# Combined Flow Control Strategy Investigation for Corner Separation and Mid-Span Boundary Layer Separation in a High-Turning Compressor Cascade

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Configurations and Computational Method

#### 2.1. Datum Cascade Configuration

#### 2.2. Flow Control Strategies

#### 2.3. Computational Details

#### 2.4. Numerical Method Validations

_{PS}, HV

_{SS}) and positions of the critical points (saddle points S

_{1}, S

_{2}and node point N). Therefore, it further proves the reliability of the simulation results at the inlet condition with uniform flow.

## 3. Performance Evaluation and Analysis

#### 3.1. Velocity Contours and Flow Turning Angles

#### 3.2. Total Pressure Loss and Limiting Streamlines

_{1}, S

_{2}, S

_{3}, S

_{4}and S

_{5}perpendicular to the Z axis are, respectively, 50%Ca, 67%Ca, 83%Ca, 105%Ca and 150%Ca. At the 0° incidence angle, a relatively serious corner separation exists in the datum cascade with the occurrence of the mid-span BL separation. The corner SL starting position is about 30%Ca away from the blade LE, and the corner separation occupies 30% of the blade span. The corner separation leads to certain passage blockage and total pressure loss, thus weakening the pressure diffusion capacity of the datum cascade. In addition, the CSV exists in the datum cascade passage.

_{2}plane, one can see that the EW suction slot behaves better than the blade-end slot in inhibiting the EW secondary flow migration. Additionally, the mixing loss between the mainstream and the blade-end slot jet is avoided, hence the loss caused by the corner separation can be further reduced. Meanwhile, the generation of CV is suppressed by the whole-chord-length EW suction slot, contributing to a further reduction in the corner separation. Therefore, the combined configuration basically eliminates the corner separation.

#### 3.3. Vortical Structures

^{−2}iso-surface and the plane (150%Ca) perpendicular to z axis is contoured by streamwise vorticity. One can see that two vortical structures of passage vortex (PV) and CSV mainly exist in the datum cascade passage, contributing to the serious loss in the corner.

#### 3.4. Overall Performance Comparison

## 4. Effect of Blade Solidity

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

${\beta}_{1}$ | Inlet flow angle |

${\beta}_{1k}$ | Geometric inlet angle |

${\beta}_{2}$ | Outlet flow angle |

${\beta}_{2k}$ | Geometric outlet angle |

${\beta}_{s}$ | Stagger angle |

$w$ | Total pressure loss coefficient without suction mass-flow |

${w}_{s}$ | Total pressure loss coefficient with suction mass-flow |

Ca | Axial blade chord |

c | Blade chord |

c/t | Blade solidity |

${C}_{P}$ | Static pressure rise coefficient |

H | Blade height |

H/c | Aspect ratio |

$M{a}_{1}$ | Inlet Mach number |

${m}_{1}$ | Inlet mass-flow |

${m}_{3}$ | End-wall suction mass-flow |

${P}_{1}$ | Inlet static pressure |

${P}_{01}$ | Inlet total pressure |

${P}_{2}$ | Local static pressure |

${P}_{02}$ | Local total pressure |

${P}_{03}$ | Total pressure at end-wall suction slot outlet |

$R{e}_{C}$ | Blade-chord-based Reynolds number |

${\mathrm{R}}_{1}$ | Outlet curve radius of blade-end slot lower wall |

${\mathrm{R}}_{2}$ | Outlet curve radius of whole-span slot lower wall |

t | Blade pitch |

${\mathrm{X}}_{1}$ | Outlet throat width of blade-end slot |

${\mathrm{X}}_{2}$ | Outlet throat width of whole-span slot |

${y}^{+}$ | Dimensionless wall first layer grid size |

Abbreviations | |

AO_{1} | Axial overlap of the blade-end slot |

AO_{2} | Axial overlap of the whole-span slot |

BL | Boundary layer |

CV | Corner vortex |

CSV | Concentrated shedding vortex |

EW | End-wall |

${\mathrm{HV}}_{\mathrm{PS}}$ | Horseshoe vortex pressure side leg |

${\mathrm{HV}}_{\mathrm{SS}}$ | Horseshoe vortex suction side leg |

LE | Leading edge |

N | Node |

PS | Pressure surface |

PV | Passage vortex |

RANS | Reynolds averaged Navier–Stokes |

SL | Separation Line |

SS | Suction surface |

SA | Spalart–Allmaras |

S | Saddle point |

TE | Trailing edge |

WV | Wall vortex |

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**Figure 5.**Loss of the combined configuration that varies with the suction flow ratio at the 0° incidence angle.

**Figure 7.**Blade surface static pressure rise coefficients comparison between simulations and experiments: (

**a**) 0.5° incidence angle (

**b**) 5° incidence angle.

**Figure 10.**Velocity contours of the datum cascade, slotted configuration and combined configuration at different H and incidence angles: (

**a**) 0° incidence angle (

**b**) 6° incidence angle.

**Figure 11.**Flow turning angle distributions of the datum cascade, slotted configuration and combined configuration: (

**a**) 0° incidence angle (

**b**) 6° incidence angle.

**Figure 12.**Total pressure loss and limiting streamlines for the datum cascade, slotted configuration and combined configuration at the 0° incidence angle.

**Figure 13.**Total pressure loss and limiting streamlines for the datum cascade, slotted configuration and combined configuration at the 6° incidence angle.

**Figure 14.**3D corner separation structures extracted by Q = 1,000,000 s

^{−2}iso-surface and contoured by streamwise vorticity at the 0° incidence angle.

**Figure 15.**3D corner separation structures extracted by Q = 1,000,000 s

^{−2}iso-surface and contoured by streamwise vorticity at the 6° incidence angle.

**Figure 16.**Aerodynamic parameters of the datum cascade, slotted configuration and combined configuration that vary with incidence angles.

**Figure 17.**Blade SS limiting streamlines of the datum cascade and combined configuration at c/t = 1.66 and 1.36: (

**a**) 0° incidence angle (

**b**) 6° incidence angle.

**Figure 18.**Total pressure loss distributions for the datum cascade and combined configuration at c/t = 1.66 and 1.36: (

**a**) 0° incidence angle (

**b**) 6° incidence angle.

**Figure 19.**Aerodynamic parameters of the datum cascade and combined configuration that vary with incidence angles at c/t = 1.66 and 1.36.

Parameters | Values |
---|---|

Blade height H/mm | 100 |

Chord c/mm Blade pitch t/mm | 63 37.95 |

Aspect ratio H/c | 1.59 |

Blade solidity c/t | 1.66 |

Geometric inlet angle ${\beta}_{1k}$/(°) | 40.17 |

Geometric outlet angle ${\beta}_{2k}$/(°) Stagger angle ${\beta}_{s}$/(°) | −13.21 15.4 |

Inlet Mach number $M{a}_{1}$ | 0.7 |

Reynolds number $R{e}_{C}$ | $7.7\times {10}^{5}$ |

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**MDPI and ACS Style**

Wang, H.; Liu, B.; Mao, X.; Zhang, B.; Yang, Z.
Combined Flow Control Strategy Investigation for Corner Separation and Mid-Span Boundary Layer Separation in a High-Turning Compressor Cascade. *Entropy* **2022**, *24*, 570.
https://doi.org/10.3390/e24050570

**AMA Style**

Wang H, Liu B, Mao X, Zhang B, Yang Z.
Combined Flow Control Strategy Investigation for Corner Separation and Mid-Span Boundary Layer Separation in a High-Turning Compressor Cascade. *Entropy*. 2022; 24(5):570.
https://doi.org/10.3390/e24050570

**Chicago/Turabian Style**

Wang, Hejian, Bo Liu, Xiaochen Mao, Botao Zhang, and Zonghao Yang.
2022. "Combined Flow Control Strategy Investigation for Corner Separation and Mid-Span Boundary Layer Separation in a High-Turning Compressor Cascade" *Entropy* 24, no. 5: 570.
https://doi.org/10.3390/e24050570