Hi,

I am simulation flow across a blunt boday. Based on force balance in a closed system, the inlet-outlet pressure drop and the total drag force (sum of friction and form drag) should have the relationship of: DeltaP*A_inlet=Drag force

Am I right? I found my simulation results do not agree with this. Can anyone help me? Thank you very much.

Li

Respected Sir,

I have a querry..If I have interfacial drag force for a single bubble as "fd" then for a swarm of bubble the total drag will be "n*fd". Now what is the total frictional pressure drop for the drag of n number of bubbles? Is it "n*fd/a" where "a" is the interfacial area between bubble and bulk liquid. Please clarify this. Thanking You Sincerely Subrata

"....then for a swarm of bubble the total drag will be "n*fd"...."

Not really. n*fd Will only give you the Total drag force per unit volume of the domain. Where,

n = (6 * disp. ph. vol. frac.) / (pi() * d^3)

For the swarm effect, you might want to check out papers like:

Behzadi, A., R. I. Issa and H. Rusche, "Modelling of dispersed bubble and droplet flow at high phase fractions" Chemical Engineering Science 59, 759-770 (2004).

Respected Sir Thanks for your valuable clarification. With reference to Joshi, (2001), the total drag force or form drag in interface of a bubble in a bulk liquid is "N*fd". Here "fd" is the form drag for a single bubble. For swarm of bubble it is N*fd. If it is form drag at interface, Can I consider the pressure drop due to form drag is N*fd/Ab where Ab is the projected surface area of single bubble? Please clarify.

If pressure drop due to skin (or wall) drag is negligible, then your equation is correct.

We know that,

Total drag = form drag + Skin (or wall) drag

So it would seem logical to estimate the form drag contribution from the total drag and then divide it by the projected area to calculate the pressure drop due to form drag.

Respected Sir, Thanks a lot for your another valuable clarification. It will be helpfull for my research. But I could not get any equation or information regarding the drag coefficient in bubble flow regime. It is available for annular slug flow. If you please help me for the same I will be highly obliged. waiting for your early reply Thanking You Subrata Majumder

There are several expressions for the drag coefficient in the bubbly flow regime. Use keywords like "drag coefficient" AND "bubbly flow" in Databases like Compendex (www.engineeringvillage.org)