Proper Plenum Planning Problem 1

[yorkjim]

Sorry - I could not resist the alliterative impulse.

I have a project that will be moving 30,000 cfm of air and the process unit requires that the air be slowed to an approximate velocity of 300 fpm. Temperature is ambient.

If the ducting carring the air stream is 4 ft diameter, the velocity of the air will be 2381 fpm.

If the ducting carrying the air stream is 5 ft diameter, the velocity of the air will be 1500 fpm.

My question is can someone point me to a reference text to find the equations to calculate needed volume of space to slow the air down to the target velocity? And if there is a simple rule of thumb that will help too!

Many thanks and happy holidays!

 

[25362]

As you yourself have estimated, it is the cross-section A, of the duct that fixes the average linear velocity v, for a given flow rate Q. Disregarding friction heating effects

Q/v= A

For a circular duct A=pi.D²/4.

In this particular case, Q=30,000 cfm; v=300 fpm. Taking pi=3.14159, the diameter D is found to be:

{(30,000)(4)/[(300)(3.14159)]}^0.5 = 11.3 ft.

Season greetings also to you.

 

[yorkjim]

Thank you 25362.

As you have noted - the face area of the process unit that will be accepting this air flow is ~ 11 ft2.

I need a plenum between the ducting and the inlet that will lower the air velocity to that of the process unit. So my design problem is how do I size this plenum? Can the area of the ducting to the entry into the process unit increase from 4ft2 to 1l ft2 in a 2 ft length? or is some other length required? 3, 4 or maybe 5 ft? The air velocity must be slowed uniformly - so that the air enters the process unit at a very uniform 300 fpm. The target is no more an a 10% variation from 300 fpm at any single point of the 11 ft2 entry area.

 

[25362]

It's a bit confusing. When you say 11 ft² do you really mean a 11 ft diameter circular section, or 11 ft x 11 ft square duct ?

If I'm not wrong the Re at the slowest velocity of 300 fpm will exceed 10⁵ at NTP. For a smooth duct the velocity profile in turbulent flow would show approximately that the ratio of the velocity v, at any point, to the maximum velocity v_max, would depend on the position (radius r) of the point in the cross section of radius r_o as follows:

v/v_max = [(r_o-r)/r_o]^1/7

Thus at a point where, say, r = 0.75 r_o (i.e., nearing the wall) the velocity would be 82% of v_max, the deviation being larger than the maximum of 10% requested.

Some sort of flow smoothening fixtures may be necessary to fulfill the target velocity profile. Good luck.

 

[yorkjim]

Thank you again 25362,

The air will be carried via either a 4 ft or 5 ft round duct.

Then the air will pass a plenum - the design problem at hand - before it enters the process unit that is square. I did answer your post above a bit to hastily.

The square unit will be 10 ft by 10 ft - 100 ft2, so the velocity through the face area of the unit will be ~ 300 fpm.

I need to get from the round duct - to the square unit - with relatively uniform air flow across the entire 100 ft2 area.

 

[Easel]

To smooth the air flow will take both a gently expanding transition, preferably about 20 degree diverging angle. Second will be a pressure drop device just before the full size duct. Items such as a dense (low open area) perforated plate, mesh-type mist eliminator or a slotted wall would help greatly.

Good Luck

 

[25362]

I remember having seen an old brochure on KOCH's flow conditioner named LAD, for large angle diffuser, that claims a uniform velocity profile all over the cross section of the expansion as well as in the final duct. Why not try to contact them ?

 

[PeterAB]

A perforated plate in front of your fully expanded cross-section would be the fail safe method of obtaining a uniform flow distribution. A 50% open area perforated plate is commonly used, but for such a slow flow as here (300 fpm) I would be inclined to go to less open area (perhaps 25%) to obtain a decent pressure drop across the plate.

Peter.