Abstract
We consider the two-dimensional steady channel flow of a rarefied gas over a backward facing step in the limit of large Knudsen numbers. The free-molecular problem is solved analytically for both diffuse and specular-reflecting channel boundaries, and the solutions are validated through comparison with direct simulation Monte Carlo calculations. Prescribing the density and temperature differences between the inlet and outlet external equilibrium conditions, the results for the density- and temperature-drop-driven flows are analysed and contrasted, revealing higher flow velocities and mass flow rates in the former. While the flow rate is unaffected by the step geometry in the specular case, it increases with the step size in the diffuse-reflecting set-up. At conditions where small flow velocities occur, flow detachment is observed in the form of streamlines connecting the step edge stagnation points. Considering the problem at finite Knudsen numbers, the collisionless-flow regime breaks down at higher Knudsen numbers for lower gas speed flows, followed by the occurrence of step flow separation and recirculation.
Highlights
The flow over a backward step is a canonical problem in fluid mechanics, which has been studied extensively over the years as a model problem for illustrating fluid flow over a sharp discontinuity (Morgan et al 1984; Chen et al 2018)
Xue et al (2005) applied direct simulation Monte Carlo (DSMC) calculations to characterize the effect of gas rarefaction on the flow regime, and reported on sudden ‘jumps’ in the hydrodynamic fields at the step section at large Kn conditions
It is assumed that the inlet and outlet channel sections are connected to equilibrium-set reservoirs, where the gas is maintained at thermodynamic and equilibrium densities and temperatures, respectively
Summary
The flow over a backward step is a canonical problem in fluid mechanics, which has been studied extensively over the years as a model problem for illustrating fluid flow over a sharp discontinuity (Morgan et al 1984; Chen et al 2018). The majority of works have otherwise used the direct simulation Monte Carlo (DSMC) method to analyse the backward step flow at arbitrary Knudsen numbers. To this end, Xue et al (2005) applied DSMC calculations to characterize the effect of gas rarefaction on the flow regime, and reported on sudden ‘jumps’ in the hydrodynamic fields at the step section at large Kn conditions. The detached zone combines the step edge stagnation points with connecting flow streamlines This result could not be effectively revealed by means of the DSMC scheme, as the simulation statistical noise obscures the flow signal at the small velocities involved.
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