Hard Sphere/Pseudo-Particle Modeling Of Hypersonic Rarefied Flow

Hypersonic flow is difficult to be comprehensively studied by traditional experimental methods or simulation methods based on continuum hypothesis because of its unique physical and chemical characteristics.In this paper,the hard-sphere/pseudo-particle modeling(HS-PPM)is improved to overcome the shortcomings of discrete simulation including large computational load and low computational efficiency to some extent,which makes HS-PPM more feasible for studying hypersonic flow.HS-PPM was originally a discrete simulation method for microscale gas-solid multiphase flow.It has been applied successfully to flow-diffusion coupled simulation at micro-and nano-scales.In order to explore its applicability in the field of hypersonic flow,this paper first analyses the flow characteristics of reentrying hypersonic vehicles,and investigates the research progress in this field.On this basis,wall description,gas-surface interaction and boundary condition settings in HS-PPM are improved to make it more suitable for describing hypersonic flow.The results of HS simulation,HS-PPM and DSMC on the same hypersonic flow past a sphere were then compared.It shows that the results of HS is closer to HS-PPM than to DSMC.The flow past a three-dimensional sphere,with a Reynolds number of 100 and Mach numbers from 4 to 19,is simulated.In HS-PPM,the upper and lower limits of the drag coefficient are obtained by using the complete thermal boundary and the complete slip boundary respectively.The corresponding HS results are in good agreement with those obtained in HS-PPM.The work above demonstrated that HS-PPM is effective for hypersonic rarefied gas flow.By extrapolating the results of flow past a sphere to zero solid volume fraction,simulating the flow past a three-dimensional sharp cone with a Mach number of 24 and Knudsen numbers from 0.11 to 4.55,and the flow past a long tail blunt cone with a Mach number of 20 and a Knudsen number of 0.03,the directions to improve HS-PPM for hypersonic rarefied gas flow are suggested.As a preliminary attempt in these directions,the Larsen-Borgnakke energy model was introduced to HS-PPM.The simulated particles have not only kinetic energy,but also internal energy including rotational and vibrational energies.The initial values of these energies of a particle were derived from the equilibrium distribution,and updated by sampling after each collision to satisfy their equilibrium distributions statistically.The comparative simulation of a long tail blunt cone proved that the introduction of energy model basically corrects the shock temperature obtained in the HS-PPM simulation of hypersonic flow without reaction.However,the simulation of the re-entry of Apollo capsule model into the atmosphere with a Mach number of 33 and a Knudsen number of 0.081 showed that it is still insufficient when the real gas effect is significant,and reaction models should also be introduced.For this purpose,a simple nitrogen-oxygen dissociation reaction model was proposed and intergrated into the Larsen-Borgnakke energy model.The particle dissociation model and its simulation algorithm were also realized to obtain again the temperature distribution in the Apollo case simulated,with significant improvement.The researches in this paper have demonstrated and improved the applicability of HS-PPM to hypersonic rarefied flow.However,in this paper,only simple air components and reaction networks are considered in the reaction model.Future researches should continue to improve HS-PPM with complex reaction model,variable collision cross section and in other aspects.