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Dimensionless Parameter and Navier Stokes

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Old   February 28, 2006, 12:26
Default Dimensionless Parameter and Navier Stokes
  #1
John
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Ok heres the problem I face, there is a question I have been given but I am damned if I can make ends meat of it.

Basically the questions asks, by using dimensionless parameter try to normalize the Navier Stokes equation.

Now my Uni friends though you differentiate the equation I have been on cfd-online but to no avail, I think it may be a little advance, the rest I can do like the closure problem etc I just do not get what he is trying to ask?
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Old   February 28, 2006, 16:14
Default Re: Dimensionless Parameter and Navier Stokes
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CFD_ACE
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Try relpacing terms with non-dimensionless quantities:

e.g.

Starting with,

d(rho*u)dt + ud(rho*u)dx + mu*d2udx2 = 0

Let U = u/Uo

T = tUo/L

X = x/L

MU = mu/MUo

RHO=rho/RHOo

where Uo,RHOo,MUo and L are all suitable reference scales (for example freestream values).

Making substitutions we have:

(Uo*Uo*RHOo/L)*d(RHO*U)dT + (Uo*Uo*RHOo/L)*Ud(RHO*U)dX + (MUo*Uo/L/L)*MU*d2UdX2 = 0

Dividing throught by the constant in front of the time derivative we obtain:

d(RHO*U)dT + Ud(RHO*U)dx + (MUo/Uo/L/RHOo)*MU*d2UdX2 = 0

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Old   February 28, 2006, 22:52
Default Re: Dimensionless Parameter and Navier Stokes
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Peter
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So I take it your Uni has no library with books in it?
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Old   March 1, 2006, 04:10
Default Re: Dimensionless Parameter and Navier Stokes
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John
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nope just comics :~)
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