Spanwise Modes Research Articles

Experimental investigation of flow past a rotationally oscillating tapered cylinder

The transition of flow from laminar to turbulent has been a topic of considerable interest for fluid dynamicists. Evolution of spanwise three-dimensionalities in the wake of an elongated bluff body occurs before the wake becomes turbulent. Several engineering structures such as industrial chimneys, marine risers, and off-shore structures have tapered geometry. In this study, we show the three-dimensional (spanwise) modes in the wake of a rotationally oscillating tapered cylinder.

Spatio-temporal dynamics of a two-layer pressure-driven flow subjected to a wall-normal temperature gradient

The present study investigates the linear spatio-temporal and weakly nonlinear stability of a pressure-driven two-layer channel flow subjected to a wall-normal temperature gradient commonly encountered in industrial applications. The liquid–liquid interface tension is assumed to be a linearly decreasing function of temperature. The study employs both numerical (pseudo-spectral method) and long-wave approaches. The general linear stability analysis (GLSA) predicts shear-flow and thermocapillary modes that arise due to the imposed pressure and temperature gradients, respectively. The previous stability analyses of the same problem predicted a negligible effect of the pressure-driven flow on the linear stability of the system. However, the GLSA reveals stabilising and destabilising effects of the pressure-driven flow depending on the viscosity ratio ( $\mu _r$ ), thermal conductivity ratio ( $\kappa _r$ ), interface position ( $H$ ) and the sign of the imposed temperature gradient ( $\beta _1$ ). The analysis predicts a range of $H$ for given $\mu _r$ and $\kappa _r$ , which can not be stabilised by the thermocapillarity. The numerically predicted long-wave instability is then captured using the long-wave asymptotic approach. The arguments based on the physical mechanism further successfully explain the role of $\mu _r$ , $\kappa _r$ , $H$ , the sign of $\beta _1$ and the interaction between the velocity and temperature perturbations in stabilising/destabilising the flow. The spatio-temporal analysis reveals the dominance of the spanwise mode in causing the absolutely unstable flow. The weakly nonlinear analysis reveals a subcritical pitchfork bifurcation without shear flow. However, with the shear flow, the streamwise mode undergoes a supercritical Hopf bifurcation.

Effect of yaw angle on vibration mode transition and wake structure of a near-wall flexible cylinder

The multi-mode transition and vortex structures in the vortex-induced vibration (VIV) of a near-wall flexible cylinder under different yaw angles are investigated through three-dimensional direct numerical simulation. Yaw angles α = 0°–60°, gap ratio G/D = 0.8, and Re = 500 are adopted. With the increase in α, the dominated vibration mode decreases from the 6th to 1st mode in the in-line (IL) direction and the 3rd to 2nd mode in the cross-flow (CF) direction. For the IL vibration, no mode transition occurs at α = 0°, whereas frequently mode transition is observed at α > 0°, due to the intermittent participation and spanwise competition of different modes, thus showing an intensified traveling-wave characteristic. For the CF vibration, mode transition is not excited at any α case even with spanwise mode competitions, due to the significant weight of the dominated mode, thus showing a strong standing-wave characteristic. The asymmetrical distributions of vibration displacements and force coefficients are established because of irregular energy transfer along the span. The spanwise vortex tubes at α = 0°–30° are separated into several cells associated with the dominated vibration mode, showing a locally parallel vortex shedding. However, positively yawed and negatively yawed vortex shedding are observed at α = 45° and 60°, respectively. The vortex strengths vary along the cylinder, where large-scale and small-scale vortices are observed at the CF anti-node and node planes, respectively. The independence principle is only valid at α < 15° for predicting the multi-mode vibrations and hydrodynamics, significantly reduced from that of α < 45° in the wall-free case or the mono-mode VIV case.

Effect of Yaw Angle on Flutter of Rectangular Plates at Low Supersonic Speeds

The stability of the infinite series of thin elastic rectangular plates simply supported along all edges and exposed to a supersonic flow is investigated. The nonzero flow yaw angle with supersonic leading edge is considered. To derive expression for the unsteady aerodynamic pressure distribution over the oscillating plate, potential flow theory was used, and an integrodifferential eigenvalue problem for finding complex eigenvalues was obtained. Flutter boundaries for the first and second modes are computed. Changing of the single-mode and coupled-mode flutter boundaries with the change of the yaw angle was shown. While they are smooth at zero angle, the boundaries become irregular, and additional isolated regions of stability and instability appear when increasing the yaw angle. This irregularity occurs due to the interaction of multiple spanwise modes, which takes place at nonzero yaw angle due to their aerodynamic coupling.

Aeroelastic mode decomposition framework and mode selection mechanism in fluid–membrane interaction

In this study, we present a global Fourier mode decomposition framework for unsteady fluid–structure interaction. We apply the framework to isolate and extract the aeroelastic modes arising from a coupled three-dimensional fluid–membrane system. We investigate the frequency synchronization between the vortex shedding and the structural vibration via mode decomposition analysis. We explore the role of flexibility in the aeroelastic mode selection and perform a systematic comparison of flow features among a rigid flat wing, a rigid cambered wing and a flexible membrane. The camber effect can enlarge the pressure suction area on the membrane surface and suppress the turbulent intensity, compared to the rigid flat wing counterpart. With the aid of our mode decomposition technique, we find that the dominant structural mode exhibits a chordwise second and spanwise first mode at different angles of attack. The structural natural frequency corresponding to this mode is estimated using an approximate analytical formula. By examining the dominant frequency of the coupled system, we show that the dominant membrane vibration mode is selected via the frequency lock-in between the dominant vortex shedding frequency and the structural natural frequency. From the fluid modes and the mode energy spectra at α=20∘ and 25°, the aeroelastic modes corresponding to the non-integer frequency components lower than the dominant frequency are observed, which are associated with the bluff body vortex shedding instability. The non-periodic aeroelastic behaviors observed at higher angles of attack are related to the interaction between aeroelastic modes caused by the frequency lock-in and the bluff-body-like vortex shedding. Using the mode decomposition analysis, we suggest a feedback cycle for flexible membrane wings undergoing synchronized self-sustained vibration. This feedback cycle reveals that the dominant aeroelastic modes are selected through the mode and frequency synchronization during fluid–membrane interaction to exhibit similar modal shapes in the membrane vibration and the pressure pulsation.

Relevance of two- and three-dimensional disturbance field explained with linear stability analysis of Orr-Sommerfeld equation by compound matrix method

Three-dimensional Orr-Sommerfeld equation is analyzed by compound-matrix method to explain the relevance of two- and three-dimensional wall excitations with respect to three-dimensional direct simulation results presented in Sharma and Sengupta, Effect of frequency and wavenumber on the three-dimensional routes of transition by wall excitation, Phys. Fluids, 31 (6), 064107 (2019). Physical variables are considered in a finite spanwise domain which allows us to consider spanwise wavenumber β as the higher harmonics of fundamental spanwise mode β0 defined by the spanwise domain. Linear stability analysis is performed for various cases with different spanwise wavenumber and neutral curves are generated in both spatial and temporal frameworks. Even though the neutral curves appear different, the critical Reynolds number remains same for all spanwise excitation wavenumbers. The significance of neutral curve in either spatial, or temporal or spatio-temporal frameworks is explained for both modal and non-modal component of the response field. It is shown that as spanwise wavenumber of input excitation increases, the critical Reynolds number increases, while the spatial amplification rate αi decreases. Thus, this establishes that increasing three-dimensionality of input excitation will shown enhanced stability of the flow, and helps one to understand the three-dimensional direct simulation of receptivity analysis for wall excitation reported very recently.

Modeling and dynamic study of rotating blades with adjustable stagger angle

A blade with an adjustable stagger angle is a type of blade that is able to partially rotate around its long axis. In fact, while a hub rotates, simultaneously the angle of the blade root section can change. The objective of this research is to develop and analyze a model of rotating cantilever orthotropic blade with adjustable stagger angle. Using Hamilton's principle, the governing partial differential equations are derived. In this formulation, both the Coriolis effects and centrifugal inertia forces are accounted for. First, the extended Galerkin method is utilized to discretize the equations of motion. Then, the multiple scales method is used to investigate the dynamic stability of the rotating blades analytically. Consequently, the possibility of internal resonances between different modes is studied and recognized. Moreover, the influence of various parameters on the instability regions is evaluated in detail, and the results are discussed. For validating the results, the modal characteristics of the system obtained by two methods of extended Galerkin and extended Kantorovich are compared with each other. Additionally, the fourth-order Runge–Kutta algorithm is employed to more deeply understand the dynamic behaviors of the system in the cases of constant and variable stagger angles and the differences between them as well as to prove the validity of the results of multiple scales method. The time histories, phase space diagrams and frequency spectrums are provided. Furthermore, a detailed investigation is carried out to determine the properties of the response under different conditions of the amplitude of the variable angle. As far as we know, the present study is the first attempt to demonstrate the effects of time-varying stagger angle for this class of problems in the literature. A stable motion in the adjustable stagger angle configuration gives a more complicated response. It can be observed that in this dynamic situation, the results are affected by Coriolis, both in quality and quantity. The findings indicate that with a change in the speed, there is a possibility of switching instability zones relative to each other. It is also found that the maximum width of the instability regions among the combination resonances is related to the second spanwise and first chordwise bending modes. The type of instability qualitatively depends on the amplitude of angle.

Wake events during early three-dimensional transition of a circular cylinder placed in shear flow

Three-dimensional (3D) direct numerical simulations are carried out for shear flows past a circular cylinder in the early 2D (two-dimensional)–3D transition regime. The effect of incoming shear is buried in a source term employing a velocity transformation. Wake transition events are inspected for both planar and span-wise shear flows. Parallel, time-mean-symmetric shedding for planar shear and oblique vortex shedding for span-wise shear are observed with a near wake roll-up vortical structure. Vortex splits and dislocations are found without any order in time for moderate shear, while they give way to visibly higher levels of instabilities at higher shear rates. Mode “B” instabilities are noted for planar shear, while opposite streamwise vortices align in parallel horizontal layers for span-wise shear. Local Strouhal frequency (Stz) drops inside a span-wise cell for span-wise shear with finite jumps across cell boundaries. Wavelet multiresolution analysis indicates a strong flushing effect, triggered by vortex dislocations, which gives rise to a new frequency event. The dominant span-wise mode indicates periodic forcing of mode “A” instabilities at a rate close to the inverse of local Strouhal number. In contrast, the streamwise velocity modes result in a global span-wise similarity. Intrinsic secondary instabilities play a vital role in span-wise shear cases. The addition of planar shear makes the downstream defect layer nearly span-wise-invariant. However, the velocity defect is entirely controlled by the span-wise shear. The momentum thickness exhibits streamwise growth, similar to the Blasius profile. The shape factor of such profiles indicates a delay in laminar–turbulent transition for span-wise shear.

Interactions between a shock and turbulent features in a Mach 2 compressible boundary layer

Large field-of-view (FOV) particle image velocimetry experiments are conducted in the vicinity of a shock wave boundary layer interaction (SWBLI) at Mach 2. The current FOV covers up to 30 boundary layer thicknesses ( ), comprising of upstream and downstream regions relative to the SWBLI, thereby allowing the turbulent boundary layer and shock to be simultaneously captured. The relationship between the boundary layer features and the instantaneous shock location is directly quantified, with the aim of better understanding the mechanisms responsible for oscillation of the reflected shock. The results show that the reflected shock location is clearly influenced by the instantaneous state of the incoming boundary layer. It is found that passage of low-/high-momentum very-large-scale turbulent features through the SWBLI region causes the reflected shock to move upstream/downstream of the mean location. Moreover, interaction with the shock is found to introduce additional velocity fluctuations across a range of spanwise length scales within the boundary layer. The spanwise scales smaller than one recover within one downstream of the SWBLI region. However, at larger spanwise wavelengths, two persistent modes at approximately one and six are observed, where they remain correlated for a longer streamwise extent ( ) than the other spanwise modes. The wall pressure measurements indicate that the low-frequency fluctuations arising from the oscillating shock foot are due to dampening of high-frequency contents beyond the critical frequency associated with the unstable global mode. Thus, the results suggest that low-frequency pressure oscillations are not necessarily an independent phenomenon from the turbulent features entering the SWBLI region and interacting with the shock. Instead, a large scale separation between their dominant time scales is due to the critical frequency of the unstable global mode occurring at frequencies that are orders of magnitudes slower than the dominant frequency of the very-large-scale features.

Flutter and gust response analysis of a wing model including geometric nonlinearities based on a modified structural ROM

In this paper, a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model (ROM). The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities. A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation. Two orthogonal spanwise modes describe the foreshortening effects of the wing. Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis, and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method (UVLM) is applied to gust response analysis. Furthermore, extended Precise Integration Method (PIM) ensures accuracy of the dynamic equation solutions. To demonstrate applicability and accuracy of the method presented, a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached. The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain. Meanwhile, the results derived highlight the effects of geometric nonlinearities obviously.

PIV measurements of the K-type transition in natural convection boundary layers

The K-type transition of a natural convection boundary layer of Ra = 9.8 × 109 is studied by PIV (Particle Image Velocimetry) measurements. To excite the transition, Tollmien-Schlitchting (TS) and oblique waves of the same frequency are introduced into the upstream boundary layer in the form of velocity perturbations. It is found that resonant interactions between the characteristic frequency of the natural convection boundary layer and the superimposed TS and oblique waves are present, which trigger the K-type transition of the boundary layer. The typical aligned Λ-shaped flow structures characterising the K-type transition present in the transition of Blasius boundary layers are also observed in the present natural convection boundary layers. They occur when the primary instability grows to a certain extent. The appearance of the spanwise mode characterised by the aligned Λ-shaped flow structures is found to be an ‘abrupt’ process, although the development of the three-dimensionality in the natural convection boundary layer is found to be a ‘gradual’ process. A peak in the typical profile of the Root-Mean-Square (RMS) of the amplitude of streamwise velocity is also noted around the transition point, beyond which distinct three-dimensional Λ-shaped flow structures are observed. The transition point has been determined consistently using different approaches. A Bicoherence analysis suggests that the interaction between the external excitation frequency and the characteristic frequency of the boundary layer is responsible for the production of new harmonic frequencies and resonance groups. The PIV measurements have been extended to a range of perturbation frequencies for the boundary layer, and the dependence of the K-type transition on the perturbation frequency is discussed.

The control of aerodynamic sound due to boundary layer pressure gust scattering by trailing edge serrations

A theoretical model is proposed in the current work to shed light on the noise-reduction mechanisms of trailing-edge serrations, which have been shown to suppress noise generated at the trailing edge due to the scattering of boundary layer pressure fluctuations. The current analytical model, which is developed by incorporating Fourier series expansions and the Wiener-Hopf method, can quickly predict noise reductions due to various types of trailing-edge serrations at low Mach numbers. The present model is validated by comparing its predictions with relevant published theoretical and experimental results. Moreover, from the Winer-Hopf analysis, an effective method based on Fourier series expansion is proposed to approximately evaluate the noise-reduction performance of different serrated geometries under various working conditions. The current work shows that trailing-edge serrations reduce noise by producing scattered waves with spanwise modes which could be evanescent, and explains why some serrated geometries are more effective than others in suppressing noise. The efficient noise prediction capability of the proposed model makes it very suitable to be used in the trailing-edge designs and evaluations of low-noise aircraft components such as wings and aero-engine fan, compressor and turbine cascades.

Linear stability of confined flow around a 180-degree sharp bend

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Numerical analysis on initial development of longitudinal vortices over a heated horizontal plate in uniform downward flow

Fluid flow and heat transfer from an upward-facing horizontal two-dimensional heated plate in uniform downward forced flow are analyzed by means of numerical simulation. We focus our attention to a case where the plate is heated so strongly that the effect of the buoyancy force is not negligible. The Reynolds number based on the plate length is 200 and 500, and the modified Grashof number ranges from 3×106 up to 1.5×108. Assuming that the working fluid is air at room condition, the Prandtl number is kept at 0.71. Longitudinal vortices, discovered in the recent experimental study, are successfully simulated. Typical structures appear as pairs of counter-rotating vortices in the vicinity of the plate with hot fluid ejection in between. They are elongated over the whole plate and regularly allocated in spanwise direction with almost uniform height. Special attention is focused on initial formation of these structures. At the beginning, germs of the structures appear either at the center or on the edge of the plate one by one until the number of them reaches a certain value. The value is subject to the natural convection instability unless the radius of the relevant vortex becomes significantly smaller than the laminar boundary layer thickness of forced stagnation flow. Streamwise contiguity of the structure is established before the power of the relevant spanwise mode comes to a stage of exponential growth inside the boundary layer.

Lumley decomposition of turbulent boundary layer at high Reynolds numbers

The decomposition proposed by Lumley in 1966 is applied to a high Reynolds number turbulent boundary layer. The experimental database was created by a hot-wire rake of 143 probes in the Laboratoire de Mécanique de Lille wind tunnel. The Reynolds numbers based on momentum thickness (Reθ) are 9800 and 19 100. Three-dimensional decomposition is performed, namely, proper orthogonal decomposition (POD) in the inhomogeneous and bounded wall-normal direction, Fourier decomposition in the homogeneous spanwise direction, and Fourier decomposition in time. The first POD modes in both cases carry nearly 50% of turbulence kinetic energy when the energy is integrated over Fourier dimensions. The eigenspectra always peak near zero frequency and most of the large scale, energy carrying features are found at the low end of the spectra. The spanwise Fourier mode which has the largest amount of energy is the first spanwise mode and its symmetrical pair. Pre-multiplied eigenspectra have only one distinct peak and it matches the secondary peak observed in the log-layer of pre-multiplied velocity spectra. Energy carrying modes obtained from the POD scale with outer scaling parameters. Full or partial reconstruction of turbulent velocity signal based only on energetic modes or non-energetic modes revealed the behaviour of urms in distinct regions across the boundary layer. When urms is based on energetic reconstruction, there exists (a) an exponential decay from near wall to log-layer, (b) a constant layer through the log-layer, and (c) another exponential decay in the outer region. The non-energetic reconstruction reveals that urms has (a) an exponential decay from the near-wall to the end of log-layer and (b) a constant layer in the outer region. Scaling of urms using the outer parameters is best when both energetic and non-energetic profiles are combined.

Three-dimensional rotating Couette flow via the generalised quasilinear approximation

We examine the effectiveness of the generalised quasilinear (GQL) approximation introduced by Marston et al. (Phys. Rev. Lett., vol. 116 (21), 2016, 214501). This approximation splits the variables into large and small scales in directions where there is a translational symmetry and removes nonlinear interactions involving only small scales. We utilise as a paradigm problem three-dimensional, turbulent, rotating Couette flow. We compare the results obtained from direct numerical solution of the equations with those from quasilinear (QL) and GQL calculations. In this three-dimensional setting, there is a choice of cutoff wavenumber for the GQL approximation both in the streamwise and in the spanwise directions. We demonstrate that the GQL approximation significantly improves the accuracy of mean flows, spectra and two-point correlation functions over models that are quasilinear in any of the translationally invariant directions, even if only a few streamwise and spanwise modes are included. We argue that this provides significant support for a programme of direct statistical simulation utilising the GQL approximation.

Turbulent boundary layer over 2D and 3D large-scale wavy walls

An experimental investigation of the flow over two- and three-dimensional large-scale wavy walls was performed using high-resolution planar particle image velocimetry in a refractive-index-matching (RIM) channel. The 2D wall is described by a sinusoidal wave in the streamwise direction with amplitude to wavelength ratio a/λx = 0.05. The 3D wall is defined with an additional wave superimposed on the 2D wall in the spanwise direction with a/λy = 0.1. The flow over these walls was characterized at Reynolds numbers of 4000 and 40 000, based on the bulk velocity and the channel half height. Flow measurements were performed in a wall-normal plane for the two cases and in wall-parallel planes at three heights for the 3D wavy wall. Instantaneous velocity fields and time-averaged turbulence quantities reveal strong coupling between large-scale topography and the turbulence dynamics near the wall. Turbulence statistics show the presence of a well-structured shear layer that enhances the turbulence for the 2D wavy wall, whereas the 3D wall exhibits different flow dynamics and significantly lower turbulence levels. It is shown that the 3D surface limits the dynamics of the spanwise turbulent vortical structures, leading to reduced turbulence production and turbulent stresses and, consequently, lower average drag (wall shear stress). The likelihood of recirculation bubbles, levels and spatial distribution of turbulence, and rate of the turbulent kinetic energy production are shown to be severely affected when a single spanwise mode is superimposed on the 2D sinusoidal wall. Differences of one and two order of magnitudes are found in the turbulence levels and Reynolds shear stress at the low Reynolds number for the 2D and 3D cases. These results highlight the sensitivity of the flow to large-scale topographic modulations; in particular the levels and production of turbulent kinetic energy as well as the wall shear stress.

Experimental investigation on the steady and unsteady disturbances in a flat plate boundary layer

Recent experiments have shown that miniature vortex generators (MVGs) are coveted devices to stabilize unsteady disturbances in flat plate boundary layers and to delay the onset of turbulence by modulating the base flow in the spanwise direction. The spanwise modulation is a result from the non-modal transient growth of steady and spanwise periodic streamwise vortices being generated by the MVGs. The present experimental investigation aims at studying the transient growth of non-modal disturbances induced by a spanwise periodic array of MVGs and its stabilizing effect on non-linear unsteady disturbances in the boundary layer originating from planar Tollmien-Schlichting (TS) waves. Measurements consist of cross-stream planes at different downstream locations in the boundary layer and a spatio-temporal analysis of different modes of the disturbances is carried out. In the streaky boundary layer generated by the MVGs the fundamental spanwise mode, with the same wavelength as the MVG pairs in the array, and its first harmonic, both undergo transient growth whereas the higher harmonics decay immediately downstream of the array. In the unstable region formed in the wake of the MVG blades, i.e., just downstream of the array, a wide range of spanwise modes contributes to an initial growth in the energy of unsteady disturbances. Similar behavior is observed upstream of branch II position of the neutral stability curve where the unsteady disturbances undergo a second energy growth in the unstable region. It is shown that the spatial gradients of the base flow in the wall-normal and spanwise directions are contributing to the amplification and attenuation of the TS wave disturbances, respectively, in the streaky boundary layer.

Unsteady aerodynamics and flow-induced vibrations of a low aspect ratio rectangular membrane wing with excess length

In this study, an experimental investigation of a low aspect ratio rectangular membrane wing with excess length was presented at angles of attack ranging from 0° to 25° at Reynolds number of 48,700. Time-accurate measurements of membrane deformation using Digital Image Correlation system, and velocity field measurements with Digital Particle Image Velocimetry system were carried out while normal forces of the wing were measured by helping a load-cell system. The experimental results showed that the camber of membrane wing with excess length excited the separated shear layer and this situation increased the lift coefficient relatively more as compared to membrane wings without excess length. At the angles of attack of α=6–10° and α=19–22°, dominant vibrational modes were obtained as a spanwise mode of two, whereas dominant spanwise modes were three at α=11–18° and α=23–25°. Moreover, the membrane wings with excess length exhibited small separated regions since the shear layer was closer to the membrane wing surface although camber of the wing increased. Consequently, it was shown that in membrane wings with low aspect ratio, unsteadiness included tip vortices and vortex shedding, and the combination of tip vortices and vortex shedding caused complex unsteady deformations of these membrane wings.

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 2.4×10 4–4.8×10 4. 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.