Page 49 - Fluid Mechanics and Thermodynamics of Turbomachinery

30 Fluid Mechanics, Thermodynamics of Turbomachinery
P
If the process is adiabatic, dQ D 0, then
s 2 = s 1 . (2.16)

If the process is reversible as well, then
s 2 D s 1 . (2.16a)

Thus, for a flow which is adiabatic, the ideal process will be one in which the
entropy remains unchanged during the process (the condition of isentropy).
Several important expressions can be obtained using the above definition of
entropy. For a system of mass m undergoing a reversible process dQ D dQ R D mTds
and dW D dW R D mpdv. In the absence of motion, gravity and other effects the
first law of thermodynamics, eqn. (2.4a) becomes

Tds D du C pdv. (2.17)
With h D u C pv then dh D du C pdv C vdp and eqn. (2.17) then gives

Tds D dh vdp. (2.18)

Definitions of efficiency

A large number of efficiency definitions are included in the literature of turboma-
chines and most workers in this field would agree there are too many. In this book
only those considered to be important and useful are included.

Efficiency of turbines
Turbines are designed to convert the available energy in a flowing fluid into useful
mechanical work delivered at the coupling of the output shaft. The efficiency of this
process, the overall efficiency 0 , is a performance factor of considerable interest to
both designer and user of the turbine. Thus,
mechanical energy available at coupling of output shaft in unit time
0 D .
maximum energy difference possible for the fluid in unit time
Mechanical energy losses occur between the turbine rotor and the output shaft
coupling as a result of the work done against friction at the bearings, glands, etc.
The magnitude of this loss as a fraction of the total energy transferred to the rotor is
difficult to estimate as it varies with the size and individual design of turbomachine.
For small machines (several kilowatts) it may amount to 5% or more, but for
medium and large machines this loss ratio may become as little as 1%. A detailed
consideration of the mechanical losses in turbomachines is beyond the scope of this
book and is not pursued further.
The isentropic efficiency t or hydraulic efficiency h for a turbine is, in broad
terms,
mechanical energy supplied to the rotor in unit time
t .or h / D .
maximum energy difference possible for the fluid in unit time