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Title: Numerical Stability Investigation of Inward Radial Rayleigh-Be'nard-Poiseuille Flow
Inward radial Rayleigh-Be'nard-Poiseuille flow can exhibit a buoyancy-driven instability when the Rayleigh number exceeds a critical value. Furthermore, similar to plane Rayleigh-Be'nard-Poiseuille flow, a viscous Tollmien-Schlichting instability can occur when the Reynolds number is high enough. Direct numerical simulations were carried out with a compressible Navier-Stokes code in cylindrical coordinates to investigate the spatial stability of the inward radial flow inside the collector of a hypothetical solar chimney power plant. The convective terms were discretized with fifth-order-accurate upwind-biased compact finite-differences and the viscous terms were discretized with fourth-order-accurate compact finite differences. For cases with buoyancy-driven instability, steady three-dimensional waves are strongly amplified. The spatial growth rates vary significantly in the radial direction and lower azimuthal mode numbers are amplified closer to the outflow. Traveling oblique modes are amplified as well. The growth rates of the oblique modes decrease with increasing frequency. In addition to the purely radial flow, a spiral flow with swept inflow was examined. Overall lower growth rates are observed for the spiral flow compared to the radial flow. Different from the radial flow, the relative wave angles and growth rates of the left and right traveling oblique modes are not identical. A plane RBP case with viscosity-driven instability by Chung et al. was considered as well. The reported growth rate and phase speed were matched with good accuracy.  more » « less
Award ID(s):
1510179
NSF-PAR ID:
10180775
Author(s) / Creator(s):
;
Date Published:
Journal Name:
AIAA Scitech 2020 Forum
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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