Normal shocks are generally treated by defining a stationary adiabatic shock discontinuity with a supersonic upstream velocity. A fundamental feature of this approach is that the problem is steady, and the stagnation enthalpy is constant across the shock, greatly simplifying the analysis. However, shocks are generally not stationary, but rather are unsteady flow features often translating into a quiescent medium. Moreover, the stagnation enthalpy of a fluid will rise in a moving shock, an often unexpected result for students studying compressible flow. In this paper, stationary normal shocks are analyzed using the classic Rankine–Hugoniot equations. The analysis is then transformed to consider a moving shock propagating into a quiescent medium. This analysis produces a simple expression relating the stagnation enthalpy rise across a moving normal shock as a function of the shock strength as measured by either the shock pressure ratio or differential pressure across the shock. An unsteady integral control volume analysis is then used to show that the cause for the stagnation enthalpy rise is the work done by the fluid downstream of the shock to compress the upstream fluid upstream.

中文翻译：

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基于物理学的移动正激波的停滞焓上升研究

通常通过定义具有超音速上游速度的静止绝热冲击不连续性来处理正常冲击。这种方法的一个基本特征是问题是稳定的，并且整个激波的停滞焓是恒定的，从而大大简化了分析。然而，冲击通常不是静止的，而是经常转化为静止介质的不稳定流动特征。此外，流体的停滞焓会在运动激波中升高，这对于研究可压缩流的学生来说往往是意想不到的结果。在本文中，使用经典的 Rankine-Hugoniot 方程来分析平稳法向冲击。然后将分析转换为考虑传播到静止介质中的移动冲击。该分析产生了一个简单的表达式，该表达式将移动法向激波上的停滞焓升作为冲击强度的函数，该强度由冲击压力比或冲击波两端的压差测量。然后使用非定常积分控制体积分析来表明停滞焓升高的原因是激波下游的流体压缩上游流体所做的功。