Transformation from open pipe flow to sealed pipe flow 2

aidanallen,

You have an interesting problem.

I am not sure I understand all your terminology, but we have been working on issues related to determining when a pipe runs full of water vs. when a pipe experiences separated flow (i.e., water filling only the lower portion of the pipe while steam or air travels along the upper portion of the pipe). If this is the same issue you are looking at, then the following information may be of interest to you.

The Froude number is often used as a criterion to determine if the liquid velocity is sufficient to allow the pipe to run full of water.

For fluid flow in pipes, the Froude number is easily calculated as,

Fr = u/sqrt(g*D)

where u is the fluid velocity, g is gravity, D is the pipe diameter, and the "sqrt" represents the square root.

If the liquid velocity is too low, then a separated flow geometry will be present with the liquid flowing underneath the gas. At high liquid velocities, the liquid will flow as a plug and push the gas in front of it to clear the line. As the liquid Froude number approaches or exceeds 0.5, the liquid velocity will be sufficient to obtain the plug flow geometry and push the gas in front of it; i.e., the pipe will run full of water.

For your sloped pipe, the fluid accelerates as it moves down the pipe. Eventually, the fluid may reach a velocity that yields a Froude number > 0.5. At that point, the pipe should be running full of water.

Let me know if this is of any use to you.

Tremolo.

Aidanallen:
Practically speaking, It is a matter of head, flow rate and friction loss.

Assume a system with a constant flow of water at the top introduced into a pipe whose bottom is 30Ft below the top.

With the elevation difference being 30FT and the flow in the pipe producing only 20Ft of head loss,then more water can flow by gravity through the pipe than is being put into the pipe. The water will try to flow faster than it would if it filled the pipe. As it flows faster the area it takes up is reduced. With the reduced area is cannot fill the pipe.

If the flow being put into the pipe produces a head loss of 40Ft (greater than the elevation difference) then the flow is being hindred by the friction loss. It cannot flow (by gravity) as fast as it is being put into the pipe. It must fill the pipe and be forced to flow faster that it could by gravity.

In order to insure that the pipe stays full the pipe should be sized so that the flow through it produces more head that the elevation difference. The pipe must be sized so that the pressure at any point in the pipe, due to the required flow, is more than the pressure drop of gravity flow (head to the bottom of the pipe).

If the height above the outlet is 30Ft and the required flow requires a head above 30FT the pipe will stay full. If the height above the outlet is 30FT and the required flow requies a head below 30FT the pipe will not be full.
If at any point in the pipe the required head falls below the head at gravity flow the pipe will not be full.

DLANDISSR:

Sorry but your post is very confusing. If I were to analyze pressure systems like you said then if I had a negative pressure in a pressure system, then the system would be in gravity flow at that point? This is not correct because lots of pressure systems have negative pressures. Pressure flow is a complicated thing, and a lot of people get confused with the flow in these systems. If there is a 30 foot head on a pipe, say Lake Michigan, then the pipe will flow in pressure flow. I say Lake Michigan because we want to assume constant head. If air were to enter the pipe from the discharge then this would be handled as a minor loss to the pressure flow system, not handled as a gravity flow system. Now if you were going to control the flow is a system designed for pressure that slopes downhill, then it would flow by gravity if you allowed the air to enter from the discharge and reference the point where the water is entering the system, but this would be an over designed system for these conditions. If the system were left to flow on its own with no control it would be pressure.

aidanallen, could you give us more information....

BobPE

Aidanallen and BobPE:
The question is not whether we have gravity or pressure flow? The question is, "Under what conditions does the flow fill or not fill the pipe?"

I agree in a closed system whether you have postive pressure or negative pressure the pipe, if it begins in a filled condition, will remain filled.(Of course, if the pressure is too low the fluid will vaporize and the pipe will not be filed with totally with fuild at that point.)

Again in an open system, a system in which the discharge is open to the atmosphere and the pipe is sloped downward from the inlet to the outlet.

As the flow moves down the pipe the total accumulated friction losses will increase and the total static head will decrease. If the static head decreases faster than the fricton losses increase the fluid will be able to flow faster than it would at full pipe conditions so the area of flow decreases and the pipe is no longer filled. Gravity is pulling it down faster than it is retarged by friction. Air moves in to fill the vacated area.

If the friction losses increase faster than the static head decreases then the pipe is flowing faster than gravity can pull it down consequently the pipe stays full. Friction retards the flow more than gravity can pull it down.

PROBLEM CAN BE SOLVED USING THE FLOW-3D CFD CODE WHICH WE HAVE IN-HOUSE. THE CODE CAN COMPUTE TRANSITIONS OF FREE SURFACE SUPERCRITICAL FLOWS TO SUBCRITICAL, POST HYDRAULIC JUMP FLOWS INCLUDING WALL FRICTION EFFECTS. THIS TYPE OF FLOW MAY CONTAIN SOME TRANSIENT INSTABILITIES, I.E,, THE HYDRAULIC JUMP MAY BE OSCILLATORY, SO ONLY A COMPUTATIONAL CODE WITH TRANSIENT, FREE SURFACE CAPABILITY IS ACCURATE.

The help you would need to complete is beyond the scope of this forum so I'm not quite sure how to help you.

DLANDISSR:

I guess where I am confused is in all the other posts that seem to be crossing gravity flow theory with pressure flow theory. A gravity pipe will flow full only when its capacity has been exceeded for the pipe. This takes into account friction and slope. The Froude number applies to this flow and if one wants, can figure it out, but it has nothing to do with pressure flow, only whether flow is sub or supercritical. Once a pipes capacity has been exceeded it surchages and that pipe will go into pressure flow as you discussed in your post and the Froude number as mentioned in other posts will not predict this.

I guess the short answer to the original post would be to place a control prior to the cyclone, like maybe the head in the cyclone or a wier box entrance into the cyclone, to ensure pressure flow prior to the cyclone.

It does get so confusing in here sometimes!!!!

BobPE

Some further comments on your supercritical-subcritical piping transition problem. While the FLOW-3D CFD code can easily handle this problem and investigate effects of piping roughness, piping angles, piping lengths and diameters, flow rates, etc., to locate the hydraulic jump transition height, some further cautions should be mentioned. If the input to the inclined piping is an open tank, then tank depth should exceed about 7X the piping diameter to avoid vortex string formation that can draw air into the inclined piping. If this occurs, then an oscillatory hydraulic jump will occur and the exit flow rate will vary considerably. In certain cases, the hydraulic jump can move up to the inlet to temporarily shut off the vortex inducing a full flow condition then migrate downstream as the vortex restarts to create an open channel flow to create ta repeating, oscillatory cycle and highly variable flow rate. Many different phenomena can occur depending upon the parameters of the problem (including the scenario just mentioned) so that only computer solutions are viable. Additionally,if piping friction is high in inclined piping, then an initial supercritical, open channel flow (presumably asymptotically approaching normal depth if the piping is long enough)can also transition to a full flow through a weak hydraulic jump due to wall friction effects. Because so many different steady and unsteady nonlinear fluid motions are possible depending upon your parameter set and feed/exit flow conditions(not specified completely),a simple algebraic method is not generally possible to use for jump position. A CFD code with free surface capability is the only way to resolve your problem and FLOW-3D is the best code available for this problem. You may also have to worry about partial vacuum regions as flow transitions from full to open channel (or vice versa)in piping as these regions and their buoyant motion can also affect the flow patterns.
tiwanaku