Absolute and Convective Instabilities of a Separated Boundary Layer Near the Leading Edge of an Aerofoil

2017 ◽  
Author(s):  
S. Sarkar ◽  
K. S. Jadhav
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Constant Thickness ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
Convective Instabilities ◽  
Image Velocimetry ◽  
Through Flow ◽  
The Mean ◽  
The Stability

Present work describes the stability analysis of a separated boundary layer over a constant thickness aerofoil subjected to an impulse at the boundary for varying angles of attack (α1) and tail flap deflections (β1), where, the Reynolds number (Rec) based on chord is 1.6 × 105 and the inlet free-stream turbulence (fst) being 1.2%. The features of the boundary layer are investigated through flow field measurement by a planar particle image velocimetry (PIV) and hotwire anemometer. The response to the impulse can grow either in space and time. The Orr-Sommerfield (O-S) equation has been solved, where the mean velocity field is obtained from the experiment. Criteria following Huerre and Monkewitz [1] are used here to decide the type of instability. It has been observed that the separated boundary layer near the leading edge is absolutely unstable for low angles of attack, whereas, it is convectively unstable for higher angles of attack, when the Kelvin-Helmholtz instability is bypassed. Further, it shows a convective instability for flap angles of ±30 deg.

Measurements in a Transitional Boundary Layer With Görtler Vortices

1996 ◽  
Author(s):  
Ralph J. Volino ◽  
Terrence W. Simon
Keyword(s):  
Boundary Layer ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Streamwise Velocity ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
Görtler Vortices ◽  
Concave Wall ◽  
The Mean ◽  
Gortler Vortices

The laminar-turbulent transition process has been documented in a concave-wall boundary layer subject to low (0.6%) free-stream turbulence intensity. Transition began at a Reynolds number, Rex (based on distance from the leading edge of the test wall), of 3.5×105 and was completed by 4.7×105. The transition was strongly influenced by the presence of stationary, streamwise, Görtler vortices. Transition under similar conditions has been documented in previous studies, but because concave-wall transition tends to be rapid, measurements within the transition zone were sparse. In this study, emphasis is on measurements within the zone of intermittent flow. Twenty-five profiles of mean streamwise velocity, fluctuating streamwise velocity, and intermittency have been acquired at five values of Rex, and five spanwise locations relative to a Görtler vortex. The mean velocity profiles acquired near the vortex downwash sites exhibit inflection points and local minima. These minima, located in the outer part of the boundary layer, provide evidence of a “tilting” of the vortices in the spanwise direction. Profiles of fluctuating velocity and intermittency exhibit peaks near the locations of the minima in the mean velocity profiles. These peaks indicate that turbulence is generated in regions of high shear, which are relatively far from the wall. The transition mechanism in this flow is different from that on flat walls, where turbulence is produced in the near-wall region. The peak intermittency values in the profiles increase with Rex, but do not follow the “universal” distribution observed in most flat-wall, transitional boundary layers. The results have applications whenever strong concave curvature may result in the formation of Görtler vortices in otherwise 2-D flows. Because these cases were run with a low value of free-stream turbulence intensity, the flow is not a replication of a gas turbine flow. However, the results do provide a base case for further work on transition on the pressure side of gas turbine airfoils, where concave curvature effects are combined with the effects of high free-stream turbulence and strong streamwise pressure gradients, for they show the effects of embedded streamwise vorticity in a flow that is free of high-turbulence effects.

Separated and Reattached Flow Over Square, Rectangular and Semi-Circular Blocks

2007 ◽  
Author(s):  
M. Agelinchaab ◽  
M. F. Tachie
Keyword(s):  
Boundary Layer ◽  
Cross Sections ◽  
Recirculation Region ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Block Height ◽  
Turbulent Statistics ◽  
Image Velocimetry ◽  
The Mean ◽  
Separated And Reattached Flow

A particle image velocimetry is used to study the characteristics of separated and reattached turbulent flow over two-dimensional transverse blocks of square, rectangular and semi-circular cross-sections fixed to the bottom wall of an open channel. The ratio of upstream boundary layer thickness to block height is considerably higher than in prior studies. The results show that the mean and turbulent statistics in the recirculation region and downstream of reattachment are significantly different from the upstream boundary layer. The variation of the Reynolds stresses along the separating streamlines is discussed within the context of vortex stretching, longitudinal strain rate and wall damping. It appears wall damping is a more dominant mechanism in the vicinity of reattachment. The levels of turbulence diffusion and production by the normal stresses are significantly higher than in classical turbulent boundary layers. The bulk of turbulence production occurs in mid-layer and transported into the inner and outer layers. The results also reveal that the curvature of separating streamline, separating bubble beneath it as well as the mean velocity and turbulent quantities depend strongly on block geometry.

scholarly journals Boundary-layer evolution over long wind farms

2021 ◽  
Vol 925 ◽  
Author(s):  
Antonio Segalini ◽  
Marco Chericoni
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Wind Farms ◽  
Internal Boundary Layer ◽  
Internal Boundary ◽  
Inertial Subrange ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
The Mean

The structure of the internal boundary layer above long wind farms is investigated experimentally. The transfer of kinetic energy from the region above the farm is dominated by the turbulent flux of momentum together with the displacement of kinetic energy operated by the mean vertical velocity: these two have comparable magnitude along the farm opposite to the infinite-farm case. The integration of the energy equation in the vertical highlighted the key role of the energy flux, and how that is balanced by the growth of the internal boundary layer in terms of energy thickness with a small role of the dissipation. The mean velocity profiles seem to follow a universal structure in terms of velocity deficit, while the Reynolds stress does not follow the same scaling structure. Finally, a spectral analysis along the farm identified the leading dynamics determining the turbulent activity: while behind the first row the signature of the tip vortices is dominant, already after the second row their coherency is lost and a single broadband peak, associated with wake meandering, is present until the end of the farm. The streamwise velocity peak is associated with a nearly constant Strouhal number weakly dependent on the farm layout and free stream turbulence condition. A reasonable agreement of the velocity spectra is observed when the latter are normalised by the velocity variance and integral time scale: nevertheless the spectra show clear anisotropy at the large scales and even the small scales remain anisotropic in the inertial subrange.

Effects of Free-Stream Turbulence on Transition of a Separated Boundary Layer Over the Leading-Edge of a Constant Thickness Airfoil

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
A. Samson ◽  
S. Sarkar
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Free Stream ◽  
Separation Bubble ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Constant Thickness ◽  
Free Stream Turbulence ◽  
Transition Mechanism ◽  
Bubble Length

This paper describes the change in the transition mechanism of a separated boundary layer formed from the semicircular leading-edge of a constant thickness airfoil as the free-stream turbulence (fst) increases. Experiments are carried out in a low-speed wind tunnel for three levels of fst (Tu = 0.65%, 4.6%, and 7.7%) at two Reynolds numbers (Re) 25,000 and 55,000 (based on the leading-edge diameter). Measurements of velocity and surface pressure along with flow field visualizations are carried out using a planar particle image velocimetry (PIV). The flow undergoes separation in the vicinity of leading-edge and reattaches in the downstream forming a separation bubble. The shear layer is laminar up to 20% of separation length, and then, the perturbations are amplified in the second-half attributing to breakdown and reattachment. The bubble length is highly susceptible to change in Tu. At low fst, the primary mode of instability of the shear layer is Kelvin–Helmholtz (K-H), although the local viscous effect may not be neglected. At high fst, the mechanism of shear layer rollup is bypassed with transient growth of perturbations along with evidence of spot formation. The predominant shedding frequency when normalized with respect to the momentum thickness at separation is almost constant and shows a good agreement with the previous studies. After reattachment, the flow takes longer length to approach a canonical boundary layer.

Characteristics of a turbulent boundary layer with an external turbulent uniform shear flow

1976 ◽  
Vol 77 (2) ◽  
pp. 369-396 ◽  
Author(s):  
Q. A. Ahmad ◽  
R. E. Luxton ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Shear Flow ◽  
Free Stream ◽  
Reynolds Shear Stress ◽  
Wall Layer ◽  
Turbulence Level ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
The Mean

Measurements are presented of both mean and fluctuating velocity components in a turbulent boundary layer subjected to a nearly homogeneous external turbulent shear flow. The Reynolds shear stress in the external shear flow is small compared with the wall shear stress. Its transverse mean velocity gradient λ (≃ 6 s−l) is also small compared with typical gradients based on outer variables (say Uw/δ, where Uwis the value of the linear velocity profile extrapolated to the wall and δ is the boundary-layer thickness), but is of the same order as Ut/δ (Ur is the friction velocity). The influence of both positive and negative transverse velocity gradients on the turbulent wall layer is investigated over a streamwise region where the normal Reynolds stresses in the external flow are approximately equal and constant in the streamwise direction. In this region, the integral length scale of the external flow is of the same order of magnitude as that of the wall layer. Measurements in the boundary layer are also given for an un-sheared external turbulent flow (λ = 0) with a turbulence level Tu of 1.5%, approximately the same as that for h = ± 6 s−1. (Tu, is defined as the ratio of the r.m.s. longitudinal velocity fluctuation to Uw.) The measurements are in good agreement with those available in the literature for a similar free-stream turbulence level and show that the external turbulence level and length scale exert a large influence on the turbulence structure in the boundary layer. The additional effect of the external shear on the mean velocity and turbulent energy budget distributions in the inner region of the boundary layer is found to be small. In the outer region, the ‘wake’ component of the mean velocity defect is lowered by the presence of free-stream turbulence and one extra effect due to the external shear is an increase in the Reynolds shear stress when h is positive and a decrease when h is negative. Another interesting effect due to the shear is the appearance near the edge of the layer of a small but distinct region where the local mean velocity is constant and the Reynolds shear stress is negligible.

Behavior of Separation Bubble and Reattached Boundary Layer Around a Circular Leading Edge

1994 ◽  
Author(s):  
B. K. Hazarika ◽  
C. Hirsch
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Separation Bubble ◽  
Low Frequency ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Low Frequency Oscillations ◽  
Lower Reynolds Number ◽  
The Mean

The flow around a circular leading edge airfoil is investigated in an incompressible, low turbulence freestream. Hot-wire measurements are performed through the separation bubble, the reattachment and the recovery region till development of the fully turbulent boundary layer. The results of the experiments in the range of Reynolds numbers 1.7×103 to 11.8×103 are analysed and presented in this paper. A separation bubble is present near the leading edge at all Reynolds numbers. At the lowest Reynolds number investigated, the transition is preceded by strong low frequency oscillations. The correlation given by Mayle for prediction of transition of short separation bubbles is successful at the lower Reynolds number cases. The length of the separation bubble reduces considerably with increasing Reynolds number in the range investigated. The turbulence in the reattached flow persists even when the Reynolds number based on momentum thickness of the reattached boundary layer is small. The recovery length of the reattached layer is relatively short and the mean velocity profile follows logarithmic law within a short distance downstream of the reattachment point and the friction coefficient conforms to Prandtl-Schlichting skin-friction formula for a smooth flat plate at zero incidence.

On the stability of attachment-line boundary layers. Part 2. The effect of leading-edge curvature

1997 ◽  
Vol 333 ◽  
pp. 125-137 ◽  
Author(s):  
RAY-SING LIN ◽  
MUJEEB R. MALIK
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Leading Edge ◽  
Mean Flow ◽  
Eigenvalue Approach ◽  
Curvature Effects ◽  
The Mean ◽  
The Stability ◽  
Attachment Line

The stability of the incompressible attachment-line boundary layer has been studied by Hall, Malik & Poll (1984) and more recently by Lin & Malik (1996). These studies, however, ignored the effect of leading-edge curvature. In this paper, we investigate this effect. The second-order boundary-layer theory is used to account for the curvature effects on the mean flow and then a two-dimensional eigenvalue approach is applied to solve the linear stability equations which fully account for the effects of non-parallelism and leading-edge curvature. The results show that the leading-edge curvature has a stabilizing influence on the attachment-line boundary layer and that the inclusion of curvature in both the mean-flow and stability equations contributes to this stabilizing effect. The effect of curvature can be characterized by the Reynolds number Ra (based on the leading-edge radius). For Ra = 104, the critical Reynolds number R (based on the attachment-line boundary-layer length scale, see §2.2) for the onset of instability is about 637; however, when Ra increases to about 106 the critical Reynolds number approaches the value obtained earlier without curvature effect.

Influence of Leading Edge and Spacing on the Near Wake of Cylinder Pairs

2009 ◽  
Author(s):  
Jonathan M. Tsikata ◽  
Samuel S. Paul ◽  
Chris Katopodis ◽  
Mark F. Tachie
Keyword(s):  
Open Channel ◽  
Particle Image ◽  
Leading Edge ◽  
Particle Image Velocimetry System ◽  
Turbulence Level ◽  
Near Wake ◽  
Mean Velocity ◽  
Rectangular Cylinder ◽  
Image Velocimetry ◽  
The Mean

An experimental study of the effects of the shape of rectangular cylinder leading edge and the cylinder spacing on the wake dynamics in an open channel turbulent flow is reported. The shapes of the rectangular cylinder leading edges were square and round with each having a square trailing edge. In each experiment, measurements were conducted for a pair of cylinders that have identical leading edge shape. Three centre-to-centre spacing (b = 30 mm, 50 mm and 75 mm) were investigated for each cylinder leading edge shape. Particle image velocimetry system was used to conduct measurements around each cylinder pair. The results show that the mean velocity and the turbulence level increases with decreasing spacing. The turbulence levels downstream of a cylinder pair with a round leading edge are relatively higher than the corresponding cylinder pair with square leading edge.

The mean velocity profile in three-dimensional turbulent oundary layers

1963 ◽  
Vol 15 (3) ◽  
pp. 368-384 ◽  
Author(s):  
H. G. Hornung ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Three Dimensional ◽  
Leading Edge ◽  
Viscous Sublayer ◽  
Scale Model ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

The mean velocity distribution in a low-speed three-dimensional turbulent boundary-layer flow was investigated experimentally. The experiments were performed on a large-scale model which consisted of a flat plate on which secondary flow was generated by the pressure field introduced by a circular cylinder standing on the plate. The Reynolds number based on distance from the leading edge of the plate was about 6 x 106.It was found that the wall-wake model of Coles does not apply for flow of this kind and the model breaks down in the case of conically divergent flow with rising pressure, for example, in the results of Kehl (1943). The triangular model for the yawed turbulent boundary layer proposed by Johnston (1960) was confirmed with good correlation. However, the value ofyuτ/vwhich occurs at the vertex of the triangle was found to range up to 150 whereas Johnston gives the highest value as about 16 and hence assumes that the peak lies within the viscous sublayer. Much of his analysis is based on this assumption.The dimensionless velocity-defect profile was found to lie in a fairly narrow band when plotted againsty/δ for a wide variation of other parameters including the pressure gradient. The law of the wall was found to apply in the same form as for two-dimensional flow but for a more limited range ofy.

Turbulent boundary layer over a compliant surface: absolute and convective instabilities

2001 ◽  
Vol 449 ◽  
pp. 141-168 ◽  
Author(s):  
K. S. YEO ◽  
H. Z. ZHAO ◽  
B. C. KHOO
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Reynolds Stress ◽  
Temporal Perspective ◽  
Mean Velocity ◽  
Compliant Surface ◽  
Convective Instabilities ◽  
Compliant Surfaces ◽  
The Mean ◽  
Spatio Temporal

A theoretical model for the instability of two-dimensional turbulent boundary layer over compliant surfaces is described. The principal Reynolds stress is modelled by a well-established mixing-length eddy-viscosity formulation of van Driest. The perturbations of the mean velocity and Reynolds stress fields are coupled via the turbulence model. The investigation of instability is carried out from a time-asymptotic spatio-temporal perspective that classifies instabilities as being either convective or absolute. The occurrence of convective and absolute instabilities over viscoelastic compliant layers is elucidated. Compliant surfaces with low damping are susceptible to convective instability, which gives way to an absolute instability when the surfaces become highly damped. The theoretical results are compared against experimental observations of surface waves on elastic and viscoelastic compliant layers.

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