Abstract— The problems of designing the contours of two-dimensional and axisymmetric bodies of minimum wave drag and maximum-thrust nozzles, such that flow past them can contain internal shocks, are considered within the ideal (inviscid and non-heat-conducting) gas model. These shocks may occur in flows past internal breaks in the optimal contours or on intersection of characteristics of the same family proceeding from these breaks. The submerged shocks occurring in the latter case are named internal, if their initial points lie within the domain of determinacy of the flowed-over optimal contour region. Further downstream the domain of determinacy is bounded by the characteristic coming to the end point of this contour. The internal submerged shocks can appear, when the optimal contour includes an interval of an isobaric streamline. The appearance of internal breaks in the optimal contours is possible due to the reflection of the pressure waves induced by them from the bow shock (for body noses) or, as might be expected, from tangential discontinuities (for afterbodies). In the case of supersonic freestreams having a tangential discontinuity the search for optimal two-dimensional afterbodies with an internal concave break flowed-over with an oblique shock is performed using the direct method with the representation of the required contours by the Bernstein—Bézier curves, a genetic algorithm, and a rapid and accurate marching scheme for calculating steady supersonic flows. While the optimal two-dimensional afterbodies with a convex internal break designed earlier using the general method of Lagrange multipliers could be reliably reproduced using the above-mentioned method, the expected optimal configurations with a concave break and an internal shock were not found. Instead, optimal contours with centered compression and expansion waves with the common focus on a tangential discontinuity and an “external” oblique shock proceeding from it were discovered. Then the new “discontinuous shock-free” solutions were constructed in the exact formulation, within the framework of the method of indefinite control contours and the method of characteristics. The solutions are generalized to include the contours of the afterbodies of revolution and supersonic parts of nozzles. In the case of a uniform freestream the flow past optimal afterbodies never includes internal shocks.

中文翻译：

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超音速流中经过最佳体和喷嘴轮廓的内部冲击

摘 要：在理想的（无粘性和非导热）气体中考虑了设计最小波阻和最大推力喷嘴的二维和轴对称体轮廓的问题，使得流过它们的流可以包含内部冲击。模型。这些冲击可能发生在经过最佳等高线内部断裂的流动中，或者发生在从这些断裂出发的同一族特征的交集上。在后一种情况下发生的淹没冲击称为内部冲击，如果它们的初始点位于溢出最优轮廓区域的确定性域内。在更下游，确定性域以到达该轮廓终点的特征为界。当最佳等高线包括等压流线的间隔时，可能会出现内部淹没冲击。由于来自弓形激波（对于机头）或切向不连续（对于后体）引起的压力波的反射，可能会在最佳轮廓中出现内部中断。在具有切向不连续性的超音速自由流的情况下，使用直接方法搜索具有斜激波的内部凹折流的最佳二维后体，并使用伯恩斯坦 - 贝塞尔曲线表示所需的轮廓，一种遗传算法，以及一种用于计算稳定超音速流动的快速准确的前进方案。虽然使用上述方法可以可靠地再现先前使用拉格朗日乘子的一般方法设计的具有凸形内部断裂的最佳二维后体，没有找到具有凹形断裂和内部冲击的预期最佳配置。相反，发现了具有中心压缩波和膨胀波的最佳轮廓，共同关注切向不连续性和由此产生的“外部”斜激波。然后在不定控制轮廓方法和特征方法的框架内，以精确的公式构建新的“不连续无冲击”解决方案。解决方案被推广到包括旋转后体和喷嘴的超音速部分的轮廓。在均匀自由流的情况下，流过最佳后体的流从不包括内部冲击。发现了具有中心压缩波和膨胀波的最佳轮廓，共同关注切向不连续性和由此产生的“外部”斜激波。然后在不定控制轮廓方法和特征方法的框架内，以精确的公式构建新的“不连续无冲击”解决方案。解决方案被概括为包括旋转后体和喷嘴的超音速部分的轮廓。在均匀自由流的情况下，流过最佳后体的流从不包括内部冲击。发现了具有中心压缩波和膨胀波的最佳轮廓，共同关注切向不连续性和由此产生的“外部”斜激波。然后在不定控制轮廓方法和特征方法的框架内，以精确的公式构建新的“不连续无冲击”解决方案。解决方案被概括为包括旋转后体和喷嘴的超音速部分的轮廓。在均匀自由流的情况下，流过最佳后体的流从不包括内部冲击。在不定控制轮廓法和特征法的框架内。解决方案被推广到包括旋转后体和喷嘴的超音速部分的轮廓。在均匀自由流的情况下，流过最佳后体的流从不包括内部冲击。在不定控制轮廓法和特征法的框架内。解决方案被概括为包括旋转后体和喷嘴的超音速部分的轮廓。在均匀自由流的情况下，流过最佳后体的流从不包括内部冲击。