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Renewable Energy 72 (2014) 154e163

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Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Off-design performance analysis of a closed-cycle ocean thermalenergy conversion system with solar thermal preheating andsuperheating

Hakan Aydin a, Ho-Saeng Lee b, Hyeon-Ju Kim b, Seung Kyoon Shin c, Keunhan Park d, *

a Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, RI 02881, USAb Deep Ocean Water Application Research Center, Korea Institute of Ocean Science and Technology, Gangwon 245-7, South Koreac College of Business Administration, University of Rhode Island, RI 02881, USAd Department of Mechanical Engineering, University of Utah, UT 84112, USA

a r t i c l e i n f o

Article history:Received 11 July 2013Accepted 1 July 2014Available online

Keywords:Ocean thermal energy conversion (OTEC)Solar thermal collectionThermodynamic system analysis

* Corresponding author.E-mail address: kpark@mech.utah.edu (K. Park).

http://dx.doi.org/10.1016/j.renene.2014.07.0010960-1481/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

This article reports the off-design performance analysis of a closed-cycle ocean thermal energy con-version (OTEC) system when a solar thermal collector is integrated as an add-on preheater or super-heater. Design-point analysis of a simple OTEC system was numerically conducted to generate a grosspower of 100 kW, representing a base OTEC system. In order to improve the power output of the OTECsystem, two ways of utilizing solar energy are considered in this study: (1) preheating of surface seawaterto increase its input temperature to the cycle and (2) direct superheating of the working fluid before itenters a turbine. Obtained results reveal that both preheating and superheating cases increase the netpower generation by 20e25% from the design-point. However, the preheating case demands immenseheat load on the solar collector due to the huge thermal mass of the seawater, being less efficientthermodynamically. The superheating case increases the thermal efficiency of the system from 1.9% toaround 3%, about a 60% improvement, suggesting that this should be a better approach in improving theOTEC system. This research provides thermodynamic insight on the potential advantages and challengesof adding a solar thermal collection component to OTEC power plants.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Ocean thermal energy conversion (OTEC) is a renewable energytechnology that makes use of the temperature difference betweenthe surface and the depth of the ocean to produce electricity byrunning a low-pressure turbine [1,2]. A closed-cycle OTEC employsa refrigerant, such as ammonia, R-134a, R-22 or R-32 as a workingfluid to allow its evaporation and condensation using warm andcold seawater, respectively. OTEC has the potential to be adoptedas a sustainable, base-load energy source that requires no fossilfuel or radioactive materials, while also causing many fewerenvironmental impacts than conventional methods of powergeneration. Several pilot OTEC plants in the order of 10 MW arecurrently under development by commercial sectors in the US,such as Ocean Thermal Energy Corporation (http://www.otecorporation.com), Makai Ocean Engineering (http://www.

makai.com), and Lockheed Martin (http://www.lockheedmartin.com/us/products/otec.html). Recently, Asian countries such asChina, Japan, and India have also initiated the construction ofOTEC plants in their territories. However, the main technicalchallenge of OTEC lies in its low energy conversion efficiency dueto small ocean temperature differences. Even in the tropical area,the temperature difference between surface and deep water isonly 20e25 �C. The thermodynamic efficiency of OTEC is in theorder of 3e5% at best, requiring large seawater flow rates forpower generation (e.g., approximately 3 ton/s of deep coldseawater and as much warm seawater to generate 1 MW ofelectrical power [3].)

Since the 1980s, considerable research efforts have been madein two directions to improve the performance of the OTEC system[4e6]. The first research direction has been targeted towardsthermodynamic optimization of Rankine-based cycles for higherefficiencies [7e10]. Two of the most popular cycles are the Kalina[11,12] and Uehara [13] cycles, which are generally suited for large-scale OTEC plants on the order of 4 MWor higher. Another researchdirection is towards the increase of temperature differences

Fig. 1. (a) Schematics of a closed-cycle OTEC system and its components and (b) T-sdiagram of the corresponding cycle.

H. Aydin et al. / Renewable Energy 72 (2014) 154e163 155

between the surface and deep seawater by utilizing renewableenergy or waste heat sources, such as solar energy [14,15],geothermal energy [16], or waste heat of a nuclear power plant [17].Among them, solar energy has been considered to be the mostappealing renewable energy source that could be integrated withOTEC due to the ever-growing solar technology and its minimaladverse impacts to the environment.

Yamada et al. [14,15] numerically investigated the feasibility ofincorporating solar energy to preheat the seawater in OTEC,demonstrating that the net efficiency can increase by around 2.7times with solar preheating. In addition, recent studies have alsosuggested the direct use of solar energy for the reheating of theworking fluid to enhance the OTEC performance [9,14,15]. Thesestudies have focused on the design of solar-boosted OTEC systems,suggesting the construction of a new power plant operating at amuch higher pressure ratio than the conventional OTEC system.However, OTEC power plants demand huge initial constructioncosts (e.g., ~ $ 1.6B for a 100 MW OTEC power plant [18]) due toenormous seawater mass flow rates and corresponding heatexchanger and seawater piping sizes. It would be more economi-cally feasible to consider improving OTEC plants by adding solarthermal collection on top of existing power-generating and pipingcomponents.

The research presented here aims to examine the system-leveleffect of integrating solar thermal collection to the power outputand efficiency of an existing OTEC power plant. To this end, thestudy begins with the design-point analysis of a closed-cycle OTECsystem with a 100 kW gross power generation capacity. Thedesigned OTEC system is considered as an illustrative base systemthat allows the thermodynamic analysis of its off-design operationwhen solar thermal collection is integrated as an additionalcomponent. Two methods that make use of solar energy areconsidered in this paper. First, an add-on solar thermal collector isinstalled to the system to preheat the surface seawater beforeentering the evaporator. The second method is directly super-heating the working fluid between the evaporator and the turbinewith an add-on solar thermal collector. Numerical analysis is con-ducted to predict the performance change (i.e., net power and ef-ficiency) in the OTEC systemwhen solar collection is integrated as apreheater/superheater. Simulated results are presented to comparethe improvement of system performances, in terms of the net po-wer output and the efficiencies, and required collector effectiveareas between the two methods.

2. Design-point analysis

As shown in Fig. 1, the closed OTEC cycle consists of two heatexchangers (evaporator and condenser), a turbine connected to agenerator, and a pump for theworking fluid. The heat source for theevaporator is warm seawater at the surface level of the ocean andthe heat sink for the condenser is cold seawater (typically pumpedout of ~1000 m or deeper in the ocean.) In this study, the temper-ature of the warm seawater is assumed to be constant at 26 �C, andthat of the cold seawater is 5 �C, which are close to the averageocean temperatures in tropical areas [2]. As for the working fluid,difluoromethane (R-32) was chosen over pure ammonia (NH3)owing to its non-corrosive, lower toxic characteristics and bettersuitability for superheated cycles [19]. Previous research has alsoshown that R-32 has a smaller vapor specific volume and thus re-quires a smaller turbine size than when ammonia is used [17]. Thepinch point temperature difference is defined as the minimumtemperature difference between the working fluid and seawaterand set to 2 �C for the evaporator and 1.8 �C for the condenser,respectively, which are similar to Ref. [14]. The vapor quality of theworking fluid is assumed to be unity at the exit of the evaporator

and zero at the exit of the condenser; neither subcooling norsuperheating is allowed during the design-point operation. Table 1summarizes the design conditions for an OTEC system with a100 kW gross power output. The proceeding section describes thethermodynamic modeling of each component of the OTEC cycle indetail.

2.1. Heat exchangers (evaporator and condenser)

Two critical parameters in the design-point analysis of the heatexchanger are the overall heat transfer coefficient and surface area.Among potential heat exchanger configurations, the present studyhas selected a titanium (Ti) shell-and-plate type heat exchangerdue to its favorable heat transfer and compact size [20]. In theevaporator, a working fluid is evaporated to saturated vapor byreceiving heat from the warm seawater. The energy balanceequation at each side of the evaporator can be written as:

_QE ¼ _mwf

�h1 � h4

�¼ _mwscp

�Twsi � Twso

�(1)

under the assumption that seawater is an ideal incompressiblefluid. Enthalpy and entropy of the working fluid, which are ingeneral a function of pressure and vapor quality during phasechange, were determined from REFPROP e NIST Reference FluidThermodynamic and Transport Properties Database [21,22]. It is

H. Aydin et al. / Renewable Energy 72 (2014) 154e163156

also assumed that the working fluid maintains at the saturationpressure without experiencing pressure loss at the evaporator.Overall heat transfer coefficient and effective surface area of theevaporator is correlated with the heat addition rate as shown in thefollowing equation:

_QE ¼ UEAEDTlm;E (2)

where DTlm;E is the logarithmic mean temperature differenceacross the evaporator expressed as DTlm;E ¼ ðTwsi � TwsoÞ=ln½ðTwsi � TEÞ=ðTwso � TEÞ�, and the effective thermal conductanceUEAE can be approximated as

1UEAE

¼ 1hwfAE

þ 1hwsAE

(3)

It should be noted that the thermal resistance of the Ti plate isignored since it is extremely small compared to other thermal re-sistances. The heat transfer coefficient of the working fluid playsthe most critical role in determining the overall thermal conduc-tance. The present study implemented the following empiricalcorrelations of the Nusselt number, or correspondingly the con-vection heat transfer coefficient, for the phase-changing workingfluid [23]:

Nuwf ¼0:023Re0:8l Pr0:4l

"1þ4:863

�� ln

�PsatPcr

�x

1�x

�0:836#

(4)

where x is the mean vapor quality, Rel is the Reynolds number, Prl isthe Prandtl number, Psat is the saturation pressure, and Pcr is thecritical pressure. The heat transfer coefficient of the seawater side isalso calculated using the Dittus-Boelter equation for single-phaseheat transfer [24]:

NuwsðcsÞ ¼ 0:023Re4=5l Pr1=3l (5)

For the calculation of the Reynolds number, the equivalent hy-draulic diameter is defined as the ratio of four times the cross-sectional channel flow area to the wetted perimeter of the duct.For a shell-and-plate type heat exchanger, the channel flow area is afunction of mean channel spacing inside the heat exchanger andhorizontal length of the plates [25].

Table 1Conditions and assumptions for the design of an OTEC system with a 100-kW grosspower capacity.

Symbol This study Yamada [14]

Seawater inlet temperature (�C)Surface seawater Twsi 26 25.7Deep seawater Tcsi 5 4.4

Pinch point temperature difference (�C)@ Evaporator DTppE 2.0 1.2

@ Condenser DTppC 1.8 1.3

Vapor quality@ Evaporator exit x1 1 1@ Condenser exit x3 0 0

Component efficiency (%)Turbine hT e 80Generator hG 95 90Working fluid pump hP;wf 75 75Seawater pumps hP;sw 80 80

Overall heat transfer coefficient (kW/m2 K)Evaporator UE e 4.0Condenser UC e 3.5

Seawater specific heat capacity (kJ/kg K) cp 4.025 e

Seawater density (kg/m3) rE 1025 e

The energy balance equation at the condenser is basically thesame as the evaporator and can be written as

_QC ¼ _mwf

�h2 � h3

�¼ _mcscp

�Tcso � Tcsi

�(6)

Likewise, the effective thermal conductance of the condenser iscorrelated with the heat transfer rate as

_QC ¼ UCACDTlm;C (7)

where dTlm,c is the logarithmic mean temperature difference acrossthe condenser, i.e., DTlm;C ¼ ðTcso � TcsiÞ=ln½ðTC � TcsiÞ=ðTC � TcsoÞ� .The effective thermal conductance of the condenser can be deter-mined using the same equations at the evaporator, i.e., Eqs. (4) and(5).

2.2. Pumps

After condensed, the working fluid is pressurized and pumpedthrough the inlet of the evaporator. The energy balance equation forthe working fluid pump can be written as

_WP;wf ¼ _mwf

�h4 � h3

�(8)

The change of enthalpy in the pump can be approximated ash4 �h3 ¼ v(P4 � P3) under the assumption that the temperature riseat the pump is negligibly small and its specific volume remains thesame throughout the pump, i.e., v3zv4. In addition, pressure of theworking fluid is raised to the evaporation pressure. The pumpworkis then calculated from the following equation:

_WP;wf ¼_mwfv4ðP4 � P3Þ

hP;wf(9)

where hP;wf is the efficiency of the working fluid pump and isassumed to be 75%. Some of the power generated by the OTEC cycleis consumed to pump the warm and cold ocean water. The powerrequired to run the seawater pumps can be simply calculated usingthe following equation [7]:

_WP;wsðcsÞ ¼_mwsðcsÞgDH

hP;sw(10)

where g is the gravitational acceleration, and hP;sw is the efficiencyof the seawater pump and is assumed to be 80%. The head differ-ence DH of each seawater pump is obtained from the previous work[7], which estimated the head difference from the friction andbending losses in the pipes.

2.3. Turbine

The vaporizedworking fluid rotates the blades of a low-pressureturbine while expanding adiabatically. Vapor pressure at the exit ofthe turbine is set equal to the saturation pressure at condensationtemperature of the condenser, i.e., P2 ¼ PsatðTCÞ. The power outputfrom the turbine connected with the generator, or the turbine-generator power, can be written as

_WT�G ¼ _mwfhThG

�h1 � h2s

�(11)

Here, h2s is the isentropic enthalpy at the exit of the turbine andcan be calculated by h2s ¼ h2f þ x2sh2fg, where h2f and h2fg are thesaturated liquid enthalpy and the enthalpy of vaporization at P2,respectively. The isentropic quality x2s can be expressed as

Table 2Design-point analysis results for the 100-kW gross power OTEC system. The ob-tained results are favorably compared to the results of Yamada et al. [14].

Symbol Thisstudy

Yamada[14]

Seawater outlet temperature (�C)Warm seawater Twso 22.83 22.9Cold seawater Tcso 8.61 7.1

Mass flow rate (kg/s)Warm seawater _mws 288.6 260Cold seawater _mcs 246.6 260Working fluid _mwf 12.3

(R-32)2.6(NH3)

EvaporatorEvaporation temperature (�C) TE 20.83 21.7Evaporation pressure (kPa) PEð¼ P1 ¼ P4Þ 1509 905Heat transfer rate (kW) _QE 3660 2934Overall heat transfer coefficient (kW/m2 K) UE 3.95 e

Surface area (m2) AE 279 232CondenserCondensation temperature (�C) TC 10.41 8.4Condensation pressure (kPa) PCð¼ P2 ¼ P3Þ 1121 582Heat transfer rate (kW) _QC 3561 2832Overall heat transfer coefficient (kW/m2 K) UC 3.26 e

Surface area (m2) AC 334 390Power output/consumption (kW)Turbine-generator power output _WT�G 100.0 100.1Working fluid pump power consumption _WP;wf (6.2) (2.1)Warm seawater pump power consumption _WP;ws (8.9) (9.5)Cold seawater pump power consumption _WP;cs (16.9) (18.6)Net power output _WN 68.0 69.9

Turbine isentropic efficiency (%) hT 80.6 e

Net thermal efficiency (%) hth 1.9 2.3

H. Aydin et al. / Renewable Energy 72 (2014) 154e163 157

x2s ¼ ðs1 � s2f Þ=s2fg by considering that the entropy at point 2 is thesame as point 1.

A radial inflow turbine is typically employed for the OTEC cycledue to its high isentropic expansion efficiency and good moistureerosion resistance [26]. The turbine efficiency for a radial turbine isdefined as [27]

hT ¼ 0:87� 1:07ðns � 0:55Þ2 � 0:5ðns � 0:55Þ3 (12)

where ns is the specific speed, a nondimensional design parameterthat characterizes the turbine performance. For the radial-inflowturbine, ns is defined as [27,28]:

ns ¼2pN _m1=2

wf

60r1=2wf Dh3=4T

(13)

where N is the rotational speed (rpm), rwf is the density of theworking fluid, and DhT is the enthalpy drop (J/kg) between theturbine inlet and outlet. Another design parameter that defines therotor tip speed is the total-to-static velocity ratio, defined as [28]

vs ¼ Vtip

. ffiffiffiffiffiffiffiffiffiffiffiffi2DhT

p(14)

where Vtip is the rotor tip speed. Once the rotor tip speed isdetermined, the rotor tip radius can be calculated using

rtip ¼ Vtip

ð2p=60ÞN (15)

2.4. Results of design-point analysis

The design-point analysis of the OTEC system producing aturbine-generator power of 100 kW was numerically conductedusing MATLAB. Since the governing equations at each componentare strongly coupled, they were solved iteratively with an initialguess of the outlet seawater temperatures (i.e. 23 �C at the evap-orator and 8 �C at the condenser exits, respectively.) From thepreset pinch point temperature differences, the saturation tem-perature and pressure of the working fluid at the evaporator andcondenser are determined by using REFPROP, which also providesthe enthalpy at each point (i.e., h1, h2, h3, and h4) as well. Once theenthalpy values are determined, the energy balance equations atthe evaporator, condenser, and turbine, i.e., Eqs. (1), (6) and (11)allow the calculation of the mass flow rates of warm seawater,cold seawater, and working fluid, respectively, along with the heattransfer rates at the evaporator and condenser. It should be notedthat in the design of the OTEC system, the most stringent designcondition is the mass flow rate of the deep seawater, as a tremen-dous cost is required to construct a pipeline reaching a ~1000 mdepth in ocean. Thus the present study identified a design point asthe operation condition requiring the minimum mass flow rate ofthe deep seawater to generate 100 kW of _WT�G, although thisdesign point may compromise the system efficiency. The previousOTEC studies suggested that the mass flow ratio of the deepseawater to the surface seawater _mcs= _mws, should be between 0.5and 1 for optimal performance [1,6], which was used as a criterionfor the validation of the obtained results. After the cold seawatermass flow rate is specified, the net power output is obtained bycalculating the turbine and pump powers:

_WN ¼ _WT�G � _WP;wf � _WP;ws � _WP;cs (16)

which allows the calculation of the net thermal efficiency, i.e.,hth ¼ _WN=

_QE. Design parameters for the evaporator and condenser,

such as the effective heat transfer coefficient and surface area canalso be obtained.

Table 2 compiles the determined design parameters of the OTECsystem that generates a 100 kW turbine-generator power output.While our results are in overall good agreement with Ref. [14] thatdesigned the same-scale OTEC system, there are noticeable differ-ences in some design parameters. It should be noted that the pre-sent study chose R-32 as a working fluid while Ref. [14] used NH3.Since the latent heat of vaporization for R-32 (218.59 kJ/kg-K at290 K) is almost five times smaller than that for NH3 (1064.38 kJ/kg-K at 290 K), more mass flow rate is required to generate the samepower when R-32 is used as a working fluid. The determined_mcs= _mws is 0.85, falling into the acceptable range. It should be notedthat the overall heat transfer coefficients computed in the presentstudy agree reasonably well with those in Refs. [14], which areexperimentally obtained values from Ref. [20]. This suggests thatEqs. (4) and (5) are valid correlations and can be used for differentflow conditions of seawater and working fluid at off-design oper-ations. The estimated net power generation is 68 kW, indicatingthat 32% of the turbine-generator power is consumed by pumps.The corresponding net thermal efficiency is estimated at 1.9%,which is slightly lower than Ref. [14] mainly due to the bigger heattransfer rate at the evaporator. Fig. 2 shows the isentropic efficiencyof the turbine as a function of the rotational speed when the tur-bine is designed to meet the system requirements. For the workingfluid mass flow rate of 12.3 kg/s and the enthalpy drop of 10.6 kJ/kg,the turbine efficiency curve demonstrates a polynomial trend witha maximum of ~87% at 8800 rpm. However, the turbine efficiency isdetermined to be 80.6% at the design-point operation, corre-sponding to 12,500 rpm, at which the mass flow rate of the deepseawater meets the design requirement. As mentioned above, themass flow rate of the deep seawater is a more stringent designcondition than the turbine efficiency for the construction andoperation of OTEC plants. Moreover, a turbine designed at higherrotational speeds is more compact and guarantees a better

Fig. 2. Turbine isentropic efficiency as a function of shaft rotational speed underdesign-point conditions, i.e., _mwf ¼ 12.3 kg/s and Dhwf ¼ 10.6 kJ/kg. The design pointof the turbine operation is determined to be at 12,500 rpm, yielding the turbine ef-ficiency of 80.6%.

H. Aydin et al. / Renewable Energy 72 (2014) 154e163158

performance when the enthalpy drop across the turbine isdemanding [28]. The rotor tip speed and the rotor tip radius aredetermined to be 102.3 m/s and 15.6 cm, respectively.

Fig. 3. Schematic illustrations of a closed-cycle OTEC system combined with a solarthermal energy collector to provide (a) preheating of the surface seawater and (b)superheating of the working fluid.

3. Off-design performance with solar preheating/superheating

Since the closed-cycle OTEC system is based on the Rankinethermodynamic cycle, its net power generation and thermal effi-ciency can be improved by increasing the temperature differencebetween the heat source and heat sink [15]. This study considerstwo different ways to improve the performance of the OTEC systemwith solar energy, i.e., preheating of the warm seawater andsuperheating of the working fluid using solar energy: see Fig. 3.When the solar preheater/superheater is integrated with the OTECsystem, the system operation shifts from its design point to find anew state of balance. For the off-design point calculation, an iter-ative algorithm was developed to revisit the energy balance equa-tions at each component and to find out a converged solution. Forthe heat exchangers, the heat transfer coefficients of each fluid andthe resultant heat transfer rate were calculated for different oper-ational conditions (i.e., different mass flow rates and inlet condi-tions) during off-design operations. However, the geometricalparameters of the OTEC system, such as the effective surface areasof the heat exchangers and the rotor tip radius of the turbine,remained as the designed values.

The net thermal efficiency for the solar preheating/superheatingOTEC system is determined by considering the additional solarenergy input, i.e., hth ¼ _WN=ð _QE þ _QSÞ, where _QS is the absorbedsolar energy. However, since solar preheating/superheating doesnot consume exhaustible energy sources, such as fossil fuels, theconventional net thermal efficiency may underestimate the OTECefficiency under off-design operation conditions. Instead of simplycomparing the net power generation to the total heat input, moreattention should be given to the increase of useful net powergeneration out of the total power increase when consuming addi-tional solar energy. To address this issue, Wang et al. [9] suggestedthe net cycle efficiency defined as

hNC ¼ _WN

._WT�G (17)

which compares the net power generation of the system to theturbine-generator power output. However, it should be noted thatsince the net cycle efficiency compares the off-design performanceof the system to its design-point; and it should not be used tocompare between different energy conversion systems.

Since the solar collector for the OTEC system does not need ahigh concentration of solar irradiation, we chose a CPC (compoundparabolic concentrator) type solar collector as a solar thermalpreheater/superheater in this study. CPC-type solar collectorsprovide economical solar power concentration for low- tomedium-pressure steam systems, allowing high collector efficiency in themoderate temperature range (i.e., 80e150 �C) [29,30]. They also caneffectively collect diffuse radiation, especially at lower concentra-tion ratios, producing satisfactory performance even in cloudyweather [30,31]. The efficiency of the CPC solar collector can bewritten as [32]

hS ¼ Fs

�h0 �

UL:DTGr,R

�(18)

where Fs is the generalized heat removal factor, h0 is the opticalefficiency and assumed to be 80%, UL is overall thermal loss coef-ficient, DT is the temperature difference between the inlet heattransfer fluid temperature and the ambient temperature, Gr is totalsolar irradiation and R is the concentration ratio. Fs is a function ofboiling status and concentration ratio and is taken from the dataavailable in literature [32]. UL is a variable that correlates withmanyfactors led by temperature and is taken from the measured data for

H. Aydin et al. / Renewable Energy 72 (2014) 154e163 159

a similar CPC type solar collector [33]. Fig. 4 shows the collectorthermal efficiency of a typical CPC solar collector as a function ofDT=Gr (m2-K/W)when h0 is set to 80% and the concentration ratio Rto 3, a typical value that would provide a high energy gain [33]. Thesolar irradiation is assumed to be 500 W/m2, which is theapproximated daytime average in Honolulu, Hawaii during thesummer [34]. From these given conditions, the solar collector ef-ficiency was determined to be 65%, which is used to estimate therequired collector effective area from the following energy balanceequation:

AS ¼½ _m,Dh�wsðwfÞ

hS,Gr(19)

Here, _m is the mass flow rate and Dh is the enthalpy change atthe preheater/superheater. The subscript ws(wf) indicates thewarm seawater for preheating and the working fluid forsuperheating.

Fig. 5. Turbine isentropic efficiency curves for several rotational speeds when theturbine is operated at off-design conditions as the inlet temperature of the surfaceseawater increases. The turbine efficiency at 12,500 rpm, the designed rotationalspeed, increases to the maximum and gradually decreases as DTwsi ¼ Twsi � TD

wsi ,where TD

wsi is the inlet surface seawater temperature and set to 26 �C, increases.

3.1. Solar preheating of seawater

As shown in Fig. 3(a), an add-on solar thermal preheater isinstalled next to the evaporator of the pre-designed OTEC system.The solar preheater has its own heat transfer fluid (typically syn-thetic/hydrocarbon oils or water [35]) that indirectly delivers solarenergy to the seawater via the auxiliary heat exchanger. The pre-heated surface seawater will alter the operation condition of theturbine, allowing more energy extraction from the working fluid.The off-design operation of the turbine should be fully character-ized to understand the off-design performance of the OTEC system.Fig. 5 shows the isentropic efficiency change of the turbine as afunction ofDTwsi, the offset of thewarm seawater inlet temperaturefrom its design point, for several turbine rotational speeds.Generally at high rotational speeds, the isentropic efficiency of theturbine reaches a maximum and gradually decreases as DTwsi in-creases. At lower rotational speeds, on the other hand, the turbineefficiency monotonically decreases without having a maximum. Itshould be noted that preheating the warm seawater increases theturbine-generator power output although the turbine efficiencydecreases. In the present study, we fixed the turbine performance

Fig. 4. Collector thermal efficiency of a CPC-type solar collector with a concentrationratio of 3, oriented in the East-West direction during daytime in the summer facingSouth in Honolulu, Hawaii. From the given conditions, the collector thermal efficiencyis calculated to be 65%.

at the design point (i.e., 80.6% at 12,500 rpm) during the off-designoperation of the OTEC system.

Fig. 6 shows the simulation results of the OTEC system whenpreheating the ocean water. In Fig. 6(a), the net power outputslightly increases as the solar power absorption at the preheaterincreases up to 3000 kW, and substantially increases with thefurther increase of the solar power absorption. The existence ofthese two regimes is mainly due to the control algorithm selectedin this study. The priority in the control algorithm is tomaintain theturbine efficiency at the design point. Thus, as can be seen in Eq.(12), ns should be constant under the solar preheating operation.Since the solar preheating enhances the enthalpy drop across theturbine, DhT in Eq. (13), the mass flow rate of the working fluidshould also increase accordingly to keep ns constant. On the otherhand, the mass flow rate of the warm seawater should be reducedto make a good balance between the energy demand of theworking fluid and the energy input from the solar preheater. Anyexcessive solar power absorption at the solar preheater would leadto the waste heat instead of being used to evaporate the workingfluid at the evaporator, which is not desirable for the cost-effectiveand eco-friendly operation of the OTEC system. Fig. 6(b) clearlyshows the continuous decrease of the warm seawater mass flowrate until the solar power absorption reaches 3000 kW. Thisdecrease of the warm seawater mass flow balances with the tem-perature increase of the preheated seawater to provide almost thesame energy to the turbine as the design point. The slight increaseof the net power generation is mainly attributed to the slight in-crease of the working fluid mass flow rate, which is required to runthe turbine at its design point. In this region, as shown in Fig. 7(a),the net thermal efficiency remains almost the same as the designpoint, indicating that the absorbed solar energy is effectively usedto generate power in the turbine.

When the solar thermal absorption reaches 3000 kW, the pre-heated seawater temperature reaches a point at which the netpower generation cannot increase any further unless the workingfluid is superheated. At this point, the surface seawater mass flowrate has been reduced to 48.5 kg/s, which is then fixed to allow thesuperheating of the working fluid. In order to run the turbine at thedesign point, i.e., constant ns in Eq. (13), the mass flow rate of the

Fig. 6. Off-design simulation results of the OTEC system when preheating of the sur-face seawater is integrated: (a) Change in net power generation of the combinedsystem and (b) change in mass flow rates of the working fluid and warm seawater.

Fig. 7. Off-design simulation results of the OTEC system when preheating of the sur-face seawater is integrated: (a) Net thermal efficiency and net cycle efficiency of thesystem as a function of solar power absorption; (b) temperature difference betweenwarm seawater and the working fluid at evaporator inlet, i.e., Twsi � T1, and temper-ature of outlet warm seawater as a function of solar power absorption; and (c) requiredcollector effective area of a solar preheater as a function of net power generation of thesystem.

H. Aydin et al. / Renewable Energy 72 (2014) 154e163160

working fluid should increase accordingly to match the increase ofDhT due to the superheating of the working fluid: see Fig. 6(b).These increases in both the mass flow rate of the working fluid andits enthalpy drop across the turbine drastically enhance the netpower generation in the second regime, which increases up to83 kW, or ~25% compared to the design point, as the solar ab-sorption reaches 8500 kW. The net thermal efficiency shown inFig. 7(a) decreases to ~1%, indicating that the absorbed solar energyis not as efficiently used in the OTEC system. However, the net cycleefficiency shows an improvement from 71% to 76%. Although theworking fluid pump consumes more power according to theincreasing mass flow rate of the working fluid, solar preheatingproduces more useful net power out of the gross power generation.

The partial use of solar energy from the excessive preheating ismanifested by the increasing outlet temperature of the seawater atthe evaporator shown in Fig. 7(b). In the first region, the warmseawater outlet temperature is lower than the design point, indi-cating that more thermal energy is transferred from the seawaterand converted to the power generation. However, further pre-heating drastically increases the exit temperature of warmseawater, which reaches up to ~50 �C when the solar power ab-sorption increases to 8500 kW. This inefficient use of absorbed solarenergy is because of the limited surface area of the evaporator andcondenser, which are originally optimized at the 100 kW turbine-generator power capacity. Unless this hot seawater is used

somewhere else, returning it back to the ocean will cause adverseenvironmental and ecological impacts. The hot seawater could beused to reheat the working fluid by installing the second turbine,which can extract more work out of the working fluid vapor beforeit enters the condenser. However, this study focuses on the effect ofsolar preheating on the existing OTEC system and thus did not

Fig. 8. Off-design simulation results of the OTEC system when superheating of theworking fluid is considered: (a) Change in net power generation of the combinedsystem with solar power absorption and (b) the net thermal efficiency and net cycleefficiency of the system as a function of solar power absorption.

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consider further modification of the system beyond the installationof the solar preheater. Fig. 7(b) also shows the temperature differ-ence between the incoming seawater and the exiting working fluidvapor, i.e., Twsi � T1 at the evaporator. In the first region, this tem-perature difference keeps increasing because the control algorithmdoes not allow the superheating of theworking fluid: thus T1 in thisrange is the evaporation temperature of the working fluid. How-ever, in the second regime, the superheating of the working fluidreduces Twsi � T1 below the preset pinch-point temperature dif-ference. Thus the practical limit of the solar preheating comes fromthe evaporator unless the evaporator is replaced with a bigger one.

Fig. 7(c) shows the required effective area of the solar collectorfor preheating. When plotted as a function of the net power output,the collector effective area has an abrupt jump to ~2000 m2 whenthe net power increases from 68 kW to 70 kW, or only a ~3% in-crease from the design point. A larger collector effective area shouldbe installed in order to take further advantage of the solar pre-heating: for example, nearly 6000m2 of the collector area is neededto increase the net power of the system by ~20%. The collector areacould be significantly reduced by improving the design of the col-lector or using a different fluid that has a higher solar absorptioncoefficient. Previous studies revealed that mixing nanoparticles inthe fluid can enhance the light absorptance to almost 100% above acertain nanoparticle concentration [36e39]. This enhancement ofthe light absorptance directly affects the solar collector efficiency,e.g., ~10% increase of the efficiency when aluminum nanoparticlesare suspended in water [37].

3.2. Superheating of working fluid

Evidently from the simulation results, preheating the oceanwater requires a huge amount of solar energy due to its massiveflow rate and high specific heat capacity. This demands a largeeffective area of the solar collector. On the other hand, difluoro-methane (R-32) has a significantly lower specific heat, and its massflow rate is much smaller than that of the warm seawater. There-fore, direct superheating of the working fluid by solar energy mayimprove the OTEC cycle with much less effective solar collectorarea. As shown in Fig. 3(b), an add-on solar thermal collector isinstalled in between the evaporator and the turbine of the OTECsystem to superheat the working fluid. The solar superheater, sameas in the preheating case, has its own heat transfer fluid and pro-vides the heating to the working fluid via the auxiliary heatexchanger.

Fig. 8 shows the simulation results for solar superheating. Thenet power generation increases from 68 kW to 85 kW, enhanced by25% from design-point, as the solar power absorption increases.This enhancement is mainly attributed to the improvement of thenet thermal efficiency from 1.9% to 3%, indicating that solarsuperheating generates more useful net power. The net cycle effi-ciency also increases from 71% to 76%. It should be noted that thenet thermal efficiency could be further increased until the criticaltemperature of R-32 is reached at around 78 �C. However, thisextreme superheating will cause the working fluid vapor to remainsuperheated at the exit of the turbine, undesirably requiring moremass flow rate of the deep seawater at the condenser. The presentstudy simulates only the sub-critical superheating case, where thevapor quality of the working fluid at the exit of the turbine remainsaround unity.

Fig. 9(a) shows the mass flow rate and the turbine inlet tem-perature of the working fluid as a function of the solar power ab-sorption. The increase of the solar power absorption yields a highertemperature of the working fluid at the inlet of the turbine,resulting in a greater enthalpy drop across the turbine. As discussedin the preheating case, the mass flow rate of the working fluid and

the enthalpy drop are correlated in Eq. (13), suggesting that thesystem should have a larger mass flow rate of the working fluid tomaintain the turbine operation at its design point. Fig. 9(b) showsthe required collector effective area as a function of net powergeneration for the superheating case. When compared to the pre-heating case, much less collector effective area is required for thesuperheater to obtain the almost same amount of net powerenhancement. For example, around 1100 m2 of effective collectorarea is required to enhance the net power by 20% with solarsuperheating, while more than 6000 m2 is required to generate thesame amount of power using solar preheating: more than fivetimes of the solar collector area should be constructed. This resultstrongly suggests that the solar superheatermay bemore beneficialin improving the thermodynamic performance of the OTEC systemalthough it requires greater care to prevent a leakage of theworking fluid during long-term operations [15].

4. Conclusions

The present study reports the effects of the solar thermal pre-heating/superheating to the performance of a closed-cycle OTECsystem. To this end, a closed-cycle OTEC system generating a100 kW turbine-generator power was designed and used as a basicsystem. The designed system, when using R-32 as its working fluid,produces 68 kW of net power with a net thermal efficiency of 1.9%

Fig. 9. Off-design simulation results of the OTEC system when superheating of theworking fluid is considered: (a) Turbine inlet temperature of the superheated workingfluid vapor and its mass flow rate as a function of solar power absorption and (b)required collector effective area of a solar superheater as a function of net powergeneration of the system.

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and the net cycle efficiency of 71%. Off-design performance analysisof the designed OTEC systemwas conducted when a CPC-type solarcollector was added as the solar preheater of warm seawater or thesuperheater of the working fluid. Simulation results demonstratethat both preheating/superheating cases increase the net powergeneration up to 20e25% from the design-point. However, super-heating of the working fluid requires up to 5 times less solar col-lector area compared to solar preheating. The superheating casealso increases the thermal efficiency of the system from 1.9% to ~3%,about a 60% improvement, suggesting that it should be a betterapproach in improving the OTEC system. The obtained results willprovide insights on the thermodynamic perspective whencombining sustainable energy conversion technologies e oceanthermal energy conversion and solar thermal energy conversion e

to improve the system performance.

Acknowledgment

This work was financially supported by projects of the“Development of Energy utilization technology with deep oceanwater,” directed by the Korea Institute of Ocean Science andTechnology. KP also acknowledges the startup support from theUniversity of Utah.

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