An overview of design methods for solar water heating systems

An overview of design methods for solar water heating systems

S , k t r ,f~ tf'~t~l Technoh~g" Vol. 2. N o 2. pp. IOI 112, 19X5 Printed in Grcat Britain 0741-983X/~5 $ 3 . 0 0 + , 0 0 Pergamon Press Ltd. AN OVE...

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S , k t r ,f~ tf'~t~l Technoh~g" Vol. 2. N o 2. pp. IOI 112, 19X5 Printed in Grcat Britain

0741-983X/~5 $ 3 . 0 0 + , 0 0 Pergamon Press Ltd.

AN OVERVIEW OF DESIGN METHODS FOR SOLAR WATER HEATING SYSTEMS H. P. G^RG Centre for Energy Studies, Indian Institute of Technology Hauz Khas, New Delhi 110 016, India (Received 20 May 1984; accepted 22 June 1984)

AlJstraet--The paper deals with the parameters which govern the relationship between the collector area and the optional economics of the collector. The paper deals also with several d c ~ n methods which require a simple computer or a hand-held programmable calculator or other simplecalculating means.Severale~¢ted methods are described in the text, they are mainly TRNSYS-simulation method, the F-chart method, the SOLCOST method, the SLR method, the SEU method, the GFL method, and the ~ F-dutrt method. The paper gives all the necessary information about each method and compares each method with the other.

INTRODUCTION Several different versions of solar water heaters have been designed and studied over the past 50-60 years by various scientists all over the world, the early work beingcarried out mainly in the United States, Australia, South Africa, Israel and India. The major concern of solar water heater design is the determination of the collector area which optimizes the system from an economic standpoint. This requires knowledge of the relationship between system performance, usually characterized by annual solar load fraction and coUector area. Several simulation models, namely by Close [1], Sheridan et aL [2], Butz et aL [31 Lof and Tybout [4], Buc~herg and Roulet [5], Brinkworth [6], etc., have developed quasi-steady state model of so[ar systems. These are capable of identifying important parameter trends in solar heating systems for specific designs. The most accurate and sophisticated computer simulation programme is the TRANSYS and was developed at the Solar Energy Labo~tory of Wisconsiw-Madison [7-10]. No doubt, this simulation programme gives good analysis, but it cannot be used as a design tool because of being expensive for optimization problems. A few simulation and design methods for solar systems which require a simple computer or a hand-held programmable calculator are reviewed by Close [I I]. Some of these methods will be described here.

components may be modeled mathematically by sets of differential and/or algebraic equations. The resulting mathematical models for these subsystem components represent the subroutines in the TRANSYS-program. The TRANSYS-program comprises an executive program which handled input and output, calculation procedures and other"house-keeping" tasks, and a set of subroutines each describing solar system components. Systems can be simulated by replacing each component in a real system by FORTRAN subroutine in the TRANSYS simulation program. Here the timedependent forcing functions such as solar insolation, ambient temperature, wind speed, etc. are interpreted as output of specialized system components. Components and combinations of c o m p o n e n t s available in the TRANSYS h'brary as on 1976 inchzde collection, differential controller, pump, liquid storage tank, heat exchanger, auxiliary heater space load and air conditioner, three stage room thermostat, card reader, packed bed energy storage tank, space heating load, time-dependent forcing functions, algebraic operations, solar radiation processor, wall, roof, heat pump, integrator, plotter, etc. These subroutines may be fairly complex, as in the ~ for the muitinode

~LOAO STORAGETANK

TRANSYS-SIMULATION METHOD In the TRANSYS-program, a modular approach is used. A simplified solar water heating system is schematically shown in Fig. 1. Each of these subsystem I01

I

~

WATERSUPPLY

Fig. I. A typlr.~l solar water heating system.

102

tl. TI

r;~

P. GAR(;

TO I T 'IvlOOE

TLY PC ETIOR I CO LE

111 TO

rh

t

O'

Cp ot UL

,T

Ti

m

To l 1

TYPE ~

Ou

I"--<

V'

",

~L

Fig. 2. Information flow diagram for a collector.

tJ

fQ

storage tank, or they may be very simple, which is the case for a constant flow rate pump. The next step is the construction of the system information flow diagram. An information flow diagram for the collector model is shown in Fig. 2. An information flow diagram of a solar water heating system is shown in Fig. 3. The user can have numerous numerical output from TRANSYS which include auxiliary heating requirement, solar fraction, and many .other component performance

I

I

I

I

I [

I T~,.

I

UNIT /-.3 TYPE 24

<,Ep [ I

INTEGRATOR]

IT° IO'u

indices. These studies can be useful for economic

analysis and feasibifity studies for a specific system at a specific location. Such detailed simulation programs like TRANSY.S are of great significance since it is used for the generation of generalised performance correlations. Several validation studies have been conducted since 1976 and are described in 1,'12] and 1,'13]. System simulations and experiments have been compared for several periods of operation of CSU House I. The agreement in the experimental and predicted collector output was within 5~/~ The heat transferred across the air heater and that delivered by the auxiliary agree within 6~/~ F r o m these studies it is concluded that the TRANSYS program provides a valid tool for the analysis of solar systems. Simulation studies have been conducted recently by Buckles and Kelin 1,,14]on four generic types of domestic solar water heaters. The range of design parameters studied is shown in Table 1. The

I AU~IARY

.... [ ON'T

TYPEpRINTER. 25

To

I--4P" T

J

I,INTERvAL

Ou OAUX

Fig. 3. Information flow diagram for a solar water heater without storage.

results of annual solar fraction are shown in Table 2. No doubt the computer simulation is an important tool for research and development, but this caanot be used as a design tool for solar energy heating applications because of the facilities and e x ~ s e required, the lack of necessary meteorological data in many locations, and the expenses and time involved. In spite of these problems, TRANSYS is presently the only completely reliable method available for designing solar systems.

Table 1. Range of design parameters used in the simulation studies (from Buckles and Klein [14]) Collector area Number of tanks Heat exchanger--type --effectiveness Tank insulation conductance Tank height to diameter ratio Tempering valve Tank volume (total) 1 tank 2 tank

: 2.88, 4.32, 5.76 m 2 : I or 2 : Internal or external coil : 0.25-1.00 : 0.0-1.67 W m-2°C-t : 1.75 : Enabled or disabled : 300-4501 : 450-600 1

103

An overview of design methods for solar water heating systems Table 2. Annual solar fraction for four domestic solar water heaters (from Buckles and Klein [14]) Location Madison Charleston Albuquerque

Collection area (m 2)

1 tank Ext-XH

2 tank Ext-XH

1 tank lnt-XH

2 tank Int-XH

2-88 4-32 5.76 2-88

0-47 0-63 0-73 0-59

0-43 0-59 069 0-54

0-42 0-59 0.70 0-52

0-38 0-55 0-66 0-49

4-32

0-79

0-74

0-73

0-69

5-76 2-88 4.32 5.76

0-88 0.75 0-92 0-96

0-85 0-69 0-89 0-95

0-85 0-67 0.89 0.95

0-82 0-62 0-85 0-93

THE F-CHART METHOD The F-chart method is a designer-oriented procedure, which has been derived from TRANSYS and can be used for estimating the fraction of total heating load that can be supplied by solar energy for a given solar heating system. The F-chart method is spedficaily developed for domestic space heating and service hot water water systems and is completely described by Beckman et al. [15] and later discussed in several papers [16, 17]. The space heating systems used in this study using fiquid and air as the medium are schematically shown in Figs. 4 and 5 respectively. The schematic diagram of the standard domestic solar water heater is shown in Fig. 6. F-charts are available for both water and air based heating systems and they differ somewhat !"!5]. The F-chart for a system using liquid heat transfer and storage medium is shown in Fig. 7. F-charts are developed for standard storage capacities of liquid or air. For hot water heating

systems, the F-charts developed and ~ above (Fig. 7) can be used to predict the performance. The F-chart program represents a correlation between the monthly solar fraetion, f, provided by a solar system and the following two dimensionless parameters that represent, respectively, the ratio between the collector losses and the load, X, and the collector gains and the load, Y.These two dimensionless parameters are given as L

and r

=

Fx(~)Rr&N

and the monthly solar fraction

f =L-E L

RELIEF

HOUSE

, HEAT EXCHANGER

..~

WATER SUPPLY HEAT EXCHANGER

Fig. 4. Schematic diagram of a liquid based solar heating system.

104

H. P.

(;Mto

W,~,R M AIR

TO HOUSE

HEAT

~

EXCHANC~ER

IANK ' (I~EA~O IA IP

DAMPER

FPI~LE

MAINS SUPPLY

IIREIURN AIR FROM H O U S E

Fig. 5. Schematic diagram of a solar air heating system.

I"'1 R E L I E F VALVE P 10 I A P S

COLLECIOR STORAGE H E A l EXCHANGER

SUPPEY

Fig. 6. Schematic diagram of a domestic solar water heating system.

where F k = collector heat exchanger efficiency factor;

collector overall heat loss coefficient (W m-2°C-~); collector area (m2); /Vr= monthly average daily radiation on plane of collector (J m - 2); g number of days in month ; L = monthly heating load (J); 7~, = reference temperature taken as 100°C ; monthly average ambient temperature (°C); Ta AI = number of seconds in month(s); (~) = monthly average transmittance absorptance product for the collector. U c ---

~1

I

Liquid sysle'ms

!

Jr=0.9 I I

-~{~ 2

- -

0.7

Ac

(3

4

8

IZ

X~ IR~IcolleciorlOSS HeOlir~gIOGS

IG

Fig. 7. The F-chart for liquid systems. (F'rom Beckman el al.

[IS].)

An overviewof design methods for solar water heating systcms

105

Table 3. Comparison of F-chart result with simulation results from three cities (from Skanvedt [19])

Collector area (m2)

Location

Solar load fraction (%) F-chart Simulation

~/oDeviation F-chart--Sim x tO0 Sire

Direct system FsJFR= 1-0 Denver

3-72 5-58 7.44 3-72 5-58 7-44 3.72 5"58 7-44

Los Angeles Boston

60 79 92 67 85 94 45 59 70

59 74 83 66 81 87 48 59 66

Average deviation

+ I-7 + 6.8 + 10-8 + 1.5 + 4-9 + 8-0 -6-3 0 +6-t + 3-7

Indirect system F~a/Fe= 0-93 Denver

3-72 5-58 7-44 3.72 5-58 7-44 3-72

Los Angeles Boston

57 76 89 69 82

80

92

87

42

46

5.58

57

7-44

67

56 64

Average deviation

X = F'aULA~(II'6+ I,STw+3-96T.- 2-32T,)At L



and y = Fa(£¢)RrA~N. L

The above two equations can be put in a more useful form as follows:

Fa

Ac

X = Fa(U~-F~a)At(II'6+I'gT,+3.86T,-2.32To)--~ and (~).

+ 1-8 + 7-0 + 12-7 - 1-5 + 2-5 + 5-7 -- 8-7 + 1-8 +4.7 +

The modified dimensionless parameters X and Y for service hot water system are given as:

Y = F,(r~).

56 7! 79 65

L

The terms (RmUD and Fa(ra). can be obtained from the slope and intercept of the standard test curve of the

2-9

collector at the desired flow rate. (F'a/Fa} is the heat exchanger penalty factor. The term (f,,)/(v,), can be approximately taken as 0.96 for one cover system and 0.94 for two cover systems. H r is determined from the procedure discussed by Garg [18]. Thus all the values in X and Yare determined. Having known X and Y,the value o f f is read from Fig. 7. The results obtained from the F-charts method and simulationare compared for a variety of systems and locations (Tables 3 and4)and the agreement has been generally very good [19]. Thus, the F-chart design method can be effectively applied for the long-term thermal performance of solar systems. With this method the effects of design parameters such as collector area, storage capacity, fluid flow rate, controls, etc. on the thermal performance can be estimated. An example ofdrect of collector area on the annual solar load fraction is shown in Fig. 8. This can help in designing a suitable collector to make the thermal system cost effective. However, the F-chart has its own limitations, like: (i) F-chart for water heating assumes a constant daily water usage distribution;

106

H.

P. G A R G

Table 4. Comparison of F-chart results with simulation results for three cities (F-chart modified such that maximum monthly solar fraction = 85%)(from Skartvedt [19]) Deviation Collector area (m 2)

Location

Solar load fraction (~) F-chart Simulation Direct system

3-72 5-58 7.44 3-72 5-58 7-44 3.72 5-58 7-44

Denver Los Angeles Boston

60 78 83 67 81 84 45 59 68

F'dFs

F-chart--Sire × 100 Sim

= I

59 74 83 66 81 87 38 59 66

+ l-7 + 5.4 0 + 1-5 0 - 3.5 -63 0 + 3-0 +0-2

Average deviation Indirect system F'dFa = 0-93 Denver

3-72 5-58 7-44 3-72 5-58 7-44 3-72 5'58 7'44

Los Angeles Boston

57 76 82 64 80 83 42 57 66

56 7l 79 65 80 78 46 56 64

+ 1-8 + 7.0 + 3"8 - 1-5 0 -4.6 - 8.7 + 1.8 + 3"1 +0.5

Average deviation

(ii) in water heating systems, it has been assumed that the energy in water above the set temperature is not useful; (iii) it is also assumed that there is no degradation in the system and that there are no leaks in the system; (iv) other assumptions like the system is well built, flow distribution is uniform, and the system configuration is similar to the one for which the Fcharts are prepared should also be valid;

l.O

t

I .....

|

I

J 25

I 50

I 75

t 100

1

08

o= O-E O-L

0.2 0

.J 125

150

Collector or¢o. m 2

Fig. 8. Annual solar load fraction vs collector area.

(v) the conditions ofweU insulated solar preheat tank are assumed and losses from the auxiliary tank are not considered in drawing the F-charts. SOLCOST

MZ-'rUOD

[2O]

As compared to the T R A N S Y S program and the Fchart method, S O L C O S T can be used to evaluate several types of solar systems, including (a) space and domestic water heating systems with air or liquid collectors, (b) absorption cycle air conditioning systems, and (c) solar-assisted heat pump system. It lies between the F-chart and T R A N S Y S programs in terms of operational costs and ease of utilization. In the S O L C O S T method the input data requirements have been simplified. A simplified S O L C O S T flow chart is shown [20] in Fig. 9. Three types of analysis are coupled together in S O L C O S T to evaluate the active solar collection system: (i) the solar collector/system performance analysis, (ii) a life cycle cost analysis, and (iii) a building heating]cooling analysis. A list of inputs [20] required by the SO L C O S T user is given i n T a b l e 5. I'or any given solar system, the S O L C O S T can

107

An overviewofdesign methods for solar water heating systems

j

INPUT 1 ROUTINE _•

f of

FRACTION LOAD SUPPLIED Bv SOLAR

I

SO',AR I FRACTION [ ~ /..~I-,

COLLECTORAREA ,.de C~CLECOST I

rx~u~ tOAD,, I+

ANALVe~SFORSOU~

I/

¥. soL.~ ~SO~T~I

I

FORCOLLECTOR TILT ANGLES

] ANDUSA~_ES(X~ COLLECTOR PERF. ENERGyPER

m2 I

O*

ANNUAL SAVINGS

1

S'}E STORAGE I FOR COST

COLLECTOR AREA

OPTIMUM AREA

OUTPUT CASH F"L(~ RATE OF'RETURN [ PAYBACK

CASH FLOW

$ -

|

BAts

YEARS

Fig. 9. SOLCOST flow chart (from Connolly et al. [20]).

determine the .optimum collector area required, load supplied by the optimum collector area, and the

payback period. The typical SOLCOST outputs are shown in Fig. 9. Results obtained from SOLCOST are compared with F-chart for several locations and solar

systems. A large difference between the two methods was observed which may range from 0 to 20% depending on the location The results obtained from annual solar load fraction by the two methods are compared in Fig. 10.

Table 5. Summary ofinpnts for SOLC~ST program (from Connoltey et aL [20]) Mandatory input* Job site Solar collector type Heating/coolingsystem type Henting/coolingloads, Monthly Buildingdescription? Fuel/utility types for reference HVAC s y s t e m solar/aux system Fuel/utility current p r i c e s Solar system Fixed initial cost Installed cost per unit area Reference HVAC system cost Interest rate and loan term Tax scenario flag Homeowner Business Non-profit

Defaulted input

V*alue

Input from SOLCOST data banks

Collector area limit Collector a,~auth angle

l0 s 0

Percent of poaibk lamlhi~ (by month) Site latitude and dennmss no.

L/quid storage size 0 m- z)

73.3

Collector efficiency data

System life(years) Building usage (day per week) Auxiliary furnace efficiency Salvage value fraction Maintenance cost ($ per year}~

20 7 0-7 0-1 80

Collector inlest temperature (by month)

Investment credit fraction First year depreciation fraction Down payment fraction

0-1

Depreciation method Depredation period (years) Property tax fraction

S.L. 10 0

0-2 0-1

* All default and data bank inputs may b¢ overridden by Direct User InpuL t Buildingdescription required if SOLCOST loads routine used. For residential users only.

Solar system etliciency (by month) Reference system eff¢iemcy(by month) Collector tilt angles Min. daily ambient temperatures Max. daily ambient temperatures Energy eost schedules and escalation rates Degree days per month Thermal properties of typical construction materials, windows ASHRAE STD 90-75 energy conservation spec for loads calculation

108

H.

P. GAR(;

M,'~DISO N WISCONSIN TILl ANGLE 1.3" 2 HOUSE UA : t,,.,69 • 10 Kcol I DD

1Of-

HOT WATER = )63 htr¢'i ; day 2 GLASS COtLECTOR BECKt4/,N & DUFFLE - CHART METHOD

05

I

I

t

20

40

60

i 80

I

100

!

120

I

I

It.0

160

k

180

COLLECTOR AREA(m2)

Fig. 10. Comparison of SOLCOST with F-chart predictions (from Connolly et al. [20]).

SLR-METHOD

This method is slightly simpler and gives comparable results on an annual basis compared to the wellrecognised F-chart method. This method has been used for predicting collector area for 85 U.S. cities using monthly climatic data. Some calculations of monthly solar load fraction using the SLR method for a solar space heating system using a double-glazed flat plate collector in Bismarck, North Dakota (U.S.A.) have been made by Kreith and Kreider [22]. The results of solar load fraction computed by the SLR method and the F-chart method are computed and results compared in Table 6. It is observed from this table that during the period of large heating demands, the SLR method consistently underpredicts the F-

chart. However, the comments on the accuracy by SLR and F-charts cannot be made since either of these methods arc not applied to large numbers of actual buildings. SEU METHOD The SEU method is a rigorous design method for solar heating systems based on a non-dimensional analysis developed by Kenna [23]. This method has been used successfully for the derivation of modified mathematical expression for monthly solar load fraction, f, given by f=

aM (b + MK*/R)

for

M<3,

Table 6. Comparison of F-chart and SLR values of monthly solar load fraction (from Kreith and Kreider [22])

Month

Monthly energy demand L (MM keal!

Average monthly solar radiation (kcal m -z day -t)

SLR

f(SLR)

f(e-ch,m

Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

6-65 5-45 4-67 2-49 1.28 0-46 0-07 0.13 0.95 2.13 4.09 5.78

4085 4840 4069 4384 4357 4262 4639 4644 4669 4671 3741 3445

1-15 1-50 1-95 3.10 5-66 5-66 5-66 5-66 5-66 4-10 1.66 1-1 I

0-43 0-52 0-63 0-83 1-00 14)0 14)0 1-00 1-00 0-92 0-57 0-41

0-46 0-00 0-73 0-94 1.00 1-00 1-00 1-00 1-00 1430 0-61 0-43

0-1
An overviewof design methods for solar water heating systems

109

where M = the collector area parameter and is the ratio of energy available to energy demand L ,,I~M L K = the collector type parameter and is the ratio of collector losses to peak rate of energy gain =

UL(T,,- T,.)/t~

for

(0"69 + O.87K) i A, = the normalised area =

\

C L O U D LOOP

01

.50

,o

,.o5

~--..~..W~--R. I.o •30

K+CM

-----

~R=

60

R = the store sizing parameter and is the ratio of useful energy contents of the store to the energy demand = M,C,(K,- Tp/t, K K* for K <0"65 (1 +O"11K)

~

R

- 2-0

K > O"65

FiZ'~o&

1~- = rr+ U L ( T . - T~) - ( ~ ' T = peak power available U~. = the effective normalized loss coefficient = ZUJ~ z = [(mc,).M(mc,l]x., 1 -- K o K t K 3 [ I -- et(a~C~(mCw)]

.10

•oo 04

I

o.z

I

o.s

I

Io

I

2.o

I

s.o

I

Io-o

,

I

soo looo

m~.m('1 R

Fig. I 1. Performance of solar heating systems (from Kenna [Z3]~

and and Z' -- correlation factor for heat loss coefficient 1 -- K o K t K 2

K1(I - Ko)

0-136R c = (1 + 1-23R)" For an open loop system with a domestic draw-off pattern:

where g o -- exp [ - u , ,4./(~=,)] K t = exp [ - - UtAt/(a~Cv) ]

1-6 am

K2 - exp F- u,A2/(,~c,)].

1-39 b~

(1 + 1-74R)'

(I + 1.13R)'

and Here At and A2 are the surface area of the inlet and outlet pipes and Ut and U 2 are the heat loss coefficient with a heat exchanger effectiveness e. H = the total energy available and q0 -- the collector efficiency at zero heat loss Thi, TI, = high temperature of the store and low temperature at which the collector will operate, respectively. The coefficients, a, b, and c are dependent on R. For the closed loop system, these are given as: a

!-67 (I + 1-74R)'

1-13 b= (1 +O.55R)

0-063R C=

(1 + O.24R)"

A plot between the monthly solar load fraction f and the parameters, M, K and R is shown in Fig. 11. Kenna [23] has shown the ufifity of the SEU method for domestic water heatiag and space heating systems. Calculations of monthly solar load fraction, f, for a few domestic solar water heaters are made and the results obtained are very encouraging. GFL METHOD Another very simple and systematic method for designing solar space heating and domestic hot water systems has been developed by Lameito and Bendt

It. P. GARG

110

Table 7. G F L coefficients for solar heating systems with air as working fluid (from Lameiro and Bendt [26]) Place

A

B

Boslon Denver Twin Falls

0"1211 E-I 0-2468 E-I ffl678 E-I

C

D

E

-0-9887 E-3 -01134 E-4 -0"1790 E-4 02348 E-5 -0-7770 E-3 -08975 E-5 0"1612E-4 -01010 E-4 -0-1414 E-2 -0-3673 E-4 -04280 E-5 0-2340E-5

F

Lo

0-6620E-6 081123 E-6 0-9722E-6

1IO10 !16-04 120-83

Table 8. GFL coefficientsfor solar heating systems with liquid as working fluid (from Lamerio and Brandt [26]) Place

A

Boston Denver Twin Falls

0.1641 E-I 0.3584 E-I 0.2255 E-I

B

D

E

F

-0-1628 E-2 -0-9557 E-5 -04022 E-4 07730 E-5 --01263 E-2 -0-1264 E-4 -0-6683 E-4 0.1598 E-4 -01688 E-2 -08680 E-5 -0-8209 E-4 08698 E-5

[26] and the same is validiated by making over 1500 side-by-side comparisons with different collector types (air and liquid), different collector design parameters, in different locations and for solar fractions from 0 to 90*/0. The method is in essence a large correlation off-chart runs. With the G F L method, the annual solar load fraction f and the actual annual energy delivered to the load, G, can be calculated in the following steps: Step 1. Calculate the heat removal efficiency factor Fe, absorptivity transmivity product (~-), and overall heat loss coefficient UL. Step 2. Calculate the annual load, L, (GJ y r - t) using the standard procedure and select a suitable collector area Ac. Step 3. Calculate X and Y as follows: X = ---FaUt

C

09990 E-6 02089 E-5 08826 E-6

Step 5. Calculate the annual fraction of load, f, met from solar energy as: f=

1-exp(--RY-SY2).

Step 6. The actual annual energy delivered to the load by the solar energy system is calculated as: G = f L ( G J yr- :). Finally the annual cost savings for fuel per year can be calculated by multiplying G by the axiliary fuel rate. For several identical hours and systems, G F L method was used and the results compared with Fchart. The correlation is shown in Fig. 12. The G F L method was found to be 99% correlated with the Fchart method with maximum RMS error of 2-09"/0from any F-chart results.

8.0 (Wm- z °C - : )

F~(T=) F ~

and

.~

VS. GFL METHODS

0.8

F~(rac) Y = (Fxra) °

----"~Ac(m 2) I._

where the reference load Lo can be read from Table 7 for the given location and (RRx=)o is 0..50 for air collector. Step 4. Calculate R and $ as follows:

S 0.7

0

~0.6 =E 0.5 .?-

,:

R = A+Bx+Cx

z (m -z)

S = D+Ex+Fx

2 (m -4)

and

..-

" IHCLUOE,~tL BUQUEROUE An.a,J~A

-

OOULOE.

LC6 ANGELES

~

-

0.~

~

-"

~K

CI'TY

COLLECIOR AREAS: $ - I 0 0 m 2

0.3



'°'-:

0-2 O.t

where the constants, A, B, C, D, E, F are tabulated location wise for air systems in Table 7 and for liquid systems in Table 8.

0

0

t

0.2

,

I

0.4 f

I

0.6

,

I

0.8

I

10.0

(GFL- M E T H O D )

Fig. 12. Correlation of F-chart and GFL methods. (From Lameiro and Bandt [26].)

An overview of design methods for solar water heating systems THE 0~, F-CHART METHOD As discussed earlier, the main limitation of the Fchart method is that it can he used strictly only with those systems for which it is developed, it cannot b¢ used to determine the performance of solar air conditioning or industrial process heating systems. Klein and Beckman [ 17] have developed a general but simple design method for closed loop solar energy systems for the type shown in Fig. 13, which is based on extensive computer simulation study useful to estimate the long term performance of a variety of solar energy systems in a relatively simpler manner. A critical factor here is that energy is delivered to the load at a temperature T > T,,i .. The ~, F-chart method is applicable to water based systems since the storage tank is assumed filled with liquid. Losses from the tank are also assumed to be zero. For such a system it can be shown that the mean monthly maximum daily energy gain can be given as:

"~W-,-v--1--,

•1.•

/

1.2'

/

x ~ ¢ , m i n ~---



rT.~R.R

where

/,= F.UL(~--/'.) F,ff=) Here rr. . is the ratio of radiation at noon to the daily total radiation and R, is the ratio ofradiation on a tilted surface to that on a horizontal surface at noon.

. . , . , . , . T~'~- ; - 1 " ~ f=09 "

1.c, ~

-

.

Oe

O.6 ~

O5

o~

04

0.1

02

OZ

0

I=

0

1"

I

'

2

~'1

= I

4

'L

I J = l -

6

I , J -

8

I0 X

I * 1 - 1 ,

12

tl

I-

14

I , J

16

18

20

Fig. 14. ~, F-Chart for a storage capacity of 350 ILlm- z°C- '. (From Klein and Beckman [17].)

where

.I

r,.. = 27 Lsin o~,-T~oJ, cos co,J

(~,,=, = A,Fe(f~,)tlr~=~. Here ¢T,u is the monthly average utilizability corresponding to the minimum critical level [¢,min" This maximum tttilizability~ . w can be calculated from the following minimum monthly average critical radiation ratio

III

and ¢0, = sunset hour angle on horizontal surface in degrees. ~=~ can now be calculated from the curves given by Klein [24]. These curves are applicable for a perfectly insulated storage tank and having a fixed capacity for effective collector area (i.e. FaA~). Such curves for two equal values of(Fa,%)equal to 350kJ m - a ° C - t and 700 kJ m - z°C - = for a uniform load distributioa between the hours at 6 a.m. and 6 p.m. and an infinjtdy hurgeload

heat exchanger are shown in Figs. 14 a a d 15 respectively. The ~T,F-chart is used.in the mmm rmmner as the F-chart for the liquid heating systems.

rr.. = rd..[l'070 + 0"025 sin (w=--60)]

t.6 1-~ 1-2

HEAT EXCHANGER

7( S TANK

Fig. 13. Schematic of closed loop heating system.

1-0

~,,ox v

08 o6

0,5

0.6 O.&

--

0.3 0.1 ~

0.2 0

it

i

2

= i

.

i

&

=

I

.

i

6

,

i

.

i

8

= ,

.

i,

I0 X

a

i

= i

12

I

I

* I

14

.

I



16

i

,

I

IB

-

t'-

~0

Fig. 15. ~. F-Chart for a storage capacity ofT00 kJ m - =oC- t. (From Klein and Beckman [17].)

112

It. P. Gt, Rc;

OTHER SIMULATION AND DESIGN METHODS A simple programme, S I M S H A C [27] was developed by Hull (1976). S I M S H A C is also modular and models all subsystem components by systems of first-order ordinary differential equations. Recently Turchan et al. [28] have developed a simple micro computer program to give the public a personalized information service on domestic hot water systems. A simple design method known as the relative area method was developed by a group of scientists [29] of C o l o r a d o State University, U.S.A and is a correlation to resuif~ obtained from the F-chart programme, and, therefore, represents a correlation to a correlation. With this method, one can calculate directly without iteration, the optical collector area based on a life cycle cost analysis, the corresponding solar fraction, and the corresponding life cycle savings of the solar system with respect to a conventional system.

REFERENCES 1. D.J. Close, A design approach for solar processes. Solar Energy 11, 112-122 (1967). 2. N. R. Sheridan, K. J. Bullock and J. A. Duffs, Study of solar processes by analogy computer. Solar Energy11, 6977 (1967). 3. L.W. Butz, W. A. Beckman and J. A. Duffle, Simulation of a solar heating and cooling system. Solar Energy 16,129136 (1974). 4. G. O. G. Lof and R. A. Taybout, A model for optimizing solar heating design. ASME paper 72-WA/Sol-8 (1972). 5. H. Buehberg and J. R. Roulet, Simulation and optimization of solar collection and storage. Solar Energy 12, 31-50(1968). 6. B.J. Brinkworth, Asymptotic behaviour as a guide to the longterm pedormanee of solar water heating systems. Solar Energy 21, 171-175 (1978). 7. S.A. Klein, TRANSYS --A transient simulation program. Solar Energy Laboratory, University of Wisconsin, Madison, Rep. 38 (1973). 8. S.A. Klein, W. A. Beckman and J. A. Duffle, A method of simulation of solar processes and its applications. Solar Energy 17, 29-37 (1975). 9. S.A. Klein, A design procedure for solar heating systems. Ph.D. dissertation, University of Wisconsin, Madison (1976). 10. S.A. Klein, W. A. Beckman and J. A. Dtdlie, TRANSYS-A transient simulation program. AHSRAE Trans. 82, Part I (1976). 1I. D.J. Close, An introduction to solar energy systems and system design. Technical Report No. TR 26, CSIRO Division of Mechanical Engineering, Highatt, Victoria, Australia.

12. J. W. Mitchell, W. A. Beckman and M. J. Pawelski, Comparison of measured and simulated performance for CSU House !. Paper presented at system simulation and economic analysis conference, San Diego, California, June 1978. 13. N. Duong and C. B. Winn, An objective approach to the validation of solar house design programs. SEEX Report, 2524 East Vine Drive, Fort Collins, Colorado, June 1977. 14. W.E. Buckles and S. A. Klein, Analysis ofsolar domestic hot water heaters. Solar Enerqy 25, 417--424 (1980). 15. W.A. Beckman, S. A. Klein and J. A. Dullie, Solar Heating Design by the F-chart Method. Wiley Interseience, New York. 16. S. A. Klein, W. A. Beckman and J. A. Duffle, A design procedure for solar heating systems. Solar Energy 18,113127. 17. S.A. Klein and W. A. Beckman, A general design method for closed-loop solar energy systems. Solar Energy 22, 269-282. 18. H. P. Garg, Treatise on Solar Energy. John Wiley and Sons, New York. 19. G. Skartvedt, Solar energy heating, in Solar Energy Handbook(Edited by J. F. Kreider and F. Kreith), Chapter 11. MacGraw-Hiil, New Delhi (1981). 20. M.Connolly, R.Ciellis, C.Jensenand R. McMordie, Solar heating and cooling computer analysis--A simplified sizing design method for non thermal specialists. Sharing the Sun, Proc. of Joint Conf. of the Am. Sec. of lSES and SolarEnergySociety of Canada, Winnipeg(Canada), 15-20 August 1976, Vol. 10, pp. 220--234 {1976). 21. J.D. Balcomb and J. C. Hedstron, A simplified method for calculating required solar collector array size for space heating. Sharing the Sun, Proc. of Joint Conf. of the Am. Sec.oflSES and Solar EnergySociety of Canada, Winnipeg (Canada), 15-20 August 1976, Vol. 4, pp. 220-234 (1976). 22. F. Kreith and J. F. Kreider, solar water heating systems, in Principles of Solar Engineering. MacGraw-Hill, New York. 23. J. P. Kenna, The SEU design method for solar heating systems. Helios 15, 8-12. 24. S.A. Klein, Calculation of flat plate collector utilizability. Solar Energy 21, 393-402 (1978). 25. B.T.H. Liu and R. C. Jordon, A rational procedure for predicting the longterm average performance of the plate solar energy collectors. Solar Energy 7, 53-74. 26. G. F. Lameiro and P. Bendt, The GFL method for designing solar energy space heating and domestic hot water systems. Pro<:. 1978 meeting of Am. Sec. of ISES, Denver 2, 113-119 (1978). 27. D.E. Hull, Documentation and validation of SIMSHAC. M.S. Thesis, Department of Mechanical Engineering, Colorado State University, U.S.A.. 28. M. P. Turchan, M. Chandrashekar and J. P. Rollefson, A computer assisted solar energy information package. ENERGEX'82, Conf. Proc. Vol. 11/I1,23-29 August 1982, Regina, Canada, pp. 978-982 (1982). 29. C. D. Barley and C. B. Winn, Optimal sizing of solar collectors by the method of relative areas. Solar Energy 2 !, 279-289 (1978).