Swept-wing boundary-layer receptivity

2012 ◽  
Vol 700 ◽  
pp. 490-501 ◽  
Author(s):  
David Tempelmann ◽  
Ardeshir Hanifi ◽  
Dan S. Henningson
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Free Stream ◽  
Stokes Equations ◽  
Cross Flow ◽  
Leading Edge ◽  
Navier Stokes ◽  
Flow Mode ◽  
Swept Wing ◽  
Worst Case

AbstractAdjoint solutions of the linearized incompressible Navier–Stokes equations are presented for a cross-flow-dominated swept-wing boundary layer. For the first time these have been computed in the region upstream of the swept leading edge and may therefore be used to predict receptivity to any disturbances of the incoming free stream as well as to surface roughness. In this paper we present worst-case scenarios, i.e. those external disturbances yielding maximum receptivity amplitudes of a steady cross-flow disturbance. In the free stream, such an ‘optimal’ disturbance takes the form of a streak which, while being convected downstream, penetrates the boundary layer and smoothly turns into a growing cross-flow mode. The ‘worst-case’ surface roughness has a wavy shape and is distributed in the chordwise direction. It is shown that, under such optimal conditions, the boundary layer is more receptive to surface roughness than to incoming free stream disturbances.

Receptivity to surface roughness near a swept leading edge

1999 ◽  
Vol 380 ◽  
pp. 141-168 ◽  
Author(s):  
S. SCOTT COLLIS ◽  
SANJIVA K. LELE
Keyword(s):  
Surface Roughness ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Convex Surface ◽  
Cross Flow ◽  
Leading Edge ◽  
Surface Curvature ◽  
Parallel Flow ◽  
Navier Stokes ◽  
Swept Wing

The formation of stationary cross flow vortices in a three-dimensional boundary layer due to surface roughness located near the leading edge of a swept wing is investigated using numerical solutions of the compressible Navier–Stokes equations. The numerical solutions are used to evaluate the accuracy of theoretical receptivity predictions which are based on the parallel-flow approximation. By reformulating the receptivity theory to include the effect of surface curvature, it is shown that convex surface curvature enhances receptivity. Comparisons of the parallel-flow predictions with Navier–Stokes solutions demonstrate that non-parallel effects strongly reduce the initial amplitude of stationary cross flow vortices. The curvature and non-parallel effects tend to counteract one another; but, for the cases considered here, the non-parallel effect dominates leading to significant over-prediction of receptivity by parallel-flow receptivity theory. We conclude from these results that receptivity theories must account for non-parallel effects in order to accurately predict the amplitude of stationary crossflow instability waves near the leading edge of a swept wing.

Leading-edge receptivity to free-stream disturbance waves for hypersonic flow over a parabola

2001 ◽  
Vol 441 ◽  
pp. 315-367 ◽  
Author(s):  
XIAOLIN ZHONG
Keyword(s):  
Boundary Layer ◽  
Hypersonic Flow ◽  
Boundary Layers ◽  
Free Stream ◽  
Stokes Equations ◽  
Leading Edge ◽  
Bow Shock ◽  
Navier Stokes ◽  
Hypersonic Boundary Layer ◽  
Disturbance Waves

The receptivity of hypersonic boundary layers to free-stream disturbances, which is the process of environmental disturbances initially entering the boundary layers and generating disturbance waves, is altered considerably by the presence of bow shocks in hypersonic flow fields. This paper presents a numerical simulation study of the generation of boundary layer disturbance waves due to free-stream waves, for a two-dimensional Mach 15 viscous flow over a parabola. Both steady and unsteady flow solutions of the receptivity problem are obtained by computing the full Navier–Stokes equations using a high-order-accurate shock-fitting finite difference scheme. The effects of bow-shock/free-stream-sound interactions on the receptivity process are accurately taken into account by treating the shock as a discontinuity surface, governed by the Rankine-Hugoniot relations. The results show that the disturbance waves generated and developed in the hypersonic boundary layer contain both first-, second-, and third-mode waves. A parametric study is carried out on the receptivity characteristics for different free-stream waves, frequencies, nose bluntness characterized by Strouhal numbers, Reynolds numbers, Mach numbers, and wall cooling. In this paper, the hypersonic boundary-layer receptivity is characterized by a receptivity parameter defined as the ratio of the maximum induced wave amplitude in the first-mode-dominated region to the amplitude of the free-stream forcing wave. It is found that the receptivity parameter decreases when the forcing frequency or nose bluntness increase. The results also show that the generation of boundary layer waves is mainly due to the interaction of the boundary layer with the acoustic wave field behind the bow shock, rather than interactions with the entropy and vorticity wave fields.

Stabilization of a swept-wing boundary layer by distributed roughness elements

2013 ◽  
Vol 718 ◽  
Author(s):  
Seyed M. Hosseini ◽  
David Tempelmann ◽  
Ardeshir Hanifi ◽  
Dan S. Henningson
Keyword(s):  
Boundary Layer ◽  
Control Method ◽  
Cross Flow ◽  
Leading Edge ◽  
Base Flow ◽  
Flow Mode ◽  
Swept Wing ◽  
Free Stream Turbulence ◽  
Flow Disturbances ◽  
Roughness Elements

AbstractThe stabilization of a swept-wing boundary layer by distributed surface roughness elements is studied by performing direct numerical simulations. The configuration resembles experiments studied by Saric and coworkers at Arizona State University, who employed this control method in order to delay transition. An array of cylindrical roughness elements are placed near the leading edge to excite subcritical cross-flow modes. Subcritical refers to the modes that are not critical with respect to transition. Their amplification to nonlinear amplitudes modifies the base flow such that the most unstable cross-flow mode and secondary instabilities are damped, resulting in downstream shift of the transition location. The experiments by Saric and coworkers were performed at low levels of free stream turbulence, and the boundary layer was therefore dominated by stationary cross-flow disturbances. Here, we consider a more complex disturbance field, which comprises both steady and unsteady instabilities of similar amplitudes. It is demonstrated that the control is robust with respect to complex disturbance fields as transition is shifted from 45 to 65 % chord.

An adjoint approach for computing the receptivity of the rotating disc boundary layer to surface roughness

2021 ◽  
Vol 926 ◽  
Author(s):  
Christian Thomas ◽  
Christopher Davies
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Stokes Equations ◽  
Flow Instability ◽  
Cross Flow ◽  
Navier Stokes ◽  
Rotating Disc ◽  
Azimuthal Mode ◽  
The Cross ◽  
Adjoint Approach

An adjoint approach is developed to compute the receptivity of the rotating disc boundary layer to surface roughness. The adjoint linearised Navier–Stokes equations, in cylindrical coordinates, are derived and receptivity characteristics are computed for a broad range of azimuthal mode numbers using a fully equivalent velocity–vorticity formulation. For each set of flow conditions (i.e. azimuthal mode number), the adjoint method only requires that the linear and adjoint solutions be computed once. Thus, the adjoint approach offers significant computational and time advantages over alternative receptivity schemes (i.e. direct linearised Navier–Stokes) as they can be used to instantaneously compute the receptivity of boundary layer disturbances to many environmental mechanisms. Stationary cross-flow disturbances are established by randomly distributed surface roughness that is periodic in the azimuthal direction and modelled via a linearisation of the no-slip condition on the disc surface. Each roughness distribution is scaled on its respective root-mean-square. A Monte-Carlo type uncertainty quantification analysis is performed, whereby mean receptivity amplitudes are computed by averaging over many thousands of roughness realisations with variable length and wavelength filters. The amplitude of the cross-flow instability is significantly larger for roughness distributions near the conditions for neutral linear instability, while roughness elements radially outboard have a negligible effect on the receptivity process. Furthermore, receptivity increases sharply for roughness distributions that encompass wavelength scales equivalent to that associated with the cross-flow instability. Finally, mean receptivity characteristics are used to predict the radial range that stationary cross-flow vortices achieve amplitudes sufficient to invalidate the linear stability assumptions.

Receptivity coefficients at excitation of cross-flow waves by free-stream vortices in the presence of surface roughness

2013 ◽  
Vol 716 ◽  
pp. 487-527 ◽  
Author(s):  
V. I. Borodulin ◽  
A. V. Ivanov ◽  
Y. S. Kachanov ◽  
A. P. Roschektaev
Keyword(s):  
Surface Roughness ◽  
Free Stream ◽  
Cross Flow ◽  
Leading Edge ◽  
Vortex Street ◽  
Swept Wing ◽  
Model Surface ◽  
Wing Model ◽  
Roughness Elements ◽  
The Stability

AbstractThe present experimental study is devoted to examination of the vortex receptivity mechanism associated with excitation of unsteady cross-flow (CF) waves due to scattering of unsteady free-stream vortices on localized steady surface non-uniformities (roughness). The measurements are carried out in a low-turbulence wind tunnel by means of a hot-wire anemometer in a boundary layer developing over a $25\textdegree $ swept-wing model. The harmonic-in-time free-stream vortices were excited by a thin vibrating wire located upstream of the experimental-model leading edge and represented a kind of small-amplitude von Kármán vortex street with spanwise orientation of the generated instantaneous vorticity vectors. The controlled roughness elements (the so-called ‘phased roughness’) were placed on the model surface. This roughness had a special shape, which provided excitation of CF-waves having basically some predetermined (required) spanwise wavenumbers. The linearity of the stability and receptivity mechanisms under study was checked accurately by means of variation of both the free-stream-vortex amplitude and the surface roughness height. These experiments were directed to obtaining the amplitudes and phases of the vortex-roughness receptivity coefficients for a number of vortex disturbance frequencies. The vortex street position with respect to the model surface (the vortex offset parameter) was also varied. The receptivity characteristics obtained experimentally in Fourier space are independent of the particular roughness shape, and can be used for validation of receptivity theories.

Swept wing boundary-layer receptivity to localized surface roughness

2012 ◽  
Vol 711 ◽  
pp. 516-544 ◽  
Author(s):  
David Tempelmann ◽  
Lars-Uve Schrader ◽  
Ardeshir Hanifi ◽  
Luca Brandt ◽  
Dan S. Henningson
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Practical Interest ◽  
Leading Edge ◽  
Constant Factor ◽  
Computationally Efficient ◽  
Swept Wing ◽  
Predictive Tool ◽  
Free Stream Turbulence ◽  
Streamwise Location

AbstractThe receptivity to localized surface roughness of a swept-wing boundary layer is studied by direct numerical simulation (DNS) and computations using the parabolized stability equations (PSEs). The DNS is laid out to reproduce wind tunnel experiments performed by Saric and coworkers, where micron-sized cylinders were used to trigger steady crossflow modes. The amplitudes of the roughness-induced fundamental crossflow wave and its superharmonics obtained from nonlinear PSE solutions agree excellently with the DNS results. A receptivity model using the direct and adjoint PSEs is shown to provide reliable predictions of the receptivity to roughness cylinders of different heights and chordwise locations. Being robust and computationally efficient, the model is well suited as a predictive tool of receptivity in flows of practical interest. The crossflow mode amplitudes obtained based on both DNS and PSE methods are 40 % of those measured in the experiments. Additional comparisons between experimental and PSE data for various disturbance wavelengths reveal that the measured disturbance amplitudes are consistently larger than those predicted by the PSE-based receptivity model by a nearly constant factor. Supplementary DNS and PSE computations suggest that possible natural leading-edge roughness and free-stream turbulence in the experiments are unlikely to account for this discrepancy. It is more likely that experimental uncertainties in the streamwise location of the roughness array and cylinder height are responsible for the additional receptivity observed in the experiments.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

Effect of Elevated Free-Stream Turbulence on Transitional Heat Transfer Over Dual-Scaled Rough Surfaces

2003 ◽  
Author(s):  
Ting Wang ◽  
Matthew C. Rice
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Surface Roughness ◽  
Vortex Shedding ◽  
Free Stream ◽  
Leading Edge ◽  
Test Surface ◽  
Dominant Effect ◽  
Free Stream Turbulence ◽  
Heat Transfer Phenomenon

The surface roughness over a serviced turbine airfoil is usually multi-scaled with varying features that are difficult to be universally characterized. However, it was previously discovered in low freestream turbulence conditions that the height of larger roughness produces separation and vortex shedding, which trigger early transition and exert a dominant effect on flow pattern and heat transfer. The geometry of the roughness and smaller roughness scales played secondary roles. This paper extends the previous study to elevated turbulence conditions with free-stream turbulence intensity ranging from 0.2–6.0 percent. A simplified test condition on a flat plate is conducted with two discrete regions having different surface roughness. The leading edge roughness is comprised of a sandpaper strip or a single cylinder. The downstream surface is either smooth or covered with sandpaper of grit sizes ranging from 100 ∼ 40 (Ra = 37 ∼ 119 μm). Hot wire measurements are conducted in the boundary layer to study the flow structure. The results of this study verify that the height of the largest-scale roughness triggers an earlier transition even under elevated turbulence conditions and exerts a more dominant effect on flow and heat transfer than does the geometry of the roughness. Heat transfer enhancements of about 30 ∼ 40 percent over the entire test surface are observed. The vortical motion, generated by the backward facing step at the joint of two roughness regions, is believed to significantly increase momentum transport across the boundary layer and bring the elevated turbulence from the freestream towards the wall. No such long-lasting heat transfer phenomenon is observed in low FSTI cases even though vortex shedding also exists in the low turbulence cases. The heat transfer enhancement decreases, instead of increases, as the downstream roughness height increases.

Similarity Solutions for the Interaction of a Potential Vortex With Free Stream Sink Flow and a Stationary Surface

1974 ◽  
Vol 96 (1) ◽  
pp. 49-54 ◽  
Author(s):  
J. A. Hoffmann
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Free Stream ◽  
Stokes Equations ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Surface ◽  
Direct Numerical Integration ◽  
Potential Vortex

Similarity equations, using an assumed transformation which reduces the partial differential equations to sets of ordinary differential equations, are obtained from the boundary layer and the complete Navier-Stokes equations for the interaction of vortex flows with free stream sink flows and a stationary surface. Solutions to the boundary layer equations for the case of the potential vortex that satisfy the prescribed boundary conditions are shown to be nonexistent using the assumed transformation. Direct numerical integration is used to obtain solutions to the complete Navier-Stokes equations under a potential vortex with equal values of tangential and radial free stream velocities. Solutions are found for Reynolds numbers up to 2.0.

scholarly journals Free-stream coherent structures in the unsteady Rayleigh boundary layer

2020 ◽  
Vol 85 (6) ◽  
pp. 1021-1040
Author(s):  
Eleanor C Johnstone ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Boundary Region ◽  
Navier Stokes ◽  
Equilibrium Solutions ◽  
Nonlinear Equilibrium ◽  
Set Up

Abstract Results are presented for nonlinear equilibrium solutions of the Navier–Stokes equations in the boundary layer set up by a flat plate started impulsively from rest. The solutions take the form of a wave–roll–streak interaction, which takes place in a layer located at the edge of the boundary layer. This extends previous results for similar nonlinear equilibrium solutions in steady 2D boundary layers. The results are derived asymptotically and then compared to numerical results obtained by marching the reduced boundary-region disturbance equations forward in time. It is concluded that the previously found canonical free-stream coherent structures in steady boundary layers can be embedded in unbounded, unsteady shear flows.

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