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3.4. TURBINE PERFORMANCE UNDER PULSATILE FLOW 19 tip, and hence, the tip vortices and the losses that they introduce. Dambach & Hodson (2001) conducted an experimental investigation of the flow over the blade tip for different axial and radial tip-clearances for a radial turbine. The tip gap was varied from 0.6% to 1.2% of the local blade height. They showed that different blade tip gap height to blade width ratio gave different behaviour for the tip leakage flow. If the ratio was below approximately 16 , the tip leakage flow was mixed with the boundary layer at the shroud, resulting in a tip leakage flow with low momentum, and hence, a less strong tip vortex at the suction side. If the ratio was larger than approximately 16 , the inertia effects dominated over the viscous effects, and the momentum of tip leakage flow from the pressure to suction side was higher, resulting in a stronger tip vortex. Also, they showed that the pressure difference over the gap remains relatively constant for the tested tip gap heights. For turbines working in pulsatile flow, mixed flow turbines have some ad- vantages compared to radial turbines. A mixed flow turbine is a turbine, with its leading edge of the blade inclined to the axial axis. This implies that the flow at the entrance to the wheel have both an axial velocity component and a radial velocity component. At higher mass flow rates, which is the same as higher pressure ratio and lower U/Cs, mixed flow turbines have better effi- ciency compared to radial turbines due to less turning of the flow in the wheel. The turning process from the radial inlet to the axial outlet gives raise to losses due to secondary flow. The U/Cs ratio is called the blade speed ratio, and U is the rotor tip speed and Cs defined as: p γ−1 Cs= 2·cp·T01·(1− 2 γ ) (3.6) p01 Mixed flow turbines have the maximum efficiency at a U/Cs ratio of ap- proximately 0.65, while a radial turbines have the best efficiency at blade speed ratio of approximately 0.7 (Chen et al. (1997)). The efficiency also drops sub- stantially for U/Cs values below 0.7 for radial turbines, while mixed flow tur- bines can maintain high efficiency over a larger region of lower U/Cs ratios. 3.4. Turbine performance under pulsatile flow As already mentioned, the flow in the exhaust system of an IC engine is highly pulsatile, and this affects the performance of the turbine. The performance of turbines working under pulsatile flow conditions has been assessed by many researches by both different numerical methods and by experiments. A typical feature of turbines working in pulsatile flow is that when plotting the mass flow versus shaft torque, as been done in Figure 3.7, the trajectory form a closed loop, enclosing the quasi-stationary trajectory. The same is valid when plotting the blade speed ratio U/Cs versus the efficiency. U/Cs varies during the pulse,PDF Image | Numerical computations of the unsteady flow in a radial turbine
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