Arterial stenosis murmurs: an analysis of flow and pressure fields

The flow field distal to an arterial stenosis is simulated by a confined turbulent jet with moderate Reynolds numbers. The wall pressure fluctuations are related to the momentum fluctuations of the jet by the Poisson equation. A Green's function was derived to satisfy the boundary conditions on a cylindrical surface. This allows the solution of the Poisson's equation to include only a volume integral of the fluctuating momentum, weighed by the relative distance between the source and the sensor. The velocity fluctuations on the jet centerline and at the middle of the shear layer were measured using a laser Doppler anemometer. The wall pressure fluctuations were detected simultaneously by an array of nine wall-mounted pressure transducers along the axial direction. Cross correlation performed between the velocity and pressure fluctuations reveals that the pressure fluctuations were mostly imposed by the passage of turbulent eddies with a convective velocity that is a function of the jet exit velocity. The Strouhal number, defined by the frequency of the passing large-scale structure, is a function of the initial conditions only very close to the jet exit. Further downstream, where the effect of the initial conditions is lost, the Strouhal number approaches a constant irrespect of the jet Reynolds number. The contribution of a source near the jet exit to wall pressure fluctuation near the reattachment is rather weak due to the rapidly decaying weighting function in the axial direction. However, for sources located within one nozzle diameter from the sensor, the cross-spectral density function has a high magnitude with maximum coherence where the pressure spectral changes its slope.