Simulation of Electroosmotic and Pressure-Driven Mixed Flow of Viscoelastic Fluids in Converging-Diverging Tubes北大核心CSCD

The electroosmotic and pressure⁃driven mixed flow was widely used in various biochemical microflu⁃ idic fields, where the elastic instability of the viscoelastic fluid cannot be ignored. A viscoelastic fluid was used to numerically simulate electroosmotic and pressure⁃driven mixed flow in a 10 ∶ 1 ∶ 10 microchannel converging⁃ diverging tube. The effects of different pressures and different polymer concentrations on the fluid flow were studied, and the superposition principle for the velocity distributions of Newtonian fluids and viscoelastic fluids in converging⁃diverging tubes was analyzed. The results show that, the reverse pressure brings the viscoelastic fluid into higher instability, which makes the inlet vortex larger by 25 μm for every 1 Pa pressure increase. The positive pressure makes the eddy current smaller. For a relatively small reverse pressure, the inlet vortex in⁃ creases with the polymer concentration and tends to be stable gradually. For a relatively large reverse pressure, the vortex size first increases and then decreases with the polymer concentration. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

基于WENO重构的真正多维黎曼求解器

具有良好守恒性与网格适应性的有限体积格式在流体力学的数值计算中占有重要地位。其中，求解数值流通量是实施有限体积法的关键步骤。一维情形下，通过求解局部黎曼问题来获得数值流通量的相关理论已经比较成熟。但是在计算多维问题时，传统的维度分裂方法仅考虑沿界面法向传播的信息，这不仅影响格式的精度，还可能会造成数值不稳定性从而诱发非物理现象。本文基于对流-压力通量分裂方法来构造真正多维的黎曼求解器，通过求解网格顶点处的多维黎曼问题来实现格式的多维特性。采用五阶WENO重构方法来获得空间的高阶精度，时间离散采用三阶TVD龙格-库塔格式。一系列数值实验的结果表明，真正多维的黎曼求解器不仅具有更高的分辨率还能有效克服多维强激波模拟中的数值不稳定性。     

高速旋转流动中泰勒涡转捩点理论研究

本文基于超临界二氧化碳涡轮主轴轴间的旋转流动过程，开展了高速转轴环形间隙中流动特性的理论研究。通过已有的实验数据对数值计算方法进行验证，并在泰勒数Ta=6.63×10¹⁰～6.37×10¹¹的范围内研究多种因素对泰勒涡形成的影响。结果表明：在研究范围内，环形间隙中会形成泰勒涡，并且泰勒涡转捩点与长宽比、半径比、泰勒数和轴向雷诺数有关。同时，增大质量流量、降低转速、减小长宽比和增大半径比能抑制泰勒涡形成，提高流动稳定性。最后，通过整理数值结果获得了针对超临界二氧化碳泰勒库埃特泊肃叶流的泰勒涡转捩点的经验关联式，其平均误差为5.3%。