*> Nick's heat exchanger can be installed in almost any orientation, but *

*> horizontal seems to be his desire. *

Horizontal is how all of my waste plumbing is arranged. I don't have any

place to put a vertical drop without adding a pump.

*> His heat exchanger will need to be cleaned out periodically of gunk,*

*> especially if toilets drain thru the same heat exchanger. *

I have never cleaned out the drains in this house.

*> The beauty of the GFX, is that it is metal, it can be stacked or daisy *

*> chained with pumps to extract even more heat in a smaller space. *

"stacked" implies a lot of vertical drop. Pumping requires energy.

--

---

Clarence A Dold - Hidden Valley (Lake County) CA USA 38.8,-122.5

*>>... physics clearly tells us that*

*>>*

*>>1. Metal conducts heat FAR more efficiently than plastics*

But the conductivity of the pipe wall is only a minor factor in fluid heat

transfer. In almost all situations, the conductivity of the film layer

*next* to the wall is the dominant factor. Just look at the R values for

two conventional water films versus that of 1/16" of Cu or 3/16" of plastic.

When conducting heat through a wall, the two films and wall material are in

series so it is appropriate to just sum the R values. (we'll neglect the

calculation accounting for the wall being cylindrical and just *assume* flat

plates)

Forced convection water films R values range from 0.02 m^2-K/W to as low as

0.0001 m^2-K/W. For a flow of about 2 m/s through a 3 cm pipe, we get a

Reynolds number of about 6.4e4. For water around 20C, that gives us a

Nusselt number of about 350, and a heat transfer coefficient of about 7000

W/m^2-K (or an R value of 1.44e-4). Cu has an R value of about 0.0025

m-K/W, or about 5.0e-6 m^2-K/W for a 2mm thick layer.

So the total R value for heat transfer across a water-water heat exchanger

tube might run about 1.44e-4 + 5.0e-6 + 1.44 e-4 = 2.93e-4 m^2-K/W

If the PEX has a conductivity of only 1/10th that of copper, and is three

times thicker, we would have about 1.44e-4 + 1.5e-4 + 1.44e-4 = 4.38e-4

m^2-K/W. Worse, true. But still about 67% that of the Cu.

And that is with rather optimal surface conditions and relatively high flow

(~2.1 m/s is a common 'rule of thumb' design flow rate, it balances between

poor film coefficients and excessive erosion).

*>>2. Water falls in a thin vertical film FAR faster than water that is*

*>>flowing horizontally in a pipe.*

But the flow through a flooded horizontal pipe means a much thicker film

layer. The novelty of the GFX design is that the water film formed by

having a small flow rate of say 2 gpm flowing over the inside surface of a

3" diameter pipe. This means the total thickness layer in the GFX flow is

about the same or *less* than the boundary layer thickness in conventional

pipe flow. So the average thickness between the bulk of the water and the

pipe wall is about 1/2 that of the flow layer. This reduces one of those

two film coefficients by an order of 2. This could be...

1.44e-4 + 1.0e-5 + 7.2e-5 = 2.26e-4 m^2-K/W (assuming twice the thickness

of Cu since it is double wall design).

With the high velocity of the water film on the drain side, overall heat

transfer could even be a bit better than this.

Flow in a horizontal pipe could be done in two ways. Flood the pipe

completely. But then you have issues of venting both sides of the drain

line, and the bore of the pipe would result in very low velocities and

correspondingly poor film coefficients. Or leave the pipe only partially

filed (like most current drain lines) and then you only have a tiny surface

area coming in contact with the drain water.

While not the *best* possible performance, like many designs it compromises

between getting better heat transfer coefficient, material costs, ease of

maintenance and installation.

*> The GFX does well with its small surface...*

*>>OK, GFX doesn't help with heat recovery for a bath, but great for hot*

*>>showers, dishwashing, clothes washing.*

*> ...60% is not "great," IMO.*

For a total surface area of just (4 in)*pi *60 in /144 = 5.24 ft^2, 60% is

pretty 'great'. How much surface area does your setup require?

*> Here's what physics tells us on page 3.4 of the 1993 ASHRAE HOF:*

*> 1. E = (Thi-Tho)/(Thi-Tci) when Ch = Cmin and*

*> = (Tco-Tci)/(Thi-Tci) when Ch = Cmin, where*

*> Ch = hot fluid capacity rate, Btu/h-F*

*> Cc = cold fluid capacity rate, Btu/h-F*

*> Cmin = smaller of the two rates*

*> Th = terminal temp of hot fluid (F). Subscript i indicates*

*> entering condition; o indicates leaving condition.*

*> Tc = terminal temp of cold fluid (F)...*

*> 2. Number of Exchanger Heat Transfer Units NTU = AUavg/Cmin.*

*> 3. Capacity rate ratio Z = Cmin/Cmax.*

*> Generally, the heat transfer effectiveness can be expressed for a given*

*> exchanger as a function of NTU and Z: E = f(NTU,Z,flow arrangement).*

*> The effectiveness is independent of the temps in the exchanger.*

*> For any exchanger with Z = 0 (where one fluid undergoes a phase change,*

*> eg in a condenser or evaporator), E = 1-e^(-NTU).*

*> For parallel flow exchangers, E = [1-e^(-NTU(1+Z))]/(1+Z).*

*> For counterflow exchangers, E = [1-e^(-NTU(1-Z))]/[(1-Z(e^(-NTU(1-Z))],*

*> = NTU/(NTU+1), when Z = 1.*

*> For instance, if we use 50 gallons per day of hot water in short bursts*

*> and Cmin = Cmax = 50x8.33/24h = 17.4 Btu/h-F and A = 78.5 ft^2 (a $0*

*> 300' piece of 1" polyethylene pipe with a 50 year guarantee) and U = 10*

*> Btu/h-F-ft^2 (with slow-moving greywater and crud outside and slow-moving*

*> fresh water inside), NTU = 78.5x10/17.4 = 45.2, and E = 0.98.*

We've been through this before Nick. You can't calculate Cmin or Cmax using

a 24 hour 'average' flow rate. When water is flowing, (say 16 lbm/minute or

960 lbm/hr), your Cmin=Cmax = 960 Btu/h-F.

So *while* the water is flowing, you might see NTUx.5*10/960 = 0.818. And

*that* would give you about E = 0.45.

By using an average flow rate that includes long periods when there is no

flow at all, you make it seem as though the heat exchanger is much longer

than just 300'. If you want to get your kind of performance with the

existing surface area and U, you would need to reduce the flow to 0.034 gpm

and keep it there all day/night. To get your kind of performance at 2 gpm,

you would need about 55 times longer tubing (~3 miles).

When you look at it that way, GFX's 0.60 performance in a 60" tall package

starts to look pretty good.

daestrom

*>> The GFX does well with its small surface...*

*>>*

*>>>OK, GFX doesn't help with heat recovery for a bath, but great for hot*

*>>>showers, dishwashing, clothes washing.*

*>>*

*>> ...60% is not "great," IMO.*

*>For a total surface area of just (4 in)*pi *60 in /144 = 5.24 ft^2, 60% is *

*>pretty 'great'.*

It might be 3 vs 4", but it's still poor overall performance.

*>How much surface area does your setup require?*

There's no requirement... 300' of 1" pipe is a convenient design choice.

*>> Here's what physics tells us on page 3.4 of the 1993 ASHRAE HOF:*

*>>*

*>> 1. E = (Thi-Tho)/(Thi-Tci) when Ch = Cmin and*

*>> = (Tco-Tci)/(Thi-Tci) when Cc = Cmin, where*

*>>*

*>> Ch = hot fluid capacity rate, Btu/h-F*

*>> Cc = cold fluid capacity rate, Btu/h-F*

*>> Cmin = smaller of the two rates*

*>> Th = terminal temp of hot fluid (F). Subscript i indicates*

*>> entering condition; o indicates leaving condition.*

*>> Tc = terminal temp of cold fluid (F)...*

*>>*

*>> 2. Number of Exchanger Heat Transfer Units NTU = AUavg/Cmin.*

*>>*

*>> 3. Capacity rate ratio Z = Cmin/Cmax.*

*>>*

*>> Generally, the heat transfer effectiveness can be expressed for a given*

*>> exchanger as a function of NTU and Z: E = f(NTU,Z,flow arrangement).*

*>> The effectiveness is independent of the temps in the exchanger.*

*>>*

*>> For any exchanger with Z = 0 (where one fluid undergoes a phase change,*

*>> eg in a condenser or evaporator), E = 1-e^(-NTU).*

*>>*

*>> For parallel flow exchangers, E = [1-e^(-NTU(1+Z))]/(1+Z).*

*>>*

*>> For counterflow exchangers, E = [1-e^(-NTU(1-Z))]/[(1-Z(e^(-NTU(1-Z))],*

*>> = NTU/(NTU+1), when Z = 1.*

*>>*

*>> For instance, if we use 50 gallons per day of hot water in short bursts*

*>> and Cmin = Cmax = 50x8.33/24h = 17.4 Btu/h-F and A = 78.5 ft^2 (a $0*

*>> 300' piece of 1" polyethylene pipe with a 50 year guarantee) and U = 10*

*>> Btu/h-F-ft^2 (with slow-moving greywater and crud outside and slow-moving*

*>> fresh water inside), NTU = 78.5x10/17.4 = 45.2, and E = 0.98.*

*>We've been through this before Nick. You can't calculate Cmin or Cmax using *

*>a 24 hour 'average' flow rate.*

Sure I can :-) You might enjoy calculating E if 50 gpd of hot water flows

in 1 second 1.25 gpm bursts, then 2 second bursts, and so on.

My shower is 1.25 gpm, so a 10 minute shower fills the 1" pipe.

*>So *while* the water is flowing, you might see NTUx.5*10/960 = 0.818.*

*>And *that* would give you about E = 0.45.*

How long between showers?

*>By using an average flow rate that includes long periods when there is no *

*>flow at all, you make it seem as though the heat exchanger is much longer *

*>than just 300'. If you want to get your kind of performance with the *

*>existing surface area and U, you would need to reduce the flow to 0.034 gpm *

*>and keep it there all day/night.*

I disagree, altho that might happen with continuous hot tub water exchange.

Nick

> nicksanspam@ece.villanova.edu wrote:>>>>>>>> Nick uses a LONG, SLOW moving body of water to extract heat. So in many>>> ways, it resembles a air conditioning condenser coil.>>>>> It also resembles a chair, if you wrap enough cotton gauze around both :-)>>>>>>> ... His heat exchanger will need to be cleaned out periodically of gunk,>>> especially if toilets drain thru the same heat exchanger.>>>>> Not a good idea. It wouldn't make a good wheelchair either.>>> No kidding. Somebody seems to need a definition of "greywater".>