Stability of buoyancy-driven flow in a vertical channel with one heated wall

Abstract

The stability of the buoyancy-driven flow in a channel between an isothermal heated vertical wall and an adiabatic vertical wall is investigated by numerical integration of the derived two-dimensional stability equations for this type of buoyant flow. Stability calculations are carried out for a Prandtl number of 0.707 inside four vertical channels at Grashof numbers of 6.1×1010 and 1.49×1011 and with length-to-width aspect ratios of 8, 10, 40/3, and 20. The flow within the channel is numerically modeled by means of two-dimensional direct numerical simulations (DNSs), and the solved temperature and velocity fields are used as the base flow properties in the derived stability equations. Solutions of the stability equations yield the phase velocity, wave number, and growth rate for upper- and lower-branch neutrally stable disturbances, disturbances with maximum growth rates, and disturbances with phase velocities equal to the maximum velocity of the base flow inside the vertical channels. The predictions of the linear stability theory are compared with the disturbance growth observed in the simulated flow by means of a short-time Fourier transform of the velocity field computed from the DNS. The results show that while a range of disturbance wave numbers may be amplified in the channel, those that sustain the largest linear amplification have phase velocities equal to the peak velocity of the flow near the heated wall. The frequency of the most amplified disturbance increases linearly with the channel aspect ratio.