The document provides an introduction and overview of the CFX Expression Language (CEL). Some key points: - CEL allows users to create equations and functions of solver/system variables to be used in CFX-Pre and CFD-Post. - CEL syntax follows standard arithmetic rules and includes variables, constants, numerical functions, and integrated quantities. - Examples are given for creating variable properties, conditional expressions, and user-defined functions in CEL. - Integrated quantity functions allow evaluating variables over locations and return area, mass, or flow-weighted averages.

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Chapter 11
CFX Expression Language
(CEL)
Introduction to CFX

2. CFX Expression Language
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• CEL - CFX Expression Language
– Allows the user to create equations (can be functions of
solution/system variables) that can be used in CFX-Pre and CFD-Post
• Example:
CEL

3. CFX Expression Language
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• The syntax rules are the same as those for conventional arithmetic.
Operators are written as:
+ (addition) - (subtraction) * (multiplication)
/ (division) ^ (exponentiation)
• Variables and expressions are case sensitive (example: t vs. T)
• Expressions must be dimensionally consistent for addition and subtraction
operations (example: 1.0 [mm] + 0.45 [yds] is OK)
– You cannot add values with inconsistent dimensions
• Fractional and decimal powers are allowed (example: a^(1/2) + 1.0^0.5)
• Units of expressions are not declared – they are the result of units in the
expression (example: a [kg m^-3] * b [m s^-1] has units of [kg m^-2 s^-1]
• Some constants are also available in CEL for use in expressions:
– e Constant: 2.7182818
– g Acceleration due to gravity: 9.806 [m s^-2]
– pi Constant: 3.1415927
– R Universal Gas Constant: 8314.5 [m^2 s^-2 K^-1]
CEL Rules

4. CFX Expression Language
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• Numerical functions and operators are also available in CEL
– Right-click when creating expressions for a complete list
– Custom functions with User Fortran can also be created
Function Operand’s Dimensions [x] Operand’s Values Result’s Dimensions
sin(x) Angle Any Dimensionless
cos(x) Angle Any Dimensionless
tan(x) *** Angle Any Dimensionless
asin(x) Dimensionless -1 ≤ x ≤ 1 Angle
acos(x) Dimensionless -1 ≤ x ≤ 1 Angle
atan(x) Dimensionless Any Angle
exp(x) Dimensionless Any Dimensionless
loge(x) Dimensionless 0 < x Dimensionless
log10(x) Dimensionless 0 < x Dimensionless
abs(x) Any Any [x]
sqrt(x) Any 0 ≤ x [x]^0.5
if(test, res1, res2)* Any Any Any (res1 and res2 must have the same dimensions)
min(x,y) **** Any Any [x]
max(x,y) **** Any Any [x]
step(x) * Dimensionless Any Dimensionless
*if functions contain a test, and two result outcomes. The first outcome, res1 will be returned if test evaluates to true. If test evaluates to false, res2 is
returned. Consider the following example, where we wish to set volume fraction to 1 when X is greater than 1 [m], and 0 if X is less than 1 [m]:
if (x>1[m], 1, 0)
In this case, if the result is precisely equal to 1[m], the result is (res1+res2)/2
**step(x) is 0 for negative x, 1 for positive x and 0.5 for x=0.
*** note that tan(x) is undefined for nπ/2 where n=1, 3, 5 .. .
**** both x and y must have the same dimensions.
Built In Functions

5. CFX Expression Language
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x Direction 1 in Reference Coordinate Frame
y Direction 2 in Reference Coordinate Frame
z Direction 3 in Reference Coordinate Frame
r Radial spatial location, r = (x^2+y^2)^0.5
theta Angle, arctan(y/x)
t Time
u Velocity in the x coordinate direction
v Velocity in the y coordinate direction
w Velocity in the z coordinate direction
p (absolute) Pressure
ke Turbulent kinetic energy
ed Turbulent eddy dissipation
T Temperature
sstrnr Shear strain rate
density Density
rNoDim Non-dimensional radius (rotating frame only)
viscosity Dynamic Viscosity
Cp Specific Heat Capacity at Constant Pressure
cond Thermal Conductivity
AV name Additional Variable name
mf Mass Fraction
• Solver variables are available for use in any expression
• Below is a partial list of the available system variables:
– When creating expressions, right-click to access a full list
Depending on your
physics, some
variables will not be
valid – e.g. you need
to solver heat transfer
to use T
Solver Variables

6. CFX Expression Language
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Training ManualHow To Create Expressions

7. CFX Expression Language
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To add more
expressions
(similar method in
CFD-Post)
How To Create Expressions
Right-click in the
Definition window
to access
Variables,
Constants,
Functions,
Locators and
existing
Expressions

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where γ is the shear strain rate
• Creating a variable viscosity
– Viscosity of a shear thickening fluid:
1−
= n
Kγµ
Solver Variable and Expression Name are both
accessed via the right mouse button
CEL in CFX-Pre: Example 1

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• Alternatively, an expression can be entered directly into a field
CEL in CFX-Pre: Example 1

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• Using an “if” Function
– Set inlet temperature to 300 K for the first 19 iterations then raise it to
320 K after 20 iterations
Solver variable
accessed with the right
mouse button
Note: On the 21st
iteration
inlet temp = 310 K
CEL in CFX-Pre: Example 2

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• You can also define your own 1-D linear, or 3-D cloud of points
interpolation functions
Import
data
points or
add
manually
User Functions

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• Example: Having the timestep change
with iteration number as shown here
Timestep size is in seconds
Continued on next
slide...
User Functions: Example
Iteration Number is
dimensionless

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• Example: Having the timestep change
with iteration number as shown here
User Functions: Example

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• Integrated quantities can be used in expressions to evaluate variables over
some location
– Examples:
– Calculate the area average of Cp on an isosurface: areaAve(Cp)@iso1
– Mass flow of particular fluid through a locator: oil.massFlow()@slice1
• Available in CFX-Pre and CFD-Post
– Usage is more strict in CFX-Pre
• E.g. the argument supplied to the function must be a variable, not an expression
• “@<locator>” syntax must always supply a named location used in the
physics definition
– A boundary condition name, a domain name, a monitor point name, etc.
• To reference general mesh regions use the syntax “@REGION:<name>”
• Phases/components can be referenced using:
[<phase name>.][<component name>.]<function>@<locator>
– E.g. Air.Nitrogen.massFlow()@outlet
Integrated Quantities

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Training ManualIntegrated Quantities
• Some functions allow an x, y or z operator:
– area_x()@boundary gives the area projected in the x-direction
– force_z()@wall gives the z component of the force on the wall
– See documentation for a full list
• These functions also allow an optional coordinate frame:
– force_z_MyCoord()@wall gives the z component of the force on the wall using the
coordinate frame “MyCoord”
• Each function requires either 0 or 1 arguments
– areaAve requires 1 argument: areaAve(Temperature)@Wall
– massFlow requires 0 arguments: massFlow()@Inlet
• Return value units depend on the argument units
– areaAve(Temperature)@Wall will return a value with units of
Temperature

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• Below is a partial list of functions
– See documentation for a complete list
– Right-clicking when creating an expression will show most functions
Function Name and Syntax
<required> [<optional>]
area( )@<Location>
Area of a boundary or
interface.
Any 2D region (e.g., boundary
or interface)
area_x( )@<Location>
area_y( )@<Location>
area_z( )@<Location>
The (signed) component of the
normal area vector in the local
x, y or z direction. Any 2D region (e.g., a
boundary or interface)
areaAve(<var>)@<Location>
Area-weighted average of <var>
on a boundary.
Any 2D region (e.g., a
boundary or interface)
areaInt(<var>)@<Location>
Area-weighted integral of <var>
on a boundary.
Any 2D region (e.g., a
boundary or interface)
ave(<var>)@<Location>
Arithmetic average of <var>
within a domain or subdomain.
Any 3D region (e.g., domain or
subdomain)
[<Fluid>.]force( )@<Location>
The magnitude of the force
vector on a boundary. Any 2D region (e.g., a wall)
Operation Valid <Location>
Integrated Quantities

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Function Name and Syntax
<required> [<optional>]
[<Fluid>.]force_x( )@<Location>
[<Fluid>.]force_y( )@<Location>
[<Fluid>.]force_z( )@<Location>
The (signed) component of the
force vector in the local x, y
or z direction. Any 2D region (e.g., a wall)
inside()@<Location>
Similar to the subdomain
variable, but allows a specific
2D or 3D location to be given.
Any 2D or 3D named sub-
region of the physical location
on which the expression is
evaluated.
mass()@<Location>
The total mass within a domain
or subdomain. This is fluid
dependent.
Any 3D region (e.g., domain or
subdomain)
massAve(<var>)@<Location>
Mass-weighted average of
<var> on a domain or
subdomain.
Any 3D region (e.g., domain or
subdomain)
massInt(<var>)@<Location>
The mass-weighted integration
of <var> within a domain or
subdomain
Any 3D region (e.g., domain or
subdomain)
[<Fluid>.]massFlow()@<Location> Mass flow through a boundary.
Any fluid surfaces (e.g., Inlets,
Outlets, Openings and fluid-
fluid interfaces)
[<Fluid>.]massFlowAve(<var>)
@<Location>
Mass flow weighted average of
<var> on a boundary.
Any fluid surfaces (e.g., Inlets,
Outlets, Openings and fluid-
fluid interfaces)
Operation Valid <Location>
Integrated Quantities

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Function Name and Syntax
<required> [<optional>]
[<Fluid>.]massFlowAveAbs(<var>)
@<Location>
Absolute mass flow weighted
average of <var> on a
boundary.
Any fluid surfaces (e.g., Inlets,
Outlets, Openings and fluid-
fluid interfaces)
[<Fluid>.]massFlowInt(<var>)
@<Location>
Mass flow weighted integration
of <var> on a boundary.
Any fluid surfaces (e.g., Inlets,
Outlets, Openings and fluid-
fluid interfaces)
maxVal(<var>)@<Location>
Maximum Value of <var>
within a domain or subdomain.
Any 3D region (e.g., domain or
subdomain)
minVal(<var>)@<Location>
Minimum Value of <var> within
a domain or subdomain.
Any 3D region (e.g., domain or
subdomain)
probe(<var>)@<Location>
Returns the value of the
specified variable on the
specified Point locator.
Any point object (e.g., a
Source Point or Cartesian
Monitor Point)
rmsAve(<var>)@<Location>
RMS average of <var> within a
domain.
Any 3D region (e.g., domain or
subdomain)
sum(<var>)@<Location>
Sum of <var> over all domain
or subdomain vertices.
Any 3D region (e.g., domain or
subdomain)
Operation Valid <Location>
Integrated Quantities

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Training ManualUseful Functions
• The inside() function returns 1 when inside the specified location and
0 when outside
– Useful to limit the scope of a function to a subdomain or boundary
• The step() function return 1 when the argument is positive and 0
when the argument is negative
– Useful as an on-off switch
– if() function can also be used as a switch
• areaAve() and massFlowAve() are used to evaluate the average of a
quantity on a location
– areaAve() is an area-weighted average. It is usually used on wall
boundaries and when the quantity is not “carried with the flow”, e.g.
Pressure at an outlet, Temperature on a wall
– massFlowAve() is an average weighted by the local mass flow. It is
usually used to evaluate quantities that are “carried with the flow”, e.g.
Temperature at an outlet