A small-disturbance model is presented for the complex dynamics of vortex flows of moist air in a straight, circular pipe with non-equilibrium and homogeneous condensation. The model explores the nonlinear interactions among the vortex near-critical swirl ratio and the small amount of water vapour in the air. The condensation rate is calculated according to classical nucleation and droplet growth models. The asymptotic analysis gives the similarity parameters that govern the flow problem. These are the flow inlet swirl ratio $\unicode[STIX]{x1D714}$ , the inlet Mach number $Ma_{0}$ , the initial humidity $\tilde{\unicode[STIX]{x1D714}}_{0}$ , the number of water molecules in a characteristic fluid element $n_{C}$ , the inlet centreline super-saturation ratio $S_{0}$ and the ratio of characteristic condensation and flow time scales $K$ . Also, the flow field may be described by an ordinary first-order nonlinear differential equation for the flow evolution coupled with a set of four first-order ordinary differential equations along the pipe for the calculation of the condensate mass fraction. An iterative numerical scheme which combines the Runge–Kutta integration technique for the flow dynamics with Simpson’s integration rule for the calculation of the condensation variables is developed. Specifically, equilibrium states are determined, including the possibility of the appearance of multiple states under the same boundary conditions, and the stability characteristics of these states are described. The model is used to study the effects of humidity and of energy supply from nanoscale condensation processes on the large-scale dynamics of vortex flows as well as the effect of flow swirl on condensation processes in swirling flows.

中文翻译：

---

具有非平衡和均匀冷凝的潮湿空气涡流

提出了一个小扰动模型，用于在具有非平衡和均匀冷凝的直管中潮湿空气涡流的复杂动力学。该模型探讨了涡流近临界涡流比与空气中少量水蒸气之间的非线性相互作用。根据经典的成核和液滴生长模型计算冷凝率。渐近分析给出了控制流动问题的相似性参数。这些是流动入口涡流比 $\unicode[STIX]{x1D714}$ ，入口马赫数 $Ma_{0}$ ，初始湿度 $\tilde{\unicode[STIX]{x1D714}}_{0}$ ，特征流体元素 $n_{C}$ 中的水分子数，入口中心线过饱和比 $S_{0}$ 以及特征凝结和流动时间尺度的比率 $K$ 。还，流场可以用流动演化的普通一阶非线性微分方程和沿管道的一组四个一阶常微分方程来描述，用于计算冷凝物质量分数。开发了一种迭代数值方案，该方案将用于流动动力学的 Runge-Kutta 积分技术与用于计算冷凝变量的 Simpson 积分规则相结合。具体地，确定了平衡状态，包括在相同边界条件下出现多个状态的可能性，并描述了这些状态的稳定性特征。