The physical characteristics inside shock waves with nonequilibrium molecular motion are difficult to describe using conventional macroscopic methods. In this paper, nonequilibrium hydrodynamic and thermodynamic effects caused by the strong nonequilibrium molecular velocity distribution at a shock wave are studied using a mesoscopic kinetic approach. This approach is based on a lattice Boltzmann method and a kinetic nonequilibrium method. The former adopts a compressible double-distribution-function model with separated density and total energy distribution functions. The latter represents the nonequilibrium effects through nonequilibrium kinetic moments based on the nonequilibrium molecular velocity distribution. The nonequilibrium effects in the steady state and the process of the formation of a regular reflection shock wave are presented. Nonequilibrium effects inside the shock wave are further investigated. First, the curvature pattern during the formation of a regular reflection shock wave is addressed. The curvature characteristic leads to distinct features of nonequilibrium effects compared with the linear pattern. A vector-based approach for visualizing nonequilibrium effects is proposed to study the curvature pattern. Second, the influence of viscosity on nonequilibrium effects, which is related to the average collision time among molecules at the shock wave, is explored. The results obtained in this paper provide mesoscopic physical insight into the flow mechanisms occurring in shock waves.
Using numerical simulations, we studied the grouping behaviors of particles settling along their line of centers in narrow channels having a Reynolds number range of 5 ≤ Re ≤ 50. The calculations are based on our previously developed lattice Boltzmann direct-forcing-fictitious-domain method. We report the grouping behavior and investigate the dependence on the number of particles n, the initial interparticle separation h_{0}, and the Reynolds number Re. In particular, the mode of grouping is found to be independent of the number of particles when the Reynolds numbers is small. The two lowermost particles always come together first and form a vertical doublet and then the next two lowest particles form another doublet, and so on. Therefore, we observe n/2 doublets or (n-1)/2 doublets when n is even or odd, respectively. The uppermost particle is always left behind when n is odd. Furthermore, the separation between these doublets remains constant, displaying a power-law dependence decreasing from top to bottom.
The dual waverider method for the integration of hypersonic inlet and waverider forebody is presented. The method connects the hypersonic internal waverider inlet and the waverider forebody by application of the osculating waverider theory. As an inverse design method, one should construct a three-dimensional shock wave surface that has continuous local curvature centers. In particular, the centers have to locate internally and externally away from the shock to obtain a proper integration configuration. Unlike most previous integration techniques, this approach jointly creates waverider lower surface and inward turning inlet configuration. As a result, the integratedcomponents become essential elements of a hypersonic vehicle design. Furthermore, detailed numerical simulations of several integration schemes demonstrate the feasibility and diversity of the new approach.
Nomenclature
FCT= flow capture tube ICC = inlet capture curve L/D = lift to drag ratio M = mach number
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