Turbulent drag reduction by spanwise wall oscillations

In the present work a technique is numerically investigated, which is aimed at reducing the friction drag in turbulent boundary layers and channel flows. A cyclic spanwise oscillation of the wall with a proper frequency and amplitude is imposed, allowing a reduction of the turbulent drag of up to 40%. The present work is based on the numerical simulation of the Navier-Stokes equations in the simple geometry of a plane channel flow. The frequency of the oscillations is kept fixed at the most efficient value determined in previous studies, while the choice of the best value for the amplitude of the oscillations is evaluated not only in terms of friction reduction, but also by taking into consideration the overall energy balance and the power spent for the motion of the wall. The analysis of turbulence statistics allows to shed some light on the way oscillations interact with wall turbulence, as illustrated by visual inspection of some instantaneous flow fields. Finally, a simple explanation is proposed for this interaction, which leads to a rough estimate of the most efficient value for the frequency of the oscillations.     

Turbulent wall pressure fluctuations over wavy surfaces

Measurements of the spectral characteristics of the wall pressure fluctuations produced by a turbulent boundary layer flow over solid sinusoidal surfaces of moderate wave amplitude to wave-length ratios have been obtained. The wave amplitudes were sufficiently small so that the flow remained attatched. The results show that the root mean square pressure level reaches a maximum on the adverse pressure gradient side of the wave at a position somewhat before the trough. Spectral analysis of the pressure fluctuations in narrow frequency bands reveals considerable differences in low and high frequency behavior. At low frequencies, the peak fluctuation amplitude was found at the trough whereas at high frequencies, the peak occurs just after the crest and a minimum is found at the trough. Pressure fluctuations having streamwise correlation lengths on the order of or larger than the wavelength of the surface do not return to their equilibrium (crest) amplitudes as they travel the length of a wave. Pressure fluctuations having streamwise correlation lengths about one order of magnitude less than a wavelength return exactly to their equilibrium amplitudes. Two-point correlation measurements show a decrease in longitudinal coherence on the adverse pressure gradient side of the wave at low frequencies and a considerable increase over a broad frequency range on the positive pressure gradient side. No change is found in the lateral coherence.List of symbols C _f skin friction coefficient - C _p pressure coefficient - C _n Fourier amplitudes of the pressure coefficient - C _dp pressure drag coefficient - d pinhole diameter - f frequency - h half the crest to trough distance - h ₊ nondimensional wave amplitude = - k _n wavenumber = - k fundamental wavenumber = - l _p pressure correlation length - p _s mean surface pressure - P ambient pressure - p fluctuating pressure - p ² mean square pressure - q dynamic head = 1/2 U ² - R space-time correlation - P Reynolds number based on wavelength = - R Reynolds number based on momentum thickness = - t time - R free stream velocity - U mean streamwise velocity - U _e streamwise velocity at the edge of the boundary layer - u ^* friction velocity = - x streamwise coordinate - y wall-normal coordinate - z spanwise coordinate - ⁺ non-dimensional wavelength = ^*) - phase of the cross-spectral density - ^* boundary layer displacement thickness - _long longitudinal coherency - _lat lateral coherency - wavelength of wavy surface - v kinematic viscosity - radian frequency = 2 f - spectral or cross-spectral density - _n phase of the Fourier series - density - time delay - _w wall shear stress - boundary layer momentum thickness     

Trapped vortex optimal control by suction and blowing at the wall

The flow due to a vortex trapped in a cavity is considered. The total circulation is constant and such that the Kutta condition is satisfied at the separation point when the vortex is on the equilibrium position S. If the vortex is slightly displaced from S it moves on closed trajectories. By using a classical variational technique, the suction/blowing intensity of the sinks/sources located on the flow boundary is determined so that the vortex is driven back to S. Examples of precomputed control and feed-back control in several flow configurations, including unstable equilibria and in the presence of random perturbations, are given.     

Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Re _θ varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re _θ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.     

The control of turbulent end-wall boundary layers using surface suction

An experimental evaluation of the effects of spatially-limited (i.e. localized) surface suction on a turbulent junction flow was performed using Particle Image Velocimetry (PIV). The results indicate that surface suction can (1) weaken both the instantaneous turbulent vortex and its associated surface interactions in the symmetry plane, (2) effectively eliminate the presence of the average turbulent necklace vortex in the symmetry plane, and (3) weaken the average downstream extensions of the vortex. It was also established that suction effectively reduces the low frequency component of the Reynolds-stress in both the symmetry plane and trailing-edge cross-stream planes, and stabilizes the behavior of the trailing vortex legs. Received: 18 May 1998/Accepted: 26 March 1999     

Turbulent drag reduction in dam-break flows

The role of turbulence is investigated in dam-break flows, where a finite volume of fluid is released from a compartment into a long, rectangular channel. After a sudden removal of the lock gate, a gravity current, undular bore, or solitary wave develops, depending on the ambient fluid height in the channel. The temporal evolution of the moving front has been measured and evaluated. It was observed that the dilution using a very small amount (a few weight ppm) of a long chain polymer (polyethylene-oxide) in the fluid strongly affected flow properties. Pronounced drag reduction has been found in dry bed flows (whereas the polymer increased the viscosity of the fluid). The presence of a few mm-thick ambient fluid layer in the channel effectively destroyed drag reduction, in spite of the fact that strong turbulence was obvious and the propagation velocity of the front was almost unchanged.     

Algebraic growth in boundary layers: optimal control by blowing and suction at the wall

The upstream perturbations that maximise the spatial energy growth in a boundary layer are called optimal perturbations. The optimal perturbations correspond to streamwise vortices and the downstream response corresponds to streamwise streaks.The aim of the present paper is to find a control by blowing and suction at the wall that zeros the energy of perturbation, when the initial disturbance is itself optimal. We shall also address the question: which kind of blowing and suction at the wall is most effective in controlling optimal disturbances?The problem is examined by a method of receptivity analysis based on a numerical solution of a system of equations adjoint to the linearised boundary layer equations. We shall investigate both cases of a flat and a concave wall.     

定常吹气对倾转旋翼机向下载荷的影响

为进一步提高倾转旋翼机悬停状态下的有效载重,开展了定常吹气流动控制对向下载荷的影响研究。首先应用延迟脱体涡模拟(DDES)方法对翼型-90°迎角下非定常大范围分离流动结构进行了数值分析;然后分别开展了前缘吹气、后缘吹气降载措施研究,揭示了吹气降载的机理,并对不同吹气口位置和吹气动量系数的影响进行了定量分析,最后开展了前、后缘同时吹气作用下降载数值模拟研究。计算结果表明:前缘最佳吹气位置在翼型的前缘点,而后缘吹气最佳位置位于襟翼弦长的15%处;前缘吹气的降载效果要优于后缘吹气,而且吹气动量系数对向下载荷的影响较小;相对于初始未施加流动控制构型,阻力系数减小量可达到32.72%。     

Pathline analysis of traveling wavy blowing and suction control in turbulent pipe flow for drag reduction

Skin friction drag is much greater in turbulent flows as compared with that in laminar flows. It is well known that traveling wave control can be used to achieve a large drag reduction. In the present study, a direct numerical simulation of a turbulent pipe flow was performed to clarify the mechanism of the drag reduction caused by the traveling wave control. The flow induced by the control was evaluated using pathline analysis. Near the wall, a “closed flow” was formed, wherein the injected particles return to the wall owing to the suction flow. The random component of Reynolds shear stress was perfectly suppressed in the closed flow, which suggests that there was no turbulence. The controlled flow was categorized into four patterns, and each flow characteristic and drag reduction effect was discussed. When the closing rate is high, the drag decreases, while when the closing rate is low, i.e., when the injected particles are released into the main flow, the turbulence is maintained. If the thickness of the layer suppressing turbulence is insufficient, a significant effect in terms of the drag reduction cannot be expected. The large drag reduction owing to the traveling wave control can be attributed to the elimination of turbulence in the region near the wall.     

Turbulent diffusion of a buoyant layer at a wall

Summary When a light fluid is injected at a steady rate at the roof of a tunnel in which there is a turbulent main flow of a heavier fluid, the turbulent diffusion of the light layer may be considerably reduced due to buoyancy. For large Richardson numbers turbulent mixing ceases altogether.The equations of motion and diffusion were solved by introducing an eddy diffusivity which is dependant on the Richardson number. Experiments were made on brine (floor) layers in a water flow, and on methane (roof) layers in an air flow. Results were essentially in agreement with theory.The motion and mixing of the layers depend mainly on the inclination of the tunnel and on a dimensionless combination of main-flow velocity, gravity, relative density difference, volume input rate of layer fluid, and tunnel width. Values of the dimensionless parameter are suggested to overcome the effects of buoyancy on mixing, and to prevent layers from moving up a slope against the main flow.     

Active control for seismic response reduction using modal-fuzzy approach

An active modal-fuzzy control method using hydraulic actuators is presented for seismic response reduction. In the proposed control system, a new fuzzy controller designed in the modal space produces the desired active control force. This type controller has all advantages of the fuzzy control algorithm and modal approach. Since it is very difficult to select input variables used in fuzzy controller among numerous state variables in the active fuzzy control system, the presented algorithm adopts the modal control algorithm to be able to consider information of all state variables in civil structures that are usually dominated by first few modes. In other words, all information of the whole structure can be considered in the control algorithm evaluated to reduce seismic responses and it can be efficient for civil structures especially. In addition, the presented algorithm is expected to magnify utility and performance caused by efficiency that the fuzzy algorithm can handle complex model more easily. An active modal-fuzzy control scheme is applied together with a Kalman filter and a low-pass filter to be applicable to real civil structures. A Kalman filter is considered to estimate modal states and a low-pass filter was used to eliminate spillover problem. The results of the numerical simulations for a wide amplitude range of loading conditions and for historic earthquake show that the proposed active modal-fuzzy control system can be beneficial in reducing seismic responses of civil structures.     

Pulsatile flow in a tube with wall injection and suction

This paper studies similarity solutions for pulsatile flow in a tube with wall injection and suction. The Navier-Stokes equations are reduced to a system of three ordinary differential equations. Two of the equations represent the effects of suction and injection on the steady flow while the third represents the effects of suction and injection on pulsatile flow. Since the equations for steady flow have been studied previously, the analysis centers on the third equation. This equation is solved numerically and by the method of matched asymptotic expansions. The exact numerical solutions compare well with the asymptotic solutions.The effects of suction and injection on pulsatile flow are the following: a) Small values of suction can cause a resonance-like effect for low frequency pulsatile flow. b) The annular effect still occurs but for large injection or suction the frequency at which this effect becomes dominant depends on the cross-flow Reynolds number. c) The maximum shear stress at the wall is decreased by injection, but may be increased or decreased by suction.Nomenclature a radius of the tube - a ₀ ² i ² - A₀, B₀, C₀, D₀, E₀ constant coefficients appearing in the expression for pressure - b a non-dimensionalized length - b ₀ ² i ^{2 2} - b _k complex coefficients of a power series - B - C ₁, C ₂, D complex constants - d - D _1,2 - f() F(a ^1/2)/aV - f ₀,f ₁,... functions of order one used in asymptotic expansions of f() - F(r) rv _r - g() - G(r) a steady component of velocity in axial direction - h() 4/C₀ a ² H(a ^1/2) - h ₀,h ₁,h ₂,...;l ₀,l ₁,l ₂,... functions of order one used in asymptotic expansions for h() in outer regions - H(r) complex valued function giving unsteady component of velocity - H ₀, H ₁, H ₂, ... K ₀, K ₁, K ₂, ...; L ₀, L ₁, L ₂, ... functions of order one used in asymptotic expansions for h() in inner regions - i - J ₀, J ₁, Y ₀, Y ₁ Bessel functions of first and second kind - k - K Rk/2b ² - O order symbol - p pressure - p ₁(z, t) arbitrary function related to pressure - r radial coordinate - r ₀ (1+16 ^{4 4})^1/4 - R Va/, the crossflow Reynolds number - t time - u() G(r)/V - v _r radial velocity - v _z axial velocity - V constant velocity at which fluid is injected or extracted - z axial coordinate - ² a ²/4 - 4.196 - small parameter; =–2/R (Sect. 4); =–R/2 (Sect. 5); =2/R(Sect. 6) - r ²/a ² - * 0.262 - Arctan (4 ^{2 2}) - , inner variables - kinematic viscosity - b - * zero of g() - density - (r, t) arbitrary function related to axial velocity - frequency     

Numerical computation of an impinging jet with uniform wall suction

The paper presents numerical predictions of a turbulent axisymmetric jet impinging onto a porous plate, based on a finite volume method of solving the Navier-Stokes equations for an incompressible air jet with the K–ε turbulence model. The velocity and pressure terms of the momentum equations are solved by the SIMPLE (semi-implicit method for pressure-linked equation) method. In this study, non-uniform staggered grids are used. The parameters of interest include the nozzle-to-wall distance and the suction velocity. The results of the present calculations are compared with available data reported in the literature. It is found that suction effects reduce the boundary layer thickness and increase the velocity gradient near the wall.     

Turbulent boundary layers with large free-stream to wall temperature ratio

Turbulent boundary layers with free-stream temperatures between 300°K and 3000°K, and wall temperature 300°K is studied numerically for air at 1 bar. Solution is started at one plane for a laminar, local similar boundary layer by solving differential equations by Runge-Kutta method. Velocity and enthalpy profiles are obtained at downstream planes by an implicit finite-difference iterative procedure. Effects of free-stream Mach number, sudden acceleration or deceleration, surface roughness, and uniform blowing or suction through the wall are studied and numerical results are compared with those available in open literatures.