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.

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow:Two-Dimensional Case

Lattice Boltzmann （LB） modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 （2007） 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests： shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

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.

Improvement and application of wall function boundary condition for high-speed compressible flows

In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simula- tion for the skin friction and heat flux, a research was performed to improve the compressible wall function boundary condition proposed by Nichols. Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation. Be- sides, the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately. Whereafter, the application study of the modified wall func- tion was carried out. The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux, and profiles of velocity, temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y＋〈400, and that the modifications to the original wall function can obviously improve the simulation precision. As for the application of separation flows, it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression comer that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall re- gion inside the separation flows, which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows, while for the region near separation and reattachment points, the wall function gives results with a rela- tively large error, because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real ve- locity profiles near the separation and reattachment points.

Optimal Design of High-Speed Partial Flow Pumps using Orthogonal Tests and Numerical Simulations

To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.

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.

Flow and sound fields of scaled high-speed trains with different coach numbers running in long tunnel

Segregated incompressible large eddy simulation and acoustic perturbation equations were used to obtain the flow field and sound field of 1:25 scale trains with three,six and eight coaches in a long tunnel,and the aerodynamic results were verified by wind tunnel test with the same scale two-coach train model.Time-averaged drag coefficients of the head coach of three trains are similar,but at the tail coach of the multi-group trains it is much larger than that of the three-coach train.The eight-coach train presents the largest increment from the head coach to the tail coach in the standard deviation(STD)of aerodynamic force coefficients:0.0110 for drag coefficient(Cd),0.0198 for lift coefficient(Cl)and 0.0371 for side coef-ficient(Cs).Total sound pressure level at the bottom of multi-group trains presents a significant streamwise increase,which is different from the three-coach train.Tunnel walls affect the acoustic distribution at the bottom,only after the coach number reaches a certain value,and the streamwise increase in the sound pressure fluctuation of multi-group trains is strengthened by coach number.Fourier transform of the turbulent and sound pressures presents that coach number has little influence on the peak frequencies,but increases the sound pressure level values at the tail bogie cavities.Furthermore,different from the turbulent pressure,the first two sound pressure proper orthogonal decomposition(POD)modes in the bogie cavities contain 90%of the total energy,and the spatial distributions indicate that the acoustic distributions in the head and tail bogies are not related to coach number.

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.

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.

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.

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.

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.

Flow structure around high-speed train in open air

According to the analysis of the turbulent intensity level around the high-speed train, the maximum turbulent intensity ranges from 0.2 to 0.5 which belongs to high turbulent flow. The flow field distribution law was studied and eight types of flow regions were proposed. They are high pressure with air stagnant region, pressure decreasing with air accelerating region, low pressure with high air flow velocity region I, turbulent region, steady flow region, low pressure with high air flow velocity region II,pressure increasing with air decelerating region and wake region. The analysis of the vortex structure around the train shows that the vortex is mainly induced by structures with complex mutation and large curvature change. The head and rear of train, the underbody structure, the carriage connection section and the wake region are the main vortex generating sources while the train body with even cross-section has rare vortexes. The wake structure development law studied lays foundation for the train drag reduction.

A BLOW-UP CRITERION FOR COMPRESSIBLE VISCOUS HEAT-CONDUCTIVE FLOWS

We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.

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.

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.

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.

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.

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.