A method using computational fluid dynamics for evaluating a correlation for shock shape with a temperature gradient over spherical nose bodies in perfect gas air

In this study a correlation for determining shock shape around spherical bodies at supersonic velocity in perfect gas air with a temperature gradient is evaluated using a computational fluid dynamics flow solver. The work is inspired by Russian experimentation with shock shape changes in weakly ionized gases where possible temperature gradients exist in the flow field. Some background information and references are given to support this data. The technique involves the use of a known flow solver (ZTUFF code) with minor modifications made to add the capability of introducing radial temperature gradients across the flow field. The resulting non-uniform flow field produces shock shape results that differ from those obtained in a uniform flow field that can be useful to determine temperature gradients in real flow field scenarios. The shock shape correlation work of Billig (4) is evaluated for accuracy with temperature gradients. The ZTUFF code is used to obtain perfect gas two dimensional axisymmetric inviscid temperature gradient solutions for Mach numbers of 2.35, 5.0, and 8.0 and Reynolds numbers of 9750,20616, and 32064 respectively around a spherical body of 0.019 meters diameter. The correlation is then used to create similar shock shape curves to determine the accuracy of the correlation versus the ZTUFF code results with an identical temperature gradient. It is found that the correlation is accurate for positive linear temperature gradients but not for negative linear temperature gradients over the range of Mach numbers presented herein with inviscid perfect gas solutions.