Mass flow distribution along parallel pipe lines 6

[pegus]

Good day,

I was performing a CFD analysis to a pipe system when I came up with this doubt.

I have a piping configuration that starts with 2 pipe(inlets)(they have different diameter) and merge into one pipe(Outlet). The data that I know is the mass flow rate at the outlet and static pressure at the inlets.

As boundaries conditions, I am setting the known mass flow rate in the outlet, and I want to set total pressure in the inlets. To obtain the total pressure for each pipe, I need to calculate the velocity for each pipe that merges in the outlet pipe. To calculate the velocity for each pipe, I am assuming a mass flow rate proportional to the inner area of each pipe. Is this assumption correct? or is there any other way to know the exact distribution?

Regards!

P.P.

 

[zdas04]

There is actually no way to ever know the exact distribution.

I always find that I never reach closure if I rely on proportional pipe sizes since the underlying equation has ID^5 in it.

The way I solve the problem is adjust the flow rate in each pipe until I get an equal dP since I know the outlet pressure and know that the inlet pressure is equal. I have solved the Isothermal gas flow equation for upstream pressure so I can plug in a flow rate and the downstream pressure to get upstream pressure. I do it in a MathCad loop q1=1/4 of total and q2=total-q1. Then I step q1 up in small increments (with a new friction factor for each iteration and each pipe) until the two upstream pressures are the same. Generally takes 2-3 seconds in MathCad.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[MikeHalloran]

I do something vaguely similar to David's method, in Excel
(because I don't have Mathcad and could never remember how to drive it when I did)

For each pipe, I model the geometry,
compute a dp for an arbitrary flow rate (wag),
... which can be done with any external pipe pressure drop calculator you like,
then compute a Cv for each branch.

Then I set up a model of the summing junction,
setting one flowrate equal to the total minus the other,
compute the dp for each branch
and goal seek on the independent branch flow to get the dps equal.


( Using an external pressure drop calculator means that the pipes can have disparate geometry, length, size, roughness, complexity, whatever; as long as your arbitrary wag flowrate guess is not too far off, the method should produce results that are credible, and may even occasionally correlate with test results.

The method of balancing flows via Cv has worked for me, on systems comprising short pipes with many elbows, always running full of liquid, i.e. seawater systems within yachts.

David's world is different.

)








Mike Halloran
Pembroke Pines, FL, USA

 

[BigInch]

You may only distribute flow based on inside cross-sectional area when the diameters and lengths of all pipes are equal. Otherwise follow the above advice.

 

[LittleInch]

If the lengths are equal, I think a reasonable start point for differential flow of liquids is (d1/d2)^5 if the ends are joined together?

The difference in flow really is huge once d1/d2 goes beyond 0.9-0.85

Gas is more complex and the lengths need to be quite long compared to the diameter otherwise entry and exit functions start to get more complex. Also how the two pipes join each other can become important (tee, wye etc)

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[davefitz]

This is a common calculation for heat exchangers which can have as many as 1000 parallel circuits, each with its own distinctive length, roughness, number of bends, ID, heat transfer etc. In that extreme case, one calculates the "average tube" and the statistically "worst tube ", but the same method can be applied to this instant case of 2 dissimilar tubes in parallel, with no heat transfer .

For each of 2 tubes you calculate and plot the curve of DP ( pressure drop) vs W ( flowrate) . You then assume a total system DP ( and draw a horizontal line on the plotted graph) , and if the sum total of the 2 W's equals the known total W, then you have the exact solution for this case of only 2 tubes. If the flow adds up to more or less than the known total W, then you perturb the assumption of DP until the sum of the 2 W's adds up to the total known W.

The fundamental parts of this graphical method are that (a) tubes in parallel have the same overall pressure drop , from inlet header to outlet header, but also considering header flow unbalance effects (b) tubes or circuits in series have the same total flowrate (if there is no dynamic mass accumulation to contend with) and (c) one can characterize variations in a statistical manner, and typical industrial margins of safety ( between average and worst tube) is 2 * the mean deviation.

The variations to be characterized in the general case for an N-tubed heat exchanger include heat absorption rate , header flow unbalance, tube length, tube ID, tube roughness, number of bends, and enthalpy unbalance at inlet( if it is not single phase flow or if there is not a full mix header upstream of the circuit). The average and worst tubes are then calculated, and the entire circuit design is modified until one is satisfied that the "worst tube" will have an acceptable life. The results of this calculation can also be used as input to the Ledinegg static stability analysis.

"Nobody expects the Spanish Inquisition!"

 

[zdas04]

Davefitz,
I've never tried to wrap my head around that problem. All I can say is better you than me.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[bimr]

Regarding "To calculate the velocity for each pipe, I am assuming a mass flow rate proportional to the inner area of each pipe. Is this assumption correct? or is there any other way to know the exact distribution?"

Velocity = Q / A

Where:

Q = Flow​

A = Cross-Sectional Area​

Where the conduit diameters and conduit lengths are equal, the conduit elevations are the same, and the flows are uniform, in theory the flows in each branch pipe will be equal.

However, in practice, because of material and construction tolerances, the flows will not be equal. The flow will adjust automatically so that the head loss in each branch pipe will be the same. For many industrial operations, most people will not notice the difference.

If ones process can't tolerate the variance, then other measures such as flow control are necessary.