Lift-to-drag ratio at supersonic speeds

Wave lift-to-drag ratio is analyzed ignoring friction and using flows behind oblique shock waves and rarefaction waves. It is shown that the lift-to-drag ratio of an infinite oblique plate can surpass considerably that of triangular plates with subsonic, sonic, or supersonic edges. The simplest finite-span oblique wing is a wing with characteristic edges. However, when the normal-to-the-edge flow velocity component behind a shock reaches the speed of sound, the wing contracts into an edge, and other means must be used to exclude the end effect. Several possible variants are indicated. A straight wedge with side plates is the optimal shape for a lifting body with fixed volume, lift, length, and width. Under the same conditions, the cross-section of a pyramidal body formed by stream planes behind one or two plane shocks has practically no effect on the lift-to-drag ratio, while the region of high lift-to-drag ratio is much narrower than for a wedge. If a pyramid fails to provide the required lift-to-drag ratio, it is necessary to turn to forms that better fill the given area. Redistribution of lift between body and wing permits an improvement in the lift-to-drag ratio.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–141, September–October, 1993.     

Optimum form of lifting bodies at hypersonic speeds

The variational problem of the form of bodies with minimum drag for given lift force, volume, and other constraints in general leads to a second-order partial differential equation even for the simplest methods of drag calculation (Newton law and averaged friction coefficient). The solution of this equation is not justified; in its place an approximate solution is suggested which consists of: a) selection of a scheme characterized by certain parameters which are determined from the solution of the extremal problem, b) determination of the optimal surface form for the selected scheme with the aid of the system of ordinary Euler equations. This paper presents a comparison of the body schemes with minimum drag and maximum L/D and presents the solution of several variational problems.At the present time we have quite complete information on the form of minimum-drag bodies for zero lift (nonlifting bodies), and both approximate and quite rigorous methods are known for solving the corresponding variational problems. This cannot be said at all of the form of lifting bodies, for which the requirements are numerous, differing essentially for vehicles of different application, and are generally not limited to a single flight regime. Account for all the mandatory requirements in solving the variational problems is not possible; therefore in the majority of cases these solutions do not yield answers which are directly suitable in practice; rather they yield limiting estimates.The natural tendency to utilize for lifting bodies the axisymmetric form which is customary for nonlifting bodies leads to the study of axisymmetric bodies at angle of attack, axisymmetric bodies with skewed base, sections of axisymmetric bodies cut by planes, etc. In order to obtain a broader view of the optimum forms of lifting bodies we must, obviously, drop the limitation to axisymmetric bodies and bodies with similar cross sections. However, in the case of an arbitrary extremal surface the Euler equation is a second-order partial differential equation, and its simple solution is difficult. In practice it seems wise to solve those variational problems whose Euler equation may be reduced to a system of ordinary differential equations. Therefore, we propose the following method for selecting the optimum forms: a) we select a scheme, a form, which is formed by a set of planes and cylindrical, conical, spherical surfaces and which is defined by parameters that are found from the solution of the extremal problem; b) for the selected scheme the generators of the scheme surface are found from the solution of the variational problem.For the calculation of the air pressure on the body surface we use the empirical Newton law, which yields in the majority of cases results which are very close to the results of the more rigorous methods.It is assumed that the pressure may vanish only at the trailing edge of the body. The frictional drag coefficient, averaged over the body surface, is assumed to be independent of the body shape. In the case of a body of simple form the hottest portion is the frontal portion and account for the thermal protection requirements reduces to the selection of suitable dimensions of this portion of the body. In the general case the problem is stated as follows: find the form of the minimum-drag body for a given lift force, volume, length, and other conditions. To the particular case of the body with maximum L/D corresponds the value of the Lagrange multiplier =–1/k.All the results of calculations presented in the paper are intended only to illustrate the method. After the present paper was submitted for publication, another study [3] appeared which also proposes a method for determining the optimal parameters.     

Velocity profiles for plate withdrawal at high speeds

A simplified Navier-Stokes equation is applied to the solution of the velocity profile in the liquid meniscus adhering to long flat supports withdrawn continuously from baths of quiescent liquids. The inertial term is included using an Oseen approximation, the inhomogeneous boundary condition is transformed, and the resulting differential equation is solved by the method of eigenfunction expansions. The series describing the velocity profile and volume flowrate are both found to be rapidly convergent.     

Experimental results on aerofoil manipulators at high subsonic speeds

An extensive series of measurements of the boundary layer development and drag downstream of aerofoil manipulators have been made in the high speed tunnels at Cambridge. This work forms part of a combined study with the University of Poitiers into the possible drag reducing properties of manipulators and was supported by Airbus Industrie. Overall the test results showed that the reduction in turbulent skin-friction downstream of the device did not compensate for the drag of the device itself in any of the cases studied, thus no overall drag saving was possible although in certain cases the overall drag penaly was small. This finding suggests that such devices may have a use in regions where a local reduction in skin-friction (and hence possible heat transfer) is needed and a low level of loss can be accepted. However, the actual drag reduction obtained was found to be extremely sensitive to changes in the aerofoil shape and incidence.     

Superposed flow between two discs contrarotating at differential speeds

This paper describes a combined computational and experimental study of the flow between two contrarotating discs for −1 ≤ Γ ≤ 0 (where Γ is the ratio of the speed of the slower disc to that of the faster one) for the case where there is a superposed radial outflow of air. The computations were conducted using an elliptic solver and a low-Reynolds-number k-ε turbulence model, and velocity measurements were made using a laser-Doppler anenometry system. Two basic flow structures can occur: Batchelor-type flow, where there are separate boundary layers on each disc with a rotating core of fluid between, and Stewartson-type flow, where there is virtually no core rotation. The main effect of a superposed flow is to reduce the core rotation and to promote the transition from Batchelor-type flow to Stewartson-type flow. For most of the results, there is good agreement between the computed and measured velocities. Computed moment coefficients show that, for Γ = −1, superposed flow has little effect on C_m: an accepted correlation of C_m for a free disc should provide a useful estimate for design purposes.     

Porous aerofoil analysis using viscous-inviscid coupling at transonic speeds

Viscous-inviscid interaction is used to compute steady two-dimensional, transonic flows for solid and porous aerofoils. A full-potential code was coupled with both a laminar/transition/turbulent integral boundary-layer/turbulent wake code and the finite-difference boundary-layer code using the semi-inverse methods of Carter and Wigton. The coupling was performed using the transpiration coupling concept, thus allowing for analysis of porous aerofoils with passive physical transpiration. The computations confirm experimental findings that passive physical transpiration can lead to a lower drag coefficient and a higher lift coefficient, a weaker shock and elimination of shock-induced separation. Nevertheless, it is very important that the extent of the porous region and permeability factor distribution of the porous region are chosen carefully if these improvements are to be achieved.     

Van Leer格式在全速域范围的推广

通过对格式耗散项的修正将Van Leer格式推广至全速域流场求解范围.对格式耗散项的分析表明,在低马赫数流动情况下格式耗散项中不应包含声速项,以此为依据对Van Leer迎风分裂格式提出了耗散项的修正方法.结合对控制方程时间导数项的预处理,修正后的格式能够成功地模拟低速流动问题,同时在其他马赫数范围内也不损失格式的收敛...     

预处理方法在全速度流场中的应用研究

应用预处理方法求解二维可压缩Navier-Stokes方程,发展出一套既适用于低速流动,也可用于可压缩流动的全速度流场解算方法.空间格式选用Ausm类格式,并采用多步Runge-Kutta时间推进方法.数值模拟了鼓包(Bump),RAE2822翼型,多段高升力翼型的不同速度绕流流场,并与实验数据进行了对比.结果表明预处...     

Dynamic structural loading using a light gas gun

A light gas gun was used to dynamically load models of the wall sections typical of those used in the construction of buried structures. Scaling of the loading time history is addressed, and the appropriate nondimensional parameters for the loading and the model structural characteristics are defined. Scaling is simplified by use of structural materials for the models which have a yield strength and material moduli close to those found in prototype structures. Methods for producing the desired loading by using a light gun are investigated, and reasonable accuracy and flexibility in achieving the desired loading time history is demonstrated. Experimental results are given for the loading conditions and the failure mode that occurs when the model wall section is breached. The loading conditions to produce failure in the model are reduced to nondimensional form and compared to results from prototype field tests, also in nondimensional form. The resulting nondimensional data are used to evaluate the suitability of the light gun to dynamically simulate ground shock loading as well as to investigate failure criteria.     

A COMPUTATIONAL METHOD FOR THE NAVIER-STOKES EQUATIONS AT ALL SPEEDS

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Drag measurements on planar riblet surfaces at high subsonic speeds

This paper presents the results of an investigation of riblet performance at high subsonic Mach numbers, and Reynolds numbers of about 20 000 based on the momentum thickness, in both zero and adverse pressure gradient boundary layers. The maximum length Reynolds number of the ribbed section was 3.4×10⁷ so the results were directly relevant to flight applications on the engine nacelles of civil airliners. Seven different sizes of riblets with heights h (equal to spacing s) ranging from 0.0007 (0.0178mm) to 0.006 (0.1524 mm) have been studied, covering a range of h+, s+ from 10 to 106. The maximum percentage skin friction reduction, as deduced from velocity profiles measured at the downstream end of the riblet surfaces, under nominally zero pressure gradient conditions was 5.5±1; rather less than that recorded in low speed studies, but consistent with a recent theoretical analysis of the effect of Reynolds number. The values of h+ required for maximum and zero skin friction reduction agreed closely with other data. In addition subsequent floating element drag balance measurements revealed little effect of yaw angles up to 15°, again in line with other findings, and also suggested that the extent of the initial development length on, and recovery length behind, the riblets was approximately 5. The adverse pressure gradient studies indicated that riblet performance was essentially unaffected by mild gradients (=0.25), but diminished to zero in a more severe gradient (=0.5).     

Shock wave interference on a fenced wing at hypersonic speeds

High-pressure zones on the wing, created by the reflected shocks, are experimentally demonstrated and their influence on the aerodynamic characteristics of the wing is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 135–140, May–June, 1992.The authors are grateful to V. E. Mosharov, V. N. Tarasov, and V. I. Plyashechnik for assisting with the experiments.     

An experimental investigation of the ELAC 1 configuration at supersonic speeds

Supersonic flight of aerospace planes is of marked interest since several flow regimes characterized by different local flow structures have to be flown through. This problem was investigated experimentally for the hypersonic research configuration ELAC 1. The aim of the study was to detect the influence of the rounded leading edge, of the thickness distribution prescribed, and of the Reynolds number, especially on the flow on the leeward side of the configuration. The experiments were carried out in the transonic wind tunnel of Aerodynamisches Institut of RWTH Aachen, at a freestream Mach number Ma _∞=2, a unit Reynolds number of Re _∞=13×10⁶, angles of attack between ?3°?α?10°, and in a wind tunnel of the Institute for Theoretical and Applied Mechanics of the Russian Academy of Sciences in Novosibirsk. The freestream Mach numbers covered in these experiments were varied between 2?Ma _∞?4, freestream Reynolds numbers per unit length between 25×10⁶?Re _∞?56×10⁶ and angles of attack between ?3°?α?10°. Flow visualization studies, measurements of surface pressure distributions and of aerodynamic forces were used to analyze the flow. The results, which will also be compared with numerical data, clearly indicate marked differences in the location of the separation and reattachment lines, and the formation of the primary, secondary and tertiary vortices, for the flow regimes investigated.     

A collocated finite volume method for predicting flows at all speeds

An existing two-dimensional method for the prediction of steady-state incompressible flows in complex geometry is extended to treat also compressible flows at all speeds. The primary variables are the Cartesian velocity components, pressure and temperature. Density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm, which in the limit of incompressible flow reduces to its well-known form. Special attention is paid to the numerical treatment of boundary conditions. The method is verified on a number of test cases (inviscid and viscous flows), and both the results and convergence properties compare favourably with other numerical results available in the literature.     

Passive shock wave/boundary layer control of wing at transonic speeds

At supercritical conditions a porous strip(or slot strip) placed beneath a shock wave can reduce the drag by a weaker lambda shock system, and increase the buffet boundary, even may increase the lift. Passive shock wave/boundary layer control(PSBC) for drag reduction was conducted by SC(2)-0714 supercritical wing, with emphases on parameter of porous/slot and bump, such as porous distribution, hole diameter,cavity depth, porous direction and so on. A sequential quadratic programming(SQP) optimization method coupled with adjoint method was adopted to achieve the optimized shape and position of the bumps.Computational fluid dynamics(CFD), force test and oil test with half model all indicate that PSBC with porous, slot and bump generally reduce the drag by weaker lambda shock at supercritical conditions.According to wind tunnel test results for angle of attack of 2? at Mach number M = 0.8, the porous configuration with 6.21% porosity results in a drag reduction of 0.0002 and lift–drag ratio increase of 0.2, the small bump configuration results in a drag reduction of 0.0007 and lift–drag ratio increase of 0.3.Bump normally reduce drag at design point with shock wave position being accurately computed. If bump diverges from the position of shock wave, drag will not be easily reduced.     

Heat transfer to surfaces of some lifting bodies at high supersonic speeds

Results are presented of an experimental study of the heat transfer and gas flow on the surface of a semicone and of planar wings with a break in the leading edges at Mach number M=5. It is shown that with the interaction of the gas streams flowing about various portions of the surface of such bodies there may occur local, relatively narrow zones of high or low values of the specific heat flux.Temperature indicating paints were used to measure the heat fluxes, and smearable paints applied to the surface in the form of individual dots were used for flow visualization.