AE3401

Pressure Distribution Around a Circular Cylinder

Objective

To measure the pressure distribution around a circular cylinder and thereby calculate the pressure drag coefficient.

Apparatus

•    T2 wind tunnel (1.12m × 0.8m working section, speed range 5 – 55 m/s).

•    Circular cylinder model (150 mm diameter), pressure tapped at 15° intervals from 0 to 180°

(tappings 1 – 13) and additionally at 210° and -30° (tappings 14 and 15 respectively), mounted to the turntable of the force balance above the test section.

•    Multi-tube manometer, inclinable, containing fluid of specific gravity 0.82.

•    Digital pressure transducer connected, in parallel with the manometer, to apitot-static tube just upstream of the cylinder model,

Procedure

The tunnel must be operated by a competent person, and will be run up to a speed of about  15 m/s (dynamic pressure of about 135 Pa).

Using the tunnel balance controls, correct the  ‘yaw’ angle of the cylinder to make sure that the 2nd  pressure tapping is aligned with the stagnation point: the manometer tubes connected to tapping  15 (-30°) and tapping 3 (+30°) should show the same reading when the cylinder is correctly aligned. Tapping 2 should now read the same as the total pressure tube from the pitot-static probe, but there may be differences which you might discuss in your report.

Note down the readings for all relevant manometer tubes, including those connected to the pitot-static probe. Note how the manometer tubes are connected and decide how high and low pressures on the model and PS tube will be displayed. Be careful not to knock the manometer which will have been levelled carefully for the lab.

Once your measurements are complete, use the balance control panel to rotate the cylinder through 180。to bring the roughness strips to the upstream side of the cylinder. Note any changes to the dynamic pressure on the digital manometer, but there is no need to adjust the tunnel speed control. Repeat the alignment procedure to position tapping  13 under the  stagnation point,  i.e.  so that the manometer tubes connected to tapping  11  (150°)  and tapping 14 (210°) show the same reading. Record all relevant manometer readings once again.

Record the inclination of the manometer, atmospheric pressure and the tunnel air temperature (required to calculate the density of air stream).

Write-Up: Contents

Write  a technical report  on  this  experiment.  In  your  introduction  you  must  both  explain  the  engineering context of the flow around a cylinder and describe the fluid phenomena you expect to encounter during the experiment. Specific requirements for the Theory, Results and Discussion sections are detailed below.

Write-up: Theory

In your write-up you should explain how the manometer height readings are converted into pressure coefficients over the surface of the cylinder, with a specimen calculation shown. Pressure coefficient cp is given by

but the tunnel dynamic pressure first needs to be corrected for ‘blockage’ . The cylinder’s presence in the tunnel means that the airflow is forced to pass through a restricted area between the cylinder and the tunnel walls , so the flow at the cylinder station is artificially faster than it would otherwise be.

We define an effective speed of air past the cylinder Ve given by Vm(1+B), where Vm is the speed measured using the pitot-static or tunnel side-wall tubes at the upstream end of the working section (the undisturbed ‘free stream’ for this flow field). Effective dynamic pressure is therefore given by

B is the sum of two terms, Bs due to solid blockage and Bw due to the wake. These two terms are given by

where D/w is the ratio of cylinder diameter to working-section width (i.e. the proportion of cross-sectional area taken up by the cylinder) and CD is the drag coefficient of the cylinder, which may be assumed to be  1.0 as a starting approximation.

So we can write

We now need to know the difference between local and free stream static pressures to calculate cp but we have only our experimentally-measured free stream pressure, pm. However we can use Bernoulli because the total pressure is the same for both actual and effective streams:

Referring to the earlier expressions we can say

Again, a specimen calculation should be provided to show how you turned your experimental readings (manometer heights) into cp  and CD  values, the latter defined here as

Use the trapezium rule, not Simpson’s rule, to integrate equation (3) numerically. Finally, you should outline how you obtained values for the Reynolds number.

Write-up: Results

This section should include a table of tunnel speeds, cylinder Reynolds numbers and drag coefficients, and plots of both cp and cpcosθ against angular position, θ, for both experiment and (inviscid) theory.

Write-up: Discussion

Include the following in your critical analysis of your results:

1.    Compare the pressure distributions and drag coefficients for both parts of the experiment with each other and with published results from textbooks, at similar Reynolds Numbers, and discuss.

2.    Comment on why you have been able to produce a pressure distribution appropriate to a turbulent boundary layer when the Reynolds number hardly changed from its laminar value in the first part of the experiment.

References

F M White                                    Fluid Mechanics              p298 & p455.

Streeter and Wylie Duncan,           Fluid Mechanics p222

Thom and Young B S                    Mechanics of Fluids p243

Massey                                        Mechanics of Fluids        p260

The Lecture notes

Report marking scheme:

Abstract - 5 marks

Introduction – 10 marks

Don’t forget to mention the relevance of the topic to practical engineering.

Experimental Arrangement / Procedure – 10 marks

Simply copying the lab sheet instructions will get zero marks!

Theory – 10 marks

Here the theory is better coming just before the results since it should concern the analysis of the experimental data rather than the details of the flow physics or any mathematical models (although the inviscid cp distribution would count as real ‘theory’). Simply copying the lab sheet analysis will get zero marks!

Results – 25 marks: 10 for data reduction; 10 for the graphs; 5 for Re, CD values and any text introducing the results.

Discussion – 20 marks: 10 for explanations of your own results; 5 for consideration of errors (i.e. more than just a list); 5 for comparison with any results published in the literature

Conclusions – 5 marks Referencing – 5 marks

Presentation – 10 marks: this includes following the standard report structure.

The length of the report should be limited to maximum of 4 pages with margnins no smaller than 15mm and minimum font size of 11.