A Discrete Boltzmann Method(DBM)with a Maxwell-type boundary condition is constructed to investigate the influence of rarefaction on laminar Shock Wave/Boundary Layer Interaction(SWBLI).Due to the complexity of compre...A Discrete Boltzmann Method(DBM)with a Maxwell-type boundary condition is constructed to investigate the influence of rarefaction on laminar Shock Wave/Boundary Layer Interaction(SWBLI).Due to the complexity of compressible flow,a Knudsen number vector Kn,whose components include the local Knudsen numbers such as Kn_(ρ)and Kn_(U),is introduced to characterize the local structures,where Kn_(ρ)and Kn_(U)are Knudsen numbers defined in terms of the density and velocity interfaces,respectively.Since first focusing on the steady state of SWBLI,the DBM considers up to the second-order Kn_(ρ)(rarefaction/non-equilibrium)effects.The model is validated using Mach number 2 SWBLI and the necessity of using DBM with sufficient physical accuracy is confirmed by the shock collision problem.Key findings include the following:the leading-edge shock wave increases the local density Knudsen number Kn_(ρ)and eventually leads to the failure of linear constitutive relations in the Navier-Stokes(N-S)model and surely also in the lower-order DBM;the non-equilibrium effect differences in regions behind the leading-edge shock wave are primarily correlated with Kn_(ρ),while in the separation region are primarily correlated with Kn_(U);the non-equilibrium quantities D_(2)and D_(4,2),as well as the viscous entropy production rate S_(NOMF)can be used to identify the separation zone.The findings clarify various effects and main mechanisms in different regions associated with SWBLI,which are concealed in N-S model.展开更多
Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas jour...Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas journal bearings based on Burgdorfer's first-order slip boundary condition is proposed that takes into account the gas rarefaction effect. The finite difference method (FDM) is adopted to solve the modified Reynolds equation to obtain the pressure profiles,load capacities and attitude angles for micro gas journal bearings at different reference Knudsen numbers,bearing numbers and journal eccentricity ratios. Numerical analysis shows that pressure profiles and non-dimensional load capacities decrease markedly as gas rarefaction in-creases. Attitude angles change conversely,and when the eccentricity ratio is less than 0.6,the attitude angles rise slightly and the influence of the reference Knudsen number is not marked. In addition,the effect of gas rarefaction on the non-dimensional load capacity and attitude angle decreases with smaller bearing numbers.展开更多
基金support from the National Key R&D Program of China(No.2020YFC2201100)the Foundation of National Key Laboratory of Shock Wave and Detonation Physics,China(No.JCKYS2023212003)+1 种基金the National Natural Science Foundation of China(No.12172061)the Opening Project of State Key Laboratory of Explosion Science and Safety Protection(Beijing Institute of Technology)(No.KFJJ25-02M).
文摘A Discrete Boltzmann Method(DBM)with a Maxwell-type boundary condition is constructed to investigate the influence of rarefaction on laminar Shock Wave/Boundary Layer Interaction(SWBLI).Due to the complexity of compressible flow,a Knudsen number vector Kn,whose components include the local Knudsen numbers such as Kn_(ρ)and Kn_(U),is introduced to characterize the local structures,where Kn_(ρ)and Kn_(U)are Knudsen numbers defined in terms of the density and velocity interfaces,respectively.Since first focusing on the steady state of SWBLI,the DBM considers up to the second-order Kn_(ρ)(rarefaction/non-equilibrium)effects.The model is validated using Mach number 2 SWBLI and the necessity of using DBM with sufficient physical accuracy is confirmed by the shock collision problem.Key findings include the following:the leading-edge shock wave increases the local density Knudsen number Kn_(ρ)and eventually leads to the failure of linear constitutive relations in the Navier-Stokes(N-S)model and surely also in the lower-order DBM;the non-equilibrium effect differences in regions behind the leading-edge shock wave are primarily correlated with Kn_(ρ),while in the separation region are primarily correlated with Kn_(U);the non-equilibrium quantities D_(2)and D_(4,2),as well as the viscous entropy production rate S_(NOMF)can be used to identify the separation zone.The findings clarify various effects and main mechanisms in different regions associated with SWBLI,which are concealed in N-S model.
基金supported by the National Natural Science Foundation of China (No. 10472101)the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070335184)
文摘Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas journal bearings based on Burgdorfer's first-order slip boundary condition is proposed that takes into account the gas rarefaction effect. The finite difference method (FDM) is adopted to solve the modified Reynolds equation to obtain the pressure profiles,load capacities and attitude angles for micro gas journal bearings at different reference Knudsen numbers,bearing numbers and journal eccentricity ratios. Numerical analysis shows that pressure profiles and non-dimensional load capacities decrease markedly as gas rarefaction in-creases. Attitude angles change conversely,and when the eccentricity ratio is less than 0.6,the attitude angles rise slightly and the influence of the reference Knudsen number is not marked. In addition,the effect of gas rarefaction on the non-dimensional load capacity and attitude angle decreases with smaller bearing numbers.
