Interaction of a laminar boundary layer with external turbulence

Gulyaev, A. N.; Kozlov, V. E.; Kuznetsov, V. R.; Mineev, B. I.; Sekundov, A. N.

doi:10.1007/bf01051722

Cited by 47 publications

(60 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first analyses the boundary-layer response to FSVDs starting from the region relatively close to the leading edge, and follows its subsequent development downstream. Gulyaev et al (1989) first considered FSVDs with characteristic streamwise and spanwise wavelengths of the same order of magnitude, but both are much larger than the local boundary-layer thickness. The induced perturbation is governed by the linearized boundary-layer equations, and its streamwise velocity is found to increase with the streamwise wavelength.…”

Section: Introductionmentioning

confidence: 99%

On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances

Dong

2013

J. Fluid Mech.

View full text Add to dashboard Cite

Small-amplitude perturbations are governed by the linearized Navier-Stokes equations, which are, for a parallel or nearly parallel shear flow, customarily reduced to the Orr-Sommerfeld (O-S) and Squire equations. In this paper, we consider continuous spectra (CS) of the O-S and Squire operators for the Blasius and asymptotic suction boundary layers, and address the issue of whether and when continuous modes can represent free-stream vortical disturbances and their entrainment into the shear layer. For the Blasius boundary layer, we highlight two particular properties of the CS: (i) the eigenfunction of a continuous mode simultaneously consists of two components with wall-normal wavenumbers ±k 2 , a phenomenon which we refer to as 'entanglement of Fourier components'; and (ii) for low-frequency disturbances the presence of the boundary layer forces the streamwise velocity in the free stream to take a much larger amplitude than those of the transverse velocities. Both features appear to be non-physical, and cast some doubt about the appropriateness of using CS to characterize free-stream vortical disturbances and their entrainment into the boundary layer, a practice that has been adopted in some recent studies of bypass transition. A high-Reynolds-number asymptotic description of continuous modes and entrainment is present, and it shows that the entanglement is a result of neglecting non-parallelism, which has a leading-order effect on the entrainment. When this effect is included, entanglement disappears, and moreover the streamwise velocity is significantly amplified in the edge layer when R −1 ω 1, where R is the Reynolds number based on the local boundary-layer thickness. For the asymptotic suction boundary layer, which is an exactly parallel flow, both temporal and spatial CS may be defined mathematically. However, at a finite R neither of them represents the physical process of free-stream vortical disturbances penetrating into the boundary layer. The latter must instead be characterized by a peculiar type of continuous modes whose eigenfunctions increase exponentially with the distance from the wall. In the limit R 1, all three types of CS are identical at leading order, and hence can be used to represent free-stream vortical disturbances and their entrainment. Lowfrequency disturbances are found to generate a large-amplitude streamwise velocity in the boundary layer, which is reminiscent of longitudinal streaks.

show abstract

Section: Introductionmentioning

confidence: 99%

On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances

Dong

2013

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…the growth of low-frequency perturbations of velocity is observed. Flow visualization shows that these 1)erturbations are narrow streaks exteuded in the streamwise direction [2]. It is ~ussu,ned that these streaky structures appear as a resul: ~ 1)enetration of ~x)rtices from the external flow into the boundary layer and their subsequent amplificat~,,a in it.…”

mentioning

confidence: 99%

Receptivity of the boundary layer on a flat plate with a blunted leading edge to steady nonuniformity of the free stream

Ustinov¹

2000

J Appl Mech Tech Phys

View full text Add to dashboard Cite

Introduction. In the case of a high level of free-stream turbulence (0.1% < ~t < 5%). the laminarturbulent transitiou occurs without fornmtion of the Tolhnien-Schlichting waves [1]. Instead of them. the growth of low-frequency perturbations of velocity is observed. Flow visualization shows that these 1)erturbations are narrow streaks exteuded in the streamwise direction [2]. It is ~ussu,ned that these streaky structures appear as a resul: ~ 1)enetration of ~x)rtices from the external flow into the boundary layer and their subsequent amplificat~,,a in it. Th~;refore, the solution of the t)rot)lem of recel)tivity of the 1)oundary layer to vortex disturbances is an important component in developing the theory of the laminar-turbulent transition in the case of an elevated level of t'ree-stream turbulence.This problem ha.s been sol~vd only for the particular case of interaction of streamwise vortices with tile boundary layer on a fiat plate [3,4]. This is tile siml)lest case, since tim free-stream vorticity field is not distorted by tile flow near the leading edge. However, such a deformation involves a(htitional amplification of pertltrbations due to the exi)ansion of vortex filaments [5]. Tile gTeatest amI)lification is experienced by I), :, bations whose vortex lines intersect tile lea(ting edge. Hence, these perturbations (and not tile streamwise vortices) should generate the streaky structure most effectively. It is shown in [5] that vorticity perpendicular to the leading edge (or nonuniformity of tile velocity profile in the spanwise (tirectit)tt) can even lead to a local separation of tile boundary layer. The analysis [5] was made for large-scale disturbances of small but finite amplitu(le. Under tim assumt)tions accel)ted, the development of disturbances is actually inviscid, and tile governing influence is exerted by nonlinear effects. However, it follows from the exl)erimental results of XNestin et al. [6] that the transverse size of the streaky structure is small, and viscosity plays a significant role in the development of this structure. In addition, the aml)litude of perturbations observed in [6] is small for manif'estation of strong nonlinear effects. In the I)resent work, the I)robleIn of interaction of a nonuniform flow with the boundary layer is solved under tile folh)wing ~lssumptions: the characteristic size of disturban('es is assumed to be of the order of the 1)oun(lary-layer thickness and the evolution of (listurbances is linear in terms of their amplitude.

show abstract

“…Its components can be decomposed in two parts as suggested in Ref. [29]: component {ū,v,w,p} and component {ū (0) ,v (0) ,w (0) ,p (0) }. The latter is dominant only in the outer part of the boundary layer [30] and is not considered here.…”

Section: Mathematical Formulation Of the Physical Problemmentioning

confidence: 99%

Closed-loop control of boundary layer streaks induced by free-stream turbulence

Papadakis

Riccó

2016

Phys. Rev. Fluids

View full text Add to dashboard Cite

The central aim of the paper is to carry out a theoretical and numerical study of active wall transpiration control of streaks generated within an incompressible boundary layer by free-stream turbulence. The disturbance flow model is based on the linearized unsteady boundary-region (LUBR) equations, studied by Leib, Wundrow, and Goldstein [J. Fluid Mech. 380, 169 (1999)], which are the rigorous asymptotic limit of the NavierStokes equations for low-frequency and long-streamwise wavelength. The mathematical formulation of the problem directly incorporates the random forcing into the equations in a consistent way. Due to linearity, this forcing is factored out and appears as a multiplicative factor. It is shown that the cost function (integral of kinetic energy in the domain) is properly defined as the expectation of a random quadratic function only after integration in wave number space. This operation naturally introduces the free-stream turbulence spectral tensor into the cost function. The controller gains for each wave number are independent of the spectral tensor and, in that sense, universal. Asymptotic matching of the LUBR equations with the free-stream conditions results in an additional forcing term in the state-space system whose presence necessitates the reformulation of the control problem and the rederivation of its solution. It is proved that the solution can be obtained analytically using an extension of the sweep method used in control theory to obtain the standard Riccati equation. The control signal consists of two components, a feedback part and a feed-forward part (that depends explicitly on the forcing term). Explicit recursive equations that provide these two components are derived. It is shown that the feed-forward part makes a negligible contribution to the control signal. We also derive an explicit expression that a priori (i.e., before solving the control problem) leads to the minimum of the objective cost function (i.e., the fundamental performance limit), based only on the system matrices and the initial and free-stream boundary conditions. The adjoint equations admit a self-similar solution for large spanwise wave numbers with a scaling which is different from that of the LUBR equations. The controlled flow field also has a self-similar solution if the weighting matrices of the objective function are chosen appropriately. The code developed to implement this algorithm is efficient and has modest memory requirements. Computations show the significant reduction of energy for each wave number. The control of the full spectrum streaks, for conditions corresponding to a realistic experimental case, shows that the root-mean-square of the streamwise velocity is strongly suppressed in the whole domain and for all the frequency ranges examined.

show abstract

Interaction of a laminar boundary layer with external turbulence

Cited by 47 publications

References 1 publication

On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances

On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances

Receptivity of the boundary layer on a flat plate with a blunted leading edge to steady nonuniformity of the free stream

Closed-loop control of boundary layer streaks induced by free-stream turbulence

Contact Info

Product

Resources

About