# Part-Load Performance Prediction and Operation Strategy Design of Organic Rankine Cycles with a Medium Cycle Used for Recovering Waste Heat from Gaseous Fuel Engines

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Description

#### 2.1. Gaseous Fuel Engine

_{2}= 73.4%, CO

_{2}= 7.11%, H

_{2}O = 14.22% (gas), O

_{2}= 5.27%. Then the specific heat capacity, enthalpy and other thermo-physical properties can be known.

#### 2.2. ORC-MC System

## 3. Mathematical Model

#### 3.1. Sub-Models for the Main Components

#### 3.1.1. Hot Water Heat Exchanger

_{1}); one referring to the state of the metal constituting the metal pipe (referred to as w); one referring to the state of the fluid in the annulus (f

_{2}). The discretization nodes are located at the centre of the different control cells and their state is represented by the average state of outlet and inlet of the control cell.

- The external pipe is assumed to be ideally insulated hence heat losses are neglected;
- The exhaust finally discharges to the environment and its pressure doesn’t change a lot, so the pressure is considered constant and the head losses of water in inner pipe is also neglected. Therefore, the momentum conservation equation is not applied to the cells of fluid.
- The hot water is considered to be incompressible and it is pressured into a constant value, while the exhaust is compressible;
- The axial conductive heat fluxes have been neglected for the fluids and pipe wall;
- No mass accumulation is considered for the fluids;
- Lumped thermal capacitance is assumed for both the metal pipe.

_{1}can be determined by Zukauskas’ correlation [36]:

_{α}and m depend on Re [36]. Subscripts f and w represent the fluid and pipe wall, respectively. There is no phase change in the tube, so the convective heat transfer coefficient for internal flow is obtained by using Sieder-Tate correlation [36]:

#### 3.1.2. Evaporator

- The heat exchanger is a long, thin, horizontal tube.
- The working fluid and exhaust flowing through the heat exchanger tube can be modeled as a one-dimensional fluid flow.
- Axial conduction of working fluid and exhaust is negligible.
- Pressure drop along the heat exchanger tube due to momentum change in refrigerant and viscous friction are negligible. Thus the equation for conservation of momentum is not needed.
- The assumption of mean void fraction is used. Void fraction is defined as the ratio of vapor volume to total volume, and has long been used to describe certain characteristics of two-phase flows.

_{0}(the heat transfer coefficient between hot water and pipe wall), α

_{1}, α

_{2}, α

_{3}(internal pipe heat transfer coefficient in subcooling region, two-phase region and superheated region), p (the pressure in evaporator), p

_{e}(the pressure of hot water), A

_{i}, A

_{o}, A

_{w}(the cross sectional area of inner pipe, outer pipe and pipe wall).

_{g}/u

_{l}between the gas and the liquid velocities. The slip flow model proposed by Zivi [37] is used here because of its simplicity:

_{1}and α

_{3}, the densities of saturated liquid (ρ

_{l}) and saturated steam (ρ

_{g}) and the average steam quality x [20]:

#### 3.1.3. Pump and Turbine

_{v}is the volumetric efficiency, ρ

_{pump}is the working fluid density at the pump inlet, V

_{cyl}is the cylinder volume and ω is revolution speed. In the pump, the working fluid goes through a non-isentropic pumping process. The ideal enthalpy of working fluid after isentropic pumping is written as h

_{spout}, h

_{pout}and h

_{pin}are the enthalpy of working fluid at the outlet and inlet of pump, respectively. η

_{sp}is the isentropic efficiency of the pump, so the consumed work of pump can be calculated as:

_{v}is a coefficient, ρ

_{out}is the outlet density from the evaporator, p is the pressure in the evaporator and p

_{c}is the condensing pressure. In the evaporator, the working fluid goes through a non-isentropic pumping process. The ideal enthalpy of the working fluid after isentropic expansion is written as h

_{stout}; h

_{tout}and h

_{tin}are respectively the enthalpy of working fluid at the outlet and inlet of turbine. η

_{st}is the isentropic efficiency of the turbine, so the output power can be calculated as:

_{s}that results from the variation of the isentropic enthalpy drop at part-load conditions, where u is the impeller tangential speed and c

_{s}is isentropic gas speed. The second correction factor (CF2) is related to the variation of the mass flow rate. a

_{1}, b

_{1}, c

_{1}and a

_{2}, b

_{2}, c

_{2}depend on the specific turbine design.

#### 3.1.4. System Performance Indicators

_{ca}) are considered and the specific power consumption of the cooling air fans is assumed to be 0.15 kW/(kg/s of air) [12]. Therefore, the net output power and thermal efficiency of the combined system can be expressed as below. Therein, W

_{e}and Q

_{ein}are respectively the output power and input heat of the gaseous fuel engine:

#### 3.2. Model Validation

#### 3.3. System Design

## 4. Results and Analysis

#### 4.1. The Effects of Mass Flow Rate of Hot Water and Working Fluid at Different Working Conditions

_{f}) on degree of superheating, evaporation pressure and isentropic efficiency of the turbine under different working conditions of the gaseous fuel engine. In these figures, including Figure 10, the mass flow rate of hot water remains unchanged. As the working conditions become small, the waste heat amount of exhaust becomes less, so the working fluid mass flow rate must decrease, otherwise the working fluid cannot evaporate totally, which leads to damage to the turbine blades. For every gaseous fuel engine working condition, the max working fluid mass flow rate is the one that makes the degree of superheating become 0 as shown in Figure 8. From Figure 8, it is known that superheat degree decreases with increasing m

_{f}, while evaporating pressure rises with it at different working conditions. The turbine is equivalent to a nozzle and when the working fluid mass flow rate increases, more working fluid goes through the turbine, so the pressure before it (evaporating pressure) must get higher.

_{f}more and more slowly, and finally they show a very small reduction. According to the basic property of ORC [31], the greater the evaporation pressure is, the more output power and thermal efficiency it has. The decreasing degree of superheating has nearly no effect on the thermal efficiency but it leads to a reduction of the output power. The increasing m

_{f}and evaporation pressure contribute to the output power, while a decreasing degree of superheating leads to a reduction of the output power. Besides, as is known to all, if the turbine works under part-load conditions, its efficiency will decrease as shown in Figure 9. Therefore, the point where n

_{st}is the highest is the design point of the turbine. For these reasons the ORC output power increases and then decreases a little. The thermal efficiency of the ORC increases with evaporation pressure more and more slowly [31], while the turbine isentropic efficiency decreases when m

_{f}exceeds the design value, so the thermal efficiency finally also decreases a little. However, under other working conditions of the gaseous fuel engine, because the turbine works under the part-load condition all the time and the increasing m

_{f}makes it closer to the design point, the n

_{st}rises with increasing m

_{f}as shown in Figure 9. Consequently the output power and thermal efficiency also increase with m

_{f}all along until m

_{f}reaches its maximum value. In a word, Figure 10 indicates that in order to get a large output power and thermal efficiency under different working conditions of gaseous fuel engine, the working fluid mass flow rate should be controlled as large as possible under the condition of no drops at the inlet of the turbine.

_{w}), which means m

_{w}cannot improve the system performance. According to the former research [42], the increase of heat source mass flow rate contributes to system output power and thermal efficiency, while a decrease of heat source inlet temperature leads to their reduction. From Figure 11, it is known that the increase of m

_{w}brings out the decrease of hot water outlet temperature in exhaust heat exchanger, which is also the heat source inlet temperature of ORC. Therefore, m

_{w}almost does not affect system output power and thermal efficiency.

#### 4.2. System Performance with Control

_{f}decreases as the working conditions become small and the degree of superheating is positive all along during the dynamic variation process, which ensures the safety of the turbine when the gaseous fuel engine working conditions change. Actually, the degree of superheating can be controlled to be lower. Figure 14 compares the system output power with different controlled degrees of superheating (10 K and 30 K). It can be found that the WHRS with a 10 K degree of superheating always has a greater output power than the system with a 30 K degree of superheating, which proves the conclusion obtained above. With the control of a constant (10K) degree of superheating of the working fluid at the evaporator outlet, the system performance under steady state under seven typical gaseous fuel engine working conditions (100%, 90%, 80, 70%, 60%, 50%, 40%) are shown in Figure 15, Figure 16 and Figure 17.

_{t}), the pump (n

_{p}) and the thermal efficiency of the ORC (n). It can be found that as the working conditions decease, n

_{t}, n

_{p}and n all become small, especially n

_{t}and n

_{p}which decrease faster and faster. As mentioned above, when the gaseous fuel engine working conditions go down, the exhaust waste heat amount decreases, therefore, the working fluid mass flow rate must be reduced and the reduction of m

_{f}leads to the decrease of P

_{e}. The lower P

_{e}the ORC has, the lower thermal efficiency it has. Added to the decrease of isentropic efficiency of pump and turbine, n decreases as the gaseous fuel engine conditions go down. At 100% working condition n is 12.9%, while n becomes 6.5% under 40% working conditions, which means the WHRS performance suffers a great reduction.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

T | Temperature (K) |

ρ | Density (kg/m^{3}) |

α | Heat transfer coefficient (W/m^{2}·K) |

C_{p} | Specific heat (J/kg·K) |

m | Mass flow rate (kg/s) |

A | Area (m^{2}) |

t | Time (s) |

D | Diameter (m) |

h | Specific enthalpy (J/kg) |

Re | Reynolds number |

Nu | Nusselt number |

Pr | Prandtl number |

γ | void fraction (m^{2}/s) |

S | Slip ratio |

μ | Density ratio |

u | Velocity (m/s) |

L | Length (m) |

p | Pressure (Pa) |

x | Vapor quality |

ω | Revolution speed (rpm) |

η_{v} | Volumetric efficiency |

V_{cyl} | Cylinder volume (m^{3}) |

$\dot{V}$ | Volume flow rate (m^{3}/s) |

C_{v} | Turbine coefficient |

W | Work (W) |

η_{st} | Isentropic efficiency of expander |

η_{sp} | Isentropic efficiency of pump |

η | Dynamic viscosity (Pa·s) or liquid fraction or efficiency |

c_{s} | Isentropic gas speed(m/s) |

l | Liquid |

g | Gas or exhaust |

e | Heat source (hot water) |

c | Cold |

f | Fluid |

i | Inside |

o | Outside |

w | Wall |

in | Inlet |

out | Outlet |

r | Working fluid |

avg | Average |

p | Pump |

s | Isentropic |

t | Turbine |

ca | Cooling air |

ORC | Organic Rankine Cycle |

MB | Moving Boundary |

WHR | Waste Heat Recovery |

WHRS | Waste Heat Recovery System |

MC | Medium Cycle |

ICE | Internal Combustion Engine |

ODP | Ozone Depression Potential |

GWP | Global Warming Potential |

## References

- Charles, S. Review of Organic Rankine cycles for internal combustion engine exhaust waste heat recovery. Appl. Therm. Eng.
**2013**, 51, 711–722. [Google Scholar] - Aghaali, H.; Ångström, H. A review of turbo compounding as a waste heat recovery system for internal combustion engines. Renew. Sustain. Energy Rev.
**2015**, 49, 819–824. [Google Scholar] [CrossRef] - Wang, T.Y.; Zhang, Y.J.; Peng, Z.J.; Shu, G.Q. A review of researches on thermal exhaust heat recovery with Rankine cycle. Renew. Sustain. Energy Rev.
**2011**, 15, 2862–2871. [Google Scholar] [CrossRef] - Chammas, R.E.; Clodic, D. Combined cycle for hybrid vehicles. SAE Pap.
**2005**. [Google Scholar] [CrossRef] - Ringler, J.; Seifert, M.; Guyotot, V.; Hübner, W. Rankine cycle for waste heat recovery of IC engines. SAE Pap.
**2009**. [Google Scholar] [CrossRef] - Teng, H.; Regner, G.; Cowland, C. Waste heat recovery of heavy-duty diesel engines by Organic Rankine cycle Part I: hybrid energy system of diesel and Rankine engines. SAE Pap.
**2007**. [Google Scholar] [CrossRef] - Battista, D.D.; Mauriello, M.; Cipollone, R. Waste heat recovery of an ORC-based power unit in a turbocharged diesel engine propelling a light duty vehicle. Appl. Energy
**2015**, 152, 109–120. [Google Scholar] [CrossRef] - Quoilin, S.; Lemort, V.; Lebrun, J. Experimental study and modeling of an Organic Rankine Cycle using scroll expander. Appl. Energy
**2010**, 87, 1260–1268. [Google Scholar] [CrossRef] - Yu, G.; Shu, G.; Tian, H.; Wei, H.; Liu, L. Simulation and thermodynamic analysis of a bottoming Organic Rankine Cycle (ORC) of diesel engine (DE). Energy
**2013**, 51, 281–290. [Google Scholar] [CrossRef] - Manente, G.; Field, R.; DiPippo, R.; Tester, J.W.; Paci, M.; Rossi, N. Hybrid solar geothermal power generation to increase the energy production from a binary geothermal plant. In Proceedings of the ASME 2011 International Mechanical Engineering Congress and Exposition, Denver, CO, USA, 11–17 November 2011.
- Jensen, J.M.; Tummescheit, H. Moving boundary models for dynamic simulation of two-phase flows. In Proceedings of the Second International Modelica Conference, Oberpfaffenhofen, Germany, 18–19 March 2002.
- Manente, G.; Toffolo, A.; Lazzaretto, A. An Organic Rankine Cycle off-design model for the search of the optimal control strategy. Energy
**2013**, 58, 97–106. [Google Scholar] [CrossRef] - Yousefzadeh, M.; Uzgoren, E. Mass-conserving dynamic Organic Rankine cycle model to investigate the link between mass distribution and system state. Energy
**2015**, 93, 1128–1139. [Google Scholar] [CrossRef] - Wei, D.; Lu, X.; Lu, Z.; Gu, J. Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery. Appl. Therm. Eng.
**2008**, 28, 1216–1224. [Google Scholar] [CrossRef] - Quoilin, S.; Aumann, R.; Grill, A.; Schuster, A.; Lemort, V.; Spliethoff, H. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Appl. Energy
**2011**, 88, 2183–2190. [Google Scholar] [CrossRef] - Mazzi, N.; Rech, S.; Lazzaretto, A. Off-design dynamic model of a real Organic Rankine Cycle system fuelled by exhaust gases from industrial processes. Energy
**2015**, 90, 537–551. [Google Scholar] [CrossRef] - Rasmussen, B.P.; Shah, R.; Musser, A.B. Control-Oriented Modeling of Transcritical Vapor Compression Systems. Master’s Thesis, University of Illinois Urbana-Champaign, Champaign, IL, USA, 2002. [Google Scholar]
- Jensen, J.M. Dynamic Modeling of Thermo-Fluid Systems. Ph.D. Thesis, Technical University of Denmark, Copenhagen, Denmark, 2003. [Google Scholar]
- Milián, V.; Navarro-Esbrí, J.; Ginestar, D. Dynamic model of a shell-and-tube condenser. Analysis of the mean void fraction correlation influence on the model performance. Energy
**2013**, 59, 521–533. [Google Scholar] [CrossRef] - Horst, T.A.; Rottengruber, H.-S.; Seifert, M.; Ringler, J. Dynamic heat exchanger model for performance prediction and control system design of automotive waste heat recovery systems. Appl. Energy
**2013**, 105, 293–303. [Google Scholar] [CrossRef] - Hou, G.; Sun, R.; Hu, G.; Zhang, J. Supervisory predictive control of evaporator in Organic rankine cycle (ORC) system for waste heat recovery. In Proceedings of the International Conference on Advanced Mechatronic Systems, Zhengzhou, China, 11–13 August 2011.
- Zhang, J.; Zhang, W.; Hou, G.; Fang, F. Dynamic modeling and multivariable control of Organic Rankine Cycles in waste heat utilizing processes. Comput. Math. Appl.
**2012**, 64, 908–921. [Google Scholar] [CrossRef] - Zhang, J.; Zhou, Y.; Gao, S.; Hou, G. Constrained predictive control based on state space model of Organic Rankine Cycle system for waste heat recovery. In Proceedings of the Chinese Control and Decision Conference (CCDC), Taiyuan, China, 23–25 May 2012.
- Benato, A.; Kærn, M.R.; Pierobon, L. Analysis of hot spots in boilers of Organic Rankine Cycle units during transient operation. Appl. Energy
**2015**, 151, 119–131. [Google Scholar] [CrossRef] [Green Version] - Luong, D.; Tsao, T.-C. Linear quadratic integral control of an Organic Rankine Cycle for waste heat recovery in heavy-duty diesel powertrain. In Proceedings of the 2014 American Control Conference (ACC), Portland, OR, USA, 4–6 June 2014.
- Gewald, D.; Siokos, K.; Karellas, S. Waste heat recovery from a landfill gas-fired power plant. Renew. Sustain. Energy Rev.
**2012**, 16, 1779–1789. [Google Scholar] [CrossRef] - Li, X. Research on Design and Performance Optimization of Diesel Engine Waste Heat Recovery Bottoming System and Key Component. Ph.D. Thesis, Tianjin University, Tianjin, China, 2014. [Google Scholar]
- Vaja, I. Definition of an Object Oriented Library for the Dynamic Simulation of Advanced Energy Systems: Methodologies, Tools and Application to Combined ICE-ORC Power Plants. Ph.D. Thesis, University of Parma, Parma, Italy, 2009. [Google Scholar]
- Sotirios, K.; Andreas, S. Supercritical fluid parameters in Organic Rankine Cycle applications. Int. J. Thermodyn.
**2008**, 11, 101–108. [Google Scholar] - Schuster, A.; Karellas, S.; Aumann, R. Efficiency optimization potential in supercritical Organic Rankine Cycles. Energy
**2010**, 35, 1033–1039. [Google Scholar] [CrossRef] - Meinel, D.; Wieland, C.; Spliethof, H. Effect and comparison of different working fluids on a two-stage Organic Rankine Cycle (ORC) concept. Appl. Therm. Eng.
**2014**, 63, 246–253. [Google Scholar] [CrossRef] - Quoilin, S.; van Den Broek, M.; Declaye, S.; Dewallef, P.; Lemort, V. Techno-economic survey of Organic Rankine Cycle (ORC) systems. Renew. Sustain. Energy Rev.
**2013**, 22, 168–186. [Google Scholar] [CrossRef] - Xie, H.; Yang, C. Dynamic behavior of Rankine cycle system for waste heat recovery of heavy duty diesel engines under driving cycle. Appl. Energy
**2013**, 112, 130–141. [Google Scholar] [CrossRef] - Zhang, J.; Zhou, Y.; Wang, R.; Xu, J.; Fang, F. Modeling and constrained multivariable predictive control for ORC (Organic Rankine Cycle) based waste heat energy conversion systems. Energy
**2014**, 66, 128–138. [Google Scholar] [CrossRef] - Bamgbopa, M.O.; Uzgoren, E. Quasi-dynamic model for an Organic Rankine Cycle. Energy Convers. Manag.
**2013**, 72, 117–124. [Google Scholar] [CrossRef] - Shiming, Y. Heat Transfer, 4th ed.; Higher Education Press: Beijing, China, 1998; pp. 162–175. (In Chinese) [Google Scholar]
- Zivi, S.M. Estimation of steady-state steam void-fraction by means of the principle of minimum entropy production. J. Heat Trans.
**1964**, 86, 247–252. [Google Scholar] [CrossRef] - Collier, J.G.; Thome, J.R. Convective Boiling and Condensation, 3rd ed.; Clarendon Press: Oxford, UK, 1994. [Google Scholar]
- Ahlgren, F.; Mondejar, M.E. Waste heat recovery in a cruise vessel in the Baltic Sea by using an Organic Rankine Cycle: A case study. J. Eng. Gas Turbines Power
**2016**, 138, 1–15. [Google Scholar] - Peralez, J.; Dufour, P. Towards model-based control of a steam Rankine process for engine waste heat recovery. In Proceedings of the 2011 IEEE Vehicle Power and Propulsion Conference, Seoul, Korea, 9–12 October 2012.
- Li, Y.-R.; Wang, J.-N.; Du, M.-T. Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Ranking cycle. Energy
**2012**, 42, 503–509. [Google Scholar] [CrossRef] - Shu, G.; Wang, X.; Tian, H. The performance of Rankine Cycle as waste heat recovery system for a natural gas engine at variable working conditions. SAE Pap.
**2016**. [Google Scholar] [CrossRef]

**Figure 8.**The effects of working fluid mass flow rate on evaporation pressure and degree of superheating.

**Figure 10.**The effects of working fluid mass flow rate on output power and thermal efficiency of the ORC system.

**Figure 11.**The effects of hot water mass flow rate on output power and hot water outlet temperature in the exhaust heat exchanger.

**Figure 14.**Comparison of the turbine output power with different controlled degrees of superheating (10 K and 30 K).

Parameter | Unit | Value | ||||||
---|---|---|---|---|---|---|---|---|

Speed | r/min | 600 | 600 | 600 | 600 | 600 | 600 | 600 |

Working condition load | - | 40% | 50% | 60% | 70% | 80% | 90% | 100% |

Effective power | kW | 400 | 500 | 600 | 700 | 800 | 900 | 1000 |

Exhaust temperature | °C | 470 | 515 | 525 | 527 | 530 | 532 | 540 |

Heat consumption rate of gas | MJ/kWh | 13.09 | 11.76 | 11.08 | 10.59 | 10.20 | 10.26 | 9.85 |

Intake air volume flow rate | m^{3}/h | 1774 | 2145 | 2465 | 2748 | 3120 | 3510 | 4180 |

Exhaust volume flow rate | m^{3}/h | 1911 | 2310 | 2654 | 2959 | 3380 | 3800 | 4500 |

Exhaust mass flow rate | kg/s | 0.69 | 0.834 | 0.958 | 1.069 | 1.221 | 1.372 | 1.625 |

Thermal efficiency of engine | % | 27.5 | 30.61 | 32.25 | 33.98 | 35.29 | 35.08 | 36.55 |

Pump and Turbine | |

η_{v} = 0.8 | V_{cyl} = 2.7313 × 10^{−6} m^{3} |

C_{v} = 0.0064 | η_{s} = 0.8 |

η_{sp} = 0.8 | |

Evaporator and Condenser Parameters | |

D_{i} = 0.02 m | T_{eout} = 373 K |

D_{o} = 0.022 m | C_{w} = 385 J/kgK |

L = 428.79 m | ρ_{w} = 8960 kg/m^{3} |

L_{1} = 117.90 m | P = 2000 kPa |

L_{2} = 75.89 m | P_{c} = 230 kPa |

L_{3} = 13.01 m | delta T_{s} = 10 K |

T_{ein} = 433 K |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, X.; Tian, H.; Shu, G.
Part-Load Performance Prediction and Operation Strategy Design of Organic Rankine Cycles with a Medium Cycle Used for Recovering Waste Heat from Gaseous Fuel Engines. *Energies* **2016**, *9*, 527.
https://doi.org/10.3390/en9070527

**AMA Style**

Wang X, Tian H, Shu G.
Part-Load Performance Prediction and Operation Strategy Design of Organic Rankine Cycles with a Medium Cycle Used for Recovering Waste Heat from Gaseous Fuel Engines. *Energies*. 2016; 9(7):527.
https://doi.org/10.3390/en9070527

**Chicago/Turabian Style**

Wang, Xuan, Hua Tian, and Gequn Shu.
2016. "Part-Load Performance Prediction and Operation Strategy Design of Organic Rankine Cycles with a Medium Cycle Used for Recovering Waste Heat from Gaseous Fuel Engines" *Energies* 9, no. 7: 527.
https://doi.org/10.3390/en9070527