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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. [ABSTRACT FROM AUTHOR]

In this paper, a high-order Navier-Stokes solver is developed for chemically reacting flow and is applied to investigate the unsteady, viscous interaction between shock wave and boundary layer in an air filled shock tube. The solver employs a high- resolution weighted essentially non-oscillatory (WENO) scheme to capture the complex flow pattern induced by shock/boundary- layer interaction, together with a point-implicit method to overcome the stiffness of chemical production term. The results show the influence of real gas effects and give insights into the mechanism of shock/boundary-layer interaction process. [ABSTRACT FROM AUTHOR]

A hybrid approach that combines a continuum approach solving the Navier–Stokes equations and a particle method called the information preservation (IP) method is implemented to simulate subsonic, rarefied gas flows accurately and efficiently. The coupling between the continuum and particle approaches relies on a continuum/particle interface, which is investigated in detail. The IP method preserves information at the macroscopic level that allows the continuum approach to directly use the information from the particle region. In order to correctly generate particles from the continuum region, two strategies are proposed. One strategy adopts a Marshak-type condition, which requires many particles in a cell to control the flux fluctuation due to the microscopic motion of particles. In the second strategy, reservoir cells and buffer cells are used, and this is the approach adopted in our general hybrid scheme. The location of the interface is determined using a continuum breakdown parameter. Studies show that the continuum breakdown parameter suggested by Garcia et al. can be used to determine the location of the interface, but the implementation of the interface also affects the location of the interface. Simulation of a flow over a flat plate shows the performance of the hybrid approach and reveals the effects of the cutoff value to a continuum breakdown parameter. This approach is also applied to study the aerodynamics of a micro-scale airfoil, which is very difficult for a single method. The hybrid approach generally spends less computational time than the IP method for rarefied gas flows, and the numerical performance of the hybrid approach depends on the number ratio of continuum cells to particle cells. [Copyright &y& Elsevier]

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well. [ABSTRACT FROM AUTHOR]