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Breakdown of continuum in lid-rotating rarefied cavity flow
Shesh N Dhurandhar1, Vishnu Mohan2, Manjul Sharma3
1Indian Institute of Technology Madras, Department of Aerospace Engineering, Tamil Nadu 600036, India.
Physical Review. E
|June 19, 2025
Summary
Rarefaction and compressibility significantly alter fluid flow in rotating cavities, deviating from standard models. This study reveals counter-intuitive heat transfer and highlights the breakdown of continuum assumptions in rarefied gas dynamics.
Area of Science:
- Fluid dynamics
- Rarefied gas dynamics
- Computational physics
Background:
- Vogel-Escudier (VE) flow describes lid-rotating cavity dynamics.
- Standard Navier-Stokes-Fourier (NSF) equations assume continuum flow.
- Rarefaction and compressibility effects are crucial in micro/nano-scale or high-speed flows.
Purpose of the Study:
- Investigate rarefaction and compressibility impacts on VE flow.
- Analyze deviations from NSF predictions.
- Identify conditions for continuum breakdown.
Main Methods:
- Direct Simulation Monte Carlo (DSMC) method.
- OpenFOAM computational fluid dynamics (CFD) software.
- Simulations across Knudsen numbers (Kn_ref) 0.025–0.5 and Mach numbers (Ma_lid) 0.5–6.
Main Results:
- Inhomogeneous number density due to lid rotation.
- Temperature and velocity slip insensitivity to Mach number in supersonic regimes.
- Observed anti-Fourier heat flux and overpredicted shear stress by NSF.
- Emergence of continuum breakdown identified by local Knudsen number (Kn_g).
Conclusions:
- DSMC simulations reveal significant deviations from NSF predictions in VE flow.
- Rarefaction and compressibility lead to altered momentum and thermal transport.
- Local Knudsen number effectively distinguishes continuum and rarefied flow regions.
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