Computation of three-dimensional transonic flow using a cell vertex finite volume method for the Euler equations

Summary A cell vertex finite volume method for the solution of the three dimensional Euler equations has been developed. The computations can be carried out block-wise after dividing the computational domain into smaller blocks to reduce the memory requirement for a single processor computer and also to facilitate parallel computing. A five stage Runge-Kutta scheme has been used to advance the solution in time. Enthalpy damping, implicit residual smoothing, local time stepping, and grid sequencing are used for convergence acceleration. The solution procedure has been studied in detail by computing transonic flow over the ONERA M-6 wing, using both C-H and O-H type structured grids. The effects of changing the artificial viscosity parameters and the distance of the far field boundary are also investigated.     

Effect of one-sided periodic pulsed energy supply on aerodynamic characteristics of wing profiles

The possibility of controlling the aerodynamic characteristics of wing profiles by means of local periodic pulsed energy supply in transonic flight regimes has been studied. A change in the flow structure near a symmetric wing profile was determined, depending on the amount of energy supplied from the lower side of the wing profile, using a numerical solution of two-dimensional nonstationary equations of gasdynamics. The results are compared to the data obtained from calculations of a transonic flow past the same profile at various incidence angles without energy supply.     

Transonic flow past thin wings

This paper is devoted to a discussion of steady inviscid transonic flow past thin wings, with subsonic free-stream Mach number M_∞ < 1, by the integral equation method. The integral equation formulation is developed for a thin unsymmetric wing at small incidence. A simple approximate analytical solution is presented for shock-free supercritical flow past a thin symmetric wing at zero incidence. The direct iteration scheme of Niyogi and Chakraborty is then extended to the three-dimensional zero incidence case, which may be used to obtain more accurate solutions for shockfree flows as well as for flows with shocks. The question of the existence and the uniqueness of a solution has been studied by means of the Banach contraction mapping principle in the spaceL ₂ (E₃), which establishes the condition of convergence of the direct iteration scheme. Simultaneously it provides us with an error estimate for the solution.     

An inverse method for transonic wing design

A fast, efficient and reliable code for wing design has been developed at INTA coupling a residual‐correction method by Bauer, McFadden and Garabedian to an inviscid solver for wing analysis in transonic flow. Smoothing procedures, including Bèzier cubic splines, are used to avoid irregularities of the wing surface, as well as the twist distribution. A modified version of FLO22 code is used as the flow solver. The original code has been adapted to improve its accuracy. Some results are presented, showing the reliability of the code. The redesign of a wing in transonic flow—which was used as test case in LARA project of BRITE‐EURAM II during 1993–94—is presented with promising results. Copyright © 1999 John Wiley & Sons, Ltd.     

Computation of transonic potential flow past wing-body configurations

Summary A simple approach has been developed to use the two dimensional grid generation method by solving elliptic partial differential equations to generate the three dimensional grid for wingfuselage configurations. This simple method can be applied to generate grids for arbitrary fuselage fitted with any swept wing with dihedral. Three dimensional transonic analysis code TWING, with approximate factorization (AF2) scheme has been suitably used as a flow solver. As an example, RAE-WING-A with body-B2 configuration has been considered. The results obtained have been compared with available numerical and experimental results. It has been observed in the present computations that AF2 scheme is not sensitive to grid stretching.     

An efficient numerical method for highly loaded transonic cascade flow

In this paper, an efficient numerical method for transonic viscous flow in a highly loaded turbine vane cascade, where the interaction of a shock wave and boundary layer often leads to very complicated flow phenomena, is developed. The numerical code, a modified implicit flux-vector-splitting solver of the Navier–Stokes equations (MIFVS), is extended to simulate such transonic cascade flow. A compressible low-Reynolds-number k–ɛ model, together with a transition-modified damping function, has been implemented into the MIFVS code. With this extended MIFVS solver, the main feature of transonic flow and shock and boundary-layer interactions in the highly loaded transonic turbine vane are efficiently predicted with satisfactory accuracy. The convergence rate is found to be three times faster than that of flux-vector-splitting (FVS) methods.     

基于多项式修正片条气动力的跨音速颤振分析方法及其试验验证

提出一种基于多项式修正片条气动力的跨音速颤振分析方法,以片条内升力和力矩随攻角变化斜率为修正目标,采用多项式方程模拟片条力矩分布,使整个翼面的气动力大小和分布都与目标相符,进而使用修正后的气动力进行跨音速区的颤振分析.计算结果经跨音速颤振风洞试验验证,该方法对翼吊发动机构型的机翼颤振型、带操纵面的尾翼颤振型都有较高的计...     

Nonlinear effects in the interaction of periodic pulsed energy supply and shock-wave structure during transonic streamlining of wing profiles

We have evaluated the possibility of controlling the aerodynamic characteristics of wing profiles by means of a local periodic pulsed energy supply in transonic flight regimes. The influence of the energy supply rate and the position and area of the zone of energy supply on the flow structure near a symmetric wing profile and on the wave drag has been studied using a numerical solution of two-dimensional nonstationary equations of gasdynamics. The energy supply in front of the breakdown shock wave within extended zones in the immediate vicinity of the streamlined contour leads to a significant decrease in the wave drag of a given wing profile. The nature of this phenomenon is elucidated and it is established that there exists a limiting rate of energy supply.     

机翼跨音速风洞颤振试验模型的计算分析

以某民机机翼跨音速颤振模型为研究对象,采用N-S方程求解固定边界流场的气动力,简化的跨音速小扰动方程求解运动边界流场的气动力,结合结构动力学的模态分析结果进行颤振特性分析。模型风洞试验前完成所有计算工作,试验后通过比较表明,计算结果与试验结果吻合:(1)颤振频率一致;(2)颤振速度随马赫数的变化趋势一致;(3)跨音速凹坑的底部位置一致;(4)颤振速度的偏差最大不超过10%,且在马赫数0.60和0.70处,偏差1%。由此可见该计算方法的计算精度高,可用于风洞试验结果的预判,提升风洞试验结果的可信度和风洞试验的效率,也可作为民机适航符合性验证的一种手段。     

Control of the aerodynamic characteristics of wing airfoils by nonstationary energy supply in transonic flow

The possibility of controlling the aerodynamic characteristics of wing airfoils in transonic regimes of flight using one-sided pulse-periodic energy supply has been studied. The flow structure near the symmetric airfoil at different angles of attack and its aerodynamic characteristics as functions of the value of energy in its nonsymmetric (about the airfoil) supply have been determined by numerical solution of two-dimensional nonstationary gasdynamic equations. A comparison of the obtained results and the data of calculation of flow past the airfoil at different angles of attack without energy supply has been made. It has been established that a prescribed lift can be obtained, using energy supply, with a much higher fineness ratio of the airfoil than that in the case of flow past it at an angle of attack. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 18–22, January–February, 2009.     

Simplified transonic integral equations for lifting profiles and wings

Summary The basic small perturbation integral equations for steady inviscid transonic flow past a thin cambered profile at small incidence have been simplified here using Oswatitsch substitution for the velocity field in terms of that on the profile axis. The resulting equations contain only one-dimensional singular integrals. These equations represent simplification of the equations of Nixon and Hancock [3], from which the two-dimensional camber integrals have been eliminated. Also the corresponding simplified equations for a thin lifting wing have been derived, which contain only two-dimensional singular integrals.     

An inverse integral 3D compressible boundary layer method and coupling with transonic inviscid solution

Summary A new velocity profile, which has a simple expression and agrees well with experimental data in a wide range, is proposed in the present paper. Based on this profile, the governing equations of the 3D compressible inverse boundary layer method are deduced. The steady transonic viscous flow around a 3D wing can be calculated as follows: the inviscid flow is calculated by using nonisentropic full potential equation; the viscous flow is calculated by using present boundary layer method; the viscous and inviscid solutions are coupled by using semi-inverse method. Numerical results agree well with the experimental data and required computer resources are less, so that it has broad prospects in the engineering application.     

气动扰流对飞机T型尾翼跨音速颤振影响的试验研究

跨音速颤振试验通常在稳定的理想流场中进行,不考虑实际非稳定流场的气动扰流对颤振特性的影响。在飞机T型尾翼跨音速颤振试验中,通过设置一种气动扰流装置对风洞流场实施干扰以研究气动扰流对飞机T型尾翼跨音速颤振特性的影响。试验结果表明,气动扰流可以将飞机T型尾翼的颤振耦合模态从平尾弯扭耦合型改变为垂尾弯扭耦合型;可显著降低飞机T型尾翼的颤振动压,翼面外气动扰流较翼面内气动扰流对飞机T尾颤振特性的影响作用大。其原因在于施加的气动扰流所诱导产生的跨音速激波作用在垂尾翼面上改变了垂尾的非定常气动力,引起气动刚度和气动阻尼发生改变,由于平尾的气动阻尼相对较大,可以预计,一旦气动扰流引起垂尾的气动阻尼迅速减小到其临界颤振阻尼,则会引起垂尾弯扭耦合颤振型先于平尾弯扭耦合颤振型发生,从而表现出T尾颤振动压的降低。在颤振模型风洞试验中,当风洞试验结果与期望不一致时,需要研究气动扰流的影响。     

Approximate factorization scheme for transonic potential flow computations

The implicit approximate factorization scheme known asaf2 is investigated here for the purpose of application to the solution of two-and three-dimensional transonic full potential equations in conservative form. The artificial viscosity used by different authors has been deduced, and is discussed in detail. A second-order correction to the implicit artificial viscosity is tested for transonic flow past a Korn aerofoil at both design and off-design conditions. The inviscid transonic flow past different aerofoils, wings and wing-body configurations has been computed using theaf2 scheme and the solutions are compared with experimental and other numerical results. It is shown that theaf2 scheme is fast, and is not sensitive to grid stretching. Modified version of the paper presented at CAARC (Commonwealth Advisory Aeronautical Research Council) Specialists Meeting on Computational Fluid Dynamics, held during 5–10 December, 1988, at National Aeronautical Laboratory, Bangalore.     

飞机T型尾翼跨音速颤振特性研究

由于飞机T型尾翼的结构与气动布局特点,T型尾翼颤振计算不能套用常规尾翼的分析方法,而需要考虑平尾面内运动以及静升力等因素的影响。而跨音速空气压缩性效应和非定常气动力计算的不准确性,使得T型尾翼跨音速颤振计算更加困难,准确性较低。因此,需要采用试验为主计算为辅的方法来研究飞机T型尾翼跨音速颤振特性。针对某T型尾翼结构,用ZAERO软件等价片条势流跨音速颤振(ZTAIC)方法计算T型尾翼跨音速颤振特性,研究了马赫数、风洞气流密度和平尾迎角对T型尾翼颤振特性的影响。通过升力系数斜率空气压缩性修正计算方法和跨音速颤振模型风洞试验方法得到了飞机T型尾翼的跨音速颤振的凹坑曲线和空气压缩性特性,两种方法得到结果一致。     

Computation of transonic viscous flow over airfoils with control by an elastic membrane and comparison with control by passive ventilation

Summary The performance of transonic wings can be influenced by control of the shock/boundary layer interaction (SBLI) using an adaptive surface in the shock region. This is achieved by inserting a cavity into the airfoil and covering it with an elastic membrane. The theoretical methods for the computation of transonic viscous flow around airfoils with control are presented. The zonal solution method consists of numerical and analytical parts. The influence of the adaptive wall on the flow field over a modern transonic airfoil has been investigated. The flow parameters have been varied up to off-design conditions to understand the physical effects of the control. Previous investigations of a second way of control, the passive ventilation, allow a comparison of these two methods.     

Time marching integral equation method for unsteady transonic flows around airfoils

A time marching integral equation method has been proposed here which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfactorily simulate the shock wave motions. Firstly, a model problem–one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method. Then the method is implemented for two dimensional unsteady transonic flow problems. The introduction of the concept of a quasi-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition. The numerical calculations show that the method is reasonable and reliable.     

A stochastic programming approach to manufacturing flow control

This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochastic programming approach on a suitably discretized and sampled system. The method proceeds through two stages: (i) the Hamilton-Jacobi-Bellman (HJB) dynamic programming equations for the finite horizon continuous time stochastic control problem are discretized over a set of sampled times; this defines an associated discrete time stochastic control problem which, due to the finiteness of the sample path set for the Markov disturbance process, can be written as a stochastic programming problem; and (ii) the very large event tree representing the sample path set is replaced with a reduced tree obtained by randomly sampling over the set of all possible paths. It is shown that the solution of the stochastic program defined on the randomly sampled tree converges toward the solution of the discrete time control problem when the sample size increases to infinity. The discrete time control problem solution converges to the solution of the flow control problem when the discretization mesh tends to zero. A comparison with a direct numerical solution of the dynamic programming equations is made for a single part manufacturing flow control model in order to illustrate the convergence properties. Applications to larger models affected by the curse of dimensionality in a standard dynamic programming techniques show the possible advantages of the method.     

Navier-Stokes analysis of Korn aerofoil

Summary Two-dimensional Reynolds-averaged Navier-Stokes equations with algebraic turbulence model have been solved using a vertex-based finite-volume space discretization and an explicit five-stage Runge-Kutta time steps. A modified artificial dissipation based on the time-step limit for convective and diffusive equation has been used for numerical stability. The off-design behaviour of the supercritical Korn aerofoil in viscous transonic flow has been considered a good test case because the numerical scheme needs more accuracy to predict the appearance of double shocks. Results have been compared with experiments and the general behaviour of the aerofoil has been studied.     

Studies in multigrid acceleration of some equations of interest in fluid dynamics

The paper describes the multigrid acceleration technique to compute numerical solutions of three equations of common fluid mechanical interest; Laplace equation, transonic full potential equation and Reynolds averaged Navier-Stokes equations. Starting with the simple and illustrative multigrid studies on the Laplace equation, the paper discusses its application to the cases of full potential equation and the Navier-Stokes equations. The paper also discusses some elements of multigrid strategies like V- and W-cycles, their relative efficiencies, the effect of number of grid levels on the convergence rate and the large CPU time saving obtained from the multigrid acceleration. A few computed cases of transonic flows past airfoils using the full potential equations and the Navier-Stokes equations are presented. A comparison of these results with the experimental data shows good agreement of pressure distribution and skin friction. With the greatly accelerated multigrid convergence, the full potential code typically takes about 10 seconds and the Navier-Stokes code for turbulent flows takes about 5 to 15 min of CPU time on the Convex 3820 computer on a mesh which resolves the flow quantities to good levels of accuracy. This low CPU time demand, made possible due to multigrid acceleration, on one hand, and the robustness and accuracy on the other, offers these codes as designer’s tools for evaluating the characteristics of the airfoils. Various parts of this paper have been presented at the following conferences; (i) 5th Asian Cong. on Fluid Mech., Taejon, Korea, 1992, (ii) Int. Conf. on Methods of Aerophysical Research, Novosibirsk, 1992, (iii) Fluid Dyn. Symp. in honour of Prof. R Narasimha on his 60th birthday, 1993.