H. S. Udaykumar

Interaction of a Synthetic Jet with a Flat Plate Boundary Layer

The interaction of a modeled synthetic jet with a flat plate boundary layer is investigated numerically using an incompressible Navier–Stokes solver. The diaphragm is modeled in a realistic manner as a moving boundary in an effort to accurately compute the flow inside the jet cavity. The primary focus of the current study is on describing the dynamics of the synthetic jet in the presence of external crossflow. A systematic parametric study has been carried out where the diaphragm amplitude, external flow Reynolds number and slot dimensions are varied. The simulations allow us to extract some interesting flow physics associated with the vortex dynamics of the jet and also provide insight into the scaling of the performance characteristics of the jet with these parameters.

An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces

A technique is presented for the numerical simulation of high-speed multimaterial impact. Of particular interest is the interaction of solid impactors with targets. The computations are performed on a fixed Cartesian mesh by casting the equations governing material deformation in Eulerian conservation law form. The advantage of the Eulerian setting is the disconnection of the mesh from the boundary deformation allowing for large distortions of the interfaces. Eigenvalue analysis reveals that the system of equations is hyperbolic for the range of materials and impact velocities of interest. High-order accurate ENO shock-capturing schemes are used along with interface tracking techniques to evolve sharp immersed boundaries. The numerical technique is designed to tackle the following physical phenomena encountered during impact: (1) high velocities of impact leading to large deformations of the impactor as well as targets; (2) nonlinear wave-propagation and the development of shocks in the materials; (3) modeling of the constitutive properties of materials under intense impact conditions and accurate numerical calculation of the elasto-plastic behavior described by the models; (4) phenomena at multiple interfaces (such as impactor-target, target-ambient and impactor-ambient), i.e. both free surface and surface-surface dynamics. Comparison with Lagrangian calculations is made for the elasto-plastic deformation of solid material. The accuracy of convex ENO scheme for shock capturing, with the Mie-Gruneisen equation of state for pressure, is closely examined. Good agreement of the present finite difference fixed grid results is obtained with exact solutions in 1D and benchmarked moving finite element solutions for axisymmetric Taylor impact.

Micro-scale Dynamic Simulation of Erythrocyte–Platelet Interaction in Blood Flow

Platelet activation, adhesion, and aggregation on the blood vessel and implants result in the formation of mural thrombi. Platelet dynamics in blood flow is influenced by the far more numerous erythrocytes (RBCs). This is particularly the case in the smaller blood vessels (arterioles) and in constricted regions of blood flow (such as in valve leakage and hinge regions) where the dimensions of formed elements of blood become comparable with that of the flow geometry. In such regions, models to predict platelet motion, activation, aggregation and adhesion must account for platelet–RBC interactions. This paper studies platelet–RBC interactions in shear flows by performing simulations of micro-scale dynamics using a computational fluid dynamics (CFD) model. A level-set sharp-interface immersed boundary method is employed in the computations in which RBC and platelet boundaries are tracked on a two-dimensional Cartesian grid. The RBCs are assumed to have an elliptical shape and to deform elastically under fluid forces while the platelets are assumed to behave as rigid particles of circular shape. Forces and torques between colliding blood cells are modeled using an extension of the soft-sphere model for elliptical particles. RBCs and platelets are transported under the forces and torques induced by fluid flow and cell–cell and cell–platelet collisions. The simulations show that platelet migration toward the wall is enhanced with increasing hematocrit, in agreement with past experimental observations. This margination is seen to occur due to hydrodynamic forces rather than collisional forces or volumetric exclusion effects. The effect of fluid shear forces on the platelets increases exponentially as a function of hematocrit for the range of parameters covered in this study. The micro-scale analysis can be potentially employed to obtain a deterministic relationship between fluid forces and platelet activation and aggregation in blood flow past cardiovascular implants.

Application of large-eddy simulation to the study of pulsatile flow in a modeled arterial stenosis.

The technique of large-eddy simulation (LES) has been applied to the study of pulsatile flow through a modeled arterial stenosis. A simple stenosis model has been used that consists of a one-sided 50 percent semicircular constriction in a planar channel. The inlet volume flux is varied sinusoidally in time in a manner similar to the laminar flow simulations of Tutty (1992). LES is used to compute flow at a peak Reynolds number of 2000 and a Strouhal number of 0.024. At this Reynolds number, the flow downstream of the stenosis transitions to turbulence and exhibits all the classic features of post-stenotic flow as described by Khalifa and Giddens (1981) and Lieber and Giddens (1990). These include the periodic shedding of shear layer vortices and transition to turbulence downstream of the stenosis. Computed frequency spectra indicate that the vortex shedding occurs at a distinct high frequency, and the potential implication of this for noninvasive diagnosis of arterial stenoses is discussed. A variety of statistics have been also extracted and a number of other physical features of the flow are described in order to demonstrate the usefulness of LES for the study of post-stenotic flows.

Ghost Fluid Method for Strong Shock Interactions Part 2: Immersed Solid Boundaries

Numerical simulation of shock waves interacting with multimaterial interface is immensely challenging, particularly when the embedded interface is retained as a sharp entity. The challenge lies in accurately capturing and representing the interface dynamics and the wave patterns at the interface. In this regard, the ghost fluid method has been successfully used to capture the interface conditions for both fluid-fluid and solid-fluid interfaces. However, the ghost fluid method results in over/underheating errors when shocks impact interfaces, and hence must be supplemented with numerical corrective measures to mitigate these errors. Such corrections typically fail for strong shock applications. Variants and extensions ofthe ghost fluid method have been proposed to remedy its shortcomings with mixed success. In this paper, the performance of approaches based on the ghost fluid method, in the case of strong shocks impinging on immersed solid boundaries in compressible flows, is evaluated. It is found that (from the viewpoint of simplicity, robustness, and accuracy) a reflective boundary condition used in conjunction with a local Riemann solver at the interface proves to be a good choice. The method is found to be stable, accurate, and robust for wide range problems involving strong shocks interacting with embedded solid objects.

Two-Dimensional Dynamic Simulation of Platelet Activation During Mechanical Heart Valve Closure

A major drawback in the operation of mechanical heart valve prostheses is thrombus formation in the near valve region. Detailed flow analysis in this region during the valve closure phase is of interest in understanding the relationship between shear stress and platelet activation. A fixed-grid Cartesian mesh flow solver is used to simulate the blood flow through a bi-leaflet mechanical valve employing a two-dimensional geometry of the leaflet with a pivot point representing the hinge region. A local mesh refinement algorithm allows efficient and fast flow computations with mesh adaptation based on the gradients of the flow field in the leaflet-housing gap at the instant of valve closure. Leaflet motion is calculated dynamically based on the fluid forces acting on it employing a fluid-structure interaction algorithm. Platelets are modeled and tracked as point particles by a Lagrangian particle tracking method which incorporates the hemodynamic forces on the particles. A platelet activation model is included to predict regions which are prone to platelet activation. Closure time of the leaflet is validated against experimental studies. Results show that the orientation of the jet flow through the gap between the housing and the leaflet causes the boundary layer from the valve housing to be drawn in by the shear layer separating from the leaflet. The interaction between the separating shear layers is seen to cause a region of intensely rotating flow with high shear stress and high residence time of particles leading to high likelihood of platelet activation in that region.

Ghost Fluid Method for Strong Shock Interactions Part 1: Fluid-Fluid Interfaces

The interaction of shocks with multimaterial interfaces can occur in several applications, including high-speed flows with droplets, bubbles, and particles and hypervelocity impact and penetration. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with level-set interface tracking is attractive. In this regard, the ghost fluid method has been widely used to capture the interface dynamics. However, ghost fluid method experiences difficulties, particularly when strong shocks impinge on the interface. It has been shown that an accurate representation and decomposition of the wave systems (by solving a Riemann problem at the interface) significantly alleviates the shortcomings confronted by the ghost fluid method. Variants of the ghost fluid method proposed in the past differed in the way in which this Riemann problem was invoked at the interface. In this work, a simple, robust, and multidimensional procedure to construct the Riemann problem at the interface is presented. The work focuses primarily on resolving interface dynamics due to strong shocks interacting with embedded fluid-fluid interfaces (gas-gas and gas-liquid interfaces) in compressible flows. Several one- and two-dimensional problems involving moderate-to-very-large deformation of the embedded interface have been computed. The numerical examples demonstrate the flexibility, stability, and versatility of the approach in successfully resolving the embedded material interface.

A FINITE-VOLUME SHARP INTERFACE SCHEME FOR DENDRITIC GROWTH SIMULATIONS: COMPARISON WITH MICROSCOPIC SOLVABILITY THEORY

We present and validate a numerical technique for computing dendritic growth of crystals from pure melts. The solidification process is computed in the diffusion-driven limit. The governing equations are solved on a fixed Cartesian mesh and a mixed Eulerian-Lagrangian framework is used to treat the immersed phase boundary as a sharp solid-fluid interface. A conservative finite-volume discretization is employed which allows the boundary conditions to be applied exactly at the moving surface. The results from our calculations are compared with two-dimensional microscopic solvability theory. It is shown that the method predicts dendrite tip characteristics in good agreement with the theory. The sharp interface treatment allows discontinuous material property variation at the solid-liquid interface. Calculations with such discontinuities are also shown to produce results in agreement with solvability and with other sharp interface simulations.

Two-Dimensional Simulation of Flow and Platelet Dynamics in the Hinge Region of a Mechanical Heart Valve

The hinge region of a mechanical bileaflet valve is implicated in blood damage and initiation of thrombus formation. Detailed fluid dynamic analysis in the complex geometry of the hinge region during the closing phase of the bileaflet valve is the focus of this study to understand the effect of fluid-induced stresses on the activation of platelets. A fixed-grid Cartesian mesh flow solver is used to simulate the blood flow through a two-dimensional geometry of the hinge region of a bileaflet mechanical valve. Use of local mesh refinement algorithm provides mesh adaptation based on the gradients of flow in the constricted geometry of the hinge. Leaflet motion is specified from the fluid-structure interaction analysis of the leaflet dynamics during the closing phase from a previous study, which focused on the fluid mechanics at the gap between the leaflet edges and the valve housing. A Lagrangian particle tracking method is used to model and track the platelets and to compute the magnitude of the shear stress on the platelets as they pass through the hinge region. Results show that there is a boundary layer separation in the gaps between the leaflet ear and the constricted hinge geometry. Separated shear layers roll up into vortical structures that lead to high residence times combined with exposure to high-shear stresses for particles in the hinge region. Particles are preferentially entrained into this recirculation zone, presenting the possibility of platelet activation, aggregation, and initiation of thrombi.

A three-dimensional sharp interface Cartesian grid method for solving high speed multi-material impact, penetration and fragmentation problems

This work presents a three-dimensional, Eulerian, sharp interface, Cartesian grid technique for simulating the response of elasto-plastic solid materials to hypervelocity impact, shocks and detonations. The mass, momentum and energy equations are solved along with evolution equations for deviatoric stress and plastic strain using a third-order finite difference scheme. Material deformation occurs with accompanying nonlinear stress wave propagation; in the Eulerian framework the boundaries of the deforming material are tracked in a sharp fashion using level-sets and the conditions on the immersed boundaries are applied by suitable modifications of a ghost fluid approach. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state and the Johnson-Cook model is employed to characterize the material response due to rate-dependent plastic deformation. Details are provided on the treatment of the deviatoric stress ghost state so that physically correct boundary conditions can be applied at the material interfaces. An efficient parallel algorithm is used to handle computationally intensive three-dimensional problems. The results demonstrate the ability of the method to simulate high-speed impact, penetration and fragmentation phenomena in three dimensions.