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INSTED CFD (test problem)

1. x coord y coord Segerlind INSTED Difference 0 0 2 0 68 97 67 70 lt 2 0 0 4 0 36 58 36 22 lt 1 0 0 2 0 140 140 lt 1 0 0 3 0 88 48 87 10 lt 2 0 0 4 0 55 71 55 36 lt 1 1 0 1 0 140 140 lt 1 0 707 0 293 140 140 lt 1 4 0 0 0 42 35 42 10 lt 1 File lola out 7 44 LEGEND 1 313E 02 1 227E 02 1 140E 02 1 053E 02 9 665E 0 G 8 797E 0 mT ec KT 7 063E 01 6 196E 0 5 329E 0 E 4462E 0 3 595E 01 C B 2u o0oo0om Number of nodes 503 Number of 9 node elements 113 a Computational Model b Contour Plot of Temperature Figure 1 2 Mesh and temperature plot for Sample Problem 1 Reference Segerlind L J 1984 Applied Finite Element Analysis Second Edition John Wiley amp Sons Ltd New York 405 408 8 44 TEST PROBLEM 2 HEAT CONDUCTION WITH VOLUMETRIC HEAT SOURCE Problem Statement Analyze the time dependent equation or Ot Q x y 0 lt x y lt 1 _V T 1 subject to the boundary conditions for t gt 0 T 0 on lines x land y 1 oT 0 on lines x 0and y 0 on and the initial boundary conditions for x y in W T 0 t 0 Physical and Computational Domain The physical and computational domain is shown below 1 0 1 0 Figure 2 1 Physical and Computational Domain Governing Equations This is written above as part of the problem statement 9 44 Initial Condition The problem will be analyzed a
2. and represent the concentrations of the two species to be calculated P i 1 2 j 1 2 3 are the three parameters index j for each of the two scalar equations index i For this sample problem Pj P 1 Pp 25 Px 1 P73 P23 0 The Prandtl number Pr is taken as 0 71 while the Rayliegh number is 10 The mathematical symbols in these equations take on their usual meaning Initial Condition The default initial conditions in INSTED is used for this problem That is u x y 0 v x y 0 hi x y 0 amp x y 0 0 Boundary Conditions Two dimensional flow of Boussinesq fluid of Prandtl number 0 71 in an upright square cavity is described in non dimensional terms by O lt x lt l O lt y lt 1 with y vertically upwards The problem assumes that both components of the velocity are zero on all boundaries and the boundaries at y 0 and y 1 are insulated OT 0 on and that T 1 at x 0 and T 0 at x 1 The boundary conditions on the scalars are the same as those for temperature Computational Grid An 8 x 8 square mesh of 9 node quadrilateral elements will be used The total number of 64elements is and the total number of nodes including those at the centroid of elements is 289 38 44 Project Files The files required to reproduce our results for this sample problem are devscala mes Input data for 8 x 8 mesh of model devscala cfd Input data for CFD solver L
3. 1 avee E p eua Jys Ot Oy Re Re Ra 0 where u v are the velocities in the coordinate directions and 77 is the non dimensional value of the absolute viscosity The Reynolds number Re is arbitrarily takes as 0 001 consistent with Stokes flow requirement 7 1 and Pr is arbitrarily set to 7 0 The mathematical symbols in these equations take on their usual meaning and are explained in greater detail in the User s Manual Initial Condition The default initial conditions in INSTED are used for this problem That is u x y 0 v x y 0 0 Boundary Conditions x 0 u 0 ty 0 Project Files The files required to reproduce our results for this sample problem are squeeze mes Input data for use in Mesh Generator to generate mesh squeeze cfd Input data for CFD solver Location of Project Files The project files above are located in the directory insted30 cfd samples Model Building and Mesh Generation The model for this sample problem will be composed of a square with a counter clockwise orientation The rectangle modeling tool in INSTED will be used to produce the square 1 Start INSTED CFD 2D Mesh Generator 2 Click the New Project button on the Main dialog box 3 Click the Limit button on the Controls dialog box The Limits dialog box appears 4 Type in 0 5 6 5 0 2 2 2 for the lower x higher x lower y and higher y screen limits in the Limits dialog box 5 C
4. 33 Click the Ok button on this dialog box to view nodes with Dirichlet temperature boundary conditions 34 Click the Refresh button on the Controls dialog box to return the screen to it original condition Turning on Node amp Element Numbering 35 Click the Display button on the Controls dialog box The Display dialog box appears 36 Click the Display Node Numbers radio button to turn on display of node numbers 37 Click the Display Element Numbers radio button to turn on display of node numbers 38 Click the OK button to dismiss the dialog box Note You should have the same result as if you loaded the file insted30 cfd samples slider mes You may also choose to save your current work Refer to the sections Loading a file and Saving a file in the first chapter of the Users Manual Obtaining a Solution to the Problem 39 Click the Solver button on the INSTED CFD 2D Mesh Generator Main dialog box 22 44 gt 40 41 gt 42 43 44 45 46 47 48 gt 49 The INSTED CFD 2D Solver program is launched The mesh generated from the Mesh Generation program is automatically loaded Click the Load Project button on the Main dialog box of the Solver program Type in the filename section of the operating system Open File dialog box that appears and press Enter A list of files in the current directory is displayed Locate the file slider cfd fr
5. 22 Click the Mesh button on the Main dialog box A mesh of the internal of our loop of lines is displayed on the Graphics dialog box 23 Click the Display button on the Controls dialog box 24 From the listbox select Dirichlet Temp 25 Click the Ok button on this dialog box to view nodes with Dirichlet temperature boundary conditions 26 Click the Refresh button on the Controls dialog box to return the screen to it original condition 16 44 Note You should have the same result as if you loaded the file insted30 cfd samples axiscond mes You may also choose to save your current work In this case refer to the sections Loading a file and Saving a file in the first chapter of the Users Manual Obtaining a Solution to the Problem 27 Click the Solver button on the INSTED CFD 2D Mesh Generator Main dialog box The INSTED CFD 2D Solver program is launched The mesh generated from the Mesh Generation program is automatically loaded 28 Click the Load Project button on the Main dialog box of the Solver program 29 Type in the filename section of the operating system Open File dialog box that appears and press Enter A list of files in the current directory is displayed 30 Locate the file axiscond cfd from the Samples directory 31 Click this file and press Enter 32 Click the Prob Description button on the Main dialog box and inspect the loaded parameters 33 Cl
6. Click the OK button on this dialog box to view nodes with Dirichlet temperature boundary conditions Click the Refresh button on the Controls dialog box to return the screen to it original condition Note You should have the same result as if you loaded the file insted30 cfd samples devahl1 mes You may also choose to save your current work Refer to the sections Loading a file and Saving a file in the first chapter of the Users Manual Obtaining a Solution to the Problem 39 gt 40 41 gt 42 43 44 45 46 47 Click the Solver button on the INSTED CFD 2D Mesh Generator Main dialog box The INSTED CED 2D Solver program is launched The mesh generated from the Mesh Generation program is automatically loaded Click the Load Project button on the Main dialog box of the Solver program Type in the filename section of the operating system Open File dialog box that appears and press Enter A list of files in the current directory is displayed Locate the file devahl1 cfd from the Samples directory Click this file and press Enter Click the Prob Description button on the Main dialog box and inspect the loaded parameters Click the OK button to dismiss the Prob Description dialog box Click the Material Properties button on the Main dialog box and inspect the loaded material properties Note particularly the heat flux parameters Click the OK button to dismiss the Mat
7. from the order in which you entered coordinates in Steps 6 through 14 that the arc represented by line 1 has a clockwise orientation relative to the loop Your dialog box should now be similar to the figure below Click the OK button to dismiss the Area Definition dialog box INSTED Mesh K Graphics New Project Load Project Save Project Mesh Control New Boundary Edit Boundary Define Area Edit Point Del Point Line Properties Enter Point Elements Lo Fa i x Controls Refresh __J Grd __J limit __H zoom Restore Display Translate Status Bar e Exit 5 44 Applying boundary conditions 28 Click the Line BC button on the Main dialog box Status bar displays message Pick Side 29 Click the Line 1 on the graphics screen or type 1 and Press Enter in the Input Box The Line BC dialog box appears with the heading Boundary Condition Side 1 confirm from the title of the dialog box that data is being received for Line 1 This will not be the case if you accidentally selected some other line 30 Click the arrow for temperature and select the Dirichlet condition from the list An input box appears beside the boundary condition listbox once Dirichlet condition is selected 31 Enter a value of 140 in the input box 32 Click the OK button to dismiss the dialog box 33 Repeat this procedure for Line 2 but only click the Nusselt No condition for this line lea
8. nodes with Dirichlet temperature boundary conditions 41 Click the Refresh button on the Controls dialog box to return the screen to it original condition Note You should have the same result as if you loaded the file devscala mes in the Samples directory of the insted30 cfd devscala mes You may also choose to save your current work Refer to the sections Loading a file and Saving a file in the first chapter of the Users Manual Obtaining a Solution to the Problem 42 Click the Solver button on the INSTED CFD 2D Mesh Generator Main dialog box The INSTED CFD 2D Solver program is launched The mesh generated from the Mesh Generation program is automatically loaded 43 Click the Load Project button on the Main dialog box of the Solver program 44 Type in the filename section of the operating system Open File dialog box that appears and press Enter A list of files in the current directory is displayed 45 Locate the file devscala cfd from the Samples directory 46 Click this file and press Enter 47 Click the Prob Description button on the Main dialog box and inspect the loaded parameters 48 Click the OK button to dismiss the Prob Description dialog box 49 Click the Material Properties button on the Main dialog box and inspect the loaded material properties Note particularly the heat flux parameters 50 Click the OK button to dismiss the Material Properties dialog box
9. on the Main dialog box and inspect the loaded parameters 45 Click the OK button to dismiss the Prob Description dialog box 46 Click the Material Properties button on the Main dialog box and inspect the loaded material properties Note particularly the heat flux parameters 47 Click the OK button to dismiss the Material Properties dialog box 48 Click the Solve button on the Main dialog box Program begins to generate a solution to the problem The graphic screen is converted to one that displays the status of the solution process 49 Wait for the solution to complete 6 44 Analyzing the Result Refer to the User s Manual for general details about INSTED CFD 2D Post Processing 50 gt Click the Post Processor button on the INSTED CFD 2D Solver Main dialog box The INSTED CFD 2D Post processor program is launched The results from the INSTED CFD 2D Solver are automatically loaded Click the Display button on the Controls dialog box The Display dialog box appears Select the most recent print step for viewing from the Time Step listbox Click the Ok button to dismiss the Display dialog box View the Contour Plot of Temperature Locate and open the file lola out in the working directory cfd for the current example Inspect and compare the values at selected nodal points Table 1 1 Heat Conduction Between Two Cylinders with Film Coefficient Boundary Conditions
10. pressure does not vary in y can be shown as p 6uU h h h h h h h pi MEET z 2u dxh h a ue U amar N DA h h h x h x CED Type This problem will be solved as CFD Type 3 that is in the dimensional form Physical and Computational Domain The physical domain is shown in the figure below In the figure h 2h 8 x 10 L 0 36 u 8x 10 Uo 30 p Caution You should be aware of the large aspect ratio of the physical system under consideration This quantity is equal to L h 900 Under this condition the truly automatic mesh generation method in INSTED defaults to the standard structured mesh generation approach 19 44 Slide block u v 0 Guide Surface u Ug v 0 Figure 4 1 Physical domain for the bearing problem The computational domain will have the same orientation and dimensions as the physical domain shown in this figure Computational Grid This problem will be analyzed with an unstructured mesh consisting of 60 9 node elements and 347 nodal points including those at the centroids of the elements Governing Equations The governing equations for CFD Type 3 Engineering CFD are used on the assumption that the data is given in dimensional quantities Note that no units have been specified Isothermal flow conditions are assumed The governing equations are Veu 0 Ope ie aay ot Py X Po 1 1 he a ds Po OY Po Initial Condition Th
11. problem go through the exercise again but this time change the input data in the project file to study the effect on the solution For example during mesh generation you could change the number of elements in each of the I and J directions During analysis you could locate the thermophysical properties dimensionless parameters solution parameters etc and change them to study the effect on the solutions LEGEND 9 172E 01 8 345E 01 7 517E 01 6 690E 01 5 862E 01 DT eK TH 3 379E 01 2 552E 01 1 724E 01 8 966E 02 6 899E 03 gt 0 U M Figure 6 3 Contour Plot of Temperature for the Natural Convection Problem Reference Davis G de Vahl 1983 Natural Convection in a Square Cavity A comparison Exercise Int J Numerical Methods in Fluids Volume 3 227 248 Davis G de Vahl 1983 Natural Convection in a Square Cavity A Benchmark Numerical Solution Int J Numerical Methods in Fluids Volume 3 249 264 36 44 TEST PROBLEM 7 NATURAL CONVECTION TRANSPORT OF TEMPERATURE AND TWO NON REACTING SPECIES Problem Statement The problem being considered is that of the two dimensional flow of a Boussinesq fluid of Prandtl number 0 71 in an upright square cavity of side L L 1 in non dimensional variables Both velocity components are zero on all the boundaries The horizontal walls are insulated and the left and right vertical sides are at temperatures T amd T respectively which are 1 a
12. the square 6 Click the Rectangle tool button among the Modeling Tools that reside on the Main dialog box Status bar displays the message Pick 1 Corner Point 7 Type in 0 0 in the Input box and press Enter Status bar displays the message Pick 2 Corner Point 8 Type in 1 1 in the Input box and press Enter Defining number of elements per line 9 Click the Line Properties button on the Main dialog box The Line Properties dialog box appears 10 Enter the values of 8 8 8 and 8 for the number of elements for lines 1 2 3 and 4 respectively Press Enter after typing each value to move to the next line I the listbox 11 Click the OK button to dismiss this dialog box Defining the area to mesh 12 Click the Define Area button on the Main dialog box The Area Definition dialog box appears 13 Click the Add button on this dialog box An area listed as l is added in the Areas listbox 14 Click the first line of the Boundaries listbox 32 44 15 Type 1 and press Enter This is meant to include boundary made of Rectangle with lines 1 2 3 and 4 in this area 16 Click the OK button to dismiss the Area Definition dialog box Applying boundary conditions 17 Click the Line BC button on the Main dialog box Status bar displays message Pick Side 18 Click the Line 1 on the graphics screen or type 1 and Press Enter in the Input Box The Line BC dialog
13. to the exact solution LEGEND 4 244E 00 3 905E 00 3 567E 00 3 229E 00 2391E 00 DEEE ETATS 2 553E 00 LEYEN EANAN LT 5 EEA NON NN Sa oe WA OSS SSE SSS 1 539E 00 he date Ra 1 201E 00 g ts Meet 8 628E 01 dd 5 248E 01 1 867E 01 Figure 5 2 Vector Plot of Velocity for Fluid Squeezed Between Parallel Plates Reference Reddy J N amp Gartling D K 1994 The Finite Element Method in Heat Transfer and Fluid Dynamics CRC Press Boca Raton Florida USA 69 70 Nadia A 1963 Theory of Flow and Fracture of Solids Volume IL McGraw Hill New York 29 44 TEST PROBLEM 6 NATURAL CONVECTION OF AIR IN A SQUARE CAVITY A BENCHMARK NUMERICAL SOLUTION Problem Statement The problem being considered is that of the two dimensional flow of a Boussinesq fluid of Prandtl number 0 71 in an upright square cavity of side L L 1 in non dimensional variables Both velocity components are zero on all the boundaries The horizontal walls are insulated and the left and right vertical sides are at temperatures T and Te respectively which are 1 and 0 in non dimensional units The solutions to this problem namely the velocities the temperature and the rate of heat transfer are to be obtained for Rayliegh numbers Ra 104 CFD Type This problem will be solved as CFD Type 1 that is using non dimensional units for free convection Physical and Computational Domain The physical and computational domain are show
14. 96 lt 1 0 002 193 06 192 68 lt 1 0 003 189 78 189 44 lt 1 0 004 185 07 184 73 lt 1 0 005 178 74 178 40 lt 1 0 006 170 50 170 12 lt 1 0 007 159 91 159 50 lt 1 0 008 146 20 145 62 lt 1 0 009 127 81 127 23 lt 1 0 010 100 0 100 0 lt 1 r z 0 0 Reddy INSTED Difference 0 000 504 64 501 30 lt 1 0 001 499 82 497 70 lt 1 0 002 488 52 486 81 lt 1 0 003 469 93 468 50 lt 1 0 004 443 70 442 49 lt 1 0 005 409 43 408 43 lt 1 0 006 366 68 365 88 lt 1 0 007 314 92 314 33 lt 1 0 008 253 61 253 22 lt 1 0 009 182 16 181 97 lt 1 0 010 100 0 100 0 lt 1 Reference Reddy J N amp Gartling D K 1994 The Finite Element Method in Heat Transfer and Fluid Dynamics CRC Press Boca Raton Florida USA 69 70 18 44 TEST PROBLEM 4 PRESSURE DISTRIBUTION IN A VISCOUS FLOW OF A LUBRICANT BEARING Problem Statement Calculate the pressure distribution in a lubricant flowing inside a slider bearing Figure 4 1 The slider bearing consists of a short sliding pad moving at a velocity u U 30 relative to a stationary pad inclined at a small angle with respect to the stationary pad as the small gap between the two pads is filled with a lubricant Since the ends of the bearing are generally open the pressure there is atmospheric which will be taken as zero The pressure distribution inside the bearing is in general a function of x and y and is set up in the gap An exact solution assuming that the
15. Analyzing the Result Refer to the User s Manual for general details about INSTED CFD 2D Post Processing 51 Click the Post Processor button on the INSTED CFD 2D Solver Main dialog box The INSTED CFD 2D Postprocessor program is launched The results from the 52 Click the Display button on the Controls dialog box The Display dialog box appears 53 Select the most recent time step for viewing from the Time Step listbox 54 Click the Ok button to dismiss the Display dialog box 55 View the Vector plot for velocity 56 View the Contour plots for velocities temperature stream function scalars 1 amp 2 and pressure 57 Locate and open the file lola out in the working directory cfd for the current example 58 Inspect and compare the values at selected nodal points 41 44 Results The contour maps for temperature and the three scalars are shown in Figures 7 1 through 7 3 Note the similarity in the results for temperature and scalar 2 Since the flow is purely thermally driven some differences no matter how small should exist between scalar 2 and temperature because of the closer tie between temperature and the velocity Finally note that because of the coarse grid used unphysical solutions were observed While scalar 1 have a high diffusivity to dissipate unphysical results scalar 2 and the temperature do show the unphysical results because of low diffusivities What s Next After reprod
16. Click the OK button to dismiss the Limits dialog box To draw the two arc segments 6 Click the Arc icon from the Modeling Tools that reside on the Main dialog box Status bar displays the message Pick Arc Center 7 Type in 0 1 in the Input Box and press Enter Status bar displays the message Pick Arc Start Point 8 Type in 0 0 in the Input Box and press Enter Status bar displays the message Pick Arc End Point 9 Type in 0 2 in the Input box and press Enter 10 Repeat steps 5 to 8 using 0 0 for the second arc center and 0 4 0 4 for the start and end points respectively To draw the two connecting lines 11 Click the Line icon from the Modeling Tools that reside on the Main dialog box Status bar displays the message Pick 1 Point 12 Type in 0 4 in the Input Box and press Enter Status bar displays the message Pick 2 Point 13 Type in 0 2 in the Input Box and press Enter 14 Repeat Steps 10 to 12 using 0 0 and 0 4 for the first and second points of the second line INSTED Mesh Ki Elements Nodes 113 390 Controls 4 Pick a task 4 144 Notice that four lines have now been created up to this point Line 1 is the smaller arc while Line 2 is the bigger arc Line 3 is the straight line closer to the top of the screen while Line 4 is the second straight line The lines are labelled in the display on the Graphics dialog box De
17. INSTED CFD Test Problems TTC Technologies Inc Centereach NY 11720 USA 1993 2013 TTC Technologies Contents Test Problem 1 Heat Conduction with Film Coefficient Boundary Conditions Test Problem 2 Heat Conduction with Volumetric Heat Source Test Problem 3 Axisymmetric Conduction in a Cylinder Test Problem 4 Pressure Distribution in Viscous Flow of a Lubricant Bearing Test Problem 5 Fluid Squeezed Between Parallel Plates Test Problem 6 Natural Convection of Air in a Square Cavity A Bench Mark Numerical Solution Test Problem 7 Natural Convection Transport of Temperature and Two Non Reacting Species 13 18 24 29 36 1 44 TEST PROBLEM 1 HEAT CONDUCTION WITH FILM COEFFICIENT BOUNDARY CONDITIONS Problem Statement Analyze the heat conduction between concentric cylinders as shown in Figure 1 1 The wall of the inner cylinder is kept fixed at 140 C while that of the outer cylinder is exposed to an ambient at T 20 C and the heat transfer coefficient is h 1 5 W cm C The thermal conductivity k of the material should be taken as 2 W cm C in all directions Governing Equations This problem is governed by the steady state heat conduction equation KV T Q 0 where k is the thermal conductivity T is temperature and Q is the volumetric heat generation rate Q is assumed to be zero for this problem CFD Type This is a heat conduction problem Therefore the values of the u and v v
18. WEEN PARALLEL PLATES Problem Statement The problem being considered is the Stokes flow of a viscous incompressible material squeezed between two long parallel plates A plane flow in the plane formed by the width of and the distance between the plates is considered Although this is a moving boundary problem we wish to determine the velocity and pressure fields for a fixed distance between the plates assuming that a state of plane flow exists Results are compared with Penalty and mixed formulations Reddy and Gartling 1994 as well as with series solutions by Nadai 1963 CFD Type This problem will be solved as a CFD Type 2 posing it in the non dimensional units We will also take advantage of symmetry in the x and y directions Physical and Computational Domain The physical and computational domain are shown below y 0 2 u 0 v l 6 2 t 0 t 0 u 0 t 0 i 6 0 0 0 v 0 f 0 a b Figure 5 1 Physical a and Computational b model for the test problem on viscous flow between parallel plates Governing Equations The governing equations are the same as those presented in the main CFD manual for CFD Type 2 Forced Mixed Convection except that the present case is isothermal and the Reynolds number is very small This problem will be solved in an inertial frame since there is no rotation of the system The resulting equations are Veu 0 Op LR Ok Ot Ox 1 A Ven Vu Vu Re 25 44
19. are P h 1 5 W cm C P 1 P3 20 C P 1 Computational Grid This problem will be analyzed with an unstructured mesh consisting of 113 9 node elements and 503 nodal points including those at the centroids of the elements Project Files The files required to reproduce the results reported here for this sample problem are Seger 1 mes Input data for use in Mesh Generator Seger cfd Input data for CFD solver Htflxmat dat Film coefficient boundary condition data Location of Project Files The project files above are located in the directory insted30 cfd samples 3 44 Model Building and Mesh Generation Refer to Section 2 3 of the User s Manual for description of the INSTED CED 2D Mesh Generation procedure The status bar Input Box modeling tools Main dialog box etc are terms that are described in the manuals The boundary of the model for this sample problem will be composed of two arcs and two lines These lines must form a counterclockwise loop in order to obtain the mesh of the area enclosed by the loop The steps for creating the mesh for the model are as follows 1 Start INSTED CFD 2D Mesh Generator 2 Click the New Project button on the Main dialog box 3 Click the Limit button on the Controls dialog box The Limits dialog box appears 4 Type in 6 5 9 0 5 0 5 0 for the lower x higher x lower y and higher y screen limits in the Limits dialog box 5
20. at displays the status of the solution process Wait for the solution to complete Analyzing the Result Refer to the User s Manual for general details about INSTED CFD 2D Post Processing 40 41 gt 42 43 44 45 46 Click the Post Processor button on the INSTED CFD 2D Solver Main dialog box The INSTED CFD 2D Postprocessor program is launched The results from the Click the Display button on the Controls dialog box The Display dialog box appears Select the most recent time step for viewing from the Time Step listbox Click the Ok button to dismiss the Display dialog box View the Vector Plot for velocity Locate and open the file lola out in the working directory cfd for the current example Inspect and compare the values at selected nodal points 28 44 Table 6 1 Comparison of Results The velocities u x at y 0 obtained from INSTED are compared in the table below with those from the references x coord Series Penalty Mixed INSTED Difference Solution 9 node Model 12x4 9 node Nadai Reddy Reddy Re 0 001 1 0 7500 7505 7497 7500 lt 1 2 0 1 500 1 499 1 503 1 502 lt 1 3 0 2 250 2 256 2 256 2 256 lt 1 4 0 3 000 3 024 3 020 3 026 lt 1 4 5 3 375 3 431 3 429 3 422 lt 1 5 0 3 750 3 803 3 816 3 811 lt 2 5 5 4 125 4 108 4 120 4 135 lt 1 6 0 4 500 4 194 4236 4 243 lt 6 Relation
21. box appears with the heading Boundary Condition Side 1 confirm from the title of the dialog box that data is being received for Line 1 This will not be the case if you accidentally selected some other line 19 Click the drop down list box for u velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 20 Click the drop down list box for v velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 21 Click the drop down list box for stream function and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 22 Click the OK button to dismiss the dialog box 23 Repeat the procedure 17 21 for Line 3 24 Click the Line BC button on the Main dialog box Status bar displays message Pick Side 25 Click the Line 4 on the graphics screen or type 4 and Press Enter in the Input Box The Line BC dialog box appears with the heading Boundary Condition Side 4 confirm from the title of the dialog box that data is being received for Line 4 This will not be the case if you accidentally selected some other line 26 Click the drop down list box for u velocity and select a Dirichlet boundar
22. ctory is displayed Locate the file reddy cfd from the Samples directory Click this file and press Enter Click the Prob Description button on the Main dialog box and inspect the loaded parameters Click the OK button to dismiss the Prob Description dialog box Click the Material Properties button on the Main dialog box and inspect the loaded material properties Note particularly the heat flux parameters Click the OK button to dismiss the Material Properties dialog box Click the Solve button on the Main dialog box Program begins to generate a solution to the problem The graphic screen is converted to one that displays the status of the solution process Wait for the solution to complete Analyzing the Result Refer to the User s Manual for general details about INSTED CFD 2D Post Processing 39 40 gt 41 42 43 44 45 Click the Post Processor button on the Main dialog box The INSTED Postprocessor program is launched The results from the Click the Display button on the Controls dialog box The Display dialog box appears Select the most recent time step for viewing from the Time Step listbox Click the Ok button to dismiss the Display dialog box View the Contour Plot of Temperature Locate and open the file lola out in the working directory cfd for the current example Inspect and compare the values at selected nodal points 12 44 Table 1 1 Comparison of Res
23. e default initial conditions in INSTED as described in Sample Problem 1 is used for this problem That is u x y 0 v x y 0 0 Boundary Conditions The appropriate boundary conditions for this sample problem is as follows Left x 0 4 0 Right x 36 t t 0 20 44 Bottom y 0 u 30 v 0 Top u 0 v 0 Project Files The files required to reproduce our results for this sample problem are slider1 mes Input data for use in Mesh Generator slider cfd Input data for CFD solver Location of Project Files The project files above are located in the directory insted30 cfd samples Model Building and Mesh Generation The CFD model for this sample problem will be generated using a structured mesh generation procedure consisting of eight sides The New Block modeling tool in INSTED will give us a structured block Note that the points of the block must be entered also in a counter clockwise direction This is illustrated in the instructions below Start INSTED CFD 2D Mesh Generator Click the New Project button on the Main dialog box Click the Limit button on the Controls dialog box The Limits dialog box appears Type in 0 02 0 4 0 0002 0 001 for the lower x higher x lower y and higher y screen limits in the Limits dialog box 5 Click the OK button to dismiss this dialog box To draw the object Click the New Boundary button on the Main dialog box Status bar displays t
24. elocities should be kept fixed during the solution stage There are also no scalars to solve for this problem This problem will be solved in dimensional form That is Type 3 solution method will be employed in the Solver refer to the Users manual We shall also take advantage of the spatial symmetry of the problem Consequently our computational model will be as shown below y T 20 C h 1 5 Wilem2 C 0 T 20 C ga T o 1 5 W cm C n x oT on a Physical Domain b Computational Model Figure 1 1 Physical and Computational Domain for Sample Problem 1 2 144 Initial Conditions This problem will be analyzed as a transient one using the default initial conditions in INSTED The default initial conditions will be zero or the minimum Dirichlet boundary conditions If there are no Dirichlet conditions for a variable INSTED sets the initial condition to zero for that variable at every nodal point Boundary Conditions Zero temperature gradient or oT o on is specified on the symmetry boundary at x 0 Temperature is specified as 140 C on the surface of the inner cylinder A film coefficient boundary condition is used on the surface of the outer cylinder This boundary condition can be written as sk Ceng on However INSTED expects the value of kOT on to be specified as opposed to kOT on Thus Cpa ae pit on Thus the 4 heat flux parameters as discussed in Chapter 3 of the User Manual
25. ements for lines 1 2 3 and 4 respectively Press Enter after typing each value to move to the next line I the listbox 11 Click the OK button to dismiss this dialog box Defining the area to mesh 12 Click the Define Area button on the Main dialog box The Area Definition dialog box appears 13 Click the Add button on this dialog box An area listed as 1 is added in the Areas listbox 14 Click the first line of the Boundaries listbox 15 Type 1 and press Enter This is meant to include boundary made of Rectangle with lines 1 2 3 and 4 in this area 16 Click the OK button to dismiss the Area Definition dialog box Applying boundary conditions 17 Click the Line BC button on the Main dialog box Status bar displays message Pick Side 18 Click the Line 2 on the graphics screen or type 2 and Press Enter in the Input Box The Line BC dialog box appears with the heading Boundary Condition Side2 confirm from the title of the dialog box that data is being received for Line 2 This will not be the case if you accidentally selected some other line 19 Click the drop down list box for temperature and select a Dirichlet boundary condition from the list and enter a value of 100 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 20 Click the OK button to dismiss the dialog box 21 Repeat the procedure 17 20 for Line 3 Mesh and Confirm Mesh Results
26. erature and Species By Natural Convection in a Cavity for Ra 10 Reference Davis G de Vahl 1983 Natural Convection in a Square Cavity A comparison Exercise Int J Numerical Methods in Fluids Volume 3 227 248 Davis G de Vahl 1983 Natural Convection in a Square Cavity A Benchmark Numerical Solution Int J Numerical Methods in Fluids Volume 3 249 264 44 44
27. erial Properties dialog box Selecting Sample Points for History Data 48 49 50 51 gt 52 Click the Select Points button on the Main dialog box Select about eight nodal points by clicking the points on the graphics display Click the Stop button on the Main dialog box to stop selecting points Click the Solve button on the Main dialog box Program begins to generate a solution to the problem The graphic screen is converted to one that displays the status of the solution process Wait for the solution to complete Analyzing the Result Refer to the User s Manual for general details about INSTED CFD 2D Post Processing Click the Post Processor button on the INSTED CFD 2D Solver Main dialog box The INSTED CFD 2D Postprocessor program is launched The results from the Click the Display button on the Controls dialog box The Display dialog box appears Select the most recent time step for viewing from the Time Step listbox Click the Ok button to dismiss the Display dialog box View the Vector plot for velocity View the Contour plots for velocities temperature stream function and pressure View the time history data for the selected sample points Locate and open the file lola out in the working directory cfd for the current example Inspect and compare the values at selected nodal points 34 44 Generating the Boundary Layer Mesh 62 Click the Line Pro
28. es 1 2 3 and 4 in this area 23 Click the OK button to dismiss the Area Definition dialog box Applying boundary conditions 24 Click the Line BC button on the Main dialog box Status bar displays message Pick Side 25 Click the Line 1 on the graphics screen or type 1 and Press Enter in the Input Box The Line BC dialog box appears with the heading Boundary Condition Side1 confirm from the title of the dialog box that data is being received for Line 1 This will not be the case if you accidentally selected some other line 26 Click the drop down list box for u velocity and select a Dirichlet boundary condition from the list and enter a value of 30 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 27 Click the drop down list box for v velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 28 Click the OK button to dismiss the dialog box 29 Repeat the procedure 20 24 for Line 3 setting Dirichlet conditions for u velocity and v velocity with values 0 0 and 0 0 respectively Mesh and Confirm Mesh Results 30 Click the Mesh button on the Main dialog box A mesh of the internal of our loop of lines is displayed on the Graphics dialog box 31 Click the Display button on the Controls dialog box 32 From the listbox select Dirichlet Temp
29. fine Area button on the Main dialog box The Area Definition dialog box appears 13 Click the Add button on this dialog box An area listed as 1 is added in the Areas listbox 14 Click the first line of the Boundaries listbox 15 Type 1 and press Enter This is meant to include boundary made of Rectangle with lines 1 2 3 and 4 in this area 16 Click the OK button to dismiss the Area Definition dialog box Entering the Number of Scalars 17 Click on the Scalars button on the Main dialog box The status bar displays the message Enter the number of scalars 18 Enter a value of 2 in the Input box and press Enter 39 44 Applying boundary conditions 19 20 gt 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Click the Line BC button on the Main dialog box Status bar displays message Pick Side Click the Line 1 on the graphics screen or type 1 and Press Enter in the Input Box The Line BC dialog box appears with the heading Boundary Condition Side 1 confirm from the title of the dialog box that data is being received for Line 1 This will not be the case if you accidentally selected some other line Click the drop down list box for u velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selec
30. fining number of elements per line 15 gt 16 17 Click the Line Properties button on the Main dialog box The Line Properties dialog box appears Enter the values of 10 20 8 and 12 for the number of elements for lines 1 2 3 and 4 respectively as shown in the figure above Press Enter after typing each value to move to the next line Click the OK button to dismiss this dialog box Defining the area to mesh 18 gt 19 20 Click the Define Area button on the Main dialog box 22 23 24 25 26 27 Click the Edit Boundary button on the Main dialog box The Edit Boundary dialog box appears The dialog box indicates that four boundaries have been created as shown in the Bdry listbox Scroll through the boundaries created to find out the constituent lines by clicking the Next button Exit the dialog box by clicking the OK button The Area Definition dialog box appears This is shown in the figure below except that the first boundary is not yet inverted Click the Add button on this dialog box An area listed as 1 is added in the Area listbox Click the first line of the Boundaries listbox Type 1 and press Enter This is meant to include boundary made of Arc line 1 in this area Repeat Step 20 to include boundaries 2 3 and 4 in the definition of the current area Click the first line of the Invert listbox to reverse the direction of Arc Line 1 You may have realized
31. he message Pick Point 1 7 Type in 0 0 in the Input box and press Enter gt 8 AL enn an Status bar displays the message Pick Point 2 Type in 0 18 0 0 in the Input box and press Enter 9 Type in 0 36 0 0 in the Input box and press Enter 10 Type in 0 36 2 0E 04 in the Input box and press Enter 11 Type in 0 36 4 0E 04 in the Input box and press Enter 12 Type in 0 18 4 0E 04 in the Input box and press Enter 13 Type in 0 0 8 0E 04 in the Input box and press Enter 14 Type in 0 0 4 0E 04 in the Input box and press Enter 15 Type in 0 0 0 0 in the Input box and press Enter The slider shape as illustrated in the Figure 4 1 is obtained Defining number of elements per line 16 Click the Line Properties button on the Main dialog box The Line Properties dialog box appears 17 Enter the values of 9 3 9 and 3 for the number of elements for lines 1 2 3 and 4 respectively Press Enter after typing each value to move to the next line I the listbox 18 Click the OK button to dismiss this dialog box 21 44 Defining the area to mesh 19 Click the Define Area button on the Main dialog box The Area Definition dialog box appears 20 Click the Add button on this dialog box An area listed as 1 is added in the Areas listbox 21 Click the first line of the Boundaries listbox 22 Type 1 and press Enter This is meant to include boundary made of Rectangle with lin
32. ick the OK button to dismiss the Prob Description dialog box 34 Click the Material Properties button on the Main dialog box and inspect the loaded material properties Note particularly the heat flux parameters 35 Click the OK button to dismiss the Material Properties dialog box 36 Click the Solve button on the Main dialog box Program begins to generate a solution to the problem The graphic screen is converted to one that displays the status of the solution process 37 Wait for the solution to complete Analyzing the Result Refer to the User s Manual for general details about INSTED CFD 2D Post Processing 38 Click the Post Processor button on the INSTED CFD 2D Solver Main dialog box The INSTED CFD 2D Post processor program is launched The results from the 39 Click the Display button on the Controls dialog box The Display dialog box appears 40 Select the most recent time step for viewing from the Time Step listbox 41 Click the Ok button to dismiss the Display dialog box 42 View the Contour Plot of Temperature 43 Locate and open the file lola out in the working directory cfd for the current example 44 Inspect and compare the values at selected nodal points 17 44 Table 3 1 Comparison of Results r z 0 009 Reddy INSTED Difference 0 000 195 86 195 21 lt 1 0 001 195 03 194
33. l Building and Mesh Generation Refer to INSTED CFD 2D manual for the description of the INSTED Mesh Generation GUI The status bar Input Box modeling tools Main dialog box are discussed in the manuals The INSTED model for this sample problem is a square in which the four enclosing lines are oriented in a counter clockwise sense The rectangle modeling tool in INSTED will be used to produce a square with counter clockwise orientation The steps for generating the mesh for the sample problem are as follows 1 Start INSTED CFD 2D Mesh Generator Skip this step if the program is already open However you should close other INSTED CFD 2D programs that may have been opened through the Mesh Generator 10 44 2 Click the New Project button on the Main dialog box 3 Click the Limit button on the Controls dialog box The Limits dialog box appears 4 Type in 0 2 1 2 0 2 1 2 for the lower x higher x lower y and higher y screen limits in the Limits dialog box 5 Click the OK button on the Limits dialog box To draw the square 6 Click the Rectangle tool button among the Modeling Tools that reside on the Main dialog box Status bar displays the message Pick 1 Corner Point 7 Type in 0 0 in the Input box and press Enter Status bar displays the message Pick 2 Corner Point 8 Type in 1 1 in the Input box and press Enter Defining number of elements per line 9 Click the Line Propertie
34. lick the OK button to dismiss this dialog box To draw the square 6 Click the Rectangle tool button among the Modeling Tools that reside on the Main dialog box 26 44 Status bar displays the message Pick 1 Corner Point 7 Type in 0 0 in the Input box and press Enter Status bar displays the message Pick 2 Corner Point 8 Type in 6 2 in the Input box and press Enter Defining number of elements per line 9 Click the Line Properties button on the Main dialog box The Line Properties dialog box appears 10 Enter the values of 12 4 12 and 4 for the number of elements for lines 1 2 3 and 4 respectively Press Enter after typing each value to move to the next line I the listbox 11 Click the OK button to dismiss this dialog box Defining the area to mesh 12 Click the Define Area button on the Main dialog box The Area Definition dialog box appears 13 Click the Add button on this dialog box An area listed as l is added in the Areas listbox 14 Click the first line of the Boundaries listbox 15 Type 1 and press Enter This is meant to include boundary 1 made of Rectangle with lines 1 2 3 and 4 in this area 16 Click the OK button to dismiss the Area Definition dialog box Applying boundary conditions 17 Click the Line BC button on the Main dialog box Status bar displays message Pick Side 18 Click the Line 3 on the graphics screen or type 3 and Pres
35. most recent time step for viewing from the Time Step listbox Click the Ok button to dismiss the Display dialog box View the Contour Plot of Pressure Locate and open the file lola out in the working directory cfd for the current example Inspect and compare the values at selected nodal points Comparison of INSTED Results with Analytical Solution x coordinate Analytic Solution INSTED Result Difference 0 0063 472 46 468 52 lt 1 0 0132 989 65 989 56 lt 1 0 0207 1551 14 1551 10 lt 1 0 0375 2804 01 2805 70 lt 1 0 0567 4221 43 4224 40 lt 1 0 0783 5785 07 5788 90 lt 1 23 44 0 1023 7462 06 7466 00 lt 1 0 1575 10886 40 10885 00 lt 1 0 1887 12367 20 12357 00 lt 1 0 2479 13465 98 13462 00 lt 1 0 2775 12627 14 12627 00 lt 1 0 3039 10634 62 10631 00 lt 1 0 3471 3477 632 3465 40 lt 1 0 3559 1188 77 1173 00 lt 1 LEGEND rc 1 245E 04 1 132E 04 1 018E 04 9 050E 03 H 7 917E 03 c X 4518E 03 3 385E 03 2 252E 03 1 120E 03 1 340E 01 gt Wu O0 mM Reference Figure 4 2 Computational Mesh of the Slider Problem Figure 4 3 Plot of Pressure Contour for the Slider Problem Reddy J N amp Gartling D K 1994 The Finite Element Method in Heat Transfer and Fluid Dynamics CRC Press Boca Raton Florida USA 69 70 24 44 TEST PROBLEM 5 FLUID SQUEEZED BET
36. n below w v 0 aT on 0 G 1 00 ee OT n 0 Figure 6 1 Physical Domain for Natural Convection Problem 30 44 Governing Equations The governing equations are the same as those presented in the main CFD manual for CFD Type 1 Free Convection However this problem will be solved in an inertial frame the rotational terms in the equations have to be set to zero That is The volumetric heat source H should also be set to zero and you should take the y coordinate as pointing in the negative direction of the normal gravity vector The governing equation can be written as Veu O Op Due vu PrVen Vu Vu t X Duevr L 4 PrV Vu Vu Ra PrT t y Due VT VekVT t where u v are the velocities in the x and y coordinate directions and n and k are the non dimensional value of the absolute viscosity and thermal conductivity respectively The Prandtl number Pr is taken as 0 71 while a Rayliegh number of 10 is used The mathematical symbols in these equations take on their usual meaning and are explained in greater detail in the Users Manual Initial Condition The default initial conditions in INSTED is used for this problem That is u x y 0 v x y 0 0 Boundary Conditions Two dimensional flow of a Boussinesq fluid of Prandtl number 1 in an upright square cavity is described in non dimensional terms by O lt x lt l O lt y lt 1 with y vertically upwards The problem assume
37. n is selected 20 Enter a value of 0 in the input box 21 Click the OK button to dismiss the dialog box 22 Repeat this procedure for Line 2 Mesh and Confirm Mesh Results 23 Click the Mesh button on the Main dialog box A mesh of the internal of our loop of lines is displayed on the Graphics dialog box 24 Click the Display button on the Controls dialog box 25 From the listbox select Dirichlet Temp 26 Click the Ok button on this dialog box to view nodes with Dirichlet temperature boundary conditions 11 44 27 Click the Refresh button twice on the Controls dialog box to return the screen to it original condition Note You should have the same result as if you loaded the file insted30 cfd samples reddy mes You may also choose to save your current work In this case refer to the sections Loading a file and Saving a file in the first chapter of the Users Manual Obtaining a Solution to the Problem 28 gt 29 30 31 32 33 34 35 36 37 gt 38 Click the Solver button on the Main dialog box The INSTED Solver program is launched The mesh generated from the Mesh Generation program is automatically loaded Click the Load Project button on the Main dialog box of the Solver program Type in the filename section of the operating system Open File dialog box that appears and press Enter A list of files in the current dire
38. nd 0 in non dimensional units The natural convection flow is used to transport two chemical species of different diffusivities within the box It is assumed that bouyancy only results from temperature differences The solution at Ra 10 is desired CFD Type This problem will be solved as a CFD Type 1 posing the solution in the non dimensional units Physical and Computational Domain The physical domain is as shown in Figure 6 1 except that we now have to include passive scalars which we assume have the same boundary conditions as temperature Governing Equations The governing equations are the same as those presented in the main CFD manual for CFD Type 1 Free Convection However this problem will be solved in an inertial frame the rotational terms in the equations have to be set to zero That is The volumetric heat source H should also be set to zero and you should take the y coordinate as pointing in the negative direction of the normal gravity vector The governing equation can be written as Veu 0 Ou Op ue Vu PrV e7 Vu Vu Ot Ox Due Vo 2s Pr eu VW Ra PrT t y Due VT VekVT t 37 44 O n sueva Ve P V P O Pal rusva Ve PaV4 Pa where u v are the velocities in the coordinate directions and 7 and k are the non dimensional value of the absolute viscosity and thermal conductivity respectively The parameters 7 and k take on the values of 1 for the test problem
39. ocation of Project Files The project files above are located in the directory insted30 cfd samples Model Building and Mesh Generation The mesh boundary for this problem is a square with counter clockwise orientation The rectangle modeling tool in INSTED will be used to produce the square Details of mesh generation follow 1 Start INSTED CFD 2D Mesh Generator 2 Click the New Project button on the Main dialog box 3 Click the Limit button on the Controls dialog box The Limits dialog box appears 4 Type in 0 2 1 2 0 2 1 2 for the lower x higher x lower y and higher y screen limits in the Limits dialog box 5 Click the OK button to dismiss this dialog box To draw the square 6 Click the Rectangle tool button among the Modeling Tools that reside on the Main dialog box Status bar displays the message Pick 1 Corner Point 7 Type in 0 0 in the Input box and press Enter Status bar displays the message Pick 2 Corner Point 8 Type in 1 1 in the Input box and press Enter Defining number of elements per line 9 Click the Line Properties button on the Main dialog box The Line Properties dialog box appears 10 Enter the values of 8 8 8 and 8 for the number of elements for lines 1 2 3 and 4 respectively Press Enter after typing each value to move to the next line I the listbox 11 Click the OK button to dismiss this dialog box Defining the area to mesh 12 Click the De
40. om the Samples directory Click this file and press Enter Click the Prob Description button on the Main dialog box and inspect the loaded parameters Click the OK button to dismiss the Prob Description dialog box Click the Material Properties button on the Main dialog box and inspect the loaded material properties Note particularly the heat flux parameters Click the OK button to dismiss the Material Properties dialog box Click the Solve button on the Main dialog box Program begins to generate a solution to the problem The graphic screen is converted to one that displays the status of the solution process Wait for the solution to complete Analyzing the Result Refer to the User s Manual for general details about INSTED CFD 2D Post Processing 50 51 gt 52 53 54 55 gt 56 57 58 59 60 Click the Post Processor button on the INSTED CFD 2D Solver Main dialog box The INSTED CFD 2D Post processor program is launched The results from the Solver is automatically loaded Note that the model does not appear clearly initially due to its high aspect ratio Click the Axis button on the Controls dialog box The Axis dialog box appears Enter a value of 1 2 for the x scale Enter a value of 140 for the y scale Click the Ok button to dismiss the dialog box Click the Display button on the Controls dialog box The Display dialog box appears Select the
41. perties button on the Main dialog box The Line Properties dialog box appears 63 Click the B L listbox for all four lines that form the boundary of the object The listbox should now have the text YES on every line 64 Click the OK button to dismiss this dialog box Specifying Boundary Layer Parameters 65 Click the Mesh Control button on the Main dialog box The Mesh Control dialog box appears 66 Click the radio button Boundary Layer Mesh to indicate that you wish to generate a boundary layer mesh 67 Enter the values 4 0 3 and 1 04 in the input boxes for the number of layers depth and packing factor 68 Click the OK button to dismiss this dialog box 69 Repeat steps 34 through 61 for this mesh Table 6 1 Comparison of Results Bench Mark Results INSTED Results Difference INSTED file Y Imax 5 071 5 074 lt 1 Psimax out Um ax 16 178 16 2 lt 1 Lola out Vmax 19 617 19 6 lt 1 Lola out Nu at left 2 238 2 23 lt 1 Numean out Numax 3 528 3 33 lt 1 Nusset out LEGEND 2467E 01 2 261E 01 2 056E 01 1 850E 01 1 645E 01 1 439E 01 1 234E 01 8 226E 00 6 171E 00 4 116E 00 2 061E 00 6 199E 03 Figure 6 2 Vector Plot of Velocity for the Natural Convection Problem 35 44 What s Next After reproducing the results for this test
42. roject Files The files required to reproduce our results for this sample problem are axiscond mes Input data for use in Mesh Generator to generate mesh axiscond cfd Input data for CFD solver Location of Project Files The project files above are located in the directory insted30 cfd samples Model Building and Mesh Generation The model for this sample problem will be composed of a square with a counter clockwise orientation The rectangle modeling tool in INSTED will be used to produce the square 15 44 1 Start INSTED CFD 2D Mesh Generator 2 Click the New Project button on the Main dialog box 3 Click the Limit button on the Controls dialog box The Limits dialog box appears 4 Type in 0 002 0 012 0 002 0 012 for the lower x higher x lower y and higher y screen limits in the Limits dialog box 5 Click the OK button to dismiss this dialog box To draw the square 6 Click the Rectangle tool button among the Modeling Tools that reside on the Main dialog box Status bar displays the message Pick 1 Corner Point 7 Type in 0 0 in the Input box and press Enter Status bar displays the message Pick 2 Corner Point 8 Type in 0 01 0 01 in the Input box and press Enter Defining number of elements per line 9 Click the Line Properties button on the Main dialog box The Line Properties dialog box appears 10 Enter the values of 5 5 5 and 5 for the number of el
43. s Enter in the Input Box The Line BC dialog box appears with the heading Boundary Condition Side 3 confirm from the title of the dialog box that data is being received for Line 3 This will not be the case if you accidentally selected some other line 19 Click the drop down list box for u velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 20 Click the drop down list box for v velocity and select a Dirichlet boundary condition from the list and enter a value of 1 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 21 Click the OK button to dismiss the dialog box 22 Repeat the procedure 17 20 for Line 4 setting Dirichlet conditions only for u velocity with a value of 0 0 23 Repeat the procedure 17 20 for Line 1 setting Dirichlet conditions only for v velocity with a value of 0 0 Mesh and Confirm Mesh Results 24 Click the Mesh button on the Main dialog box A mesh of the internal of our loop of lines is displayed on the Graphics dialog box 25 Click the Display button on the Controls dialog box 26 From the listbox select Dirichlet Temp 27 Click the Ok button on this dialog box to view nodes with Dirichlet temperature boundary conditions 28 Click the Refresh button on the Controls dialog box to return the screen to it original condi
44. s a transient one for which the initial condition T 0 is used everywhere This is also the default initial condition in INSTED for this problem Boundary Conditions This is written above as part of the problem statement Computational Grid This test problem will be analyzed with a mesh consisting of 64 9 node elements and 289 nodal points including the nodes at the centroids of the elements Project Files The files required to reproduce our results for this sample problem are reddy mes Input data for use in Mesh Generator to generate mesh reddy cfd Input data for CFD solver Location of Project Files The project files above are located in the directory insted30 cfd samples CFD Type This is a transient heat conduction problem Therefore the velocities are not solved There are also no scalars Since this problem is posed in terms of non dimensional parameters one could in principle analyze this problem using CFD Type 1 or Type 2 However the temperature equation for this problem resembles the form in CFD Type 1 if k H 1 H is non dimensional volumetric heat source Moreover for Type 2 it is not clear what Re value must be used to obtain the right temperature equation and at the same time ensure a motionless state The reason for this is the appearance of the Peclet number Pe RePr in the temperature equation for CFD Type 2 We have selected CFD Type 1 for this problem to avoid any ambiguities Mode
45. s button on the Main dialog box The Line Properties dialog box appears 10 Enter the values of 8 8 8 and 8 for the number of elements for lines 1 2 3 and 4 respectively Press Enter after typing each value to move to the next line I the listbox 11 Click the OK button to dismiss this dialog box Defining the area to mesh 12 Click the Define Area button on the Main dialog box The Area Definition dialog box appears 13 Click the Add button on this dialog box An area listed as l is added in the Areas listbox 14 Click the first line of the Boundaries listbox 15 Type 1 and press Enter This is meant to include boundary 1 made of Rectangle with lines 1 2 3 and 4 in this area 16 Click the OK button to dismiss the Area Definition dialog box Applying boundary conditions 17 Click the Line BC button on the Main dialog box Status bar displays message Pick Side 18 Click the Line 3 on the graphics screen or type 3 and Press Enter in the Input Box The Line BC dialog box appears with the heading Boundary Condition Side 3 confirm from the title of the dialog box that data is being received for Line 3 This will not be the case if you accidentally selected some other line 19 Click the temperature boundary condition listbox s drop down arrow and select the Dirichlet condition from the list An input box appears beside the boundary condition listbox once Dirichlet conditio
46. s that both components of the velocity are zero on all boundaries and the boundaries are y 0 and y 1 are insulate OT Et on and that T 1 atx O andT Oatx 1 31 44 Computational Grid Two different mesh models are used an 8 x 8 square mesh and a 10 x 10 boundary layer mesh with 4 layers 0 3 depth and a packing factor of 1 04 The 8 x 8 square is consists of 64 elements and 289 nodes including the nodes at the center while the boundary layer mesh includes 81 elements and 361 nodes Project Files The files required to reproduce our results for this sample problem are Devahl1 mes Input data for 8 x 8 mesh of model Devahl2 mes Input data for boundary layer mesh of model Devahl cfd Input data for CFD solver Location of Project Files The project files above are located in the directory insted30 cfd samples Model Building and Mesh Generation The mesh boundary for this problem is a square with counter clockwise orientation The rectangle modeling tool in INSTED will be used to produce the square Details of mesh generation follow 1 Start INSTED CFD 2D Mesh Generator 2 Click the New Project button on the Main dialog box 3 Click the Limit button on the Controls dialog box The Limits dialog box appears 4 Type in 0 2 1 2 0 2 1 2 for the lower x higher x lower y and higher y screen limits in the Limits dialog box 5 Click the OK button to dismiss this dialog box To draw
47. ted Click the drop down list box for v velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected Click the drop down list box for stream function and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected Click the OK button to dismiss the dialog box Repeat the procedure 19 23 for Line 3 Click the Line BC button on the Main dialog box Status bar displays message Pick Side Click the Line 2 on the graphics screen or type 2 and Press Enter in the Input Box The Line BC dialog box appears with the heading Boundary Condition Side 2 confirm from the title of the dialog box that data is being received for Line 2 This will not be the case if you accidentally selected some other line Click the drop down list box for u velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected Click the drop down list box for v velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected Click the drop down list box for stream function and select a Dirichlet boundary condition from the list and en
48. ter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected Click the drop down list box for temperature and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected Click the drop down list box for scalar 1 Scalar 1 is the scalar that is selected by default for boundary condition input and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected Change the selected scalar to Scalar 2 by clicking the drop down arrow of the Scalar listbox and clicking on Scalar 2 Click the drop down list box for Scalar 2 and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected Click the OK button to dismiss the dialog box Repeat the procedure 26 35 for Line 4 setting Dirichlet conditions for temperature with a value of 1 0 while executing step 29 Mesh and Confirm Mesh Results 37 Click the Mesh button on the Main dialog box 40 44 A mesh of the internal of our loop of lines is displayed on the Graphics dialog box 38 Click the Display button on the Controls dialog box 39 From the listbox select Dirichlet Temp 40 Click the Ok button on this dialog box to view
49. the Axisymetric Conduction Problem The computational model is shown in Fig 3 1 b Governing Equations The present sample problem is a conduction one with the equation yl TG 0 0 r r Or Oz where k 25W cm C is the thermal conductivity and Q 5 x 108 W m is the volumetric heat generation The coordinates r z y x are the radial and axial coordinates respectively 14 44 You must specify the axial coordinate z as the x coordinate in INSTED and the radial coordinate as the y coordinate This is the convection for axisymmetrical problems in INSTED CFD Type This problem will be solved as CFD Type 3 that is without non dimensionalization We will also take advantage of symmetry to simplify the problem As a result the computational domain shown above was derived based on symmetry along the r and z axis Initial Condition The problem will be analyzed as a transient one for which the initial condition T 0 is used everywhere This is also the default initial condition in INSTED Boundary Conditions This is illustrated in Figure 3 1 b and summarized below Pe pea On x 0 01 T 100 C oT 0 0 gt On y 0 01 T 100 C Also note that there is additional heat generation Q 5 x 10 W m Computational Grid This problem will be analyzed with an unstructured mesh consisting of 25 9 node elements and 121 nodal points including those at the centroids of the elements P
50. tion Note You should have the same result as if you loaded the insted30 cfd samples axiscond mes You may also choose to save your current work Refer to the sections Loading a file and Saving a file in the first chapter of the Users Manual 27 44 Obtaining a Solution to the Problem 29 gt 30 31 32 33 34 35 36 37 38 gt 39 Click the Solver button on the INSTED CFD 2D Mesh Generator Main dialog box The INSTED CFD 2D Solver program is launched The mesh generated from the Mesh Generation program is automatically loaded Click the Load Project button on the Main dialog box of the Solver program Type in the filename section of the operating system Open File dialog box that appears and press Enter A list of files in the current directory is displayed Locate the file squeeze cfd from the Samples directory Click this file and press Enter Click the Prob Description button on the Main dialog box and inspect the loaded parameters Click the OK button to dismiss the Prob Description dialog box Click the Material Properties button on the Main dialog box and inspect the loaded material properties Note particularly the heat flux parameters Click the OK button to dismiss the Material Properties dialog box Click the Solve button on the Main dialog box Program begins to generate a solution to the problem The graphic screen is converted to one th
51. ucing the results for this test problem go through the exercise again but this time change the input data in the project file to study the effect on the solution For example during mesh generation you could change the number of elements in each of the I and J directions During analysis you could locate the thermophysical properties dimensionless parameters solution parameters etc and change them to study the effect on the solutions TU LEGEND uw u W 9 172E 01 8 345E 01 7 517E 01 6 690E 01 5 862E 01 5 034E ET SA 3 379E 0 2 552E 0 1 724E 0 8 966E 02 6 899E 03 gt M Figure 7 1 Contour Plot of Temperature for the Test Problem on the Transport of Temperature and Species By Natural Convection in a Cavity for Ra 10 42 44 EE ex gt U O0 M LEGEND E 9 176E 01 8 351E 01 7 527E 01 L 6 703E 01 5 879E 01 5 054E 01 es 3 406E 01 2 581E 01 1 757E 01 9 328E 02 1 085E 02 ae Q a es wm oH Figure 7 2 Contour Plot of Scalar 1 for the Test Problem on the Transport of Temperature and Species By Natural Convection in a Cavity for Ra 10 43 44 LEGEND 9 172E 01 8 344E 01 7 516E 01 6 689E 01 5 861E 01 3E 01 w Se oS Se 3 377E 01 2 549E 01 1 722E 01 8 938E 02 6 600E 03 2 DO Om Figure 7 3 Contour Plot of Scalar 2 for the Test Problem on the Transport of Temp
52. ults with Source x coord y coord Exact Solution INSTED Difference 0 0 0 0 0 2947 0 2947 lt 1 0 0 0 25 0 2789 0 2789 lt 1 0 0 0 5 0 2293 0 2293 lt 1 0 0 0 75 0 1397 0 1397 lt 1 0 0 1 0 0 0 0 0 lt 1 File lola out LEGEND L 2 708E 01 K 2 469E 01 J 2230E 01 1 991E 01 H 1 752E 01 E 1 036E 01 D 7 968E 02 C 5 579E 02 B 3 190E 02 A 8 013E 03 Number of nodes 289 Number of 9 node elements 64 Figure 1 2 Mesh and temperature plot for Sample Problem 1 Reference Reddy J N 1984 An Introduction to the Finite Element Method McGraw Hill Book Co New York 303 305 13 44 14 44 TEST PROBLEM 3 AXISYMETRIC CONDUCTION IN A CYLINDER Problem Statement Consider a cylinder of height L 0 02 m radius r 0 01m thermal conductivity k 25W cm C and constant internal heat generation Q 5 x 10 W m The top and bottom faces and the curved surface of the cylinder are maintained at T 100 C Calculate the axisymmetric temperature distribution in the 7 z plane of the cylinder Physical and Computational Domain The physical domain is shown in Fig 3 1 a 4 0 0 0 0 _ at an 0 i 0 0 0 01 T n 0 T 100 C 0 01 0 0 T 100 C 0 01 0 01 X b a Figure 3 1 Physical Domain for
53. ving the remaining variables intact Mesh and Confirm Mesh Results 34 Click the Mesh button on the Main dialog box A mesh of the internal of our loop of lines is displayed on the Graphics dialog box 35 Click the Display button on the Controls dialog box 36 From the listbox select Nusselt No 37 Click the Ok button on this dialog box to view nodes with Nusset number boundary conditions 38 Click the Refresh button twice on the Controls dialog box to return the screen to it original condition Note You should have the same result as if you loaded the file seger1 mes located in the directory insted30 cfd samples segerl mes You may also choose to save your current work Refer to the sections Loading a file and Saving a file in the first chapter of the Users Manual Obtaining a Solution to the Problem 39 Click the Solver button on the INSTED CFD 2D Mesh Generator Main dialog box The INSTED CFD 2D Solver program is launched The mesh generated from the Mesh Generation program is automatically loaded 40 Click the Load Project button on the Main dialog box of the Solver program 41 Type in the filename field of the operating system Open File dialog box that appears and press Enter A list of files in the current directory is displayed 42 Locate the file Seger cfd from the Samples directory 43 Click this file and press Enter 44 Click the Prob Description button
54. y condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 27 Click the drop down list box for v velocity and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 28 Click the drop down list box for stream function and select a Dirichlet boundary condition from the list and enter a value of 0 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 29 Click the drop down list box for temperature and select a Dirichlet boundary condition from the list and enter a value of 1 0 in the accompanying Input box that appears as soon as Dirichlet condition is selected 30 Click the radio button Nusset No BC on Side to indicate that you with to calculate the Nusset number along this line 31 Click the OK button to dismiss the dialog box 32 Repeat the procedure 24 29 for Line 2 setting Dirichlet conditions for temperature with a value of 0 0 while executing step 29 33 Click the OK button to dismiss the dialog box Mesh and Confirm Mesh Results 34 Click the Mesh button on the Main dialog box A mesh of the internal of our loop of lines is displayed on the Graphics dialog box 35 Click the Display button on the Controls dialog box 36 From the listbox select Dirichlet Temp 33 44 37 38

INSTED CFD (test problem)

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