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Incompressible Turbulent Boundary Layer

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Question 4 (30 marks)

Clauser's experiment II is the background to this question. The objective is to find an approximate analytical solution for an equilibrium ( = constant) turbulent flow. The free stream velocity at the edge of the boundary layer and the measured values of friction coefficient, Cf are given against distance along the wall in the table below:

x (m) 2,286 2,743 3,353 3,862 4,929 5,483 7,300 8,129
U (m/s) 7,955 7,559 7,163 6,949 6,492 6,157 5,761 5,517
Cf-measured 0,0013 0,0012 0.0011 0,0010 0,0011 0,0011 0,0010 0,0009

a) Show that the velocity distribution is approximated well by U = U0 xm where U0 = 10,2
and m = -0,29

b) Use the incompressible momentum integral equation to prove that for U = U0 xm:

c) Recognise this as a linear first order differential equation and prove that, when  and Cf are constant its solution is:

where c is an integration constant.

d) According to Clauser,  = 8 for this experiment. Assuming that  = 0,8( + 0,5)0,75, and that Cf = 0,00127 at x = 2,286, calculate , H, *, and Cf for each x-value in the table.

e) Discuss the validity of the assumptions.

f) Discuss the possibility of extending this method to non-equilibrium flows.

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Solution Summary

Incompressible turbulent boundary layers are examined. Integration constants for Clauser experiments are determined.

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