Posted by *nicksanspam* on April 15, 2006, 5:02 am

*>While I agree that 'batch' flows that do not fully purge your apparatus will *

*>give you some improvements, we haven't seenn any of your 'numbers' for that. *

Here are some numbers for that. If 100' of 3 1" pipes (polyethylene, with

a 0.07" wall thickness) has 78.5 ft^2 of surface with U = 10 Btu/h-F-ft^2,

10' has 78.5 Btu/h-F...

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>10 GOTO 170'rest vs shower

90 TF(0)=TF(1)'move fresh water up from below

100 TG(0)=(100*CFRESH+TG(0)*CGREY)/(CFRESH+CGREY)'move greywater in at the top

110 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out)

120 TF(S)=TF(S+1)'move fresh water up

130 TG(S)=(TG(S-1)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY)'move greywater down

140 NEXT S

150 TF(9)U'move cold water in at the bottom

160 TG(9)=(TG(8)*CFRESH+TG(9)*CGREY)/(CFRESH+CGREY)'move greywater down

170 FOR S=0 TO 9'rest

180 HEATFLOW=(TG(S)-TF(S))*UPIPE/60'heatflow into fresh water (Btu)

190 TF(S)=TF(S)+HEATFLOW/CFRESH'new fresh temp (F)

200 TG(S)=TG(S)-HEATFLOW/CGREY'new grey temp (F)

210 NEXT S

220 NEXT M

230 NEXT SHOWER

240 FOR S=0 TO 9'results

250 PRINT S,TF(S),TG(S)

260 NEXT S

270 E=(TF(0)-55)/(100-55)'effectiveness

280 PRINT E

pipe fresh water greywater

section temp (F) temp (F)

0 93.32178 93.3218

1 90.556 90.55602

2 87.60851 87.60853

3 84.60492 84.60494

4 81.62819 81.62821

5 78.71178 78.71181

6 75.86447 75.8645

7 73.08838 73.0884

8 70.3852 70.38522

9 67.75679 67.75681

effectiveness

.8515951

The fresh and greywater temps are very close, about 6 hours after

a shower, since the pipe time constant is much shorter (less than

8 minutes.) These results wouldn't change much with only a half-hour

between showers. The effectiveness would be higher for shorter bursts.

Maybe it's worth adding 2 more $0 100' pieces of 1" pipe (altho that

would be a tight squeeze), or a handheld showerhead that only runs

when a button is pushed. Who sells them?

Nick

Posted by *nicksanspam* on April 15, 2006, 6:14 am

*>>While I agree that 'batch' flows that do not fully purge your apparatus will *

*>>give you some improvements, we haven't seenn any of your 'numbers' for that. *

*>Here are some numbers for that...*

Oops. Fixing lines 100, 130, and 160 improves the effectiveness to 88%.

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>10 GOTO 170'rest vs shower

90 TF(0)=TF(1)'move fresh water up

100 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top

110 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out)

120 TF(S)=TF(S+1)'move fresh water up

130 TG(S)=(TG(S-1)*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down

140 NEXT S

150 TF(9)U'move cold water in at the bottom

160 TG(9)=(TG(8)*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down

170 FOR S=0 TO 9'rest

180 HEATFLOW=(TG(S)-TF(S))*UPIPE/60'heatflow into fresh water (Btu)

190 TF(S)=TF(S)+HEATFLOW/CFRESH'new fresh temp (F)

200 TG(S)=TG(S)-HEATFLOW/CGREY'new grey temp (F)

210 NEXT S

220 NEXT M

230 NEXT SHOWER

240 FOR S=3 TO 9'results

250 PRINT 300+S;"'";S;TF(S),TG(S)

260 NEXT S

270 E=(TF(0)-55)/(100-55)

280 PRINT 410;"'";E

pipe fresh water greywater

section temp (F) temp (F)

0 94.53323 94.53326

1 92.54844 92.54847

2 90.32916 90.32919

3 87.93309 87.93311

4 85.42671 85.42674

5 82.85161 82.85163

6 80.22588 80.2259

7 77.55527 77.55529

8 74.8424 74.84241

9 72.08957 72.0896

effectiveness

.8785163

Nick

Posted by *daestrom* on April 15, 2006, 3:55 pm

*>>>While I agree that 'batch' flows that do not fully purge your apparatus *

*>>>will*

*>>>give you some improvements, we haven't seenn any of your 'numbers' for *

*>>>that.*

*>>*

*>>Here are some numbers for that...*

*> Oops. Fixing lines 100, 130, and 160 improves the effectiveness to 88%.*

*> 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>10 GOTO 170'rest vs shower*

*> 90 TF(0)=TF(1)'move fresh water up*

*> 100 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the *

*> top*

*> 110 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out)*

*> 120 TF(S)=TF(S+1)'move fresh water up*

*> 130 TG(S)=(TG(S-1)*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down*

*> 140 NEXT S*

*> 150 TF(9)U'move cold water in at the bottom*

*> 160 TG(9)=(TG(8)*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down*

*> 170 FOR S=0 TO 9'rest*

*> 180 HEATFLOW=(TG(S)-TF(S))*UPIPE/60'heatflow into fresh water (Btu)*

*> 190 TF(S)=TF(S)+HEATFLOW/CFRESH'new fresh temp (F)*

*> 200 TG(S)=TG(S)-HEATFLOW/CGREY'new grey temp (F)*

*> 210 NEXT S*

*> 220 NEXT M*

*> 230 NEXT SHOWER*

*> 240 FOR S=3 TO 9'results*

*> 250 PRINT 300+S;"'";S;TF(S),TG(S)*

*> 260 NEXT S*

*> 270 E=(TF(0)-55)/(100-55)*

*> 280 PRINT 410;"'";E*

Not bad, apparantly you've chosen a flow rate and section length so the time

step corresponds to exactly one section length.

Because the greywater drain cross-section is so much larger than the

freshwater, your Cmin/Cmax ratio ends up being about 0.24 (IIRC a 4-inch

pipe with three 1-inch pipes inside). So a high efficiency of 87% doesn't

really tell us how much energy we're saving. While your efficiency is 87%,

it looks like you're still putting (72-55)*1.25*8.337 BTU/minute down the

drain. Out of a total of 468.6 BTU/minute needed to heat 1.25 gpm from 55

to 100, that's nearly 38% of the heating.. Print out the data *during* the

last shower, not 350 minutes later. I'd like to see what the greywater

outlet temperature is while it's flowing. I think it's going to be a lot

cooler than 72, but not sure. Better yet, print out the freshwater and

greywater outlet temperatures *during* the ten time steps of the last

shower.

After all, it is the temperatures out *during* flow that matter. The

temperatures at the end of the stagnation period only tell us the initial

startup point for the next shower. How quickly they change *during* the

shower, and in what direction would be more telling.

After all, if the freshwater outlet during the shower really is at 94F, and

the greywater really leaves at 72F, then you don't have conservation of

energy (freshwater side picks up (94-55)*1.25*8.33 = 406 btu/min, while the

greywater side gives off (100-72)*1.25*8.33)1 btu/min). That's a clue

that something is wrong with these results.

daestrom

Posted by *nicksanspam* on April 15, 2006, 7:27 pm

*>I'd like to see what the greywater outlet temperature is while it's flowing.*

How about the fresh water outlet temp? Line 100 below accumulates

the heat energy that needs to be added during the last shower...

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 required

110 PRINT 300+M;"'";M,TF(0),RHEAT

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)'total heat energy with no gwhx

290 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY

time fresh cum reheat

(min) temp (F) (Btu)

0 94.56091 56.6345

1 92.93514 130.1973

2 91.38136 219.9389

3 89.96538 324.4244

4 88.72086 441.8685

5 87.6472 570.492

6 86.72784 708.6885

7 85.94302 855.0568

8 85.27464 1008.385

9 84.70704 1167.623

cum reheat shower effectiveness

(Btu) heat (Btu) (fraction)

1167.623 4685.625 .7508075

Nick

Posted by *daestrom* on April 18, 2006, 8:28 pm

*>>I'd like to see what the greywater outlet temperature is while it's *

*>>flowing.*

*> How about the fresh water outlet temp? Line 100 below accumulates*

*> the heat energy that needs to be added during the last shower...*

*> 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 required*

*> 110 PRINT 300+M;"'";M,TF(0),RHEAT*

*> 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)'total heat energy with no gwhx*

*> 290 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY*

*> time fresh cum reheat*

*> (min) temp (F) (Btu)*

*> 0 94.56091 56.6345*

*> 1 92.93514 130.1973*

*> 2 91.38136 219.9389*

*> 3 89.96538 324.4244*

*> 4 88.72086 441.8685*

*> 5 87.6472 570.492*

*> 6 86.72784 708.6885*

*> 7 85.94302 855.0568*

*> 8 85.27464 1008.385*

*> 9 84.70704 1167.623*

*> cum reheat shower effectiveness*

*> (Btu) heat (Btu) (fraction)*

*> 1167.623 4685.625 .7508075*

More like I expect. Your system's outlet temperature drops from the high of

94F the longer you run the shower. The fact that it's a 'batch' process

allows you to get better performance than the steady-state parameters would

allow.

But show the greywater too. As I said before, if the greywater is giving

off less energy than the freshwater is picking up, then something's broke.

I notice you chose to show the more optimistic of the two numbers. I'll bet

the greywater shows more energy going down the drain than physics would

allow if these numbers were accurate.

So then it's just a matter of adjusting gwhx versus shower time to keep

performance high. Too long a shower, or too short a gwhx and performance

drops.

How would two showers spaced fairly close together look? Looks like this

would support four, 10-minute showers a day, spaced 6 hours apart right now.

daestrom

>While I agree that 'batch' flows that do not fully purge your apparatus will>give you some improvements, we haven't seenn any of your 'numbers' for that.