PERFORMANCE ANALYSIS OF A CLOSED-CYCLE OCEAN THERMAL ENERGY CONVERSION SYSTEM WITH SOLAR PREHEATING AND SUPERHEATING

The research presented in this thesis provides thermodynamic insights on the potential advantages and challenges of adding a solar thermal collection component into ocean thermal energy conversion (OTEC) power plants. In that regard, this article reports the off-design performance analysis of a closed-cycle OTEC system when a solar thermal collector is integrated as an add-on preheater or superheater into the


LIST OF TABLES
(OTEC) is a technology that aims to take advantage of that free energy. In other words OTEC is a renewable energy technology that makes use of the temperature difference between the surface and the depth of the ocean to produce the electricity by running a low-pressure turbine [1], [2]. In the tropics the surface temperature levels can reach

Previous Related Studies
A closed-cycle OTEC employs a refrigerant, such as ammonia, R-134a, R-22 or R-32, as a working fluid to allow its evaporation and condensation using warm and cold seawater, respectively. OTEC has the potential to be adopted as a sustainable, base-load energy source that requires no fossil fuel or radioactive materials, which also makes much less environmental impacts than conventional methods of power generation. However, the main technical challenge of OTEC lies in its low energy conversion efficiency due to small ocean temperature differences. Even in the tropical area, the temperature difference between surface and deep water is only 20 -25 °C. 1 The thermodynamic efficiency of OTEC is in the order of 3 to 5% at best, requiring large seawater flow rates for power generation, e.g., approximately 3 ton/s of deep 1 Reprinted with permission from Journal of Renewable and Sustainable Energy published by American Institute of Physics. Copyright 2010, AIP Publishing LLC. cold seawater and as much warm seawater to generate 1 MW of electrical power [3].
These large quantities of seawater result in the consumption of a substantial portion of the power generated to be used in the operation of the pumps that are needed to provide seawater from the surface and the depth of the ocean.
Since the 1980s, considerable research efforts have been made into two directions to improve the performance of the OTEC system [4], [5], [6]. The first research direction has been targeted to the thermodynamic optimization of Rankinebased cycles for higher efficiencies [7], [8], [9], [10]. Two of the most popular cycles are Kalina [11], [12] and Uehara [13] cycles, both of which are generally suited for large-scale OTEC plants in the order of 4 MW and higher. Another research direction is towards the increase of temperature difference between the surface and deep seawater by utilizing renewable energy or waste heat sources, such as solar energy [14], [15], geothermal energy [16], or waste heat at the condenser of a nuclear power plant [17]. Among them, solar energy has been considered as the most appealing renewable energy source that could be integrated with OTEC due to the ever-growing solar technology and its minimal adverse impacts to the environment.
Yamada et al. [15] numerically investigated the feasibility of incorporating solar energy to preheat the seawater in OTEC, demonstrating that the net efficiency can increase by around 2.7 times with solar preheating. In addition, recent studies also suggested the direct use of solar energy for the reheating of the working fluid to enhance the OTEC performance [9], [14], [15]. However, these studies have focused on the design of solar boosted OTEC systems, suggesting the construction of a new power plant operating at a much higher pressure ratio than the conventional OTEC 5 system. However, OTEC power plants demand huge initial construction costs (e.g., ~$1.6 Billion for a 100 MW OTEC power plant [18]) due to massive seawater mass flow rates and corresponding heat exchanger and seawater piping sizes. It would be economically more appropriate to consider improving OTEC plants by adding solar thermal collection to existing components and piping.

OTEC System Components
A basic single stage closed-cycle OTEC system consists of two heat exchangers (an evaporator and a condenser), a working fluid pump and a turbine connected to a generator by its shaft. Heat source for the evaporator is warm seawater at the surface level of the ocean and heat sink for the condenser is cold seawater, typically pumped out of ~1000 m or deeper in the ocean. Therefore two seawater pumps are required to provide the seawater. Under operation, the working fluid is vaporized at the evaporator, expanded through the turbine, condensed back to its liquid state and pumped back to the evaporator thus completing its cycle.

Heat Exchangers
In the evaporator, a working fluid is evaporated to saturated vapor by receiving heat from the warm seawater. The energy balance equation at each side of the evaporator can be written as The energy balance equation at the condenser is basically the same as the evaporator and can be written as Likewise, the effective thermal conductance of the condenser is correlated with the heat transfer rate as where lm,C T  is the logarithmic mean temperature difference across the condenser which can be expressed as The effective thermal conductance of the condenser can be determined by using the following equation:

Pumps
After condensed, the working fluid is pressurized and pumped to the inlet of the evaporator. The energy balance equation for the working fluid pump can be written as The change of enthalpy in the pump can be approximated as Under the assumption that the temperature rise at the pump is negligibly small and its specific volume remains the same throughout the pump, i.e., 34 vv  . In addition, pressure of the working fluid is raised to the evaporation pressure. The pump work is then calculated from the following equation: where P,wf  is the efficiency of the working fluid pump. Some of the power generated by the OTEC cycle is consumed to pump the warm and cold ocean water. The power required to run the seawater pumps can be simply calculated using the equation given by [7] ws(cs) P,ws(cs) P,sw where g is the gravitational acceleration, and P,sw  is the efficiency of the seawater pump. Previous study [7] makes it possible to estimate the head difference H  from the friction and bending losses in the pipes.

Turbine
The vaporized working fluid rotates the blades of a low-pressure turbine while expanding adiabatically. Vapor pressure at the exit of the turbine is set equal to the saturation pressure at condensation temperature of the condenser, i.e., 2 @ sat C P P T  . 9 The power output from the turbine connected with the generator, or the turbinegenerator power, can be written as Here, h 2 s is the isentropic enthalpy at the exit of the turbine and can be calculated by where h 2 f and 2 fg h are the saturated liquid enthalpy and the enthalpy of vaporization at 2 P , respectively. The isentropic quality 2s x can be expressed as by considering that the entropy at point 2 is the same as point 1.
A radial inflow turbine is typically employed for the OTEC cycle due to its high isentropic expansion efficiency and good moisture erosion resistance [19]. The specific speed n s is a dimensionless design parameter that characterizes the performance of a turbine. For the radial-inflow turbine, n s is defined as [20], [21]: where N is the rotational speed (rpm), wf  is the density of the working fluid, and T h  is the enthalpy drop (J/kg) between the turbine inlet and outlet. The total-to-static efficiency of a turbine is defined as a function of the dimensionless specific speed Aungier also defines total-to-static velocity ratio which is defined as where tip U is rotor tip speed and 0 C is discharge spouting velocity which can be calculated from the equation: Once the rotor tip speed is determined, the rotor tip radius can be calculated using Radius of the turbine determines the size of the turbine, and it is inversely proportional to turbine rotational speed.

CHAPTER II:
Design-Point Analysis of OTEC

Methodology
As mentioned in the previous chapter, first part of the study requires the design of a closed-cycle OTEC system with gross power generation of 100 kW. Design-point analysis is conducted numerically with the help of a MATLAB code specifically written for this purpose. The design parameters to be determined from numerical simulation at the end of this chapter will constitute the basis of the OTEC system that this research will suggest ways to improve.
In this study, the temperature of the warm seawater is assumed to be constant at 26 °C, and that of the cold seawater is 5 °C, which are close to the average ocean temperatures in tropical areas [2]. As for the working fluid, difluoromethane (R-32) was chosen over pure ammonia (NH 3 ) owing to its non-corrosive and lower toxic characteristics and better suitability for superheated cycles [22], [23]. Previous research has also shown that R-32 has a smaller vapor volume than ammonia and thus requires a smaller turbine size for same scale power production [17]. The pinch point temperature difference is defined as the minimum temperature difference between the working fluid and seawater and set to 2 °C for the evaporator and 1.8 °C for the condenser, respectively. The vapor quality of the working fluid is assumed to be unity at the exit of the evaporator and zero at the exit of the condenser; neither sub-cooling nor superheating is allowed during the design-point operation. Table 2.1 summarizes the design conditions for an OTEC system with 100 kW gross power generation.
Two critical parameters in the design-point analysis of the heat exchanger are the overall heat transfer coefficient and surface area. Among potential heat exchanger configurations, the present study has selected a titanium (Ti) shell-and-plate type heat exchanger due to its solid heat transfer and compact size [24]. Enthalpy and entropy of the working fluid at the heat exchangers, which are in general a function of pressure and vapor quality during phase change, were determined from REFPROP -NIST Reference Fluid Thermodynamic and Transport Properties Database [25], [26]. It is also assumed that the working fluid maintains at the saturation pressure without experiencing pressure loss at the evaporator. It should be noted that the thermal   16 required mass flow rate on the warm sea water side to be high. On the other hand designing for a lower temperature will require higher effective thermal conductance which means higher heat exchanger costs. In the next plot, again, changes in mass flow rate of cold & warm seawater and the effective thermal conductance of the heat exchangers is shown but this time as a function of cold seawater output temperature, cso T . Designing this temperature to be high will increase heat exchanger costs but will decrease the necessary cold sea water mass flow rate. Previous OTEC studies suggested that the mass flow ratio of the deep seawater to the surface seawater, m cs / m ws , should be between 0.5 and 1 for optimal performance [1], [6], which was used as a criterion for the validation of the obtained results. After the cold seawater mass flow rate is specified, the net power output is obtained by calculating the turbine and pump powers: which allows the calculation of the net thermal efficiency, i.e.,

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However, the turbine efficiency is determined to be 80.6 % at the design-point operation, corresponding to ~12500 rpm, at which the mass flow rate of the deep seawater meets the design requirement. As aforementioned, the mass flow rate of the deep seawater is a more stringent design condition than the turbine efficiency for the economic construction and operation of OTEC plants. Moreover, a turbine designed at higher rotational speeds is more compact and guarantees a better performance when the enthalpy drop across the turbine is demanding. For the design rotational speed of 12500 rpm; rotor tip speed and rotor tip radius of the radial inflow turbine to be used

CHAPTER III:
Off-Design Performance Analysis of OTEC

OTEC with Solar Thermal Collection
Since the closed-cycle OTEC system is based on the Rankine thermodynamic cycle, its net power generation and thermal efficiency can be improved by increasing the temperature difference between the heat source and the heat sink [15]. This study considers two different ways to improve the performance of the OTEC system, i.e., preheating of the warm seawater and superheating of the working fluid using solar energy. When the solar preheater/superheater is integrated with the base OTEC system, the system will shift from its design point to find its new state of balance. For the off-design point calculation, an iterative algorithm is developed to revisit the energy balance equations at each component and to find out a converged solution.
During the off-design analysis, the geometrical parameters of the OTEC system, such as the effective surface areas of the heat exchangers and the rotor tip radius of the turbine, remains the same as the pre-designed values.
The net thermal efficiency for the solar preheating/superheating OTEC system is determined by considering the additional solar energy input, i.e., where Q S is the absorbed solar energy. However, since solar preheating/superheating does not consume exhaustible energy sources, such as fossil fuels, the conventional net thermal efficiency may underestimate the OTEC efficiency at off-design operation conditions. Instead of simply comparing the net power generation to the total heat 24 input, more emphasis should be given to the increase of the useful net power generation out of the total power increase when consuming additional solar energy. To address this issue, Wang et al [9] suggested the net cycle efficiency defined as which compares the net power generation of the system to the turbine-generator power output. However, it should be noted that since the net cycle efficiency compares the off-design performance of the system to its design-point; it should not be used to compare between different energy conversion systems.
Since the solar collector for the OTEC system does not need a high concentration of solar irradiation, a CPC (compound parabolic concentrator) type solar collector is chosen as the solar thermal preheater/superheater in this study. CPC-type solar collectors provide economical solar power concentration for low-to medium-pressure steam systems, providing high collector efficiency in the moderate temperature range (i.e., 80-150 °C) [30], [31]. They also can effectively collect diffuse radiation, especially at lower concentration ratios, demonstrating satisfactory performance even in cloudy weather [31], [32]. The overall thermal efficiency of the CPC solar collector can be written as [33] S0 where F s is the generalized heat removal factor, 0  is the optical efficiency, U L is overall thermal loss coefficient, T  is the temperature difference between the inlet heat transfer fluid temperature and the ambient temperature, G r is total solar irradiation and R is the concentration ratio. Generalized F s is a function of boiling 25 status and concentration ratio and is taken from the data available in literature [33].
Optical efficiency is assumed to be constant and taken as 80%. U L is a variable that correlates with many factors led by temperature and is taken from measured data for a similar CPC type solar collector [34]. approximately the daytime average in Honolulu, Hawaii during the summer [35], and the concentration ratio is set to be 3, a typical value that would provide the high 26 energy gain [36]. At the given circumstances, the resulting collector efficiency is determined to be 65%, which is used to estimate the required collector effective area from the following energy balance equation: Here, m is the mass flow rate and h  is the enthalpy change at the preheater or superheater. The subscript "ws(wf)" indicates that the warm seawater should be considered for preheating and the working fluid for superheating.

Solar Preheating of Seawater
As shown in Fig. 3.2, an add-on solar thermal preheater is installed next to the evaporator side of the pre-designed OTEC system to preheat the incoming surface seawater. The solar preheater has its own heat transfer fluid (typically 27 synthetic/hydrocarbon oils or water [37]) that indirectly deliver solar energy to the seawater via the auxiliary heat exchanger. The preheated surface seawater will alter the design operation condition of the turbine, allowing more energy extraction from the working fluid. The off-design operation of the turbine should be fully characterized to understand the off-design performance of the OTEC system. Figure   3.3 shows the isentropic efficiency change of the turbine as a function of the warm seawater inlet temperature for several turbine rotational speeds. Generally at high rotational speeds, the isentropic efficiency of the turbine increases to the maximum

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The partial use of the solar energy for the excessive preheating is manifested by the increase of the outlet seawater temperature at the evaporator shown in Fig. 3.5(b).   Simulation results for superheating, as can be seen in Fig. 3.7, reveals that   Secondary applications that are popular with OTEC are also on the table such as desalination to produce potable water or to be used in irrigation. 38 Figure 3.10 shows the required collector effective area as a function of net power generation for the superheating case. When compared to the preheating case, much less collector effective area is required for the superheater to obtain the same amount of net power enhancement. For example, around 1100 m 2 of collector effective area is needed to obtain 20% more net power in the superheating case, which needs only ~18% of the collector area when the preheating is used. This result strongly suggests that the solar superheater may be more beneficial in improving the OTEC system although it requires more care to prevent leakage of the working fluid into the environment during long-term operation [15].