Numerical simulation of unsteady laminar flow through a tilting disk heart valve: prediction of vortex shedding

Heart valves induce flow disturbances which play a role in blood cell activation and damage, but questions of the magnitude and spatial distribution of fluid stresses (wall shear stress and turbulent stress) cannot be readily addressed with current experimental techniques. Therefore, a numerical simulation procedure for flow through artificial heart valves is presented. The algorithm employed is based on the Navier-Stokes equations in generalized curvilinear coordinates with artificial compressibility for coupling of velocity and pressure. The algorithm applies a finite-difference technique on a body-conforming composite grid around the heart valve disk on which the numerical simulations are performed. Steady laminar flow over a backward-facing step and unsteady laminar flow inside a square driven cavity are computed to validate the algorithm. Two-dimensional, time-accurate simulation of flow through a tilting disk valve with a steady upstream Reynolds number as high as 1000 reveals the complex behavior of 'vortex shedding'. By scaling the results at the Reynolds number of 1000 to peak systolic flow conditions, the maximum value of shear stress on the valve disk is estimated to be 770 dyn cm-2. The 'apparent' Reynolds stress associated with vortex shedding is estimated to be as high as 3900 dyn cm-2 with a vortex shedding frequency of about 26 Hz. The 'apparent' Reynolds stress value is of similar magnitude as reported in experiments but would not be expected to damage blood cells because the spatial scales associated with vortex shedding are much larger than blood cell dimensions.