第十四章 CEL表达式语言.doc

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Specify complex boundary conditions. Add terms to the solved equations.You can also monitor the value of an expression during the solution using monitor points.Important: There is some CEL that works elsewhere in ANSYS CFX, but not in CFD-Post. Any expression created in CFX-Pre and used as a Design Exploration output parameter could potentially cause fatal errors during the Design Exploration run, so you should create all expressions for Design Exploration output parameters in CFD-Post.14.1.1.Values and ExpressionsCEL can be used to generate both values and expressions. Values are dimensional (that is, with units) or dimensionless constants. The simplest type of definition is the dimensionless value, for example:b = 3.743You can also specify a value with units, for example:g = 9.81 m s-2The dimensions of the quantities of interest for CFD calculations can be written in terms of mass, length, time, temperature and angle. The concept of units is fundamental to the behavior of values and expressions.Values can be used directly, or they can be used as part of an expression. For example, you can use an expression to add two values together:=+In this example, you may want to predefineand, but this is not required. However, in order to add two quantities together,they must have the same dimension; that is, it is meaningful to add a quantity in inches to one expressed in meters, but it is not meaningful to add one expressed in kilograms to one in square feet.Expressions can also be functions of other (predefined) expressions:=+Units follow the conventions in the rest of CFX, in that a calculation has a set of solution units (by default, SI units), and that any quantity can be defined either in terms of the solution units, or any other set of units with the correct form.An expression does not have its own units string, but if it references quantities that have dimensions, these will determine the resulting units for the expression. For example, if an expression depends inversely on the square of the xcoordinate, then it hasimplied dimensionsof length to the power -2.14.1.1.1.Using Locators in ExpressionsA CFX simulation has physics areas and mesh areas; physics areas are boundaries while mesh areas are regions. These two types of area can occupy completely different spaces in a simulation; however, there is no requirement that area names be unique between physics and mesh. This can lead to ambiguities when you use these names in expressions.To avoid these ambiguities, ANSYS CFX first checks to see if is a physics name; if this is not found, the name is checked in the list of mesh names. Thus if in1 is both the name of a physics area and the name of a mesh area, is taken to indicate the physics area.ANSYS CFX also has REGION CEL syntax so that you can identify a named area as being a mesh area. Thus to identify the mesh area in1, you would use the syntax:REGION:in1Note that if does not appear as a physics name or a mesh name, the expression fails.14.1.2.CFX Expression Language StatementsThe CFX Expression Language is declarative. You declare the name and definition of the expression using expression language statements. The statements must conform to a predefined syntax that is similar to Fortran mathematical statements and to C statements for logical expressions.The statement must consist of the following: a number, optionally with associated units. This defines aconstant. Constants without units are termeddimensionless. for mathematical expressions, one or more references to mathematical constants, system variables, or existing user variables, separated by+(addition),-(subtraction),*(multiplication),/(division) and(exponentiation), with optional grouping of these by parentheses. The syntax rules for these expressions are the same as those for conventional arithmetic. for logical expressions involving relational operators, one or more references to mathematical constants or results from mathematical expressions, separated by=(is less than or equal to),(is greater than) and=(is greater than or equal to) with optional grouping of these by parentheses. for logical expressions involving logical operators, one or more references to logical constants or results from relational operations separated by!(negation),&(logical AND) and|(logical OR), with optional grouping by parentheses.14.1.2.1.Use of ConstantsConstants do not need to be defined prior to being used in an expression. For example, you could choose to evaluate the expressionx + 5 m. Or, you could define a constant,b = 5 mand then create an expressionx + b.The logical constants arefalseandtrue. Results of logical expressions are either false or true, which are evaluated as0and1(corresponding tofalseandtrue, respectively) when a numerical representation is required.The use of constants may be of benefit in generating complicated expressions or if you have several expressions that use the same constants.14.1.2.2.Expression SyntaxAll numbers are treated as real numbers.The precedence of mathematical operators is as follows (from highest to lowest): The power operatoras inxy. The unary minus or negation operator-as in-x. Multiplication and division as inx*y/z. Addition and subtraction as inx+y-z.The precedence of logical and relational operators is as follows (from highest to lowest): The negation operator!as in!x. The relational operators involving less than or greater than (=,and=) as inx = y. The relational operator is equal to and is not equal to (=and!=) as inx != y. The logical AND operator (&) as inx & y. The logical OR operator (|) as inx | y.14.1.2.3.Multiple-Line ExpressionsIt is often useful, particularly with complex expressions, to use more than one line when creating your expression. CFX allows you to use multiple lines to generate an expression, provided each line is separated by an appropriate operator.For example, you may have an equation, A + B/C, that consists of three complex terms, A, B, and C. In this case, you could use three lines to simplify creating the expression:A +B/ CNote that the operator may be used at the end of a line (A +) or at the beginning of a line (/ C). You do not need to enter the operator twice.Once the expression has been created, it will appear in the Existing Definitions list box as if it were generated on a single line (A + B/C).14.2.1.CEL OperatorsCFX provides a range of mathematical, logical and operational operators as built-in functions to help you create complex expressions using theExpressiondetails view.Table14.1:CEL OperatorsOperatorFirst Operands Dimensions xSecond Operands Dimensions yOperands Values (Approx)aResults Dimensions-xAnyAnyxx+yAnyxAnyxx-yAnyxAnyxx*yAnyAnyAnyx*yx/yAnyAny0x/yxy (if y is a simple, constant, integer expression)AnyDimensionlessAnybxyxy (if y is any simple, constant, expression)AnyDimensionlessx 0xyxy (if y is not simple and constant)DimensionlessDimensionlessx 0Dimensionless!xDimensionlessfalse or trueDimensionlessx = yAnyxfalse or trueDimensionlessx yAnyxfalse or trueDimensionlessx = yAnyxfalse or trueDimensionlessx = yAnyxfalse or trueDimensionlessx != yAnyxfalse or trueDimensionlessx & yDimensionlessDimensionlessfalse or trueDimensionlessx | yDimensionlessDimensionlessfalse or trueDimensionlessaThe logical constants true and false are represented by 1 and 0 when a numerical representation is required.bFor y 0, 1/x, 1.0). In this case, whenx=0.0, a division by zero will still occur because the expression1/xis evaluated independent of whetherx0is satisfied or not.14.2.3.CEL ConstantsRight-click in theExpressiondetails view to access the following useful constants when developing expressions:Table14.2:CEL ConstantsConstantUnitsDescriptionRJK-1mol-1Universal Gas Constant: 8.314472avogadromol-16.02214199E+23boltzmannJ K-11.3806503E-23clightm s-12.99792458E+08eDimensionlessConstant: 2.7182817echargeA sConstant: 1.60217653E-19epspermo1./(clight*clight*mupermo)gms-2Acceleration due to gravity: 9.8066502mupermoN A-24*pi*1.E-07piDimensionlessConstant: 3.141592654planckJ s6.62606876E-34stefanW m-2 K-45.670400E-0814.2.4.Using ExpressionsThe interaction with CEL consists of two phases: a definition phase, and, a use phase.The definition phase consists of creating a set of values and expressions of valid syntax. The purpose of theExpressiondetails view is to help you to do this.14.2.4.1.Use of Offset TemperatureWhen using temperature values in expressions, it is generally safer to use units of K only. When units are used that posses an offset (for example, C), they are converted internally to K. For terms that have temperature to the power of unity, any unit conversion will include the offset between temperature scales. However, in all other cases the offset is ignored because this is usually the most appropriate behavior. You should therefore take care when specifying an expression involving non-unit powers of temperature. For example, each of the expressions below is equivalent:Temperature = 30 CTemperature = 303.15 KTemperature = 0 C + 30 KTemperature = 273.15 K + 30 KThese are only equivalent because all units are to the power of unity and units other than K appear no more than once in each expression. The following expression will not produce the expected result:Temperature = 0 C + 30 CThis is equivalent to576.30Kbecause each value is converted to K and then summed. The two expression below are equivalent (as expected) because the offset in scales is ignored for non-unit powers of temperature:Specific Heat = 4200 J kg-1 C-1Specific Heat = 4200 J kg-1 K-115.5.Quantitative Function ListThe available quantitative functions are outlined in the sections that follow.In the table that follows, applies to CFD-Post only. CFX-Pre and CFX-Solver can only accept variables as arguments to quantitative functions. Note that for CFX-Pre and CFX-Solver, an Additional Variable can be used to pass an expression indirectly into a quantitative function.The behavior of the functions in the table below depends on the type of . Typically: On domains and subdomains, the functions use vertex (node) values for the operand. On a boundary, the functions use conservative values for the operand unless this is overridden by theBoundconvariable operator in CFX-Pre. On user locations in CFD-Post, the functions use values interpolated from nodal values.Table15.4:CEL Functions in CFX-Pre/CFX-Solver and in CFD-PostFunction Name and Syntax OperationAvailabilityarea( )Area of a boundary or interface.Supports “”.Seearea.Allarea_x_( )area_y_( )area_z_( )The (signed) component of the normal area vector in the local x, y or z direction. The normal area vectors are always directed out of the domain, therefore you may obtain positive or negative areas depending on the orientation of your domain and the boundary you are operating on. The area of a closed surface will always be zero.Supports “”.AllaareaAve()Area-weighted average of on a boundary.Supports “”.SeeareaAve.AllareaAve_x_( )areaAve_y_( )areaAve_z_( )The (signed) component of the normal area vectorweighted averagein the local x, y or z direction. The normal area vectors are always directed out of the domain, therefore you may obtain positive or negative areas depending on the orientation of your domain and the boundary you are operating on. The area of a closed surface will always be zero.Supports “”.CFD-PostareaInt()Area-weighted integral of on a boundary.TheareaIntfunction projects the location onto a plane normal to the specified direction (if the direction is not set toNone) and then performs the calculation on the projected location (the direction specification can also beNone). The direction of the normal vectors for the location is important and will cancel out for surfaces such as closed surfaces.Supports “”.SeeareaInt.AllareaInt_x_( )areaInt_y_( )areaInt_z_( )The (signed) component of the normal area vectorweighted integralin the local x, y or z direction. The normal area vectors are always directed out of the domain, therefore you may obtain positive or negative areas depending on the orientation of your domain and the boundary you are operating on. The area of a closed surface will always be zero.Supports “”.Allave()Arithmetic average of over nodes within a domain or subdomain.Supports “”.Seeave.Allcount( )Counts the number of evaluation points (for example, nodes) on the named region.Seecount.AllcountTrue()Counts the number of nodes at which the Variable or logical expression evaluates to true.Supports “”.SeecountTrue.Allforce( )The magnitude of the force vector on a boundary.Supports “.” and “”.Seeforce.AllforceNorm _( )The length of the normalized force on a curve in the specified direction.Supports “.” and “”.SeeforceNorm.CFD-Postforce_x_( )force_y_( )force_z_( )The (signed) component of the force vector in the local x, y or z direction.Supports “.” and “”.Allainside()Similar to thesubdomainvariable, but allows a specific 2D or 3D location to be given.Supports “”.Seeinside.CFX-Pre, CFX-Solverlength()Length of a curve.Supports “”.Seelength.CFD-PostlengthAve()Length-weighted average.Supports “”.SeelengthAve.CFD-PostlengthInt()Length-weighted integration.Supports “”.SeelengthInt.CFD-Postmass()The total mass within a domain or subdomain. This is fluid-dependent.Supports “”.Seemass.CFX-Pre, CFX-SolvermassAve()Mass-weighted average of on a domain or subdomain.Supports “”.SeemassAve.CFX-Pre, CFX-SolvermassFlow()Mass flow through a boundary.Supports “.” and “”.SeemassFlow.AllmassFlowAve()Mass flow w