By Rama S.R. Gorla, Aijaz A. Khan
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Extra resources for Turbomachinery: Design and Theory (Dekker Mechanical Engineering)
Sample text
P 0 Also, DT ¼ D T /hc P by definition of hc , and thus: hs /hc ¼ DT s 0 /DT 0 . It is clear from Fig. 12 that DT 0 s . DT 0 . Hence, hc , hs and the difference will increase with increasing pressure ratio. , small stage efficiency) is less than the overall efficiency of the turbine. The above discussions have led to the concept of polytropic efficiency, h1, which is defined as the isentropic efficiency of an elemental stage in the process such that it is constant throughout the entire process. The relationship between a polytropic efficiency, which is constant through the compressor, and the overall efficiency hc may be obtained for a gas of constant specific heat.
The net torque of the rotor t (tau). Under steady flow conditions, using mass flow rate m, the torque exerted by or acting on the rotor will be: t ¼ mðC w1 r1 2 C w2 r2 Þ Therefore the rate of energy transfer, W, is the product of the torque and the angular velocity of the rotor v (omega), so: W ¼ tv ¼ mvðC w1 r 1 2 C w2 r 2 Þ For unit mass flow, energy will be given by: W ¼ vðC w1 r 1 2 C w2 r 2 Þ ¼ ðC w1 r 1 v 2 Cw2 r 2 vÞ But, v r1 ¼ U1 and v r2 ¼ U2. Hence; W ¼ ðC w1 U 1 2 C w2 U 2 Þ; ð1:78Þ where, W is the energy transferred per unit mass, and U1 and U2 are the rotor speeds at the inlet and the exit respectively.
The change in magnitude of the radial velocity components produces radial force. Neither has any effect on the angular motion of the rotor. The whirl or tangential components Cw produce the rotational effect. This may be expressed in general as follows: The unit mass of fluid entering at section 1 and leaving in any unit of time produces: The angular momentum at the inlet: Cw1r1 The angular momentum at the outlet: Cw2r2 And therefore the rate of change of angular momentum ¼ Cw1r1 – Cw2r2 Copyright 2003 by Marcel Dekker, Inc.