In recent years, coupled with traditional turbulence models, the second-order gas-kinetic scheme (GKS) has been used in the turbulent flow simulations. At the same time, highorder GKS has been developed, such as the two-stage fourth-order scheme (S2O4) GKS, and used for laminar flow calculations. In this paper, targeting on the high-Reynolds number engineering turbulent flows, an implicit high-order GKS with Lower-Upper Symmetric Gauss-Seidel (LU-SGS) technique is developed under the S2O4 framework. Based on Vreman-type LES model and k − ω SST model, a turbulent relaxation time is obtained and used for an enlarged particle collision time in the implicit high-order GKS for the high-Reynolds number turbulent flows. Numerical experiments include incompressible decaying homogeneous isotropic turbulence, incompressible high-Reynolds number flat plate turbulent flow, incompressible turbulence around NACA0012 airfoil, transonic turbulence around RAE2822 airfoil, and transonic high-Reynolds number ARA M100 wing-body turbulence. Comparisons among the numerical solutions from current implicit high-order GKS, the explicit high-order GKS, the implicit second-order GKS, and experimental measurements have been conducted. Through these examples, it is concluded that the high-order GKS has high accuracy in space and time, especially for smooth flows, obtaining more accurate turbulent flow fields on coarse grids compared with second-order GKS. In addition, significant acceleration on computational efficiency, as well as super robustness in simulating complex flows are confirmed for current implicit high-order GKS. This study also indicates that turbulence modeling plays a dominant role in the capturing physical solution, such as in the transonic three-dimensional complex RANS simulation, in comparison with numerical discretization errors.
International Journal of Thermal Sciences, Vol. 110, pp. 270-284, 2016, DOI: 10.1016/j.ijthermalsci.2016 AbstractThermo-hydrodynamic behaviour of bidirectional dry gas seals with trapezoidal shaped symmetric grooves is studied. A multi-physics model, coupling compressible laminar flow and heat transfer in both the fluid and the solid bodies is used in a multi-physics modelling environment. The multi-physics model also includes slip flow conditions, corresponding to relatively high Knudsen numbers, as well as the effect of asperity interactions on the opposing seal faces. A comparison of the seal performance under isothermal and thermal flow conditions shows the importance of including the thermal effects. The difference in the predicted opening force between isothermal and thermal model can exceed 2.5%, which is equivalent to a force of around 1kN. The importance of designing gas seals to operate at the minimum possible gap to reduce power losses as well as leakage from the contact is highlighted. However, it is shown that there exists a critical minimum gap, below which the power loss in the contact can abruptly increase due to asperity interactions, generating significantly increased operating temperatures. Relative depths at the triangular and middle trunk parts of the grooves ℎ Convection heat transfer coefficient ℎ , , ℎ , Convection heat transfer coefficient from outer rims of rotor and stator Thermal conductivity of the gas Thermal conductivity of seal ring material Keywords Gas temperature at the inlet (outer radius), , , Gas temperature near rotor and stator contact face surfaces Temperature of the solid wall in contact with sealing gas
In this study, the high-resolution numerical simulations of the two-dimensional (2D) multi-component inert and reactive highly underexpanded jets are conducted to quantify the influences of the injected gas mixture properties on the flow structure. First, the gas mixture with the specified species mass fractions is imposed to exhaust into the quiescent air with a Mach number of 1.0, of which the specific heat ratios (γe) range from 1.3 to 1.6. Our results indicate that the larger γe yields a relatively shorter and thinner jet core under the same inlet pressure ratio due to the sound speed increasing. Next, we focus on the chemical reaction effects on the jets with a premixed hydrogen–air mixture injection. The results reveal that the shock-induced combustion develops into a detonation, inducing numerous vortices behind the combustion wave, while the combustion in the mixing layer cannot be preserved due to the instability of the supersonic shearing. During the detonation process, the increasing pressure accompanied by the heat release forces the Riemann wave to move upstream compared with the inert one. The violent detonation periodically propagates between the two jet triple points. The detonation collision leads to the intersection of their slip lines, which causes distinct vortex formation. In addition, the main frequencies, corresponding to the Riemann wave movement, the oscillation of the shock-induced ignition positions, the periodical propagation of the detonation, and the collision of the detonation triple points, are explored to explain the unsteady process of the reactive highly underexpanded jet.
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