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the mechanical efficiency of the turbocharger, and the efficiency of the compressor, it is possible to relate the blade speed to the boost pressure ratio of the compressor. This is shown in Fig. 2 for a turbine stage loading coefficient of 0.95 and a range of compressor efficiencies. For many applications the maximum compressor efficiency that is realistically achievable today is about 0.85, and in this case a boost pressure ratio of 6, for example, requires a turbine blade tip speed of approximately 500 m/s. Higher boost pressures, or lower compressor efficiencies, require larger turbine blade tip speeds. The maximum blade speed that can be tolerated is limited by the turbine rotor stress. The largest component of this is centrifugal and hence is a function of the square of the blade speed. Other stress components include pressure, thermal and vibratory loads and so the actual relation between peak stress and blade speed is not a simple one, but peak stress does increase rapidly with blade speed. The maximum allowable stress is a function of the rotor material, the quality of the casting, and the duty cycle of the engine. For engines that undergo many cycles, low cycle fatigue limits the rotor life, and with the commonly used Inconel alloys, the blade speed limit is usually found to be in the region of 500 m/s. For engines that run continuously for long periods this limit may be extended somewhat. Further increases in boost pressure therefore require an increase in either the turbine stage loading coefficient or the blade tip speed. The former is a function of the turbine design and it is clearly important to understand what it is about the conventional radial-inflow turbine that prevents higher stage loadings from being achieved with good efficiency. The latter requires developments in blade materials and manufacturing technology, and the prospects for this are discussed later in this paper. LOADING LIMITS The specific work output of the turbine can be written in terms of the blade speed U and the tangential component Cθ of the gas velocity at the inlet (station 2) and exit (station 3) of the rotor using the Euler turbomachine equation: ∆h0 =U2Cθ2 −U3Cθ3 Because of the radius change in the rotor, the blade speed at exit is smaller than that at inlet, and for a turbine working at its design point the flow leaving the rotor is usually in, or close to, the axial direction. The second term on the right hand side of the equation is therefore much smaller than the first, and to a good approximation the equation can be written as ∆h0 =U2Cθ2 The stage loading coefficient can therefore be written as ψ=Cθ2 U2 and then, using the geometry of the rotor inlet velocity triangle, it can be shown that the inlet flow angle of gas relative to the rotor isPDF Image | HIGH BOOST TURBOCHARGERS radial and mixed flow turbines
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