1. Complex, Time and/or Spatially-Varying Boundary Conditions Chapter 6

2. Training Manual Inventory #001445 March 15, 2001 6-2 Tabular Thermal Boundary Conditions (Loads) Up to this point, all boundary conditions applied to the solid model and/or FEA model were applied as known constant values or temperature-dependent values. When complex time-dependent and/or spatially-dependent boundary conditions need to be applied, tabular boundary conditions may be much more convenient. –Definition - A tabular boundary condition is a condition that is applied via a look-up table whose values are evaluated and applied during the solution process.

3. Training Manual Inventory #001445 March 15, 2001 6-3 Tabular BCs - Primary Variables Primary Variable time coordinate location in the global Cartesian system temperature velocity, only for use with the Fluid116 element, the 1-D thermal-flow element Corresponding ANSYS Labels TIME X, Y, Z TEMP VELOCITY Tables may be constructed with the following primary variables:

4. Training Manual Inventory #001445 March 15, 2001 6-4 Additional Table Definitions Independent Variable –Variable that directly or indirectly describes a tabular relation to a primary variable, e.g., hf = f(time) film coefficient (independent variable) is defined as a function of the primary variable, time hf = f(x,rpm) in this case, hf and rpm rpm = g(time )are independent variables.

5. Training Manual Inventory #001445 March 15, 2001 6-5 Additional Table Definitions Multivariate tables –Tables which are a function of more than one variable, e.g., hf = f(x,y,time) Recursive tables –Tables which reference other tables through a common independent variable, e.g., hf = f(x,y,rpm) rpm = g(time)

6. Training Manual Inventory #001445 March 15, 2001 6-6 Tabular Input Applicability Tabular BCs can generally be used with all solid model and/or FE model thermal boundary conditions: –Applied temperatures via D, DK, DL, DA commands –Heat flow via F, FK commands –Convections (film coefficients and bulk fluid temperatures) via SF, SFE, SFL, SFA commands –Heat fluxes via SF, SFE, SFL, SFA commands –Internal heat generation (heat/volume) via BF, BFE, BFL, BFA, BFV commands Use the HELP command to see the appropriate menu picks for the commands listed.

7. Training Manual Inventory #001445 March 15, 2001 6-7 Important Note Concerning Tabular BCs If tabular boundary conditions are not functions of time, they are effectively stepped across time, regardless of the KBC command setting (see Chapter 4 ).

8. Training Manual Inventory #001445 March 15, 2001 6-8 Primary Variables - Boundary Condition Applicability Thermal Boundary Condition Applied Temperatures Heat Flow Film Coefficient Bulk Temperature Heat Flux Internal Heat Generation (heat/volume) Uniform Heat Generation (heat/volume) Primary Variables TIME,X,Y,Z TIME,X,Y,Z,TEMP TIME,X,Y,Z,TEMP,VELOCITY TIME,X,Y,Z TIME,X,Y,Z,TEMP TIME

9. Training Manual Inventory #001445 March 15, 2001 6-9 Element-Specific Tabular Support Fluid116 1-D Thermal-Flow Element –Loads Flow Rate as function of primary variable, TIME Pressure as function of primary variables, TIME,X,Y,Z SURF151, 152 Surface Effect Elements –Real Constants Rotational Speed and Slip Factor (primarily for use in gas turbine applications such as rotating disks) as function of primary variables TIME, X, Y, Z

10. Training Manual Inventory #001445 March 15, 2001 6-10 Defining ANSYS Tables Tables can be defined using any of the following methods: –ANSYS commands (*DIM) –In the GUI, under Utility Menu>Parameters>Array Parameters>Define/Edit –In the GUI, at the time the boundary condition is applied the program will allow the use of an existing table or allow the user to define a new table. From an external file created using an editor or a spreadsheet, e.g., EXCEL. The data must be in tab- delimited text format to be used by the ANSYS command, *TREAD.

11. Training Manual Inventory #001445 March 15, 2001 6-11 Review of ANSYS APDL Arrays There are two types of ANSYS array parameters: –array type used to define discrete functions –table type used to define continuous functions via linear interpolation between tables entries Arrays can be one, two, or three-dimensional. A two-dimensional array has m rows and n columns; –rows are identified by a row index number I, which varies from 1 to m –columns are identified by a column index number J, which varies from 1 to n. The quantities that make up the array are called array elements. Each array element is identified by indices (I,J) where I is its row number and J is its column number.

12. Training Manual Inventory #001445 March 15, 2001 6-12 Review of ANSYS APDL Arrays For ARRAY type, all data values are stored and retrieved using the subscripts to point to the particular row/column/plane location. All subscript input values are treated as integers. Typical row and column indices for a 5x3 ARRAY are shown below.

13. Training Manual Inventory #001445 March 15, 2001 6-13 Review of ANSYS APDL Arrays For example, the use of the ARRAY element, NSTR(2,4) in an ANSYS command field would substitute the value 19.1 if the NSTR ARRAY (3 rows and 4 columns) was defined as:

14. Training Manual Inventory #001445 March 15, 2001 6-14 Review of ANSYS APDL Tables TABLE arrays also consist of numbers arranged in a tabular fashion but a TABLE array allows retrieval of “in-between” values of array elements. This is done by linear interpolation. In addition, the J=0 column, which normally consists of the row index integers (I=1 through m), must be changed and filled with monotonically increasing numbers (not necessarily integers). Similarly, the I=0 row, which normally consists of the column index integers (J=1 through n), must be changed and filled with monotonically increasing numbers (not necessarily integers). By default, all index numbers are initialized with a near-zero number.

15. Training Manual Inventory #001445 March 15, 2001 6-15 1-D Table Example For example, the 1-D TABLE array A can be interpreted as follows: A(1.5) evaluates as 20.0 (halfway between 12.0 and 28.0) A(2.5) evaluates as 87.2 (halfway between 28.0 and 146.4)

16. Training Manual Inventory #001445 March 15, 2001 6-16 2-D Table Example The 2-D TABLE array PQ can be interpreted as follows: –PQ(1,1.5) evaluates to 3.5 (halfway between 2.8 and 4.2) –PQ(3.5,1.3) evaluates to 14.88 (average 42.0 and -4.5, average 9.7 and 2.0, then take 30% of the difference and add it to the average of 42.0 and -4.5).

17. Training Manual Inventory #001445 March 15, 2001 6-17 Conventions for Load Tables Although parameter names can, in general, be up to 8 characters in length, table parameters that will be used in command fields (where constant values are normally given) are limited to seven (7) characters.

18. Training Manual Inventory #001445 March 15, 2001 6-18 Example: Using a Table To Define A “Load” The use of TABLE arrays for loads allows the user to define functions using table entries with automatic linear, bilinear, or trilinear interpolation between table entries. Consider the loading shown below (FORCE might be a nodal heat flow):

19. Training Manual Inventory #001445 March 15, 2001 6-19 Procedure to Define APDL Tables Via Commands The TABLE array (FORCE) whose array elements are the force values and whose row index numbers are time values, would be defined using the ANSYS commands: *DIM,FORCE,TABLE,5,1,1,TIME FORCE(1,1)=0,560,560,238.5,0 FORCE(1,0)=1.E-6,0.8,7.2,8.5,9.3 FORCE(0,1)=1.0 (not really necessary) –and would appear schematically as shown on the right.

20. Training Manual Inventory #001445 March 15, 2001 6-20 Procedure to Define APDL Tables Via GUI Table Editor Using the GUI, in the Utility Menu>Parameters>Array Parameters>Define/Edit>Add 1 2

21. Training Manual Inventory #001445 March 15, 2001 6-21 Procedure to Define APDL Tables Via External Spreadsheet (e.g., EXCEL) Define the table entries, including the “0” row, “0” column entries in EXCEL. One can separate the “planes” of data using blank lines to make the data more readable. An example of a 3-D table is shown below, note that y, the plane variable, only has two entries in this example: Write out the data in tab-delimited text format, in EXCEL, click under File>Save As>change Save As Type to text (tab delimited)

22. Training Manual Inventory #001445 March 15, 2001 6-22 Procedure to Define APDL Tables Via External Spreadsheet (continued) Note that one can include headers that document the purpose of the EXCEL data, etc. and that blank lines can be included to make the data more user-readable. In ANSYS, define array type and dimensions under Utility Menu>Parameters>Array Parameters>Define/Edit>Add this is a 3-D Table

23. Training Manual Inventory #001445 March 15, 2001 6-23 To read in the EXCEL data, click under Utility Menu>Parameters>Array Parameters>Read from File>Table array and fill out the dialog box. Procedure to Define APDL Tables Via External Spreadsheet (continued) Note-skip first 4 lines at top of the EXCEL spreadsheet.

24. Training Manual Inventory #001445 March 15, 2001 6-24 Checking the Table in the GUI The data can be checked in the Utility Menu under Parameters>Define/Edit> pick the Table to be edited Plane data

25. Training Manual Inventory #001445 March 15, 2001 6-25 Plotting APDL Tables TABLES can be plotted under Utility Menu> Plot> Arrays. Employing this for the earlier 1-D example, filling out the dialog box produces the plot in the next viewgraph.

26. Training Manual Inventory #001445 March 15, 2001 6-26 Plotting APDL Tables (continued) After filling out the dialog box and clicking “OK”, the following plot appears:

27. Training Manual Inventory #001445 March 15, 2001 6-27 Applying Tables Via Commands Tables can be applied as loads using standard ANSYS load commands. The use of tabular input is indicated by using the table name between percent signs in the “value” field of the command. No table indices are required. A few examples are shown below: SF,all,HFLUX,%fluxtab% D,all,TEMP,%temptab% SFL,all,CONV,%hftab%,1000

28. Training Manual Inventory #001445 March 15, 2001 6-28 Applying Tables Via GUI In the GUI, when the user picks the entity for “load” application and then clicks APPLY, the resulting dialog box gives the user the option to specify: –a constant value –an existing table –or a new table

29. Training Manual Inventory #001445 March 15, 2001 6-29 Checking Boundary Conditions Applied Via Table Input When a tabular boundary conditions are applied to solid model or FE model entities, the table name will be shown when boundary conditions are listed or plotted in the Preprocessor. If solid model loads are transferred to the FE model via SBCTRAN (Solution>Loads>Operate>Transfer to FE), the evaluated table boundary conditions (numerical values) can be listed or plotted on the nodes and elements in the Solution processor. If the tabular BCs are functions of time, the evaluation is done at TIME = 0. If a Load Step File (jobname.SXX) is written after the transfer, the load step file boundary conditions on the nodes and elements (solid model loads are not stored on LS files) will still reference the table arrays, not the evaluated numerical values.

30. Training Manual Inventory #001445 March 15, 2001 6-30 Checking Boundary Conditions Applied Via Table Input (continued) After a solution has been performed, listing or plotting of node and element BCs (in the Solution processor) will show numerical values evaluated at the TIME of the last substep. In POST1 (General Postprocessor), the evaluated boundary conditions can be listed or plotted on the nodes and elements at the time value associated with the results stored in the database.

31. Training Manual Inventory #001445 March 15, 2001 6-31 Other Options - Tabular Input In some instances, the type of load may be known but specific table values of loads may not be known at the time the model is being built. In such cases the user may simply want to identify the various load regions. To do this: –Apply the boundary condition as a new table, take all the defaults for the table dimensions and values (empty). –When the boundary conditions are known at a later date, simply redefine the table size and values to be consistent with the known values. You do not need to reapply loads.

32. Training Manual Inventory #001445 March 15, 2001 6-32 Example: Film Coefficient as a Function of Length [HF = f(x )] Assume that the film coefficient on a surface is a nonlinear function of the surface’s global x-coordinate only. Assuming that 6 bilinear interpolation points are to be used, a table array can be defined in the GUI as follows:

33. Training Manual Inventory #001445 March 15, 2001 6-33 Assuming the x-coordinate in the Global Cartesian coordinate system varies from 2 to 4 along the surface to be loaded, the film coefficient table might be defined as shown: Example: Film Coefficient as a Function of Length [HF = f(x )] (continued)

34. Training Manual Inventory #001445 March 15, 2001 6-34 Example: Film Coefficient as a Function of Length [HF = f(x )] (continued) Using the GUI to apply the convection on a line, causes a dialog box to appear. Choose “existing table” for the film coefficient and “constant value” for Bulk temperature (since it is not defined by a tabular function). Enter the constant TBULK value and press OK.

35. Training Manual Inventory #001445 March 15, 2001 6-35 Example: Film Coefficient as a Function of Length [HF = f(x )] (continued) The next dialog box allows the user to pick the appropriate load table from the group of currently defined tables (in this case, only one table, HF, is currently defined).

36. Training Manual Inventory #001445 March 15, 2001 6-36 To display the convection boundary condition, we turn on the plotting in the Utility Menu under PlotCtls>Symbols Example: Film Coefficient as a Function of Length [HF = f(x )] (continued)

37. Training Manual Inventory #001445 March 15, 2001 6-37 Example: Film Coefficient as a Function of Length [HF = f(x )] (continued) To display the table name on the plot, in the Utility Menu, under PlotCtls> Numbering, turn on Table Names

38. Training Manual Inventory #001445 March 15, 2001 6-38 Example: Film Coefficient as a Function of Length [HF = f(x )] (continued) A plot of lines shows the tabular film coefficient, HF, using the table name.

39. Training Manual Inventory #001445 March 15, 2001 6-39 In the General Postprocessor (POST1), the numerical values can be displayed by turning table names off and turning the numerical values on (Utility Menu>PlotCtls>Numbering) Turn off Turn on Example: Film Coefficient as a Function of Length [HF = f(x )] (continued)

40. Training Manual Inventory #001445 March 15, 2001 6-40 Numerical values cannot be displayed on the solid model; numerical values can only be displayed on the FE model: Example: Film Coefficient as a Function of Length [HF = f(x )] (continued) Notice that these are ELEMENT plots.

41. Training Manual Inventory #001445 March 15, 2001 6-41 Time-Stepping and Output Controls Tabular boundary conditions allow the user to define and solve complex, transient heat transfer problems in a single load step. Multiple load steps can also be used with tabular boundary conditions. However, with Automatic Time-Stepping (ATS), the solver might inadvertently “jump” over key events in time (e.g., abrupt load changes). To prevent this, the user can define keytimes (times at which the time step is to be reset to the initial NSUB/DELTIM value). These settings are specified via the ANSYS command, TSRES. The frequency with which results are written to the thermal results file (jobname.rth) is controlled via an option on the OUTRES command.

42. Training Manual Inventory #001445 March 15, 2001 6-42 Keytimes and Output Times RPM Time Output Times Keytimes

43. Training Manual Inventory #001445 March 15, 2001 6-43 Time Step Reset (TSRES command) Resetting the time step size to the initial value (specified on the NSUB/DELTIM command) at particular time points can be accomplished by referencing an array (not a table) of time point values with the TSRES command: TSRES, array name The named array must be an ANSYS array parameter of dimension Nx1, where N is the number of keytimes and the values of the array elements are the numerical values of time at which the time step must be reset. The time increments between time points specified in this array must be greater than the initial time step given by NSUB or DELTIM.

44. Training Manual Inventory #001445 March 15, 2001 6-44 Time Step Reset - Using the GUI 3 4 1 2

45. Training Manual Inventory #001445 March 15, 2001 6-45 Results File Output Controls (OUTRES) The OUTRES command allows the user to control how often the calculated results are written to the thermal results file (jobname.rth). The form of the command is, OUTRES, item, FREQ, Cname To control the frequency of output using an array parameter (not a table), use %array name% in the FREQ field where array name is the name of an array parameter of dimension Nx1 and the array is filled with the N values of time at which the results are to be written to the results file. No indices are required.

46. Training Manual Inventory #001445 March 15, 2001 6-46 Results File Controls Using GUI 1 3 4 2

47. Training Manual Inventory #001445 March 15, 2001 6-47 Results File Controls Using GUI (continued) Indicate whether a new or existing array is to be used. Then respond to the subsequent dialog prompts. 5 6

48. Training Manual Inventory #001445 March 15, 2001 6-48 Note: Arrays used with TSRES and OUTRES need not be the same. This is important since output is usually requested at more time points than those at which the time step is reset. Example of Arrays Used With TSRES and OUTRES Examples of arrays that might be used to reset the time step (TSRES) and write output to the results file at specified time (OUTRES) are shown below:

49. Training Manual Inventory #001445 March 15, 2001 6-49 Function Tool There are three ways to apply time history loads: –Multiple load steps –Tabular input –Function tool The Function Tool can also be used to apply complex spatially varying loading Load t t t

50. Training Manual Inventory #001445 March 15, 2001 6-50 Function Tool The Function Tool… Allows building a library of functions that can be used to apply complex boundary conditions easily –Calculator like functionality to build equations –Supports all primary variables (x, y, z, temp, pres, time etc.) –Each function must be saved to a file (archived) –Functions can be retrieved from archived files and applied as TABLE array loads

51. Training Manual Inventory #001445 March 15, 2001 6-51 Function Tool There are two steps in using the Function Tool to apply loads in ANSYS: 1.Use the Function Editor to create an arbitrary equation. 2.Load the function into TABLE arrays using the Function Loader. Create functions using function builder Save functions to files and create an archive of various functions Step 1: Function Editor When needed, read in any saved function Supply a parameter name for the array and any other required data as directed Apply load using ‘existing table’ and the parameter name Step 2: Function Loader

52. Training Manual Inventory #001445 March 15, 2001 6-52 Function Tool … Function Editor Function Editor –Solution > Loads-Apply > Functions-Define/Edit –Or from the utility menu as shown below. –Define the equation using TIME as the primary variable. –Save the function for later use.

53. Training Manual Inventory #001445 March 15, 2001 6-53 Use the Function Editor like a calculator to create your time or spatially varying equation For time-history loading, define the equation using TIME as the primary variable. Save the function for later use. Function Tool … Function Editor

54. Training Manual Inventory #001445 March 15, 2001 6-54 Function Tool … Function Loader The function must be stored as a table array before it can be applied as a load. This conversion is done using the Function Loader. To use the equation, choose –Solution > Loads-Apply > Functions- Read File –Or pick from the utility menu as shown before. Load the function (“.func” file) Fill in the dialog box shown Provide a table parameter name. Assign values to all equation variables.

55. Training Manual Inventory #001445 March 15, 2001 6-55 The function can now be applied as a tabular boundary condition (e.g. F,ALL,FZ,%PPULSE%) Recommendation: Do not use the Function Tool if the boundary conditions can be expressed directly with tabular input Function Tool … Function Loader For more information refer to “Applying Loads Using Function Boundary Conditions” in the Basic Analysis Guide.

56. Training Manual Inventory #001445 March 15, 2001 6-56 Function Tool Goal: Allow user to apply any arbitrary function to describe HT film coefficients Examples:

57. Training Manual Inventory #001445 March 15, 2001 6-57 Function Tool … Example Problem Convection over a flat plate 0.1 0.55 1.1 x

58. Training Manual Inventory #001445 March 15, 2001 6-58 Equation for regime variable. {X} comes from the primary variable “X” Function Tool … Example Problem Regime variable: xloc

59. Training Manual Inventory #001445 March 15, 2001 6-59 Function Tool … Example Problem The Reynolds number is constructed first and stored in Memory 1 A constant “Velo” is defined for the free stream velocity Regime 1 will now be prepared

60. Training Manual Inventory #001445 March 15, 2001 6-60 Function Tool … Example Problem The Prandtl number is constructed next and stored in Memory 2

61. Training Manual Inventory #001445 March 15, 2001 6-61 Function Tool … Example Problem Regime 1 is now prepared. The Regime variable limits are defined The film coefficient is now constructed. The Reynolds and Prandlt numbers are recalled from memory using the “ins mem” key.

62. Training Manual Inventory #001445 March 15, 2001 6-62 Function Tool … Example Problem Regime 2 is now prepared. The Regime variable limits are defined The film coefficient is now constructed. The Reynolds and Prandlt numbers are recalled from memory using the “ins mem” key. The function is saved as “FlatePlate4.func” using the “Editor” tab.

63. Training Manual Inventory #001445 March 15, 2001 6-63 Function Tool … Example Problem Select function from directory. Assign name to imported function Assign values to the function constants. Function Loader

64. Training Manual Inventory #001445 March 15, 2001 6-64 Function Tool … Example Problem Apply the function to the plate as the tabular boundary condition “PLATE”.

65. Training Manual Inventory #001445 March 15, 2001 6-65 Function Tool … Example Problem

66. Training Manual Inventory #001445 March 15, 2001 6-66 Film coefficient distribution Function Tool … Example Problem