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The DS2G Program User's Guide

1. ee ax a ao a R lt 3 8 3 ox Qs g gt o gt o Q gt ct gt fo lt W 3 a PF lt o m a Q y a v Q Enter 1 if groups are not implemented roup in which the species lies otherwise the group Zero for monatomic molecules two for diatomic molecules and generally three o of rotational degrees of freedom for polyatomic Required only for species with rotational degrees of freedom Choices are a CONSTANT value or a second order POLYNOMIAL in emperature depend of rotl relax temperature Required only for mixtures and a species with internal degrees of freedom Choices are to have relaxation rates SURI E Ce peM Ces Ge OURS ALES that are COMMON to all collision 2 2 5 Rotational Mode Data Screen Alsoin theloop over the molecular species of CUSTOM gases and is required only if the species has rotational degres of freedom Should the rates in a mixture be species dependent se amp as final item on previous screen the values in this screen ate for collisions between like molecules Rotational relax coll number This is a the constant value of the rotational relaxation collision number if that option has been chosen in the second last item in the previous screen If the Coefficient of temperature The coefficient of temperature in the second order polynomial Required only if thereis a polynomial for the rotational collis
2. 650 625 600 575 550 525 500 475 450 425 400 375 350 325 Fig 6 Temperature contours for DS2GD001 DAT PNKORUARHRYM OER DWAUHMHA 3 2 Steady 2 D internal expansion DS2GD002 DAT This is the expansion of the stream from an infinite set if regular two dimensional sonic slits The upper and lower boundaries are therefore planes of symmetry The flow is divided into two regions as shown in Fig 6 The lower region is bounded on the left by a diffusely reflecting surface and the upper region by the sonic inflow boundary The right hand boundary is a vacuum and that between the regions is of course an interface With the exception of those along the surface the cell spacing is regular A representative set of streamlines are shown in Fig 7 while the contours of constant Mach number are shown in Fig 8 The expansion in the upper region of the flow is supersonic but the lower region is largely subsonic The vacuum boundary exerts a strong influence on the subsonic region and the sonic line very nearly intersects the downstream end of the lower plane of symmetry A vortex is formed downstream of the diffusely reflecting vertical surface The magnitudes of the flow velocities in this vortex are small in comparison with the velocities in the bulk of the stream 37 ETT Tea ETT TT He TET TTT TT I DAT Fig 7 Cell structure for test case DS2GD002 the internal expansion flow ine
3. A further application of the molecule file input output feature is to allow a single upstream flow calculation to be used as the input toa number of downstream flows In many cases the upstream flow will be more dense and its re use can save considerable re calculation Program DS2G employs data and parameter files DS2GD DAT and DS2GP DAT In general these are generated by the data screens within DS2G and the user need not be aware of their existence However these are ASCII files and their content is specified in Appendix B It is therefore possible to produce front end programs as an alternative to the use of the data screens Only DS2GD DAT need be generated externally because DS2GP DAT is generated automatically when DS2GD DAT is reviewed by cycling through the data screens These may allow graphical input from CAD programs or simplified data set up for a restricted class of flow There are a number of demonstration data files DS2GDn DAT where n ranges from 1 to 999 and these may be selected as one of the menu items when starting a new run Theinitial menu also makes provision for the existing data file to be archived as DS2GAn DAT where n ranges from 1 to 999 The program automatically selects the smallest available value for n and an archive record file is opened under the DOS EDIT program so that a description of the archived file may be recorded ALTERNATIVE DATA GENERATION GRAPHICAL DEDICATED ARCHIVED DEMONSTRAT
4. c u Q o e A 3 Required only for the first segment Angle from x dirn to startpoint rad This is at the intersection with side 2 This is nearest the intersection with Angle from x dirn to endpt rad side 4 If this item is left at its default value of unity the cell elements along the segment are of equal angular extent If it is other than unity the elements are in an arithmetic progression Positive values define the ratio of the cell element nearest to side 4 to that nearest to side 2 The absolute value of a negative number defines the ratio of the size of the central element to that of the end elements egment angular size ratio 2 2 35 Side 3 Segment Screen for Coincident Option 29 he adjacent region number Ves region in which the identical side Number of the corresponding side The code number of Ihe side ot that region If the points are in reverse order the negative of the side number is entered The coordinates of all points along the segment and side must be coincident 2 2 36 Side 2 Screen for Arithmetic Progression Option z z z z If this number is positive it is the cell Size rau O MONA JESO element length ratio from side 3 to side 1 The magnitude of a negative number defines the ratio of the central element to the end elements 2 2 37 Side 2 Screen for the Arbitrary Option This screen is repeated for each cdl dement along side 2 gt These numbers are summed and the NUDE
5. creep is a tendency for a transition regime flow to move towards a region od high temperature It vanishes in the free molecule and continuum limits and is not 46 present at the level of approximation that is provided by the Navier Stokes equations This is an axially symmetric version of the One way flow of a rarefied gas induced in a channel with a periodic temperature distribution of Sone Waniguchi and Aoki Phys Fluids 8 2227 2235 1996 The results are shown in Fig 21 This is a periodic flow and represents the maximum flow rate with no pressure change The maximum surface temperature is at the ends of the flow and the creep velocities adjacent to the surfaces are towards the ends A vortex forms in the enlarged section and there is a net flow to the right ARGUN rin OUU IN K 0 05 Tma 900 K Axial velocity m s Fig 21 Streamlines and axial velocity distribution 47 APPENDIX A Installation and run time considerations The program requires an IBM compatible computer with a 386DX 486DX or Pentium family processor the mathematics co processor is mandatory While the program will run under DOS it will generally be run in a Windows 95 environment It is a 32 bit application and can use all the memory that is available It can be run in a DOS window or by simply clicking on the executable The files on the distribution disc are the self extracting compressed execution program DS2GZ EXE and the set of de
6. 1 for constant polynomial rotational relaxation number Required only for gas mixtures 0 1 for common or collision partner species dependent rotational and vibrational relaxation rate 49 The constant value or constant in the polynomial for Zr either the common or the like collision value Required only if thereis a polynomial for Zr Coefficient of temperature in the polynomial Coefficient of temperature squared in the polynomial Number of vibrational modes of this species Required only if there are vibrational modes in a loop over the modes Characteristic temperature of the mode Constant C1 in eqn 6 53 for the relaxation collision number or if C2 is negative the relaxation collision number either the common or like collision value at this stage Constant C2 in eqn 6 53 or 1 to indicate a constant Zv Required only for a gas mixture in a loop over species but only for collisions between molecules of different species and when the cross collision values are to be s amp as data rather than through mean values Reference diameter for the cross collisions Reference temperature for the cross collisions Viscosity temperature power law for the cross collisions Reciprocal of the VSS scattering parameter for the cross collisions Required only for rotational degrees of freedom and collision partner dependent rdaxation rates Constant value or constant in the polynomial for Zr in the cross collision Required only
7. 20 was applied to the latter in order to equalize the samples About 1 in 30 of the outgassed molecules return tothe disk 42 Fig 15 The number fraction of outgassed molecules in the flow 3 7 Hypersonic re entry DS2G007 DAT This considers the flow of real air at 200 K and 3x10 m past the spherically nosed cone that is shown in Fig 16 There are only two regions and the segmented side option has been used to have both a circle and straight line along the side 1 and 3 boundaries The surface is diffusely reflecting at a temperature of 1000 K There is almost a two order of magnitude increase in the density from the stream to the surface in such a flow and advantage is taken of the variable DTM FNUM feature to set very thin cells in the region adjacent to the surface It has been found that while the pressure is insensitive to the cell height near the surface the shear stress and the heat transfer are very sensitive to it The gradients parallel to the surface are relatively small and the cell dimension in this direction may be larger than the local mean free path These examples are to demonstrate and test the operation of the program and some further optimization possibly involving the introduction of additional regions would be required in a serious engineering calculation The build up in the number of simulated molecules is more than a factor of three and the memory required for the molecules increases automatically duri
8. a loop over the cdl segments for variable input and in a loop over the species Temperature if 1 the reflection is specular or if 2 the reflection follows the diffuse adiabatic model with zero heat transfer For other than specular or diffuse adiabatic reflection 1 for full diffuse reflection or between O and 1 for internal energy accommodation coefficient For other than diffuse reflection Normal energy accommodation coefficient Tangential momentum accommodation coefficient Fraction of molecules adsorbed at the surface If the side is type 6 Outgas mass flux The tangential velocity component of the surface in the plane of the flow 54 The tangential velocity component of the surface in the plane normal to the flow The following item was introduced in Version 1 1 The probability of catalytic recombination at the surface for this species If the sideis type 7 in a loop over the adjacent sides Code 1 to 4 of the adjoining side Code number of the region in which side NSD lies If there are molecule input files in a loop over the files Region into which the molecules enter Side of this region at which they enter Number of molecules in each record of the entry file Number of records in the molecule entry file If molecule input files are to be generated in a loop over the files Required only for axially symmetric flows with radial wa ghting factors 0 1 if weighting factors are to be removed kept 0 1 if program continu
9. based on momentum while the previous one was gt ke Q o gt Z lt ma 3 O rc 3 2 2 angential mom acc coeff based on energy This avoids a singularity This fraction of this species are simply removed from the calculation on striking the surface This can simulate a cryogenic surface raction adsorbed at surface 32 Applies only to outgassing surfaces This is the flux for this species and it is assumed that the molecules leaving the surface are completely accommodated to the surface temperature and effuse with a he outgas mass flux kg m 2 s While the geometry is fixed the surfaces may have a velocity that is parallel to the surface This is the component of that velocity that lies in the plane of the flow 7 2 y Cc nn D fan D gt amp c fan 2 nH Z T am m fe gt urface in plane velocity m s This is the component of the surface velocity that is normal to the plane of A S oO xh 2 ot fo 2 g a je v urf cross plane velocity m s the flow or for axially symmetric flows For positive values this is the circumferential velocity component of the surface velocity However for negative values it is an angular velocity urf cross plane vel m s or rad s A surface may act as a catalyst for the recombination of atoms to a molecule It is assumed that the residence time of the atoms on the surface is
10. exchange reaction The species code of the recombined molecule for a recombination econd post collision parameter The species code of the third post collision species for a dissociation The species code of the second post collision species for an exchange reaction In the case of a recombination it is the species code of the third body molecule or if this is not fixed the negative of the code number of the third body table hird post collision parameter The logic converts the reaction rates into steric factors This is based on eqn 6 10 of Bird 1994 Thisis an arbitrary parameter but the temperature exponent in the Arrhenius equation cannot be more negative than the negative of the sum of this number and 3 2 Large negative values of this exponent are associated with reactions in which there is a large contribution from the internal degrees of freedom umber of internal deg of freedom The relative translational energy and contributing internal energy must exceed this energy for a reaction to be possible Activation energy J The reaction rate coefficient is assumed to be in the form k T AT exp kT Pre exponential factor where E is the activation energy A is the pre exponential factor and n is the temperature exponent The units are such that the rate coefficient k T is in m molecule s for a binary reaction and m moleculets for a ternary reaction he temperature exponent T
11. file 7 This selects one of the demonstration EUa eteinen iei SS data files DS2GDn DAT as the data file When either an archived or demonstration file is chosen the data screens must be traversed by the enter key in order to generate a matching DS2GP DAT file Appears only when an archived or demonstration file is to be sd ected Godatumberorinanla A integer less than equal to the number of available files is specified as the number n in the archive or demonstration file name The help window displays the maximum integer that is available Appears only for the continue option with a time averaged flow Extend an existing sample Generate a new sample The first option causes the existing sample for an assumed steady flow to be continued The second option causes a new sample to be started and is useful if the number of print intervals to steady flow has been set in the data to an excessively small value The screen has no effect if the flow has not reached the stage at which steady flow is assumed Appears only for the TECPLOT option with interfaces betwern regions Average across interfaces Discontinuity at interfaces The TECPLOT output file is divided into blocks that correspond to the flow regions If the first option is chosen the values in the two regions in either side of an interface between regions are averaged on the interface so that there will no discontinuities in the contours at theinterface Theaveraging requ
12. if there are to be no alterations to the data This is to produce a matching DS2GP DAT file In the case of an ensemble averaged unsteady flow there is an option to either bypass or generate the cell report files DS2GC TXT and DS2GC PLT There is a further screen with three options to completely bypass the generation of the text output files to generate text output for the surface properties only or to generate the full output enerate and run a new case This should be chosen only when a run has proceeded to the point where a restart file DS2GR DAT has been produced for a time averaged flow or an unsteady sampling file has been produced for an unsteady flow In the case of a steady flow there is a subsidiary screen that provides a choice between the continuation of the existing time average or the commencement of a new average New run from existing data file This starts a run from zero time and in the case of an unsteady flow removes any preceding runs from consideration in forming averages It should only be chosen when a consistent DS2GP DAT file exists z In the case of a time averaged flow this generates the file DS2GT TEC that is formatted according to the requirements of the TECPLOT post processing program For an unsteady flow a series of files U 001 TEC U002 TEC are generated where the number corresponds to the print interval These files may be used to generate a series of TECPLOT representations that may be capture
13. molecules that will be generated and largely controls the memory requirement The parameter FNUM is ideally chosen such that the number of simulated molecules grows to just under this value Should it be exceeded the DIMENSION s are reallocated in order toincrease it by 10 as long as the additional memory is available Maximum number of molecules 35 3 DEMONSTRATION CASES A set of data files DS2GDnnn DAT serve as both tutorial examples for the application of the program and as a Suite of test cases for its continuing validation as new features are added In order to run one of these files the Generate and run a new case option must be chosen from the first screen followed by the Run demonstration case from the second screen The enter key should then be used to step through the data file This is necessary to generate the consistent DS2GP DAT file and also provides a tutorial overview of the data 3 1 Steady supersonic flow of air past sphere DS2GDO001 DAT This calculates the flow of a 1 000 m s stream of ideal air past a sphere of radius 0 1 m The stream number density is 3x10 m and there is diffuse reflection at the surface with complete accommodation to the surface temperature which is equal to the freestream static temperature of 300 K The mean free path is about 1 twentieth of the sphere radius and the computational grid of Fig 3 was adequate only because the transient sub cells reduced the mean spacing of the col
14. side 4 to that adjacent to side 2 The absolute value of a negative number defines the ratio of the size of the central element to that of the end elements egment size ratio 2 2 18 Side 1 Screen for Conic Section Option The side is a segment of the general conic section with the radial coordinate r and the angular measured from the x axis which fixes the alignment of the conic coordinate 6 both relative to the focus given by r p 1 ecos where p is the value of the radial coordinate when 9 is 2 2 and eis the eccentricity The side is specified by the coordinates of the focus the values of p and e the angular coordinates of the endpoints of the side from the line through the focus parallel to the x axis and the size ratio of the elements these are in arithmetic progression based on the angle Note that when the eccentricity is zero the side is an arc of the circle with its center at the focus and radius equal top The side is a portion of an ellipse if the eccentricity is less than unity a parabola if it is equal to one and a hyperbola if it is greater than one Note that the major axes must be coordinate of focus m he parameter p m he eccentricity e Angle from x dirn to startpoint rad This is at the intersection with side 2 Angle from the x dirn to endpoint This is at the intersection with side 4 If this item is left at its default value of unity the cell elements along side 1 are of equ
15. the data generation process be abandoned by pressing the esc key the original DS2GD DAT file is restored through the renaming of DS2GD OLD The altered or new values are confirmed in the new DS2GD DAT fileif the screens are progressed through to the end of the program by successive depression of the enter key All data is set in base SI units 2 2 1 Introductory Data Screen The space bar is used to toggle between the options of TWO DIMENSIONAL in the x y plane and AXIALLY SYMMETRIC about the x axis low geometry The flow is always unsteady but with teady or unsteady sampling the STEADY option the flow is assumed to be steady after a specified time and a time average of the flow properties is then accumulated UNSTEADY averaging is employed when the unsteady flow is to be studied If multiple runs are specified in the final screen there is an ensemble average of the results over these runs Required only for axially symmetric flows These are used to increase the sample near the axis and decrease it at large radii Molecules that are outside the reference radius and move towards the axis may be duplicated and those moving away from the axis may be removed Molecule duplication can produce undesirable statistical effects although a delay is imposed on duplication in steady flows Radial weighting factors should be used with caution adial weighting factors Required only for axially symmetric flows with waghti
16. the flow regions need not overlap In the case of a wake flow or plume impingement problem where there is upstream influence the output file may be generated within the flow The next section of the flow may then be calculated with a much larger sample because of its limited extent and the free choice of both FNUM and DTM which may be different from their values in the calculation that produced the file Each molecule input side must be coincident with the side at which the molecule file was generated The number of cells should be the same along curved sides but may differ if the sides are straight For axially symmetric flows with radial weighting factors the output files can either retain or remove these factors If they are removed the flow into which the molecules flow must not have radial weighting factors The molecule entry side should be specified as a type 8 side because no molecules other than file molecules should enter the flow across this side but molecules should be free to leave the flow across the file entry side The inflow may be subsonic as long as the upstream moving molecules are allowed to leave the flow Note that the flow will be affected by the sample size of the input molecule file The scatter in this sample will be transmitted as a systematic error to the flow generated from this file The molecule input file should therefore be as large as possible Note that only one record of this input file is in memory at any time
17. General Program for the Computation of Two Dimensional or Axially Symmetric Flows by the Direct Simulation Monte Carlo DSMC Method The DS2G Program User s Guide Version 3 2 J une 1999 G A B Consulting Pty Ltd 5 Fiddens Wharf Rd Killara N S W 2071 Australia Country code 61 City code 2 498 7809 gabird compuserve com http ourworld compuserve com homepages gabird Table of Contents INTRODUCTION 1 1 TheDSMC method 1 2 The scope of the program 1 3 General description of the program OPERATION OF THE PROGRAMS 2 1 Program Screens 2 2 Data Screens DEMONSTRATION CASES 3 1 Steady supersonic flow of air past a sphere DS2GD001 DAT 3 2 Steady 2 D internal expansion DS2GD002 DAT 3 3 Unsteady flow past a vertical flat plate DS2GD003 DAT 3 4 Supersonic jet plume DS2GD004 DAT 3 5 Plume backflow DS2GD005 DAT 3 6 Satellite contamination DS2GD006 DAT 3 7 Hypersonic re entry DS2GD007 DAT 3 8 Flow past curved plate DS2G008 DAT 3 9 Taylor Couette flow DS2G009 DAT 3 10 Thermal creep flow DS2G010 dat APPENDIX A_ Installation and run time considerations APPENDIX B_ Specification of ASCII data files 10 13 35 36 38 39 41 41 42 44 45 45 47 48 1 INTRODUCTION 1 1 The DSMC Method The direct simulation Monte Carlo method is a technique for the computer modelling of a real gas by some thousands or millions of simulated molecules The velocity components
18. ION DATA FILES DATA FILES DS2GAn DAT DS2GDn DAT RECORD IN DS2GA TXT y ASCII DATA FILES DS2GD DAT DS2GP DAT CELL CONFIGURATION DATA FILES SUMMARY DS2GC TXT DS2GD TXT DS2GC PLT GENERAL MOLECULE TWO DI M INPUT FILES BINARY OR DGMIFn DAT RESTART DS2GR DAT DSMC MOLECULE OUTPUT FILES PROGRAM DGMOFn DAT DS2G EXE UNSTEADY SAMPLING FILES TEXT Un DGF OUTPUT FILES TECPLOT DS2GS TXT OUTPUT DS2GF TXT FILES DS2GM TXT DS2GT TEC Un TEC Fig 3 The files associated with the DS2G program ASCII files in rectangular shapes and binary files in rounded shapes 10 2 OPERATION OF THE PROGRAM The program is operated through succession of on screen forms or menus The appropriate option is chosen or numerical data entered into each screen The user progresses from screen to screen by pressing the enter key 2 1 Program screens 2 1 1 Introductory Program Screen Orange One of five options is chosen from this screen The selection of this option causes the program to cycle through the data screens in order to generate a completely new set of data or to modify an existing data file This choice is made through a subsidiary screen which presents a two way choice If the data file DS2GD DAT is produced through the renaming of one of the DS2GDn DAT files or a similar file it is necessary to choose the modify option and to cycle through the data screens even
19. RIOR ALD SUB eS NSUenES element fractional lengths are equal to the number divided by the sum 2 2 38 Side 4 Screen for Arithmetic Progression Option E homadaatons If this number is positive it is the cell and cell element length ratio from side 3 to side 1 The magnitude of a negative number defines the ratio of the central element to the end elements 2 2 39 Side 4 Screen for the Arbitrary Option This screen is repeated for each cdl dement along side 4 7 These numbers are summed and the NUMPERPLOP TASHE CSM SEJMENE element fractional lengths are equal to the number divided by the sum 2 2 40 Side Specification Screen he type of the side There are eight options Axis This is valid only for axially symmetric flows and the side must lie on the x axis Plane of symm This must be a straight side and for axially symmetric flows it must be normal to the axis It is functionally equivalent to a specularly reflecting side with so sampling of surface properties 30 Stream bound An interface with the uniform stream Specified flow A non uniform entry flow is defined by the gas composition and flow properties at each element along the side Solid surface This may have uniform or non_uniform properties and may have a velocity in its plane Outgas surface A surface with superimposed outgassing Interface A boundary with one or more sides of other regions Vacuum or M E Either an interface with a vacuum o
20. ables the segment to be specified as a segment of a conic Coincident sets the segment as being coincident with a previously defined side These are cell elements and the total umber of elem along the segment over all segments must equal the 5 3 gt a Q ia om wn ov fa 5 Ke ct 5 D u 2 2 2 22 Side 1 Segment Screen for Point by Point Option The x coordinate of the point lt x 3 alB Sig ct 2 gt a 2 Fly e et Q u Qa R He fan D gt Qa A NEEN The y coordinate of the point 2 2 23 Side 1 Segment Screen for Straight Line Option The startpoint coordinates are required only for the first segment The startpoint is at the intersection x coordinate of startpoint m With side gt coordinate of startpoint m The endpoint is nearest the intersection x coordinate of endpoint m sieht Sead 25 coordinate of endpoint m If this item is left at its default value of unity the cell elements along side 1 are of equal length If it is other than unity the elements are in an arithmetic progression Positive values define the ratio of the cell element nearest to side 4 to that nearest to side 2 The absolute value of a negative number defines the ratio of the size of the central element to that of the end elements egment size ratio 2 2 24 Side 1 Segment Screen for Conic Section Option The conic section is as described for the ful
21. al angular extent If it is other than unity the elements arein an arithmetic progression Positive values define the ratio of the cell element adjacent to side 4 to that adjacent to side 2 The absolute value of a negative number defines the ratio of the size of the central element to that of the end element H lt x A o 9 v 5 o a s h s 3 fo e x fe u x Q n A O gt A Ca 3 Masaa dl egment angular size ratio 2 2 19 Side 1 Screen for Coincident Option The region in which the identical side lies he adjacent region number 24 The code number of the side of that region If the points are in reverse order the negative of the side number is entered The coordinates of all points along the sides must be coincident umber of the corresponding side 2 2 20 Side 1 Screen for Segmented Option This sets the number od input type segments into which the side is divided he number of type segments 2 2 21 Side 1 Segment Type Screen This and the following side segment screns are repeated in a loop over the number that was set in the preceding seren There are four choices for the specification of the geometry of each he type of the segment segment Point by point requires the specification of every cell vertex along the segment Straight line is the default choice and this requires only the coordinates of the startpoint first segment only and the endpoint Conic section en
22. and position coordinates of these molecules are stored in the computer and are modified with time as the molecules are concurrently followed through representative collisions and boundary interactions in simulated physical space This direct simulation of the physical processes contrasts with the general philosophy of computational fluid dynamics which is to obtain solutions of the mathematical equations that model the processes The computational task associated with the direct physical simulation becomes feasible when the gas density is sufficiently low It also becomes necessary under these conditions because the Navier Stokes equations do not provide a valid model for rarefied gases and conventional CFD methods are unable to cope with the large number of independent variables that are involved in applications of the Boltzmann equation to realistic multi dimensional problems The degree of rarefaction of a gas flow is generally expressed through the Knudsen number which is the ratio of the mean free path to a typical dimension of the flowfield The Navier Stokes equations are valid when the Knudsen number is very small in comparison with unity and the limit as the Knudsen number tends to zero may be identified with the inviscid limit that is modelled by the Euler equations The opposite limit as the Knudsen number tends to infinity is the collisionless or free molecule flow limit in which intermolecular collisions may be neglected The flow regime bet
23. ate of the point 2 2 27 Side 3 Screen for Straight Line Option The startpoint is at the intersection with side 2 coordinate of startpoint m The endpoint is at the intersection with side 4 coordinate of endpoint m If this item is left at its default value of unity the cell elements along side 3 are of equal length If it is other than unity the edements are in an arithmetic progression Positive values define the ratio of the cell element adjacent to side 4 to that adjacent to side 2 The absolute value of a negative number defines the ratio of the size of the central element to that of the end elements m lt x lt lt x lt A A 2 2 a a 0 oO 9 9 3 g 2 xe ct fe xe 5 O rF a et 3 3 egment size ratio 2 2 28 Side 3 Screen for Conic Section Option The conic is similar to that described in 2 2 18 coordinate of focus m he parameter p m he eccentricity e Angle from x dirn to startpoint rad This is at the intersection with side 2 Angle from x dirn to endpoint rad This is at the intersection with side 4 If this item is left at its default value of ment angular size ratio NS ae SESS ple edo reio unity the cell elements along side 1 are r lt x O 8 Fa Q g c u 9 O O O 3 27 of equal angular extent If it is other than unity the elements arein an arithmetic progression Positive values define the ratio of the cell e
24. between unlike molecules cross collisions to be set to the mean of the values for the separate species The SEPARATE option leads to requests for values for all cross collisions ype of data for cross collisions Required only for gas mixtures Species groups may be employed to increase the efficiency of collision between particles with very different masses Studies Bird 1994 have shown that umber of species groups 15 in general this is worthwhile only when one of the species is an electron The groups may also be used to implement species weighting factors see next item Species weighting factors may be used to increase the sample of a trace species However in collisions between molecules with different weighting factors the velocity components of one of the molecules will sometimes not be altered This means that momentum and energy are not exactly conserved and there will bea step of a random walk at every such collision This can lead to serious errors and species weighting factors should only be used when absolutely necessary 3 Q gt EE Q T A ct e 5 v j 5 v 8 Q Q jad fe is xo n Required only for gas mixtures Set to the total number of chemical umber of reactions reactions in the gas Set to zero in a non reacting gas Required only for gas mixtures with reactions umber of third body tables This is greater than zero only when there are recombination reactions in wh
25. center to the end segments If side 3 is type 3 x coord of the focus of the conic section y coord of the focus of the conic section Parameter p for the conic section Eccentricity of the conic section Angle rads from x dirn to the int of sides 1 and 2 Angle rads from x dirn to the int of sides 1 and 4 Size ratio defined as for type 2 but applied to angular segments If side 3 is type 4 Number of the region with an identical side Number of the side ve for points in reverse order If side 3 is type 5 Number of type segments along the side In a loop over the segments starting at side 2 Either 1 2 3 or 4 for the type of the segment The number of cell segments along the type segment If the segment is type 1 in a loop over the number of points on the segment x coordinate of the point y coordinate of the point If the segment is type 2 x coord of the first point first segment only y coord of the first point first segment only x coord of the final point y coord of the final point Size ratio of the segment defined as for the side If the segment is type 3 x coord of the focus y coord of the focus Parameter p for the conic Eccentricity of the conic Angle from x direction to first point first segment only Angle rad from x dirn to last point on segment Size ratio defined as for the side If the segment is type 4 Number of the region with an identical side 53 Number of corres side ve for point
26. d within TECPLOT to produce a moving picture representation of the flow This may be displayed through the FRAMER utility The tecplot files are generated during the run when unsteady sampling is specified with a single run no ensemble averaging The TECPLOT files deal only with the flowfield values The surface values will generally be plotted as scatter or x y plots and if the descriptive text is edited out the text data output in DS2GS TXT is in a suitable form for TECPLOT For unsteady flows the word ZONE should be inserted between the records for the successive time intervals The time interval may be included as the zone title ontinue an existing calculation 11 The flow variables that are plotted in TECPLOT are distinguished by a code The key to this is x coordinate m y coordinate or for axially symmetric flows the radius m z coordinate only for axi sym flow and only if 3 D option is chosen number density n density kg m velocity component in either the x or axial direction m s velocity component in either the y or radial direction m s velocity component in either the z or circumferential direction m s translational temperature K rotational temperature K vibrational temperature K overall temperature K flow Mach number MC the average number of simulated molecules per cell CTR the ratio of the time step DTM to the local mean collision time MFP the local m
27. e jet is in the horizontal direction in the lower left of the figure The very small cells arein the boundary layer region of the flow within the nozzle Fig 11 The cell system for the jet plume problem 40 The central portion of the jet is a uniform stream of 20 argon and 80 helium by number at a Mach number just under 2 5 The boundary layer inside the nozzle is represented by a specified stream at the left hand boundary of the small region with very small cells The boundary layer velocity profile is assumed to be sinoidal with no slip at the wall The Mach number contours are shown in Fig 12 The two unlabelled contours are for M 0 5 and M 1 0 The subsonic flow accelerates and as expected the sonic line intersects the lip of the nozzle ee YY KKU a Fig 12 Mach number contours in the plume Fig 13 Streamlines and number density ratio contours 41 3 5 Plume backflow DS2GD005 DAT A molecule output file DGMOF1 DAT was generated at the upstream boundary of the upper left region in the flow in 3 4 This was renamed DGMIF1 DAT and was used as the sole molecule input source for this case There is a single region which matches region 5 along sides 3 and 4 but extends further in the backflow direction The molecule entry boundary is side 4 and as is required this is coincident with although the cells need not match side 2 of region 4 of the previous calculation where the molecule file was generated Bo
28. ean free path CSR theratio of the mean separation between collision partners to the local mean free path Fl fraction by number of species 1 in the flow mixture only F2 fraction by number of species 2 in the flow and so on the code output assumes a maximum of 20 species a JHiAandtnarse lt COZN lt x z335 This causes the program to search for the lowest value of n that has not already been applied to an archived file DS2GAn DAT The current data file is copied as this file and the program then opens the archive record file DS2GA TXT under the DOS text editor This enables the details of the archived data file to be entered for future reference 2 1 2 Subsidiary Screens Green These appear after the Introductory Program Screen and the combination of screens depends on the choice that is made from the introductory screen Appears only for the new case option choice of one of four options z The first option puts default values into STERLE M Completely Nevius all of the Data Screen items The combination of default items does not lead to a valid data file and the desired data must be entered z ae z The second reads in the values from the odiy Migexisting DS GD DATAE existing DS2GD DAT file Any desired modifications may then be made as the data screens are cycled z z z This option leads to the selection of one Recep onmedia AENEA of the archived data files DS2GAn DAT 12 files as the current data
29. ell and region structure Fig 19 Ratio of the temperature to the freestream value 45 3 9 Taylor Couette flow DS2G009 DAT The Taylor Couette flow is generated in the gap between two concentric cylinders when the outer cylinder is stationary and the inner cylinder rotates about the axis This case is concerned with the case in which the radius of the outer cylinder is twice that of the inner cylinder and the region is defined by two planes of symmetry normal to the axis The width of the flow is equal to the radius of the inner cylinder and the rotation commences at zero time The density of the monatomic hard sphere gas is such that there are initially 100 mean free paths between the inner and outer cylinder and the speed ratio of the circumferential velocity of the inner cylinder is 3 0 This flow is a consequence od an instability and differs from the others in that it is not repeatable to within the statistical scatter More than one vortex may be formed initially their directions of rotation is not predictable and the evolution to a single vortex may occur at different times Q Fig 20 Typical streamlines in the Taylor Couette vortex 3 10 Thermal creep flow DS2G010 DAT This case demonstrates several of the features that were added to Version 2 3 They are the use of offsets on interfaces in order to set up periodic boundaries and the ability to set flow and surface conditions as power law distributions Thermal
30. er of real molecules by a very much smaller number of simulated molecules must always be kept in mind The statistical scatter generally decreases as the square root of the sample size and in order to attain a sufficiently small standard deviation the programs employ either time averaging for steady flows or ensemble averaging for unsteady flows The most serious statistical problem is when a significant effect in the real gas is a consequence of the few molecules towards the extremities of the distribution A detailed exposition of the method is available in the reference which will be referred to as Bird 1994 Reference BIRD G A Molecular Gas Dynamics and the Direct Simulation of Gas Flows Oxford University Press 1994 1 2 The Scope of the Program 1 2 1 Geometry The DS2G program has a flexible system for the specification of the flow geometry This enables the program to be applied to a wide variety of flows ranging from the flow past aerodynamic bodies and rocket plume flows through to internal flows in high vacuum equipment The flow may be either a plane two dimensional flow or an axially symmetric flow There may be velocity components in the direction normal tothe plane or in the case of axially symmetric flows circumferential velocity components However there must not be any flow gradients in these directions The time averaged flow properties may be sampled if the flow is such that it becomes steady at large times Alternative
31. er of molecule output files Required only if thereis a stream Stream temperature Stream number density Stream velocity in the x direction along the axis for axially symmetric flows Stream velocity in the y direction The following item was required only for a stream in versions below 2 1 0 1 2 3 if the flowfield is initially a vacuum uniform stream specified by region or from the restart file Required only if thereis a stream and a gas mixturein a loop over the species Fraction by number of the species in the initial stream Required only if theinitial gas is s amp for each region in a loop over the regions These items were introduced in version 2 1 0 1 2 if the region is initially a vacuum a stream or is specified below Required only if the gas is specified for the region Initial temperature for the region Initial number density for the region Initial velocity in the x direction Initial velocity in the y direction Required only for a mixturein a loop over all the species Initial fraction of the species in the region In a loop over the regions For a steady flow The ratio of FNUM and DTM to basic values For an unsteady flow If positive a density ratio to basic value or if negative a temperature ratio 0 for a vacuum Number of cell elements along sides 1 and 3 Number of cell elements along sides 2 and 4 Either 1 2 3 4 5 to indicate type of side 1 1 if the co ordinates of the points are read individually o
32. es stops when file is completed Region containing the output side Code of the output side Number of molecules in each record Number of records in the output file Number of DTM time steps between sampling Number of samples between prints Number of prints to the assumed start of steady flow or the number of prints in one run of the unsteady flow Required only for a steady flow The factor for the molecule multiplication at 80 of the steady flow time Number of prints to STOP in a steady flow or the total number of runs in an unsteady flow The maximum number of simulated molecules Specification of parameter file DS2GP DAT If externally generated data in DS2GD DAT is sdected through the Generate and run a new case option in the Introductory Program Screen followed by Modify the existing DS2GD DAT in the subsidiary screen the DS2GP DAT file is generated automatically as the data screams are cyded However if it is sdected through the New run from an existing data file in the Introductory Program Screen a consistent DS2GP DAT file must also have been generated externally Maximum number of simulated molecules Maximum number of molecules in the duplication buffer Number of molecular species 3 for all monatomic species or 4 if some species have internal modes 2 for a simple gas or 3 for a gas mixture Number of species groups Number of reactions Number of third body tables Number of regions Number of cells Nu
33. f cells along the side 2 2 32 Side 3 Segment Screen for Point by Point Option This screen is repeated in a loop over the number of points on the segment The first point is that nearest the intersection of sides 3 and 2 while the final point is that nearest the intersection of sides 3 and 4 x Coordinate m The x coordinate of the point The y coordinate of the point coordinate m 2 2 33 Side 3 Segment Screen for Straight Line Option 28 The startpoint coordinates are required only for the first segment The startpoint is at the intersection with side 2 coordinate of startpoint m The endpoint is nearest the intersection with side 4 coordinate of endpoint m If this item is left at its default value of unity the cell elements along side 1 are of equal length If it is other than unity the elements are in an arithmetic progression Positive values define the ratio of the cell element nearest to side 4 to that nearest to side 2 The absolute value of a negative number defines the ratio of the size of the central element to that of the end elements egment size ratio vM lt x lt lt x lt A A 8 2 2 f g ot et 0 0 9 9 3 g 2 xe ce o 3 5 o rF Pah rF 3 3 2 2 34 Side 3 Segment Screen for Conic Section Option The conic section is as described for side 1 coordinate of focus m he parameter p m he eccentricity e lt x a 8 2 Q h a
34. f the seren he constant C1 in eqn 6 53 As for the like collisions AS for the like collisions he constant C2 in eqn 6 53 2 2 9 Basic Reaction Data Screen This is required only for CUSTOM gases if there are chemical reactions and is repeated in a loop over the reactions The logic assumes that the reaction is one of A dissociation reaction in which one moleculein a binary collision splits into two separate molecules or atoms An exchangereaction in which thetwo molecules or atoms in a binary reaction change their species A recombination reaction which requires a ternary or threebody collision Two of the atoms or molecules combineinto a single molecule whilethethird body molecule does not change its identity The pre collision species code number of one of the molecules other than the pecies of first pre coll mol third body molecule in a recombination The pre collision species code number of the second molecule other than the pecies of second pre coll mol third body molecule in a recombination This varies with the type of the reaction and identifies the type of reaction For a dissociation it is the code of the first post collision species It is set to zero for an exchange reaction or to 1 for a recombination First post collision parameter 19 The species code of the second post collision species in a dissociation The species code of the first post collision species for an
35. for polynomial rotational rdaxation rate Coefficient of temperature in the polynomial Coefficient of temperature squared in the polynomial Required only for specie with vibration in a loop over the modes Constant C1 in eqn 6 53 for the relaxation collision number or if C2 is negative the constant value of the relaxation collision number Constant C2 in eqn 6 53 or 1 to indicate a const Zv Required only when there are chemical reactions in a loop over the reactions Species code of the first molecule Species code of the second molecule If it is a dissodation First post reaction species code Second post reaction species code Third post reaction species code If it is a recombination 1 Species code of the recombined molecule Species code of the third body or if negative the code of the third body table If it is an exchange reaction 0 First post reaction species code Second post reaction species code Number of internal degrees of freedom that contribute energy to the reaction Activation energy for the reaction 1 E 10 times the pre exponential parameter in the Arrhenius rate equation 50 Temperature exponent in the rate equation Energy of the reaction Required only when there are third body probability tables in a loop over the tables In a loop over the species The relative efficiency of the species in recombinations 0 1 for stream or initial gas no stream or initial gas Number of molecule input files Numb
36. h numbers type 8 boundaries would be preferable Side 3 of region 4 should be upstream of the disturbance The boundary at the base is almost exact in the outer part of the flow as long as the x component of the velocity is well supersonic Unless this boundary is very far downstream there will be subsonic flow in the wake and some error in the flow The magnitude of this could be determined by placing the downstream boundary at different locations This system of flow boundaries has proved to be sufficiently flexible to cope with almost all flow problems that have been encountered When an interface between regions lies along curved sides the cell elements will match exactly only if they are equal in number and identically distributed along the interface Any mismatch will result in small gaps or overlaps at the interface The program procedures are designed to cope with this eventuality but it greatly increases the normally very small probability of simulated molecules going astray It is strongly recommended that the cell divisions be chosen such that curved interfaces are exactly matched There are no problems with cell size discontinuities across straight interfaces as far as the flow calculations are concerned However if contour output is chosen the contours will be continuous across the region boundaries only if the cells match exactly If the Knudsen number for the flow shown in Fig 2 was sufficiently small for the flow to be near c
37. he parameter n in the above equation This is positive for an exothermic reaction and negative for an endothermic reaction In the latter case it is generally the negative of the activation energy he energy of the reaction J 2 2 10 Third body Screen This is only for CUSTOM gases It is repeated for each table in a loop over the number set as the last item in the introductory gas screen It is repeated for each species and the screm title lists the table number and the species code If this is set to unity the rate coefficient is as set for the reaction Otherwise it is the factor by which the rate coefficient is multiplied elative effectiveness of species 20 2 2 11 Stream Data Screen There are two options PRESENT if there is a stream or initial gas or tream or initial gas ABSENT if there is not These generate input molecules along one side of one of the regions There can be up to three files DGMIFn DAT and they must have been produced by the renaming of molecule output files from other runs of DS2G umber of molecule input files Up to three files DGMOFn DAT are generated from the molecules crossing umber of molecule output files the specified sides and regions The next four items are required only if the stream is PRESENT The stream is in equilibrium at this tream temperature K temperature tream number density m TF z There are four options to indicate nical
38. ich the identity of the third body molecule is not specified Each table provides data on the relative efficiency of the species as third bodies in one recombination 2 2 3 Group Weighting Factor Screen Appears only for CUSTOM gas mixtures with more than one group and when group weighting factors are employed The screen is repeated for each group This weighting factor multiplies FNUM for this species A value greater than unity decreases the relative prevalence of this group and vice versa 3 Q gt EE Q T A ct e 5 9 Q 3 fe is 2 2 4 Main Species Data Screen Appears only for CUSTOM gases It is the first seren in a loop over the molecular species and the code number of the species being set appears with thetitle at the top of the screen eference diameter m The effective diameter of the molecule at the reference temperature eference temperature K The reference temperature for the molecular diameter This controls the way in which the cross section changes with relative velocity in collisions It is 0 5 for hard sphere molecules 1 0 for Maxwell molecules and of the order of 0 75 for real molecules lt J 7 A Q 2 T 3 o 5 g et i s o 8 0 5 o eciprocal of VSS scattering param Unity for the VHS model The VSS j N oz Q3 Blo 88 8 a Sie 25 o 2 a v Q lt 3 ag 9 o O IV m S10 ow Q lax ox IIR R Q Q 95 3 5 82
39. ide 2 A plane of symmetry For an axially symmetric flow such a plane would have to be normal to the x axis The flow velocity component normal to such a planeis zero and all flow gradients normal to the plane are zero At the molecular level the plane is equivalent to a specularly reflecting boundary 3 An interface with a specified uniform freestream flow A set of molecules appropriate to those crossing the boundary into the region are generated at the side Molecules crossing the side from the region are removed from the flow The boundary is an exactly correct physical representation even in subsonic or stationary flow as long as the flow disturbance does not extend to the boundary 4 An interface with a non uniform specified flow the macroscopic properties of which can vary at each cell element The flow gradients should be such that it can be regarded as effectively isentropic because the molecules are generated from the appropriate Maxwellian distribution 5 A solid surface A specified fraction which may vary with the molecular species of the gas may be absorbed by the surface 6 A solid surface similar to the previous option but which is outgassing at a specified rate 7 An interface with one or more sides of other regions 8 A boundary with a vacuum or a boundary with a molecule input file This option is also suitable for an outflowing gas with a highly supersonic velocity component across such a bounda
40. ing Required only for axially symmetric flows 0 1 for no weighting factors or factors proportional to radius Required only for axially symmetric flows with weighting factors Reference radius below which the weighting factors are unity The basic value for the number of real molecules that are represented by each simulated molecule The basic time step for uncoupling movement and collisions Gas menu code Number of regions Number of molecular species in the flow Required only for gas mixtures 0 if the diameter viscosity exponent and VSS scattering parameter for the cross collisions are to be set to the mean values or 1 if these quantities are to be set as data Number of species groups Required only if the number of species groups is greater than one 0 1 for group weighting factors not implemented implemented Number of chemical reactions Required only if there are chemical reactions Number of third body probability tables for recombinations Required only if there are more than one species group and is repeated for each group Weighting factor of species group L The following data is repeated for each species Reference diameter Reference temperature Viscosity temperature power law Reciprocal of the VSS scattering parameter 1 for VHS Molecular mass Required only for gas mixtures Species group in which the molecule lies Number of rotational degrees of freedom Required only if there are rotational degrees of freedom 0
41. ion number The coefficient of temperature squared oeff of the square of temperature in the second order polynomial Set to zero if there are no vibrational modes or if these need not be taken into account In the case of degenerate modes the degeneracy should be added to the total he number of vibrational modes 2 2 6 Vibrational Mode Data Screen Also in the loop over the species of CUSTOM gases and is required only if there are 17 vibrational modes It is repeated in a loop over the number of vibrational modes Should the rates in a mixture be species dependent the values for like molecules are set in this screen he characteristic vibrational temp Enter the value for this species in degrees K The vibrational relaxation collision number is assumed to be either a constant or available in the form of eqn 6 53 of Bird 1994 This is Z C T exp C T 3 he constant C1 in eqn 6 53 where T is the temperature and is the temperature exponent of the coefficient of viscosity Depending on the following item either the constant value or the constant C is entered here Either 1 or the constant C is entered here The negative value indicates that the vibrational relaxation collision number is a constant equal to the preceding value Both constants are in SI units he constant C2 in eqn 6 53 2 2 7 Cross collision Basic and Rotational Data Screen Also in the loop over species Required onl
42. ires extrapolation and this can sometimes cause problems that are avoided by the second option which bypasses the averaging Appears only for ensemble averaged unsteady flows Bypass cell report file Generate cell report file The cell report files can require significant time and this option allows them to be bypassed Appears only for ensemble averaged unsteady flows Bypass generation of text output Text output for surface values only Flowfield and surface text output The output files DS2GF TXT and DS2GM TXT can be very large because they are generated at each print interval in an unsteady flow Also if many runs are made the file need only generated after the final run The first of the three vertically listed choices bypasses the generation of the output file The second option provides output for the surface values only As noted above the TECPLOT output files are for flowfield values only so that this will bea widely used 13 option The third option leads to text output for both surface and flowfield properties 2 2 Data Screens The data screens are all blue in color They are processed in a forward direction and the DS2GD DAT file is modified progressively as enter is pressed for each screen However one can return to the first data screen by pressing the F1 key If one returns in this way the changes that have already been made are preserved The program first copies DS2GD DAT as DS2GD OLD and should
43. ires the input of numbers proportional to the length of each cell element he cell spacing along side 4 ie options are similar to those for side The corresponding points on sides 1 and 3 are joined by straight lines These lines are divided into intervals by the lines that define the cells Theintervals along sides 2 and 4 are defined in the above two items and the intervals along the intermediate lines are a weighted mean of these This data defines the weighting for these mean values Weighting on 1 3 divisions 2 2 16 Side 1 Screen for Point by Point Option This screm is repeated in a loop over thenumber of points on theside Thefirst point is at the intersection of sides 1 and 2 while the final point is at the intersection of sides 1 and 4 The points are at the cdl vertices x Coordinate m The x coordinate of the point AEN The y coordinate of the point 2 2 17 Side 1 Screen for Straight Line Option The startpoint is at the intersection with side 2 x coordinate of startpoint m coordinate of startpoint m The endpoint is at the intersection with side 4 lt x lt lt A 8 2 5 d et 9 fe 5 2 e o 5 rF 3 coordinate of endpoint m 23 If this item is left at its default value of unity the cell eements along side 1 are of equal length If it is other than unity the elements are in a arithmetic progression Positive values define the ratio of the cell element adjacent to
44. it is initially set as stream or AS BELOW if it is set to the conditions specified below The STREAM option is valid only if a stream has been defined nitial state The gas is in equilibrium at this egion temperature K temperature egion number density m Velocity component in x dirn m s Velocity comp in the y dirn m s 2 2 14 Initial Gas Composition Screen Required only if the BY REGION option was chosen and the gas is a mixture Itis then repeated for each of the species These are number fractions and their sum must be unity raction of species 2 2 15 Basic Region Data Screen The first screen in a loop over the regions atio of FNUM and DTM FNUM isthe number of real molecules represented by each simulated molecule apart from the effects of radial and species weighting factors and DTM is the time step over which the molecular motion and collisions are decoupled The basic values of these quantities were specified in the introductory data screen and are multiplied by this factor in this region Because both FNUM and DTM are altered by the same amount the fluxes of the molecules between regions is not affected This essentially allows the regions of steady flows to be calculated on different time scales The unsteady phase in not then physically accurate and this ratio is unity for all regions in an ensemble averaged unsteady flow For unsteady flows a positive value other than unity sets the
45. l side coordinate of focus m he parameter p m lt x A 8 9 h 8 c v 9 A e A 2 he eccentricity e Required only for the first segment Angle from x dirn to startpoint rad This is at the intersection with side 2 This is nearest the intersection with Angle from x dirn to endpoint rad ide A If this item is left at its default value of unity the cell elements along the segment are of equal angular extent If it is other than unity the elements are in an arithmetic progression Positive values define the ratio of the cell element nearest to side 4 to that nearest to side 2 The absolute value of a negative number defines the ratio of the size of the central element to that of the end elements egment angular size ratio 2 2 25 Side 1 Segment Screen for Coincident Option he adjacent region number Vis region in which the identical side The code number of the side of that region If the points are in reverse order the negative of the side number is entered The coordinates of all points along the segment and side must be coincident umber of the corresponding side 2 2 26 Side 3 Screen for Point by Point Option This scr n is repeated in a loop over thenumber of points on theside Thefirst point 26 is at the intersection of sides 3 and 2 while the final point is at the intersection of sides 3 and 4 x Coordinate m The x coordinate of the point EEA The y coordin
46. lement adjacent to side 4 to that adjacent to side 2 The absolute value of a negative number defines the ratio of the size of the central element to that of the end element 2 2 29 Side 3 Screen for Coincident Option The region in which the identical side he adjacent region number lies The code number of the side of that region If the points are in reverse order the negative of the side number is entered The coordinates of all points along the sides must be coincident umber of the corresponding side 2 2 30 Side 3 Screen for Segmented Option This sets the number od input type segments into which the side is divided he number of type segments 2 2 31 Side 3 Segment Type Screen This and the following side segment screens are repeated in a loop over the number There are four choices for the MEY PEO ihe Sees specification of the geometry of each ct D cr D n u Q ct S D D g a wn Q g segment Point by point requires the specification of every cell vertex along the segment Straight line is the default choice and this requires only the coordinates of the startpoint first segment only and the endpoint Conic section enables the segment to be specified as a segment of a conic Coincident sets the segment as being coincident with a previously defined side These are cell elements and the total over all segments must equal the umber of elem along the segment number o
47. lision pairs to a value well below the mean free path Fig 4 Cell structure associated with DS2GD001 DAT There is just one region in the flow Side 1 is the surface of the sphere side 2 is the upstream portion of the axis side 3 is a boundary with the stream and side 4 is the downstream region of the axis The stream boundary is exact for the upstream region of the undisturbed flow but there will be some boundary interference to the disturbed region of the flow The contours of constant Mach number are shown in Fig 4 and these show that the Mach number based on the velocity component normal to the outer boundary would be supersonic over most of the downstream boundary It is almost certain that the outer boundary is sufficiently far from the body for there to be no serious boundary interference but the only way to prove this is to make matching calculations with the outer boundary in different locations The contours of Mach number and those for the overall temperaturein Fig 5 have been generated by the TECPLOT post processing program using the file DS2GT TEC that is generated by choosing the TECPLOT option in the menu for the initial options 36 The quantity CTR in the TECPLOT file time step exceeds the mean collision time in the stagnation region and DTM should be reduced in the data BPNYHWORUADASOOSCHD WALD HW m vn Fig 5 Contours of constant Mach number for DS2GDO001 PLT T E 700 675
48. ly an ensemble average may be made over multiple runs of an unsteady flow 1 2 2 Gas Model The program employs the physical gas models that have been described and validated in Bird 1994 The gas may be a mixture of VHS or VSS models and the cross sections the viscosity temperature index which determines the way in which the cross section changes with the relative velocity and the may VSS scattering parameter may be specified separately for every combination of molecular species A classical Larsen Borgnakke model is employed for the rotational degrees of freedom while a quantum model is used for the vibrational modes The chemical reaction model calculates reactive cross sections that are consistent with the measured rate constants 1 2 3 Gas Surface Interactions The classical diffuse reflection model with complete accommodation of the gas to the surface temperature is appropriate to engineering surfaces that have not been exposed for a long period to ultra high vacuum The other classical model of specular reflection may be specified for the artificial case of complete slip and no energy transfer at the surface Alternatively the CLL model may be employed and this is capable of modelling realistic non classical reflection cases Version 3 2 adds a diffuse adiabatic reflection option and gives the recovery temperature distribution 1 3 General Description of the DS2G Program For the two dimensional option the flow is in the x y
49. mber of cell corner points 55 Number of boundary elements Max number of specification type segments on any side Number of surface cell elements Number of molecule entry elements Number of interface elements Maximum number of adjacent sides Maximum number of adjacent elements Specified Maximum number of points along 1 3 sides in any one region Maximum number of points along 2 4 sides in any one region Maximum number of points on any side Maximum number of vibrational modes of any species Number of molecule input files Number of molecules in one record repeated for each molecule input file Number of molecule output files Number of molecules in one record repeated for each molecule output file 0 1 if weighting factors are removed retained repeated for each output file Number of prints to assumed steady flow or total number of runs in unsteady flow 0 1 for steady unsteady flow
50. monstration data files DS2GD001 DAT DS2GD002 DAT and soon A directory say DSM C should be created on the hard disk and the executable and all demonstration files on the distribution disc should be copied to it The execution of DS2GZ produces the executable file DS2G EXE This is the only file that is required for the operation of the program Apart from the demonstration data files all files in Fig 3 and additional self deleting scratch files are created during the execution of DS2G The general operation of the program is described in 2 1 The input of invalid data will lead to an error which may or may not lead to a diagnostic that identifies the error The cell configuration file DS2GC PLT may be useful in detecting inconsistent geometry input and should in any case be viewed in order to check the geometry This is an HPGL file and may be viewed by importing it directly toa graphics or a wordprocessing program This has been tested with both WordPerfect and Microsoft Word In addition the data summary file DS2GD TXT may be studied and compared with its specification in Appendix B The geometry logic that is employed when moving the molecules traces their motion through all cells is sensitive to round off error If a molecule becomes lost during this process it is discarded from the flow and produces a removal error These are indicated on the screen during the running of the program and the total number is listed in DS2GS TXT Thi
51. ng factors The weighting factors are all unity ErErence LACUS TOWNS ELIS EOL S AM within this radius and are set equal to the ratio of the radius to the reference radius outside it The molecular radius is used to define a molecule based weighting factor during the molecule move and output For collisions the weighting factor is based on the cell radius so that it does not vary from molecule to molecule within the cell z ae This is the number of real molecules SSE ENUMTANS that are represented by each of the simulated molecules If the number density was uniform and in the absence of weighting factors the number of simulated molecules would be equal to the product of the number density and the total volume of the flow divided by FNUM When setting FNUM account should be taken of the probable average number density the presence of ant weighting factors which will tend to reduce the required FNUM 14 and the fact that FNUM may vary with region in steady flows A trial run will often be necessary to establish the value of FNUM that leads to the desired number of simulated molecules In calculating the volume a two dimensional flow has a width of 1 m while an axially symmetric flow occupies the full 2x azimuth angle This is the time step or interval over which the molecular motion is uncoupled from the intermolecular collisions This is normally set to a value such that the faster molecules move about one third of a cell width du
52. ng the running of the program from the 50 000 that is set in the data to more than 80 000 The time to steady flow is large and this example could well use the molecule multiplication feature There is about 4 by number atomic oxygen in the stream and this represents degree of oxygen dissociation of 0 1 The increase in this degree of dissociation due to chemical reactions in the flowfield is shown in Fig 17 The maximum degree of dissociation is approximately 0 6 Thereis also considerable dissociation of nitrogen accompanied by the formation of a small fraction of NO The surface is non catalytic and at there densities no recombination reactions occur 43 LURAY Sn i SSSR Fig 16 The cells for the reentry flow Fig 17 Degree of dissociation of oxygen in the flowfield 44 3 8 Flow past a curved plate DS2G008 DAT This is the flow of argon at 300 K 10 m3 and 1000 ms past a curved flat plate with its leading edge parallel to the flow The plate is in the shape of one quadrant of a sine wave and the purpose of the test case is to check the point input option for region sides surfaces with a variable temperature and arbitrary cell spacing r r r 7 J Ga Un L 1 1__J Fig 18 The c
53. number density in the region to this ratio times the standard number density while a negative value similarly sets a temperature ratio However it is recommended that region dependent values be set explicitly through the Initial Gas Data screen which was introduced in Version 2 1 The cells are used for the sampling of the flow properties and for setting the collision rate Sides 1 and 3 may be curved Sides 2 and 4 are always straight ell segments along sides 1 and 3 ell segments along sides 2 and 4 There are five choices for the specification of the geometry of side 1 Point by point requires the specification of every cell vertex along the side he geometry specification of side 1 22 Straight line is the default choice and this requires only the coordinates of the intersection of side 1 with side 2 and those of the intersection of side 1 and side 4 Conic section enables the side to be specified as a segment of a conic Coincident sets the side as being coincident with a previously defined side Segmented allows the side to be specified by a combination of the above four choices he geometry specification of side 3 oe are the same as those for z z The straight side 2 may be divided in EISEN spacings Ong Ade z three ways to form the cell divisions Equal elements is the default choice Arithmetic progression leads to the elements being in an arithmetic progression Arbitrary requ
54. one third of the cell dimension at each time step This satisfies the above requirement for the size of time step in stationary low Knudsen number flows and is conservative for moving gases and or high Knudsen numbers The DSMC method uses the cell system only for the sampling of the macroscopic properties and for the selection of possible collision partners although the sampled density is used in the procedures for establishing the collision rate This means that the cell geometry should be chosen to minimise the changes in the macroscopic properties across an individual cell Primitive implementations of the DSMC method choose the collision partners from anywhere in the same cell Later implementations including Versions 1 and 2 of DS2G employed fixed sub cells to reduce the spacing of collision partners Version 3 of DS2G introduces an adaptive transient rectangular background grid to one cell at a time within the collision routine This yields nearest neighbour collisions and is efficient with regard to both computation time and storage requirements Version 3 1 adds output to the TECPLOT files that indicates whether the DSMC numerical criteria have been met The ratio of the time step to the local mean collision time and the ratio of the 4 mean separation between collision partners to the local mean free path should be well under unity over the whole of the flowfield The statistical consequences of the replacement of the extremely large numb
55. ontinuum very thin cells would be necessary in the region of high vorticity near the surface Should the desirable cell size lead to an excessively small number of simulated molecules in the cell the problem can be overcome in a steady flow by calculating the boundary layer on a shorter timescale The number of molecules in the cell is increased by reducing the number of real molecules that are represented by each simulated molecule If the time step is reduced by exactly the same fraction the flux of molecules across the interfaces with the outer flow are exactly matched This simultaneous change in DTM and FNUM is ideal for flows in the stagnation region where FNUM is reduced in order to increase the number of molecules in very thin cells near the surface The reduction is DTM is also desirable because of the thin cells However for problems 8 such a plume backflow a reduction in FNUM is desirable because of the very low density but the cells should be large and the reduction in DTM is most undesirable The above problem may be overcome by splitting separate calculations for the near and far plume Up to three files of molecules G2MOFn DAT n to 3 are generated at the low density boundary and these files may be renamed G2MIFn DAT and used as the input files for the next section of the flow This process may be repeated If the normal component of the flow is well supersonic across the output input boundary so there is no upstream influence
56. owever as the density decreases the collision rate in the gas eventually becomes too low to maintain the isotropy of the pressure tensor A breakdown parameter can then be defined as the ratio of the density scale time following the fluid element to the mean collision rate For a steady flow this parameter can be related to the local Knudsen number based on the density scale length 3 Although it was shown many years ago that the Chapman E nskog expansion for the distribution function is not uniformly valid attempts are still being made to extend the range of validity of the Navier Stokes equations to lower densities However the low density effects such as the development of an anisotropic pressure tensor are of a very basic nature and it is unlikely that much progress will be made for other than one dimensional steady flows In addition effects such as thermal and pressure diffusion become more prominent at low densities and these are not generally included in the Navier Stokes formulations It is certain that the necessary extensions in the event that adequate ones can be developed will add greatly to the difficulty of the continuum approach On the other hand once the density becomes sufficiently low for the DSMC solution to be computationally feasible it is a much easier method to apply The main reasons for this are i The calculation is always unsteady with physical time as one of the principal variables in the simulation A stead
57. plane Alternatively in G2 the axis of an axially symmetric flow lies along the x axis and the y coordinate is a radius from that axis The flowfield is divided into a number of four sided regions the four sides being numbered from 1 to 4 in clockwise manner as shown in Fig 1 ZZ lt gt IEA AALA AA Fig 1 A typical flow region Sides 1 and 3 of each region may be curved but they must not be reentrant These sides are divided into a number of cell segments or elements and the number of elements on each side must be the same The cell structure is defined by joining the corresponding points on each side by straight lines and then dividing each of these lines into the same number of cell elements Sides 2 and 4 must therefore be straight There are a number of options that relate to the way this geometry is defined and the cells may be quite irregular as long as none of the joining lines cross The lines of cells in the direction of sides 1 and 3 are referred to as rows and lines in the direction of sides 2 and 4 as columns The numbering of cells is along successive rows starting rom the cell at the intersection of sides 1 and 2 As noted earlier the cells are used for the sampling of the flow information and the establishment of the collision rate Each side is one of the following 1 On the axis of the flow This would occur only for an axially symmetric grid and no molecules would collide with such a s
58. r 2 if the side is straight the endpoints are specified and the spacing is an arithmetic progression or 3 if the side is a segment of a conic section or 4 if the points are identical with another side or 5 if the side is defined by more than one segment Either 1 to 5 as defined above but for side 3 Either 1 2 or 3 to indicate the type of input for side 2 1 if the segments are of equal length or 2 if the segments are in a arithmetic progression or 3 if the segment lengths are arbitrarily distributed 51 Either 1 2 or 3 as above but for side 4 Weighting lt 1 towards side 2 or gt 1 towards side 4 when dividing the intermediate lines joining sides 1 and 3 If side 1 is type 1 in a loop over the number of call points on the side x coordinate of the point y coordinate of the point If side 1 is type 2 x coord of intersection with side 2 y coord of intersection with side 2 x coord of intersection with side 4 y coord of intersection with side 4 Size ratio if positive of cell at side 4 to that at side 2 or if negative of the center to the end elements If side 1 is type 3 x coord of the focus of the conic section y coord of the focus of the conic section Parameter p for the conic section Eccentricity of the conic section Angle rads from x dirn to the int of sides 1 and 2 Angle rads from x dirn to the int of sides 1 and 4 Size ratio defined as for type 2 but applied to angular elements If side 1 is
59. r a surface across which file entry molecules are introduced Distribution of properties There are three options gt ko no R o gt lt ctr ro wn 8 2 re wn Q wn Cc 3 fed a R Uniform This indicates that a single set of values applies to the whole side Variable Requires the specification of the flow or surface properties at every cell element along the side Power Law The values at the ends of the side are specified and the other values follow a power law distribution Applies only to the Power Law option If the powerlaw is n the value at distance s along a side of length is ndex of power law v v S I v v Here v and v are the values at the beginning and end of the side respectively The number of sides of other regions ie MSs Cae onge that wholly or partially adjoin this side gt xe kok R o gt lt ar o or Q i o a BR 2 2 41 Specified Flow Property Screen If the uniform option has b n chosen a single screen applies to the whole side although this is titled Element 1 If the variable option has been chosen the screen is repeated for each cdl dement If the power law option has been chosen a screen appears for each end of the line velocity component m s emperature K umber density m 3 z z x Z A O 2 fa rr 3 31 2 2 42 Specified Flow Composition Screen This scregm is req
60. ring a time step It should be small in comparison with the local mean collision time The time step may vary along with FNUM from region to region asic time step s This chooses the gas species either as one of the eight preset cases or aS a CUSTOM gas that requires the details to be entered in subsequent screens Once a data file has been generated with a preset option the CUSTOM option may be chosen in the modification of this file The detailed gas screens then appear and the preset values for the gas may be modified ype of gas If the preset gas is a mixture it is necessary to know the species code numbers of the constituents These are IDEAL AIR Oxygen is species 1 and nitrogen is species 2 REAL AIR Oxygen is species 1 nitrogen is species 2 atomic oxygen is species 3 atomic nitrogen is species 4 and NO is species 5 REAL NITROGEN Nitrogen is species 1 and atomic nitrogen is species 2 ARGON HELIUM Argon is species 1 and helium is species 2 This sets the number of four sided regions that will be set up by the data umber of regions 2 2 2 Introductory Gas Data Screen This screen appears only when the CUSTOM gas option has b n chosen Umber OL Molecular SPECIES Unity for a simple gas or the number of molecular species in a gas mixture Required only for gas mixtures The MEAN option causes the cross sections viscosity temperature power laws and VSS scattering parameters for collisions
61. ry This is because there are virtually no upstream moving molecules in a flow with Mach number or speed ratio greater than about three The whole of each side must be of the same type so that changes in boundaries such as the end of a surface can occur only at the corners of the regions The orientation of a region with respect to the x and y axes is quite arbitrary and any face of a region can interface with more than one other region A typical set of regions is shown in Fig 2 Fig 2 Typical arrangement of regions If the regions in Fig 2 were for the supersonic flow past a blunt cone with a flat base and assuming that side 1 is the lowest side in each case the specification of the sides is as follows Region 1 Side1 A surface type 5 Side2 On the axis type 1 Side 3 An interface with side 1 of region 4 type 7 Side 4 An interface with side 2 of region 3 type 7 Region 2 Sidel On the axis type 1 Side2 A surface type 5 Side 3 An interface with side 1 of region 3 type 7 Side 4 A stream boundary type 3 Region 3 Side1 An interface with side 3 of region 2 type 7 Side 2 An interface with side 4 of region 1 type 7 Side 3 An interface with side 1 of region 4 type 7 Side 4 A stream boundary type 3 Region 4 Sidel An interface with side 3 of region 1 and side 3 of region 3 type 7 Side2 On the axis type 1 Side 3 A stream boundary type 3 Side 4 A stream boundary type 3 For high Mac
62. s in Fig 8 Streami If the Knudsen number was reduced the flow speeds within the vortex would be ize if the d eventually it would be desirable to double the s Id because the lower boundary would not necessar Increase an expected to ly be a plane of symmetry become unsteady 1 l IN a rea flowfi but it would be a ion may The separated reg formidable task to study this case as an unsteady flow flow 38 Fig 9 Contours of constant Mach number 3 3 Unsteady flow past a vertical flat plate DS2GD003 DAT This case involves a vertical flat plate of height 0 2 m that is placed instantaneously into a uniform supersonic stream of argon at 1000 ms The undisturbed number density is 3x10 m and the temperature of both the stream and the surface is 300 K The flow is symmetrical about the centreline of the plate and only the upper half is computed There are three rectangular regions the first extends 0 15 m directly upstream of the plate the second directly downstream by an equal amount and the third extends across the other two and has a height equal to the semi height of the plate The cell size is uniform across the regions The problem has been set up with unsteady sampling and ensemble averaging in order to study the establishment of steady flow about the plate The most useful indicator of the establishment of steady flow is generally given by the total number of molecules in the flow Thi
63. s in reverse order If side 2 is type 2 Ratio of cell size if positive at side 3 to that at side 1 or if negative at centre segment to the end segments If side 2 is type 3 in a loop over the cell segments Number proportional to segment length side 1 to side 3 If side 4 is type 2 Ratio of cell size if positive at side 3 to that at side 1 or if negative at centre segment to the end segments If side 4 is type 3 in a loop over the cdl segments Number proportional to segment length side 1 to side 3 In a loop over the four sides of the region Either 1 2 3 4 5 6 7 or 8 for the type code for the side 1 for an axis of symmetry or 2 for a plane of symmetry or 3 for a stream boundary or 4 for a specified flow boundary or 5 for a surface or 6 for an outgassing surface or 7 an interface with another side or sides or 8 the side is a vacuum or molecule entry file boundary If the side is type 4 5 or 6 0 1 for constant variable input along the side If the side is type 7 Number of sides that adjoin this side If the side is type 4 input a single value for constant input or in a loop over the cdl segments for variable input Velocity component in the x or axial direction Velocity component in the y direction Temperature of the stream Number density Required only for a mixturein a loop over the species Fraction of the species in the stream If the side is type 5 or 6 input a single value for constant input or in
64. s is included in the on screen information during the running of the program In this case the build up in front of the plate is initially matched by the decline in the number of molecules behind the plate There is then a systematic increasein the number with the steady flow value being attained before 1 ms The change in pressure on a vertical plate from the initial impulsive value to the steady flow value is comparatively small in a supersonic flow This is illustrated for this case by the pressure distribution along the upstream face of the plate This is shown for a number of time intervals in Fig 9 This shows that the pressure effectively reaches the steady flow value by 0 6 ms The number of molecules is still increasing at this time so that the total number of molecules is a conservative indicator as far as the surface values are concerned The pressure is uniform at zero time but a gradient develops quickly 39 30 p 25 N So 0 0 to 0 04 ms a 0 2 to 0 24 ms v0 4 to 0 44 ms e 0 6 to 0 64 ms 5 m 0 8 to 0 84 ms 1 5 to 16 0 ms Steady Flow Pressure n m Nn o 0 00 0 02 0 04 0 06 0 08 0 10 Height m Fig 10 The pressure distribution along the plate as a function of time 3 4 Supersonic jet plume DS2GD004 DAT The cell system for this flow involves five regions as shown in Fig 11 The lip of the nozzle is at the boundary of the small cells with the large cells and th
65. s number should be compared with the similar listing of the total number of molecules that enter the flow The ratio of removed to entering molecules is normally about one in ten thousand The total number of simulated molecules in the flow is preserved through the duplication of another molecule in the cell from which the molecule is removed The program has been compiled without the activation of array bounds checking or full floating point error detection Should an isolated execution error occur the restarting of the program will generally involve a different random number sequence and the problem should not recur Systematic errors will generally be a consequence of inconsistent data that leads to gaps between regions time steps that are excessively large and so on Should problems persist with valid data the problem should be reported to Graeme Bird on 100250 1101 compuserve com advice on new versions together with instructions for the downloading of revised files is available at http ourworld compuserve com homepages gabird 48 APPENDIX B Specification of data file DS2GD DAT A data file may be gnerated externally to conform to these specifications All dimensioned quantities are in base SI units n in version number n m m in version number n m The following specification is for n 3 and m i e Version 3 0 0 1 for two dimensional axially symmetric flows respectively 0 1 for steady time averaged unsteady averaged sampl
66. such that collisions effectively occur at the surface The data is the probability that a single atom striking the surface recombines This fraction obviously cannot exceed 0 5 and will generally be very much smaller The necessary physical data for the recomb ination is taken from the data for the corresponding gas phase recombination A finite value for this fraction therefore requires that the data for this reaction be set robability of catalytic recomb 2 2 44 Interface Screen This scree is repeated for each of the sides that adjoin the side he adjacent side The code number of the adjacent side he region in which it lies The code number of the region The x coordinate of the molecule is pisplacementim the cdir altered by this amount in the transfer The y coordinate of the molecule is PiSPIacementinthe yidirn altered by this amount in the transfer For periodic boundaries the adjacent side may be another side in the same region 33 2 2 45 Molecule Input File Screen This is repeated for each of the up to 3 files he region code This is the region into which the molecules enter z z R This side must have been specified as a he side of this region aumo ME SiGe The entry file is divided into records that are read at random Only one record is in the memory at any time and entry molecules are read from it at random Ks o R Q ge e 3 s R Q The file is a renamed outpu
67. t file and these must correspond to the corresponding settings for the original output file ecords on the file 2 2 46 Molecule Output File Screen This is repeated for each of the up to 3 files he region code This may be within the flow eg an he side of this region interface rod Ks o R Q ge e 3 s R 3 foe ecords in the file Required only for an axially symmetric flows with radial weighting factors REMOVE writes the files as if Me OMe G eel weighting factors were not present RETAIN preserves the weighting factors ile completion action The computation may either continue or stop when the output file has been completed If there are other output files the program will not stop until they have all been completed 2 2 47 Computational Parameter Screen The first five items are for timeaveraged steady flows The time step is usually chosen such that a typical molecule moves about one third of the way across a cell in one step This number is usually in the range two to four ime steps between sampling 34 This sets the interval at which the restart file DS2GR DAT and the output files DS2GS TXT DS2GF TXT and DS2GM TXT are written amples between prints The flowfield and surface sampling is reset at the start of each print interval less than value The time average starts with this interval but if the program is re started there is an opportunit
68. tele ofthe NOWE whether the flowfield is initially a uniform stream or a VACUUM a STREAM as specified above is specified BY REGION through the next two screens or is filled with molecules from the current RESTART FILE DS2GM DAT The last option is primarily to allow the calculation of a lower Knudsen number case to start from the fully developed steady flow in a higher Knudsen number case This greatly reduces the time preceding the development of steady flow in very low Knudsen number case particularly when the unsteady process largely depends on the diffusion of viscosity The geometry of the flow must be the same in each case as far as the region boundaries are concerned although the number and spacing of cells may be changed Also the FNUM ratio must be increased in direct proportion to the freestream density so that the total number of simulated molecules is the same in each case E lt lt i 7 Oo A A fo fo 3 3 xe xe Q 5 b rt er er oO lt 2 x lt 2 a gt 3 2 2 12 Stream Composition Screen Required only if there is a stream and the gas is a mixture Itis then repeated for each of the species These are number fractions and their sum must be unity raction of species 2 2 13 Region Dependent Initial Gas Screen Required only if the BY REGION option was chosen for the initial state 21 There are three options VACUUM if there is initially no gas in this region STREAM if
69. th the number of molecules per cell and the time step were significantly larger than in the earlier calculation The contours of number density ratio are shown in Fig 14 The total number of molecules in the input file was only 250 000 the current data file would produce 1 000 000 This was excessively small and was probably responsible for the higher density contours not being exactly matched with those from the preceding calculation Note that a surface could be placed in the backflow region and that as long as the resulting disturbance did not reach the input boundary the single input file could be used for a number of cases Fig 14 Number density ratio in the backflow region 3 6 Satellite contamination DS2GD006 DAT This is concerned with the flow of atomic oxygen at 7 500 m s and 1000 K past a vertical disk of radius 1 m The number density of the stream is 3x10 and the there is an outgas mass flux of 5x10 of a gas with molecular weight 500 from the disk The disk is diffusely reflecting at a temperature of 300 K There are no radial weighting factors and the flowfield extends 10 m upstream of the disk and toa radius of 5 m There is a rectangular region upstream of the disk and another rectangular region outside the disk The number fraction of the outgassed molecules in the flowfield is shown in Fig 15 The number of outgassed molecules is small compared with the stream molecules and a species weighting fraction of
70. type 4 Number of the region with an identical side Number of the side ve for points in reverse order If side 1 is type 5 Number of type segments along the side In a loop over the segments starting at side 2 Either 1 2 3 or 4 for the type of the segment The number of cell segments along the type segment If the segment is type 1 in a loop over the number of points on the segment x coordinate of the point y coordinate of the point If the segment is type 2 x coord of the first point first segment only y coord of the first point first segment only x coord of the final point y coord of the final point Size ratio of the segment defined as for the side If the segment is type 3 x coord of the focus y coord of the focus Parameter p for the conic Eccentricity of the conic Angle from x direction to first point first segment only Angle rad from x dirn to last point on segment Size ratio defined as for the side If the segment is type 4 52 Number of the region with an identical side Number of corres side ve for points in reverse order If side 3 is type 1 in a loop over the number of points on the side x coordinate of the point y coordinate of the point If side 3 is type 2 x coord of intersection with side 2 y coord of intersection with side 2 x coord of intersection with side 4 y coord of intersection with side 4 Size ratio if positive of cell at side 4 to that at side 2 or if negative of the
71. uired only for gas mixtures and is then repeated for each species If the uniform option has b n chosen a single screen applies to the whole side although this is titled Element 1 If the variable option has been chosen the scree is repeated for each cal dement If the power law option has been chosen a screen appears for each end of theline raction of species 2 2 43 Surface Screen This scree is repeated for each species If the uniform option has bem chosen a single screen applies to the whole side If the variable option has been chosen the scree is repeated for each cal dement If the power law option has been chosen a screen appears for each end of the line If this is set as a negative number the Spel EONS Senaeue surface is regarded as specularly reflecting for this species The default value is 1 and this leads to diffuse reflection with complete thermal accommodation A value other than 1 specifies that the CLL Cercignani Lampis Lord model is to be used and if the species has internal energy modes this value is the accommodation coefficient for the internal modes of this species and must be between 0 and 1 ndicates diffuse or CLL model The accommodation coefficient for the energy based on the normal component of the translational velocity of the incident molecule az pez Q o gt Z lt ct 3 O rc 3 8 ormal energy accomm coeff Note that this coefficient is
72. ween free molecule and the limit of validity of the Navier Stokes equations is generally referred to as the transition flow regime A Knudsen number of 0 1 has traditionally been quoted as the boundary between the continuum and transition regimes but the characteristic dimension of complex flow fields may be specified in many different ways and the use of an overall Knudsen number may be misleading The conservation equations of fluid mechanics are valid for all flow regimes but the Navier Stokes equations depend also on the Chapman Enskog theory for the shear stresses heat fluxes and diffusion velocities as linear functions of the velocity temperature and concentration gradients The Chapman Enskog theory assumes that the velocity distribution is a small perturbation of the equilibrium or Maxwellian distribution In an isentropic flow for which the Euler equations are valid the distribution function conforms everywhere to the Maxwellian The formulation of the Chapman Enskog distribution incorporates local Knudsen numbers which are the ratios of the local mean free paths to the scale lengths of the velocity and temperature gradients It has been found that errors become significant when these local Knudsen numbers exceed 0 1 and the continuum theory is hardly useable when they exceed 0 2 The transport property terms become Zero in an isentropic flow and it might be thought that the Euler equation yield correct results at all Knudsen numbers H
73. y flow is obtained as the large time state of the unsteady flow The method does not require an initial approximation to the flow field and there is no iterative procedure for convergence to the final solution In the case of a time averaged steady flow or an ensemble averaged unsteady flow there will bea gradual declinein thestatistical scatter as the sample increases but convergence is not the appropriate description of this process ii Additional effects such as non equilibrium chemistry may be included simply by adding to the complexity of the molecular model and the fact that these may change the basic nature of the continuum equations is of no consequence iii Most importantly there are no numerical instabilities The uncoupling of the molecular motion and collisions over small time steps and the division of the flow field into small cells are the key computational assumptions associated with the DSMC method The time step should be much less than the mean collision time and a typical cell dimension should be much less than the local mean free path The cell dimension should also be small compared with the distance over which there is a significant change in the flow properties This latter condition will dictate the cell size in high Knudsen number flows and in practice the cell size in low Knudsen number flows is set to about one third or one half the cell size The time step is then set such that a typical molecule moves about
74. y for gas mixtures in which the ather the SEPARATE option has been chosen in the basic gas data screm or the DEPENDENT option has been chosen in combination of species is shown in the title of the seren First four items are required only for the SEPARATE option Based on the collision cross section for he reference diameter m this pair of species The temperature on which the above at the reference temperature K Pee cara ie based Viscosity data is available for many Viscosity temperature power law ombras These can be quite different from the eciprocal of VSS scatter parameter mean values Final thr items arerequired only for species with rotational degres of freedom and only if the DEPENDENT option was chosen in the main data screen for this species Depends on the choice that was made in the main species data screen onstant or const in polynomial Final two items are required only if the POLYNOMIAL option was chosen in the main data screen for this species 18 oeff of temperature in polynom oeff of temp squared in poly 2 2 8 Cross collision Vibrational Screen The final screen in the loop over species Required only for gas mixtures when the species has vibrational modes and when the DEPENDENT option has b n chosen in the main species data screen The screen is repeated for all species other than that in the current loop and the combination of species is shown in the title o
75. y to start a new average This is useful if the original estimate of the steady flow time is too small rints to assumes steady flow The unsteady phase of the flow may require an excessively long computation time This enables the flow to be started with a small number of molecules and at 80 of the steady flow time the molecules are multiplied by this factor 7 A run is usually stopped interactively Umber of punts O ROR by Ctrl C and this is usual set to a very large integer such that it would not be reached in any reasonable time The flow should not be stopped by Ctrl C while the restart file is being written because this may result in a defective file Molecule multiplication factor For unsteady flows the preceding items are replaced by the following five items This is the number of time steps between the generation of the unsteady sampling file Un DGF and the updating of the text output file record ime steps between sample print A local average is taken over this teps for short time average number of time steps umber of prints in each run This sets the length of the run dimberobruneto STOP The run is repeated this number of _times unless stopped interactively The number of runs should be set to one if the flow is not repeatable eg In the study of flow instabilities When it is set to unity the TECPLOT files are generated during the run This is an estimate of the number of simulated

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