Immersed boundary method for cavitating and biological flows

The aim of the present work is the development of a computational tool to ease the numerical simulation of cavitating flows in domains of complex topology or with arbitrary moving boundaries. Within the framework of Computational Fluid Dynamics(CFD), an Immersed Boundary (IB) Method has been developed. According to the IB methodology, the grid that discretises the computational domain does not need to conform to the geometry and the solid boundaries are modelled on a fixed canonical grid by alternations of the governing equations in their vicinity. This modelling strategy is beneficial in terms of both computational cost and numerical solution. The grid generation, which is a complex and time consuming process, is simplified as a regular canonical grid, non-conformal to the boundaries, can be used. In addition, when moving boundaries are present, a conformal grid would need to adapt or deform following the motion of boundaries, which would increase the computational cost of the simulations in the first case and affect the solution in the latter case; the use of IB method alleviates these issues. The developed method follows the direct-forcing approach, which simply adds to the governing equations a source term to account for the body force acting on the fluid. The simplicity of the method makes it suitable for complex flow regimes, including phase change, strong shocks and compressibility effects, as well as Fluid Structure Interaction (FSI). Since cavitation dynamics regard a wide range of applications of engineering interest, from hydraulic machines to novel therapeutic techniques, the method is designed to be applicable in a wide range of flow regimes. Turbulent modelling and flow induced motion has been taken into account. The method has been successfully applied to cavitating and incompressible cases where conventional techniques are not easily or at all applicable. The shock-wave interaction with material interfaces is studied via the high-speed impact of a solid projectile on a water jet, which has been studied only experimentally before and only qualitative observations existed. The numerical investigation with the proposed methodology unveiled rich information regarding the physics of the impact, the resulting shock formation, cavitation development and interface instabilities initiation. Moreover, the methodology was applied on the thoroughly studied pulsatile flow through a bi leaflet Mechanical Heart Valve, to provide additional information regarding shear stress development. The methodology aids an experimental campaign employing novel shear stress measuring techniques, carried out by our collaborators. The research work and the developed method described in the present Thesis, intend to set the foundations for more elaborate numerical investigations of highly complex problems of Fluid Dynamics

Cavitation Induction by Projectile Impacting on a Water Jet

The present paper focuses on the simulation of the high-velocity impact of a projectile impacting on a water-jet, causing the onset, development and collapse of cavitation. The simulation of the fluid motion is carried out using an explicit, compressible, density-based solver developed by the authors using the OpenFOAM library. It employs a barotropic two-phase flow model that simulates the phase-change due to cavitation and considers the co-existence of non-condensable and immiscible air. The projectile is considered to be rigid while its motion through the computational domain is modelled through a direct-forcing Immersed Boundary Method. Model validation is performed against the experiments of Field et al. [Field, J., Camus, J. J., Tinguely, M., Obreschkow, D., Farhat, M., 2012. Cavitation in impacted drops and jets and the effect on erosion damage thresholds. Wear 290–291, 154–160. doi:10.1016/j.wear.2012.03.006. URL http://www.sciencedirect.com/science/article/pii/S0043164812000968 ], who visualised cavity formation and shock propagation in liquid impacts at high velocities. Simulations unveil the shock structures and capture the high-speed jetting forming at the impact location, in addition to the subsequent cavitation induction and vapour formation due to refraction waves. Moreover, model predictions provide quantitative information and a better insight on the flow physics that has not been identified from the reported experimental data, such as shock-wave propagation, vapour formation quantity and induced pressures. Furthermore, evidence of the Richtmyer-Meshkov instability developing on the liquid-air interface are predicted when sufficient dense grid resolution is utilised

Cavitation Induction by Projectile Impacting on a Water Jet

Following the work of Field et al. [4], who experimentally visualised cavity formation and shock propagation in impacted liquids at high velocities, the present study focuses on the simulation of the high velocity impact of a solid projectile on a water jet. The undeformable solid projectile is modelled through a direct forcing Immersed Boundary Method. The simulation is carried out using an explicit density based compressible solver, developed by Kyriazis et al. [6], which employs a two-phase flow model and includes phase change. This study gives a better insight on the phenomena following the impact of solids on liquids, including shock propagation and vapour formation, and demonstrates the capabilities of the presented Immersed Boundary Method to handle compressible cavitating flows

Micro-pillar sensor based wall-shear mapping in pulsating flows: In-Situ calibration and measurements in an aortic heart-valve tester

Accurate wall-shear stress (WSS) in-vitro measurements within complex geometries such as the human aortic arch under pulsatile flow are still difficult to achieve, meanwhile such data are important for classifying impacts of prosthetic valves on aortic walls. Micro-cantilever beams can serve to sense the WSS in such flows for applications in in-vitro flow tester. However, within pulsatile flows and complex 3D curved geometries such as the aortic arch, the flexible sensor structures are subject to oscillating boundary layer thickness and profile shape, which may not have been taken into account in the calibration procedure. The fluid-structure 13 interaction is sensitive to these changes, thus reflecting also the flow-induced deflection of the sensor tip which is actually the sensing signal. We develop herein a methodology for in-situ calibration of the response of the sensors directly in the complex geometry of the aortic arch, assisted by reference data from numerical simulations of the flow under the same boundary conditions. For this procedure, a quick exchange of the heart valve in the tester with a tubular insert is done to provide a smooth contour in the curved aorta model. Arrays of 500µm long micro-pillar WSS sensors in the aorta model are calibrated under physiological pulsatile flow and used then for mapping the WSS evolution in the arch induced by two different heart valves, showing their difference of impact. The developed methodology completes the in-house built in-vitro flow tester with a reliable WSS measurement technique and provides a unique hydrodynamic testing facility for heart valve prostheses and their impact on the WSS distal along the aortic walls

A direct forcing Immersed Boundary Method for Cavitating Flows

In the current study, an Immersed Boundary Method for simulating cavitating flows with complex or moving boundaries is presented, which follows the discrete direct forcing approach. Although the Immersed Boundary Methods are widely used in various applications of single phase, multiphase and particulate flows, either incompressible or compressible, and numerous alternative formulations exist, to the best of the authors' knowledge, a handful of computational works employ such methodologies on cavitating flows. The herein proposed method, following the works of the author's group1,2,3, tries to fill this gap and to solidify the development of a computational tool of a simple formulation capable to tackle complex numerical problems of cavitation modelling. The method aims to be used in a wide range of applications of industrial interest and treat flows of engineering scales. Therefore, a validation of the method is performed by numerous benchmark test-cases, of progressively increasing complexity, from incompressible low Reynolds number to compressible and highly turbulent cavitating flows