The EnSight calculator functions are listed below. All of the calculator functions are threaded except as follows. ElemToNode ^* , Lambda2, MassedParticle, MatSpecies, MatToScalar, NormC, OffsetVar, Q_criteria, Radiograph_grid, Radiograph_mesh, SOSConstant, StatRegVal1, StatRegVal2, TempMean, TempMinmaxField. All of the Math functions are threaded. For more details on this topic see Threading.

Variable units are discussed in a previous section (see Variable Units). The EnSight calculator is integrated into the unit system in two ways. First, variables generated via pre-defined functions and the general expression system will have appropriate unit dimensions generated for them. When the resulting variable units are unknown, or the expression is invalid, the resulting variable will appear unitless (unit dimensions = "/"). For example, the simple expression Coordinates[X] + TEMPERATURE, where TEMPERATURE has the unit dimensions K is, from a units perspective, invalid (one cannot add variables of type L and K) so the resulting variable would be unitless. Whereas the expression Coordinates[X] / TEMPERATURE is valid and will have the unit dimensions L/K.

Some predefined functions may require careful treatment. For example, consider variables: MakeScalNode(plist,1.0) which will generate a unitless variable (1.0 has no units). If one needed a nodal variable of specific dimensionality, one can first create a constant variable with the appropriate units and pass it to the predefined function. The variable resulting from MakeScalNode(plist, v) will have the same units as the constant variable v.

An additional feature of the calculator general expression system can help simplify the creation of a constant (or any variable) with specific unit dimensions. If any general expression ends with the @ symbol, the characters after the @ will be used to explicitly set the variable unit dimensions, overriding the dimensions computed by default. For example, the expression: 1.0@L/T will create a new constant with the value of 1 and the units of velocity. The calculator graphical user interface has a simple interface for previewing and setting these values.

Choose Override dimensions.

The Override dimensions menu can be used to bring up the dialog shown here as well as simply set the dimensions to common values which will be shown as follows: Velocity (@L/T) or Density (@M/LLL).

The other calculator units feature relates to the predefined function editor. In this editor, where variable selection occurs, the variables are (by default) filtered to only those variables with unit dimensions that are appropriate for the argument. For example, only the variables with M/LT dimensions are displayed for viscosity.

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Note:  Viscosity is filtered using variable dimensions.

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Unit conversions are performed as part of server I/O operations. All data in memory (client and server) will be in the session unit system. This ensures that datasets from different sources that might have overlapping variable names will always be consistently displayed in the client. One implication of this is that files saved from EnSight (context files, geometric entities export, etc) will all be written in the session unit system. For example, the geometric entities case gold file export writes out the unit system from the current session (including the metadata files), not in the original source dataset unit system.

Area (any part(s) [, Compute_Per_part])

Computes a constant or constant per part variable whose value is the area of the selected parts. If a part is composed of 3D elements, the area is of the border representation of the part. The area of 1D elements is zero.

BL_aGradOfVelMag (boundary part(s), velocity)

Computes a vector variable which is the gradient of the magnitude of the specified velocity variable on the selected boundary part(s) defined as:

where:

	on boundary part
	velocity vector
	magnitude of velocity vector =
x, y, z	coordinate directions
i, j, k	unit vectors in coordinate directions

Function Arguments

BL_CfEdge (boundary part(s), velocity, density, viscosity, ymax, flow comp(0,1,or2), grad)

Computes a scalar variable which is the edge skin-friction coefficient (that is, using the density and velocity values at the edge of the boundary layer - not the free-stream density and velocity values) defined as:

Component: 0 = Total tangential-flow (parallel) to wall:

Component: 1 = Stream-wise (flow) component tangent (parallel) to wall:

Component: 2 = Cross-flow component tangent (parallel) to wall:

where:

	fluid shear stress magnitude at the boundary
	stream-wise component of
	cross-flow component of
	dynamic viscosity of the fluid at the wall
	magnitude of the velocity-magnitude gradient in the normal direction at the wall
	stream-wise component of the velocity-magnitude gradient in the normal direction at the wall
	cross-flow component of the velocity-magnitude gradient in the normal direction at the wall
	density at the edge of the boundary layer
	velocity at the edge of the boundary layer

Function Arguments

Provides a measure of the skin-friction coefficient in the tangent (parallel to surface) direction, and in its tangent's respective stream-wise and cross-flow directions, respective to the decomposed velocity parallel to the surface at the edge of the boundary layer.

This is a non-dimensionalized measure of the fluid shear stress at the surface based on the local density and velocity at the edge of the boundary layer. The following figure illustrates the derivations of the computed 'edge' related velocity values , , & .

Figure 8.4: Figure Illustrating Derivation of Edge Velocity Related Values and Components

BL_CfWall (boundary part(s), velocity, viscosity, free density, free velocity, grad)

Computes a scalar variable which is the skin-friction coefficient , defined as:

where:

This is a non-dimensionalized measure of the fluid shear stress at the surface. An important aspect of the Skin Friction Coefficient is that indicates boundary layer separation.

Function Arguments

BL_CfWallCmp (boundary part(s), velocity, viscosity, free-stream density, free-stream velocity-mag., ymax, flow comp(1or2), grad)

Computes a scalar variable which is a component of the skin-friction coefficient Cf tangent (or parallel) to the wall, either in the stream-wise or in the cross-flow Cfc(·) direction defined as:

Component 1 = Stream-wise (flow) component tangent (parallel) to wall:

Component 2 = Cross-flow component tangent (parallel) to wall:

where:

	stream-wise component of
	cross-flow component of
	fluid shear stress magnitude at the wall
	dynamic viscosity of the fluid at the wall
	stream-wise component of the velocity-magnitude gradient in the normal direction at the wall
	cross-flow component of the velocity-magnitude gradient in the normal direction at the wall
	density at the edge of the boundary layer
	velocity at the edge of the boundary layer

Function Arguments

BL_CfWallTau (boundary part(s), velocity, viscosity, ymax, flow comp(0,1,or 2), grad).

Computes a scalar variable which is the fluid's shear-stress at the wall or in its stream-wise , or cross-flow component direction defined as:

Component 0 = Total fluid shear-stress magnitude at the wall:

Component 1 = Stream-wise component of the fluid shear-stress at the wall:

Component 2 = Cross-flow component of the fluid shear-stress at the wall:

where:

	dynamic viscosity of the fluid at the wall
	magnitude of the velocity-magnitude gradient in the normal direction at the wall
	stream-wise component of the velocity-magnitude gradient in the normal direction at the wall
	cross-flow component of the velocity-magnitude gradient in the normal direction at the wall

Function Arguments

BL_DispThick (boundary part(s), velocity, density, ymax, flow comp(0,1,or 2), grad).

Computes a scalar variable which is the boundary-layer displacement thickness , , or defined as:

Component: 0 = Total tangential-flow parallel to the wall

Component: 1 = Stream-wise flow component tangent (parallel) to the wall

Component: 2 = Cross-flow component tangent (parallel) to the wall

Provides a measure for the effect of the boundary layer on the outside flow. The boundary layer causes a displacement of the streamlines around the body.

Function Arguments

BL_DistToValue (boundary part(s), scalar, scalar value).

Computes a scalar variable which is the distance from the wall to the specified value defined as:

Function Arguments

BL_MomeThick (boundary part(s), velocity, density, ymax, flow compi(0,1,or2), flow compj(0,1,or2), grad).

Computes a scalar variable which is the boundary-layer momentum thickness , , , , or defined as:

Components: (0,0) = Total tangential-flow parallel to the wall

Components: (1,1) = stream-wise, stream-wise component

Components: (1,2) = Stream-wise, cross-flow component

Components: (2,1) = cross-flow, stream-wise component

Components: (2,2) = cross-flow, cross-flow component

where:

Relates to the momentum loss in the boundary layer.

Function Arguments

BL_Scalar (boundary part(s), velocity, scalar, ymax, grad).

Computes a scalar variable which is the scalar value of the corresponding scalar field at the edge of the boundary layer. The function extracts the scalar value while computing the boundary-layer thickness (see Boundary Layer: Thickness).

Function Arguments

BL_RecoveryThick (boundary part(s), velocity, total pressure, ymax, grad).

Computes a scalar variable which is the boundary-layer recovery thickness defined as:

This quantity does not appear in any physical conservation equations, but is sometimes used in the evaluation of inlet flows.

Function Arguments

BL_Shape is not explicitly listed in the general function list, but can be computed as a scalar variable via the calculator by dividing a displacement thickness by a momentum thickness:

Used to characterize boundary-layer flows, especially to indicate potential for separation.

This parameter increases as a separation point is approached, and varies rapidly near a separation point.

In a Blasius Laminar layer (for example, a flat plate boundary layer growth with zero pressure gradient), H = 2.605. Turbulent boundary layer, H ~= 1.4 to 1.5, with extreme variations ~= 1.2 to 2.5.

BL_Thick (boundary part(s), velocity, ymax, grad).

Computes a scalar variable which is the boundary-layer thickness defined as:

The distance normal from the surface to where: ,

.

Function Arguments

See the following references for more detailed explanations.

P.M. Gerhart, R.J. Gross, & J.I. Hochstein, Fundamentals of Fluid Mechanics, 2nd Ed.,(Addison-Wesley: New York, 1992)

P. Spalart, A Reasonable Method to Compute Boundary-Layer Parameters from Navier-Stokes Results, (Unpublished: Boeing, 1992)

H. Schlichting & K. Gersten, Boundary Layer Theory, 8th Ed., (Springer-Verlag: Berlin, 2003)

BL_VelocityAtEdge (boundary part(s), velocity, ymax,comp(0,1,2),grad).

Extracts a vector variable which is a velocity vector , , or defined as:

	= velocity vector at the edge of the boundary layer
	= the decomposed velocity vector normal to the wall at the edge of the boundary layer
	= the decomposed velocity vector parallel to the wall at the edge of the boundary layer

Computes a scalar variable which is the boundary-layer thickness defined as:

	= the decomposed velocity vector normal to the wall at the edge of the boundary layer
	= the decomposed velocity vector parallel to the wall at the edge of the boundary layer

Computes a scalar variable which is the boundary-layer thickness defined as:

BL_Y1Plus (boundary part(s), density, viscosity, grad option, vector variable).

Computes a scalar variable which is the coefficient off the wall to the first field cell centroid, defined as:

where:

Normally is used to estimate or confirm the required 1st grid spacing for proper capturing of viscous-layer properties. The values are dependent on various factors including, what variables at the wall are sought, the turbulent models used, and whether the law of the wall is used or not. Consult a boundary-layer text for correct interpolation of the values for your application.

Function Arguments

BL_Y1PlusDist (boundary part(s), velocity).

Computes a scalar variable which is the off-the-wall distance, , which is the distance off the wall to the first field cell centroid. The velocity variable is only used to determine whether the variable is nodal or elemental to maintain consistency with the calculation above.

Function Arguments

CaseMap (2D or 3D part(s), case to map from, scalar/vector/tensor, parts to map from, search option flag)

For all locations on the selected part(s) this function finds the specified variable value (scalar, vector, or tensor) from the case to map from using a variety of user-specified search options. If the variable in the case to map from is located at the nodes, then the casemapped variable will be defined on the nodes of the selected part(s), and if the variable is located at the elements, then the casemapped variable will be defined at the elements of the selected part(s).

The idea is to map onto the selected part(s), a variable from another case, usually for comparison purposes. It does this by taking the location of the nodes or centroid of the elements and looking at the other case to see if the variable in question is defined at that location in the field. If so, the value is mapped to the parts nodes or element value. The algorithm can be fairly expensive, so there are options to inform the search that finds a matching variable location.

There are several options available in this function that can greatly impact the performance as follows.

CaseMapDiff (2D or 3D part(s), case to map from, scalar/vector/tensor, 0/1 0=search only 1=if search fails find closest)

This function is equivalent to Variable - CaseMap[Variable]. See CaseMap function for details on how that function works.

See Compare Cases.

CaseMapImage (2D or 3D part(s), part to map from, scalar, viewport number, Undefined value limit)

This Function does a projection of a 2D part variable from a different case onto a 3D geometry taking into account the view orientation from the specified viewport number, similar to a texture mapping. The function in effect maps 2D results to a 3d geometry taking into account view orientation and surface visibility.

Function Arguments

Coeff (any 1D or 2D part(s), scalar, component)

Computes a constant or constant per part variable whose value is a coefficient , , or such that , ,

where:

Function Arguments

Specify [X], [Y], or [Z] to get the corresponding coefficient.

Cmplx (any part(s), scalar/vector(real portion), scalar/vector(complex portion), [optional frequency(Degrees)])

Creates a complex scalar or vector from two scalar or vector variables. The frequency is optional and is used only for reference.

Z = A + Bi

Function Arguments

CmplxArg (any part(s), complex scalar or vector)

Computes the Argument of a complex scalar or vector. The resulting scalar is given in degrees and will be in the range -180 and 180 degrees.

CmplxConj (any part(s), complex scalar or vector)

Computes the Conjugate of a complex scalar of vector. Returns a complex scalar or vector where:

CmplxImag (any part(s), complex scalar or vector)

Extracts imaginary portion of a complex scalar or vector into a real scalar or vector.

CmplxModu (any part(s), complex scalar or vector)

Returns a real scalar/vector which is the modulus of the given scalar/vector

CmplxReal (any part(s), complex scalar or vector)

Extracts the real portion of a complex scalar or vector into a real scalar or vector.

CmplxTransResp (any part(s), complex scalar or vector, constant PHI(0.0-360.0 Degrees))

Returns a real scalar or vector which is the real transient response:

which is a function of the transient phase angle defined by:

where:

t	the harmonic response time parameter
f	frequency of the complex variable

and the complex field , defined as:

where:

Function Arguments

ConstPerPart (any part(s), constant)

This function is assigns a value to the selected part(s). The value can either be a floating point value entered into the field, or it can be a case constant. This value does not change over time. At a later point, any other part(s) can be selected and this can be recalculated and these other part(s) will be assigned the new value and the exisiting part(s) that were previously selected will retain their previously assigned value. Each successive time that this is recalculated for an existing variable, values assigned to the most recently selected parts are updated without removing previously assigned values.

Curl (any part(s), vector)

Computes a vector variable which is the curl of the input vector

Consider a mesh with a scalar per element variable representing the micro porosity of each cell, where 0 means no porosity (the cell is completely full) and 100 means the cell is fully porous (the cell is empty). Cells with a non zero porosity are considered to have defects. Defects that span multiple cells may indicate an unacceptable defect.

Six Defect functions are provided to help calculate factors of interest in characterizing these defects that occur over multiple cells. To use the Defect_* functions, you would create an isovolume of your porosity variable between desired ranges (perhaps 5 to 100) and select this isovolume part..

Density (any part(s), pressure, temperature, gas constant)

Computes a scalar variable which is the density , defined as:

where:

	pressure
	temperature
	gas constant

Function Arguments

DensityLogNorm (any part(s), density, freestream density)

Computes a scalar variable which is the natural log of Normalized Density defined as:

where:

	density
	freestream density

Function Arguments

DensityNorm (any part(s), density, freestream density)

Computes a scalar variable which is the Normalized Density defined as:

where:

	density
	freestream density

Function Arguments

DensityNormStag (any part(s), density, total energy, velocity, ratio of specific heats, freestream density, freestream speed of sound, freestream velocity magnitude)

Computes a scalar variable which is the Normalized Stagnation Density defined as:

where:

	stagnation density
	freestream stagnation density

where:

DensityStag (any part(s), density, total energy, velocity, ratio of specific heats)

Computes a scalar variable which is the Stagnation Density defined as:

where:

	density
	ratio of specific heats
	mach number

Function Arguments

Dist2Nodes (any part(s), nodeID1,nodeID2)

Computes a constant, positive variable that is the distance between any two nodes. Searches down the part list until it finds nodeID1, then searches until it finds nodeID2 and returns Undef if nodeID1 or nodeID2 cannot be found. Nodes are designated by their node ID's, so the part must have node IDs.

Function Arguments

Dist2Part (origin part + field part(s), origin part, origin part normal)

Computes a scalar variable on the origin part and field parts that is the minimum distance at each node of the origin and field parts to any node in the origin part. This distance is unsigned by default. The origin part is the origin of a Euclidean distance field. So, by definition the scalar variable will always be zero at the origin part because the distance to the origin part will always be zero.

The origin part normal vector must be a per node variable. If the origin part normal is calculated using the Normal calculator function, then it is a per element variable and must be moved to the nodes using the calculator ElemToNode function. If this per node, origin part normal vector variable defined at the origin part is supplied then the normal vector is used to return a signed distance function (with positive being the direction of the normal). The signed distance is determined using the dot product of the vector from the given field node and its closest node on the origin with the origin node's normal vector.

This function is computed between the nodes of the origin and field parts. As a result, the accuracy of its approximation to the distance field is limited to the density of nodes (effectively the size of the elements) in the origin part. If a more accurate approximation is required, use the Dist2PartElem() function. It is slower, but is less dependent on the nodal distribution in the origin part because it uses the nodes plus the element faces to calculate the minimum distance.

Usage: A typical usage would be to use an arbitrary 2D part to create a clip in a 3D field. Use the 2D part as your origin part, and select the origin part as well as your 3D field parts. No need to have normal vectors. Create your scalar variable, called say distTo2Dpart, then create an isosurface=0 in your field using the distTo2Dpart as your variable.

Function Arguments

Dist2PartElem (origin part + field part(s), origin part, origin part normal)

Computes a scalar variable that is the minimum distance at each node of the origin part and field parts and the closest point on any element in origin part. This distance is unsigned (if the origin part normal vector is not supplied).

If the origin part normal vector is supplied, then the distance is signed.

Once the closest point in the origin part has been found for a node in an field part, the dot product of the origin node normal and a vector between the two nodes is used to select the sign of the result.

This function is a more accurate estimation of the distance field than Dist2Part() because it allows for distances between nodes and element surfaces on the origin part. This improved accuracy results in increased computational complexity and as a result this function can be several times slower than Dist2Part().

Function Arguments

Div (2D or 3D part(s), vector)

Computes a scalar variable whose value is the divergence defined as:

where:

EleMetric (any part(s), metric_function).

Calculates an element mesh metric, at each element creating a scalar, element-based variable depending upon the selected metric function. The various metrics are valid for specific element types. If the element is not of the type supported by the metric function, the value at the element will be the EnSight undefined value. Metrics exist for the following element types: tri, quad, tet, and hex. A metric can be any one of the following:

EnSight Element types:

The implementation is based on the BSD implementation of the Sandia Verdict Library. See the following links:

http://cubit.sandia.gov/public/documents/Verde_UG-2.5B.pdf Verde User's Manual

Verdict Mesh Verification Library

Detail of Elemetric Equations

For more detail on individual metrics, see the following reference:

C. J. Stimpson, C. D. Ernst, P. Knupp, P. P. Pebay, & D. Thompson, The Verdict Library Reference Manual, May 8, 2007.

EleSize (any part(s)).

Calculates the Volume/Area/Length for 3D/2D/1D elements respectively, at each element creating a scalar, element-based variable.

ElemToNode (any part(s), element-based scalar or vector).

Averages an element based variable to produce a node-based variable.

For each node[i] →

For each node[i] →

Results: node[i] →

where:

By default, this uses all parts that share each node of the selected part(s). So, parts that are not selected whose elements are shared by nodes of the selected part(s) will have their element values averaged in with those of the selected parts.

ElemToNodeWeighted (any part(s), element-based scalar or vector, element-based weighting scalar).

Same as ElementToNode, except that the value of the variable at the element is weighted by an element scalar. That is, elem[j]->wt is the value of the weighting scalar in the ElemToNode algorithm description above.

One use of this function might be to use the element size as a weighting factor so that larger elements contribute more to the nodal value than smaller ones.

EnergyT (any part(s), density, pressure, velocity, ratio of specific heats).

Computes a scalar variable of total energy per unit volume.

	Total Energy
	Internal Energy
	Stagnation Energy
	density
	velocity

Or based on gamma, pressure and velocity:

Function Arguments

KinEn (any part(s), velocity, density)

Computes a scalar variable whose value is the kinetic energy defined as:

where:

	density
	velocity variable

Function Arguments

Enthalpy (any part(s), density, total energy, velocity, ratio of specific heats)

Computes a scalar variable which is Enthalpy defined as:

	total energy per unit volume
	density
	velocity magnitude
	ratio of specific heats

Function Arguments

EnthalpyNorm (any part(s), density, total energy, velocity, ratio of specific heats, freestream density, freestream speed of sound)

Computes a scalar variable which is Normalized Enthalpy defined as:

	enthalpy
	freestream enthalpy

Function Arguments

EnthalpyStag (any part(s), density, total energy, velocity, ratio of specific heats)

Computes a scalar variable which is Stagnation Enthalpy defined as:

	enthalpy
	velocity magnitude

EnthalpyNormStag (any part(s), density, total energy, velocity, ratio of specific heats, freestream density, freestream speed of sound, freestream velocity magnitude)

Computes a scalar variable which is Normalized Stagnation Enthalpy defined as:

	stagnation enthalpy
=	freestream stagnation enthalpy

Entropy (any part(s), density, total energy, velocity, ratio of specific heats, gas constant, freestream density, freestream speed of sound)

Computes a scalar variable which is Entropy defined as:

where:

where pressure, is calculated from the total energy, , and velocity

with freestream pressure,

Function Arguments

Flow (any 1D or 2D part(s), velocity [,Compute_Per_part]).

Computes a constant or constant per part variable whose value is the volume flow rate defined as:

where:

	Velocity vector
	Unit vector normal to surface
	1D or 2D domain

Function Arguments

FlowRate (any 1D or 2D part(s), velocity).

Computes a scalar which is the component of velocity normal to the surface, defined as:

where:

	Velocity
	Unit vector normal to surface
	1D or 2D

Function Arguments

FluidShear (2D part(s), velocity magnitude gradient, viscosity)

Computes a scalar variable tau whose value is defined as:

where:

	shear stress
	dynamic viscosity
	Velocity gradient in direction of surface normal

Function Arguments

FluidShearMax (2D or 3D part(s), velocity, density, turbulent kinetic energy, turbulent dissipation, laminar viscosity)

Computes a scalar variable defined as:

where:

	force
	unit area
	turbulent (eddy) viscosity
	laminar viscosity (treated as a constant)
	local strain

The turbulent viscosity is defined as:

where:

	density
	turbulent kinetic energy
	turbulent dissipation

A measure of local strain (local elongation in 3 directions) is given by

where:

given the Euclidean norm defined by

;

and the rate of deformation tensor defined by

with:

given the strain tensor defined by

Function Arguments

Force (2D part(s), pressure)

Computes a vector variable whose value is the force defined as:

where:

	pressure
	unit area

Function Arguments

Force1D (1D planar part(s), pressure, surface normal)

Computes a vector variable whose value is the force defined as:

where:

	pressure
	unit length normal vector

Function Arguments

Grad (2D or 3D part(s), scalar or vector(Magnitude will be used))

Computes a vector variable whose value is the gradient defined as:

where:

	any scalar variable (or the magnitude of the specified vector)
	coordinate directions
	unit vectors in coordinate directions

Algorithm

If the variable is at the element, then it is moved to the nodes. Then each element is mapped to a normalized element and the Jacobian is calculated for the transformation from the element to the normalized element; and then, its inverse Jacobian is calculated for this transformation and used to compute the Jacobian for the scalar variable. Therefore, the chain rule is used with the inverse Jacobian of the transformation and the Jacobian of the scalar variable to calculate the gradient for each node of each element. The contributions of the gradient from all the elements are moved to all the nodes using an unweighted average. Finally, if the original variable is per element, the gradient is moved from the nodes to the elements using an unweighted average.

GradTensor (2D or 3D part(s), vector)

Computes a tensor variable whose value is the gradient defined as:

where:

	any vector variable
	coordinate directions
	unit vectors in coordinate directions

HelicityDensity (any part(s), velocity)

Computes a scalar variable whose value is:

where:

	velocity
	vorticity

Function Arguments

HelicityRelative (any part(s), velocity)

Computes a scalar variable whose value is:

where:

	the angle between the velocity vector and the vorticity vector
V	velocity
Ω	vorticity

Function Arguments

HelicityRelFilter (any part(s), velocity, freestream velocity magnitude).

Computes a scalar variable whose value is:

, if or , if

where:

	relative helicity (as described above)
	helicity density (as described above)
filter	0.1(V∞)2

Function Arguments

IblankingValues (Any iblanked structured part(s))

Computes a scalar variable whose value is the iblanking flag of selected parts. Returns undefined for unstructured part(s).

IJKValues (Any structured part(s))

Computes a vector variable whose value is the I/J/K values of the selected parts. Returns undefined for unstructured part(s).

IntegralLine (1D part(s), scalar or (vector, component) [,Compute_Per_part])

Computes a constant or constant per part variable whose value is the integral of the input variable over the length of the specified 1D part(s). Nodal variables are first converted to elemental variable using a weighted average of the shape function.

IntegralSurface (2D part(s), scalar or (vector, component) [,Compute_Per_part])

Computes a constant or constant per part variable whose value is the integral of the input variable over the surface of the specified 2D part(s). Nodal variables are first converted to elemental variable using a weighted average of the shape function.

IntegralVolume (3D part(s), scalar or (vector, component) [,Compute_Per_part])

Computes a constant or constant per part variable whose value is the integral of the input variable over the volume of the specified 3D part(s). Nodal variables are first converted to elemental variable using a weighted average of the shape function.

Length (any 1D part(s) [,Compute_Per_part])

Computes a constant or constant per part variable whose value is the length of selected parts. While any part can be specified, it will only return a nonzero length if the part has 1D elements.

See Integrals: Line Integral.

LineVectors (any 1D part(s))

Computes a nodal, vector variable which is the

Lambda2 (any part(s), Grad_Vel_x, Grad_Vel_y, Grad_Vel_z)

Computes a scalar variable which is the second eigenvalue, or , of the second invariant (or Q-criterion) of the velocity gradient tensor. Vortex shells may then be visualized as an iso-surface of = 0. The following describes the calculation of the inputs to this function:

Explicitly calculate the three components of Velocity

Vel_x = Velocity[X] = x-component of the velocity vector

Vel_y = Velocity[Y] = y-component of the velocity vector

Vel_z = Velocity[Z] = z-component of the velocity vector

and then

Grad_Vel_x = Grad(any part(s), Vel_x) = gradient of x component Velocity

Grad_Vel_y = Grad(any part(s), Vel_y) = gradient of y component Velocity

Grad_Vel_z = Grad(any part(s), Vel_z) = gradient of z component Velocity

where:

Algorithm

The three gradient vectors of the components of the velocity vector constitute the velocity gradient tensor. Using the 9 components of this (anti-symmetric) velocity gradient tensor, Lv, construct both the symmetric, S, and the anti-symmetric, , parts of the velocity gradient tensor,

where:

Ω

then combine to compute the symmetric tensor

Next compute and sort the eigenvalues of (using Jacobi eigen analysis), and assign the 2nd eigenvalue, or , as the scalar value at the node.

The vortex is to be visualized as an iso-surface with

See also the Q_criteria calculator function.

References

Haller, G., "An objective definition of a vortex," Journal of Fluid Mechanics, 2005, vol. 525, pp. 1-26.

Jeong, J. and Hussain, F., "On the identification of a vortex," Journal of Fluid Mechanics, 1995, vol. 285, pp. 69-94.

Mach (any part(s), density, total energy, velocity, ratio of specific heats)

Computes a scalar variable whose value is the Mach number defined as:

where:

	momentum
	density
	speed, computed from velocity input.
	ratio of specific heats (1.4 for air)
	pressure (see Pressure below)
	speed of sound

See Energy: Total Energy for a description.

Function Arguments

MakeScalElem (any part(s), constant number or constant or constant per part variable)

Assigns the specified constant value to each element, making a scalar variable.

MakeScalElemId (any part(s))

Creates a scalar variable set to the element IDs of the part. If the element ID does not exist or is undefined the scalar value is set to the Undefined value.

MakeScalNode (any part(s), constant number or constant or constant per part variable)

Assigns the specified constant value to each node, making a scalar variable.

MakeScalNodeId (any part(s))

Creates a scalar variable set to the node IDs of the part. If the node ID does not exist or is undefined the scalar value is set to the Undefined value.

MakeVect (any part(s), scalar or zero, scalar or zero, scalar or zero)

Computes a vector variable formed from scalar variables. First scalar becomes the X component of the vector, second scalar becomes the Y component, and the third scalar becomes the Z component. A zero can be specified for some of the scalars, creating a 2D or 1D vector field.

MassedParticle (massed particle trace part(s))

This scalar creates a massed-particle per element scalar variable for each of the parent parts of the massed-particle traces. This per element variable is the mass of the particle times the sum of the number of times each element is exited by a mass-particle trace. See Particle-Mass Scalar on Boundaries.

MassFluxAvg (any 1D or 2D part(s), scalar, velocity, density [,Compute_Per_part])

Computes a constant or constant per part variable whose value is the mass flux average defined as:

where:

	any scalar variable, (pressure, mach, a vector component, and so on)
	density (constant or scalar) variable
	velocity (vector) variable
	area of some 2D domain
	unit vector normal to

Function Arguments

MatSpecies (any model part(s), any material(s), any specie(s), scalar per element).

Computes a scalar per element variable whose value is the sum of all specified material and species combinations multiplied by the specified element variable on specified 'model' parts with defined material species.

where:

	scalar per element variable value or value
	The product of the material fraction and its corresponding specie value 0, if specie does not exist for material if no species are specified

This function only operates on model part(s) with pre-defined species. The specified material(s) can either be a list of materials or a single material value. The specified species can either be a list, a single specie, or no specie (for example, a null species list which then computes an element value based on only material fraction contributions). The scalar per element value can either be an active variable, or a scalar value (for example, the value 1 would give pure material fraction and/or specie value extraction).

Both material and specie names are selected from the context sensitive Active Variables list which changes to a Materials list and then a Species List for their respective prompts.

For more information on Species see both Material Section and Example Material Dataset (With Species).

MatToScalar (any model part(s), a material)

Computes a scalar per element variable whose value s is the specified material's value m of the element on the specified part(s).

s = m

where:

This function only operates on model part(s) with pre-defined materials that are given by sparse mixed material definitions. Only one material may be converted into one per element scalar variable at a time. The material cannot be the null material.

For more information on Materials,(see Material Interface Parts), and both MATERIAL Sections under EnSight Gold Case File Format, and Example Material Dataset in Utility Programs.

Max (any part(s), scalar or (vector, component))

Computes a constant or constant per part variable whose value is the maximum value of the scalar (or vector component) in the parts selected. The component is not requested if a scalar is selected.

Min (any part(s), scalar or (vector, component))

Computes a constant or constant per part variable whose value is the minimum value of the scalar (or vector component) in the parts selected.

Moment (any part(s), vector, component)

Computes a constant or constant per part variable (the moment about the cursor tool location) whose value is the x, y, or z component of Moment .

where:

	force vector component in direction i of vector
	signed moment arm (the perpendicular distance from the line of action of the vector component to the moment axis (which is the current cursor tool position)).
vector	any vector variable
component	[X], [Y], or [Z]

MomentVector (any part(s), force vector).

Computes a nodal vector variable (the moment is computed about each point of the selected parts) whose value is the x, y, or z component of Moment .

where:

	force vector component in direction i of vector
	signed moment arm (the perpendicular distance from the line of action of the vector component to the moment axis (model point position)).

Function Arguments

Momentum (any part(s), velocity, density).

Computes a vector variable , which is:

where:

	density
	velocity

Function Arguments

NodeCount (any part(s) [,Compute_Per_part])

Produces a constant or constant per part variable containing the node count of the part(s) specified.

NodeToElem (any part(s), node-based scalar or vector)

Averages a node based variable to produce an element based variable.

For each: elem[j]->val += node[i]->val | elem[j]

Results: elem[j]->val /= elem[j]->num_cell_nodes

where:

Normal (2D part(s) or 1D planar part(s))

Computes a vector variable which is the normal to the surface at each element for 2D parts, or for 1D planar parts - lies normal to the 1D elements in the plane of the part.

NormC (2D or 3D part(s), pressure, velocity, viscosity [,Compute_Per_part])

Computes a constant or constant per part variable whose value is the Normal Constraints defined as:

where:

	pressure
	velocity
	dynamic viscosity
	direction of normal
	border of a 2D or 3D domain

Function Arguments

NormVect (any part(s), vector)

Computes a vector variable whose value is a unit vector of the given vector .

	vector variable field

OffsetField (2D or 3D part(s))

Computes a scalar field of offset values. The values will be in model distance units perpendicular to the boundary of the part.

OffsetVar (2D or 3D part(s), scalar or vector, constant offset value)

Computes a scalar (or vector) variable defined as the offset value into the field of that variable that exists in the normal direction from the boundary of the selected part. This assigns near surface values of a variable to the surface of the selected part(s) from the neighboring 3D field (which is found automatically using the selected part(s) surface(s).

This function gets the value of a variable from surrounding field(s), a fixed distance from the surface of the selected part(s) and assigns it to the surface fo the selected part. For example, you might use this function to get the value of the velocity in the flow field a slight distance above your vehicle surface and assign that value to your vehicle surface.

To use this function, select part(s) in the part list that you want to use, enter a variable and an offset. EnSight will auto detect the 3D field part(s) adjacent to your selected part(s) surface(s) and reach into these fields by your offset in the normal direction to obtain the variable value and then assign it to the surface of your selected part(s).

Function Arguments

PartNumber (any part(s) [,Compute_Per_part])

Computes a constant per part variable which is the GUI part number, if the part is a server-side part. If computed as ‘Compute_Per_case’, the value will be the maximum part number.

Pres (any part(s),density, total energy, velocity, ratio of specific heats)

Computes a scalar variable whose value is the pressure defined as:

	momentum
	total energy
	density
	velocity
	ratio of specific heats (1.4 for air)

Function Arguments

PresCoef (any part(s), density, total energy, velocity, ratio of specific heats, freestream density, freestream speed of sound, freestream velocity magnitude)

Computes a scalar variable which is Pressure Coefficient defined as:

	pressure
	freestream pressure
	freestream density
	freestream velocity magnitude

Function Arguments

PresDynam (any part(s), density, velocity)

Computes a scalar variable which is Dynamic Pressure defined as:

See Kinetic Energy.

Function Arguments

PresNorm (any part(s), density, velocity, ratio of specific heats, freestream density, freestream speed of sound)

Computes a scalar variable which is Normalized Pressure defined as:

where:

	freestream pressure =
	ratio of specific heats
	pressure

Function Arguments

PresLogNorm (any part(s), density, total energy, velocity, ratio of specific heats, freestream density, freestream speed of sound)

Computes a scalar variable which is the natural log of Normalized Pressure defined as:

	freestream pressure =
	ratio of specific heats
	pressure

Function Arguments

PresStag (any part(s), density, total energy, velocity, ratio of specific heats)

Computes a scalar variable which is the Stagnation Pressure defined as:

Function Arguments

PresNormStag (any part(s), density, total energy, velocity, ratio of specific heats, freestream density, freestream speed of sound, freestream velocity magnitude)

Computes a scalar variable which is Normalized Stagnation Pressure

defined as:

where:

	stagnation pressure
	freestream stagnation pressure

Function Arguments

PresStagCoef (any part(s), density, total energy, velocity, ratio of specific heats, freestream density, freestream speed of sound, freestream velocity magnitude)

Computes a scalar variable which is Stagnation Pressure Coefficient

defined as:

where:

	stagnation pressure
	freestream pressure =
	ratio of specific heats
	freestream density
	velocity magnitude

Function Arguments

PresPitot (any part(s), density, total energy, velocity, ratio of specific heats)

Computes a scalar variable which is Pitot Pressure defined as:

where:

	ratio of specific heats
	total energy per unit volume
	density
	velocity magnitude
	pressure

Function Arguments

PresPitotRatio (any part(s), density, total energy, velocity, ratio of specific heats, freestream density, freestream speed of sound)

Computes a scalar variable which is Pitot Pressure Ratio defined as:

where:

	(defined above in Pitot Pressure)
	ratio of specific heats
	total energy per unit volume
	density
	velocity magnitude

Function Arguments

PresT (any part(s), pressure, velocity, density)

Computes a scalar variable whose value is the total pressure defined as:

where:

	density
	velocity
	pressure

Function Arguments

Q_criteria (any part(s), Grad_Vel_x, Grad_Vel_y, Grad_Vel_z)

Computes a scalar variable which is the second invariant, or Q-criterion, of the velocity gradient tensor. Vortex shells may then be visualized as an iso-surface of Q-criterion > 0. The following describes the calculation of the inputs to this function:

First, calculate the intermediate variable:

Vel_x = Velocity[X] = x-component of the velocity vector

Vel_y = Velocity[Y] = y-component of the velocity vector

Vel_z = Velocity[Z] = z-component of the velocity vector

Then calculate the gradient using the intermediate variable:

Grad_Vel_x = Grad(any part(s), Vel_x) = gradient of x component Velocity

Grad_Vel_y = Grad(any part(s), Vel_y) = gradient of y component Velocity

Grad_Vel_z = Grad(any part(s), Vel_z) = gradient of z component Velocity

with

Velocity = velocity vector variable

Algorithm

The three gradient vectors of the components of the velocity vector constitute the velocity gradient tensor. Using the nine components of this (anti-symmetric) velocity gradient tensor, Lv, construct both the symmetric, , and the anti-symmetric, , parts of the velocity gradient tensor, the criteria is established as follows.

where

solving for (hence criteria) when

which (in terms of our EnSight variables) reduces to:

Q = - 0.5 * ( Grad_Vel_x[X] * Grad_vel_x[X] + Grad_Vel_y[Y] * Grad_vel_y[Y] + Grad_Vel_z[Z] * Grad_Vel_z[Z] + 2 * (Grad_Vel_x[Y] * Grad_Vel_y[X] + Grad_Vel_x[Z] * Grad_Vel_z[X] + Grad_Vel_y[Z] * Grad_Vel_z[Y])) > 0

Now, to find the vortices, create an isosurface where Q is positive (Q > 0). This is because an isosurface with positive Q isolates areas where the strength of the rotation overcomes the strain, making those surfaces eligible as vortex envelopes.

See also the Lambda2 calculator function.

References

Dubief, Y and Delcayre, F., "On coherent-vortex identification in turbulence", Journal of Turbulence, (jot.iop.org) 1 (2000) 11, pp.1-22.

Haller, G., "An objective definition of a vortex," Journal of Fluid Mechanics, 2005, vol. 525, pp. 1-26.

Jeong, J. and Hussain, F., "On the identification of a vortex," Journal of Fluid Mechanics, 1995, vol. 285, pp. 69-94.

Radiograph_grid (1D or 2D part(s), dir X, dir Y, dir Z, num_points, variable, [component])

Computes a per element scalar variable on the designated 1D or 2D parts, that is a directional integration from these parts of a scalar variable or vector component through the model.

Think of rays being cast from the center of each element of the 1D or 2D parents in the direction specified (and long enough to extend through the model). Along each ray, the desired variable is integrated and the integral value is assigned to the element from which the ray was cast. This function integrates the ray in a constant delta, grid-like fashion. You control the delta by the number of points that is specified in the integration direction.

Function Arguments

Advanced usage: set the following environmental variable ENSIGHT_RADIOGRAPH_OPTION to 0 which integrates the ray (default), or 1 which finds min along ray, or 2 which finds max along ray.

Radiograph_mesh (1D or 2D part(s), dir X, dir Y, dir Z, variable, [component])

Computes a per element scalar variable on the designated 1D or 2D parts, that is a directional integration from these parts of a scalar variable or vector component through the model. Think of rays being cast from the center of each element of the 1D or 2D parents in the direction specified (and long enough to extend through the model). Along each ray the desired variable is integrated and the integral value is assigned to the element from which the ray was cast. This function integrates the ray at each domain element face intersection.

Function Arguments

Advanced usage: set the following environmental variable ENSIGHT_RADIOGRAPH_OPTION to 0 which integrates the ray (default), or 1 which finds min along ray, or 2 which finds max along ray.

RectToCyl (any part(s), vector)

Produces a vector variable with cylindrical components according to frame 0.

(Intended for calculation purposes)

x = radial component, y = tangential component, z = z component

ServerNumber (any part(s))

Produces a per-element scalar variable that is the server number containing the element. This function is useful for decomposed models using Server of Servers (SOS) mode so that the distribution can be visualized.

ShockPlot3d (2D or 3D part(s), density, total energy, velocity, ratio of specific heats)

Computes a scalar variable ShockPlot3d, whose value is:

where:

	velocity
	speed of sound
	pressure
	gradient of pressure

Function Arguments

To compute candidate shock surface(s), create an isosurface of the calculated variable, shockplot3d = 1.0. These shock region(s) can be verified by overlaying them with

Also consider comparing with the Shock Region/Surface feature visualization.

Shock Regions/Surfaces Parts.

SmoothMesh (any 1D or 2D part(s), number of passes, weight)

Performs a mesh “smoothing” operation. This function returns a vector variable which, when applied to the mesh as a displacement, results in a “smoother” mesh representation. The function computes new node locations resulting from a “normalization” of the mesh elements.

The result of this function tends to be a mesh with equal-sized elements. The algorithm applies a form of convolution to the mesh edges repeatedly (number of passes) using a weighting factor to control how much change in position is allowed in each pass. In most cases, the weight is supplied as a constant, but the weight can be specified as a nodal scalar array. This allows for local control over the region of the mesh to be smoothed. The algorithm is fully threaded.

For each pass, the following formula is applied:

where = nodal position at pass (i)

= nodal weight

= edge connected nodes

Function Arguments

SOSConstant (any part(s), variable, reduction operation (0-3))

Computes a constant variable whose value is the result of applying a reduction operation on that constant variable over the values on each of the servers. If there is no SOS involved or only a single server, the result is the same as the constant variable value on the single server.

The selected part is used to select the case from which the constant variable is used. The constant variable itself is specified (from the dataset or a computed value). The operation to perform is selected as an integer from 0 to 3:

Function Arguments

SpaMean (any part(s), scalar or (vector, component) [,Compute_Per_part])

Computes a constant or constant per part variable whose value is the volume (or area or length) weighted mean value of a scalar (or vector component) at the current time. This value can change with time. The component is not requested if a scalar variable is used

The spatial mean is computed by summing the product of the volume (3D, or area 2D, or length 1D) of each element by the value of the scalar (or vector component) taken at the centroid of the element (nodal variables are interpolated at each cell centroid using cell shape blending or metric functions), for each element over the entire part. The final sum is then divided by the total volume (or area) of the part.

where: = Scalar taken at centroid of element i

= Volume (or Area, or Length) of element i

Function Arguments

SpaMeanWeighted (any part(s), scalar or (vector, component), weight, component [,Compute_Per_part])

Computes a constant or constant per part variable whose value is weighted both by the volume (or area or length) and a weighting variable. This value can change with time. For both the variable itself and the weighting variable, the component is not requested if a scalar variable is used.

The weighted spatial mean is computed by summing the product of the volume (3D, area 2D, or length if 1D) of each element by the value of the scalar (or vector component) taken at the centroid of the element (nodal variables are interpolated at each cell centroid using cell shape blending or metric functions) with the product of the weighting scalar/vector component taken at the centroid of the element (again, if a nodal variable, similarly evaluated at the element centroid) for each element over the entire part. The final sum is then divided by the total scalar/vector weighted (again if a nodal weighting variable is similarly evaluated at the element centroid) volume (or area or length) of the part as follows:

where: = Scalar or vector component taken at centroid of element i

where: = Scalar or vector component taken at centroid of element i

= Volume (or Area, or Length) of element i

Function Arguments

Speed (any part(s), velocity)

Computes a scalar variable whose value is the speed. This function is defined as:

where: = velocity components in the directions.

Function Arguments

SonicSpeed (any part(s), density, total energy, velocity, ratio of specific heats).

Computes a scalar variable , whose value is:

where = ratio of specific heats