Abstract

In high-speed flows, blunt body elements having an irregular shape due to which gas dynamic parameters undergo significant changes are, as a rule, the most thermally loaded parts. In this respect, a quick evaluation of the thermal load on blunt bodies is important. Laminar boundary-layer equations given in special coordinates in a constant axisymmetric flow of a compressible perfect gas are considered. The adhesion condition is accepted as a boundary condition on the wall and it is assumed that the speed and temperature on the boundary correspond to the values of the external flow. The Pohlhausen method introduces the concepts of the displacement thickness and momentum thickness, finds relations between these values and the boundary-layer thickness, and derives a differential equation to determine the boundary-layer form parameter such that all other characteristics of the boundary layer are determined via it. The Pohlhausen method is modified in order to simplify the calculation by excluding the differential equations from it. Similarly to the velocity, a special function including the enthalpy and dimensionless kinetic parameter to be determined is introduced as a biquadratic polynomial. The boundary conditions on the wall and on the border of the boundary layer are used to determine the polynomial coefficients. The kinetic parameter is defined in different ways for bodies of various shapes. We provide the results of applying the proposed method for the calculation of heat flux that have been analyzed numerically (in various papers) in complete systems of Navier-Stokes and Prandtl equations. The comparison of the results shows the efficiency of the proposed method.

中文翻译：

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钝体附近层流边界层的分析研究

摘要

在高速流动中，具有不规则形状的钝体元件通常是受热负荷最大的部分，由于这些因素，气体动力学参数会发生显着变化。在这方面，快速评估钝体上的热负荷很重要。考虑在可压缩的理想气体的恒定轴对称流中以特殊坐标给出的层流边​​界层方程。粘附条件被接受为壁上的边界条件，并且假定边界上的速度和温度对应于外部流动的值。Pohlhausen方法引入了位移厚度和动量厚度的概念，找到了这些值与边界层厚度之间的关系，并导出微分方程以确定边界层形式参数，以便通过边界方程确定边界层的所有其他特征。修改了Pohlhausen方法，以便通过从中排除微分方程来简化计算。与速度相似，将包含待确定的焓和无量纲动力学参数的特殊函数引入为双二次多项式。使用墙和边界层边界上的边界条件来确定多项式系数。对于各种形状的物体，以不同的方式定义了动力学参数。我们提供了将拟议方法应用于热通量计算的结果，该方法已在完整的Navier-Stokes和Prandtl方程组中进行了数值分析（在各种论文中）。结果的比较表明了该方法的有效性。