# On the wall pressure fluctuations and the flow field structure distal to a modeled stenosis

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## Abstract

The flow field distal to an arterial stenosis is simulated by a confined turbulent jet under moderate Reynold's numbers. The wall pressure fluctuations are related to the momentum fluctuations in the flow field distal to the stenosis through the Poisson's equation. A mathematical derivation has been performed to obtain the Green's function that is tailored to satisfy the boundary conditions on a cylindrical rigid surface. Accordingly, the integral representation for the solution of the Poisson's equation includes only a volume integral of the fluctuating momentum, weighted by a function of the relative distance between the source and the observation point. The present experimental study is concentrated on investigating the distribution and statistical characteristics of the wall pressure fluctuations and the velocity fluctuations in the flow field. The velocity fluctuations on the centerline and at the middle of the shear layer were measured using a laser Doppler anemometer system. The wall pressure fluctuations were simultaneously detected by an array of nine wall-mounted pressure transducers in the axial direction. The frequency analysis of the laser Doppler anemometer signal has been found to exhibit peaks or corner frequencies suggesting that the flow field is dominated by large scale structures similar to that observed in the case of free turbulent jets. The cross-correlation between the wall pressure fluctuations and the axial velocity fluctuations revealed that the fluctuations in the pressure signal were mostly imposed by the passage of the turbulent eddy with a convection velocity that is a function of the jet exit velocity. The Strouhal number formed with the frequency passage of the large-scale structure is a function of the initial conditions only very close to the nozzle exit. Further downstream, the effect of the initial condition is lost, leading to a constant Strouhal number irrespective of the jet Reynold's number. The contribution of the sources in the close vicinity of the nozzle exit to the wall pressure fluctuations near the reattachment is rather weak due to the fast decaying distance function in the axial direction. On the other hand, for sources located within one nozzle diameter from the observation point, the cross-spectral density function has a higher magnitude with its coherence function maxima at a lower frequency range. This frequency range coincides with the frequency domain at which the pressure fluctuation spectrum changes its slope to form a corner frequency that scales with the nozzle diameter and the jet exit speed resulting in a constant Strouhal number equal to 0.1 - 0.2 irrespective of the jet Reynold's number.