We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we dis...We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we discuss is the derivation of the Euler system from the BGK equation.The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.展开更多
Based on the governing equations which include the heat conduction equation in the target and the fluid equations of the vapor plasma,a two-dimensional axisymmetric model for ns-laser ablation considering the Knudsen ...Based on the governing equations which include the heat conduction equation in the target and the fluid equations of the vapor plasma,a two-dimensional axisymmetric model for ns-laser ablation considering the Knudsen layer and plasma shielding effect is developed.The equations of state of the plasma are described by a real gas approximation,which divides the internal energy into the thermal energy of atoms,ions and electrons,ionization energy and the excitation energy of atoms and ions.The dynamic evolution of the silicon target and plasma during laser ablation is studied by using this model,and the distributions of the temperature,plasma density,Mach number related to the evaporation/condensation of the target surface,laser transmissivity as well as internal energy of the plasma are given.It is found that the evolution of the target surface during laser ablation can be divided into three stages:(1)the target surface temperature increases continuously;(2)the sonic and subsonic evaporation;and(3)the subsonic condensation.The result of the internal energy distribution indicates that the ionization and excitation energy plays an important role in the internal energy of the plasma during laser ablation.This model is suitable for the case that the temperature of the target surface is lower than the critical temperature.展开更多
Ablation excited by current pulses is a very critical physical process in pulse plasma thrusters(PPT).Its effects on wall-plasma interaction directly determine the PPT performances.In order to reveal the process of th...Ablation excited by current pulses is a very critical physical process in pulse plasma thrusters(PPT).Its effects on wall-plasma interaction directly determine the PPT performances.In order to reveal the process of the ablated wall interaction with the discharge plasma in PPT,ablation models formulated by three different boundary conditions at the wall-plasma interface are studied.These are the two widely used high-speed evaporation models(Model-L and Model-M),and the recently developed Keida-Zaghloul model(Model-K)of the Knudsen layer that takes into account the internal degrees of freedom on the energy flux conservation.First,fundamental mechanisms of the three ablation models are clarified by comparative analysis in order to gain a comprehensive understanding of the wall-plasma interaction.Then,the applicability of different ablation models with the numerical solutions of LES-6 PPT is investigated in detail using magnetohydrodynamic(MHD)modeling.Results show that Model-L and Model-M are actually special cases of Model-K when a simplified jump conditions limited by high velocity at the vapor/plasma interface is used;A ratio of ablation rate in Model-L to that in Model-M is about 0.8at the same wall surface temperature,while it rises to 1 at different surface temperature determined by Model-L and Model-M in PPT.Even though Model-K solution requires significant computational time,it shows more accurate ablation feature for the wall-plasma interaction and possesses better computing precision of impulse bit during post-pulse which is useful for future studies of the late time ablation.展开更多
For simple hydrodynamic solutions, where the pressure and the velocity arepolynomial functions of the coordinates, exact microscopic solutions are constructedfor the two-relaxation-time (TRT) Lattice Boltzmann model w...For simple hydrodynamic solutions, where the pressure and the velocity arepolynomial functions of the coordinates, exact microscopic solutions are constructedfor the two-relaxation-time (TRT) Lattice Boltzmann model with variable forcing andsupported by exact boundary schemes. We show how simple numerical and analyticalsolutions can be interrelated for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) multi-reflection (MR) type schemes. Special care is taken toadapt themfor corners, to examine the uniqueness of the obtained steady solutions andstaggered invariants, to validate their exact parametrization by the non-dimensionalhydrodynamic and a “kinetic” (collision) number. We also present an inlet/outlet“constant mass flux” condition. We show, both analytically and numerically, that thekinetic boundary schemes may result in the appearance of Knudsen layers which arebeyond the methodology of the Chapman-Enskog analysis. Time dependent Dirichletboundary conditions are investigated for pulsatile flow driven by an oscillating pressuredrop or forcing. Analytical approximations are constructed in order to extend thepulsatile solution for compressible regimes.展开更多
To understand lattice Boltzmann model capability for capturing nonequilibrium effects,the model with first-order expansion of the equilibrium distribution function is analytically investigated.In particular,the veloci...To understand lattice Boltzmann model capability for capturing nonequilibrium effects,the model with first-order expansion of the equilibrium distribution function is analytically investigated.In particular,the velocity profile of Couette flows is exactly obtained for the D2Q9 model,which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit.Meanwhile,it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer.展开更多
基金This work is supported by Thales Alenia Space.We are gratefully indebted to J.-F.Coulombel,F.GolseK.Aoki for many useful advices concerning this work and for their kind encouragements。
文摘We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we discuss is the derivation of the Euler system from the BGK equation.The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.
基金supported by the National Key Research and Development Program of China (No. 2017YFA0402300)National Natural Science Foundation of China (Nos.11904293, 12064040 and 11874051)+2 种基金the Science and technology project of Gansu Province (No. 20JR5RA530)the Young Teachers Scientific Research Ability Promotion Plan of Northwest Normal University (No. NWNU-LKQN-18-32)the Funds for Innovative Fundamental Research Group Project of Gansu Province (No. 20JR5RA541).
文摘Based on the governing equations which include the heat conduction equation in the target and the fluid equations of the vapor plasma,a two-dimensional axisymmetric model for ns-laser ablation considering the Knudsen layer and plasma shielding effect is developed.The equations of state of the plasma are described by a real gas approximation,which divides the internal energy into the thermal energy of atoms,ions and electrons,ionization energy and the excitation energy of atoms and ions.The dynamic evolution of the silicon target and plasma during laser ablation is studied by using this model,and the distributions of the temperature,plasma density,Mach number related to the evaporation/condensation of the target surface,laser transmissivity as well as internal energy of the plasma are given.It is found that the evolution of the target surface during laser ablation can be divided into three stages:(1)the target surface temperature increases continuously;(2)the sonic and subsonic evaporation;and(3)the subsonic condensation.The result of the internal energy distribution indicates that the ionization and excitation energy plays an important role in the internal energy of the plasma during laser ablation.This model is suitable for the case that the temperature of the target surface is lower than the critical temperature.
基金Project supported by Ph.D.Programs Foundation of Ministry of Education of China(20121101120004)Basic Research Foundation of Beijing Institute of Technology(20120142015)
文摘Ablation excited by current pulses is a very critical physical process in pulse plasma thrusters(PPT).Its effects on wall-plasma interaction directly determine the PPT performances.In order to reveal the process of the ablated wall interaction with the discharge plasma in PPT,ablation models formulated by three different boundary conditions at the wall-plasma interface are studied.These are the two widely used high-speed evaporation models(Model-L and Model-M),and the recently developed Keida-Zaghloul model(Model-K)of the Knudsen layer that takes into account the internal degrees of freedom on the energy flux conservation.First,fundamental mechanisms of the three ablation models are clarified by comparative analysis in order to gain a comprehensive understanding of the wall-plasma interaction.Then,the applicability of different ablation models with the numerical solutions of LES-6 PPT is investigated in detail using magnetohydrodynamic(MHD)modeling.Results show that Model-L and Model-M are actually special cases of Model-K when a simplified jump conditions limited by high velocity at the vapor/plasma interface is used;A ratio of ablation rate in Model-L to that in Model-M is about 0.8at the same wall surface temperature,while it rises to 1 at different surface temperature determined by Model-L and Model-M in PPT.Even though Model-K solution requires significant computational time,it shows more accurate ablation feature for the wall-plasma interaction and possesses better computing precision of impulse bit during post-pulse which is useful for future studies of the late time ablation.
文摘For simple hydrodynamic solutions, where the pressure and the velocity arepolynomial functions of the coordinates, exact microscopic solutions are constructedfor the two-relaxation-time (TRT) Lattice Boltzmann model with variable forcing andsupported by exact boundary schemes. We show how simple numerical and analyticalsolutions can be interrelated for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) multi-reflection (MR) type schemes. Special care is taken toadapt themfor corners, to examine the uniqueness of the obtained steady solutions andstaggered invariants, to validate their exact parametrization by the non-dimensionalhydrodynamic and a “kinetic” (collision) number. We also present an inlet/outlet“constant mass flux” condition. We show, both analytically and numerically, that thekinetic boundary schemes may result in the appearance of Knudsen layers which arebeyond the methodology of the Chapman-Enskog analysis. Time dependent Dirichletboundary conditions are investigated for pulsatile flow driven by an oscillating pressuredrop or forcing. Analytical approximations are constructed in order to extend thepulsatile solution for compressible regimes.
基金supported by the Engineering and Physical Sciences Research Council U.K.under Grants No.EP/F028865/1The research leading to these results has received the funding from the European Community’s Seventh Framework Programme FP7/2007-2013 under grant agreement ITN GASMEMS No.215504.
文摘To understand lattice Boltzmann model capability for capturing nonequilibrium effects,the model with first-order expansion of the equilibrium distribution function is analytically investigated.In particular,the velocity profile of Couette flows is exactly obtained for the D2Q9 model,which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit.Meanwhile,it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer.
