This article shows the importance of flow compressibility on the heat transfer in confined impinging jets, and how it is driven by both the Mach number and the wall heat-flux. Hence, we present a collection of cases at several Mach numbers with different heat-flux values applied at the impingement wall. The wall temperature scales linearly with the imposed heat-flux and the adiabatic wall temperature is found to be purely governed by the flow compression. Especially for high heat-flux values, the non-constant wall temperature induces considerable differences in the thermal conductivity of the fluid. This phenomenon has to date not been discussed and it strongly modulates the Nusselt number. In contrast, the heat transfer coefficient is independent of the varying thermal properties of the fluid and the wall heat-flux. Furthermore, we introduce the impingement efficiency, which highlights the areas of the wall where the temperature is influenced by compressibility effects. This parameter shows how the contribution of the flow compression to raising the wall temperature becomes more dominant as the heat-flux decreases. Thus, knowing the adiabatic wall temperature is indispensable for obtaining the correct heat transfer coefficient when low heat-flux values are used, even at low Mach numbers. Lastly, a detailed analysis of the dilatation field also shows how the compressibility effects only affect the heat transfer in the vicinity of the stagnation point. These compressibility effects decay rapidly further away from the flow impingement, and the density changes along the developing boundary layer are caused instead by variable inertia effects.

中文翻译：

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湍流冲击射流中的可压缩性和可变惯性对传热的影响

本文展示了流动可压缩性对受限撞击射流中传热的重要性，以及它是如何受马赫数和壁面热通量驱动的。因此，我们在几个马赫数下展示了一系列案例，这些案例在冲击壁上应用了不同的热通量值。壁温与施加的热通量成线性比例，绝热壁温被发现完全由流动压缩控制。特别是对于高热通量值，非恒定的壁温会导致流体热导率的显着差异。迄今为止，这种现象还没有被讨论过，它强烈地调节了努塞尔特数。相比之下，传热系数与流体和壁面热通量变化的热特性无关。此外，我们介绍了冲击效率，它突出显示了温度受可压缩性影响的壁区域。该参数显示了随着热通量的降低，流动压缩对提高壁温的贡献如何变得更加重要。因此，当使用低热通量值时，即使在低马赫数下，了解绝热壁温对于获得正确的传热系数也是必不可少的。最后，对膨胀场的详细分析还显示了压缩效应如何仅影响驻点附近的传热。这些可压缩性效应在远离流动冲击的地方迅速衰减，并且沿发展边界层的密度变化是由可变惯性效应引起的。它突出显示了温度受可压缩性影响的壁区域。该参数显示了随着热通量的降低，流动压缩对提高壁温的贡献如何变得更加重要。因此，当使用低热通量值时，即使在低马赫数下，了解绝热壁温对于获得正确的传热系数也是必不可少的。最后，对膨胀场的详细分析还显示了压缩效应如何仅影响驻点附近的传热。这些可压缩性效应在远离流动冲击的地方迅速衰减，并且沿发展边界层的密度变化是由可变惯性效应引起的。它突出显示了温度受可压缩性影响的壁区域。该参数显示了随着热通量的降低，流动压缩对提高壁温的贡献如何变得更加重要。因此，当使用低热通量值时，即使在低马赫数下，了解绝热壁温对于获得正确的传热系数也是必不可少的。最后，对膨胀场的详细分析还显示了压缩效应如何仅影响驻点附近的传热。这些可压缩性效应在远离流动冲击的地方迅速衰减，并且沿发展边界层的密度变化是由可变惯性效应引起的。