#
Performance of a 250 kW Organic Rankine Cycle System for Off-Design Heat Source Conditions^{ †}

^{*}

^{†}

## Abstract

**:**

_{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 m

_{W}; a higher m

_{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 m

_{W}. For the range of m

_{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.

## 1. Introduction

## 2. System Description

_{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 Figure 2, has recently been under construction at the Industrial Technology Research Institute, Taiwan.

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 |

_{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 (T

_{w,in}) and mass flow rate (m

_{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.

## 3. Analysis Methodology

_{sys}) can be obtained from the following equations:

_{sys}= W

_{net}/ Q

_{tot}

_{net}= W

_{out}− W

_{in}

_{out}= W

_{tur}/ E

_{gen}

_{tur}= m

_{R}(h

_{4}− h

_{5s}) · E

_{tur}

_{in}= m

_{R}(h

_{2s}− h

_{1}) / E

_{pump}

_{tur}= (h

_{4}− h

_{5}) / (h

_{4}− h

_{5s})

_{pump}= (h

_{2s}− h

_{1}) / (h

_{2}− h

_{1})

_{tot}= Q

_{pre}+ Q

_{eva}

_{pre}= m

_{R}(h

_{3}− h

_{2}) = (UA·∆T

_{lm})

_{pre}

_{eva}= m

_{R}(h

_{4}− h

_{3}) = (UA·∆T

_{lm})

_{eva}

_{net}is the net power output of the system; W

_{out}is the power output of the generator; W

_{in}is the power requirement of the pump; W

_{tur}is the power output of the turbine; h

_{i}is the specific enthalpy for i = 1–5, 2s, and 5s; Q

_{tot}is the total heat transfer rate of the preheater and evaporator; Q

_{pre}is the heat transfer rate of the preheater; Q

_{eva}is the heat transfer rate of the evaporator; m

_{R}is the mass flow rate of the working fluid, i.e., R245fa; E

_{gen}, E

_{tur}, and E

_{pump}are the efficiencies of the generator, turbine, and pump, respectively; U is the overall heat transfer coefficient; A is the total heat transfer area; ∆T

_{lm}is the logarithmic mean temperature difference (LMTD); h

_{R}and h

_{W}are the heat transfer coefficients of the shell side (R245fa side) and tube side (water side), respectively, of the heat exchanger; d

_{o}and d

_{i}are the outer and the inner diameters, respectively, of the tube; and k is the thermal conductivity of the tube.

_{R}= h

_{0}· J

_{c}· J

_{l}· J

_{b}· J

_{s}· J

_{r}

^{−2}

_{0}is the heat transfer coefficient for an ideal tube bundle; J

_{c}, J

_{l}, J

_{b}, J

_{s}, and J

_{r}are the correction factors for the baffle cut, baffle leakage effects, bundle bypass flow, laminar flow, and unequal baffle spacing, respectively, in the inlet and outlet sections; f is the friction factor; Re is the Reynolds number; and Pr is the Prandtl number.

## 4. Results and Discussion

_{R}), and evaporation/saturation temperature (T

_{R,eva}) as a function of the heat source flow rate (m

_{W}). As shown in Figure 4, the operating pressure and evaporation temperature increased from 0.775 MPa to 1.675 MPa and from 79.3 °C to 113.2 °C, respectively, as the heat source flow rate increased from 9.39 kg/s to 27.39 kg/s. Both P

_{R}and T

_{R,eva}increased rapidly for m

_{W}< 17.39 kg/s and gradually for m

_{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 m

_{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.

**Figure 4.**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 Figure 3) increased slightly from 39.3 °C to 39.7 °C (due to the different operating pressures in the preheater and evaporator), and the outlet temperature of the hot water increased from 72.9 °C to 110.9 °C. In addition, this figure also illustrates that the minimum temperature difference between the hot and cold streams occurred at the midpoint between the preheater and evaporator; this particular location is considered to be the pinch point of the heat exchanger system. The pinch point temperature differences for cases (a), (b), and (c) are 10.1 °C, 10.1 °C, and 8.8 °C, respectively. These results indicate that for this system the pinch point temperature difference was not significantly affected by m

_{W}. In previous work by Wang et al. [16], the optimal recommended pinch point temperature difference at the evaporator was ≤15 °C when the heat source temperature in the ORC system was between 100 °C and 220 °C. Their results also demonstrated that a higher pinch point temperature difference leads to a decrease of the total net power output of an ORC system. Moreover, for engineering applications, the acceptable range of the pinch point temperature difference was 6 °C to 20 °C [2]. Therefore, when considering ORC system performance, the pinch point temperature differences of the heat exchanger system presented here may be suitable for such applications.

_{pre}) and the evaporator (Q

_{eva}) as a function of the heat source flow rate. In this figure, the total heat transfer rate (Q

_{tot}) is the sum of Q

_{pre}and Q

_{eva}. It is clearly shown that with an increase in m

_{W}, Q

_{pre}increased from 654 kW to 1258 kW but Q

_{eva}decreased from 1773 kW to 1392 kW. This figure also demonstrates that the increase of Q

_{pre}was larger than that of Q

_{eva}. As a result, the total heat transfer rate increased from 2427 kW to 2650 kW with an increase in m

_{W}. In addition, the change rates of Q

_{pre}, Q

_{eva}, and Q

_{tot}for m

_{W}< 17.39 kg/s were significantly higher than that for m

_{W}≥ 17.39 kg/s. In summary, Figure 6 indicates that a higher heat source flow rate resulted in a better heat transfer performance of the designed preheater and required a smaller evaporator heat capacity.

_{W}increased, the heat transfer coefficient of the tube side (h

_{W,pre}) increased rapidly from 3362 W/m

^{2}K to 9162 W/m

^{2}K, i.e., increasing by 272.5%, at an almost constant increase rate. In contrast, the heat transfer coefficient of the shell side (h

_{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 (U

_{pre}) increased gradually from 308 W/m

^{2}K to 373 W/m

^{2}K, i.e., increasing by only 21.1%. The increase of Q

_{pre}, shown in Figure 6, resulted from the increase of the overall heat transfer coefficient and the logarithmic mean temperature difference (∆T

_{lm}), shown in Figure 7. ∆T

_{lm}increased from 19.6 °C to 29.9 °C, i.e., increasing by 52.6%, for the investigated range of m

_{W}values.

_{W}, the net power output (W

_{net}) and system thermal efficiency (E

_{sys}) increased from 172 kW to 282 kW and from 7.1% to 10.7%, respectively, as shown in Figure 8. The result also illustrates that the power requirement for the pump (W

_{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 (W

_{out}). Moreover, it is worth mentioning that for the studied range of m

_{W}values, the net power output increased by 64.0% (from 172 kW to 282 kW) while the total heat transfer rate (Q

_{tot}) increased by only 9.2% (from 2427 kW to 2650 kW). This result indicates that the system performance was significantly enhanced by increasing m

_{W}. It is also interesting to note that W

_{net}, W

_{out}, W

_{in}, and E

_{sys}increased rapidly for m

_{W}< 17.39 kg/s but gradually for m

_{W}≥ 17.39 kg/s, which is similar to the characteristics of P

_{R}and T

_{R,eva}, as shown in Figure 4. The trend demonstrated by these results can be used as a reference for predicting the operational performance of this system when using off-design heat source flow rates. Finally, it is shown that for off-design operations, a pressure control approach where the heat source flow rate varied between –39.0% to +78.0% with respect to the designed parameters resulted in –29.2% to +16.0% and –25.3% to +12.6% variations in the net power output and system thermal efficiency, respectively.

## 5. Summary and Conclusions

_{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%.

_{W}; (2) a higher m

_{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 [2,16]; and (4) the net power output and system thermal efficiency increased with an increase in m

_{W}, especially for m

_{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 m

_{W}values. This result indicates that the performance of this system was significantly improved by increasing m

_{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.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Fu, B.-R.; Hsu, S.-W.; Lee, Y.-R.; Hsieh, J.-C.; Chang, C.-M.; Liu, C.-H.
Performance of a 250 kW Organic Rankine Cycle System for Off-Design Heat Source Conditions. *Energies* **2014**, *7*, 3684-3694.
https://doi.org/10.3390/en7063684

**AMA Style**

Fu B-R, Hsu S-W, Lee Y-R, Hsieh J-C, Chang C-M, Liu C-H.
Performance of a 250 kW Organic Rankine Cycle System for Off-Design Heat Source Conditions. *Energies*. 2014; 7(6):3684-3694.
https://doi.org/10.3390/en7063684

**Chicago/Turabian Style**

Fu, Ben-Ran, Sung-Wei Hsu, Yuh-Ren Lee, Jui-Ching Hsieh, Chia-Ming Chang, and Chih-Hsi Liu.
2014. "Performance of a 250 kW Organic Rankine Cycle System for Off-Design Heat Source Conditions" *Energies* 7, no. 6: 3684-3694.
https://doi.org/10.3390/en7063684