Compressible Flow through a Nozzle/Diffuser

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This Demonstration models compressible flow of air through a reversible nozzle/diffuser. The inlet pressure , exit velocity
, and exit temperature
are calculated from mass and energy balances. Because the system is reversible, the entropy change is zero. The air exits as a free jet at atmospheric pressure (
). Set the outlet diameter
and inlet velocity
with sliders. When
, the device acts as a nozzle, with the inlet pressure higher than the exit pressure (
) in order to provide the energy needed to accelerate the air through the nozzle. When
, the device operates as a diffuser, and the exit pressure is higher than the inlet pressure (
). Select "plots" to plot the outlet velocity or outlet temperature as a function of outlet diameter for compressible air flow (blue) and incompressible air flow (green). Air is assumed to behave as an ideal gas and all flow is subsonic.
Contributed by: Rachael L. Baumann (March 2016)
Additional contributions by: Jeffrey S. Knutsen andJohn L. Falconer
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The mass balance around a nozzle/diffuser for compressible flow where for the inlet and
for the outlet is given by:
,
where is the area,
is the velocity (m/s),
is the density calculated from the ideal gas law,
is diameter (m),
is pressure (kPa),
is the ideal gas constant and
is temperature (K).
The mass balance simplifies to:
for incompressible flow , and thus
.
The energy balance for an adiabatic nozzle/diffuser is:
,
where is enthalpy (J/kg), and conservation of mass means that
, so the energy balance simplifies to:
,
where is the ideal gas heat capacity of air (J/[kg K]).
For compressible flow, the inlet pressure is calculated from an entropy balance on an adiabatic reversible system:
,
which simplifies to
.
Permanent Citation