Numerical instability investigation of inward radial Rayleigh–Bénard–Poiseuille flow

Abstract

The spatial instability of inward radial Rayleigh–Bénard–Poiseuille flow was investigated using direct numerical simulations with random and controlled inflow forcing. The simulations were carried out with a higher-order-accurate compact finite difference code in cylindrical coordinates. Inward radial Rayleigh–Bénard–Poiseuille flows can be found, for example, in the collectors of solar chimney power plants. The conditions for the present simulations were chosen such that both steady and unsteady three-dimensional waves are amplified. The spatial growth rates are attenuated significantly in the downstream direction as a result of strong streamwise acceleration. For the oblique waves, the growth rates and wave angles decrease and the phase speeds get larger with increasing frequency. As the oblique waves travel downstream, the phase speeds decrease and the wave angles increase. Overall, steady waves with a wave angle of 90 ° are the most amplified. In general, because of the finite azimuthal extent, only certain azimuthal wavenumbers are possible. As a result, the steady waves appear to merge in the streamwise direction. When the inflow is at an angle such that a spiral flow is formed, one family of oblique waves is favored over the other and the mode shapes of the left- and right-traveling oblique waves are asymmetric with respect to the radius. As the inflow angle increases, this asymmetry is aggravated and the wavenumber of the most amplified disturbances is diminished.