Viscous tails in Hele-Shaw flow

1971 ◽  
Vol 46 (3) ◽  
pp. 569-576
Author(s):  
C. J. Wood
Keyword(s):  
Reynolds Number ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Quantitative Discrepancy ◽  
Edge Flow ◽  
Hele Shaw Cell

An experiment has been performed, using pulsed dye injection on an aerofoil in a Hele-Shaw cell. The purpose was to observe the form of the trailing-edge flow when the Reynolds number was high enough to permit separation and the initiation of a Kutta condition. The experiment provides a successful confirmation of the existence of a ‘viscous tail’ as predicted by Buckmaster (1970) although there is an unexplained quantitative discrepancy.

Two-dimensional impervious sails: experimental results compared with theory

1984 ◽  
Vol 144 ◽  
pp. 445-462 ◽  
Author(s):  
B. G. Newman ◽  
H. T. Low
Keyword(s):  
Reynolds Number ◽  
Dynamic Instability ◽  
Two Dimensional ◽  
Poor Agreement ◽  
Trailing Edge ◽  
Small Incidence ◽  
Visualization Experiments ◽  
Drag Ratio ◽  
Lift To Drag Ratio ◽  
Edge Flow

Experiments have been made on quasi two-dimensional sails of small camber and at small incidence. Four excess-length ratios have been tested at a Reynolds number of 1.2 x 105. The results for lift, tension, centre of lift, maximum camber and its position, and leading- and trailing-edge membrane angles have been compared with existing inviscid theories and show poor agreement in general. This is attributed to leading- and trailing-edge flow separations as indicated by supplementary flow-visualization experiments. The optimum incidences in particular are much greater than the theoretical value of 0°. Luffing occurs at slightly negative incidences and appears to be a dynamic instability. The highest lift-to-drag ratio obtained was 16.5 on a membrane with an excess-length ratio of 0.03.

Correlated unsteady and steady laminar trailing-edge flows

1981 ◽  
Vol 108 ◽  
pp. 171-183 ◽  
Author(s):  
S. N. Brown ◽  
H. K. Cheng
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Small Amplitude ◽  
Frequency Parameter ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Sinusoidal Oscillations ◽  
Steady Laminar ◽  
Uniform Stream

The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of small amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. It is shown that if the frequency parameter is of any order less than R¼ the viscous correction to the Kutta condition and hence to the lift and moment may be determined from the results for the steady case. Justification of this correlation requires discussion of the flow in an additional region not encountered in previous studies.

On the viscous flow about the trailing edge of a rapidly oscillating plate

1975 ◽  
Vol 67 (4) ◽  
pp. 743-761 ◽  
Author(s):  
S. N. Brown ◽  
P. G. Daniels
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Frequency ◽  
Analytic Solutions ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Sinusoidal Oscillations ◽  
Low Amplitude ◽  
Oscillating Plate ◽  
Uniform Stream

The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of high frequency and low amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. The aerofoil is replaced by a flat plate on the assumption that leadingedge stall does not take place. It is shown that, for oscillations of non-dimensional frequency $O(R^{\frac{1}{4}})$ and amplitude $O(R^{\frac{9}{16}})$, a rational description of the flow at the trailing edge is based on a subdivision of the boundary layer above the plate into five distinct regions. Asymptotic analytic solutions are found in four of these, whilst in the fifth a linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

The Effect of Pulsed Blowing on the Boundary Layer of a Highly Loaded Low Pressure Turbine Blade

2013 ◽  
Author(s):  
Marion Mack ◽  
Roland Brachmanski ◽  
Reinhard Niehuis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Trailing Edge ◽  
Low Pressure Turbine ◽  
Wide Range ◽  
Highly Loaded

The performance of the low pressure turbine (LPT) can vary appreciably, because this component operates under a wide range of Reynolds numbers. At higher Reynolds numbers, mid and aft loaded profiles have the advantage that transition of suction side boundary layer happens further downstream than at front loaded profiles, resulting in lower profile loss. At lower Reynolds numbers, aft loading of the blade can mean that if a suction side separation exists, it may remain open up to the trailing edge. This is especially the case when blade lift is increased via increased pitch to chord ratio. There is a trend in research towards exploring the effect of coupling boundary layer control with highly loaded turbine blades, in order to maximize performance over the full relevant Reynolds number range. In an earlier work, pulsed blowing with fluidic oscillators was shown to be effective in reducing the extent of the separated flow region and to significantly decrease the profile losses caused by separation over a wide range of Reynolds numbers. These experiments were carried out in the High-Speed Cascade Wind Tunnel of the German Federal Armed Forces University Munich, Germany, which allows to capture the effects of pulsed blowing at engine relevant conditions. The assumed control mechanism was the triggering of boundary layer transition by excitation of the Tollmien-Schlichting waves. The current work aims to gain further insight into the effects of pulsed blowing. It investigates the effect of a highly efficient configuration of pulsed blowing at a frequency of 9.5 kHz on the boundary layer at a Reynolds number of 70000 and exit Mach number of 0.6. The boundary layer profiles were measured at five positions between peak Mach number and the trailing edge with hot wire anemometry and pneumatic probes. Experiments were conducted with and without actuation under steady as well as periodically unsteady inflow conditions. The results show the development of the boundary layer and its interaction with incoming wakes. It is shown that pulsed blowing accelerates transition over the separation bubble and drastically reduces the boundary layer thickness.

Effect of riblets on the drag of a body of revolution with trailing-edge flow separation

1998 ◽  
Vol 33 (1) ◽  
pp. 135-139
Author(s):  
S. F. Konovalov ◽  
Yu. A. Lashkov ◽  
V. V. Mikhailov
Keyword(s):  
Flow Separation ◽  
Body Of Revolution ◽  
Trailing Edge ◽  
Edge Flow

Computational Study of the Risø-B1-18 Airfoil with a Hinged Flap Providing Variable Trailing Edge Geometry

2005 ◽  
Vol 29 (2) ◽  
pp. 89-113 ◽  
Author(s):  
Niels Troldborg
Keyword(s):  
Reynolds Number ◽  
Unsteady Flow ◽  
Computational Study ◽  
Turbine Blades ◽  
Aerodynamic Characteristics ◽  
Flow Conditions ◽  
Wind Turbine Blades ◽  
Trailing Edge ◽  
Edge Geometry ◽  
Fully Developed Turbulent Flow

A comprehensive computational study, in both steady and unsteady flow conditions, has been carried out to investigate the aerodynamic characteristics of the Risø-B1-18 airfoil equipped with variable trailing edge geometry as produced by a hinged flap. The function of such flaps should be to decrease fatigue-inducing oscillations on the blades. The computations were conducted using a 2D incompressible RANS solver with a k-w turbulence model under the assumption of a fully developed turbulent flow. The investigations were conducted at a Reynolds number of Re = 1.6 · 106. Calculations conducted on the baseline airfoil showed excellent agreement with measurements on the same airfoil with the same specified conditions. Furthermore, a more widespread comparison with an advanced potential theory code is presented. The influence of various key parameters, such as flap shape, flap size and oscillating frequencies, was investigated so that an optimum design can be suggested for application with wind turbine blades. It is concluded that a moderately curved flap with flap chord to airfoil curve ratio between 0.05 and 0.10 would be an optimum choice.

scholarly journals Oscillating foils of high propulsive efficiency

1998 ◽  
Vol 360 ◽  
pp. 41-72 ◽  
Author(s):  
J. M. ANDERSON ◽  
K. STREITLIEN ◽  
D. S. BARRETT ◽  
M. S. TRIANTAFYLLOU
Keyword(s):  
Reynolds Number ◽  
High Efficiency ◽  
Leading Edge ◽  
Half Cycle ◽  
Trailing Edge ◽  
Propulsive Efficiency ◽  
Principal Characteristics ◽  
Theoretical Predictions ◽  
Power Measurements ◽  
Oscillating Foils

Thrust-producing harmonically oscillating foils are studied through force and power measurements, as well as visualization data, to classify the principal characteristics of the flow around and in the wake of the foil. Visualization data are obtained using digital particle image velocimetry at Reynolds number 1100, and force and power data are measured at Reynolds number 40 000. The experimental results are compared with theoretical predictions of linear and nonlinear inviscid theory and it is found that agreement between theory and experiment is good over a certain parametric range, when the wake consists of an array of alternating vortices and either very weak or no leading-edge vortices form. High propulsive efficiency, as high as 87%, is measured experimentally under conditions of optimal wake formation. Visualization results elucidate the basic mechanisms involved and show that conditions of high efficiency are associated with the formation on alternating sides of the foil of a moderately strong leading-edge vortex per half-cycle, which is convected downstream and interacts with trailing-edge vorticity, resulting eventually in the formation of a reverse Kármán street. The phase angle between transverse oscillation and angular motion is the critical parameter affecting the interaction of leading-edge and trailing-edge vorticity, as well as the efficiency of propulsion.

The Effect of Reynolds Number and Velocity Distribution on LP Turbine Cascade Performance

1986 ◽  
Author(s):  
D. J. Patterson ◽  
M. Hoeger
Keyword(s):  
Reynolds Number ◽  
Pressure Distribution ◽  
Guide Vane ◽  
Flow Visualisation ◽  
Suction Surface ◽  
Trailing Edge ◽  
Wide Range ◽  
Oil Flow ◽  
Low Reynolds ◽  
Lp Turbine

Because of the laminar boundary-layer’s inability to withstand moderate adverse pressure gradients without separating, profile losses in LP turbines operating at low Reynolds numbers can be high. The choice of design pressure distribution for the blading is thus of great importance. Three sub-sonic LP turbine nozzle-guide-vane cascade profiles have been tested over a wide range of incidence, Mach number and Reynolds number. The three profiles are of low, medium and high deflection and, as such, display significantly different pressure distributions. The tests include detailed boundary-layer traverses, trailing-edge base-pressure monitoring and oil-flow visualisation. It is shown that the loss variation with Reynolds number is a function of pressure distribution and that the trailing-edge loss component is dominant at low Reynolds number. The importance of achieving late flow transition — rather than separation — in the suction-surface trailing-edge region is stressed. The paper concludes by remarking on the advantages and practical implications of each loading design.

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