粘性圆柱液体喷射进入不可压缩气流中的线性稳定性分析

发布时间：2018-01-28 21:55

本文关键词： 圆柱液膜线性稳定性色散关系式表面波增长率　出处：《长安大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文主要对圆柱液膜射流的线性稳定性进行了分析,从已知理论我们可以知道表面波增长率是影响圆柱液膜射流稳定性的一个特征因素。但是从推导得到的色散关系式中,我们可以看出表面波增长率和表面波数之间的关系是隐含给出的,它的解析解不能通过直接求解得到,所以需应用Fortran语言,采用Muller迭代方法编制相应的程序求得数值解。在分析过程中,通过改变输入参数的值来得到不同条件下的表面波增长率随表面波数的变化关系,可以得知液流速度lU、雷诺数lRe、马赫数Ma、韦伯数lWe、欧拉数lEu、欧尼索数lOh这些量纲一参数对圆柱液体射流的稳定性都有着十分重要的影响。把编程输出的数据绘制成图,对圆柱液膜的线性稳定性进行了分析:圆射流的单股状正对称波形(n=0)、反对称波形(n=1)、双股状正对称波形(n=2)、三股状反对称波形(n=3)这四种情况所绘制出的曲线的形状都呈倒U型,当表面波数k值增大时,表面波增长率r?出现先增大后减小的趋势。也就是随表面波数的增加,表面波增长率都有一个最大值,这个峰值表示了圆柱液膜射流在此表面波增长率下最有可能碎裂,此时相对应的波数称为支配波数即为最易导致圆柱液膜射流碎裂的表面波波数;本文也论述了韦伯数对圆射流的影响,随着韦伯数lWe逐渐增大,支配波数domk在逐渐增大,与其对应的支配表面波增长率domr,?也在增大,这可以说明在表面张力很小的情况下,空气动力的作用越大,液体表面波碎裂的可能性越大;在本文中通过比较单股状圆柱液体的正对称波形和反对称波形,可以得知韦伯数相同时,正对称波形的表面波增长率要比反对称波形的表面波增长率大,这可以说明比起正对称波形来,反对称波形的表面波更稳定。也就是说正对称波形的表面波比反对称波形的表面波更易碎裂。所以,在雾化过程中,正对称波形的表面波将起主导作用,反对称波形的表面波起次要作用;比较正对称与反对称波形的韦伯数,它们的大小是不相同的,反对称波形的韦伯数比正对称波形的韦伯数大,当韦伯数比较大时,圆柱液体的表面波增长率较大,此时圆柱液体更容易碎裂。由于圆射流速度为低、中速时容易形成正对称波形的表面波,而中高速圆柱液体则易形成反对称波形的表面波,所以对于许多实际喷雾来说,对于反对称波形的研究比对正对称波形的研究更有重大意义;在本文中还对不同阶数下的圆柱液体的表面波增长率进行了分析,可以得知单股状圆柱液体的雾化效果比双股状、三股状圆柱液体的雾化效果要好;本文还论述了液体粘性对圆射流的影响,从分析结果可知随着圆柱液体粘度的增大,表面波增长率在逐渐地变小,这可以说明液体粘性的增大使得液体表面波愈趋于稳定,圆柱液体更不容易碎裂,使得雾化效果变差。
[Abstract]:In this paper, the linear stability of liquid film jet is analyzed. From the known theory we can know that the growth rate of surface wave is a characteristic factor affecting the stability of cylindrical liquid film jet. We can see that the relationship between the growth rate of surface wave and the number of surface wave is given implicitly, its analytical solution can not be obtained by direct solution, so we need to use Fortran language. The numerical solution is obtained by using the Muller iterative method. In the process of analysis, the relationship between the surface wave growth rate and the surface wave number under different conditions is obtained by changing the value of the input parameters. The velocity of liquid flow, Reynolds number, Mach number, Weber number and Euler number lEu can be obtained. The dimensionality parameters of lOh are very important to the stability of liquid jet. The linear stability of cylindrical liquid film is analyzed as follows: the single-strand normal symmetric waveform of circular jet, the anti-symmetric waveform, and the double-strand normal-symmetric waveform. The shape of the curves drawn in these four cases is inverted U shape. When the surface wave number k increases, the growth rate of the surface wave is r? With the increase of the surface wave number, the growth rate of the surface wave has a maximum value, which indicates that the cylindrical liquid film jet is most likely to break down under the growth rate of the surface wave. The corresponding wave number is called dominant wave number which is the surface wave number which is the most likely to lead to the breakup of cylindrical liquid film jet. The influence of Weber number on circular jet is also discussed in this paper. With the increasing of Weber number lWe, the dominating wavenumber domk is gradually increasing, and the corresponding dominating surface wave growth rate is domr? It can be concluded that the greater the effect of aerodynamic force is, the greater the possibility of surface wave fragmentation is when the surface tension is very small. In this paper, by comparing the normal and antisymmetric waveforms of single-stranded cylindrical liquids, we can find that the growth rate of the surface waves of the normal symmetric waveforms is higher than that of the antisymmetric waveforms when the Weber number is the same. This shows that the surface wave of the antisymmetric waveform is more stable than that of the symmetric waveform. That is to say, the surface wave of the symmetric waveform is more easily broken than the surface wave of the antisymmetric waveform. Therefore, in the atomization process. The surface wave of the symmetric waveform will play a leading role, and the surface wave of the antisymmetric waveform will play a secondary role. The Weber numbers of symmetric and antisymmetric waveforms are different. The number of Weber of antisymmetric waveforms is larger than that of positive symmetric waveforms, when the number of Weber numbers is larger. The growth rate of surface wave of cylindrical liquid is large, and the cylindrical liquid is more easily broken. Due to the low velocity of circular jet, the surface wave with normal symmetry wave can easily be formed at medium velocity. But the medium and high speed cylindrical liquid is easy to form the surface wave of the antisymmetric waveform, so for many practical spray, the research on the antisymmetric waveform is more important than the study of the normal symmetric waveform. In this paper, the surface wave growth rate of cylindrical liquid with different order is also analyzed. It can be found that the atomization effect of single-stranded cylindrical liquid is better than that of double-stranded cylindrical liquid, and the atomization effect of triplicate cylindrical liquid is better than that of double-stranded cylindrical liquid. The effect of liquid viscosity on circular jet is also discussed in this paper. The results show that the growth rate of surface wave becomes smaller with the increase of liquid viscosity. It can be concluded that the increase of liquid viscosity makes the surface wave of liquid more stable and the cylindrical liquid more difficult to break down, which makes the atomization effect worse.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TK05

【引证文献】