Aerodynamics of high speed trains passing by each other

A three-dimensional flow field induced by two trains passing by each other inside a tunnel is studied based on the numerical simulation of the three-dimensional compressible Euler/Navier-Stokes equations formulated in the finite difference approximation. A domain decomposition method with the FSA (fortified solution algorithm) interface scheme is used to treat this moving-body problem. The computed results show the basic characteristics of the flow field created when two trains pass by each other. The history of the pressure distributions and the aerodynamic forces acting on the trains are the main areas discussed. The results indicate that the phenomenon is complicated due to the interaction of the flow induced by the two trains. Strong side forces occur between the two trains when the front portion of the opposite train passes by. The forces fluctuate rapidly and the maximum suction force occurs when two trains are aligned side by side. The results also indicate the effectiveness of the present numerical method calculating moving boundary problems.     

Numerical studies in high Reynolds number aerodynamics

Two numerical approaches are presented for the computation of viscous compressible flows at high Reynolds' numbers. In the first approach, named global approach, the whole flow field, which includes viscous and inviscid regions, is determined as the solution of a single set of equations, which may be the full Navier-Stokes equations, or some approximate form of these equations. The second approach, named coupling approach, consists in solving two different sets of equations in their respective domains simultaneously; one of the two sets governs an inviscid flow whose boundary conditions are provided by the viscous effects, determined by the other set.The discussion of the global approach is centred on two particular features of the finite-difference method used: a discretization technique, directly in the physical plane with arbitrary meshes: and a mesh adaptation technique, which combines a coordinate transformation to fit the mesh system to particular lines in the flow, and a technique of dichotomy for mesh refinement. Numerical results are presented for an axisymmetric compression corner and a shock-boundary layer interaction on a flat plate, both in supersonic regime, and for a transonic nozzle flow.For the coupling approach, emphasis is given firstly to the improvement resulting from an interacting analysis where the viscous and inviscid computations are matched, and not only patched. It is shown that the parabolic problems associated with simple viscous theories are always replaced by elliptic problems, even for supersonic flows, and that “supercritical interactions” or “critical points”, as defined by Crocco-Lees, are removed. Secondly, a new coupling method, fully automatized and capable of solving directly a well-posed problem for supersonic flow, is illustrated by examples involving shock wave-boundary layer interactions and reverse flow bubbles; they concern flows over symmetrical transonic airfoils and supersonic compression ramps.     

Boundary conditions for subsonic compressible Navier-Stokes calculations

A systematic study of inflow and outflow boundary conditions for the numerical solution of the compressible Navier-Stokes equations is presented. Combinations of several representative inflow and outflow boundary conditions are applied in the solution of subsonic flow over a flat plate in a finite computational domain. These boundary conditions are evaluated in terms of their effect on the accuracy of the solution and the rate of convergence to a steady state. It is shown that errors in the data specified at the inflow boundary can produce significant errors in the computed flow field. It is also shown that a non-reflecting outflow boundary condition can significantly reduce the total computational time required.     

GPU acceleration for general conservation equations and its application to several engineering problems

In the this paper, shock/shock and shock/boundary layer interactions in thermochemical nonequilibrium flow have been analyzed. The analysis is limited to flow at Mach 9 around a double-wedge selected to generate an interaction of type IVr that does not fit into Edney’s classification. It is generally known that the interaction of type IV are associated with very high local loads in pressure and heat transfer. The numerical resolution of the Navier Stokes equations allows the prediction of the structure of flow field. The numerical method used is based on a finite volume formulation defined on a structured multi block mesh. Particular emphasis is given to the contribution of real gas effects on the topological characteristics and dynamic structure of the flow field. A comparative study of the contours of Mach numbers and pressure is shown. The results obtained showed that the flow field is highly sensitive to real gas effects.     

含激波、旋涡和声波的复杂多尺度流动的直接数值模拟

本文主要报道了我们近年来在银河并行机上采用五阶WENO格式所做的一系列直接数值模拟研究,主要包括激波与单旋涡相互作用、激波与旋涡对相互作用、激波与三维纵向旋涡的相互作用,以及可压缩各向同性湍流。研究的主要目的是揭示激波与旋涡间相互作用中的激波动力学特性、旋涡变形、旋涡破裂和声波的产生机理,以及湍流等多尺度复杂流动的流场结构和流动机理。研究表明,高阶WE-NO格式具有很好的分辨率和稳定性,是研究上述包含强间断与复杂流场结构的流动的理想数值方法。研究发现,激波与强旋涡相互作用具有多级特征,即激波与初始旋涡的相互作用、反射激波与变形旋涡的相互作用、小激波与变形旋涡的相互作用。激波与旋涡对相互作用中产生的声波包含两个区域:线性区和非线性区。在线性区,激波与旋涡对相互作用产生的声波是激波分别与每个旋涡单独作用产生的声波的线性叠加;而在非线性区则与激波和耦合旋涡对的作用有关。在激波与纵向旋涡的相互作用过程中,发现旋涡破裂区存在多螺旋结构。在高初始湍流马赫数的各向同性湍流脉动场中,也发现了广泛报导的"小激波"的存在,这是可压缩湍流有别于不可压缩湍流的显著结构特征。     

Study of subsonic�Csupersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver

We use an extended direct simulation Monte Carlo (DSMC) method, applicable to unstructured meshes, to numerically simulate a wide range of rarefaction regimes from subsonic to supersonic flows through micro/nanoscale converging–diverging nozzles. Our unstructured DSMC method considers a uniform distribution of particles, employs proper subcell geometry, and follows an appropriate particle tracking algorithm. Using the unstructured DSMC, we study the effects of back pressure, gas/surface interactions (diffuse/specular reflections), and Knudsen number on the flow field in micro/nanoscale nozzles. If we apply the back pressure at the nozzle outlet, a boundary layer separation occurs before the outlet and a region with reverse flow appears inside the boundary layer. Meanwhile, the core region of inviscid flow experiences multiple shock-expansion waves. In order to accurately simulate the outflow, we extend a buffer zone at the nozzle outlet. We show that a high viscous force creation in the wall boundary layer prevents any supersonic flow formation in the divergent part of the nozzle if the Knudsen number exceeds a moderate magnitude. We also show that the wall boundary layer prevents forming any normal shock in the divergent part. In reality, Mach cores would appear at the nozzle center followed by bow shocks and expansion region. We compare the current DSMC results with the solution of the Navier–Stokes equations subject to the velocity slip and temperature jump boundary conditions. We use OpenFOAM as a compressible flow solver to treat the Navier–Stokes equations.     

An immersed-boundary method for compressible viscous flows

This paper combines a state-of-the-art method for solving the preconditioned compressible Navier-Stokes equations accurately and efficiently for a wide range of the Mach number with an immersed-boundary approach which allows one to use Cartesian grids for arbitrarily complex geometries. The method is validated versus well documented test problems for a wide range of the Reynolds and Mach numbers. The numerical results demonstrate the efficiency and versatility of the proposed approach as well as its accuracy, from incompressible to supersonic flow conditions, for moderate values of the Reynolds number. Further improvements, obtained via local grid refinement or non-linear wall functions, can render the proposed approach a formidable tool for studying complex three-dimensional flows of industrial interest.     

Computational simulation of transient blast loading on three-dimensional structures

A computing technique is described for the numerical solution of three-dimensional, time-dependent fluid dynamic problems with irregularly shaped and movable boundaries (or internal obstacles) confining the flow. This paper presents in detail the method used in treating the three-dimensional boundary conditions. The numerical solution technique for the full nonlinear Navier-Stokes equations has been presented elsewhere. The general method is illustrated here through comparison of computed surface pressure time histories with the corresponding experimental data for a plane-shock wave (5 psi overpressure) passing over a rectangular parallelepiped.     

Numerical simulation of a compressible turbulent boundary layer over a conductive wall with line heat source

A conjugated problem of supersonic turbulent flow over a conductive solid wall with an embedded line heat source has been investigated as a model of a separation detector and skin friction gage. The 2-D Navier-Stokes equations for compressible fluid, including a two layer eddy viscosity model, are solved simultaneously with the heat transfer equation for the solid, written in general coordinates. The effect of the interface boundary condition on the stability of the implicit scheme of the flow field has been checked. A careful investigation of the effect of heat source strength, solid and fluid conductivity and Mach and Reynolds numbers on flow and temperature fields has been performed. The results of this investigation may be used to design an optimal gage with a minimum influence on the flow field.     

A numerical method for the transonic cascade flow problem

An implicit time-marching finite-difference method for solving the three-dimensional compressible Navier-Stokes equations for the relative flow of a turbomachine impeller in general curvilinear coordinates is presented. The fundamental equations of the method have the distinctive feature that the momentums of the contravariant velocities are employed as the dependent variables. The use of the momentum equations of the contravariant velocities makes possible correct and simple treatments of some boundary conditions. In order to obtain the stable solution for high Reynolds number turbulent flow, the Navier-Stokes equations and the k-ε turbulence model equations are solved simultaneously, and a high-resolution TVD upwind scheme is introduced. The calculated results of some two-dimensional turbulent flows agreed well with the experimental data. The calculated results of an axial-flow transonic compressor rotor flow showed that the leakage vortex from the tip clearance as well as the shock waves can be captured vividly, in spite of the relatively coarse grid.     

Analysis of unsteady compressible boundary layer flow via finite elements

This paper is concerned with the discrete formulation and numerical solution of unsteady compressible boundary layer flows using the Galerkin-finite element method. Linear interpolation functions for the velocity, density, temperature and pressure are used in the momentum equation and equations of continuity, energy and state. The coupled nonlinear finite element equations are approximated by a third order Taylor series expansion as temporal operator to integrate in time with Newton-Raphson type iterations performed until convergence within each time step. As an example, a boundary layer problem of a perfect gas behind a normal shock wave is solved. A comparison of the results with those by other method indicates a favorable agreement.     

Computational study of the transonic flow around a rocket-shaped body

Transonic flows around a rocket were computed using the second-order TVD scheme proposed by Harten for solving the two- and three-dimensional unsteady, compressible Navier-Stokes equations in the conservation-law form. LU-ADI and DD-ADI schemes were employed to the implicit part. The influences of the Reynolds number on the shock-wave/boundary-layer and the shock-wave/vortex interaction were clarified by the two-dimensional analysis. The three-dimensional computations show that there is no stationary shock-wave except near the nose cone. In the wake region, a pair of asymmetrical vortices separates periodically, and the shear layer oscillates. The computed pressure distribution on the surface of the body was compared with that of the three-dimensional experiment. The qualitative agreement of the general profile was good.     

Flow about a spherically blunted body in a supersonic wake

Stationary flows about the nose of a spherically blunted body in a supersonic wake-type, nonuniform oncoming stream are investigated. The flow calculation is carried out using the Navier-Stokes equations which are solved by means of the implicit finite-difference, unidirectional scheme. Oncoming stream nonuniformity, rarefaction and wall cooling effects on the shock layer structure and the distributions of the drag and heat transfer parameters along the body surface are investigated. The solutions of the full Navier-Stokes equations are compared with the results obtained using the reduced Navier-Stokes and Euler equations.     

Direct computation of perturbed impinging hot jets

The unsteady flow and temperature fields of an impinging hot jet at a Reynolds number of 1000 and a nozzle-to-plate distance of 6 jet diameters have been obtained by direct numerical solution of the compressible time-dependent three-dimensional Navier-Stokes equations using highly accurate numerical methods. Effects of an external perturbation on the flow and heat transfer characteristics of the transitional impinging jet have been examined. Oscillatory behaviour induced by the external perturbation has been observed for the impinging jet. The external perturbation leads to the large-scale vortical structures in the primary jet stream, which subsequently lead to the strong oscillatory behaviour of the impinging jet. The vortical structures lead to flow transitional behaviour that enhances mixing of the hot jet with the ambient fluid. It has been observed that the wall boundary layer of the impinging jet is thin. Both the instantaneous and time-averaged wall shear and normal stresses and Nusselt number are examined. Although the external perturbation strongly affects the flow structures in the primary jet stream, it does not have significant effects on the wall stresses and heat transfer characteristics of the impinging jet due to the re-laminarization effect of the wall.     

Development of a MEMS-based control system for compressible flow separation

A MEMS-based sensor and actuator system has been designed and fabricated for separation control in the compressible flow regime. The MEMS sensors in the system are surface-micromachined shear stress sensors and the actuators are bulk-micromachined balloon vortex generators (VGs). A three-dimensional (3-D) wing model embedded with the shear stress sensors and balloon VGs was tested in a transonic wind tunnel to evaluate the performance of the control system in a range of Mach number between 0.2 and 0.6. At each Mach number tested, the shear stress sensors quantify the boundary layer on the surface of the wing model while the balloon VGs interact with the boundary layer in an attempt to provide flow control. The shear stress measurements indicate the presence of a separated flow on the trailing ramp section of the wing model at all Mach numbers tested when the balloon VGs are not activated. This result is confirmed by total pressure measurements downstream from the wing model where a wake profile is observed. When the balloon VGs are activated, the shear stress level on the trailing ramp increases with the Mach number. At the highest Mach number tested, this increase elevates the shear stress on the ramp to almost the same level as the unseparated flow, suggesting the possibility of a boundary layer reattachment. This result is supported by the downstream pressure measurements which show a large pressure recovery when the balloon VGs are activated. The wind tunnel experiment successfully demonstrated two aspects of the MEMS flow control system: the effectiveness of the microshear stress sensors in measuring the separation characteristics of a high-speed compressible flow and the ability of the microballoons in positively enhancing the aerodynamic performance of a high-speed wing through boundary layer modification.     

A higher order finite element algorithm for the unsteady Navier-Stokes equations

A higher order element, the Tocher 10 or C₀ Cubic on triangles, is the base for formulation of a finite element algorithm for numerical calculation of fluid flows governed by the unsteady Navier-Stokes equations. Results from the calculation of supersonic free shear layer flow are numerically accurate and in excellent agreement with finite difference solutions. Diverse characteristics for these two classes of methods emerge when the requirements of core storage and computer time are considered.     

Vectored injection into compressible laminar and turbulent boundary layers

A fundamental analysis of two-dimensional supersonic boundary layer flow, both laminar and turbulent, is presented for a wide range of normal and nonnormal mass-transfer velocities. The analysis is based on the numerical solution of the Navier-Stokes equations, and results are compared with available theoretical and experimental data. Certain cases of practical importance, for which results are not presently available, are referred to.     

Separation-bubble flow solution using Euler/Navier-Stokes zonal approach with downstream compatibility conditions

An Euler/Navier-Stokes zonal scheme is developed to numerically simulate the two-dimensional flow over a blunt leading-edge plate. The computational domain has been divided into inner and outer regions where the Navier-Stokes and Euler equations are used, respectively. On the downstream boundary, compatibility conditions derived from the boundary-layer equations are used. The grid is generated by using conformal mapping and the problem is solved by using a compressible Navier-Stokes code, which has been modified to treat Euler and Navier-Stokes regions. The accuracy of the solution is determined by the reattachment location. Bench-mark solutions have been obtained using the Navier-Stokes equations throughout the optimum computational domain and size. The problem is recalculated with sucessive decrease of the computational domain from the downstream side where the compatibility conditions are used, and with successive decrease of the Navier-Stokes computational region. The results of the zonal scheme are in excellent agreement with those of the benchmark solutions and the experimental data. The CPU time saving is about 15%.     

Numerical study of passive and active flow separation control over a NACA0012 airfoil

This paper is focused on numerical investigation of subsonic flow separation over a NACA0012 airfoil with a 6° angle of attack and flow separation control with vortex generators. The numerical simulations of three cases including an uncontrolled baseline case, a controlled case with passive vortex generator, and a controlled case with active vortex generator were carried out. The numerical simulation solves the three-dimensional Navier-Stokes equations for compressible flow using a fully implicit LU-SGS method. A fourth-order finite difference scheme is used to compute the spatial derivatives. The immersed-boundary method is used to model both the passive and active vortex generators. The characteristic frequency that dominates the flow is the natural frequency of separation in the baseline case. The introduction of the passive vortex generator does not alter the frequency of separation. In the case with active control, the frequency of the sinusoidal forcing was chosen close to the natural frequency of separation. The time- and spanwise-averaged results were used to examine the mean flow field for all three cases. The passive vortex generators can partially eliminate the separation by reattaching the separated shear layer to the airfoil over a significant extent. The size of the averaged separation zone has been reduced by more than 80%. The flow control with active vortex generator is more effective and the separation zone is not visible in the averaged results. The three-dimensional structures of the flow field have also been studied.     

Iterative methods for stationary solutions to the steady-state compressible Navier-Stokes equations

Numerical experiments are presented for the solution of the steady-state compressible Navier-Stokes equations. One test problem is fixed supersonic flow past a double ellipse, and the various solution methods studied. The problem is discretized using Osher's scheme, first- and second-order accurate. The fastest convergence to steady state is obtained using Newton's method. Simplifications of Newton's method based on domain decomposition are shown to perform well, whereas line relaxation methods meet with difficulties.