Numerical investigation of leading edge separated flow over cranked wings using a vortex lattice model

Numerical models based on the vortex lattice concept using free vortex lines have been developed for the calculation of separated flow about cranked wings. Various separated flow models are developed assuming the flow to be separated along the leading edges of (i) the inner wing, (ii) the entire wing and (iii) the inner wing and the outboard part of the outer wing. To illustrate the effects of separation, attached flow solutions are also obtained. Results are compared with available experimental results. Agreement with separated flow solutions is usually good except at very high incidence.     

On identification of flow separation and vortices in internal periodic flows

To permit simplified analysis of complex time-dependent flows, possible relationship between the near-wall flow, flow separation and vortices are studied numerically for a flow in a constricted two-dimensional channel. The pulsating incoming wave-form consists of a steady flow, followed by a half-sinus flow superimposed on the steady component. One pair of vortices is created in each cycle, one vortex near each wall. The vortices propagate downstream in the next cycles, promoting flow separation as they move. Existing flow separation criteria were not found to be uniformly valid. A relation between the near-wall flow and the vortical system exists only during the steady incoming flow phase of the cycle. It seems that local criteria of flow separation cannot be found for complex internal pulsating flow fields. However, the vorticity field can be utilized, even in complex time-periodic flows, for identifying vortices that have been formed by the roll-up of shear layers.     

An experimental study of the effect of the blow-in rate on the size of the flow separation region

Experimental results are presented concerning the effect of the air blow-in rate on the size of the flow separation region downstream of a rearward-facing step at different step heights. The stream function is found from the experimental velocity profiles, the streamline = 0 being taken as the boundary line. It is shown that the separation region increases as the blow-in rate is increased. Generalization of the experimental results for different blow-in rates and step heights has made it possible to obtain an analytical expression describing the location of some characteristic lines in the separation region (boundary streamline, reverse-flow boundary, line of reverse-flow maximum velocity, line of variable-velocity layer thickness, and the displacement thickness line). Velocity profiles are obtained by means of a hot-wire anemometer. Analytical expressions are written as polynomials with unknown coefficients. The results obtained may be helpful in developing techniques for the treatment of heat transfer under flow separation conditions.     

低浓度固液两相流的颗粒相动理学模型

用广义Fokker-Planck扩散模型描述液相湍动对颗粒的挟带作用,用修正的BGK模型描述粒间碰撞效应,建立了封闭的颗粒相PDF输运方程．运用Chapman-Enskog迭代法求得方程的二阶近似解,获得颗粒相脉动速度二阶矩和三阶矩闭合关系．模型与颗粒流模型相容,与液相湍流闭合模型是否相容依赖于扩散模型的具体形式,并据此比较了不同的涡一颗粒作用模型．模型与二维明渠流轻质沙和天然沙试验资料符合很好．表明细小粒径颗粒能够充分跟随水流运动;大粒径颗粒的相间平均速度差和壁面滑移速度明显,近壁区内的颗粒沿流向和垂向脉动强度都可能大于水流,并存在一定程度的颗粒碰撞效应．     

Applications of URANS on predicting unsteady turbulent separated flows

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.     

超音速流动中侧向喷流干扰特性的实验研究

在超音速流动中,进行了侧向喷流干扰特性的实验研究,研究了喷流压力、攻角、迎风侧及背风侧喷流对侧向喷流干扰特性的影响. 结果表明,随喷流压力增大,喷流前的高压区向前扩展,喷流的包裹作用加强. 有攻角时,背风侧喷流前的高压区更大,喷流包裹作用的影响区域前移,喷流的控制效果更好,这一趋势随攻角的增大更加明显.     

Computation of field structure and aerodynamic characteristics of delta wings at high angles of attack

A numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics that are dominated by the effect of the breakdown of the leading-edge vortices. The methods that analyze the flowfield structure quantitatively were given by using flowfield data from the computational results. In the region before the vortex breakdown, the vortex axes are approximated as being straight line. As the angle of attack increases, the vortex axes are closer to the root chord, and farther away from the wing surface. Along the vortex axes, as the adverse pressure gradients occur, the axial velocity decreases, that is, A is negativee, so the vortex is unstable, and it is possible to breakdown. The occurrence of the breakdown results in the instability of lateral motion for a delta wing, and the lateral moment diverges after a small perturbation occurs at high angles of attack. However, after a critical angle of attack is reached the vortices breakdown completely at the wing apex, and the instability resulting from the vortex breakdown disappears.     

Computation of backward-facing step flows by a second-order Reynolds stress closure model

This paper scrutinizes the predictive ability of the differential stress equation model in complex shear flows. Two backward-facing step flows with different expansion ratios are solved by the LRR turbulence model with an anisotropic dissipation model and the near-wall regions of the separated side resolved by a near-wall model. The computer code developed for solving the transport equations is based on the finite-volume-finite-difference method. In the numerical solution of the time-averaged momenum equations the Reynolds stresses are treated partially as a diffusion term and partially as a source term to avoid numerical instability. Computational results are compared with experimental data. It is found that the near-wall region of the separated side resolved by the near-wall model, the LRR model with a simple modification of an anisotropic dissipation model can predict backward step flows well.     

Vortex control by the spanwise suction flow on the upper surface of delta wing

The numerical investigation has been performed to explore the feasibility of vortex control by leading edge sucking excitation on a delta wing. The results reveal that the flow on the upper surface of the delta wing changes significantly in a wide range of the angle of attack. For the vortical flow at moderate angle of attack, the secondary and tertiary vortices are weakened or suppressed, and the total lift is almost unchanged. For the stalled flow at high angle of attack, the leading edge concentrated vortex is recovered, and the lift is enhanced with increasing suction rate. For the bluff-body flow at even high angles of attack, the lift can still be improved. The concentrated vortex disappears on the upper surface, and the load increment is nearly unchanged along the chordwise direction. The project supported by the National Natural Science Foundation of China (19802018).     

3-D measurements of separated flow over rigid plates with spanwise periodic cambering at low Reynolds number

Measurements of the flow field around a flat plate and rigid plates with spanwise periodic cambering were performed using volumetric three-component velocimetry (V3V) at a Reynolds numbers of 28,000 at α=12° where the flow is fully separated. The Reynolds normal and shear stresses, and the streamwise, spanwise and normal components of the vorticity vector are investigated for three-dimensionality. Flow features are discussed in context of the periodic cambering and corresponding aerodynamic force measurements. The periodic cambering results in spanwise variation in the reversed-flow region, Reynolds stresses and spanwise vorticity. These spanwise variations are induced by streamwise and normal vortices of opposite directions of rotation. Moreover, measurements were carried out for the cambered plates at α=8°, where a long separation bubble exists, to further understand the behavior of the streamwise and normal vortices. These vortices become more organized and increase in strength and size at the lower angle of attack. It is also speculated that these vortices contribute to the increase in lift at and beyond the onset of stall angle of attack.     

Control of vortex shedding behind circular cylinder for flows at low Reynolds numbers

It has been observed by researchers in the past that vortex shedding behind circular cylinders can be altered, and in some cases suppressed, over a limited range of Reynolds numbers by proper placement of a second, much smaller, ‘control’ cylinder in the near wake of the main cylinder. Results are presented for numerical computations of some such situations. A stabilized finite element method is employed to solve the incompressible Navier–Stokes equations in the primitive variables formulation. At low Reynolds numbers, for certain relative positions of the main and control cylinder, the vortex shedding from the main cylinder is completely suppressed. Excellent agreement is observed between the present computations and experimental findings of other researchers. In an effort to explain the mechanism of control of vortex shedding, the streamwise variation of the pressure coefficient close to the shear layer of the main cylinder is compared for various cases, with and without the control cylinder. In the cases where the vortex shedding is suppressed, it is observed that the control cylinder provides a local favorable pressure gradient in the wake region, thereby stabilizing the shear layer locally. Copyright © 2001 John Wiley & Sons, Ltd.     

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

The effect of Lorentz force on particle transport and deposition is studied by using direct numerical simulation of turbulent channel flow of electrically conducting fluids combined with discrete particle simulation of the trajectories of uncharged, spherical particles. The magnetohydrodynamic equations for fluid flows at low magnetic Reynolds numbers are adopted. The particle motion is determined by the drag, added mass, and pressure gradient forces. Results are obtained for flows with particle ensembles of various densities and diameters in the presence of streamwise, wall-normal or spanwise magnetic fields. It is found that the particle dispersion in the wall-normal and spanwise directions is decreased due to the changes of the underlying fluid turbulence by the Lorentz force, while it is increased in the streamwise direction. The particle accumulation in the near-wall region is diminished in the magnetohydrodynamic flows. In addition, the tendency of small inertia particles to concentrate preferentially in the low-speed streaks near the walls is strengthened with increasing Hartmann number. The particle transport by turbophoretic drift and turbulent diffusion is damped by the magnetic field and, consequently, particle deposition is reduced.     

Investigation of the influence of the transverse sweepback of delta wings on their vortex structures and aerodynamic characteristics in the case of flow separation at low subsonic velocities

The results are given of theoretical and experimental investigations into the influence of transverse sweepback of delta wings of small aspect ratio on their lifting properties and the stability of the vortex structure in the case of flow separation. Theoretical investigations have been made using the method of discrete vortices. The physical experiment included weight tests and also investigations on the breakup of vortex filaments by means of aerometric and schlieren methods. The results of the investigations are given and the calculated and experimental data are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 173–175, September–October, 1982.     

A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. A generalized Maxwell model with the fractional calculus was considered. Exact solutions of some unsteady flows of a viscoelastic fluid between two parallel plates are obtained by using the theory of Laplace transform and Fourier transform for fractional calculus. The flows generated by impulsively started motions of one of the plates are examined. The flows generated by periodic oscillations of one of the plates are also studied.     

A time‐accurate scheme for the calculations of unsteady reactive flows at low Mach number

The artificial compressibility method is extended to the case of unsteady turbulent reacting flows at low Mach number. The resulting scheme is applied to the calculation of a propagating one‐dimensional (1D) planar turbulent flame with a realistic heat release parameter. An eddy break‐up‐like approach, with a conventional gradient expression for the turbulent fluxes, is retained to model this reacting turbulent flow. A quenched form of the mean reaction rate is used to ensure the existence of a steady regime of propagation, for which the present results are compared with those obtained by a steady analysis of the mean flame brush structure, with excellent agreement. A sensitivity analysis of the convergence rate to the values of the artificial compressibility factor and the pseudo‐time is carried out. It is shown that a reduced artificial compressibility factor of 5–10, combined with a pseudo‐Courant number of ≈1000, represents a good compromise to optimize the convergence rate. Copyright © 1999 John Wiley & Sons, Ltd.     

A low Reynolds number variant of partially-averaged Navier-Stokes model for turbulence

A low Reynolds number (LRN) formulation based on the Partially Averaged Navier-Stokes (PANS) modelling method is presented, which incorporates improved asymptotic representation in near-wall turbulence modelling. The effect of near-wall viscous damping can thus be better accounted for in simulations of wall-bounded turbulent flows. The proposed LRN PANS model uses an LRN k-ε model as the base model and introduces directly its model functions into the PANS formulation. As a result, the inappropriate wall-limiting behavior inherent in the original PANS model is corrected. An interesting feature of the PANS model is that the turbulent Prandtl numbers in the k and ε equations are modified compared to the base model. It is found that this modification has a significant effect on the modelled turbulence. The proposed LRN PANS model is scrutinized in computations of decaying grid turbulence, turbulent channel flow and periodic hill flow, of which the latter has been computed at two different Reynolds numbers of Re = 10,600 and 37,000. In comparison with available DNS, LES or experimental data, the LRN PANS model produces improved predictions over the standard PANS model, particularly in the near-wall region and for resolved turbulence statistics. Furthermore, the LRN PANS model gives similar or better results - at a reduced CPU time - as compared to the Dynamic Smagorinsky model.