Dynamic performance and wake structure of flapping plates with different shapes

The dynamic performance and wake structure of flapping plates with different shapes were studied using multi-block lattice Boltzman and immersed boundary method.Two typical regimes relevant to thrust behavior are identified.One is nonlinear relation between the thrust and the area moment of plate for lower area moment region and the other is linear relation for larger area moment region.The tendency of the power variation with the area moment is reasonably similar to the thrust behavior and the efficiency decreases gradually as the area moment increases.As the mechanism of the dynamic properties is associated with the evolution of vortical structures around the plate,the formation and evolution of vortical structures are investigated and the effects of the plate shape,plate area,Strouhal number and Reynolds number on the vortical structures are analyzed.The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to flapping locomotion.     

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.     

The effect of a splitter plate on the flow around a finite prism

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height square prism was investigated experimentally in a low-speed wind tunnel. Measurements of the mean drag force and vortex shedding frequency were made at Re=7.4×10⁴ for square prisms of aspect ratios AR=9, 7, 5 and 3. Measurements of the mean wake velocity field were made with a seven-hole pressure probe at Re=3.7×10⁴ for square prisms of AR=9 and 5. The relative thickness of the boundary layer on the ground plane was δ/D=1.5–1.6 (where D is the side length of the prism). The splitter plates were mounted vertically from the ground plane on the wake centreline, with a negligible gap between the leading edge of the plate and rear of the prism. The splitter plate heights were always the same as the heights of prisms, while the splitter plate lengths ranged from L/D=1 to 7. Compared to previously published results for an “infinite” square prism, a splitter plate is less effective at drag reduction, but more effective at vortex shedding suppression, when used with a finite-height square prism. Significant reduction in drag was realized only for short prisms (of AR≤5) when long splitter plates (of L/D≥5) were used. In contrast, a splitter plate of length L/D=3 was sufficient to suppress vortex shedding for all aspect ratios tested. Compared to previous results for finite-height circular cylinders, finite-height square prisms typically need longer splitter plates for vortex shedding suppression. The effect of the splitter plate on the mean wake was to narrow the wake width close to the ground plane, stretch and weaken the streamwise vortex structures, and increase the lateral entrainment of ambient fluid towards the wake centreline. The splitter plate has little effect on the mean downwash. Long splitter plates resulted in the formation of additional streamwise vortex structures in the upper part of the wake.     

Mechanical forcing of the wake of a flat plate

We report experimental results of the forced wake of a thin symmetric flat plate, placed parallel to an uniform air stream, in the range of thickness-based Reynolds number 50< Re _e <200. External wake forcing was introduced by small harmonic oscillations of a moving flap, placed at the trailing-edge of the flat plate. When the flap remains in a fixed horizontal position, the mean velocity profiles obtained by hot wire measurements, for different Reynolds numbers, are self similar. In the presence of harmonic forcing, within a certain range of the forcing frequency, the mean velocity profiles change and coherent structures are formed in the wake. Two independent flow-type resonances were observed: (i) when the inverse of the forcing frequency matches the flight time of the fluid particles along the flap. (ii) when the forcing frequency of the flap equals one half of the vortex shedding frequency of the flat plate and flap system. Implications of the two observed resonances on the wake structure are important. The first resonance (i) is associated to a wide but less intense (energy fluctuations) wake flow and the second resonance (ii) generates a thin but intense resultant wake flow.     

Generation of coherent structures in supersonic flow past a finite-span flat plate

The formation of coherent structures on a flat plate in a supersonic flow is numerically investigated both in the case of strong shock incidence on the plate and in the problem of oncoming harmonic waves having an intensity of 1–5% of the freestream pressure P ₀. The same mechanism of the coherent structure formation is noticed in both nonstationary problems; it is due to the manifestation of the secondary instability generated in the gas flow owing to the influence of the vortices formed at the lateral edges of the plate. An analysis of the incident wave enhancement at the rear of the plate is made for different wave intensities and wavelength to plate width ratios. The flow patterns in the plate wake indicate the generation of an intense expansion wave in this region, which accelerates the gas flow to the freestream velocity.     

Experimental study of three-dimensional vortex structures in translating and rotating plates

Motivated by the unsteady force generation of flying animals, vortex formation and vorticity transport processes around small aspect-ratio translating and rotating plates with a high angle of attack are investigated. Defocusing Digital Particle Image Velocimetry was employed to explore the structure and dynamics of the vortex generated by the plates. For both translating and rotating cases, we observe the presence of a spanwise flow over the plate and the consequent effect of vorticity transport due to the tilting of the leading-edge vortex. While the spanwise flow is confined inside the leading-edge vortex for the translating case, it is widely present over the plate and the wake region of the rotating case. The distribution of the spanwise flow is a prominent distinction between the vortex structures of these two cases. As the Reynolds number decreases, due to the increase in viscosity, the leading-edge and tip vortices tend to spread inside the area swept by the rotating plate. The different vorticity distributions of the low and high Reynolds number cases are consistent with the difference in measured lift forces, which is confirmed using the vorticity moment theory.     

Vortex dynamics of a sphere wake in proximity to a wall

Toward getting the vortex dynamics characteristics and wake structure of a sphere in proximity to a wall, the effect of a proximal flat plate on the wake of a stationary sphere is investigated via direct numerical simulation. The vortex shedding process and the significant variation of the wake structure are described in detail. The drag coefficient reduces and the wake structure of the sphere becomes complex due to the combined effect of the wake flow and the wall. A jet flow forms between the sphere and the flat plate, which suppresses the vortex separation on the bottom of the sphere. The asymmetric distributions of the coherent structures and the recirculation region behind the sphere are discussed. Besides vortex shedding patterns, the time-averaged velocity distribution, vortex dynamics, distribution regularities of turbulent kinetic energy and enstrophy are investigated.     

Turbulent wake behind a T-shaped plate: Comparison with a cross-shaped plate

The wake behind T-shaped intersecting flat plates has been studied by direct numerical simulations and compared with the wake behind intersecting plates forming a cross. The Reynolds number based on the uniform inflow velocity and the plate width d was 1000. Similar to the cross-plate the vortex shedding was suppressed in a 4d wide intersection region with a substantial base suction pressure reduction. Shear-layer (K-H) instabilities have been observed and its characteristic frequency obtained. In contrast to the cross-plate, a main feature of the mean wake structure behind the T-plate is the formation of two symmetrically positioned swirling vortices close to the internal corners of the T. This was examined by considering pressure contours and the turbulent production terms of mean streamwise vorticity. In spite of some similarities, major features of the wake behind the T-plate turned out to be distinctly different from the wake behind a cross-plate configuration.     

Low Reynolds number flow over a square cylinder with a detached flat plate

A numerical study of the alteration of a square cylinder wake using a detached downstream thin flat plate is presented. The wake is generated by a uniform flow of Reynolds number 150 based on the side length of the cylinder, D. The sensitivity of the near wake structure to the downstream position of the plate is investigated by varying the gap distance (G) along the wake centerline in the range 0 ⩽ G ⩽ 7D for a constant plate length of L = D. A critical gap distance is observed to occur at G_c ≈ 2.3D that indicates the existence of two flow regimes. Regime I is characterised by vortex formation occurring downstream of the gap while for regime II, formation occurs within the gap. By varying the plate length and gap distance, a condition is found where significant unsteady total lift reduction can occur. The root mean square lift reduction is limited by an unsteady stall process on the plate.     

Effect of Large Scale 3-D Structures on the Flow Around a Heated Cylinder at Low Reynolds Number

This work presents results of flow around a heated circular cylinder in mixed convection regime and demonstrates that Prandtl number and angle of attack of the incoming flow have a large influence on the characterisation of the flow transition from 2-D to 3-D. Previous studies show that heat transfer can enhance the formation of large 3-D structures in the wake of the cylinder for Reynolds numbers between 75 and 127 and a Richardson number larger than 0.35. This transitional mode is generally identified as “mode E”. In this work, we compare the results for water-based flow (large Prandtl number) with the ones for air-based flows (low Prandtl number). The comparison is carried out at two Reynolds numbers (100 and 150) and at a fixed Richardson number of 1. It shows that at the low Reynolds number of 100 the low Prandtl number flow does not enter into transition. This is caused by the impairment of the baroclinic vorticity production provoked by the spanwise temperature gradient. At low Prandtl number temperature gradients are less steep. For an air-based flow at Reynolds number 150, several Richardson numbers have been simulated. In this situation, the flow enters into transition and exhibits the characteristics of “mode E”, with the development of Λ-shaped structures in the near wake and mushroom-like structures in the far wake. It is also observed that the transition is delayed at Richardson number of 0.5. Simulations are also carried to investigate the effect of the angle of attack on the incoming flow on the development of large coherent structures. When the angle of attack is positive, the development of the wake tends to return to a more bi-dimensional configuration, where large scale coherent structures are impaired. In contrast, when the angle of attack is negative, large scale tri-dimensional structures dominate the flow in the wake, but with a very chaotic behaviour and the regular pattern of zero angle of attack is destroyed. The different behaviour of the flow with the variation of the angle of attack is also related to the baroclinic vorticity production, where new terms appear in the equations, leading to a positive effect of the vorticity production in case of a negative angle of attack and the opposite for a positive angle of attack.     

Interaction of circular cylinder wake with a short asymmetrically located downstream plate

This study reveals the interaction patterns of separated shear layers from a circular cylinder with a short downstream plate and their reflection on the frequency and the formation length of the vortices from the cylinder as a function of plate location relative to the cylinder. The effect of horizontal (G/D) and vertical (Z/D) distances between the cylinder and the plate on the near wake is studied via Digital Particle Image Velocimetry (DPIV) in a water channel for Reynolds numbers of 200, 400 and 750, based on the cylinder diameter D. It is shown that the interaction of wake with the plate of length D can be categorized depending on the horizontal and the vertical distances between the cylinder and the plate. For the vertical distance range of Z/D ≤ 0.7, there is a critical horizontal spacing before which the shear layers from the cylinder are inhibited to form vortices in front of the plate. Resulting elongated recirculation region between the plate and the cylinder suggests modification of the absolutely unstable near wake of free circular cylinder in favor of convective instability. Z/D = 0.9 provides a passage from Z/D ≤ 0.7 to ≥1.1 and is associated with a dominant effect on the near-wake characteristics of interaction of shear layers from the cylinder with those from the downstream plate. For Z/D ≥ 1.1, there is again, yet a smaller critical horizontal spacing after which vortices interact with decreased downstream plate interference. In this vertical separation distance range, a gap flow between the plate and the cylinder plays a determining role on the formation length and St number of vortices for small horizontal spacing values.     

Passive Control of the Vortex Wake Past a Flat Plate at Incidence

A passive control, based on wall suction acting at the leading edge, is proposed to stabilize the vortex shedding from a flat plate at incidence. The correct suction amount is determined by a potential flow model where the large-scale vortical structures formed near the plate edges are represented by point vortices of variable intensity, and the wall suction by an adequately placed sink. We concentrate on the case of a plate that is broadside to the flow and show that the stabilization of the vortex wake can be obtained by simple passive backside suction. In such a case geometric shaping and passive suction have similar effects on the vortex Hamiltonian. The model predictions compare well with the results obtained by blob-vortex simulations, thus confirming the stabilization of the unsteady wake past the plate. Received 5 April 2002 and accepted 6 August 2002 Published online 3 December 2002 Communicated by M.Y. Hussaini     

An experimental investigation of the interaction of swirl flow with partially premixed disk stabilized propane flames

The present work describes the experimental investigation of reacting wakes established through fuel injection and staged premixing with air in an axisymmetric double cavity arrangement, formed along three concentric disks, and stabilized in the downstream vortex region of the afterbody. The burner assembly is operated with a co-flow of swirling air, aerodynamically introduced upstream of the burner exit plane, to allow for the study of the interaction between the resulting partially premixed recirculating afterbody flames with the surrounding swirl. At low swirl the primary afterbody disk stabilizes the partially premixed annular jet in the downstream reacting wake formation region. As swirl increases, a system of two successive vortices emerges along the axis of the developing wake; the primary afterbody vortex is cooperating with an adjacent, swirl induced, central recirculation zone and this combination further promotes turbulent mixing in the hot wake.Complementary measurements of the counterpart isothermal turbulent velocity fields provided important information on the near wake aerodynamics under the interaction of the variable swirl and the double cavity produced annular jet stabilized by the afterbody. Under reacting conditions, measurements of turbulent velocities, temperatures and statistics together with an evaluation of the exhaust emissions were performed using LDV, thin digitally-compensated thermocouples and gas analyzers. A selected number of lean and ultra-lean flames were investigated by regulating the injected fuel and the air supply ratio, while the influence of the variation of the imposed swirl on wake development, flame characteristics and emission performance was documented for constant fuel injections. The differences and similarities between the present partially premixed stabilizer and other types of axisymmetric configurations are also highlighted and discussed.     

Coherent Structures Formation During Wake-Boundary Layer Interaction on a LP Turbine Blade

Particle Image Velocimetry (PIV) measurements have been analyzed in order to characterize the dynamics of coherent structures (eddies and streaks) within the suction side boundary layer of a low pressure turbine cascade perturbed by impinging wakes. To this end, the instantaneous flow fields at low Reynolds number and elevated free-stream turbulence intensity level (simulating the real condition of the blade row within the engine) were investigated in two orthogonal planes (a blade-to-blade and a wall-parallel plane). Proper Orthogonal Decomposition (POD) has been employed to filter the instantaneous flow maps allowing a better visualization of the structures involved in the transition process of the boundary layer. For the unsteady case properly selected POD modes have been also used to sort the instantaneous PIV images in the wake passage period. This procedure allows computing phase-averaged data and visualizing structures size and intensity in the different parts of the boundary layer during the different wake passage phases. The contributions to the whole shear stress due to the largest spanwise oriented scales at the leading and trailing boundaries of the wake-jet structures and those associated with streaky structures observed in the bulk of the wake are discussed. Instantaneous images in the wall-parallel plane are filtered with POD and they allow us to further highlight the occurrence of low and high speed traveling streaks (Klebanoff mode). The periodic advection along the suction side of the high turbulent content regions carried by the wakes anticipates both formation and sinuous instability of the streaks inside the boundary layer as compared with the steady case. The dynamics driving the breakdown of the streaks and the consequent formation of nuclei with high wall-normal vorticity have been found to be almost the same in the steady and the unsteady cases. Auto-correlation of the instantaneous images are also presented in order to highlight analogies and differences in the size and spacing of streaks in the two cases. These results are also compared with the available literature concerning simplified geometries (i.e flat plate) operating under steady inflow.     

Effect of vortex shedding in unsteady aerodynamic forces for a low Reynolds number stationary wing at low angle of attack

This study elucidates the relation between wake vortex shedding and aerodynamic force fluctuations for a low Reynolds number wing from time resolved particle image velocimetry (TR-PIV) experimental measurements. The results reveal a periodic lift and drag variation within the shedding cycle and resolve the frequencies of those fluctuations from a proper orthogonal decomposition (POD) and power spectral density (PSD) analysis. To show the effect of vortex shedding on the body force fluctuations, the evolution of instantaneous aerodynamic forces is compared to the pressure field of the fluid flow and to the vortical structures in the wake of the airfoil. A six step model describing the vortex-force relation is proposed. It shows that changes in lift such as maximum lift and minimum lift are associated with the detachment of a vortex. It also shows that the minimum or local minimum drag value is obtained at the onset formation of a vortex on the airfoil wake. Similarly, the maximum or local maximum drag is obtained at the onset formation of the saddle on the airfoil wake. The model further explains the asymmetry observed in the unsteady drag force evolution. The model can be used to optimize flow control and fluid-structure interaction applications.     

Numerical simulation of the turbulent wake behind a normal flat plate

The three-dimensional wake flow behind a flat plate placed normal to the free stream has been investigated by means of direct numerical simulations. The Reynolds number Re based on the homogeneous inflow velocity and the uniform width d of the plate was 750. Coherent vortices were alternately shed from the sides of the plate with a frequency corresponding to a Strouhal number 0.168. The wake was distinctly turbulent downstream of the plate whereas the mean recirculation bubble extended 1.96d downstream. A steady 2D mean flow and the accompanying Reynolds stresses were obtained by averaging in time and along the span of the plate. These Reynolds-averaged statistics exhibited the same qualitative features as corresponding data from cylinder wakes.     

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.     

带有柔性薄板三维方柱流固耦合的数值模拟研究

采用双向流固耦合方法,对带有柔性薄板三维方柱的流场变化特性进行了研究。通过对比单方柱,分析了带有柔性薄板三维方柱阻力系数、升力系数以及斯特劳哈尔数的变化规律。研究表明,在方柱尾流区域附加一柔性薄板可以使其阻力系数降低34.6%,同时其变化幅值大大减小;其升力系数的均方根减小84.8%,流场脉动大幅度减小;斯特劳哈尔数降低79.5%。研究结果表明,在三维方柱后设置柔性薄板可有效抑制涡脱落,从而改善三维方柱的尾流特性。     

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.     

Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations

Symmetric perturbations imposed on cylinder wakes may result in a modification of the vortex shedding mode from its natural antisymmetric, or alternating, to a symmetric one where twin vortices are simultaneously shed from both sides of the cylinder. In this paper, the symmetric mode in the wake of a circular cylinder is induced by periodic perturbations imposed on the in-flow velocity. The wake field is examined by PIV and LDV for Reynolds numbers about 1200 and for a range of perturbation frequencies between three and four times the natural shedding frequency of the unperturbed wake. In this range, a strong competition between symmetric and antisymmetric vortex shedding occurs for the perturbation amplitudes employed. The results show that symmetric formation of twin vortices occurs close to the cylinder synchronized with the oscillatory component of the flow. The symmetric mode rapidly breaks down and gives rise to an antisymmetric arrangement of vortex structures further downstream. The downstream wake may or may not be phase-locked to the imposed oscillation. The number of cycles for which the symmetric vortices persist in the near wake is a probabilistic function of the perturbation frequency and amplitude. Finally, it is shown that symmetric shedding is associated with positive energy transfer from the fluid to the cylinder due to the fluctuating drag.