GFX vs home brew

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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.

I have never cleaned out the drains in this house.

"stacked" implies a lot of vertical drop. Pumping requires energy.
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Clarence A Dold - Hidden Valley (Lake County) CA USA 38.8,-122.5
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Stacked or daisy chained does NOT mean increased height. It merely means we hook up two shorter GFX lengths in series, pumping effluent from the outlet of the first one to the inlet of the second one. Overall efficiency rises. For instance we could get two S4-40s and set them on the wall parallet to each other. Inlet for the first one is from house sewer. Outlet of first is pumped (100W power used) to inlet of second, outlet of second is piped to city sewer/septic tank. One BIG advantage of this system in a septic tank is that you can put BOILING water down the kitchen drain, something you cannot do with a plain ole septic tank.
One issue with this configuration is water pressure drop GFX Tech will argue for manifolding, that is, connect potable water supply to coil inlet on BOTH GFX units and tie the coil outlets from BOTH units to a common pipe to hot water heater and cold side of showers, That produces a pressure drop of about 2-3 psi A full series connection with potable water to the coil inlet on the one connected to city sewer/septic tank, its output then connected to coil input of the GFX attached to the house sewer, and the coil outlet then connected to house hot water and shower cold side. This produces a pressure drop of 5-6 psi.
In my configuration, the inlet water pressure will be a constant 65psi So dropping to about 60psi is no big deal, and the water temp to the house rises. Effluent temp in both series and parallel configs drops by at least 20F, maybe much more
In 40 inches of vertical height, we get 80 inches of heat recovery.
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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).

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.

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?

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

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

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.

How long between showers?

I disagree, altho that might happen with continuous hot tub water exchange.
Nick
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But you also claim you don't need to breathe oxygen for the full 10 minute shower so that you can seal your shower stall.

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Guess again. If your setup was restricted to just 5 feet long, would its performance be anywhere near as good as the GFX??? And that's the point. To get performance on par with GFX, you have to resort to something several tens of feet long.
Heck, If I had someone build a GFX that was 100 feet tall, I'm sure it's performance would put your setup to shame. But who has space for 100' of 4" pipe (vertical, coiled or otherwise).
<snip ASHRAE calculations for steady-state problem>

Well, *you* can calculate using average flow, but the results are *NOT* meaningful. Just because you found a formula in a book, doesn't mean you can apply it to different situations, like intermittent and 'average' flow and still get meaningful results. Those ASHRAE formula are for calculating the steady-state performance of a heat-exchanger. Trying to apply them to 'burst' mode is a waste of time. The results do *not* mean anything. And they don't prove anything except that you don't know when to apply them.
But just to humor you, if the 'bursts' are 1.25 gpm, then the steady-state answer would be Cmin-Cmax=1.25*60*8.33 = 624.75 Btu/h-F. With an area of 78.4 ft^2 and U Btu/h-f-ft^2, NTUx.5*10/624.75 = 1.26 and EU.7%.
Notice how the answer depends on the flow rate *when water is flowing*?? Not the average amount of water that flows during some arbitrary time period.
The fact that the two different flow rates give such drasticly different answers should be a clue that you're missing something.

The formulae you are using from ASHRAE are for steady-state, *flowing* heat-exchangers. The NTU and effectiveness assume *steady-state* conditions (i.e. a constant flow rate). So the efficiency of your system when water flows and has reached steady-state is only 0.45. But since your showers are less than the time needed to reach steady-state, even that number is useless.

Your other post with a step-wise simulation is probably much closer for this sort of transient behavior, but it too has some flaws. You posted the outlet temperature for the greywater as 72F while the outlet for freshwater as 94F. This is with constant 55F inlet freshwater and 100F inlet greywater. The fact that your freshwater is picking up more energy [(94-55)*flowrate] than your greywater is losing [(100-72)*flowrate] is a clue that something is wrong in your calculation.
Your simulation printed out the numbers after 350 minute stagnation period, not when there is flowing water. You should print out the temperatures *during* the last shower, when there is actual flow. *That* is when there is energy flowing down the drain. Print out the numbers for fresh and grey water outlet temperatures *during* the last ten minute shower.
Calculate the energy removed from the greywater during those ten minutes and the energy being picked up by the fresh-water during those same ten minutes. Since the inlet temperatures are both assumed fixed (100F and 55F), if the energy picked up by fresh-water does not equal the energy given off by the greywater during those ten minutes of flow, then something is wrong with your calculations because energy must be conserved. (we're neglecting any ambient losses)
To find the true effectiveness for this non-steady-state operation, just calculate the amount of energy picked by the freshwater during the shower and divide by the total energy to heat that same water to the greywater inlet temperature.
*hint*, if the water outlet temperatures change a lot while the shower is running, you might reduce the time step to less than one minute intervals so as to get better resolution. This would make for better integration of the temperature versus time to get total energy. Too course a time step could lead to mismatch between greywater and freshwater energy calculations.
daestrom
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daestrom wrote:

water tubing and the pressure required to get a reasonable flow rate thru the 100ft stack.
As it is on a 60 inch GFX, manifolding is performed to limit pressure loss (coil height is about 27 inches each) with the base of each coil tied to the inlet water, and the top of each coil tied to the outlet.
The engineering drawings on gfxtech's web site clearing indicate an asymptotic behavior. Adding additional length brings lower and lower incremental benefit. Still with two S4-40s in series, pressure loss is about 2.5psi on a 2 gal/hr flow rate. and 80 inches of gfx recovery will get efficiency up another 5-10% over a 60 inch model and a 40inch height is easier, in many cases, to find a spot for.
daestrom is doing us a great service by pointing out the issues with the home brew system. I too do not believe that the home brew system proposed will work as well as a 60 inch GFX to recover waste heat from grey/black water and pump that heat to DHW and cold side showers.
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wrote:

I wasn't seriously recommending a 100' GFX. Just pointing out that 100' of any sort of piping takes considerably more space than a 5' GFX.

Yes, that is exactly how mine is constructed. The problem with piping the freshwater side in parallel is that the two coils form a sort of series-parallel flow heat exchanger. One heat exchanger cannot heat its outlet as much because it only receives already-cooled greywater from the other heat-exchanger. So when it's cooler freshwater outlet water mixes with the warmer water from the upper one, there is a reduction in overall efficiency. I can detect this when someone is in the shower by touch alone on the two coil outlets.
This is the same sort of thing that multiple-pass conventional heat-exchangers suffer from. Less than ideal, but a compromise of heat-transfer performance versus hydraulic performance (pressure drop).
I've toyed with the idea of restricting the flow through the lower coil to improve on this. Would increase the pressure drop some, but not as bad as the full series model. Some weekend project I may put a throttle valve in series with the lower coil and play around with different settings.

True, but you would need two 40inch heights, or a pumping arrangement. Since mine is installed in the main waste line for the entire house, pumping blackwater did not seem very attractive.

It could perform rather well. And if I know Nick at all from his postings over the years, it will cost less than my GFX did, even though I installed in myself. I'm just trying to keep Nick 'honest' by not letting him apply steady-state calculations to a transient system. But it does require more space to install, and may have some maintenance issues.
Hopefully when Nick is done building it, he'll post his performance numbers (good or bad). Direct measurements and experimentation are always better than theory.
daestrom "In theory, theory and practice are the same. In practice, they're different"
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GFX nick efficiency 6 7 price 5 3 convenience 9 1 wife likes 6 0 ---------------------- total score 26 11
wrote:

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Solar Flare wrote:

Particularly since GFX is non clogging and works with ALL sewer waters (grey and black).
Efficiency is NOT the only criteria here. If we recover 40% to 60% of the waste heat, we have made MAJOR strides in overall DHW production efficiency. Convenience, non-clogging, wife friendly are all MAJOR concerns.
Price is NOT the only factor either, but price and efficiency are Nick's main concerns.
Nick's will have to be connected ONLY to non-toilet drains. Nick's will have to be periodically cleaned of matter that goes down kitchen sinks and out the clothes washer drain.
None of these are concerns with GFX.
If we can afford one of these, either of these, these other factors, besides price and efficiency may well be MORE of a concern to the rest of us.
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Well the efficiency of heat exchange factor is not the only efficiency. A purchased and installed product at 5% efficiency is much more economical than a well designed, thought out, project that will be implemented sometime after getting a 'Round Tuit
Efficiency of installation ease. Efficiency of installation time. Efficiency of product parts and pieces aquisition Efficiency of marriage after the home space displacement. Efficiency of trial and error costs. Efficiency of maintenance. Efficiency of computer time arguing about imaginary issues. Efficiency of home resale after the newfangled frankenstein paraphenalia is seen.

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Le mieux est l'ennemi du bien. I'm better at thinking up things than getting round tuits.

I can relate to that, having spent about 40 hours in the last 2 weeks visiting various plumbing supply stores. It's been fun learning names of fittings, like "bullnose T" and "Dismukes crampon lifter."

Spouses care a lot more about what's on the lawn or in the living room than what's in the basement.

It might be nice to build more than one, with careful directions at http://BuildItSolar.com

And only empty the crud once a year, using a hose instead of a toothbrush.

Some issues are more important than others, eg daestrom's.

This leads me to make things easy to remove.

Nah. Efficiency should be 8 vs 7, a lower price should give me more vs fewer points, convenience is TBD, and wives may like saving more money, or having more to spend in other directions.
20 UPIPEx.5'U-value of 10' section of pipe (Btu/h-F) 30 CFRESH=1.25*8.33'thermal capacitance of 10' of fresh water (Btu/F) 40 VGREY*3.14159*(2/12)^2'volume of 10' of greywater (ft^3) 50 CGREY=VGREY*62.33-CFRESH'thermal capacitance of 10' of greywater (Btu/F) 60 FOR SHOWER = 1 TO 1000'simulate showers 70 FOR M=0 TO 359'simulate 10 min shower + 350 min rest 80 IF M>9 GOTO 200'rest vs shower 90 IF SHOWER <1000 GOTO 120 100 RHEAT=RHEAT+1.25*8.33*(100-TF(0))'reheat energy 105 GLOSS=GLOSS+1.25*8.33*(TG(9)-55)'greywater heat loss 110 PRINT 300+M;"'";M,TF(0),RHEAT,TG(9),GLOSS 120 TF(0)=TF(1)'move fresh water up 130 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top 140 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out) 150 TF(S)=TF(S+1)'move fresh water up 160 TG(S)=(TG(S-1)*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down 170 NEXT S 180 TF(9)U'move cold water in at the bottom 190 TG(9)=(TG(8)*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down 200 FOR S=0 TO 9'rest 210 HEATFLOW=(TG(S)-TF(S))*UPIPE/60'heatflow into fresh water (Btu) 220 TF(S)=TF(S)+HEATFLOW/CFRESH'new fresh temp (F) 230 TG(S)=TG(S)-HEATFLOW/CGREY'new grey temp (F) 240 NEXT S 250 NEXT M 260 NEXT SHOWER 280 SHOWERGY=1.25*10*8.33*(100-55) 290 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY
0 94.56091 56.6345 71.68895 173.7736 1 92.93514 130.1973 72.0242 351.0381 2 91.38136 219.9389 72.44145 532.6472 3 89.96538 324.4244 72.83433 718.3472 4 88.72086 441.8685 73.20448 907.9012 5 87.6472 570.492 73.55341 1101.089 6 86.72784 708.6885 73.88255 1297.703 7 85.94302 855.0568 74.19321 1497.553 8 85.27464 1008.385 74.4866 1700.457 9 84.70704 1167.623 74.76389 1906.248
1167.623 4685.625 .7508075
This is confusing. The greywater output seems to warm during the course of a shower, but I wouldn't expect that in a real system with 100' of 4" pipe.
Nick
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snipped-for-privacy@ece.villanova.edu wrote:

If you wanted to clean a GFX, its simple to remove and HOSE it down also, but there is no need to do so.
Yours WILL need interior cleaning

heat exchanger as the time required to recapture the heat exceeds the amount of time that the greywater remains in the heat exchanger. Need higher surface area (i.e. longer, or larger diameter tubes).
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snipped-for-privacy@ece.villanova.edu (in e1t523$ snipped-for-privacy@acadia.ece.villanova.edu) said:
<much snippage throughout>
|| Efficiency of installation ease. || Efficiency of installation time. || Efficiency of product parts and pieces aquisition | | I can relate to that, having spent about 40 hours in the last 2 | weeks visiting various plumbing supply stores. It's been fun | learning names | of fittings, like "bullnose T" and "Dismukes crampon lifter."
This may be some of the best and most encouraging news I've seen posted to alt.solar.thermal!
I've admired Nick's tenacity in dealing with the math of solar issues; but deplored his seeming inability to "get his wheels on the ground."
Nick, bless you! Get out even more. Take some of those fittings home with you and play with 'em! Build at least rough prototypes of your ideas and take pictures to share...
-- Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto
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So you are saying "Better nick's wife batting him around than ours"?
wrote:

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Mine objected to 300 55 gallon drums on the lawn. When I moved 200 into a greenhouse and the rest into the basement, that was OK. Go figure.

Fat plumbers in grimy jeans come in and say "Gimmie a 45 degree Thomson slidearm and a couple of 16" vertical Whittakers with the purple nibs."

Do what you do best. Lots of people can build things that don't leak. I'd like to know why the energy that flows into the gwhx is less than the energy that flows out during a shower, in that simulation.

My 4th HP digital camera stopped working. They seem fragile. Otherwise, you might see me stretching the curves out of 300' of 1" pipe with a tree and a pickup truck.
Nick
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Changing the heatflow from linear to a more accurate exponential (two caps equalizing voltage through a resistor) made little difference...
20 UPIPEx.5'U-value of 10' section of pipe (Btu/h-F) 30 CFRESH=1.25*8.33'thermal capacitance of 10' of fresh water (Btu/F) 40 VGREY*3.14159*(2/12)^2'volume of 10' of greywater (ft^3) 50 CGREY=VGREY*62.33-CFRESH'thermal capacitance of 10' of greywater (Btu/F) 60 CSERIESRESH*CGREY/(CFRESH+CGREY)'caps in series (Btu/F) 70 RC=CSERIES/UPIPE'combined time constant (hours) 80 EXPF=EXP(-1/60/RC)'exponential factor 100 FOR SHOWER = 1 TO 100'simulate showers 110 FOR M=0 TO 59'simulate 10 min shower + 50 min rest 120 IF M>9 GOTO 250'rest vs shower 130 IF SHOWER <100 GOTO 170 140 RHEAT=RHEAT+CFRESH*(100-TF(0))'reheat energy 150 GLOSS=GLOSS+CFRESH*(TG(9)-55)'greywater heat loss 160 PRINT 400+M;"'";M,TF(0),RHEAT,TG(9),GLOSS 170 TF(0)=TF(1)'move fresh water up 180 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top 190 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out) 200 TF(S)=TF(S+1)'move fresh water up 210 TG(S)=(TG(S-1)*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down 220 NEXT S 230 TF(9)U'move cold water in at the bottom 240 TG(9)=(TG(8)*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down 250 FOR S=0 TO 9'rest 260 TFINAL=(TF(S)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY) 270 TF(S)=TFINAL+(TF(S)-TFINAL)*EXPF'new fresh temp (F) 280 TG(S)=TFINAL+(TG(S)-TFINAL)*EXPF'new grey temp (F) 290 NEXT S 295 NEXT M 310 NEXT SHOWER 320 SHOWERGY*CFRESH*(100-55) 330 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY
0 94.38332 58.48365 71.9481 176.4721 1 92.75861 133.8847 72.28975 356.5016 2 91.17551 225.7697 72.71021 540.9092 3 89.71318 332.8812 73.10856 729.4646 4 88.41459 453.5143 73.48615 921.9516 5 87.28408 585.919 73.84426 1118.167 6 86.30738 728.4934 74.18405 1317.921 7 85.46612 879.8273 74.50663 1521.034 8 84.74309 1038.69 74.81306 1727.338 9 84.12328 1204.006 75.10433 1936.674
1204.006 4685.625 .7430426
Why 1204 Btu in and 1936 out?
Nick
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20 UPIPEx.5'U-value of 10' section of pipe (Btu/h-F) 30 CFRESH=1.25*8.33'thermal capacitance of 10' of fresh water (Btu/F) 40 VGREY*3.14159*(2/12)^2'volume of 10' of greywater (ft^3) 50 CGREY=VGREY*62.33-CFRESH'thermal capacitance of 10' of greywater (Btu/F) 60 CSERIESRESH*CGREY/(CFRESH+CGREY)'caps in series (Btu/F) 70 RC=CSERIES/UPIPE'combined time constant (hours) 80 EXPF=EXP(-1/60/RC)'exponential factor 90 FOR SHOWER = 1 TO 100'simulate showers 100 FOR M=0 TO 59'simulate 10 min shower + 50 min rest 110 IF M>9 GOTO 270'rest vs shower 120 IF SHOWER <100 GOTO 160 130 RHEAT=RHEAT+CFRESH*(100-TF(0))'reheat energy 140 GLOSS=GLOSS+CFRESH*(TG(9)-55)'greywater heat loss 150 PRINT 400+M;"'";M,TF(0),RHEAT,TG(9),GLOSS 160 TF(0)=TF(1)'move fresh water up 170 TGT=TG(0)'save original Tg(0) for later Tg(1) calc 180 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top 190 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out) 200 TF(S)=TF(S+1)'move fresh water up 210 TGP=TG(S)'save original Tg(s) for later Tg(s+1) calc 220 TG(S)=(TGT*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down 230 TGT=TGP'prepare for Tg(s+1) calc 240 NEXT S 250 TF(9)U'move cold water in at the bottom 260 TG(9)=(TGT*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down 270 FOR S=0 TO 9'rest 280 TFINAL=(TF(S)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY) 290 TF(S)=TFINAL+(TF(S)-TFINAL)*EXPF'new fresh temp (F) 300 TG(S)=TFINAL+(TG(S)-TFINAL)*EXPF'new grey temp (F) 310 NEXT S 320 NEXT M 330 NEXT SHOWER 340 SHOWERGY*CFRESH*(100-55)'if no GWHX (Btu) 350 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY
0 93.72946 65.29199 67.76752 132.9418 1 91.50189 153.7785 68.01705 268.4818 2 89.30461 265.1443 68.32899 407.2698 3 87.3519 396.8427 68.61366 549.0221 4 85.71924 545.5411 68.89086 693.6606 5 84.37411 708.2456 69.15711 841.0716 6 83.2604 882.5468 69.41382 991.1554 7 82.33891 1066.443 69.66134 1143.817 8 81.58043 1258.237 69.90021 1298.965 9 80.95963 *1456.495 70.13091 *1456.516
1456.495 4685.625 .6891568
Ah. Much better with buffering in lines 170, 210, and 230. The effectiveness dropped to 69%, but it still beats a GFX, esp. for baths, with no large vertical space requirement. And the pipe conductance might end up larger, with greywater vs liquid manure, and warm greywater bouyancy (not simulated) might also help.
Thanks, daestrom :-)
Nick
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... 5 vs 3 100' pipes only raised the effectiveness from 68 to 77%. A 200' version makes 82%... 200' of 4" drainpipe would wrap around the lower 3' of an 86" diam x 48" tall STSS heat storage tank.
15 DIM TF(20),TG(20) 20 UPIPEx.5'U-value of 10' section of pipe (Btu/h-F) 30 CFRESH=1.25*8.33'thermal capacitance of 10' of fresh water (Btu/F) 40 VGREY*3.14159*(2/12)^2'volume of 10' of greywater (ft^3) 50 CGREY=VGREY*62.33-CFRESH'thermal capacitance of 10' of greywater (Btu/F) 60 CSERIESRESH*CGREY/(CFRESH+CGREY)'caps in series (Btu/F) 70 RC=CSERIES/UPIPE'combined time constant (hours) 80 EXPF=EXP(-1/60/RC)'exponential factor 90 FOR SHOWER = 1 TO 100'simulate showers 100 FOR M=0 TO 59'simulate 10 min shower + 50 min rest 110 IF M>9 GOTO 270'rest vs shower 120 IF SHOWER <100 GOTO 160 130 RHEAT=RHEAT+CFRESH*(100-TF(0))'reheat energy 140 GLOSS=GLOSS+CFRESH*(TG(19)-55)'greywater heat loss 150 PRINT 400+M;"'";M,TF(0),RHEAT,TG(19),GLOSS 160 TF(0)=TF(1)'move fresh water up 170 TGT=TG(0)'save original Tg(0) for later Tg(1) calc 180 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top 190 FOR S=1 TO 18'pipe section (19<->fresh water in and greywater out) 200 TF(S)=TF(S+1)'move fresh water up 210 TGP=TG(S)'save original Tg(s) for later Tg(s+1) calc 220 TG(S)=(TGT*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down 230 TGT=TGP'prepare for Tg(s+1) calc 240 NEXT S 250 TF(19)U'move cold water in at the bottom 260 TG(19)=(TGT*CFRESH+TG(19)*(CGREY-CFRESH))/CGREY'move greywater down 270 FOR S=0 TO 19'rest 280 TFINAL=(TF(S)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY) 290 TF(S)=TFINAL+(TF(S)-TFINAL)*EXPF'new fresh temp (F) 300 TG(S)=TFINAL+(TG(S)-TFINAL)*EXPF'new grey temp (F) 310 NEXT S 320 NEXT M 330 NEXT SHOWER 340 SHOWERGY*CFRESH*(100-55)'if no GWHX (Btu) 350 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY
0 96.58958 35.51103 62.44146 77.4842 1 95.26726 84.79071 62.58688 156.4826 2 93.96446 147.6357 62.76867 237.3738 3 92.78384 222.7741 62.93455 319.9923 4 91.76805 308.4892 63.09611 404.293 5 90.9036 403.2055 63.25129 490.2096 6 90.16348 505.6282 63.40093 577.6842 7 89.52875 614.6602 63.54522 666.6613 8 88.98529 729.3508 63.68448 757.0885 9 88.52072 848.8789 63.81895 848.9157
848.8789 4685.625 .8188334
Nick
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But that's pretty big. How about this?
We collect all the shower water in a tank, with an infinite cold water tank next to it, then circulate the cold water through a coil in the shower tank until it all cools to the cold water temp... Then again, infinite tanks are hard to come by.
So maybe mix hot and cold fresh water to 90 F and circulate that through the coil until the shower tank drops from 100 to 95, then pump some of the 95 F fresh water back into the hot water tank and add enough cold fresh water to make the fresh mix 85, then circulate for a while, then pump some 90 F fresh water back into the hot water tank and add enough cold water to make the fresh mix 80, and so on. How can we do this automatically, on a continuous basis? We need a 20 gallon expansion tank too. Lots of pumping, but little energy, if the hot and cold supplies stay pressurized.
Nick
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