Numerical Analysis on Turbulent Transition of Thermal Plume : Formulations and Numerical Methodology

The three-dimensional, time-dependent thermal plume with variable density and properties is rising upward in non-stratified air from a heated square plate on a horizontal, solid ground with an extremely wide area. Formulations and numerical methodology without assuming laminar, transitional, or turbulent state in this complicated plume are presented. The grid size and time step employed in the present computation give computed results without a grid dependency at laminar conditions, and resolve the Kolmogorov's microscale at turbulent conditions. The Courant number and the diffusion number are valid because time-records of turbulent velocity and temperature are stable. Furthermore, the x -shape distribution of the limiting vectors in the present model agree well with that by the experimental visualization in the similar model. As shown above, the present formulation, numerical methods, and computed results satisfy the necessary condition of validation.