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Nomenclature

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Acronym Description Unit
C_p Specific heat at constant pressure J/kgK
C_v Specific heat at constant volume J/kgK
e Internal energy J/kg
e_0 Total energy J/kg
h Enthalpy J/kg
k Turbulent kinetic energy J/kg = m^2/s^2
p Static pressure Pa
R Specific gas constant J/kgK
S_{ij}^* Trace-less viscous strain-rate tensor s^{-1}
t Time s
T Static temperature K
u^* Friction velocity m/s
u_i Velocity m/s
\gamma Specific heat ratio = C_p/C_v
\epsilon Turbulence dissipation J / kg s = m^2 / s^3
\delta_{ij} Kronecker's delta function
\mu Dynamic viscosity Ns/m^2
\nu Kinematic viscosity m^2/s
\rho Density kg/m^3
\tau_{ij} Shear stress tensor N/m^2
\omega Specific dissipation s^{-1}
Y_k Mass Fraction of species k
X_k Molar Fraction of species k
[X_k] Molar Concentration of species k mol/m^3
W_k Molecular weight of species k kg/mol
  \overline{W} Mean molecular weight of a mixture kg/mol
 \dot \omega_k  k-species reaction rate kg/m^3 s

Dimensionless parameters:

Parameter Description Definition
Nu Nusselt number \frac{h L}{k}
Pr Prandtl number \frac{\mu C_p}{k}
Re Reynolds number \frac{\rho VL}{\mu}
St Strouhal number \frac{fL}{V}
Ma Mach number \frac{v}{C}

Subscript:

tTurbulent property
0Stagnation / total property

Superscript:

convConvective part
diffDiffusive part
lamLaminar part
totLaminar + turbulent part
turbTurbulent part
'Reynolds fluctuating part
''Favre fluctuating part
\widetilde{\cdot}Density weighted (Favre) average
\overline{\cdot}Normal average (time or space)
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