Poiseuille-Rayleigh-Bénard (P-R-B) flow is an interesting and important topic which is frequently encountered in nature phenomenon and various industrial applications, such as the chemical vapor deposition process, the cooling of electronic components, the air flow in solar collector and so on. In this work, a series of three-dimensional numerical simulations were conducted by means of the finite volume method in order to understand the flow pattern, stability and heat transfer ability of P-R-B flow of air in a horizontal rectangular channel subjected to constant vertical temperature gradient. The horizontal channel with a streamwise aspect ratio of 100 and spanwise aspect ratio ranging from 2 to 10 was heated from below at a higher temperature Th and cooled from above at a lower temperature Tc. An air flow with the Prandtl number of 0.71 was induced into the channel at cold temperature Tc. A wide variety of flow patterns such as stable longitudinal rolls, transversal rolls, transverse traveling waves and wavy rolls were observed in the range of 0≤Re≤350, 1708≤Ra&lt;105. Results show that the number of longitudinal rolls depends not only on the spanwise aspect ratio but possibly on the Rayleigh number. When the aspect ratio is 2, 5 and 10, the number of longitudinal rolls is 2, 4 and 10 at a small Rayleigh number. However, the split of rolls is observed in channel with relatively large aspect ratio when the Rayleigh number is large enough. Furthermore, the entrance length of longitudinal rolls increases with the increase of Reynolds number, that is, the streamwise position where the flow is fully developed moves downstream with the increase of horizontal inflow. The flow pattern strongly depends on the Reynolds number and Rayleigh number. For small Reynolds numbers, the instability appears as a combination of transverse traveling waves and longitudinal rolls. When the symmetrical transverse traveling waves flow through, the Nusselt numbers on the upper and lower wall show sinusoidal oscillation with time and the peaks of the upper wall are opposite to the valleys of the lower wall. An evolution from stable longitudinal rolls to unstable wavy rolls which offset to the center or sidewall alternately on the cross section of the channel is observed with the increase of Rayleigh number. The dimensionless reduced temperature of the wavy rolls oscillates in a sinusoidal manner along the streamwise direction and is stronger at high Rayleigh numbers. In this case, the local Nusselt numbers of the upper and lower wall vary periodically along the channel, while the spanwise averaged Nusselt number is oscillatory in the streamwise direction. The stability of P-R-B flow of air in rectangular channel with finite transverse aspect ratio mainly depends on Reynolds number, Rayleigh number and spanwise aspect ratio. Owing to the lateral confinement of the sidewall in channel with small aspect ratio, the basic flow is stabilized and the critical Reynolds number is smaller. As expected, the critical Raleigh number of longitudinal rolls decreases from 2100 to 1900 as the aspect ratio increases from 2 to 10. The heat transfer rate of P-R-B flow is enhanced with the increase of Rayleigh number and spanwise aspect ratio. A scaling relationship for the average Nusselt number in terms of the Rayleigh member and spanwise aspect ratio is proposed. The predicted results based on the scaling correlation are consistent with those from simulations.

Numerical Simulation of Poiseuille-Rayleigh-Bénard Flow of Air in a Horizontal Rectangular Channel Heated From Below

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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