Heat Transfer in a Drainage Pipe

[PEDARRIN2]

Trying to determine how quickly the water temperature in a partially full sanitary drainage pipe will drop from 180 F to 140 F.

The rationale is to determine where in the piping system I can transition from Cast Iron pipe to PVC when I have a discharge to the system from a boiler/water heater/dishwasher.

I am trying to come up with a "general" numerical model which can be used over different pipe sizes (2" to 4") and different pipe full fractions (25%, 50%, 66%).

Considerations/Issues

1. How to account for the partial flow in a pipe heat transfer equations. Do I use hydraulic radius for r? How do I account for heat transfer to the air space above the water line in the pipe? How do I account for the portion of the pipe wall that is not in contact with the water?
2. If I assume the flow is turbulent (which I am not sure I can since I have never tried with partially full pipe), how do I calculate the Reynold's number? Do I again use the hydraulic radius?

Any thoughts?

 

[BronYrAur]

I know this doesn't help quantify your answer, but I think the time will be much longer than the water will be in the piping. In other words, the water will probably hit the municipality sewer before it cools down.

You probably need to mix cold water in with the hot discharge, similar to a drain cooler on a boiler blowdown separator.

 

[IRstuff]

Those are part of the questions, but the big one is how does the heat get out of the pipe itself? Buried in dry soil, presumably?

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[PEDARRIN2]

BronYrAur: It depends on how much water is going down the drain, but I would hope the cast iron would "soak" up a lot of the heat before it goes out to the street. We do sometimes specify the drain cooler, but those require maintenance and "waste" water.

IRstuff: The pipe is under the slab for this example, but it could be above slab. In the former, heat transfer would be conductive to the soil. In the latter, it would be convective to the air.

 

[IRstuff]

OK, so ignoring the niceties of the internal heat transfer, there are existing correlations for both external conditions that can tell you how fast heat can be removed from the pipe.

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[MintJulep]

The equations are the easy part.

It will be the coeficients that are hard.

 

[PEDARRIN2]

IRstuff,

Agree that if the pipe were full, it would be a simple formula exercise.

But the pipe is not full which is why I am asking the questions I am. I guess I could make the assumption the pipe is full, calculate the length of pipe required to get to 140, than multiply by the actual percentage the pipe is full of water. That is pretty close to using the hydraulic radius.

 

[danschwind]

I haven't read it, but the title seems to be helpful:

https://www.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782005000100004&lang=en

Daniel
Rio de Janeiro - Brazil

 

[IRstuff]

You can still assume 50% full, or whatever, that just means the heat transfer is split between conductive and convective/radiative within the pipe.

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[PEDARRIN2]

Ok, as I looked at some examples of how to calculate this, I ran into an issue I do not know how to deal with.

I backed up the assumptions I was making and was using a full pipe that is buried and how heat transfer happens with that.

Looking online and even on some posts here, I saw examples using a horizontal isothermal cylinder of length L buried in a semi-infinite medium for a buried pipe losing heat. It used a shape factor and other easily determined quantities.

The problem I cannot seem to wrap my head around is the isothermal part and how that applies to a pipe with contents that are cooling. I broke it down into segments where the water temperature drops 1 F (close to isothermal?). That allows me to have a constant Q loss per segment. So as it cooled, the delta T got smaller, but my segments got larger, which I would expect. The problem (maybe it is not really a problem), is my total length of pipe is about 1100 meters. Though I have never put a thermometer on the end of a sanitary pipe connected to a kitchen, I do not see how it would take 2/3 mile of pipe to get from 212 to 140.

I am using 3" cast iron pipe with a OD of 0.085 m buried at 0.61 m below grade (neglecting slope).
The k for the pipe is 51.9 W/mK. This is not included in the calculations, since it is much larger than the k for the soil, I am thinking I can neglect the heat transfer across the pipe wall.
The k I am using for the backfill soil(stiff dark grey sandy gravelly clay) is 3.28 W/mK
Flow rate I am using is 35.2 gpm which is what a 3" pipe flows full by gravity at 1/8" per foot slope.
Since the pipe is buried under a building, I am using a surface temp of 70 F.

What, if anything, am I missing?

 

[LittleInch]

In a buried situation, you need to look at soil properties as well and not just as a transmission substance.

Given the much higher heat conduction rate of the iron pipe I would forget about any issues with heat transfer due to different %full. The pipe all the way around will be within a degree or two if the pipe is 25% full or 100% full.

The thing that changes is the mass flow.

Is this flow transient or continuous?

If occasional then the soil around the pipe won't have enough time to heat up and impact the temperature gradient and you can use the soil as simply a layer between the pipe and a vast heat sink. Probably use 500mm as the maximum soil impact.

However if the flow is continuous then the soil will, over time heat up itself and reduce heat outflow. This can be seen where initial temperature at the end of a pipe containing worm fluid start off as one temperature then over the space of 2-3 days or maybe a week, slowly climbs to a new higher temperature before reaching an equilibrium. These calcualtions are difficult to do in an equation based way as the temperature around the pipe falls away in a non uniform manner the further you get away from the pipe.

K factor for your soil looks quite high - I usually use something between 1 and 1.5

But water has a high heat capacity and depending on your velocity and flow rate I wouldn't be too surprised at 1100m from 212 to 140F ( initially you said 180F was the start temperature?)

If you do it on energy, your flow ( 35.2 gpm = 2 l/sec) water is 4200J/kg/C, your temp drop is 40C, so it looses 340,000J as the 2 l parcel goes from start to finish, which takes about 2,200 sec.

So average heat outflow is 150W. Sounds about right to me for an un-insulated 3" line.



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[PEDARRIN2]

Thanks for the feedback.

Flow would be an occasional dump load from a commercial dishwasher or small autoclave.

I pulled the soil k factor from a table I found and matched it as close as I could to what would be expected for the backfill material in the pipe trench.

Does "use the soil as simply a layer between the pipe and a vast heat sink. Probably use 500mm as the maximum soil impact." mean use 500 mm of soil as the layer of "insulation" around the pipe?

We typically use 55 F as a soil temperature in our area so would that be the "ambient" temperature in the conduction equation?

My calculation would use a range of temperatures that could enter the pipe, from near 212 F down to around 160 F.

 

[BronYrAur]

I know my comment really side-stepped the question and was of no help to quantify your answer. Just curious however if your length is short enough to allow you to switch materials. It would just seem to me (based on no calculations) that the distance would be "long." Long enough that you will need to stay with cast iron for all practical purposes unless you introduce cooling water.

 

[PEDARRIN2]

BronYrAur

You are likely right.

Our "rule of thumb" has always been provide 20 feet of cast iron pipe and then you could transition to PVC

As an engineer, I hate rules of thumb that I do not understand the basis behind them. This is looking to be one of those cases that the rule of thumb is going to be very wrong.

But I have to have a basis for going against "That's how we have always done it."

 

[LittleInch]

Yes the soil as an insulation layer for a short term event. Yes use 55F as the ambient temperature.

You will be surprised how far the temperature goes before it gets down to your lower limit, especially for a full pipe.

The key to lower flows only part filling the pipe is to use a lower mass flow rate.

But you really need to be dumping a lot of water to get this. Small volumes will use up a fair bit of energy just heating the DI up.

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

 

[BronYrAur]

I love "That's how we have always done it." I posted in a different thread the other day how I was asked to review a chilled water system has been pumping water through a non-operating chiller since the building opened in 1984. The original building engineer is still there. Unless both chillers are running, they blend return water from the non-operating unit with supply from the operating chiller. I am trying to convince them to change the operation, but it has "always been that way."