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MOUSE PIPE FLOW

1. 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Figure 3 3 Degree of Filling function applied MOUSE In order to make an approach to pressurised flow the following assumption has been made An increase in pressure gradient gives rise to an increased flow rate according to 9 e 00232 ag 3 21 17 Io 1 15 the remaining part of the pipe length This correction corresponds to an empirical deviation from the kinematic wave theory so that the pressure grade line is no longer parallel to the pipe slope 1046 of the excess pressure is now used to increase the pressure gradient see Figure 3 4 DHI Software MOUSE PIPE FLOW Reference Manual 3 9 DHI Water amp Environment 54 lt DESCRIPTION OF UNSTEADY FLOW IN LINKS Pressure Gradeline 2 Figure 3 4 The assumption that 10 of the excess pressure is used to increase the pressure gradient 3 5 Diffusive Wave It was mentioned above that numerical errors in connection with the numerical solution of the kinematic wave equations produce a diffusive dampened wave motion If the pressure term is included in the equation of momentum then a damping term will automatically be included in the equations the correct solution is a dampened wave motion The momentum equation for diffusive wave approximation reads gA0 eAlo 3 22 By retaining the pressure term in the computation it is possible to implement the downstr
2. Figure 7 1 Relative variation of the Manning number with relative depth h D Manning 1 100 90 000 90 000 90 000 90 000 90 000 90 000 1 000 90 000 90 000 90 000 90 000 90 000 90 000 0 900 89 686 89 374 88 461 87 000 84 300 81 870 0 800 89 338 88 691 86 833 84 000 79 200 75 360 0 700 88 949 87 934 85 100 81 000 74 700 70 290 0 600 88 506 87 086 83 238 78 000 70 800 66 480 0 500 87 991 86 117 81 213 75 000 67 500 63 750 0 400 87 373 84 977 78 974 72 000 64 800 61 920 0 300 86 597 83 580 76 432 69 000 62 700 60 810 0 200 85 540 81 743 73 416 66 000 61 200 60 240 0 100 83 830 78 929 69 487 63 000 60 300 60 030 0 000 60 000 60 000 60 000 60 000 60 000 60 000 Exponent 0 1 0 2 0 5 1 0 2 0 3 0 Figure 7 2 Variation of the Manning M for Manningy 260 and Manning 90 with different values of the variation exponent DHI Software 7 4 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment FLOW RESISTANCE 54 lt The Manning number variation is specified through the ASCII file ADP The specified Manning numbers in the ADP file must follow the selected option for the Manning number convention Syntax of the format of the files must be as shown in the DHIAPP INI and ADP Reference Manual The lines of the ADP file related to the Manning number variation may be easily compiled by copy and paste operations from the MOUSE650 O0UT file This ASCII file is generated by every computat
3. RERO NR ER EE REN eo EG 3 5 DIFFUSIVE WAVE 3 6 DYNAMIC WAVE APPROXIMATION 3 0 1 General iiec re RON tM 3 6 2 Supercritical flow simulations with dynamic wave approximation 3 7 FLOW DESCRIPTION IN LINKS SUMMARY sent rn nnns ener nennen VA MENT Ip EC as 3 52 Which flow description RP NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE LINK NETWORKS 4 23 Ai mee 4 2 COMPUTATIONAL GRID 4 37 INUMERIGAL SCHEMEB 4 3 1 Continuity egat Onsiris ieri neea sasoin ETE 4 3 2 Momentum equation sie iti rm ENER EEE aTa GI IR ae en 4 4 THE DOUBLE SWEEP 44 1 Branch matrix 4 5 STABILITY CRITERIA PERI E HEY 4 6 OPTIMISING THE SIMULATION TIME STEP 4 6 1 Pre defined time step variation 4 6 2 Automated self adaptive time step variation 4 23 4 6 3 Criteria controlling the self adaptive time step variation eese 4 23 47 MASS GONTINUITY BALANCE e de a ee AN eese et qu Deve 4 71 Improved Continuity Balance for Links 4 72 User defined minimum water depth eese nennen INITIAL COND
4. 2 Overflow submerged 4 Underflow submerged Figure 2 11 Flow regimes through an orifice This flow regime is identified when the downstream water level has no influence on the discharge over the weir The water surface is free and the solution is therefore a pure free overflow weir solution The weir is considered to be ventilated and sharp crested The discharge over a unit width of a weir for a given water level is given by 2 2 19 4 The discharge pr m of the weir m s Upstream water level above the crest Cy The level discharge coefficient for the sharp crested weir obtained as Cy 2 3Cq see Weir Function The coefficient Cy is given in Table 2 2 for different values of the weir height divided by the water level above the crest w H Value of wi H 2 agg zi w H 0 673 0 05 0 707 1 3 i H Table 2 2 Variation of for different values of w H DHI Software MOUSE PIPE FLOW Reference Manual 2 21 DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM DHI Software In the interval from w H 0 05 to 0 1 the coefficient Cy is interpolated linearly between 0 761 and 0 757 In the interval from Wyi H 0 1 to 0 2 the coefficient is interpolated linearly between 0 757 and 0 673 Ignoring the energy loss from the upstream section to the weir section the energy equation reads 2 2 44 Ud 5 2g H w 2g w
5. WL upstream WL downstream BL upstream BL downstream Figure 2 10 Illustration of a general shape orifice For the given upstream and downstream water levels flow through the orifice is computed as an integral of the flows through individual slices with the total flow corrected for lateral contraction Orifice Flow Regimes DHI Software Basically there are four different types of flow regimes through an orifice i e for individual slice for the approaching flow in sub critical regime These are classified as e Free overflow e Submerged overflow e Free underflow and e Submerged underflow A definition sketch of the four types of flow regimes is shown on Fig 2 11 Further the theory distinguishes different forms of overflow jets depending on the geometrical and hydraulic relations In the current implementation equations for the ventilated jet for the free overflow and the momentum equation for the filled jet with a simplified correction for the downstream pressure for the submerged case have been adopted These types are the most common The solution for the approaching flow in super critical regime has not been implemented 2 20 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM 54 gt lt Free Overflow LLL Overflow free 3 Underflow free m
6. M 4 N NEZ 1 2 n At Centrepoint N 4 M ie 1 n Figure 4 2 Centred 6 point Abbott scheme The flow equations are approximated by finite differences 4 3 1 Continuity equation In the continuity equation the storage width b is introduced as QA oh g mro 4 2 giving 90 oh _ 2 ay tbe a 4 3 DHI Software 4 2 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE cone LE As only has a derivative with respect to x the equation can be centred at an point see Figure 4 3 A2 xj Timestep Po om nri Q 0 j ji Gridpoin Figure 4 3 Centring of the continuity equation in the Abbott scheme a generalised scheme Note that in MOUSE and are always equal The individual derivative terms in Equation 4 3 are expressed by finite difference approximations at the time level 2 as follows oso 90 _ 2 2 2 4 dh _ pitt Qt A 552 is approximated by _ Ao jt Ao jl 4 6 5 2 xj where Aoj the surface area between grid points j j DHI Software 4 3 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS MOUSE NETWORKS Aoj 1 the surface area between grid points j and
7. 9A ABP NIS 3 10 ox p ox ot p For a circular pipe it can be shown that the density of the water can be approximated as p 122 3 11 0 where Po the density of water for a free surface flow kgm the speed of sound water ms the water depth m the pipe diameter Furthermore it can be shown that the cross sectional area in the case of the excess pressure pg y D approximately equals to 122297 3 12 ar where the area without excess pressure and is given as DHI Software MOUSE PIPE FLOW Reference Manual 3 5 DHI Water amp Environment 54 lt DESCRIPTION UNSTEADY FLOW IN LINKS z a 3 13 with the Young s modulus of elasticity Nm the pipe wall thickness m The a has the dimension ms and is in the order of 1400 ms for most concrete pipes Combining these equations yields 9A dy 1 1 oy 8 4 3 14 a where a a 2 3 15 ala la represents the speed of sound in water considering the compressibility of water and the deformation of the pipe wall Equation 3 10 can now be written as 90 0 4840 9 _0 3 16 ox p ox The analogy with the continuity equation can thus be maintained in case that the fictitious slot width is specified as bstor 840 3 17 a is in the order of 1000 ms fo
8. gAl p 7 3 18 i e the friction slope is equal to the bottom slope uniform flow conditions In MOUSE the Manning s formula for uniform flow is used and the momentum equation reads DHI Software MOUSE PIPE FLOW Reference Manual 3 7 DHI Water amp Environment 54 lt DESCRIPTION OF UNSTEADY FLOW IN LINKS 3 4 2 Implementation DHI Software M Ag 2 3 19 The kinematic wave is independent of the downstream conditions meaning that disturbances only propagate downstream The kinematic wave description can therefore only be applied in cases when the flow is independent of the downstream conditions which is the case in supercritical flow Froude s number Fr gt 1 The analysis of the characteristics of the kinematic wave approximation see e g Sj berg 1976 reveals that a solution obtained for partly filled pipes is physically unrealistic as the characteristic wave speed 20 9 increases with increasing depth in a circular pipe filled for less than 60 and decreases with increasing depth when the pipe is filled for more than 60 This points that an uncritical use of the kinematic wave approach can lead to incorrect results caused by an unrealistic deformation of the propagating wave The kinematic wave is by nature undamped The flow rate and the water depth will therefore remain unchanged for an observer moving downstream with the velocity 20 04 Generally it is not realistic to neglect pre
9. where DHI Software MOUSE PIPE FLOW Reference Manual 3 1 DHI Water amp Environment 54 lt DESCRIPTION UNSTEADY FLOW IN LINKS discharge m 1 flow area m7 y flow depth m g x t a acceleration of gravity ms B distance in the flow direction m time s velocity distribution coefficient bottom slope friction slope Ex The derivation of these equations is described number of textbooks and scientific papers The general flow equations are non linear hyperbolic partial differential equations The equations determine the flow condition variation in water depth and flow rate in a pipe or channel when they are solved with respect to proper initial and boundary conditions Analytical solutions are only possible in special cases with a rather limited number of applications therefore the general equations have to be solved numerically 3 2 Implementation of the Saint Venant Equations in MOUSE The Saint Venant equations can be rewritten as follows 3 Ao 3 3 ox Qt and 2 44 90 oy _ i ye ey E 2 5 with the same nomenclature for Equations 3 1 and 3 2 The sketch of the system being described by the equations is presented in Figure 3 1 DHI Software 3 2 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment DESCRIPTION UNSTEADY FLOW IN LINKS Figure 3 1 Sketch of the pipe section
10. The parameters in the table are W surface width m L height relative depth m cross section area m R A P hydraulic radius m In case of a closed link MOUSE automatically provides an appropriate slot for pressurised flow computations see paragraph 3 3 Intermediate values are linearly interpolated The first set of values is associated with depth equal to zero y 0 and the last set with the maximum specified value relative to the bottom For open channels MOUSE will compute the flow as long as the water level is below the lower end of the cross section If this level is exceeded the computation will be stopped For closed conduits 2 6 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM Ss 2 3 2 3 1 Nodes MOUSE allows an unlimited raise of pressure i e Preismann slot is extended indefinitely in the height Processed data for a cross section is specified as a table with depth Y width B area A and hydraulic radius R Conveyance is computed automatically by MOUSE as C AR The processed cross section data table for an open cross section should cover the whole range of the expected oscillation of the water surface If the water surface exceeds the maximum specified elevation in the table the computation is stopped For closed cross sections the processed data table has to cover the entire range from the bottom to
11. h h H1 H2 4 16 and similarly Q Q Hpi H2 4 17 4 6 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE cone La Manhole 1 Manhole 2 Manhole 3 ao Yo Energy E Q Bi Y Q a2 Bo 2 Cont E Q P3 Q4 4 4 O5 P5 15 06 Y 4 Energy Figure 4 5 Branch matrix with coefficients derived from the node energy level momentum and continuity equations 0 Oyo 1 1 1yo 1 2 2 2yo 2 3 3yo 4 4 4yo 4 5 5 5yo 5 6 6yo Figure 4 6 Branch matrix after local elimination The continuity equation around a node can in principle be expressed as n l ntl n l 6 b hpranchi e 4 hp ranch Qpranchz Teema 4 18 where a z are quasi constants If Equation 4 15 is substituted herein a global relation can be obtained 2 1 4 19 where to Z are quasi constants Equation 4 19 shows that the water level in a node can be described as a function of the water levels in the neighbouring nodal points It is therefore possible to set up a nodal point matrix at each time step using the coefficients from Equation 4 19 and the solution to the DHI Software MOUSE PIPE FLOW Reference Manual 4 7 DHI Water amp Envi
12. 0 0 has been performed on the same example The differences in computed water levels Figure 7 8 are not so pronounced as in the previous case Ej 500 0 450 0 250 0 euer EHE eae Sea 200 0 150 0 0 0 4 pec 100 0 50 0 0 0 50 0 100 0 1500 2000 2500 3000 3500 400 0 Figure 7 6 Head Loss Computation System lay out DHI Software 7 14 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment m3 s 0 800 0 800 0 800 0 800 0 800 WATER LEVEL BRANCHES 1 1 1994 01 00 FIGUR22 PRF 0 800 0 800 0 800 Discharge FLOW RESISTANCE ox z PEAS gE e tao URINE S D s L3 bor og op de fle poo 404404 8 bo pod f2 ge M 8 specie pe FSS aie N 4 2 pos oc p moa sept o f fa Ko esl cs al gh aed ca LE 1 ee gel ae aL g je g d Kd ee EES aS ae YT mE L N Fog kom qd REC 2 gt medo dimus e ee HH Mie m WS uS L rod P MES amp ce S EE 1 ifo 8 1 e e 4 l N iho 5 IE 3 a SI An S LN LN Fe S ilg ple mim med d aes a e muri s 3 M 9 819 H IE S Qu ae rri J lt Ep o L E 2 og 9 ua el Le Y
13. 1 3 The implemented algorithm includes a combination of the parabolic and the momentum solution The parabolic solution is applied if the combined energy and momentum equation does not give applicable solutions for the given AH H i e if is rejected The discharge is solved for decreasing values of AH H and for each value of AH H 1 3 is the combined energy and momentum equation evaluated As soon as the combined energy and momentum equation begin to give applicable solutions a swap from the approximate parabolic solution to the combined energy and momentum solution is performed The contraction coefficient will in this case be based on the criteria that the discharge applying the combined momentum and energy solution is the same as from the parabolic solution at the point of intersection The underflow is free if the issuing jet of the supercritical flow is open to the atmosphere and is not overlaid or submerged by tail water Following an approach similar to the one developed in the section related to free overflow the discharge through the opening e g gate can be expressed as 2 26 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM LEA q C w A2gE 2 30 where q the specific discharge E the energy level upstream of the opening Wo the gate opening the discharge coefficient with respect to the energy level The energy level at the upstream side can
14. 7 4 AN ALTERNATIVE SOLUTION BASED ON WEIGHTED INLET ENERGY LEVELS eese 7 23 7 5 SELECTING AN APPROPRIATE LOCAL HEAD LOSS DESCRIPTION 7 23 7 5 1 Alternative interpretations of head loss coefficient eese eene nnne 7 23 7 5 2 Alternative head loss descriptions eese 7 23 7 5 3 Example 1 Impact of alternative head loss formulations on the results sese 7 23 7 5 4 Example 2 Node Outlet Head Losses variation as function of head loss coefficient mode 7 23 7 5 5 Implementation of head loss description in kinematic wave simulations eene 7 23 8 SOME SPECIAL 2 21 2 2 e eene stats sonata enses sonata sense esses eene ta stes snae 8 23 8 1 SURFACE FLOODING PUER EN UN 8 23 8 2 SEALED NODES T 8 23 0 3 SPILLING NODES 5 nior oiihtivasiu ne D ante es apne 8 23 PRESSURE MAINS Reciente essei luu tidie ise 8 23 8 5 DRY CONDUITS E r seed 8 23 9 NOMENCLATURE 0044002 0 9 23 10 REFERENCES C 10 23 e E 10 23 1 IMPORT EXPORT OF SEWER NETWORK DATA FRO
15. 9 reg gt im g 1 Fl Bg potato T8 E So 518 pem cec sga eene eoe S S gt 2 FS e ES or ICR US 2 amp m Sg Ie cd Se Lo 5 ug Wesesedesetercbeledecos or M om 1 S 505 d Eig r 2 M 2 S E 8 o S pue 2 Os g if Ped Sar Pere SM 8 gt Ze Fe se a Lo N a pq ue 4 3B l l uu S N fois d dp eee to a MES la Lia A d NE E tot fms ud T qw 1 1 1 IP o L T3 Ca rr rr YES 20 8 8 REN RON EC RE I pur Ry o 1 1 1 Ira ae ae e ie npe Ss lt 1 T es 4 4 r r prE9 Htt tta tata 9S8 s b PSS Sie OQ 0000000 0 o 9 0 S o e e specs es cd Xs HOS T USED INDE Um ps Quom S 6 hom Om oH OH o9 4 o o o 9 7 15 m DHI Software DHI Water amp Environment MOUSE PIPE FLOW Reference Manual 54 gt lt FLOW RESISTANCE Figure 7 8 Computed Water Levels Left branch Option 4 Right branch Option 6 7 5 4 Example 2 Node Outlet Head Losses variation as function of head loss co
16. Basin geometry 0 000 100 000 16 200 16 000 220 000 19 200 49 000 220 000 Figure 2 6 Definition of a basin an example Purpose of storage nodes is a controlled simulation of the surface flooding i e controlled return of the water into the sewer system Storage nodes are fully defined with the identification string alone The only other parameter associated with a storage node is the content of water the capacity is not limited currently stored in the storage node Water enters to a storage node from any manhole or structure either through a weir or a pump A storage node may be emptied by an emptying function 2 12 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM LEA Outlets Outlets are nodes specified at locations where the modelled system interacts with receiving waters External water volume is assumed so large that the outlet water level is not affected by the outflow from the sewer system As such outlets are appropriate for simulation of the sewer flow recipients river lake and sea An outlet can behave as an inlet which depends on the flow conditions in the link s attached to the outlet and the water level specified at the outlet This means that the flow in both directions can occur Outlets are defined with the following parameters bott outlet bottom elevation m water surface elevation at outlet m Water surf
17. Qinf follows 2 Gwlev follows Qinf or GWlev see comment As 1 Circular pipe D diameter 2 3 4 see details in the MOUSE documentation D dimension diameter m ft real number Comments The Nodel and Node2 will normally be chosen so Node is the upstream node and Node2 the down stream end of a pipe However also the opposite selection will work in MOUSE The pipe will be connected to the nodes as indicated MOUSE will define the flow direction from 4 1 to Node2 as the direction of positive flow The Material code is in MOUSE related to a user specified set of Manning resistance values If Ai 2 then the two invert levels should not be written In this case MOUSE will connect the pipe to the invert levels of the nodes at Appendix 1 16 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual Example NUMBER CONDUITS NODE U NODE D M Ai BL U BL D Af FLOW B4 B4 B4 B4 B4 B4 B4 B4 B4 AO B4 B4 B4 B4 B4 B4 B4 B4 B4 B4 10 1520 1502 1501 1501 1491 1500 1200 1485 1490 1480 1510 1501 1500 1491 1490 1490 1485 1480 1485 0327 each end If lt Ai gt 1 then the invert level of the pipe should be given for both ends even if the pipe at one of the ends are connected at the node invert level lt Af gt indicates if the following value are to be interpreted as an infiltration inflow Af 1 or as a ground water
18. The equations above are valid for free surface flow only They can however be generalised to include flow in full pipes pressurised flow as discussed in section 3 3 below The continuity equation expresses that the volume of water 20 which is added in pipe section of length ok is balanced by an increase in cross sectional area dA storage The first two terms on the left side of the momentum equation represent the inertia forces local and convective acceleration while the third term represents pressure forces The two terms on the right hand side of the equation represent gravity and friction forces respectively The velocity distribution coefficient accounts for an uneven velocity distribution across a section and corresponding difference in the actual momentum compared to those obtained with an average velocity It is defined as ZI i 0 Assuming that the bottom slope Z is small y 0 then J can be expressed as a function of the water depth and water surface gradient 1 3 6 DHI Software MOUSE PIPE FLOW Reference Manual 3 3 DHI Water amp Environment 54 lt DESCRIPTION UNSTEADY FLOW IN LINKS It is thus possible to use the height h above a certain reference level as the dependent variable instead of the water depth y The equation of momentum can hence be written as 4 90 3 7 X X Pressure and gravity forces can be expressed in one
19. 45 3 14 45 15 20 17 00 0 070 0 150 0 300 NUMBER CONTROL FUNCTIONS FORM KF3 0 NUMBER CRITICAL WATER LEVELS FORM KK 0 NUMBER OUTLETS FORM KU 1 DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 21 DHI Water amp Environment X COOR Y COOR BOTTL OUTL 0 0327 630 0 0 0 16 00 17 00 NUMBER CONDUITS PIPES FORM 11 10 NODE U NODE D M A BL U BL D A FLOW GW LE A DIAM 4 1520 4 1510 12 1 0 000000 1 0 300 B4 1502 B4 1501 4 2 1 0 000000 1 0 200 B4 1501 B4 1500 4 2 1 0 000000 1 0250 B4 1501 B4 1491 1 2 1 0 000000 1 0 200 B4 1491 B4 1490 4 2 1 0 000000 I 0 250 B4 1500 B4 1490 3 2 1 0 000000 1 0 400 B4 1200 B4 1485 5 2 1 0 000000 3 0 700 B4 1485 B4 1480 1 2 1 0 000000 1 1 200 B4 1490 B4 1485 1 2 1 0 000000 1 1 200 B4 1480 A0 0327 1 2 1 0 000000 1 1 200 NUMBER CONDUITS TRAPEZOIDAL SECTION FORM L2 0 NUMBER CONDUITS ARBITRARY SECTION FORM L3 0 NUMBER CONDUITS CROSS SECTION Data Base FORM L4 3 NODE U NODE D M A BL U BL D BASE CROSS ID SCALAR 4 1310 4 1320 3 2 OLDSYS N1 4 1 6 1 000 2 4 1300 4 1320 3 2 OLDSYS N1 4 1 6 1 000 2 B4 1320 B4 1485 12 OLDSYS N1 4 1 6 1 000 2 DHI Software Appendix 1 22 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment
20. 70 0 0143 7 Stone 80 0 0125 8 Other 50 0 0200 Table 2 1 Manning s Numbers MOUSE Default Values The default values can be edited by the user The modified default values are associated with the current project only i e will affect any simulation carried out with a MOUSE project file MPR Also the default Manning number for any individual link can be overwritten by a user specified link specific value Longitudinal Profile A link is longitudinally defined by bottom elevations of the upstream and downstream end By default link bottom elevations are assumed to be equal to the adjacent node s bottom elevations The default setting can be over ruled by specification of the actual link end elevations but not below the node bottom Normally length of a link is calculated on the basis of the nodes co ordinates assuming a straight link layout Optionally For links connected to circular manholes it is possible to calculate the length from the manhole perimeter In cases where actual link length significantly deviates from the calculated value a user specified length can be supplied instead Longitudinal slope of a link is assumed constant It is calculated using link end elevations and the link length Specification of a node as upstream or downstream has in principle only a declarative meaning and does not affect the computations exception is if the functions located in the link see 2 4 2 2 4
21. 80 80 Appendix l 6 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual 1 4 2 Section KGt The section is used for definition of circular manholes Typically most of the nodes in a network will be defined in this section Definition of data elements lt Node gt lt X coor gt lt Y coor gt lt Invert level gt lt Ground level gt lt Out Shape gt lt Diameter gt where lt Node gt 7 character string followed by one blank lt X coor gt X coordinate m ft real number lt Y coor gt Y coordinate m ft real number lt Invert level gt Invert level node bottom m ft real number lt Ground level gt Ground level m ft real number lt Out Shape gt Outlet shape code For head loss computation 1 6 integer lt Diameter gt Diameter of circular manhole m ft real number Comments Example NUMBER CIRCULAR MANHOLES FORM KG1 11 X COOR Y COOR BOTTL SHP DIAM 4 1520 945 0 594 0 16 50 021022 1 25 4 1500 630 0 594 0 16 70 19 20 1 1 50 4 1501 330 0 564 0 17 30 20 47 1 1 25 4 1502 120 0 564 0 17 86 21 32 1 1 00 4 1490 630 0 330 0 16 39 19 801 2 50 4 1485 630 0 180 0 16 35 19 80 1 1 25 4 1320 900 0 180 0 17 10 20 201 1 50 4 1310 1200 0 300 0 17 30 20 231 1 50 4 1300 1200 0 180 0 17 42 19 90 1 1 50 4 1200 150 0 180 0 16 80 19 90 1 1 50 B4 1491 390 0 330 0 16 89 20 15 1 1 25 DHI Software
22. H gt WaterLevDiffMaxRel 4 26 where is the relative depth the water depth divided by the height e g by diameter for circular pipes is the relative depth before the attempted time step and H is the relative depth at the end of the time step AH is the difference in the relative depth through the time step The WaterLevDiffMaxRel value can be user controlled from DHIAPP INI file If limitation is violated at any H point in the model then the obtained solution is scaled down with respect to dt 4 12 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE cone gt The default value of WaterLevDiffMaxRel is 0 3 which corresponds to maximum relative change of 30 Variation of cross section parameters The variation of cross section parameters A R and B where A is the cross section area R is the hydraulic radius and the width of water surface can be included as additional criterion for limiting the simulation time step Whether the check on the cross section parameters is to be activated or not is specified through the variable Crosscheck in the DHIAPP INI file the value 0 means that the is de activated while the values 1 or 2 mean that the check is activated in one of the two available variants If the check on the cross section parameters is activated then it is carried out in all H grid points The variation in the three cro
23. Relation Built in Overflow Energy loss coefficient The relation between the water level in the structure or manhole and the released discharge can be defined as a specific Q H relation or the built in overflow formula can be used In the later case the discharge is calculated on the basis of a given structure geometry crest elevation structure width orientation relative to the flow crest type It is important that the width of the overflow is realistic compared to the physical dimensions of the manhole or structure E g an overflow width of 10 m in a manhole having a diameter of 2 m will inevitably cause numerical problems when the overflow is in function The user defined Q H relation consists of at least 2 pairs of tabulated values for water level above the weir crest H m and corresponding discharge Q m s Intermediate values are linearly interpolated The Q H table has to fulfil certain conditions e the first H value has to be the overflow weir crest elevation e the H values have to be given in a monotonously increasing order the largest H value given in the table shall not be less than the largest H value to be computed The model does not extrapolate beyond the tabulated values Formula MOUSE provides two different methods for the computation of the free overflow e Flow computation based on the energy loss coefficient and weir orientation This is applied if the field for the discharge coefficient on
24. U NODE D M A BL U BL D A FLOW A DIAM B4 1520 B4 1510 1 2 1 0 000000 1 0 300 ABC12 1 2 1 0 000 1 0 2000 N 34 ABC13 1 2 1 0 0000 1 0 25 KKE KKK KKK KKEKK KKK k ck ck ck ck ck ck ck k kk k lt fixed format gt lt free format gt DHI Software Appendix 1 4 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment SS 1 4 SVK 19 Data blocks 1 4 1 Section D NOTE this description is only valid for MOUSE releases 1999B and older In the releases 2000 and newer this section is empty The catchment data are used by the MOUSE Runoff simulation In this section each data element will always be in one line The data element have two alternative types Definition of data elements Node Area Slope Length A PE Q H Pct Or Node Area Slope Length A PE Q lt H gt lt S gt al a7 where Node 7 character string followed by one blank Area catchment area ha acre real number Slope the slope of the area in per mille 0 00 0 oo finteger Length length of catchment m ft integer A z Area type code Type code 1 7 is used in MOUSE integer PE Inhabitants per area Inhabitants ha Inhabitants acre integer lt Q gt Additional inflow m3 sec cft sec real number lt H gt Hydrological level 1 simple 2 detailed description if lt H gt 1 t
25. and less important the smaller the values of AH H are Secondly the contraction coefficient has a significant effect on the discharge e g this approach is very sensitive to the choice of the vertical contraction coefficient DHI Software MOUSE PIPE FLOW Reference Manual 2 25 DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM Free Underflow DHI Software The submerged overflow solution must be compatible with the free overflow at the transition between the two flow regimes In other words introducing the submerged solution at AH H 1 3 requires that the submerged discharge for this water level difference is equal to the free flow discharge This is not achievable in all cases and sometimes another pragmatic solution must be adopted for the transitional regime Following the approximate rule as for the flow over a broad crested weir a flow reduction is introduced as soon as the difference between upstream and downstream water level is less than one third of the upstream water level The remaining submerged discharge is proportional to the square root of the difference in upstream and downstream water levels above the weir crest The free flow is taken from the sharp crested case as described above The flow in the submerged flow can be approximated as 4 a p forest 2 29 3 where AH the water level difference between the upstream and downstream section qr the free flow at the level where AH
26. basins e Surcharge of manholes The scale of the problem is usually related to the length of the simulation time step 4 7 1 Improved Continuity Balance for Links In order to reduce the amount of water generated in conduits due to the changes of surface width as function of water depth i e to improve the DHI Software 4 14 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE cone LE continuity balance the Taylor expansion of the general continuity equation 3 1 has been applied Since the surface width is assumed to be constant during two time steps the continuity equation can be rearranged as 10 A 0 4 30 wo ot where A is the water level m and w is the surface width m The term a in the equation above can be expanded in a Taylor w series as n n n n 1 222 204 2 w Ox w a che w ox ox 4 31 where represents the time centering of the numerical scheme and n and refer to the simulation time steps This modification is applicable only for conduits with relatively smooth changes of the surface width As the width for arbitrary pipes and pipes from the cross section database may vary in a very unpredictable way the Taylor expanded equation is only applied to standard pipes and trapezoidal canals 47 2 User defined minimum water depth Further means of controlling the volume continuity balance for
27. be expressed as 2 q E H W f H 2 31 2g H 4 w 2 31 where H the upstream water level measured from the crest of the weir q the discharge w is the weir height at the upstream side Usually discharge is given as a function of the upstream water depth above the crest rather than by energy level q Cyw 28H 2 32 with C C es 2 33 m wo H w 1 9 where is a constant representing the contraction coefficient of the jet Substitution of equation 2 33 into equation 2 32 leads to the expression 2 2 w H B 14 C Ea 2 34 Further the relationship between Cg and Cy may be derived as DHI Software MOUSE PIPE FLOW Reference Manual 2 27 DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM DHI Software C VA From above equations the underflow discharge can be computed However it should be noted that the compatibility of discharge values at the transition from the free overflow equation to the free underflow equation must be secured Theoretically this transition should take place at the moment where the upstream water level touches the top of the gate This point is difficult to define as the water level is drawn down towards the contracted section Another complication is the fact that the underflow equation is accurate only for upstream depths considerably exceeding the depth of the gate opening C 2 35 For this r
28. controllable rectangular sluice gates Orifice functions can be specified in nodes defined either as manholes as structures but not at an outlet An orifice is topologically fully defined with two node identifiers defining the orifice upstream node FROM and the orifice downstream node TO Basic Geometrical Assumptions Bottom is considered horizontal both in the sections upstream and downstream from the orifice The upstream overflow crest height w is calculated as the distance between the orifice invert level and the bottom level of the upstream node Similarly the overflow crest height from downstream w is given as the distance between the orifice sill level and the bottom level of the downstream node Other parameters are described in the following text or illustrated on drawings Approximation of Arbitrary Geometrical Shapes An orifice opening is defined as a closed polygon through the MOUSE cross section editor Any form of convex and concave shapes is allowed as long as there are no intersected arcs see Figure 2 9 NOT ALLOWED ALLOWED Figure 2 9 Examples of an illegal left and correct definition of an orifice polygon For the computational purpose a polygon is cut into a number of narrow rectangles slices which approximate the shape of an orifice see Figure 2 10 DHI Software MOUSE PIPE FLOW Reference Manual 2 19 DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM
29. in the momentum equation This allows the user to take downstream boundary conditions into account and thus simulate backwater effects The diffusive wave description ignores the inertia terms and is therefore suitable for backwater analyses in cases where the link bed and wall resistance forces dominate and for slowly propagating waves where the change in inertia is negligible 3 Kinematic wave approach where the flow is calculated on the assumption of a balance between the friction and gravity forces This means that the kinematic wave approach cannot simulate backwater effects Thus this description is appropriate for steep pipes without backwater effects 3 7 2 Which flow description Depending on the type of problem the most appropriate description can be selected three approaches simulate branched as well as looped networks The dynamic wave description is recommended to be used in all cases except where it can be shown that either the diffusive or kinematic descriptions are adequate The diffusive and kinematic wave approximations are simplifications of the full dynamic descriptions They are implemented to offer improved computational efficiency but should only be used when the omitted terms have insignificant influence When there is any doubt it is better to use the full dynamic description or trials should be undertaken to establish the difference between the alternative methods and advice sought from experienced pers
30. level Af 2 at the location of the pipe MOUSE will only accept Af 1 It is recommended to set Af 1 and Qinf 0 000 and instead use the MOUSE Boundary Data system for entering additional inflows PIPES PRPPUWARPA ARB 2 NN 1 RoR RoR RR 0 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 GW LE As FAs Rt p FORM 11 DIAM 300 200 250 200 250 400 700 200 200 200 DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 17 DHI Water amp Environment 1 4 11 Section 12 L2 section is intended for trapezoidal open channels This section does work with MOUSE but it is strongly recommended to use the more flexible L4 section for defining this type of links Definition of data elements Nodel1 Node2 Mat Ai Invert1 lt Invert2 gt Af lt Qinf or GWlev lt gt lt gt lt gt where B Bottom width m ft real number A The side wall angle real number lt gt Height of the channel m ft real number other parameters See definition for the L1 section Comments The side wall angle is defined as the width per 1 m ft height That is a 45 degree side wall will have A 1 0 a vertical side wall will have A 0 0 Example NUMBER
31. level in the manhole This implies that the expansion loss at the inlet is automatically assumed All calculated energy losses are assumed to occur at the outlet pipe 1 manhole E pipe AH 7 20 or expressed by using the notation in Figure 7 9 2 2 2 2 Zn ES Your Zour 6 p 7 21 4 a coefficient expressing the total outlet energy loss see the paragraph above Data Discharge Q 2 0 mis Diameter in outlet pipe Dou 1 0 m Diameter in manhole Dun 1 5 m Velocity in outlet pipe Q is capacity assumed Vout 2 55 ms Length of outlet pipe L 50 0 m Manning number M 70 m s Water level in outlet 15 0 Bottom level in manhole Zi 14 0 m Head shape loss coefficient Km 0 5 Friction loss in outlet pipe from manhole to outlet DHI Software MOUSE PIPE FLOW Reference Manual 7 17 DHI Water amp Environment 54 gt lt FLOW RESISTANCE DHI Software OL 2 02 50 0 7 22 f MARO 70 0 7854 0 25 8 The water level the manhole be found from 2 2 2 H 4 Hoythrt Vout Vout gp ccu MU d 2g 7 23 Vm is approximated by assuming that Ym Your CN SE 20 0 94 ms 7 24 Am Dm Yn 15 150 042 140 2 2 a 2 55 ms Vout 0 33m 7 25 Aout 0 78 2g 2 0 045 7 26 28 Es an dir 2 2Km l Aout Qin gp Qi A 7 27 Qo 90 2 OS 15 142 90 Sub
32. links with no or little water are provided as user controlled minimum water depth for links running dry or with very little flow The default minimum water depth can be modified in the DHIAPP INI file In this file two parameters can be changed BRANCH MIN REL 20 This is the relative minimum water depth in promille of the characteristic dimension in a link BRANCH MIN H ABS 20 This is the absolute minimum water depth mm in a link The minimum water depth in a link will be set to BRANCH MIN H REL calculated as promille of the link size e g pipe diameter or height of the open channel but never larger than BRANCH MIN H ABS mm In the presented example the DHI Software MOUSE PIPE FLOW Reference Manual 4 15 DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE LINK NETWORKS DHI Software minimum water depth is set to 20 promille of the link size but with a maximum of 20 mm This means that for links smaller than 1 meter the minimum water depth is set to 20 promille of the link size For links larger than 1 meter the minimum water depth is kept at 20 mm independently of the link dimensions 4 16 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual INITIAL CONDITIONS 54 lt 5 INITIAL CONDITIONS The hydrodynamic computation is started from the flow conditions in the systems specified for time t 0 MOUSE provides two different options for establish
33. not the case This problem is reduced by applying the effective flow area in the manhole but this is available in MOUSE only for circular pipes and for the flow through manholes i e with one pipe in and one pipe outflow An alternative solution is available which fully ignores the energy loss at the inlet For a flow through manhole this practically means that the energy level in the manhole is set to be equal as at the downstream end of the inlet pipe For manholes with multiple inlets the energy level is calculated as the weighted average of the inlet flows i e large flows contribute most to the energy level Thus this formulation the total loss at the manhole is concentrated computationally at the outlet and can be fully controlled by the user Without doubt this approach proves valuable for some specific situations particularly for the flow through manholes with normal flow conditions However due attention must be paid for cases with high inlet energy levels e g a small pipe with high velocity flow entering a large basin In such a case the energy level of otherwise still water in the basin would be calculated as equal to the energy level of the approaching flow i e much higher than realistic with erroneous results as a consequence 7 5 Selecting an appropriate local head loss description In some cases results from using different approach for node head loss calculation can be considerably different and d
34. term only as dh 3 8 The friction slope J is equal to the slope of the energy grade line and is introduced into the equation using the Manning s formulation for more details see paragraph 4 1 3 3 Modelling The Pressurised Flow The full flow capacity of a closed conduit pipe can be defined as a discharge at which the flow depth is equal to the conduit height Any further increase of discharge fundamentally changes the conditions of flow i e basic assumptions for the derivation of the Saint Venant equations are not valid Namely the flow changes from the free surface flow to the pressurised flow However it is possible to generalise the equations for free surface flow so that the pressurised flow in closed conduits is covered This is done by introducing a fictitious slot in the top of the conduit see Figure 3 2 The idea of introducing a fictitious slot was first presented by Preissmann and Cunge 1961 and has since been used by Cunge and Wagner 1964 see ref 4 The derivation can be obtained from the continuity equation which can be written as MOD NPA pog 3 9 ox ot assuming the density of water constant over the cross section DHI Software 3 4 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment DESCRIPTION OF UNSTEADY FLOW LINKS B B giot 9 BB slot Figure 3 2 Pipe with a fictitious slot By partial differentiation is found QUE
35. the weir dialog is left empty Flow computation based on a standard rectangular overflow weir formula with user specified discharge coefficient This is applied if a discharge coefficient is specified In case of a free overflow the water depth above the weir crest will be equal to the critical water depth Certain energy loss occurs with a magnitude depending on the structural configuration The overflow situation is schematised in Figure 2 7 DHI Software MOUSE PIPE FLOW Reference Manual 2 15 DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM DHI Software Figure 2 7 Free Overflow In the critical flow section the Froude s number Fr equals to 1 and the critical flow condition can be written as Fr 2 7 mean flow velocity ms 1 critical depth 9 81 028 E Conservation of energy between the upstream and critical cross section yields with 2 2 8 28 with 2 9 28 where energy level at the section just upstream the structure m AE entrance energy loss Ke energy loss coefficient Based on the energy conservation and critical flow principles discharge over a plane overflow having a structure width B m is calculated for a weir orthogonal to the flow axis 90 as 3 2 2 gt 5 H 2 10 2 16 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual M
36. to be familiar with the MOUSE software and to have the MOUSE User Manual available Recent move to the new data file structure in MOUSE have introduced for the first time that the MOUSE native file format 1s an ASCII format This is the so called Parameter File System PFS with a flexible structure The transition to the new PFS reduced the need for the SVK19 format However it will be maintained in MOUSE until the new file system is completely implemented This Appendix provides a full reference to the original SVK19 format SVK19 File Structure The format divides the data describing the sewer network into a number of sections Each section has the following structure Headline 1 Number of data elements Headline 2 Data element Data element Data element DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 1 DHI Water amp Environment DHI Software The lt Number of data elements gt must match the actual number of lt Data elements gt following lt Headline2 gt If no elements are present in a section then lt Headline 2 gt is omitted but lt Headline gt and the succeeding line with a zero are mandatory The headlines are simply skipped by MOUSE and they may contain any text Also other reading routines should do this and NOT base any reading by identifying e g the type of section from the contents of the header line Different language versions of MOUSE may pro
37. 3 O H relation at the outlet Q Q H m s Internal boundary conditions can be defined as follows At manholes and structures 1 Weir discharging to another manhole or structure Q m where H stands for energy level above the weir crest in case of a free overflow and for difference of energy levels upstream and downstream of the weir in case of a submerged overflow If an alternative formulation for the weir is specified with a user specified Q H relation such conditions should be provided that the overflow is always free i e that holds the unique relation between the water level and the flow 2 Pump discharging to another manhole or structure Q Q H ms or Q AH m s where H stands for water level in the manhole or structure and AH level difference between the two manholes or structures associated with the pump Some of the listed boundary conditions are illustrated in Figure 6 1 6 2 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual BOUNDARY CONDITIONS 54 lt OUTLET Figure 6 1 Supplying Boundary Conditions Examples to be continued DHI Software MOUSE PIPE FLOW Reference Manual 6 3 DHI Water amp Environment O 1 Supplying Boundary Conditions Examples continue FLOW RESISTANCE 54 lt 7 FLOW RESISTANCE 7 1 Friction Losses in Free Surface Flow Links 7 1 1 Numerical description Head losses caused by th
38. 3 and 2 4 4 are present in the model In the flow regulation DHI Software MOUSE PIPE FLOW Reference Manual 2 3 Water amp Environment MODELLING THE PHYSICAL SYSTEM restriction only positive flow is affected by the regulation Similarly the non return valve function allows only positive flow By convention positive flow values represent the flow in the direction from upstream to downstream node Link Cross sections DHI Software As a built in feature MOUSE supports five different pipe cross section types Any other non standard pipe tunnel or open canal can be described through the Cross section database facility by specifying geometric shape of the cross section or a table of geometrical parameters MOUSE includes the following standard pipes 1 Circular pipe 2 Rectangular pipe B H 3 Danish egg shaped 0 shaped pipe H B 1 5 1 4 Egg shaped pipe H B 1 5 1 5 Quadratic pipe B Egg shaped pipe Danish egg shaped pipe 0 shape 1 5D H gt B 2 3D B D Figure 2 1 MOUSE egg shaped cross sections Note the difference in selection of the characteristic dimension D Any of the five standard pipe cross sections is fully defined by specifying the pipe type and characteristic dimension s While for the circular rectangular and square shape this is straightforward attention should be paid for the definition of the egg shaped cross sections For th
39. C Z A B Z a bs Dstot B AR Din Diy Dout drop_ factor quasi constants in a modified continuity equation around a node quasi constants in a generalised continuity equation around a node the speed of sound in water with actual pipe walls rigidity ms vertical distance from the point where the jet intercepts the manhole to the centreline of the inlet the speed of sound in water for absolutely rigid pipe walls ms the speed of sound along pipe walls ms cross section area m effective flow area in a manhole m cross section area of the jet at the point of interception with the manhole m cross section area of the wet part of the manhole cross section area at full pipe flow m the cross section area without excess pressure structure wetted cross section area m structure water surface area surface area between grid points and j surface area between grid points j and j vertical distance from the point where the side of the outlet enters the manhole to the centreline of the inlet surface width m storage width m width of Preismann slot m overflows width m cross section conveyance m Courant number Coefficient of discharge Coefficient of discharge energy based Coefficient of discharge level based pipe diameter m diameter of the inlet pipe m diameter of the manhole m diameter of the ou
40. CONDUITS TRAPEZOIDAL SECTION FORM L2 1 NODE U NODE D BL U BL D A FLOW GW LE B WI ANG MAX H R15 0 R14 0 1 2 1 0 000000 0 7 1 0 0 7 DHI Software Appendix 1 18 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment 1 4 12 Section 13 The L3 section is intended for arbitrary shaped channels This section does work with MOUSE but it is strongly recommended to use the more flexible L4 section for defining this type of links Each data element in this section will always cover five lines Definition of data elements lt 4 1 gt lt Node2 gt lt Mat gt lt Ai gt lt Invert1 gt lt Invert2 gt lt Af gt lt Qinf or GWlev gt lt Op Cl gt lt Nval gt lt 1 gt Y2 Yn W W2 Wn lt 1 gt A2 An R1 R2 Rn where lt gt 1 Open channel 2 Closed channel integer Nval Number of value sets in the geometry description 2 10 integer lt gt lt W gt lt A gt lt R gt depth m ft real number width m ft real number flow cross section area m2 ft2 real number hydraulic radius m ft real number other parameters See definition for the L1 section Comments The geometry is described as function of the water depth Example NUMBER CONDUITS 1 NODE U NODE D M A BL U R14 0 813 0 12 0 00 0 10 0 20 0 01 0 30 0 60 0 0000 0 0150 0 0600 0 0000 0 0450 0 1200 ARBITRARY SEC
41. I Software MOUSE PIPE FLOW Reference Manual 4 9 DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS MOUSE LINK NETWORKS conditions of variable flow dynamics as usually occur during the simulated interval the total computational effort is minimised while preserving stable and accurate computations MOUSE includes two different concepts for optimising the simulation time step The user specified pre defined time step variation specified as a time series e The automated self adaptive time step variation controlled by the actual hydraulic and operational conditions within the entire model area throughout the numerical simulation Both of these concepts can be applied in connection with the Dynamic and Diffusive flow descriptions while they cannot be used with the Kinematic flow description In this context it is important to note that a constant time step is simply a restricted case of these concepts 4 6 1 Pre defined time step variation Pre defined time dependent time step variation must be specified in the MOUSE time series database system as a time series If the variation is to be applied in the simulation a reference to the time series must be made in the boundary system BSF file currently applied in the simulation It must be noted that the pre defined variation of the time step has precedence over the automatically generated self adaptive time step 4 6 2 Automated self adap
42. I Water amp Environment L MODELLING THE PHYSICAL SYSTEM Submerged Overflow 2 4 2 Orifice Function DHI Software The model calculates the flow rate for the submerged overflow using the same critical depth formulation in the case of a submerged overflow In this situation the head that is driving the flow is expressed as the difference between the upstream and downstream water surface elevations NS Weir Crest Weir defined in this node node Figure 2 8 Principle of submerged overflow The submerged weir flow is then with user specified level discharge coefficient approximated as H 2 Q7 Cu B 428 2 16 or with energy loss coefficient for orthogonal overflow weir 3 2 2 B VASE Q soir V8 x 2 17 and for a side overflow weir 0 3 2 2 H pom AH Q veir 8 E 2 18 Orifice is an opening of any shape allowing water passage between otherwise separated parts of the network Usually an orifice represents a flow restriction Like an overflow weir orifice is defined in MOUSE as a function between two nodes MOUSE supports the computation of flows through orifices of any shape in all possible flow regimes Further a rectangular orifice with 2 18 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM moveable top is used for the simulation of
43. ITIONS DHI Software iii DHI Water amp Environment 5 1 DEFAULT INITIAL CONDITIONS scierie erinran eian aara nR Ear Ea EEE EERTE A EE EE A PS NEON EEEn NERDC IEEE RETS 5 23 5 2 INITIAL CONDITIONS PROVIDED BY 5 5 23 6 BOUNDARY CONDITIONS sees eese enne tns 6 23 7 FLOW 8 0020412 7 23 7 1 FRICTION LOSSES FREE SURFACE FLOW 5 7 23 ALI Numericabdescription U HY orte Eee o Ma ES ae Re Lp I 7 23 7 1 2 The friction resistance described by the Manning formula eene 7 23 7 1 3 Depth variable Manning coefficient esee 7 23 7 1 4 Colebrook White Formula for Circular Pipes eese nennen enne 7 23 7 2 HEAD LOSSES IN MANHOLES AND STRUCTURES INTRODUCTION 2 41 220004000000 nennen enne rennen 7 23 7 3 STANDARD MOUSE SOLUTION F A 73 Headlossatihemodeanlet ese ORE ERE NI ene es 7 3 2 Head losses at the outlet from a node esses eerte nnne 7 3 3 Implementation of the total energy loss computation
44. L4 3 NODE U NODE D M A BL U BASE CROSS ID SCALAR 4 1310 4 1320 3 2 OLDSYS N1 4 1 6 1 000 2 4 1300 4 1320 3 2 OLDSYS N1 4 1 6 1 000 2 4 1320 4 1485 1 2 OLDSYS N1 4 1 6 1 000 2 DHI Software Appendix 1 20 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual 1 5 Example Version 2000 and newer NUMBER CATCHMENTS FORM D 0 NUMBER CIRCULAR MANHOLES FORM KG1 11 X COOR Y COOR BOTTL SHP DIAM 4 1520 945 0 594 0 16 50 19 101 1 25 4 1500 630 0 594 0 16 70 19 201 1 50 4 1501 330 0 564 0 17 30 20 47 1 1 25 4 1502 120 0 564 0 17 86 21 32 1 1 00 4 1490 630 0 330 0 16 39 19 80 1 2 50 4 1485 630 0 180 0 16 35 19 80 1 1 25 4 1320 900 0 180 0 17 10 20 201 1 50 4 1310 1200 0 300 0 17 30 20 23 1 1 50 4 1300 1200 0 180 0 17 42 19 901 1 50 4 1200 150 0 180 0 16 80 19 901 1 50 4 1491 390 0 330 0 16 89 20 15 1 1 25 NUMBER STRUCTURES FORM KG2 2 X COOR Y COOR BOTTL SHP B4 1480 630 0 120 0 16 25 18 50 1 4 1510 710 0 594 0 14 20 19 20 1 NUMBER GEOMETRY OF STRUCTURES FORM KG3 2 NODE NO H AT AO 4 1480 3 0 00 17 10 18 50 0 00 0 90 2 40 3 5 315 345 4 1510 2 0 00 19 20 0 00 1 50 10 0 10 0 NUMBER WEIR FUNCTIONS FORM KF1 1 NODE OVFLPT WIDT NO 4 1480 0 16 80 2 1 2 00 1 NUMBER PUMP FUNCTIONS FORM KF2 1 NODE PUMP AR STA K STO K NO 4 1510 B4 15002 1 14 86 14 45 2 14 45 15 46 0 030 0 060 15 46 14
45. M TO ASCII FILES 23 LS P 23 BEC 4 d IDE FKE STRUCTURE PPM 23 1 3 PROGRAMMING Tita iii Es 23 14 SVK 19 DATA BLOCKS 1 4 1 Section 1 4 2 Section 1 4 3 Section 1 4 4 Section 1 4 5 Section 1 4 6 Section 1 4 7 Section 1 4 8 Section 1 4 9 Section 1 4 10 Section 1 4 11 Section 1 4 12 Section 1 4 13 Section DHI Software 2004 iv DHI Water amp Environment 1 5 EXAMPLE VERSION 2000 AND NEWER scscscssssssssssssssesssssscssssscsessssessscscacscssuessscssssscseseessusacscscsesessusececacscseeeees 23 DHI Software v DHI Water amp Environment COPYRIGHT WARRANTY Copyright Warranty This document refers to proprietary computer software which is protected by copyright All rights are reserved Copying or other reproduction of this manual or the related programs is prohibited without prior written consent of DHI Water amp Environment The warranty given by DHI Water amp Environment is limited as specified in your Software License Agreement The following should be noted Because programs are inherently complex and may not be completely free of errors you are advised to validate your work When using the programs you acknowledge that DHI has taken every care in the design of them DHI shall not be responsible for any damages arising out of t
46. MOUSE MOUSE PIPE FLOW Reference Manual WATER amp ENVIRONMENT DHI Software DHI Water amp Environment 1 2 5 5 22221 General description ER i ette dete qat Ege EIE bre 2 2 2 pecificalion Of lk i ciet aet i RS SUI er 2 39 NODES 23 11 General description 2 32 Types and definition of nodes netu 2AL 2 42 Orifice PUNCH ON uias tate Ue LAB EEG OUAIS E 244 Flow regulation 2 45 Non ret rivalve ci 2 46 Combined regulation non return valve regulation 2 23 DESCRIPTION OF UNSTEADY FLOW IN LINKS e eeeeee estes eene stent tn tintas tns en 3 23 3 1 SAINT VENANT EQUATIONS GENERAL ccce eet tette ettet tette 3 23 3 2 IMPLEMENTATION OF THE SAINT VENANT EQUATIONS IN MOUSE ceret tette 3 23 3 3 MODELLING THE PRESSURISED 422 4 2 seen eene nenne nter enn nnnn sse n nets ssi n nnne n rennen sss n tents sss enne r nnn 3 23 3 4 KINEMATIC WAVE APPROXIMATION 2 0 2 82441 2 224000011000000000 50220000000000 0 555 se erri nnn nn 3 23 n SEE CC LU E 342
47. MOUSE PIPE FLOW Reference Manual Appendix 1 7 DHI Water amp Environment 1 4 8 Section KG2 The KG2 KG3 sections defines nodes which have a special description of the geometry First the location of the node and the levels are given in the KG2 section Secondly each of these nodes must also appear in the section The nodes found in KG2 KG3 are not allowed to appear in and vice versa Definition of data elements Node X coor Y coor Invert level Ground level Out Shape where see description for KG1 Comments Identical to except that the node diameter found in is omitted Example NUMBER STRUCTURES FORM KG2 2 NODE X COOR Y COOR BOTTL SHP B4 1480 630 0 120 0 16 25 18 50 1 B4 1510 710 0 594 0 14 20 19 201 DHI Software Appendix 1 8 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment SS 1 4 4 Section KG3 Description of the geometry of nodes defined in the KG2 section Definition of data elements Node Number of values hl h2 h6 atl at2 lt gt aol ao2 ao6 where Node 7 character string followed by one blank Number of values number of h at ao value sets 2 6 h level m ft real number at vertical crossection area m2 ft2 real number ao horizontal crossection area m2 ft2 real number Comments Calculation of flo
48. Manual DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM LEA Structures basins This type of nodes is associated with arbitrarily shaped structures of significant volume non circular manholes tanks reservoirs basins and natural ponds Structure geometry is defined by a table of data sets min two related to monotonously increasing elevations containing the following H elevation m A cross section area used in calculation of the flow velocity in the structure assuming uniform velocity distribution m water surface area used for calculation of volume m7 outlet shape types 1 9 The first set of values corresponds to the structure bottom The last set corresponds to the surface level Intermediate values are linearly interpolated Definition of the outlet shape is connected with calculation of head losses in nodes see paragraph 7 2 A structure volume contributes to the overall system volume and is included in the computations If the water level raises above the highest elevation value in the table describing the structure geometry the program extends the basin geometry following the principle as described in Paragraph 8 1 An example of a definition of a basin is given in Figure 2 6 DHI Software MOUSE PIPE FLOW Reference Manual 2 11 DHI Water amp Environment L MODELLING THE PHYSICAL SYSTEM Storage Nodes DHI Software Name example Type
49. NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE cone LE 4 5 6 7 2 3 8 RS TI x x x 2 x x x x M x 3 x C x 4 x x I X 5 X x X 6 TX x x 7 c x 8 X x x Figure 4 8 Minimised matrix band width 45 Stability Criteria A criterion for a stable solution of the finite difference scheme is given by the Courant condition At Cv dy 4 20 Ax where mean flow velocity ms At time step s Ax distance between computational points in the conduit m y water depth m Theoretically the implemented numerical scheme is unconditionally stable for all Courant numbers In practice however this is restricted because the numerical implementation and the accuracy criteria impose some additional limitations The most conservative condition for a correct and stable solution of the implemented finite difference scheme is the velocity condition v At E Ax 4 21 The automatically generated computational grid fulfils this condition 46 Optimising the Simulation Time Step At The computational efficiency of any discrete time numerical simulation algorithm is highly dependent on the time step applied in the simulations In turn the feasible time step in a concrete situation depends on apart from the inherent performance properties of the computational scheme the dynamics of the flows in the simulated network It is therefore desirable to optimise the algorithm so that in DH
50. ODELLING THE PHYSICAL SYSTEM and for a side overflow weir 0 3 2 2 H 2 11 0 8 E RT 2 11 where water depth above the weir crest level energy loss coefficient associated with the outlet head loss specified for the weir node see Paragraphs 7 3 to 7 6 This actually corresponds to the standard overflow formula for a rectangular notch Quy CHB 2g 2 12 where is a discharge coefficient expressed for an orthogonal weir as COME NM 24 Key 2227 and for a side overflow weir 3 C7 GE KJ 2 14 E g this method if used with 0 5 sharp edged outlet is equivalent to a standard weir formula with 0 7589 and 0 4582 for orthogonal and for side weir respectively The side overflow yields a smaller discharge for the same overflow level because in this case the kinetic energy of the approaching flow is excluded from the computations User Specified Discharge Coefficient If the method with default energy loss coefficient is not applicable for a particular weir the standard overflow formula 2 12 is applied with a user specified level discharge coefficient Cy 2 3C which gives Q veir Cu 4528 2 15 This implies that the head loss coefficient specified for the weir node and the weir orientation are ignored in the weir computation DHI Software MOUSE PIPE FLOW Reference Manual 2 17 DH
51. TION FORM L3 BL D A FLOW GW LE OP CL NO 1 0 000000 I 6 0 30 1 00 4 00 0 70 0 70 0 70 0 0700 0 5700 2 6700 0 1300 0 2900 0 3330 DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 19 DHI Water amp Environment 1 4 13 Section 14 The L4 section is MOUSE specific extension of the original file format The L4 section has been introduced for providing a more flexible way of defining arbitrary pipe and channel cross section shapes The cross sections are defined through the MOUSE Cross Section Editor Any number of cross sections can be defined Each cross section is identified by a name the Cross section ID The ID is a string with maximum 12 characters Except for the difference in length the same rules apply for this ID string as for node names Definition of data elements Nodel Node2 Mat Ai Invert1 lt Invert2 gt lt CrsBase gt CrsId Scale lt Op Cl gt where CrsBase Cross section Data Base name max 8 characters file name lt CrsId gt Cross section ID name maximum 12 characters Scale Scaling factor Applied both vertical and horizontal lt Op Cl gt 1 Opencross section 2 Closed cross section other parameters See definition for the L1 section Comments A separate ASCII text file format is available for import export of the Cross section Data base file to from MOUSE Example NUMBER CONDUITS CROSS SECTION Data Base FORM
52. The minimum number of computational points N in a conduit is 3 i e two h points and one point in between The points are all equally spaced with a distance Ax equal to Ax 4 1 where is the conduit length On the basis of the input data and the specified time step The model automatically generates a complete computational grid based on the velocity condition see paragraph 4 5 The velocity used in the calculation is a full flow velocity obtained from the Manning formulation assuming completely filled conduit If the velocity condition can not be satisfied for the specified simulation time step which often happens with short and steep pipes then the model issues a warning with proposal for a shorter time step required for the condition to be satisfied DHI Software MOUSE PIPE FLOW Reference Manual 4 1 DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE NETWORKS The grid generated by the model can be altered individually for each conduit i e can be made more dense or sparse according to the needs of the current application see documentation on ADP file Manhole 1 Manhole 2 Manhole 3 Figure 4 1 A section of the network with Computational Grid 43 Numerical Scheme The implemented numerical scheme is a 6 point Abbott scheme see ref 2 The scheme for the method is shown in Figure 4 2 Timestep 4 M o Ns o
53. USE PIPE FLOW Reference Manual 2 7 DHI Water amp Environment 54 lt MODELLING THE PHYSICAL SYSTEM Circular Manholes Circular manhole is a vertical cylinder defined by the following parameters Hrot bottom elevation m surface elevation m Dun diameter m K outlet shape types 1 9 Definition of the outlet shape is connected with calculation of head losses in nodes see paragraph 7 2 MANHOLE DATA X coordinate Y coordinate Diameter m Ground Level mabs Invert Level mabs Critical Level mabs Outlet Shape level m Figure 2 4 MOUSE manhole Flow conditions in a manhole are an important element of the overall flow description The following parameters are calculated An water level in a manhole m velocity calculated per default as Q 3 E Hm Hyon 2 1 i e uniform velocity distribution is assumed The flow area calculated as above gives a very conservatively low estimate of the velocity head and hence a conservative energy loss in the manhole causing higher water levels in the manholes than observed in reality DHI Software 2 8 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM An alternative formula for a more realistic calculation of the flow area in manholes is also available however only for flow through manholes with one inlet pipe in and one outlet
54. ace elevation Hou be specified as constant or as time dependent see Chapter 6 Boundary Conditions Depending on the specified outlet water level the model applies the following elevation of the water surface in the link adjacent to the outlet H out forH out 2 H bot min ye h else 2 6 H bot min ye where Ye critical depth m Yn normal depth m In the later case the outlet is considered to be a free outlet meaning that the outlet water level does not influence the flow in the adjacent link Otherwise the model applies the specified water level with the corresponding backwater effect and a possibility for reverse flow DHI Software MOUSE PIPE FLOW Reference Manual 2 13 DHI Water amp Environment 54 lt MODELLING THE PHYSICAL SYSTEM 2 4 Functions 2 4 1 Overflow weirs Functions are used for the calculation of the flow between the two nodes or in specified links according to the functional relation and the hydraulic conditions at relevant points in the system There can be more functions defined simultaneously between the two nodes of the network One or more functions can be defined in a link between the two nodes The overflow structures are normally found in sewer systems with purpose to lessen the hydraulic load in the pipe system during extreme flow conditions by allowing a part of the flow to be spilled to a recipient Also overflow structures can be u
55. an be expressed by applying the vertical contraction coefficient given as W y2 W2 There are two unknowns in these two equations By rearranging the equations and substituting the q actually 4 28 from one of equations into another the remaining unknown in the obtained equation is 2 The equation can be transformed into a 4 degree polynomial of a general form Cy Oy 0 2 28 The polynomial is solved iteratively applying the Newton Raphson principle The initial value of y applied in the iterations is 2 y W W2 1 2 The iterative process terminates when 2 converges within the specified threshold or if the number of iterations exceeds the specified number If the convergence is achieved the discharge can then be derived from equation 2 26 The value of is rejected if the maximum number of iterations is exceeded or in the following cases e If y gives a negative argument to the square root for the discharge e If y2 gt yy w w2 lt w2 The equations applied above have some shortcomings At first the effect of the curved streamlines is not taken into account properly in contrast to the free overflow case which is derived from empirical expressions The curved streamlines will in this case give a different pressure distribution over the crest deviating from the hydrostatic pressure and the pressure will be smaller The curved streamlines will become less
56. duce different contents of the headlines The lt Data elements gt are in most cases on one line but for some sections a lt Data Element gt will cover more lines For a few types of data elements the number of lines may vary depending on the actual data contents The remaining part of this description will be based on the example file which is enclosed at the end of this chapter The example shows most of types of data which can be found in the SVK19 files Note that the example contains 13 sections sections must be present even if some sections do not contain any data elements Note also that the sections are identified in the headline 1 gt by names as FORM D FORM etc This identification will be used as reference in the detailed description for each section The following sections exists D Catchment data for the hydrology simulation 1 Circular manholes KG2 Nodes manholes with specific geometry KG3 Geometry description for nodes in KG2 section Weir description KF2 Pump description KF3 Regulator description 2 KK Critical level 3 KU Outlet description L1 Circular pipes L2 Channels with trapezoidal cross section 4 L3 Channels with arbitrary cross section 5 L4 Pipes with cross section database reference 6 Notes 1 This group of data has been moved to the hydrological data file HGF which is an ASCII PFS file The SVK19 files generated by the Export funct
57. e 7 6 with a constant inflow of 0 8 m s into both branches at nodes A 3 1 and A 3 2 The nodes in the left branch have specified outlet shape coefficients Km as option Sharp Edged K 0 5 while the nodes in the right branch are specified with option Energy Loss where Km also equals to 0 5 On the profile plot Figure 7 7 a significant difference in computed water levels in nodes B 3 1 and B 3 2 can be observed The result in node B 3 1 is incorrect which is caused by the strong limitation of the outlet head loss when option 2 is used This result gives an inaccurate too low water level in node B 3 1 needed to supply 0 8 m s into the downstream pipe or in other words artificially adds energy into the DHI Software MOUSE PIPE FLOW Reference Manual 7 13 DHI Water amp Environment 54 gt lt FLOW RESISTANCE system On the contrary energy levels in the right example are correctly computed but the solution appears as unrealistic Namely after a fully submerged inlet computed water level in the outlet pipe is so low that the pipe is filled less than 1 3 This is a consequence of the MOUSE incapability to compute negative pressures At other two nodes C 3 1 and D 3 1 results are identical as in corresponding two nodes in the right branch because the computed head loss does not exceed the limitation Similarly comparison between the option 4 left branch and 6 right branch in both cases with Km
58. e Danish egg shape i e 0 shape the dimension to be specified is the width D m and for the standard egg shape the dimension to be specified is the cross section height 2 4 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM Ss The non standard link cross sections can be specified and maintained through the Cross section Editor Cross sections are distinguished as opened and closed i e open canals on the one side and pipes and tunnels on the other The data required for description of a non standard cross section can be entered in a raw form either in a X Z or in Height Width format see MOUSE User Guide paragraph Network Cross Section which gives six options in total Pairs of X Z co ordinates in a counter clockwise direction Z X Z Open 8 3 X Z Closed Figure 2 2 X Z types of cross sections DHI Software MOUSE PIPE FLOW Reference Manual 2 5 DHI Water amp Environment L MODELLING THE PHYSICAL SYSTEM DHI Software Pairs of H W co ordinates in an upwards direction _ Hs H W Closed v Figure 2 3 H W types of Cross sections The raw geometrical data are then automatically processed in order to create tables with parameters suitable for flow computations Such a table contains 50 data sets covering the range from the lowest to the highest point specified in equal increments
59. e corrected discharges are overwritten by new values for the submerged flow case Submerged Underflow The submerged underflow is identified when the upstream water level is above the gate level and the downstream water level influences the discharge through the gate The threshold for swapping from free underflow to submerged underflow is for the simplification purpose defined at AH H 1 3 This ensures that the same criterion is applied both in the overflow and underflow cases and a consistency of the solution is maintained when wy H approaches unity A definition sketch of the submerged underflow is shown on Fig 2 13 DHI Software MOUSE PIPE FLOW Reference Manual 2 29 DHI Water amp Environment Ss MODELLING THE PHYSICAL SYSTEM DHI Software mi ns n2 H a Wa hs yY wW Ya y2 Ww nos Figure 2 13 Definition of submerged underflow A combined energy and momentum formulation is applied the same principle as for the submerged overflow If the energy loss from section 1 to 2 is ignored the energy equation reads 4 4 2 38 momentum equation from section 2 to 3 be written as 2 2 2 2 2 92 2 39 where the shear stress on the bottom from section 2 3 is neglected The contracted overflow area can then be expressed by applying the vertical contraction coefficient given as y y wo By rearranging the two equations and eliminating one of the tw
60. e resistance in free surface flow links are introduced as a friction slope term into the momentum equation see paragraph 3 2 The friction slope J is equal to the slope of the energy grade line and is defined as 2 1 Jer 7 1 where T tangential stress caused by the wall friction Nm density of water kgm hydraulic radius m where P is the wetted parameter The friction slope can be derived as a function of an appropriate combination of the flow parameters Q A and R and the water and conduit wall properties v Generally the friction slope can be expressed as 0 7 2 where is generalised friction factor By these means the friction slope is explicitly determined as a function of instantaneous values of local flow parameters A more stable formulation is achieved through an implicit description of the friction term It is derived from a variational principle at a grid point 7 as I7 1 0dl 20 0 61 7 3 This results 1n DHI Software MOUSE PIPE FLOW Reference Manual 7 1 DHI Water amp Environment 54 gt lt FLOW RESISTANCE nc n I I 0dl fy E 7 4 f Qj Qi gt The coefficient 9 determines the time weighting of the scheme For stability reasons the coefficient should be above 0 5 The recommended also default value is 1 0 i e a fully forward time weighting o
61. eam boundary conditions and thus consider backwater effects The diffusive wave approximation is therefore from a theoretical and practical point of view a better ap proach than the kinematic wave approximation The computational basis for the diffusive wave approximation is in principle identical to the one applied for the dynamic wave approximation for Froude number Fr gt 1 supercritical flow Further more for stability reasons a moving average in time is applied to the slope of the water surface Ai ox in order to dampen the short periodic fluctuations This means that only relatively steady backwater phenomena compared to the time step are resolved 3 6 Dynamic Wave Approximation 3 6 1 General DHI Software The general flow equations form the best theoretical foundation for a flow model because the full equation of momentum makes it possible to describe all forces affecting the flow conditions However larger computational load in comparison with the kinematic and diffusive 3 10 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual DESCRIPTION UNSTEADY FLOW IN LINKS wave approximations involves correspondingly larger CPU time for the same analysis Additionally difficulties are present when simulating the supercritical flow conditions 3 6 2 Supercritical flow simulations with dynamic wave approximation The full Saint Venant equations 3 1 and 3 2 are applicable in the dynamic wave appr
62. eason the transition is simply assumed to take place at an upstream water level equal to the top of the gate while the difference between overflow and underflow equations is fully corrected in the underflow computation at that level This requires a correction in the free underflow equation through the use of a correction coefficient For increasing upstream water levels this correction coefficient is gradually reduced as follows 0 2 36 where _ overflow 2 37 C C ume with E and Cz taken at the top of the gate level For increasing upstream levels the discharge coefficient approaches the constant value usually taken as 0 608 The free flow equations require a further correction based on the pressure distribution at the outflow side There are two extreme cases the jet can either emanate surrounded by free atmosphere like an orifice or it can have full contact with the bottom on the downstream side the vertical sluice gate In the first case the pressure over the height of the jet is approximately atmospheric In the other case the pressure follows a hydrostatic distribution The real situation usually is somewhere in between these two extreme cases and the flow through the gate is corrected for the influence from the pressure on the downstream side 2 28 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM T
63. efault value 1 The spilling nodes are defined in the ADP file 8 4 Pressure Mains The pressure mains also referred to as rising mains in earlier versions of MOUSE feature is intended for modeling the permanently pressurized individual pipes or networks in connection to pumps Computationally MOUSE assumes that a rising main network always runs under pressure and therefore the reaction time within the rising main network is insignificant Solution in pressure mains is based on the two equations 90 0 8 3 90 3r amp Jr 8 8 4 where discharge m s flow area m7 y flow depth m g acceleration of gravity ms distance in the flow direction m x time s Ip bottom slope l friction slope All nodes within the pressure main networks are assumed to be sealed DHI Software MOUSE PIPE FLOW Reference Manual 8 3 DHI Water amp Environment 54 gt lt SOME SPECIAL TECHNIQUES 8 5 Dry Conduits DHI Software MOUSE supports modeling of an arbitrary number of pressure main networks and there is no limitation on the number of elements in each sub network Pressure main networks must always converge down to one receiving manhole which is called the tail node The tail node is the point of transition between domains where the hydraulic solution is based on the St Venant equation and the special pressure main model The computation o
64. efficient mode DHI Software In this example a simple sewer system consisting of two pipes two manholes and one outlet is constructed Tests for different head loss formulations a b and c have been performed with various modifications in flow direction or drop height or both Table 7 1 shows a complete test matrix Four variants of the model setup have been constructed I Straight sewer pipelines with no drops and no changes in directions A change in direction is introduced in variant I A drop is introduced in variant I IV Adrop anda change in direction are introduced in variant I A definition sketch of the setups I IV is shown in Figure 7 9 The manual calculation example corresponds to test No 4 in the test matrix Figure 7 9 Example definition sketch In the performed tests the value of the HEADLOSS COEFFICIENT has been set to 0 5 for all three modes a b and c The head loss coefficients for drop in the setup IIT and IV is 0 4 inlet pipe is 0 6 m 7 16 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual FLOW RESISTANCE 254 lt above the bottom manhole The head loss for direction in the setup and IV is 0 25 angle between pipes are 45 The example also includes calculation of the friction loss in the downstream pipe Manual head loss calculation Assumptions The water level in the inlet pipe is assumed equal to the water
65. eme cases where head losses in nodes play a crucial role for the correct solution it is advisable to perform a more detailed analysis in order to assess the approximation errors inherent to this approach In acase of a free inlet of a sub critical flow i e when the water level in the junction is lower than the critical depth level in the inlet link the water level in the link is assumed to be equal to the critical depth For different cross sections appropriate approximations are applied e g for a circular pipe as follows lo 32 7 12 where Di diameter of the circular pipe m Similarly in a case of a low water level in the junction with supercritical flow steep inlet links the downstream water level is set equal to normal depth in the link 7 3 2 Head losses at the outlet from a node the individual losses in a node except the inlet loss calculated by the model are added up at the outlet separately for each outlet link The outlet loss for the link is assumed to be proportional to the velocity head in the outlet link j DHI Software MOUSE PIPE FLOW Reference Manual 7 7 Water amp Environment 54 gt lt FLOW RESISTANCE 2 T Ani ty 7 13 k where bx are individual head loss coefficients for link j calculated on the basis of geometrical set up of the node and flow distribution among the links attached to the node The model distinguishes among the following lo
66. es difficulties in fitting the computed stage discharge curve based on a single M value specified for a link with the actual measured stage discharge relation This is usually related to old systems where significant sediment deposits and pipe wall erosion are present The MOUSE Pipe Flow Model accepts a specification of a non linear variation of Manning number with relative elevation water depth in the conduit Three parameters define the Manning s number variation bottom value full flow value and a non linear exponent Intermediate values are calculated by a general expression exp y Mas Mon M op 2 7 8 where Mact calculated Manning s number Manning s numbers specified for the conduit bottom and top respectively exp Manning s number variation exponent default yD the relative water depth in a conduit The formula is used for relative depths h D in the interval 0 0 1 0 For relative depth gt 1 0 the Manning number is set to the Manningiop value The variation between Manning and Manning is controlled by the Variation Exponent The variation of the Manning number in relative terms is illustrated in Figure 7 1 An example of the variation is shown in Figure 7 2 with Manning M values DHI Software MOUSE PIPE FLOW Reference Manual 7 3 DHI Water amp Environment FLOW RESISTANCE h D A 10 Variation exponent 1 3 0 0 5 0 1 Manning of
67. f the scheme MOUSE provides an optional choice between the explicit and implicit flow resistance description through The DHIAPP INI file see relevant documentation The explicit description is selected per default 7 1 2 The friction resistance described by the Manning formula DHI Software The classic explicit application of the Manning s formula reads as 210 7 5 with the friction factor 1 MAR 3 7 6 f where M is the Manning number A the area and R the hydraulic radius Usage of the ol Q instead of facilitates computations of the reverse flow The Manning s number M or n 1 M is the parameter used as a measure of the conduit s wall roughness Default values are given in paragraph 2 2 2 The implicit formulation of the Manning s formula is obtained by the differentiation of f with respect to h which results in Ff __ f 90M 2 4f9R h M h Adh 3R h 7 7 and substituting the derivative into the Equation 7 4 7 2 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual FLOW RESISTANCE 54 lt 7 1 3 Depth variable Manning coefficient Per default MOUSE assumes a constant Manning s number over the link section height However in real situations conduit wall roughness often changes with water depth because different parts of the link cross section are exposed to quite different flow conditions during its lifetime This introduc
68. f the special pressure main sub models uses the maximum of the water level in the St Venant governed domain and the water level at the tail nodes as downstream boundary conditions As default it is assumed that the tail node water level is equal to the maximum of the up vert level of all pipes attached to the tail node but the user can change this default value The upstream pressure main network must be linked with the St Venant controlled domain through pumps The pressure mains feature can handle an unlimited number of pumps attached to one pressure main network but the solution feature can only handle networks where the upstream link to the St Venant domain is modeled by pumps If parts of the sewer system dry out during the simulation then the model artificially maintains a minimum water depth in those conduits corresponding per default to 2 of the characteristic dimension of the conduit diameter for circular pipes or max 0 02 m This is necessary with regards to the numerical stability in the solution of the flow equations This correction practically means artificial generation of water i e some water volume is added to the system As a consequence of that the continuity status report shown at the end of the simulation does not give a fair impression of the accuracy of the simulation 8 4 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual NOMENCLATURE Ss NOMENCLATURE a D
69. ferent for the different inlet links DHI Software MOUSE PIPE FLOW Reference Manual 7 19 DHI Water amp Environment SOME SPECIAL TECHNIQUES 54 lt 8 SOME SPECIAL TECHNIQUES 8 1 Surface Flooding If the water level in a manhole or a basin reaches the ground level an artificial inundation basin is inserted above the node The surface area of this basin is gradually over one meter increased from the area in the manhole or the basin to a 1000 times larger area thus simulating the surface inundation The maximum level of inundation is 10 meter above the specified ground level When the outflow from the node surmounts the inflow the water stored in the inundation basin re enters the system When the water level in the node increases and is above ground level the following is assumed During a time step the surface area in the basin is calculated using the water level from the start of the actual time step A situation like this is shown in Figure 8 1 If the water level passes through the transition region between the actual manhole or structure and the artificial basin this assumption leads to generation of water In Figure 8 1 the shaded area illustrates the generated volume of water Water level and area in timestep n 1 A 1000 Am Ground level Generated volume from timestep n to n 1 Generated volume from timestep n to n 1 Water level and area in timestep n Figure 8 1 Simulat
70. finition of a numerical model in MOUSE are 3 Links pipes standard and arbitrary cross sections open channels arbitrary cross sections Nodes manholes basins structures storage nodes outlets Functions for description of certain physical components of sewer systems including 4 overflow weirs orifices pumps non return valves flow regulators Controllable structures for the simulation of reactive or time dependent operation real time control including rectangular underflow gate with movable blade rectangular overflow weir with changeable crest elevation Principles underlying the concept of controllable structures are described in the MOUSE RTC User Manual and Tutorial DHI Software MOUSE PIPE FLOW Reference Manual 2 1 DHI Water amp Environment 54 lt MODELLING THE PHYSICAL SYSTEM 2 2 Links 2 2 1 General description Links in MOUSE Pipe Flow Model are defined as one dimensional water conduits connecting two nodes in the model The link definition allows that the dependent flow variables e g water levels and discharges can be uniquely described as functions of time and space A link is featured by constant cross section geometry constant bottom slope and constant friction properties along the entire length A straight layout is assumed MOUSE supports two classes of links closed conduit links pipes e open channel links Closed conduit
71. ge obtained as explicit estimate based on the known water levels in the previous time step on each side of the regulation point m s water level at the control point m Anininax water levels at the control point A defining the range in which the regulation is to be applied m 2 34 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM Ss 2 4 5 Non return valve The function for simulation of non return valves is included into the model structure identically as the flow regulation function The flow is applied according to the following Q for 2 H down 4 else 0 where Q Qreg Hup Haown 2 47 calculated discharge m s applied discharge ms water levels at the computational points upstream and downstream respectively m 2 46 Combined regulation non return valve regulation A combination of the two previous functions results with min Q Ha for H min SHASH max and H up H down Cres uis 2 48 0 where Qreg applied discharge m s discharge defined by the regulation function m s natural discharge obtained as an explicate estimate based on the known water levels in the previous time step on each side of the regulation point m s 1 water level at the control point m HminHmas water levels at the control point A defining the range in w
72. he free overflow formula according to the following for lt o T AP Q pin 0 8 2 Jor H H AP top Relative Weir Coefficient 0 63 B 28 AP where Ospitt is the spill discharge m s B is a conceptual spill width m An is the water level in the manhole m Hop is the ground level in the manhole m AP is the Buffer Pressure Level for the spill m g is the acceleration of gravity ms RelativeWeirCoefficient is the linear scaling coefficient for the spill The level i e head at which the spill starts can be controlled by optionally specifying the Buffer Pressure Level as a relative elevation above or below the ground surface default value 0 For circular manholes the spill width B equals to 1 5 times the manhole diameter for the water level Hm With increasing water level the spill width B increases following the same functional DHI Software 8 2 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment SOME SPECIAL TECHNIQUES Ss relation as used for the basin area above surcharging nodes i e increases exponentially to approximately max 1000 times the manhole diameter see paragraph 8 1 For nodes defined as basins the spill width B is set equal to the square root of the basin surface area The spilling capacity of a spilling manhole can be controlled by specifying the Relative Weir Coefficient d
73. he underflow equation has been derived on the basis of experiments where the downstream bottom level is the same as the sill level of gates w2 0 This implies a hydrostatic pressure distribution in the contracted flow section With positive values for w2 drop structure however these pressures drop to lower values with nearly atmospheric pressure over the height of the jet In this case the discharge will be higher due to the lower counter pressure Comparison of the orifice flow equation and the underflow equation reveals that this difference may be up to 9 The same reasoning applies to some extent for the case of overflow where the discharge equation for the case of a free overfall w 0 1s also based on hydrostatic pressure distribution assumption To cover most cases in a reasonable way therefore the free flow discharges are increased by 5 for the case where the downstream water level is found below the crest level of the gate For the range of downstream water levels between the crest level and the upstream level the correction applied is reduced quadratically as the downstream water level is increasing The quadratic reduction follows from the quadratic relation between the integrated hydrostatic pressure force and the water depth Although the matrix of free flow discharges is set up for the complete range of downstream water levels up to the level which equals the upstream level it should be realised that some of thes
74. he use and application of the programs and you shall satisfy yourself that the programs provide satisfactory solutions by testing out sufficient examples DHI Software DHI Water amp Environment COPYRIGHT WARRANTY DHI Software DHI Water amp Environment GENERAL DESCRIPTION Ss 1 GENERAL DESCRIPTION The MOUSE Pipe Flow Model is a computational tool for simulations of unsteady flows in pipe networks with alternating free surface and pressurised flow conditions The computation is based on an implicit finite difference numerical solution of basic 1 D free surface flow equations Saint Venant The implemented algorithm provides efficient and accurate solutions in multiply connected branched and looped pipe networks The computational scheme is applicable to vertically homogeneous flow conditions which occur in pipes ranging from small profile collectors for detailed urban drainage to low lying often pressurised sewer mains affected by the varying water level at the outlet Hydrodynamics of prismatic open channels can also be simulated Both sub critical and supercritical flows are treated by means of the same numerical scheme that adapts according to the local flow conditions Naturally flow features such as backwater effects and surcharges are precisely simulated Pressurised flow computations are facilitated through implementation of a narrow slot as a vertical extension of a closed pipe cross sect
75. hen follow by lt Pct gt Percent impervious area 0 0 integer if lt H gt 2 then follow by S Soil parameter 1 3 Always set to 1 not used in MOUSE al steep roof integer a2 flat root integer a3 paved area 0 o integer a4 semi pervious large infiltratiron 0 o 0 o integer a5 semi pervious small infiltratiron 0 0 0 o integer a6 pervious area unplanted integer a pervious area planted integer DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 5 DHI Water amp Environment Example NUMBER CATCHMENTS AREA SLOPE LENG A Comments lt Q gt additional inflow is recommended to set to zero 0 000 for MOUSE However the alternative options for specifying additional inflow exists in MOUSE is recommended lt H gt hydrological level 1 is recommended for use in MOUSE 9 B4 1520 B4 1500 B4 1501 B4 1502 B4 1491 B4 1490 B4 1480 B4 1300 4 1310 DHI Software 30 2 440 680 400 000 500 000 000 NO 000 550 0 40 40 50 40 40 40 40 40 Qe OO Q O OQ O1 000 1 000 1 000 1 000 1 000 1 000 1 000 1 000 1 000 1 FORM D H PCT S DISTR OF SURFACES 20 60 60 65 50 50 50
76. here will be used during the simulation as a constant water level MOUSE also offers an option for applying a time varying water level input through the Boundary Data system in MOUSE Example NUMBER OUTLETS FORM KU 1 NODE X COOR Y COOR BOTTL OUTL A0 0327 630 0 0 0 16 00 17 00 DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 15 DHI Water amp Environment 1 4 10 Section 11 DHI Software The section is used for defining links pipes connecting nodes in the sewer network In the L1 section pipes with simple cross section shapes can be defined That is primarily circular pipes but also special egg shape pipes and pipes with a square cross section can be defined For pipes with arbitrary cross sections it is recommended to use the L4 section in combination with the cross section data base found in MOUSE Please refer to the MOUSE documentation for details Definition of data elements Nodel1 Node2 Mat Ai Invert1 lt Invert2 gt Af Qinf or GWlev As D where Node1 7 character string followed by one blank lt Node2 gt 7 character string followed by one blank lt Mat gt Material code 1 7 relates to Manning numbers in MOUSE lt Ai gt 1 Invert levels are given 2 Invert levels are NOT given lt Invert1 gt Pipe invert level at Nodel m ft real number lt Invert2 gt Pipe invert level at Node2 m ft real number Af 1
77. hich the regulation is to be applied m water levels at the computational points upstream and downstream respectively DHI Software MOUSE PIPE FLOW Reference Manual 2 35 DHI Water amp Environment DESCRIPTION UNSTEADY FLOW IN LINKS 3 DESCRIPTION OF UNSTEADY FLOW IN LINKS 3 1 Saint Venant Equations General Computations of the unsteady flow in the links MOUSE Pipe Flow Model applied with the dynamic wave description performs by solving the vertically integrated equations of conservation of continuity and momentum the Saint Venant equations based on the following assumptions e the water is incompressible and homogeneous i e negligible variation in density e the bottom slope is small thus the cosine of the angle it makes with the horizontal may be taken as 1 e the wavelengths are large compared to the water depth This ensures that the flow everywhere can be regarded as having a direction parallel to the bottom i e vertical accelerations can be neglected and a hydrostatic pressure variation along the vertical can be assumed e the flow is sub critical Super critical flow is also modelled in MOUSE but using more restrictive conditions The general form of the equations takes the form as follows Conservation of mass continuity equation 90 9A 3 1 Conservation of momentum momentum equation 2 90 EAT Fg AI p BAL y 3 2
78. ing or as effect of external water level These disturbances may be constant stationary or time variable By default MOUSE supplies all necessary boundary conditions founded on the topology and geometry of the system Therefore the simulations can be run even if no boundary conditions of the other type are specified by the user With respect to the volume balance in the system two groups of boundary conditions can be distinguished External boundary conditions describing the interaction of the modelled system with its surroundings 2 Internal boundary conditions describing relations between certain parts of the model The external boundary conditions comprise the following At manholes and structures 1 Constant inflow or extraction const m s 2 Time variable inflow or extraction Q Q t 113 3 Computed inflow hydrograph Q t m s 4 Weir discharging out of the system m 1 5 Pump discharging out of the system 002871 DHI Software MOUSE PIPE FLOW Reference Manual 6 1 DHI Water amp Environment 54 gt lt BOUNDARY CONDITIONS DHI Software Application of negative inflows extraction should be done with due care because extraction of more volume than the system can supply would end up with error in computations At outlets 1 Constant outlet water level H const m 2 Time variable outlet water level H H t m
79. ion Free surface and pressurised flows are thus described within the same basic algorithm which ensures a smooth and stable transition between the two flow types The complete non linear flow equations can be solved for user specified or automatically supplied boundary conditions In addition to this fully dynamic description simplified flow descriptions are available Within the Pipe Flow Model advanced computational formulations enable description of a variety of pipe network elements system operation features and flow phenomena e g flexible cross section database including standard shapes circular manholes detention basins overflow weirs pump operation passive and active flow regulation constant or time variable outlet water level DHI Software MOUSE PIPE FLOW Reference Manual 1 1 DHI Water amp Environment GENERAL DESCRIPTION constant or time variable inflows into the sewer network e head losses at manholes and basins e depth variable friction coefficients The features implemented in conceptualisation of the physical system and the flow process enable realistic and reliable simulations of the performance of both existing sewer systems and those under design DHI Software 1 2 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM Ss 2 MODELLING THE PHYSICAL SYSTEM 2 1 The model elements inventory Elements available for de
80. ion of MOUSE release 2000 and newer contain an empty form D When importing a SVK19 file which was generated Appendix l 2 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual by the Export function of an earlier MOUSE release the catchment information is ignored In order to avoid the loss of data when loading such an old data file both in binary SWF and ASCII SVK19 formats an external conversion program has been made available in the MOUSE BIN directory mouse swf2hgf exe which extracts all the catchment information from the network data file combines it with the hydrological data from the ROF file and creates the new HGF ASCII file 2 Do not apply the KF3 form MOUSE handles regulated weirs and gates based on data in separate input files Please refer to the MOUSE documentation 3 The section must be present but MOUSE does not apply the critical level data 4 Itis recommended to apply the L4 form instead of the L2 for input of trapezoidal cross sections 5 It is recommended to apply the L4 form instead of L3 for input of arbitrary crossections 6 This section is not part of the original format definition The L4 section has been defined by DHI for use in MOUSE as an enhanced alternative to the L2 and L3 sections Data can be given in either SI metric or US American units 1 3 Programming Aspects The loading routines in MOUSE require that the data are separated by blank characte
81. ion of the surface flooding When the increase of the water level during a time step is relatively small then the generated water volume is negligible If the water level is changing rapidly the generated volume of water is important and due to that an appropriate correction is built in the program to ensure no generation of water An alternative to the assumption of constant surface area during a time step is to introduce iterations in the simulation Iterations would significantly increase the simulation time DHI Software MOUSE PIPE FLOW Reference Manual 8 1 DHI Water amp Environment 54 gt lt SOME SPECIAL TECHNIQUES 8 2 Sealed Nodes Any manhole or basin can be defined as sealed If a node is defined as a sealed node then the maximum water level at a node is set to the ground surface In this case the pressure will rise without any water on the ground surface The following relations are valid H m m and 8 1 H for gt H o m P for lt T where An is the water level in the node m Pin is the pressure level in the node m is the ground level for the node m sealed nodes are defined in the ADP file 8 3 Spilling Nodes Any manhole or basin can be defined as spilling If the water level in a node defined as a spilling node reaches the ground level the water will start spilling irreversibly out of the system The flow will be computed using t
82. ion with the MOUSE Pipe Flow Model Before using the ADP file the Manning number parameters for the selected lines must be modified i e values for bottom and top of pipe Manning numbers and possibly the variation exponent must be adjusted for the pipes or canals where varying Manning numbers are to be used 7 1 4 Colebrook White Formula for Circular Pipes In 1939 Colebrook and White derived an approximate formula which unifies the description of the turbulent flow in both rough and smooth circular pipes This formula is extensively used for the computation of flow resistance in predominantly full flowing pipe networks According to Colebrook and White the friction factor fis computed iteratively using one of the several formulations known from the literature The formula implemented in MOUSE reads 2 2 k cw tcew In 7 9 Saw Re Faw R where k the equivalent wall roughness m R the hydraulic radius Re the Reynolds number CW CW2 cw4 empirical constants The default values of the constants are cw 6 4 CW 2 45 3 3 CW4 1 0 The default values can be modified through DHIAPP INI file DHI Software MOUSE PIPE FLOW Reference Manual 7 5 DHI Water amp Environment 54 gt lt FLOW RESISTANCE The actual friction slope is calculated by using the following relation 2gA R sfata 1 10 If f ds 2gA R The Colebrook Whi
83. ions between Cz P q E for different values of Ww Starting with values for H and w given the energy level can be derived by iteration The iteration implemented in the program is based on a Newton Raphson technique The discharge over the weir can then be determined by inserting the energy level into equation 2 21 Submerged Overflow The submerged overflow is identified when the downstream water level influences the discharge over the weir and water surface is free i e the upper of the gate is not in contact with the water surface as can be seen in Fig 2 11 The submerged overflow case will be applied when the wy H gt 1 0 and AH H lt 1 3 The submerged overflow case is illustrated in Fig 2 12 also giving the meaning of the geometrical parameters used in the sequel hi od ha hs H hs y w y2 W Ww T Ys Figure 2 12 Definition of submerged overflow Since the energy loss from section 1 to 2 is much smaller than the energy loss from 2 to 3 the energy loss is neglected i e E E2 energy equation now reads 2 2 X 2 26 28 22 DHI Software 2 24 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM The momentum equation from section 2 to 3 can be written as q 93 4 23 2 27 where the shear stress the bottom between section 2 and 3 is neglected The contracted overflow area c
84. ity but instead the pump discharge is gradually increased over some time steps If pumps are present in the model set up it might be necessary to introduce relatively small time steps 5 10 sec In computational terms the flow regulation differ fundamentally from the weir orifice and pump function by the fact that the control is simulated within the pipe connecting two nodes and NOT by replacing the pipe with a functional relation This means that the conduit connecting the two specified nodes is treated by the algorithm as a normal link The flow is controlled by setting the general equation coefficients at the control location first upstream Q point in the pipe The control function is specified as a function of water level in a control node A The control is applied only within the specified range of water levels and if the water level is outside the specified range an unregulated flow applies Therefore it is important that the specified range covers all expected water levels at point A Otherwise a sharp transition between the Q defined by the control function and natural unregulated discharge would occur at the range bounds causing numerical instabilities The following expression determines the flow min Q Ha 0 for H min S HAS H max Qreg else 2 46 Qua where applied regulated discharge m s Q H discharge defined by the regulation function m s natural unregulated dischar
85. j A2xj distance between points j and j Substituting for the finite difference approximations in Equation 4 3 and rearranging gives a formulation of the following form aj Bailey 0511 8 4 7 where yare functions of b and moreover depend on and at time level n and on time level 12 4 3 2 Momentum equation DHI Software The momentum equation is centred at Q points as illustrated in Figure 4 4 The derivatives of Equation 3 7 are expressed as finite difference approximations in the following way Q 0 as n nl j Q 2 2 2 2 1 1 1 2 xj 4 9 nl n nn n ju Werth oh 2 2 A2 x a 4 4 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE cone A2xj ro gt lt l nr 1 h 0 h 777 2227 40117 EN N At Centrepoint 7 fos 4 Fos cc Ko n h Gridpoint j1 j j 1 Figure 4 4 Centring of the momentum equation in the Abbott scheme For the quadratic term in Equation 4 9 a special formulation is used to ensure the correct sign for this term when the flow direction is changing during a time step Q fg g f 1 9 Q 4 11 where 1 2 9 0 Oy0j 0 Q Q f 4 12 As
86. junctions are of the same order of magnitude as those caused by the pipe wall friction Knowledge about the magnitude of these energy losses based on experimental data is very limited but some theoretical results are available e g ref 3 Importance of a detailed evaluation of these losses is related to the relative length of the links D and grows with relative shortening of the conduits 7 3 Standard MOUSE Solution F A Engelund A simplified computational model for energy losses in junctions implemented in MOUSE is based on F A Engelund s energy loss DHI Software 7 6 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment FLOW RESISTANCE 54 lt formulae see ref 5 Furthermore a critical depth formulation with approximation of critical flow conditions is used in MOUSE for simulation of a free inlet to a manhole 7 3 1 Head loss at the node inlet It is assumed that the water levels in the inlet conduit and in the manhole or structure are the same This assumption implies that the energy loss of the flow entering and expanding in the node amounts to the difference of the velocity heads in the inlet conduit i and the node m respectively Ag 2t um 2g 7 11 Essentially one dimensional analysis in MOUSE relies on this simplification also in nodes with multiple inlet and outlet conduits i e where mixing of flows of different energy levels occurs Therefore in some extr
87. lative water depth generalised flow variable substituting h and Coriolis velocity distribution coefficient coefficients in finite difference equations total calculated node head loss coefficient for outlet conduit j calculated node head loss coefficient due to change of direction calculated node head loss coefficient due to change of elevation calculated outlet contraction head loss coefficient for outlet conduit j weighting coefficent of the numerical scheme horizontal angle between inlet conduit i and outlet conduit j water density density of water for a free surface flow tangential stress caused by the wall friction Nm kinematic viscosity vertical contraction coeff DHI Software MOUSE PIPE FLOW Reference Manual 9 3 DHI Water amp Environment NOMENCLATURE DHI Software 9 4 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment 5 Ss 10 REFERENCES 1 MOUSE User Manual and Tutorial 1999 2 Abbott M B Computational Hydraulics Elements of the Theory of Free Surface Flows Pitman 1979 3 Pedersen F B Mark O Head Losses in Storm Sewer Manholes Submerged Jet Theory Journal of Hydraulic Engineering Vol 116 No 11 November 1990 4 Cunge and Wegner M 1964 Integration numerique des equations d ecoulement de Barre de Saint Venant par un schema implicite de differences finies Applicatio
88. ly as for the options listed above overwritten for selected nodes Options No CRS change 1 and No CRS change 2 ignore all calculated losses Both perform similar Regardless of the shape of the outlets geometrical set up of the junction and distribution of flows among inlet and outlet conduits water levels in the junction and the outlet conduit are set equal as if there is no change of geometry and the flow conditions between the junction and outlet conduit This literary means that this option should be applied only where there is no change in cross section If inappropriately applied inconsistent results may be generated If an artificial node is introduced somewhere on a straight section of a conduit where no losses occur then one of these two options can be recommended for use Options Effective Flow Area 1 and Effective Flow Area 2 apply the same concept as for Round edged Sharp edged and Orifice but with the calculated reduced effective flow area after the submerged jet theory see paragraph 2 3 The option 1 takes the effective flow area fully while the option 2 reduces the area further by 50 These two option can be used only for flow trough manholes with circular pipes attached Option Mean energy Approach is an alternative approach as described in paragraph 7 5 7 5 3 Example 1 Impact of alternative head loss formulations on the results A symmetric system is assumed Figur
89. ment of proper initial conditions 5 1 Default Initial Conditions MOUSE automatically specifies the initial conditions establishing a default initial water depth equal to 0 5 of the characteristic dimension of the conduit diameter for circular pipes but not more than 0 005 m and flow rates are calculated based on the Manning formulation for uniform flow In case of dry weather flow applications the volume of artificially generated water may be significant compared to the dry weather flows This may compromise the volume balance the analysis For such cases the default initial depth can be reduced by setting the parameters BRANCH MIN H REL controls the initial depth relative to the conduit size and BRANCH MIN H ABS controls the absolute depth of the initial water depth to appropriate values in the DHIAPP INI file If there are outlets in the system with initial water level specified higher than the outlet bottom a horizontal water surface is assumed extending inside the system until the point in the pipe system where the water level coincides with the bottom level see Figure 5 1 DHI Software MOUSE PIPE FLOW Reference Manual 5 1 DHI Water amp Environment INITIAL CONDITIONS WATER LEVEL BRANCHES 1 1 1994 00 00 FIGPF16 PRF Discharge 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 5 2 DHI Software ie T ro rA rri T
90. n au cas d une galerie tantot en charge tantot a surface libre La Houille Blance No 1 5 Engelund og Fl Bo Pedersen Hydraulik Den Private Ingenigrfond Danmarks Tekniske Hgjskole ISBN 87 87245 64 7 In Danish DHI Software MOUSE PIPE FLOW Reference Manual 10 1 DHI Water amp Environment 5 DHI Software 10 2 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment APPENDIX DHI Software MOUSE PIPE FLOW Reference Manual DHI Water amp Environment DHI Software MOUSE PIPE FLOW Reference Manual DHI Water amp Environment SS 1 1 1 1 2 IMPORT EXPORT OF SEWER NETWORK DATA FROM TO ASCII FILES Introduction The MOUSE software package for hydraulic simulation and analysis of Urban Drainage and Sewer networks has originally operated with input files in a proprietary binary format In order to enable an easier data exchange with external applications an export import facility has been provided This has enabled import and export of the network data to from ASCII formatted files The ASCII file format used by MOUSE is known as the SVK19 format This format was originally defined by the Danish Wastewater Committee The original documentation is only available in Danish This document gives a brief overview of the file format and how it is implemented in MOUSE Before building routines for exchanging data with MOUSE it is recommended
91. ng relative to the flow rates in the inlet links relative to the outlet link is also included n Qi Zj Zi Zj Dj Zi Di Coi gt j 1 7 15 5 9 Dr Dy If the calculated head loss coefficient is smaller than 0 a zero value is assumed Loss due to contraction The flow leaving the manhole and entering the outlet conduit is more or less contracted and due to subsequent expansion there occurs an energy loss The outlet head loss coefficient depends on the shape of the manhole outlet manhole and the link cross sections and distribution of flow among multiple inlet and outlet links DHI Software MOUSE PIPE FLOW Reference Manual 7 9 DHI Water amp Environment 54 gt lt FLOW RESISTANCE MOUSE calculates the outlet head loss coefficient according to the following A C contr j Km 1 7 16 j 0 i l where Km specified outlet shape coefficient for the node For relatively large basins Km approaches contr Am flow cross sectional area in the node 7 3 8 Implementation of the total energy loss computation DHI Software Theoretically the total energy loss at the outlet from the node expressed as a function of the velocity head in the outlet pipe can be as high as the available energy level in the node The limiting case occurs e g with completely clogged outlet Km gt with no flow in the outlet pipe However in computational reality in orde
92. o unknowns 4 and 2 the combined equation reads 1 1 yy w 1 Me 0 2 40 Introducing the constants C z wo 1 y3 and 2 12 0 V wo 2 the equation can be reduced to a second degree polynomial in the form 2 30 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM 1 Gwv w y 106 0 2 41 Introducing A 1 4 Ci w Wwa y1 1 4 Coy 2 42 it can be shown that the only realistic solution for the second degree polynomial is the negative one So 2 can be expressed as 4AC T 2 43 and the discharge can then be derived from eq 2 38 The solution is sensible to the selection of the vertical contraction coefficient The contraction coefficient must be determined so that smooth transition between free and submerged underflow is maintained For a certain range of contraction coefficient values only imaginary solutions to the Eq 2 43 exist In such cases i e as long as the combined energy and momentum equation fail to deliver reasonable results the parabolic solution is applied similarly as for the transition between free and submerged overflow Practical Computational Aspects Computation of the flows through an orifice is based on a pre processed 4 D table containing the flows through a vertical slice of unit width computed as a function of four dimensionles
93. on the local geometrical parameters e Discharge from the dimensionless 4D table for the given upstream and downstream water level and if relevant gate position are read and interpolated e The unit discharges are scaled by multiplying the discharge by the upstream depth above the crest i e slice bottom to the power of 1 5 e The discharge is corrected reduced for the effect of lateral contraction e The discharge for entire orifice is summed up The actual flow through an orifice in a given hydraulic situation is obtained during the simulation by interpolating the flow derivatives with respect to h2 and wo in the 3 D table and inserting these directly into the MOUSE pipe flow algorithm By these means accuracy and stability of the computation is preserved even with very rapid water level changes and fast movement of the gate DHI Software 2 32 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM 2 43 Pump Function Pump functions can be specified in nodes defined either as manholes as structures but not at an outlet A pump is topologically fully defined with two node identifiers defining the pump sump basin node FROM and the downstream recipient node If the pump discharges out of the contemplated runoff system then the downstream node identifier is left unspecified empty The pump operation is specified by defining
94. ons It is very important to have a solid understanding of the influence of the different terms None of the three wave descriptions includes detailed hydraulic descriptions of hydraulic jumps However the chosen formulations ensure a correct description upstream and downstream of the jump DHI Software 3 12 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE cone gt 4 NUMERICAL SOLUTION OF THE FLOW EQUATIONS MOUSE LINK NETWORKS 4 1 General The implemented algorithm solves the flow equations by an implicit finite difference method Setting the numerical scheme into the frame of the Double Sweep algorithm ensures preservation of the mass continuity and compatibility of energy levels in the network nodes The solution method is the same for each model level kinematic diffusive and dynamic 42 Computational Grid The transformation of Equations 3 1 and 3 2 to a set of implicit finite difference equations is performed on a computational grid consisting of alternating Q and A points staggered grid i e points where the discharge and water level h respectively are computed at each time step see Figure 4 1 The computational grid is generated automatically by the model or with user specified number of grid points The computational grid for a conduit contains an odd number N of Q and h points with points at both ends
95. oot 0 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 100 0 110 0 120 0 130 0 140 0 Figure 5 1 Initial conditions with backwater outlet Initial Conditions provided by Hotstart Realistic initial conditions can be specified by taking the water levels and discharges from previously calculated result file Flow conditions at any time level contained in the interval covered by the result file can be chosen as initial condition The result file used as a HOTSTART file has to be complete i e water levels and flows at all computational points have to be saved 5 2 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual mi BOUNDARY CONDITIONS Ss 6 BOUNDARY CONDITIONS Unique solution of the flow equations requires appropriate set of boundary conditions Flow equations are solved for each conduit between two nodes and the boundary conditions are required at both end of the conduit at each time step throughout the computation In some situations boundary conditions are specified as unique relations of two flow variables e g stage discharge relation i e as hydraulic boundaries in certain points These are defined as functions i e as a part of the system description In other cases proper boundary conditions are constructed by the model as a consequence of current flow situation and of various user specified disturbances in form of e g adding or extracting water controlling the flow adding energy pump
96. oximation only for sub critical flow conditions i e for Froude number Fr lt 1 In supercritical flow conditions the equations are reduced to the diffusive wave approximation In the sub critical regime the contribution of the inertia terms 90 9 and aQ0 A cx is gradually taken out by a reduction factor according to Figure 3 5 Reduction Facter 0 5 0 0 5 1 0 1 5 Froude Number Figure 3 5 Gradual reduction of momentum terms during transition to supercritical flow Similarly the differential equation is gradually centred upstream as the influence of the upstream conditions increases according to the same function 3 7 Flow Description in Links Summary 3 7 1 Inventory The MOUSE Pipe Flow Model provides a choice between 3 different levels of flow description approximations 1 Dynamic wave approach which uses the full momentum equation including acceleration forces thus allowing correct simulation of fast transients and backwater profiles The dynamic flow description should be used where the change in inertia of the water body over time and space is of importance This is the case when the bed slope is small and bed resistance forces are relatively small DHI Software MOUSE PIPE FLOW Reference Manual 3 11 DHI Water amp Environment 54 lt DESCRIPTION OF UNSTEADY FLOW IN LINKS 2 Diffusive wave approach which only models the bed friction gravity force and the hydrostatic gradient terms
97. pe length which gives rise to pressurised flow m M Manning number m s Mac calculated Manning s number 3 1 Moon Manning s numbers specified for the conduit bottom ms Mau Manning number at full pipe flow s n invers of manning number M N number of grid points in a pipe q specific discharge m s Q discharge 33 Qni full pipe flow for uniform flow conditions ms regulation discharge defined by the regulation function ms regulation natural discharge mis DHI Software 9 2 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment NOMENCLATURE Ss Qreg Qweir R A P Ax y 1 2 Yn yD 60 ett Cconir 7 0 0 Po 4 V Y regulation applied discharge overflows discharge m s hydraulic radius m hydraulic radius at full pipe flow m time computational time step s mean flow velocity ms flow velocity in a node gate opening distance from the overflow crest to the upstream bottom m distance from the overflow crest to the downstream bottom m distance in the flow direction m distance between two computational points m node co ordinates m depth m depth in a contracted section m depth in upstream central and downstream section m critical depth m normal natural depth m the re
98. pipe The alternative formulation is based on the assumption that the inflow behaves like a submerged jet which entrains water from the ambient fluid and increases the discharge through the manhole The angle of entrainment is approximately 6 8 The cross section area of the jet thus depends on the distance from the inlet As a generalisation it is assumed that the effective flow area in the manhole equals the cross section area of the jet at the outlet This is valid in the case of no change in direction from inlet to outlet It is calculated as 2 T 6 8 4 D in 2 tan E 2 2 2 where Dj is the diameter of the inlet pipe So far the alternative formula is only applicable in MOUSE for manholes with one inlet and one outlet However the implementation includes the possibility for a change in elevation and a change in flow direction from inlet to outlet Figure 2 5 Manhole with one inlet one outlet and a change in flow direction In the case of a change in flow direction the effect of the jet at the outlet will gradually diminish with increasing angle The effective flow area is therefore linearly interpolated between the full cross section area of the manhole and the area of the jet as the angle increases DHI Software MOUSE PIPE FLOW Reference Manual 2 9 DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM The distance a from the point where the je
99. r most pipes DHI Software 3 6 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment DESCRIPTION UNSTEADY FLOW IN LINKS Ss 3 4 3 4 1 In order to obtain a smooth transition between the free surface flow computations and pressurised flow computations it is required to apply a soft transition between the actual pipe geometry and the fictitious slot Such a smooth transition has been designed based on a series of tests with various slot configurations The slot configuration thus obtained ensures stable computations without affecting the accuracy significantly The applied slot width is larger than the theoretical value The default relation between relative depth and the slot width as implemented in MOUSE is given in Table 3 1 y D B D D 1m 0 98 0 36 1 00 0 19 1 10 0 0166 1 20 0 0151 1 50 0 0105 gt 1 50 0 0100 Table 3 1 Relation between relative depth and slot width The default slot width can be modified for individual links through the ADP file Kinematic Wave Approximation General The flow conditions in steep partly full pipelines are mainly established by the balance between gravity forces and friction forces Consequently the inertia and pressure terms in the momentum equation are less dominant Accelerations are comparably small and the flow is almost uniform so that the kinematic wave approximation is a reasonable approach The momentum equation reduces to
100. r to preserve a robustness of the computation various additional limitations could be introduced With respect to that MOUSE offers two possibilities The first older limitation relates the maximum head loss to the depth in the outlet pipe 2 2 AH min hj 146 54 7 17 It also introduces the limitation on the total head loss coefficient as 26 10 7 18 These limitations have caused that the computed head losses and the corresponding flow conditions around nodes in some cases were inexact Due to the advances in the computational implementation the limitation from Equation 7 18 could been removed allowing the total head loss for the outlet pipe j being computed as 7 10 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual FLOW RESISTANCE 54 lt 2 AH j min dir j C levei j contri d 2g 7 19 The limitation of the total head loss coefficient to 1 0 is however still present 74 Alternative Solution Based on Weighted Inlet Energy Levels The assumption applied in the MOUSE standard solution that the water level in the manhole and all downstream water levels of the inflowing conduits are the same often leads to overestimates of the energy loss at the inlet In many cases the wetted cross section area in the inlet pipe is smaller than in the manhole leading to almost entire loss of the kinetic energy of the incoming flows which is
101. re MOUSE PIPE FLOW Reference Manual 4 11 DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE LINK NETWORKS The boundary resolution criteria is tested on all time series defined in either the boundary database the BSF file or results from a runoff simulation the RRF file However the test is only applied to boundary conditions which are larger than QlowLimitM3s a minimum flow threshold value The default value of QacceptLimitRel is 0 1 and QlowLimitM3s 0 01 Variation in the operation of the pump flow The variation in the pump flow through one time step is limited by AQ lt MaxPumpFlowVar 4 23 where is the variation in the pumped flow is the current value of the pumped flow and MaxPumpFlowVar is the user specified maximum relative variation The default value of MaxPumpFlowVar is 0 1 which corresponds to a 10 maximum variation in the pumped flow during one time step It should be noted that this test also implies that the simulation is always decelerated down to the minimum time step whenever a pump is switched ON or OFF Variations in the water level in grid points DHI Software The variation of the water level in all H grid points is limited by the following functions AH lt JWaterLevDiffMaxRel H 4 24 for lt WaterLevDiffMaxRel gt AH lt H for H lt WaterLevDiffMaxRel HI lt 0 4 25 lt WaterLevDiffMaxRel for
102. re then computed by multiplying the velocity head in the respective link by the specified 7 5 2 Alternative head loss descriptions DHI Software MOUSE allows to chose among nine different options for calculation of energy losses at junctions Some of these options differ purely by the value of the default supplied head loss coefficient value while some other represent a different concept of the head loss calculation Behind some of the available choices there is a default value for the head loss coefficient The default values can be modified for individual nodes MOUSE menu options Round edged Sharp edged and Orifice provide identical way of calculation but with various outlet shape coefficients Km The computed head losses are subject to limitations from equations 7 17 and 7 18 The model uses defaults values provided by MOUSE Round edged 0 25 Sharp edged 0 50 Orifice Km 0 50 7 12 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual FLOW RESISTANCE Ss For any node a special user specified value of can be supplied to the model which will override the default value Value of Km specified for certain junction is assumed for all outlets from the junction Option Energy Loss is based on the modified approach i e it retains only the limitation on the total head loss as given in the Equation 7 19 The default value of Km is 0 50 which can be similar
103. ronment NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE LINK NETWORKS DHI Software matrix yields by backward substitution the water levels in all nodal points at the next time step Figure 4 7 shows an example with 8 nodal points and 9 branches 5 6 7 8 RS 1 TO 2 9 3 x b x 4 x x x 5 x x x 6 x x x 7 x x x x x 8 x x x Figure 4 7 Principle of a nodal matrix for a system with 8 nodes and 9 branches The crosses in the matrix symbolise coefficients meaning that for instance the water level in node 4 can be expressed as a function of the water levels in nodes 1 5 and 6 When the nodal point matrix has been solved the solution in the branches is found by backward local elimination The bandwidth of the nodal point matrix as indicated by the stippled lines depends on the order in which the nodal points are defined The bandwidth of the matrix in Figure 4 7 is equal to 5 The computational time required for solution of the nodal point matrix depends on the bandwidth size and sharply increases with increasing bandwidth In order to minimise the computational time an automatic minimisation of the bandwidth is performed by internal perturbation of the nodal points The bandwidth displayed in Figure 4 7 for the network with 8 nodal points and the 9 branches could be reduced to 4 as shown in the matrix in Figure 4 8 below 4 8 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual
104. rs Do not use other separators like lt gt character or comma Use period as the decimal divider character E g 123 4567 MOUSE will read all data in free format This means that there can be any number of blank spaces between the data values The only exception is for the reading of node names All data elements described are identified by one or two node names Catchments manholes and outlets are identified by one node name Links pipes weirs and pumps are identified by two node names A node name in MOUSE is defined as a string of maximum 7 characters Node names may contain letters and digits and special characters like and but blanks are not allowed Always use upper case characters Legal node names are e g ABCI234 12 347 71258 DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 3 DHI Water amp Environment The following is not allowed as node name C12 The node name 0 zero has a special meaning for weirs and pumps and should not be used in other places Writing node names to the text file should be done by always starting in column one left adjusting the node name string and patch with blank characters up to 7 characters followed by one blank separator character The first character of second node name of branches pumps or weirs must always be given in column 9 Example NUMBER CONDUITS PIPES FORM L1 3 NODE
105. s parameters wgH w H w2 H and AH H and using the equations described in previous paragraphs The unit flows are computed at discrete points determined by the following set of the dimensionless parameter values wo H 0 00 0 05 0 10 0 30 0 50 0 80 1 00 w H 0 00 0 05 0 10 0 30 1 00 5 00 100 00 w2 H 0 00 0 05 0 10 0 30 1 00 5 00 100 00 AH H 0 00 0 01 0 04 0 09 0 16 0 25 0 36 0 49 0 64 0 70 0 80 0 85 0 90 0 95 1 00 This table is stored in a binary file MOUSE650 ORI and is supplied as a part of MOUSE installation DHI Software MOUSE PIPE FLOW Reference Manual 2 31 Water amp Environment 54 lt MODELLING THE PHYSICAL SYSTEM At the simulation start MOUSE generates a structure specific 3 D table for each orifice where actual flows to be applied in the computation are stored This table of the size 28 x 28 x 10 contains discharges for all the combinations of 28 upstream and downstream water levels covering the full range of possible water levels When the algorithm is used for a gate the third dimension is used for 10 different gate openings A non equidistant scaling approximating logarithmic scaling is applied for the water levels while the scaling of the gate position is linear During the pre processing the following operations are executed e Grids for the full range of upstream and downstream water levels are generated The grid spacing depends
106. s under certain hydraulic conditions may become pressurised In such a case the confinement of the flow fundamentally changes the environment in which the flow process takes place but the MOUSE Pipe Flow Model continues to perform the computations using the same flow description as for open channel flow This is possible because MOUSE furnishes actually closed conduits pipes with a fictitious slot Preismann slot on the top of the cross section thus replacing a pipe with an open channel featuring a cross section shaped to approximate the hydraulic behaviour of a pressurised pipe 2 22 Specification of a link Link Material DHI Software Specification of a Link requires specification of the associated nodes see paragraph 2 3 the link material longitudinal parameters and the cross section definition shape and size The parameter which characterises the link material is the link friction expressed as Manning s number M or n 1 The link can be defined as constituted of one of 8 predefined material types Table 2 1 lists the available link materials with MOUSE default values for Manning s number 2 2 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM MOUSE Default Value MOUSE Code Material M N 1 M 1 Smooth Concrete 85 0 0118 2 Normal Concrete 75 0 0133 3 Rough Concrete 68 0 0147 4 Plastic 80 0 0125 5 Iron 70 0 0143 6 Ceramics
107. sed for internal distribution of the flow within the pipe system According to hydraulic conditions two different types of overflow are possible e free overflow e submerged overflow The free overflow is a more frequent of the two types and the present conceptualisation is therefore concentrated on this phenomenon The computation of the submerged overflow is based on the same concept as the free overflow and therefore inherently yields approximate results Definition of an Overflow Weir General DHI Software Overflow weirs structures can be specified in nodes defined either as manholes or as structures but not at an outlet weir is topologically fully defined with two node identifiers defining the upstream node FROM and downstream node The definition of the upstream and downstream nodes does not restrict direction of the flow because the weir function allows the flow in both directions depending on the current hydraulic conditions Practically this means that if the water level in the downstream node is higher than the water level in the upstream node then the water flows backwards i e the computed flow rates are given a negative sign If an overflow structure discharges out of the contemplated pipe system then the downstream node identifier is left unspecified empty 2 14 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM Q H
108. ss section parameters is limited by AX lt MaxVarCrossConstant Max X 4 2 7 where the variable X is one of the three cross section variables and the meaning of Max X depends on the value of Crosscheck If Crosscheck is given as 1 then Max X is the maximum value of the actual parameter over the cross section while a value of Crosscheck which is equal to 2 means that Max X is given as the actual value of the respective cross section parameters However the check is carried out only if the relative depth in the cross section is larger than the variable CrossLowDepthLimit check of these limitations is carried out at the end of a time step simulation If limitations are violated then the solution is scaled down with respect to dt The default value of MaxVarCrossConstant is 0 03 of Crosscheck 18 and CrossLowDepthLimit is 0 04 Variation in Courant Number In the dynamic flow conditions the Courant number see 4 5 is continuously changing from time step to time step In order to avoid stability and accuracy problems the Courant number is limited by V dt C lt MaxCourant where C 4 x 4 28 Vis flow velocity and dx the distance between two computational grid points DHI Software MOUSE PIPE FLOW Reference Manual 4 13 DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE LINK NETWORKS Check of this limitation is carried out after the simulation of a time
109. sses Change in flow direction Change in elevation Loss due to contraction at outlet Loss due to change in flow direction DHI Software This loss is a function of the angles between the inlet and outlet links and distribution of the discharge in the inlet and outlet links as shown in Figure 7 3 and Figure 7 4 Pipe 1 Q1 V1 13 Q3 V3 Pipe 3 Vm 23 A Q2 V2 A2 Pipe 2 Figure 7 3 Manhole consisting of 2 inlet links and 1 outlet link Q2 V2 A2 2 12 91 a V3 Figure 7 4 Manhole consisting of 1 inlet link and 2 outlet links 7 8 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual FLOW RESISTANCE 54 lt Based on the generalised notation the calculation of the head loss coefficient is performed individually for each outlet link as follows n Qi 82 Lari Dig gos 7 14 i j where i stands for inlet links and j stands for outlet links Loss due to change in elevation Vertical changes in flow direction occur and cause energy losses if there is a difference in elevation between inlet and outlet link These losses are described considering the magnitude of the difference in elevation see Figure 7 5 Figure 7 5 Manhole with a difference in elevation between inlet and outlet pipe The individual head loss coefficient is calculated according to the following expression where the weighti
110. ssure and inertia terms in the momentum equation in most real flow situations Therefore the kinematic wave approximation has to be used with care The computations of the kinematic wave approximation in MOUSE are facilitated with the so called degree of filling function The filling function can be determined from the Manning s formula assuming uniform flow conditions ie 10 2 3 r 2 MEE le 3 20 Dj M fuit A fut where suffix full indicates values corresponding to a filled pipe and y D indicates the degree of filling This theoretically determined filling function has an over capacity at y D 0 9 The filling function applied in MOUSE does not include this over capacity but follows the Manning function up to a value of y D 0 8 see Figure 3 3 According to the kinematic wave theory will not increase further after the pipe runs full as the pressure grade line is assumed to 3 8 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual DESCRIPTION UNSTEADY FLOW IN LINKS remain parallel to the pipeline In reality however pressurised flow often gives rise to an increased pressure gradient and thus an increased flow rate The kinematic wave theory is therefore not suitable for computations of pressurised flow without special adaptations y D Mouse Degree of Filling 1 0 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 Manning Q Q tun gt
111. standard fis set to 1 0 With all the derivatives substituted by finite difference approximations and appropriately rearranged the momentum equation can be written in the following form 8 0 5 where DHI Software MOUSE PIPE FLOW Reference Manual 4 5 DHI Water amp Environment NUMERICAL SOLUTION OF THE FLOW EQUATIONS MOUSE LINK NETWORKS aj f A B f 0 At M A 4 14 y f A Ax A a q v QUI hip OT 44 The Double Sweep Algorithm 4 41 Branch matrix DHI Software As shown earlier the continuity equation and momentum equation can be formulated in a similar form compare Equation 4 7 and Equation 4 13 Using instead of and Q the general variable Z which thus becomes A in grid points with odd numbers and in grid points with even numbers the general formulation will be Zi B Zi 2 4 15 Writing the appropriate equation for every grid point a system of equations is obtained for each conduit branch in the network constituting the branch coefficient matrix as illustrated in Figure 4 5 Applying a local elimination the branch coefficient matrix can in principle be transformed as shown in Figure 4 6 below It is thus possible to express any water level or discharge variable within the branch as a function of the water levels in the upstream and downstream nodes e g manholes and i e
112. step If the limitation is violated the solution is scaled down with respect to Recommended value of MaxCourant specified in DHIAPP INI file is 20 60 Weir oscillations If the storage volume in one of the nodes connecting a weir is small weir oscillations might occur for free flow conditions This phenomenon results in a continuous change in flow direction over the weir until the instability is dampened In order to avoid this situation a criterion related to the change in water levels between up and downstream nodes around the weir is implemented The criterion relates to dt by possible d AH 0 02 4 29 where is the difference in water level between the two nodes connected to the weir and n corresponds to the time step level The absolute allowed change of 0 02 m is hard coded in the program and cannot be controlled by the user 47 Mass continuity balance Theoretically what concerns the mass continuity balance the applied computational scheme is inherently conservative for prismatic conduits with vertical walls In practical applications the continuity balance may be jeopardised in a number of situations such as e Relatively sharp changes of surface width due to rapid changes of water depth or a sharp change of cross section shape with depth This may be e g the case at relatively small depths in circular pipes and in arbitrary cross sections e Sharp changes in surface area of
113. stituting values to the Equation 7 24 and calculating H yields 15 89m 7 28 The deviation between the MOUSE simulation and manual calculation result is due to the fact that MOUSE calculates vou by using the following area in the pipe 2 D oul Preismann slot area Aout The table shows which setups have been used for the calculation and also which head loss types are included are all head loss coefficients due to contraction and correspond to the modes a b and c 7 18 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual FLOW RESISTANCE Table 7 1 Test matrix for implementation of Head Loss Type 7 5 5 Implementation of head loss description in kinematic wave simulations When applying the kinematic wave approximation the head loss description in nodes is based on the same equations as described above However in order to reduce the computational time the energy losses are computed once for a number of different flow conditions and tabulated for use during the simulation In cases where there is more than one inlet link in a manhole the losses are calculated on the basis of the assumption that the flow in each link relative to the flow in the other inlet links is proportional to the corresponding full flow capacity This assumption affects the energy losses due to changes in elevation and direction only when these losses are dif
114. t intercepts the manhole to the centreline of the inlet see Figure 2 5 is conservatively calculated as half the diameter of the inlet Din thus neglecting the entrainment angle of 6 8 2 3 The distance b from the point where the side of the outlet enters the manhole to the centreline of the inlet is approximated with b 2m Dou 2 4 2 360 2 where is the angle between the centrelines of the inlet outlet and Dout is the diameter of the outlet pipe In the case of a change in elevation the effective flow area is diminished with a factor drop_factor which is equal to 1 when the inlet flows directly into the outlet and 0 when there is no interception between the incoming jet calculated conservatively without the entrainment angle and the outlet In between these two conditions the drop factor is interpolated linearly The effective flow area is then interpolated as A flow A jet 2 drop_factor drop_factor f 3J 2 5 For a straight inlet outlet with no change in elevation the formula gives that the effective flow area equals the jet area The manhole volume contributes to the overall system volume and is included in the computations If the water level exceeds the ground elevation then the surface flooding occurs consequently followed by appropriate treatment by the model see paragraph 8 1 DHI Software 2 10 MOUSE PIPE FLOW Reference
115. tc A list of all possible limiting factors is given below If any of these criteria are exceeded i e if the generated variation is too large then a revised solution is calculated The revised solution is obtained as a linear interpolation between the last two simulation results the previous time step solution and the solution with preliminary time step so that all specified criteria are fulfilled The different criteria which control the variation in the time step are outlined below The user has the option to modify the individual criteria through variation in the parameters All of these parameters must be defined in the DHIAPP INI file 46 3 Criteria controlling the self adaptive time step variation Resolution of the boundary conditions The time step is limited by the excessive errors generated due to the difference in the boundary time series resolution In case of relatively fine resolution of boundary time series application of long time steps may e g cause volume errors The maximum allowed error in the boundary conditions is given by lt QacceptLimitRel Bvar 4 22 where is the largest error between the given and simulated boundary conditions see Figure 4 9 Bvar is the value of the given boundary conditions and QacceptLimitRel is a user specified value given in the DHIAPP INI file A Given boundary Simulated boundary t t dt Figure 4 9 Resolution of the boundary conditions DHI Softwa
116. te friction resistance can only be used if an implicit friction formulation is activated The links where Colebrook White computation is required are specified individually in the file see DHIAPPINI and ADP Reference Manual Use of the Colebrook White formula must be restricted to circular pipes only Also the Colebrook White formula is fully valid for full flowing pipes 7 2 Head Losses in Manholes and Structures Introduction The general flow equations are valid only for continuous conduits where in principle the only resistance to the flow originates from the bottom and side wall friction Hydraulic conditions in nodes i e at manholes and structures take the role of boundary conditions for computation of the flows in the conduits In turn hydraulic conditions in a node depend on the flows in the inlet and outlet conduits These hydraulic conditions expressed in terms of the energy conservation principle are calculated as water levels and velocity heads The calculation is based on the mass continuity and formulation of more or less advanced energy relation between the node and the neighbouring links with inclusion of some energy losses caused by local flow disturbances at different locations in the node The implemented solution ensures that mutual dependence of the flows in links and hydraulic conditions in nodes are correctly resolved even for complex branched and looped conduit networks Energy losses in
117. ter string followed by one blank Crest level weir crest level m ft real number Method 1 2 or 3 if Method 2 then Type 1 weir parallel to flow direction 2 weir perpendicular to flow direction Width width length of the weir crest m ft real number Shape 1 sharp crested weir 2 broad crested weir if Method 3 then lt Number of values number of h value sets 2 6 H level m ft real number lt gt discharge at water level m3 s cfs real number Comments If the weir discharges out of the network then Node 2 should be set to 0 zero Example NUMBER WEIR FUNCTIONS FORM KF1 1 NODE OVFLPT CRLE M AFV T WIDT KF NO H 9 B4 1480 0 16 80 2 1 2 00 1 DHI Software Appendix 1 10 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment 1 4 6 Section KF2 The section describes pumps located in the drainage network The pump description may cover from one to three pumps in each data element The data element will consist of one line indicating the location of the pump Then follows three lines per pump Definition of data elements Node1 Node2 Number of pumps Rel then follows for each pump Start level Stop level lt Number of values d H1 d H2 lt d H4 gt Q1 Q2 gt Q4 where Nodel 7 character string followed by one blank Node2 7 charac
118. ter string followed by one blank Number of pumps 1 2 or3 Rel Pump characteristic 1 given as H Q relation 2 given as dH Q relation Start level pump start level m ft real number Stop level 2 pump stop level m ft real number lt Number of values the number of H Q or dH Q values that follows 2 4 H water level at the pump m ft real number dH difference in water level m ft real number lt gt corresponding discharge m3 s cfs real number Comments If the pump capacity is given by the H Q relation then the first H value must be equal to the value given as stop level for that pump If the dH Q relation is used then the dH value are interpreted as the difference in water level between the receiving node and the node where the pump is located The start level should always be above the stop level restrictions are checked by the MOUSE error checking facility at the start of each simulation DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 11 DHI Water amp Environment Example NUMBER PUMP FUNCTIONS 1 NODE PUMP AR 5 STO K NO B4 1510 B4 1500 2 1 14 86 14 45 2 15 46 14 45 3 DHI Software 14 45 0 030 14 45 0 070 FORM KF2 15 46 0 060 15 20 17 00 0 150 0 300 Appendix 1 12 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual SS 1 4 7 Section KF3 Originally intended for defini
119. the range of operation start level H 4 m and stop level m and one of the two available relations in a form of tabulated pairs of values 1 AH m and Qpump m s or 2 H m and Qpump m s The Qpump H table consists of min two data sets there is no upper limit Intermediate values are linearly interpolated Variables and Hstop denote water level in a pump sump basin pump wet well node Relation 1 correlates water level in the pump sump basin and the pump discharge Q H if H stop SH if H decreases in time or if Hstart lt H if increases in time 2 44 0 E else Relation 2 defines the pump performance as a function of the water level difference between the two nodes Q AH if H stop if H decreases in time or if H starn SH if increases in time 2 45 Q pump else A number of pumps with different operation strategies can be simultaneously defined between the two nodes As the pump performance can be quite significant even during the start up it has been necessary to dampen the pump dynamics in order to sustain the numerical stability The dampening is obtained by DHI Software MOUSE PIPE FLOW Reference Manual 2 33 DHI Water amp Environment MODELLING THE PHYSICAL SYSTEM 2 44 Flow regulation DHI Software centring the pump rate backwards in time so that the pump performance does not instantaneously reach the full capac
120. the top of the cross section MOUSE adds the Preissmann slot see ref 4 automatically To ensure the computational stability the cross section conveyance should be maintained monotonously increasing or at least constant with increase of water level This is normally not the case with closed conduits where the value of conveyance drops in the region near the top of the section For such cases when raw data are input MOUSE adjusts the hydraulic radius so that the limiting conveyance for the cross section corresponds to the actual conveyance value for the full profile When closed cross section data are input in the processed form attention should be paid in the upper region of the profile so that decreasing conveyance is avoided General description Points associated with link ends and junctions are called nodes Each link is actually defined with exactly two nodes Depending on the position in a network layout a node is associated with one or more links In the later case a node is called a junction An arbitrary number of links can be attached to a junction thus allowing construction of arbitrary network layouts 2 3 2 Types and definition of nodes Every node in a network is defined by its identification max 7 characters and its x and y co ordinates m Exception is storage nodes which do not require co ordinates Further according to the type of node an appropriate set of parameters is required DHI Software MO
121. tion of controllable weirs and gates MOUSE does not use this section Alternative and extended input facilities exists in MOUSE for defining RTC elements in the sewer and drainage networks Please refer to the MOUSE documentation for details Number of elements of this section must be zero Definition of data elements not used not described Example NUMBER CONTROL FUNCTIONS FORM KF3 0 DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 13 DHI Water amp Environment 1 4 8 Section KK The section is intended for defining critical level at selected nodes The section may contain data elements but the data has no impact on the MOUSE simulation Definition of data elements Node Critical level where Node 7 character string followed by one blank lt Critical level gt Critical level m ft real number Comments Not used by MOUSE Example NUMBER CRITICAL WATER LEVELS FORM KK 0 DHI Software Appendix 1 14 MOUSE PIPE FLOW Reference Manual DHI Water amp Environment SS 1 49 Section KU The section defines location of outlets Definition of data elements lt Node gt lt X coor gt lt Y coor gt lt Invert level gt lt Water level at outlet gt where lt Node gt lt X coor gt lt Y coor gt lt Invert level gt see description for KG1 lt Water level at outlet gt Constant water level at the outlet Comments The water level at the outlet given
122. tive time step variation DHI Software The automated self adaptation of the simulation time step is performed during the running simulation Such on the fly calculation of the time step is performed through a three step procedure e Before the actual time step is taken a preliminary value of the time step is calculated on the basis of the following The instantaneously time step is increased by a user specified fraction the time step acceleration Acceptance of this time step is validated through checking the resolution of boundary conditions and pump operations see below Finally the suggested time step is validated with respect to user specified minimum and maximum values The minimum and maximum values and acceleration factors are specified as a part of the simulation configuration If the maximum and minimum values of are equal the program will use a constant time step 4 10 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual NUMERICAL SOLUTION OF THE FLOW EQUATIONS IN MOUSE cone LL e The preliminary hydrodynamic solution is calculated with the preliminary time step value e Based on an assessment of the preliminary solution a judgement is made whether the used time step is acceptable or not The user has the opportunity to specify numerous different limitation factors such as a maximum allowed variation in the water level in grid points a maximum allowed variation in the courant number e
123. tlet pipe m factor diminishing the effective flow area in manhole due to drop in elevation 8 3 the pipe wall thickness m E energy level just upstream overflow m DHI Software MOUSE PIPE FLOW Reference Manual 9 1 DHI Water amp Environment NOMENCLATURE exp Manning s number variation exponent default 1 00 E the Young s modulus of elasticity Nm f coeff for flow direction change default f 21 g 9 81 constant acceleration of gravity ms Fr Froude s number h water level m H Cross sections elevation relative to bottom m pumps water level in a pump sump m overflows water level just upstream the overflow m AH overflows entrance energy loss m pumps level difference between two nodes regulation water level at the control point node bottom elevation Hm water level in a node m H min H max regulation water levels at the control point A defining the range in which the regulation is to be applied m Hout water surface elevation at outlet m FA start pumps start and stop level for a pump Hio node surface elevation m Hp Haown or water levels at the computational points upstream and downstream respectively m 10 bottom slope m I friction slope m k wall roughness m overflows energy loss coefficient Ky specified outlet shape coefficient for a node l conduit length m 1 pi
124. ue attention must be paid to the selection of the most appropriate approach DHI Software MOUSE PIPE FLOW Reference Manual 7 11 DHI Water amp Environment 54 gt lt FLOW RESISTANCE 7 5 1 Alternative interpretations of head loss coefficient The head loss calculation for individual nodes can be controlled by selecting one of the three computational modes for the head loss calculation These modes distinguish the meaning of the specified head loss coefficient Per default a the specified value is interpreted as the outlet shape coefficients Km In addition to the default interpretation of the head loss coefficient Km for individual nodes two alternative interpretations can be selected These are b Contraction head loss coefficient and c Total head loss coefficient For the case b the model ignores the geometrical relations between the node and the outlet links outlet shape and applies the specified value Contraction HCL directly as the Conr The contraction losses in the outlet links are then computed by multiplying the velocity head the respective link by the Conr The total head loss for an outlet link is computed as a sum of the contraction direction and elevation loss In case c the model completely ignores the geometry of the node links and applies the specified value Total HLC directly as the Gu the same for all outlet links at the node The total head losses in the outlet links a
125. unt One effect is the change of the velocity term in the energy equation v7 2g For large values of w is the upstream energy level E approximately equal to the depth over the crest and is equal Cy For smaller values of the upstream velocity term becomes more important and Cg and Cy will deviate from each other The other effects are the curved streamlines the change in the Coriolis coefficient 0 the vertical contraction coefficient w the surface tension and the friction The latter effects influence both and Cy By moving from 9 relation to a q E relation the variation in the discharge coefficient should be expected to be smaller The energy level is given as 2 aq 2 23 28 2g H wy n where fi Coefficient of the relation between energy and water level By combining Eq 2 23 with 2 22 8 can be expressed as 2 2 24 A lisi and the coefficient Cg can be expressed as 2 25 The table below shows the relation between Cy Cz D and q for 1 for different values of w H showing indeed that the coefficient Cg shows less variation than the values for Cg TG qe TR 0 407 1 00 1 81 0 460 0 426 1 053 2 04 0 423 1 474 3 35 0 707 0 385 1 500 3 13 1 500 3 15 DHI Software MOUSE PIPE FLOW Reference Manual 2 23 DHI Water amp Environment Ss MODELLING THE PHYSICAL SYSTEM Table 2 3 Relat
126. w velocity in the manhole is based on the vertical cross section area The flow velocity is used in the head loss computation The horizontal area is used for computing the volume of water stored in the node basin at a given level MOUSE takes a maximum of six set of values describing the node geometry Each data element in the KG3 section will always cover four lines Example NUMBER GEOMETRY OF STRUCTURES FORM KG3 2 NODE NO H AT AO 4 1480 3 0 00 17 10 18 50 0 00 0 90 2 40 34 5 3 55 355 4 1510 2 0 00 19 20 0 00 1 50 10 0 10 0 DHI Software MOUSE PIPE FLOW Reference Manual Appendix 1 9 DHI Water amp Environment 1 4 5 Section This section is used for data describing overflow weirs The weirs be internal discharging from one node in the network to another node or the weir may discharge out of the network e g a weir discharging to a river The original format allows three different possible definitions method 1 2 3 MOUSE only uses method 2 and method 3 Definition of data elements lt 1 gt Node2 Crest level lt Method 1 gt lt Q const gt or Node1 lt Node2 gt Crest level lt Method 2 gt Type Width Shape Or Nodel1 Node2 Crest level lt Method 3 gt lt Number of values H1 H2 H6 Q1 Q2 Q3 where Nodel 7 character string followed by one blank Node2 7 charac
127. y 2 20 where y the distance from the sill level to the surface at the weir crest m amp the Coriolis factor yw the vertical contraction coefficient E the energy level m The depth at the weir crest is considered to be critical i e y 2 3E This assumption is very rough because the streamlines are curved As a consequence the depth over the crest will be less than the critical depth In the context of the present implementation curvature of the streamlines is ignored since the expression is only used to evaluate the effect the velocity term have on the coefficient The effect of curved streamlines is indeed incorporated in the coefficients and By inserting 2 3E in the right hand side of equation 2 20 the following relation is obtained 2 4 4 gt q a CLE 2E 2 21 28y GEY where CE the energy discharge coefficient for the sharp crested weir Since the discharge q can be expressed either via the water level above the crest upstream of the weir or the energy level at the upstream section the following relation between the level discharge coefficient and the energy discharge coefficient can be derived 2 Ce 51 2 2 22 2gH w 2 22 DHI Water amp Environment MOUSE PIPE FLOW Reference Manual MODELLING THE PHYSICAL SYSTEM As it can be seen from the relation above the coefficient takes several effects into acco

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