Flow Field Functions Reference

Absolute Pressure

The sum of the working pressure, the reference pressure, and, when gravity is present, the hydrostatic pressure. It is used to obtain density by the Ideal Gas Law, Eqn. (671).

Absolute Total Pressure

The pressure that results from isentropically bringing the flow to rest in the absolute frame of motion.

For ideal gas:

P_{t,abs} = P_{abs} {(1 + \frac{γ - 1}{2} M^{2})}^{γ / (γ - 1)}

where $γ$ is the ratio of specific heats and $M$ is the Mach number.

For incompressible fluid:

P_{t,abs} = P_{abs} + \frac{1}{2} ρ v^{2}

For alternate equations of state, or a non-constant specific heat, $P_{t,abs}$ is obtained by integrating $d h = d P / ρ$ from static conditions to total conditions.

Axial Velocity

The axial component of velocity

v_{a x}

relative to the axis and origin in the coordinate system given under the Axis node of the region.

This field function is not available in Eulerian multiphase models for 3-D cases.

Cell Relative Velocity

The fluid flow velocity at the cell centroid relative to the cell centroid due to motion.

CFL Number (CF)

The CFL number controlled by the expert driver.

Convective Courant Number

For unsteady simulations, the local convective Courant number, which is the ratio of the physical time-step to the mesh convection time scale,

Δ t / (d x / V)

V * Δ t / d x

. For moving mesh cases,

V

is the velocity relative to the mesh.

When you use this field function in a Eulerian multiphase model, it plots the value for the phase that has the maximum convective Courant number in a cell.

Density

The density of the fluid.

Effective Volume

Explicit relaxation factor

Flow Direction

Defined on any boundary that has a Flow Direction physics condition. For each Flow Direction option, it gives a vector which is parallel to the flow direction specification. See the Flow Direction boundary value.

Helicity

The scalar defined by

H = V \cdot Ω

where

V

is velocity and

Ω

is vorticity.

Lamb Vector

The cross product of velocity and vorticity, which is defined as

L \equiv v \times \nabla \times v

Lambda 2 Criterion

The scalar defined by the second eigenvalue of

(S^{2} + Ω^{2})

when sorted from minimum to maximum, where

S

is the strain-rate tensor and

Ω

is the spin tensor. Values of

λ_{2} < 0

can be interpreted as vortex regions, while values equal to or greater than 0 have no physical interpretation.

Local Time Step

The time-step used in the cell under consideration.

Mass Flow Rate

The rate at which mass flows through a boundary.

Mass Flux

The face mass flux,

{\dot{m}}_{f}

Mass Imbalance

The imbalance of mass in any cell that results from evaluating the discrete continuity equation at the given iteration or time-step. For incompressible flows with no source terms this equation reduces to

\sum_{f}^{} {\dot{m}}_{f}

for each cell.

Number of AMG cycles, for Expert-Driver (CF, with Expert Driver enabled)

Pressure

The working pressure that is the solution variable in the flow models in Simcenter STAR-CCM+. It is the quantity

p

in Eqn. (947).

Pressure Coefficient

The pressure coefficient is defined as:

C_{p} = (p - p_{ref}) / (\frac{1}{2} ρ_{ref} v_{ref}^{2})

where

p_{ref}

ρ_{ref}

, and

v_{ref}

are the Reference Pressure (gauge), Reference Density, and Reference Velocity that you specify in the field function, respectively.

This field function is not available in Eulerian multiphase models.

PressureGrad

The pressure gradient

Δ P

times the cell volume. This becomes available when you activate the Coupled Solver and the Temporary Storage property.

Q Criterion

The scalar value defined by:

$Q := \frac{1}{2} ({‖ Ω ‖}^{2} - {‖ S ‖}^{2})$

where $Ω$ is the spin tensor and $S$ is the strain-rate tensor. Where positive, this is vorticity-dominated flow; a negative value implies strain-dominated.

Radial Velocity

The radial component of velocity

v_{r}

relative to the axis and origin in the coordinate system given under the Axis node of the region.

This field function is not available in Eulerian multiphase models for axisymmetric cases.

Reference Velocity (CF)

Relative Tangential Velocity

Relative Total Pressure

The pressure that is obtained from isentropically bringing the flow to rest in the relative frame of motion.

This field function is not available in Eulerian multiphase models.

Rhie-Chow Unsteady Scale

For unsteady simulations, based on the value of Limiting Acoustic-CFL that you specify when Unsteady Flux Dissipation Corrections is activated, the Segregated Flow model computes the scale to adjust numerical dissipation and so reduce or even eliminate spurious numerical noise due to the insufficient Rhie-Chow dissipation at very small time-steps.

Make sure that the scale is of value 1 in the regions where physical sound sources are generated; these must be preserved accurately. Make sure the scale is less than 1 (or much less than 1) outside these regions, which should include the region where spurious noise occurs—typically at larger cells or at cell-size jump interfaces when the time-step is very small.

To extend the region where the Rhie-Chow scale is 1 (no numerical corrections applied), lower the value of Limiting Acoustic-CFL.
To increase the region where the solver applies numerical corrections to mitigate spurious noise (Rhie-Chow scale is less than 1), increase the value of Limiting Acoustic-CFL.

This field function becomes available when you activate Temporary Storage Retained for the Segregated Flow solver.

Relative Velocity

Static Pressure

The spherical part of the stress tensor acting in fluids, which is the same as the actual thermodynamic pressure of the fluid. When the gravity model is active, it is related to the working pressure, (which becomes the piezometric pressure), by Eqn. (863) for variable density flows and by Eqn. (862) for constant density flows.

Tangential Velocity

The tangential component of velocity

v_{t}

relative to the axis and origin in the coordinate system given under the Axis node of the region.

This field function is not available in Eulerian multiphase models for axisymmetric cases.

Total Pressure

The absolute total pressure minus the reference pressure and, when gravity is present, the hydrostatic pressure:

p_{t} = p_{t,abs} - p_{ref} - p_{hydro}

Total Pressure Coefficient

The total pressure coefficient is defined as:

C_{p} = (P_{t} - P_{ref}) / (\frac{1}{2} ρ_{ref} v_{ref}^{2})

where

$P_{t}$ is the total pressure.
$P_{ref}$ , $ρ_{ref}$ , and $v_{ref}$ are the Reference Pressure, Reference Density, and Reference Velocity that you specify in the field function, respectively.

This field function is not available in Eulerian multiphase models.

Total Temperature

The temperature that is obtained from bringing the fluid to rest, defined as:

C_{p} = (v_{ref}^{2}) / 2 (T_{0} - T)

where

$T_{0}$ is the total temperature.
$T$ , and $v_{ref}$ are the Reference Temperature, and Reference Velocity that you specify in the field function.

Turbulent Charge

The value that is defined as

n = \nabla \cdot L

, where

L

is the lamb vector.

This field function is not available in Eulerian multiphase models.

Velocity

The velocity vector field.

Vorticity

The vector variable with components

ζ_{x}

ζ_{y}

ζ_{z}

defined as:  

ζ_{x} = \frac{\partial w}{\partial y} - \frac{\partial v}{\partial z}, ζ_{y} = \frac{\partial u}{\partial z} - \frac{\partial w}{\partial x}, ζ_{z} = \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}

  where

u

v

and

w

are velocity components in the x, y and z directions.

$\nabla\times v$ is the curl of the velocity field.