Unified Gas Kinetic Simulations of Lid-Driven Cavity Flows: Effect of Compressibility and Rarefaction on Vortex Structures

Vishnu Venugopal, Haneesha Iphineni (), Divya Sri Praturi and Sharath S. Girimaji ()
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Vishnu Venugopal: Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
Haneesha Iphineni: Department of Ocean Engineering, Texas A&M University, College Station, TX 77843, USA
Divya Sri Praturi: Department of Ocean Engineering, Texas A&M University, College Station, TX 77843, USA
Sharath S. Girimaji: Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA

Mathematics, 2024, vol. 12, issue 18, 1-12

Abstract: We investigate and characterize the effect of compressibility and rarefaction on vortex structures in the benchmark lid-driven cavity flow. Direct numerical simulations are performed, employing the unified gas kinetic scheme to examine the changes in vortex generation mechanisms and the resulting flow structures at different Mach and Knudsen numbers. At high degrees of rarefaction, where inter-molecular interactions are minimal, the molecules mainly collide with the walls. Consequently, the dominant flow structure is a single vortex in the shape of the cavity. It is shown that increasing compressibility or decreasing rarefaction lead to higher molecular density in the cavity corners, due to more frequent inter-molecular collisions. This results in lower flow velocities, creating conditions conducive to the development of secondary and corner vortices. The physical processes underlying vortex formations at different Knudsen numbers, Mach numbers, and cavity shapes are explicated. A parametric map that classifies different regimes of vortex structures as a function of compressibility, rarefaction, and cavity shape is developed.

Keywords: vorticity; cavity flow; Knudsen number ( Kn ); Mach number ( Ma ); unified gas kinetic scheme (UGKS) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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