One large fireplace flue versus two smaller ones

Question

I am a mason contractor whom specializes in Rumford Fireplaces. I am helping design a fireplace that had a problem fitting in a single 18" x 18" flue pipe. So I installed two 13" x 13" pipes adjacent to each other.
They start at the smoke chamber tight together with a smooth as possible connecting partition. I'm cutting out the connecting flue walls some 12" down from the chimney top so as to form a plenum in order to avoid pressure variations from wind on one side more than the other.

The two flue pipes will be equal in height and length and have the same amount of masonry surrounding them to keep temperatures even. They will be centered in the smoke chamber and their total area is 256 $in^2$, which is nearly equal to 1/9th of the 48" x 48" fireplace opening as required by all codes.

My masonry teacher built a design like this long ago as have I, and I have had no problems. However, I am being told on certain blogs that this design will cause turbulence and double the drag resistance. I'm also told that I should have used a single 13" x 20" flue with a inside area of 192 $in^2$.

I believe that having my pipes connected at the top and bottom prevents turbulence from pressure and flow differences. And that having more cross sectional area from the combined flues should easily compensate for the added drag of the extra 12" of smooth tile partition.

I also believe that in a smoke chamber, a intermittent vortex exists below the damper blade and never rises into the flue area because the flow changes to laminar flow before entering the pipes and the parting divider.

Normally, I don't use double flues. However, I really can't see how two pipes connected at both ends and being larger in combined area will hurt flow via turbulence to a point of where you would see enough flow loss to generate eddy's in the flow.

If anyone can help verify if two flue pipes is sufficient or not in this design, I'd appreciate it.

To summarize my thoughts: I don't believe the air flow will be negatively affected from using two flue pipes instead of a single flue pipe because of the connection between the two pipes and having a larger overall combined area within the pipes.

Answer 1

I am attacking this problem from the point of view of the flow of the gas itself through the chimney. So what I am looking at is whether using two vents vs one increases speeds of the flow to the point where it is inherently turbulent as determined by the critical Reynolds number. To do this I make some assumptions and base calculations. The sources I used for most of this are:

1. How Chimneys Work : General info for my education!
2. Characterization of residential chimney conditions for flue gas flow measurements: Typical data.
3. Critical Reynolds number for Newtonian flow in rectangular ducts: Calculation of Reynolds number.
4. Impact of Chimney-top Appurtenances on Flue Gas Flow: Correlation for flow rate of flue gas.
5. Rumford Fireplaces: Information about Rumford fireplaces.

The first thing I did is calculate the critical Reynolds number for the flow on the two different ducts. I assume the ducts where $11.3\times 11.3$ inches for the square one and $17.2\times 11.2$ inches for the rectangular one. The Reynolds number for a rectangular duct is defined as: $$ Re=\frac{D_{h}\rho<v>}{\mu} $$ where $D_h$ is the hydraulic diameter, $\rho$ is density, $\mu$ is viscosity, and $<v>$ is the average velocity of the flue gas. The hydraulic diameters are 11.2 and 13.6 in for the square and rectangular vents, respectively. Using Ref. 3 above the critical Reynolds numbers for laminar/turbulent transition are 1688 and 1548 for square and rectangular ducts, respectively.

Now assuming that I have the flow rate that yields the critical Reynolds number for the rectangular duct, that the flow rate remains the same when moving to the two square ducts, and that density and viscosity of the flue gas do not vary between the two choices, the effect of moving to the two square vents results in obtaining a Reynolds number of 966, which is lower than the critical value for that piping system.

This calculation suggests that all things remaining equal, it is unlikely that the flow will become turbulent because of switching to two smaller vents. Instead, switching to the two square ducts should decrease the velocity of flow and therefore the Reynolds number. However, this does not take into account any other effects like the induced disturbances due to the wall in between the two ducts and at the end of the chimney. Although you seem to have taken precautions to deal with those.

Also, I did not perform calculations to determine whether the flow rate will actually stay the same. I noted that in some of the references above it is explained that the flow rate will depend on the area of the vents among other factors.