# Numerical Analysis of Flatback Trailing Edge Airfoil to Reduce Noise in Power Generation Cycle

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Large Eddy Simulation

**I**,

**T**, and

**f**

_{b}denote the pressure, density, identity tensor, stress tensor, and body force, respectively. Every velocity component is included in vector

**v**.

**S**is the mean strain rate tensor and k is the sub-grid scale turbulent kinetic energy.

#### 2.2. Acoustic Analogy

**x**. The FW-H equation for the pressure that is radiated into a medium at rest by a flow in a region or a set of surfaces is:

- The procedure starts with a sequence of emission times (conveniently taken as the flow times).
- The source strengths are calculated (thickness surface noise and loading surface noise) at all source elements (faces of the integration surfaces) for a given emission time.
- The contributions of the sources are interpolated in the far-field time domain to build the sound signal.

#### 2.3. Numerical Conditions

^{−4}times the airfoil chord length, with a stretching factor of 1.2 so that the boundary layer was created until the 20 layers had a thickness of 5.5% of the chord length (Figure 3). Table 1 shows the aspect ratio of each layer at the mid-chord region and the leading-edge region. At the leading edge, dx/dy fell below 30 from the 8th layer, and the thickness from surface to 8th layer was 0.049% of the chord length. At the mid chord region where the aspect ratio was the largest, dx/dy fell below 30 from the 12th layer. The thickness from the surface to the 12th layer was 1.1 × 10

^{−3}of the chord length. In this case, pressure and velocity change in boundary layer normal direction were larger than the change in stream-wise direction. Thus, a large dx/dy did not result in a serious error. In addition, the aspect ratio near the leading edge was half of the other regions because pressure and velocity change in stream-wise direction was large in this region. Similar research by Mendonca, Kumar and Kim [50] used similar aspect ratio of dx/dy and showed the expected results. The aspect ratio of chord-wise to span-wise (dx/dz) was one. Figure 4 shows the surface mesh on the airfoil—they were built up to the external boundary, the same as the dx/dz ratio. The dx on the airfoil surface was 0.5% of airfoil’s chord length. The total mesh number was 17 million for each airfoil. Figure 5 shows the resulting y+ distribution on the surface of the airfoil after calculation was converged. Around the T.E. area where the vortex shedding occurs, the values are maintained under two. Figure 6 shows convective courant number contour that was calculated in the present mesh. Convective courant number was under 0.7 in most of the flow regions, except a few cells near the T.E. corner. It is considered that the present mesh quality was enough for the analysis.

^{−5}s intervals in the second order while simulation was conducted for 0.8 s for an adequate convection of vortex shedding flow in the T.E. for the condition with a chord length of 0.92 m and an inflow speed of 28.7 m/s.

#### 2.4. Test Cases

^{6}). The measurement point was 3.04 m towards the suction side from the center of rotation of the airfoil.

^{6}but inaccuracy was increased as Re. No. was increased to Re. = 2.4 × 10

^{6}or Re. = 3.2 × 10

^{6}. Our study focused on the reduction of tonal noise by vortex shedding between 100 Hz and 200 Hz. This tonal noise could not be seen in the Re. = 1.64 × 10

^{6}case in Sandia’s measurement. In addition, the Re. = 1.46 × 10

^{6}data has a poor S/N ratio because of background noise of the wind tunnel. However, Re. = 2.4 × 10

^{6}data showed clear tonal noise and a good S/N ratio. Since our research target was to see the tonal noise reduction effect, an acoustic comparison for validation was implemented for Re. = 2.4 × 10

^{6}despite there data being not corrected. Sandia’s report stated that the error might not be serious. For this reason, Re. = 1.64 × 10

^{6}data were used for the validation of aerodynamic performance and Re. = 2.4 × 10

^{6}data were used for noise analysis.

^{6}), which is are the same conditions as the noise measurement.

## 3. Results and Discussion

#### 3.1. Validation of Aerodynamic and Aero-Acoustic Results

^{6}, and for a geometric AOA of 5.1° with a flow speed of 58.6 m/s and Re. No. = 3.2 × 10

^{6}. Here, the pressure coefficient (C

_{p}) is defined as in Equation (23).

_{p}distribution and the comparison of the airfoil surface measured under ${\alpha}_{eff}=4.4\xb0$, Re. No. = 1.6 × 10

^{6}. The x-axis shows the normalized chord length while the y-axis shows the –Cp values. In this case, the Sandia National Laboratories test results were corrected with an effective AOA of 4.4° while the CFD simulation was calculated by setting the geometric AOA = 4.4°. The overall CFD analysis results matched the test values well but show a slight difference with the L.E and T.E. regions of the upper surface. In the wind tunnel test, transition occurred from the laminar boundary layer to the turbulent boundary layer on the LE region, and such an error was the result of the fact that CFD analysis basically assumes full turbulent flow for the entire numerical domain. Therefore, slight over-prediction was observed for –C

_{p}of the upper surface near the LE area compared to the experimental value, but the location of the apex was predicted relatively accurately, with values in the range of 20–25%.

_{p}distribution comparison of a geometric AOA of 5.1°, Re. No. = 3.2 × 10

^{6}. In the case of the Sandia National Laboratories test, the test conditions are not corrected by an effective AOA and only [35] geometric AOA is indicated; the same goes for noise measurements, which are described later, as they are also indicated in geometric AOA. Therefore, the AOA experienced by the airfoil in an actual test is smaller than 5.1°; as such, when the geometric AOA was calculated with a 5.1° in CFD analysis, the –C

_{p}value in the upper surface turned out to be greater than the measured value, and the error also increased.

^{2}value for the Q-criterion while Figure 12 shows the non-dimensional vortices contour. All calculation conditions are of geometric AOA of 5.1°, Re. No. = 2.4 × 10

^{6}, the same as the noise measurement condition. The vortices occurring in the boundary layer of the T.E. flow out to the back, creating a turbulent vortex street, and a visible wake pattern. The eddy created in the upper and lower surfaces convexed downstream, creating a 2D coherent structure, which also becomes the primary mechanism of generation for the vortex shedding noise in the case of a blunt T.E. [53]. Figure 11 and Figure 12 clearly show a trend similar to that of the results from the experiment by Shannon and Morris [28].

^{6}.

#### 3.2. Noise Analysis of Oblique Trailing Edge Airfoils

_{p}distribution of each airfoil. Modification of the T.E. shape reduced C

_{p}near T.E., and resulted in a decreased Cl (Table 2). However, as for the peak tonal noise, noise level was maintained or slightly increased in the case of Oblique60 and Oblique45. This means that an improper oblique angle could reduce aerodynamic performance and structural property, and increase noise level.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Rotating machine geometry (

**a**) axial fan [6]; (

**b**) axial impulse turbine; (

**c**) screw compressor.

**Figure 2.**Grid system for RANS and LES analyses. (

**a**) Whole gird structure; (

**b**) grid structure near airfoil wall.

**Figure 5.**The wall y+ distribution (Geometric AOA (angle of attack) = 5.1°, Re. No. = 2.4 × 10

^{6}): (

**a**) Flatback; (

**b**) Oblique60; (

**c**) Oblique45; (

**d**) Oblique30.

**Figure 8.**Oblique T.E. airfoils: (

**a**) Airfoil geometry comparison; (

**b**) oblique angle definition and T.E. comparison.

**Figure 9.**Comparison of the pressure coefficient (Cp) between the CFD prediction and the experimental data (Effective AOA = 4.4°, Re. No. =1.6 × 10

^{6}).

**Figure 10.**Comparison of the pressure coefficient (C

_{p}) between the CFD prediction and experimental data (Geometric AOA = 5.1°, Re. No. = 3.2 × 10

^{6}).

**Figure 11.**Visualization of the Q-criterion. Iso-surface Q = 100/s

^{2}(Geometric AOA = 5.1°, Re. No. =2.4 × 10

^{6}).

**Figure 14.**Noise comparison between the measurement and calculation (Geometric AOA = 5.1°, Re. No. = 2.4 × 10

^{6}).

**Figure 16.**Comparison of the pressure coefficient (C

_{p}) between each airfoil (CFD results, Geometric AOA = 5.1°, Re. No. = 2.4 × 10

^{6}).

**Figure 17.**The 1/12th octave band noise calculation of oblique T.E. airfoils (Geometric AOA = 5.1°, Re. No. = 2.4 × 10

^{6}).

**Figure 18.**Non-dimensional vortices contour and streamline (Geometric AOA = 5.1°, Re. No. = 2.4 × 10

^{6}): (

**a**) Flatback; (

**b**) Oblique60; (

**c**) Oblique45; (

**d**) Oblique30.

**Figure 20.**Power spectral density (PSD) behind T.E. (Geometric AOA = 5.1°, Re. No. = 2.4 × 10

^{6}): (

**a**) Vertical velocity PSD along the chord behind T.E.; (

**b**) pressure PSD behind the T.E. point.

**Figure 21.**Lambda2 criterion (Geometric AOA = 5.1°, Re. No. = 2.4 × 10

^{6}): (

**a**) Flatback; (

**b**) Oblique60; (

**c**) Oblique45; (

**d**) Oblique30.

**Table 1.**The dx/dy in the prism layer mesh. dx: stream-wise direction, dy: surface normal direction.

Layer Number from the Surface Wall | Mid-Chord Region | Leading Edge Region |
---|---|---|

No. | dx/dy | dx/dy |

1 | 186.7 | 93.3 |

2 | 155.6 | 77.8 |

3 | 129.6 | 64.8 |

4 | 108 | 54 |

5 | 90 | 45 |

6 | 75 | 37.5 |

7 | 62.5 | 31.3 |

8 | 52.1 | 26.1 |

9 | 43.4 | 21.7 |

10 | 36.2 | 18.1 |

11 | 30.2 | 15.1 |

12 | 25.1 | 12.6 |

13 | 20.9 | 10.5 |

14 | 17.4 | 8.7 |

15 | 14.5 | 7.3 |

16 | 12.1 | 6.1 |

17 | 10.1 | 5 |

18 | 8.4 | 4.2 |

19 | 7 | 3.5 |

20 | 5.8 | 2.9 |

Airfoil Name | Sectional Stiffness Based on Flatbak Airfoil (%) | Cl | Peak Noise Level (dB) |
---|---|---|---|

Flatback | 100 | 0.98 | 94.2 |

Oblique60 | 95.8 | 0.79 | 97.7 |

Oblique45 | 94.6 | 0.72 | 97.9 |

Oblique30 | 93.6 | 0.66 | 84.8 |

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**MDPI and ACS Style**

Shin, H.; Kim, H.; Kim, T.; Kim, S.-H.; Lee, S.; Baik, Y.-J.; Lee, G. Numerical Analysis of Flatback Trailing Edge Airfoil to Reduce Noise in Power Generation Cycle. *Energies* **2017**, *10*, 872.
https://doi.org/10.3390/en10070872

**AMA Style**

Shin H, Kim H, Kim T, Kim S-H, Lee S, Baik Y-J, Lee G. Numerical Analysis of Flatback Trailing Edge Airfoil to Reduce Noise in Power Generation Cycle. *Energies*. 2017; 10(7):872.
https://doi.org/10.3390/en10070872

**Chicago/Turabian Style**

Shin, Hyungki, Hogeon Kim, Taehyung Kim, Soo-Hyun Kim, Soogab Lee, Young-Jin Baik, and Gilbong Lee. 2017. "Numerical Analysis of Flatback Trailing Edge Airfoil to Reduce Noise in Power Generation Cycle" *Energies* 10, no. 7: 872.
https://doi.org/10.3390/en10070872