# Numerical Research on the Jet Mixing Mechanism of the De-Swirling Lobed Mixer Integrated with OGV

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## Abstract

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## 1. Introduction

## 2. Numerical Method

^{−6}.

#### 2.1. Model of Lobed Mixer

#### 2.2. CFD Domain and Mesh

_{h}(where D

_{h}is the hydraulic diameter of the core flow at the lobe exit) and an axial extent of 20 D

_{h}to simulate jet mixing with ambient air.

^{4}based on the hydraulic diameter of the core outlet and the core axial velocity in all cases, which was greater than the critical value defined by Manning [6].

#### 2.3. Verification

_{h}to 1.2 D

_{h}, while it is slightly larger than the latter in the range of 0.44 D

_{h}to 0.7 D

_{h}. The simulated total pressure coefficients (Figure 8b) are consistent with the experimental results throughout the radial range, except for the two peak regions. As shown in Figure 8c, the simulated location and shape of the azimuthal vortices have good consistency with experimental results, but the calculated azimuthal vorticity is higher than the experimental one. These differences may be due to errors in the seven-hole probe, which identifies the velocity gradient as the flow angle in high-velocity gradient regions (such as high shear layers) [21]. Overall, CFD simulation can accurately capture the parameter distributions and vortex structures downstream of IRLM.

#### 2.4. Data Reduction

_{re}), total pressure loss (Y), and their relative changes compared to the baseline case. The relative thrust (T

_{re}) and total pressure loss (Y) were defined as follows:

_{T}is calculated by dividing T by $0.5\rho {\overline{u}}_{core,in}^{2}{D}_{h}^{2}$. The non-dimensional total pressure coefficient C

_{p}

_{0}is calculated using the total pressure at the measuring point and the mass-averaged static & total pressure in the inlet of the exhaust system, including the core inlet and bypass inlet. The total pressure loss is the difference between the mass-averaged value of C

_{p}

_{0}at the nozzle inlet and nozzle exit.

_{g}, is used to evaluate the dispersion degree of the flow parameter. It is defined as follows:

_{g}is supported to be 0. This paper chooses the total pressure as the parameter ‘g’ to calculate the mixing coefficient. A lower value of I

_{p}

_{0}indicates the core and bypass flows are mixing more effectively.

_{s}) and azimuthal vorticity (ω

_{a}) are used to analyse the development of the vortex system. The definition of ω

_{s}and ω

_{a}is derived from the partial derivative of velocity under the Cartesian coordinate system:

_{w}

_{s}and C

_{wa}are dimensionless vorticity parameters calculated by dividing ω

_{s}and ω

_{a}by u

_{core,in}/D

_{h}, respectively.

## 3. Results and Discussion

#### 3.1. Mixing Mechanism of IDLM on Design Condition

_{ws, max}= 31.3) in the IRLM case, maximum streamwise vorticity in the IDLM case increases by 8% on x = 0.4 Ln section, and then the decay rate of maximum vorticity shown on downstream sections is also greater than that in IRLM case. As analyzed above, this is mainly due to the design concept of DLM, which reserves a certain strength of residual swirling flow. In addition, the strength of the trailing edge shedding vortex downstream of IOGV in the IDLM case is also greater than that in the IRLM case, with their maximum values on x = 0.4 Ln section being 35.5 and 27.7, respectively. Therefore, compared to the IRLM case, stronger streamwise vortices interact with stronger trailing edge shedding vortex in the IDLM case, inevitably accelerating the dissipation of streamwise vortices in this area: streamwise vortices in the IDLM case have almost dissipated on x = 0.55 Ln section, while there are still two clear vortex cores on this section in IRLM case until x = 0.7 Ln section.

_{re}) on the nozzle outlet for the four cases with core inlet swirl of 20°, and also gives their gain (ΔY and ΔT

_{re}) relative to those of the RLM case. The total pressure loss in the DLM case has increased by 7.78% compared with that of the RLM case, which may be related to the enhanced jet mixing and the stronger leakage swirl between the lobe trough and central body in the DLM case. Similarly, it can also see that the total pressure loss in the IDLM case is greater than that of the IRLM case. However, the total pressure losses of the two integrated lobed mixers are significantly lower than those of the non-integrated lobed mixers due to the effective suppression of leakage swirling flow.

_{re}= 3.01% in Table 1) of the IRLM case, indicating that IDLM has the best comprehensive effect of improving the output thrust of the exhaust system.

#### 3.2. Performance of IDLM on off-Design Condition

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

RLM | Scalloped Reference Lobed Mixer | C_{wa} | Azimuthal Vorticity Coefficient |

DLM | Scalloped de-swirling Lobed Mixer | C_{ws} | Streamwise Vorticity Coefficient |

IRLM | Integrated RLM | C_{p}_{0} | Total Pressure Coefficient |

IDLM | Integrated DLM | C_{T} | Thurs Coefficient |

OGV | Outlet Guide Vane | w_{a} | Azimuthal Vorticity |

IOGV | Integrated Outlet Guide Vane | w_{s} | Streamwise Vorticity |

LPT | Low-Pressure Turbine | T | Thrust |

x, y, z | x, y, and z Coordinate | T_{re} | The Relative Thrust |

u, v, w | Velocity in the x, y and z-Direction | u_{core,in} | Axial Velocity of Core Inlet |

α | Inlet Swirl Angle, ° | D_{h} | Hydraulic Diameter of Core Exit |

H | height | I_{g} | Mixing Index |

H | Channel Height | I_{p}_{0} | Total Pressure Mixing Index |

L_{n} | Length of Nozzle | y^{+} | Non-dimensional wall distance |

P_{0} | Total Pressure, Pa | Y | Total Pressure Loss |

P_{s} | Static Pressure, Pa | R | Radius of Bypass Nozzle |

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**Figure 8.**Comparison Between Experimental Results and Numerical Ones on the x = 1.0 Ln Section for the IRLM Case with an Inlet Swirl of 20°: (

**a**) Radial distribution of tangential flow angle; (

**b**) Radial distribution of total pressure coefficient; (

**c**) Contour of azimuthal vorticity.

**Figure 9.**The radial distribution of the pitch-wise mass-averaged flow angle at the outlet of the lobed mixer (x = 0.4 Ln) for cases with a core inlet swirl of 20°.

**Figure 10.**The limiting streamlines on the IOGV, central body and the inner surface of different lobed mixers for the cases with inlet swirl of 20°: (

**a**) RLM; (

**b**) DLM; (

**c**) IRLM; (

**d**) IDLM.

**Figure 11.**The streamwise vorticity contour at different axial sections in the IOGV channel: (

**a**) IRLM; (

**b**) IDLM.

**Figure 12.**The streamwise vorticity contour downstream of the lobed mixers under different conditions with the core inlet swirl of 20°: (

**a**) RLM; (

**b**) DLM; (

**c**) IRLM; (

**d**) IDLM.

**Figure 14.**The radial distribution of pitch-wise mass-averaged thrust coefficient on the nozzle outlet for the four cases with core inlet swirl of 20°.

**Figure 15.**The radial distribution of the tangential flow angle on the x = 0.4 Ln section downstream of the two integrated lobed mixers for the different inlet swirl cases.

**Figure 16.**The streamwise vorticity contours on the x = 0.4 Ln section downstream of IRLM and IDLM in the cases with the core inlet swirl of 0°, 10° and 30°: (

**a**) α = 0°; (

**b**) α = 10°; (

**c**) α = 30°.

Location | Boundary Condition |
---|---|

Core Inlet | u = 40 m/s |

α = 0°, 5°, 10°, 15°, 20°, 25°, 30° and 35° | |

Bypass Inlet | u = 30.8 m/s |

α = 0° | |

Far-field | P_{s} = 101,325 Pa |

Outlet | P_{s} = 101,325 Pa |

Solid Surfaces | No-slip Wall |

**Table 2.**The total pressure loss and thrust coefficient on the nozzle outlet for the four cases with core inlet swirl of 20°.

Cases | Y | ΔY | T_{re} | ΔT_{re} |
---|---|---|---|---|

RLM | 24.29% | - | 1.060 | - |

DLM | 26.18% | 7.78% | 1.074 | 1.32% |

IRLM | 15.38% | −36.69% | 1.092 | 3.01% |

IDLM | 16.72% | −31.17% | 1.094 | 3.18% |

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**MDPI and ACS Style**

Lei, Z.; Deng, H.; Ouyang, X.; Zhang, Y.; Lu, X.; Xu, G.; Zhu, J.
Numerical Research on the Jet Mixing Mechanism of the De-Swirling Lobed Mixer Integrated with OGV. *Energies* **2023**, *16*, 4394.
https://doi.org/10.3390/en16114394

**AMA Style**

Lei Z, Deng H, Ouyang X, Zhang Y, Lu X, Xu G, Zhu J.
Numerical Research on the Jet Mixing Mechanism of the De-Swirling Lobed Mixer Integrated with OGV. *Energies*. 2023; 16(11):4394.
https://doi.org/10.3390/en16114394

**Chicago/Turabian Style**

Lei, Zhijun, Hanliu Deng, Xiaoqing Ouyang, Yanfeng Zhang, Xingen Lu, Gang Xu, and Junqiang Zhu.
2023. "Numerical Research on the Jet Mixing Mechanism of the De-Swirling Lobed Mixer Integrated with OGV" *Energies* 16, no. 11: 4394.
https://doi.org/10.3390/en16114394