水下超声速气体射流线性稳定性研究

Linear Stability of Underwater Supersonic Gas Jet

关键词:  水下射流  超声速气体射流  线性稳定性  Chebyshev配置点法  气液两相流

Key words:  Underwater jet  Supersonic gas jet  Linear stability  Chebyshev collocation point method  Gas-liquid two-phase flow

摘要:

水下超声速气体射流稳定性是水下推进、水下焊接技术研究的焦点领域。通过建立线化小扰动气液混合流体控制方程，开展水下超声速气体射流线性稳定性研究。控制方程的形式表明，射流基本流分布（速度与浓度分布）、雷诺数、相对密度、相对粘度能够影响水下超声速气体射流稳定性。使用Chebyshev配置点法对控制方程进行求解。计算结果表明，射流基本流分布以及相对密度是影响射流稳定性的主要因素。射流基本流分布越平缓，射流最大扰动增长率越小；相对密度越小，即气液密度差越小，射流最大扰动增长率越小。随雷诺数增大，射流最大扰动增长率先减小后增大，当雷诺数>10⁵时，射流最大扰动增长率趋于常数。对不同相对粘度，射流扰动增长率-特征波数曲线高度重合。同时分析了射流不同截面的稳定性特征，计算结果表明，随射流截面与喷管出口距离的增加，最大扰动增长率减小。

Abstract:

Linear stability of underwater supersonic gas jet is the core field of underwater propulsion and underwater welding. The linearized small disturbance gas-liquid two-phase flow governing equations have been established to study the linear stability of underwater supersonic gas jet. The form of the governing equations indicate that the stability of underwater supersonic gas jet can be affected by the jet’s velocity and concentration distribution， Reynolds number， relative density and relative viscosity. Chebyshev collocation point method has been used to solve the governing equations. The calculation results show that the velocity and concentration distribution of the jet and the relative density are the main factors affecting the stability of the jet. The more flat the velocity and concentration distribution of the jet， the smaller the maximum growth rate of the jet. The smaller the relative density， means the smaller the density difference between gas and liquid， the smaller the maximum growth rate of the jet. As the Reynolds number increases， the maximum growth rate of the jet decreases first and then increases. The maximum growth rate of the jet approaches a constant when the Reynolds number is greater than 10⁵. The jet maximum growth rate-wavenumber curves are highly coincident for different relative viscosities. The stability of different jet’s cross-sections also has been analysed. The maximum growth rate of the jet decreases with increasing the distance from the nozzle， which is shown by the calculation.