# Performance of Siloxane Mixtures in a High-Temperature Organic Rankine Cycle Considering the Heat Transfer Characteristics during Evaporation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Thermodynamic Process Analysis

T_{EG-IN} (K) | ṁ_{EG} (kg/s) | p_{EG} (bar) | Composition (mol %) | ||||
---|---|---|---|---|---|---|---|

733.15 | 0.48 | 1 | N_{2} | H_{2}O | CO_{2} | O_{2} | Ar |

64.55 | 18.15 | 9.74 | 6.63 | 0.93 |

#### 2.1. Methodology

Case | Fluid | T_{HS-IN} (K) | T_{HS-OUT} (K) | ṁ_{HS} (kg/s) | p_{HS} (bar) |
---|---|---|---|---|---|

heat sink (electricity) | air | 288.15 | 303.15 | variable | 1 |

heat sink (CHP) | water | 323.15 | 343.15 | variable | 2 |

PP_{EG heat exchanger} (K) | PP_{evaporator} (K) | PP_{condenser} (K) (min) | PP_{internal recuoerator} (K) (min) | η_{turbine} (%) | η_{generator} (%) | η_{pump} (%) | η_{driver} (%) |
---|---|---|---|---|---|---|---|

20 | 30 | 10 | 10 | 60 | 90 | 70 | 90 |

_{net}(power of turbine P

_{el,turb}minus power of pump P

_{pump}) divided by the exergy of heat source Ė

_{EG}:

_{EG}, mass flow rate ṁ

_{EG}, enthalpy h

_{EG,in}as well as entropy of heat source s

_{EG,in}are used. The index 0 corresponds to the reference state (288.15 K, 1 bar). In the case of combined heat and power generation the exergy content of the condenser duty Ė

_{cond}has to be taken into account:

_{HS,in/out}) and entropies (s

_{HS,in/out}) of the cooling water as well as its mass flow rate ṁ

_{HS}.

_{in}and T

_{out}describe the inlet and outlet temperatures of the heat sink. For the irreversibilities of the evaporator the temperatures of Dowtherm G have to be used.

#### 2.2. Results of Process Simulation

_{net}< 30 kW). The results of the process simulation are displayed in Figure 2. On the left hand side the exergetic efficiency against the mass fraction of MM in case of pure electricity generation is presented, whereas the results for the combined heat and power case are shown on the right hand side. Next to the efficiency, the corresponding upper working pressure, that yields the highest efficiency in each case, is added in the diagrams.

**Figure 2.**Exergetic efficiencies and respective maximum working pressures against mass fraction of MM ((

**a**): pure electricity generation, (

**b**): combined heat and power generation).

_{ex}= 31.73%) an efficiency increase of 2.9% is possible when using mixtures (60 wt % MM: η

_{ex}= 32.65%). Next to this improved cycle efficiency, lower working pressures are needed compared to pure MM. As shown in Figure 3, this increase in second law efficiency derives from an irreversibility minimum in the condenser. Regarding the irreversibilities in the evaporator, smaller differences between the fluids can be observed. Therefore, they do not affect the overall cycle efficiency.

**Figure 3.**Irreversibilities in evaporator and condenser in case of (

**a**) pure electricity generation and (

**b**) combined heat and power generation.

**Figure 4.**Temperature profiles during (

**a**) evaporation and (

**b**) condensation for the pure fluids as well as for the most efficient mixture (60 wt % MM) in case of CHP.

## 3. Heat Transfer Coefficients of Siloxanes and Siloxane Mixtures

#### 3.1. Experimental Setup

_{w,o}for one measurement site is therefore calculated by:

_{w,t}), middle (T

_{w,m}) and bottom (T

_{w,b}) of the tube.

_{evap}is evaluated by:

_{el}corresponds to the power supplied by the DC power device. The temperature at the inner face of the tube, T

_{w,i}, can be determined with respect to the outer wall temperature, T

_{w,o}, by applying the law of heat conduction. T

_{sat}represents the bulk temperature and therefore corresponds to the respective boiling point temperature, which depends on pressure and regarding mixtures as well on vapour quality. Its value is obtained by REFPROP (Reference Fluid Thermodynamic and Transport Properties Database) [27] assuming a linear pressure profile along the test section.

#### 3.2. Experimental Results

**Figure 7.**Average heat transfer coefficients for different mass fractions of MM at a pressure of (

**a**) 0.4 p

_{crit}[28] as well as (

**b**) a saturation temperature of 198 °C.

#### 3.3. Examination of Appropriate Correlations

_{TP}):

_{NBD}describes the heat transfer coefficient in the nucleate boiling region:

_{CBD}is used for regions where convective boiling is dominant:

_{Fl}. For the single-phase heat transfer coefficient α

_{lo}the correlations by Petukhov and Popov (Equation (12), for 0.5 ≤ Pr

_{L}≤ 2000 and 10

^{4}≤ Re

_{LO}≤ 5 × 10

^{6}) or Gnielinski (Equation (13), for 0.5 ≤ Pr

_{L}≤ 2000 and 2300 ≤ Re

_{LO}≤ 10

^{4}) are applied:

_{l}as well as the inner diameter d

_{i}of the tube contribute to the heat transfer coefficient.

_{1}and the boiling number Bo [29]:

- Near azeotropic region—V
_{1}< 0.03. In this domain the correlation for pure fluids is adopted (Equations (9)–(14)). - Moderate diffusion-induced suppression region—0.03 < V
_{1}< 0.2 and Bo > 10^{−4}. Heat transfer is dominated by convection. Therefore, Equation (12) is used to predict heat transfer coefficients. - Severe diffusion-induced suppression region—0.03 < V
_{1}< 0.2 and Bo ≤ 10^{−4}or V_{1}≥ 0.2. This region is still dominated by convection. Moreover, additional mass diffusion resistance due to large composition differences has to be taken into account. Due to that, Equation (12) is extended by the diffusion-induced suppression factor F_{D}:$${\text{\alpha}}_{\text{CBD}}=1.136\text{C}{\text{o}}^{-0.9}{(1-x)}^{0.8}{\text{\alpha}}_{\text{lo}}+667.2{\text{Bo}}^{0.7}{(1-x)}^{0.8}{F}_{\text{Fl}}{\text{\alpha}}_{\text{l}o}{F}_{\text{D}}$$$${F}_{D}=\frac{0.678}{1+{V}_{1}}$$_{1}is defined by:$${V}_{1}=\frac{{c}_{p,\text{l}}}{\text{\Delta}{h}_{\text{LG}}}{\left(\frac{\kappa}{{D}_{12}}\right)}^{0.5}\left|\left({y}_{1}-{x}_{1}\right)\left(\frac{dT}{d{x}_{1}}\right)\right|$$

_{p,}

_{l}, the latent heat of vaporisation Δh

_{LG}, the thermal diffusivity κ and the diffusion coefficient D

_{12}. Moreover, the mass fraction of component 1 in vapour (y

_{1}) and liquid (x

_{1}) phase as well as the slope of the bubble point curve (dT/dx

_{1}) contribute.

_{Fl}= 1 as suggested by Kandlikar for all fluids in stainless steel tubes. The results are demonstrated in Figure 8.

_{Fl}is used to adapt the values. It is fitted to the average heat transfer coefficients of the pure siloxanes.

**Figure 8.**Comparison of experimental results and Kandlikar’s correlation (F

_{Fl}= 1): Average heat transfer coefficients for different mass fractions of MM at a pressure of (

**a**) 0.4 p

_{crit}as well as (

**b**) a saturation temperature of 198 °C.

_{Fl,MM}= 0.1 and F

_{Fl,MDM}= 0.8 results in maximum deviations of 15% in case of MM and 1.5% regarding MDM. For mixtures, the fluid-surface parameter is derived from those of the pure components as suggested by Kandlikar:

_{MM}corresponds to the mass fraction of MM in liquid phase, x

_{MDM}to that of MDM, respectively.

**Figure 9.**Comparison of experimental results and Kandlikar’s correlation (F

_{Fl,MM}= 0.1, F

_{Fl,MDM}= 0.8): Average heat transfer coefficients for different mass fractions of MM at a pressure of (

**a**) 0.4 p

_{crit}as well as (

**b**) a saturation temperature of 198 °C.

_{Fl}when calculating heat transfer coefficients of MM/MDM-mixtures.

## 4. Estimation of Required Heat Exchanger Area

Geometry Data | Maximum Velocities (m/s) [30,31] | ||||
---|---|---|---|---|---|

outer tube radius r_{a} (mm) | wall thickness Δd (mm) | thermal conductivity λ_{steel} (W/mK) | ORC liquid | ORC vapour | Dowtherm |

9.5 | 2.1 | 15 | 4 | 20 | 4 |

Fluid | ṁ_{TO} (kg/s) | T_{TO-IN} (K) | T_{TO-OUT} (K) | ṁ_{ORC} (kg/s) | T_{ORC-R-E} (K) | T_{ORC-E-T} (K) | p_{ORC} (bar) |
---|---|---|---|---|---|---|---|

MM | 0.35 | 645.94 | 449.68 | 0.50 | 419.68 | 511.59 | 17.23 |

MDM | 0.35 | 645.41 | 502.74 | 0.51 | 472.74 | 541.93 | 10.30 |

MM/MDM 95/05 | 0.35 | 646.32 | 452.51 | 0.50 | 422.51 | 513.32 | 16.92 |

Fluid | ṁ_{TO} (kg/s) | T_{TO-IN} (K) | T_{TO-OUT} (K) | ṁ_{ORC} (kg/s) | T_{ORC-R-E} (K) | T_{ORC-E-T} (K) | p_{ORC} (bar) |
---|---|---|---|---|---|---|---|

MM | 0.35 | 646.32 | 452.58 | 0.57 | 422.56 | 480.22 | 10.46 |

MDM | 0.35 | 647.04 | 457.78 | 0.65 | 427.78 | 472.37 | 3.00 |

MM/MDM 60/40 | 0.35 | 645.99 | 450.09 | 0.57 | 420.30 | 480.90 | 6.77 |

Pure Electricity | Heat Exchange Area (m^{2}) | Number of Tubes | Heat Transfer Coefficient (kW/m^{2}·K) ORC/Dowtherm | Heat Duty (kW) | ||||
---|---|---|---|---|---|---|---|---|

PH | EVAP | PH | EVAP | PH | EVAP | PH | EVAP | |

MM | 0.725 | 0.120 | 2 | 2 | 5.761/7.202 | 26.414/8.343 | 113.35 | 30.725 |

MDM | 0.741 | 0.187 | 2 | 2 | 5.141/7.450 | 40.502/8.256 | 86.901 | 36.500 |

MM/MDM 95/05 | 0.728 | 0.125 | 2 | 2 | 5.699/7.201 | 32.575/8.336 | 111.6 | 32.135 |

CHP | Heat Exchange Area (m^{2}) | Number of Tubes | Heat Transfer Coefficient (kW/m^{2}·K) ORC/Dowtherm | Heat Duty (kW) | ||||
---|---|---|---|---|---|---|---|---|

PH | EVAP | PH | EVAP | PH | EVAP | PH | EVAP | |

MM | 0.583 | 0.270 | 2 | 3 | 5.756/6.942 | 34.394/8.660 | 77.76 | 65.276 |

MDM | 0.536 | 0.379 | 2 | 9 | 4.869/6.806 | 60.753/10.312 | 63.873 | 83.795 |

MM/MDM 60/40 | 0.602 | 0.373 | 2 | 4 | 5.245/6.762 | 37.859/8.914 | 64.009 | 80.192 |

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Weith, T.; Heberle, F.; Preißinger, M.; Brüggemann, D.
Performance of Siloxane Mixtures in a High-Temperature Organic Rankine Cycle Considering the Heat Transfer Characteristics during Evaporation. *Energies* **2014**, *7*, 5548-5565.
https://doi.org/10.3390/en7095548

**AMA Style**

Weith T, Heberle F, Preißinger M, Brüggemann D.
Performance of Siloxane Mixtures in a High-Temperature Organic Rankine Cycle Considering the Heat Transfer Characteristics during Evaporation. *Energies*. 2014; 7(9):5548-5565.
https://doi.org/10.3390/en7095548

**Chicago/Turabian Style**

Weith, Theresa, Florian Heberle, Markus Preißinger, and Dieter Brüggemann.
2014. "Performance of Siloxane Mixtures in a High-Temperature Organic Rankine Cycle Considering the Heat Transfer Characteristics during Evaporation" *Energies* 7, no. 9: 5548-5565.
https://doi.org/10.3390/en7095548