# Analysis of an Internal Combustion Engine Using Porous Foams for Thermal Energy Recovery

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## Abstract

**:**

## 1. Introduction

_{2}O

_{3}), silicon carbide (SiC), and zirconium dioxide (ZrO

_{2}) were suitable materials for porous applications. These materials have advantageous characteristics compared to other materials, such as better resistance to high temperature, higher mechanical strength, and better suitability for heat transfer [10].

- Using constant contact recovery porous combustion chamber
- Due to the permanent regenerator, combustion was modeled in three areas: above, below and in the regenerator.
- Differential equations for heat transfer were analyzed completely with the software SOPHT.

## 2. System Description

## 3. Mathematical Modeling

- (1)
- The heat capacity of the porous medium is much larger than that of the gas. Thus the temperature of the porous medium can be assumed constant.
- (2)
- Heat losses from the piston, cylinder wall, and PM-chamber are neglected. The compression and expansion processes are assumed adiabatic.

^{2}K), ε is a porosity factor, T

_{g}is the porous media gas phase temperature (K), T

_{S}is the porous media solid phase temperature (K), ρ

_{g}is the gas density (kg/m

^{3}), c

_{p}is the specific heat at constant pressure (kJ/kgK), ω is the fuel mole fraction rate (mol/m

^{3}s), u is the gas speed (m/s), and λ’

_{g}is the corrected gas thermal conductivity coefficient (W/mK), which is related to the gas heat conduction coefficient (W/mK), λ

_{g}, as follows [15]:

_{p}is the porous diameter (cm), ppc is a regenerator structure specification that can be selected to be 6, 9, or 11, ε is the porosity factor for the porous regenerator, and Pr is the Prandtl number [15].

_{p}is the volumetric convection coefficient between the solid and gas phases (W/m

^{3}K), λ

_{s}is the solid thermal conductivity coefficient (W/mK), ρ

_{s}is the solid density (kg/m

^{3}), T

_{s}is the porous solid phase temperature (K), which can be evaluated as follows [16]:

_{s}is the solid temperature (K). With Equations (5)–(7), Equation (4) can be rewritten as follows [14]:

_{s}is the solid specific heat (kJ/kg/K), and λ

_{eff}is the effective heat transfer coefficient in the porous material (W/mK), which can be calculated as follows [14]:

_{e}is the porous conduction coefficient (W/mK), and λ

_{r}is the porous radiation heat transfer coefficient (W/mK).

_{i}is calculated as [17]:

_{i}is the flow velocity in the x direction (m/s), u

_{j}is flow velocity in the y direction (m/s), P is the pressure (Pa), and S

_{i}is the dissipation energy by viscosity (kJ), which can be written as follows [3]:

^{3}). The inlet heat, output work, and PM engine efficiency can be determined respectively as follows [17]:

_{in}is the input heat (kJ), W is output work (kJ) and η is the thermal efficiency. The volumetric efficiency for the PM engine can be expressed as follows [17]:

_{air}is the mass of air in the cylinder when the inlet valve is closed (kg), ρ

_{a,i}is the inlet air density (kg/m

^{3}), and V

_{d}is the displacement volume (m

^{3}).

## 4. Results and Discussion

- (1)
- The maximum operating pressure rapidly increases with increasing compression ratio because a higher engine mass is required to resist the pressure, and this somewhat offsets the advantage of the increasing thermal efficiency [13].
- (2)
- The abnormal combustion process at high compression ratios results in an increase in noise and potential damage of engine parts. This type of abnormal combustion is known as explosive or detonation combustion [13].

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## Nomenclature

${\mathrm{c}}_{\mathrm{p}}$ | Specific heat at constant pressure (kJ/kgK) |

${\mathrm{c}}_{\mathrm{s}}$ | Solid specific heat at constant pressure (kJ/kgK) |

H | Convection coefficient (W/m^{2}K) |

${\mathrm{h}}_{\mathrm{p}}$ | Volumetric convection coefficient between solid and gas phases (W/m^{3}K) |

L | Regenerator length (m) |

m_{air} | Air mass (kg) |

${\dot{\mathrm{m}}}_{\mathrm{f}}$ | Fuel mass flow rate (kg/s) |

p | Pressure (Pa) |

Pr | Prandtl number |

${\mathrm{Q}}_{\text{in}}$ | Input heat (kJ) |

${\mathrm{q}}_{\mathrm{r}}$ | Radiation heat transfer from solid surface (W/m^{2}) |

R | Gas constant (kJ/kmoleK) |

Re | Reynolds number |

${\mathrm{S}}_{\mathrm{i}}$ | Dissipation energy by viscosity (kJ) |

${\mathrm{T}}_{\mathrm{g}}$ | Porous media gas phase temperature (K) |

T_{i} | Cyclic temperature (K) |

${\mathrm{T}}_{\mathrm{s}}$ | Porous media solid phase temperature (K) |

u_{j} | Speed in j direction (m/s) |

u | Gas speed (m/s) |

${\mathrm{V}}_{\mathrm{d}}$ | Displacement volume (m^{3}) |

$\mathrm{W}$ | Output work (kJ) |

$\overline{\mathrm{W}}$ | Volume of compound (m^{3}) |

z | Compression ratio |

Greek Symbols | |

${\lambda}_{g}$ | Gas thermal conductivity coefficient (W/mK) |

${\rho}_{g}$ | Gas density (kg/m^{3}) |

${\omega}_{i}$ | Fuel mole fraction rate (mol/m^{3}s) |

${\lambda}_{s}$ | Solid heat conduction coefficient (W/mK) |

${\rho}_{s}$ | Solid density (kg/m^{3}) |

${{\lambda}^{\prime}}_{g}$ | Corrected gas heat conduction coefficient (W/mK) |

$\mu $ | Fluid viscosity (Pa.s) |

$\sigma $ | Stephan-Boltzman constant (W/m^{2}K^{4}) |

${\lambda}_{eff}$ | Effective heat transfer coefficient in porous material (W/mK) |

$\epsilon $ | Porosity factor |

$\mathsf{\Psi}$ | Compression ratio |

$\eta $ | Thermal efficiency |

${\rho}_{a,i}$ | Inlet air density (kg/m^{3}) |

${\lambda}_{e}$ | Effective porous heat conduction coefficient (W/mK) |

${\lambda}_{r}$ | Porous radiation heat transfer coefficient (W/mK) |

$\phi $ | Expansion ratio |

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**Figure 1.**Idealized heat engine cycle with a PM regenerator [8].

**Figure 2.**Variation of position of piston and regenerator with crank angle for one complete cycle of a regenerative engine.

**Figure 3.**Variation of fuel efficiency with crank angle for one complete cycle of a regenerative engine.

**Figure 4.**Variation of thermal efficiency with crank angle for one complete cycle of a regenerative engine.

**Figure 5.**Variation of volumetric efficiency with crank angle for one complete cycle of a regenerative engine.

**Figure 6.**Variation of net-work output with crank angle for one complete cycle of a regenerative engine.

**Figure 7.**Variation of net-work output of the internal combustion engine with crank angle for two compression ratios.

**Figure 8.**Variation of thermal efficiency of the internal combustion engine with crank angle for two compression ratios.

Engine Specification | |
---|---|

Bore (mm) | 90 |

Stroke (mm) | 140 |

Compression ratio | 16 |

Engine speed (rpm) | 1450 |

Chamber pressure (MPa) | 0.12 |

Valve thickness (mm) | 1.2 |

Valve diameter (mm) | 17 |

Start of computation (degrees) | 130 |

End of computation (degrees) | 160 |

Injection speed (m/s) | 70 |

Injection temperature (K) | 310 |

Equivalence ratio | 0.268 |

Parameter | Engine without Regenerator | Engine with Porous Regenerator |
---|---|---|

Fuel mass flow rate (g/s) | 0.2165 | 0.2165 |

Intake air mass flow rate (g/s) | 6.494 | 6.494 |

Air-fuel ratio | 30 | 30 |

Maximum compression pressure (MPa) | 23.9 | 30.3 |

Maximum temperature of compression stroke (K) | 1619 | 2305 (compartment above porous regenerator) 964 (compartment below porous regenerator) |

Compression ratio | 16 | 10 |

Temperature of engine exhaust gas (K) | 882 | 780 |

Mean effective pressure (MPa) | 2.31 | 2.82 |

Volumetric efficiency (%) | 94 | 92 |

Thermal efficiency (%) | 43 | 53 |

© 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 by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Ali Ehyaei, M.; Tanehkar, M.; Rosen, M.A.
Analysis of an Internal Combustion Engine Using Porous Foams for Thermal Energy Recovery. *Sustainability* **2016**, *8*, 267.
https://doi.org/10.3390/su8030267

**AMA Style**

Ali Ehyaei M, Tanehkar M, Rosen MA.
Analysis of an Internal Combustion Engine Using Porous Foams for Thermal Energy Recovery. *Sustainability*. 2016; 8(3):267.
https://doi.org/10.3390/su8030267

**Chicago/Turabian Style**

Ali Ehyaei, Mehdi, Mehdi Tanehkar, and Marc A. Rosen.
2016. "Analysis of an Internal Combustion Engine Using Porous Foams for Thermal Energy Recovery" *Sustainability* 8, no. 3: 267.
https://doi.org/10.3390/su8030267