balancing flow through perforated pipe

[KimBellingrath]

I have a problem to solve
we have a vertical inlet duct 51"L x 26"W that needs heat added to it using the following criteria:

injector pipe: .62dia x 51"L
psia = 57.8
temp = 375F
mass flow* = .17 lbs/sec through 11 pairs of horizontally opposed .125"dia holes.

How can I optimize the flow down the entire length of the pipe by varying the hole diameters?

*this has been calculated to add required heat load to flow

 

[davefitz]

the "dead end" of teh pipe has the lowest velocity head, so it has the highest static pressure and will use either the smallest hole or the farthest hole spacing. The source end of the pipe has the highest velocity head and teh lowest static pressure, so it needs the largest hole or the msallest spacing of holes.

There are som 1970's papers by Pignewski + Sha on this "manifold " problem- when I find my copies, I'll cite the source.

 

[davefitz]

here are some references that are useful for determining the flow unbalance in manifolds/ headers ( as I listed in a earlier thread):

Bajura, RA "A model for flow distr...: trans ASME 98-A-4,473-479 Oct 76

Acrivos, A Chem Eng Sci V10 p112 1959

Keffer, JF J Fluid Mech 15 p 481 & , 1963

Bajura, RA, Jones, EH J trans ASME V93 ser A no 1 pp 7-12 Jan 71

Ahn, H KSME Int J 12(1):87-95 feb 98

Hager,WH P I Mech Eng C-J Mech 201(6):439-448 1987

Greskovi, EJ , Obara, J T Ind Eng chem proc DD 7(4):593 1968

A science citation search of newer articles that reference these papers may provide more modern techniques, such as using FLUENT etc 3D CFD to simulate the flow in the headers.

As I recall, some of the older correlations were based on the assumption that the header internal design was formed using "set-thru" tube welds, which led to a higher internal header friction pressure drop then the now normal design of a set-in flush weld of tubes to header.

Another detail to note is that the headers are often drilled with smaller holes than the attached piping, to allow fit-up if a set-on stub weld is used ( ie ASME sect I fig "Z" weld).So, it isnot always corect to assume the header drilled holes equals the attached piping ID.

 

[timbones]

davefitz, your reasoning confuses me.

If the dead end of the pipe has the highest static head, then flow would be going in the reverse direction towards the source. Your reasoning only makes sense if you assume the total head remains constant as you move down the pipe, which is not the case since air is escaping out the holes along the way.

I would have reasoned that the dead end has both the lowest static head and the lowest dynamic head and would therefore require the largest and/or most closely spaced holes.

This is all acedemic of course as it doesn't really quantify any solution. You might be able to solve it with friction factors across the holes. Use orifice correlations for different hole sizes. Is a scale model flow study an option? Or maybe a CFD model?

 

[davefitz]

Timbones:
A thoughtful reply, since it is easy to get confused on this topic. There may be some confusion between "static pressure" and "stagnaton , or total" pressure.

Fluids must flow from higher stagnation pressure to lower stagnation pressure, but can flow from lower static pressure to higher static pressure . Consider the case of water flowing down a downcomer from a steam drum down to a waterwall inlet header at a 200 ft lower elevation. The fluid at the steam drum has a higher stagantion pressure, but lower static pressure, than the water in the waterwall inlet header; it flows from low static pressure to high static pressure.

Less obvious is the effect of the other terms in Bernouli's equation- the stagnation pressure is the sum of static P plus 1/2 rho v^2 + rho *g* H. The above steam drum case illustrates the effect of rho *g*H. The header issue under consideration illustrates how V^2 can also cause the static pressure to increase along the direction of flow.

An easier way of realizing this is to consider what some people call the "venturi effect" . If the header inlet has a gas flowing at 100 fps, then the velocity at the halfway point along the perforated header is about 50 fps, and at the dead end it is nearly 0 fps. The 100 fps velocity blowing perpendicular to the perforation's 1st hole could be considered to be causing a venturi effect, effectively lowering the pressure that the 1st hole sees .This venturi effect ( 1/2 rho V^2) basically doesn't exist at the dead end of the header, so the last hole has he advantage of the largest static pressure. There is of course frictionalloss along the length of the header, and predicting that loss is the primary unknown to be determined .

The same affect occurs in collecting headers ( or "outlet headers" ), but in reverse. The dead end of that header has the highest static pressure , so it's end recieves the least flow. To arrange inlet and outlet headers so that this effect cancels each other out is boiler design 101- a so called U-shaped configuration of a heat exchanger with headers.

 

[katmar]

The missing bit of information that would tell us whether davefitz's or timbones' analysis is correct is the pressure in the large duct. In my experience, when a perforated pipe is used to sparge one fluid into another the pressure inside the sparger is usually significantly higher than the pressure outside it. If this is the case then the pressure drop through the perforations can be high enough to make the pressure losses/gains down the sparger pipe negligible. On the other hand, if you had a very low pressure drop through the orifices then the pressure changes down the inside of the pipe would be critical.

Whenever I have to design such a device I do my damndest to make sure that the pressure drop/gain down the pipe is negligible. This makes it possible to use holes of constant size and spacing and still get nice even flows on the outside.

Kim did not specify what the fluid is here, but if it is steam or air then the diameter of the internal pipe is too small to neglect the pressure changes inside the pipe. A rough estimate is that the ID would have to be increased to 1.0" to make the pressure changes negligible. If you cannot increase the pipe size you have a tough analysis to perform. Depending on the accuracy required you could have a reasonable go at it with a spreadsheet using trial and error, or do it properly with CFD. But either way you would still be faced with a design that is optimized for a very specific condition. As soon as you vary the pressures, temperatures or flows you are immediately back to a non-ideal situation. A design where the pressure changes down the pipe are negligible is much more forgiving in this regard.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[timbones]

Yikes, how much we do forget over time!

Davefitz, I am not sure I agree with your statement that fluid must flow from higher to lower stagnation pressure but I do feel in serious jeopardy of actually relearning something!

I'm not saying your reasoning is wrong, but I'm going to challenge it by throwing in a few monkey wrenches.

I have a bit of a contradiction in my head. From your reasoning, the driving force pushing air out the holes is the static pressure difference across the hole, not the stagnation pressure (otherwise I would need bigger holes at the dead end of the pipe). And yet it is the stagnation pressure that determines which way the air flows in the pipe? Both seem reasonable on their own, but they don't work together.

In your steam downcomer example, I don't see how I could have a higher stagnation pressure in the drum. If i look at the top of a downcomer pipe verus the bottom of that pipe, the velocity pressure would be the same for both cases, but the static pressure would be much higher at the bottom due to the change in elevation. Therefore the stagnation pressure would have to be higher at the bottom.

An example more specific to the current problem, if I made the supply pipe small enough to push the velocities in the pipe up high enough I could actually push the static pressure lower than the static pressure in the duct and start sucking air into the pipe, much like an eductor. In this case I am moving from a lower stagnation pressure in the duct to a higher stagnation pressure in the pipe.

If I put static pressure taps (ie just regular pressure gauges) along the length of the pipe, provided the pipe is big enough that frictional losses don't overwhelm everything, should I see an increasing pressure from 57.8 psi to something higher near the dead end of the pipe?

Tim

 

[25362]

Visit thread378-90783.

 

[davefitz]

timbones:
an easier way of envisioning it is to recall the common elevated water towers many cities have. If you drill a 1/8" hole in the tank wall about 1" below the water level, the water will leak thru the hole very slowly. If you then drill another 1/8" hole at a level about 40 ft lower , you will have a lot of water flowing thru the same hole.

The first hole, at the top of the tank , has the highest stagnation pressure, but the lowest static pressure , so it flows the least amount of water thru its 1/8" hole. The 2nd hole, 40 ft lower elevation, has a lower stagnation pressure ( due to the friction loss from its flow down from above) but a higher static pressure.

as far as the bernouli eqn is concerned, it treats velocity head variations as equally as it treats gravity head variations.

IN any case , the papers I had cited provide theoretical proofs that the dead end of the header has the highest static pressure, and the practice among large mfrs' of large process equipment ( boilers, reactors) design their equipment using commonly accepted engineering principles that are simliar to what I have described. More to the point, they are competing with each other, and need to absolutley minimize the cost of the equipment they are trying to sell. This means minimize the size of these headers, while managing the effect this associated flow unbalance has on the life and performance of their heat exchangers.