Flow-induced vibrations of low aspect ratio rectangular membrane wings

An experimental study of a low aspect ratio rectangular membrane wing in a wind tunnel was conducted for a Reynolds number range of 2.4×10⁴–4.8×10⁴. Time-accurate measurements of membrane deformation were combined with the flow field measurements. Analysis of the fluctuating deformation reveals chordwise and spanwise modes, which are due to the shedding of leading-edge vortices as well as tip vortices. At higher angles of attack, the second mode in the chordwise direction becomes dominant as the vortex shedding takes place. The dominant frequencies of the membrane vibrations are similar to those of two-dimensional membrane airfoils. Measured frequency of vortex shedding from the low aspect ratio rigid wing suggests that membrane vibrations occur at the natural frequencies close to the harmonics of the wake instabilities. Vortex shedding frequency from rigid wings shows remarkably small effect of aspect ratio even when it is as low as unity.     

Scaling of flow separation on a pitching low aspect ratio plate

We use two different dye injection approaches, in two different water tunnels, to visualize the formation and subsequent evolution of leading-edge vortices and related separated structures, for a pitching low aspect ratio plate. The motion is a smoothed linear pitch ramp from 0° to 40° incidence, brief hold, and return to 0°, executed at reduced pitch rates ranging from 0.1 to 0.35 and about various pivot locations. All cases evince a leading edge vortex with pronounced axial flow, which leads to formation of large-scale, three-dimensional flow structures, culminating in a large vortical structure centered at the wing symmetry plane. Pitch is also compared to plunge, where the plunge-induced angle of attack is taken as the geometric pitch incidence angle, ignoring pitch-rate effects. At successively increasing values of convective time C/U, the three-dimensional patterns of the flow structure are remarkably similar for the pitching and plunging motions. The similarity of these patterns persists, though they are shifted in time, for variation of either the location of the pitching axis or the dimensionless pitch rate.     

Low Reynolds number aerodynamics of free-to-roll low aspect ratio wings

The aerodynamics of thin, flat-plate wings of various planforms (rectangular, elliptical and Zimmerman) have been studied in free-to-roll experiments in a wind tunnel. Non-zero trim angles at low angles of attack, self-induced roll oscillations with increasing angle of attack and even autorotation in some cases were observed. The rectangular wings with round leading-edge had non-zero trim angles at low incidences due to the asymmetric development of the three-dimensional separation bubble at these low Reynolds numbers. With increasing angle of attack, the bubble increases in length and once reattachment is lost, large amplitude roll oscillations develop. The Strouhal number of the roll oscillations is of the order of 10⁻², which is in the same range as those expected for small aircraft experiencing atmospheric gusts. Velocity measurements revealed that variations in the strength of the vortices drove the rolling motion. At the mean roll angle, because of the time lag in the strength of the vortices, an asymmetric flow is generated, which results in a net rolling moment in the direction of the rolling motion.     

Experimental study of vortex flow about low aspect ratio wings and circular cones at M = 2

Characteristic of the flow about wings of low aspect ratio with subsonic leading edges and bodies of revolution at angles of attack is the formation of spiral vortices as a result of rolling-up of the transverse flow, which separates near the wing leading edge and on the lateral generator of the body. The vortices, concentrated in a pair of free vortex cores, interact with the boundary layer, causing a complex flow pattern on the surface of the model in question.There are several methods which make it possible to study the flow about the model. Pickups may be used to measure the pressure field or the velocity field near the model. This technique has found wide application and was used for studying the flow pattern about wings and bodies of revolution at both subsonic and supersonic speeds (see, for example, [1–4]). However, this method is very tedious and, in addition, the probes always introduce disturbances into the flow, particularly for supersonic speeds.A visual picture of the vortex flow may be obtained in a towing basin by adding to the water metal powder in the suspended state, or by introducing filaments of colored liquid [1, 5].The vapor screen [6] and smoke [3] methods are also used for flow visualization.The boundary layer flow on the model may be studied with the aid of oil or evaporting coatings. These methods have been used in [1, 7] to study flow about wings and in [8] to study flow about circular cones.According to the studies presented in [9] of an electric discharge with the application of high voltage to electrodes located in an air stream, a stable glow occurs as a result of the prebreakdown discharge.The properties of the prebreakdown discharge have been used by the authors of the present paper to study visually the vortex flows (high voltage electric discharge method). This technique was used to obtain the trajectories of the vortex trails for low aspect ratio wings and circular cones mounted at various angles of attack in a stream with Mach number M=2 and Reynolds number R=0.9·10⁶.In conclusion the author wishes to thank B. V. Kalachev, R. V. Bertyn, and E. D. Korolev for assistance in carrying out the experiments.     

Asymptotic theory of laminar flow separation at a corner

The development of the reverse flow structure in the neighborhood of a corner in a viscous incompressible laminar flow at high Reynolds numbers is investigated numerically. It is found that as the angle of inclination increases the internal structure of the reverse flow zone becomes more complex as a result of secondary separation. The effect of the curvature of the surface is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 180–182, January–February, 1991.     

Asymptotic theory of turbulent separation

The flow of an incompressible fluid in the viscous wall sublayer of a turbulent boundary layer in the neighborhood of a point of separation is considered. On the basis of an asymptotic analysis of the Reynolds equations and without the use of any hypotheses about their closure it is shown that at large Reynolds numbers the velocity profile satisfies the well-known “half-power law,” and as a result of a large self-induced pressure gradient separation is preceded by the appearance of reverse flows in a thin viscous sublayer.     

Asymptotic theory of nonstationary separation

Nonstationary separation of a laminar boundary layer in a incompressible fluid is studied on the basis of asymptotic analysis of the Navier-Stokes equations at large Reynolds numbers. The case when the point of separation moves upstream is considered. It is shown that under certain restrictions on the acceleration with which the motion of the point of separation occurs the local solution depends on the time as on a parameter. As in the stationary case, the separation occurs spontaneously under the influence of the large local pressure gradient. An important difference is however that the mechanism of nonstationary separation is inviscid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 21–32, November–December, 1979.I thank A. I. Ruban for great interest and assistance in the work, and also O. S. Ryzhov for a number of helpful comments.     

Asymptotic theory of separation flows

A review is given of the results of theoretical investigations of the separation of laminar and turbulent boundary layers in an incompressible fluid obtained on the basis of matched asymptotic expansions valid at large Reynolds numbers (Re). The global picture of the separation flow behind a body of finite size as Re is investigated.Paper presented at Fifth All-Union Symposium on Theoretical and Applied Mechanics, Alma-Ata, 1981.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 20–30, March–April, 1982.     

On vortex shedding from low aspect ratio dual step cylinders

A dual-step cylinder is comprised of two cylinders of different diameters. A large diameter cylinder (D) with low aspect ratio (L/D) is attached to the mid-span of a small diameter cylinder (d). The present study investigates the effect of Reynolds number (Re_D) and L/D on dual step cylinder wake development for D/d=2, 0.2≤L/D≤3, and two Reynolds numbers, Re_D=1050 and 2100. Experiments have been performed in a water flume facility utilizing flow visualization, Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV). The results show that vortex shedding occurs from both the large and small diameter cylinders for 1≤L/D≤3 at Re_D=2100 and 2≤L/D≤3 at Re_D=1050. At these conditions, large cylinder vortices predominantly form vortex loops in the wake and small cylinder vortices form half-loop vortex connections. At lower aspect ratios, vortex shedding from the large cylinder ceases, with the dominant frequency in the large cylinder wake attributed to the passage of vortex filaments connecting small cylinder vortices. At these lower aspect ratios, the presence of the large cylinder induces periodic vortex dislocations. Increasing L/D increases the frequency of occurrence of vortex dislocations and decreases the dominant frequency in the large cylinder wake. The identified changes in wake topology are related to substantial variations in the location of boundary layer separation on the large cylinder, and, consequently, changes in the size of the vortex formation region. The results also show that the Reynolds number has a substantial effect on wake vortex shedding frequency, which is more profound than that expected for a uniform cylinder.     

Finite-span rotating wings: three-dimensional vortex formation and variations with aspect ratio

We investigate experimentally the effect of aspect ratio ( ) on the time-varying, three-dimensional flow structure of flat-plate wings rotating from rest at 45° angle of attack. Plates of = 2 and 4 are tested in a 50 % by mass glycerin–water mixture, with a total rotation of ? = 120° and a matched tip Reynolds number of 5,000. The time-varying, three-component volumetric velocity field is reconstructed using phase-locked, phase-averaged stereoscopic digital particle image velocimetry in multiple, closely-spaced chordwise planes. The vortex structure is analyzed using the $\mathcal{Q}$ -criterion, helicity density, and spanwise quantities. For both s, the flow initially consists of a connected and coherent leading-edge vortex (LEV), tip vortex (TV), and trailing-edge vortex (TEV) loop; the LEV increases in size with span and tilts aft. Smaller, discrete vortices are present in the separated shear layers at the trailing and tip edges, which wrap around the primary TEV and TV. After about ? = 20°, the outboard-span LEV lifts off the plate and becomes arch-like. A second, smaller LEV and the formation of corner vortex structures follow. For = 4, the outboard LEV moves farther aft, multiple LEVs form ahead of it, and after about ? = 50° a breakdown of the lifted-off LEV and the TV occurs. However, for = 2, the outboard LEV lift-off is not progressive, and the overall LEV-TV flow remains more coherent and closer to the plate, with evidence of breakdown late in the motion. Inboard of about 50 % span, the = 4 LEV is stable for the motion duration. Up to approximately 60 % span, the = 2 LEV is distinct from the TV and is similarly stable. The = 2 LEV exhibits substantially higher spanwise vorticity and velocity. The latter possesses a “four-lobed” distribution at the periphery of the LEV core having adjacent positive (outboard) and negative (inboard) components, corresponding to a helical streamline structure. Both s show substantial root-to-tip velocity aft of the stable LEV, which drives outboard spanwise vorticity flux; flux toward the root is also present in the front portion of the LEV. For = 2, there is a strong flux of spanwise vorticity from the outboard LEV to the tip, which may mitigate LEV lift-off and is not found for = 4. The TV circulation for each is similar in magnitude and growth when plotted versus the chord lengths travelled by the tip, prior to breakdown. Streamwise vorticity due to the TV induces high spanwise velocity, and for = 2, the tilted LEV creates further streamwise vorticity which corresponds well to spanwise-elongated regions of spanwise velocity. For = 2, the TV influences a relatively greater portion of the span and is more coherent at later times, which coupled with the tilted LEV strongly contributes to the higher overall spanwise velocity and vorticity flux.     

On the theory of a wing with small aspect ratio in a hypersonic flow

A study is made of flow over three-dimensional wings of small aspect ratio with shape close to that of a flat delta-shaped wing. The obtained results make it possible to estimate the influence of the plan shape of the leading edge and the curvature of the wing on the pattern of the flow over its windward surface and on the corresponding gas-dynamic functions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 112–117, July–August, 1980.     

Bluff body wakes with free, fixed, and discontinuous separation at low Reynolds numbers and low aspect ratio

Some comparative experimental results are presented of bluff body wakes with free, fixed, and discontinuous separation. The particular examples considered are a circular cylinder, a plain blunt trailing edge aerofoil and a segemented blunt trailing edge aerofoil. The evolution of the near wake and vortex shedding modes are compared and discussed.     

Method of calculating subsonic gas flow with separation past wings

The steady nonlinear problem of subsonic compressible gas flow past a wing of arbitrary shape in plan is considered. A numerical method was devized for solving the problem; this is a further development of the method of discrete vortices. The surface of the body and the vortex wake behind it are simulated by systems of discrete vortex sections, but, in contrast to the case of an incompressible medium, it is necessary in this case for the sources to be distributed outside the wing. The circulations of the attached vortices, the strengths of the sources, and the shape of the wake are determined by iterations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 140–147, July–August, 1984.     

Numerical modeling of supersonic flow over wings with varying aspect ratio on a broad range of angles of attack using the law of plane sections

A method and a program based on it for solving the problem of flow in the neighborhood of bodies of different shapes introduced into a high-supersonic stream at arbitrary angles of attack are proposed. The equations of the law of plane sections are integrated by Godunov's method. It is shown that the region of applicability of Sychev's theory is much broader than indicated in [1].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 113–120, March–April, 1992.     

Effects of aspect ratio on unsteady solutions through curved duct flow

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.     

Effects of aspect ratio and orientation on the wake characteristics of low Reynolds number flow over a triangular prism

The wake characteristics of unconfined flows over triangular prisms of different aspect ratios have been numerically analysed in the present work. For this purpose, a fixed Cartesian-grid based numerical technique that involves the porous medium approach to mimic the effect of solid blockage has been utilised. Correspondingly, laminar flow simulations ranging from the sub-critical regime (before the onset of vortex shedding) to the super-critical regime have been considered here within the limits of two-dimensionality. In the sub-critical regime, correlations relating the wake bubble length with Reynolds number (Re) have been proposed for various aspect ratios. Also, the effects of aspect ratio and Reynolds Number on the drag force coefficient (C_D) have been characterised for two different geometrical orientations of the prism (base or apex facing the flow). Subsequently, the critical Reynolds number at the onset of vortex shedding has been predicted for each of the aspect ratio considered, by an extrapolation procedure. The unsteady flow characteristics of the super-critical regime are finally highlighted for different aspect ratios and triangular orientations considered in the study.