Spanwise Motion Research Articles

Boundary-layer transition at high free-stream disturbance levels – beyond Klebanoff modes

We consider a nominally uniform flow over a semi-infinite flat plate and show how a small slowly modulated (predominantly streamwise) disturbance of the upstream flow is amplified by leading-edge bluntness effects and eventually develops into a small-amplitude but nonlinear spanwise motion far downstream from the edge. This motion is then imposed on the viscous boundary layer at the surface of the plate – causing an order-one change in its profile shape, which can reduce the wall shear to zero and thereby causes the boundary layer to separate. The present study is similar to an earlier steady flow analysis, but the unsteady effects now cause the upstream boundary layer to develop inflectional profiles which can support rapidly growing inviscid instabilities that give rise to transition before the separation can occur.

Drag reduction in turbulent channel flow with periodically arrayed heating and cooling strips

A new technique giving significant drag reduction in turbulent shear flows has been proposed by using the buoyancy effect to generate periodic spanwise motion. Such spanwise motion can be obtained by arranging heating and cooling strips periodically aligned in the spanwise direction of a vertical channel, where the streamwise mean flow is perpendicular to the gravity vector. The strip size has been changed in order to obtain the optimum size corresponding to the maximum drag reduction. Series of direct numerical simulation have been performed where the bulk Reynolds number, Rem=Umδ∕ν is fixed at 2270 whereas the Grashof number is changed to between 106 and 107. At the lowest Grashof number, the buoyancy forces are not strong enough to disturb the flow and no apparent variation of drag compared to the plane channel is observed. However, as the Grashof number increases, considerable drag reduction can be obtained. At the highest Grashof number, an optimum strip size of about 250 wall units gives drag reduction of about 35%. The greater the Grashof number, the smaller the strip size which attains the maximum drag reduction. The similarity between the induced lateral motions by the buoyancy forces and those induced by the spanwise wall oscillations is highlighted.

Drag reduction in a turbulent boundary layer on a flexible sheet undergoing a spanwise traveling wave motion

The effect of a spanwise traveling-wave motion on a zero-pressure-gradient turbulent boundary layer over a flexible sheet was investigated at low Reynolds numbers using a single hot-wire anemometer for turbulence statistics and two laser displacement sensors for displacements of the flexible sheet. It was found that the log-law region of the mean velocity on the flexible sheet was slightly narrower compared with a rigid wall. The energy spectra of streamwise velocity fluctuations on the flexible sheet undergoing the spanwise traveling-wave motion were smaller in a region of frequency which corresponded to the bursting frequency in the canonical wall turbulence. This indicates that the bursting event near the flexible sheet was directly affected by the surface wave motion. It was revealed that a drag reduction of up to 7.5% could be obtained by the spanwise traveling-wave motion, estimating the friction coefficients through the growth rate of the momentum thickness.

난류 채널 내 냉·열판 부착에 의한 마찰저항 감소

A new technique giving significant drag reduction in turbulent shear flows has been proposed by using the buoyancy effect to generate periodic spanwise motion. Such spanwise motion can be obtained by arranging heating and cooling strips periodically aligned in the spanwise direction of a vertical channel, where the streamwise mean flow is perpendicular to the gravity vector The strip size has been changed in order to obtain the optimum size corresponding to the maximum drag reduction. The bulk Reynolds number, <TEX>$ Re_{m} = U_{m} \delta / \nu \$</TEX> is fixed at 2270 while Grashof numbers is changed between <TEX>$10^{6}$</TEX> to <TEX>$10^{7}$</TEX>. As Grashof number increases, considerable drag reduction can be obtained, At the highest Grashof number, an optimum strip size of about 250 wail units gives drag reduction of about 35<TEX>$\%$</TEX>. The greater the Grashof number, the smaller the strip size attains the maximum drag reduction.

Dynamic shape control of sub-sections of moderately thick beams

The present paper is concerned with dynamic shape control of Timoshenko beams by self-stress actuation. In many practical applications, it is sufficient to control a sub-section of the beam by self-stress actuation applied only within the sub-section. Given the transient external disturbances, we seek for a self-stress actuation, which results in a span-wise constant motion of the sub-section. We show that we achieve this behavior, if the resultant and the couple of the self-stress actuation correspond to the statically admissible transverse shear force and bending moment. Finally, we discuss the application of discretely acting piezoelectric actuators.

Destruction Process of Near-wall Streamwise Vortices and Low-speed Streaks under Spanwise Wall Motion

Two dimensional Poiseuille turbulent flow is subjected to spanwise motion of the lower wall of a channel flow. Direct Numerical Simulation (DNS) is used to investigate the response of coherent structures which exist in the near-wall region to the wall motion for the initial period (t+δ≤0.5). There is asymmetry in the response of streamwise vortices. Upstream ends of positive vortices leave away from the wall and lose the ability to wind up the spanwise vortex line, while those of negative vortices are bent towards the positive spanwise direction but remain close to the wall. This difference makes the positive vortices decay earlier than the negative vortices. Low-speed streak is torn into pieces at the overlapped region between the positive and the negative vortices. The bottom of the low-speed streak is also pared off due to the strong enstrophy.

Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst

Two time-periodic solutions with genuine three-dimensional structure are numerically discovered for the incompressible Navier–Stokes equation of a constrained plane Couette flow. One solution with strong variation in spatial and temporal structure exhibits a full regeneration cycle, which consists of the formation and breakdown of streamwise vortices and low-velocity streaks; the other one, of gentle variation, represents a spanwise standing-wave motion of low-velocity streaks. These two solutions are unstable and the corresponding periodic orbits in the phase space are connected with each other. A turbulent state wanders around the strong one for most of the time except for occasional escapes from it. As a result, the mean velocity profile and the root-mean-squares of velocity fluctuations of the plane Couette turbulence agree very well with the temporal averages of those of this periodic motion. After an occasional escape from the strong solution, the turbulent state reaches the gentle periodic solution and returns. On the way back, it experiences an overshoot accompanied by strong turbulence activity like an intermittent bursting phenomenon.

Turbulence Modification Due to Wave Action at Low Reynolds Numbers in Horizontal Open-Channel Flow

Wave-turbulence interaction was experimentally investigated in turbulent open-channel flows with a shear-free wavy surface using a photochromic dye activation technique. In the experiments conducted, two-dimensional waves of different amplitudes, wavelengths, and frequencies were superimposed on a liquid surface via a mechanical wave maker. The range of Reynolds numbers varied from 3900 to 5000 based on the hydraulic diameter, with the corresponding aspect ratio of the channel width to liquid depth varying from 7.5 to 5.Within the range of Reynolds numbers investigated, the results showed that the streamwise turbulence intensity increased in the bulk and interfacial regions in comparison to the undisturbed flow.Furthermore, video sequences of the flow visualization experiments clearly revealed that the spanwise motion of the liquid was significantly suppressed; the traces did not immediately deform in the spanwise direction but retained their shape with increasing wave amplitude and frequency as compared to smooth interface flows. This suggests that waves may have suppressed longitudinal vortices generated near the smooth interface. The suppression of the longitudinal vortices in wavy open-channel flows has been proposed as a mechanism responsible for the turbulence energy redistribution, different from that for smooth open-channel flows.

Near-wall turbulence structures in three-dimensional boundary layers

We examine the structure of near-wall turbulence in three-dimensional boundary layers (3DBLs), which we approximate by applying an impulsive spanwise motion to the lower wall of a turbulent channel flow. Direct numerical simulation (DNS) data are analysed using probability density functions (PDFs), conditional-averaged quadrant analysis about Reynolds-stress-producing events, and visualization of vortices with the ?2-criterion. The evidence suggests that mean three-dimensionality breaks up the symmetry and alignment of near-wall structures, disrupting their self-sustaining mechanisms, and thereby causing a reduction in the turbulence kinetic energy (TKE).

Numerical prediction of eddy structure in a shear-driven cavity

We present in this paper a detailed numerical study of the vortical flow structure in a confined lid-driven cavity which is defined by a depth-to-width aspect ratio of 1:1 and a span-to-width aspect ratio of 3:1. In this study we have carefully examined the computed data that the useful to gain an in-depth knowledge of the complex interactions among secondary eddies, primary eddies, and spiraling spanwise motions. Chief of conclusions drawn from this study is to explain how the secondary eddies are intimately coupled with the primary recirculating flow. We also enlighten in this paper why spiraling vortices inside the upstream secondary eddy tend to destabilize the incompressible flow system and aid development of laminar instabilities.

Three-Dimensional Vortex Dynamics in a Shear-Driven Rectangular Cavity

We investigate the vortical flow structure which has evolved in a rectangular cavity defined by a depth-to-width aspect ratio of 1:1 and a span-to-width aspect ratio of 3:1. The vortical system of interest consists of a dominant eddy, secondary motions, and spiraling spanwise motion. The objective of this study was to broaden knowledge of: 1) how the Taylor-Görtler vortices emerge and modify the flow structure; 2) why the left vortex differs from its right counterpart in each unsymmetric pair of TGL vortices. Most importantly, the intent of this study is to discuss the formation of flow instabilities from the energy standpoint.

The interaction between a steady jet flow and a supersonic blade tip

The potentially high level of noise generated by modern counter-rotation propellers has attracted considerable interest and concern, and one of the most potent mechanisms involved is the unsteady interaction between the tip vortex shed from the tips of the forward blade row and the rear row. In this paper a model problem is considered, in which the tip vortex is represented by a jet of constant axial velocity, which is convected at right angles to itself by a uniform supersonic mean flow, and which is cut by a rigid airfoil with its chord aligned along the mean flow direction. Ffowcs Williams &amp; Guo have previously considered this problem for an infinite-span airfoil and a circular jet; in this paper we extend their analysis to include the effects of the presence of the second-row blade tip on the interaction, by considering a semi-infinite-span airfoil. As a first attempt, the case of a highly compact jet, represented by a delta-function upwash on the airfoil, is considered, and both the total lift on the airfoil and the radiation are investigated. The presence of the airfoil corner and side edge is seen to cause the lift to decay in time from its infinite-span value towards zero, due to a spanwise motion round the side edge; whilst the radiation is shown to be composed of two Signals, the first received directly from the interaction between the jet and the leading edge, and the second resulting from the diffraction of sound waves emanating from the leading edge by the side edge. The effect of choosing a more diffuse upwash distribution is then considered, in which case it becomes clear that the first signal has a considerably larger amplitude, and shorter duration, than the second, diffracted signal.

Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate

We consider a nominally uniform flow over a semi-infinite flat plate. Our analysis shows how a small streamwise disturbance in the otherwise uniform flow ahead of the plate is amplified by leading-edge bluntness effects and eventually leads to a small-amplitude but nonlinear spanwise motion far downstream from the leading edge of the plate. This spanwise motion is then imposed on the viscous boundary-layer flow at the surface of the plate – causing an order-one change in its profile shape. This ultimately reduces the wall shear stress to zero – causing the boundary layer to undergo a localized separation, which may be characterized as a kind of bursting phenomenon that could be related to the turbulent bursts observed in some flat-plate boundary-layer experiments.

Transition to turbulence in a rotating channel

Direct numerical simulation is used to determine the flows that occur as the Reynolds number, Re, is increased in a plane channel undergoing system rotation about a spanwise axis. (Plane Poiseuille flow occurs for zero rotation rate and low Re.) A constant system rotation speed of 0.5, non-dimensionalized with respect to the bulk streamwise velocity and channel full width, is used throughout. The spectral numerical method solves the three-dimensional, time-dependent, incompressible Navier-Stokes equations using periodic boundary conditions in the streamwise and spanwise directions. On increasing the Reynolds number above the temporally periodic wavy vortex regime, near Re = 4Rec (Rec = 88.6 is the critical Re for development of vortices), a second temporal frequency, ω2, occurs in the flow that corresponds to slow, constant, spanwise motion of the vortices, superposed on the much faster, constant, streamwise motion of the wavy vortex waves. Curiously, ω2 is always frequency locked with the wavy vortex frequency ω1 for the parameter range explored, although the locking ratio varies. At the slightly higher Re of 4.1 Rec, ω2 is replaced by a new frequency ω′2 that corresponds to a modulation of the wavy vortices like that seen in modulated wavy Taylor vortex flow. However, unlike the Taylor-Couette geometry, the modulation frequency here can become frequency locked with the wavy vortex frequency. Increasing Re further to Re = 4.2 Rec results in the appearance of a second incommensurate modulation frequency ω3, yielding a quasi-periodic three-frequency flow, although there are only two frequencies (ωω′2 and ω3) present in the reference frame moving with the travelling wave associated with ω1. At still higher Re (Re = 4.5 Rec), weak temporal chaos occurs. This flow is not turbulent however. Calculations of the instantaneous largest Lyapunov exponent, λ(t), and the spatial structure of small perturbations to the flow show that the chaos is driven by spanwise shear instability of the streamwise velocity component. At the highest Re of 6.7 Rec considered, quasi-coherent turbulent boundary layer structures occur as transient, secondary streamwise-oriented vortices in the viscous sublayer near the inviscidly unstable (high-pressure) wall. Calculations of λ(t) and the spatial structure of small perturbations to the flow show that the coherent structures are not caused by the local growth of small disturbances to the flow.

Evolution and dynamics of shear-layer structures in near-wall turbulence

Near-wall flow structures in turbulent shear flows are analysed, with particular emphasis on the study of their space–time evolution and connection to turbulence production. The results are obtained from investigation of a database generated from direct numerical simulation of turbulent channel flow at a Reynolds number of 180 based on half-channel width and friction velocity. New light is shed on problems associated with conditional sampling techniques, together with methods to improve these techniques, for use both in physical and numerical experiments. The results clearly indicate that earlier conceptual models of the processes associated with near-wall turbulence production, based on flow visualization and probe measurements need to be modified. For instance, the development of asymmetry in the spanwise direction seems to be an important element in the evolution of near-wall structures in general, and for shear layers in particular. The inhibition of spanwise motion of the near-wall streaky pattern may be the primary reason for the ability of small longitudinal riblets to reduce turbulent skin friction below the value for a flat surface.

Secondary Flow, Turbulent Diffusion, and Mixing in Axial-Flow Compressors

The relative importance of convection by secondary flows and diffusion by turbulence as mechanisms responsible for mixing in multistage, axial-flow compressors has been investigated by using the ethylene tracer-gas technique and hot-wire anemometry. The tests were conducted at two loading levels in a large, low-speed, four-stage compressor. The experimental results show that considerable cross-passage and spanwise fluid motion can occur and that both secondary flow and turbulent diffusion can play important roles in the mixing process, depending upon location in the compressor and loading level. In the so-called freestream region, turbulent diffusion appeared to be the dominant mixing mechanism. However, near the endwalls and along airfoil surfaces at both loading levels, the convective effects from secondary flow were of the same order of magnitude as, and in some cases greater than, the diffusive effects from turbulence. Calculations of the secondary flowfield and mixing coefficients support the experimental findings.

Interaction of chord and spanwise oscillations in a flow past a yawed cylinder and asymptotic solutions

The aim of the work is to study the interaction of the chord and spanwise oscillations which induce perturbations in both magnitude and direction as in Sarma [4], in a three-dimensional incompressible oscillatory boundary layer flow past a yawed infinite cylinder. Asymptotic and matched asymptotic solutions are found for small and large frequencies and for chord and spanwise motions. In turn, the matched asymptotic solution given in this paper for large frequencies for the chordwise motion generalises the work of Ackerberg and Phillips [5] to a wedge flow. As examples yawed flat plate, yawed cylinder with a stagnation point and yawed wedge are studied in detail. The skin friction coefficients for small and large frequencies are represented graphically. Their joining and behaviours are discussed for different values of the interaction, and elongation parameters.