The numerical investigations are performed by each partner applying either inhousedeveloped or commercial computational tools. The aerodynamic simulations necessary for the aeroacoustic predictions are conducted with a range of different fidelity numerical methods, varying from lifting line to CFD.
3.1. CIRA
The CIRA aerodynamic simulations were carried out by using the mediumfidelity code RAMSYS [10], which is an unsteady, inviscid and incompressible freewake vortex lattice boundary element methodology (BEM) solver for multirotor, multibody configurations developed at CIRA. It is based on Morino's boundary integral formulation [11] for the solution of Laplace's equation for the velocity potential φ. The surface pressure distributions are evaluated by applying the unsteady version of Bernoulli equation, which is then integrated to provide the forces and moments on the configuration and the surrounding obstacles. A computational acceleration is obtained by applying the module for symmetrical flows and geometries implemented in the solver and the parallel execution via the OpenMP API.
The ACOFWH solver is used for computing the acoustic freefield generated by the rotor blades. It is based on the FWH formulation [12] described in [13] [14] and [15]. The advancedtime formulation of Farassat 1A is employed, and the linear terms (the socalled thickness and loading noise contributions) are computed through integrals on the moving blades’ surface (impermeable/rigid surface formulation). The computational acceleration is obtained by a parallel execution via the MPI API. The simulation of the aeroacoustic freefield was carried out by using the aerodynamic database evaluated by RAMSYS, and consisting of the rotor blade pressure distributions.
3.2. DLR
The freewake panel method UPM [3][16][17] is based on a velocitybased, indirect potential formulation using a combination of source and vortex distribution on the solid surfaces and vortex panels in the wake. Compressibility effect of the flow are considered by applying the PrandtlGlauert correction. The blade vortex interaction (BVI) is captured thanks to the free wake model used in UPM. Depending on the configurations, all interactions among rotors, rotor, pylon are considered. The validation effort is supported by CFD TAU steady simulations on selected hover test cases. The unstructured CFD code TAU is based on the solution of the Reynolds averaged NavierStokes equations on hybrid unstructured meshes. The solver uses a cell vertex scheme to discretize the mass, momentum and energy fluxes [18]. In the current paper, the secondorder accuracy central scheme was used for spatial discretization. Scalar dissipation has been used as the central dissipation scheme. The temporal discretization is based on an explicit Runge–Kutta scheme. As turbulence model, the twoequation turbulence model Menter SST was used. Furthermore, all surfaces were simulated fully turbulent.
The Aeroacoustic Prediction System based on an Integral Method, APSIM [19], is designed to calculate wave propagation over large distances in uniform flows. The methodology is based on FfowcsWilliams/Hawkings (FWH) formulation [32] and only linear sound propagation is considered. In general, the aeroacoustic computation into the far field is split into two steps for current applications: In a first step the pressure data on the rotor is computed by aerodynamic codes and provided to APSIM; in a second step the sound propagation into the far field is calculated with APSIM. Validations of UPM, TAU and APSIM were intensively conducted during various projects.
3.3. ONERA
The aerodynamic simulations performed by ONERA are realized with the PUMA code [21]. PUMA (potential unsteady methods for aerodynamics) is an unsteady lifting line / freewake solver developed at ONERA since 2013. It is built on a coupling between an aerodynamic module and a kinematic module. The aerodynamic module relies on a lifting line method with a freewake model using the Mudry theory [20], which describes the unsteady evolution of a wake modeled by a potential discontinuity surface. The lifting line method relies on twodimensional airfoils characteristics through lookup tables computed preliminary by CFD with the ONERA elsA11 code [22]. Some blade sweep correction and dynamic stall models are added. Concerning the kinematic module, it is based on a rigid multibody system approach using a treelike structure with links and articulations. It enables any arbitrary motion between the different elements. To speed up the computation the code has been parallelized using OpenMP and the Multilevel Fast Multipole Method has been implemented.
Concerning the numerical parameters used for the computations, they are based on previous experience. The lifting line is divided in 30 radial stations using a square root distribution. A time step of 5° was used over 25 rotor revolutions over which the last 6 are used for postprocessing. The computations do not account for the rotor hub or other test rig components.
The unsteady spanwise distribution of loads obtained with PUMA are used as input for the KIM code [23][24] to determine the noise emission of the rotor thanks to a FfowcsWilliams and Hawkings formulation implemented in a noncompact advanced time approach. Since only sectional forces are available and in order not to consider noise sources compacted in the chord direction, the surface pressure is reconstructed over the entire blade thanks to interpolation based on the pressure distributions computed and stored during the airfoil polar computations.
3.4. Polimi
The single propeller case was simulated with a midfidelity and a highfidelity aerodynamics solver, respectively DUST and SU2. DUST is an opensource software developed by Polimi to simulate the interactional aerodynamics of unconventional rotorcraft configurations. The code, released as free software under the opensource MIT license, relies on an integral boundary element formulation of the aerodynamic problem and a vortex particle model of the wakes [25]. SU2 is an opensource toolkit distributed by the SU2 Foundation [27], freely available and licensed under the GNU Lesser General Public License. It uses the finite volume approach to solve partial differential equations (PDE) on unstructured meshes. It solves the Unsteady Reynoldaveraged NavierStoke (URANS) equations to analyze typical aeronautical problems that involve turbulent flows in the compressible regime. Aerodynamic results obtained with both solvers are not trimmed. The aeroacoustic signature is computed by solving Ffowcs WilliamsHawkings[32] (FWH) equations. The surface pressure field on the propeller computed with the two solvers is provided as input to the same acoustic module [28]. The pylon for both DUST/SU2 simulations is not modelled.
3.5. Roma Tre University/CNRINM (ROMA3)
The RM3 aerodynamic and aeroacoustic analyses rely on tools developed by the Roma Tre University unit in the last twenty years and widely validated in the past in helicopter and tiltrotor configurations [29][30]. The aerodynamic module is based on the boundary integral formulation for the velocity potential presented in [31], suited for helicopter configurations where bladevortex interaction (BVI) occurs. This formulation is fully 3D, can be applied to bodies with arbitrary shape and motion, and allows the calculation of both wake distortion and blade pressure field. It assumes the potential field to be divided into an incident field, generated by doublets over the wake portion not in contact with the trailing edge (far wake), and a scattered field, generated by sources and doublets over the body and doublets over the wake portion very close to the trailing edge (near wake). This procedure allows one to overcome the instabilities arising when the wake comes too close to or impinges on the body. Recalling the equivalence between the surface distribution of doublets and vortices, the contribution of the wake portion experiencing BVI (far wake) is expressed in terms of thick vortex (i.e., Rankine vortices) distributions. The shape of the wake can be either assigned (prescribedwake analysis) or obtained as a part of the solution (freewake analysis) by a timemarching integration scheme in which the wake is moved accordingly to the velocity field computed from the potential solution. Once the potential field is known, the Bernoulli theorem yields the pressure distribution on the body that, in turn, is used both to determine the aerodynamic loads and as an input to the aeroacoustic solver to predict the radiated noise.
The aeroacoustic analysis is performed by a prediction tool based on the Ffowcs Williams and Hawkings equation (FWH) [32]. The solution of the FWH equation is achieved through the boundary integral representation known as the Farassat Formulation 1A [33].
3.6. Uni Stuttgart (IAG)
For highfidelity simulations, a framework consisting of FLOWer and ACCO was used at the Institute of Aerodynamics and Gas Dynamics (IAG) at the University of Stuttgart. CFD results are obtained with the blockstructured code FLOWer, originally developed by DLR [34] and continuously extended at the IAG for rotorcraft and multirotor applications [35]. Acoustic coupling was provided by IAG’s FWH solver ACCO [36] which uses the transient flow data provided by FLOWer as an input.
FLOWer solves the threedimensional, compressible RANS equations and enables unsteady flow solutions (URANS). The discretization of time and space is applied separately by the method of lines. For temporal discretization a secondorder dual time stepping is used [37] with a time step of 0.5° to resolve acoustic waves, while for spatial discretization a 5th highorder weighted essentially nonoscillatory (WENO) scheme by Borges [38] is used. Furthermore, the komega turbulence model was applied to close the URANS equations. Using the Chimera technique separate meshes were created for the background and rotor, utilizing hanging grid nodes to reduce the numerical expense. The spatial resolution of a single rotor was achieved by 6.6 million cells. The rotor surface was meshed with 144 cells in radial and 80 cells in chordwise direction with a refinement towards the blade tip, leading edge and trailing edge with cell sizes of less than one thousandth of the radius. The rotor mesh is extruded in wall normal direction with 52 cells. The first surface cells satisfy y + < 1 and an extrusion up to cell sizes corresponding 10% of the chord length is applied. The spatial discretization in the background mesh was based on the resolution of the first harmonic wave length, with 15 cells discretizing the wave length of the blade passing frequency (BPF).
The acoustic code ACCO is an inhouse code of the IAG, which uses an acoustic integration surface for the generation of sound emissions. For the integration either the physical surfaces or a permeable surface surrounding the object of interest can be used. For the performed simulations, the physical blade data of 4 full rotor revolutions are used and the integration is achieved through the physical surface of the rotor blade, which includes all tonal sound sources.
3.7. UoG (University of Glasgow, Glasgow)
Helicopter MultiBlock (HMB3) code is employed in this study. The solver can accurately predict the aerodynamic performance, acoustics of propagation, and has been widely used in the investigation of rotorcraft flows [41], helicopter rotor aeroelasticity [42], and missile trajectory prediction [43]. Moreover, a good agreement when compared to experimental results in aerodynamics, acoustics and aeroelasticity of propellers, can be seen in a previous study [44]. Most recently, its ability to capture the interactions of multirotor flows and ducted propeller flows was documented [45]. HMB3 solves the Unsteady Reynolds Averaged NavierStokes(URANS) equation in integral form using the Arbitrary LagrangianEulerian formulation for timedependent domains, including moving boundary layers. HMB3 uses a cellcentred finite volume approach to discrete NavierStokes equations on multiblock, structured grids. The 3rdorder MUSCL (Monotone Upstreamcentered Schemes for Conservation Laws) approach is applied to provide highorder accuracy in space. In the present work, simulations are performed with the k − ω shear stress transport (SST) [46]turbulence model.
Regarding acoustics, the present work estimates the nearfield information derived from pressure fields computed with the highfidelity HMB3 tool. The sound pressure signal was obtained by subtracting the timeaveraged pressure from the timedependent data. All CFD grids are designed to have at least 20 cells in the nearfield region to capture the target wavelength, which is calculated based on four times the Blade Passing Frequency (BPF = 400 Hz). approach has also been applied in previous work by Smith [47].
3.8. Summary
The numerical methodologies used in the group are summarized in Table 1.
Table 1
Main Characteristics of the codes used by the partners For a midfidelity aerodynamic tool based on potential formulation and free wake, the specific number of panels on the blade and pylon utilized in this paper is listed in Table 2. The numbers are derived according to the convergence of the code results.
Partner

Code

Description

CIRA

RAMSYS, ACOsuite

Unsteady, inviscid and incompressible freewake Boundary Element Method (BEM), Ffowcs Williams /Hawkings (FWH)

DLR

UPM, TAU APSIM

Free Wake Panel method, unstructured CFD, FWH

ONERA

PUMA, KIM

Unsteady lifting line / freewake solver, FWH

Polimi

DUST, SU2

Free Wake Panel method and unsteady, compressible (URANS) CFD, FWH

RomaTre
University

RM3

Free wake boundary element method (BEM) + FWH

Uni Stuttgart

FLOWer, ACCO

Flower: unsteady, compressible (URANS) CFD solver with Chimera technique, FWH Solver with sourcetime dominant algorithm

UoG

HMB3HFWH

HM3 CFD solver, FWH coupled with HMB3

For a midfidelity aerodynamic tool based on potential formulation and free wake, the specific number of panels on the blade and pylon utilized in this paper is listed in Table 2. The numbers are derived according to the convergence of the code results
Table 2
Summary of the numerical resolution for mid fidelity aerodynamic tool used by the partners The summary of CFD grids utilities is given in Table 3.
Partner

Panel per Blade

Panel per Pylon

Time step
ISO/Multi

Num. of revs
ISO/Multi

DLR UPM

1624

1470

5°/2°

16/8

CIRA RAMSYS

1450

1392

2°/2°

9/9

ONERA PUMA

N.A.

No Pylon

5°/5°

25/25

Polimi DUST

1050

No Pylon

3°/3°

15/15

ROMA3 RM3

3150

No Pylon

3°/3°

20/20

The summary of CFD grids utilities is given in Table 3.
Table 3
Summary of CFD grids used by the partners
Partner

Grid Cells
Rotor
(Million)

Grid Cells
Total
ISO/Multi
(Million)

Time step
ISO/Multi

Num. of revs
ISO/Multi

DLR TAU

N.A

34.2

stationary

stationary

IAG
FLOWer

6.6

14.3/24

0.5°/0.5°

25/25

Polimi
SU2

15

30

1°/1°

20/20

UoG

4.7

18.3

1°/2°

10/10
