Wall Interference Research Articles

Some Remarks on Glauert's General Interference Theorem

SummaryAfter a retrospective discussion of Glauert's theorem concerning the wall interference on a small lifting aerofoil in a wind tunnel with mixed boundaries, a simple proof of the theorem is given for a tunnel having one rigid and one free boundary. It is shown that the theorem does not necessarily hold when there are two rigid walls and two free boundaries.

An Anomaly in the Theory of Tunnel-Wall Interference on a Lifting Wing

SummaryThere appear in the literature some discrepancies in the various mathematical expressions for the upwash constituting the wall interference on a small lifting wing placed symmetrically in a rectangular tunnel with closed side-walls and open floor and roof. The representation of the interference field as that of a doubly infinite array of image doublets is shown to lead to divergence. An independent calculation by relaxation confirms the correctness of an analytical solution by expansion in Fourier series. The discrepancies are found to arise from incomplete flow conditions at the open boundaries, and it is shown in this paper how the various theories are reconciled.

Viscosity and Boundary Effects in the Dynamic Behavior of Hydraulic Systems

The use of hydraulic mechanisms in low-energy transfer and information-transmittal devices requires a working understanding of dynamic hydraulic behavior. In this paper the effects of fluid viscosity and wall interference on wave motion in a simple hydraulic device are considered. It is shown that for the applications considered these phenomena may be treated by boundary-layer methods. Calculations are carried out to show their effect on piston displacement, and these effects are compared with the behavior when viscosity is not taken into account.

The aerodynamic forces on an aerofoil in non-uniform unsteady motion in a closed tunnel

The two-dimensional unsteady motion of an aerofoil, situated midway between parallel walls, and moving through an inviscid, incompressible fluid, is investigated. A completely general upwash distribution is taken, and expressions are obtained for the pressure on the aerofoil surface and the lift and moment about the mid-chord point. By a conformal transformation involving Jacobian elliptic functions the physical plane is mapped into a rectangle, and the theory is based on a solution of Laplace’s equation satisfying certain given boundary conditions on this rectangle. Special cases are considered in which the upwash is ( a ) sudden upgust, and ( b ) a harmonic oscillation. Detailed examination is made of a rigid-body aerofoil performing translational and rotational harmonic oscillations. The aerodynamic forces are expressed in terms of dimensionless ‘air-load coefficients’, which are then compared with corresponding coefficients for an aerofoil in an infinitely deep stream. The air-load coefficients are obtained in a form which readily enables first-order corrections for wall interference to be evaluated. It is shown that the formulae derived are at variance with corresponding results obtained by other authors using different methods.

One Method of calculating the Wind Tunnel Interference in the Cascade Test

This paper deals with the theoretical calculation of the wind tunnel interference in the cascade test on the assumption of two-dimensional potential flow. Using the theory of the wind tunnel wall interference upon the turning angle, as mentioned in the other paper, we can calculate the induced velocities and velocity gradients on each airfoil in the cascade by the tunnel walls. Hence we can introduce the induced ones into the theory of cascade composed of airfoils with arbitrary shape and obtain the theory of the wind tunnel interference with the airfoil characteristics in the cascade test. A numerical example is shown in the case of cascade composed of N. A. C. A. 6409.

On the Wind Tunnel Interference and the Wall Boundary Layer Effects in the Airfoil Cascade

This paper deals with the theoretical calculation of the wind tunnel interference in the cascade test on the assumption of two-dimensional potential flow and then with the influence of the wall boundary layer upon the tuning angle of flow in the cascade. Part I contains the theory of the wind tunnel wall interference upon the turning angle, and Part II the method of calculating the wall boundary layer effects upon the turning angle.

遷音速風洞における風洞効果の線型理論

It has been proved that a linearized theory is consistent for three dimensional lifting case at sonic and nearly sonic speeds and is also applicable to a nonlifting case in the field of Mach number nearly one which has boundaries at finite distances. In the present paper, problems of wall interference in a transonic wind tunnel are discussed by the method of linearized theory. Linearized relations are also assumed for the boundary conditions at slotted or porous walls, usually being used in transonic tunnels. It is shown that a slotted wall is better than a porous wall for lifting and nonlifting bodies in transonic range.

Cavitation Tests on Hydrofoils in Cascade

Abstract First treated is theoretical basis of the cavitation tunnel for experimental hydrofoils in cascade, the following two points especially being taken into account: (a) The impossibility of arranging an infinite number of hydrofoils in an actual experiment. (b) The inevitable effects of wall interference in the working section.

The Effects of Compressibility on the Two-Dimenstional Subsonic Wind-Tunnel Constriction Correction

Relaxation methods were applied to the determination of the effects of compressibility on two-dimensional wind-tunnel interference. Calculations were made for a 10-per cent-thick symmetrical section, both isolated and symmetrically placed between two walls, for ratios of chord to tunnel height c/h of 1 and 2. Flows at Mach Numbers of both 0 (incompressible flow) and 0.5 were obtained. The incompressible velocities agreed well with those obtained by conformal mapping methods and the compressible velocities for the free-stream case were in satisfactory agreement with those given by Kaplan. Evaluation of the wall interference showed tha t the effect of compressibility averaged linearly along the chord was about the same as given by the linear-perturbation theories of Goldstein and Young, and Allen and Vincenti. The variations along the chord were so great, however, tha t the use of these theories for correcting local quantities is problematical.

Research in the Region between Subsonic and Supersonic Speeds

THERE is a large gap in our knowledge which must be bridged before we can take decisive steps from present aircraft subsonic speeds to supersonic speeds. There is first of all the question as to what happens when actually passing through the range of speed about that of sound. It is known that we must expect a steep rise of drag in this region, but we have no quantitative information. There is the further question of change of trim and stability in level flight as one passes from subsonic to supersonic speeds. There are other questions of aerodynamic and structural significance, and the whole problem is rather complex. Normally one would expect to get a large part of this information from wind tunnels, and although the capabilities of existing wind tunnels will be used to the limit, nobody knows how to design or use a practicable wind tunnel at or about the speed of sound. The phenomenon known as 'choking' and the effect of wall interference prohibit the use of tunnels for model tests at Mach numbers between about 0.9 and 1.15. This is the main reason for going into the air, and a series of experiments has been planned to use flying model aircraft launched from a great height from another aircraft and powered by rockets. This form of propulsion should enable the models to be driven through the speed-range of that of sound to various supersonic speeds.

Wind‐Tunnel Wall Interference

AN attempt is made here to summarize the present state of the theory of wind tunnel wall interference in a form that will be of some value to those using wind tunnels. The type of wind tunnel work frequently carried out without a complete knowledge of the corrections is also mentioned as it is of interest to those asking for, and using, wind tunnel results. A list of the most useful published reports on the subject is given at the end of the article, it is, however, by no means a complete guide to the literature of the subject, much of which is contained in academic volumes not usually available to the engineer using a wind tunnel.

The Glauert-Prandtl Approximation for Subsonic Flows of a Compressible Fluid

RECENT INTEREST in the compressibility effects has encouraged various investigations in the field of hydrodynamics of compressible fluids, or gas dynamics. Because of the inherent complexity of the problem, the * main effort up until now seems to be concentrated in finding a satisfactory approximate solution. One of these approximations is the Glauert-Prandtl method. The only conditions required for its validity are the vanishing of vorticity and that the deviation from the undisturbed parallel flow must be small. It is realized, of course, that these conditions are not always satisfied. For instance, near the nose of a thin airfoil, the deviation from the undisturbed parallel flow is not small. Furthermore, the flow behind a detached shock wave is subsonic but not irrotational. However, there are many problems in airplane design and its related fields which can be treated by the Glauert-Prandtl method, at least in first approximation. The method itself is simple and is applicable to three-dimensional flows as well as two-dimensional flows. These features are not present in other more refined approximations, such as the hodograph method. The authors therefore believe that such a powerful method should have a wider recognition of its potentiality beyond its present restricted application to thin airfoil theory. The first part of the present paper gives a general formulation of the three-dimensional flow problem with application to the calculation of wall interference in wind-tunnel testing at high speeds. This part of the work is prompted by a paper of the late Wieselsberger, which seems to be erroneous. Prandtl himself has formulated the general problem arid applied the method to the three-dimensional wing theory. Kiissner in his general wing theory has also touched upon this question. However, both treatments are brief and use the concept of acceleration potential, which is, perhaps, not so well known as the,concept of trailing vortices. Hence, it seems desirable to re-examine the wing theory from the usual point of view. This, of course, involves the derivation of the Biot-Savart law for the compressible flow by the Glauert-Prandtl approximation. This investigation constitutes the second part of the present paper where the mistake in Husk's treatment of the down-wash problem will be pointed out. The first order effect of compressibility

The Effect of Wind Tunnel Wall Interference on the Stalling Characteristics of Wings

In this paper it is shown that the distortion of the lift distribution of a wing in a wind tunnel caused by the wind tunnel wall interference can be considered as an induced twist in the wing. The magnitude of this twist is calculated for a wing in a circular closed wind tunnel. In numerical examples and an experimental check it is seen that this induced twist (washin for a closed wind tunnel working section) is large enough to cause very marked changes in the stalling characteristics of a wing unless the wing span is less than eighty per cent of the wind tunnel diameter. T ALMOST universal use of highly tapered and highly loaded monoplane wings has made the problem of stalling characteristics one of great importance. A wing with a tendency toward tip-stall will almost invariably have undesirable lateral stability and control characteristics near the stall. The normal induction effect, which can be calculated by the Prandtl wing theory, causes the effective angle of attack of the tip sections of an untwisted highly tapered wing to be considerably greater than that of the central portion of the wing; consequently the stalling angle is first reached at the wing tips as the angle of attack is increased; and a tip-stall is produced. This effect may be counteracted either by twisting the wing so that the geometrical angle of attack of the tip sections is less than that of the center or by changing the airfoil section so that the tip sections have more camber than the central portion of the wing. A combination of these two methods is normally used to prevent tip-stall. As both of these methods increase the wing drag, the optimum design uses only sufficient twist or camber to prevent tip-stall. The theoretical methods of solving this problem are generally satisfactory; however, it is advisable to obtain an experimental check of the results in a model test. Wind tunnel investigations of the stalling of tapered wings, utilizing both force measurements and floss tufts to show the flow over the wing, have been carried out and described by Nazir and by C. B. Millikan, and such tests are now generally included in any wind tunnel test program. In all such tests which the author has observed, the distortion of the lift distribution due to the interference of the wind tunnel walls has been neglected. Although this distortion is generally of little significance below the stall, it will be shown in the present paper to be of considerable importance in connection with the spanwise development of the stall. The pertinent calculation will be carried out for the case of a closed wind tunnel having a circular cross-section; similar results would be found for any other shape of closed wind tunnel working section. The general problem of the lift distribution for a wing of arbitrary plan form in a circular wind tunnel has been solved by C. B. Millikan. His method is very similar to that developed by Lotz for determining the lift on a wing in an unbounded fluid. For the present investigation it will, however, be sufficient to consider the much simpler inverse problem of determining the plan form necessary to produce a given lift distribution. In the analysis, the following notations will be used : T = Circulation about the wing (in the wind tunnel) T0 = Circulation about the center of the wing (in the wind tunnel) CL = Lift coefficient (in the wind tunnel) U = Velocity of airstream w' = Down wash velocity due to wind tunnel wall interference S = Wing area b = Wing span AR = b/S = Wing aspect ratio r = Wind tunnel radius x = Distance along the wing span from the center of the wing, positive to the right a = Angle of attack corrected for wind tunnel wall interference a i = CL/r AR = Self-induced angle of attack a i = w'/U = Induced angle of attack due to wind tunnel wall interference Aa'j = Induced washin of wing due to wind tunnel wall interference If a wing in a wind tunnel has an elliptic lift distribution as in Fig. 1, the circulation is r = r 0 / i (2x/b) 2 The downwash at the wing due to the wind tunnel wall interference can be calculated from the image vortex system and is

楕圓形の斷面を有する風洞の干渉に就て

楕圓形の斷面を有する風洞の壁が模型翼の空気力學的性質に及ぼす干渉の係數を固定壁自由壁の兩場合に就て求めた。其方法としては近似解法及嚴密解法を併用して實用上殆ど一致せる結果を得た。固定壁の時ほGlauertが矩形の壁に就て下した結論に對應して斷面楕圓の短長径の比が1 : √<2>のものが干渉最小となる。但しこれは翼長が風洞の幅に比較して小さい時に限り、大きくなればもつと扁たい楕圓が適當である。自由壁の時は圓形斷面の風洞が最小の干渉を與へる。

The Wall Interference of a Wind Tunnel of Elliptic Cross-Sertion

The Wall Interference of a Wind Tunnel of Elliptic Cross-Sertion

Historical Sketch of the Development of Aerodynamic Theory

Abstract This paper is intended to give, in brief historical outline, a sketch of the development of aerodynamic theory from the time of Newton to the present day. Newton’s theory of fluid motion and the resulting formula for the force reaction resulting between an inclined plane and a fluid in relative motion are briefly stated and the insufficiency of the formulas noted. Reference is then made to the various mathematical aids which were developed during the next century, and which made possible the investigation of fluid motion based on the concept of continuous change and the “perfect fluid” of the mathematician. The limitations of this concept, especially with reference to the explanation of force reactions between the body and the fluid, are then noted, together with the introduction of the idea of “circulation” and generally of the physical picture as developed by Lanchester and then in mathematical form by Prandtl and his school. These are then briefly sketched and the results of the introduction of these new ideas indicated. Reference is then made to the problem of the drag, only in part taken care of by the Lanchester-Prandtl vortex theory, and to von Karman’s work leading to his concept of the “Karman vortex street” and thence to the measurement of a further element of the drag; and finally to the third element (depending on skin friction) as at present dependent chiefly on direct physical measurement. In addition to the problem of lift and drag, the problems of stability and control in the air are briefly referred to, followed by mention of the dependence of theory on experimental research and to the vast amount of wind-tunnel investigation which has been made during the past two decades. Brief mention is then made of the two problems introduced by such work—the correction for “wall interference” and the “scale factor” due to the imperfect fulfilment of the conditions for kinematic similitude. This section closes with a mention of some of the problems which characterize the advancing fringe of progress in aerodynamic theory and which in large part still remain for future examination and study. Then follows a brief section dealing with the screw propeller with reference to the chief stages of the development of propeller theory as suggested by the names Rankine, Froude, Drzewiecki, Prandtl, and closing with a suggestion of some of the problems which characterize the advancing fringe of this phase of general aerodynamic theory.

Research on Channel Wall Interference

SummaryAn investigation of channel wall interference with the object of verifying experimentally the accuracy of the results given by the theory developed by Prandtl and extended by Glauert. Tests were made, with cylinders and aerofoils, using the “ mirror ” method, for some ten different channel sizes. The results show :1.The presence of the channel walls results in an increase in the drag of a symmetrical body, such as a cylinder.2.Agreement with the theoretial corrections for incidence and drag for channels of reasonable size.3.The extent and nature of the wall interference effects on the aerodynamic characteristics of aerofoils in much restricted streams, beyond the limits of applicability of the theory.