# Prediction of Heat Transfer and Fluid Flow Effects on Entropy Generation in a Monolithic Catalytic Converter Using Large-Eddy Simulation

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## Abstract

**:**

## 1. Introduction

## 2. Large-Eddy Simulation

## 3. Test Case: The Catalytic Converter

#### 3.1. Experimental Setup

#### 3.2. Numerical Setup

## 4. Results and Discussion

#### 4.1. Comparison with Experimental Data (Case 1–12)

#### 4.2. Predictions of Heat and Fluid Flow Features (Case 9 and 12)

#### 4.3. Predictions of Entropy Production Rates

## 5. Conclusions

- The Darcy-Forchheimer equation is well suited to describe the pressure drop in this specific catalytic converter. Correlation equations based on the experimental data are provided.
- Important characteristic flow features are identified in the catalytic converter, namely the impinging flow with stagnation, recirculation, flow separation, and laminarization within the fine ducts of the monolith.
- The rms velocity decreases rapidly in the monolith, attributing to the flow laminarization process in the narrow monolith channels. This physical process is influenced by the heat transfer dynamics through temperature-dependent thermophysical properties as simulations with and without heat transfer testify.
- The entropy production by viscous dissipation (${\Pi}_{v}$) occurs predominantly in the monolith region due to high-velocity gradients at the walls of the narrow monolith ducts. This suggests that the laminarization inside the monolith is purely a fluid flow process through temperature-dependent thermophysical properties.
- The entropy production rate due to heat transport ${\Pi}_{q}$ is relatively small in the monolith region, while it overwhelms viscous dissipation effects in the pipe regions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ICEV | Internal Combustion Engine Vehicle |

BEV | Battery Electric Vehicle |

EGM | Entropy Generation Minimization |

EGAS | Exhaust Gas After-treatment System |

CFD | Computation Fluid Dynamics |

VANS | Volume-Averaging Navier–Stokes |

RANS | Reynolds-Averaging Navier–Stokes |

LES | Large-Eddy Simulation |

## Appendix A. Thermodynamic Properties of Applied Exhaust Gas

^{−6}and ${T}_{Suth}=1$95.6627, respectively. A comparison of the fitted values and the theoretical values are depicted in Figure A1. An excellent agreement is observed; the presented coefficients are therefore applied in the simulation.

species [-] | $C{O}_{2}$ | ${H}_{2}O$ | ${O}_{2}$ | ${N}_{2}$ | $CO$ |

fraction [%] | 12.3 | 13.8 | 0.7 | 72.3 | 0.9 |

NASA Coefficient | ${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}$ | ${\mathit{a}}_{3}$ | ${\mathit{a}}_{4}$ | ${\mathit{a}}_{5}$ | ${\mathit{a}}_{6}$ | ${\mathit{a}}_{7}$ |
---|---|---|---|---|---|---|---|

$T\le 1000$ K | 3.48 | 7.08 × 10^{−4} | −2.61 × 10^{−7} | 1.24 × 10^{−9} | −7.77 × 10^{−13} | −1.10 × 10^{4} | 4.15 |

$T>1000$ K | 3.13 | 1.77 × 10^{−3} | −5.91 × 10^{−7} | 9.04 × 10^{−11} | −5.10 × 10^{−15} | −1.10 × 10^{4} | 5.88 |

**Figure A1.**Comparison of the thermodynamic and transport properties calculated by the existing material laws and their coefficients (in circles) and calculated by the new material laws of exhaust gas, in which the coefficients are generated by least-square fits (in lines).

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**Figure 1.**Illustration of the exhaust after-treatment catalytic converter; (

**a**) assembly and dimensions; (

**b**) measurement locations.

**Figure 2.**Numerical treatment of the catalytic converter configuration: domain coupling fluid/solid/catalyst regions.

**Figure 3.**The representation of applied numerical grids for solid and fluid regions that are coupled via interfaces.

**Figure 4.**Pressure drop characteristic of a three-way catalytic converter of a Lada Niva 21214. U denotes the bulk velocity inside the monolith.

**Figure 5.**Instantaneous velocity field in the catalytic converter and instantaneous pressure field in the monolith along with velocity profile in various cross sectional planes S1–S5.

**Figure 6.**Velocity distributions in the main flow direction at different cross-sections for isohermal case (black lines) and nonisothermal nonreacting case (red lines). The dashed lines represent the velocity profile inside the monolith region.

**Figure 8.**Instantaneous temperature fields in the catalytic converter and instantaneous pressure field in the monolith along with velocity profile in various cross-sectional planes S1–S5.

**Figure 12.**Entropy production rates by viscous dissipation ${\Pi}_{v}$ on selected planes for the isohermal case (black lines), and nonisothermal case (red lines). The dashed lines represent the quantities at the ceramic–fluid wall in the monolith.

Coarse | Medium | Fine | |
---|---|---|---|

solid part | 1,499,560 | 2,348,408 | 2,348,408 |

fluid part | 5,556,400 | 13,959,292 | 46,349,536 |

**Table 2.**The list of the test cases considered in the numerical study. (See Table 1 for numerical grids.) The Reynolds number $R{e}_{pipe}$ is specified for the pipe inflow and pipe diameter. $R{e}_{monolith}$ represents the Reynolds number inside the monolith channels.

Case | Grid | Flow Rate | Fluid | Temperature | ${\mathit{Re}}_{\mathit{pipe}}$ | ${\mathit{Re}}_{\mathit{monolith}}$ |
---|---|---|---|---|---|---|

1 | coarse | 40.3 m${}^{3}$/h | air | 298 K | 15,921 | 73 |

2 | medium | 40.3 m${}^{3}$/h | air | 298 K | 15,921 | 73 |

3 | fine | 40.3 m${}^{3}$/h | air | 298 K | 15,921 | 73 |

4 | coarse | 79.8 m${}^{3}$/h | air | 298 K | 31,527 | 144 |

5 | medium | 79.8 m${}^{3}$/h | air | 298 K | 31,527 | 144 |

6 | fine | 79.8 m${}^{3}$/h | air | 298 K | 31,527 | 144 |

7 | coarse | 160 m${}^{3}$/h | air | 298 K | 63,213 | 289 |

8 | medium | 160 m${}^{3}$/h | air | 298 K | 63,213 | 289 |

9 | fine | 160 m${}^{3}$/h | air | 298 K | 63,213 | 289 |

10 | coarse | 160 m${}^{3}$/h | exhaust gas | 900 K | 10,020 | 46 |

11 | medium | 160 m${}^{3}$/h | exhaust gas | 900 K | 10,020 | 46 |

12 | fine | 160 m${}^{3}$/h | exhaust gas | 900 K | 10,020 | 46 |

**Table 3.**Entropy production rates related to viscous dissipation ${\Pi}_{v}$ and heat transport ${\Pi}_{q}$ integrated over the monolith and pipe flow regions.

Monolith Region | Pipe Regions | Conditions | |
---|---|---|---|

$\langle {\overline{\Pi}}_{v}\rangle $ | 182.877 | 5.104 | isothermal |

$\langle {\overline{\Pi}}_{v}\rangle $ | 102.886 | 3.112 | non-isothermal |

$\langle {\overline{\Pi}}_{q}\rangle $ | 82.221 | 1249.484 | non-isothermal |

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**MDPI and ACS Style**

Li, Y.; Rico Cortes, L.F.; Hamel, H.; Nishad, K.; Biondo, L.; Ries, F.
Prediction of Heat Transfer and Fluid Flow Effects on Entropy Generation in a Monolithic Catalytic Converter Using Large-Eddy Simulation. *Entropy* **2022**, *24*, 602.
https://doi.org/10.3390/e24050602

**AMA Style**

Li Y, Rico Cortes LF, Hamel H, Nishad K, Biondo L, Ries F.
Prediction of Heat Transfer and Fluid Flow Effects on Entropy Generation in a Monolithic Catalytic Converter Using Large-Eddy Simulation. *Entropy*. 2022; 24(5):602.
https://doi.org/10.3390/e24050602

**Chicago/Turabian Style**

Li, Yongxiang, Luis Felipe Rico Cortes, Hardy Hamel, Kaushal Nishad, Luigi Biondo, and Florian Ries.
2022. "Prediction of Heat Transfer and Fluid Flow Effects on Entropy Generation in a Monolithic Catalytic Converter Using Large-Eddy Simulation" *Entropy* 24, no. 5: 602.
https://doi.org/10.3390/e24050602