#
Design of a Tandem Compressor for the Electrically-Driven Turbocharger of a Hybrid City Car^{ †}

^{1}

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^{†}

## Abstract

**:**

## 1. Introduction

_{2}emissions led to stricter regulations on the exhaust limitation of internal combustion engines (ICE). With specific reference to gasoline-fueled ICE, the automotive industry response has been articulated in three directions (listed here in order of decreasing “perceived emission levels”): the downsizing of existing engine [1,2], the introduction of hybrid propulsion systems [3], and the design of all-electric vehicles. The three solutions are not equivalent in terms of feasibility, cost, and time-to-market, and only the first one is based on a sufficiently mature technology to be immediately implemented without substantial modifications to the production and assembly lines. Within this scenario, the Italian Ministry of Research launched a series of R&D projects aimed at a better definition of short-term modifications to existing gasoline ICE.

## 2. The Original Turbocharged Engine

## 3. Rationale of the Proposed Modifications

## 4. The Modified Radial Compressor: Geometry and Computational Mesh

#### 4.1. The Original GT12 Compressor Geometry

- The obtained geometries were digitalized.
- The virtual design was adjusted for the CFD simulations: first, the domain occupied by the actual rotor was lengthened by 1.5 diameters of the inlet eye (30 mm) on the intake side, to allow for a numerical “smoothing” of the flow quantities from the inlet boundary condition to the blade leading edge. The outlet was lengthened by 10% of the blade tip diameter (2 mm) to account for the rotor/diffuser clearance.
- The blade profile was generated as a cubic spline. The incidence β (angle between the relative velocity vector and the blade tangent at leading edge) was specified from the geometrical drawing, and a blade overlap of θ = 60° was imposed. The splitter was set to begin at mid channel length. Blade maximum thickness was set to 1.3% of the chord of the blade and clearance to 2% of the blade span.
- The computational domain consists in a 60° solid slice of the impeller and includes one main and one splitter blade. This configuration take advantage of the axisymmetric nature of the impeller, to save computational time (Figure 9).
- The final values of the analytical design for the conventional impeller were compared with the available data for the Garrett GT12 and found to agree with exceptional accuracy [7].

#### 4.2. The Tandem Impeller Geometry

- More accurate leading and trailing edge profiles for the inducer blade;
- Both the inducer chord and stagger were made to vary spanwise;
- The inducer maximum thickness, set to 3.5% of the chord, is located at mid-chord;
- The exducer is obtained by trimming the original centrifugal blades on the inlet side until they reach the same chord length as the splitter blades: in practice, we are thus dealing with a 12-blade radial rotor (this geometry was modified later, see below, for better performance).

#### 4.3. The Diffuser

- The axial span of the diffuser is equal to the blade thickness at rotor exit;
- The radial extension of the diffuser is the same as in the original GT12 compressor;
- Again an extension of the domain by 1.5 diameters was introduced to smooth the downstream boundary condition (Figure 10);
- The mixing plane method was used at the rotor/diffuser interface.

## 5. Performance Comparisons

- Stationary flow: all parameters are assumed constant in time;
- No preswirl at inlet: V
_{t}= 0 on the inlet section; - Radially constant inlet meridional flow;
- Air inlet conditions as in Table 1.

#### 5.1. The Tandem Compressor

^{6}and 1.2 × 10

^{6}nodes for the standard and tandem rotor, respectively. The diffuser mesh contained 1.6 × 10

^{5}(Garrett) and 1.2 × 10

^{5}(Tandem) nodes. The final rotor meshes are shown in Figure 12.

#### 5.1.1. CFD Results

- The inducer trailing edge and the exducer leading edge were made radial, to enforce a radially constant angular gap between the two blades;
- The exducer stagger was redesigned to match the relative fluid flow at inducer exit;
- The angular overlapping of the exducer was reduced to 40°, to increase the critical mass flowrate.

- “Tandem B”: 75% clock and 0.5 mm of axial clearance, overlap 40°. Obtained by a Design-Of-Experiment (DOE) campaign;
- “Tandem C”: 75% clock and 0.5 mm of axial clearance, overlap 50°.

#### 5.1.2. Discussion

## 6. Maps of the Entropy Generation Rate

_{0}is a fixed reference temperature, conveniently taken to be that of the surrounding environment. The rate of entropy generation contains a viscous and a thermal term, [23]:

## 7. Further Developments

- (1)
- The 50% and 75% clock configurations show a better resistance to stall (upper left corner of Figure 28 right);
- (2)
- Choking characteristics are virtually independent on clock;
- (3)
- Whereas previous published results predicted higher efficiencies for 0% clock, in the high-flow regions the 75% clock is outperforming all other configurations (Figure 28, right).

- 40° blade overlapping angle;
- b parameter equal to 3 mm;
- Clock 75%;
- Axial displacement 0.5 mm.

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Symbol and Units | Definition | Symbol and Units | Definition |

AR | Diffuser area ratio (Exit/Inlet) | S, W/°K; s, W/(kg°K) | Entropy, specific entropy |

BL | Boundary Layer | SFC, kg/s | Specific fuel consumption |

CFD | Computational Fluid Dynamics | SR | Diffuser slenderness ratio (length/inlet diameter) |

DOE | Design of Experiments | T, K | Temperature |

ECU | Electronic Control Unit | W, J | Mechanical work |

K, J/kg | Turbulent kinetic energy | β | Pressure ratio |

K, J/kg | Turbulent kinetic energy | ε, W/kg | Turbulent dissipation |

KERS | Kinetic Energy Recovery System | λ, W/(m°K) | Thermal conductivity |

m, kg/s | Mass flowrate | μ, kg/(ms) | Dynamic viscosity |

NGV | Nozzle guide vanes | ϕ, W(m^{3}°K) | Viscous dissipation function |

P_{0},T_{0} (Pa, K) | Thermodynamic Inlet conditions | - | - |

K = 1.4 | Polytropic transformation coefficient | - | - |

D_{0} (m) | Inlet compressor diameter | - | - |

R = 287 J/Kg∙K | Thermodynamic gas constant | - | - |

m (kg/s) | Mass flow in | - | - |

## Appendix A

## References

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**Figure 12.**The final mesh for the conventional (

**left**) and tandem compressor (

**right**). Arrows indicate flow direction.

**Figure 17.**Effects of the incidence correction m

_{r}= 0.36. Countour of Mach number (

**left**) and velocity vector plot (

**right**).

**Figure 18.**Relative Mach number contours at 50% span in tandem A (

**left**) and Tandem B (

**right**) (m

_{r}= 0.35).

**Figure 20.**Relative velocity maps for 0% clock, clearance 0.5 mm (

**left**) and 1.5 mm (

**right**). m

_{r}= 0.33.

**Figure 22.**Entropy generation map (

**left**) and Mach number (

**right**) for 75% clock, 0.5 mm clearance. m

_{r}= 0.33.

**Figure 24.**Entropy generation map at 50% span, 0% clock. Axial gap 0.5 mm (

**A**), 1 mm (

**B**), and 1.5 mm (

**C**). m

_{r}= 0.33.

**Figure 25.**Entropy generation map at 50% span, 25% clock. Axial gap 0.5 mm (

**A**), 1 mm (

**B**), and 1.5 mm (

**C**), m

_{r}= 0.33.

**Figure 27.**Mach number contour at choking condition, Impeller with blade channel modification (

**left**) and without (

**right**).

**Figure 28.**Graphical results of second generation DOE campaign. Isentropic efficiency-Corrected mass flowrate Plot (

**left**), Characteristic map of the second generation of impellers (

**right**).

**Table 1.**Air inlet conditions (British units shown for comparison with original Garrett documentation).

Inlet pressure (p_{1}) | Pa | 101,000 |

Inlet temperature (T_{1}) | K | 298 |

Intake mass flow rate, Design Point | (kg/s) | 0.05598 |

Corrected mass flow, Design Point | (lb/min) | 7.00 |

Unit | Value | |
---|---|---|

Inducer tip diameter (D_{1}) | mm | 22.47 |

Inducer hub diameter (D_{1i}) | mm | 8.20 |

Exducer tip diameter (D_{2}) | mm | 38.00 |

Blade tip span (b) | mm | 2.38 |

Z_{n} | - | 6 + 12 |

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**MDPI and ACS Style**

Cuturi, N.; Sciubba, E.
Design of a Tandem Compressor for the Electrically-Driven Turbocharger of a Hybrid City Car. *Energies* **2021**, *14*, 2890.
https://doi.org/10.3390/en14102890

**AMA Style**

Cuturi N, Sciubba E.
Design of a Tandem Compressor for the Electrically-Driven Turbocharger of a Hybrid City Car. *Energies*. 2021; 14(10):2890.
https://doi.org/10.3390/en14102890

**Chicago/Turabian Style**

Cuturi, Nicolò, and Enrico Sciubba.
2021. "Design of a Tandem Compressor for the Electrically-Driven Turbocharger of a Hybrid City Car" *Energies* 14, no. 10: 2890.
https://doi.org/10.3390/en14102890