Gauss-Hermite quadratures and accuracy of lattice Boltzmann models for non-equilibrium gas flows

Recently, kinetic theory-based lattice Boltzmann (LB) models have been developed to model nonequilibrium gas flows. Depending on the order of quadratures, a hierarchy of LB models can be constructed which we have previously shown to capture rarefaction effects in the standing-shearwave problems. Here, we further examine the capability of high-order LB models in modeling nonequilibrium flows considering gas and surface interactions and their effect on the bulk flow. The Maxwellian gas and surface interaction model, which has been commonly used in other kinetic methods including the direct simulation Monte Carlo method, is used in the LB simulations. In general, the LB models with high-order Gauss-Hermite quadratures can capture flow characteristics in the Knudsen layer and higher order quadratures give more accurate prediction. However, for the Gauss-Hermite quadratures, the present simulation results show that the LB models with the quadratures obtained from the even-order Hermite polynomials perform significantly better than those from the odd-order polynomials. This may be attributed to the zero-velocity component in the odd-order discrete set, which does not participate in wall and gas collisions, and thus underestimates the wall effect

Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows

In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is shown to be able to reduce to the linearized Bhatnagar–Gross–Krook (BGK) equation. Therefore, when the same Gauss–Hermite quadrature is used, LB method closely resembles the discrete velocity method (DVM). In addition, the order of Hermite expansion for the equilibrium distribution function is found not to be directly correlated with the approximation order in terms of the Knudsen number to the BGK equation for incompressible flows. Meanwhile, we have numerically evaluated the LB models for a standing-shear-wave problem, which is designed specifically for assessing model accuracy by excluding the influence of gas molecule/surface interactions at wall boundaries. The numerical simulation results confirm that the high-order terms in the discrete equilibrium distribution function play a negligible role in capturing non-equilibrium effect for low-speed flows. By contrast, appropriate Gauss–Hermite quadrature has the most significant effect on whether LB models can describe the essential flow physics of rarefied gas accurately. Our simulation results, where the effect of wall/gas interactions is excluded, can lead to conclusion on the LB modeling capability that the models with higher-order quadratures provide more accurate results. For the same order Gauss–Hermite quadrature, the exact abscissae will also modestly influence numerical accuracy. Using the same Gauss–Hermite quadrature, the numerical results of both LB and DVM methods are in excellent agreement for flows across a broad range of the Knudsen numbers, which confirms that the LB simulation is similar to the DVM process. Therefore, LB method can offer flexible models suitable for simulating continuum flows at the Navier–Stokes level and rarefied gas flows at the linearized Boltzmann model equation level

Analytical solution of axi-symmetrical lattice Boltzmann model for cylindrical Couette flows

Analytical solution for the axi-symmetrical lattice Boltzmann model is obtained for the low-Mach number cylindrical Couette flows. In the hydrodynamic limit, the present solution is in excellent agreement with the result of the Navier-Stokes equation. Since the kinetic boundary condition is used, the present analytical solution using nine discrete velocities can describe flows with the Knudsen number up to 0.1. Meanwhile, the comparison with the simulation data obtained by the direct simulation Monte Carlo method shows that higher-order lattice Boltzmann models with more discrete velocities are needed for highly rarefied flows

Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows

A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0:5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations that have been chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased

The Effect of the Inlet Total Pressure and the Number of Detonation Waves on Rotating Detonation Engines

AbstractThis paper presented a three-dimensional numerical study of rotating detonation engines, exploring the effect of the inlet total pressure and the number of detonation waves on the performance of rotating detonation engines. It was found that under the same total pressure of the inlet fuel, the number of detonation waves had little influence on the specific impulse, the thrust and the outlet flow of RDE. The number of detonation waves, however, affected the time needed to reach stable detonation.Besides, there was instability phenomenon in the development of detonation waves due to the relation between the number of detonation waves and the inlet total pressure. In order to speed up the process from ignition to stable detonation, the total pressure of the inlet fuel should match with the ignitions

Modeling and simulation of brake judder considering the effects of thermo-mechanical coupling

Reproducing the real behavior of brake judder in time domain is useful for brake judder reduction, but it is hard to establish a time-domain model of brake judder due to the effects of thermo-mechanical coupling. To solve this problem, a modeling method is proposed taking into account the effects of thermo-mechanical coupling before hotspot occurs. In this method, an eight-degree-of-freedom dynamics model of brake caliper assembly with multi-contact points is established, and a semi-empirical model of friction coefficient is proposed by magic formula tyre model. The input of the dynamics model is the initial disc thickness variation (DTV) and the DTV caused by uneven heating, which is calculated by a transient FE model of thermo-mechanical coupling considering initial DTV. On this basis, a simulation of brake judder is conducted and an experiment is designed to validate the method. The simulated brake pressure and brake torque without and with thermo-mechanical coupling are compared with the experiment results respectively, and it indicates that the simulated results considering thermo-mechanical coupling have a good agreement with experiment results. Brake pressure variation (BPV) and brake torque variation (BTV) increase gradually in time domain because of the effects of thermo-mechanical coupling and the increments of BPV and BTV can reach 45 % and 50 % respectively in the simulation

Linezolid and Rifampicin Combination to Combat cfr-Positive Multidrug-Resistant MRSA in Murine Models of Bacteremia and Skin and Skin Structure Infection.

Linezolid resistance mediated by the cfr gene in MRSA represents a global concern. We investigated relevant phenotype differences between cfr-positive and -negative MRSA that contribute to pathogenesis, and the efficacy of linezolid-based combination therapies in murine models of bacteremia and skin and skin structure infection (SSSI). As a group, cfr-positive MRSA exhibited significantly reduced susceptibilities to the host defense peptides tPMPs, human neutrophil peptide-1 (hNP-1), and cathelicidin LL-37 (P < 0.01). In addition, increased binding to fibronectin (FN) and endothelial cells paralleled robust biofilm formation in cfr-positive vs. -negative MRSA. In vitro phenotypes of cfr-positive MRSA translated into poor outcomes of linezolid monotherapy in vivo in murine bacteremia and SSSI models. Importantly, rifampicin showed synergistic activity as a combinatorial partner with linezolid, and the EC50 of linezolid decreased 6-fold in the presence of rifampicin. Furthermore, this combination therapy displayed efficacy against cfr-positive MRSA at clinically relevant doses. Altogether, these data suggest that the use of linezolid in combination with rifampicin poses a viable therapeutic alternative for bacteremia and SSSI caused by cfr-positive multidrug resistant MRSA