Flow Transient Near the Leading Edge of a Flat Plate Moving Through a Viscous Fluid

1974 ◽  
Vol 41 (4) ◽  
pp. 919-924 ◽  
Author(s):  
R. B. Kinney ◽  
M. A. Paolino
Keyword(s):  
Free Stream ◽  
Infinite Plate ◽  
Leading Edge ◽  
Viscous Flows ◽  
Stream Velocity ◽  
Viscous Layer ◽  
Two Dimensional Flow ◽  
Essential Input ◽  
Vorticity Production ◽  
Vorticity Transport

An investigation is made of the unsteady flow in the leading-edge region of a semi-infinite plate impulsively started from rest. Based entirely on the vorticity concepts outlined by Lighthill, numerical results are obtained for the complete two-dimensional flow field by solving the single vorticity transport equation. An essential input to the calculations is the distribution of vorticity production at the plate surface. This is determined at each instant of time from the no-slip condition at the plate and represents a departure from conventional numerical analyses of viscous flows. Departing further from conventional approaches, the velocity field is computed from the law of induced velocities (Biot-Savart law) rather than the stream function. Because of vorticity diffusion well ahead of the plate, a significant disturbance propagates upstream, thereby destroying the uniformity of the approaching flow. Calculations are carried sufficiently forward in time for an approximately steady state to be reached at a distance downstream of the leading edge equal to the thickness of the viscous layer. As viewed by an observer moving with the plate, the flow transient exhibits a velocity overshoot relative to the apparent free-stream velocity. This effect was unexpected for a semi-infinite plate and represents a novel aspect of the flow not found in transient analyses based on the boundary-layer approximations.

On fluctuating flow of an elastico-viscous fluid past an infinite plate with variable suction

1969 ◽  
Vol 35 (3) ◽  
pp. 561-573 ◽  
Author(s):  
V. M. Soundalgekar ◽  
Pratap Puri
Keyword(s):  
Skin Friction ◽  
Free Stream ◽  
Infinite Plate ◽  
Porous Wall ◽  
Frequency Parameter ◽  
Stream Velocity ◽  
Suction Parameter ◽  
Suction Velocity ◽  
Elasticity Parameter ◽  
Two Dimensional Flow

An exact solution is obtained for the two-dimensional flow of an elastico-viscous (Walters fluid B’) incompressible fluid past an infinite porous wall under the following conditions: (i) the suction velocity normal to the plate oscillates in magnitude but not in direction about a non-zero mean; (ii) the free-stream velocity oscillates in time about a constant mean.The response of the skin-friction to the fluctuating stream and suction velocity is studied for variations in the suction parameter A, the elasticity parameter k and the frequency parameter μ. It is found that the back-flow at the wall is enhanced by k. For the same value of A, the amplitude of the skin-friction decreases with increasing k. Also an increase in k and μ leads to a decrease in the phase of the skin-friction. For moderately large A and k, the phase of the skin-friction may be completely negative.

scholarly journals Added mass of a circular cylinder oscillating in a free stream

2013 ◽  
Vol 469 (2156) ◽  
pp. 20130135 ◽  
Author(s):  
Efstathios Konstantinidis
Keyword(s):  
Circular Cylinder ◽  
Free Stream ◽  
Transverse Velocity ◽  
Inertial Force ◽  
Added Mass ◽  
Stream Velocity ◽  
Virtual Experiment ◽  
Classical Formulation ◽  
Fundamental Understanding ◽  
Two Dimensional Flow

The fundamental understanding of the added mass phenomenon associated with the motion of a solid body relative to a fluid is revisited. This paper focuses on the two-dimensional flow around a circular cylinder oscillating transversely in a free stream. A virtual experiment reveals that the classical approach to this problem leads to a paradox. The inertial force is derived afresh based on analysis of the motion in a frame of reference attached to the cylinder centroid, which overcomes the paradox in the classical formulation. It is shown that the inertial force depends not only on the acceleration of the cylinder per se , but also on the relative motion between body and fluid embodied in a parameter called alpha, α , which represents the ratio of the maximum transverse velocity of the cylinder to the free-stream velocity; the induced inertial force is directionally varying and non-harmonic in time depended on the alpha parameter. It is further shown that the component of the inertial force in the transverse direction is negligible for α <0.1, increases quadratically for α <0.5, and tends asymptotically to the classical result as , i.e. in still fluid.

scholarly journals Numerical Analysis of Effect of Leading-Edge Rotating Cylinder on NACA0021 Symmetric Airfoil

2019 ◽  
Vol 4 (7) ◽  
pp. 11-17
Author(s):  
Md. Abdus Salam ◽  
Vikram Deshpande ◽  
Nafiz Ahmed Khan ◽  
M. A. Taher Ali
Keyword(s):  
Free Stream ◽  
Numerical Study ◽  
Tangential Velocity ◽  
Leading Edge ◽  
Rotating Cylinder ◽  
Aerodynamic Performance ◽  
Stream Velocity ◽  
Surface Boundary ◽  
Lower Velocity ◽  
Numerical Studies

The moving surface boundary control (MSBC) has been a Centre stage study for last 2-3 decades. The preliminary aim of the study was to ascertain whether the concept can improve the airfoil characteristics. Number of experimental and numerical studies pointed out that the MSBC can superiorly enhance the airfoil performance albeit for higher velocity ratios (i.e. cylinder tangential velocity to free stream velocity). Although abundant research has been undertaken in this area on different airfoil performances but no attempt was seen to study effect of MSBC on NACA0021 airfoil for and also effects of lower velocity ratios. Thus, present paper focusses on numerical study of modified NACA 0021 airfoil with leading edge rotating cylinder for velocity ratios (i.e.) between 1 to 1.78 at different angles of attack. The numerical study indicates that the modified airfoil possess better aerodynamic performance than the base airfoil even at lower velocity ratios (i.e. for velocity ratios 0.356 and beyond). The study also focusses on reason for improvement in aerodynamic performance by close look at various parameters.

Heat Transfer and Effectiveness for a Turbulent Boundary Layer With Tangential Fluid Injection

1960 ◽  
Vol 82 (4) ◽  
pp. 303-312 ◽  
Author(s):  
R. A. Seban
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Free Stream ◽  
Cooling System ◽  
Leading Edge ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
The Heat Transfer Coefficient

Experimental results are presented for the effectiveness and for the heat-transfer coefficient for a film cooling system in which air was used both for the film and for the free-stream fluids. Injection occurred at a single tangential slot near the leading edge of the plate and the slot size was varied. All flows were turbulent and the injection velocities covered a range from much less to much greater than the free-stream velocity. Correlations are realized for both the effectiveness and for the heat-transfer coefficient and, as in the past experience with such systems, separate specifications are needed for injection velocities greater and less than the free-stream velocity.

Linear stability of a gas boundary layer flowing past a thin liquid film over a flat plate

2001 ◽  
Vol 436 ◽  
pp. 321-352 ◽  
Author(s):  
NIKOLAOS A. PELEKASIS ◽  
JOHN A. TSAMOPOULOS
Keyword(s):  
Boundary Layer ◽  
Liquid Film ◽  
Flat Plate ◽  
Free Stream ◽  
Leading Edge ◽  
Critical Value ◽  
Stream Velocity ◽  
Absolute Instability ◽  
Interfacial Waves ◽  
The Family

The flow of a gas stream past a flat plate under the influence of rainfall is investigated. As raindrops sediment on the flat plate, they coalesce to form a water film that flows under the action of shear from the surrounding gas stream. In the limit of (a) large Reynolds number, Re, in the gas phase, (b) small rainfall rate, r˙, compared to the free-stream velocity, U∞, and (c) small film thickness compared to the thickness of the boundary layer that surrounds it, a similarity solution is obtained that predicts growth of the liquid film like x3/4; x denotes dimensionless distance from the leading edge. The flow in the gas stream closely resembles the Blasius solution, whereas viscous dissipation dominates inside the film. Local linear stability analysis is performed, assuming nearly parallel base flow in the two streams, and operating in the triple-deck regime. Two distinct families of eigenvalues are identified, one corresponding to the well-known Tollmien–Schlichting (TS) waves that originate in the gas stream, and the other corresponding to an interfacial instability. It is shown that, for the air–water system, the TS waves are convectively unstable whereas the interfacial waves exhibit a pocket of absolute instability, at the streamwise location of the applied disturbance. Moreover, it is found that as the inverse Weber number (We−1) increases, indicating the increasing effect of surface tension compared to inertia, the pocket of absolute instability is translated towards larger distances from the leading edge and the growth rate of unstable waves decreases, until a critical value is reached, We−1 ≈ We−1c, beyond which the family of interfacial waves becomes convectively unstable. Increasing the inverse Froude number (Fr−1), indicating the increasing effect of gravity compared to inertia, results in the pocket of absolute instability shrinking until a critical value is reached, Fr−1 ≈ Fr−1c, beyond which the family of interfacial waves becomes convectively unstable. As We−1 and Fr−1 are further increased, interfacial waves are eventually stabilized, as expected. In this context, increasing the rainfall rate or the free-stream velocity results in extending the region of absolute instability over most of the airfoil surface. Owing to this behaviour it is conjectured that a global mode that interacts with the boundary layer may arise at the interface and, eventually, lead to three-dimensional waves (rivulets), or, under extreme conditions, even premature separation.

CFD Study of Effects of Boundary Layer Suction on Transonic SC(2)-0714 Airfoil Performance

2017 ◽  
Author(s):  
Ruslan Khamedov ◽  
Ruslan Baitlessov ◽  
Luis Rojas-Solórzano
Keyword(s):  
Boundary Layer ◽  
Shock Waves ◽  
Isotropic Turbulence ◽  
Free Stream ◽  
Computational Study ◽  
Leading Edge ◽  
Design Stage ◽  
Stream Velocity ◽  
Local Boundary ◽  
Boundary Layer Suction

The complete understanding of the aerodynamics of wings and blades under transonic conditions represents a substantial challenge in the design of modern airplanes and turbomachinery. Transonic flow over airfoils may result in appearance of shock waves, which lead to increase in drag if not properly considered during the design stage. Therefore, it is a major challenge to design transonic airfoils such that potential appearance of shock waves is foreseen and negative drag effects are minimized. This paper presents the computational study of the SC(2)-0714 airfoil, focusing on its aerodynamics characteristics at Reynolds number of 35 × 106 and angle of attack of 2 and 10 degrees which are the most common operational conditions of transonic wings using this airfoil. The study was undertaken at free-stream Mach 0.72. The numerical simulation was conducted using the finite volume method on platform ANSYS CFX™ and solving the Reynolds-Averaged Navier-Stokes, mass conservation and energy equations. Mesh verification and model validation are presented. The latter is developed by using two different isotropic turbulence models: k-ω and Shear Stress Transport (SST) and the comparison of results with NASA experimental data to determine the best among the treated models. Thereafter, effects of local boundary-layer suction on shock wave strength and characteristics during transonic speed are analyzed for the two aforementioned angles of attack. Two suction slots were placed along the airfoil contour to determine their control effectiveness when compared to standard closed-contour airfoil. Suction slots were placed at the leading edge and in the middle of the upper camber of the airfoil with inflow in the normal direction to the surface. The slot length was 2.5 % of the chord with inflow velocity of 30%, 40% and 50% of free-stream velocity. Effects of suction slots were assessed on the wake region and by computing the resulting lift-to-drag ratio. Concluding remarks on the turbulence model and global aerodynamics performance of the airfoil are presented.

Experiments on Leading-Edge Induced Separated Shear Layer Under Various Imposed Pressure Gradients

2014 ◽  
Author(s):  
K. Anand ◽  
S. Sarkar ◽  
N. Thilakan
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Free Stream ◽  
Separation Bubble ◽  
Leading Edge ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Separated Shear Layer

The behaviour of a separated shear layer past a semi-circular leading edge flat plate, its transition and reattachment downstream to separation are investigated for different imposed pressure gradients. The experiments are carried out in a blowing tunnel for a Reynolds number of 2.44×105 (based on chord and free-stream velocity). The mean flow characteristics and the instantaneous vector field are documented using a two-component LDA and a planar PIV, whereas, surface pressures are measured with Electronically scanned pressure (ESP). The onset of separation occurs near the blend point for all values of β (flap angle deflection), however, a considerable shift is noticed in the point of reattachment. The dimensions of the separation bubble is highly susceptible to β and plays an important role in the activity of the outer shear layer. Instantaneous results from PIV show a significant unsteadiness in the shear layer at about 30% of the bubble length, which is further amplified in the second half of the bubble leading to three-dimensional motions. The reverse flow velocity is higher for a favourable pressure gradient (β = +30°) and is found to be 21% of the free stream velocity. The Reynolds number calculated based on ll (laminar shear layer length), falls in the range of 0.9×104 to 1.4×104. The numerical values concerning the criterion for separation and reattachment agree well with the available literature.

Estimation of Time Dependent Flow Properties in an Open Cavity

2005 ◽  
Author(s):  
Lawrence Ukeiley ◽  
Nathan Murray
Keyword(s):  
Velocity Field ◽  
Free Stream ◽  
Leading Edge ◽  
Open Cavity ◽  
Time Dependent ◽  
Stream Velocity ◽  
Estimation Technique ◽  
Flow Features ◽  
Dependent Flow ◽  
Low Dimensional

Experiments have been performed to measure the velocity field and surface pressure synchronously for flow over an open cavity. Specifically, an l/d = 6 full span cavity with a Mach 0.6 free stream flow and a turbulent boundary layer at the cavities leading edge was studied. The study focuses on using these measurements in a mean-square estimation technique to study the time dependence of a low-dimensional formulation of the velocity field. Utilizing select modes from the Proper Orthogonal Decomposition in the estimation technique, flow features associated with select Rossiter modes were reconstructed. The time dependent estimated flow field demonstrates how the shear layer structures and free stream velocity interact with the aft wall of the cavity to form the source of the intense areoacoustic environment known to exist in cavity flows.

Unsteady boundary-layer transition in low-pressure turbines

2011 ◽  
Vol 681 ◽  
pp. 370-410 ◽  
Author(s):  
JOHN D. COULL ◽  
HOWARD P. HODSON
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Separation Bubble ◽  
Leading Edge ◽  
Transition Process ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Free Stream Turbulence

This paper examines the transition process in a boundary layer similar to that present over the suction surfaces of aero-engine low-pressure (LP) turbine blades. This transition process is of significant practical interest since the behaviour of this boundary layer largely determines the overall efficiency of the LP turbine. Modern ‘high-lift’ blade designs typically feature a closed laminar separation bubble on the aft portion of the suction surface. The size of this bubble and hence the inefficiency it generates is controlled by the transition between laminar and turbulent flow in the boundary layer and separated shear layer. The transition process is complicated by the inherent unsteadiness of the multi-stage machine: the wakes shed by one blade row convect through the downstream blade passages, periodically disturbing the boundary layers. As a consequence, the transition to turbulence is multi-modal by nature, being promoted by periodic and turbulent fluctuations in the free stream and the inherent instabilities of the boundary layer. Despite many studies examining the flow behaviour, the detailed physics of the unsteady transition phenomena are not yet fully understood. The boundary-layer transition process has been studied experimentally on a flat plate. The opposing test-section wall was curved to impose a streamwise pressure distribution typical of modern high-lift LP turbines over the flat plate. The presence of an upstream blade row has been simulated by a set of moving bars, which shed wakes across the test section inlet. Further upstream, a grid has been installed to elevate the free-stream turbulence to a level believed to be representative of multi-stage LP turbines. Extensive particle imaging velocimetry (PIV) measurements have been performed on the flat-plate boundary layer to examine the flow behaviour. In the absence of the incoming bar wakes, the grid-generated free-stream turbulence induces relatively weak Klebanoff streaks in the boundary layer which are evident as streamwise streaks of low-velocity fluid. Transition is promoted by the streaks and by the inherent inflectional (Kelvin–Helmholtz (KH)) instability of the separation bubble. In unsteady flow, the incoming bar wakes generate stronger Klebanoff streaks as they pass over the leading edge, which convect downstream at a fraction of the free-stream velocity and spread in the streamwise direction. The region of amplified streaks convects in a similar manner to a classical turbulent spot: the leading and trailing edges travel at around 88% and 50% of the free-stream velocity, respectively. The strongest disturbances travel at around 70% of the free-stream velocity. The wakes induce a second type of disturbance as they pass over the separation bubble, in the form of short-span KH structures. Both the streaks and the KH structures contribute to the early wake-induced transition. The KH structures are similar to those observed in the simulation of separated flow transition with high free-stream turbulence by McAuliffe & Yaras (ASME J. Turbomach., vol. 132, no. 1, 2010, 011004), who observed that these structures originated from localised instabilities of the shear layer induced by Klebanoff streaks. In the current measurements, KH structures are frequently observed directly under the path of the wake. The wake-amplified Klebanoff streaks cannot affect the generation of these structures since they do not arrive at the bubble until later in the wake cycle. Rather, the KH structures arise from an interaction between the flow disturbances in the wake and localised instabilities in the shear layer, which are caused by the weak Klebanoff streaks induced by the grid turbulence. The breakdown of the KH structures to small-scale turbulence occurs a short time after the wake has passed over the bubble, and is largely driven by the arrival of the wake-amplified Klebanoff streaks from the leading edge. During this process, the re-attachment location moves rapidly upstream. The minimum length of the bubble occurs when the strongest wake-amplified Klebanoff streaks arrive from the leading edge; these structures travel at around 70% of the free-stream velocity. The bubble remains shorter than its steady-flow length until the trailing edge of the wake-amplified Klebanoff streaks, travelling at 50% of the free-stream velocity, convect past. After this time, the reattachment location moves aft on the surface as a consequence of a calmed flow region which follows behind the wake-induced turbulence.

On the flow past a quarter infinite plate using Oseen's equations

1960 ◽  
Vol 7 (1) ◽  
pp. 1-21 ◽  
Author(s):  
K. Stewartson ◽  
L. Howarth
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Potential Flow ◽  
Infinite Plate ◽  
Leading Edge ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Side Edge ◽  
Flow Past ◽  
Two Dimensional Flow

This paper is concerned with the determination, on the basis of Oseen's equations, of the flow past a quarter-plane with its leading edge normal to, and its side edge parallel to, a uniform incident stream. The solution is completed, except for a region in the vicinity of the corner, correct to orderv1/2for small kinematic viscosity ν.Away from the vicinity of the side edge the flow will approximate to the two-dimensional flow past a semi-infinite plate. This two-dimensional flow can be built up successively, if we like to think in terms of boundary conditions at the plate rather than at the edge of the boundary layer, from the potential flow associated with the uniform stream, a shear layer introduced to remove the tangential slip and a potential flow to remove the normal velocity at the plate associated with the shear layer. In the vicinity of the plate the three together give the usual boundary-layer solution.We start our solution from this same basis, namely, the potential flow associated with the uniform stream and the shear layer to restore the no-slip condition. As a first approximation, neglecting the effects of the edges, this will be the same as for the two-dimensional problem. The normal velocity introduced by this shear layer has to be compensated by a potential flow (see §4). This potential flow in turn (and here our problem diverges significantly from the two-dimensional problem) introduces tangential velocities with components parallel to both leading and side edges which require the introduction of a further shear layer. Over the main body of the plate this secondary shear layer is of a conventional form (§5) but requires special examination near the edges. In §6 it is shown how Carrier & Lewis's (1949) solution can be modified to give the flow near the leading edge away from the tip and in §7, the core of the paper, the flow near the side edge is determined.In the vicinity of the side edge the extra potential flow has no component in the direction of that edge and so the solution given by Howarth (1950) for the corresponding unsteady problem is applicable. What emerges from the present calculations, however, is that Howarth's application of Rayleigh's analogy to give the excess skin friction is seriously incomplete. For, whilst this argument gives correctly the local increase of order ν in skin friction in the immediate vicinity of the side edge, it omits the widespread effects of the secondary shear layer. These are found to be of the same order in ν as the local effects.The cross-flow in the side edge region has features of special interest. Its determination depends on a knowledge of the potential flow associated with the primary shear layer and so it depends, for instance, on the shape of the leading edge and is not, as appears to have been assumed up to now, determined completely by local conditions. This is further exemplified by the fact that it cannot be expressed in terms of what would be regarded as the natural boundary-layer variables but involves quite separately the distance from the leading edge.

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