层流泡状流的近似解析解

当前描述泡状流的双流体模型无法求得解析解，只能通过数值计算的方法进行模拟.本文则针对最基本的泡状流（垂直圆管内稳态层流泡状流），通过对其双流体模型进行积分，得到比较直观的揭示层流泡状流流场成因的近似解析表达式.并用数值积分的方法迭代求解该表达式，所得到的数值结果与实验数据吻合很好.虽然该表达式是积分形式的，仅能算是近似的解析解，但它揭示了影响泡状流流场的因素，在理论上向前迈进了一步.

Approximate analytical results for two-fluid model of laminar bubbly flow

The two-fluid model is usually taken to predict the bubbly flow.The direct numerical calculation is often used for it, because it can not get the analytical results.In this paper, the results in integration type (i.e. the approximate analytical results) of the most simple type of bubbly flow and fully developed laminar bubbly flow in vertical pipe, are derived by symbol integration of the two-fluid model.Then they are calculated in numerical integration and compared with the experimental data.The numerical results coincide with the experimental data.Though the integration type results are not the analytical results of two-fluid model of bubbly flow, they can show what influences the flow field of bubbly flow.So they are good approximation of analytical results and have an advantage over direct numerical calculation.