Accuracy of 1D microvascular flow models in the limit of low Reynolds numbers.

We describe results of numerical simulations of steady flows in tubes with branch bifurcations using fully 3D and reduced 1D geometries. The intent is to delineate the range of validity of reduced models used for simulations of flows in microcapillary networks, as a function of the flow Reynolds number Re. Results from model problems indicate that for Re less than 1 and possibly as high as 10, vasculatures may be represented by strictly 1D Poiseuille flow geometries with flow variation in the axial dimensions only. In that range flow rate predictions in the different branches generated by 1D and 3D models differ by a constant factor, independent of Re. When the cross-sectional areas of the branches are constant these differences are generally small and appear to stem from an uncertainty of how the individual branch lengths are defined. This uncertainty can be accounted for by a simple geometrical correction. For non-constant cross-sections the differences can be much more significant. If additional corrections for the presence of branch junctions and flow area variations are not taken into account in 1D models of complex vasculatures, the resultant flow predictions should be interpreted with caution.

Application of Computational Fluid Dynamics Techniques to Blood Pumps.

Present-day computational fluid dynamics (CFD) techniques can be used to analyze the behavior of fluid flow in a variety of pumps. CFD can be a powerful tool during the design stage for rapid virtual prototyping of different designs, analyzing performance parameters, and making design improvements. Computational flow solutions provide information such as the location and size of stagnation zones and the local shear rate. These parameters can be correlated to the extent of hemolysis and thrombus formation and are critical to the success of a blood pump. CFD-ACE, an advanced commercial CFD code developed by CFD Research Corporation, has been applied to fluid flows in rotary machines, such as axial flow pumps and inducers. Preprocessing and postprocessing tools for efficient grid generation and advanced graphical flow visualization are integrated seamlessly with CFD-ACE. The code has structured multiblock grid capability, non-Newtonian fluid treatment, a variety of turbulence models, and an Eulerian-Lagrangian particle tracking model. CFD-ACE has been used successfully to study the flow characteristics in an axial flow blood pump. An unstructured flow solver that greatly automates the process of grid generation and speeds up the flow simulation is under development.