Chapter: Mechanical : Gas Dynamics and Jet Propulsion : Flow Through Ducts
Adiabatic Flow of a Compressible Fluid Through a Conduit
Adiabatic Flow of a
Compressible Fluid Through a Conduit
Flow through pipes in a typical plant where line lengths
are short, or the pipe is well insulated can be considered adiabatic. A typical
situation is a pipe into which gas enters at a given pressure and temperature
and flows at a rate determined by the length and diameter of the pipe and
downstream pressure. As the line gets longer friction losses increase and the
following occurs:
Ø Pressure
decreases
Ø Density
decreases
Ø Velocity
increases
Ø Enthalpy
decreases
Ø Entropy
increases
The question is “will the velocity continue to increasing
until it crosses the sonic barrier?” The answer is NO. The maximum velocity
always occurs at the end of the pipe and continues to increase as the pressure
drops until reaching Mach 1. The velocity cannot cross the sonic barrier in
adiabatic flow through a conduit of constant cross section. If an effort is
made to decrease downstream pressure further, the velocity, pressure,
temperature and density remain constant at the end of the pipe corresponding to
Mach 1 conditions. The excess pressure drop is dissipated by shock waves at the
pipe exit due to sudden expansion. If the line length is increased to drop the
pressure further the mass flux decreases, so that Mach 1 is maintained at the
end of the pipe.
The
effect of friction in supersonic flow of the following parameters
a)
velocity b) pressure c) temperature
Flow
properties at M = M* = 1 are used as reference values for non-
dimensionalizing various properties at any section of the duct.
a) Velocity
Variation of flow properties
The flow properties (P,T,ρ,C)at M=M*=1are used
as reference values for non-dimensionalizing various properties at any section
of the duct.
Temperature
Stagnation temperature –Mach
number relation
At critical state
M=1
T0 = T0*
Variation of Mach number
with duct length
The duct length required for the flow to pass from a
given initial mach number M1 to a given final mach number m2can be obtained
from the following expression.
Mean friction coefficient with respect
to duct length is given by
The distance (L) between two section of
duct where the ach numbers M1 &M2 are given by
Related Topics