Numerical Methods for Fluid-Structure Interaction in a Pilot-Operated Valve

Over the last three decades, the increasing demand for miniaturization and precise control across diverse fields, from biomedical diagnostics to advanced manufacturing, has contributed to the development of advanced microfluidic control systems. Among these, pilot-operated control valves (POCVs) represent a crucial component for providing precise, low-power, and potentially automated regulation of fluid flow in hydraulic circuits. Nevertheless, the design of reliable microfluidic valves is inherently complex, as it is governed by the intricate interplay of multiple physics; for instance, fluid dynamics, structural mechanics, and contact interactions at small scales, to name a few. To this end, simulation-based engineering (SBE) offers powerful tools to analyze these complex systems numerically, and provide insights that can be difficult to obtain through traditional physical experiments alone.This thesis confronts a specific challenge encountered in the industrial development of a particular microfluidic POCV. As this valve is originally designed to operate for ON/OFF switching, it exhibited functional issues during proportional control operations. The emergence of severe flow-induced vibrations during experimental testing, along with noise and turbulent flow, limited its potential market value and functional versatility. As such, the present study aims to leverage simulation tools to address the POCV's instability issues by proposing a numerical design framework for the POCV. Therefore, the primary objectives of the thesis are to (i) develop advanced numerical methods that can simulate the fluid-structure-contact interactions within the microfluidic POV, (ii) assess the instability in valve function by systematically analyzing design imperfections and reducing the reliance on iterative experimentation through predictive models for design validation, and (iii) investigate and overcome numerical bottlenecks associated with FSCI analysis. Chapter 2 presents a comprehensive numerical investigation of this original valve. We developed an FSCI model using advanced numerical methods and stabilization techniques to address the challenges associated with the strongly coupled system, i.e. an incompressible fluid interacting with a soft, flexible structure with a similar density, in a nearly-closed configuration during transient operation. The simulations showed reliable ON/OFF performance, thereby aligning with experimental results. Additionally, they successfully reproduced the flow-induced vibrations during the proportional control regime. A detailed analysis was conducted to identify the root cause of the issue. It showed that the onset of flow-induced vibrations was due to an interplay between the pressure drop in the valve-seat gap and the subsequent Venturi effect, resulting in a self-excited oscillation cycle. Understanding the underlying cause of the vibrations enabled a targeted approach to redesign. Chapter 3 presents a proposal for a redesigned POCV, engineered to mitigate flow-induced vibrations. A computational framework is employed to assess its performance prior to conducting extensive experimentation. The simulations demonstrate that the redesigned valve successfully eliminates vibrations during proportional control, exhibiting improved stability, more uniform membrane deflection, and faster response times. Although direct experimental validation was constrained, comparisons with analogous configurations support the simulation-driven design process. This work demonstrates the merits of employing advanced SBE tools to facilitate design enhancements, thereby reducing reliance on iterative prototyping processes. The simulations in Chapters 2 and 3 highlighted persistent numerical challenges, particularly concerning the stability and convergence of partitioned FSI methods in nearly-closed domains. Chapter 4 addresses the limitations of partitioned FSI solvers, in particular the widely used Dirichlet-Neumann (DN) coupling scheme. We identify and characterize a phenomenon we term as the added-damping effect, which arises in DN schemes for nearly-closed, incompressible FSI problems. Using a prototypical leaky piston model, we derived the interface operator, which reveals that the added-damping emerges alongside the well-established added-mass effect. The corresponding operator is of Volterra type, non-normal, and scales with the time step and flow resistance. This characterization explains observed non-monotonous convergence behavior and provides critical insight into the limitations and sensitivities of DN coupling in these challenging FSI scenarios. This thesis provides a twofold contribution: First, it leverages numerical methods for FSCI to analyze and design microfluidic POCVs. Second, it delivers a fundamental contribution by identifying and characterizing the added-damping effect, clarifying convergence issues in DN schemes for nearly-closed domains. The results support the exploration of alternative coupling methods (e.g. Robin-Neumann) and the use of High Performance Computing (HPC) resources to effectively tackle the demanding simulations that are crucial for the advancement of microfluidic technology and other complex Multiphysics applications.