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Title: Numerical Investigation of Hydrodynamic Stability of Inward Radial Rayleigh-Bènard-Poiseuille Flow
Since the generation of green and clean renewable energy is a major concern in the modern era, solar energy conversion technologies such as the solar chimney power plant are gaining more attention. In order to accurately predict the performance of these power plants, hydrodynamic instabilities that can lead to large-scale coherent structures which affect the mean flow, have to be identified and their onset has to be predicted accurately. The thermal stratification of the collector flow (resulting from the temperature difference between the heated bottom surface and the cooled top surface) together with the opposing gravity can lead to buoyancy-driven instability. As the flow accelerates inside the collector, the Reynolds number can get large enough for viscous (Tollmien-Schlichting) instability to occur. A new highly accurate compact finite difference Navier-Stokes code in cylindrical coordinates has been developed for the spatial stability analysis of such radial flows. The new code was validated for a square channel flow. Stability results for different stable and unstable Reynolds/Rayleigh number combinations were in good agreement with temporal stability simulations as well as linear stability theory. To investigate the radial flow effect, spatial stability simulations were then carried out for a computational domain with constant streamwise extent and different outflow radii. The Reynolds and Rayleigh number were chosen such that buoyancy-driven instability occured. more » For cases with significant radial flow effect, the spatial growth rates of the azimuthal modes were found to vary considerably in the streamwise direction. « less
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2018 AIAA Aerospace Sciences Meeting
Sponsoring Org:
National Science Foundation
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  1. The hydrodynamic stability of the radial Rayleigh-Benard-Poiseuille flow inside the collector of solar chimney power plants has not attracted much attention in the literature. Because the ground is heated, buoyancy driven instability is possible. In addition, viscosity driven instability may occur. Temporal and spatial simulations are employed for investigating the hydrodynamic stability of the radial flow. Towards this end a new compact finite difference Navier-Stokes code is being developed. Square channel ow simulations were performed for code validation purposes using both the new code and an existing finite-volume code. For certain Reynolds and Rayleigh number combinations transverse rolls or longitudinalmore »rolls appear while for others the ow remains stable. A Fourier mode decomposition of the wall-normal velocity component at mid-channel height reveals linear (exponential) growth for the unstable modes and nonlinear interactions once the mode amplitudes exceed a certain threshold. The present square channel flow results are consistent with the neutral curves from the linear stability theory analysis by Gage and Reid. Simulations were also carried out for the collector of a 1:30 scale model of the Manzanares solar chimney power plant at the University of Arizona. The Rayleigh number is well above the critical Rayleigh number and steady longitudinal rolls appear shortly downstream of the collector inflow.« less
  2. 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 aremore »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.« less
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