# Experimental and Numerical Analysis of a Compressor Stage under Flow Distortion

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Numerical Setup

## 4. Results

#### 4.1. Stable Operation

_{1}and X

_{2}were created, X

_{2}being the time shifted matrix, and X

_{1}the matrix of the individual snapshots. The DMD computed the leading eigenmodes of the linear operator A that best advanced the data X

_{1}to X

_{2}, i.e., X

_{2}

^{N}≈ A X

_{1}

^{N−1}, where N denotes the time of the current snapshot. For N→∞, hence marching continuously in time, the corresponding linear system reads

_{DMD}indicates the reconstruction with 21 modes, p

_{1}the first mode reconstruction (the linear least-squares fit of the signal), p

_{2}the reconstruction up to the second order (linear least-squares fit plus the second mode with its complex conjugate), and so on. In Figure 5a,b, p

_{5}and p

_{9}respectively represent the DMD reconstruction with the minimum number of modes that have an error less or equal to 5% with respect to the DMD with 21 modes.

#### 4.2. Stall Inception

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Roman | $t$ | Time [s] | |

b | Initial amplitude of DMD modes | $U=\mathsf{\Omega}\mathrm{r}$ | Blade velocity [m/s] |

$d$ | hole diameter of the grid [m] | $v$ | Axial velocity [m/s] |

DMD | Dynamic Mode Decomposition | ||

$f$ | Porosity of the grid [-] | Greek | |

$h$ | grid inter-hole distance [m] | σ | Real part of ω |

$p$ | Static pressure [Pa] | $\varphi =v/U$ | Flow coefficient [-] |

p_{DMD} | DMD reconstruction | ψ | Eigenvectors of DMD |

$r$ | Compressor mean radius [m] | ω | Growth rate of DMD modes |

$s$ | Diagonal matrix of the SVD | $\mathsf{\Omega}$ | Compressor Angular velocity [rad/s] |

SVD | Singular Value Decomposition | ${\mathsf{\Omega}}_{p}$ | Perturbation angular velocity [rad/s] |

## References

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**Figure 1.**(

**a**) CAD representation of the equilateral triangular pattern of the grid holes; (

**b**,

**c**) CAD representation of the CME2 compressor showing grid position with respect to instrumented window.

**Figure 2.**Scheme representing rotor blades and pressure probe locations highlighted in red (mid chord circumferential positions) and blue (axial position from z = −2 mm to z = 50 mm); probe used for DMD (green), wake of the grid (yellow).

**Figure 4.**(

**a**,

**b**) Comparison between raw signal (blue) and DMD reconstruction (light blue) for the case of 5 kg/s; (

**c**,

**d**) comparison between raw numerical signal (blue) and DMD reconstruction (light blue) for the case of 4.85 kg/s. Difference between raw signal and DMD reconstruction plotted in orange.

**Figure 5.**Partial DMD reconstruction; p

_{1}: least-squares fit, p

_{i}+ cc: DMD modes plus complex conjugate (cc) up to i

^{th}order. (

**a**) 11 modes 5 kg/s without grid; (

**b**) 19 modes 5 kg/s with 60° grid.

**Figure 6.**Partial DMD reconstruction; p

_{1}: least-squares fit, p

_{i}+ cc: DMD modes plus complex conjugate (cc) up to i

^{th}order; (

**a**) 13 modes 4.85 kg/s without grid, (

**b**) 13 modes 4.85 kg/s with 60° grid.

**Figure 7.**Relative energy in the modes calculated from SVD. Experimental signals. (

**a**) 5 kg/s; (

**c**) 4.2 kg/s; numerical signal (

**b**) 4.85 kg/s.

**Figure 8.**Stall transient with no grid; on the x axis the number of revolutions, on the y axis: (

**a**) angular position of the signal, (

**b**) non-dimensional pressure amplitude, (

**c**) non-dimensional perturbation speed.

**Figure 9.**Stall transient with 60° grid; on the x axis the number of revolutions, on the y axis: (

**a**) angular position of the signal, (

**b**) non-dimensional pressure amplitude, (

**c**) non-dimensional perturbation speed.

**Figure 10.**Four (

**a**–

**d**) repetitions of rotating stall transient with 60° grid. Black rectangles: position of the 60° grid. Dashed line in the bottom panel: threshold for spike development; red continuous line: polynomial fit, which appears also in Figure 8 and Figure 9. Green background: part of the signal below threshold; yellow background: part of the signal above the threshold.

Rotational speed | 3200 | rpm |

Design mass flow rate at 3200 rpm | 5.3 | kg/s |

Design total to static pressure ratio at | 1.03 | |

Rotor blade number | 30 | |

Stator blade number | 40 | |

Casing diameter | 550 | mm |

Rotor tip chord | 84 | mm |

Rotor tip stagger angle | 54 | ° |

Rotor tip gap | 0.5 | mm |

Number of structural struts | 4 |

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## Share and Cite

**MDPI and ACS Style**

Baretter, A.; Godard, B.; Joseph, P.; Roussette, O.; Romanò, F.; Barrier, R.; Dazin, A.
Experimental and Numerical Analysis of a Compressor Stage under Flow Distortion. *Int. J. Turbomach. Propuls. Power* **2021**, *6*, 43.
https://doi.org/10.3390/ijtpp6040043

**AMA Style**

Baretter A, Godard B, Joseph P, Roussette O, Romanò F, Barrier R, Dazin A.
Experimental and Numerical Analysis of a Compressor Stage under Flow Distortion. *International Journal of Turbomachinery, Propulsion and Power*. 2021; 6(4):43.
https://doi.org/10.3390/ijtpp6040043

**Chicago/Turabian Style**

Baretter, Alberto, Benjamin Godard, Pierric Joseph, Olivier Roussette, Francesco Romanò, Raphael Barrier, and Antoine Dazin.
2021. "Experimental and Numerical Analysis of a Compressor Stage under Flow Distortion" *International Journal of Turbomachinery, Propulsion and Power* 6, no. 4: 43.
https://doi.org/10.3390/ijtpp6040043