Secondary instability and subcritical transition of the leading-edge boundary layer

2016 ◽  
Vol 792 ◽  
pp. 682-711 ◽  
Author(s):  
Michael O. John ◽  
Dominik Obrist ◽  
Leonhard Kleiser
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Instability ◽  
Bypass Transition ◽  
Wall Suction ◽  
Transition Mechanism

The leading-edge boundary layer (LEBL) in the front part of swept airplane wings is prone to three-dimensional subcritical instability, which may lead to bypass transition. The resulting increase of airplane drag and fuel consumption implies a negative environmental impact. In the present paper, we present a temporal biglobal secondary stability analysis (SSA) and direct numerical simulations (DNS) of this flow to investigate a subcritical transition mechanism. The LEBL is modelled by the swept Hiemenz boundary layer (SHBL), with and without wall suction. We introduce a pair of steady, counter-rotating, streamwise vortices next to the attachment line as a generic primary disturbance. This generates a high-speed streak, which evolves slowly in the streamwise direction. The SSA predicts that this flow is unstable to secondary, time-dependent perturbations. We report the upper branch of the secondary neutral curve and describe numerous eigenmodes located inside the shear layers surrounding the primary high-speed streak and the vortices. We find secondary flow instability at Reynolds numbers as low as$Re\approx 175$, i.e. far below the linear critical Reynolds number$Re_{crit}\approx 583$of the SHBL. This secondary modal instability is confirmed by our three-dimensional DNS. Furthermore, these simulations show that the modes may grow until nonlinear processes lead to breakdown to turbulent flow for Reynolds numbers above$Re_{tr}\approx 250$. The three-dimensional mode shapes, growth rates, and the frequency dependence of the secondary eigenmodes found by SSA and the DNS results are in close agreement with each other. The transition Reynolds number$Re_{tr}\approx 250$at zero suction and its increase with wall suction closely coincide with experimental and numerical results from the literature. We conclude that the secondary instability and the transition scenario presented in this paper may serve as a possible explanation for the well-known subcritical transition observed in the leading-edge boundary layer.

Darryl E. Metzger Memorial Session Paper: Comparison of Calculated and Measured Heat Transfer Coefficients for Transonic and Supersonic Boundary-Layer Flows

1995 ◽  
Vol 117 (2) ◽  
pp. 248-254 ◽  
Author(s):  
C. Hu¨rst ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Supersonic Boundary Layer ◽  
Nozzle Wall ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Three Dimensional Finite Element

The present study compares measured and computed heat transfer coefficients for high-speed boundary layer nozzle flows under engine Reynolds number conditions (U∞=230 ÷ 880 m/s, Re* = 0.37 ÷ 1.07 × 106). Experimental data have been obtained by heat transfer measurements in a two-dimensional, nonsymmetric, convergent–divergent nozzle. The nozzle wall is convectively cooled using water passages. The coolant heat transfer data and nozzle surface temperatures are used as boundary conditions for a three-dimensional finite-element code, which is employed to calculate the temperature distribution inside the nozzle wall. Heat transfer coefficients along the hot gas nozzle wall are derived from the temperature gradients normal to the surface. The results are compared with numerical heat transfer predictions using the low-Reynolds-number k–ε turbulence model by Lam and Bremhorst. Influence of compressibility in the transport equations for the turbulence properties is taken into account by using the local averaged density. The results confirm that this simplification leads to good results for transonic and low supersonic flows.

Three-Dimensional Vortex Structure in a Leading-Edge Separation Bubble at Moderate Reynolds Numbers

1991 ◽  
Vol 113 (3) ◽  
pp. 405-410 ◽  
Author(s):  
Kyuro Sasaki ◽  
Masaru Kiya
Keyword(s):  
Reynolds Number ◽  
Separation Bubble ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Vortex Filaments ◽  
Separated Shear Layer ◽  
Hydrogen Bubbles ◽  
Edge Separation

This paper describes the results of a flow visualization study which concerns three-dimensional vortex structures in a leading-edge separation bubble formed along the sides of a blunt flat plate. Dye and hydrogen bubbles were used as tracers. Reynolds number (Re), based on the plate thickness, was varied from 80 to 800. For 80 < Re < 320, the separated shear layer remains laminar up to the reattachment line without significant spanwise distortion of vortex filaments. For 320 < Re < 380, a Λ-shaped deformation of vortex filaments appears shortly downstream of the reattachment and is arranged in-phase in the downstream direction. For Re > 380, hairpin-like structures are formed and arranged in a staggered manner. The longitudinal and spanwise distances of the vortex arrangement are presented as functions of the Reynolds number.

Simulation of blunt-fin-induced shock-wave and turbulent boundary-layer interaction

1985 ◽  
Vol 154 ◽  
pp. 163-185 ◽  
Author(s):  
Ching-Mao Hung ◽  
Pieter G. Buning
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Flat Plate ◽  
High Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Horseshoe Vortex ◽  
Layer Interaction ◽  
Boundary Layer Interaction

The Reynolds-averaged Navier–Stokes equations are solved numerically for supersonic flow over a blunt fin mounted on a flat plate. The fin shock causes the boundary layer to separate, which results in a complicated, three-dimensional shock-wave and boundary-layer interaction. The computed results are in good agreement with the mean static pressure measured on the fin and the flat plate. The main features, such as peak pressure on the fin leading edge and a double peak on the plate, are predicted well. The role of the horseshoe vortex is discussed. This vortex leads to the development of high-speed flow and, hence, low-pressure regions on the fin and the plate. Different thicknesses of the incoming boundary layer have been studied. Varying the thicknesses by an order of magnitude shows that the size of the horseshoe vortex and, therefore, the spatial extent of the interaction are dominated by inviscid flow and only weakly dependent on the Reynolds number. Coloured graphics are used to show details of the interaction flow field.

Numerical investigation of wake flow regimes behind a high-speed rotating circular cylinder in steady flow

2019 ◽  
Vol 878 ◽  
pp. 875-906
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu ◽  
Lin Lu
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Rotation Rate ◽  
High Speed ◽  
Three Dimensional ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Rotating Circular Cylinder

Flow around a high-speed rotating circular cylinder for $Re\leqslant 500$ is investigated numerically. The Reynolds number is defined as $UD/\unicode[STIX]{x1D708}$ with $U$, $D$ and $\unicode[STIX]{x1D708}$ being the free-stream flow velocity, the diameter of the cylinder and the kinematic viscosity of the fluid, respectively. The aim of this study is to investigate the effect of a high rotation rate on the wake flow for a range of Reynolds numbers. Simulations are performed for Reynolds numbers of 100, 150, 200, 250 and 500 and a wide range of rotation rates from 1.6 to 6 with an increment of 0.2. Rotation rate is the ratio of the rotational speed of the cylinder surface to the incoming fluid velocity. A systematic study is performed to investigate the effect of rotation rate on the flow transition to different flow regimes. It is found that there is a transition from a two-dimensional vortex shedding mode to no vortex shedding mode when the rotation rate is increased beyond a critical value for Reynolds numbers between 100 and 200. Further increase in rotation rate results in a transition to three-dimensional flow which is characterized by the presence of finger-shaped (FV) vortices that elongate in the wake of the cylinder and very weak ring-shaped vortices (RV) that wrap the surface of the cylinder. The no vortex shedding mode is not observed at Reynolds numbers greater than or equal to 250 since the flow remains three-dimensional. As the rotation rate is increased further, the occurrence frequency and size of the ring-shaped vortices increases and the flow is dominated by RVs. The RVs become bigger in size and the flow becomes chaotic with increasing rotation rate. A detailed analysis of the flow structures shows that the vortices always exist in pairs and the strength of separated shear layers increases with the increase of rotation rate. A map of flow regimes on a plane of Reynolds number and rotation rate is presented.

scholarly journals Global stability of swept flow around a parabolic body: features of the global spectrum

2011 ◽  
Vol 669 ◽  
pp. 375-396 ◽  
Author(s):  
CHRISTOPH J. MACK ◽  
PETER J. SCHMID
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Temporal Stability ◽  
Three Dimensional ◽  
Leading Edge ◽  
Parameter Study ◽  
Acoustic Modes ◽  
Stabilizing Effect ◽  
Unstable Boundary Layer ◽  
Temporal Perturbation

The global temporal stability of three-dimensional compressible flow about a yawed parabolic body of infinite span is investigated using an iterative eigenvalue technique in combination with direct numerical simulations. The computed global spectrum provides a comprehensive picture of the temporal perturbation dynamics of the flow, and a wide and rich variety of modes has been uncovered for the investigated parameter choices: stable and unstable boundary-layer modes, different types of stable and unstable acoustic modes, and stable wavepacket modes have been found. A parameter study varying the spanwise perturbation wavenumber and the sweep Reynolds number reproduced a preferred spanwise length scale and a critical Reynolds number for a boundary-layer or acoustic instability. Convex leading-edge curvature has been found to have a strongly stabilizing effect on boundary-layer modes but only a weakly stabilizing effect on acoustic modes. Furthermore, for certain parameter choices, the acoustic modes have been found to dominate the boundary-layer modes.

Development of a Tip-Leakage Flow—Part 1: The Flow Over a Range of Reynolds Numbers

2006 ◽  
Vol 128 (4) ◽  
pp. 751-764 ◽  
Author(s):  
Ghanem F. Oweis ◽  
David Fry ◽  
Chris J. Chesnakas ◽  
Stuart D. Jessup ◽  
Steven L. Ceccio
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Leakage Flow ◽  
Core Size ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Downstream Distance ◽  
Secondary Vortices

An extensive experimental investigation was carried out to examine the tip-leakage flow on ducted propulsors. The flow field around three-bladed, ducted rotors operating in uniform inflow was measured in detail with three-dimensional laser Doppler velocimetry and planar particle imaging velocimetry. Two geometrically similar, ducted rotors were tested over a Reynolds number range from 0.7×106 to 9.2×106 in order to determine how the tip-leakage flow varied with Reynolds number. An identification procedure was used to discern and quantify regions of concentrated vorticity in instantaneous flow fields. Multiple vortices were identified in the wake of the blade tip, with the largest vortex being associated with the tip-leakage flow, and the secondary vortices being associated with the trailing edge vortex and other blade-wake vortices. The evolution of identified vortex quantities with downstream distance is examined. It was found that the strength and core size of the vortices are weakly dependent on Reynolds number, but there are indications that they are affected by variations in the inflowing wall boundary layer on the duct. The core size of the tip-leakage vortex does not vary strongly with varying boundary layer thickness on the blades. Instead, its dimension is on the order of the tip clearance. There is significant flow variability for all Reynolds numbers and rotor configurations. Scaled velocity fluctuations near the axis of the primary vortex increase significantly with downstream distance, suggesting the presence of spatially uncorrelated fine scale secondary vortices and the possible existence of three-dimensional vortex-vortex interactions.

Unsteady Transition Phenomena at a Compressor Blade Leading Edge

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Alan D. Henderson ◽  
Gregory J. Walker ◽  
Jeremy D. Hughes
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Leading Edge ◽  
Inviscid Flow ◽  
Surface Boundary ◽  
Bypass Transition ◽  
Suction Surface ◽  
Film Sensor ◽  
Rotor Wake

Wake-induced laminar-turbulent transition is studied at the leading edge of a C4-section compressor stator blade in a 1.5-stage axial compressor. Surface hot-film sensor observations are interpreted with the aid of numerical solutions from UNSFLO, a quasi-three-dimensional viscous-inviscid flow solver. The passage of a rotor wake, with its associated negative jet, over the stator leading edge is observed to have a destabilizing effect on the suction surface boundary layer. This leads to transition closer to the stator leading edge than would have occurred under steady flow conditions. The strength of this phenomenon is influenced by the rotor-stator axial gap and the variability of individual rotor wake disturbances. A variety of transition phenomena is observed near the leading edge in the wake path. Wave packets characteristic of Tollmien-Schlichting waves are observed to amplify and break down into turbulent spots. Disturbances characteristic of the streaky structures occurring in bypass transition are also seen. Examination of suction surface disturbance and wake-induced transitional strip trajectories points to the leading edge as the principal receptivity site for suction surface transition phenomena at design loading conditions. This contrasts markedly with the pressure surface behavior, where transition at design conditions occurs remotely from leading-edge flow perturbations associated with wake chopping. Here, the local receptivity of the boundary layer to the wake passing disturbance and turbulent wake fluid discharging onto the blade surface may be of greater importance.

Unsteady Transition Phenomena at a Compressor Blade Leading Edge

2006 ◽  
Author(s):  
Alan D. Henderson ◽  
Gregory J. Walker ◽  
Jeremy D. Hughes
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Leading Edge ◽  
Inviscid Flow ◽  
Surface Boundary ◽  
Bypass Transition ◽  
Suction Surface ◽  
Film Sensor ◽  
Rotor Wake

Wake-induced laminar-turbulent transition is studied at the leading edge of a C4-section compressor stator blade in a 1.5-stage axial compressor. Surface hot-film sensor observations are interpreted with the aid of numerical solutions from UNSFLO, a quasi three-dimensional viscous-inviscid flow solver. The passage of a rotor wake, with its associated negative jet, over the stator leading edge is observed to have a destabilizing effect on the suction surface boundary layer. This leads to transition closer to the stator leading edge than would have occurred under steady flow conditions. The strength of this phenomenon is influenced by the rotor-stator axial gap and the variability of individual rotor wake disturbances. A variety of transition phenomena are observed near the leading edge in the wake path. Wave packets characteristic of Tollmien–Schlichting waves are observed to amplify and break down into turbulent spots. Disturbances characteristic of the streaky structures occurring in bypass transition are also seen. Examination of suction surface disturbance and wake-induced transitional strip trajectories points to the leading edge as the principal receptivity site for suction surface transition phenomena at design loading conditions. This contrasts markedly with the pressure surface behavior, where transition at design conditions occurs remote from leading edge flow perturbations associated with wake chopping. Here the local receptivity of the boundary layer to the wake passing disturbance and turbulent wake fluid discharging onto the blade surface may be of greater importance.

scholarly journals On the Flow Along Swept Leading Edges

1967 ◽  
Vol 18 (2) ◽  
pp. 165-184 ◽  
Author(s):  
M. Gaster
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Wave Length ◽  
Leading Edge ◽  
Propagation Speed ◽  
Reynolds Numbers ◽  
Amplification Ratio ◽  
Tollmien Schlichting ◽  
High Reynolds ◽  
Attachment Line

SummaryFlight tests on the Handley Page suction wing showed that turbulence at the wing root can propagate along the leading edge and cause the whole flow to be turbulent. The flow on the attachment line of a swept wing was studied in a low speed wind tunnel with particular reference to this problem of turbulent contamination.The critical Reynolds number, RθL, of the attachment-line boundary layer for the spanwise spread of turbulence was found to be about 100 for sweep angles in the range 40°–60°. A device was developed to act as a barrier to the turbulent root flow so that a clean laminar flow could exist outboard. This device was shown to be effective up to an Rθ of at least 170, so that experiments were possible on a laminar boundary layer at Reynolds numbers above the lower critical value. A spark was used to introduce spots of turbulence into the attachment-line boundary layer and the propagation speeds of the leading and trailing edges were measured. The spots expanded, the leading edge moving faster than the trailing edge, at high Reynolds numbers, and contracted at low values.The behaviour of Tollmien-Schlichting waves was also investigated by exciting the flow with sound emanating from a small hole on the attachment line. Measurements of the perturbation phase and amplitude were made downstream of the source and, although accurate values of wave length and propagation speed could be found, difficulties were experienced in evaluating the amplification ratio. Nevertheless, all small disturbances decayed at a sufficient distance from the source hole up to the highest available Reynolds number of 170.

The wake behind a cylinder rolling on a wall at varying rotation rates

2010 ◽  
Vol 648 ◽  
pp. 225-256 ◽  
Author(s):  
B. E. STEWART ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Number Range ◽  
Rotation Rates ◽  
Transition Mechanism ◽  
Three Dimensional Simulations

A study investigating the flow around a cylinder rolling or sliding on a wall has been undertaken in two and three dimensions. The cylinder motion is specified from a set of five discrete rotation rates, ranging from prograde through to retrograde rolling. A Reynolds number range of 20–500 is considered. The effects of the nearby wall and the imposed body motion on the wake structure and dominant wake transitions have been determined. Prograde rolling is shown to destabilize the wake flow, while retrograde rotation delays the onset of unsteady flow to Reynolds numbers well above those observed for a cylinder in an unbounded flow.Two-dimensional simulations show the presence of two recirculation zones in the steady wake, the lengths of which increase approximately linearly with the Reynolds number. Values of the lift and drag coefficient are also reported for the steady flow regime. Results from a linear stability analysis show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for all rotation rates. The critical Reynolds number Rec of transition and the spanwise wavelength of the dominant mode are shown to be highly dependent on, but smoothly varying with, the rotation rate of the cylinder. Varying the rotation from prograde to retrograde rolling acts to increase the value of Rec and decrease the preferred wavelength. The structure of the fully evolved wake mode is then established through three-dimensional simulations. In fact it is found that at Reynolds numbers only marginally (~5%) above critical, the three-dimensional simulations indicate that the saturated state becomes time dependent, although at least initially, this does not result in a significant change to the mode structure. It is only at higher Reynolds numbers that the wake undergoes a transition to vortex shedding.An analysis of the three-dimensional transition indicates that it is unlikely to be due to a centrifugal instability despite the superficial similarity to the flow over a backward-facing step, for which the transition mechanism has been speculated to be centrifugal. However, the attached elongated recirculation region and distribution of the spanwise perturbation vorticity field, and the similarity of these features with those of the flow through a partially blocked channel, suggest the possibility that the mechanism is elliptic in nature. Some analysis which supports this conjecture is undertaken.

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