Numerical study of turbulent blood flow through a caged-ball prosthetic heart valve using a boundary-fitted co-ordinate system

A numerical model is developed for steady turbulent flow through a fully open Starr-Edwards caged-ball prosthetic heart valve in the aortic position. An orthogonal boundary-fitted co-ordinate system is generated for the axisymmetric flow domain in the vicinity of the valve. The boundary lines follow the left ventricular wall, an idealised sinus, the aortic wall, and the ball occluder. The governing partial differentiation equations, written in a stream function-vorticity formulation, are recast into their curvilinear equivalents before being discretised into finite-difference equations. The equations are then solved iteratively. Regions of separated flow and elevated fluid stress are identified at several flow rates. Analysis of the numerical solutions reveals a simple power-law relationship between the computed turbulent shear stress and the steady flow rate at important flow field locations. The maximum turbulent shear stress occurs consistently near the sewing-ring tip. However, the peak turbulent shear stress in the sinus separation zone is observed to increase significantly with higher flow rates, exceeding values in many other regions. The numerical solutions compare satisfactorily with experimental measurements.