Derivation and stability analysis of two-fluid model equations for bubbly flow with bubble oscillations and thermal damping
Derivation and stability analysis of two-fluid model equations for bubbly flow with bubble oscillations and thermal damping
复制标题
DOI：
10.1016/j.ijmultiphaseflow.2023.104456
复制
发表时间：
2023-05-03
影响因子：
3.8
通讯作者：
Kanagawa, Tetsuya
中科院分区：
文献类型：
--
作者：
Ayukai, Takahiro;Kanagawa, Tetsuya
Egashira等人（2004）提出的含气泡振荡的双流体模型可以较好地解释空泡泡流的特性和压力波在泡状液体中的传播。然而，粘性效应以及能量守恒导致的气泡内的温度变化与气泡振荡尚未被考虑。因此，本研究的目的是将粘性（体积粘度和阻力）和热效应，以前提出的双流体模型与气泡振荡。体粘度通过平均牛顿流体单相动量守恒中的剪切应力项来考虑，阻力通过转换界面剪切应力来引入。我们推导了一般的两相流的平均能量守恒与气泡内的热传导和两相之间的热传递，并限制这个方程的泡状流通过封闭的界面温度梯度项通过本构方程为一个单一的气泡。此外，我们研究了我们提出的一维模型方程的稳定性，使用色散分析。该分析提供了以下见解：（i）温度梯度模型的差异对所提出的模型方程的稳定性有轻微影响;（ii）气泡内的热传导在泡状流的热阻尼中占主导地位，而不是两相之间的热传递;（iii）将体积粘度和阻力两者结合在一起稳定了所提出的模型方程。我们的研究结果提供了深入了解的数学模型的发展，以调查泡状流与气泡振荡，如空化泡状流和波在气泡液体中的传播的热效应。
The two-fluid model with bubble oscillations, proposed by Egashira et al. (2004), can explain the properties of cavitating bubbly flow and pressure wave propagation in the bubbly liquid. However, the viscous effect as well as energy conservation leading to temperature changes inside the bubble with bubble oscillations have not yet been considered. Hence, this study aimed to incorporate the viscous (bulk viscosity and drag) and thermal effects to the previously proposed two-fluid model with bubble oscillations. Bulk viscosity was considered by averaging the shear stress term in the single-phase momentum conservation for a Newtonian fluid, and the drag was introduced by transforming the interfacial shear stress. We derived the averaged energy conservation for a general two-phase flow with a thermal conduction inside bubbles and heat transfer between the two phases, and limited this equation to that for a bubbly flow by closing the interfacial temperature gradient term via constitutive equations for a single bubble. Furthermore, we investigated the stability of our proposed one-dimensional model equations using the dispersion analysis. This analysis provided the following insight: (i) The difference in the temperature gradient models had a slight effect on the stability of the proposed model equations; (ii) the thermal conduction inside the bubbles was dominant in the thermal damping in bubbly flows rather than the heat transfer between the two phases; (iii) incorporating both the bulk viscosity and drag stabilized the proposed model equations. Our results provide insights into the development of mathematical models to investigate the thermal effects in bubbly flow with bubble oscillations, such as cavitating bubbly flow and wave propagation in bubbly liquids.