ENG5091 - Assignment
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ENG5091 - Assignment
Part 1
You are required to compare the results of laminar boundary layer analysis between an exact analytic method (Falkner-Skan) with an approximate integral method (Thwaites) for flows of the general type ue = uo xm .
Calculate, tabulate and plot the distribution of 6* , 9 , c f for the cases of m = 1, 0.6 , 0.2 , 0 , -0.04, -0.06, obtained from F-S and Thwaites method.
In each case take uo = 15m/s plot the distributions over a surface of length of 0.25m.
Solutions of the Falkner-Skan equation can be obtained modifying the Matlab code provided on the course Moodle page. The code can be edited to specify the required beta value. Include sample outputs from the code in your report.
Part 2
You are required to compare the laminar boundary layer development, using Thwaites’ method, around a circular cylinder at freestream Reynolds Number Rea = 9500 using two different external flows:
Potential Flow theory: = 2x − 0.333x3 + 0.0167x5
Experimental data: = 1.814x − 0.271x3 − 0.0471x5
where x’ = x/a
Calculate, tabulate and plot the variation in cf from the front stagnation point to the point of boundary layer separation for the two external flows and comment on the results. (You will have to implement an iterative solution procedure – e.g. via Excel or Matlab, using sufficient resolution along surface to capture behaviour). Show sample working.
Report
Students are require to submit a typed report on Moodle on both parts of the assignment. These should be kept as brief as possible, whilst presenting the necessary information. A standard report header and statement of originality should be attached to the report. Deadline for submission is before 12am, 3rd January 2023.
Hints
92 (x1 ) = x1j0 u e(5)dx
1 1
j • dx = aj • dx'
Re a =
v
m = −
a dx'
→ f (Re a , x 1('))
→ l
→ cf = → f (Re a , x1 )
e
2023-01-05