COMPARATIVE ANALYSIS OF TWO SOLAR DRIVEN CYCLES [615840]

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COMPARATIVE ANALYSIS OF TWO SOLAR DRIVEN CYCLES
UNDER CLEAR AND CLOUDY SKY CONDITIONS

Bogdan Borcila 1a, Camelia Stanciu a, Monica Costea a, Stoian Petrescu a, Michel Feidt b
aUniversity POLITEHNICA of Bucharest, Bucharest, Rom ania
bLorraine University, Nancy, France

ABSTRACT

The paper presents a comparative analysis of two so lar powered systems aiming to produce
electricity. The potential user could be a duplex h ouse or an office building. One system consists of an
Organic Rankine Cycle (ORC) modeled to operate at v ariable mass flow rate, constraint by the heat
source temperature which is provided by a parabolic dish collector. The second one is a Stirling engine
modeled by taking into account the internal and ext ernal irreversibilities, using the concentrated sol ar
radiation from dish collector , too . Both engines have to deliver the same electrical power (constraint),
according to the user’s daily energy consumption pr ofile. The study considers the daily solar radiatio n
and ambient temperature variation under cloudy sky conditions , and the receiver heat losses
dependence on these data. The analysis results emph asize the required solar collector dimensions in
each case. The comparison is done to previous obtained results under clear sky condit ions.

1. INTRODUCTION

In the recent past, the solar energy has proven to be an actual alternative and clean source
of energy for the sustainable development of the so ciety worldwide. It is cheap, abundant and
everlasting as source of renewable energy and thus it can be integrated in different systems to
overcome the dependency of present society on conve ntional fuels [1-2].
Such integration of solar energy has given an oppor tunity for several studies based on the
energy and economic approaches of solar-powered Sti rling engine system. Ferreira et al [3]
developed a methodology for the thermal-economic op timization of micro cogeneration units,
showing its great potential for applications in the residential sector, with a payback period of
approximately 10 years. As a performant solar radia tion concentrator, the parabolic dish
coupled with a Stirling engine was modelled and its operation was simulated for insolation
conditions in Egypt [4] or in Brazil [5]. Both stud ies aimed to find the best performance in
terms of energy production and efficiency, and deve loped sensitivity analysis for the receiver
working fluid [4], or for collector diameter, wind speed and tilt angle of the cavity [5].
Among the under development micro-scale power gener ation technologies the ORC
concept is a promising solution for smaller units f or domestic users [6-8]. The operation of a
solar power plant associated with a latent heat the rmal storage and an ORC unit was simulated
under dynamic (time-varying) solar radiation condit ions [9] showing that the system is able to
provide power in 78.5% of the time, with practical efficiency for the ORC unit. The working
fluid for ORC system is important to improve effici ency and achieve better economy [10].
In this paper, a comparative analysis of two solar powered systems performance for
residential consumers, one with Stirling engine, an d the other with Organic Rankine Cycle is
done. The aim of the analysis is to provide informa tion that could help the consumer to
choose the system that best suits his needs taking into account the two extrema for sky
conditions – cloudy and clear ones.

1Department of Engineering Thermodynamics, +40-21-40 29339, bbd1188@yahoo.com

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2. DESCRIPTION OF THE TWO SOLAR DRIVEN SYSTEMS

The Stirling system consists of a Dish-Receiver assembly that will pro vide the
necessary heat input, a Stirling engine and an elec trical generator, as shown in Fig. 1. The
power output of the electrical generator can be use d directly by the consumer and the surplus
is stored in a battery, to be supplied for covering the pick consume or the periods without sun.

Figure 1: The Stirling system

Experimental data obtained from the V-160 Stirling engine [11] are used for the Stirling
engine modeling.
The Organic Rankine Cycle system is also driven by the assembly of a Dish
Receiver and coupled to a storage tank (ST), which will ensure a stable operation. The fluid is
circulated through the receiver of the dish solar c ollector and heated along the day,
simultaneously feeding the evaporator of the organi c Rankine cycle, as presented in Fig. 2.

Figure 2: The Organic Rankine Cycle system

Therminol XP is chosen as heat transfer fluid in th e solar receiver tubes, with a mass
flow rate of 0.7 kg/s. The storage tank module is a fully mixed one, assuring a uniform
temperature in its bulk volume, having a capacity o f 100 kg.
The parabolic dish collector feeds the storage tank ST, to which the evaporator of the
Organic Rankine Cycle (ORC) is coupled ensuring the heat exchange between the organic
fluid (n-pentane in this case) and the ST fluid. A lower limit is set for ORC operation at 80°C
in order to avoid instability and poor operation. T he ORC operates between ambient
condensation temperature and a vaporization level i mposed by the ST fluid temperature,
higher than the lower set limit and lower than the optimum vaporization temperature for
maximum power output, 140°C [12]. The main target o f this study is to compare the results
Electric
generator
Pel ORC
turbine

ST ORC
evaporator
Pump
Pump ORC
condenser
Pump Sink at Ta Dish-
Receiver
system
Electric
generator
Pel

Pump Dish-
Receiver
system
Stirling
engine

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obtained with this technic arrangement under cloudy sky conditions, to previous results
obtained under clear sky conditions [13].

3. MODELLING OF THE TWO SYSTEMS

Stirling engine performance evaluation based on the Direct Method from TFS
In the frame of Thermodynamics with Finite Speed an d using the Direct Method ,the
Stirling engine efficiency will be given by the equ ation [14]:
( )
( )
, , ,, , 11
,
, , ,
, , 1 /
1 1 1 1 ln i
CC II irrev T opt power II irrev X L H S L L
SE CC II irev II irev P
H S H S X T T T T
T T
η ηηη η η η γ ε
Δ−−
ΣΔ   −       = ⋅ = − ⋅ + +         −        
 
  
 , (1)
where: – ηII, irrev – the second law efficiency cumulating the cycle i rreversibility effect;
– T H,S – the receiver temperature (hot source);
– TL – the cold end temperature;
– ΔTopt, power – the optimum temperature difference at the source for maximum power
delivered by the Stirling engine;
– ηII, irrev,X – the second law efficiency due to incomplete rege neration of heat;
– γ – the specific heat ratio (= cp/c v);
– ε – the volumetric ratio, ε = Vmax /V min ;
– ηII, irrev, ΔP – the second law efficiency due to pressure losses , expressed as [14, 15]:

( )( )
εητετγ
ηln 'Pw. .
wwN ln ww
SL gR
S
SL
P irrev , II i⋅ ⋅++


⋅ + +
−=ΣΔ 5
12
10 4045 094 0 35 1
1 (2)
with:
( )
( )1
11
1 1−




−−
+⋅



−=εγηln T /T X
TT'S , H L
S , HL (3)
and w – the average speed of the piston; wSL – the speed of the sound corresponding to the
sink parameters; τ – the ratio of the gas extreme temperature in the cycle (T max /T min ); NS –
number of screens of the regenerator
Equation (1) emphasizes the main causes of irrevers ibility in actual Stirling Machines
that decrease the ideal cycle efficiency (equal wit h the Carnot cycle efficiency), namely heat
transfer at finite ΔT at the hot end, incomplete heat regeneration in th e Regenerator evaluated
by the losses coefficient X [14, 15] that contains one of the adjustment coefficient of the
model, and pressure losses due to friction.
Finally, the analytical expression for the power ou tput results as :
ε η ln zw
g , HmRT zSE irrev , SE Power 2⋅ ⋅ ⋅= , (4)
where the second adjustment coefficient, z, accounts for the finite heat rate at the source. Its
value is equal to 0.55 or 0.8 [15].
ORC system performance evaluation
For the ORC system, the storage tank is a fully mix ed one, characterized by a constant
heat loss coefficient ( U)ST = 0.7 W/(m 2K) [16]. The mathematical expression of the First L aw
of Thermodynamics allows us to compute the storage tank temperature at the next time-step
(n + 1) based on the value from the previous time-step ( n):

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, (5)

The time-step Δτ = 10 min for the simulations along a day or more c onsecutive days.
The term is the useful heat rate absorbed by the receiver f luid, while
represents the heat rate transferred to the organic fluid in the organic Rankine cycle
evaporator. At system start-up, the initial storage tank temperature is set to ambient one
, while the ORC is turned off, so that . For each simulation day, the
computation is implemented for 24 hours starting fr om midnight.
The sky conditions are determined based on Meteonorm database [17], a s 10-years-
averaged measured values, for Bucharest, thus inclu ding cloudy days radiation and ambient
temperature.

4. RESULTS
The results are presented for two consecutive days, July 15 th and 16 th (the 196 th and 197 th
days respectively out of 365 yearly days). The sola r assembly is composed by the parabolic
dish and the associate receiver of 18 cm diameter a perture, the same for both systems. Heat
losses from the receiver to the surroundings, due t o convection and radiation are considered.
Different values of the dish diameter were consider ed, namely 8m, 12m, and 16m, in order to
evaluate the most economical solution that suits to the consumer needs.
The Stirling engine system daily power output toget her with the consumption profile of
the user are illustrated in Fig. 3. One can see tha t the 16 m dish largely covers the pick
consumption of 2 kW, thus 12 m diameter would be a better choice, due to the battery use.

Figure 3: Stirling system power output with respect to the required one

Regarding the ORC system, the clear sky conditions revealed [13] that a dish diameter of
6m was sufficient to cover daily electric energy ne ed of 8kWh. In the present study, authors
have found that, under the same system characterist ics, at least 18m diameter should be used
(Fig. 4). Cloudy sky conditions imposed much lower solar radiation values and consequently
the ST fluid heated insufficiently to run the ORC a t desired rate.
Due to obviously technical difficulties in using su ch very large diameter dish, authors
decided to modify some operating parameters in orde r to find a suitable solution. In this
regards, the simulations were redone for a mass flo w rate of fluid circulating the receiver
reduced to 0.3kg/s and a period of two days chargin g the ST before ORC start-up. In this two-

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days period, the ST fluid was heated, so that the O RC starts at an upper temperature level and
having a previously stored thermal energy.

Figure 4: ORC daily electric energy produced under cloudy sky (and same parameters used
for clear sky simulation in paper [13])

Figure 5: ORC daily electric energy produced under cloudy sky for a reduced value of
receiver fluid mass flow rate (0.3kg/s) and two cha rging days before ORC start;
12m diameter dish

The simulation was performed for different dish dia meters and the most suitable results
were obtained for a dish diameter of 12m. Results a re presented in Fig. 5. The ST fluid
temperature attaint 320°C after 40 hours of operati on. ORC module was started in the third
day and produced 8.3 kWh electric energy in 24 hour s. The next days, the ORC module
produced 5.56 kWh daily and the ST fluid temperatur e did not drop under 96°C, thus a stable
operation condition was met.

5. CONCLUSIONS

Performance of Stirling engine and Organic Rankine Cycle systems, in terms of electric
power, electrical energy provided by several dish d iameter systems have been simulated,
namely 8m, 12m, 16m for Stirling, completed by 18m and 20m for ORC respectively.

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The results have been compared to previously obtain ed ones under clear sky conditions
[13] and emphasized that the electric energy supply which is the closest to demand is
provided by a system with a much larger dish diamet er for the same system parameters, in the
simulated case under cloudy sky. The ORC module req uires a 18m dish diameter, compared
to 6m one, while the Stirling engine, a 12 m diamet er parabolic dish, compared to 5m one.
Modifying operating parameters, the ORC module requ ired a 12m diameter dish for
covering daily electric energy need and a two-days charging period of the ST before start.
Further development of the analysis for different v alues of other operating and technical
parameters and sink temperature levels (so that hea t rejected could be used in cogeneration) is
in due course.

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