Y. H. Kuo

At The Annual Meeting of the Institute of the Aeronautical Sciences, January, 1956, James M. Kendall, Jr., presented a set of highly interesting data on the characteristics of the flow over a flat plate at Mach number 5.8, obtained from the GALCIT 5- by 5-in. hypersonic wind tunnel. By measuring the impact pressure profiles and the static pressure along the plate, as previously reported by H. T. Nagamatsu, he was able to deduce the detailed structural features of the flow field. These results reveal definitely that the flow field between the shock and the plate has two distinct regions—the one which is close to the plate is of the boundary-layer type, and the other which is far from the plate is nearly inviscid and of the simple-wave type. This picture is in complete accord with the model that has been used in a theoretical calculation. To substantiate this point of view, it is proposed to make further quantitative comparisons.

Of the results reported by Kendall, the surface pressure was measured with the greatest degree of certainty. As the leading edge of the plate was thin (0.0002 in.), the thickness effects must have been very much reduced, if not entirely eliminated. The surface pressure affords, for this reason, the best chance of a check of the theoretical result. This comparison is made. The experimental points for three different Reynolds numbers fall very close to the theoretical curve for the parameter, less than 2 and lie below it beyond that value of ,i. e. very close to the leading edge.

Previously, D. Coles has made a similar measurement at Mach 3.7, which, when compared with theoretical values, was found consistently high. The good agreement now achieved by Kendall’s results shows definitely that the leading-edge geometry of Cole’s plate caused an additional deflection of the flow, as in the case of a wedge and, therefore, gave rise to a slightly higher pressure.

The divergence of the measurements and calculations beyond equals to 2 may well be attributed to the inaccuracies of either the pressures measured or those calculated in the neighborhood of the leading edge (less than 0.08 in. from the leading edge, say). Without further careful measurements nothing definite can be said at this moment.

Based on the impact-pressure profiles, Kendall deduces approximately the flow properties behind the shock, such as velocity, mass flow, static pressure, etc. Of these quantities, the static-pressure profile is the most interesting. It shows not only the behavior of the pressure inside the boundary layer and in the inviscid field but also the outer edge of the flow field—namely, the shock curve. The comparison with the estimated values at x=0.64 in. is given. That the measured surface pressure at x=0.64 in. is too high—an anomaly pointed out by Kendall—seems to be borne out by the calculations. On the whole, the agreement in this case is qualitative only.

From the impact-pressure profiles, Kendall also defines the shock curve and the edge of the boundary layer. These are compared with the corresponding calculated ones. The shock curve has been calculated not by means of the accurate formula but by its asymptotic form and is fitted to the measured value at x=0.25 in. As a result, the agreement for large x is not so good as expected. On the other hand, the calculated boundary-layer edge lies consistently below the estimated curve. This discrepancy can possibly be explained by the fact that the calculation was based on the choice of the similarity parameter to be 7 instead of 8. In any case, the agreement in the boundary-layer curve is quite close.

沿高速运动平板的粘性流动

郭永怀

在1956年1月的航空科学院的年会上，James M。Kendall给出了一组非常有意义的数据，描述了以马赫数5.8绕平板流动的特征，它们是在GALCIT的5×5英寸高超声速风洞中得到的。正如早先H. T. Nagamatsu报告的那样，测量沿平板冲击压力与静压分布，并导出流场详细的结构特征。这些结果明确地揭示出，激波与平板之间的流场有两个不同的区域——靠近平板的区域为边界层类型，远离平板的另一区域是几乎无粘性的、简单波类型的。这个图像完全与理论计算采用的模型一致。为证实这一观点，需要做进一步的定量比较。

在Kendall报告的结果中，极精确地测量了表面压力。由于平板的前缘薄(0.0002英寸)，厚度效应如果不是完全消除了的话，也已极大地减小了。由于这个原因，表面压力提供了检验理论结果的最好机会。三个不同雷诺数的实验点落在理论曲线位置上；若 < 2（也就是非常靠近前缘），实验点位于理论曲线下方。

以前，D. Coles曾给出马赫数为3.7时的类似测量，与理论值进行比较时发现总偏高。现在理论与Kendall结果很符合，这明确地表示，像尖劈的情况一样，Cole因平板前缘的几何形状产生的流动进一步偏折导致了略高的压力。

< 2时测量结果与计算之间的偏差很可能是由于压力测量不准确，或者是由于前缘附近（譬如距前缘小于0.08英寸）计算不准确造成的。没有进一步更仔细的测量，目前还不能肯定地说些什么。

根据冲击压力分布，Kendall近似地推导出激波后的流动性质，诸如速度，流量，静压等。在这些量中，静压剖面最有意义。它不仅给出边界层内和无粘性场中的压力特性，而且还给出流场的外缘，即激波曲线。给出了与x=0.64英寸时理论计算值的比较。在x=0.64英寸时测量的表面压力过高，看来Kendall指出的这一异常也得到了计算证实。总体看来，这种情况的一致性只是定性的。

Kendall还用压力分布确定激波和边界层边缘。与计算结果进行了比较。激波曲线并未采用准确公式进行计算，而是用渐近的形式，使与x=0.25英寸处的测量值符合。所以，大x时的一致性不像预期的那么好。另一方面，计算的边界层边缘总是低于计算值。这一不一致性也许可以用计算时选择的相似参数是7而不是8来解释。无论如何，边界层曲线还是十分接近的。

原文发表于Journal of the Aeronautical Sciences, 1956,23(11):1058-1059. 见《郭永怀文集》北京：科学出版社出版，pp. 573-574, 2009.