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Influence of the sweepback angle and the unit reynolds number on boundarylayer transition at supersonic velocities


Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30° for a sweepback angle of 67.6°.




 In this paper, the blunt leadingedge of a wing is taken as mesh points, and there the exact velocity potential equation with central difference scheme and the exact boundary condition are used, while in the other places, the approximate velocity potential equation, which assumes small perturbation in the transverse plane but allows large perturbation in the longitudinal direction, and the corresponding boundary condition are employed. Two numerical examples are following:(1) A rectangular wing having airfoil... In this paper, the blunt leadingedge of a wing is taken as mesh points, and there the exact velocity potential equation with central difference scheme and the exact boundary condition are used, while in the other places, the approximate velocity potential equation, which assumes small perturbation in the transverse plane but allows large perturbation in the longitudinal direction, and the corresponding boundary condition are employed. Two numerical examples are following:(1) A rectangular wing having airfoil NACA0012, aspect ratio λ = 12, angle of attack α=2°, free stream Mach number M∞ = 0.63. The computed pressure distribution of the root section agrees with the exact numerical subsonic solution given by Sells (1968).( 2 ) The sweepback wing tested by NACA RM A51G31 having airfoil NACA64A010 which is perpendicular to 1/4 chord line with sweepback angle X1/4 = 45°, λ = 3 and taper ratio η = 2 ,α=2°, M∞=0.4, 0.8 and 0.9. The computed pressure distributions agree well with those obtained by tests.Under the assumption of local linearization, the stability of the difference equation in line relaxation with Seidel iteration is studied by the von Neumann method and the convergence of the solution of the differential equation equivalent to the above difference equation to the solution of the original differen tial equation is discussed by the method of separation of variables.The following conclusions are obtained:( 1 ) The stability condition for the line relaxation with Seidel iteration is 0<ω≤2 at locally subsonic points, where ω is the relaxation factor.( 2 ) At locally supersonic points, the relaxation is always unstable. The convergence conditions are as follows. Let the steps Δx (chordwise) and Δz (spanwise) perpendicular to the relaxation line.(3) 0<ω<2, at locally subsonic points.(4) 0 <ω<1+ , at locally supersonic points.The numerical experiences agree with the conclusions ( 1 ), ( 3 ) and ( 4 ), but do not agree with the conclusion ( 2 ).  本文在机翼钝前缘处用精确速势方程和精确的边界条件,其他地方用纵向大扰动而横向小扰动的速势方程和相应的边界条件,联立求解。数值算例1为矩形机翼,展弦比λ=12,翼剖面为NACA0012,自由流的马赫数M_∞=0.63,迎角α=2°,翼根剖面压力分布的计算结果与二元亚音速精确数值解(Sells,1968)接近。算例2为NACA RM A51G31实验的机翼,垂直于1/4弦线的翼剖面为NACA64A010,其后退角χ_(1/4)=45°,λ=3,根梢比η=2,M_∞=0.4,0.8,0.9,α=2°。计算与实验接近。 本文建立跨音速定常小扰动速势差分方程的线松弛改进迭代在局部线化假设下的稳定性条件和松弛解收敛到原来的微分方程解的条件。这些条件大多数与数值实验相符。  The paper concerns separated flow patterns of delta wings and its boundaries, topological analysis of separated flows and vortex flows, vortex breakdown, as well as controlled separation and vortex interaction.Flow patterns about upper and lower surfaces of a series of delta plate wings with sharpened leadingedge sweepback of 15 to 85 deg. at angles of attack up to 90 deg. at low speeds are given. There are nine types of leadingedge separated flows about upper surface; bubble, bubble vortex, streamwise vortex,... The paper concerns separated flow patterns of delta wings and its boundaries, topological analysis of separated flows and vortex flows, vortex breakdown, as well as controlled separation and vortex interaction.Flow patterns about upper and lower surfaces of a series of delta plate wings with sharpened leadingedge sweepback of 15 to 85 deg. at angles of attack up to 90 deg. at low speeds are given. There are nine types of leadingedge separated flows about upper surface; bubble, bubble vortex, streamwise vortex, concentrated stable vortex, bursting vortex, spiral flow, reversed flow, completely separated flow and asymmetric vortex. Boundary diagrams of the separated flows in the angle of attack versus leadingedge sweepback angle plane are discussed.Qualitative theory of differential equations and topology are very useful in analysing three dimensional flows and vortex flows. Local properties near singular points, global properties and topological rules of differences between the numbers of. nodal and saddle points, as well as the evolution of the topological structures as a function of parameters have been investigated by previous authors. Now concentrated vortex of a slender wing and spiral flow of a moderate sweepback cropped delta wing are studied.Vortex breakdown usually arises in either of two predominant forms, bubblelike and spiral, and the bursting vortex flowfields of the twoforms are described, moreover, subspecies are mentioned. The Position of vortex bursting point can be determined by jetlike distribution of axial velocity in front of it and wakelike one behind it. Theories of vortex breakdown and theoretical methods to evaluate the position of vortex bursting point are stated. Upstream movement of the bursting point of a: strakewing is different from that of a very slender wing.Concept of controlled separation in threedimensional flows is very important in air vehicle configuration design. The types of unstable separated flows about wings and the stability of vortex flows can be controlled by a concentrated stable vortex. The effect of strake vortex on wing vortex is studied. Displacement, coiling or merging may appear due to interaction between two stable vortices rotating in same direction. The merging of two vortices of a double delta wing and that of spanwise blowing on a wing are shown.  本文简要介绍研究旋涡运动在以下问题上的某些结果:低速不同后掠角三角翼在各个迎角下的九种分离流类型及其边界;应用微分方程定性论与拓扑学对三维分离流与旋涡流的分析;旋涡破裂形态,对三角翼前缘涡破裂的实验研究与理论分析;受控分离与旋涡的干扰,二旋涡的位移、绕转与合并等。  This paper uses the threedimensional waving plate model and optimummotion theory to analyse lunatetail swimming propulsion, and so a comparatively systmatic study of the three classes of fish propulsive modes has been carried out. Theoretical results show that lunatetail, with highaspectratio, spanwise tapering tip and moderate sweepback angle, of many fastswimming ocean animals, may gain the nearly best propulsive characteristics. Estimation of a porpoise swimming performance gives satisfactory... This paper uses the threedimensional waving plate model and optimummotion theory to analyse lunatetail swimming propulsion, and so a comparatively systmatic study of the three classes of fish propulsive modes has been carried out. Theoretical results show that lunatetail, with highaspectratio, spanwise tapering tip and moderate sweepback angle, of many fastswimming ocean animals, may gain the nearly best propulsive characteristics. Estimation of a porpoise swimming performance gives satisfactory results.  本文运用三维波动柔板位流模型与最佳游动方式理论,继续分析了新月形鱼尾的推进性能,从而实现了对鱼类三种主要推进模式的较为系统的研究。理论分析表明,高速海洋动物所具有的大展弦比、尖叶梢、中等后掠的新月形尾能获得接近于最佳的推进性能。对海豚游动特性的理论估算也给出了令人满意的结果。   << 更多相关文摘 
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