Computation of unsteady transonic flow over a fighter wing using a zonal Navier–Stokes/full‐potential method

An improved hybrid method for computing unsteady compressible viscous flows is presented. This method divides the computational domain into two zones. In the inner zone, the Navier–Stokes equations are solved using a diagonal form of an alternating‐direction implicit (ADI) approximate factorisation procedure. In the outer zone, the unsteady full‐potential equation (FPE) is solved. The two zones are tightly coupled so that steady and unsteady flows may be efficiently solved. Characteristic‐based viscous/inviscid interface boundary conditions are employed to avoid spurious reflections at that interface. The resulting CPU times are about 60% of the full Navier–Stokes CPU times for unsteady flows in non‐vector processing machines. Applications of the method are presented for a F‐5 wing in steady and unsteady transonic flows. Steady surface pressures are in very good agreement with experimental data and are essentially identical to the full Navier–Stokes predictions. Density contours show that shocks cross the viscous/inviscid interface smoothly, so that the accuracy of full Navier–Stokes equations can be retained with significant savings in computational time. Copyright © 1999 John Wiley & Sons, Ltd.     

跨音速湿空气非平衡凝结流动的数值研究

跨音速流动条件下湿空气中的水蒸气由于快速膨胀而发生非平衡凝结,凝结潜热对跨音速气流进行加热,会显著改变气流的流动特性。通过对商用计算流体动力学软件FLUENT进行二次开发,建立了湿空气非平衡凝结流动的数值求解方法。该方法可用于二维或三维、粘性或无粘、内流或外流的求解中。采用该方法分剐对缩放喷管、透平叶栅以及绕CA-0.1圆弧翼型的湿空气非平衡凝结流动进行了数值分析。计算结果表明：湿空气凝结手l起缩放喷管中的凝结激波、导致叶橱流动中总压降低;对于翼型周围的流动,在相对湿度分别为50％、57．1％、64.1％时,依次计算得到了单激波、五激波、双激波。     

Numerical study of vortex-breakdown over a slender wing in transonic flow at high incidence

The transonic flowfields and vortex-breakdown over a slender wing with the angle of attack from 10° to 28° are studied numerically, and the emphasis is on the secondary separation and the charateristics of vortex-breakdown. The results indicated that: (a) TVD schemes have strong capability for capturing vortices in three-dimensional transonic separated flow at large angle of attack. (b) The development of secondary vortices is more complex than that of leading-edge ones, and is affected by wing's configuration, angle of attack and compressibility simultaneously, and the effect of compressibility is more severe at low angle of attack. (c) The starting angle of attack for vortex-breakdown (when vortex bursting point crosses trailing-edge) is about 18° forM∞=0.85, then the bursting point moves upstream quickly with increasing angle of attack. (d) At α=24°, breakdown occurs over most part of upper side, and the wing begins to stall. Therefore, there is a large lag of angle of attack between the beginning of vortex-breakdown and the stall of the wing. (e) This lag increase with the decreasing of Mach number.     

跨音速翼型反设计的一种大范围收敛方法

求解跨音速翼型的反设计问题时,传统的梯度型方法一般均为局部收敛. 为增大求解的收敛范围,依据同伦方法的思想,通过构造不动点同伦,将原问题的求解 转化为其同伦函数的求解,并依据拟Sigmoid函数调整同伦参数以提高计算效率,进而构造 出一种具有较高计算效率的大范围收敛反设计方法. 数值算例以RAE2822翼型的表面压力分 布为拟合目标,分别采用B样条方法, PARSEC方法及正交形函数方法等3种不同的 参数化方法,并分别以NACA0012, OAF139及VR15翼型为初始翼型进行迭代计 算. 计算结果证明,该方法适用于多种参数化方法,且具有较好的计算效率,从多 个不同的初始翼型出发,经较少次数迭代后, 均能与目标翼型很好地拟合,是一种高效的大范围收敛方法.     

Buffeting in transonic flow prediction using time‐dependent turbulence model

In transonic flow conditions, the shock wave/turbulent boundary layer interaction and flow separations on wing upper surface induce flow instabilities, ‘buffet’, and then the buffeting (structure vibrations). This phenomenon can greatly influence the aerodynamic performance. These flow excitations are self‐sustained and lead to a surface effort due to pressure fluctuations. They can produce enough energy to excite the structure. The objective of the present work is to predict this unsteady phenomenon correctly by using unsteady Navier–Stokes‐averaged equations with a time‐dependent turbulence model based on the suitable (k–ε) turbulent eddy viscosity model. The model used is based on the turbulent viscosity concept where the turbulent viscosity coefficient (Cμ) is related to local deformation and rotation rates. To validate this model, flow over a flat plate at Mach number of 0.6 is first computed, then the flow around a NACA0012 airfoil. The comparison with the analytical and experimental results shows a good agreement. The ONERA OAT15A transonic airfoil was chosen to describe buffeting phenomena. Numerical simulations are done by using a Navier–Stokes SUPG (streamline upwind Petrov–Galerkin) finite‐element solver. Computational results show the ability of the present model to predict physical phenomena of the flow oscillations. The unsteady shock wave/boundary layer interaction is described. Copyright © 2005 John Wiley & Sons, Ltd.     

翼身组合体气动力计算研究

采用求解Euler方程结合附面层修正的方法在结构网格上对翼身组合体跨音速流场进行了数值模拟.附面层方程的求解应用Whitfield提出的动量积分方程和平均流动能积分方程,为了保持Euler方程求解过程中计算网格的固定性,用加在物面上的溢出速度来模拟附面层效应.针对传统的近场方法计算阻力,计算精度较低、误差较大并且不能给出各阻力分量值的缺点,将基于动量定理的远场方法用于飞机的阻力估算,采用远场法将阻力分解为:粘性阻力,激波阻力,诱导阻力,并对各个分量分别进行了求解,将计算结果与近场法以及风洞实验值做了比较.以DLR-F4翼身组合体为考核算例,对所述方法进行了验证,结果显示远场法的计算结果与风洞实验值吻合的很好.     

Nonlinear effects caused by pulsed periodic supply of energy in the vicinity of a symmetric airfoil in a transonic flow

Changes in the structure of a transonic flow around a symmetric airfoil and a decrease in the wave drag of the latter, depending on the energy-supply period and on localization and shape of the energy-supply zone, are considered by means of the numerical solution of two-dimensional unsteady equations of gas dynamics. Energy addition to the gas ahead of the closing shock wave in an immediate vicinity of the contour in zones extended along the contour is found to significantly reduce the wave drag of the airfoil. The nature of this decrease in drag is clarified. The existence of a limiting frequency of energy supply is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 64–71, May–June, 2006.     

Numerical solution of single and multi‐phase internal transonic flow problems

This paper presents numerical methods for solving turbulent and two‐phase transonic flow problems. The Navier–Stokes equations are solved using cell‐vertex Lax–Wendroff method with artificial dissipation or cell‐centred upwind method with Roe's Riemann solver and linear reconstruction. Due to a big difference of time scales in two‐phase flow of condensing steam a fractional step method is used. Test cases including 2D condensing flow in a nozzle and one‐phase transonic flow in a turbine cascade with transition to turbulence are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

跨超声速风洞扩散段流动分离控制设计参数研究

为抑制跨超声速风洞扩散段的分离,提出了一种较为完备的设计方法。由于影响扩散段性能的参数较多,完全通过试验方法进行设计的成本过高,该方法通过数值模拟,结合适当的边界条件,详细描述了扩散段角度、分流锥角度与长度、孔板开孔率对扩散段性能的影响;从数值模拟的结果可以看出,孔板开孔率和扩开角对扩散段性能有显著影响,通过比较得出较为合理的参数匹配,提高了扩散段的防分离性能,并改善了出口气流质量。数值结果与试验结果结论一致,表明本文所用的方法用于扩散段气动设计是可行的,为数值模拟方法应用于风洞部段气动设计创造了一定的条件。     

用隐式方法和WENO格式计算悬停旋翼跨声速无粘流场

寻找一种能够准确计算以涡为主要特征的复杂流场和克服尾迹耗散问题的数值方法,一直是旋翼空气动力学研究的热点和难点。本文发展了一种基于高阶迎风格式计算悬停旋翼无粘流场的隐式数值方法。无粘通量采用Roe通量差分分裂格式,为提高精度,使用五阶WENO格式进行左右状态插值,并与MUSCL插值进行比较。为提高收敛到定常解的效率,时间推进采用LU-SGS隐式方法。用该方法对一跨声速悬停旋翼无粘流场进行了数值计算,数值结果表明WENO-Roe的激波分辨率高于MUSCL-Roe,体现出了格式精度的提高对计算结果的改善,LU-SGS隐式方法的计算效率比5步Runge-Kutta显式方法的高。     

Transonic flow past an airfoil with mini-flaps

The effect of mini-flaps located on either the lower or upper side of an airfoil near its trailing edge on the flow around the trailing edge and the global flow past the airfoil is numerically investigated. The flow pattern near the trailing edge is compared with that on which the Chaplygin-Joukowski hypothesis is based. The mini-flap effect on the aerodynamic characteristics of the airfoil is studied.     

Aerodynamic drag of bodies in transonic flow. Theory and applications to computational aerodynamics

Formulas for all the components of the aerodynamic drag (total, friction, inductive, wave, pressure, and heat-transfer) are uniformly derived as applied to flows governed by the Navier-Stokes and Reynolds equations. For flows of this type the definition of the aerodynamic drag components is refined and the physical basis of the chosen method of breaking up the total drag into components is discussed. Ways of calculating the aerodynamic drag components using the methods of computational aerodynamics are considered. On the basis of the refined formulas the drag components are calculated for flows around airfoils and a high-aspect-ratio wing in transonic flow.     

Calculation of pressure on an airfoil contour in an unsteady separated flow

Simple formulas for calculating the pressure and the total hydrodynamic reactions acting on an arbitrarily moving airfoil are derived within the framework of the model of plane unsteady motion of an ideal incompressible fluid. Several vortex wakes may be shed from the airfoil owing to changes in velocity circulation around the airfoil contour. Cases with nonclosed and closed contours are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 109–113, May–June, 2008.     

Input-output reduced-order modeling of unsteady flow over an airfoil at a high angle of attack based on dynamic mode decomposition with control

Due to the damage caused by stall flutter, the investigation and modeling of the flow over a wind turbine airfoil at high angles of attack are essential. Dynamic mode decomposition (DMD) and dynamic mode decomposition with control (DMDc) are used to analyze unsteady flow and identify the intrinsic dynamics. The DMDc algorithm is found to have an identification problem when the spatial dimension of the training data is larger than the number of snapshots. IDMDc, a variant algorithm based on reduced dimension data, is introduced to identify the precise intrinsic dynamics. DMD, DMDc and IDMDc are all used to decompose the data for unsteady flow over the S809 airfoil that are obtained by numerical simulations. The DMD results show that the dominant feature of a static airfoil is the adjacent shedding vortices in the wake. For an oscillating airfoil, the DMDc results may fail to consider the effect of the input and have an identification problem. IDMDc can alleviate this problem. The dominant IDMDc modes show that the intrinsic flow for the oscillating case is similar to the unsteady flow over the static airfoil. Moreover, the input–output model identified by IDMDc can give better predictions for different oscillating cases than the identified DMDc model.     

A study on the mechanism of high-lift generation by an airfoil in unsteady motion at low reynolds number

The aerodynamic force and flow structure of NACA 0012 airfoil performing an unsteady motion at low Reynolds number (Re=100) are calculated by solving Navier-Stokes equations. The motion consists of three parts: the first translation, rotation and the second translation in the direction opposite to the first. The rotation and the second translation in this motion are expected to represent the rotation and translation of the wing-section of a hovering insect. The flow structure is used in combination with the theory of vorticity dynamics to explain the generation of unsteady aerodynamic force in the motion. During the rotation, due to the creation of strong vortices in short time, large aerodynamic force is produced and the force is almost normal to the airfoil chord. During the second translation, large lift coefficient can be maintained for certain time period and , the lift coefficient averaged over four chord lengths of travel, is larger than 2 (the corresponding steady-state lift coefficient is only 0.9). The large lift coefficient is due to two effects. The first is the delayed shedding of the stall vortex. The second is that the vortices created during the airfoil rotation and in the near wake left by previous translation form a short “vortex street” in front of the airfoil and the “vortex street” induces a “wind”; against this “wind” the airfoil translates, increasing its relative speed. The above results provide insights to the understanding of the mechanism of high-lift generation by a hovering insect. The project supported by the National Natural Science Foundation of China (19725210)     

双三角翼拉升流场特性数值模拟研究

发展了适用于双三角翼大攻角非定常分离流场模拟的数值方法,开展双三角翼拉升运动的动态流场特性研究。通过减缩频率、转轴位置和起始攻角的变化,仔细分析了这些运动参数对动态流场施加影响的物理机制,有利于提高对双三角翼在拉升条件下的非定常特性和流场滞后效应等非线性现象的认识。     

Numerical experiments with several variant WENO schemes for the Euler equations

Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd.     

To formulating a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil

A general formulation of a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil by an ideal incompressible fluid is considered. The problem is formulated for a complex velocity. Conditions of shedding of vortex wakes from the airfoil are analyzed in detail. The proposed system of functional relations allows constructing algorithms for solving a wide class of problems of the wing theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 48–56, March–April, 2007.     

Finite element computation of turbulent flow past a multi-element airfoil

Flow past multi-element airfoil is studied via two-dimensional numerical simulations. The incompressible Reynolds averaged Navier–Stokes equations, in primitive variables, are solved using a stabilized finite element formulation. The Spalart–Allmaras and Baldwin–Lomax models are employed for turbulence closure. The implementation of the Spalart–Allmaras model is verified by computing flow over a flat plate with a specified trip location. Good agreement is seen between the results obtained with the two models for flow past a NACA 0012 airfoil at 5° angle of attack. Results for the multi-element airfoil, with the two turbulence models, are compared with experiments for various angles of attack. In general, the pressure distribution, from both the models matches quite well with the experimental results. However, at larger angles of attack, the computational results overpredict the suction peak on the slat. The velocity profiles from the Baldwin–Lomax model are, in general, more diffused compared to those from the Spalart–Allmaras model. The agreement between the computed and experimental results is not too good in the flap region for large angles of attack. Both the models are unable to predict the stall; the flow remains attached even for relatively large angles of attack. Consequently, the lift coefficient is over predicted at large α by the computations. Overall, compared to the Baldwin–Lomax model, the predictions from the Spalart–Allmaras model are closer to experimental measurements.