Circular-arc Aerofoil Research Articles

Numerical Investigation of Viscous Laminar Supersonic Flow Past an Asymmetric Biconvex Circular-Arc Aerofoil

A numerical investigation of two-dimensional unsteady, viscous and laminar compressible flow past an asymmetric biconvex circular-arc aerofoil in supersonic regime is carried out. The focus of the present work is to investigate the effects of variation of Mach number, at two different angles of attack, on the flow and force characteristics on NACA 2S-(50)(04)-(50)(20) aerofoil. The value of Reynolds number is taken as 5x105. The computations are carried out at Mach numbers of 1.25, 1.5 and 2.0 at an angle of attack of α=0° and α=10°. It is found that the aerofoil works well in the supersonic flow and, unlike the conventional symmetric biconvex aerofoil, generates finite lift at α=0° due to stronger shock waves at the lower surface. Moreover, the L/D ratio at α=10° is always found to be more than 2.5.

Numerical investigation of the compressible flow past an aerofoil

Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach numberM∞= 0.76 and a Reynolds numberRe= 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock wave characteristics, three typical flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.

Wing in Ground Effect Characteristics of Circular-Arc Aerofoils for Aero-Train

In this paper, the aerodynamic characteristics of a symmetrical ground effect wing are measured in a low turbulence wind tunnel. To change the directions of an Aero-Train in practical use, it must shuttle back and forth. Circular-arc aerofoil seems to be suitable for the Aero-train, while it can run back and forth by changing only the attack angle of wings. Lift and drag characteristics of NACA 6412-modified, circular-arc aerofoils with thickness ratio 9% and 12% were clarified by the 6-component balance. Suction and moving-belt system were used to simulate the ground. Characteristics of two-dimensional aerofoils and three-dimensional wings were compared, and lift-to-drag rations of three aerofoils were compared. Separations on the upper surface of the circular-arc aerofoils were visualized by tuft and oil spot method. It was found that increase of drag in ground effect condition was caused by increase of the induced drag and by enlargement of the separation area on upper surface of circular-arc aerofoils. A circular-arc aerofoil with thickness ratio 9% at the angle of attack 2 degrees had enough lift-to-drag ratio for Aero-Train.

Measurement of Aerofoil Characteristics by Method of Towing Model.

Recently a new transport system Aerotrain has been proposed, and test using the first and second stage models are conducted in a 3 km guide way of old MAGLEV test facility in Miyazaki prefecture. Aerotrain has wings, and flies close to the ground of an open channel to take advantage of the ground effect. Characteristics of wing in ground effect (WIG) have been investigated using conventional wind tunnels. But this type of experiment cannot estimate the ground effect correctly because of the existence of boundary layer developed between bottom of the wings and the ground surface. Therefore, it is necessary to experiment using a towing wind tunnel to clarify characteristics of wing in the real ground effect. The aerodynamic charactersistis of two kinds of aerofoil sections: NAGA 4412 and circular arc aerofoil were clarified by the experriment towing the aerofoils in 3 km guide way of MAGLEV test facility. In addition, we examined problems to utilize the guide way of old MAGLEV as a towing wind tunnel.

Vibration—Analysis of circular-arc aerofoil shaped plates

Circular-arc aerofoil flat plates are analysed for their vibrational characteristics using the finite element approach. The effect of variation in the lune angles of the aerofoil plates, on natural frequencies and mode shapes is investigated. Two types of plate bending finite elements are used in the investigation; one is the conventional nine degree of freedom triangular element and the other is a modified triangular element with one edge curved. The later element has been specially developed and used near the curved boundaries of the plate, whereas the former straight edged element is used in the interior. The results of the finite element analysis are verified through experimental investigations.

A uniformly asymptotic solution for incompressible flow past thin sharp-edged aerofoils at zero incidence

Expansions obtained from classical subsonic thin-aerofoil theory break down in the neighbourhood of the aerofoil edges. At sharp edges the method of matched asymptotic expansions fails to remedy this. Here this failure is explained, and in the case of incompressible flow past a symmetric aerofoil at zero incidence it is shown that by proper choice of the dependent variable an expansion may be obtained which is uniformly asymptotic. Finally, the case of a circular-arc aerofoil is considered in more detail.

The Effect of Jet Entrainment on Lift and Moment for a Thin Aerofoil with Blowing

SummaryJet flap theory for thin aerofoils has been extended to include the effect of jet entrainment on the external flow when the jet is blown over the upper surface of the aerofoil. The effective camber of the aerofoil is increased by the sink effect due to entrainment and the increase of lift at zero incidence is proportional to the square root of the jet momentum coefficient. Formulae and charts are presented to facilitate the determination of the increments of lift and pitching moment due to this effect. The theory is shown to be in first-order agreement with the exact solution for a circular-arc aerofoil of small camber with distributed sinks on the upper surface.The new theory is compared with four old sets and one new set of experimental data. It greatly improves the accuracy of prediction for cases where the incidence and flap angle are small. The new theory substantiates the usefulness of a small flap in applications of the jet flap principle.

Effect of Shock Boundary Layer Interaction on Aerofoil Pressure Distributions at Transonic Speeds

SummaryA method of improving pressure distributions predicted by inviscid theory over two-dimensional aerofoils at transonic speeds taking into account shock-wave turbulent boundary layer interaction as obtained in the case of the flat plate is described.The method was applied to a non-lifting circular arc aerofoil of eight per cent relative thickness. The shock wave location, pressure distribution and drag coefficient were calculated and compared with experimental and inviscid theoretical results.It has been found that the method gives results which are consistent with experimental results in various aspects.

Erratum: “Theoretical Prediction of the Pressure Distribution on a Non-lifting, Thin Symmetrical Aerofoil at Various Transonic Speeds”

Theoretical pressure distributions on a non-lifting, circular-arc aerofoil at various transonic speeds are obtained by application of a new method recently published by the author. The method consists essentially of a refinement of the linearized transonic flow theory in which the nonlinear characteristics of the fundamental equation are taken into account. The results reveal most of principal phenomena observed in experimental studies throughout the whole Mach number range.

A Refinement of the Linearized Transonic Flow Theory

A new method is proposed to calculate the velocity and pressure distributions around a thin symmetrical aerofoil or a slender body of revolution flying at transonic speed. It is essentially a refinement of the linearized transonic flow theory due to Oswatitsch and Maeder, such that a correction term is introduced to take account of the nonlinear character of the transonic flow. As examples of application, a symmetrical circular-arc aerofoil and a circular-arc body of revolution in the sonic flow are dealt with, and the results are found to be in good agreement with experiments, except for the rear portion in the latter case.

High Subsonic Flow with Normal Shock Wave at Nearly Critical Mach Number

High subsonic flow past a biconvex circular arc aerofoil with a pair of normal shock waves at nearly critical Mach number is discussed by a very simple approximation procedure. The shock waves are assumed to be the normal shock waves which start from the surface of the aerofoil and stand perpendicularly to the direction of the uniform flow. The locations of the sonic line and the shock waves are treated as unknown parameters to be determined in the course of analysis. The results show that these parameters have real physical meaning only when the Mach number exceeds the usual critical Mach number calculated by means of Prandtl-Glauert approximation. The results also suggest that the curvature of the profile must change discontinuously at its intersection with the shock wave. This fact is also confirmed by applying Lin's exact consideration. Thus, it is concluded that there can exist no high subsonic flow of ideal fluid with normal shock waves starting form the surface past a profile having continuous curv...

Note on the Lift acting On a Circular-arc Aerofoil in a Stream bounded by a Plane Wall

Being a continuation of the preceding paper, Green's new method, somewhat extended by the present writer, is applied to the evaluation of the lift acting on a circular-arc aerofoil in the presence of an infinite plane rigid wall. The expression for the lift is obtained in the form of a power series. By performing detailed numerical calculations, a discussion is made on the manner in which the ground-effect on the lift of an aerofoil is modified by its camber. It is thus found that in accordance with the prediction made by Tomotika et al. , as the arc-aerofoil of sufficiently small camber approaches the wall, the lift first decreases and then tends to increase to values which are greater than the corresponding values for the same arc-aerofoil in an unlimited stream, especially when the angle of attack takes small values as used in practice. It is also found that the rate of increase in the lift becomes smaller as the camber of the aerofoil increases.

Further Studies on the Lift and Moment of a Circular Arc Aerofoil which touches the Ground with its Trailing Edge

Further Studies on the Lift and Moment of a Circular Arc Aerofoil which touches the Ground with its Trailing Edge

The Forces Acting on a Circular arc Aerofoil in a Stream Bounded by a Plane Wall

The Forces Acting on a Circular arc Aerofoil in a Stream Bounded by a Plane Wall

Note on the Lift and Moment of a Circular Arc Aerofoil which touches the Ground with its Trailing Edge

Note on the Lift and Moment of a Circular Arc Aerofoil which touches the Ground with its Trailing Edge