Page 65 - Fluid Mechanics and Thermodynamics of Turbomachinery

46 Fluid Mechanics, Thermodynamics of Turbomachinery
p 02 . Also, using the continuity equa-
where the loss in total pressure, p 0 D p 01
tion across the diffuser, c 1 A 1 D c 2 A 2 , we obtain
c 1 /c 2 D A 2 /A 1 D A R , (2.49)

where A R is the area ratio of the diffuser.
From eqn. (2.48), by setting p 0 to zero and with eqn. (2.49), it is easy to show
that the ideal pressure rise coefficient is

1
2
C pi D 1 .c 2 /c 1 / D 1 (2.47b)
A 2
R
Thus, eqn. (2.48) can be rewritten as
C p D C pi p 0 /q 1 . (2.50)
Using the definition given in eqn. (2.46), then the diffuser efficiency (referred to as
the diffuser effectiveness by Sovran and Klomp (1967)), is
D D C p /C pi . (2.51)

(2) A total pressure recovery factor, p 02 /p 01 , is sometimes used as an indicator
of the performance of diffusers. From eqn. (2.45a), the diffuser efficiency can be
written

1/. (2.52)
D D .T 2s /T 1 1//.T 2 T 1
For the isentropic process 1 2s:

.
1//
T 2s p 2
D .
T 1 p 1
For the constant temperature process 01 02, Tds Ddp/ which, when combined
with the gas law, p/ D RT, gives ds DRdp/p:

p 01
∴ s D R ln .
p 02
For the constant pressure process 2s 2, Tds D dh D C p dT,

T 2
∴ s D C p ln .
T 2s
Equating these expressions for the entropy increase and using R/C p D .
1//
,
then

.
1//
T 2 p 01
D ,
T 2s p 02
.
1//
∴ T 2 D T 2 T 2s D p 01 p 2 .
T 1 T 2s T 1 p 02 p 1