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This paper was previously presented in the 1st International e-Conference on Energies, 2014, c010; doi:10.3390/ece-1-c010, available online:

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

An organic Rankine cycle system comprised of a preheater, evaporator, condenser, turbine, generator, and pump was used to study its off-design performance and the operational control strategy. R245fa was used as the working fluid. Under the design conditions, the net power output is 243 kW and the system thermal efficiency is 9.5%. For an off-design heat source flow rate (_{W}), the operating pressure was controlled to meet the condition that the R245fa reached the liquid and vapor saturation states at the outlet of the preheater and the evaporator, respectively. The analytical results demonstrated that the operating pressure increased with increasing _{W}; a higher _{W} yielded better heat transfer performance of the preheater and required a smaller evaporator heat capacity, and the net power output and system thermal efficiency increased with increasing _{W}. For the range of _{W} studied here, the net power output increased by 64.0% while the total heat transfer rate increased by only 9.2%. In summary, off-design operation of the system was examined for a heat source flow rate which varied by –39.0% to +78.0% from the designed rate, resulting in –29.2% to +16.0% and –25.3% to +12.6% variations in the net power output and system thermal efficiency, respectively.

An organic Rankine cycle (ORC) employs the same general principles as the steam Rankine cycle, but uses organic fluids with a low boiling point as the working fluid, enabling power generation for a low heat source temperature [

Because an ORC system provides the heat to power a process, the heat exchanger is a very important component of the system. Moreover, the evaporation temperature related to the working fluid flow rate and the specific enthalpy change is a crucial parameter in an ORC system. Li

Another important parameter is the pinch point temperature difference of the heat exchanger system, which also significantly influences the performance of an ORC system. Li

Although there have been many studies examining the effect of various system parameters on the performance of ORC systems [

The ORC system studied here is depicted in _{R}) was set to be 11.58 kg/s, which was chosen based on the optimal operating range of the designed turbine. The working fluid R245fa flowed in the shell side of the heat exchangers while hot and cooling water flowed in the tube side. This ORC prototype, the engineering drawing of which is shown in

Schematic diagram of the studied ORC system.

Detailed parameters of the designed preheater.

Parameter | Value or type |
---|---|

Tube inner/outer diameter | 1.471/1.587 cm |

Tube thickness | 0.058 cm |

Tube number | 200 |

Tube in window | 83 |

Tube bundle | 1 pass |

Tube inner type | Rifled |

Tube outer type/Fin per inch (FPI) | Low-finned/42 |

Tube arrangement | Staggered |

Tube pitch transverse | 1.984 cm |

Tube pitch longitudinal | 1.718 cm |

Tube/Shell length | 360 cm |

Shell inner diameter | 32.45 cm |

Bundle hole diameter | 1.61 cm |

Bundle diameter | 31.66 cm |

Sealing strips number | 0 |

Nozzle inner diameter | 10 cm |

Baffle plate diameter | 31.95 cm |

Baffle thickness | 0.4 cm |

Baffle spacing | 20 cm |

Baffle cut | 30% |

Baffle plate number | 17 |

Tube side enhanced factor | 1.2 |

Shell side enhanced factor | 1.6 |

Engineering drawing of the ORC prototype: (

_{R,eva}, is 100 °C) and 0.242 MPa (the condensation temperature is 39 °C), respectively. The designed set point for the heat source (hot water) temperature (_{w,in}) and mass flow rate (_{W}) are 133.9 °C and 15.39 kg/s, respectively. Under the design conditions, the net power output is 243 kW and the system thermal efficiency is 9.5%. The analyzed heat source flow rate ranged from 9.39 kg/s to 27.39 kg/s.

The following assumptions were made for the present analysis: (1) Each component is in the steady state under both flow and thermal conditions; (2) pressure drops in the heat exchangers (preheater, evaporator, and condenser) can be neglected; (3) the heat loss in each of the components and in the system pipes can be ignored; (4) the pump, turbine, and generator efficiencies are assumed constant of 90%, 80%, and 90%, respectively; (5) for an off-design flow rate of the heat source, a new operating pressure of the preheater/evaporator has to be chosen to meet the following requirements: R245fa reaches the saturation liquid state at the outlet of the preheater (point 3 in

The mathematical models of each component as well as of the system performance are presented below in brief. The system thermal efficiency (_{sys}) can be obtained from the following equations:
_{sys} = _{net} / _{tot}
_{net} = _{out} − _{in}
_{out} = _{tur} / _{gen}
_{tur} = _{R} (_{4} − _{5s}) · _{tur}
_{in} = _{R} (_{2s} − _{1}) / _{pump}
_{tur} = (_{4} − _{5}) / (_{4} − _{5s})
_{pump} = (_{2s} − _{1}) / (_{2} − _{1})
_{tot} = _{pre} + _{eva}
_{pre} = _{R} (_{3} − _{2}) = (_{lm})_{pre}
_{eva} = _{R} (_{4} − _{3}) = (_{lm})_{eva}

Here, _{net} is the net power output of the system; _{out} is the power output of the generator; _{in} is the power requirement of the pump; _{tur} is the power output of the turbine; _{i}_{tot} is the total heat transfer rate of the preheater and evaporator; _{pre} is the heat transfer rate of the preheater; _{eva} is the heat transfer rate of the evaporator; _{R} is the mass flow rate of the working fluid, _{gen}, _{tur}, and _{pump} are the efficiencies of the generator, turbine, and pump, respectively; _{lm} is the logarithmic mean temperature difference (LMTD); _{R} and _{W} are the heat transfer coefficients of the shell side (R245fa side) and tube side (water side), respectively, of the heat exchanger; _{o} and _{i} are the outer and the inner diameters, respectively, of the tube; and

Moreover, in this study the heat transfer functioning of the preheater was calculated by the classical effectiveness–NTU method [_{R} = _{0} · _{c} · _{l} · _{b} · _{s} · _{r}
^{−2}
_{0} is the heat transfer coefficient for an ideal tube bundle; _{c}, _{l}, _{b}, _{s}, and _{r}

_{R}), and evaporation/saturation temperature (_{R,eva}) as a function of the heat source flow rate (_{W}). As shown in _{R} and _{R,eva} increased rapidly for _{W} < 17.39 kg/s and gradually for _{W} ≥ 17.39 kg/s. This result is mainly due to the fact that the heat source temperature is set to be 133.9 °C. Therefore, for _{W} ≥ 17.39 kg/s, the evaporation/saturation temperature increases slowly until it approaches the plateau value, which may be approximately 120 °C. Thus these results can be used as guidelines for this system when choosing the operating pressure and evaporation temperature for off-design heat source flow rates.

Operating pressure and evaporation temperature as a function of the heat source flow rate.

_{W} increased, the inlet temperature of the compressed fluid state R245fa (point 2 in _{W}. In previous work by Wang

Temperature distribution of water and R245fa for different heat source flow rates.

_{pre}) and the evaporator (_{eva}) as a function of the heat source flow rate. In this figure, the total heat transfer rate (_{tot}) is the sum of _{pre} and _{eva}. It is clearly shown that with an increase in _{W}, _{pre} increased from 654 kW to 1258 kW but _{eva} decreased from 1773 kW to 1392 kW. This figure also demonstrates that the increase of _{pre} was larger than that of _{eva}. As a result, the total heat transfer rate increased from 2427 kW to 2650 kW with an increase in _{W}. In addition, the change rates of _{pre}, _{eva}, and _{tot} for _{W} < 17.39 kg/s were significantly higher than that for _{W} ≥ 17.39 kg/s. In summary,

Heat transfer rate as a function of the heat source flow rate.

_{W} increased, the heat transfer coefficient of the tube side (_{W,pre}) increased rapidly from 3362 W/m^{2}K to 9162 W/m^{2}K, _{R,pre}) remained nearly constant at about 815 W/m^{2}K. In addition, because the heat transfer coefficient of the shell side was much smaller than that of the tube side, the overall heat transfer coefficient (_{pre}) increased gradually from 308 W/m^{2}K to 373 W/m^{2}K, _{pre}, shown in _{lm}), shown in _{lm} increased from 19.6 °C to 29.9 °C, _{W} values.

Preheater heat transfer coefficient as a function of the heat source flow rate.

Most importantly, these results further demonstrate that with an increase in _{W}, the net power output (_{net}) and system thermal efficiency (_{sys}) increased from 172 kW to 282 kW and from 7.1% to 10.7%, respectively, as shown in _{in}) is 5.5 kW to 14.4 kW, which is only about 3.1% to 4.9% of the power output of the generator (_{out}). Moreover, it is worth mentioning that for the studied range of _{W} values, the net power output increased by 64.0% (from 172 kW to 282 kW) while the total heat transfer rate (_{tot}) increased by only 9.2% (from 2427 kW to 2650 kW). This result indicates that the system performance was significantly enhanced by increasing _{W}. It is also interesting to note that _{net}, _{out}, _{in}, and _{sys} increased rapidly for _{W} < 17.39 kg/s but gradually for _{W} ≥ 17.39 kg/s, which is similar to the characteristics of _{R} and _{R,eva}, as shown in

Net power output and system efficiency as a function of the heat source flow rate.

In this paper, an analysis of the effect of the heat source flow rate on the heat transfer characteristics of a preheater and the system performance of a 250 kW organic Rankine cycle (ORC) system was conducted. The refrigerant R245fa was used as the working fluid, with a constant flow rate of 11.58 kg/s. The design conditions for the operating pressures of the preheater/evaporator and the condenser are 1.265 MPa (_{W}) ranged from 9.39 kg/s to 27.39 kg/s with a constant inlet temperature of 133.9 °C. The efficiencies of the pump, turbine, and generator were assumed to be 90%, 80%, and 90%, respectively. For the design conditions, the net power output is 243 kW and the system thermal efficiency is 9.5%.

For an off-design heat source flow rate, a new operating pressure of the preheater/evaporator was chosen to meet the following limitation: R245fa reaches the liquid saturation state at the outlet of the preheater and the vapor saturation state at the outlet of the evaporator, _{W}; (2) a higher _{W} yielded better heat transfer performance of the preheater and required a smaller heat capacity of the evaporator; (3) the pinch point temperature differences (8.8 °C to 10.4 °C) of this ORC system were appropriate from a system performance point of view [_{W}, especially for _{W} < 17.39 kg/s. Most importantly, these results illustrated that the net power output increased by 64.0% while the total heat transfer rate increased only by 9.2% for the investigated range of _{W} values. This result indicates that the performance of this system was significantly improved by increasing _{W}. In conclusion, an off-design operation of this ORC system is studied using a pressure control approach for a heat source flow rate which varied by –39.0% to +78.0% from the designed rate, resulting in –29.2% to +16.0% and –25.3% to +12.6% variations in the net power output and system thermal efficiency, respectively.

The authors would like to express their gratitude for the financial support provided by the Energy R&D Foundation of the Energy Bureau of the Ministry of Economic Affairs, Taiwan, under the Efficient Geothermal Energy Technology Research Project (grant number: 103-D0102).

The corresponding author was mainly responsible for analysis/interpretation of data and initial writing. The other authors had been involved in the discussion and preparation of the manuscript.

The authors declare no conflict of interest.