Blunt-Body Heat Transfer at Hypersonic Speed and Low Reynolds Numbers

Abstract

with the computed value given by the analysis of Fay and Riddell using the actual measured pressure gradient which, in turn, agrees with the modified Newtonian formula; therefore, the analytical results are made nondimensional with respect to the value given by the analysis of Fay and Riddell. In order to make a correct comparison between these results and others, one must insure that the Reynolds number is calculated in the same way, and the qzeTO vorticity used is equal to the value given by the Fay and Riddell method, with the actual pressure gradient at the stagnation point. If these points are kept in consideration , then the results given by the methods of Refs. 2-4 are apparently in good agree­ ment with the experimental results and with the analysis of Ref. 1. Fig. 1 presents a comparison between experimental results, the results of Cheng's method, and the method of Ref. 1. The figure has been obtained in the following way. The ana­ lytical data of CH published in Ref. 2 have been used. These values have been divided by the CH value given by the Fay and Riddell method, using the actual pressure gradient at the stagna­ tion point of a sphere. In the figure other experimental results published by Witliff and Wilson are also included.4 In Fig. 11 of Ref. 4, the results of Ref. 4 and those of Ref. 1 are compared. Again, the differences are small. Similar considerations appear to be valid for the numerical comparison made in Ref. 3. In this case the ratio between the heat transfer with and without vorticity is given in the form 1 + Ke, where e is a function of the Reynolds number and Mach number. First, it is not .clear from the report if the value of heat transfer with zero vorticity obtained for this analysis is in agreement with the value given by Fay and Riddell or with experiments. We are discussing differences of 10 percent; therefore, any small difference in the value for zero vorticity is surely important. The second point is that some of the numbers presented in the report do not seem consistent with the definitions used. Specifically, on p. 43 of Ref. 3 a numerical analysis for Ma> = °°, for 7 = 7/5, is presented. The results are compared with results of Ref. 1 at Mm = 8. In this process the following transformation is presented [Eq. (3-28)]: Re«_A>_R:/hi~