In hypersonic low density nozzle flow, the vibrational temperature is frozen, causing serious non-equilibrium relative to the translational and rotational temperatures. In related numerical simulations, the vibrational temperature is completely frozen, but the experimental data is obviously lower than the simulation result. To address this issue, analyses have been performed on the numerical method in the applications of low temperature conditions. Based on the simulation method of thermal non-equilibrium used in direct simulation Monte Carlo (DSMC), by modifying the number of vibrational relaxation collision, a numerical method for vibrational non-equilibrium flow at low temperature is proposed, in which the modified coefficient is set to be 1×10⁻⁷. The flow in a M16 nozzle of the low density wind tunnel and the plume of 10 N attitude control thruster is simulated, and the vibrational temperature agrees with the experimental result. It is shown that, due to the large value of the number of vibrational relaxation collision in the low temperature condition, gas molecules can rarely have vibrational relaxation collisions, and the vibrational energy cannot transform to the translational energy, thus the vibrational temperature is completely frozen. With the present introduced modification, the number of vibrational relaxation collision is reduced, the probability of vibrational relaxation collision is increased, and the vibrational temperature can be reduced to match the experimental results.

The influence of main/side jet and plume exists in a wide area around the intercepting maneuvering aircraft, and the traditional Navier-Stokes (N-S) equation cannot simulate the flow near the outlet of the engine nozzle expansion well, so a new method is needed to deal with the whole flow regime flow problem. In order to solve this problem, the Boltzmann model equation governing the flow in an axisymmetric nozzle under the rarefied environment of different Knudsen numbers is mathematically derived, and the numerical scheme and gas kinetic unified algorithm for the model equation are established. Numerical results for steady/unsteady rotating flow between two coaxial cylinders, as well as flow in an axisymmetric nozzle, both agree with existing studies, which verifies the reliability of the present algorithm in the whole flow regime. By comparing with the low-density wind tunnel experiment, the plume structure in the core area of the nozzle outlet and the pressure profile along the plume axis from the simulation show good agreement with the experiment, which suggests that the proposed algorithm can effectively solve the problem of mixing in the multi-flow regime from the nozzle compression section to the expansion section, especially in the low-pressure vacuum environment near the outlet.

The kinetic Boltzmann-Rykov model is used to explore the influence of rotating non-equilibrium on the inner flow of the nozzle, based on the computing principle of the gas-kinetic unified algorithm (GKUA). Mathematical models for the boundary conditions of nozzle flows were developed under the level of molecular velocity distribution function, and a numerical scheme of gas-kinetic was constructed to solve the molecular velocity distribution function directly. The Boltzmann-Rykov model equation considering the effect of rotational energy was numerically solved. The inner flow problems including the one-dimensional unsteady shock tube, one-dimensional steady positive shock structure, and two-dimensional planar nozzle flow were numerically simulated. The computed results match the theoretical solution, simulation value, and experimental data. It verifies the feasibility and accuracy of the unified algorithm for the inner flow problems. Lastly, an analysis was conducted on the nozzle’s inner flow field while taking rotational energy into account. The results show that the Knudsen number can be used as the characterization of nozzle flow characteristics and performance.