# CFD Methodology for an Underhood Analysis towards the Optimum Fan Position in a Compact Off-Road Machine

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of the Compact Off-Road Vehicle

## 3. Physical Phenomena Involved

## 4. Simplified Geometries for the CFD Analysis

## 5. Validation of the Model

#### 5.1. Virtual Test for the Validation of the Fan Model

_{max}, to the smallest, A

_{min}, areas of the integration points for each element surrounding a node.

_{02}[Pa] and p

_{01}[Pa], respectively [43].

_{0}= p

_{02}− p

_{01}

_{0}is the static pressure averaged over the local mass flow that can be obtained by the general expression reported in Equation (2) [41], where ϕ represents any variable or expression being averaged (p

_{0}in this case) and m represents the local mass flow:

#### 5.2. Mesh-Independent Analysis for the Validation of the Underhood Model

^{3}/h.

## 6. Numerical Simulation

^{−4}. With these settings for the steady-state simulations, the global imbalances were normally kept below ±3%. With these settings, the convergence was achieved in about 500 iterations and the necessary time calculation was around 6 h with an Intel Xeon CPU.

## 7. Parametric Analysis and Simulated Test Cases

#### 7.1. Test Cases with Different Positions

#### 7.2. Test Cases with Different Conveyor Geometries

#### 7.3. Test Cases with Different Blade Angles

#### 7.4. Additional Test Case

## 8. Results and Discussion

- the pressure rise $\Delta {p}_{0}^{31}$ between the air vents ${p}_{0}^{1}$ and the fan conveyor ${p}_{0}^{3}$

- the pressure rise $\Delta {p}_{0}^{41}$ between the air vents ${p}_{0}^{1}$ and the radiator outlet ${p}_{0}^{4}$

- the hydraulic and mechanical powers, as defined in [41]:

_{idr}= Δp

_{0}Q P

_{mec}= M

_{t}ω

_{0}is difference in the static pressure, Q is the flow rate, M

_{t}is the torque acting on the impeller, and ω is the fan rotational velocity.

- the fan efficiency η [41]

- the sound pressure level SPL, both in terms of peak and averaged values. The acoustics pressure, p
_{a}, is computed by the Lowson model [45].

_{a}

^{ref}is the acoustic reference pressure of 20 µPa.

#### 8.1. Test Cases a to f—Different Positions

#### 8.2. Test Cases g and h—Different Conveyor Geometries

#### 8.3. Test Case i—Different Blade Angles

#### 8.4. Test Case j

^{3}/s and reached 42%. Conversely, in all the simulated cases, the efficiency was between 28% and 35%, due to the off-design conditions.

## 9. Conclusions and Future Perspectives

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Lateral and A-A section views of the fan cooling system. a is the engine-fan distance and b is the engine-radiator distance (courtesy of MultiOne s.r.l.).

**Figure 4.**Engine vane modelling: (

**A**) original 3D CAD; (

**B**) surface simplification; (

**C**) surface meshing; and (

**D**) volume meshing.

**Figure 5.**(

**A**) Blade surface in the MRF domain; (

**B**) surface of the shroud conveyor domain; and (

**C**) surface of the heat exchanger domain.

**Figure 11.**Test cases with different conveyor geometries. (

**a**) Original (test case a). (

**b**) Curved shape (test case g). (

**c**) Divergent shape (test case h).

Fan Parameter Specification | Engine Parameter Specification | ||
---|---|---|---|

Shroud diameter, Ds | 455 mm | Engine Power Rating | 54.5 kW |

Tip blade diameter, D | 435 mm | Engine Speed | 2200 rpm |

Hub diameter, Dh | 250 mm | Radiator Coolant Flow | 56 L/min |

Eye diameter, Do | 35 mm | Radiator Pressure Drop | 24 bar |

Inlet blade angle, β1 | 35° | Radiator Water/glycol | 50% |

Outlet blade angle, β2 | 25° | Radiator Heat to Coolant | 38 kW |

Rotational speed, ω | 1800–3000 rpm | Cooling System Parameter SpecificationAfter cooler (CAC) | |

Number of blades, z | 8 | Air temp. after charger | 150 °C |

Blade thickness, s | Variable | Mass Air Flow | 252 kg/h |

Engine–fan distance, a | 40 mm | Charge pressure | 1.1 bar |

Engine–radiator distance, b | 200 mm | Heat to CAC | 6.2 kW |

Max Coolant Temp | 105 °C |

Mesh Tested | Number of Elements (10^{3}) | Quality Parameters | |||||
---|---|---|---|---|---|---|---|

iTS | Fan (MRF and Conveyor) | oTC | Total | Orthogonality Angle [°] | Expansion Factor [-] | Aspect Ratio [-] | |

Mesh 1 | 900 | 360 | 1200 | 2460 | 8 | 81 | 22 |

Mesh 2 | 1300 | 865 | 1580 | 3745 | 20 | 173 | 54 |

Mesh 3 | 1750 | 1140 | 2150 | 5040 | 25 | 267 | 70 |

Mesh 4 | 2100 | 1720 | 2430 | 6250 | 20 | 176 | 46 |

Setting | Value |
---|---|

Advection scheme | Second Order |

Fan rotational speed | 2926 rpm |

Air density | 1.185 kg/m^{3} |

Inlet | PAtm. [Pa] |

Outlet | Mass Flow Rate [kg/s] |

Convergence level | 10-4 |

Turbulence model | SST k-ω |

Mesh Tested | Number of Elements (∙10^{3}) | Quality Parameters | ||||||
---|---|---|---|---|---|---|---|---|

Heat Exchanger | Fan (MRF and Conveyor) | Engine Vane | Outlet | Total | Orthogonality Angle [°] | Expansion Factor [-] | Aspect Ratio [-] | |

Mesh A | 1025 | 1140 | 1301 | 140 | 3606 | 16 | 300 | 89 |

Mesh B | 1356 | 1140 | 1704 | 252 | 4452 | 28 | 450 | 113 |

Mesh C | 1653 | 1140 | 2090 | 352 | 5208 | 34 | 546 | 138 |

Mesh D | 1908 | 1140 | 2456 | 401 | 5905 | 30 | 484 | 122 |

Test Case | Engine-Fan Distance a [mm] | Engine-Radiator Distance b [mm] |
---|---|---|

a | Std | Std |

b | Std + 18 | Std |

c | Std + 36 | Std |

d | Std | Std + 30 |

e | Std + 18 | Std + 30 |

f | Std + 36 | Std + 30 |

Case | a | b | c | d | e | f | g | h | i | j |
---|---|---|---|---|---|---|---|---|---|---|

Engine–fan a [mm] | Std | Std + 18 | Std + 36 | Std | Std + 18 | Std + 36 | Std | Std | Std | Std + 36 |

Engine–radiator b [mm] | Std | Std | Std | Std + 30 | Std + 30 | Std + 30 | Cur | Div | Std | Std + 30 |

Conveyor geometry | Std | Std | Std | Std | Std | Std | Cur | Div | Std | Cur + Div |

Pitch angle [°] | 35 | 35 | 35 | 35 | 35 | 35 | 35 | 35 | 30 | 30 |

ω [rpm] | 2927 | 2927 | 2927 | 2927 | 2927 | 2927 | 2927 | 2927 | 2927 | 2927 |

Q [m^{3}/s] | −2.11 | −2.11 | −2.11 | −2.11 | −2.11 | −2.11 | −2.11 | −2.11 | −2.11 | −2.11 |

Results | ||||||||||

Δp^{31} [Pa] | 429 | 359 | 311 | 437 | 588 | 495 | 454 | 451 | 423 | 418 |

Δp^{41} [Pa] | 203 | 133 | 91 | 222 | 282 | 204 | 229 | 216 | 189 | 190 |

P_{idr} [W] | 905 | 757 | 656 | 921 | 1241 | 1045 | 958 | 951 | 892 | 882 |

P_{mec} [W] | 2715 | 2688 | 2642 | 2747 | 3618 | 3038 | 2743 | 2682 | 2633 | 2486 |

η | 0.333 | 0.281 | 0.248 | 0.335 | 0.343 | 0.344 | 0.349 | 0.355 | 0.339 | 0.355 |

SPL_{peak} [dB] | 114.5 | 113.7 | 108.8 | 114.5 | 108.3 | 104.2 | 114.3 | 114.4 | 113 | 110.4 |

SPL_{average} [dB] | 61.7 | 64.8 | 63.9 | 64.6 | 52.4 | 51.8 | 63.3 | 64.6 | 59 | 53 |

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**MDPI and ACS Style**

Ferrari, C.; Beccati, N.; Pedrielli, F.
CFD Methodology for an Underhood Analysis towards the Optimum Fan Position in a Compact Off-Road Machine. *Energies* **2023**, *16*, 4369.
https://doi.org/10.3390/en16114369

**AMA Style**

Ferrari C, Beccati N, Pedrielli F.
CFD Methodology for an Underhood Analysis towards the Optimum Fan Position in a Compact Off-Road Machine. *Energies*. 2023; 16(11):4369.
https://doi.org/10.3390/en16114369

**Chicago/Turabian Style**

Ferrari, Cristian, Nicolò Beccati, and Francesca Pedrielli.
2023. "CFD Methodology for an Underhood Analysis towards the Optimum Fan Position in a Compact Off-Road Machine" *Energies* 16, no. 11: 4369.
https://doi.org/10.3390/en16114369