Dimensionless Parameter and Navier Stokes
 

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?

Re: Dimensionless Parameter and Navier Stokes
 

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

Re: Dimensionless Parameter and Navier Stokes
 

So I take it your Uni has no library with books in it?

Re: Dimensionless Parameter and Navier Stokes
 

nope just comics :~)