Heat-source driven convection in tall cavities

This investigation considers a tall, two-dimensional cavity with adiabatic side and bottom walls and a fixed temperature at the upper boundary. All boundaries are rigid, no-slip surfaces. The energy generation within the fluid is treated as a constant. Six aspect ratios are investigated. A commercially available CFD code is used to solve the turbulent equations of conservation of mass, momentum, and energy. These equations are normalized, and the effects of reference velocity on convergence are investigated. The choice of reference velocity affects numerical stability, and the most favorable scaling is when the Reynolds number is the square root of the Grashof number, as opposed to the conventional inverse of the Prandtl number. Mesh convergence is confirmed. Under-relaxation, steady-state modeling is used. Typical convergence criteria are not feasible at higher Rayleigh numbers. Rather, the maximum difference convergence criteria is set at unobtainable values, and steady-state convergence is based on an acceptable energy balance between the internal heat generation and heat transfer at the free surface. The model is validated using published experimental data and numerically verified using available finite difference and finite element solutions. Rayleigh numbers range from 10⁴ to 10⁸ for the six aspect ratios and the fixed Prandtl number of 6.5. Temperature, stream function, turbulent kinetic energy, and velocity vectors are calculated for each of these cases and selected results are presented. Heat transfer results indicate the absence of a universal correlation of the Nusselt number with Rayleigh number and aspect ratio.