Correlation of loss coeffient
 

Hello friends,

I have a fluid mechanics question:

A pressure drop vs flow rate is measured for air flow through a porous medium. This gives a relation DP=1/2*density(air)*C(air)*v^2, where C(air) is the loss coefficient.

If the fluid is changed to water through the same porous medium, I am wondering if the above formulation for air can be used in some way for predicting the pressure drop (water) or the loss coefficient C(water).

Please help. Thanks!

Suping

Re: Correlation of loss coeffient
 

As far as the mach number of the flow is very low so that the fluid can be regarded as incompressible, the loss coefficient depends on the Reynolds number only, as simple dimensional analysis shows. This means that the loss coefficients obtained for water and for air are the same if Reynolds numbers are the equal.

Hope it helps

Re: Correlation of loss coeffient
 

Note that this formula is only valid for very thin porous media, for thicker media you need to use Darcy's Law which has a linear dependence on the velocity (instead of the quadratic). The type of formula you give is commnly used for perforated plates and screens (used for example to even out and calm the flow in wind-tunnels etc.) - if you need correlations for C let me know - I have a couple of good references which I recently digged up for modeling a screen in a CFD simulation of a jet-engine test-cell.

Re: Correlation of loss coeffient
 

Jonas,

Thanks for the helpful message. I am very interested in reading the references you mentioned.

Our model based on Darcy's law is developed for general porous media including thick media and thin perforated screen. According to Darcy's law, the pressure drop increases linearly with velocity in thick porous media. For thin perforated screens, however, we intent to use DP=1/2*density*C*v^2.

Since some experimental measurements are available for air flow, it will be helpful to know the correlation for loss coefficient in order for predicting other fluids through the same screens.

Thanks again.

Suping

Re: Correlation of loss coeffient
 

Exactly how thick is a thick porous medium? Is for instance a water-air heat exchanger featuring bundles of tubes with/without fins placed in the air stream thick enough to follow a linear dependence on velocity?

Re: Correlation of loss coeffient
 

The best reference I found was:

Cornell, W. G., "Losses in Flow Normal to Plane Screens", Transactions if the ASME, May 1958, pp 791-799 (since it is a bit old it can be a bit tought to get - let me know if you want me to fax it to you).

Another reference is:

Salmirs, S & Aljabari, S., "Prediction of the Pressure Loss Coefficient of Wind Tunnel Turbulence Reducing Sreens", AIAA Paper 92-0568, 30th Aerospace Sciences Meeting & Exhibit, January 1992, Reno

You can also find a quite long list of other references on:

http://vonkarman.stanford.edu/tsd/pb...el/rscreen.txt

and

http://vonkarman.stanford.edu/tsd/pb...el/screen.html

I hope that helps.

Re: Correlation of loss coeffient
 

Generally a laminar type loss has a linear relationship between velocity and dP, a turbulent loss has a quadratic one. Transitional flows obey a combination of the two of the form:

f = A/Re + B/Re^n

values for A, B and n can be found in the literature, Try Idelchik.

Good luck!

Re: Correlation of loss coeffient
 

Suping,

We apply the Darcy-Forschheimer model

-dp/dx = A*mu*u + B*rho*u^2

where A and B are nondimensional correlation coefficients, mu is the dynamic viscosity and rho is the density.

We have used this form for various types of porous media (e.g., ceramic foam, tube banks and honeycomb) at various Re ranges. The A and B are found based on experimental data (e.g., Zukauskas for tube banks) for the appropriate porous medium micro-structures, and are generally related to the micro-structure parameters (e.g., the tube arrangement, diameter and pitches in tube banks).

Having the correlation coefficients for the needed Re range, the model may be applied to any fluid.

Re: Correlation of loss coeffient
 

I am not quite sure for your case.

In general, for high Reynolds number flows where Re=rho*U*k^0.5/mu >=1, Darcy law is inadequate, where rho is density, k permeability, and mu viscosity. A remedy to this problem is to employ an inertia term, containing a loss coefficient, to the standard Darcy equation.

Re: Correlation of loss coeffient
 

Dear Friends,

From your responses, I really found valuable information. Many Thanks to all of you.

Best Wishes.

Suping