Optimal design for non-Newtonian flows using a topology optimization approach

AbstractWe study non-Newtonian effects on the layout and geometry of flow channels using a material distribution based topology optimization approach. The flow is modeled with the single-relaxation hydrodynamic lattice Boltzmann method, and the shear dependence of viscosity is included through the Carreau–Yasuda model for non-Newtonian fluids. To represent the viscosity of blood in this model, we use non-Newtonian similarity. Further, we introduce a scaling to decrease the effects of the non-Newtonian model in porous regions in order to stabilize the coupling of the LBM porosity and non-Newtonian flow models. For the resulting flow model, we derive the non-Newtonian sensitivity analysis for steady-state conditions and illustrate the non-Newtonian effect on channel layouts for a 2D dual-pipe design problem at different Reynolds numbers

Non-Newtonian Rheology in Blood Circulation

Blood is a complex suspension that demonstrates several non-Newtonian rheological characteristics such as deformation-rate dependency, viscoelasticity and yield stress. In this paper we outline some issues related to the non-Newtonian effects in blood circulation system and present modeling approaches based mostly on the past work in this field.Comment: 26 pages, 5 figures, 2 table

Modelling wall shear stress in small arteries using LBM and FVM

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.In this study a finite-volume discretisation of a Lattice Boltzmann equation over unstructured grids is presented. The new scheme is based on the idea of placing the unknown fields at the nodes of the mesh and evolve them based on the fluxes crossing the surfaces of the corresponding control volumes. The method, named unstructured Lattice Boltzmann equation (ULBE) is compared with the classical finite volume method (FVM) and is applied here to the problem of blood flow over the endothelium in small arteries. The study shows a significant variation and a high sensitivity of wall shear stress to the endothelium corrugation degree

Severity parameter and global importance factor of non-newtonian models in 3D reconstructed human left coronary artery

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The capabilities and limitations of various molecular viscosity models, when testing Left Coronary Artery (LCA) tree, were analyzed via: molecular viscosity, local and global non-Newtonian importance factors, Wall Shear Stress (WSS) and Wall Shear Stress Gradient (WSSG). Seven non-Newtonian molecular viscosity models, plus the Newtonian one, were compared. Dense grid of 620000 nodes located, mostly, at near to low WSS flow regions (endothelium regions) is needed for current LCA application. The WSS distribution yields a consistent LCA pattern for nearly all non-Newtonian models. High molecular viscosity, low WSS low WSSG values appear at proximal LCA regions at the outer walls of the major bifurcation. The global importance factor for the non-Newtonian power law model yields 76.7% (non-Newtonian flow), while for the Generalized power law model this value is 6.1% (Newtonian flow). The capabilities of the applied non-Newtonian law models appear at low strain rates. The Newtonian blood flow treatment is considered to be a good approximation at mid-and high-strain rates. In general, the non-Newtonian power law and the Generalized power law blood viscosity models are considered to approximate the molecular viscosity and WSS calculations in a more satisfactory way

Wall Orientation and Shear Stress in the Lattice Boltzmann Model

The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.Comment: 9 pages, 11 figure

Near wall hemodynamics: Modelling the glycocalyx and the endothelial surface

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.In this paper a coarse-grained model for blood flow in small arteries is presented. Blood is modelled as a two-component incompressible fluid: the plasma and corpuscular elements dispersed in it. The latter are modelled as deformable liquid droplets having greater density and viscosity. Interfacial surface tension and membrane effects are present to mimic key properties and to avoid droplets’ coalescence. The mesoscopic model also includes the presence of the wavy wall, due to the endothelial cells and incorporates a representation of the glycocalyx, covering the vessel wall. The glycocalyx is modelled as a porous medium, the droplets being subjected to a repulsive elastic force when approaching it, during their transit. Preliminary simulations are intended to show the influence of the undulation on the wall together with that of the glycocalyx