Compressible Flow through a Nozzle/Diffuser
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
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