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slaxmi September 10, 2007 05:48

Actual drag force from dimensionless equations
 
If the equations of motion are solved in dimensionless form in CFX, how to calculate the actual drag force?

The equations of motion in dimensional form are converted into dimensionless form. Since there is no provision to solve in dimensionles form in CFX, the dimensionless variables are assigned some units (viz, SI system) in CFX. After the solver is run, how is the drag force obtained in Post related to actual drag force?

Stumpy September 10, 2007 14:23

Re: Actual drag force from dimensionless equations
 
I don't think the equations are solved in dimensionless form. The solver has units that it solves in - the "Solution Units".

Glenn Horrocks September 10, 2007 18:36

Re: Actual drag force from dimensionless equations
 
Hi,

Stumpy is correct. The solver uses the dimensional form. You can define a set of non-dimensional numbers which are consistent and solve for them, I think this is discussed in the manual.

Glenn Horrocks

slaxmi September 11, 2007 00:55

Re: Actual drag force from dimensionless equations
 
Hi,

Thanks for the response. Yes, the dimensionless form of the equations are solved after assigning some units (cgs or SI). But our problem is how to relate the drag force obtained in Post to the actual drag force if the equations were in dimensional from?

Terje September 11, 2007 07:15

Re: Actual drag force from dimensionless equations
 
Hi,

If I understand you correctly you want to know how the drag force is scaled in a dimensionless calculation. The unit of drag force is the same as pressure and should therefor scale accordingly. The answer to your question is thus completely dependent on how you have scaled your equations to get them on a dimensionless form.

A common way to scale the Navier Stokes equations is to introduce a characteristic length and velocity and get the Reynolds number as a characteristic dimensionless number. In this case a characteristic pressure which reduces the NS to

Du/Dt = Re^-1 nabla^2 u - nabla p

is

p* = rho* U*^2

where rho* is the characteristic density and U* the characteristic velocity of your system. Meaning that in this case you would have to scale your dimensionless pressure / drag force by rho* U*^2 in order to get it back on dimensionful form.

- Terje

slaxmi September 12, 2007 23:53

Re: Actual drag force from dimensionless equations
 
Hi Terje,

Thanks for the response. But the dimensions of force and pressure differ by area.


Terje September 13, 2007 03:29

Re: Actual drag force from dimensionless equations
 
Hi,

if you have the total drag force and not per area just use the method described and scale by the characteristic length squared.

Terje

slaxmi September 13, 2007 05:19

Re: Actual drag force from dimensionless equations
 
Hi,

If we solve the dimenionless form of the equations, will simple scaling give the actual force? We solve the dimensionless equations after assigning some units in CFX. Since the values of velocity etc, now, are different from actual velocity, the physics of the problem will change completely, viz., separation of boundary layer, size of wake region will be different. Then, will simple scaling in Post represent actual conditions?

Terje September 13, 2007 07:18

Re: Actual drag force from dimensionless equations
 
Hi slaxmi,

If, as you say, the physics of the problem changes completely when you scale it, of course simple scaling in post will not give any useful information. And the simulation done with the dimensionless quantities will not be of much use.

However, the idea of scaling is that the physics of the problem is the same on different size scales and can be described with the same equations. And this is the trick, if the equations describing the physics of the problem are the same, and all your dimensionless quantities are the same on the different size scales then you can also scale your solution.

If the probelem scales or not in your case is probably best decided by you.

- Terje

slaxmi September 13, 2007 23:42

Re: Actual drag force from dimensionless equations
 
Hi Terje,

Thanks for your inputs.

Glenn Horrocks September 14, 2007 19:20

Re: Actual drag force from dimensionless equations
 
That will obviously depend on the non-dimensional scheme you have set up.

In general I see nothing to be gained by using non-dimensional solver variables in a dimensional solver like CFX. If you are comparing to published data in non-dimensional form I recommend you solve using dimensional variables and convert the results to non-dimensional numbers after extracting your results.

Glenn Horrocks


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