Compressible Flow in a Convergent-Divergent
A Convergent- Divergent or Laval Nozzle is a device that, under different conditions
of fluid flow is capable of generating the full range of Mach numbers from the
subsonic, (M <1) through to the supersonic (M>1). Although air is a compressible
fluid, the effects of change in density on the flow parameters only become significant
at Mach numbers above approximately 0.6 Bernoulli's equation can be used to
characterise incompressible flow but the effects of change in density at higher Mach
numbers rule out its use in transonic and supersonic flow.
The aim of this experiment is to demonstrate the relationships between the pressure,
temperature, density and Mach number in flowing fluid as the Mach number
approaches and potentially reaches unity.
A convergent-divergent nozzle has been machined into a length of transparent bar
(see figures & below). Tappings have been drilled into the nozzle to allow
temperature and pressure sensors to be introduced into the flow before, at and after
the throat of the nozzle. Air under pressure is supplied to the lower end of the nozzle
from the building compressed air system and some control over its flow rate provided
with valve upstream of the nozzle. Following its passage through the nozzle, the
is allowed to expand ina larger diameter tube, in which its velocity and temperature
are recorded, before is discharged to atmosphere
Figures 1& 2. Schematic
diagram and photograph of
Some key dimensions:
1. Use the anemometer to measure the maximum possible air velocity at the exit
of the discharge tube when the inlet valve is fully opened
Determine suitable flow velocities at which to take readings. The flow rate
can be controlled by changing the opening of the inlet valve,
3. At each flow rate, measure the pressure and temperature at the inlet, throat
and exit of the nozzle (stations 1, 2 & 3) and the temperature in the
discharge tube (station 4).
4. Ensure you have recorded all the physical dimensions of the apparatus
required to analyse the flow The ambient temperature and pressure should
also be recorded
Results and discussion:
1. Calculate the air mass flow rate through the system for each inlet valve
setting. Care should be given to ensuring that the measurements recorded
have the appropriate units and baseline.
2. From continuity equation, calculate the velocity at each section (inlet, throat
and exit) of the nozzle
3. Calculate the speed of sound at each section (inlet, throat and exit) of the
4. Calculate the Mach number at each section (inlet, throat and exit) of the
5. Plot the pressure density and Mach number distributions in the axial
direction for each flow rate
6. Discuss the results in detail In addition to considering the variation in the flow
parameters given above, you should also consider whether the system is
isentropic and the impact that this might have on the results achieved
The experiment should be properly documented as formal lab report of
approximately 1000 words in length. The report is to be correctly formatted and
referenced in accordance with the Harvard referencing system Although the
experiment will be conducted as a group activity, each student is to submit their
own individual report via Turnitin which should be their work except where stated
otherwise. If academic misconduct of any nature is suspected (e g plagiarism or
collusion) it will be considered using the appropriate procedures.
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A convergent-divergent (C-D) nozzle is used to produce supersonic flow from a reservoir of pressure and a particular geometry. This geometry consists of a section of decreasing area which reaches a minimum and then increases again. The purpose of this shape is creation of supersonic flow. The nozzle contracts the flow by decreasing area continually until the smallest portion of area called the throat....