Numerical study of effects of pulsatile amplitude for transitional turbulent pulsatile flow in pipes with ring-type constrictions

The effects of pulsatile amplitude on sinusoidal transitional turbulent flo ws through a rigid pipe in the vicinity of a sharp-edged mechanical ring-ty pe constriction have been studied numerically. Pulsatile flows were studied for transitional turbulent flow with Reynolds number (Re) of the order of 10(4), Womersley number (Nw) of the order of 50 with a corresponding Strouh al number (St) of the order of 0.04. The pulsatile flow considered is a sin usoidal flow with dimensionless amplitudes varying from 0.0 to 1.0. Transit ional laminar and turbulent flow characteristics in an alternative manner w ithin the pulsatile flow fields were observed and studied numerically. The flow characteristics were studied through the pulsatile contours of streaml ines, vorticity, shear stress and isobars. It was observed that fluid accel erations tend to suppress the development of flow disturbances. All the ins tantaneous maximum values of turbulent kinetic energy, turbulent viscosity, turbulent shear stress are smaller during the acceleration phase when comp ared with those during deceleration period. Various parametric equations wi thin a pulsatile cycle have also been formulated through numerical experime ntations with different pulsatile amplitudes. In the vicinity of constricti ons, the empirical relationships were obtained for the instantaneous flow r ate (Q), the pressure gradient (dp/dz), the pressure loss (P-loss), the max imum velocity (V-max), the maximum vorticity (zeta(max)) the maximum wall v orticity (zeta(w,max)), the maximum shear stress (tau(max)) and the maximum wall shear stress (tau(w,max)). Elliptic relation was observed between flo w rate and pressure gradient. Quadratic relations were observed between flo w rate and the pressure loss, the maximum values of shear stress, wall shea r stress, turbulent kinematic energy and the turbulent viscosity. Linear re lationships exist between the instantaneous flow rate and the maximum value s of vorticity, wall vorticity and velocity. The time-average axial pressur e gradient and the time average pressure loss across the constriction were observed to increase linearly with the pulsatile amplitude. Copyright (C) 1 999 John Wiley & Sons, Ltd.