Page 250 - Fluid Mechanics and Thermodynamics of Turbomachinery

Centrifugal Pumps, Fans and Compressors 231
Impeller

In the rotating impeller passages, flow conditions are referred to the factor I D
1
2
h C .w 2 U /, which is constant according to eqn. (7.2). At the impeller inlet
2
1 2
and for the special case c 1 D 0, note that I 1 D h 1 C c D h 01 . When choking
2 1
occurs in the impeller passages it is the relative velocity w which equals the
2
2
speed of sound at some section. Now w D a D
RT and T 01 D T C .
RT/2C p /
2
.U /2C p /, therefore
2
T 2 U
D 1 C . (7.34)
T 01
C 1 2C p T 01
Assuming isentropic flow, / 01 D .T/T 01 / 1/.
1/ . Using the continuity equation,
.
C1//2.
1/
P m T
D 01 a 01
A T 01
2 .
C1//2.
1/
2 U
D 01 a 01 1 C

C 1 2C p T 01
2 2
C1//2.
1/
2 C .
1/U /a
01
D 01 a 01 .7.36/

C 1
If chocking occurs in the rotating passages, eqn. (7.36) indicates that the mass flow
is dependent on the blade speed. As the speed of rotation is increased the compressor
can accept a greater mass flow, unless choking occurs in some other component of
the compressor. That the choking flow in an impeller can vary, depending on blade
speed, may seem at first rather surprising; the above analysis gives the reason for
the variation of the choking limit of a compressor.
Diffuser

The relation for the choking flow, eqn. (7.34) holds for the diffuser passages,
it being noted that stagnation conditions now refer to the diffuser and not the
inlet. Thus
.
C1//2.
1/
P m 2
D 02 a 02 . (7.37)
A 2
C 1
Clearly, stagnation conditions at diffuser inlet are dependent on the impeller
process. To find how the choking mass flow limit is affected by blade speed it
is necessary to refer back to inlet stagnation conditions.
Assuming a radial bladed impeller of efficiency i then,

2
T 01 / D i U /C p .
T 02s T 01 D i .T 02
2
Hence
2
p 02 /p 01 D .T 02s /T 01 /
/.
1/ D [1 C i U /C p T 01 /]
/.
1/
2