Page 72 - Fluid Mechanics and Thermodynamics of Turbomachinery

Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency 53
Solution. From eqns. (2.47a) and (2.58):

p 2 p 1 2
C p D ˛ 2 /A / $
D .˛ 1
R
q 1
D 1.059 1.543/4 0.09 D 0.583.
Using eqn. (2.59) directly,
2
D D C p /C pi D C p /.1 1/A / D 0.583/0.75
R
∴ D D 0.7777.
Stevens and Williams observed that an incipient transitory stall was in evidence
on the diffuser outer wall which affected the accuracy of the results. So, it is not
surprising that a slight mismatch is evident between the above calculated result and
the measured result.

References
¸ Cengel, Y. A. and Boles, M. A. (1994). Thermodynamics: An Engineering Approach. (2nd
edn). McGraw-Hill.
Japikse, D. (1984). Turbomachinery Diffuser Design Technology, DTS-1. Concepts ETI.
Kline, S. J. and Johnson, J. P. (1986). Diffusers flow phenomena and design. In Advanced
Topics in Turbomachinery Technology. Principal Lecture Series, No. 2. (D. Japikse, ed.)
pp. 6 1to6 44, Concepts, ETI.
Kline, S. J., Abbott, D. E. and Fox, R. W. (1959). Optimum design of straight-walled
diffusers. Trans. Am. Soc. Mech. Engrs., Series D, 81.
Horlock, J. H. (1966). Axial Flow Turbines. Butterworths. (1973 Reprint with corrections,
Huntington, New York: Krieger.)
Reynolds, William C. and Perkins, Henry C. (1977). Engineering Thermodynamics. (2nd
edn). McGraw-Hill.
Rogers, G. F. C. and Mayhew, Y. R. (1992). Engineering Thermodynamics, Work and Heat
Transfer. (4th edn). Longman.
Rogers, G. F. C. and Mayhew, Y. R. (1995). Thermodynamic and Transport Properties of
Fluids (SI Units). (5th edn). Blackwell.
Runstadler, P. W., Dolan, F. X. and Dean, R. C. (1975). Diffuser Data Book. Creare TN186.
Sovran, G. and Klomp, E. (1967). Experimentally determined optimum geometries for
rectilinear diffusers with rectangular, conical and annular cross-sections. Fluid Mechanics
of Internal Flow, Elsevier, pp. 270 319.
Stevens, S. J. and Williams, G. J. (1980). The influence of inlet conditions on the perfor-
mance of annular diffusers. J. Fluids Engineering, Trans. Am. Soc. Mech. Engrs., 102,
357 63.

Problems
1. For the adiabatic expansion of a perfect gas through a turbine, show that the overall
efficiency t and small stage efficiency p are related by
t D .1 ε //.1 /,
p
where D r .1
//
, and r is the expansion pressure ratio,
is the ratio of specific heats.