Jet-flapped Wing Research Articles

Computational analysis of the aerodynamic performance of a jet-flap airfoil in transonic flow

The needed shift in next generation aircraft design is expected to bring novel concepts for civil aviation as the jet-flap wing. The aircraft efficiency improvements with the jet-flap wing directs its use for future aircraft designs reinforced by the tendency for more synergistic systems as active flow control, boundary layer ingestion and distributed propulsion, making the jet-flap wing a very suitable option for the latter concept. The analysis carried out in this paper is aimed at the application of the jet-flap wing concept for manoeuvrability and cruise efficiency improvement of an airliner. A 2D computational model of a jet-flapped transonic airfoil is developed in order to assess the jet-flap wing technology for a commercial aircraft at cruise conditions. This paper provides an insight into the parameters that affect the performance of a jet-flap under various flight conditions. To do this, a general parametrical analysis is performed, studying numerically the influences of main flow parameters like Mach number, Reynolds number, angle of attack, jet deflection angle and jet thickness. Changes in pressure distribution and flow circulation around the airfoil yield strong modifications in lift and drag due to jet angle variation. Improvements are encountered in the performance of an airfoil with a jet-flap system compared with a standard airfoil with no jet. Enhancements in lift and reduction in drag, as well as an increase of the lift-to-drag ratio is possible with a proper combination of the jet deflection and the angle of attack of the airfoil. In summary, this paper shows the conditions under which the benefits of the jet-flapped wing, for lift enhancement and manoeuvrability as an active flow control are promising.

Errata: Subsonic and Transonic Similarity Rules for Jet-Flapped Wings

F convenience in discussion, the above journal article will be designated as Ref. 1. Also, Ref. 4 in the journal article will be referred to as Ref. 2. Reference 2 is a more detailed version of Ref. 1. The notation herein follows Ref. 1, except for the introduction of the new symbol m, where m = ( d r / d n ) 0 . In the appendices of Refs. and 2 it is incorrectly assumed that (1 m) < . The correct assumption is (1 + m ) < . The purpose in making an approximating assumption regarding m was to eliminate m from some of the jet internal flowfield relations and thereby simplify those relations for possible future use. This goal was peripheral to the main thrust of the analysis in the aforementioned appendices and has no impact upon any of the final results in Refs. and 2; only the intermediate internal field relations are affected. The lack of impact upon the final results is associated with the order of the terms retained in the analysis in con j unction with some symmetric and antisymmetric function properties. The corrections which must be applied are as follows. The term (/^(n/R) must be added to Eqs. (A6) and (A6) in Refs. and 2 respectively. The term U^ (h/R)/4 must be added to each of Eqs. (A10) and (Al 1) in Ref. 2, and 1 should be replaced by 3 in Eq. (A20) of Ref. 2. For an additional unrelated correction, also note that an infinity subscript should be appended to the Mach number term in Eq. (A8) of Ref. .

Subsonic and Transonic Similarity Rules for Jet-Flapped Wings

Abstract : Linear-subsonic and nonlinear-transonic similarity rules are derived for a finite-span jet-flapped wing with partial or full-span blowing. Although some subsonic rules previously have been published for jet-flapped wings, those presented herein are more general. The nonlinear transonic rules are new. The rules for both flow regimes employ a new jet-sheet compatibility condition that is second order relative to the jet-sheet internal flow and yields a jet-momentum coefficient similarity parameter differing from the conventional parameter in that it includes the effect of the jet-supply pressure ratio. The examples presented show that the second-order effect is significant only for conditions under which a convergent jet nozzle chokes at a relatively low free-stream Mach number, say, less than 0.5. The relation of the present rules to previously published rules for both blown and unblown wings is discussed briefly. The experimental data available for validation of the linear rules is rather sparse and is plagued with uncertainties regarding wind-tunnel interference corrections. Nevertheless, some comparisons with experiment are made and fair agreement is achieved. These comparisons revealed that camber-line effects associated with blowing could be significant in transonic applications. There is no experimental data of appropriate configurational simplicity and of sufficient generally in parametric variations to permit validation of the nonlinear rules. (Author)

An Alternative Approach to the High Aspect Ratio Wing With Jet Flap by Matched Asymptotic Expansions

SummaryAn alternative method is described for solving the problem of a three-dimensional jet-flapped wing with a high aspect-ratio. This method is similar to the lifting-line theory of Kerney6 or Tokuda7, but differs in that the method of matched asymptotic expansions is applied to an integral equation, derived from the lifting surface theory, rather than a partial differential equation. The advantage of the present method over those used previously is that the necessary outer solutions are obtained directly; it is not necessary to rely upon physical insight or considerable ingenuity. The final results are different from those obtained by the previous authors; it is shown that the present result is correct, by noting some errors in the earlier theories.

A Relaxation Solution for Transonic Flow over Three-Dimensional Jet-Flapped Wings

An algorithm has been developed which treats transonic flow over jet-flapped wings of general plan form within a small disturbance framework. The numerical method represents a generalization of the relaxation solutions developed by Bailey and Ballhaus for unblown wings and the authors' previous work for twodimensional jet-flapped airfoils, and it incorporates a new far field which accounts for the vorticity on the jet. Supercritical results presented for a variety of blown planforms indicate repeal of the Kutta condition, as in two dimensions, appreciable spanwise load carryover for partial span blowing, and reduction in lift augmentation due to sweepback. Comparison of lift coefficients with experimental values shows good agreement for various planforms.

A non-linear crack model

Elliott's crack model which accounts for non-linearity of material behaviour in the vicinity of a crack tip is difficult to investigate analytically in view of the mathematical complexities associated with the governing singular integral equation. However, with a particular force law, the governing equation can be transformed into one that arises in the theory of the lift coefficient of a thin jet-flapped wing, and for which a solution has been obtained. The displacement variation ahead of the crack tip is therefore known, and the results show that the width of the crack front decreases as the force law becomes sharper, a state of affairs which is analogous to that for the dislocation width in the Peierls-Nabarro model. The fact that a solution of the governing equation has been obtained without the use of inverse methods, should act as a spur to the search for solutions for other force laws.

Analysis of High-Aspect Ratio Jet-Flap Wings of Arbitrary Geometry

An analytical technique to compute the performance of an arbitrary jet-flapped wing is developed. The solution technique is based on the method of Maskell and Spence in which the well-known lifting-line approach is coupled with an auxiliary equation providing the extra function needed in jet-flap theory. The present method is generalized to handle straight, uncambered wings of arbitrary planform, twist, and blowing (including unsymmetrical cases). An analytical procedure is developed for continuous variations in the above geometric data with special functions to exactly treat discontinuities in any of the geometric and blowing data. A rational theory for the effect of finite wing thickness is introduced as well as simplified concepts of effective aspect ratio for rapid estimation of performance.

Jet-Flapped Wings in Very Close Proximity to the Ground

The method of matched asymptotic expansions is applied to the problem of jet-flapped wings of finite span in very close proximity to the ground. For the linearization of this problem, the order of small parameters, the angle of attack and jet deflection, are assumed to be smaller than the ratio of the ground clearance to the root chord. This linearized problem is solved as a direct problem represented by a source distribution on the upper surface of the wing and jet sheet with concentrated sources around the leading and side edges plus a separate confined channel flow region under the wing and jet sheet. The two-dimensional, jet-flapped airfoil is examined in detail, and the calculated lift coefficients lie within 5% of corresponding results by Lissaman.1 In the three-dimensional case, a simple analytic solution is obtained for a flat plate semi-elliptic wing with a straight trailing edge, zero angle of attack and uniform momentum distribution of the jet. Spanwise lift distributions and lift coefficients are derived and the distributions of the jet momentum are discussed for minimum induced drag.

An Investigation of the Trailing Vortex System Generated by a Jet‐Flapped Wing Operating at High Wing Lift Coefficients

Abstract : The purpose of the investigation was to measure the geometry of the trailing vortex generated behind a jet-flapped wing. Such vortices can pose a serious hazard to aircraft that penetrate them. Previous investigations performed on conventional wings indicate that these vortices persist for some time and have maximum tangential velocities which increase linearly with the lift coefficient. As future aircraft may employ high lift devices such as jet-flapped wings, the vortices generated could be even stronger. Two semispan models of a jet-flapped wing were tested in a subsonic wing tunnel. Parameters varied during testing included the jet flap angle, angle of attack, aspect ratio, and jet momentum coefficient. Vortex measurements were obtained using a vortex meter which measured the rotational speed of the fluid within the vortex. Values obtained were numerically integrated to yield the tangential velocity and circulation distributed through the vortex. Experimental results indicate that the maximum tangential velocity increases to a maximum and then decreases with continually increasing jet blowing. At high values of jet blowing, the vortex was found to decay rapidly downstream. (Author)

An asymptotic theory of the jet flap in three dimensions

A uniformly valid asymptotic solution has been constructed for three-dimensional jet-flapped wings by the method of matched asymptotic expansions for high aspect ratios. The analysis assumes that the flow is inviscid and incompressible and is formulated on the thin airfoil theory in accordance with the well-established Spence (1961) theory in two dimensions.A simple method emerges in treating the bound vortices along the jet sheet which forms behind the wing with the aid of the following physical picture. Three distinct flow regions—namely inner, outer and Trefitz—exist in the problem. Close to the wing the flow approximates to that in two dimensions. Therefore, Spence's solution in two dimensions applies. In the outer region a wing shrinks to a line of singularities from which the main disturbances of flow in this region arise. In particular, we find that the shape of the jet sheet, hence the strength of vortices, is now predetermined by the strength of the singularities there. Hence a complete flow field in the outer region can now be determined first by evaluating the flow due to various degrees of singularities along this line and then adding the effect of the jet bound vortices which is now known. Far removed from the wing, the well-known Trefftz region exists in which calculations of aerodynamic forces can be most easily done.The result has been applied to various wing planforms such as cusped, elliptic and rectangular wings. The present result breaks down for rectangular wings. However, we can apply Stewartson's (1960) solution for lifting-line theory for semi-infinite rectangular wings, because, to this second-order approximation it is established that the jet sheet in the outer region makes no contribution to lift, with the direct contribution of the deflected jet at the exit being cancelled by the reduced circulation in the jet vortices. This result for the rectangular wing gives excellent agreement with the experiments made on a rectangular wing, while the result for elliptic wings underestimates them considerably.

Performance, operation, and use of low aspect ratio jet-flapped wings

The characteristics of a jet-flapped wing of aspect ratio 6 are presented, discussed, and evaluated for STOL application. Again, as for high aspect ratio (AR = 20) jet-flapped wings, a range for most economical jet-flap operation is well denned. The angle of attack as an efficient means of lift production loses its usefulness with low aspect ratio jet-flapped wings, whereas the optimum jet deflection angle seems hardly to be affected (0 ^ 55°). A most efficient jet-flap application for STOL calls for a complete integration of the lifting and propulsive systems. In the range of most economical jet-flap operation, semi-empirical relationships predict parameter changes accurately enough for many practical purposes.

Further Comments on "A Drag Hypothesis for Jet-Flapped Wings"

Further Comments on "A Drag Hypothesis for Jet-Flapped Wings"

The Problem of Strain Accumulation Under Thermal Cycling

Eqs. (1) and (2), as pointed out in reference 2, are not applicable to a jet-flapped wing; likewise, neither is Eq. (6). However, Hancock has made the necessary extension to Eq. (2) and found the added terms to be small. The experimental data cited in references 1 and 2 lie above Eq. (2) for the planar wake (and above its extended form), but below Eq. (6) for the rolled-up vortex pair. (The full predicted maximum of Eq. (6) is probably unattainable since it is predicated on a wake angle of 90°). Thus, perhaps the rolling up of the trailing vortex sheet, not previously considered in this problem, plays an important role.

A Note on the Induced Drag of Jet-Flapped Wings

The main purpose of this note is to explain the apparent discrepancy which arises when the change in effective aspect ratio due to blowing, as predicted by the theoretically derived expression for the induced drag coefficient, is compared with what one intuitively expects from the general flow picture. If the jet sheet is considered as a chordwise extension of the wing (mechanical flap analogy), the general flow picture suggests that the effective aspect ratio of a wing without blowing is reduced by blowing. Maskell and Spence's relation for the induced drag coefficient, however, indicates that the effect of jet blowing is to increase the effective aspect ratio.

Comments on "Limiting Circulatory Lift of a Wing of Finite Aspect Ratio"

The second point questions the direct application of Eq. (1) to the finite jet-flapped wing. In the derivation of Eq. (1), it is assumed tha t the wing has an elliptic spanwise loading distribution and tha t the trailing vorticity lies in a plane inclined to the free stream at the induced down wash angle calculated at the wing lifting line. But, the ultimate downwash angle far behind the wing will be twice the inclination at the wing. Thus, the effects of the curvature of the trailing vorticity in the stream direction are neglected. However, it is possible to include these effects by considering the forces on a control surface at infinit}^ in the usual manner. A wing, which has an elliptic load distribution given by r = r0(i v A) (2)

A theory of the jet flap in three dimensions

The treatment of two-dimensional jet-flapped wings in incompressible flow by the methods of thin-aerofoil theory given by one of the authors (Spence 1956) has been extended to the case of a thin wing of finite aspect ratio which possesses a deflected jet sheet of zero thickness emerging with a small angular deflexion at its trailing edge. The restriction is imposed that the streamlines of the jet flow lie in planes perpendicular to the wing-span, transverse momentum-transport being thus excluded. As in classical theories, the downwash field is assumed to arise from elementary horseshoe vortices proportional in strength to the local lift distribution; a new feature is the ability of the sheet formed by these elements to sustain a pressure difference on account of the longitudinal flux of momentum of the jet within it. The induced downwash w i ( x, y ) in the plane z = 0 at intermediate distances x from the wing cannot be calculated, and is therefore replaced by an interpolation formula having the correct values U ∞ α i at the wing and U ∞ α i ∞ far downstream. To ensure that the errors so introduced are small the aspect ratio A must be large, its permissible minimum increasing with the jet momentum coefficient C J . Two methods of interpolating to w i ( x, y ), both of which lead within close limits to the same expression for C L , are discussed. They are chosen so as to allow the two-dimensional equation for loading, whose solution is known, to be used to calculate the loading in a streamwise section in three dimensions. The spanwise variation of loading could be calculated for arbitrary planforms and jet-momentum distributions, but the present paper is confined to the case in which the loading and downwash distribution depend only on x/c , where x measures distance from the leading edge and c ( y ) is the local chord. This is shown to require both c and the jet-momentum flux per unit span to be elliptically distributed, the deflexion τ and incidence a being constant over the span. The relation between the coefficients of induced drag and lift is then C D i = C (2) L /( πA + 2 C J ) induced drag being defined as the difference between the thrust and the (constant) flux of momentum in the jet. (The interpolations for induced downwash are not used in deriving this relation.) The ratio of C L to the value C (2) L which it would have in two dimensions is C L / C (2) L = { A + (2/π) C J } / { A + 2/π ) (∂ C (2) L /∂α) - 2(1+ σ)}, where ∂ C (2) L /∂α is the two-dimensional derivative of lift with respect to incidence, a known function of C J and σ = 1 — α i /(½ α i ∞ ). An expression for σ is found in terms of known quantities by equating the induced drag calculated from the detailed forces on the wing to that given above. The results have been compared with experimental measurements made on an 8:1 elliptic cylinder of rectangular planform at aspect ratios 2⋅75, 6⋅8 and infinity. Remarkably close agreement with observed values of C L is obtained in all cases, and the difference C D — C Di = C D 0 , say, between the total- and induced-drag coefficients, is virtually independent of the aspect ratio. C D 0 represents the effects of the Reynolds number, section shape and jet configuration, which are excluded from the present theory.

The lift coefficient of a thin, jet-flapped wing

A solution is given for the inviscid, incompressible flow past a thin, two-dimensional wing at a small incidenceα, at the trailing edge of which a thin jet emerges at a small deflexionז. The flow inside the jet is assumed to be irrotational, and bounded by vortex sheets across which it is prevented from mixing with the main stream. The effect of the jet on the outside flow is the same as that of a vortex sheet of strength proportional to its curvature and to the jet momentum flux, together with a doublet distribution proportional to the jet thickness (and vanishing in the present limiting case). An integral equation is obtained for the slope of the jet, by aligning the trailing vortex sheet in the undisturbed-stream direction. The solution is expressed as the sum of a Fourier series, together with a function possessing the correct (i. e. logarithmic) form of singular behaviour at the trailing edge. The coefficients of a 9-term interpolation to the series have been calculated on an electronic computer, for a number of momentum-flux coefficientsCJlying between 0.01 and 10. The convergence is sufficient to justify the truncation of the Fourier seriesa posteriori. Simple expressions have been obtained for lift, pressure distribution and pitching moment. In particular, the lift coefficient is given byCL= 4πA0τ+ 2π(1+ 2B0)α, whereA0andB0are the leading Fourier coefficients associated with deflexion and incidence respectively. Close interpolations to their values are provided by the formulae 4πA0= 3.54C½J+ 0.325CJ+ 0.156C3/2J, 4πB0= 1.152C½J+ 1.106CJ+ 0.051C3/2J. For smallCJthese exhibit the dependence onC½Jwhich has been predicted by the empirical theories of Stratford (1956) and Woods (1955). Close agreement with the theory is found in tests made at the National Gas Turbine Establishment, Pyestock, by Dimmock (1955) on an 8:1 elliptic cylinder with a narrow deflected jet exit close to its trailing edge, both forτ≑ 30° and forτ≑ 60°. The measured lift coefficients lie within 5% of the corresponding calculated curves (an allowance of 12½% having been made for thickness), and the observed centres of lift lie within 2% of the chord of those calculated for a thin aerofoil, over the whole range ofCJ. The ‘shallow jet’ approxi­mations used in the theory had not been expected to apply forτas large as 60°, but the experimental agreement still found in this case resembles that obtained at large deflexion angles by the Glauert (1927) small angle theory for hinged flaps, in which similar approxima­tions occur.