Linearized stability analysis of two-dimension Burnett equations |
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Authors: | FB BaoZH Zhu JZ Lin |
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Affiliation: | a Institute of Fluid Measurement and Simulation, China Jiliang University, Hangzhou 310018, China b Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China |
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Abstract: | The linearized stability analyses of two-dimension Burnett equations were studied in present paper for the first time. The characteristic stability equation of two-dimension original Burnett equation was first derived and the characteristic curve was achieved. The material derivatives in original Burnett equations are then replaced with the Euler and Navier-Stokes equations. The stabilities of these two alternative Burnett equations are then analyzed. The linearized stability analyses show that the two-dimension original Burnett and Euler-based Burnett equations are not stable while the Navier-Stokes-based Burnett equations are stable. The critical Knudsen number for the original Burnett and Euler-based Burnett equations are 0.074 and 0.353, respectively. These critical Knudsen number are smaller than those of corresponding one-dimension equations. The two-dimension Burnett equations are more unstable than one-dimension equations. |
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Keywords: | Linearized stability analysis Burnett equations Critical Knudsen number Slip/transition flow Rarefied effect |
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