# Nomenclature

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 $J/kg$
$p$ 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 = $C_p/C_v$
$\delta_{ij}$ 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 $mol/m^3$
$\dot \omega_k$ k-species reaction rate $kg/m^3 s$

## Dimensionless parameters:

Parameter Description Definition
$Nu$ Nusselt number $\frac{q_w L}{k \Delta T}$
$Pr$ Prandtl number $\frac{\mu C_p}{k}$
$Re$ Reynolds number $\frac{\rho VL}{\mu}$
$St$ Strouhal number $\frac{fL}{V}$

## Subscript:

 $t$ Turbulent property $0$ Stagnation / total property

## Superscript:

 $conv$ Convective part $diff$ Diffusive part $lam$ Laminar part $tot$ Laminar + turbulent part $turb$ Turbulent part $'$ Reynolds fluctuating part $''$ Favre fluctuating part $\widetilde{\cdot}$ Density weighted (Favre) average $\overline{\cdot}$ Normal average (time or space)