Parametric analysis and optimization of an Organic Rankine Cycle with nanofluid based solar parabolic trough collectors

Accepted Manuscript Parametric analysis and optimization of an Organic Rankine Cycle with nanofluid based solar parabolic trough collectors Evangelos Bellos, Christos Tzivanidis PII:

S0960-1481(17)30557-8

DOI:

10.1016/j.renene.2017.06.055

Reference:

RENE 8922

To appear in:

Renewable Energy

Received Date: 10 May 2017 Revised Date:

31 May 2017

Accepted Date: 14 June 2017

Please cite this article as: Bellos E, Tzivanidis C, Parametric analysis and optimization of an Organic Rankine Cycle with nanofluid based solar parabolic trough collectors, Renewable Energy (2017), doi: 10.1016/j.renene.2017.06.055. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Parametric analysis and optimization of an Organic Rankine Cycle

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with nanofluid based solar parabolic trough collectors

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Evangelos Bellos, Christos Tzivanidis

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Thermal Department, School of Mechanical Engineering, National Technical

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University of Athens, Zografou, Heroon Polytechniou 9, 15780 Athens, Greece.

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Corresponding author: Evangelos Bellos ([email protected], tel:+302107722340)

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Abstract

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The main objective of this work is to investigate the utilization of nanofluids in the

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solar field in order to achieve higher system performance. An Organic Rankine Cycle

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(ORC) driven by solar parabolic trough collectors (PTCs) is the examined system.

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Four different nanoparticles are examined (Al2O3, CuO, TiO2 and Cu) in the base

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fluid (Syltherm 800), as well as the pure thermal oil is examined as working fluid.

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The examined ORC is a regenerative cycle and four organic fluids are also tested

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(toluene, MDM, cyclohexane and n-pentane). In every combination between the

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organic fluid in ORC and working fluid (nanofluid) in the solar field, an optimization

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procedure is followed. The concentration of every nanoparticle and the pressure ratio

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(pressure in the turbine inlet to critical pressure) are the optimization parameters.

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According to the final results, toluene is the best organic fluid and CuO is the most

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suitable nanoparticle. The combination of these two working fluids leads to

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167.05kW electricity production and to 20.11% system efficiency with concentration

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4.16%. The enhancement by the use of nanofluids is found up to 1.75% compared to

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the respective case with pure thermal oil and this result indicates that the use of them

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is able to improve the performance of solar driven ORCs. For the other nanoparticles

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ACCEPTED MANUSCRIPT and Toluene in the ORC, Cu, Al2O3 and TiO2 lead to 166.18 kW, 165.72 kW and

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165.60 kW electricity productions respectively with optimum concentrations 3.98%,

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2.51% and 2.57% respectively.

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Keywords

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ORC, PTC, Nanofluid, Solar energy, Toluene, CuO/Syltherm

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1. Introduction

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Energy production and management are among the most discussed issues of the last

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years due to many factors, as the fossil fuel depletion, the increasing energy need of

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the humanity, the increasing price of electricity and the global warming problems [1-

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2]. The exploitation of renewable and alternative energy sources as solar, geothermal,

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wind, waste heat and biomass seems to be the sole sustainable solution. Among them,

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solar energy presents many advantages, especially in countries with high solar

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potential, and thus a lot of research has been focused on this energy source [3].

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Solar collectors are the devices which capture the incident solar irradiation and

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convert it into useful heat (solar thermal collectors), into electricity (photovoltaic

40

panels) or both into useful heat and electricity (hybrid collectors) [4]. However, at this

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time, it is difficult for many solar-driven systems to compete for the conventional and

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non-clean energy systems. In this direction, a lot of research has been focused on the

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improvement of solar thermal collectors in order to increase their performance and to

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make them the best candidate for thermal processes [5-6].

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One of the most promising ways is the utilization of nanofluids are working fluids in

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the solar collectors [7]. Nanofluids are working fluids which are created by adding

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metallic nanoparticles inside a usual base fluid (water or thermal oil). The term of

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nanofluids is introduced by Choi in 1995 for the first time [8]. The most usual

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ACCEPTED MANUSCRIPT nanoparticles are the following: CuO, Cu, Fe, Al, Al2O3, TiO2, SiO2, and carbon

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nanomaterial which have different thermal properties compared to the base fluid [9].

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More specifically, these metallic particles present high thermal conductivity [8] and

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density, two factors which can increase the thermal performance of the solar collector,

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increasing the heat transfer coefficient in the working fluid (nanofluid) [10-11].

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Up to this time, the majority of the literature studies are focused on the preparation of

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nanofluids and of their thermal properties investigation (for instance in Refs [12-13]).

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A smaller but increasing number of studies are focused on the performance of them in

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the solar collector. Mwesigye et al. have been performed a great number of

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simulations for nanofluid operation in parabolic trough collectors (PTCs) [14-16].

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Mwesigye et al. [14] examined the use of Al2O3 inside the water for concentrations up

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to 6% and they determined the optimum Reynolds numbers for various nanoparticle

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concentrations. Mwesigye et al. [15] examined the use of Al2O3 in Syltherm 800 for

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concentrations up to 8%. According to their results, thermal efficiency enhancement

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up to 7.6% can be achieved. In the last study of these researchers [16], Cu

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nanoparticle inside Therminol VP1 is investigated for concertation up to 6% and the

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maximum thermal efficiency enhancement is found to be 12.6%. The use of Al2O3

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inside thermal oils is examined also in Refs [17-19], as well as in Ref [20-21], with

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encouraging results. Ghasemi et al. [22] compared the use of Al2O3 and CuO

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nanoparticles in water base fluid by performing CFD simulations. According to their

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results, both nanoparticles lead to thermal enhancement with CuO to be the best

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candidate. Kasaeian et al. [23] examined the use of carbon nanotube/oil nanofluid in a

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pilot PTC and they found significant enhancement. Moreover, other interesting

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studies as the utilization of gas-phase nanofluids in transparent collectors are found in

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the literature [24].

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ACCEPTED MANUSCRIPT It is obvious that the examination of nanofluids in solar thermal collectors is a recent

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topic of research and thus the examination of nanofluids in the thermal application has

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not been extensively studied. There are an extremely small number of studies which

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examine the nanofluids in greater solar-driven systems. More specifically, about one

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or two studies in some applications can only be found in the literature. Kabeel and El-

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Said [25] examined a hybrid solar desalination system with nanofluid (Al2O3/H2O) as

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working fluid in a flat plate solar thermal collector. The experimental installation

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included solar air heater, water solar collector, storage tank, humidifier and

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dehumidifier. According to their results, the system performance is affected by the

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nanoparticle concentration. Abu-Hamdeh and Almitani [26] investigated the use of

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nanofluid in a solar driven liquid desiccant cooling system. They examined various

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nanoparticles, as ZnO, Fe3O4, and Al2O3 and they found high thermal enhancements

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up to 40% for various nanoparticle concentrations. Boyaghchi et al. [27] examined the

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use of CuO nanofluid in the solar driven compression-absorption cascade refrigeration

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system. They performed single and multi-objective optimization procedures in order

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to determine the optimum values of the examined parameters, as well as the optimum

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organic working fluid in the compression cycle. Finally, R134a is found to be the best

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candidate. Their optimization parameters were the nanoparticle concentration, the

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collector title angle, the collecting area, the intermediate pressure level and the mass

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flow rate of the strong solution in the absorption chiller.

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The next part of literature studies, which examines nanofluid in solar thermal

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applications, is associated with the electricity production. Boyaghchi et al. [28]

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examined a combined cooling, heating and power system which utilizes solar energy,

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geothermal energy as well as there is auxiliary heat supply. The authors used

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nanofluid as working fluid in solar thermal collectors and more specifically the used

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ACCEPTED MANUSCRIPT CuO inside water. Their multi-objective optimization proved that R134a is the best

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candidate as working fluid in the ORC. In another study with similar configuration,

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the same nanofluid is examined [29]. The last two literature studies examine

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electricity production system with Rankine cycles, driven by PTC, which operate with

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nanofluids. Alashkar and Gadalla [30] examined three different nanoparticles (Cu,

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Al2O3 and SWCNT) in Therminol and in Syltherm. They finally found that the Cu

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nanoparticle to be the best candidate for both thermal oils. More specifically, the

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optimum concentration of Cu is found to be 3% in the Therminol and 5% in Syltherm.

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Toghyani et al. [31] examined the use of CuO, SiO2, TiO2 and Al2O3 nanoparticles in

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thermal oil for feeding a water/steam Rankine cycle. They found that CuO is the best

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nanoparticle and its optimum concentration is 4.28%.

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As it is obvious from the previous literature review, the utilization of nanofluids in

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solar thermal applications takes more and more attentions by the researchers. Up

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today, there is a small number of studies which have examined the nanofluids in

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thermodynamic cycles for electricity production. Thus, this study is devoted to the

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detailed analysis and optimization of a solar driven ORC with parabolic trough

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collectors. The innovative part of this study is the examination of various nanofluids

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and organic fluids, as well as the optimization of all the possible combinations of the

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previous working fluids. This strategy leads to a totally optimum system which

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combines high thermal output in the solar field and high thermodynamic efficiency at

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the ORC. The optimization of the energy systems is a very important issue in order to

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design sustainable configurations [32]. The examined nanofluids are oil based, with

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Syltherm 800 to be used. Al2O3, CuO, TiO2 and Cu are selected as the most usual and

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efficient nanoparticles. Toluene, MDM, cyclohexane and n-pentane are the selected

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organic fluids for the ORC. These fluids are selected because they have high critical

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ACCEPTED MANUSCRIPT temperature and they can be optimally combined with PTC [33]. The optimization

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parameters are the nanoparticle concentration and the pressure ratio which are directly

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associated with the pressure in the turbine inlet of ORC. The analysis is performed

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with EES (Engineering Equation Solver) in steady state condition in order to give the

128

emphasis in the thermal comparison of the different design cases.

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2. Materials and Methods

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2.1 The examined system

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The examined system of this study is depicted in figure 1 with many details. This

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system is examined with the commercial software EES (Engineering Equation

133

Solver). Parabolic trough collectors are selected for capturing the solar irradiation

134

(Qsol,t) and convert it into high-temperature heat (Qu,t). Eurotrough [34] module is

135

selected to be examined and 15 modules exist in the collector field. The working fluid

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in this loop is nanofluid. The base fluid is Syltherm 800 [35] which is usual thermal

137

oil for operation from -40oC up to 400oC [35]. For different usual nanoparticles are

138

examined in this thermal oil: Al2O3, CuO, TiO2 and Cu. Moreover, the case of

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operation with pure Syltherm 800 in the collector loop is examined in order to

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perform suitable comparisons.

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The storage tank includes pure Syltherm 800 and there is sensible heat storage. The

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heat from the collector loop to the storage tank is transferred to a suitable heat

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exchanger inside the storage tank. Hot thermal oil from the upper part of the storage

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tank (Ts,in) goes to the heat recovery system (HRS) and it gives the demanded heat

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input in the ORC (Qin). The cold thermal oil, after the HRS), has a temperature equal

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to (Ts,out) and it is delivered in the down part of the storage tank.

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ACCEPTED MANUSCRIPT The next step is the description of the regenerative ORC. Four different organic

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working fluids are examined: toluene, MDM, cyclohexane and n-pentane. In the heat

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recovery system, heat is transferred to the organic fluid and it becomes vapor. More

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specifically, organic fluid in a liquid phase (state point 3) enters the heat recovery

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system. Firstly in the economizer (ECO) part, it is converted to saturated liquid (state

152

point 34) and after in the evaporator (EVAP) heat exchange surfaces, it becomes

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saturated vapor (state point 4). It is important to state that in the present study, the

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system operates without superheating. The produced saturated steam goes to the

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turbine where it expanded and electricity (Pel) is produced in the electrical generator

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(G). The outlet of the turbine (state point 5) is a low-pressure superheated vapor of

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high temperature. This steam is used in the recuperator in order the colder stream after

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the condenser to be warmed up, a fact that leads to lower energy input demand in the

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heat recovery system. More specifically, in the recuperator, the hot stream leaves this

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device (state point 6) and enters to the condenser where heat is rejected to the

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absorption heat pump in temperature level (Tcon). The saturated organic liquid (state

162

point 1) becomes subcooled liquid of high pressure after the pump (state point 2) with

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electricity consumption (Wp) and this quantity is driven to the recuperator. In this

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device, the enthalpy of the inlet stream (state point 1) increases and the warmer

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stream (state point 3) enter the heat recovery system.

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Figure 1. The examined solar ORC system

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2.2 Working fluids

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2.2.1 Nanofluids

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In this study, four different nanoparticles are examined inside the base fluid (Syltherm

171

800). These nanoparticles are the following: Al2O3, CuO, TiO2 and Cu. The thermal

172

properties of these nanoparticles are given in table 1 [36]. It is important to state that

173

the thermal properties of Syltherm 800 have been taken by the EES libraries [35, 37].

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ACCEPTED MANUSCRIPT Table 1. Properties of the examined nanoparticles [36]

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ρ (kg/m3) 3970 6320 4250 8933

k (W/mK) 40 77 8.95 401

cp (kJ/kgK) 0.765 0.532 0.686 0.385

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Particle Al2O3 CuO TiO2 Cu

The thermal properties of the nanofluids can be calculated according to equations 1 to

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4, using the properties of the base fluid (bf) and of the nanoparticles (np). The density

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of the mixture is given by equation 1 [38] and the specific heat capacity according to

182

equation 2 [39]:

183

ρ nf = ρ bf ⋅ (1 − φ ) + ρ np ⋅ φ ,

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c p ,nf =

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The thermal conductivity of the nanofluid is calculated according to the suggested

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equation by Yu and Choi [40]:

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ρ bf ⋅ (1 − φ ) ρ np ⋅ φ ⋅ c p ,bf + ⋅ c p ,np , ρ nf ρ nf

k np + 2 ⋅ k bf + 2 ⋅ (k np − k bf ) ⋅ (1 + β ) ⋅ φ

(1)

(2)

3

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k nf = k bf ⋅

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The parameter β is the ratio of the nanolayer thickness to the original particle radius

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and usually, this parameter is taken equal to 0.1 for calculating the thermal

190

conductivity of the nanofluids [41].

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The mixture viscosity can be calculated according to equation 4a and 4b [42-44]:

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µ nf = µ bf ⋅ (1 + 2.5 ⋅ φ + 6.5 ⋅ φ 2 ) ,

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µ nf =

k np + 2 ⋅ k bf − (k np − k bf ) ⋅ (1 + β ) ⋅ φ

,

(3)

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µ bf

(1 − φ )2.5

,

(4a)

(4b)

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ACCEPTED MANUSCRIPT These equations are general and do not include the nanoparticle diameter and other

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characteristics. It is essential to state that equation 4a is the Batchelor model and

196

equation 4b is the Brinkman model (ideal for spherical nanoparticles). These two

197

equations are evaluated and the give similar results (figure 3). Finally, equation 4a is

198

selected in this study.

199

The thermal properties of the examined nanofluids are presented in figures 2-3. In

200

these figures, the thermal conductivity, specific heat capacity, density and dynamic

201

viscosity are given for various temperatures (T) and nanoparticle concentrations (φ).

202

In every case, different depictions are selected in order to present the properties with

203

the clearest and simplest way.

204

Figure 2 shows the specific heat capacity (subfigures 2a and 2b), the density

205

(subfigures 2c and 2d) and the thermal conductivity (subfigures 2e and 2f). In

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subfigures 2a, 2c and 2e, the four examined nanofluids with 3% concentration are

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compared with the Syltherm 800 for temperatures from 25oC to 375oC. The other

208

subfigures (2b, 2d and 2f) compare the thermal properties of the four nanofluids for

209

different concentrations (from 0% to 6%) with a temperature equal to 300oC. The

210

followed presentation technique makes obvious the impact of temperature and of

211

concentration in these thermal properties. It is important to state that the

212

concentrations of 3%, as well as the temperature of 300oC, are representative values

213

for the examined cases in this work.

214

Subfigure 2a shows that the specific heat capacity of the nanofluids is lower than the

215

specific heat capacity of Syltherm 800. This result is explained by the low specific

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heat capacity of the nanoparticles, as table 1 indicates. Al2O3 and TiO2 lead to similar

217

properties, while CuO and Cu lead to lower specific heat capacities respectively.

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ACCEPTED MANUSCRIPT Subfigure 2b proves that higher concentration leads to lower specific heat capacity for

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all the nanofluids. The density of nanofluids is greater than the Syltherm 800 case, as

220

subfigure 2c shows. Cu, CuO, TiO2 and Al2O3 create the order from the highest to the

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lowest density values. Moreover, higher concentration leads to greater density,

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according to subfigure 2d. Subfigures 2e and 2f prove that the thermal conductivity of

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the examined nanofluids is similar and it is greater than the Syltherm 800 case. Also,

224

higher concentration leads to greater thermal conductivity, while higher temperature

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leads to lower thermal conductivity.

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Figure 2. a) Specific heat capacity for different temperatures b) Specific heat capacity for different concentrations c) Density for different temperatures d) Density for different concentrations e) Thermal conductivity for different temperatures f) Thermal conductivity for different concentrations

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ACCEPTED MANUSCRIPT Figure 3 depicts the dynamic viscosity variation with temperature (subfigure 3a) and

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concentration (subfigure 3b). According to equations 4a and 4b, the nanofluid

233

dynamic viscosity is depended on the base fluid viscosity and the concentration. Thus,

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the present modeling leads to the same viscosity values among the examined

235

nanofluids. This is the reason for presenting only one general curve for nanofluids in

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the subfigures of figure 3. Following the same methodology, as in figure 3, subfigure

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3a compared the dynamic viscosity of the Syltherm 800 with the nanofluid case for

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various temperatures. It is obvious that the nanofluid has higher viscosity with a small

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difference with the Syltherm 800. Moreover, subfigure 3b proves that higher

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concentration leads to higher nanofluid viscosity, a reasonable result according to

241

equation 4. Both models of equations 4a and 4b are depicted in figure 3. It is obvious

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that the viscosity is approximately the same for both models and thus these models are

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adopted as reliable. In this study, the model of equation 4a is selected to be used.

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The results of figure 3 and 4 make clear the impact of the nanoparticles in the thermal

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properties of the nanofluids. The basic conclusions from this mini-analysis are the

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following: The nanofluids present higher density, thermal conductivity and viscosity,

247

compared to the base fluid. On the other hand, the specific heat capacity is lower. All

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the thermal properties, except the specific heat capacity, have an increasing rate of the

249

increase in the nanoparticle concentration. Moreover, the density and the specific heat

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capacity are depended on the kind of nanoparticle, with the thermal conductivity to be

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influenced in an extremely small way and the viscosity to be the same among the

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nanofluids.

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Figure 3. a) Dynamic viscosity between nanofluids and thermal oil for various

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temperatures b) The impact of concentration in the dynamic viscosity for

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temperature equal to 300oC

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2.2.2 Organic fluids

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In the ORC, four different organic fluids are investigated. Toluene, cyclohexane,

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MDM and n-pentane are the examined working fluid in this study. Table 2 includes

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the examined working fluids and their basic properties as the critical temperature, the

261

critical pressure and the molecular weight, as well as the ASHRAE safety group of

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every working fluid, ODP and GWP. Moreover, figure 4 shows the saturation lines of

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the examined organic fluids in T-s figures. It is essential to state that these data are

264

taken from EES libraries [37], as well as the data of table 1 have taken from the same

265

libraries. All the examined working fluids are dry fluids and they are common in

266

similar studies with ORCs.

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The most important parameter for all the working fluids is critical temperature

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because it determines the maximum evaporating temperature level in the subcritical

269

cycle. Working fluids with critical temperature in the region close to 200-300oC are

270

selected to be examined because the heat sources temperature levels of this study are

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close to this region. It is essential to state that the maximum examined heat source

272

temperatures in this study are close to 300oC – 350oC.

Toluene

MDM

Cyclohexane

n-pentane

350

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300

200

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T (oC)

250

150

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100 50 0 -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

s (kJ/kg K)

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Figure 4. The saturation lines of the examined organic fluids in T-S diagram

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Table 2. The examined organic fluids in the ORC [37, 45] Working

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Tcrit o

pcrit

MW

ODP

GWP ASHRAE group

( C)

(bar)

(kg/kmol)

Toluene

318.60

41.26

92.14

0

3

B3

MDM

290.90

14.15

236.5

0

n.a

A2

Cyclohexane

280.49

40.75

84.16

0

n.a

A3

n-pentane

196.55

33.70

72.15

0

5

A3

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fluids

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ACCEPTED MANUSCRIPT 2.3 Mathematical formulation

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This subsection is devoted to describing the basic mathematical modeling if the

280

present system. The given equation concern energy balances, index definitions and

281

other useful modeling assumptions.

282

2.3.1 Solar field modeling

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In this subsection, a detailed thermal modeling for the module Eurotrough is

284

presented. These equations can be combined together and finally, the thermal

285

efficiency of the solar collector can be calculated in every case.

286

Parabolic trough collectors are imaging concentrating collectors with high

287

concentration ratio and they exploit only the direct beam part of the incident solar

288

irradiation [20]. Thus, the available solar energy is calculated as the product of the

289

outer aperture (Aa) and the solar beam irradiation (Gb).

290

Qs = Aa ⋅ Gb ,

291

The outer absorber area is calculated according to equation 6, using the outer absorber

292

diameter (Dro) and the length (L) of the evacuated tube. The inner absorber area, as

293

well as the cover areas (inner and outer), can be calculated with similar formulas as

294

equation 6.

295

Aro = π ⋅ Dro ⋅ L ,

296

The useful energy that the heat transfer fluid gains are able to be calculated according

297

to the energy balance of its volume, as it is given in equation 7. It is important to state

298

that this quantity represents the useful heat of one module of the total system. The

299

specific heat capacity (cp) corresponds to the working fluid of the solar collector which

300

is nanofluid in the majority of the cases and pure thermal oil in only some cases.

(5)

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(6)

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ACCEPTED MANUSCRIPT 301

Qu = mcol ⋅ c p ⋅ (Tcol ,out − Tcol ,in ) ,

302

It is useful to state that the mass flow rate (m) is calculated as the product of the fluid

303

density (ρ) and the volumetric flow rate (V):

304

mcol = ρ ⋅ V / 3600 ,

305

The most important index for the evaluation of the solar collector is the thermal

306

efficiency (ηth). This parameter is calculated as the ratio of the useful energy to the

307

available solar energy:

308

η th =

309

If the solar collector modules are connected in parallel series, as in the present study,

310

then the thermal efficiency of one module is the same for the entire collector field [46].

311

So, the total useful energy of the collector field is calculated as:

312

Qu ,t = ηth ⋅ Qsol ,t ,

313

For “N” PTC modules, the total available solar irradiation Qsol,t is calculated as:

314

Qsol ,t = N ⋅ Qsol ,

315

The thermal losses of the absorber (Qloss), for one module, are radiation losses, as

316

equation 12 shows. It is important to state that in the evacuated tube collectors the heat

317

convection losses are neglected due to the vacuum between absorber and cover [47].

318

Qloss =

(7)

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(8)

(9)

(10)

(11)

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Qu , Qs

(

)

Aro ⋅ σ ⋅ Τr4 − Tc4 , 1 1 − ε c  Aro   + ⋅ εr ε c  Aci 

(12)

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ACCEPTED MANUSCRIPT 319

The emissivity of the absorber (εr) is calculated as a function of its mean temperature

320

[48]:

321

ε r = 0.000327 ⋅ Tr − 0.065971,

322

In steady-state conditions, as in the present modeling, the thermal losses of the

323

absorber to the cover are equal to the thermal losses of the cover to the ambient. Cover

324

losses thermal energy due to radiation and to convection, as equation 14 shows [49]:

325

4 , Qloss = Aco ⋅ hout ⋅ (Tc − Tam ) + Aco ⋅ σ ⋅ ε c ⋅ Tc4 − Tsky

326

The sky temperature is calculated as [50]:

327

Tsky = 0.0553 ⋅ Tam ,

328

The heat convection coefficient between cover and ambient (hout) is estimated

329

according to equation 16 [49]:

330

0.58 hout = 4 ⋅ Vwind ⋅ Dco−0.42 ,

331

The wind velocity (Vwind) has a low impact on the results due to the evacuated tube. In

332

this study, this parameter is selected to be 1 m/s which leads approximately to hout = 10

333

W/m2K [49].

334

The energy balance on the absorber is a basic equation in the presented analysis

335

because this equation correlates the useful energy and the thermal losses, as equation

336

17 indicates. More specifically, this equation shows that the absorbed solar energy

337

(Qs· ηopt) is separated to useful heat and to thermal losses.

338

Qs ⋅ η opt = Qu + Qloss ,

SC

(14)

(15)

(16)

AC C

EP

TE D

1.5

)

M AN U

(

RI PT

(13)

(17)

17

ACCEPTED MANUSCRIPT 339

The optical efficiency (ηopt) is depended on the incident angle. The indecent angle

340

modifier K is used in order to calculate the optical efficiency of the collector for

341

various incidents angles [51].

342

ηopt (θ ) = ηopt (θ = 0ο )⋅ Κ (θ ) ,

343

In order to correlate the temperature level on the absorber and the fluid operational

344

temperature level, the heat transfer analysis inside the absorber tube has to be

345

examined. The next equation describes that heat transfer from the absorber to the

346

working fluid.

347

Qu = h ⋅ Ari ⋅ (Tr − T fm ) ,

348

The mean temperature of the working fluid is calculated as:

349

T fm =

350

A critical parameter of this modeling is the heat transfer coefficient (h) between

351

absorber tube and fluid. The tube geometry, the flow rate and the properties of the fluid

352

with the thermal conductivity play a significant role in the determination of the heat

353

transfer coefficient. The following equation shows the way that the heat transfer

354

coefficient can be calculated with the use of the dimensionless Nusselt number (Nu).

355

h=

356

Generally, the Nusselt number is determined with experimental analysis and there are

357

many literature equations about this number, for different operating conditions.

358

Usually, some other dimensionless numbers are used in these equations. These

359

numbers are presented below:

,

(19)

(20)

AC C

EP

TE D

2

M AN U

Tcol ,in + Tcol ,out

SC

RI PT

(18)

Nu ⋅ k , Dri

(21)

18

ACCEPTED MANUSCRIPT 360

Reynolds number (Re) in circular tubes is given below:

361

Re =

362

Prandtl number (Pr) is presented below:

363

Pr =

364

In this study, the Reynolds number is over 2300 and thus the flow is assumed to be

365

turbulent. More specifically, the Reynolds number is varied from 11,000 to 25,000

366

approximately. Different equations about the Nusselt number have been used for the

367

different working fluids in the PTC.

368

For the pure thermal oil case, the Dittus-Boelter equation for turbulent flow is used

369

[52]. This equation is valid for Reynolds numbers over 10,000 and Prandtl number

370

between 0.7 and 160.

371

Nu = 0.023 ⋅ Re 0.8 ⋅ Pr 0.4 ,

372

For Syltherm 800 and Al2O3, the equations 25, which is suggested by Pak and Cho

373

[53], is used. This equation is valid for Prandtl number between 6.5 and 12, for

374

Reynolds numbers between 10,000 and 100,000, and for concentrations up to 10%.

375

Nu = 0.021 ⋅ Re 0.8 ⋅ Pr 0.5 ,

376

For operation with Cu and CuO as nanoparticles inside the thermal oil, the equation of

377

Xuan and Li is applied [54]. The experiments of this Ref have been made for Reynolds

378

number between 10,000 and 25,000, while the concentration was up to 2%.

379

Nu = 0.059 ⋅ 1 + 7.68 ⋅ φ 0.6886 ⋅ (Re⋅ Pr )

4⋅m , π ⋅ Dri ⋅ µ

,

(23)

TE D

M AN U

SC

k

RI PT

µ ⋅ cp

(22)

AC C

EP

(24)

[

(25)

0.001

]⋅ Re

0.9238

⋅ Pr 0.4 ,

(26) 19

ACCEPTED MANUSCRIPT 380

For the case of TiO2, the equation of Duangthongsuk and Wongwises [41] is selected

381

to be used. The experiments of this Ref have been made for Reynolds number between

382

3,000 and 28,000, while the concentration was up to 2%.

383

Nu = 0.074 ⋅ Re 0.707 ⋅ Pr 0.385 ⋅ (100 ⋅ φ )

384

2.3.2 Storage tank and heat recovery system modeling

385

In the storage tank of the system, heat is stored in the thermal oil. This storage is

386

sensible and it is based on the increase on the thermal oil temperature increase. In the

387

present study, there is a heat exchanger in order the nanofluid not to be mixed with

388

the thermal oil. The heat exchanger is designed properly in order high heat amounts to

389

be transferred from the collector loop to the storage tank. The heat transfer from the

390

collector loop to the storage tank is assumed to be equal to the useful energy

391

production every time moment, a reasonable assumption for the steady state model.

392

This assumption practically leads to zero thermal storage on the collector loop,

393

something acceptable because of the low mass quantity in this loop tubes. So, the

394

following equation is used in this modeling:

395

Qu ,t = (UA)c − st ⋅

396

The total heat transfer coefficient (UA)c-st is taken equal to 12 kW/m2K in this study.

397

This parameter can be modified by designing greater or smaller heat exchanger, as

398

well as changing the shape of the heat exchanger area. It is also important to state that

399

the storage tank is assumed to have uniform temperature level equal to Tst. The

400

general energy balance on the storage tank is given below [46]:

401

Q stored = Qu ,t − Qloss − m s ⋅ c p s ⋅ (Ts ,in − Ts ,out ) ,

(27)

RI PT

,

TE D

M AN U

SC

0.074

EP

Tcol ,out − Tcol ,in

,

(28)

AC C

 Tcol ,out − Tst  ln    Tcol ,in − Tst 

(29) 20

ACCEPTED MANUSCRIPT 402

In steady state conditions, the stored energy (Qstored) is equal to zero. For the

403

definition of the thermal losses (Qloss), the following equation is used:

404

Qloss = U st ⋅ Ast ⋅ (Tst − Tam ) ,

405

The heat transfer coefficient (Ust) includes radiation, convection and conduction

406

losses and it is taken equal to 0.5 · 10-3 kW/m2K [55]; a value which corresponds to a

407

well-insulated storage tank. The outer area of the storage tank (Ast) can be calculated

408

according to Ref [55] for a cylindrical storage tank. The volume of the storage tank is

409

selected to be 10 m3. This parameter has a low impact on the system performance,

410

especially in steady state conditions as in this work.

411

On the other side of the system, heat is transferred to the ORC. Hot thermal oil from

412

the upper part of the storage tank with temperature (Ts,in) goes to the heat recovery

413

system and heat (Qin) is transferred in the ORC. The colder thermal oil, in the outlet

414

of the heat recovery system, has a temperature (Ts,out). Figure 5 depicts the general

415

heat exchange process inside the storage tank. The pinch point is observed at the start

416

of the evaporator and the temperature of the thermal oil at this point is calculated as:

417

Ts , m = Tsat + PP ,

418

At this study, the pinch point is taken equal to 20 oC, a typical value according to the

419

literature [33].

(31)

AC C

EP

TE D

M AN U

SC

RI PT

(30)

21

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

420

TE D

Figure 5. The heat transfer process in the heat recovery system

421

2.3.3 ORC modeling

423

The basic equations which describe the thermodynamic performance and operation of

424

the ORC are given in this subsection. These equations express mainly the energy

425

balances in the devices of the ORC.

426

The expansion in the turbine is modeled with the isentropic efficiency which is

427

defined as:

428

η is =

AC C

EP

422

h4 − h5 , h4 − h5is

(32)

22

ACCEPTED MANUSCRIPT The state point 5is has the same entropy with the state point 4 and its pressure is equal

430

to pl. This pressure level (pl) is the saturation pressure for heat rejection temperature

431

level (Tc).

432

The produced power (Pel) in the electrical generator is calculated according to

433

equation 33:

434

Pel = η mg ⋅ mo ⋅ (h4 − h5 ) ,

435

The power consumption (Wp) in the organic fluid heat pump is calculated as:

436

Wp =

437

The net power production (Pnet) of the ORC is the difference between the power

438

production in the electrical generator and the power consumption of the pump.

439

Pnet = Pel − W p ,

440

The high-pressure of the system is an important variable parameter in this study. The

441

pressure ratio (PR) is a dimensionless parameter which expresses the high-pressure.

442

This parameter is defined as the ratio of the high pressure to the critical pressure of

443

the fluid. The maximum value of this parameter is 0.9 for safety and stability reasons

444

[33].

SC

(33)

(34)

(35)

EP

TE D

M AN U

mo ⋅ ( ph − pl ) , ρ o ⋅η pum

AC C

445

RI PT

429

PR =

ph , p crit

(36)

446

The thermal efficiency (or thermodynamic efficiency) of the ORC (ηorc) is the ratio of

447

the net produced electricity to the heat input:

23

ACCEPTED MANUSCRIPT Pnet , Qin

448

η orc =

449

The heat input (Qin) can be calculated by the energy balance on the HRS by assuming

450

an ideal heat exchange:

451

Qin = mo ⋅ (h4 − h3 ) = m s ⋅ c ps ⋅ (Ts ,in − Ts ,out )

452

The system thermodynamic efficiency (ηsys) is calculated as:

453

η sys =

454

2.4 Methodology

455

In this study, the depicted system on figure 1 is examined and optimized. The basic

456

goal is to achieve maximum electricity production by keeping constant the collector

457

field area. Different working fluids are examined in the ORC and in the solar field

458

loop. More specifically, toluene, MDM, cyclohexane and n-pentane are the examined

459

organic fluids in the ORC cycle. In the solar field loop, four different nanofluids are

460

tested (Al2O3, CuO, TiO2 and Cu) inside Syltherm 800. Thus, four different

461

nanofluids, as well as pure Syltherm 800 are examined as working fluids in PTCs.

462

Totally twenty combinations of working fluids are investigated in this work.

463

At this point, it is essential to explain the way that this analysis is performed. The first

464

step (subsection 3.1) is the preliminary analysis of the system. In this analysis

465

(subsection 3.1.1), a simple strategy is followed in order to find how the examined

466

parameters (mainly nanoparticle concentration and pressure in the turbine inlet)

467

influence on the results. In this direction, the two main subsystems (solar field and

468

ORC) are examined separately. In the analysis of the PTC system, all the nanofluids

(38)

SC

,

RI PT

(37)

(39)

AC C

EP

TE D

M AN U

Pnet , Q s ,t

24

ACCEPTED MANUSCRIPT are examined for different concentrations ratios and for a typical inlet temperature in

470

the solar field (Tcol,in = 300oC). Moreover, the four organic fluids are compared for

471

different pressure ratios (PR). The best candidates from these sensitivity analyses are

472

selected to be examined deeper. In this analysis, different combinations of

473

nanoparticle concentration (φ) and pressure ratio (PR) are examined simultaneously

474

and the optimum combination of these parameters, which maximizes the system

475

electricity production (PTC and ORC) is found. In the next part of the preliminary

476

analysis, two different sensitivity analyses are performed (subsection 3.1.2). In the

477

first sensitivity analysis, the optimum nanofluid concentration is kept constant and the

478

pressure ratio is examined parametrically. In the second sensitivity analysis, the

479

pressure ratio is kept to its optimum value and the concentration is examined

480

parametrically. This strategy indicates how the parameters influence the system

481

performance and give reasons for the existence of an optimum solution.

482

The next step is the optimization of the total system with a more accurate way

483

(subsection 3.2). For all the working fluids combinations (20 combinations), an

484

optimization procedure is followed using the “Conjugate Directions Method” or

485

“Powell's method”. This method is supported by the utilized tool which is EES

486

(Engineering Equation Solver) by f-chart [37]. The relative convergence tolerance is

487

selected equal to 10-8 and a maximum number of iterations (function calls) is selected

488

to 104 (usually the solution was found after 200 to 300 iterations). A simple flow chart

489

for the optimization procedure is given in figure 6.

490

In this optimization procedure, the concentration of the nanoparticles is the first

491

optimization variable and it is varied from zero up to 6%. The second optimization

492

variable is the pressure ratio which varies from 10% up to 90%. For all the organic

493

fluids, 10% of pressure ratio is greater than the condensation temperature and so it

AC C

EP

TE D

M AN U

SC

RI PT

469

25

ACCEPTED MANUSCRIPT pressure ratio leads to acceptable values. Moreover, the upper limit is set to 90% in

495

order to keep a relatively safe distance to the critical point. It is important to note that

496

in the cases with pure Syltherm 800 in the collector loop, the nanoparticle

497

concentration is set to zero and only the pressure ratio is the optimization variable.

498

After performing twenty optimization procedures, the final optimum cases are

499

compared to each other in order to determine the global optimum solution. This global

500

optimum solution is a result of four different optimization parameters: nanoparticle

501

type, organic fluid, nanoparticle concentration and pressure ratio.

502

At the last part of this subsection, the basic parameters of the system simulation are

503

given in table 3. The majority of these parameters have typical values in order to

504

perform a representative study of the real systems. For the solar collector, the data

505

have been taken by Refs [48, 56] and the efficiencies have been taken from Ref [33].

506

Table 3. System constant parameters Parameters Values Ambient temperature (Tam) 25oC Solar beam irradiation (Gb) 0.8 kW/m2 Condenser temperature (Tcon) 40 oC Pinch point (PP) 20 oC Temperature difference in recuperator (∆Trc) 20 oC Electromechanical efficiency of the generator (ηmg) 98% Turbine isentropic efficiency (ηis) 85% Organic fluid pump efficiency (ηpum) 70% Thermal loss coefficient of the storage tank (Ust) 0.5·10-3 kW/m2K Storage tank volume (Vst) 10 m3 Heat exchanger effectiveness (UA)c-st 12 kW/m2K Volumetric flow rate on the collector module (V) 3 m3/h Number of modules (N) 15 Module collecting area (Aa) 69.2 m2 Collector module length (L) 12 m Incident angle modifier (K) ~1 Maximum optical efficiency [ηopt(θ=0ο)] 0.741 Absorber inner diameter (Dri) 0.066 m Absorber outer diameter (Dro) 0.070 m Cover inner diameter (Dci) 0.120 m Cover outer diameter (Dco) 0.125 m Cover emittance (εc) 0.90 Wind speed (Vwind) 1 m/s

AC C

EP

TE D

M AN U

SC

RI PT

494

26

ACCEPTED MANUSCRIPT It is essential to state that the solar irradiation has been kept constant during this

508

analysis. This strategy is followed in order to give the emphasis in the selection of the

509

proper working fluids and of the proper system characteristics. The selected value of

510

0.8 kW/m2 is a usual value in real applications and it is a reliable solution for sizing

511

the system in realistic conditions. It is useful to state that for the financial examination

512

of the system, the daily variation of the solar irradiation has to be examined, but this is

513

the objective of future studies on this system. It is important to state that the

514

developed model has been validated and used in other previous literature studies and

515

thus there is no reason for giving again theis validation evidence. More specifically,

516

the ORC modeling has been validated in Ref [33] and the parabolic trough collector

517

modeling has been validated in Refs [9, 57].

AC C

EP

TE D

M AN U

SC

RI PT

507

518 519

Figure 6. Flow chart of the optimization procedure

27

ACCEPTED MANUSCRIPT 3. Results

521

3.1 System performance with the parameter variation

522

3.1.1 Preliminary analysis

523

The objective of this subsection is to present the energetic behavior of the various

524

subsystems for different values of critical parameters. Firstly, the ORC is examined

525

and results for the thermal efficiency (ηorc) are presented in figure 7. In this figure,

526

different pressure ratios (Pratio) are applied for all the examined working fluids. In this

527

analysis, only the ORC is examined without the solar field. According to the results of

528

figure 7, higher pressure ratio leads to higher thermal efficiency. This result is based

529

on the simultaneous increase of the saturation temperature with the increase of the

530

high pressure or the pressure ratio. This fact makes the cycle to operate with a greater

531

high-temperature level and according to the ideal Carnot cycle, the thermal efficiency

532

is getting higher. The increase in the thermal efficiency is getting lower for greater

533

pressure ratios and the curves tend towards to horizontal. This fact is explained by the

534

decrease of (dTsat/dp) for higher pressures. The most efficient working fluid is toluene

535

with MDM, cyclohexane and n-pentane to follow respectively. The first three

536

working fluids lead to similar performance while the n-pentane leads to lower

537

performance. This result can be explained by the relatively lower critical temperature

538

(see table 2) of the n-pentane which creates a restriction in the system thermal

539

efficiency.

540

Figure 8 depicts the thermal efficiency of the solar collector (ηth) for the examined

541

nanofluids and for various concentrations. The zero concentration represents the

542

operation with pure Syltherm 800 and thus all the curves start from the same point.

543

These results concern operation with inlet temperature equal to 300oC. This

544

temperature level is representative for this study and thus it is selected. However, the

AC C

EP

TE D

M AN U

SC

RI PT

520

28

ACCEPTED MANUSCRIPT conclusions are the same for all the inlet temperature levels because in all cases, an

546

enhancement is achieved with the use of nanofluids. It is obvious that higher

547

nanoparticle concentration leads to higher thermal efficiency. The use of Al2O3 and

548

TiO2 leads to similar results and their curves are approximately the same. On the other

549

hand, the use of Cu and CuO presents similar behavior with Cu to leads to higher

550

thermal performance. Moreover, figure 8 shows that the use of CuO and Cu in the

551

thermal oil leads to a significant enhancement of the thermal performance, especially

552

for great concentrations.

MDM

0.35 0.30

0.20 0.15 0.10 0.05 0.00

554 555

0.3

EP

0.2

AC C

0.1

TE D

ηorc

0.25

553

Cyclohexane

n-pentane

M AN U

Toluene

SC

RI PT

545

0.4

0.5

0.6

0.7

0.8

0.9

Pressure Ratio - PR

Figure 7. Thermal efficiency of the ORC without the solar field for various working fluids and pressure ratios

29

ACCEPTED MANUSCRIPT 0.700

Syltherm 800 + Al₂O₃

Syltherm 800 + CuO

Syltherm 800 + TiO₂

Syltherm 800 + Cu

0.695

RI PT

ηth

0.690 0.685 0.680

0.00

0.01

0.02

0.03

φ

0.04

0.05

0.06

M AN U

556

SC

0.675

Figure 8. Thermal efficiency of nanofluids for various concentrations with the

558

inlet temperature equal to 300oC

559

Figures 7 and 8 proved that toluene and Syltherm 800 with Cu are the best candidates

560

for utilization in the examined system. Thus, the operation with these fluids is

561

examined with more details in this subsection. Figure 9 shows the electricity

562

production for various concentrations and for six pressure ratios (from 0.4 to 0.9). In

563

every curve of this figure, the maximum point is depicted. According to the results,

564

the global maximum is observed for pressure ratio equal to 0.8 and concentration

565

2.50%, with the electricity production to be 166.19 kW. The next case is for pressure

566

ratio 0.7 and concentration 2.75% where the electricity production is 166.18 kW.

567

These solutions are similar and maybe equivalent. The next choice is for pressure

568

ratio 0.6 and 3% concentration with 165.06 kW. An interesting observation is that the

569

optimum concentration is getting lower for higher pressure ratios and it is ranged

570

from 2.25% (for PR=0.9) to 3.75% (for PR=0.4). Figure 10 is a three-dimensional

571

depiction of figure 9 and it is presented for giving a better image of the optimization

AC C

EP

TE D

557

30

ACCEPTED MANUSCRIPT need. In other words, the green-top area in the electrical output surface is the optimum

573

area. All the optimum solutions are located in the projection of this area to the

574

horizontal surface (PR - φ). This observation proves the need of a deeper optimization

575

procedure in order to determine in every case an optimum couple of pressure ratio and

576

nanoparticle concentration.

577

The results of figures 9 and 10 prove that there is an internal optimum solution which

578

maximizes the electricity production. However, this result is maybe strange because

579

the separate analysis in figures 7 and 8 does not indicate this. More specifically, figure

580

7 shows that higher pressure ratio leads to greater ORC efficiency and figure 8 shows

581

that higher nanoparticle concentration leads to higher solar thermal collector

582

efficiency. Figures 9 and 10 prove that the combination of the solar system and the

583

ORC operates optimally for intermediate values of concentration and pressure ratio.

584

This result is very interesting and it will be examined in subsection 3.1.2 in details.

585

Moreover, the system efficiency (ηsys) is illustrated in figure 11. This figure proves

586

that the system efficiency surface has a similar shape with the one of the electricity

587

production (figure 10). The maximum efficiency is 20.00%, while the lowest system

588

efficiency, for the depicted cases, is 18.85%.

AC C

EP

TE D

M AN U

SC

RI PT

572

31

ACCEPTED MANUSCRIPT PR = 0.8 PR = 0.5

PR = 0.7 PR = 0.4

RI PT

167 166 165 164 163 162 161 160 159 158 157 156 0.00

0.01

0.02

0.03

φ

0.05

0.06

M AN U

589

0.04

SC

Pel (kW)

PR = 0.9 PR = 0.6

Figure 9. Electricity production for operation with toluene and Cu nanofluid.

591

The red points represent the maximum points of the examined curves.

592

AC C

EP

TE D

590

593

Figure 10. Three-dimensional depiction for the optimization procedure of

594

electricity output. These results correspond the case with toluene and Cu

595

nanofluid.

32

0.1975-0.2000 0.1900-0.1925 0.1825-0.1850

0.1950-0.1975 0.1875-0.1900 0.1800-0.1825

0.2025 0.2000 0.1975 0.1950 0.1925 0.1900 0.1875 0.1850 0.1825 0.1800

RI PT

0.2000-0.2025 0.1925-0.1950 0.1850-0.1875

ηsys

ACCEPTED MANUSCRIPT

0.0%

1.0%

2.0% 3.0% 4.0% 0,5

PR

5.0% 6.0%

φ

SC

596

0,7

M AN U

0,9

597

Figure 11. System efficiency for various concentrations and pressure ratios.

598

These results correspond the case with toluene and Cu nanofluid. 3.1.2 Parametric analysis

600

In order to perform a deeper analysis, two cases will be examined with more details.

601

The first is for constant nanoparticle concentration and variable pressure ratio, while

602

the second is for constant pressure ratio and different nanoparticle concertation. This

603

method will try to approximate the maximum point with two lines, one parallel to the

604

nanoparticle axis (see the black line in figure 10) and the other parallel to the pressure

605

ratio axis (see the red line in figure 10).

606

Figures 12 to 14 are devoted to the first case with constant nanoparticle concentration

607

(2.5%). Figure 12 shows that the saturation temperature increases with the increase of

608

the pressure ratio. This result makes all the system temperature levels to increase.

609

More specifically, the thermal oil temperature in the heat recovery system is getting

610

greater with the increase of the saturation temperature. The thermal oil outlet

611

temperature (Ts,out) has similar values with the saturation temperature, as the Q-T

AC C

EP

TE D

599

33

ACCEPTED MANUSCRIPT diagram of figure 5 also indicates. The inlet temperature in the HRS (Ts,in) is higher

613

than (Ts,out) in order to give the demanded heat to the ORC. The temperature levels of

614

the nanofluid in the collector loop are higher that the thermal oil temperature levels in

615

the thermal oil loop (storage tank and HRS). The inlet temperature in the collector

616

field (Tcol,in) is a bit higher than the storage tank temperature (which equal to Tl,in in

617

the present modeling), while the collector field outlet temperature (Tcol,out) is the

618

highest temperature in the system.

619

The temperature level variation, which is depicted in figure 12, influence on the

620

various subsystem efficiencies (ORC and PTC), as well as in the total system

621

efficiency (ηsys). All these indexes are given in figure 13 for various pressure ratios.

622

Higher pressure ratio leads to higher temperature level in all the points of the system,

623

a fact that makes the subsystem to have different behavior. The higher temperature in

624

the solar collector makes its thermal efficiency to get lower. On the other hand, higher

625

temperature in the ORC and especially in the turbine inlet (or higher saturation

626

temperature) makes the thermodynamic efficiency to be higher. The system

627

performance is strongly influenced by these two parameters and thus the system

628

efficiency presents maximum point for an intermediate pressure ratio. This is a very

629

interesting result and it proves the need for a detailed optimization procedure of the

630

cycle. Figure 13 shows that the thermal efficiency on PTC is ranged from 65.59% to

631

71.43%, the ORC efficiency from 20.97% 30.52% and the system efficiency from

632

14.90% to 20.00%. The system efficiency is maximized for pressure ratio equal to

633

0.8, and for this pressure ration the PTC efficiency is 66.13%, the ORC efficiency is

634

30.52% and the system efficiency 20.00%.

AC C

EP

TE D

M AN U

SC

RI PT

612

34

ACCEPTED MANUSCRIPT Tcol,out

Tcol,in

Ts,in

Ts,out

Tsat

400

300

RI PT

Temperature (oC)

350

250 200 150 0.2

0.3

0.4

0.5

0.6

0.7

SC

0.1

0.8

0.9

Pressure ratio - PR

M AN U

635

Figure 12. Temperature levels in the system for various pressure ratios when the

637

Cu concentration is 2.5% and toluene is the organic working fluid

638

The next step is to investigate the energy flow inside the system. Figure 14 depicts the

639

basic heat and electricity streams in the system for various pressure ratios. More

640

specifically, the electricity production (Pel), the heat input in the ORC (Qin) and the

641

useful energy production in the collector field (Qu,t) are given for various pressure

642

ratios in this figure. The heat input in the ORC is lower than the useful energy

643

production in the collector field (Qin < Qu,t) due to the thermal losses in the storage

644

tank. The electricity production is a small fraction of the heat input in the ORC

645

because of the relatively small thermodynamic efficiency of the cycle (ηorc).

646

The electricity production curve presents maximum for pressure ratio close to 0.8.

647

This result is interesting and it can be explained by the results of figure 14. For this

648

pressure ratio, the electricity production is 166.19 kW, the heat input in the system is

649

544.4 kW and the useful heat production in the collector field is 549.4 kW.

AC C

EP

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636

35

ACCEPTED MANUSCRIPT System

ORC

PTC

0.8 0.7

0.5 0.4

RI PT

Efficiency

0.6

0.3 0.2 0.1 0.0 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

SC

0.1

Pressure ratio - PR

M AN U

650 651

Figure 13. Efficiencies (ORC, PTC and system) for various pressure ratios when

652

the Cu concentration is 2.5% and toluene is the organic working fluid

Pel

TE D

170 165 160 155 150 145 140 135 130 125 120

580 570 560

EP

Energy (kW)

590

Qu,t

550

AC C

540 530

0.1

653

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Electricity (kW)

Qin 600

0.9

Pressure ratio - PR

654

Figure 14. Electricity production, useful energy production in the collector field

655

and heat input in the ORC for various pressure ratios (Cu concentration 2.5%

656

and toluene)

36

ACCEPTED MANUSCRIPT The next step in this analysis is to examine the cases of constant pressure ratio equal

658

to 0.8 and the nanoparticle concentration to be a variable parameter. Figures 15 and

659

16 include the respective results for this case with toluene and Cu nanoparticles.

660

Figure 15 gives the various temperature levels in the system and the most variable

661

properties of the nanofluid with the different concentrations (specific heat capacity

662

and density). These thermal properties are calculated for the mean nanofluid

663

temperature in the solar collector. It is obvious that the temperature difference in the

664

nanofluid circuit (Tcol,out - Tcol,in) is getting lower with the increase in concentration

665

(blue color curves). The main reason for this result is the variation of the thermal

666

properties. Higher density is achieved with the increase in the concertation and this

667

fact makes the mass flow rate to be higher. This situation makes the temperature

668

difference to be lower for higher φ. However, the simultaneous decrease in the

669

specific heat capacity comes to counterbalance this situation and the phenomenon is

670

not very intense. The temperature difference in the thermal oil circuit (black color

671

curves) has also decreasing rate. This result is explained by the increase in the thermal

672

oil specific capacity and the decrease in the heat transfer quantity in high

673

concentrations, as figure 15 shows.

674

Figure 16 proves that there is an optimum concentration where the electricity

675

production is maximized. For the present case, this concentration is 2.5% and the

676

electricity production is 166.19 kW. The heat input in the system is 544.4 kW and the

677

useful heat production is 549.4 kW. These numbers are the same as it is presented in

678

figure 14. This result is reasonable because the optimum point of figure 14 is the same

679

to the optimum point of figure 16. This optimum point is the global optimum point of

680

figure 10 and it is the cross-section of the read and the black curves in figure 10.

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657

37

ACCEPTED MANUSCRIPT It would be valuable to state that the existence of the optimum concentration is an

682

important result which has to be explained more. The decreasing rate of temperature

683

difference (Tcol,out - Tcol,in) in figure 15, leads to lower heat input (Qin) in the storage

684

tank. On the other hand, higher concentration leads to greater thermal efficiency

685

(figure 8). These reverse factors lead to an optimum concentration which leads to

686

maximum system performance.

Tcol,in

Ts,in

Ts,out

SC

355 345

M AN U

Temperature (oC)

ρ

335 325 315 305 295 275 0.00

TE D

285 0.01

0.02

0.03

cp 2500 2000 1500 1000 500

ρ (kg/m3) , cp (J/kg K)

Tcol,out 375 365

RI PT

681

0 0.04

0.05

0.06

concentration - φ

687

Figure 15. Temperature levels in the system, nanofluid density and nanofluid

689

specific heat capacity for various concentrations of Cu nanoparticles (PR=0.8)

AC C

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688

38

ACCEPTED MANUSCRIPT Qin

Qu,t

Pel

552

166.5

550

544

165

542

RI PT

Energy (kW)

165.5

546

164.5

540

Electricity (kW)

166

548

164

538 536

163.5

0.01

0.02

0.03

0.04

concentration - φ

690

0.05

0.06

SC

0.00

Figure 16. Electricity production, useful energy production in the collector field

692

and heat input in the ORC for various concentrations of Cu (PR=0.8)

693

The results of subsection 3.1.2 showed that for every pressure ratio, there is an

694

optimum concentration and for every concentration, there is an optimum pressure

695

ratio which maximizes the electricity production. These results are taken for the case

696

with Cu nanoparticle and toluene as organic fluid.

697

3.2 Optimization results

698

The results of the previous analysis proved that there is need of systematic

699

optimization. In this section, the optimum pressure ratio and concentration are

700

determined for all the combinations between nanoparticles and organic working

701

fluids. A more detailed methodology is followed, by using the “Conjugate Directions

702

Method” which is supported by EES. More specifically, for every combination of

703

organic fluid and fluid in the PTC circuit, an optimization procedure is followed. In

704

this procedure, the nanofluid concentration and the pressure ratio are the optimized

705

parameters. For the case of thermal oil in the PTC circuit, the concentration is kept

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39

ACCEPTED MANUSCRIPT equal to zero in the optimization. So, twenty different combinations are examined and

707

the results are given below in figures 17 to 20 and in table 4.

708

Figure 17 illustrates the electricity production for the all the optimized cases. It is

709

obvious that toluene is the best working organic fluid in all the cases. MDM comes

710

second with cyclohexane and n-pentane to follow respectively. It is important to state

711

that n-pentane is the less suitable working fluid for this system because of its lower

712

critical temperature which makes restriction in the maximum work production from

713

the thermodynamic cycle. Among the nanofluids, CuO is the best candidate and it

714

leads to 167.05 kW electricity production combined with toluene. The next candidate

715

is Cu with 166.32 kW, while Al2O3 and TiO2 follow with 165.72 kW and 165060 kW

716

respectively. The case with pure thermal oil leads to the lowest electricity production

717

with 164.18 kW. This consequence (CuO, Cu, Al2O3, TiO2, thermal oil) in the

718

performance is the same for all the organic fluids and this is an important result.

719

Moreover, it is useful to comment about the exact electricity productions for all the

720

organic fluids with the best nanoparticle (CuO). As it has been said, the electricity

721

production with toluene is 167.05 kW. MDM, cyclohexane and n-pentane lead to

722

164.86 kW, 160.01 kW and 117.02 kW respectively.

723

It is obvious that the impact of the organic fluid selection in higher on the electricity

724

production than the impact of the proper nanofluid selection. This result indicates that

725

the utilization of the best organic working fluid is the major step in every optimization

726

procedure. On the other hand, the use of nanofluid leads always to higher

727

performance, compared to the pure thermal oil case. This result indicates the use of

728

nanoparticles inside the base fluid in order to achieve higher performance in all the

729

cases. Figure 18 shows the system efficiency results for all the optimized cases. The

730

results of this figure are similar to the results of figure 17 but they are expressed in

AC C

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SC

RI PT

706

40

ACCEPTED MANUSCRIPT efficiency terms. More specifically, again toluene is the best organic working fluid

732

and CuO is the best nanoparticle. The system efficiency with toluene is 20.11% with

733

CuO, 20.02% with Cu, 19.95% with Al2O3 and 19.93% with TiO2. The system

734

efficiency with pure thermal oil is 19.76% and it is the lower than all the cases with

735

nanofluids.

Toluene 180

MDM

167.05

165.72

Cyclohexane 165.60

n-pentane

166.32

140

100 80 60 40 20 0

Al₂O₃

TiO₂

TE D

CuO

M AN U

Pel (kW)

120

737

164.18

SC

160

736

RI PT

731

Cu

Thermal oil

Figure 17. Optimum electricity production for all the examined cases

0.25

0.1995

0.2011

Cyclohexane

0.1993

n-pentane

0.2002

0.1976

AC C

0.20

MDM

EP

Toluene

ηsys

0.15 0.10 0.05 0.00

738 739

Al₂O₃

CuO

TiO₂

Cu

Thermal oil

Figure 18. Optimum system efficiency for all the examined cases 41

ACCEPTED MANUSCRIPT Figures 19 and 20 exhibit the optimum values of the variable parameters. Figure 19

741

gives the optimum nanoparticle concentration for all the examined cases. It is

742

important to state that for the cases with thermal oil, the concentration is set equal to

743

zero. Figure 20 gives the optimum values of the pressure ratio for all the cases. The

744

optimum concentration, in figure 19, presents significant variations in the examined

745

range (0% - 6%). Generally, the n-pentane performs better with the highest possible

746

concentrations close to the upper limit (~6%). Moreover, the Al2O3 inside the

747

cyclohexane obtains it upper limit value for the optimum operation. In the other cases,

748

concentrations from 2.5% to 4.35% are found as optimum. Toluene is the working

749

fluid which needs the lowest concentrations, with MDM, cyclohexane and n-pentane

750

to need higher concentrations respectively. Al2O3 and CuO have to be used in higher

751

concentrations, compared to TiO2 and Cu, as the results proved. For example, toluene

752

needs 4.16% Al2O3 and 3.98% CuO for optimum operation, while 2.57% TiO2 and

753

2.51% Cu. Taking into account all the above, as well as the ORC efficiency results of

754

figure 7, the most efficient working fluids (toluene and MDM), need relatively lower

755

nanofluid concentration in order to achieve maximum system performance. On the

756

other hand, the less efficient working fluids, n-pentane mainly and cyclohexane in

757

some cases, need high concentrations in the nanofluid in order the higher thermal

758

efficiency in the PTC to counterbalance the lower ORC efficiency.

759

Figure 20 depicts the optimum pressure ratios for all the examined cases. It is useful

760

to state again that the maximum value of this parameter is set to 90% in order not to

761

go extremely close to the critical point. Generally, values between 75% and 90% are

762

the optimum, a fact that proves the need for high pressure in the turbine inlet. It is also

763

obvious that the kind of nanofluid (or the pure thermal oil case) does not play a

764

significant role on the optimum pressure ratio. So, for toluene, a pressure level close

AC C

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SC

RI PT

740

42

ACCEPTED MANUSCRIPT to 75% is optimum for all the cases. MDM needs to operate at the highest possible

766

pressure level (PR=90%), while cyclohexane and n-pentane need pressure ratio close

767

to 87%. Practically, the exact curvature of the saturation line is the determining factor

768

for the optimum pressure level in every fluid. As a final result, the pressure ratio has

769

to be selected close to highest possible values except for the case of toluene.

770

However, it is important to state that toluene has the highest critical temperature

771

compared to the other examined organic fluids and this also makes the optimum

772

pressure ratio to bit relatively lower, in order to achieve the suitable (optimum)

773

saturation temperature inside the HRS.

M AN U

Toluene

MDM

0.06 0.05

0.01 0.00

775

n-pentane

Al₂O₃

CuO

TiO₂

Cu

Thermal oil

AC C

774

Cyclohexane

TE D

0.02

EP

φopt

0.04 0.03

SC

RI PT

765

Figure 19. Optimum concentration for all the examined cases

43

ACCEPTED MANUSCRIPT Toluene

MDM

Cyclohexane

n-pentane

0.90 0.85

RI PT

0.75 0.70 0.65

Al₂O₃

CuO

TiO₂

Cu

Thermal oil

M AN U

776

SC

PRopt

0.80

Figure 20. Optimum pressure ratio for all the examined cases

778

Table 4 summarizes the presented results of figures 17 to 20, as well as includes data

779

about the ORC efficiency, the PTC efficiency and the optimum saturation

780

temperatures. It is useful to be commented that the thermal efficiency in the solar field

781

is close to 67%, while the ORC efficiency is close to 28-30% for the three more

782

efficient fluids (toluene, MDM, cyclohexane) and close to 20% about n-pentane. The

783

system efficiency is approximately the product of the previous efficiencies and it is

784

close to 20% for the three more efficient working fluids and close to 14% for n-

785

pentane. The saturation temperature which leads to the optimum operation is variable

786

among the examined working fluid. It is close to 296oC for toluene, 284oC for MDM,

787

269oC for toluene and 187oC for n-pentane. The critical temperature is one parameter

788

which influences on the previous optimum temperature level by creating restrictions

789

in the highest possible saturation temperature (remember the constraint of 90% higher

790

pressure ratio).

AC C

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777

44

ACCEPTED MANUSCRIPT It is valuable to comment about the impact of nanoparticle kind on the final results.

792

Comparing the optimized cases with the same organic fluid, it is obvious that there is

793

a small difference in the system efficiency among the different nanofluids. These

794

results can be explained by two factors. The first one is that the final results are

795

optimized and for every nanofluid, the optimum parameters have been obtained. Thus,

796

this result indicates that all the examined nanoparticles can lead to system

797

performance enhancement. The second factor is based on the high PTC thermal

798

efficiency which gives a small margin of thermal improvement by the use of

799

nanoparticles.

800

Moreover, it is essential to state in the optimum nanoparticles concentrations. Table 4

801

shows that different concentrations are optimum among the examined cases. This

802

result indicates the need of optimization for determining the most suitable

803

concentration in every case. The reason for the existence of optimum concentration

804

has been explained in subsection 3.1.2 and especially with figures 15 and 16. More

805

specifically, for some nanofluids, higher nanoparticle concentration leads to a

806

different temperature in the collector field and in the storage tank and this fact makes

807

the system performance to be variable.

808

Figure 21 illustrates the temperature-specific entropy diagram of the process. This

809

figure depicts the optimum case with toluene and CuO nanofluid. The concentration is

810

3.98% and the pressure ratio 75.51% in order to give the best case. It is obvious that

811

the ORC covers a great part of the saturation area, a fact that proves great temperature

812

difference between the turbine inlet and the condensation temperature. Moreover, the

813

heat transfer from the nanofluid to the thermal oil and from the thermal oil to the

814

organic fluid is also given. It is important to state that the heat transfer from the

815

nanofluid to the thermal oil is achieved with the storage tank, while the heat transfer

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791

45

ACCEPTED MANUSCRIPT 816

from the thermal oil to the nanofluid is done in the heat recovery system. It is also

817

useful to state that the state point 7 is inside the condenser and this is the saturation

818

vapor in the low pressure.

ηorc (%) 30.42 30.42 30.42 30.42 30.43 29.63 29.63 29.63 29.63 29.62 28.42 28.43 28.43 28.43 28.43 19.80 19.80 19.80 19.80 19.79

φ (%) 4.16 3.98 2.57 2.51 0.00 4.35 4.20 2.70 2.66 0.00 6.00 4.75 4.16 3.04 0.00 6.00 6.00 6.00 5.88 0.00

TE D

PR (%) 75.25 75.51 75.48 75.22 75.79 90.00 90.00 90.00 90.00 90.00 86.68 86.83 86.78 86.71 87.13 86.78 86.80 86.75 86.64 86.87

SC

ηth (%) 66.17 66.68 66.10 66.41 65.54 67.05 67.53 67.00 67.26 66.47 67.82 68.28 67.76 68.03 67.18 71.17 71.51 71.15 71.39 70.51

M AN U

ηsys (%) 19.95 20.11 19.93 20.02 19.76 19.70 19.84 19.68 19.76 19.52 19.12 19.26 19.11 19.19 18.94 14.01 14.08 14.01 14.06 13.88

Tsat (oC) 295.6 295.9 295.8 295.5 296.1 283.9 283.9 283.9 283.9 283.9 269.1 269.2 269.2 269.1 269.5 186.7 186.8 186.7 186.6 186.8

AC C

820

Al2O3 CuO TiO2 Cu Thermal oil Al2O3 CuO TiO2 Cu Thermal oil Al2O3 CuO TiO2 Cu Thermal oil Al2O3 CuO TiO2 Cu Thermal oil

Pel (kW) 165.72 167.05 165.60 166.18 164.18 163.66 164.86 163.55 164.19 162.21 158.90 160.01 158.77 159.41 157.41 116.45 117.02 116.41 116.82 115.35

EP

n-pentane

Cyclohexane

MDM

Toluene

Working fluids

RI PT

Table 4. Optimum results for all the examined cases

819

46

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

821 822 823

Figure 21. Temperature – specific entropy diagram for the optimum case with toluene and CuO nanofluid (φ = 3.98% and PR = 75.51%) 3.3 Discussion

825

This subsection is devoted to summarizing the results and to discussing them on a

826

deeper basis. This work is an optimization of a solar driven ORC by using nanofluids

827

inside the PTCs. The main scope of this work is to determine the performance

828

enhancement of the system by using nanofluids, compared to the conventional

829

thermal oil case. Figure 22 gives the enhancement for all the examined cases with

830

nanofluids compared to the respective with pure thermal oil and of course the same

831

organic working fluid. The highest enhancement is found with CuO and they are close

832

to 1.7%. Cu case follows with 1.25%, while Al2O3 leads to 0.95% enhancement and

833

TiO2 to 0.85% enhancement. This enhancement is in the electrical production but it is

834

the same for the system performance. It is essential to state that the comparison is

835

performed with the optimized thermal oil case for the same organic fluid in every

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824

47

ACCEPTED MANUSCRIPT case. So, the results are compared to also optimized cases and the shown enhancement

837

is associated only with the nanofluid utilization.

838

The global maximum enhancement is observed for toluene with CuO nanofluid and it

839

is 1.75%. The next is with cyclohexane and CuO (1.65%) and the third with MDM

840

and CuO (1.63%). Generally, it is obvious that the thermal enhancement is not so

841

great but it is important for improving the performance of the systems. If financial and

842

environmental parameters are taken into account, this enhancement is able to make

843

the investment more sustainable in the total project life horizon. However, the higher

844

cost of working fluid with the nanoparticles, as well as the preparation cost and the

845

operating - maintenance costs have to be taken into account for the final decision of

846

the nanofluid utilization. Moreover, it would be important to state that the equations

847

about the thermal properties of nanofluids (equations 1-4) and the equations about the

848

Nusselt number (equations 25-27) have taken from literature studies. This strategy

849

leads to reliable results but an extra experimental for them would be important and it

850

can be performed in the future.

TE D

M AN U

SC

RI PT

836

1.6% 1.4%

1.75%

1.2% 1.0%

Cyclohexane

n-pentane

1.65% 1.63% 1.45% 1.27% 1.30% 1.27% 1.22%

AC C

Performance enhancement

1.8%

MDM

EP

Toluene

0.95% 0.94% 0.95% 0.89%

0.86% 0.86% 0.92% 0.83%

0.8% 0.6% 0.4% 0.2% 0.0%

851 852

Al₂O₃

CuO

TiO₂

Cu

Figure 22. Performance enhancement with the use of nanofluids 48

ACCEPTED MANUSCRIPT Another interesting result of this study is the results about the best nanoparticle.

854

According to the preliminary study of the solar collector (see figure 8), the best

855

nanoparticle is Cu. However, the analysis of the total system proves that CuO is the

856

best candidate (see for example figure 21). This result is very interesting and proves

857

that a combined analysis (with solar and ORC together) has to be made in order to

858

determine the optimum nanofluid for the examined application. As a final conclusion,

859

the utilization of CuO is the most suitable in the solar driven system because the final

860

optimization results indicated this as the best candidate. However, the performance

861

different between CuO and Cu cases are relatively small.

862

In the last part of the discussion section, it is important to discuss about the

863

assumptions of this study. The adoption of equations 26 and 27 for concentrations up

864

to 6% is an important assumption of this study because the respective experimental

865

studies have been performed for concentrations up to 2%. Moreover, the selection of

866

viscosity models which take into account only the concentration (φ) is a questionable

867

issue. Thus, an extra analysis is given below. The following model of Corcione [58] is

868

selected to be used as a reliable model which takes into account the nanoparticle

869

diameter (dp), as well as the equivalent diameter of the base fluid molecule (df). The

870

nanofluid viscosity is given as [58]:

871

µ nf =

AC C

EP

TE D

M AN U

SC

RI PT

853

µ bf

 dp 1 − 34.87 ⋅  d  f

   

,

− 0.3

(40)

⋅ φ 1.03

872

The equivalent diameter of the base fluid molecule is given as [58]:

873

 6 ⋅ MW d f = 0.1 ⋅   N ⋅π ⋅ ρ bf  a

1

3  ,  

(41)

49

ACCEPTED MANUSCRIPT For Syltherm 800, the molecular weight (MW) is 317 kg/kmol, the density at 293 K

875

(ρbf) is 935.3 kg/m3, while the Avogadro number (Na) is equal to 6.022 · 1026 kmol-1.

876

The nanoparticle diameter (dp) has taken equal to 100 nm or 10-7 m for all the

877

nanoparticles. This diameter selection is the same as in Refs [53-54] and it is a

878

representative value for performing a simple comparative analysis. Equation 40 is

879

valid for concentrations up to 7%, for nanoparticle diameters from 25 nm to 200 nm

880

and for temperatures from 20oC to 60oC. Figure 23 give the comparison between the

881

calculation of viscosity with equation 4a (used in this paper) and equation 40. It can

882

be shown that in low concertation up to 3%, the curves are relatively close. For higher

883

concentration, their difference is getting higher with deviation up to 20%

884

approximately. Figure 24 shows the thermal efficiency of the collector using the two

885

viscosity models when the inlet temperature is equal to 300oC. This temperature level

886

is characteristic of the examined system and thus it is selected as a representative

887

value for this analysis. It is obvious that the thermal efficiency is about the same with

888

the two viscosity models with maximum deviation about 0.15% for high

889

concentrations. This extremely low difference has no practical impact on the final

890

results and the utilization of equation 4 is acceptable. Moreover, equation 40 is valid

891

up to 60oC, something that maybe makes it unsuitable for the present study. In any

892

case, it is proved that a deviation in viscosity of about 20% (maximum deviation)

893

leads to an extreme low deviation in the PTC thermal efficiency (about 0.15%).

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874

50

ACCEPTED MANUSCRIPT Nanofluid - T = 300˚C (equation 4a) 0.00080

Nanofluid - T = 300˚C (equation 40)

0.00075 0.00065 0.00055 0.00050 0.00045 0.00040 0.00

0.01

0.02

0.03

φ

0.05

0.06

Figure 23. Nanofluid dynamic viscosity with two different models

896

AC C

EP

TE D

895

0.04

M AN U

894

RI PT

0.00060

SC

μ (Pa s)

0.00070

897

Figure 24. Comparison of collector thermal efficiency for different viscosity models

898

with inlet temperature equal to 300oC

899 900 51

ACCEPTED MANUSCRIPT 4. Conclusions

902

This work examines the impact of nanofluids in the performance of a solar driven

903

Organic Rankine Cycle with parabolic trough collectors. Four different nanoparticles

904

(Al2O3, CuO, TiO2, Cu) are tested in the thermal oil (Syltherm 800) which is used in

905

the solar field loop. A storage tank with thermal oil is used for storing the heat and

906

this thermal fluid carries the heat to the heat recovery system of the ORC. In the ORC,

907

a regenerative system is used and four different organic working fluids are tested

908

(toluene, MDM, cyclohexane, n-pentane). The system is optimized by selecting the

909

proper nanoparticle concentration and the ideal pressure at the turbine inlet (with the

910

pressure ratio parameter) for all the combinations of nanofluids and organic fluids.

911

The main conclusions of this study are the following:

912

- Toluene is the best organic working fluid, with MDM, cyclohexane and n-pentane to

913

follow respectively. According to the optimization results, CuO is the best candidate,

914

while Cu, Al2O3 and TiO2 are following respectively. Moreover, it is proved that all

915

the nanofluids perform better than the pure thermal oil case.

916

- In the preliminary analysis for the solar field without the ORC, Cu is proved to be

917

the best nanoparticle. This difference between the preliminary analysis and the

918

optimization of the total system indicates that the optimization should be made for the

919

total system and not for each part separately.

920

- The best case is the one with toluene and CuO nanoparticle inside the Syltherm 800.

921

The optimum concentration is found to be 3.98% and the optimum pressure ratio is

922

75.51%. In this case, the electricity production is 167.05 kW and the system

923

efficiency is found to be 20.11%.

AC C

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M AN U

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RI PT

901

52

ACCEPTED MANUSCRIPT - The electricity production enhancement for the optimum case, compared to the

925

optimized case with pure thermal oil as working fluid in the solar field, is found to be

926

1.75%.

927

- It is found that the most efficient organic working fluids (toluene and MDM) need

928

relatively lower concentration in order to achieve maximum system performance.

929

Furthermore, it is proved that Al2O3 and CuO have to be used in higher

930

concentrations, compared to TiO2 and Cu.

931

- The results of this work indicate that the use of nanofluids as working fluids in

932

concentrated collectors (PTC) can enhance the system performance, achieving

933

enhancement up to 1.75% compared to operation with pure thermal oil. This fact

934

encourages the utilization of nanofluids in applications as the solar driven Organic

935

Rankine Cycles in order to achieve higher performances.

936

- It is essential to state that the proper working fluid selection is more important than

937

the suitable nanoparticle selection. This result is based on the small margin on the

938

solar thermal efficiency enhancement due to the high performance of PTCs.

939

Nomenclature

940

Aa

Area of the module, m2

941

Ast

Storage tank outer area, m2

942

cp

Specific heat capacity under constant pressure, kJ/kg K

943

D

Diameter, mm

944

df

Equivalent diameter of a base fluid molecule, m

945

dp

Diameter of the nanoparticle, m

AC C

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RI PT

924

53

ACCEPTED MANUSCRIPT Gb

Solar beam radiation, kW/m2

947

h

Heat transfer coefficient, W/m2K

948

hout

Convection coefficient between cover and ambient, W/m2K

949

k

Thermal conductivity, W/mK

950

K

Incident angle modifier, -

951

L

Tube length, mm

952

m

Mass flow rate, kg/s

953

MW

Molecular weight, kg/kmol

954

N

Number of modules, -

955

Na

Avogadro number, kmol-1

956

Nu

Mean Nusselt number

957

p

Pressure, bar

958

Pel

Electricity production in the generator, kW

959

Pnet

Net electricity production, kW

960

PP

Pinch point, oC

961

Pr

Prandtl number, -

962

PR

Pressure ratio, -

963

Q

Heat flux, W

964

Re

Reynolds number, -

AC C

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M AN U

SC

RI PT

946

54

ACCEPTED MANUSCRIPT s

Specific entropy, kJ/kgK

966

T

Temperature, oC

967

Ust

Storage tank thermal loss coefficient, kW/m2K

968

(UA)st Heat exchanger effectiveness, kW/m2K

969

V

Volumetric flow rate, m3/h

970

Vst

Volume of storage tank, m3

971

Vwind Ambient wind velocity, m/s

972

Wp

973

Greek symbols

974

β

Nanolayer thickness to the original particle radius, -

975

∆Τrc

Temperature difference in the recuperator, oC

976

ε

Emittance, -

977

ηis

Turbine isentropic efficiency, -

978

ηmg

Electromechanical efficiency of the generator, -

979

ηorc

ORC thermodynamic efficiency, -

980

ηopt

Optical efficiency, -

981

ηpum

Organic fluid pump efficiency, -

982

ηsys

System efficiency, -

983

ηth

Thermal collector efficiency, -

SC M AN U

AC C

EP

TE D

Pump consumption, kW

RI PT

965

55

θ

Incident angle, o

985

µ

Dynamic viscosity, Pa s

986

ρ

Density, kg/m3

987

σ

Stefan–Boltzmann constant [= 5.67 · 10-5 kW/m2 K4]

988

φ

Concentration of nanoparticles, %

989

Subscripts and superscripts

990

am

ambient

991

bf

base fluid

992

c

cover

993

ci

inner cover

994

co

outer cover

995

col

collector

996

col,in collector in

997

col,out collector out

998

con

condenser

999

crit

critical

1000

G

generator

1001

fm

mean fluid

1002

h

high

AC C

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RI PT

ACCEPTED MANUSCRIPT

56

ACCEPTED MANUSCRIPT in

input

1004

is

isentropic

1005

l

low

1006

loss

losses

1007

max

maximum

1008

nf

nanofluid

1009

np

nanoparticle

1010

o

organic

1011

opt

optimum

1012

r

receiver

1013

ri

inner receiver

1014

ro

outer receiver

1015

s

source – thermal oil

1016

sat

saturation

1017

sky

sky equivalent

1018

sol

solar

1019

st

storage

1020

stored stored quantity

1021

s,in

AC C

EP

TE D

M AN U

SC

RI PT

1003

source in 57

ACCEPTED MANUSCRIPT s,m

source intermediate (in pinch point position)

1023

s,out

source out

1024

sol,t

solar total

1025

u

useful

1026

u,t

useful total

1027

Abbreviations

1028

CFD

Computational Fluid Dynamics

1029

ECO

Economizer

1030

EES

Engineer Equator Solver

1031

EVAP Evaporator

1032

GWP Global Warming Potential

1033

HRS

Heat Recovery System

1034

n.a.

Not available

1035

ODP

Ozone Depletion Potential

1036

ORC Organic Rankine Cycle

1037

PTC

AC C

EP

TE D

M AN U

SC

RI PT

1022

Parabolic Trough Collector

1038

1039

1040 58

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1043

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1105

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1138

investigation of a stand-alone solar-thermal Organic Rankine Cycle power plant,

1139

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