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首页> 外文期刊>Applied Mathematical Modelling >Analyzing The Longitudinal Effect Of Hypersonic Flow Past A Conical Cone Via The Perturbation Method
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Analyzing The Longitudinal Effect Of Hypersonic Flow Past A Conical Cone Via The Perturbation Method

机译：通过摄动法分析高音速流通过圆锥体的纵向效应

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To analyze the hypersonic flow past a conical cone, the variations of gasdynamic properties subjected to the longitudinal curvature effect by using the perturbation method. An outer perturbation expansion has been carried out by recent researchers, but a problem occurred, the outer expansion solutions are not uniformly valid in the shock layer, however, the outcome near the conical body surface called vortical layer remains deflective. This study intends to discover uniformly valid analytical solutions in the shock layer by applying the inner perturbation expansions matching with the out expansions to analyze the characteristics in the whole region including shock layer and vortical layer. Starting from the zero-order approximate solutions for hypersonic conical flow is then applied as the basic solutions for the outer perturbation expansions of a flow field. The governing equations and boundary conditions are also expanded via outer perturbations. Using an approximate analytical scheme in the derivation process, first-order perturbation equations can be simplified and the approximate closed-form solutions are obtained; furthermore, the various flow field quantities, including the normal force coefficient on the cone surface, have been calculated. According to the variations of gasdynamic properties, the longitudinal curvature effect for the hypersonic flow past a conical cone can be determined. Thicknesses of shock layer and vortical layer can be predicted as well. The physical phenomena inside both layers can be investigated carefully, the conditions for an elliptic cone with longitudinal curvature, m = 1 and n = 2 and other conditions of parameters; the perturbation parameter, ε_(m2) = 0.1, semi-vertex angle of the unperturbed cone, δ = 10°, and hypersonic similarity parameter, K_δ = M_∞δ = 1.0, the thickness of vortical layer, η_(VL), can be calculated at the position angle of conical cone body, φ = 30° was demonstrated here. Results show how very thin the vortical layer is approximately only 10% of the shock layer close to the body, the pressure in the whole shock layer is verified to be uniformly valid which agrees with previous studies. Large gradient changes in entropy and density are found when the flow approaches the cone surface, the most important is, this method provides a benchmark solution to the hypersonic flow past a conical cone and to assist the grids and numerics for numerical computation should be fashioned to accommodate the whole flow field region including the vortical layer of rapid adjustment, and let the analysis become more effective and low cost.
机译：为了分析通过圆锥体的高超声速流动，通过使用扰动方法，使气体动力学特性的变化受到纵向曲率的影响。最近的研究人员已经进行了外部摄动扩展，但是出现了一个问题，即外部扩展解在冲击层中并不一致，但是在圆锥体表面（称为涡旋层）附近的结果仍然是偏斜的。本研究旨在通过应用内部扰动扩展与外部扩展相匹配的方法来分析激波层中统一有效的解析解，从而分析整个区域（包括激波层和涡旋层）的特征。从高超声速圆锥流的零阶近似解开始，然后将其用作流场外部摄动扩展的基本解。控制方程和边界条件也通过外部扰动扩展。在推导过程中使用近似解析方案，可以简化一阶摄动方程，并获得近似的闭式解。此外，已经计算出各种流场量，包括锥面上的法向力系数。根据气体动力学特性的变化，可以确定通过圆锥体的超音速流的纵向曲率效应。冲击层和涡旋层的厚度也可以预测。可以仔细研究两层内部的物理现象，纵向曲率为m = 1和n = 2的椭圆锥的条件以及其他参数条件；摄动参数ε_（m2）= 0.1，无扰动锥的半顶点角δ= 10°，高超声速相似性参数K_δ=M_∞δ= 1.0，涡旋层的厚度η_（VL）在圆锥体的位置角处计算出φ= 30°。结果表明，涡旋层非常薄，仅是靠近人体的震荡层的10％，整个震荡层中的压力被证明是一致有效的，这与以前的研究相吻合。当流体接近圆锥体表面时，会发现熵和密度的大梯度变化，最重要的是，该方法为通过圆锥体的高超声速流体提供了基准解决方案，并有助于网格和用于数值计算的数值的形成。容纳包括快速调节涡旋层在内的整个流场区域，并使分析变得更加有效和低成本。

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