# Reciprocating Expander for an Exhaust Heat Recovery Rankine Cycle for a Passenger Car Application

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## Abstract

**:**

## 1. Introduction

## 2. Modelling of the Expander

_{S}and clearance volume V

_{0}were taken from the expander manufacturer’s data. The ratio C between the clearance and the expander displacement is 0.072.

#### 2.1. Supply and Exhaust Pressure Drops

_{crit}and the exhaust pressure P

_{ex}according to Equation (4):

#### 2.2. Mass Flow Rate

_{2}is specific volume of the working fluid after closing of the supply valve, m

^{3}/kg; v

_{6}isspecific volume of the working fluid before opening of the supply valve, m

^{3}/kg.

_{thr}

_{,leak}—specific enthalpy of the fluid at the throat, J/kg; h

_{su}

_{,2}—initial specific enthalpy of the fluid, J/kg.

#### 2.3. Expander Power Output

#### 2.4. Heat Transfer

_{w}and fluid during suction can be evaluated from Equation (11):

_{su}—global heat transfer coefficient between working fluid and metallic envelope, W/K; T

_{w}—wall temperature, K.

_{su}depends on the mass flow rate of the working fluid and is given by Equation (12) proposed by Lemort et al. [24]:

_{su}

_{,n}—nominal overall heat transfer coefficient estimated at nominal mass flow rate , W/K.

_{amb}—overall heat transfer coefficient between metallic envelope and the ambient, W/K.

#### 2.5. Efficiency

## 3. Validation of the Expander Model

_{s}and clearance volume V

_{0}. The operational parameters correspond to valve timing i.e., f

_{a}and f

_{p}, leakage i.e., A

_{leak}, suction and exhaust orifice areas i.e., A

_{su}and A

_{ex}and overall heat transfer coefficients i.e., AU

_{su}, AU

_{ex}and AU

_{amb}. The nominal values of these parameters are summarized in Table 1. In order to achieve the performances given by the expander manufacturer, the operational parameters of the expander model have to be optimized.

f_{a} | f_{p} | AU_{amb}, W/K | AU_{ex}, W/K | AU_{su}, W/K | A_{leak}, m^{2} | d_{trh,su,n}, m | d_{thr,ex,n}, m |
---|---|---|---|---|---|---|---|

0.25 | 0.4 | 2.5 | 45 | 22.2 | 0.2386 × 10^{−6} | 6 × 10^{−6} | 11 × 10^{−6} |

## 4. Expander Analysis

**Figure 6.**Evolution of the expander internal power output and shaft power at different pressure ratios and rotary speeds.

## 5. Conclusions

## Nomenclature:

A | leakage area, m ^{2} |

AU | global heat transfer coefficient, W/K |

C | clearance coefficient, - |

d | diameter of the orifice, m |

f_{a} | supply cut-off ratio, - |

f_{p} | exhaust cut-off ratio, - |

h | specific enthalpy, J/kg |

m | mass flow rate, kg/s |

N | expander rotation speed, rpm |

n | piston number |

P | pressure, Pa |

Q | heat flow, W |

Rp | pressure ratio, - |

T | temperature, K |

u | specific internal energy, J/kg |

v | specific volume, m ^{3}/kg |

V_{S} | displacement, m ^{3} |

V_{0} | clearance volume, m ^{3} |

power, W | |

ΔP | pressure drop, Pa |

ε | efficiency, - |

γ | gamma of ideal gas, - |

## Subscripts and Superscripts:

adm | admission |

amb | ambient |

cp | compression |

ex | exhaust |

exp | expander; experimental value |

f | fluid |

in | internal |

leak | leakage |

loss | losses |

mec | mechanical |

n | nominal |

net | net |

s | isentropic |

sh | shaft |

su | supply |

thr | throat |

vol | volumetric |

w | wall |

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**MDPI and ACS Style**

Glavatskaya, Y.; Podevin, P.; Lemort, V.; Shonda, O.; Descombes, G.
Reciprocating Expander for an Exhaust Heat Recovery Rankine Cycle for a Passenger Car Application. *Energies* **2012**, *5*, 1751-1765.
https://doi.org/10.3390/en5061751

**AMA Style**

Glavatskaya Y, Podevin P, Lemort V, Shonda O, Descombes G.
Reciprocating Expander for an Exhaust Heat Recovery Rankine Cycle for a Passenger Car Application. *Energies*. 2012; 5(6):1751-1765.
https://doi.org/10.3390/en5061751

**Chicago/Turabian Style**

Glavatskaya, Yulia, Pierre Podevin, Vincent Lemort, Osoko Shonda, and Georges Descombes.
2012. "Reciprocating Expander for an Exhaust Heat Recovery Rankine Cycle for a Passenger Car Application" *Energies* 5, no. 6: 1751-1765.
https://doi.org/10.3390/en5061751