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Velocity boundary condition at solid walls in rarefied gas calculations
Duncan A Lockerby1, Jason M Reese, David R Emerson
1Department of Mechanical Engineering, King's College London, London WC2R 2LS, United Kingdom.
Summary
Misapplication of Maxwell's slip boundary condition in rarefied gas dynamics is common. A new Maxwell-Burnett boundary condition improves accuracy for complex geometries and phenomena like thermal-stress slip flow.
Area of Science:
- Fluid dynamics
- Rarefied gas dynamics
- Computational physics
Background:
- Maxwell's slip boundary condition is widely used but often misapplied in rarefied gas flow simulations.
- This misapplication leads to the loss of crucial physics, especially for flows over curved or moving surfaces.
- Existing higher-order slip conditions may not be universally applicable to all surface geometries.
Purpose of the Study:
- To address the misapplication of Maxwell's slip boundary condition in rarefied gas dynamics.
- To propose a novel, higher-order boundary condition applicable to complex surface geometries.
- To improve the accuracy of simulations involving rarefied gas flows over curved or moving surfaces.
Main Methods:
- Derivation of a higher-order boundary condition based on Maxwell's general equation.
- Incorporation of constitutive relations derived by Burnett.
- Application and validation of the proposed "Maxwell-Burnett" boundary conditions.
Main Results:
- The proposed Maxwell-Burnett boundary conditions are applicable to any surface geometry.
- These conditions show reasonable agreement with experimental data for Poiseuille flow.
- The Maxwell-Burnett conditions successfully predict Sone's thermal-stress slip flow, a phenomenon missed by conventional methods.
Conclusions:
- The Maxwell-Burnett boundary conditions offer a more accurate and versatile alternative to conventional slip conditions in rarefied gas dynamics.
- This advancement is crucial for accurate simulations in fields like hypersonics and microfluidics.
- The proposed conditions enhance the prediction of complex gas flow phenomena.
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