Contact Problems Involving the Flow Past an Inflated Aerofoil

1982 ◽  
Vol 49 (2) ◽  
pp. 263-265 ◽  
Author(s):  
J.-M. Vanden-Broeck
Keyword(s):  
Potential Flow ◽  
Weber Number ◽  
Angle Of Attack ◽  
Contact Problems ◽  
Critical Value ◽  
Cavitation Number ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Trailing Edges ◽  
Steady Potential

Steady potential flow around a two-dimensional inflated airfoil is considered. The aerofoil consists of a flexible and inextensible membrane which is anchored at both leading and trailing edges. The flow and the aerofoil shape are determined as functions of the angle of attack α, the cavitation number γ, and the Weber number λ. When γ decreases to a critical value γ0 (α, λ), opposite sides of the membrane become tangent to each other at the trailing edge. For γ < γ0 the aerofoil is partially collapsed near the trailing edge. The length of the region of collapse increases as γ decreases and for γ = −∞, the aerofoil is completely collapsed. The shape of the aerofoil and the value of γ0 are determined analytically by a perturbation solution for λ small. Graphs of the results are presented.

Two-Dimensional Experimental Investigation on the Effects of a Fowler Flap Gap and Overlap Size on the Wake Flow Field

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
David Demel ◽  
Mohsen Ferchichi ◽  
William D. E. Allan ◽  
Marouen Dghim
Keyword(s):  
Experimental Investigation ◽  
Flow Field ◽  
Angle Of Attack ◽  
Wake Flow ◽  
Two Dimensional ◽  
Edge Region ◽  
Suction Surface ◽  
Trailing Edge ◽  
Piv Measurements ◽  
Image Velocimetry

This work details an experimental investigation on the effects of the variation of flap gap and overlap sizes on the flow field in the wake of a wing-section equipped with a trailing edge Fowler flap. The airfoil was based on the NACA 0014-1.10 40/1.051 profile, and the flap was deployed with 40 deg deflection angle. Two-dimensional (2D) particle image velocimetry (PIV) measurements of the flow field in the vicinity of the main wing trailing edge and the flap region were performed for the optimal flap gap and overlap, as well as for flap gap and overlap increases of 2% and 4% chord beyond optimal, at angles of attack of 0 deg, 10 deg, and 12 deg. For all the configurations investigated, the flow over the flap was found to be fully stalled. At zero angle of attack, increasing the flap gap size was found to have minor effects on the flow field but increased flap overlap resulted in misalignment between the main wing boundary layer (BL) flow and the slot flow that forced the flow in the trailing edge region of the main wing to separate. When the angle of attack was increased to near stall conditions (at angle of attack of 12 deg), increasing the flap gap was found to energize and improve the flow in the trailing edge region of the main wing, whereas increased flap overlap further promoted flow separation on the main wing suction surface possibly steering the wing into stall.

scholarly journals Two-Dimensional Supercavitating Plate Oscillating Under a Free Surface

1965 ◽  
Vol 9 (02) ◽  
pp. 40-55
Author(s):  
C. S. Song
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Region ◽  
Integral Form ◽  
Cavitation Number ◽  
Two Dimensional ◽  
First Order ◽  
Upper Half Plane ◽  
Order Quantities

The problem of a supercavitating flat plate at zero and nonzero cavitation numberoscillating under a free surface is analyzed by a linearized method using the accelerationpotential. The analysis is based on the concept of small velocity perturbations where in all second-order quantities are neglected. The flow is assumed two-dimensional, irrotational, incompressible, and gravitation-free. The potential-flow region is mapped on to an upper half-plane and the solution is expressed in an integral form using Cheng andRott's method. Special attention is given to the effect of approximate wake boundary conditions on the computed force and moment. It was estimated that the effect is of secondorder when the cavitation number is a first-order small quantity.

Transonic flow around the leading edge of a thin airfoil with a parabolic nose

1993 ◽  
Vol 248 ◽  
pp. 1-26 ◽  
Author(s):  
Z. Rusak
Keyword(s):  
Pressure Distribution ◽  
Stagnation Point ◽  
Asymptotic Expansions ◽  
Potential Flow ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Outer Expansion ◽  
Inner Region

Transonic potential flow around the leading edge of a thin two-dimensional general airfoil with a parabolic nose is analysed. Asymptotic expansions of the velocity potential function are constructed at a fixed transonic similarity parameter (K) in terms of the thickness ratio of the airfoil in an outer region around the airfoil and in an inner region near the nose. These expansions are matched asymptotically. The outer expansion consists of the transonic small-disturbance theory and it second-order problem, where the leading-edge singularity appears. The inner expansion accounts for the flow around the nose, where a stagnation point exists. Analytical expressions are given for the first terms of the inner and outer asymptotic expansions. A boundary value problem is formulated in the inner region for the solution of a uniform sonic flow about an infinite two-dimensional parabola at zero angle of attack, with a symmetric far-field approximation, and with no circulation around it. The numerical solution of the flow in the inner region results in the symmetric pressure distribution on the parabolic nose. Using the outer small-disturbance solution and the nose solution a uniformly valid pressure distribution on the entire airfoil surface can be derived. In the leading terms, the flow around the nose is symmetric and the stagnation point is located at the leading edge for every transonic Mach number of the oncoming flow and shape and small angle of attack of the airfoil. The pressure distribution on the upper and lower surfaces of the airfoil is symmetric near the edge point, and asymmetric deviations increase and become significant only when the distance from the leading edge of the airfoil increases beyond the inner region. Good agreement is found in the leading-edge region between the present solution and numerical solutions of the full potential-flow equations and the Euler equations.

scholarly journals Flow Past a Flat Plate With a Vortex/Sink Combination

1996 ◽  
Vol 63 (2) ◽  
pp. 543-550 ◽  
Author(s):  
N. J. Mourtos ◽  
M. Brooks
Keyword(s):  
Flat Plate ◽  
Current Model ◽  
Angle Of Attack ◽  
Separated Flow ◽  
Leading Edge ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Attached Flow

This paper presents a potential flow model for the leading edge vortex over a two-dimensional flat plate at an angle of attack. The paper is an extension of a model by Saffman and Sheffield (1977). A sink has been added in this model in an effort to satisfy the Kutta condition at both the leading edge and the trailing edge of the plate. The introduction of the sink was inspired by the fact that most steady vortices in nature appear in combination with a flow feature which can be interpreted as a sink at their cores when the flow is analyzed in a two-dimensional observation plane. As in the Saffman and Sheffield model, the presence of a vortex results in increased lift; however, in the current model a unique vortex/sink position is found at each angle of attack. A comparison has also been made between the lift and the drag of this model and the corresponding results for two classical solutions of flow over a flat plate: (a) the fully attached flow with the Kutta condition satisfied at the trailing edge only and (b) the Helmholtz solution of fully separated flow.

On the roll-up of a trailing vortex sheet in the very near field

2003 ◽  
Vol 217 (5) ◽  
pp. 263-269 ◽  
Author(s):  
A L Heyes ◽  
S J Hubbard ◽  
A J Marquis ◽  
D A Smith
Keyword(s):  
Vortex Core ◽  
Near Field ◽  
Angle Of Attack ◽  
Point Vortex ◽  
Vortex Sheet ◽  
Measured Data ◽  
Tip Vortex ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Naca 0012

This paper addresses a discrepancy found between the rate of roll-up of a trailing vortex sheet calculated from point vortex simulations and that from measured data. Measurements of the wake behind a rectangular planform NACA 0012 section wing at 7.5° angle of attack show that some 50 per cent of the circulation in the wake is already present in the vortex core or “rolled-up region” at the trailing edge of the wing, and that there is no increase in the circulation contained within this region within one chord length downstream of the trailing edge. This conflicts with two-dimensional point vortex simulations of sheet roll-up which predict no initial core at the trailing edge and a constantly increasing value of circulation in the vortex in the downstream direction. A modification to include the effect of the tip vortex in the simulation is proposed and is shown to represent the behaviour of the vortex sheet in the very near field accurately.

scholarly journals Computational fluid dynamics investigation into flow behavior and acoustic mechanisms at the trailing edge of an airfoil

2018 ◽  
Vol 49 (1) ◽  
pp. 20-31 ◽  
Author(s):  
Beren R Jackson ◽  
Sam M Dakka
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Power Level ◽  
Angle Of Attack ◽  
Acoustic Power ◽  
Dynamics Simulation ◽  
Turbulent Intensity ◽  
Two Dimensional ◽  
Computational Fluid Dynamics Simulation ◽  
Trailing Edge

Airfoil self-noise or trailing edge noise and shear noise were investigated computationally for a NACA 0012 airfoil section, focusing on noise mechanisms at the trailing edge to identify and understand sources of noise production using ANSYS Fluent. A two-dimensional computational fluid dynamics simulation has been performed for 0°, 8°, and 16° airfoil angles of attack capturing surface pressure contours, contours of turbulent intensity, contours of surface acoustic power level, vorticity magnitude levels across the airfoil profile, and x- and y-directional self-noise and shear noise sources across the airfoil profile. The results indicate that pressure gradients at the upper surface do increase as the angle of attack increases, which is a measure of vortices near the surface of the trailing edge associated with turbulence cease as the boundary layer begins to separate. Comparison of the turbulent intensity contours with surface acoustic power level contours demonstrated direct correlation between the energy contributed by turbulent structures (i.e. vortices) and the level of noise measured at the surface and within the boundary layer of the airfoil. As angle of attack is increased, both x and y sources have the same trends; however, y sources (perpendicular to the free-stream flow) appear to have a bigger impact as angle of attack is increased. Furthermore, as the angle of attack increased, shear noise contributes less and less energy further downstream of the airfoil and becomes dominated by noise energy from vortical structures within turbulence. The two-dimensional computational fluid dynamics simulation revealed that pressure, turbulent intensity, and surface acoustic power contours further corroborated the previously tested noise observations phenomena at the trailing edge of the airfoil.

scholarly journals Potential flow of a second-order fluid over a tri-axial ellipsoid

2005 ◽  
Vol 2005 (4) ◽  
pp. 341-364 ◽  
Author(s):  
F. Viana ◽  
T. Funada ◽  
D. D. Joseph ◽  
N. Tashiro ◽  
Y. Sonoda
Keyword(s):  
Potential Flow ◽  
Flow Fields ◽  
Second Order ◽  
Stress Fields ◽  
Harmonic Potential ◽  
Gas Bubble ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Principal Axes

The problem of potential flow of a second-order fluid around an ellipsoid is solved, and the flow and stress fields are computed. The flow fields are determined by the harmonic potential but the stress fields depend on viscosity and the parameters of the second-order fluid. The stress fields on the surface of a tri-axial ellipsoid depend strongly on the ratios of principal axes and are such as to suggest the formation of gas bubble with a round flat nose and two-dimensional cusped trailing edge. A thin flat trailing edge gives rise to a large stress which makes the thin trailing edge thinner.

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