cases:case047

# Homogeneous Isotropic Flow with/without Mean Temperature Gradient

Direct numerical simulation (DNS) of homogeneous decaying, almost isotropic, turbulence with a mean temperature gradient imposed in one direction was carried out by using a spectral method. Each term in the budget equations of the Reynolds stresses and turbulent heat flux were calculated, together with turbulence spectra and lengthscales.

The numerical databases to be analysed are of decaying homogeneous anisotropic turbulence with a mean temperature gradient (figure 1).

Fig. 1: Flow configuration

These computations were carried out by Iida and Kasagi (1991) using a spectral method with 963 grid points on a cubic box of side $L = 2\pi$, with periodic conditions imposed across its boundaries.

The Navier-Stokes equations and energy equation were solved for an incompressible fluid with dimensionless kinematic viscosity $\nu=1/300$. Cases are reported for Prandtl numbers $Pr = 0.2$, $0.71$ and $1.5$.

The initial energy spectrum was given as follows: $E(k) = (q_ok/k_p^2) \exp(-k/k_p)$ where $k$ is the three-dimensional wave number, $q_o = 0.49$ and $k_p = 5.0$. The initial distribution of the Reynolds stresses is a fairly small anisotropy, with $\overline{u^2} = \overline{v^2} < \overline{w^2}$.

A constant mean temperature gradient, which would create a turbulent heat flux, was imposed in the $y$ direction, with non-dimensional gradient $dT/dy=-1$. In most cases the initial thermal field had no fluctuations, although for one case with $Pr=0.71$ non-zero initial thermal fluctuations were imposed, with the same spectral distribution as the dynamic field.

Data available include:

• Time development of the Reynolds stresses, temperature variance and turbulent heat flux
• Budgets of the above second moments
• Dynamic and thermal inertial lengthscales
• One dimensional energy spectra and two-point correlations

Sample plots of selected quantities are available.

The data can be downloaded as compressed archives from the links below, or as the single uncompressed file.

 Datafile Dynamic and thermal field data is_2_ut_hm1.dat
1. Iida, O., Kasagi, N. (1991). Prandtl number effect on scalar transport in homogeneous isotropic turbulence, Proc. 5th Symposium of Numerical Fluid Dynamics, Tokyo, Japan.
2. Iida, O., Kasagi, N. (1993). Redistribution of the Reynolds Stresses and destruction of the turbulent heat flux in homogeneous decaying turbulence. Proc. 9th Turbulent Shear Flow Symposium, Kyoto, Japan.

Indexed data:

case047 (dbcase, free_flow)
case047
titleHomogeneous Isotropic Flow with/without Mean Temperature Gradient
authorIida, Kasagi
year1992
typeDNS
flow_taghomogeneous, scalar