Modeling the Interaction of a Vortex Pair with the Ground

The results of a numerical investigation of the interaction between an aircraft vortex wake (vortex pair) and the ground during the takeoff and landing phases are presented. The calculations were performed within the framework of the time-dependent two-dimensional Reynolds-averaged Navier-Stokes equations using the Spalart-Shur turbulence model generalizing the turbulent viscosity transport model of Spalart and Allmaras to the case of the flows with curved streamlines and rotation. Similar calculations were carried out on the basis of the original Spalart-Allmaras model and the k- model of Menter. Some new qualitative and quantitative data on the distinctive features of the phenomenon under consideration are obtained.     

Effect of a Thin Longitudinal Inviscid Vortex on a Two-Dimensional Pre-Separation Boundary Layer

For large Reynolds numbers, an asymptotic solution of the Navier-Stokes equations describing the effect of a thin longitudinal vortex with a constant circulation on the development of an incompressible steady two-dimensional laminar boundary layer on a flat plate is obtained. It is established that, in a narrow wall region extending along the vortex filament, the viscous flow is described by the 3-D boundary layer equations. A solution of these equations for small values of the vortex circulation is studied. It is found that the solution of the two-dimensional pre-separation boundary layer equations collapses. This is attributable to the singular behavior of the 3-D disturbances near the zero-longitudinal-friction points.     

Optical Analysis and Qualitative Discrimination of Vortex-Flame Interaction in a Plane Premixed Shear Layer

To obtain practical schemes of vortex–flame interactions, a series of organized eddies formed in the plane premixed shear layer is investigated, instead of a single vortex ring or a single vortex tube. The plane premixed shear layer is first formed between two parallel uniform propane–air mixture streams. For getting clear qualitative pictures of vortex–flame interactions in the plane premixed shear layer, two extreme ignition points are assigned; one is assigned at the center of an organized eddy where the vortex motion plays an important role, the other at the midpoint between two adjacent organized eddies where the rolling-up motion prevails. A premixed flame is initiated by an electric discharge at one of the two assigned points and propagates either in the large scale organized eddy or along the interface between two uniform mixture streams. Propagation and deformation processes of the flame are observed using the simultaneously two-directional and high-speed Schlieren photography. The tangential velocity of organized eddy and the equivalence ratio of premixed shear flow are varied as two main parameters. The outline of propagating flame after the midpoint ignition is numerically analyzed by superposing the flame propagation having a constant burning velocity on the vortex flow field simulated with the discrete vortex method. The results obtained show that there exists another type of vortex–flame interaction in the plane shear layer in addition to the vortex bursting, and that it is caused by the rolling-up motion particular to the coherent structure in the plane shear layer and is simply named the vortex boosting. It is qualitatively concluded therefore that, in the ordinary turbulent premixed flames formed in the plane premixed shear layer, these two fundamental vortex-flame interactions get tangled with each other to augment the propagation velocity. An empirical expression which qualitatively takes into account of the effects of both vortex and chemical properties is finally proposed.     

Interaction of Spontaneous Vortex Structure with a Flame Front

Spontaneous vortex formation in combustion products near a flame front propagating in a combustible mixture down a vertical tube has been studied experimentally. It is shown that under certain conditions, free convection suppresses or stimulates vortex perturbations at the flame front. It is found that periodic changes in vortex intensity depend on oscillations of the flame front. This dependence is controlled by the rate of heat exchange among the flame front, combustion products, and pipe walls. The vortex flow structure depends on the shape of the closed trajectory along which the leading point of the flame moves in the coordinate system attached to the vortex.     

Interaction of a Streamwise Vortex with an Oblique Shock Wave

Interaction of a supersonic streamwise vortex with an oblique shock wave is considered. A mathematical model of the streamwise vortex is constructed. Three interaction regimes (weak, moderate, and strong) are found. It is shown numerically that vortex breakdown is possible in the case of strong interaction. The influence of the governing parameters on the interaction type is studied. It is shown that the main effect on the interaction type is exerted by the streamwise velocity and angle of the wedge forming the shock wave. The effect of splitting of the primary vortex on the shock wave in the case of moderate and strong interaction regimes is found.     

Interaction of a Traveling Pressure Perturbation with a Boundary Layer

The interaction between a traveling pressure perturbation and a laminar compressible boundary layer is investigated for a perturbation level higher than that needed to initiate steady-state flow separation. It is found that if the velocity of the pressure perturbation is fairly high the flow may remain unseparated and its direction of motion determines the nature of the perturbation propagation in the boundary layer. It is shown that even in the linear approximation the perturbations are mainly induced by the linear wall layer and not by the critical layer, which always remains nonlinear. It is also found that in the unsteady case shortwave perturbation oscillations are damped with time while the longwave ones grow and that the growth of the perturbations with time amplifies their damping along the streamwise coordinate while damping reduces it.     

Vortex Induced Vibrations of a Pair of Cylinders at Reynolds Number 1000

Vortex induced vibrations of two equal-sized cylinders in tandem and staggered arrangement placed in uniform incompressible flow is studied. A stabilized finite element formulation is utilized to solve the governing equations. The Reynolds number for these 2D simulations is 1000. The cylinders are separated by 5.5 times the cylinder diameter in the streamwise direction. For the staggered arrangement, the cross-flow spacing between the two cylinders is 0.7 times the cylinder diameter. In this arrangement, the downstream cylinder lies in the wake of the upstream one and therefore experiences an unsteady inflow. The wake looses its temporal periodicity, beyond a few diameters downstream of the front cylinder. The upstream cylinder responds as an isolated single cylinder while the downstream one undergoes disorganized motion. Soft-lock-in is observed in almost all the cases.     

Vortex Shedding from a Hemisphere in a Turbulent Boundary Layer

Supercritical turbulent boundary layer flow over a hemisphere with a rough surface (Re= 150000) has been simulated using Large Eddy Simulation (LES) and analyzed using the Karhunen--Loève expansion (“Proper Orthogonal Decomposition,” POD). The time-dependent inflow condition is provided from a separate LES of a boundary layer developing behind a barrier fence and a set of vorticity generators. LES results using significantly different grid resolutions are compared with a corresponding wind tunnel experiment to demonstrate the reliability of the simulation. The separation processes are analyzed by inspecting second-order moments, time spectra, and instantaneous velocity distributions. Applying POD, a detailed study of the spatiotemporal structure of the separation processes has been carried out. From this analysis it can be concluded that the major event in the separated flow behind the obstacle is the shedding of “von Kármán”-type vortices, which can be represented by the first three energetically dominant modes. Received 23 January 1997 and accepted 19 February 1998     

Turbulent Channel Flow with an Artificial Two-Dimensional Wall Layer

Turbulent flow of an incompressible fluid in a plane channel with parallel walls is considered. The three-dimensional time-dependent Navier-Stokes equations are solved numerically using the spectral finite-difference method. An artificial force which completely suppresses lateral oscillations of the velocity is introduced in the near-wall zone (10 % of the channel half-width in the neighborhood of each wall). Thus, the three-dimensional flow zone, in which turbulent oscillations can develop, is separated from the wall by a fluid layer. It is found that the elimination of three-dimensionality in the neighborhood of the walls leads to a significant reduction in the drag. However, complete laminarization does not occur. The flow in the stream core remains turbulent and can be interpreted as a turbulent flow in a channel with walls located on the boundary of the two-dimensional layer and traveling at the local mean-flow velocity. The oscillations developing inside the two-dimensional layer, which have significant amplitude, distort the flow only in the adjacent zone. Beyond this zone the distributions of the mean characteristics and the structure of instantaneous fields completely correspond to ordinary turbulent flow in a channel with rigid walls. The results obtained confirm the hypothesis of the unimportance of the no-slip boundary conditions for the fluctuating velocity component in the mechanism of onset and self-maintenance of turbulence in wall flows.     

Flat-Plate Boundary Layer Receptivity to a Steady Free-Stream Vortex Disturbance

A single trailing vortex developed behind a micro-wing immersed in a free stream was used to study the vortex receptivity of the boundary layer on a flat plate. As a result of the interaction, in the boundary layer there develop longitudinal-velocity disturbances which grow almost linearly in the longitudinal coordinate. The parameters of the excited steady disturbances agree with the data of previous experiments performed under natural conditions and dealing with an indirect scenario of laminar-turbulent transition at high free-stream turbulence. It is shown that the leading edge of the plate does not play a decisive role in the mechanism of growth of disturbances of this kind and the receptivity is non-local in nature.     

Swept-Wing Boundary Layer Receptivity to a Steady Free-Stream Vortex Disturbance

A single trailing vortex developed behind a micro-wing immersed in a free stream was used to study the vortex receptivity of a swept-wing boundary layer. As a result of the interaction, longitudinal-velocity disturbances develop in the boundary layer. On the swept wing, disturbance transformation occurs near the leading edge and is accompanied by the formation of a wave packet consisting of waves typical of cross-flow instability. Disturbances with other characteristics are also detected. These disturbances may be attributable to distributed boundary-layer receptivity to the free-stream vortex disturbance considered.     

激波与沉积可燃粉尘相互作用的实验研究

在新建立的激波管中实现了激波对沉积可燃粉尘的卷扬与点火。利用自行设计的瞬态阴影摄影系统和高空间分辨率的新型红外光敏二极管成功拍摄了激波后燃烧粉尘云的阴影图像和测量了激波后可燃粉尘的点火诱导时间。通过对实验结果的较深入的分析，揭示了激波与可燃粉尘床相互作用的基本特征     

Asymptotic Theory of the Viscous Interaction Between a Vortex and a Plane

The problem of the viscous interaction between a flow induced by a vortex filament and an orthogonal rigid surface is solved for high Reynolds numbers using the method of matched asymptotic expansions. In view of the impossibility of matching the principal terms of the asymptotic expansions directly for the near-axial boundary layer and the main flow zone, the solution is obtained by introducing two intermediate zones. In this case a logarithmic singularity of the axial velocity arises inevitably on the vortex filament. In the near-axial and intermediate zones the solution is obtained numerically and analytically, respectively, while in the main zone the problem reduces to the problem of the flow induced by a line of weakly swirled vortex-sinks.     

Simulations of Spatially Developing Two-Dimensional Shear Layers and Jets

A computational study of spatially evolving two-dimensional free shear flows has been performed using direct numerical simulation of the Navier–Stokes equations in order to investigate the ability of these two-dimensional simulations to predict the overall flow-field quantities of the corresponding three-dimensional “real” turbulent flows. The effects of inflow forcing on these two-dimensional flows has also been studied. Simulations were performed of shear layers, as well as weak (large co-flow and relatively weak shear) and strong (small co-flow and relatively strong shear) jets. Several combinations of discrete forcing with and without a broadband background spectrum were used. Although spatially evolving direct simulations of shear layers have been performed in the past, no such simulations of the plane jet have been performed to the best of our knowledge. It was found that, in the two-dimensional shear layers, external forcing led to a strong increase in the initial growth of the shear-layer thickness, followed by a region of decreased growth as in physical experiments. The final downstream growth rate was essentially unaffected by forcing. The mean velocity profile and the naturally evolving growth rate of the shear layer in the case of broadband forcing compare well with experimental data. However, the total and transverse fluctuation intensities are larger in the two-dimensional simulations with respect to experimental data. In the weak-jet simulations it was found that symmetric forcing completely overwhelms the natural tendency to transition to the asymmetric jet column mode downstream. It was observed that two-dimensional simulations of “strong” jets with a low speed co-flow led to a fundamentally different flow with large differences even in mean velocity profiles with respect to experimental data for planar jets. This was a result of the dominance of the two-dimensional mechanism of vortex dipole ejection in the flow due to the lack of spanwise instabilities. Experimental studies of planar jets do not show vortex dipole formation and ejection. A three-dimensional “strong”-jet simulation showed the rapid evolution of three-dimensionality effectively preventing this two-dimensional mechanism, as expected from experimental results. Received: 25 November 1996 and accepted 17 April 1997     

Convective-Absolute Transition of Non-Isothermal Compressible Shear Layer

The linear stability of inviscid compressible shear layers is studied. When the layer develops at the vicinity of a wall, the two parallel flows can have velocity of the same sign or of opposite sign. This situation is examined in order to obtain first hints on the stability of separated flows in the compressible regime. The shear layer is described by an hyperbolic tangent profile for the velocity component and the Crocco relation for the temperature profile. The gravity effects and the superficial tension are neglected. By examining the temporal growth rate at the saddle point in the wave number space, the flow is characterized as being either absolutely unstable or convectively unstable. This study principally shows the non-isothermal effect on the absolute-convective transition in compressible shear flow. Results are presented, showing the amount of the backflow necessary to have this type of transition for a range of primary flow Mach number M ₁ up to 3.0. The boundary of the absolute-convective transition is defined as a function of the velocity ratio, the temperature ratio and the Machnumber.     

On the Interaction of Turbulent Shear Layers with Harmonic Perturbations

The problem of coherent perturbations in a turbulent shear layer is considered for the purpose of developing a mathematical model based on a triple decomposition that extracts the coherent components of random fluctuations. The governing equations for the mean and the coherent parts of flow are derived, assuming the eddy-viscosity equivalence for the random part of flow, and solved by iterations to provide a coupled solution of the problem as a whole. Calculations agree well with experimental data in the upstream part of the layer where the mean–coherent flow interaction is the most important. In this region, the interaction changes the mean flow velocity distribution in such a manner that the neutral stability curve is shifted upstream relative to its position in the undisturbed layer and the perturbation intensity decreases further downstream. Experiments show that the coherent waves suppress the turbulent Reynolds stress production downstream of this region, but the model fails to predict the layer spreading correctly probably due to an inadequate turbulence closure of the mean flow. For the case of a turbulent mixing layer, we suggest a new closure relation that takes into account this coherent-random interaction.     

Generation of Three-Dimensional Disturbances in a Boundary Layer on Strong Interaction with a Hypersonic Flow

Laminar boundary layer flow over an infinite-span, finite-length flat plate is investigated in the regime of strong interaction with a hypersonic gas flow. Under the assumption that an additional condition dependent on the transverse coordinate can be imposed on the trailing edge of the plate the flow functions are expanded in power series in the vicinity of the leading edge. It is shown that these expansions include an indefinite function dependent on the transverse coordinate. The corresponding boundary value problems are formulated and solved and the eigenvalues are determined. It is established that in this case the two-dimensional boundary layer can rearrange itself into a three-dimensional boundary layer.     

一种新的运动激波--非定常边界层相互干扰现象

本文探讨了一种新的激波－非定常边界层相互干扰现象，这种激波－边界层干扰现象既不同于定常激波－边界层干扰现象，又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象，而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象，本文对这种现象用微波动力学理论进行分析，并把这种干扰现象看成激波的绕射现象，同时在稀疏波破膜的双驱动激波管中进行实验观察，最后把理论分析与实验观察进行了比较。