A stagnation streamline model incorporating quantum-state-resolved chemistry is proposed to study hypersonic nonequilibrium flows along the stagnation streamline. This model is developed by reducing the full Navier–Stokes equations to the stagnation streamline with proper approximations for equation closure. The thermochemical nonequilibrium is described by either the state-to-state approach for detailed analysis or conventional two-temperature models for comparison purpose. The model is validated against various data, and nearly identical results are obtained as compared with those from full field computational fluid dynamics data. In addition, the calculated distributions agree well with the measurement data of a shock tube experiment for the dissociation and vibrational relaxation of O2, including the distributions of species mole fractions and vibrational temperature of the first excited state of O2 molecules. Furthermore, the results with the state-resolved chemistry show that the flow within a shock layer exhibits a strong thermochemical nonequilibrium behavior, which is beyond the capability of commonly used two-temperature models to correctly evaluate the dissociation rate and the associated reaction energy. The present model is also employed to calculate the nonequilibrium re-entry flow along the stagnation streamline for a five-species air mixture as an example to demonstrate the model capability. It is found that both species and internal energy are in a nonequilibrium state, especially the vibrational distributions are strongly deviated from the Boltzmann distribution right behind the bow shock and near the wall surface. The results demonstrate that the proposed stagnation streamline model is very useful to understand thermochemical nonequilibrium phenomena in hypersonic flows.

Cryocoolers working in the liquid hydrogen temperature are important for applications such as cryo-pump, superconductor cooling and cryogenic electronics. This paper analyzes and compares the 20K gas-coupled two-stage Stirling type pulse tube cryocooler with and without pre-cooling. The pre-cooling uses some of the cooling power generated by the first stage cold head to pre-cool the middle of the second stage pulse tube. Given the same input acoustic power, the simulation results show that the cooling capacity of the second stage increase from 0.64 W to 2 W@20 K while the first stage available cooling capacity decrease from 5.84 W to 3 W@77 K when the pre-cooling is used. Meanwhile, the cryocooler relative Carnot Efficiency in terms of acoustic power increases from 10.3% to 14.6%.