Numerical Hydrodynamics Assignment

Force prediction on three geometries

The assignment is to use numerical methods to generate pressure and friction force predictions for the laminar flow around three geometries:

1. A circular cylinder,
2. A jukowski foil with $t/c=0.15$, and
3. A mystery geometry which will be assigned individually.

Specifically, for the circular cylinder you will:

• Compute the pressure coefficient $c_p$ on the surface for three resolutions $N=32,64,128$, and compare the results to the exact potential flow solution.
• Compute the friction drag coefficient $C_F$, and an estimate for the pressure drag coefficient $C_D$ for the same three resolutions at $Re_D=10^5$.

For the jukowski foil you will:

• Compute the lift coefficient $C_L$ as a function of the angle of attack $\alpha\le 10^o$ for three resolutions $N=32,64,128$, and and compare the results to the exact potential flow solution.
• Compute the separation point location on either side of the foil for the same angle of attack range for $N=128$.

The mystery geometry will require a similar computation. Correct results for this geometry will demonstrate independent excellence and will be marked accordingly.

Submission requirements

The project will be submitted in the form of an iPython notebook, like this one. This means your report will be a reproducible scientific document; all of your results will be generated and displayed inside the document itself.

You may use the code in the VortexPanel.py and BoundaryLayer.py files, but all other code must be embedded in the notebook itself. All results must be generated in the notebook and be publication quality; axis labeled, plot legends included, etc.

Your report should follow the standard format, with a short Introduction and Conclusion, and a short Method, Results, and Discussion section for each geometry. Please keep the text brief and to the point. In particular, do not explain how VortexPanel.py and BoundaryLayer.py work - explain how your code works. What method did you use? What do your results mean?

Submit the report by email to me directly with the subject SESS 3023 report: <your student ID>.

iPython help

The text in iPython notebooks is written in Markdown, which is extremely simple to use. The best part is that it let's you embed latex-style equations like this

without latex installed. The worst part is that spell-checking doesn't work automatically. You can copy-paste into a text editor, or try installing a spell checker.

Please avoid embedding images in your report since it would require sending additional files and the path information might be corrupted.

In the course you will become familiar with how code blocks work:

but my #1 tip is: Make sure to restart the kernel and Run all cells in the notebook frequently. That will avoid unpleasant surprises and ensure that the document you submit will work as you intend it to.

I'll add more tips to this document and post announcements as common problems present themselves.

Ignore the line below - it just loads the style sheet.