Definitions of Variables

Variable

Definition

Equation or Value

µ_T

Turbulent Viscosity

${\mu }_T=\rho \ast C_{\mu }\left(\frac{k^2}{ϵ}\right)$

ρ

Fluid Density—depends on temperature, pressure, and fluid

Constant for incompressible flow

C_µ

Constant

0.09

k

Turbulent Kinetic Energy

Equation (1)

ε

Turbulent Dissipation Rate

Equation (2)

u

Velocity Field

User Input

$\nabla$

Gradient/Partial Differential

µ

Fluid Dynamic Viscosity—relates the shear stress and shear rates of a liquid

σ_k

Constant

1.0

P_k

Production Term

$P_k={\mu }_T\left(\nabla u:\left(\nabla u+{\left(\nabla u\right)}^T\right)-\frac{2}{3}{\left(\nabla \cdot u\right)}^2\right)-\frac{2}{3}\rho k\nabla \cdot u$

T

Temperature – user-defined reference temperature or calculated from other model inputs

σ_ε

Constant

1.3

C_ε1

Constant

1.44

C_ε2

Constant

1.92

B

Surface roughness (Constant or user-defined)

5.2

κ_v

von Kárman constant

0.41