153
Chapter 4
Compressible Fluids
© Springer Science+Business Media Dordrecht 2015
E. Dick, Fundamentals of Turbomachines, Fluid Mechanics and Its Applications 109,
DOI 10.1007/978-94-017-9627-9_4
Abstract In further chapters we will study machines that function with compressible fluids, first steam turbines (Chap. 6), then gas turbines and compressors
(Chaps. 11–15). For analysis of these machines, knowledge of fundamentals of
compressible fluid flow is a necessity. We study compressible fluid flow fundamentals in the present chapter, for one-dimensional steady flows. This term refers to a
flow whose properties change in one single spatial direction, namely an average
streamline, and that is uniform in the spatial directions perpendicular to this streamline and constant in time. The streamline need not be straight. The discussion is
limited to what is strictly necessary for the fundamental analysis of turbomachines.
We refer to books on fluid mechanics for a more in-depth study.
4.1 Basic Laws
The fundamental equations for one-dimensional flows have already been derived in
Chap. 1. We apply them here to compressible fluids. The one-dimensional flow is an
approximation of the flow in a blade passage of a turbomachine. This approximation is
not very accurate. It is primarily intended to acquire fundamental insight. Multi-dimensional effects occur in real machines. We will study them introductorily in the chapter
on steam turbines. More in-depth study of multi-dimensional effects is dealt with in
the gas turbine and compressor chapters. We mainly discuss turbine flow. Within most
components of a turbine, flow is accelerating. A stationary channel between two spaces
in which a flow accelerates is called a nozzle, as shown in Fig. 4.1. Nozzle flow allows
analysis of the functioning of steam turbines. In the present chapter, relations are derived for accelerating flow, but most apply to decelerating flow as well.
The mass conservation equation is vA
r = constant, where A is the cross-section
area of the channel. Logarithmic differentiation results in
(4.1)
The work equation is
.
d
dv dA 0
v
A
r
r
+ +
=
Chapter 4
Compressible Fluids
© Springer Science+Business Media Dordrecht 2015
E. Dick, Fundamentals of Turbomachines, Fluid Mechanics and Its Applications 109,
DOI 10.1007/978-94-017-9627-9_4
Abstract In further chapters we will study machines that function with compressible fluids, first steam turbines (Chap. 6), then gas turbines and compressors
(Chaps. 11–15). For analysis of these machines, knowledge of fundamentals of
compressible fluid flow is a necessity. We study compressible fluid flow fundamentals in the present chapter, for one-dimensional steady flows. This term refers to a
flow whose properties change in one single spatial direction, namely an average
streamline, and that is uniform in the spatial directions perpendicular to this streamline and constant in time. The streamline need not be straight. The discussion is
limited to what is strictly necessary for the fundamental analysis of turbomachines.
We refer to books on fluid mechanics for a more in-depth study.
4.1 Basic Laws
The fundamental equations for one-dimensional flows have already been derived in
Chap. 1. We apply them here to compressible fluids. The one-dimensional flow is an
approximation of the flow in a blade passage of a turbomachine. This approximation is
not very accurate. It is primarily intended to acquire fundamental insight. Multi-dimensional effects occur in real machines. We will study them introductorily in the chapter
on steam turbines. More in-depth study of multi-dimensional effects is dealt with in
the gas turbine and compressor chapters. We mainly discuss turbine flow. Within most
components of a turbine, flow is accelerating. A stationary channel between two spaces
in which a flow accelerates is called a nozzle, as shown in Fig. 4.1. Nozzle flow allows
analysis of the functioning of steam turbines. In the present chapter, relations are derived for accelerating flow, but most apply to decelerating flow as well.
The mass conservation equation is vA
r = constant, where A is the cross-section
area of the channel. Logarithmic differentiation results in
(4.1)
The work equation is
.
d
dv dA 0
v
A
r
r
+ +
=