ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

Artificial neural network-based subgrid-scale models for LES of compressible turbulent channel flow

Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers.The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point.The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43,with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model(DSM).In a posteriori test,the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles,mean temperature profiles,turbulent intensities,total Reynolds stress,total Reynolds heat flux,and mean SGS flux of kinetic energy,and outperformed the Smagorinsky model.

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

A discrete Boltzmann model(DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional(2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin.40 98108(2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142(2019)].In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman–Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod’s shock tube, sound wave, compressible Rayleigh–Taylor instability,and translational motion of a 2D fluid system.

Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.

FLOW STRESS MODELING FOR AERONAUTICAL ALUMINUM ALLOY 7050-T7451 IN HIGH-SPEED CUTTING

The high temperature split Hopkinson pressure bar （SHPB） compression experiment is conducted to obtain the data relationship among strain, strain rate and flow stress from room temperature to 550 C for aeronautical aluminum alloy 7050-T7451. Combined high-speed orthogonal cutting experiments with the cutting process simulations, the data relationship of high temperature, high strain rate and large strain in high-speed cutting is modified. The Johnson-Cook empirical model considering the effects of strain hardening, strain rate hardening and thermal softening is selected to describe the data relationship in high-speed cutting, and the material constants of flow stress constitutive model for aluminum alloy 7050-T7451 are determined. Finally, the constitutive model of aluminum alloy 7050-T7451 is established through experiment and simulation verification in high-speed cutting. The model is proved to be reasonable by matching the measured values of the cutting force with the estimated results from FEM simulations.

Study on compressibility of traffic flow

In order to describe the compressibility of traffic flows and determine the compression factors, the Mach number of gas dynamics is introduced, and the concept and the formula of the compression factor are obtained. According to the concept of the compression factor and its differential equation, a stop-wave model is built. The theoretical value and the observed one are obtained by the survey data in Changchun city. The relative error between the two values is 20. 3%. The accuracy is improved 39% compared with the result from the traditional stop-wave model. The results show that the traffic flow is compressible, and the methods of research on gas compressibility is also applicable to the traffic flow. The stop-wave model obtained by the compression factor can better describe the phenomenon of the stop wave at a signalized intersection when compared with the traditional stop-wave model.

COMPRESSIBLE FLOW SIMULATION AROUND AIRFOIL BASED ON LATTICE BOLTZMANN METHOD

The flow around airfoil NACA0012 enwrapped by the body-fitted grid is simulated by a coupled doubledistribution-function （DDF） lattice Boltzmann method （LBM） for the compressible Navier-Stokes equations. Firstly, the method is tested by simulating the low Reynolds number flow at Ma =0. 5,a=0. 0, Re=5 000. Then the simulation of flow around the airfoil is carried out at Ma：0. 5, 0. 85, 1.2; a=-0.05, 1.0, 0.0, respectively. And a better result is obtained by using a local refined grid. It reduces the error produced by the grid at Ma=0. 85. Though the inviscid boundary condition is used to avoid the problem of flow transition to turbulence at high Reynolds numbers, the pressure distribution obtained by the simulation agrees well with that of the experimental results. Thus, it proves the reliability of the method and shows its potential for the compressible flow simulation. The suecessful application to the flow around airfoil lays a foundation of the numerical simulation of turbulence.

Numerical simulation of the dimensional transformation of atomization in a supersonic aerodynamic atomization dust-removing nozzle based on transonic speed compressible flow

To simulate the transonic atomization jet process in Laval nozzles,to test the law of droplet atomization and distribution,to find a method of supersonic atomization for dust-removing nozzles,and to improve nozzle efficiency,the finite element method has been used in this study based on the COMSOL computational fluid dynamics module.The study results showed that the process cannot be realized alone under the two-dimensional axisymmetric,three-dimensional and three-dimensional symmetric models,but it can be calculated with the transformation dimension method,which uses the parameter equations generated from the two-dimensional axisymmetric flow field data of the three-dimensional model.The visualization of this complex process,which is difficult to measure and analyze experimentally,was realized in this study.The physical process,macro phenomena and particle distribution of supersonic atomization are analyzed in combination with this simulation.The rationality of the simulation was verified by experiments.A new method for the study of the atomization process and the exploration of its mechanism in a compressible transonic speed flow field based on the Laval nozzle has been provided,and a numerical platform for the study of supersonic atomization dust removal has been established.

Lattice Boltzmann Flux Solver:An Efficient Approach for Numerical Simulation of Fluid Flows

A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the governing differential equations,but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers.Instead,it is evaluated from local solution of lattice Boltzmann equation(LBE)at cell interface.Two versions of LBFS are presented in this paper.One is to locally apply one-dimensional compressible lattice Boltzmann(LB)model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves.The other is to locally apply multi-dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows.The present solver removes the drawbacks of conventional lattice Boltzmann method(LBM)such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.

A NOVEL SLIGHTLY COMPRESSIBLE MODEL FOR LOW MACH NUMBER PERFECT GAS FLOW CALCULATION

By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.

On the Liquid-Vapor Phase-Change Interface Conditions for Numerical Simulation of Violent Separated Flows

Numerous models have been proposed in the literature to include phase change into numerical simulations of two-phase flows.This review paper presents the modeling options that have been taken in order to obtain a model for violent separated flows with application to sloshing wave impacts.A relaxation model based on linear non-equilibrium thermodynamics has been chosen to compute the rate of phase change.The integration in the system of partial differential equations is done through a non-conservative advection term.For each of these modelling choices,some alternative models from the literature are presented and discussed.The theoretical framework for all phase change model(conservation equations and entropy growth)is also summarized.

A GHOST FLUID BASED FRONT TRACKING METHOD FOR MULTIMEDIUM COMPRESSIBLE FLOWS

Recent years the modify ghost fluid method （MGFM） and the real ghost fluid method （RGFM） based on Riemann problem have been developed for multimedium compressible flows. According to authors, these methods have only been used with the level set technique to track the interface. In this paper, we combine the MCFM and the RGFM respectively with front tracking method, for which the fluid interfaces are explicitly tracked by connected points. The method is tested with some one-dimensional problems, and its applicability is also studied. Furthermore, in order to capture the interface more accurately, especially for strong shock impacting on interface, a shock monitor is proposed to determine the initial states of the Riemann problem. The present method is applied to various one- dimensional problems involving strong shock-interface interaction. An extension of the present method to two dimension is also introduced and preliminary results are given.

GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA

By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.

Effects of the jet-to-crossflow momentum ratio on a sonic jet into a supersonic crossflow

Numerical investigation of a transverse sonic jet injected into a supersonic crossflow was carried out using large-eddy simulation for a free-stream Mach number M = 1.6 and a Reynolds number Re = 1.38×10~5 based on the jet diameter.Effects of the jet-to-crossflow momentum ratio on various fundamental mechanisms dictating the intricate flow phenomena,including flow structures, turbulent characters and frequency behaviors,have been studied.The complex flow structures and the relevant flow features are discussed to exhibit the evolution of shock structures,vortical structures and jet shear layers.The strength of the bow shock increases and the sizes of the barrel shock and Mach disk also increase with increasing momentum ratio.Turbulent characters are clarified to be closely related to the flow structures.The jet penetration increases with the increase of the momentum ratio.Moreover,the dominant frequencies of the flow structures are obtained using spectral analysis.The results obtained in this letter provide physical insight in understanding the mechanisms relevant to this complex flow

Characteristics of compressible flow of supercritical kerosene

In this paper, compressible flow of aviation kerosene at supercritical conditions has been studied both numerically and experimentally. The thermophysical properties of supercritical kerosene are calculated using a 10- species surrogate based on the principle of extended corresponding states （ECS）. Isentropic acceleration of supercritical kerosene to subsonic and supersonic speeds has been analyzed numerically. It has been found that the isentropic relationships of supercritical kerosene are significantly dif- ferent from those of ideal gases, A two-stage fuel heating and delivery system is used to heat the kerosene up to a tem- perature of 820 K and pressure of 5.5 MPa with a maximum mass flow rate of 100 g/s. The characteristics of supercritical kerosene flows in a converging-diverging nozzle （Laval nozzle） have been studied experimentally. The results show that stable supersonic flows of kerosene could be established in the temperature range of 730 K-820 K and the measurements in the wall pressure agree with the numerical calculation.

COMPUTATION OF COMPRESSIBLE FLOW PAST SLENDER WING－BODY USING FULL－POTENTIAL EQUATION

The H-O grid is suggested to compute compressible flow past highly swept slender wing-body combinations. Full-potential equation, finite difference method and approximate factorization scheme are used. The computations for the AGARD-B wing-body show that the code developed can apply to the cases from subsonic up to low supersonic free stream. The computed lift and pitching moment are in good agreement with the experimental results.

Gas flow characteristics of argon inductively coupled plasma and advections of plasma species under incompressible and compressible flows

In this work, incompressible and compressible flows of background gas are characterized in argon inductively coupled plasma by using a fluid model, and the respective influence of the two flows on the plasma properties is specified. In the incompressible flow, only the velocity variable is calculated, while in the compressible flow, both the velocity and density variables are calculated. The compressible flow is more realistic; nevertheless, a comparison of the two types of flow is convenient for people to investigate the respective role of velocity and density variables. The peripheral symmetric profile of metastable density near the chamber sidewall is broken in the incompressible flow. At the compressible flow, the electron density increases and the electron temperature decreases. Meanwhile, the metastable density peak shifts to the dielectric window from the discharge center, besides for the peripheral density profile distortion, similar to the incompressible flow.The velocity profile at incompressible flow is not altered when changing the inlet velocity, whereas clear peak shift of velocity profile from the inlet to the outlet at compressible flow is observed as increasing the gas flow rate. The shift of velocity peak is more obvious at low pressures for it is easy to compress the rarefied gas. The velocity profile variations at compressible flow show people the concrete residing processes of background molecule and plasma species in the chamber at different flow rates. Of more significance is it implied that in the usual linear method that people use to calculate the residence time, one important parameter in the gas flow dynamics, needs to be rectified. The spatial profile of pressure simulated exhibits obvious spatial gradient. This is helpful for experimentalists to understand their gas pressure measurements that are always taken at the chamber outlet. At the end, the work specification and limitations are listed.

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiplerelaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time （SRT） lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations, it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version.

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional （31）） Lattice Boltzmann （LB） model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 （2004） 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative （NND） scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model is validated by well-known benchmarks, （i） Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; （ii） reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.

ADAPTIVE DELAUNAY TRIANGULATION WITH MULTIDIMENSIONAL DISSIPATION SCHEME FOR HIGH-SPEED COMPRESSIBLE FLOW ANALYSIS

Adaptive Delaunay triangulation is combined with the cell-centered upwinding algorithm to analyze inviscid high-speed compressible flow problems. The multidimensional dissipation scheme was developed and included in the upwinding algorithm for unstructured triangular meshes to improve the computed shock wave resolution. The solution accuracy is further improved by coupling an error estimation procedure to a remeshing algorithm that generates small elements in regions with large change of solution gradients, and at the same time, larger elements in other regions. The proposed scheme is further extended to achieve higher-order spatial and temporal solution accuracy. Efficiency of the combined procedure is evaluated by analyzing supersonic shocks and shock propagation behaviors for both the steady and unsteady high-speed compressible flows.