The similarity of ideal gas flow at different scales is investigated analytically and nu-merically. With the compressible and rarefied effects considered, two dimensionless parameters, Mach number and Knudsen number, ...The similarity of ideal gas flow at different scales is investigated analytically and nu-merically. With the compressible and rarefied effects considered, two dimensionless parameters, Mach number and Knudsen number, are proposed as the similarity criterions, because the Rey-nolds number can be expressed by the Mach number and the Knudsen number of ideal gases. A DSMC method is used to simulate flows at different scales with the same Ma and Kn, including subsonic channel flows and the supersonic flows over a hot plate. Comparisons between the re-sults of different scales show that the normalized fields of macroscopic quantities are the same. This confirms the similarity. Especially, the results indicate that the micro flow are similar to the rarefied flow of ideal gas, which suggests that many transformations are available from the existing rarefied flow results to the micro flow.展开更多
In gas-solid flows, particle-particle interaction （typical, particle collision） is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical ...In gas-solid flows, particle-particle interaction （typical, particle collision） is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles （e.g., agglomeration and fragmentation） in spite of their initial monodisperse particle distribution. The conventional direct simulation Monte Carlo （DSMC） method for particle collision tracks equally weighted simulation particles, which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions. In this study, a new differentially weighted DSMC （DW-DSMC） method for collisions of particles with different number weight is proposed within the framework of the general Eulerian-Lagrangian models for hydrodynamics. Three schemes （mass, momentum and energy conservation） were developed to restore the numbers of simulation particle while keeping total mass, momentum or energy of the whole system unchanged respectively. A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency. The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best. Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC, compared with the equally weighted DSMC. Meanwhile, computational cost can be largely reduced in contrast with direct numerical simulation.展开更多
基金This work was supported by the State Key Lab of Applied Optics,Changchun Institute of Optics and Fine Mechanics and Physics,and Joint Academy of Nankai Universityand Tianjin University.
文摘The similarity of ideal gas flow at different scales is investigated analytically and nu-merically. With the compressible and rarefied effects considered, two dimensionless parameters, Mach number and Knudsen number, are proposed as the similarity criterions, because the Rey-nolds number can be expressed by the Mach number and the Knudsen number of ideal gases. A DSMC method is used to simulate flows at different scales with the same Ma and Kn, including subsonic channel flows and the supersonic flows over a hot plate. Comparisons between the re-sults of different scales show that the normalized fields of macroscopic quantities are the same. This confirms the similarity. Especially, the results indicate that the micro flow are similar to the rarefied flow of ideal gas, which suggests that many transformations are available from the existing rarefied flow results to the micro flow.
基金supported by the National Natural Science Foundation of China(51276077 and 51390494)the National Key Basic Research and Development Program(2010CB227004)
文摘In gas-solid flows, particle-particle interaction （typical, particle collision） is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles （e.g., agglomeration and fragmentation） in spite of their initial monodisperse particle distribution. The conventional direct simulation Monte Carlo （DSMC） method for particle collision tracks equally weighted simulation particles, which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions. In this study, a new differentially weighted DSMC （DW-DSMC） method for collisions of particles with different number weight is proposed within the framework of the general Eulerian-Lagrangian models for hydrodynamics. Three schemes （mass, momentum and energy conservation） were developed to restore the numbers of simulation particle while keeping total mass, momentum or energy of the whole system unchanged respectively. A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency. The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best. Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC, compared with the equally weighted DSMC. Meanwhile, computational cost can be largely reduced in contrast with direct numerical simulation.
