| 摘要: | 本研究針對微尺度液滴撞擊彈性平板之流固耦合行為，建立一套具備穩定性與實驗再現能力之數值模擬流程，並採用廣義插值物質點法（Generalized Interpolation Material Point Method, GIMP）作為核心計算工具。現有多數相關研究集中於宏觀尺度之衝擊或結構反應，對於微觀尺度下流固耦合的細部機制探討相對稀少。液滴撞擊問題同時涉及非線性變形、自由界面運動與複雜接觸行為，對數值方法之穩定性與解析能力提出高度挑戰。
為補足實驗觀測中對內部流場與應力場資訊不足之缺口，本研究結合本系中央大學土木系水資源組黃冠嶺教授團隊所建立之高速攝影實驗影像資料，並透過廣義插值物質點法進行數值模擬，評估水滴模型在撞擊後之變形過程、展開對稱性與再現能力。數值模型中，流體部分採近似不可壓縮牛頓流體之假設，僅透過體積模數所控制之壓力項進行模擬；固體部分則以線彈性模型定義應力–應變關係，探討材料楊氏模數與邊界支承條件對變形模式之影響。
模擬設計中以五種楊氏模數（200GPa至2MPa）與兩種邊界條件（四邊固定端與下方滾支承）模擬受水滴撞擊之平板，系統性探討水滴撞擊行為於不同結構彈性條件下之展開形貌與變形特徵。模擬程式以福傳程式語言(Fortran)撰寫，並於國家高速網路與計算中心之超級電腦進行運算；相關結果則透過可視化軟體Ovito進行呈現，並與實驗影像進行對照分析。
結果顯示，平板強度與邊界拘束型式顯著影響水滴的展開方向及對稱性。當平板楊氏模數設定為20 MPa且採固定邊界條件時，水滴展開輪廓、帽狀隆起位置及水滴壓縮程度相較於其他條件顯得與實驗結果最為接近。此外，廣義插值物質點法在處理網格穿越與自由界面變形時展現高度穩定性，避免傳統物質點法在形函數不連續處產生之數值擾動，亦能自然描述撞擊過程中的能量傳遞與界面變化。
本研究驗證廣義插值物質點法於微尺度流固耦合模擬中之可行性與實用性，所建立之模擬流程具備良好再現能力與參數擴充彈性，未來可進一步納入黏滯係數、應力場分析、表面張力模型與破壞機制，以深化對微觀撞擊問題中流體–固體交互動態之理解，並拓展其於噴霧技術、微流體元件設計與材料微觀響應分析等領域之應用潛力。
;This study develops a numerically stable and experimentally verifiable simulation framework to investigate the fluid–structure interaction (FSI) behavior of a microscale droplet impacting an elastic plate. The Generalized Interpolation Material Point Method (GIMP) is adopted as the core numerical scheme. While most existing studies focus on macroscopic-scale impacts or structural responses, the detailed mechanisms of microscale FSI remain largely unexplored. The droplet impact problem involves nonlinear deformation, free-surface evolution, and complex contact phenomena, posing significant challenges to the stability and accuracy of numerical methods.
To address the lack of internal flow field and stress distribution data in experimental observations, this study incorporates high-speed imaging data obtained from the Water Resources Division of the Department of Civil Engineering at National Central University, under the direction of Professor Kuan-Ling Huang. GIMP is employed to simulate the droplet deformation process after impact and to evaluate expansion symmetry and the model’s ability to reproduce physical behavior. In the numerical model, the fluid is assumed to be a nearly incompressible Newtonian fluid, with the pressure governed solely by the bulk modulus; the solid is modeled using a linear elastic constitutive law to examine how variations in Young’s modulus and boundary support conditions influence deformation patterns.
The simulation design includes five different Young’s modulus values (ranging from 200 GPa to 2 MPa) and two types of boundary conditions (fully clamped and bottom roller support). These conditions are used to systematically explore the spreading behavior and deformation characteristics of the elastic plate subjected to droplet impact. The simulation code is written in Fortran and executed on a supercomputer at Taiwan’s National Center for High-Performance Computing (NCHC). Simulation results are visualized using Ovito and compared with experimental images.
The results indicate that both the plate stiffness and boundary constraints significantly affect the droplet’s spreading direction and symmetry. When the plate has a Young’s modulus of 20 MPa with fully clamped boundaries, the simulated droplet profile, crown-shaped elevation, and compression depth show the best agreement with experimental observations. Moreover, GIMP demonstrates high numerical stability when handling grid-crossing and free-surface deformation, avoiding the numerical artifacts associated with discontinuous shape functions in conventional MPM, and effectively capturing energy transfer and interface dynamics during impact.
This study confirms the feasibility and practicality of applying GIMP to microscale FSI simulations. The developed simulation framework demonstrates strong reproducibility and parameter scalability. Future extensions may incorporate viscosity, stress field analysis, surface tension models, and fracture mechanisms to further advance the understanding of fluid–solid interaction dynamics at small scales and expand its applicability in spray technologies, microfluidic device design, and microscale material response analysis. |
