Disturbance growth and its effect on convection in a buoyancy-driven vertical channel with one heated wall

Three-dimensional buoyancy-driven flow in a vertical channel with one heated wall that resembles a solar chimney is studied employing direct numerical simulation in order to capture the instability and disturbance growth in this flow. The aspect ratio of the simulated channel is 20, and the Grashof number is 6.1 x 1010. Linearly-unstable sinusoidal perturbations are individually applied to the pressure, velocity, and temperature fields at the entrance of the channel. It is shown that the imposed perturbations grow in time and change the characteristics of the flow from a laminar to a transitional character with a range of active scales of flow disturbances. Two dominant vortical structures identified in the transitional flow consist of two-dimensional spanwise and three-dimensional predominantly streamwise vortices, both growing spatially near the heated wall as the flow rises. For the ranges studied, both vortical structures appear to be independent of the amplitude or the type of the introduced perturbations. Budgets of the fluctuation kinetic energy show that buoyancy plays the main role in producing the fluctuating energy, although the role of shear production becomes more important as the flow rises along the channel. The effect of the disturbance growth on bulk convection in the solar chimney is to increase the friction coefficient, lowering the flow rate by 14% compared to a laminar condition. Moreover, the turbulent Prandtl number diverges significantly from unity near the heated wall, suggesting that the assumption of near-unity turbulent Prandtl number that is commonly made in Reynolds-averaged Navier-Stokes simulations of solar chimneys may lead to inaccurate predictions.