【摘要】 本文应用摄动法给出了一种简便的计算任意二元和轴对称细长喷管可压缩有势流动的近似解析方法。流场的解是相对于一个表示喷管细长程度的小参数进行渐近展开,而展开式的首项就取喷管当地截面处的一元流的解。对于速度分量,文中给出了展开式中的前两项的表达式。数值算例的结果表明,当喷管壁的斜率大约不超过20°,喷管壁的曲率半径大约不小于喷管截面半高度的4～5倍时,用本方法计算的速度的模的相对误差不超过1％。本方法可用于计算Laval喷管内由亚音速加速到超音速时的流场。更多还原

【Abstract】 A simple and approximate analytical method for calculations of compressible potential flows in arbitrary two-dimensional and axially symmetric slender nozzles is given using perturbation technique. The solutions of the flow field are expanded asymptotically with respect to a small parameter defining the slenderness of the nozzle, whereas the local one-dimensional solutions are taken as the leading terms in the expansions. Two term expansions are obtained for the velocity components. Numerical examples show that the relative error for the magnitude of the v.elocity is less than 1%, provided the slope of the nozzle wall is less than about 20° and the radius of the curvature of the nozzle wall is greater than about 4-5 times of the half height of the nozzle throat. The present theory can be used for the calculations of the flow field in Laval nozzles accelerating from subsonic to supersonic.更多还原