马赫数3到7的变比热正冲波的改进解析解及近似解

IMPROVED ANALYTICAL SOLUTION AND APPROXIMATE SOLUTION OF VARYING SPECIFIC HEAT NORMAL SHOCK WAVES FOR MACH NUMBERS 3 TO 7

关键词:  变比热  正激波  改进解析解  近似解法

Key words:  Varying specific heat  Normal shock wave  inproed analytical solution  Approximate solution

摘要:

作者提出的变比热正冲波改进解析解,延伸用于马赫数从3到7情况,求出过冲波后全部气动参数,按马赫数间隔为1列表给出。并附列定比热结果误差。同时提出了只取初温到终温平均比热的单比热比k₁₂近似解,平行列出结果及误差。

Abstract:

The author first derived varying specific heat gasdynamic functions formulae[1], and applied them to analytical solution of normal shock waves[2]. In view of the physical process of shock wave not including total temperature at all, an improved analytical solution was initiated,including only specific heat ratios kT1, kT2 for initial and final temperatures and k12 for the average specific heat between them, which is simpler, quicker, more rational and accurate[3].In this paper, the improved solution extends from Mach number 3 to a range of 3 to 7. All parameters after shock are tabulated. The corresponding results and errors of fixed specific heat k = 1. 4 solution are also shown, which give rapid error increase when M1 increases.An approximate solution using single k12 is then proposed with the results alsoaccompanying. In general, the errors are smaller than the fixed specific heat solution, and might thus be accepted in primary evaluations.The rapid increase of errors of approximate and fixed specific heat solution, however, enlightens a field of vision that at higher Mach numbers, the varying specific heat effect should be carefully distinguished from viscous effects and experimental errors.Varying specific heat,Normal shock wave,improved analytical solution, Approximate solution