Lubrication analysis based on consistent direct discretisation and its application to particle-dispersed multiphase flows

2021 Fiscal Year Final Research Report

• Project/Area Number: 17H03174
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fluid engineering
• Research Institution: Osaka University
• Principal Investigator: Takeuchi Shintaro 大阪大学, 工学研究科, 准教授 (50372628)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 潤滑 / 粒子を含む流れ / 離散化

Outline of Final Research Achievements

Aiming at the analysis of transport phenomena occurring in a multiphase flow of dispersed particles, a numerical method is proposed for the lubrication flow occurring in the narrow regions between particles. It was shown that the concept of "consistent direct discretisation" in the finite-difference method is essential for velocity-pressure coupling and capturing a particle-fluid interface, and its effectiveness for the flow analysis in a narrow passage was demonstrated.
The method was extended to permeate flows through membrane, which aims a number of particles covered with a permeable membrane (e.g. biological cells). The uniqueness of the method is imposing the pressure discontinuities at the front and rear sides of the interface to the pressure Poisson equation for coupling the velocity and pressure fields of an incompressible fluid. The proposed method was also proved to be effective for analysing the permeate flow driven by the lubrication-induced pressure.

Free Research Field

数値流体力学

Academic Significance and Societal Importance of the Research Achievements

従来、多数の粒子を含む流れでは粒子間の狭隘流路における流れを解く際は、解像度の低下が問題であった。提案した手法により狭隘流路の流れを正確に解くために必要な条件が明らかになり、それを数値解析コードに実装するユニークな方法を示した。また、狭隘流路において、壁面圧力から壁垂直方向の圧力分布を構成する数理モデルを提案した。これは従来の潤滑流れ解法の解像度を補う手法と位置付けられる。
さらに、提案した数値解法を膜透過流れの解法へ発展させる過程をとおして、より一般に膜表裏における物理量の不連続性を考慮する方法が明らかになりつつあり、将来的に流れ中の輸送現象の理解に貢献する方法論への展開が期待される。