Asymmetric vortex shedding flow past an inclined flat plate at high incidence

This paper reports an experimental investigation of the vortex shedding wake behind a long flat plate inclined at a small angle of attack to a main flow stream. Detailed velocity fields are obtained with particle-image velocimetry (PIV) at successive phases in a vortex shedding cycle at three angles of attack, α=20°, 25° and 30°, at a Reynolds number Re≈5,300. Coherent patterns and dynamics of the vortices in the wake are revealed by the phase-averaged PIV vectors and derived turbulent properties. A vortex street pattern comprising a train of leading edge vortices alternating with a train of trailing edge vortices is found in the wake. The trailing edge vortex is shed directly from the sharp trailing edge while there are evidences that the formation and shedding of the leading edge vortex involve a more complicated mechanism. The leading edge vortex seems to be shed into the wake from an axial location near the trailing edge. After shedding, the vortices are convected downstream in the wake with a convection speed roughly equal to 0.8 the free-stream velocity. On reaching the same axial location, the trailing edge vortex, as compared to the leading edge vortex, is found to possess a higher peak vorticity level at its centre and induce more intense fluid circulation and Reynolds stresses production around it. It is found that the results at the three angles of attack can be collapsed into similar trends by using the projected plate width as the characteristic length of the flow.     

Calculation of flow around a lifting surface in the case of large deformations

Many studies have been made of the nonstationary flow of an ideal incompressible fluid around a lifting surface. The present state of the numerical methods of solution of this problem is reviewed in [1]. The present paper studies three-dimensional nonstationary flow around a lifting surface which undergoes deformation and behind which a wake vortex surface is formed. The lifting and wake vortex surfaces are represented in parametric form. The metrics of these surfaces are used, and the introduced vortex function is approximated by bicubic splines. For the convenient application of the theory developed here to the flapping flight of insects, for which it is sometimes difficult to distinguish the lateral and trailing edges of the wings, the following terminology is introduced. The part of the edge of the lifting surface from which the wake vortex surface is shed is called the trailing edge. The remaining part is called the leading edge. On the leading edge, the velocity has a singularity. Test calculations have demonstrated the effectiveness of the method.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 72–79, July–August, 1980.     

Wake formation when shock wave is shed from the edge of a plate

The formation of a laminar wake in the flow behind a shock wave when the latter is shed from the trailing edge of a semi-infinite plate is investigated in this paper. It is shown that the flow on the plate and in the wake turns out to be self-similar, dependent on two dimensionless combinations of variables, and the flow on the plate, including the trailing edge, remains steady in a coordinate system coupled to the shock wave (the fact of the flow self-similarity in the wake was first noted in [1]). An analytic solution of the problem of the wake in the neighborhood of the trailing edge is obtained, from which it follows that, in contrast to [2], there is no line of singularities in the nonstationary boundary-layer equations in the flow domain. This fact is also verified by the analysis of the flow in the neighborhood of a line of tagged particles leaving the trailing edge simultaneously with the shock wave. Hence the problem under consideration is solved by the traditional numerical methods using conditions in the initial section (which is taken to be the section in the neighborhood of the trailing edge), on the wake axis, and at an infinite distance away. Approximate formulas are obtained for the longitudinal velocity profiles in the whole range of shock-wave intensities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 59–66, July–August, 1978.     

Features of the turbulent flow around symmetric elongated bluff bodies

The flow fields around three elongated bluff bodies with the same chord-to-thickness ratios but distinct leading and trailing edge details were measured at a Reynolds number of 3×10⁴. These models each represent a case where: leading edge shedding dominates, trailing edge shedding dominates and a case where there is a balance between the two. The results show that the vortex street parameters vary between the models, and in particular, the shedding frequencies are significantly altered by the geometry. However, contrary to the current understanding for shorter bluff bodies, the scale of the recirculation region is found to be similar for each model, even though the shedding frequency changes within the range from 0.15 to 0.24. Also, the base pressure does not follow trends with shedding frequency expected from shorter bluff bodies. A force balance of the recirculation region shows that the near wake of each body is significantly affected by the Reynolds shear stress distribution and the resultant force due to the pressure field in the mean recirculation region. These differences infer that the distinct vortex formation characteristics depend on the state of the trailing edge shear layers. The boundary layers at the trailing edge have been quantified, as have the leading edge separation bubbles, and the marked differences in the wake details are shown to depend on the leading edge separation.     

Experimental investigation of a blunt trailing edge flow field with application to sound generation

The unsteady lift generated by turbulence at the trailing edge of an airfoil is a source of radiated sound. The objective of the present research was to measure the velocity field in the near wake region of an asymmetric beveled trailing edge in order to determine the flow mechanisms responsible for the generation of trailing edge noise. Two component velocity measurements were acquired using particle image velocimetry. The chord Reynolds number was 1.9 × 10⁶. The data show velocity field realizations that were typical of a wake flow containing an asymmetric periodic vortex shedding. A phase average decomposition of the velocity field with respect to this shedding process was utilized to separate the large scale turbulent motions that occurred at the vortex shedding frequency (i.e., those responsible for the production of tonal noise) from the smaller scale turbulent motions, which were interpreted to be responsible for the production of broadband sound. The small scale turbulence was found to be dependent on the phase of the vortex shedding process implying a dependence of the broadband sound generated by the trailing edge on the phase of the vortex shedding process.     

Turbulent flow of a fluid in the neighborhood of the trailing edge of a plate at zero angle of attack

The laminar flow regime of an incompressible fluid at the trailing edge of a plate was studied by Stewartson and Messiter [1, 2] by means of the method of matched asymptotic expansions. In. the present paper, this method is used to analyze the same problem, but in the case of turbulent flow in the boundary layer and the wake. A system of linear equations of elliptic type with variable coefficients is obtained for the averaged values of the flow parameters in the main part of the boundary layer and the wake that is responsible for the change in the displacement thickness. A solution of this system is constructed by the Fourier method in the case of a power law of the velocity in front of the interaction region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 17–23, November–December, 1983.     

Experimental investigation of vortex formation in the wake of a flat plate for subsonic and supersonic freestream Mach numbers

The wake of a flat plate with thickness H = 6 mm whose surface was either smooth or rough by pasting smooth or rough paper on to it was investigated with optical methods. The studies showed that for supersonic freestream Mach numbers the wake of the smooth flat plate seems to be turbulent in the observation field. In contrast the wake of the rough plate can exhibit a vortex street if certain conditions are met. The most important parameters are the roughness of the paper and the distance from the location where the rough paper ends to the trailing edge, abbreviated with d. It turned out that a vortex street develops in the wake if the roughness exceeds a critical value and if the distance d is of the order of some millimeters. If these conditions are not met the wake of the rough plate is turbulent in the observation field. The dependence of the vortex formation upon the Mach number, the roughness and the distance d was investigated with holographic interferometry, two component laser-Doppler-anemometry and a laser-optics for measuring the vortex shedding frequency.     

Interaction between Taylor bubbles rising in stagnant non-Newtonian fluids

The interaction between Taylor bubbles rising in stagnant non-Newtonian solutions was studied. Aqueous solutions of carboxymethylcellulose (CMC) and polyacrylamide (PAA) polymers were used to study the effect of different rheological properties: shear viscosity and viscoelasticity. The solutions studied covered a range of Reynolds numbers between 10 and 714, and Deborah numbers up to 14. The study was performed with pairs of Taylor bubbles rising in a vertical column (0.032 m internal diameter) filled with stagnant liquid. The velocities of the leading and trailing bubbles were measured by sets of laser diodes/photocells placed along the column. The velocity of the trailing bubble was analysed together with the liquid velocity profile in the wake of a single rising bubble (Particle Image Velocimetry data obtained from the literature). For the less concentrated CMC solutions, with moderate shear viscosity and low viscoelasticity, the interaction between Taylor bubbles was similar to that found in Newtonian fluids. For the most concentrated CMC solution, which has high shear viscosity and moderate viscoelasticity, a negative wake forms behind the Taylor bubbles, inhibiting coalescence since the bubbles maintain a minimum distance of about 1D between them. For the PAA solutions, with moderate shear viscosity but higher viscoelasticity than the CMC solutions, longer wake lengths are seen, which are responsible for trailing bubble acceleration at greater distances from the leading bubble. Also in the PAA solutions, the long time needed for the fluid to recover its initial shear viscosity after the passage of the first bubble makes the fluid less resistant to the trailing bubble flow. Hence, the trailing bubble can travel at a higher velocity than the leading bubble, even at distances above 90D.     

The effect of viscoelasticity on a rising gas bubble

This paper investigates the role of viscoelasticity on the dynamics of rising gas bubbles. The dynamics of bubbles rising in a viscoelastic liquid are characterised by three phenomena: the trailing edge cusp, negative wake, and the rise velocity jump discontinuity. There is much debate in the literature over the cause of the jump discontinuity, which is observed once the bubble exceeds a certain critical volume. In this paper, the employment of some choice modelling assumptions allows insights into the mechanisms of the jump discontinuity which cannot be ascertained experimentally. The ambient fluid is assumed incompressible and the flow irrotational, with viscoelastic effects included through the stress balance on the bubble surface. The governing equations are solved using the boundary element method. Some Newtonian predictions are discussed before investigating the role of viscoelasticity. The model predicts the trademark cusp at the trailing end of a rising bubble to a high resolution. However, the irrotational assumption precludes the prediction of the negative wake. The corresponding absence of the jump discontinuity supports the hypothesis that the negative wake is primarily responsible for the jump discontinuity, as mooted in previous studies.     

Numerical simulation of flapping‐wing insect hovering flight at unsteady flow

A computational fluid dynamics (CFD) analysis was conducted to study the unsteady aerodynamics of a virtual flying bumblebee during hovering flight. The integrated geometry of bumblebee was established to define the shape of a three‐dimensional virtual bumblebee model with beating its wings, accurately mimicking the three‐dimensional movements of wings during hovering flight. The kinematics data of wings documented from the measurement to the bumblebee in normal hovering flight aided by the high‐speed video. The Navier–Stokes equations are solved numerically. The solution provides the flow and pressure fields, from which the aerodynamic forces and vorticity wake structure are obtained. Insights into the unsteady aerodynamic force generation process are gained from the force and flow‐structure information. The CFD analysis has established an overall understanding of the viscous and unsteady flow around the virtual flying bumblebee and of the time course of instantaneous force production, which reveals that hovering flight is dominated by the unsteady aerodynamics of both the instantaneous dynamics and also the past history of the wing. A coherent leading‐edge vortex with axial flow and the attached wingtip vortex and trailing edge vortex were detected. The leading edge vortex, wing tip vortex and trailing edge vortex, which caused by the pressure difference between the upper and the lower surface of wings. The axial flow, which include the spanwise flow and chordwise flow, is derived from the spanwise pressure gradient and chordwise pressure gradient, will stabilize the vortex and gives it a characteristic spiral conical shape. Copyright © 2006 John Wiley & Sons, Ltd.     

Mean and turbulence measurements in the boundary layer and wake of a symmetric aerofoil

Detailed measurements of two-dimensional profiles of static pressure, mean velocity, turbulence intensity and Reynolds shear stress were carried out with conventional pressure probes and hot wire probes at preselected streamwise stations in the boundary layer and wake of a 12.5% thick, 600 mm chord two-dimensional symmetric aerofoil mounted at zero incidence in a low speed wind tunnel. The chord Reynolds number was one million and the wake measurements extended up to three chord lengths (or nearly 660 trailing edge momentum thicknesses) downstream of the trailing edge. The data indicate rapid interaction of the wall layers immediately behind the trailing edge, leading to significant changes in the flow parameters close to the trailing edge. The relaxation of the wake is preceded by initial ‘overshoot’ in the streamwise profiles of mean-flow parameters and peak values of turbulence components. Further growth of the wake towards similarity/equilibrium is discussed.     

Secondary wake instabilities of a blunt trailing edge profiled body as a basis for flow control

Flow in the wake of a blunt trailing edge profiled body, comprised of an elliptical leading edge and a rectangular trailing edge, has been investigated experimentally, to identify and characterize the secondary instabilities accompanying the von Kármán vortices. The experiments, which involve laser-induced fluorescence for visualization and particle image velocimetry for quantitative measurement of the wake instabilities, cover Reynolds numbers ranging from 250 to 2,150 based on thickness of the body, to include the wake transition regime. The dominant secondary instability appears as spanwise undulations in von Kármán vortices, which evolve into pairs of counter-rotating vortices, with features resembling the instability mechanism predicted by Ryan et al. (J Fluid Mech 538:1–29, 2005). Feasibility of a flow control approach based on interaction with the secondary instability using a series of discrete trailing edge injectors has also been investigated. The control approach mitigates the adverse effects of vortex shedding in certain conditions, where it is able to amplify the secondary instability effectively.     

Flows around two airfoils performing fling and subsequent translation and translation and subsequent clap

The aerodynamic forces and flow structures of two airfoils performing “fling and subsequent translation“ and “translation and subsequent clap“ are studied by numerically solving the Navier-Stokes equations in moving overset grids. These motions are relevant to the flight of very small insects. The Reynolds number, based on the airfoil chord length c and the translation velocity U, is 17. It is shown that: (1) For two airfoils performing fling and subsequent translation, a large lift is generated both in the fling phase and in the early part of the translation phase. During the fling phase,a pair of leading edge vortices of large strength is generated; the generation of the vortex pair in a short period results in a large time rate of change of fluid impulse, which explains the large lift in this period. During the early part of the translation, the two leading edge vortices move with the airfoils;the relative movement of the vortices also results in a large time rate of change of fluid impulse, which explains the large lift in this part of motion. (In the later part of the translation, the vorticity in the vortices is diffused and convected into the wake.) The time averaged lift coefficient is approximately 2.4 times as large as that of a single airfoil performing a similar motion. (2) For two airfoils performing translation and subsequent clap, a large lift is generated in the clap phase. During the clap, a pair of trailing edge vortices of large strength are generated; again, the generation of the vortex pair in a short period (which results in a large time rate of change of fluid impulse) is responsible for the large lift in this period. The time averaged lift coefficient is approximately 1.6 times as large as that of a single airfoil performing a similar motion. (3) When the initial distance between the airfoils (in the case of clap, the final distance between the airfoils) varies from 0.1 to 0.2c, the lift on an airfoil decreases only slightly but the torque decreases greatly. When the distance is about lc， the interference effects between the two airfoils become very small.     

Active flow control for reduction of fluctuating aerodynamic forces of a blunt trailing edge profiled body

Vortex shedding in the wake of two-dimensional bluff bodies is usually accompanied by three dimensional instabilities. These instabilities result in streamwise and vertical vorticity components which occur at a certain spanwise wavelength. The spanwise wavelength of the instabilities (λ_Z) depends on several parameters, including profile geometry and Reynolds number. The objective of the present work is to study the three dimensional wake instabilities for a blunt trailing edge profiled body, comprised of an elliptical leading edge and a rectangular trailing edge, and to manipulate these instabilities to control the aerodynamic forces. Results of numerical simulations of flow around the body at Re(d) = 400, 600, and 1000, as well as planar Laser Induced Fluorescence (LIF) flow visualizations at Re(d) = 600 and 1000 are analyzed to determine the wake vorticity structure and λ_Z. Based on the findings of these analyses, an active flow control mechanism for attenuation of the fluctuating aerodynamic forces on the body is proposed. The flow control mechanism is comprised of a series of trailing edge injection ports distributed across the span, with a spacing equal to λ_Z. Injection of a secondary flow leads to amplification of the three dimensional instabilities and disorganization of the von Kármán vortex street. Numerical simulations indicate that the flow control mechanism can attenuate the fluctuating aerodynamic forces at lower Reynolds numbers (Re(d) = 400 and 600) where λ_Z is constant in time. However, the control mechanism loses its effectiveness at Re(d) = 1000, due to the temporal variations of λ_Z.     

Numerical simulation of a low-Reynolds-number turbulent wake behind a flat plate

A numerical simulation of a plane turbulent wake at a very low Reynolds number has been performed using finite volume methods. The wake was produced by allowing two turbulent boundary layers, simulated separately in advance, to interact downstream of the trailing edge of a thin flat plate. A number of innovative numerical techniques were required in the simulation, such as the provision of fully turbulent time-dependent inflow data from a separate simulation, advective outflow boundary conditions and the approximate representation of an internal solid surface by a method which is computationally efficient. The resulting simulation successfully reproduced many of the statistical properties of the turbulent near-wake flow at low Reynolds number.     

Numerical investigation on effects of induced jet on boundary layer and turbulent models around airfoils

In this study the effects of induced jet at trailing edge of a two dimensional airfoil on its boundary layer shape, separation over surface and turbulent parameters behind trailing edge are numerically investigated and compared against a previous experimental data. After proving independency of results from mesh size and obtaining the required mesh size, different turbulent models are examined and RNG k-epsilon model is chosen because of good agreement with experimental data in velocity and turbulent intensity variations. A comparison between ordinary and jet induced cases, regarding numerical data, is made. The results showed that because of low number of measurement points in experimental study, turbulent intensity extremes are not captured. While in numerical study, these values and their positions are well calculated and exact variation of turbulent intensity is acquired. Also a study in effect of jet at high angles of attack is done and the results showed the ability of jet in controlling separation and reducing wake region.     

Changes in flat plate wake characteristics obtained with decreasing plate thickness

The near and very near wake of a flat plate with a circular trailing edge is investigated with data from direct numerical simulations. Computations were performed for four different Reynolds numbers based on plate thickness (D) and at constant plate length. The value of θ/D varies by a factor of approximately 20 in the computations (θ being the boundary layer momentum thickness at the trailing edge). The separating boundary layers are turbulent in all the cases. One objective of the study is to understand the changes in wake characteristics with changing θ/D (as obtained by decreasing D). Vortex shedding is vigorous in the low θ/D cases with a substantial decrease in shedding intensity in the largest θ/D case (for all practical purposes shedding becomes almost intermittent). Other characteristics that are significantly altered with increasing θ/D are the roll-up of the detached shear layers and the magnitude of fluctuations in shedding period. These effects are explored in depth. The effects of changing θ/D on the distributions of the time-averaged, near-wake velocity statistics are discussed.     

Elliptic cylinder in inviscid shear flow

We examine the flow of a plane parallel inviscid stream about an elliptic contour. There is vorticity far ahead of the body because of nonuniformity of the velocity profile. In the case of a small vorticity parameter the velocity profile will be parabolic. In contrast with [1] and [2], we assume the existence of additional circulational flow around the contour. The magnitude of this flow circulation is determined from the condition under which the flow leaves the trailing edge of the body (the analog of the Chaplygin-Zhukovskii postulate in potential flow).The results obtained in this study can be used, in particular, to evaluate the flow past a two-dimensional body in the wake behind another body.The author wishes to thank G. A. Dombrovskii for his interest in this study.     

Suppression of force fluctuations in flow past an aerofoil

Force fluctuations on a solid body are associated with unsteadiness in the wake, e.g. vortex shedding. Therefore, the control of force fluctuations can be realised by suppressing the flow unsteadiness. A NACA0024 aerofoil closed with a round trailing edge is chosen to represent the solid body throughout this investigation, with the Reynolds number fixed at Re = 1000 and angle of attack α ≤ 15^o, at which the uncontrolled flow is two-dimensional. A linear optimal control is calculated by analysing the distribution of sensitivity of unsteadiness to control around the entire surface of the body. The nonlinear effects of the calculated control, which can be actuated through surface-normal suction and blowing across the surface of the aerofoil, are tested through two-dimensional direct numerical simulations. It is observed that a surface-normal velocity control with a maximum magnitude less than 8% of the free stream velocity completely suppresses unsteadiness at α = 10° with an overall drag reduction of 14% and a 138% increase of lift.     

绕振荡水翼流动及其转捩特性的数值计算研究简

通过对比标准k-ω SST 湍流模型和基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型对绕振荡NACA66 水翼流动的数值计算结果与实验结果,对水翼振荡过程的水动力特性和流场结构变化进行了分析研究. 结果表明：与标准k-ω SST 湍流模型的数值计算结果相比,基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型能有效预测绕振荡翼型流场结构和水动力特性,捕捉流场边界层发生的流动分离和转捩现象;绕振荡水翼的流动过程可分为5 个特征阶段,当来流攻角较小时,在水翼前缘发生层流向湍流的转捩现象,水翼动力特征曲线出现变化拐点;随着来流攻角的增大,顺时针尾缘涡逐渐形成并向水翼前缘发展;当攻角较大时,前缘涡分离导致动力失速,水翼的动力特征曲线出现大幅波动;水翼处于顺时针向下旋转阶段,绕水翼的流动状态逐渐由湍流过渡为层流.