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8 2. NON-PULSATILE AND PULSATILE INTERNAL FLOW where the Womersley number was varied from 40 to 60. The results showed that the axial pressure gradient has a phase lag of about 90◦ to the veloc- ity. The results also showed that the instantaneous velocity profile was flat at the centre of the pipe. In the region between the core region and the wall a velocity overshoot occurred at some instants. These overshoots had a veloc- ity that was larger than the velocity in the core region, and more heat was transported at these instances. The thermal boundary layer thickness varied with the pulsation of the flow and was during a period, sometimes thinner and sometimes thicker than in a corresponding steady state flow case. The local Nusselt number was, for different Womersley numbers, higher than it was for the corresponding steady case. The heat transfer was greatly enhanced by the pulsative flow, especially in the entrance region. Wang and Zhang also showed that the local instantaneous Nusselt number had its maximum when the ve- locity reached its peak value and the Nusselt number reached its lowest value when the velocity was zero. The heat transfer was also enhanced when the velocity amplitude of the pulse was increased. The results from Dec & Keller (1989) experiments with a pulse combustor fitted with a tail-pipe showed that the Nusselt number in oscillating flow was significantly higher than for steady flow with the same mean Reynolds number. The experiments also showed that the Nusselt number increased with increasing frequency and pulsation ampli- tude. Habib et al. (2004) studied pulsatile pipe flow in a range of Re of 8 000 < Re < 50 000 and both enhancement and reduction in mean Nusselt number was reported. The Nusselt number decreased for low pulsating frequency. The maximum mean Nusselt number was obtained when the pulsating frequency was in the vicinity of the turbulent bursting frequency. At this pulsating fre- quency, the interaction of the pulsations and the turbulent bursting increased the heat transfer, and hence the Nusselt number increased. These phenom- ena can be explained by the turbulent bursting model, which states that the viscous sublayer is unstable, and due to turbulent structures, its growth and destruction occur periodically. These different effects, such as the phase lag and increased heat transfer in pulsatile flow, will affect the performance of the radial turbine working under pulsatile flow conditions. The phase shift will imply that the static and dynamic pressure will be out of phase, which can affect the shaft power of the turbine. The pulsatile flow also increases the losses; for example the heat-losses to the ambient. The losses due to viscous effects will probably also increase, due stronger shear layers. This will most probably imply that the turbine cannot be treated as being a quasi-stationary flow device.PDF Image | Numerical computations of the unsteady flow in a radial turbine
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