高超声速非定常流动的数值模拟与气动热计算

高超声速飞行器研究中的一个重点问题是飞行器表面的气动加热,它对飞行器的气动、热特性及安全性有重要的影响.受到当前实验技术的限制,地面实验无法准确模拟真实飞行条件,所以采用数值模拟研究气动加热问题成为目前重要的研究手段.本文采用数值方法求解三维N-S方程,得到钝头体再入模型绕流的瞬态流场,驻点温度及表面热流沿轨道变化规律.计算中采用变边界条件模拟沿轨道飞行的非定常性.     

Effects of unsteady deformation of flapping wing on its aerodynamic forces

Effects of unsteady deformation of a flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations on a dynamically deforming grid.Aerodynamic forces on the flapping wing are not much affected by considerable twist,but affected by camber deformation.The effect of combined camber and twist deformation is similar to that of camber deformation.With a deformation of 6% camber and 20°twist(typical values observed for wings of many insects),lift is increased bv 10%～20%and lift-to-drag ratio by around 10%compared with the case of a rigid flat-plate wing.As a result.the deformation can increase the maximum lift coefficient of an insect.and reduce its power requirement for flight.For example,for a hovering bumblebee with dynamically deforming wings(6?mber and 20°twist),aerodynamic power required is reduced by about 16%compared with the case of rigid wings.     

随机风作用下高速列车非定常气动载荷的计算方法

基于Cooper理论和谐波叠加法计算随车移动点的脉动风速,分析不同风向角下脉动风速的功率谱密度特性.在横风下高速列车非定常气动载荷计算方法的基础上,建立了侧风下高速列车非定常气动载荷的计算方法,并用此方法分析了侧向随机风作用下非定常气动载荷的统计特性,给出了各气动载荷的峰值因子.研究表明,当风向角接近90°时,无量纲功率谱会往高频移动,风向角对脉动风速的影响较小;在各个风向角下,气动载荷的标准差与平均值的比值仅依赖于侧偏角,侧力与侧滚力矩的峰值因子相同,摇头力矩与点头力矩的峰值因子相同.     

Implementation of phase change thermodynamic probability for unsteady simulation of cavitating flows

The aim of this work is to investigate the non‐equilibrium effects of phase change in cavitating flows. For this purpose, the concept of phase change thermodynamic probability is used along with homogeneous model to simulate two‐phase cavitating flows. For simulation of unsteady behaviors of cavitation, which have practical applications, unsteady PISO algorithm based on the non‐conservative approach is utilized. For multi‐phase simulation, single‐fluid Navier–Stokes equations, along with the volume fraction transport equation, are employed. In this paper, phase change thermodynamics probabilities and cavitation model is briefly summarized. Thus, derivation of the cavitation model, starting from the basic thermodynamic equations to the mass and momentum conservation equations at a liquid–vapor two‐phase flow, is presented to explain the numerical model. Unsteady simulations of cavitation around a flat plate normal to flow direction are presented to clarify the accuracy of the model. The accuracy of the numerical results is good, and it is possible to apply this method to more complex geometries. Copyright © 2010 John Wiley & Sons, Ltd.     

近似黎曼解对高超声速气动热计算的影响研究

高超声速流场计算一般采用TVD型格式,这些格式中,大多采用了不同形式的近似黎曼解. 通过分析和数值验证,论述了激波捕捉格式中近似黎曼解的耗散性质,说明其对高超声速热流计算的影响. 数值实验证明,采用低耗散格式可大大提高热流计算精度,降低热流计算对网格的依赖程度,从而获得精确的热流数值解.      

Numerical study of a piston-driven unsteady flow in a pipe with sudden expansion

This paper presents results of the numerical study of a piston-driven unsteady flow in a pipe with sudden expansion. The piston closes the larger-diameter pipe and moves between two limiting positions with strong acceleration or deceleration at the beginning and end of each stroke and constant velocity in between. The piston velocity in the exhaust stroke is about four times higher than in the intake stroke. Periodic piston movement in this fashion creates a complex unsteady flow between the piston head and the plane of sudden expansion. The numerical method is implicit and of finite volume type, using a moving grid and a collocated arrangement of variables. Second-order spatial discretization, fine grids and a multigrid solution method were used to ensure high accuracy and good efficiency. Spatial and temporal discretization errors were of the order of 1% and 0.1% respectively. The features of the flow are discussed and the velocity profiles are compared with experimental data, showing good qualitative and quantitative agreement.     

三维非稳定渗流自由面边界积分项的精确数值计算

利用固定网格法分析三维非稳定渗流问题时,将要面对两项积分难题:以自由面及单元表面为边界的空间积分及以自由面为边界的曲面积分。针对常用的任意8结点6平面三维普通单元,提出采用坐标变换及等参变换技术求取空间积分项的精确数值解;至于曲面积分项,建议改用单元非饱和区部分表面作为积分边界,经过坐标变换及等参变换处理积分边界后,利用高斯数值积分可求出曲面积分项的精确数值解。通过一个普通单元及一项均质半无限边界堤坝的实例分析,表明此方法的精确性和稳定性良好。     

Numerical solution of the unsteady Euler equations for airfoils using approximate boundary conditions

This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary rectilinear grids. Boundary conditions on the surface of an airfoil are implemented by using their first-order expansions on the mean chord line. The method is not restricted to flows with small disturbances since there are no restrictions on the mean angle of attack of the airfoil. The mathematical formulation and the numerical implementation of the wall boundary conditions in a fully implicit time-accurate finite-volume Euler scheme are described. Unsteady transonic flows about an oscillating NACA 0012 airfoil are calculated. Computational results compare well with Euler solutions by the full boundary conditions on a body-fitted curvilinear grid and published experimental data. This study establishes the feasibility for computing unsteady fluid-structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in saving computer time and program design since it does not require the generation and implementation of time-dependent body-fitted grids.     

Control of unsteady vortical lift on an airfoil by leading-edge blowing-suction

The effects of leading-edge blowing-suction on the vortex flow past an airfoil at high incidence are investigated numerically by solving the Navier-Stokes equations. The results indicate that the frequency of the flowfield excited by the periodic blowing-suction locks into the forcing frequency, which is half of the dominant frequency for the flow past a fixed airfoil without injection. In that case, a well-developed primary leading-edge vortex occupies the upper surface of the airfoil and the largest lift augmentation is obtained. The project supported by the National Defence Research Fund of China     

Numerical simulation of the unsteady flow over an elliptic cylinder at different orientations

A numerical method is developed for investigating the two‐dimensional unsteady viscous flow over an inclined elliptic cylinder placed in a uniform stream of infinite extent. The direction of the free stream is normal to the cylinder axis and the flow field unsteadiness arises from two effects, the first is due to the flow field development following the start of the motion and the second is due to vortex shedding in the wake region. The time‐dependent flow is governed by the full conservation equations of mass and momentum with no boundary layer approximations. The parameters involved are the cylinder axis ratio, Reynolds number and the angle of attack. The investigation covers a Reynolds number range up to 5000. The minor–major axis ratio of the elliptic cylinder ranges between 0.5 and 0.6, and the angle of attack ranges between 0° and 90°. A series truncation method based on Fourier series is used to reduce the governing Navier–Stokes equations to two coupled infinite sets of second‐order differential equations. These equations are approximated by retaining only a finite number of terms and are then solved by approximating the derivatives using central differences. The results reveal an unusual phenomenon of negative lift occurring shortly after the start of motion. Various comparisons are made with previous theoretical and experimental results, including flow visualizations, to validate the solution methodology. Copyright © 2001 John Wiley & Sons, Ltd.     

Extrapolation-to-flight of aerodynamic heating measurements and determination of in-flight radiation-equilibrium surface temperature in hypersonic/high enthalpy flow conditions

The previously demonstrated success of the reference enthalpy concept in heat transfer prediction at hypersonic flow conditions is utilized herein to propose a cost-effective methodology for extrapolation-to-flight of Stanton number measurements (or baseline computational results), and the determination of radiation-equilibrium surface temperatures that develop on actual vehicle surfaces during hypersonic/high enthalpy flight conditions. The methodology couples the (analytical) generalized reference enthalpy solution with Euler computations (providing input data along the edge of thin boundary layers) and is, therefore, significantly cheaper and more efficient than the execution of full Navier–Stokes computations that are presently incorporated, particularly so in the thermo-chemically active high enthalpy flow regime. The validity of the proposed methodology is demonstrated in a first step by means of two-dimensional test cases, whereby extrapolated data accuracy is better than 20%.

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风力机叶片的三维非定常气动特性估算

结合动量-叶素理论、非定常空气动力和动态失速模型来计算风力机叶片的二维非定常气动特性,并在此基础上经过适当修正后考虑三维旋转效应的非定常气动特性。分析比较二维和三维两种计算结果,给出更为合理的计算叶片非定常气动特性的方法。计算结果表明,风力机叶片的三维非定常气动特性计算结果与二维时的计算结果相比有较大改善。     

运动物体与运动激波干扰流场特性数值研究

用数值方法求解非定常可压缩Navier—Stokes方程，模拟了运动物体分别以超声速和亚声速穿越激波的全过程。在这两种情况下，激波都是从高压区运动到低压区，阻力急剧地减小，但在亚声速情况下，会在物体上产生不对称力和力矩，导致运动物体的不稳定。     

Approximate method for determining the maximum temperature during quasistationary heating of a piecewise-homogeneous half-space

A method is proposed to calculate the maximum temperature of the surface of a piecewise-homogeneous half-space heated by a uniformly moving, locally distributed heat flow. Analytical solutions of the corresponding quasistationary heat-conduction problems are obtained for small and large values of the Peclet number. These solutions are used to derive formulas for calculating the maximum temperature in the case of intermediate (moderate) values of the Peclet number. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 85–97, May–June, 2005.     

Interpretation of gas-film cooling against aero-thermal heating for high-speed vehicles

The possible application of the film-cooling technique against aero-thermal heating for surfaces of high-speed flying vehicles is discussed. The technique has been widely used in the heat protection of gas turbine blades. It is shown in this paper that, by applying this technique to high-speed flying vehicles, the working principle is fundamentally different. Numerical simulations for two model problems are performed to support the argument. Besides the heat protection, the appreciable drag reduction is found to be another favorable effect. For the second model problem, i.e., the gas cooling for an optical window on a sphere cone, the hydrodynamic instability of the film is studied by the linear stability analysis to observe possible occurrence of laminar-turbulent transition.     

改进的有自由面非稳定渗流分析复合单元渗透矩阵调整法

应用连续的罚函数,提出了一种改进的自由面边界条件渗流分析复合单元渗透矩阵调整法,优化了此类算法的稳定性,提高了收敛速度和精度,并将此改进算法编制成相应的有限元分析程序,应用于上海地铁4号线董家渡隧道修复基坑降水工程的优化设计,解决了基坑降水过程中复杂三维渗流场的高效精细模拟问题,同时预测了基坑中心水位降至地面以下40 m,位于承压含水层顶面以下,基坑内外自由面落差很大时基坑周边渗流场以及地面沉降的分布特征.     

Numerical simulation of axisymmetric unsteady incompressible flow by a vorticity-velocity method

A new numerical method for solving the axisymmetric unsteady incompressible Navier-Stokes equations using vorticity-velocity variables and a staggered grid is presented. The solution is advanced in time with an explicit two-stage Runge-Kutta method. At each stage a vector Poisson equation for velocity is solved. Some important aspects of staggering of the variable location, divergence-free correction to the velocity field by means of a suitably chosen scalar potential and numerical treatment of the vorticity boundary condition are examined. The axisymmetric spherical Couette flow between two concentric differentially rotating spheres is computed as an initial value problem. Comparison of the computational results using a staggered grid with those using a non-staggered grid shows that the staggered grid is superior to the non-staggered grid. The computed scenario of the transition from zero-vortex to two-vortex flow at moderate Reynolds number agrees with that simulated using a pseudospectral method, thus validating the temporal accuracy of our method.     

A numerical study on the unsteady evolution of weak axisymmetric fountain flows in a homogeneous ambient

Weak axisymmetrical fountains resulting from the injection of a dense fluid upwards into a large container of homogeneous fluid of lower density has been studied numerically in this paper using a time-accurate finite volume scheme. The behaviour of fountains for both the uniform and parabolic profiles of the discharge velocity at the fountain source has been investigated. The evolution of transient fountain flow has been analysed and two distinct stages of evolution have been identified. The time trace of the position of the fountain front has been presented and the initial, temporary and final fountain height and fountain width have been determined. The project is jointly supported by the National Natural Science Foundation of China, the Special Fund for the Young and Middle-aged Academic and Technical Leaders Training Scheme of Yunnan Province, and the Australian Development Cooperation Scholarship to Prof. Lin Wenxian. Author for correspondence: Li Yuncang.     

Investigation of temperature statistic characteristics in turbulent water flow with unsteady heat transfer

The results of an experimental study of a temperature field and its statistical characteristics in turbulent water flow upon a sudden change of heat generation in the channel wall are reported. Measurements were performed in 5 mm × 40 mm, 10 mm × 40 mm, and 20 mm × 40 mm channels in the regions of thermal stabilization and stabilized heat transfer at Reynolds numbers of (0.8–6.8) × 10⁴. The measurement results are generalized using a dimensionless time scale. The results of the calculation of heat transfer coefficients at unsteady heat transfer are presented.     

Effect of one-sided unsteady energy supply on aerodynamic characteristics of airfoils in a transonic flow

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of one-sided pulsed-periodic energy supply is studied. Based on the numerical solution of two-dimensional unsteady gas-dynamic equations, the change in the flow structure in the vicinity of a symmetric airfoil at different angles of attack and the aerodynamic characteristics of the airfoil as functions of the amount of energy supplied asymmetrically (with respect to the airfoil) are determined. The results obtained are compared with the data calculated for the flow past the airfoil at different angles of attack without energy supply. It is found that a given lift force can be obtained with the use of energy supply at a much better lift-to-drag ratio of the airfoil, as compared to the case of the flow past the airfoil at an angle of attack. The moment characteristics of the airfoil are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 82–87, November–December, 2008.