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首页> 外文期刊>Journal of Heat Transfer >Explicit Inversion of Stodola's Area-Mach Number Equation
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Explicit Inversion of Stodola's Area-Mach Number Equation

机译：Stodola的面积-马赫数方程的显式反演

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摘要

Stodola's area-Mach number relation is one of the most widely used expressions in compressible flow analysis. From academe to aeropropulsion, it has found utility in the design and performance characterization of numerous propulsion systems; these include rockets, gas turbines, microcombustors, and microthrusters. In this study, we derive a closed-form approximation for the inverted and more commonly used solution relating performance directly to the nozzle area ratio. The inverted expression provides a computationally efficient alternative to solutions based on traditional lookup tables or root finding. Here, both subsonic and supersonic Mach numbers are obtained explicitly as a function of the area ratio and the ratio of specific heats. The corresponding recursive formulations enable us to specify the desired solution to any level of precision. In closing, a dual verification is achieved using a computational fluid dynamics simulation of a typical nozzle and through Bosley'sformal approach. The latter is intended to confirm the truncation error entailed in our approximations. In this process, both asymptotic and numerical solutions are compared for the Mach number and temperature distributions throughout the nozzle.
机译：Stodola的面积-马赫数关系是可压缩流动分析中使用最广泛的表达式之一。从学术界到航空推进，它已在许多推进系统的设计和性能表征中找到了实用工具。其中包括火箭，燃气轮机，微型燃烧器和微型推进器。在这项研究中，我们得出了倒置和更常用的解决方案的闭合形式近似值，该解决方案将性能直接与喷嘴面积比相关。反向表达式为基于传统查找表或根查找的解决方案提供了计算有效的替代方案。在这里，亚音速和超音速马赫数都明确地作为面积比和比热比的函数获得。相应的递归公式使我们能够以任何精度级别指定所需的解决方案。最后，使用典型喷嘴的计算流体动力学模拟并通过Bosley的形式方法进行了双重验证。后者旨在确认我们的逼近法所带来的截断误差。在此过程中，比较渐近解和数值解的马赫数和整个喷嘴的温度分布。

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