# Basic Heat Exchanger Performance Evaluation Method on OTEC

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## Abstract

**:**

## 1. Introduction

## 2. Heat Exchanger Performance and Power Output

#### 2.1. Maximum Power Output of a Heat Engine

_{W}and that of the cold deep seawater is Q

_{C}, respectively:

_{p}is the specific heat of seawater, and the subscription of

_{W}is warm sweater,

_{W,O}is the warm seawater outlet after heat exchange with the heat engine,

_{C}is the deep seawater and

_{C,O}is the deep seawater outlet after the heat exchange. Figure 2 shows the conceptual T − s diagram of an OTEC with a reversible heat engine. In the case of a reversible heat engine, the entropy generation will be zero:

_{H}and T

_{L}show the high and low temperatures of the heat engine in the reversible heat engine, respectively. The thermal efficiency η

_{th}and the power output W can be calculated as:

_{m}, the heat transfer rates can be expressed as:

_{W,O}or T

_{C,O}. Then the work output can be maximized by $\partial W/\partial {T}_{W,O}=0$ or $\partial W/\partial {T}_{C,O}=0$. The maximum work considering the heat exchanger performance W

_{m,NTU}is expressed as:

_{HS}is the total heat capacity flow rate (C

_{HS}= C

_{W}+ C

_{C}, C = $\dot{m}{c}_{p}$), r is the ratio of the heat capacity flow rate of the surface seawater (r = C

_{W}/C

_{HS}), and NTU is the net transfer unit defined as follows:

_{m,NTU}/W

_{m}as a function of the net transfer unit in the case in which NTU

_{W}and NTU

_{C}are identical. According to Figure 3, the ratio of maximum available power will be 63%, 86%, and 95% when NTU is 1.0, 2.0, and 3.0, respectively.

#### 2.2. Relationship between Net Power and Heat Exchanger Performance

^{3}), η

_{P}is the mechanical efficiency of the seawater pumps and ∆P is the pressure drop of the heat exchangers (kPa). Although the total pressure drop of the seawaters are related to each heat exchanger, piping, valve, and the configuration of seawater intake facility, ∆P is assumed that the considerable pressure drop is only inside the heat exchanger in order to directly represent the effect of the performance of the heat exchangers on the net power. Then, the net power output is calculated as:

_{W}and P

_{C}are the pumping power of the warm surface seawater and the cold deep seawater, respectively. The maximum net power using a reversible heat engine will then be:

## 3. Basic Performance Evaluation Method

#### 3.1. Basic Heat Exchanger Performance Evaluation Index

_{P}= 1) in order to avoid the effect of the efficiency on the heat exchanger performance evaluation: the total performance of the heat exchangers, including the net transfer unit and pressure drop, are the same, and the ratio of warm seawater heat capacity flow rate is 0.5 in order to conduct independent evaluations as a heat exchanger, an evaporator, or a condenser.

#### 3.2. Assumptions and Evaluation Procedure

_{HS}is the forced convention heat transfer coefficient of seawater (W/m

^{2}K), t is the plate thickness (m), L

_{pt}is the coefficient of thermal conductivity (W/mK), α

_{WF}is the heat transfer coefficient of the working fluid (W/m

^{2}K) and Rf is the thermal resistance due to fouling (m

^{2}K/W). The heat transfer coefficient of the working fluid is the mix of the forced convection with the boiling or condensing heat transfer coefficient. In general, the boiling or condensing heat transfer coefficients are much higher than the forced convection heat transfer coefficient. Thus, this study assumes that the working fluid heat transfer coefficient is much higher than the seawater forced heat transfer coefficient and is constant, which are then applied in the Wilson plot method [30], and then even in an evaporator and a condenser, the effect of superheating and subcooling are negligible. Then, the overall heat transfer coefficient is approximated as an exponential function of seawater mean velocity in the plate heat exchanger. In addition, the thermal resistance due to the fouling is assumed to be negligible.

- To make the approximate formula of the overall heat transfer coefficient and pressure drop a function of the mean velocity of seawater by experimentation, which is shown in Figure 4a:$$U=\xi {V}_{HS}^{\beta},\text{}\Delta P=\zeta {V}_{HS}^{\theta},$$
- To calculate the maximum net power output per heat transfer area, which are represented by Equation (20), and the optimum mean velocity of seawater, which maximizes the net power output, in the design seawater temperature condition shown in Figure 4b,
- To calculate ω represented by Equation (23) as the performance index for an OTEC heat exchanger.

## 4. Results and Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Martin, B.; Okamura, S.; Nakamura, Y.; Yasunaga, T.; Ikegami, Y. Status of the “Kumejima Model” for advanced deep seawater utilization. In Proceedings of the IEE Conference Publications, Kobe, Japan, 6–8 October 2016; pp. 211–216. [Google Scholar]
- Takahashi, M. DOW: Deep Ocean Water as Our Next Natural Resource; Terra Scientific Publishing Company: Tokyo, Japan, 2000; ISBN 488704125x. [Google Scholar]
- Claude, G. Power from the tropical sea. Mech. Eng.
**1930**, 52, 1039–1044. [Google Scholar] - Avery, H.W.; Wu, C. Renewable Energy from the Ocean; Oxford University Press: Oxford, UK, 1994; pp. 90–151. ISBN 9780195071993. [Google Scholar]
- Kalina, A.I. Generation of Energy by Means of a Working Fluid, and Regeneration of a Working Fluid. U.S. Patents 4346561, 31 August 1982. [Google Scholar]
- Marston, C.H. Parametric analysis of the Kalina cycle. Trans. ASME J. Eng. Gas Turb. Power
**1990**, 112, 107–116. [Google Scholar] [CrossRef] - Uehara, U.; Ikegami, Y.; Nishida, T. OTEC System Using a New Cycle with Absorption and Extraction Process; Physical Chemistry of Aqueous Systems, Begell House, Inc.: Danbury, CT, USA, 1995; pp. 862–869. [Google Scholar]
- Anderson, J.H.; Anderson, J.H., Jr. Thermal power form seawater. Mech. Eng.
**1966**, 88, 41–46. [Google Scholar] - Morisaki, T.; Ikegami, Y. Maximum power of a multistage Rankine cycle in low-grade thermal energy conversion. Appl. Ther. Eng.
**2014**, 69, 78–85. [Google Scholar] [CrossRef] - Sun, F.; Ikegami, Y.; Arima, H.; Zhou, W. Performance analysis of the low-temperature solar-boosted power generation system—Part I: Comparison between Kalina solar system and Rankine solar system. Trans. ASME J. Sol. Energy Eng.
**2013**, 135. [Google Scholar] [CrossRef] - Sun, F.; Ikegami, Y.; Arima, H.; Zhou, W. Performance analysis of the low-temperature solar-boosted power generation system—Part II: Thermodynamic characteristics of the Kalina solar system. Trans. ASME J. Sol. Energy Eng.
**2013**, 135. [Google Scholar] [CrossRef] - Bombarda, P.; Invernizzi, C.; Gaia, M. Performance analysis of OTEC plants with multilevel organic Rankine cycle and solar hybridization. Trans. ASME J. Eng. Gas Turb. Power
**2013**, 135. [Google Scholar] [CrossRef] - Sinama, F.; Martins, M.; Journoud, A.; Marc, O.; Lucas, F. Thermodynamic analysis and optimization of a 10 MW OTEC Rankine cycle in Reunion Island with the equivalent Gibbs system method and generic optimization program. Appl. Ocean Res.
**2015**, 53, 54–66. [Google Scholar] [CrossRef] - Johnson, D.H. The exergy of the ocean thermal resource and analysis of second-law efficiencies of idealized ocean thermal energy conversion power cycles. Energy
**1983**, 8, 927–946. [Google Scholar] [CrossRef] - Owens, W.L.; Trimble, L.C. Mini-OTEC operational results. Trans. ASME J. Sol. Energy Eng.
**1981**, 103, 233–240. [Google Scholar] [CrossRef] - Mitsui, T.; Ito, F.; Seya, Y.; Nakamoto, Y. Outline of the 100 kW OTEC pilot plant in the Republic of Nauru. IEEE Trans. Power App. Syst.
**1983**, PAS-102, 3167–3171. [Google Scholar] [CrossRef] - Yasunaga, T.; Ikegami, Y.; Monde, M. Performance test of OTEC with ammonia/water as working fluid using shell and plate type heat exchangers (effect of heat source temperature and flow rate). Trans. JAME B
**2008**, 74, 445–452. [Google Scholar] [CrossRef] - Bejan, A. Advanced Engineering Thermodynamics; Wiley: New York, NY, USA, 1998; ISBN 0471677639. [Google Scholar]
- Ibrahim, O.M. Effect of irreversibility and economics on the performance of a heat engine. Trans. ASME J. Sol. Energy Eng.
**1992**, 114, 267–271. [Google Scholar] [CrossRef] - Wu, C. Performance bound for real OTEC heat engines. Ocean Eng.
**1987**, 14, 349–354. [Google Scholar] [CrossRef] - Yasunaga, T.; Ikegami, Y. Application of finite-time thermodynamics for evaluation method on heat engine. Energy Procedia
**2017**, 129, 995–1001. [Google Scholar] [CrossRef] - Ikegami, Y.; Bejan, A. On the thermodynamic optimization of power plants with heat transfer and fluid flow irreversibility. Trans. ASME J. Sol. Energy Eng.
**1998**, 120, 139–144. [Google Scholar] [CrossRef] - Owens, W.L. Optimization of closed-cycle OTEC system. In Proceedings of the ASME/JSME Thermal Engineering Joint Conference, Honolulu, HI, USA, 20–24 March 1980; Volume 2, pp. 227–239. [Google Scholar]
- Uehara, H.; Ikegami, Y. Optimization of a closed-cycle OTEC system. Trans. ASME J. Sol. Energy Eng.
**1990**, 112, 247–256. [Google Scholar] [CrossRef] - Ikegami, Y.; Uehara, H. Performance analysis of OTEC plants at off-design conditions: Ammonia as working fluid. Trans. ASME J. Sol. Energy Eng.
**1992**, G0656A, 633–638. [Google Scholar] - Novikov, I.I. The efficiency of atomic power stations. J. Nuclear Energy II
**1958**, 7, 125–128. [Google Scholar] - Curzon, F.L.; Ahlborn, B. Efficiency of a Carnot engine at maximum power output. Am. J. Phys.
**1975**, 43, 22–24. [Google Scholar] [CrossRef] - Chen, I.; Yan, Z.; Lin, G.; Andersen, B. On the Curzon-Ahlborn efficiency and its connection with the efficiencies of the real heat engines. Energy Convers. Manag.
**2001**, 42, 173–181. [Google Scholar] [CrossRef] - Jones, J.B.; Hawkins, G.A. Engineering Thermodynamics an Introductory Textbook, 2nd ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 1986; p. 578. ISBN 0471812021. [Google Scholar]
- Wilson, E.E. A basis for rational design of heat transfer apparatus. Trans. ASME J. Heat Trans.
**1915**, 37, 47–82. [Google Scholar] - Kushibe, M.; Ikegami, Y.; Monde, M.; Uehara, H. Evaporation heat transfer of ammonia and pressure drop of warm water for plate type evaporator. Trans. JSRAE
**2005**, 22, 403–415. [Google Scholar] - Nakaoka, T.; Urata, K.; Ikegami, Y.; Nishida, T.; Ohhara, J.; Horita, M. Heat transfer coefficient and pressure drop of plate-type condenser using OTEC (using NH
_{3}/H_{2}O as working fluid). OTEC**2009**, 15, 1–8. [Google Scholar] - Uehara, H.; Nakaoka, T.; Miyara, A.; Murakami, H.; Dilao, C.O.; Miyazaki, K. A shell and plate type condenser. In Proceedings of the 2nd International Symposium on Condenser and Condensation, Bath, UK, 28–30 March 1990; pp. 347–356. [Google Scholar]
- Uehara, H.; Nakaoka, T.; Hagiwara, K. Plate type condenser (cold water side heat transfer coefficient and friction factor). Refrigeration
**1984**, 59, 3–9. [Google Scholar]

**Figure 2.**Conceptual T − s diagram of an OTEC power generation system using a reversible heat engine.

**Figure 3.**Dependency of the ratio of maximum available power output and net transfer unit in the case in which NTU

_{W}and NTU

_{C}are identical.

**Figure 4.**Concept of performance evaluation of a heat exchanger as a function of mean velocity of the heat source. (

**a**) an overall heat transfer coefficient and a pressure drop; and (

**b**) a maximum power output, a required pumping powers and a net power output as a function of mean velocity of the heat source.

**Figure 5.**The net power output per the heat transfer area as function of the mean velocity of heat source in the plate when T

_{W}= 30 °C, T

_{C}= 5 °C, c

_{p}= 4.0 kJ/kgK and $\rho $ = 1025 kg/m

^{3}. The open circles show the maximum point of power output, i.e., the optimum mean velocity of the heat source in each plate heat exchanger.

**Figure 6.**The ratio of net power, loss in the heat exchange process (e

^{−NTU}), and backwork ratio at the optimum mean velocity of heat source in the plate when T

_{W}= 30 °C, T

_{C}= 5 °C, c

_{p}= 4.0 kJ/kgK and $\rho $ = 1025 kg/m

^{3}.

No. | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Type of Heat Exchanger (Application) | Plate (Evaporator) | Plate (Evaporator) | Plate (Evaporator) | Plate (Condenser) | Plate (Condenser) | Plate (Condenser) |

Length (mm) | 960 | 718 | 1765 | 1213 | 1765 | 1450 |

Width (mm) | 576 | 325 | 605 | 709 | 605 | 235 |

Plate thickness (mm) | 0.7 | 0.5 | 0.6 | 0.6 | 0.6 | 1.0 |

Clearance of plates (mm) | 4.00 | 3.96 | 2.68 | 2.80 | 3.40 | 2.20 |

Equivalent diameter (mm) | 8.0 | 7.9 | 5.36 | 5.6 | 6.8 | 4.4 |

Material | SUS316 | Titanium | Titanium | Titanium | Titanium | SUS304 |

Surface pattern | Herringbone (72°) | Herringbone (30°) | Fluting & drainage | Emboss | Herringbone (58°) | Fluting & drainage |

Number of plates | 120 | 20 | 52 | 100 | 30 | 5 |

Heat transfer area per path (m^{2}) | 1.686 | 0.417 | 1.592 | 3.683 | 1.683 | 0.560 |

Total passage cross sectional are (m^{2}) | 0.14 | 0.012 | 0.041 | 0.099 | 0.031 | 0.0005 |

Reference | [31] | [31] | [31] | [32] | [33] | [34] |

No. | Overall Heat Transfer Coefficient U | Pressure Drop ∆P | Water Inlet Temperature (°C) | Ref. | |||||
---|---|---|---|---|---|---|---|---|---|

Multiplier Factor ξ * | Exponential Factor β * | Mean Velocity Data Range (m/s) | Heat Flux (kW/m^{2}) | Multiplier Factor ζ * | Exponential Factor θ * | Mean Velocity Data Range (m/s) | |||

1 | 4.20 | 0.22 | 0.20–0.444 | 4.51–16.6 | 306.3 | 1.86 | 0.16–0.45 | 36.7–75.1 | [31] |

2 | 5.64 | 0.36 | 0.59–1.20 | 45.4–121.9 | 65.4 | 2.21 | 0.60–1.19 | 27.6–45.6 | [31] |

3 | 3.25 | 0.46 | 0.29–0.59 | 10.2–16.1 | 182.3 | 2.00 | 0.48–0.59 | 23.8–44.0 | [31] |

4 | 2.40 | 1.10 | 0.40–0.70 | N.A. | 311.3 | 1.86 | 0.40–0.70 | 10.0 | [32] |

5 | 1.80 | 0.22 | 0.51–0.94 | 11.9–12.5 | 9.4 | 1.79 | 0.51–0.94 | 7.1–15.8 | [33] |

6 | 1.66 | 0.65 | 0.55–0.29 | N.A. | 7.0 | 1.42 | 0.55–1.80 | 6.85 | [34] |

_{HS}

^{β}and ∆P = ζV

_{HS}

^{θ}shown in Equation (25).

Plate No. | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

V_{HS,opt} (m/s) | 0.39 | 0.60 | 0.49 | 1.03 | 0.33 | 2.00 |

U_{HS,opt} (kW/m^{2}K) | 1.57 | 0.62 | 1.14 | 0.34 | 0.48 | 0.27 |

∆P_{HS,opt} (-) | 51.8 | 21.3 | 44.3 | 9.8 | 39.6 | 18.8 |

NTU_{HS,opt} (-) | 1.57 | 0.62 | 1.14 | 0.34 | 0.48 | 0.27 |

(W_{net}/A)_{m} (kW/m^{2}) | 0.18 | 0.39 | 0.14 | 0.18 | 0.05 | 0.22 |

ω (1/m^{2}) | 0.36 | 0.92 | 0.33 | 0.15 | 0.13 | 0.38 |

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**MDPI and ACS Style**

Yasunaga, T.; Noguchi, T.; Morisaki, T.; Ikegami, Y.
Basic Heat Exchanger Performance Evaluation Method on OTEC. *J. Mar. Sci. Eng.* **2018**, *6*, 32.
https://doi.org/10.3390/jmse6020032

**AMA Style**

Yasunaga T, Noguchi T, Morisaki T, Ikegami Y.
Basic Heat Exchanger Performance Evaluation Method on OTEC. *Journal of Marine Science and Engineering*. 2018; 6(2):32.
https://doi.org/10.3390/jmse6020032

**Chicago/Turabian Style**

Yasunaga, Takeshi, Takafumi Noguchi, Takafumi Morisaki, and Yasuyuki Ikegami.
2018. "Basic Heat Exchanger Performance Evaluation Method on OTEC" *Journal of Marine Science and Engineering* 6, no. 2: 32.
https://doi.org/10.3390/jmse6020032