Card 9 - EXPRESSION Symbolic Expression Definition

KODE

KODE is the code EXPRESSION (or 100)

N1

N1 is the expression number.

An expression cannot have the same number as a table or array in the model. An expression number can be referenced the same way as a table number in most of the places where a table number is accepted. Expressions are mainly supported for the cards and definitions (including emissivity and heat transfer coefficients) where the actual evaluation of the expression or table is done in (or postponed until) the Analyzer module execution. Those normally include, but may not be limited to, INTERP, SINK, PSINK, QNODE, and RELTEMP cards, material properties, thermal couplings, as well as various fields in VOID_NONGEOM, VOID_REGION, TSTREAM, and ZONE_CONVECTION cards.

Expression numbers can also be referenced as dependent variable values in TABDATA cards for tables whose dependent and independent variable types (in TABTYPE card) are TABLE and OPERATION, respectively. This is supported provided that such a TABLE-OPERATION table is not referenced from another expression. For places where a table with number n can be referenced using Tn or -n convention, you can also use the En notation, which is an equivalent intended for cases when n is an expression number.

T1

T1 is the code for the dependent variable type, which has the same meaning and can accept the same values as the dependent variable type in TABTYPE cards

For a list of supported types and for their descriptions, see Card 9 - TABDATA Analyzer Table Data.

T2

T2 is the symbolic expression string, which could be either enclosed in double quotes (") or left unquoted. The expression string consists of:

• Constants
• Operators
• Backed variables
• Built-in functions
• Table references (fields) registered functions
• Punctuation (parentheses and if/then/else statements)

For example:

where:

The expression strings in the INPF should not contain any unit specifications, such as "[mm/sec]". All unit conversions should be done before the expression string is written to the INPF file. In that expression string all quantities are assumed to be in the same units as in other INPF cards.

Expression constants can be of type:

• integer, for example 257
• real, for example 0.1, 1E6, 2.3d4
• boolean, for example true or false or various capitalized versions of those
• string enclosed in quotes, for example "string 1(a)#$%^&"

Those are also the types used in arguments or return values of expression functions.

Expression operators include standard mathematical operators (+, -, *, /, and ^ for power), comparison operators (==, !=, <, >, <=, >=), and boolean operators (!, &&, ||). The meaning of those operators (except using ^ for power) is the same as in C or C++ programming languages.

The built-in function symbols include:

• abs
• acosine
• asine
• atangent
• atangent2 (two arguments, x and y)
• ceiling (returns integer for a real argument)
• cos
• floor (returns integer for a real argument)
• hypcos
• hypsin
• hyptan
• log
• log10
• max
• minimum
• mod
• pi (pi constant, 3.14159.., no arguments)
• round (returns integer for a real argument)
• sin
• sqrt
• tan

Note that in the INPF file expression strings, all angular quantities in arguments or return values of those built-in functions should be in degrees, not radians (for example cos(90.0) is the cosine of a 90 degree angle).

Expression backed variables is an Analyzer-supported set of variable names to access various quantities in the expression evaluation context, which is for a given element or conductance number to which the expression is applied at a given moment in the solve integration time, that can be used as independent variables. Many of those names have a corresponding equivalent with the same definition in the list of possible independent variable types for TABTYPE cards, which are listed in the following table. For more information on the types, see Card 9 - TABDATA Analyzer Table Data.

EXPRESSION 14 QNODE 2.0*(fd("Field Name (1)"") + Table2)
EXPTAB  15 "Field Name (1)"
EXPTAB  16 Table2
TABTYPE 15 VALUE EID
TABDATA 15 ...
TABTYPE 16 VALUE TIME
TABDATA 16 ...

Parentheses, with any number of matching “(” and “)”, could be used to structure an expression. The if-then-else construct can be used according to the following syntax:

if <expr1> then <expr2> else <expr3>

For example:

Note that spaces are required before and after each of the “if”, “then”, and “else” keywords.

Other functions, besides the built-in functions and fd(...) fields, should be registered in the expression evaluation system by loading plugins (dynamic library files loaded at run time by the solver) that contain definitions (names, numbers and types of mandatory and optional arguments, type of the return value) and implementations of those functions. A generally available standard set of registered functions is supported through solver built-in plugins that are distributed with the thermal solver executable. Those ones include general function, solution-dependent function, and fluid properties function plugins. Other functions that are not part of that pre-supplied set can be registered by loading additional user-provided plugins specified by EXPPLUGIN cards.

Registered functions can have required and optional arguments (parameters) or no arguments. In the latter case, the parentheses “()” should still follow the function name. When optional arguments for a given function are not provided, then their function-specific defaults are used. For example, possible uses of required and optional arguments of the function ABS2REL could be:

ABS2REL(300.0)
ABS2REL(300.0,0.99*radius)
ABS2REL(300.0,radius,0.5*rotational_speed)
ABS2REL(300.0,radius,rotational_speed,0,0.5*
swirl_velocity)

To set a desired optional argument (for example, the third one) one should also provide all of the preceding ones (for example, the first two).

Note that when there are expressions with significant sensitivity to temperature through backed variables or registered functions and/or there are expressions with critical inter dependencies (an expression result on one boundary condition depends on the quantities on another boundary condition which is governed by another expression), then use of the fully implicit integration method setting for GRADNT field on Card 2b is recommended for increased accuracy and consistency of the results.

The following table lists registered functions from the general category.

The following table lists registered functions from the solution dependent category.

Note that for the functions that return pressure, swirl, or temperature for convecting zone, void, or stream BCs (ZT, ZP, etc), when there are spatial variations of that quantity along the BC, then the output result is the maximum value over those spatial variations. In the functions where temperature is returned, the temperature is either total absolute or total relative temperature, depending on the type of rotational effects specified in the ROT_FXS option of the ROT_FX card, referenced in the given BC.

The following table lists registered functions from the additional solution dependent category.

The following table lists registered functions from the fluid properties category.