In an early approach, a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 （2007）] to simulate non-equilibrium flows was proposed. In this paper, instead of us...In an early approach, a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 （2007）] to simulate non-equilibrium flows was proposed. In this paper, instead of using three temperatures in the x, y and z-directions, we define the translational temperature as a second-order symmetric tensor. Under the new framework, the differences between the temperature tensor and the pressure tensor will be explicitly pointed out. Based on a multiple stage BGK-type collision model and the Chapman-Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The zeroth-order expansion gives 10 moment closure equations similar to that of Levermore [C.D. Levermore, J. Stat. Phys 83, pp.1021 （1996）]. The derived gas dynamic equations can be considered as a regularization of the 10 moments equations in the first-order expansion. The new gas dynamic equations have the same structure as the Navier-Stokes equations, but the stress-strain relationship in the Navier-Stokes equations is replaced by an algebraic equation with temperature differences. At the same time, the heat flux, which is absent in Levermore＇s 10 moment closure, is recovered. As a result, both the viscous and the heat conduction terms are unified under a single anisotropic temperature concept. In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier-Stokes equations. Our gas dynamic equations are natural extensions of the Navier-Stokes equations to the near continuum flow regime and can be used for microfiow computations. Two examples, the force-driven Poiseuille flow and the Couette flow in the transition flow regime, are used to validate the model. Both analytical and numerical results are presented. Theoretically, the Boltzmann equation can be also applied to the current multiple stage gas evolution model to derive generalized macroscopic governing equations in the near continuum flow regime. Instead of using 展开更多
The integrative process of a quiescent projectile accelerated by high-pressure gas to shoot out at a supersonic speed and beyond the range of a precursor flow field was simulated numerically. The calculation was based...The integrative process of a quiescent projectile accelerated by high-pressure gas to shoot out at a supersonic speed and beyond the range of a precursor flow field was simulated numerically. The calculation was based on ALE equations and a second-order precision Roe method that adopted chimera grids and a dynamic mesh. From the predicted results, the coupling and interaction among the precursor flow field, propellant gas flow field and high-speed projectile were discussed in detail. The shock-vortex interaction, shockwave reflection, shock-projectile interaction with shock diffraction, and shock focus were clearly demonstrated to explain the effect on the acceleration of the projectile.展开更多
This paper presents a gaskinetic study on high-speed, highly rarefied jets expanding into a vacuum from a cluster of planar or annular exits. Based on the corresponding exact expressions for a planar or annular jet, i...This paper presents a gaskinetic study on high-speed, highly rarefied jets expanding into a vacuum from a cluster of planar or annular exits. Based on the corresponding exact expressions for a planar or annular jet, it is convenient to derive the combined multiple jet flowfield solutions of density and velocity components. For the combined temperature and pressure solutions, extra attention is needed. Several direct simulation Monte Carlo simulation results are provided to validate these analytical solutions. The analytical and numerical solutions are essentially identical for these high Knudsen number jet flows.展开更多
This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al...This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.展开更多
Nonequilibrium process for cracking ethane and n-buthane in the manufacture of ethene has been analytically and numerically investigated in a Heaviside function temperature field and through a normal shock wave. The ...Nonequilibrium process for cracking ethane and n-buthane in the manufacture of ethene has been analytically and numerically investigated in a Heaviside function temperature field and through a normal shock wave. The results demonstrate that, while the reaction temperature increases, the maximum value of ethene yield is increased, and the optimal reaction duration is sharply shortened. For the identical initial reaction temperature, the maximum value of ethene yield through a stationary normal shock wave is less than that in a Heaviside function temperature field. However, the ethene consumption after the maximum value in the former case is less than that in the latter. Higher ethene yield will be obtained by using the gasdynamic heating method than by using the current methods. (Edited author abstract) 5 Refs.展开更多
A set of new gasdynamic functions with varying specific heat are derived for the first time.An original analytical solution of normal shock waves is worked out therewith.This solution is thereafter further improved by...A set of new gasdynamic functions with varying specific heat are derived for the first time.An original analytical solution of normal shock waves is worked out therewith.This solution is thereafter further improved by not involving total temperature.Illustrative examples of comparison are given,including also some approximate solutions to show the orders of their errors.展开更多
文摘In an early approach, a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 （2007）] to simulate non-equilibrium flows was proposed. In this paper, instead of using three temperatures in the x, y and z-directions, we define the translational temperature as a second-order symmetric tensor. Under the new framework, the differences between the temperature tensor and the pressure tensor will be explicitly pointed out. Based on a multiple stage BGK-type collision model and the Chapman-Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The zeroth-order expansion gives 10 moment closure equations similar to that of Levermore [C.D. Levermore, J. Stat. Phys 83, pp.1021 （1996）]. The derived gas dynamic equations can be considered as a regularization of the 10 moments equations in the first-order expansion. The new gas dynamic equations have the same structure as the Navier-Stokes equations, but the stress-strain relationship in the Navier-Stokes equations is replaced by an algebraic equation with temperature differences. At the same time, the heat flux, which is absent in Levermore＇s 10 moment closure, is recovered. As a result, both the viscous and the heat conduction terms are unified under a single anisotropic temperature concept. In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier-Stokes equations. Our gas dynamic equations are natural extensions of the Navier-Stokes equations to the near continuum flow regime and can be used for microfiow computations. Two examples, the force-driven Poiseuille flow and the Couette flow in the transition flow regime, are used to validate the model. Both analytical and numerical results are presented. Theoretically, the Boltzmann equation can be also applied to the current multiple stage gas evolution model to derive generalized macroscopic governing equations in the near continuum flow regime. Instead of using
基金the National Key Laboratory of Transient Physics of China
文摘The integrative process of a quiescent projectile accelerated by high-pressure gas to shoot out at a supersonic speed and beyond the range of a precursor flow field was simulated numerically. The calculation was based on ALE equations and a second-order precision Roe method that adopted chimera grids and a dynamic mesh. From the predicted results, the coupling and interaction among the precursor flow field, propellant gas flow field and high-speed projectile were discussed in detail. The shock-vortex interaction, shockwave reflection, shock-projectile interaction with shock diffraction, and shock focus were clearly demonstrated to explain the effect on the acceleration of the projectile.
基金NSF-DMS-0914706the Research Enhancement Awards from the New Mexico Space GrantsNSF-CBET-0854411
文摘This paper presents a gaskinetic study on high-speed, highly rarefied jets expanding into a vacuum from a cluster of planar or annular exits. Based on the corresponding exact expressions for a planar or annular jet, it is convenient to derive the combined multiple jet flowfield solutions of density and velocity components. For the combined temperature and pressure solutions, extra attention is needed. Several direct simulation Monte Carlo simulation results are provided to validate these analytical solutions. The analytical and numerical solutions are essentially identical for these high Knudsen number jet flows.
基金supported by the National Natural Science Foundation of China(Grant Nos.12102365,91752202,11472016,11621202,and 12272371).
文摘This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.
基金The project supported by the National Natural Science Foundation of China(19632002)
文摘Nonequilibrium process for cracking ethane and n-buthane in the manufacture of ethene has been analytically and numerically investigated in a Heaviside function temperature field and through a normal shock wave. The results demonstrate that, while the reaction temperature increases, the maximum value of ethene yield is increased, and the optimal reaction duration is sharply shortened. For the identical initial reaction temperature, the maximum value of ethene yield through a stationary normal shock wave is less than that in a Heaviside function temperature field. However, the ethene consumption after the maximum value in the former case is less than that in the latter. Higher ethene yield will be obtained by using the gasdynamic heating method than by using the current methods. (Edited author abstract) 5 Refs.
基金Improved solution belongs to a project supported by the National Science Foundation of China
文摘A set of new gasdynamic functions with varying specific heat are derived for the first time.An original analytical solution of normal shock waves is worked out therewith.This solution is thereafter further improved by not involving total temperature.Illustrative examples of comparison are given,including also some approximate solutions to show the orders of their errors.
