Direct Numerical Simulation of Turbulent Thermal Plume in Stably Stratified Ambient: Formulation, Numerical Methodology, Reverse Transition, Relaminarization, and Turbulent Enhancement

Abstract

For the turbulent thermal plume of air developing in stably stratified air above a square heated plate on a horizontal solid surface with infinite area, the formulation and numerical methodology for direct numerical simulation (DNS) are developed, the DNS data at the Rayleigh number Ra = 1 × 10⁷ are obtained by DNS computation, and the reverse transition, relaminarization, and turbulence enhancement are elucidated by the present DNS. Main conclusions are as follows.

1. The governing equation system for DNS of the turbulent plume in stratified ambient is 3-D and time-dependent with buoyancy and varying density and properties and without assumption of turbulent, transitional, or laminar state, and is applicable to any thermal conditions of heated plate and any stratification degree.

2. In the present DNS, the turbulent behavior, i.e., the high-frequency motion, the viscous dissipation, etc. can be reasonably considered, but the viscous dissipation heat is omitted because it is extremely small in the thermal plume.

3. The numerical method for DNS of the above governing equation system is developed.

4. The criterion determining the turbulent, transitional, and laminar states is obtained. The turbulent, transitional, and laminar regions in the plume are shown in the region map.

5. The grid size, the time step, and the frequency and resolution of space and time of the Kolmogorov microscale are validated for DNS by using the power spectrum density (PSD).

6. The variations and mechanisms of the distributions of temperature and velocity in the upward direction in the stable stratification are elucidated.

7. At the weakly stratified ambient, turbulence is enhanced near the plate center.

8. At any degree of stable stratification, the turbulence is suppressed. Whether turbulence exists or not near the plate center leads to different mechanisms of the turbulence suppression, i.e., the reverse transition and relaminarization.

Notes

Symbols Tu, Tr, and L mean turbulent, transitional, and laminar.