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Theoretical and experimental studies of pressurized and non-pressurized solar water heating systems of thermosyphonic type
Renewable Ener~cy VoL 2. No, 4/5, pp. 371-384. 1992 Printed in Great Britain.
0960 1481/92 $5.00+.D0 Pergamon Press Ltd
THEORETICAL A N D EXPERIMENTAL STUDIES OF PRESSURIZED A N D NON-PRESSURIZED SOLAR WATER HEATING SYSTEMS OF THERMOSYPHONIC TYPE R. S. MISHRA*
Mechanical Engineering Department, Haryana Agricultural University, Hisar, India 125004 (Received 13 May 1991 ; accepted 16 January 1992) Abstract--A method for calculating the thermosyphonic flow rate in the single and multipass systems of pressurized and non-pressurized type is presented. The experiments were conducted over several days on various systems fabricated and tested at T.1.E.T. Patiala, India. Close agreement between the theoretical calculations and experimental results shows verification of the present method.
INTRODUCTION
THERMOSYPHONIC FLOW RATE IN NONPRESSURIZED SOLAR WATER HEATING SYSTEMS
Various theoretical and experimental studies performed on the thermosyphonic solar water heating system are readily available in the literature [1]-[30]. The studies of Metrol [3] and others attempted to show very detailed equations for each of the components. This analysis, if employed in practice, required the use of large computers and was expensive and time consuming. The studies of Close [2], Ong [12], Sodha and Tiwari [13] and Bansal [14] based on the simple assumption that the whole system is at some average temperature, lack a comparison with detailed experimental investigation. Also, the basis for estimating thermosyphonic flow rate has not been established for pressurized solar water heating systems. The study presented in this paper covers both these points with the derivation of thermosyphonic flow rate from basic principles. The eight thermosyphonic solar water heating systems were fabricated in the institute for hot water requirement of the T.I.E.T. guest house. Measurements were taken for several days in October. The numerical calculations for thermosyphonic flow rate, water temperature in the storage with the given hot water demand pattern and thermal efficiency were carried out by computer at the Indian Institute of Technology, Delhi, India. The experimental measurements are in close agreement with the calculated values.
A density difference created by the temperature difference causes the fluid being heated to flow without any pump. This effect of natural flow due to the density difference is usually known as thermosyphonic effect. The total pressure responsible for the thermosyphonic flow is APt = .q sin 0
(pf~ - p(y)) dy + y h , p , ~ - ( h t +h2)gp,.~,,
(l)
where L is the length of solar energy collector. The energy balance in the whole system can be expressed as
Q. = rhc(t)Cw(Tfo(t)- T~(t)) = F'A~[(zc~)~l~(t)-- Uc~(Tm(t) - T.(t))]
(2)
and Qu = MwCw - - - d ~
+ g r A y ( T i n ( t ) - T,(t)) +f2rh~(t)Cw(Tm(t)--T~M)).
(3)
Assuming the density variation to be linear it can be expressed as (p~-p(y))dy
*Present address: Faculty House, H.A.U. Hisar-125004 Hisar, Haryana, India.
and
371
L = (pn(t)-Pt.o(t))~
(4)
372
R.S. MISHRA
Vent ------b.~ Float valve
Hot water out Shut off valve
Check valve Cold water in
'-'-" Drain Fig. 1(a). Simple non-pressurized thermosyphonic solar water-heating system components.
Tank
Hot water out
Cold
C
w a t e r out
Fig. 1(b). Simple, pressurized thermosyphonic solar water-heating system I.
Thermosyphonic solar water heating systems
373
Ti Pe Ti iPi ~ i l ~
I
T
i
¢1 2000 mm
hi
1
-'= W
I-
1000m m
--1
Fig. l(c). Modified single-pass non-pressurized thermosyphonic solar water-heating system.
Tank
~oO
~o,~ •
I
Fig. 1(d). Principle of thermosyphonic solar water-heating system.
Ti Pe
Ti
2000ram = 120mm 1000m m
hi
1
~ Ti
)L _~)0 T10
l
Fig. l(e). Modified single-pass pressurized thermosyphonic solar water-heating system.
374
R.S. MISHRA
v
v
v
1
w
D f
D L1
B
L'll -w-4 Parallel tube thermosyphon I
L
B
Parallel plate thermosyphon Tr
Fig. 1(f). Collector configurations of non-pressurized thermosyphonic solar water-heating systems.
.- Air vent [r ~- Float valve Heverse Ir ~ ~ '_ r FlOw o-'~"~' t I ~'Check valve ~ "1~ ~_-'-" ~--~ Cold.water
Ill ~" -'---1=upp,~
c,O\\~/~6~ !iI ~-'r'~~J'~er Makeuptank Fig. 1(g). Modified single-pass thermosyphonic solar water-heating systems.
Fig. 1(h). Modified multi-pass thermosyphonic solar water-heating system design.
375
Thermosyphonic solar water heating systems Details of various system configurations shown in Fig. 1. Collector type
Parallel
Absorber plate Total tube length Number of fluid-channels Thickness of absorber plate Painton absorber z~
Absorber area Tube diameter : internal external Header diameter: external Number of tubes Inclination angle of collector F'(TZQI F'UL~
Tank capacity Tank loss coefficient Reynolds number Coefficient of friction (riser) and headers Geometric length (a) headers (b) risers
Parallel
Copper
Copper
7 0.7 m m Black 0.88 0.88 1.89 m 2
7 0.7 m m Black 0.88 0.88 1.89 m:
15.5 m m 15.75 m m 31.75 m m 32.25 m m 7 40
15.5 m m 15.7 m m 31.75 m m 32.25 m m 7 40'
0.660 2.583 Honeycomb 100 1 1.9 W/m2~'C 350 0.18 0.005 14.40 m 12.20 m
Meander
Meander
Copper 16.6 m 7 0.7 m m Black 0.88 0.88 1.89 m 2
Copper 16.6 m 7 0.7 m m Black 0.88 0.88 1.89 m 2
15.5 m m ! 5.75 m m
15.5 m m 15.75 m m --
7 40
7 40
0.720 6.50 -100 1 1.9 W/m2°C 350 0.18 0.055
0.6605 3.375 Honeycomb 100 1 1.9 W/m2~C 560 0.125
0.720 6.580
14.40 m 12.20 m
16.6 m
16.6 m
AP, = [gh~p~ - (h~ + h2)g/h-o]
100 1 1.9 W/m2~C 560 0.125
p(T) = p ¢ ) ( l - - f i T ) ,
+ [ ( g s i n O ) x (p,~(t)-p:o(t))
~ ,
(5)
w h e r e [fl] is t h e coefficient o f t h e r m a l v o l u m e e x p a n s i o n a n d is o b t a i n e d by l e a s t - s q u a r e fit o f t h e d e n s i t y variation with temperature
w h e r e p~(t) a n d pro(t) a r e t h e d e n s i t i e s o f fluid at t h e inlet a n d o u t l e t o f t h e s y s t e m s . O v e r t h e s m a l l t e m p e r a t u r e c h a n g e s , t h e v a r i a t i o n in d e n s i t y w i t h t e m p e r a t u r e c a n be a s s u m e d to be g i v e n by a l i n e a r relationship
.
+,,2>1 × [T,~,(t)- Tt~(t)]--pogh2(1 -[~T~(t).
1000
50-
800
o0"40 -- • v ¢ I(t)l
• ~t.oj~
. ~
. ...... - -
600
/ 400
E
~
- ~.
m..m.l=O.o I ~
~30-1 .
•
I ~ ~
I-- 20 ~ , ~
10 8AM
o .o3
I 16
.E
-200
I 12
(6)
"~
I o 20
24
4
8AM
T i m e (hr)
Fig. 2(a). Variation of solar intensity, temperature with time of non-pressurized thermosyphonic solar water-heating system for different withdrawal mass-flow rates.
(7)
376
R . S . M]SHRA T w (t) 5O
_
/
['q'
i
I?
I 4O
_ i,¢tl__,/' -
"°"°"°-~''°'°~_o...a
~/
9/~/\ /J '\
Exp.
o "
'\
System System
-
/ e/ __4_._
/Ta
20
f 10
N°n-pressurizedsystem
y 7~.=.o
o/'/
,'
=E
N o n - w i t h d r a w l case
il '\,g ,~'Tw¢tl
/ ,I' I
v
Pressurized system
(t)
'\,
I 8AM
I 12
I 16
\
I 20
I
I
24
4
T i m e (hr)
Fig. 2(b). Variation of solar intensity and temperatures of non-pressurized and pressurized thermosyphonic solar water-heating systems.
55--
o
50--
~;;ory
...-.Qq~
Tin(t)
o'-o-.=.
40-35-:
25 ,,.
/
!\
.L/
\
700
_
300
~ o
-~
20-15
R"
500
Ta(t)
== 3 0 - E
900
°_
,(tl "oY"
45--
--
IO0
I ..-'"
5
0
I
I
10
15
,I 20
25
Fig. 2(c). Variation of solar intensity and temperatures of non-pressurized thermosyphonic solar waterheating system.
Exp. 50 vo
--
. . , . ' . . I(t) : ; Tin(t)
Theory
45
1 900
E 700
P 40 Q. 30 E 25
i
300
i .;
° 100
0
5
10 Time
15 (hr)
c
.E I
20 15
o~
500
35
20
o 09
25
Fig. 2(d). Variation of solar intensity and temperatures of non-pressurized thermosyphonic solar waterheating system.
377
Thermosyphonic solar water heating systems 0.6
-
System 1T F' ( ~ c~) = 0.735 a d F' U L= 6.5625
.
0.6 -
E ~"
N N ~ ~
" ~ k - ~ ~ \K~.. " ~ /
-
F'({c~)
F' u o
= 0 . 7 2 0 a dn " ~
~
System'~rF'(~cc) 0765and F' U L= 6.12 (copper fin absorber)
/S)/stemTrr
~
~
r C.¢~)Z o.73 __~"o,,
I
I
I
0.01
0.03
0.05
\
"~",,.
I
I
0.07
0.09
0.11
Fig. 2(e). Performance curves of modified pressurized and non-prcssurized lhermosyphonic solar waterheating systems.
The value of [qh2[~T.(t)] is small compared with the total pressure created in the whole system and can be neglected. Using eqs (2) and (3) for [T,o(t) L~(t)] and rearranging one gets
For the thermosyphonic flow to occur, the total pressure drop through system has to equal AP~.(1 +G), where [128vL]
'
:
{]/~[~o[~sinOq-(hl+h2)lF'Ac[('~OOlIc(t) -
u,
(8)
For the balance point [AP~] = 0
and
L~,(t) = Th(t)
(9)
(,2)
and
BPL]
~(T(t)- T.U))]
-.qh2pl,.
"J < ( ' )
"'
LAP,. J
(13)
is the ratio of resistance of flow in the connecting tubes to the resistance in the collector, assuming there is no resistance in the storage tank. Equating APt = AP,.(1 + rp) yields ~nd~(t) + A #h,U) + A : = 0.
(14)
where
gh,ND ~ ] xL
~:(OC,,,
-gh2po]
= 0
(10)
and A, = LI28vL(1 + r p ) C ~ J
yielding
x
T,,(t) = T,,(t)+
× F'A~.[(r~),I{(t)- ULc(Tm(t)- T,,(t))] 1.
haqPo
fi(LsinO+(h,+h2))(F'A[(~),l~(t)
(16)
Hence -
g,ATm(t)-
L,(t))]
(11)
m~.(t) = -
~ +
Ell
:2 [ ( A ~ 2 + 4 A j I : 2 ] '
(17)
378
R. S. MISHRA
From eq. (3) the variation in tank temperature can be expressed in the following form dTm(t)
dt ]+g1(t)Tm(t)=g2(t),
[1281aLrh~(t)( l +rp)] APL = APc(1 +rp) = L Az+A ,rhc(t)] x A~q-A6m~t)]"
(18)
(26)
Yielding
where =
rA,,] ~
3
UTAT +frh, (t)C~ + F'A~ UL~]
g l(t)
FA,~]
+[-A,~] LA,oj=0. (27)
(19)
t._
where and
g,(t) =
J
MwCwm
]
exp(9~t)dt x[exp(-glt)].
(30)
ULcTa(t)]
(31)
A6= gp0 ( 2 sin O+(h, +h2))
(33)
128/tL ..
T~(t) = TmoeXp(-g,t)
i
(29)
A5 = F'Acpo(ULc--~(ULcT,~(t)+(z~),It(t))) (32)
In principle, lift), T~(t), T~i(t) and thermosyphonic mass flow rate (m~(t)) are functions of time, but for small time intervals (t) the values of these parameters may be assumed to be constant and at t = 0, [T~ = T~o] yields
[i
A 2 = F'Ac ULo A 3 = F'Ac[(ZOOllt(t)+
(20)
+
(28)
A4 = gpo(1--[~T,;(t))
r uTAv .(t) + fdh,(t) + F'A [(zcO,It(t) + Ut~Ta(t))]] .
L
A I = 2Cw
(21)
AT=[~N~-]tl+rp))rh~(t )
(34)
A8 = .qhzpo(l -flT~(t)) A 7 = A~,A7
(35)
Aio =
(36) (37)
A~*A 7
A,~ = A,(2AvA2+aA,A4As) PRESSURIZED SYSTEMS
The energy balance equation in the pressurized system can be written as Fig. 1(b)
Q~(t) = F'A~[(zot)I~(t) [Tfo(t) + T~(t)
--el.c~
~
--Ta(t)) ]
Q. = rh~(t)Cw(T~o(t)- T~(t))
A,2 = A7A2+(A,As)(A2A4+As)-A4A9A~ A,3 = As(AsA2-A6Ag).
and
arm(,)] dt j+g~(t)Tm(t)=g2(t).
Q. = MwCw dt
=L
k UrAT(Tm(t)- T~(t))
+f2rh,(t)Cw(Tm(t)-- Tci(t)). (24) The total pressure due to buoyancy force created by density difference for the thermosyphonic flow is
(40)
(41)
where
rUvAv+J~rh,(t)Cw] dTm(t)
(39)
From eq. (24) the variation of tank temperature can be expressed in the following form
(22) (23)
(38)
[-F'AcULc]
-J+LM Cw ] r
2mc(,)c.
x L2m~(t)C~+F'AcU~J
]
(42)
+f2rh, (t) CwT~,(t)
gz(t)=[UvAvT"(t)MwCw
]
L
P, = gflpo(~sinO+(hl +t12)) x [ f'A~UL~[(z~),I~(t)Mww(Tw + ULcZ.(t)]]
x (Too(t)-- T,;(t))-gh2po(l -flTf;(t))
(25)
and pressure losses due to friction can be calculated as
[
2th~(t)C~ ] x L2mc(t)Cw+F,A~ULcj. (43)
379
Thermosyphonic solar water heating systems
In principle, l~(t), Z,(t) and thermosyphonic flow rate (the(t)) and may be functions of time but for the small time interval of 0 time (t), these values of parameters may be assumed to be constant and solution of eq. (24) may be written as
T~(t)
~
~
$
~
~
g
;
~
~
Tin(t) = Tmoexp ( - g , t )
+ f" [q,exp~q,t)]dtexp(-q,t). ,,
(44)
i
II
RESULTS AND DISCUSSIONS
The experiments were conducted at Patiala (India) for several days of October 1987 and data for typical days of 23 October 1987 and 28 October 1987 are given in Tables 1-7, respectively. The evaluation of collector temperatures and mean temperature of storage and calculation of thermosyphonic flow rate, thermal efficiencies (hourly variation and average values) are shown in Tables 2 8 and in Fig. I. The close agreement between the theoretical and experimental results shows the validity of the present method. NOMENCLATURE
A¢
AT Cr
d F" g H H~ H2 h,. h2
h; h4
h~ h~ h~ its h,) 1,(l) L
m~(~) r~,(t) m~ II
N
0_o(~) f
R Re l
T
area of solar energy collector, m'area of hot water storage tank, m : specific heat of water, J/kg C diameter of tube, m collector efficiency factor acceleration due to gravity, m/s 2 height of storage tank from collector inlet, m height of tank bottom from collector inlet, m height of tank water from collector outlet, m height of collector outlet from top absorber's water level, m height of control valve from collector outlet, m height of tank bottom from collector outlet, m height of tank bottom from ground, m height of collector inlet from ground, m header diameter, m distance between two headers, m m height of control valve (or tank top) from ground, m m outer diameter of tube, m m solar intensity, W / m ~ length of flow channels, m mass flow rate in the system, kg,'s withdrawal flow rate of hot water, kg/s mass flow rate of water in the (collector + storage tank) system, kg number of bends (curves etc) number of lubes useful energy collected from system, W ' h radius of tube, m radius of header tubes, m Reynolds n umber time interval, h temperature, C
e~
E =
~' e~ .= p) ~"
.~ .?.
"~
[...
e. ~ .~.
E
e. E -~
...~
~'-
~ ~.,~ ~ ~ ~
_~ ~" ~2 ~
~
~
~
i
~
i
27.6 28.1 28.63 28.78 30.61 31.23 31.70 32.03 32.13 32.61 32.64 32.84 32.80 32.40 32.10
9 a.m. 9.30 10.0 10.30 11.0 11.30 12.0 12.30 13.00 13.30 14.0 14.30 15.0 15.30 16.0
26.8 27.7 28.4 29.1 29.9 31.l 32.5 33.2 34.3 35.5 36.1 35.9 33.1 31.9 29.7
71,(t) (C)
273.1 432.9 670.33 782.47 812.45 850.92 905.51 891.73 910.88 785.58 772.01 624.118 524.0 432 1 387.0
IM) (Win:) 63.20 78.90 90.50 95.60 95.95 96.20 96.10 96.30 96.40 96.30 94.30 92.70 87.30 68.20 57.(!
Experimental 61.915 78.621 91.134 96.891 96.986 96.999 97.329 97.4216 97.5973 97.5032 96.9532 94.932 88.892 67.982 56.437
-Theoretical
7~,(1)
0.50 2.10 3.54 4.20 4.95 5.50 6.0 6.13 5.75 4.82 4.65 4.52 4.10 2.93 2. I7
Experimental 0.435 2.203 3.571 4.352 5.029 5.718 6.097 6.246 5.749 4.874 4.693 4.5252 4.0998 2.9567 2.189
Theoretical
rh~(t) (kg/~h)
35.60 50.70 60.90 64.90 64.35 62.93 62.75 62.85 62.81 62.50 60.13 58.49 53.11 34.183 23.9
Expcrimental
Ttz,(t)
34.315 50.421 61.534 65.891 65.386 63.729 63.979 63.912 64.007 63.703 62.783 60.722 55.702 34.483 22.337
Thcoretical
Tt~(l) Q,(t) 4[.535 248.430 503.034 633.080 743.242 807.60 878.50 898.9645 842.70 702.917 652.4105 616.8745 508.0857 345.180 121.0136
(W/~h) 0.05855 0.24373 0.49352 0.46075 0.50475 0.53391 0.57541 0.59016 0.5800 0.50787 0.498634 0.500221 0.504652 0.321313 0.255602
Efficiency qh
((7)
(C)
27.61t 28.20 29.6 31.0 31.6 33.27 33.45 33.45 33.59 33.80 34.17 34.2J 34.19 33.8{I 33.1
9 a.m. t~.30 10.0 lu.30 ll.0 11.30 12.11 I2,30 l 3.00 13.30 14.0 14.30 ! 5.i/ [ 5.?0 lo.0
21.80 22.60 23.50 24.91i 26.10 27.10 28.5O 29.0 "~ "~ ~)..~ 29.5 .:9.6~ ~'~ _"9 .(~ 29.70 29.85 29.95
"l~,(t)
T,~(t)
Time (h)
375.'~0 539.30 637.811 627.1t 799.73 807.80 807.811 805.95 768.67 699.7/) 698.7!) 639.7 532.7 387.3 25{}.{}
~W m-')
IM) 64.0 72. l 76.5 79.8 82.5 82.9 83.5 83.3 83.0 82.0 82.0 79.8 77.5 71.3 55.5
l~xperimental
.
.
. 61.30 72.90 76.70 80.10 82.80 83.04 83.55 83.45 83.59 82.10 82. I 0 78.8 77.7 71.8 53.9
Theoretical
Tr,,(t) (C)
. 1.0 3.5 5.0 6.5 8.5 9.2 9.5 9.3 8.8 7.0 7.0 6.2 5.7 4.7 2.5
1.4 3.6 5.09 6.53 8.62 9.0 9.5 9.43 9.04 7.1 7.0 6.37 6.0 4.8 2.9
Theoretical
22.4
36.40 43.90 46.9 48.8 50.9 49.63 50.15 49.85 49.41 48.20 47.83 45.59 43.3 I 32.5
Experimental
33.70 44.70 47.10 50.10 51.20 49.74 50.25 50.0 50.0 49.10 47.93 44.59 43.47 38.0 22.0
Theoretical
(C)
Experimental
.
Tfo(t)- Tli(t)
ti~c(t) (kg '~h)
169.867 353.520 547.167 740.133 1009.517 1065.390 1111.6583 1081.7368 1014.552 960.40 781.222 659.535 576.023 411.25 t30.67
(W/h)
Qu(t)
0.55674
1/day
0.23948 0.351736 0.453914 0.538659 0.685580 0.704860 0.728125 0.71015 0.69835 0.69390 0.59075 0.5455065 0.57213 0.56182 0.276
Efficiency qh
T:~b[c ~ Thc~'mv,~.~pi~v;nic evin}:le p;~ss {non p,'essurizcd) domestic solar water heating syslcm using parallel tube absorber and copper lins (A~ = 1.89 m'-)
"Fdt) (C)
Time (h)
Table 2. Thermos 5 phonic single pass domestic solar water heating system using meander tube absorber and aluminum fins (A~ = 1.89 m 2) of pressurized type
27.6 28.10 28.63 28.78 30.61 31.23 31.70 32.(13 32.13 32.6l 32.64 32.64 32.80 32.40 32.10
9 a.m. 9.30 10.0 10.3(I ll.0 I 1.30 12.0 12.30 13.00 13.30 14.(t 14.30 [5.0 15.30 16.0
26.8 27.70 28.4 29.1 29.9 31.1 32.5 33.2 34,3 35.5 36.1 35.9 33.1 31.9 29.7
71,(z (C)
273.1 432.90 67(/.33 782.47 812.45 850.92 905.51 891.73 910.88 785.58 772.01 624.08 524.0 432. l 387.6
l~(z) /W/m:) 61.8 70.90 74.80 77.4 80.6 81.3 82.0 82.30 82.5 82.6 82.1 79.0 76.1 70.1 55.0
Experimental 59.86 70.15 75.10 77.34 81.05 81.40 82.5 82.9 83.13 83.31 82.14 79.05 76.21 69.8 53.9
Theoretical 1.50 2.90 4.7 5.9 7.8 9.1 9.6 9.3 8,8 8.1 7.4 6.1 5.0 3.7 1.76
Experimental 1.39 2.98 4.71 6.0 8.0 9.05 9.6 9.4 8.9 8.09 7.4 6.2 5.15 3.69 1.78
Theoretical
#~3t) kg'~h)
33.20 42.80 46.17 48.62 49.99 50.07 50.30 50.27 50.37 49.99 49.46 46.16 43.3 37.7 22.9
Experimental 32.06 42.05 46.47 48.56 50.44 50.17 50.80 50.87 51.0 50.7 44.5 46.21 43.41 37.4 24.2
Theoretical
1],,(0 - T~(t) (C)
119.0 289.613 506.331 669.335 909.818 1063.153 1126.72 1090.86 1034.264 944.811 900.172 657.010 505.167 325.477 94.040
Q~(t) (W/~h) (Experimental)
0.23064 0.35397 0.399654 0.45260 0.59250 0.661067 0.658356 0.6473 0.60008 0.63633 0.61695 0.55708 0.51008 0.39864 0.1285153
Efficiency qh
I'~M) (C)
21.0 24.0 28.0 32.0 32.5 34.5 35.5 35.0 33.5 31.0
Time (h)
9 a.m. 10.0 I 1.0 12.0 13.0 14.0 15.0 16.(1 17.0 18.0
21.7 23.4 26.(/5 28.40 29.32 29.6 29.8 29.9 28.75 27.00
li~(t) ((') 431.0 534.5 674.5 758.5 763.75 692.25 387.25 182.0 0.0 0.0
l~(t) (W,m:l 45.0 65.0 71.0 76.0 77.0 74.9 67.0 55.0 50.0 49.5
Experimental
T,,,(1) C)
46.0 65.5 72.0 75.9 78. l 74.9 66.1 54. I 50.1 49.5
. Theoretical
.
22.0 29.0 33.0 38.(I 42.0 46.0 48.0 49.0 50.0 49.5
. l-xpcrin3enlal
.
T,,,(t) (C)
22.1 29.1 34.1 39.1 42.9 47.3 49.8 49.5 50.0 49.5
. Theoretical
.
23.0 34.0 38.0 38.0 35.0 28.9 19.0 6.0 0.0 0.0
. Experimental
24.0 34.9 37.9 36.8 35.2 27.6 17.3 4.6 0.0 0.0
Theoretical
T,,,(1) T,,,(0 (C)
Table 5. Thermosyphonic mullipass domestic solar ~ater heating system (ftv]rth) without rc~crsc 11o~ ~sing copper fins absorber (parallel tubes) in closed loop cycle
T,,(z) (C)
imp, (h)
7~,~(0 ((7')
F;tblc 4 l'hermosyphonic single pass (non-pressurizcdl domestic ,tHat walcr heating s',~,lcm using2',parallel tube absorber and aluminuln lins (A~ = 1.89 m e)
~
2-
©
"O
g
21.0 24.0 28.0 32.0 32.5 34.5 35.5 35.0 33.5 31.0
9 a.m. 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0
21.7 23.42 26.05 28.40 29.375 29.6 29.8 29.9 28.75 27.0
Ta(t) (°C) 431.0 534.5 674.5 758.5 763.75 692.75 560.0 385.25 182.0 0.0
It(t) ( W / m 2) 41.0 53.5 65.0 68.0 65.0 61.5 55.5 48.0 45.0 44.0
Experimental 40.5 53.1 64.9 69.1 66.5 61.4 54.8 48.5 44.8 44.0
Theoretical 21.0 27.0 30.0 33.5 36.0 40.0 42.0 43.0 43.5 44.0
Experimental
(of)
Tin(t)
21.0 26.9 30.1 34.0 35.9 40.4 41.8 42.9 43.3 44.0
Theoretical 20.0 26.5 35.0 34.5 29.0 21.5 13.5 5.0 2.5 0.0
Experimental
(of)
20.5 26.2 34.8 35.1 30.6 21.0 13.0 4.6 1.5 0.0
Theoretical
Tro(t) -- Tin(t)
Tn(t) CC)
21.0 24.0 28.0 32.0 32.5 34.5 35.5 35.0 33.5 31.5
Time (h)
9 a.m. 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0
21.7 23.4 26.05 28.40 29.32 29.6 29.8 29.9 28.75 27.0
Ta(t ) (~'C) 431.0 534.5 674.5 758.5 763.75 692.75 560.5 387.25 182.0 0.0
I~(t) (W/m 2) 65.0 78.5 91.5 96.0 97.5 98.0 91.5 80.0 57.5 50.0
Experimental
Cc)
Tfo(t)
64.5 78.5 92.0 95.9 97.9 98.5 90.8 80.5 56.9 49.9
Theoretical
22.0 29.0 33.0 38.0 43.0 47.0 48.0 49.0 49.5 49.4
Experimental
(oc)
Tin(t)
22.1 28.9 33.5 37.9 43.2 46.9 48.1 49.0 49.6 49.5
Theoretical
43.0 49.5 58.5 58.0 54.5 51.0 43.5 31.0 8.0 0.6
Experimental
(of)
42.4 49.6 58.5 58.0 54.7 51.6 42.7 31.5 7.3 0.4
Theoretical
Tro(t) -- Tn(t)
Table 7. Thermosyphonic domestic multipass solar water heating system without reverse flow using meander tube absorber (in closed loop cycles) with no water withdrawal
Tci(t) (°C)
Time (h)
(°c)
Tfo(t)
Table 6. Thermosyphonic multipass domestic solar water-heating system (fifth) without reverse flow using parallel tube absorber a l u m i n i u m fins in the closed loop cycle
>
bo
(C)
(~C)
27.60 26.20 27.1 29.1 30.9 33.6 34.3 35.0 35.6 36.1 35.8 35.4 35.0 34.9 34.1 33.5 33.1 32.9 32.5 32.2 31.8 31.0
9 a.m. 9.30 10.00 10.30 I 1.0 11.30 12.00 12.30 13.0 13.30 14.0 14.30 15.0 15.30 t 6.0 16.30 17.0 17.30 18.0 18.30 19.0 t9.30
26.80 25.6 26.5 27.2 28.0 28.5 29.2 29.6 30.1 30.4 30.8 31.0 31.5 31.9 32.2 32.4 32.5 32.(/ 31.7 33.14 30.9 30.1
T.(t)
T~(t)
Time (h) 273.10 350.0 444.0 505.0 638.0 715.0 805.0 925.0 958.0 943.0 932.0 885.0 885.0 820.0 809.0 641.0 253.0
(W/n121
It(t)
--
65.10 71.40 91.80 93.41 95.05 96.1 96.5 94.0 93.2 91.8 90.1 88.7 86.8 84.7 80.2 70.0 60.0
(~'C)
T~(t) 25.20 25.9 26.9 28.4 30.1 33.6 35.7 38.0 40.2 42.4 42.4 44.3 46.1 47.7 49.2 50.6 51.8 51.2 50.7 50.2 49.7 49.2
Tin(t) (~C) O.550 45.5 64.9 65.01 64.95 64.30 62.9 58.3 54.8 51.6 47.7 44.7 40.7 37.0 31.0 19.4 8.2
ATc(t) (~C) O.570 0.70 1.0 1.5 1.7 t .7 1.8 2.1 2.3 2.2 2.2 1.9 1.8 1.6 1.5 1.4 1.2 0.6 -0.5 -0.5 0.5 -0.5
ATm(t) ('C) 0.00194 0.0010256 0.001284 0.001284 0.001454 0.001469 0.00159 0.0020 0.00233 0.00237 0.00256 0.00236 0.002457 0.00240 0.003276 0.00481 l --
n'*c(t) (kg/s) 46.93 196.0 280.0 420.0 476.0 476.0 504.0 588.0 644.0 616.0 616.0 532.0 504.0 448.0 420.0 392.0 336.0
Q~(t)
0.09 0.29630 0.33370 0.440 0.39475 0.35224 0.331263 0.336336 0.3557 0.34563 0.34970 0.31806 0.3119 0.28907 0.2747 0.32357 --
rlh
Efficiency
Table 8. Thermosyphonic solar ~atc~ heating system of pressurized type using a rneandcr tube absorber (A~ = 1.89 m 2) connected with a hot water storage tank of capacity of 120 1 in closed loop cycle
,.~,a
0~
0
o
,..q
g
384
R. S. MISHRA T~,(t) ambient temperature, °C T~(t) temperature of cold water in the collector inlet in single pass system, ' C T,-o(t) temperature of hot water at collector outlet, ' C Tin(t) mean temperature of the system, C fl coefficient of volumetric thermal expansion, C i 0 collector inclination angle, ). triction factor thermal viscosity of water, N/s m-' v kinematic viscosity of water, m:/s coefficient of flow-resistance p,,(t) density of water, kg/m ~ p,(t) density of water at zero degree centigrade, kg/m:~ pit) density of water at collector inleL kg/m 3 p~,(t) density of water at collector outlet, kg/m -~ pro(t) density of water at mean temperature, kg/m 3 (r:~)~ effective transmitivity absorptivity products
13.
14.
15. 16. 17. 18.
19. 20. 21.
REFERENCES I. R. S. Mishra, Investigation in solar hot water systems. Ph.D. Thesis, Indian Institute of Technology, Delhi, India (1986). 2. D.J. Close, The performance of solar waters with natural circulation. Solar Enerqy 6, 33 40 (1962). 3. A. Metrol, Detailed loop model analysis of liquid solar thermosyphonic system with heat exchangers. Solar Enew.v 27, 367 (1981). 4. C. L. Gupta, System design in solar water heaters with natural circulation. Solar Ener,qy 12, 163 182 (1968). 5. M. IqbaI, Free convection effects inside tubes of flat plate solar energy collector. Solar E)wr,qy 10, 207 (1964). 6. A. Shitzer, Experiments with flat plate solar water heating system in thermosyphonic flow. Solar Enerqy 22, 27 35 (1979). 7. G. L. Morrision, Transient response of thermosyphonic collectors. Solar Energy 24, 55 (1980). 8. M. F. Young, Performance characteristics of thermosyphonic hot water systems. Solar Ener.qy Enyn,q, Trans. A.S.M.E. 103, 193 ([981). 9. B. Norton, Achieving thermal stratification in natural circulation in solar water heaters. Appl. Enerqy 4, 211 225 (1983). 10. B.J. Haung, Similarity theory of solar water heaters with natural circulation. Solar Enerqy 25, 105 116 (1980). 11. K. S. Ong, A finite difference method to evaluate the thermal performance of a solar water heaters. Solar Ener,qv 16, 137 147 (1974). 12. K. S. Ong, Improved computer programme for thermal
22. 23. 24. 25.
26.
27.
28.
29.
30.
31.
32.
performance of solar water heaters. Solar Energy 18, 183 191 (1976). M. S. Sodha and G. N. Tiwari, Analysis of natural circulation solar water heating systems. Energy Convers. Mgmt 21,283 (1981). N. K. Bansal, Side by side comparison of pressurised and non pressurised solar water heating systems of thermosyphonic type. Solar Ener.qy 34, 317- 328 (1985). Y. F. Wang, Once through solar water heating system. Solar Energy 29, 541 547 (1982). G. Grossman, Heat transfer analysis of a flat plate solar energy collectors. Solar Ener,qy 19, 493 502 (1977). A. 1. Kudish, Direct measurement and analysis of thermosyphonic flow. Solar Enerqy 35, 167-173 (1986). S. G. Tzafestas, A finite difference modelling, identification and simulation of solar water heaters. Solar Energy 16, 25 31 (1974). J. M. Gorden, Thermosyphonic systems : single vs multipass. Solar Ener.qy 27, 441M42 (1981). G. L. Morrision, Reverse circulation in thermosyphonic solar water beaters. Solar Enerqy 36, 377 379 (1986). G. L. Morrision, Long term performance simulation of thermosyphonic solar water beaters. Sohtr Ener!Lv 35, 515 520 (1984). B. J. Haung, A simulation method For thermosyphonic solar collectors. Solar Ener,qy 35.3l 43 (1986). M. Vaxman, Analysis of free flow solar collector. Solar Energl' 34, 287 290 (1985). M. Sokolov. Experiments with compact solar water heaters. Solar Enerq3' 34, 447 454 (1986). M. Vaxman, Effects of connecting pipes in thermosyphonic solar water heating systems. Solar Ener.oy 37, 323 330 (1986). W. F. Phillips, Effects of stratification on the performance of liquid based solar heating systems. Solar L>wr,qy 29, 11 [ 120 (1982). G. L. Morrision, Long tern1 performance of thermosyphonic solar water heaters. Solar Ener,qy 30, 341 350 (1983). J.W. Baughn, The calculated performance of solar domestic hot water system with hot water removal. Solar Enerqy 32, 303 305 (1984). M. F. Young, The performance of thermosyphonic solar domestic bot water systems witb hot water removal. Solar Enerqy 32, 655 658 (1984). M. Sokolov and M. Vaxman, Analysis of integral con> pact solar water beaters. Solar E~wrqy 30. 237 246 (1983). A. S. I. Khalik, Heat removal factor for a flat plate collector with serpentine tube. Solar Enep~qv 18, 59 64 (1976). N. K. Bansal, Solar sterilization of" water. Solar Enerqy 40, 35 39(1988).
0960 1481/92 $5.00+.D0 Pergamon Press Ltd
THEORETICAL A N D EXPERIMENTAL STUDIES OF PRESSURIZED A N D NON-PRESSURIZED SOLAR WATER HEATING SYSTEMS OF THERMOSYPHONIC TYPE R. S. MISHRA*
Mechanical Engineering Department, Haryana Agricultural University, Hisar, India 125004 (Received 13 May 1991 ; accepted 16 January 1992) Abstract--A method for calculating the thermosyphonic flow rate in the single and multipass systems of pressurized and non-pressurized type is presented. The experiments were conducted over several days on various systems fabricated and tested at T.1.E.T. Patiala, India. Close agreement between the theoretical calculations and experimental results shows verification of the present method.
INTRODUCTION
THERMOSYPHONIC FLOW RATE IN NONPRESSURIZED SOLAR WATER HEATING SYSTEMS
Various theoretical and experimental studies performed on the thermosyphonic solar water heating system are readily available in the literature [1]-[30]. The studies of Metrol [3] and others attempted to show very detailed equations for each of the components. This analysis, if employed in practice, required the use of large computers and was expensive and time consuming. The studies of Close [2], Ong [12], Sodha and Tiwari [13] and Bansal [14] based on the simple assumption that the whole system is at some average temperature, lack a comparison with detailed experimental investigation. Also, the basis for estimating thermosyphonic flow rate has not been established for pressurized solar water heating systems. The study presented in this paper covers both these points with the derivation of thermosyphonic flow rate from basic principles. The eight thermosyphonic solar water heating systems were fabricated in the institute for hot water requirement of the T.I.E.T. guest house. Measurements were taken for several days in October. The numerical calculations for thermosyphonic flow rate, water temperature in the storage with the given hot water demand pattern and thermal efficiency were carried out by computer at the Indian Institute of Technology, Delhi, India. The experimental measurements are in close agreement with the calculated values.
A density difference created by the temperature difference causes the fluid being heated to flow without any pump. This effect of natural flow due to the density difference is usually known as thermosyphonic effect. The total pressure responsible for the thermosyphonic flow is APt = .q sin 0
(pf~ - p(y)) dy + y h , p , ~ - ( h t +h2)gp,.~,,
(l)
where L is the length of solar energy collector. The energy balance in the whole system can be expressed as
Q. = rhc(t)Cw(Tfo(t)- T~(t)) = F'A~[(zc~)~l~(t)-- Uc~(Tm(t) - T.(t))]
(2)
and Qu = MwCw - - - d ~
+ g r A y ( T i n ( t ) - T,(t)) +f2rh~(t)Cw(Tm(t)--T~M)).
(3)
Assuming the density variation to be linear it can be expressed as (p~-p(y))dy
*Present address: Faculty House, H.A.U. Hisar-125004 Hisar, Haryana, India.
and
371
L = (pn(t)-Pt.o(t))~
(4)
372
R.S. MISHRA
Vent ------b.~ Float valve
Hot water out Shut off valve
Check valve Cold water in
'-'-" Drain Fig. 1(a). Simple non-pressurized thermosyphonic solar water-heating system components.
Tank
Hot water out
Cold
C
w a t e r out
Fig. 1(b). Simple, pressurized thermosyphonic solar water-heating system I.
Thermosyphonic solar water heating systems
373
Ti Pe Ti iPi ~ i l ~
I
T
i
¢1 2000 mm
hi
1
-'= W
I-
1000m m
--1
Fig. l(c). Modified single-pass non-pressurized thermosyphonic solar water-heating system.
Tank
~oO
~o,~ •
I
Fig. 1(d). Principle of thermosyphonic solar water-heating system.
Ti Pe
Ti
2000ram = 120mm 1000m m
hi
1
~ Ti
)L _~)0 T10
l
Fig. l(e). Modified single-pass pressurized thermosyphonic solar water-heating system.
374
R.S. MISHRA
v
v
v
1
w
D f
D L1
B
L'll -w-4 Parallel tube thermosyphon I
L
B
Parallel plate thermosyphon Tr
Fig. 1(f). Collector configurations of non-pressurized thermosyphonic solar water-heating systems.
.- Air vent [r ~- Float valve Heverse Ir ~ ~ '_ r FlOw o-'~"~' t I ~'Check valve ~ "1~ ~_-'-" ~--~ Cold.water
Ill ~" -'---1=upp,~
c,O\\~/~6~ !iI ~-'r'~~J'~er Makeuptank Fig. 1(g). Modified single-pass thermosyphonic solar water-heating systems.
Fig. 1(h). Modified multi-pass thermosyphonic solar water-heating system design.
375
Thermosyphonic solar water heating systems Details of various system configurations shown in Fig. 1. Collector type
Parallel
Absorber plate Total tube length Number of fluid-channels Thickness of absorber plate Painton absorber z~
Absorber area Tube diameter : internal external Header diameter: external Number of tubes Inclination angle of collector F'(TZQI F'UL~
Tank capacity Tank loss coefficient Reynolds number Coefficient of friction (riser) and headers Geometric length (a) headers (b) risers
Parallel
Copper
Copper
7 0.7 m m Black 0.88 0.88 1.89 m 2
7 0.7 m m Black 0.88 0.88 1.89 m:
15.5 m m 15.75 m m 31.75 m m 32.25 m m 7 40
15.5 m m 15.7 m m 31.75 m m 32.25 m m 7 40'
0.660 2.583 Honeycomb 100 1 1.9 W/m2~'C 350 0.18 0.005 14.40 m 12.20 m
Meander
Meander
Copper 16.6 m 7 0.7 m m Black 0.88 0.88 1.89 m 2
Copper 16.6 m 7 0.7 m m Black 0.88 0.88 1.89 m 2
15.5 m m ! 5.75 m m
15.5 m m 15.75 m m --
7 40
7 40
0.720 6.50 -100 1 1.9 W/m2°C 350 0.18 0.055
0.6605 3.375 Honeycomb 100 1 1.9 W/m2~C 560 0.125
0.720 6.580
14.40 m 12.20 m
16.6 m
16.6 m
AP, = [gh~p~ - (h~ + h2)g/h-o]
100 1 1.9 W/m2~C 560 0.125
p(T) = p ¢ ) ( l - - f i T ) ,
+ [ ( g s i n O ) x (p,~(t)-p:o(t))
~ ,
(5)
w h e r e [fl] is t h e coefficient o f t h e r m a l v o l u m e e x p a n s i o n a n d is o b t a i n e d by l e a s t - s q u a r e fit o f t h e d e n s i t y variation with temperature
w h e r e p~(t) a n d pro(t) a r e t h e d e n s i t i e s o f fluid at t h e inlet a n d o u t l e t o f t h e s y s t e m s . O v e r t h e s m a l l t e m p e r a t u r e c h a n g e s , t h e v a r i a t i o n in d e n s i t y w i t h t e m p e r a t u r e c a n be a s s u m e d to be g i v e n by a l i n e a r relationship
.
+,,2>1 × [T,~,(t)- Tt~(t)]--pogh2(1 -[~T~(t).
1000
50-
800
o0"40 -- • v ¢ I(t)l
• ~t.oj~
. ~
. ...... - -
600
/ 400
E
~
- ~.
m..m.l=O.o I ~
~30-1 .
•
I ~ ~
I-- 20 ~ , ~
10 8AM
o .o3
I 16
.E
-200
I 12
(6)
"~
I o 20
24
4
8AM
T i m e (hr)
Fig. 2(a). Variation of solar intensity, temperature with time of non-pressurized thermosyphonic solar water-heating system for different withdrawal mass-flow rates.
(7)
376
R . S . M]SHRA T w (t) 5O
_
/
['q'
i
I?
I 4O
_ i,¢tl__,/' -
"°"°"°-~''°'°~_o...a
~/
9/~/\ /J '\
Exp.
o "
'\
System System
-
/ e/ __4_._
/Ta
20
f 10
N°n-pressurizedsystem
y 7~.=.o
o/'/
,'
=E
N o n - w i t h d r a w l case
il '\,g ,~'Tw¢tl
/ ,I' I
v
Pressurized system
(t)
'\,
I 8AM
I 12
I 16
\
I 20
I
I
24
4
T i m e (hr)
Fig. 2(b). Variation of solar intensity and temperatures of non-pressurized and pressurized thermosyphonic solar water-heating systems.
55--
o
50--
~;;ory
...-.Qq~
Tin(t)
o'-o-.=.
40-35-:
25 ,,.
/
!\
.L/
\
700
_
300
~ o
-~
20-15
R"
500
Ta(t)
== 3 0 - E
900
°_
,(tl "oY"
45--
--
IO0
I ..-'"
5
0
I
I
10
15
,I 20
25
Fig. 2(c). Variation of solar intensity and temperatures of non-pressurized thermosyphonic solar waterheating system.
Exp. 50 vo
--
. . , . ' . . I(t) : ; Tin(t)
Theory
45
1 900
E 700
P 40 Q. 30 E 25
i
300
i .;
° 100
0
5
10 Time
15 (hr)
c
.E I
20 15
o~
500
35
20
o 09
25
Fig. 2(d). Variation of solar intensity and temperatures of non-pressurized thermosyphonic solar waterheating system.
377
Thermosyphonic solar water heating systems 0.6
-
System 1T F' ( ~ c~) = 0.735 a d F' U L= 6.5625
.
0.6 -
E ~"
N N ~ ~
" ~ k - ~ ~ \K~.. " ~ /
-
F'({c~)
F' u o
= 0 . 7 2 0 a dn " ~
~
System'~rF'(~cc) 0765and F' U L= 6.12 (copper fin absorber)
/S)/stemTrr
~
~
r C.¢~)Z o.73 __~"o,,
I
I
I
0.01
0.03
0.05
\
"~",,.
I
I
0.07
0.09
0.11
Fig. 2(e). Performance curves of modified pressurized and non-prcssurized lhermosyphonic solar waterheating systems.
The value of [qh2[~T.(t)] is small compared with the total pressure created in the whole system and can be neglected. Using eqs (2) and (3) for [T,o(t) L~(t)] and rearranging one gets
For the thermosyphonic flow to occur, the total pressure drop through system has to equal AP~.(1 +G), where [128vL]
'
:
{]/~[~o[~sinOq-(hl+h2)lF'Ac[('~OOlIc(t) -
u,
(8)
For the balance point [AP~] = 0
and
L~,(t) = Th(t)
(9)
(,2)
and
BPL]
~(T(t)- T.U))]
-.qh2pl,.
"J < ( ' )
"'
LAP,. J
(13)
is the ratio of resistance of flow in the connecting tubes to the resistance in the collector, assuming there is no resistance in the storage tank. Equating APt = AP,.(1 + rp) yields ~nd~(t) + A #h,U) + A : = 0.
(14)
where
gh,ND ~ ] xL
~:(OC,,,
-gh2po]
= 0
(10)
and A, = LI28vL(1 + r p ) C ~ J
yielding
x
T,,(t) = T,,(t)+
× F'A~.[(r~),I{(t)- ULc(Tm(t)- T,,(t))] 1.
haqPo
fi(LsinO+(h,+h2))(F'A[(~),l~(t)
(16)
Hence -
g,ATm(t)-
L,(t))]
(11)
m~.(t) = -
~ +
Ell
:2 [ ( A ~ 2 + 4 A j I : 2 ] '
(17)
378
R. S. MISHRA
From eq. (3) the variation in tank temperature can be expressed in the following form dTm(t)
dt ]+g1(t)Tm(t)=g2(t),
[1281aLrh~(t)( l +rp)] APL = APc(1 +rp) = L Az+A ,rhc(t)] x A~q-A6m~t)]"
(18)
(26)
Yielding
where =
rA,,] ~
3
UTAT +frh, (t)C~ + F'A~ UL~]
g l(t)
FA,~]
+[-A,~] LA,oj=0. (27)
(19)
t._
where and
g,(t) =
J
MwCwm
]
exp(9~t)dt x[exp(-glt)].
(30)
ULcTa(t)]
(31)
A6= gp0 ( 2 sin O+(h, +h2))
(33)
128/tL ..
T~(t) = TmoeXp(-g,t)
i
(29)
A5 = F'Acpo(ULc--~(ULcT,~(t)+(z~),It(t))) (32)
In principle, lift), T~(t), T~i(t) and thermosyphonic mass flow rate (m~(t)) are functions of time, but for small time intervals (t) the values of these parameters may be assumed to be constant and at t = 0, [T~ = T~o] yields
[i
A 2 = F'Ac ULo A 3 = F'Ac[(ZOOllt(t)+
(20)
+
(28)
A4 = gpo(1--[~T,;(t))
r uTAv .(t) + fdh,(t) + F'A [(zcO,It(t) + Ut~Ta(t))]] .
L
A I = 2Cw
(21)
AT=[~N~-]tl+rp))rh~(t )
(34)
A8 = .qhzpo(l -flT~(t)) A 7 = A~,A7
(35)
Aio =
(36) (37)
A~*A 7
A,~ = A,(2AvA2+aA,A4As) PRESSURIZED SYSTEMS
The energy balance equation in the pressurized system can be written as Fig. 1(b)
Q~(t) = F'A~[(zot)I~(t) [Tfo(t) + T~(t)
--el.c~
~
--Ta(t)) ]
Q. = rh~(t)Cw(T~o(t)- T~(t))
A,2 = A7A2+(A,As)(A2A4+As)-A4A9A~ A,3 = As(AsA2-A6Ag).
and
arm(,)] dt j+g~(t)Tm(t)=g2(t).
Q. = MwCw dt
=L
k UrAT(Tm(t)- T~(t))
+f2rh,(t)Cw(Tm(t)-- Tci(t)). (24) The total pressure due to buoyancy force created by density difference for the thermosyphonic flow is
(40)
(41)
where
rUvAv+J~rh,(t)Cw] dTm(t)
(39)
From eq. (24) the variation of tank temperature can be expressed in the following form
(22) (23)
(38)
[-F'AcULc]
-J+LM Cw ] r
2mc(,)c.
x L2m~(t)C~+F'AcU~J
]
(42)
+f2rh, (t) CwT~,(t)
gz(t)=[UvAvT"(t)MwCw
]
L
P, = gflpo(~sinO+(hl +t12)) x [ f'A~UL~[(z~),I~(t)Mww(Tw + ULcZ.(t)]]
x (Too(t)-- T,;(t))-gh2po(l -flTf;(t))
(25)
and pressure losses due to friction can be calculated as
[
2th~(t)C~ ] x L2mc(t)Cw+F,A~ULcj. (43)
379
Thermosyphonic solar water heating systems
In principle, l~(t), Z,(t) and thermosyphonic flow rate (the(t)) and may be functions of time but for the small time interval of 0 time (t), these values of parameters may be assumed to be constant and solution of eq. (24) may be written as
T~(t)
~
~
$
~
~
g
;
~
~
Tin(t) = Tmoexp ( - g , t )
+ f" [q,exp~q,t)]dtexp(-q,t). ,,
(44)
i
II
RESULTS AND DISCUSSIONS
The experiments were conducted at Patiala (India) for several days of October 1987 and data for typical days of 23 October 1987 and 28 October 1987 are given in Tables 1-7, respectively. The evaluation of collector temperatures and mean temperature of storage and calculation of thermosyphonic flow rate, thermal efficiencies (hourly variation and average values) are shown in Tables 2 8 and in Fig. I. The close agreement between the theoretical and experimental results shows the validity of the present method. NOMENCLATURE
A¢
AT Cr
d F" g H H~ H2 h,. h2
h; h4
h~ h~ h~ its h,) 1,(l) L
m~(~) r~,(t) m~ II
N
0_o(~) f
R Re l
T
area of solar energy collector, m'area of hot water storage tank, m : specific heat of water, J/kg C diameter of tube, m collector efficiency factor acceleration due to gravity, m/s 2 height of storage tank from collector inlet, m height of tank bottom from collector inlet, m height of tank water from collector outlet, m height of collector outlet from top absorber's water level, m height of control valve from collector outlet, m height of tank bottom from collector outlet, m height of tank bottom from ground, m height of collector inlet from ground, m header diameter, m distance between two headers, m m height of control valve (or tank top) from ground, m m outer diameter of tube, m m solar intensity, W / m ~ length of flow channels, m mass flow rate in the system, kg,'s withdrawal flow rate of hot water, kg/s mass flow rate of water in the (collector + storage tank) system, kg number of bends (curves etc) number of lubes useful energy collected from system, W ' h radius of tube, m radius of header tubes, m Reynolds n umber time interval, h temperature, C
e~
E =
~' e~ .= p) ~"
.~ .?.
"~
[...
e. ~ .~.
E
e. E -~
...~
~'-
~ ~.,~ ~ ~ ~
_~ ~" ~2 ~
~
~
~
i
~
i
27.6 28.1 28.63 28.78 30.61 31.23 31.70 32.03 32.13 32.61 32.64 32.84 32.80 32.40 32.10
9 a.m. 9.30 10.0 10.30 11.0 11.30 12.0 12.30 13.00 13.30 14.0 14.30 15.0 15.30 16.0
26.8 27.7 28.4 29.1 29.9 31.l 32.5 33.2 34.3 35.5 36.1 35.9 33.1 31.9 29.7
71,(t) (C)
273.1 432.9 670.33 782.47 812.45 850.92 905.51 891.73 910.88 785.58 772.01 624.118 524.0 432 1 387.0
IM) (Win:) 63.20 78.90 90.50 95.60 95.95 96.20 96.10 96.30 96.40 96.30 94.30 92.70 87.30 68.20 57.(!
Experimental 61.915 78.621 91.134 96.891 96.986 96.999 97.329 97.4216 97.5973 97.5032 96.9532 94.932 88.892 67.982 56.437
-Theoretical
7~,(1)
0.50 2.10 3.54 4.20 4.95 5.50 6.0 6.13 5.75 4.82 4.65 4.52 4.10 2.93 2. I7
Experimental 0.435 2.203 3.571 4.352 5.029 5.718 6.097 6.246 5.749 4.874 4.693 4.5252 4.0998 2.9567 2.189
Theoretical
rh~(t) (kg/~h)
35.60 50.70 60.90 64.90 64.35 62.93 62.75 62.85 62.81 62.50 60.13 58.49 53.11 34.183 23.9
Expcrimental
Ttz,(t)
34.315 50.421 61.534 65.891 65.386 63.729 63.979 63.912 64.007 63.703 62.783 60.722 55.702 34.483 22.337
Thcoretical
Tt~(l) Q,(t) 4[.535 248.430 503.034 633.080 743.242 807.60 878.50 898.9645 842.70 702.917 652.4105 616.8745 508.0857 345.180 121.0136
(W/~h) 0.05855 0.24373 0.49352 0.46075 0.50475 0.53391 0.57541 0.59016 0.5800 0.50787 0.498634 0.500221 0.504652 0.321313 0.255602
Efficiency qh
((7)
(C)
27.61t 28.20 29.6 31.0 31.6 33.27 33.45 33.45 33.59 33.80 34.17 34.2J 34.19 33.8{I 33.1
9 a.m. t~.30 10.0 lu.30 ll.0 11.30 12.11 I2,30 l 3.00 13.30 14.0 14.30 ! 5.i/ [ 5.?0 lo.0
21.80 22.60 23.50 24.91i 26.10 27.10 28.5O 29.0 "~ "~ ~)..~ 29.5 .:9.6~ ~'~ _"9 .(~ 29.70 29.85 29.95
"l~,(t)
T,~(t)
Time (h)
375.'~0 539.30 637.811 627.1t 799.73 807.80 807.811 805.95 768.67 699.7/) 698.7!) 639.7 532.7 387.3 25{}.{}
~W m-')
IM) 64.0 72. l 76.5 79.8 82.5 82.9 83.5 83.3 83.0 82.0 82.0 79.8 77.5 71.3 55.5
l~xperimental
.
.
. 61.30 72.90 76.70 80.10 82.80 83.04 83.55 83.45 83.59 82.10 82. I 0 78.8 77.7 71.8 53.9
Theoretical
Tr,,(t) (C)
. 1.0 3.5 5.0 6.5 8.5 9.2 9.5 9.3 8.8 7.0 7.0 6.2 5.7 4.7 2.5
1.4 3.6 5.09 6.53 8.62 9.0 9.5 9.43 9.04 7.1 7.0 6.37 6.0 4.8 2.9
Theoretical
22.4
36.40 43.90 46.9 48.8 50.9 49.63 50.15 49.85 49.41 48.20 47.83 45.59 43.3 I 32.5
Experimental
33.70 44.70 47.10 50.10 51.20 49.74 50.25 50.0 50.0 49.10 47.93 44.59 43.47 38.0 22.0
Theoretical
(C)
Experimental
.
Tfo(t)- Tli(t)
ti~c(t) (kg '~h)
169.867 353.520 547.167 740.133 1009.517 1065.390 1111.6583 1081.7368 1014.552 960.40 781.222 659.535 576.023 411.25 t30.67
(W/h)
Qu(t)
0.55674
1/day
0.23948 0.351736 0.453914 0.538659 0.685580 0.704860 0.728125 0.71015 0.69835 0.69390 0.59075 0.5455065 0.57213 0.56182 0.276
Efficiency qh
T:~b[c ~ Thc~'mv,~.~pi~v;nic evin}:le p;~ss {non p,'essurizcd) domestic solar water heating syslcm using parallel tube absorber and copper lins (A~ = 1.89 m'-)
"Fdt) (C)
Time (h)
Table 2. Thermos 5 phonic single pass domestic solar water heating system using meander tube absorber and aluminum fins (A~ = 1.89 m 2) of pressurized type
27.6 28.10 28.63 28.78 30.61 31.23 31.70 32.(13 32.13 32.6l 32.64 32.64 32.80 32.40 32.10
9 a.m. 9.30 10.0 10.3(I ll.0 I 1.30 12.0 12.30 13.00 13.30 14.(t 14.30 [5.0 15.30 16.0
26.8 27.70 28.4 29.1 29.9 31.1 32.5 33.2 34,3 35.5 36.1 35.9 33.1 31.9 29.7
71,(z (C)
273.1 432.90 67(/.33 782.47 812.45 850.92 905.51 891.73 910.88 785.58 772.01 624.08 524.0 432. l 387.6
l~(z) /W/m:) 61.8 70.90 74.80 77.4 80.6 81.3 82.0 82.30 82.5 82.6 82.1 79.0 76.1 70.1 55.0
Experimental 59.86 70.15 75.10 77.34 81.05 81.40 82.5 82.9 83.13 83.31 82.14 79.05 76.21 69.8 53.9
Theoretical 1.50 2.90 4.7 5.9 7.8 9.1 9.6 9.3 8,8 8.1 7.4 6.1 5.0 3.7 1.76
Experimental 1.39 2.98 4.71 6.0 8.0 9.05 9.6 9.4 8.9 8.09 7.4 6.2 5.15 3.69 1.78
Theoretical
#~3t) kg'~h)
33.20 42.80 46.17 48.62 49.99 50.07 50.30 50.27 50.37 49.99 49.46 46.16 43.3 37.7 22.9
Experimental 32.06 42.05 46.47 48.56 50.44 50.17 50.80 50.87 51.0 50.7 44.5 46.21 43.41 37.4 24.2
Theoretical
1],,(0 - T~(t) (C)
119.0 289.613 506.331 669.335 909.818 1063.153 1126.72 1090.86 1034.264 944.811 900.172 657.010 505.167 325.477 94.040
Q~(t) (W/~h) (Experimental)
0.23064 0.35397 0.399654 0.45260 0.59250 0.661067 0.658356 0.6473 0.60008 0.63633 0.61695 0.55708 0.51008 0.39864 0.1285153
Efficiency qh
I'~M) (C)
21.0 24.0 28.0 32.0 32.5 34.5 35.5 35.0 33.5 31.0
Time (h)
9 a.m. 10.0 I 1.0 12.0 13.0 14.0 15.0 16.(1 17.0 18.0
21.7 23.4 26.(/5 28.40 29.32 29.6 29.8 29.9 28.75 27.00
li~(t) ((') 431.0 534.5 674.5 758.5 763.75 692.25 387.25 182.0 0.0 0.0
l~(t) (W,m:l 45.0 65.0 71.0 76.0 77.0 74.9 67.0 55.0 50.0 49.5
Experimental
T,,,(1) C)
46.0 65.5 72.0 75.9 78. l 74.9 66.1 54. I 50.1 49.5
. Theoretical
.
22.0 29.0 33.0 38.(I 42.0 46.0 48.0 49.0 50.0 49.5
. l-xpcrin3enlal
.
T,,,(t) (C)
22.1 29.1 34.1 39.1 42.9 47.3 49.8 49.5 50.0 49.5
. Theoretical
.
23.0 34.0 38.0 38.0 35.0 28.9 19.0 6.0 0.0 0.0
. Experimental
24.0 34.9 37.9 36.8 35.2 27.6 17.3 4.6 0.0 0.0
Theoretical
T,,,(1) T,,,(0 (C)
Table 5. Thermosyphonic mullipass domestic solar ~ater heating system (ftv]rth) without rc~crsc 11o~ ~sing copper fins absorber (parallel tubes) in closed loop cycle
T,,(z) (C)
imp, (h)
7~,~(0 ((7')
F;tblc 4 l'hermosyphonic single pass (non-pressurizcdl domestic ,tHat walcr heating s',~,lcm using2',parallel tube absorber and aluminuln lins (A~ = 1.89 m e)
~
2-
©
"O
g
21.0 24.0 28.0 32.0 32.5 34.5 35.5 35.0 33.5 31.0
9 a.m. 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0
21.7 23.42 26.05 28.40 29.375 29.6 29.8 29.9 28.75 27.0
Ta(t) (°C) 431.0 534.5 674.5 758.5 763.75 692.75 560.0 385.25 182.0 0.0
It(t) ( W / m 2) 41.0 53.5 65.0 68.0 65.0 61.5 55.5 48.0 45.0 44.0
Experimental 40.5 53.1 64.9 69.1 66.5 61.4 54.8 48.5 44.8 44.0
Theoretical 21.0 27.0 30.0 33.5 36.0 40.0 42.0 43.0 43.5 44.0
Experimental
(of)
Tin(t)
21.0 26.9 30.1 34.0 35.9 40.4 41.8 42.9 43.3 44.0
Theoretical 20.0 26.5 35.0 34.5 29.0 21.5 13.5 5.0 2.5 0.0
Experimental
(of)
20.5 26.2 34.8 35.1 30.6 21.0 13.0 4.6 1.5 0.0
Theoretical
Tro(t) -- Tin(t)
Tn(t) CC)
21.0 24.0 28.0 32.0 32.5 34.5 35.5 35.0 33.5 31.5
Time (h)
9 a.m. 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0
21.7 23.4 26.05 28.40 29.32 29.6 29.8 29.9 28.75 27.0
Ta(t ) (~'C) 431.0 534.5 674.5 758.5 763.75 692.75 560.5 387.25 182.0 0.0
I~(t) (W/m 2) 65.0 78.5 91.5 96.0 97.5 98.0 91.5 80.0 57.5 50.0
Experimental
Cc)
Tfo(t)
64.5 78.5 92.0 95.9 97.9 98.5 90.8 80.5 56.9 49.9
Theoretical
22.0 29.0 33.0 38.0 43.0 47.0 48.0 49.0 49.5 49.4
Experimental
(oc)
Tin(t)
22.1 28.9 33.5 37.9 43.2 46.9 48.1 49.0 49.6 49.5
Theoretical
43.0 49.5 58.5 58.0 54.5 51.0 43.5 31.0 8.0 0.6
Experimental
(of)
42.4 49.6 58.5 58.0 54.7 51.6 42.7 31.5 7.3 0.4
Theoretical
Tro(t) -- Tn(t)
Table 7. Thermosyphonic domestic multipass solar water heating system without reverse flow using meander tube absorber (in closed loop cycles) with no water withdrawal
Tci(t) (°C)
Time (h)
(°c)
Tfo(t)
Table 6. Thermosyphonic multipass domestic solar water-heating system (fifth) without reverse flow using parallel tube absorber a l u m i n i u m fins in the closed loop cycle
>
bo
(C)
(~C)
27.60 26.20 27.1 29.1 30.9 33.6 34.3 35.0 35.6 36.1 35.8 35.4 35.0 34.9 34.1 33.5 33.1 32.9 32.5 32.2 31.8 31.0
9 a.m. 9.30 10.00 10.30 I 1.0 11.30 12.00 12.30 13.0 13.30 14.0 14.30 15.0 15.30 t 6.0 16.30 17.0 17.30 18.0 18.30 19.0 t9.30
26.80 25.6 26.5 27.2 28.0 28.5 29.2 29.6 30.1 30.4 30.8 31.0 31.5 31.9 32.2 32.4 32.5 32.(/ 31.7 33.14 30.9 30.1
T.(t)
T~(t)
Time (h) 273.10 350.0 444.0 505.0 638.0 715.0 805.0 925.0 958.0 943.0 932.0 885.0 885.0 820.0 809.0 641.0 253.0
(W/n121
It(t)
--
65.10 71.40 91.80 93.41 95.05 96.1 96.5 94.0 93.2 91.8 90.1 88.7 86.8 84.7 80.2 70.0 60.0
(~'C)
T~(t) 25.20 25.9 26.9 28.4 30.1 33.6 35.7 38.0 40.2 42.4 42.4 44.3 46.1 47.7 49.2 50.6 51.8 51.2 50.7 50.2 49.7 49.2
Tin(t) (~C) O.550 45.5 64.9 65.01 64.95 64.30 62.9 58.3 54.8 51.6 47.7 44.7 40.7 37.0 31.0 19.4 8.2
ATc(t) (~C) O.570 0.70 1.0 1.5 1.7 t .7 1.8 2.1 2.3 2.2 2.2 1.9 1.8 1.6 1.5 1.4 1.2 0.6 -0.5 -0.5 0.5 -0.5
ATm(t) ('C) 0.00194 0.0010256 0.001284 0.001284 0.001454 0.001469 0.00159 0.0020 0.00233 0.00237 0.00256 0.00236 0.002457 0.00240 0.003276 0.00481 l --
n'*c(t) (kg/s) 46.93 196.0 280.0 420.0 476.0 476.0 504.0 588.0 644.0 616.0 616.0 532.0 504.0 448.0 420.0 392.0 336.0
Q~(t)
0.09 0.29630 0.33370 0.440 0.39475 0.35224 0.331263 0.336336 0.3557 0.34563 0.34970 0.31806 0.3119 0.28907 0.2747 0.32357 --
rlh
Efficiency
Table 8. Thermosyphonic solar ~atc~ heating system of pressurized type using a rneandcr tube absorber (A~ = 1.89 m 2) connected with a hot water storage tank of capacity of 120 1 in closed loop cycle
,.~,a
0~
0
o
,..q
g
384
R. S. MISHRA T~,(t) ambient temperature, °C T~(t) temperature of cold water in the collector inlet in single pass system, ' C T,-o(t) temperature of hot water at collector outlet, ' C Tin(t) mean temperature of the system, C fl coefficient of volumetric thermal expansion, C i 0 collector inclination angle, ). triction factor thermal viscosity of water, N/s m-' v kinematic viscosity of water, m:/s coefficient of flow-resistance p,,(t) density of water, kg/m ~ p,(t) density of water at zero degree centigrade, kg/m:~ pit) density of water at collector inleL kg/m 3 p~,(t) density of water at collector outlet, kg/m -~ pro(t) density of water at mean temperature, kg/m 3 (r:~)~ effective transmitivity absorptivity products
13.
14.
15. 16. 17. 18.
19. 20. 21.
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22. 23. 24. 25.
26.
27.
28.
29.
30.
31.
32.
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