Solar Energy Vol. 69, No. 5, pp. 377–401, 2000
2000 Elsevier Science Ltd
Pergamon PII: S 0 0 3 8 – 0 9 2 X ( 0 0 ) 0 0 1 0 8 – 0 All rights reserved. Printed in Great Britain
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EXPERIMENTAL AND THEORETICAL EVALUATION OF DYNAMIC TEST
PROCEDURES FOR SOLAR FLAT-PLATE COLLECTORS
J. K. NAYAK* , † and E. H. AMER**
*Department of Mechanical Engineering, IIT, Bombay, Powai, Mumbai 400 076, India
**Department of Mechanical Engineering, Faculty of Engineering, Menoufia University, Menoufia, Egypt
Received 11 November 1999; revised version accepted 12 May 2000
Communicated by BRIAN NORTON
Abstract—This communication presents a critical evaluation of nine dynamic test methods for solar flat-plate
collectors. The theoretical basis, the technique of parameter estimation and the test procedure of each method
have been reviewed and compared. Extensive experimental studies have been carried out under a wide range of
weather and operating conditions. Two commercially available collectors (from two different manufacturers)
have been used in the investigation. The tests were carried out at the same location using a common test-rig,
measuring transducers and controlling and data-acquiring facilities. The characteristic parameters of the
collectors have been obtained on the basis of each procedure and compared with those based on the
steady-state ASHRAE 93-86 standard. Further, for the methods which prescribe similar test sequences, the
collector parameters have been extracted from the same data sets according to their procedures for providing a
direct and very clear comparison between the methods. A sensitivity study has also been carried out in order to
examine the effect of uncertainties in measurements on the values of the estimated parameters from different
methods. Also investigated is the error propagation wherever applicable. Among the methods evaluated, the
new dynamic method (NDM) seems to be quite reliable. The quick dynamic test (QDT) method is the most
simple method and could be adopted by manufacturers as an effective tool for the purpose of quality control of
their products. From the point of view of theoretical completeness, Perers’ method accounts for almost all
effects. 2000 Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION 1981; Emery and Rogers, 1984; BS 6757, 1986;
Wang et al., 1987).
Transient methods for outdoor testing of solar
In addition to these methods, the literature also
flat-plate collectors have attracted the attention of
contains several studies on dynamic modelling of
many investigators during the last two decades.
collectors which are developed either to investi-
Several methods have been reported in the litera-
gate the collector response to transient inputs or
ture. Amer (1998) has classified these methods
predict its performance under varying weather
into the following three broad categories based on
conditions. Among these, only a few studies
their similarities in approach:
(Gicquel, 1979; De Ron, 1980; Matter, 1982;
(a) One-node methods (e.g., Arranovitch, 1977;
Hotchkiss et al., 1985) lead to definition of
Munroe, 1983; Saunier and Chungpaibulpatana,
certain parameters which can also be used to
1983; Stronskii et al., 1986; Chungpaibulpatana
compare different collectors.
and Exell, 1988, 1990a, 1990b; Perers et al.,
The motivation behind the development of all
1990; Perers and Walletun, 1991; Perers, 1993,
these methods is to circumvent the difficulties
1997; Souproun, 1992; Muschaweck and Spirkl,
associated with conventional steady-state outdoor
1993; Bosanac et al., 1994; Spirkl et al., 1997;
test methods. It is well known that steady-state
Zeroual et al., 1994; Wijeysundera et al., 1996;
methods specify certain strict limits for weather
Amer et al., 1998b, 1999).
and operating conditions during tests. Conse-
(b) Multi-node methods (e.g., Wijeysundera and
quently, a long time is taken to test a collector and
Hawlader, 1984; Kamminga, 1985a, 1985b; Haw-
in some regions, which experience rapid weather
lader and Wijeysundera, 1987; Frid, 1990).
fluctuations, conducting steady-state outdoor tests
(c) Response function methods (e.g., Rogers,
may become impossible. Based on transient pro-
cedures, however, experimental tests can be car-
†
Author to whom correspondence should be addressed. Tel.: ried out throughout the year even when the
191-22-578-2544; fax: 191-22-578-3480; e-mail: weather conditions are changing continuously.
jknayak@me.iitb.ernet.in Amer (1998) and Amer et al. (1997) have carried
377
,378 J. K. Nayak and E. H. Amer
out a detailed review of transient methods. The Further, for the methods which prescribe similar
review shows that most of these methods have test sequences, the collector parameters have been
been compared individually with the results of the extracted from the same data sets according to
steady-state ASHRAE standard (ASHRAE, 1986). their procedures. This provides a direct and very
Very limited work has been reported so far on clear comparison between the methods.
the relative comparisons of various transient The transient methods evaluated in the current
methods. Wang et al. (1987) have proposed a investigation are:
method, known as the filter method and compared (a) Rogers’ method (Rogers, 1981), which has
it with three other transient methods, namely been adopted by the British Standard Institution
Arranovitch’s method (1977), Talarek’s method as a standard (BS, 1986).
(Gillett et al., 1983) and Rogers’ method (1981) (b) Saunier’s method (Saunier and Chun-
and a steady-state method. They have reported gpaibulpatana, 1983).
that the results obtained on the basis of the filter (c) The filter method (Wang et al., 1987).
method have shown agreement with the transient (d) Exell’s method (Chungpaibulpatana and
as well as steady-state method. Schnieders (1997) Exell, 1988, 1990a,b).
has made theoretical studies and comparison of (e) Perers’ method (Perers et al., 1990; Perers
one stationary and four dynamic models by and Walletun, 1991; Perers, 1993)
applying to a small module of vacuum tube (f) Dynamic Solar Collector (DSC) Procedure
collector. The stationary model has been taken (Muschaweck and Spirkl, 1993; Bosanac et al.,
from the simulation system TRNSYS (TRNSYS, 1994; Spirkl et al., 1997).
1994). The dynamic models considered are (1) (g) Wijeysundera’s method (Wijeysundera et
Kamminga, 1985b; (2) Isakson and Eriksson, al., 1996).
1991 and Isakson, 1995; (3) Muschaweck and (h) Quick Dynamic Testing (QDT) Procedure
Spirkl, 1993, and, (4) Henning, 1994. The com- (Amer et al., 1998b).
parison lacks detailed experimental investigation (i) New Dynamic Method (NDM) (Amer et al.,
on the implementation of these models and pa- 1999).
rameters estimation; but whatever has been re- The steady-state ASHRAE 93-86 standard is
ported, they refer to vacuum tube collector. Amer taken as a reference for comparing the parameters
et al. (1998a) have reported the results of a obtained on the basis of the above methods.
relative comparison of Saunier’s (Saunier and
Chungpaibulpatana, 1983) and Exell’s method
2. COMPARISON OF THEORETICAL ASPECTS
(Chungpaibulpatana and Exell, 1988, 1990a,
OF MODELS
1990b). Thus a very detailed comparison of
various transient methods has not been made. It The theoretical basis of each method is summa-
would be desirable to evaluate these methods on a rised in Table 1. The model equation and the
common basis by implementing them for the parameters defined to characterise a collector in
same collector at one location. Such an ex- each method is presented in the table. Also shown
perimental comparison would be useful in iden- are the conditions for which the model is valid. A
tifying their advantages and difficulties associated scrutiny of the model equations reveals that all
with the implementation of these methods. With models, except Rogers’, the filter and Wijeysun-
this objective in view, a critical evaluation of a dera’s method, are based on one-node concept.
number of transient methods has been undertaken. The thermal capacitance of the collector is
In this investigation, theoretical as well as lumped and is referenced to the mean temperature
extensive experimental studies have been carried of the working fluid. The DSC method is based on
out to compare nine different transient test pro- segmented collector model; it means that the
cedures. The experimental conditions refer to a collector is divided into a number of segments
wide range of weather and operating conditions. along the flow direction, typically 30 segments.
Two collectors from different manufacturers have The thermal capacitance of the collector is distrib-
been used in the study. The tests are carried out at uted equally over the segments. For each segment,
the same location using a common test-rig, the energy balance equation similar to the one
measuring transducers and controlling and data- referred in Table 1 is written and solved. On the
acquiring facilities. The characteristic parameters other hand, Wijeysundera’s method does not
of the collectors have been obtained on the basis consider the heat capacity effect of the collector
of each procedure and compared with those based and Rogers’ and the filter method are based on a
on the steady-state ASHRAE 93-86 standard. response function approach. In case of Rogers’
, Table 1. Comparison of theoretical aspects of models
Method Model equation Characteristic Conditions a
Experimental and theoretical evaluation of dynamic test procedures for solar flat-plate collectors
parameters
]] ~ 5 C; T fi 5 C; IT ± C;
m
Rogers qu ( j) 5 o nN51 [FR (ta ) e Kn ITj (n)] 2 FRUL(T fi 2 TA ) FR (ta ) e , FRUL
TA 5 slowly varying
Filter qu 5 e0` FR (ta ) e h(t)IT (t 2 t)dt 2 FRUL (T fi 2 TA ) FR (ta ) e , FRUL ~ 5 C; T fi 5 C; IT ± C; TA ± C
m
≠T fm
Saunier (Ma 1 Me )c p ] 5 ho A p IT 2 (U1 1 Ua )A p (T fm 2 TA ) 2 U2 A p (T fm 2 TA )2 1 (Pp 1 d Pe ) M e , ho , U 1 , U 2 Pe 5 C; qu 5 0; m
~ 5 very high
≠t
]
HT [T fm (t 2 ) 2 T fm (t 1 )] 5 ett12 (PP 1 d Pe 1 ho IT )dt 2 (U1 1 UA )A p ett12 [T fm (t) 2 TA ]dt
Exell ho , U 1 , U 2 Pe 5 C; qu 5 0
2 U2 A p ett12 [T fm (t) 2 TA ] 2 dt
qu 5 F9(ta ) e Kta b (u )Ib 1 F9(ta ) e Kta d (u )Id 2 F9U1 DT 2 F9U2 DT 2 F9(ta ) e , Kta b , Kta d ,
Perers dT fm F9U1 , F9U2 , F9U3 , T fi 5 C; m
~ ± C; IT ± C
2 F9U3 DTw 2 F9Usky DT sky 2 (mc) e ] 2 Up DT F9Usky , (mc) e
dt
(mc) e dT fm,p F9
DSC ]] ]] 5 ] [(ta ) e IT 2 UL (T fm,p 2 TA )] 2 mc ~ p (T fm,p 2 T fm,p21 ) F9(ta ) e , F9UL , (mc) e ~ ± C; IT ± C; TA ± C
m
Nc dt Nc
dT s FR (ta ) e , FRUL , Ct ,
Wijeysundera Ct ] 5 A p FR [(ta ) e IT (t) 2 UL (T fi 2 TA )] 2 (AU ) t (T s 2 TA ) ~ 5 C; IT ± C; TA ± C
m
dt (AU ) i , (AU ) o , (AU ) t
2 (AU ) i ei (T s 2 TA ) 2 (AU ) o eo (T fo 2 TA )
dT fm
QDT qu 5 F9(ta ) e IT 2 F9UL (T fm 2 TA ) 2 (mc) e ] F9(ta ) e , F9UL , (mc) e ~ 5 C; T fi 5 C, IT 5 forced, TA ± C
m
dt
NDM
T fo (t ) 5 T 0 exp S
F9UL
]]td
(mc) e D 21
1 o kN50 F F9(ta ) e F9UL
]] IT (t 2 kDt ) 1 ]] TA (t 2 kDt )
(mc) e (mc) e G F9(ta ) e , F9UL , (mc) e ~ 5 C; IT ± C; TA ± C; T fi ± C
m
exp SF9UL
]] kDt
(mc) e D Dt
ASHRAE H
h 5 FR (ta ) e 2 FRUL FT fi 2 TA
]]
IT GJ AP
]
AC
FR (ta ) e , FRUL
or F9(ta ) e , F9UL
Steady conditions
a
C: Constant.
379
