Abstract Membrane distillation is an emerging desalination process with important applications to the energy-water nexus. Its performance depends, however, on heat and mass transport phenomena that are uniquely challenging to simulate. Difficulties include two adjacent channel flows coupled by heat and mass transport across a semi-permeable membrane. Within the channels, heat and mass boundary layers interact with the membrane surface and vortical flow structures generated by complicated geometries. The presence of multiple inlets and outlets also complicates the application of mass-conserving outlet conditions. Moreover, even small amounts of outlet noise affect the resolution of important near-membrane fluid velocities. We show these phenomena can be simulated to second-order spatial and temporal accuracy using finite volume methods with immersed boundaries and projection methods. Our approach includes a projection method that staggers the coupled channel flows and applies Robin boundary conditions to facilitate mass conservation at the outlets. We also develop an immersed boundary method that applies Neumann boundary conditions to second-order spatial accuracy. The methods are verified and validated against manufactured solutions and theoretical predictions of vortex shedding. They are then applied to the simulation of steady and unsteady transport phenomena in membrane distillation. The methods have important applications to the broad field of chemical engineering and deal with long-standing issues in both theoretical and computational fluid dynamics.

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投影法和浸入式边界法在模拟膜蒸馏传热传质中的应用

摘要 膜蒸馏是一种新兴的海水淡化工艺，在能源-水关系中具有重要应用。然而，它的性能取决于对模拟具有独特挑战性的热量和质量传输现象。困难包括两个相邻的通道流动通过跨半透膜的热量和质量传输耦合。在通道内，热量和质量边界层与膜表面和由复杂几何形状产生的涡流结构相互作用。多个入口和出口的存在也使质量守恒出口条件的应用复杂化。此外，即使是少量的出口噪音也会影响重要的近膜流体速度的分辨率。我们展示了这些现象可以使用具有浸入边界和投影方法的有限体积方法模拟到二阶空间和时间精度。我们的方法包括一种投影方法，该方法交错耦合通道流并应用罗宾边界条件以促进出口处的质量守恒。我们还开发了一种浸入边界方法，该方法将诺依曼边界条件应用于二阶空间精度。这些方法针对制造的解决方案和涡旋脱落的理论预测进行了验证和验证。然后将它们应用于模拟膜蒸馏中的稳态和非稳态传输现象。这些方法在广泛的化学工程领域具有重要的应用，并且可以解决理论和计算流体动力学中长期存在的问题。