Efficient prediction method for Kelvin-Helmholtz instability growth on transcritical droplet surface in composite coordinate system
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摘要:
针对混合动力专用内燃机实际运行的跨临界条件，传统方法对于主导可燃混合气形成质量的液滴表面Kelvin-Helmholtz不稳定性分析方法难以实现跨临界宽范围的有效预测。采用复合坐标系方法，建立跨临界强对流环境的等效液滴不稳定性高效预测模型，分别采用全局扩散动力学模型、热力学控制模型及局部液滴表面切向不稳定模型。在全局坐标系模型可以通过模态坐标变换求得解析解，局部坐标系引入势函数等，提高求解速度。而对于可实用性流体计算仿真模型，可通过无量纲物理参数描述不同跨临界条件下空气动力、惯性力、黏性力、表面张力、加速度等控制因素的变化规律，以及其对液滴表面切向和法向不稳定波增长的影响规律。结果表明：液滴表面的空气动力仍然支配着跨临界条件液滴表面切向不稳定波的发展；压力增大时，液相雷诺数控制的流动特性减小与欧尼索控制的液滴黏性力减弱基本抵消；环境温度增加时，雷诺数表征的流动特性对Kelvin-Helmholtz波增长的贡献越来越小，液滴的惯性力影响也越来越弱。
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关键词:
- 复坐标系 /
- 跨临界 /
- 液滴 /
- 表面Kelvin-Helmholtz不稳定 /
- 高效预测
Abstract:Traditional methods for analyzing the Kelvin-Helmholtz instability on the surface of droplets that dominate the formation mass of combustible mixtures are difficult to achieve effective predictions over a wide range of critical conditions for the actual operation of hybrid internal combustion engines. In this paper, the composite coordinate system method was used to establish an efficient prediction model of equivalent droplet instability in a transcritical strong convection environment. The global diffusion dynamics model, thermodynamics control model, and tangential instability model of local droplet surface were used, respectively. The analytical solution could be obtained by the modal coordinate transformation in the global coordinate system model, and the potential function was introduced in the local coordinate system to improve the solution speed. To realize a practical fluid computational simulation model, the dimensionless physical parameters were used to describe the changes in aerodynamic force, inertial force, viscous force, surface tension, and other control factors under different transcritical conditions and analyze their influence on the growth of tangential and normal unstable waves on the droplet surface. The results show that the aerodynamic forces on the droplet surface still dominate the development of tangential unstable waves on the droplet surface under transcritical conditions. When the pressure increases, the decrease in the flow characteristics controlled by Reynolds number in liquid phase and the decrease in the viscous force of the droplet controlled by Ornisol number basically offset. With the increase in ambient temperature, the contribution of flow characteristics controlled by Reynolds number to the growth of the Kelvin-Helmholtz wave becomes small, and the influence of the inertial force of the droplet becomes weak.
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图 1 跨临界复合坐标系统液滴切向不稳定模型示意
Figure 1. Tangential instability model of droplet in transcritical composite coordinate system
图 2 局部表面坐标系K-H不稳定表面波示意
Figure 2. K-H unstable surface waves in local surface coordinate system
图 3 液滴迎风面破碎高速摄影图像
Figure 3. High-speed photographic image of droplets breaking up on the windward side
图 4 不同环境压力下各参数随无量纲时间的变化曲线
Figure 4. Variation of variables with dimensionless time under different ambient pressures
图 5 不同环境压力下最大K-H增长率随无量纲时间的变化曲线
Figure 5. Variation of maximum K-H growth rate with dimensionless time under different environmental pressures
图 6 不同环境温度下各参数随无量纲时间的变化曲线
Figure 6. Variation of variables with dimensionless time under different ambient temperatures
图 7 不同环境温度下最大K-H增长率随无量纲时间的变化曲线
Figure 7. Variation of maximum K-H growth rate with dimensionless time under different ambient temperatures
表 1 不稳定波长与初始粒径比的试验与数值模拟结果
Table 1. Experimental and numerical simulation results of ratio of unstable wavelength to initial particle size
对比态环境压力Pr 对比态初始液滴温度Trdrop0 对比态环境温度Tramb 气流速度urel /(m·s−1) λ/d0计算值 λ/d0试验值 1.1 0.53 0.95 80 0.53 0.6 1.6 0.53 0.95 80 0.4 0.4 1.0 0.59 0.95 80 0.62 0.7 1.0 0.78 0.95 80 0.3 0.3 1.0 0.53 0.66 80 0.60 0.7 1.0 0.53 1.15 80 0.56 0.6 1.0 0.53 0.95 80 0.59 0.6 1.0 0.53 0.95 100 0.43 0.5 
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