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2.2. INTERNAL PULSATILE FLOW 7 the flow in the core region. The laminar flow solution also shows a sharper overshoot relative to the core region profile, while the turbulent flow has a smoother axial velocity profile. The reason is, according to Dec et al. (1991), that in turbulent flow the additional momentum transport by the turbulence rapidly dissipates the oscillations. The turbulence intensity is uniform across the core region of the flow, but the behaviour in the boundary layer has two different modes. When the streamwise pressure gradient is adverse, the tur- bulent intensity increases from the core to a maximum in the boundary layer and then going to zero at the wall. When the pressure gradient is favourable, the turbulent intensity drops from the core value throughout the boundary layer. The turbulent intensity also shows a maximum at times of zero-velocity crossings. From the measured velocity profiles, the instantaneous wall shear stresses were calculated. A trend of increasing cycle-averaged wall shear stress with increasing pulsation amplitude can be noted but no dependence on the fre- quency was found. The cycle-averaged wall shear stress is slightly greater than the wall shear stress predicted for steady turbulent flow at the same averaged mean Reynolds number. For laminar pulsating flow in a bent pipe, the secondary flow changes ro- tational direction from being outward to inward in the centre when Reynolds number is increased for a certain Womersley number. Hamakiotes & Berger (1988) showed using numerical computations, that the Dean vortices do change rotation direction when Re exceeds 300. The Womersley number was 15 and curvature ratio was 1/7. The reversed vortices are called the Lyne vortices. Lyne (1970) showed analytically that the fluid is driven along the wall from the outer side to inner side under action of the pressure gradient in the same man- ner as for the Dean vortices. However, the pressure gradient in the boundary layer is not balanced by the centrifugal forces, and at the edge of the boundary layer, the flow returns centrifugally within in the boundary layer, and drags the fluid in the interior around in a pair of vortices, that are counter-rotating compared to the Dean vortex. It may be expected that the heat transfer to or from a flow in a pipe should depend on the pulsation frequency, since the pulsations will affect the boundary layer. Both increase and decrease of the Nusselt number in pulsating flow has been reported in the literature for different pulsation frequencies, amplitudes and mean Reynolds numbers. The Nusselt number is defined as the ratio between the convective and conductive heat transfer: NuL = hcoef ยท L (2.2) kf hcoef is the heat-transfer coefficient, L is a characteristic length scale and kf is the thermal conductivity. Wang & Zhang (2005) performed numerical computations of turbulent pulsatile flow in a straight pipe with Uosc/Umean=3,PDF Image | Numerical computations of the unsteady flow in a radial turbine
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