# ACAT1 Benchmark of RANS-Informed Analytical Methods for Fan Broadband Noise Prediction—Part I—Influence of the RANS Simulation

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## Abstract

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## 1. Introduction

- the RANS input,
- the preparation of the RANS input (i.e the extraction of flow and geometry, the reconstruction of wake flow and turbulence, the determination of integral turbulent length scales, etc.),
- and the applied acoustic model.

## 2. Methods

#### 2.1. Experimental Setup and Used Measurement Data

#### 2.2. RANS-Informed Analytical Methods

#### 2.2.1. RANS Simulations and Turbulence Modeling

#### Linear Eddy Viscosity Turbulence Models

**Wilcox**k-$\omega $ turbulence model [19]. It is a two-equation linear eddy viscosity model solving transport equations for the turbulent kinetic energy k and the specific turbulent dissipation rate $\omega $. The model is particularly suited for computing the turbulence in near-wall flow fields but it is formulated for equilibrium flows, that is, the turbulence is self-preserving. Non-equilibrium flows are typically characterized by large pressure gradients like in stagnation points. Thus, a turbulence model extension is often used in combination with this turbulence model in order to overcome this issue.

**Shear-Stress-Transport (SST)**k-$\omega $ turbulence model [20,21] combines the advantages of two turbulence models. The Wilcox k-$\omega $ turbulence model is used for near-wall flows and the k-$\u03f5$ turbulence model, for free stream flows. A blending function is used to transition between the two models. However, the blending function is empirically motivated and a known weak point of the model as it is prone to fail, particularly for complex flow fields and in the presence of high turbulence levels in free stream flows. Compared to the Wilcox k-$\omega $ model, the Menter SST model is formulated for non-equilibrium flows. If turbulence production is higher than dissipation, the eddy viscosity is limited so that the ratio of turbulent shear stress and turbulent kinetic energy remains constant. If turbulence production is not higher than dissipation, the standard k-$\omega $ formulation is applied. However, as turbulence production exceeds dissipation in flow regimes featuring adverse pressure gradients and separated flow, Menter’s model predicts larger flow separation bubbles than other commonly used models.

**Smith k-l**turbulence model [22,23]. Instead of solving a time-scale based transport equation like the previous models, it uses a length-scale based formulation. The length scale l can be directly related to the specific turbulent dissipation rate $\omega $:

**Note that the length scale l is not the same as an integral turbulent length scale**. Whereas the Menter SST model uses a simple limiter to treat non-equilibrium flows, the k-l Smith model incorporates a more sophisticated, continuous non-equilibrium function. The model is suited for both near-wall and free-stream flows without relying on a blending function. Compared to the other two featured linear eddy viscosity model, its grid resolution requirements are less restrictive in the buffer zone and in the viscous sublayer.

#### Non-Linear Eddy Viscosity Turbulence Models

**Hellsten EARSM k-$\omega $**turbulence model [24]. It is essentially an extension of the Menter baseline k-$\omega $ turbulence model, which in contrast to the previously described Menter SST k-$\omega $ does not feature a limiter. The transport equations and the blending functions are identical to Menter’s baseline model but a non-linear term is added to Boussinesq’s turbulence stress definition to account for the Reynolds stress anisotropy in terms of the strain-rate and vorticity tensors. This additional, algebraic term was formulated using recalibrated data from a Launder, Reece, and Rodi DRSM [25].

#### Extensions of Eddy Viscosity Turbulence Models

**Kato-Launder modification**, which can be used in combination with most two-equation turbulence models. It replaces one mean strain rate tensor ${S}_{ij}$ by the vorticity tensor ${\mathrm{\Omega}}_{ij}$. The Reynolds stress tensor ${\tau}_{ij}$ of the production term of the turbulence model in the transport equation for turbulent kinetic energy k is thus modified as follows:

**Schwarz limiter**. Using this inequality, a lower bound for the specific dissipation rate $\omega $ can be formulated:

**$\gamma $-$R{e}_{\vartheta t}$ transition model**[27], a common correlation-based model, was used during this benchmark. This transition model introduces two further transport equations—one for the transition Reynolds number based on the momentum thickness $R{e}_{\vartheta t}$ and one for the intermittency $\gamma $, which triggers transition. Advantages of this model are that it relies on local variables and can be adjusted based on experimental data.

#### Differential Reynolds Stress Turbulence Models

**Wilcox stress-$\omega $**turbulence model [18] is closely related to the Wilcox k-$\omega $ model. For computing the Reynolds stress tensor, Wilcox decided to use the simpler, linear pressure-strain correlation of Launder, Reece and Rodi (LRR) rather than the non-linear, more complex formulation of Speziale-Sarkar-Gatski (SSG) [28]. While this model solves the Reynolds stress tensor, the underlying transport equation for the specific turbulent dissipation rate remains the same and the turbulent kinetic energy transport equation can be recovered from the Reynolds stress equations. This also means that all closure coefficients are exactly the same for both models and that both models are particularly suitable for computing boundary layer flows. Wilcox [18] also states that both models therefore produce similar results.

**SSG/LRR-$\omega $**turbulence model [29] is formulated analogously to the Menter SST k-$\omega $ turbulence model. It blends two pressure-strain models: the LRR model—using the same formulation as the Wilcox stress-$\omega $ model—for boundary layer flows and the SSG model in free shear flows. The LRR model’s formulation is a simpler, linear model and therefore more robust than the SSG model, especially in near-wall flows. The SSG/LRR-$\omega $ model uses the same specific dissipation rate transport equation and the same blending function as both the Menter SST k-$\omega $ and Hellsten EARSM k-$\omega $ models.

**JH stress-${\omega}^{h}$**turbulence model [30,31,32] follows a different approach than the other two DRSM’s. Data of direct numerical simulations (DNS) were used to model the pressure-strain correlation. While the formulation of the pressure-strain is rather simple and linear, the coefficients are defined as functions of the turbulence anisotropy invariants as constant coefficients are not adequate for describing flows in areas close to walls. The formulation of the turbulent eddy viscosity was also optimized to match DNS data. Based on the transport equation for the two-point correlation, Jovanović et al. [33] showed that the dissipation tensor can be divided into a homogeneous part and contributions due to the inhomogeneity of the flow, which are equal to the viscous diffusion of the Reynolds stresses. Thus the scale-determining transport equation is formulated in terms of the specific homogeneous dissipation rate ${\omega}^{h}$. As the focus of formulating this model was to correctly describe the turbulence in boundary layer flows, the JH stress-${\omega}^{h}$ turbulence model was proven to be superior to the Menter SST k-$\omega $, Hellsten EARSM k-$\omega $, and SSG/LRR-$\omega $ models in predicting the flow features of streamline curvature, boundary layer, flow separation, and shock wave/boundary layer interaction [34].

#### 2.2.2. Preparation of the RANS Input

- a length scale determined by fitting the circumferential average of turbulence velocity frequency spectra $\overline{{\mathrm{\Phi}}_{ii}\left(f\right)}=\frac{1}{2\pi}\underset{0}{\overset{2\pi}{\int}}{\mathrm{\Phi}}_{ii}(f,\vartheta )d\vartheta $ with a target spectrum [38],
- a Pope-based length scale computed from circumferentially averaged turbulence characteristics $\overline{\mathrm{\Lambda}}=\frac{{C}_{\mathrm{Re}}}{{C}_{\mu}}\frac{\sqrt{\overline{k}}}{\overline{\omega}}$,
- and a Ganz-based, empirically motivated length scale $\overline{\mathrm{\Lambda}}=0.2\frac{A}{d}$ (where A represents the wake area and d the wake velocity deficit) [39].

#### 2.2.3. Analytical Acoustic Model

#### 2.2.4. Post-Processing of Acoustic Results

#### 2.3. Overview of Used RANS Simulations

#### 2.3.1. Solvers and Turbulence Models

#### 2.3.2. Operating Conditions

#### 2.3.3. Geometry and Meshing

## 3. Results and Discussion

#### 3.1. Influence of the Menter SST k-$\omega $ Turbulence Model

- The wake width is a bit larger in the experiment than in the simulations, especially at lower radial positions. One explanation for this phenomenon is that the hot-wire probes cover a measuring volume of 1 × 2 × 2 mm [10], which defines the spatial resolution. Therefore, the slope of the shear layers are “smeared” and wakes appear to be wider as they are in reality.
- The wake velocity deficit is smaller in the experiment than in the simulations. Part of the reason for this offset is likely physical in nature. Particularly near the tip region, the wake velocity deficit in the experiment is less pronounced due to a less severe (or absent) leading edge flow detachment compared to the simulations, where it causes deeper and thicker wakes. Another part of the explanation may be due to the hot-wire measurement. The previously mentioned control volume can also cause flatter peaks. In addition, the hot-wire probes were calibrated at one radial position upstream of the rotor blades. Since the in-duct calibration was performed for circumferentially uniform flow, it can be expected that the calibration may not work as well within the wake as outside of it as the temperature increases inside the wakes.
- There are some offsets in mean velocities outside of the wakes. Smaller offsets are indeed expected as the hot-wire probes are less accurate in measuring mean velocities as opposed to fluctuating velocities. Offsets in the radial velocity can occur if the yaw angle of an X-wire probe intended to measure axial and radial velocities is not well aligned with the mean flow. The circumferential velocity component then creates an additional cooling effect, which will be interpreted as partly axial and radial velocity. Since the radial component is significantly smaller than the axial and circumferential components, it is most susceptible to such an effect. The trends of the circumferential velocities at 25% of the stator height diverge, which may be due to the fact that the differences are quite small and likely difficult to capture.
- Turbulent RMS velocities are overpredicted in the RANS simulations, particularly at 75% and 90% stator heights. It should be noted that there is some uncertainty regarding the measured fluctuating velocities. The lower, experimental line in Figure 9 are values directly determined from the measured data, while the upper line includes a factor of 1.5. The thickness of the hot-wires reduces the frequency resolution of the measured data. In this case, the cut-off frequency (or resolution limit) was a posteriori estimated to be around 7–8 kHz. Polacsek et al. [51] have introduced a correction factor of 1.5, which was determined by extrapolating the measured levels beyond the cut-off limit relative to the results of a scale-resolving simulation. For this reason, the raw as well as the corrected experimental values are shown in subsequent figures featuring either turbulent kinetic energies or RMS velocities. It should again be highlighted that the hot-wire calibration may be less suited for determining values within the wake than outside of the wake. Part of the observed offset in RMS velocities may, however, be physical as the higher turbulence levels in the RANS simulations are probably caused by a larger separation at the rotor leading edge than in the experiment. At 90% of the stator height, the measured values also capture the structure of the tip vortex resulting in two peaks.

#### 3.2. Influence of Linear Eddy Viscosity Turbulence Models

#### 3.3. Influence of More Advanced Turbulence Models

## 4. Conclusions

- The Menter SST k-$\omega $ turbulence model and related turbulence models (like the Hellsten EARSM k-$\omega $ or the SSG/LRR-$\omega $) tend to exaggerate flow separations leading to increased turbulence production. This leads to an increase of sound power levels leading to a better agreement with measured sound power levels but increases the offset between simulated and measured velocities. The Hellsten EARSM k-$\omega $ also causes an increase in turbulent length scale, which is advantageous in terms of sound power levels.
- The Smith k-l turbulence model predicts a weaker flow separation resulting in a better agreement with hot-wire measurements. Due to an increase in predicted TLS, the predicted sound power levels are similar to sound power levels predicted using a Menter SST k-$\omega $ turbulence model. For the investigated case, the Smith k-l turbulence model may be the best compromise between matching hot-wire and acoustic measurements.
- The use of differential Reynolds stress models did not improve results in terms of flow and turbulence characteristics and in terms of fan broadband noise. Unless the objective is to study anisotopic turbulence in more detail, simpler models should be used as they are more robust and require less computational resources.
- Stagnation fixes need to be used for turbulence model featuring an equilibrium formulations. For other turbulence models, stagnation fixes further reduce turbulence production. The reduction of turbulence production leads to a further reduction of predicted fan broadband noise leading to a worse agreement with measurements. The use of stagnation fixes does not significantly improve the agreement with hot-wire data. If the use of stagnation point is necessary, a simple limiter or a local modification of transport equations limited to areas of non-equilibrium flows are preferable.
- Rotational fixes can be used to achieve a better agreement between hot-wire measurements and simulated velocities.
- The use of transition model does not improve fan broadband noise predictions or the agreement with hot-wire measurements.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | wake area, m${}^{2}$ |

${C}_{\mathrm{Re}}$ | Reynolds number-dependent constant |

${C}_{\mu}$ | turbulence model-dependent constant |

d | wake velocity deficit, m/s |

f | frequency, Hz |

k | turbulent kinetic energy, m${}^{2}$/s${}^{2}$ |

${L}_{w}$ | wake width, m |

l | pseudo turbulent length scale (Smith), m |

$PWL$ | sound power level, dB ref. ${10}^{-12}$ W/Hz |

${r}_{tip}$ | averaged tip rotor radius, 0.428 m |

$R{e}_{\vartheta t}$ | transition Reynolds number based on the momentum thickness |

${S}_{ij}$ | mean strain rate tensor, 1/s |

$St$ | Strouhal number |

u | velocity, m/s |

${u}_{0}$ | total mean velocity at the HW 1 position, 128 m/s |

$\gamma $ | intermittency |

$\u03f5$ | turbulent dissipation rate, m${}^{2}$/s${}^{3}$ |

$\vartheta $ | angle, rad |

$\mathrm{\Lambda}$ | integral turbulent length scale, m |

${\mu}_{T}$ | eddy viscosity, m${}^{2}$/s |

$\rho $ | density, kg/m${}^{3}$ |

${\tau}_{ij}$ | Reynolds stress tensor, kg/(s${}^{2}$ m) |

${\mathrm{\Phi}}_{ii}$ | turbulence velocity frequency spectrum (relative to direction i), m${}^{2}$/s |

${\mathrm{\Omega}}_{ij}$ | vorticity tensor, 1/s |

$\omega $ | specific turbulent dissipation rate, 1/s |

${\omega}^{h}$ | specific homogeneous dissipation rate, 1/s |

## Abbreviations

ACAT1 | AneCom AeroTest Rotor 1 |

CFD | Computational Fluid Dynamics |

DNS | Direct Numerical Simulation |

DRSM | Differential Reynolds Stress Model |

EARSM | Explicit Algebraic Reynolds Stress Model |

HW | Hot-Wire |

ISA | International Standard Atmosphere |

JH | Jakirlic-Hanjalic |

LE | Leading Edge |

LRR | Launder-Reece-Rodi |

NASA | National Aeronautics and Space Administration |

PWL | Sound Power Level |

RANS | Reynolds-Averaged Navier-Stokes |

RMS | Root Mean Square |

RSI | Rotor-Stator-Interaction |

TE | Trailing Edge |

TKE | Turbulent Kinetic Energy |

TLS | Turbulent Length Scale |

SDT | Source Diagnostic Test |

SSG | Speziale-Sarkar-Gatski |

SST | Shear-Stress-Transport |

UFFA | Universal Fan Facility for Acoustics |

## Appendix A. Velocities

## Appendix B. Turbulence Characteristics

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**Figure 1.**Sketch of the UFFA test rig at AneCom AeroTest (

**top**): Positions of acoustic instrumentation in the free field (FF), in the inlet duct (CMD1), and in the bypass duct (CMD3 and AX1) are shown in red (TurboNoiseBB consortium, reprint with permission); Example of a Reynolds-Averaged Navier-Stokes (RANS) domain (

**bottom**): Streamlines at relative stator heights of 1%, 25%, 50%, 75%, 90%, and 97% are shown in blue and radial measurement positions in the fan inlet section (HW 0) and in the fan interstage section (HW 1) are indicated by green markers.

**Figure 2.**Impact of choice of turbulent length scale (TLS) definition on predicted sound power levels.

**Figure 3.**Comparison of extracted turbulence characteristics at HW 1 position and extrapolated turbulence characteristics at the stator leading edge: Radial distributions of turbulent kinetic energy k and turbulent length scale $\mathrm{\Lambda}$ at HW 1 and stator leading edge positions are shown.

**Figure 4.**Impact of choice of analysis plane on predicted rotor-stator-interaction (RSI) broadband noise: Sound power level spectra downstream of the stator vanes for HW 1 and stator leading edge positions are shown.

**Figure 5.**Flow separation near rotor leading edge: Streamlines are shown in black and the contours show non-dimensional turbulent kinetic energies. The interstage slice corresponds to the HW 1 position and the black contour lines indicate the considered domain between the streamlines of 1% and 97% of the stator height.

**Figure 6.**Non-dimensional turbulent kinetic energy values measured by the hot-wire probes at position HW 1 in the interstage region.

**Figure 7.**Impact of choice of solver and mesh topology on turbulence characteristics for simulations using a Menter SST k-$\omega $ turbulence model: Radial distributions of turbulent kinetic energy k and turbulent length scale $\mathrm{\Lambda}$ are shown.

**Figure 8.**Impact of choice of solver and mesh topology on velocities at 90%, 75%, 50%, 25% (top to bottom) stator height for simulations using a Menter SST k-$\omega $ turbulence model

**Figure 9.**Impact of choice of solver and mesh topology on fluctuating velocities at 90%, 75%, 50%, 25% (top left to bottom right) for simulations using Menter SST k-$\omega $ turbulence model

**Figure 10.**Comparison of wake velocity deficits for all RANS simulations at 75% (top) and 50% (bottom) of the stator height. The dashed, black lines mark the experimental values.

**Figure 11.**Comparison of wake widths for all RANS simulations at 75% (top) and 50% (bottom) of the stator height. The dashed, black lines mark the experimental values.

**Figure 12.**Impact of choice of solver and mesh topology on predicted RSI broadband noise using a Menter Shear-Stress-Transport (SST) k-$\omega $ turbulence model: Sound power level spectra downstream are shown.

**Figure 13.**Impact of type of linear eddy viscosity turbulence model on velocities at 90%, 75%, 50%, 25% (top to bottom) stator height for simulations using a linear eddy viscosity turbulence model.

**Figure 14.**Impact of type of linear eddy viscosity turbulence model on fluctuating velocities at 90%, 75%, 50%, 25% (top left to bottom right) for simulations using a linear eddy viscosity turbulence model.

**Figure 15.**Impact of type of linear eddy viscosity turbulence model on turbulence characteristics: Radial distributions of turbulent kinetic energy k and turbulent length scale $\mathrm{\Lambda}$ are shown.

**Figure 16.**Impact of type of linear eddy viscosity turbulence model on predicted RSI broadband noise: Sound power level spectra downstream of the stator vanes are shown.

**Figure 17.**Impact of choice of a more advanced turbulence model on velocities at 90%, 75%, 50%, 25% (top to bottom) stator height.

**Figure 18.**Impact of choice of a more advanced turbulence model on fluctuating velocities at 90%, 75%, 50%, 25% (top to bottom) for simulations.

**Figure 19.**Impact of choice of a more advanced turbulence model on turbulence characteristics: Radial distributions of turbulent kinetic energy k and turbulent length scale $\mathrm{\Lambda}$ are shown.

**Figure 20.**Impact of choice of a more advanced turbulence model on predicted RSI broadband noise: Sound power level spectra downstream of the stator vanes are shown.

Turbulence | Turbulence Model | ||
---|---|---|---|

RANS | Solver | Model | Extensions |

1, 2 | TRACE [41] | Menter SST k-$\omega $ | none |

3, 5, 8 | elsA [42] | Menter SST k-$\omega $ | none |

4, 7 | ANSYS CFX v19.2 / v19.1 [43] | Menter SST k-$\omega $ | none |

6 | G3D::Flow [44] | Menter SST k-$\omega $ | none |

9 | $M{u}^{2}{s}^{2}t$ [45,46] | Menter SST k-$\omega $ | Kato-Launder mod. |

10 | TRACE | Menter SST k-$\omega $ with Vorticity Source Term | none |

11 | TRACE | Menter SST k-$\omega $ | Kato-Launder mod. modified vortex extension (rotational fix) |

12 | HYDRA [47] | Menter SST k-$\omega $ | modifications for turbulent Mach number, rotation, low Re etc. |

13 | $M{u}^{2}{s}^{2}t$ | Wilcox k-$\omega $ | Kato-Launder mod. |

14 | $M{u}^{2}{s}^{2}t$ | Wilcox k-$\omega $ | Kato-Launder mod., $\gamma -R{e}_{\vartheta t}$ transition model |

15 | TRACE | Wilcox k-$\omega $ | Schwarz limiter |

16 | TRACE | Wilcox k-$\omega $ | Kato-Launder mod. |

17, 18 | elsA | Smith k-l | none |

19 | TRACE | Hellsten EARSM k-$\omega $ | none |

20 | TRACE | Wilcox stress-$\omega $ | none |

21 | TRACE | SSG/LRR-$\omega $ | none |

22 | TRACE | JH stress-${\omega}^{h}$ | none |

Bypass | Core | Inlet | Inlet | Ambient | Ambient | ||
---|---|---|---|---|---|---|---|

Fan | Mass | Mass | Turbulence | Turbulent | Pressure | Temperature | |

RANS | RPM | Flow [kg/s] | Flow [kg/s] | Intensity [%] | Length Scale [m] | [hPa] | [K] |

1, 2, 4, 10, 15, 16, 19-22 | 3828.1 | 48.75 | 6.41 | 0.3 | 0.04 | 995.6 | 292.8 |

3 | 3828.2 | 49.02 | 6.37 | 1.0 | 6.4 × 10${}^{-6}$ | 995.6 | 292.8 |

5 | 3828.2 | 48.75 | 6.41 | 0.3 | - | 995.6 | 292.8 |

6 | 3828.1 | 48.76 | 6.39 | 1.0 | 0.01 | 995.6 | 292.8 |

7 | 3828.2 | 48.75 | 6.44 | 0.3 | 0.04 | 995.3 | 292.8 |

8 | 3828.3 | 48.72 | 6.43 | 0.23 | 0.01 | 995.3 | 292.8 |

9 | 3828.2 | 48.75 | 6.41 | 0.36 | 0.043 | 1013.25 | 288.15 |

11 | 3856.1 | 49.85 | 6.70 | 0.88 | 0.00018 | 1013.25 | 288.15 |

12 | 3828.1 | 49.10 | 6.45 | 0.30 | 0.04 | 995.3 | 292.8 |

13, 14 | 3828.2 | 48.75 | 6.41 | 0.36 | 0.043 | 1013.25 | 288.15 |

17 | 3828.2 | 48.75 | 6.41 | 0.3 | - | 995.6 | 292.8 |

18 | 3828.3 | 48.72 | 6.43 | 0.23 | 0.01 | 995.3 | 292.8 |

Tip | Total | Azimuthal Wake | Boundary | Spatial | |
---|---|---|---|---|---|

Clearance | Mesh Size | Resolution | Layer | Discretization | |

RANS | [mm] | [Mio. cells] | at R = 75% [cells] | Resolution | Scheme |

1, 10, 12, 15, 16, 19–22 | 0.78 | 6.5 | ≈30 | resolved | 2nd order |

2 | 0.78 | 4.8 | ≈20 | resolved | 2nd order |

3 | 0.63 | 63 | ≈30 | resolved | 3rd order |

4 | 0.78 | 70 | >25 | resolved | CFX high resolution |

5 | 0.78 | 4.5 | ≈30 | resolved | 2nd order |

6 | 0.78 | 15.4 | ≈20 | resolved | 3rd order convective, 2nd order diffusive |

7 | 0.63 | 7.0 | ≈20 | resolved | CFX high resolution |

8, 18 | 0.63 | 38.0 | ≈20 | resolved | 2nd order |

9, 13, 14 | 0.63 | 35.5 | ≈30 | wall functions (OGV), resolved (rotor) | 2nd order |

11 | 0.58 (LE) 0.69 (TE) | 11.3 | ≈15 | resolved | 2nd order |

17 | 0.78 | 4.5 | ≈30 | resolved | 2nd order |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kissner, C.; Guérin, S.; Seeler, P.; Billson, M.; Chaitanya, P.; Carrasco Laraña, P.; de Laborderie, H.; François, B.; Lefarth, K.; Lewis, D.; Montero Villar, G.; Nodé-Langlois, T. ACAT1 Benchmark of RANS-Informed Analytical Methods for Fan Broadband Noise Prediction—Part I—Influence of the RANS Simulation. *Acoustics* **2020**, *2*, 539-578.
https://doi.org/10.3390/acoustics2030029

**AMA Style**

Kissner C, Guérin S, Seeler P, Billson M, Chaitanya P, Carrasco Laraña P, de Laborderie H, François B, Lefarth K, Lewis D, Montero Villar G, Nodé-Langlois T. ACAT1 Benchmark of RANS-Informed Analytical Methods for Fan Broadband Noise Prediction—Part I—Influence of the RANS Simulation. *Acoustics*. 2020; 2(3):539-578.
https://doi.org/10.3390/acoustics2030029

**Chicago/Turabian Style**

Kissner, Carolin, Sébastien Guérin, Pascal Seeler, Mattias Billson, Paruchuri Chaitanya, Pedro Carrasco Laraña, Hélène de Laborderie, Benjamin François, Katharina Lefarth, Danny Lewis, Gonzalo Montero Villar, and Thomas Nodé-Langlois. 2020. "ACAT1 Benchmark of RANS-Informed Analytical Methods for Fan Broadband Noise Prediction—Part I—Influence of the RANS Simulation" *Acoustics* 2, no. 3: 539-578.
https://doi.org/10.3390/acoustics2030029