Direct numerical simulation of laminar–turbulent flow over a flat plate at hypersonic flow speeds

A method for direct numerical simulation of a laminar–turbulent flow around bodies at hypersonic flow speeds is proposed. The simulation is performed by solving the full three-dimensional unsteady Navier–Stokes equations. The method of calculation is oriented to application of supercomputers and is based on implicit monotonic approximation schemes and a modified Newton–Raphson method for solving nonlinear difference equations. By this method, the development of three-dimensional perturbations in the boundary layer over a flat plate and in a near-wall flow in a compression corner is studied at the Mach numbers of the free-stream of M = 5.37. In addition to pulsation characteristic, distributions of the mean coefficients of the viscous flow in the transient section of the streamlined surface are obtained, which enables one to determine the beginning of the laminar–turbulent transition and estimate the characteristics of the turbulent flow in the boundary layer.     

Numerical solution of turbulent jet flows

The work deals with numerical modelling of several turbulent 3D jet flows: steady impinging jet, steady free jet in cross–flow, synthetic free jet (unsteady) and synthetic impinging jet (unsteady). The numerical method is based on artificial compressibility method with dual time extension for unsteady cases. Space discretization uses cell–centered finite volume method with third order accurate upwind approximation for convection, the time discretisations are implicit. Turbulence is modelled using two–equation eddy viscosity models and by explicit algebraic Reynolds stress model (EARSM by Wallin and Hellsten). The results of first three cases are compared with measurements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of spatially unsteady jets of compressible gas on a multiprocessor computer system

Vortex structures in subsonic and transonic jets of various initial profiles are numerically simulated. The mathematical models are based on conservative finite difference schemes that approximate conservation laws in the framework of the model of nonviscous perfect gas. The unsteady vortex structures are visualized. Pulsating characteristics of the flow are examined and compared with experimental data. Computations are performed using parallel algorithms implemented on a cluster architecture system. The influence of the parallelization scheme and the number of computing units on the performance of the algorithms is investigated. The approximation errors of real-life computations are estimated using the differential approximation method.     

Theorie zur Berechnung des Abströmwinkels bei Turbinengittern

Summary A simple method is given for the approximate calculation of the outlet flow angle for cascades of narrow-spaced blades of the type used in steam and gas turbines. The method is based on continuity and momentum equation and may be applied to compressible flow.      

Numerical modeling of unsteady flow in steam turbine stage

This work deals with numerical solution of unsteady flow in turbine stage. We use models of compressible single-phase flow of air and two-phase flow of wet steam. Presented numerical methods are based on different stator-rotor matching algorithms, as well as different numerical schemes. Numerical results achieved by both methods and flow models are discussed.     

A corrected smoothed particle hydrodynamics method for solving transient viscoelastic fluid flows

In this work, a corrected smoothed particle hydrodynamics (CSPH) method is proposed and extended to the numerical simulation of transient viscoelastic fluid flows due to that its approximation accuracy in solving the Navier–Stokes equations is higher than that of the smoothed particle hydrodynamics (SPH) method, especially near the boundary of the domain. The CSPH approach comes with the idea of combining the SPH approximation for the interior particles with the modified smoothed particle hydrodynamics (MSPH) method for the exterior particles, this is because that the later method has higher accuracy than the SPH method although it also needs more computational cost. In order to show the validity of CSPH method to simulate unsteady viscoelastic flows problems, the planar shear flow problems, including transient Poiseuille, Couette flow and transient combined Poiseuille and Couette flow for the Oldroyd-B fluid are solved and compared with the analytical and SPH results. Subsequently, the general viscoelastic fluid based on the eXtended Pom–Pom (XPP) model is numerically investigated and the viscoelastic free surface phenomena of impacting drop are simulated by the CSPH for its extended application and the purpose of illustrating the ability of the proposed method. The numerical results are presented and compared with available solutions, which shows a very good agreement. All the numerical results show the higher accuracy and better stability of the CSPH than the SPH, especially for larger Weissenberg numbers.     

Verification of software codes for simulation of unsteady flows in a gas centrifuge

A simple semi-analytical solution is proposed for the problem of an unsteady gas flow in a gas centrifuge. The circulation in the centrifuge is driven by a source/sink of energy and by an external force (deceleration/acceleration of the gas rotation) acting on the gas at a given frequency. In the semi-analytical solution, the rotor is infinite, while the given forces vary harmonically with a given wave-length along the axial coordinate. As a result, the unsteady flow problem is reduced to a system of ordinary differential equations, which can be quickly solved to any prescribed accuracy. This problem is proposed for verifying numerical codes designed for the simulation of unsteady processes in gas centrifuges. A similar unsteady problem is solved numerically, in which case the cylinder is finite with the rotor length equal to the wavelength of the external force along the axis of rotation. The periodicity of the solution is set at end faces of the cylinder. As an example, the semi-analytical solution is compared with the numerical one obtained with these boundary conditions. The comparison confirms that the problem formulations are equivalent in both cases.     

A tracking method for gas flow into vacuum based on the vacuum Riemann problem

In this paper, a tracking method is proposed for the expansion of gas flow into vacuum which may be combined with numerical methods for the equations of gas dynamics, the Euler equations. This tracking prevents the difficulties of the numerical approximation introduced by the vacuum as a region where the Euler equations are not valid due to the failure of the continuum assumption. The tracking algorithm is based on the exact or an approximate solution of the vacuum Riemann problem. This is the initial value problem with two constant states, one being the gas and the other the vacuum state, and a limit case of the usual Riemann problem. In this approach, the gas–vacuum boundary is sharply resolved within one mesh interval. For a test problem, the numerical results of gas flow into vacuum are presented which indicate that the gas vacuum boundary is captured very well.     

Direct numerical simulation of the laminar–turbulent transition at hypersonic flow speeds on a supercomputer

A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar–turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier–Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton–Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar–turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar–turbulent transition.     

直管束流固耦合振动的数值模拟

为了研究反应堆结构中的诸如燃料棒、蒸汽发生器和其它换热器传热管束等的流体-结构交互作用问题,利用有限体积法离散大涡模拟(large eddy simulation, LES)的流体控制方程,用有限元方法求解结构动力学方程,并结合动网格技术,建立三维流体诱发振动的数值模型,模拟直管束中流体的流动及结构振动,实现计算结构动力学(computational structure dynamics, CSD)与计算流体力学(computational fluid dynamics, CFD)之间的联合仿真．首先,基于流固耦合方法对单管的流致振动特性进行了详细分析,得到了其动力学响应与流场特性;其次基于建立的传热管束流致振动计算模型,研究了两并列管、两串列管以及3×3正方形排列管束的流致振动行为．     

Relaxation approximation to bed-load sediment transport

In this work we propose and apply a numerical method based on finite volume relaxation approximation for computing the bed-load sediment transport in shallow water flows, in one and two space dimensions. The water flow is modeled by the well-known nonlinear shallow water equations which are coupled with a bed updating equation. Using a relaxation approximation, the nonlinear set of equations (and for two different formulations) is transformed to a semilinear diagonalizable problem with linear characteristic variables. A second order MUSCL-TVD method is used for the advection stage while an implicit–explicit Runge–Kutta scheme solves the relaxation stage. The main advantages of this approach are that neither Riemann problem solvers nor nonlinear iterations are required during the solution process. For the two different formulations, the applicability and effectiveness of the presented scheme is verified by comparing numerical results obtained for several benchmark test problems.     

Splitting over physical processes as applied to the construction of a numerical method for solving the system of kinetic equations governing a hall thruster rarefied plasma jet

A numerical method is constructed for solving the system of kinetic equations describing the behavior of a rarefied plasma jet exhausted from a Hall thruster. A similar problem was previously considered in the steady case. Now the same problem is solved in the unsteady formulation. The numerical method is based on a generalization of the splitting method with respect to physical processes, which is widely used in rarefied gas dynamics. The basic difficulty faced in the natural generalization of this method as applied to thruster jets is that a boundary condition has to be taken into account when the ion distribution function is determined. This difficulty is overcome by analytically selecting the corresponding term at the stage of free-molecular motion. Another difficulty that can be coped with by the splitting method is that the ion and neutral velocity spaces have widely different scales. Techniques for making the method conservative are described, and situations in which this is necessary are discussed. Qualitative characteristics of some numerical computations are compared with experimental data. The comparison shows that the numerical method constructed adequately reproduces the behavior of the modeled object.     

带激波的一维非定常两相流动的数值模拟

本文将处理带激波的单相气体非定常流动问题的两种高分辨数值方法(随机取样法和二阶GRP有限差分法)推广应用于气固悬浮体(亦称含灰气体)两相情况,计算了含灰气体激波管中两相激波特性、波后流场结构及气固两相流动参数随时间的变化.数值结果表明:这两种方法均能给出带有尖锐间断阵面的两相激波松弛结构.二阶GRP方法在计算精度和机时耗用等方面优于随机取样法.     

Numerical Study on Hypersonic Flow and Aerodynamic Heating北大核心CSCD

基于有限差分法开发了高超声速流动与换热问题气热耦合仿真求解器,运用该求解器对三种典型高超声速流动与换热问题开展了仿真研究,得到了相应的气动参数、热流密度分布。高超声速后台阶的存在使表面气动参数、热流分布不再连续;随着缝深的提高,缝隙局部流速迅速降低,对流换热效应减弱;高超声速无限长圆管绕流中,边界层外部区域气动参数随时间变化不大,边界层内存在较大的温度梯度,壁面温度随时间升高。三个算例的仿真结果均与试验测量值进行了对比,验证了所开发的求解器的计算能力。     

Seismic-generated unsteady motions in shallow basins and channels. Part II: Numerical modelling

In this paper, unsteady motions generated by seismic-type excitation are simulated by a 2D depth-averaged mathematical model based on the classic shallow water approximation. A suitable time-dependent forcing term is added in the governing equations, and these are solved by a MUSCL-type shock-capturing finite volume scheme with a splitting treatment of the source term. The HLL approximate Riemann solver is used to estimate the numerical fluxes. The accuracy of the numerical scheme is assessed by comparison with novel exact solutions of test cases concerning sinusoidally-generated sloshing in a prismatic tank, a rectangular open channel, and a parabolic basin. A sensitivity analysis is performed on the influence of the relevant dimensionless parameters. Moreover, numerical results are validated against experimental data available in literature concerning shallow water sloshing in a swaying tank. Finally, real‐scale applications to a reservoir created by a dam and an urban water-supply storage tank are presented. The results show that the model provides accurate solutions of the shallow water equations with a seismic-type source term and can be effectively adopted to predict the main flow features of the unsteady motion induced by horizontal seismic acceleration when the long wave assumption is valid.     

Unsteady Flow and its Influence to Aerodynamic and Aeroacoustic of VAWT's

A study is reported of the influence of unsteady flow on the aerodynamics and aeroacoustics of vertical axis wind turbines by numerical simulation. The combination of aerodynamic predictions with a discrete vortex method and aeroacoustic predictions based on Ffowcs Williams-Hawkings equation is used to achieve this goal. The numerical results show that unsteady flow of the turbine has a significant influence on the turbine aerodynamics and can lead to a decrease in generated noise as compared to the conventional horizontal axis wind turbine at the similar aerodynamic performance. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

膛口流场动力学过程数值研究

采用基于ALE方法的动网格及嵌入网格技术,运用有限体积方法,结合二阶精度Roe格式,对弹丸由高压气体驱动从静止状态加速至超音速,射出膛口到完全飞离初始流场的整个过程进行了数值模拟．根据数值结果,详细讨论了初始流场、火药燃气流场的形成与发展以及与弹丸的耦合和相互作用过程,揭示了在这一变化过程中激波与激波、激波与漩涡、激波与弹丸等的相互作用以及激波衍射、聚焦等对弹丸加速的影响．     

Three-dimensional generalization for <Emphasis Type="Italic">W</Emphasis> modification of a Godunov method

A high-accuracy modification of Godunov’s method for three-dimensional unsteady ideal gas flows is proposed. For the linear advection equation, a fully three-dimensional second-order accurate monotone scheme is designed with corrections computed on a variable stencil whose orientation depends on the signs of the equation coefficients. For the linear scalar advection equation, the scheme is proved to possess the positive approximation property. The method is tested by computing the flow in a three-dimensional Ludwieg tube with a square cross section.     

The modeling and numerical simulation of gas flow networks

Summary. A network formulation is introduced for the modeling and numerical simulation of complex gas transmission systems like a multi-cylinder internal combustion engine. Several simulation levels are discussed which result in different network representations of a specific system. Basic elements of a network are chambers of finite volume, straight pipes and connections like valves or nozzles. The pipe flow is modeled by the unsteady, one-dimensional Euler equations of gas dynamics. Semi-empirical approaches for the chambers and the connections yield differential-algebraic equations (DAEs) in time. The numerical solution is based on a TVD scheme for the pipe equations and a predictor-corrector method for the DAE-system. Simulation results for an internal combustion engine demonstrate the practical interest of the new approach. Received May 12, 1994 / Revised version received August 26, 1994