锥形液膜空间稳定性分析

对离心喷嘴喷出的锥形液膜做了空间不稳定性分析,导出了锥形液膜的色散方程,并对色散方程进行了数值求解和分析研究。研究结果表明,在液膜表面存在着对称扰动波和反对称扰动波。对于对称扰动波,液膜半锥角的增大使得液膜的不稳定范围和波增长率缩小,并且将扰动波的主波向长波的方向移动。而反对称扰动波既有类似于对称扰动波的变化规律,又有其自身的特点。仅考虑液膜曲率半径的变化时,半锥角的增大使得波增长率的减小趋缓。而同时考虑曲率半径和液膜形状的变化时,液膜的波增长率出现了两个局部峰值。这两个峰值分别对应长短不同的两个波长,并且短波的稳定范围和增长率均远小于长波。这说明锥形液膜的破碎受到两种长短不同的扰动波的共同影响,且在短波的影响下液膜更易破碎。 

On the Spatial Instability of a Conical Sheet

A temporal instability analysis of a conical sheet is carried out.A dispersion relation of a conical sheet for both axisymmetrical and antisymmetrical disturbances is presented.The dispersion relation has been solved numerically and typical results are given.For both axisymmetrical and antisymmetrical disturbances,the increase in sheet cone half-angle reduces the wave growth rate and the range of instability,and shifts the dominant wave of the disturbances to a longer wavelength.For antisymmetrical disturbances,the sheet cone half-angle inhibits the reduction of the growth rate, and two local maxima of the growth rate exist in this case.The two maximum growth rates correspond to waves with different wavelengths,and the growth rate and the range of instability of the short wavelength wave are much less than that of the long one.It is shown that both long and short wavelength waves affect the breakup of the conical sheet,and sheet is easy to breakup under the effect of short wavelength wave.