Enhancement of a 2D front-tracking algorithm with a non-uniform distribution of Lagrangian markers

The 2D front tracking method is enhanced to control the development of spurious velocities for non-uniform distributions of markers. The hybrid formulation of Shin et al. (2005) [7] is considered. A new tangent calculation is proposed for the calculation of the tension force at markers. A new reconstruction method is also proposed to manage non- uniform distributions of markers. We show that for both the static and the translating spherical drop test case the spurious currents are reduced to the machine precision. We also show that the ratio of the Lagrangian grid siz

Numerical Model for the Determination of Erythrocyte Mechanical Properties and Wall Shear Stress in vivo From Intravital Microscopy.

The mechanical properties and deformability of Red Blood Cells (RBCs) are important determinants of blood rheology and microvascular hemodynamics. The objective of this study is to quantify the mechanical properties and wall shear stress experienced by the RBC membrane during capillary plug flow in vivo utilizing high speed video recording from intravital microscopy, biomechanical modeling, and computational methods. Capillaries were imaged in the rat cremaster muscle pre- and post-RBC transfusion of stored RBCs for 2-weeks. RBC membrane contours were extracted utilizing image processing and parametrized. RBC parameterizations were used to determine updated deformation gradient and Lagrangian Green strain tensors for each point along the parametrization and for each frame during plug flow. The updated Lagrangian Green strain and Displacement Gradient tensors were numerically fit to the Navier-Lame equations along the parameterized boundary to determined Lame's constants. Mechanical properties and wall shear stress were determined before and transfusion, were grouped in three populations of erythrocytes: native cells (NC) or circulating cells before transfusion, and two distinct population of cells after transfusion with stored cells (SC1 and SC2). The distinction, between the heterogeneous populations of cells present after the transfusion, SC1 and SC2, was obtained through principle component analysis (PCA) of the mechanical properties along the membrane. Cells with the first two principle components within 3 standard deviations of the mean, were labeled as SC1, and those with the first two principle components greater than 3 standard deviations from the mean were labeled as SC2. The calculated shear modulus average was 1.1±0.2, 0.90±0.15, and 12 ± 8 MPa for NC, SC1, and SC2, respectively. The calculated young's modulus average was 3.3±0.6, 2.6±0.4, and 32±20 MPa for NC, SC1, and SC2, respectively. o our knowledge, the methods presented here are the first estimation of the erythrocyte mechanical properties and shear stress in vivo during capillary plug flow. In summary, the methods introduced in this study may provide a new avenue of investigation of erythrocyte mechanics in the context of hematologic conditions that adversely affect erythrocyte mechanical properties

Computations of Multiphase Fluid Flows Using Marker-Based Adaptive, Multilevel Cartesian Grid Method

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76194/1/AIAA-2007-336-338.pd

Adaptive Lagrangian–Eulerian computation of propagation and rupture of a liquid plug in a tube

Liquid plug propagation and rupture occurring in lung airways can have a detrimental effect on epithelial cells. In this study, a numerical simulation of a liquid plug in an infinite tube is conducted using an Eulerian–Lagrangian approach and the continuous interface method. A reconstruction scheme is developed to allow topological changes during plug rupture by altering the connectivity information about the interface mesh. Results prior to the rupture are in reasonable agreement with the study of Fujioka et al . in which a Lagrangian method is used. For unity non‐dimensional pressure drop and a Laplace number of 1000, rupture time is shown to be delayed as the initial precursor film thickness increases and rupture is not expected for thicknesses larger than 0.10 of tube radius. During the plug rupture process, a sudden increase of mechanical stresses on the tube wall is recorded, which can cause tissue damage. The peak values of those stresses increase as the initial precursor film thickness is reduced. After rupture, the peaks in mechanical stresses decrease in magnitude as the plug vanishes and the flow approaches a fully developed behavior. Increasing initial pressure drop is shown to linearly increase maximum variations in wall pressure and shear stress. Decreasing the pressure drop and increasing the Laplace number appear to delay rupture because it takes longer for a fluid with large inertial forces to respond to the small pressure drop. Copyright © 2010 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/88023/1/2422_ftp.pd

Mechanistic modeling of evaporating thin liquid film instability on a bwr fuel rod with parallel and cross vapor flow

This work has been aimed at developing a mechanistic, transient, 3-D numerical model to predict the behavior of an evaporating thin liquid film on a non-uniformly heated cylindrical rod with simultaneous parallel and cross flow of vapor. Interest in this problem has been motivated by the fact that the liquid film on a full-length boiling water reactor fuel rod may experience significant axial and azimuthal heat flux gradients and cross flow due to variations in the thermal-hydraulic conditions in surrounding subchannels caused by proximity to inserted control blade tip and/or the top of part-length fuel rods. Such heat flux gradients coupled with localized cross flow may cause the liquid film on the fuel rod surface to rupture, thereby forming a dry hot spot. These localized dryout phenomena can not be accurately predicted by traditional subchannel analysis methods in conjunction with empirical dryout correlations. To this end, a numerical model based on the Level Contour Reconstruction Method was developed. The Standard k- turbulence model is included. A cylindrical coordinate system has been used to enhance the resolution of the Level Contour Reconstruction Model. Satisfactory agreement has been achieved between the model predictions and experimental data. A model of this type is necessary to supplement current state-of-the-art BWR core thermal-hydraulic design methods based on subchannel analysis techniques coupled with empirical dry out correlations. In essence, such a model would provide the core designer with a "magnifying glass" by which the behavior of the liquid film at specific locations within the core (specific axial node on specific location within a specific bundle in the subchannel analysis model) can be closely examined. A tool of this type would allow the designer to examine the effectiveness of possible design changes and/or modified control strategies to prevent conditions leading to localized film instability and possible fuel failure.Ph.D.Committee Chair: Abdel-Khalik, Said; Committee Member: Ammar, Mostafa H.; Committee Member: Ghiaasiaan, S. Mostafa; Committee Member: Hertel, Nolan E.; Committee Member: Liu, Yingji

An Edge-based Interface Tracking (EBIT) Method for Multiphase-flows Simulation with Surface Tension

We present a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method for multiphase flow simulations. In the EBIT method, the markers are located on the grid edges and the interface can be reconstructed without storing the connectivity of the markers. This feature makes the process of marker addition or removal easier than in the traditional Front-Tracking method. The EBIT method also allows almost automatic parallelization due to the lack of explicit connectivity. In a previous journal article we have presented the kinematic part of the EBIT method, that includes the algorithms for interface linear reconstruction and advection. Here, we complete the presentation of the EBIT method and combine the kinematic algorithm with a Navier--Stokes solver. To identify the reference phase and to distinguish ambiguous topological configurations, we introduce a new feature: the Color Vertex. For the coupling with the Navier--Stokes equations, we first calculate volume fractions from the position of the markers and the Color Vertex, then viscosity and density fields from the computed volume fractions and finally surface tension stresses with the Height-Function method. In addition, an automatic topology change algorithm is implemented into the EBIT method, making it possible the simulation of more complex flows. A two-dimensional version of the EBIT method has been implemented in the open-source Basilisk platform, and validated with five standard test cases: (1) translation with uniform velocity, (2) single vortex, (3) capillary wave, (4) Rayleigh-Taylor instability and (5) rising bubble. The results are compared with those obtained with the Volume-of-Fluid (VOF) method already implemented in Basilisk

A Unified Adaptive Cartesian Grid Method for Solid-Multiphase Fluid Dynamics with Moving Boundaries

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76397/1/AIAA-2007-4576-676.pd

Numerical simulations of a sphere settling in simple shear flows of yield stress fluids

We perform $3$D numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross shear flow is a secondary flow with amplitude $10\%$ of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modeled using the elastovisco-plastic (EVP) constitutive laws proposed by \cite{saramito2009new}. The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary (IB) method. Our results show that the fore-aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly as compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross shear flow cannot be derived from the pure sedimentation drag law owing to the non-linear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield-stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.Comment: 41 pages, 24 figure