## Measurements in Supersonic Flow

The aim of this laboratory experiment is to familiarise students with a simple application of the rules of gas dynamics. To complete the work successfully a student will need to understand the behaviour of supersonic flow along with the equipment and techniques required to perform measurement of this flow. A secondary aim is to familiarise students with alternate methods of theoretical flow prediction. In this case direct molecular simulation of gas flow can be applied to the near-continuum region to determine its accuracy against the known solutions provided by classical gas dynamic theory.

Experimental Procedure.

Observe the set up of the apparatus. Take note of each piece of equipment and its function. The high-pressure gas supply line is attached via a manually operated valve to the converging-diverging two-dimensional nozzle. Once the valve is open to give sufficient upstream stagnation pressure, the nozzle will choke giving Mach 1 flow at the throat. Downstream of the throat (area A*) the flow Mach number will depend primarily on the area ratio of the channel (A/A*) and a supersonic flow slightly above Mach 2 will be obtained. Click here to see nozzle geometry.
With a steel wall containing static pressure ports on the side of the nozzle, static pressure variation along the nozzle length can be determined. The static pressure to stagnation pressure ratio at any point along the channel can be used to predict local Mach number. This result can be compared to area ratio predictions and discrepancies due to boundary layer effects, shock waves or surface imperfections can be evaluated. Click here to see a diagram of the manometers used for this experiment.
With an empty test section, open the control valve and establish supersonic flow in the channel. Measure the static pressure readings along the length of the nozzle. Measure the total pressure reading for the upstream flow. Measure the atmospheric pressure in the lab. Recorded data can be written in the Tables shown here.
With glass walls on the side of the nozzle and by means of a Schlieren optical system, the shock/expansion wave system produced by objects placed in the flow can be seen. These flow patterns can be recorded on film. Click here to see a diagram of Schlieren optical system.
Install a test shape into the test section of the channel. Again open the valve to establish supersonic flow. Record the shock and expansion wave patterns using the Schlieren optical system.
Some examples are shown below,

Axi-symmetric Cone at M=1.7, M=2.2 and M=3.0

Image enhanced versions of the above Cone flow

Flow at the nose of a bluff body at Mach 2.2

Experimental Results

Plot a graph of Mach number versus axial length from throat based on the above experimental measurements. Include both methods, Mach number predicted from nozzle area ratio and Mach number predicted from static/stagnation pressure ratios.
Comment on the differences in Mach number predicted by these two methods. Give explanations.
Estimate the flow Mach number in the part of the channel section into which objects are placed.
Compare oblique shock wave angles and Prandtl-Meyer expansion fan angles for the measured flow with perfect gas theory models.

Extended comparison with DSMC Gas Simulation Method

Using the experimental result for Mach number determined above, set up a direct molecular simulation (DSMC) of the flow for one of the test objects used in the experiment.
Compare the simulation flow patterns to those obtained experimentally in the nozzle test section. Quantitative comparisons can be made of the wave angles and percentage errors estimated. Include comparisons with ideal perfect gas flow theory. Click here for a demonstration program showing ideal gas solutions of supersonic flow over a two-dimensional wedge.
Give a brief discussion of the accuracy obtained by molecular simulation theory in comparison to experimental results and in comparison to simple perfect gas theory. Based on these comparisons give your view on the type of flow problems to which DSMC is suited as compared to other conventional CFD methods.

© School of Aerospace, Mechanical and Mechatronic Engineering
University of Sydney, 1998-2004