Triangular Wing Research Articles

Global Solutions for Supersonic Flow Past a Delta Wing

In this paper we study the mathematical aspects of supersonic flow past a delta wing. The flow is described by the potential flow equation, and the delta wing is assumed to be a triangular plate or a triangular wing with specific thickness. In the self-similar coordinates, the problem can be reduced to a boundary value problem of a nonlinear degenerate elliptic equation with a free boundary. By constructing a nonlinear iteration scheme and applying the Schauder fixed point theorem, we prove the existence of a solution to this problem, provided that the incident angle of the oncoming flow is less than a critical value determined by the data.

Leading-edge vortex shedding from rotating wings

This paper presents a numerical investigation of the leading-edge vortices generated by rotating triangular wings at Reynolds number Re = 250. A series of three-dimensional numerical simulations have been carried out using a Fourier pseudo-spectral method with volume penalization. The transition from stable attachment of the leading-edge vortex to periodic vortex shedding is explored, as a function of the wing aspect ratio and the angle of attack. It is found that, in a stable configuration, the spanwise flow in the recirculation bubble past the wing is due to the centrifugal force, incompressibility and viscous stresses. For the flow outside of the bubble, an inviscid model of spanwise flow is presented.

Drepanolejeunea actinogyna(Lejeuneaceae), a new species from southern Thailand

Abstract The new species, Drepanolejeunea actinogyna J. Inuthai, R. L. Zhu & Chantanaorr., is described and illustrated from southern Thailand. The new species belongs in the subgenus Pristolejeunea Grolle because of the presence of median ocelli in the leaf lobe. It is closely related to D. thwaitesiana (Mitt.) Steph. and D. nymanii Steph., but differs in the smaller plant size, the radially-symmetric perianth with triangular wings equal in size and a 2–3 cells long beak of the perianth, the free lateral margin of leaf lobule proximal to the notch bordered by 4 rectangular cells, and the curved tooth of the lobule.

Attitude Control Methodology for Large Solar Sails

In this paper, an attitude control methodology for large-size (on the order of kilometer squared) solar sails is proposed. The methodology is demonstrated for the case of a square sail divided into four equal triangular wings held together by two rigid perpendicular booms. By adjusting the position of a wing tip along the boom, the shape of the wing is altered. Under the effect of solar radiation pressure, the wing will naturally curve. This curvature in the wing will cause a change in the position of the center of pressure as well as the total solar radiation force vector acting on the wing, resulting in a torque that can be used for attitude control. This methodology exploits the sail film geometry itself to generate the necessary control forces and torques, rather than introducing extra control elements into the system. The mathematical relationship between the displacement of the wing tip and the control torque generated is fully developed under quasi-static conditions and assuming the wing takes on the shape of a right cylindrical shell. A case study that shows the effectiveness of the proposed method for a typical large solar sail is also presented.

Jumping mechanisms in flatid planthoppers (Hemiptera, Flatidae)

The jumping performance of three species of hemipterans from Australia and Europe belonging to the family Flatidae was analysed from images captured at a rate of 5000 s(-1). The shape of a flatid was dominated by large triangular or wedge-shaped front wings, which, when folded, covered and extended above and behind the body to give a laterally compressed and possibly streamlined appearance. The body lengths of the three species of adults ranged from 7 to 9 mm and their mass from 8 to 19 mg. The propulsive hind legs were 30% longer than the front legs but only 36-54% of the body length. Jumps with the fastest take-off velocities of 2.8-3.2 m s(-1) had acceleration times of 1.4-1.8 ms. During such jumps, adults experienced an acceleration of 174-200 G: . These jumps required an energy expenditure of 76-225 μJ, a power output of 13-60 mW and exerted a force of 9-37 mN. The required power output per mass of jumping muscle in adults ranged from 24,000 to 27,000 W kg(-1) muscle, 100 times greater than the maximum active contractile limit of normal muscle. The free-living nymphs were also proficient jumpers, reaching take-off velocities of 2.2 m s(-1). To achieve such a jumping performance requires a power amplification mechanism. The energy store for such a mechanism was identified as the internal skeleton linking a hind coxa to the articulation of a hind wing. These pleural arches fluoresced bright blue when illuminated with UV light, indicating the presence of the elastic protein resilin. The energy generated by the prolonged contractions of the trochanteral depressor muscles was stored in distortions of these structures, and the rapid elastic recoil of these muscles powered the synchronous propulsive movements of the hind legs.

Computation of heat transfer enhancement in a plate‐fin heat exchanger with triangular inserts and delta wing vortex generator

AbstractLongitudinal vortices disrupt the growth of the thermal boundary layer, thereby the vortex generators producing the longitudinal vortices are well known for the enhancement of heat transfer in compact heat exchangers. The present investigation determines the heat transfer characteristics with secondary flow analysis in plate fin triangular ducts with delta wing vortex generators. This geometrical configuration is investigated for various angles of attack of the wing i.e. 15°, 20°, 26° and 37° and Reynolds numbers 100 and 200. The constant wall temperature boundary condition is used. The solution of the complete Navier Stokes equation and the energy equation is carried out using the staggered grid arrangement. The performance of the combination of triangular secondary fins and delta wing with stamping on slant surfaces has also been studied. Copyright © 2009 John Wiley & Sons, Ltd.

Simple method for estimating shape functions of optical spectra

A simple method for estimating shape functions of optical spectra is proposed, based on the numerical correlation with an assumed optical spectrum composed of a central main rectangular component and two right-angled triangular wings on either side of the main component. The degrees of correlation between observed and assumed spectra were examined using spectral and coherence widths of those spectra and pulsewidths of Fourier-transform-limited pulses calculated from those spectra. By using this method, shape functions of output spectra from superluminescent diodes and a self-pulsating laser diode were evaluated in detail over a relatively wide injection current range beyond their rated currents.

Mathematical simulation of a supersonic flow around complex objects. Influence of the position of a wing on the gasdynamic characteristics of a complex object

Results of numerical simulation of a supersonic flow around spatial configurations of flying vehicles with the use of the Euler equations are presented. A model of a complex object was constructed on the basis of simpler base objects. Results of numerical solution of the problem on a three-dimensional flow around objects with an ogival-cylindrical airframe and a triangular wing with a diamond-shaped profile, arranged in different ways, at a Mach number M∞ = 4.03 and an angle of attack α = 10.1o have been analyzed. Calculation data were compared with the analogous data of a physical experiment.

Effect of counter-rotating vortices on the development of aircraft wakes

AbstractA two-dimensional vortex particle model is used for studying the development of the vortex wake generated by the wing of an aircraft in the Trefftz plane. Two-dimensional, finite-area vortex structures simulate the initial vorticity distribution at a near-field cross-section of the wing, as provided by either measurements or simulations. The code is used for studying the effect of weak or strong counter-rotating vortices on the development of an aircraft wake. Application in a three-vortex configuration, consisting of the tip and flap vortices, plus a weak negative vorticity sheet lying between them, supports the hypothesis of Graham that the merging of the tip and flap vortices is prevented, because in such an arrangement the counter-rotating vorticity sheet is wrapped around the primary vortices. The present results indicate that even in the far field the tip and flap vortices remain distinct and follow a helical trajectory with large-pitch and small-radius. The code is next applied to the two-vortex system of Savas’s triangular wing, in which the circulation of the flap vortex is comparable to that of the tip. Although a 2D analysis is inappropriate for stability analysis it is still useful for a quick qualitative investigation. Results indicate that the flap and tip vortices follow a helical trajectory with large-pitch but also very large radius. During one period, the flap vortex covers a span wise distance equal to the wing span. Such a flow has not been observed in flight or in laboratory tests. Actually, Ortega et al, who studied experimentally the triangular wing of O. Savas, found out that before concluding one full spiral, the vortices are literally destroyed (rapid spreading of their vorticity) by an instability mechanism.

Inverse problem of wing aerodynamics in a supersonic flow

The inverse problem of wing aerodynamics—the determination of the lifting surface shape from a specified load—is solved within the framework of linear theory. Volterra's solution of the wave equation is used. Solutions are found in the class of bounded functions if certain conditions imposed on the governing parameters of the problem are satisfied. Solutions of inverse problems of supersonic flow are presented for an infinite-span wing, a triangular wing with completely subsonic edges, and a rectangular wing.

Linear Approximation for Supersonic Flow Past a Delta Wing

When a supersonic projectile moves in the air, a shock front generally appears ahead of it. If the head of the projectile has a sharp edge, the shock front is usually attached. Such a phenomenon is observed in physical experiment for both a wing and a cone-shape body. In this paper we are mainly concerned with the flow past a wing. In the case of a thin wing with a constant section, the corresponding boundary-value problem for the Euler system for compressible fluids has been solved explicitly in [1, 2]. Moreover, when the wing has variable sections or when its leading edge is a smooth curve, the local existence of the solution is obtained in [3]. The present paper studies supersonic flow past a triangular plate, as motivated by the modern design of delta wings. Much computational work has been done for the study of this problem (see [4–6]), but its mathematical theory is still open. In this paper we study the supersonic flow past a triangular plate with vertex angle near π, and take the point of view that locally the flow past such a triangular wing is a perturbation of the same flow past a plate in the same plane with its leading edge perpendicular to the oncoming flow. Under such assumptions we linearize the nonlinear problem at the unperturbed state, and solve the linearized problem as an approximation to the original nonlinear problem. Our linearization preserves the basic character of the equation as one of mixed type. Since the solution in the hyperbolic region and the boundary of degeneracy are easily determined, our problem is then reduced to a boundary-value problem for a degenerate elliptic equation, because in the hyperbolic region the solution is easily determined. The main result is

On the onset of high-Reynolds-number grid-generated wind tunnel turbulence

Using an active grid devised by Makita (1991), shearless decaying turbulence is studied for the Taylor-microscale Reynolds number, Rλ, varying from 50 to 473 in a small (40 × 40 cm2 cross-section) wind tunnel. The turbulence generator consists of grid bars with triangular wings that rotate and flap in a random way. The value of Rλ is determined by the mean speed of the air (varied from 3 to 14 m s–1) as it passes the rotating grid, and to a lesser extent by the randomness and rotation rate of the grid bars. Our main findings are as follows. A weak, not particularly well-defined scaling range (i.e. a power-law dependence of both the longitudinal (u) and transverse (v) spectra, F11(k1) and F22(k1) respectively, on wavenumber k1) first appears at Rλ ∼ 50, with a slope, n1, (for the u spectrum) of approximately 1.3. As Rλ was increased, n1 increased rapidly until Rλ ∼ 200 where n ∼ 1.5. From there on the increase in n1 was slow, and even by Rλ = 473 it was still significantly below the Kolmogorov value of 1.67. Over the entire range, 50 [les ] Rλ [les ] 473, the data were well described by the empirical fit: . Using a modified form of the Kolmogorov similarity law: F11(k1) = C1*e2/3k1–5/3(k 1η)5/3–n1 where e is the turbulence energy dissipation rate and η is the Kolmogorov microscale, we determined a linear dependence between n1 and C1*: C1* = 4.5 – 2.4n1. Thus for n1 = 5/3 (which extrapolation of our results suggests will occur in this flow for Rλ ∼ 104), C1* = 0.5, the accepted high-Reynolds-number value of the Kolmogorov constant. Analysis of the p.d.f. of velocity differences Δu(r) and Δv(r) where r is an inertial subrange interval, conditional dissipation, and other statistics showed that there was a qualitative difference between the turbulence for Rλ 200 (strong turbulence). For the latter, the p.d.f.s of Δu(r) and Δv(r) had super Gaussian tails and the dissipation (both of the u and v components) conditioned on Δu(r) and Δv(r) was a strong function of the velocity difference. For Rλ 200 are consistent with the predictions of the Kolmogorov refined similarity hypothesis (and make a distinction between the dynamical and kinematical contributions to the conditional statistics). They have much in common with similar statistics done in shear flows at much higher Rλ, with which they are compared.

Numerical calculation of a three-dimensional laminar compressible boundary layer on profiled triangular wings with supersonic front edges

Numerical calculation of a three-dimensional laminar compressible boundary layer on profiled triangular wings with supersonic front edges

Waverider configurations according to thin shock-layer theory

This paper shows that the thin shock-layer theory can be completed in an analytical manner when the shock wave is attached to the leading edges of a non-planar triangular conical wing. Discontinuities appear only in the derivatives and not in the functions. Thus, the second derivative of each body and the shock is discontinuous at one point, and the first derivative of the transverse velocity components and pressure are discontinuous at one point. Bodies for which the slope is discontinuous at one point are also possible. A differentiable shock wave is assumed known and the body is calculated. Thus, bodies with smooth differentiable cross-sections in the inboard which are attached to planar segments in the outboard are obtained while bodies having infinite slope at the central axis are also possible. It is found that a parabolic arc shock in the inboard cannot permit an attached shock solution but other higher order polynomials can. Surface pressure coefficient, coefficients of normal and axial force, and the lift and drag forces of waveriders constructed from these bodies are calculated in closed-form for a wide range of the flow parameters.

Behaviour of [Ru(CO)2(MeCO2)2(PBun3)2] in the presence of carbon monoxide and/or hydrogen: crystal structure of [Ru6(µ-H)6(CO)10(µ-PHBun)(µ-PBun2)2-(PBun3)2(µ6-P)

The behaviour of [Ru(CO)2(MeCO2)2(PBun3)2] in the presence of N2, CO, H2, or a mixture of the last two gases has been investigated. When heated, especially in the presence of CO and/or H2, acetato and phosphido ligands are lost. At higher temperature, under hydrogen, but in the absence of alternative free ligands, a metal cluster hydride derivative, [Ru6(µ-H)6(CO)10(µ-PHBun)(µ-PBun2)2(PBun3)2(µ6-P)], is formed. An X-ray crystal structure analysis has shown that the shape of this metal cluster is ‘butterfly’ like with two pairs of triangular wings, encapsulating a bare phosphide phosphorus and carrying three bridging phosphides and two terminal phosphine ligands. The sides of the wings not bridged by the phosphido phosphorus are bridged by hydride hydrogens in such a way that the moiety formed by the metal, phosphorus, and hydride hydrogen atoms shows a local non-crystallographic C2 symmetry. Two carbonyl ligands complete the metal co-ordination about each ruthenium atom except those of the base hinge that are bound to only one carbonyl each.

Supersonic leeward heating of a triangular wing

Supersonic leeward heating of a triangular wing

Effect of viscosity on the lift-drag ratio of a thin blunt wing at hypersonic rates of flow round it

The effect of viscosity on the carrying properties of hypersonic aircraft appears at great flight altitudes, where an important factor is the interaction of the laminar boundary layer with inviscid flow. In the present study the method of bands is used to make an approximate calculation of this effect for a regime of weak viscous interaction [1]. The results of [2] are used for conditions of inviscid flow round a body. The local coefficient of friction and coefficients of the additional pressure induced by the boundary layer are determined from the data for a plate of infinite width [3]. Simple relationships are obtained which make it possible to estimate the effect of viscosity on the magnitude of the maximum lift-drag ratio and the value of the angle of attack corresponding to it. The results are given of an experimental study of hypersonic flow round a plane triangular wing in a broad range of Reynolds numbers, and these confirm the relationships obtained and indicate the region in which they are applicable.

AERODYNAMIC CHARACTERISTICS OF QUASI-SLENDER WING - BODY COMBINATIONS AT SUPERSONIC VELOCITIES

A procedure for determining the lift and pitching moment derivatives of not so slender wing-body combination in supersonic flow is presented. It is based on an introduced extension of the approximate slender body theory by retaining additional terms that have been neglected by virtue of body slenderness.The extension included the dependence of the solution on body geometry and flow Mach number. An application is given for the case of thin flat triangular wing mounted on conical pointed body. Computed results are compared with the original theory and other publish-ed theoritical and experimental data where good agreement is obtained.

Supersonic flow over a triangular wing

Supersonic flow over a triangular wing

Flow in the hypersonic boundary layer on a finite triangular wing in the presence of an angle of attack

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