Isolated propeller aeroacoustics at positive and negative thrust

Using propellers in negative thrust conditions can potentially result in many beneﬁts, such as a steeper descent, a reduced landing run, reduced community noise, energy regeneration, etc. However, the aerodynamics and aeroacoustics of propellers in this regime are not well understood. This paper presents an aeroacoustic analysis of an isolated propeller operating in both positive and negative thrust conditions, using scale-resolved lattice-Boltzmann very large eddy simulations and the Ffowcs Williams & Hawkings analogy. The propeller was operated at a constant tip Mach number so that any diﬀerences in tonal noise between positive and negative thrust conditions were due to changes in blade loading. Results showed that the ﬂow separation around the blades in the negative thrust case led to a 2 to 6 times higher standard deviation in integrated thrust compared to the positive thrust case. The blade loading in the negative thrust case shows the amplitude of ﬂuctuations up to 18% for inboard sections and up to 30% near the blade tip compared to the time-averaged loads. The noise in the propeller plane is 10 dB higher in the positive thrust regime than in the negative thrust regime at a given absolute thrust level of | 𝑇 𝐶 | = 0 . 08 . The lower noise at negative thrust is caused by two factors: the lower magnitude of the negative torque compared to the positive torque at a given thrust level and the shift of the blade loading inboard in the negative thrust condition due to the stall of the blade tip. Along the propeller axis, the negative thrust regime has 13-15 dB higher noise because of the increased broadband noise generated by the ﬂow separation. In the negative thrust case, the noise along the propeller axis (89 dB) and propeller plane (92 dB) are comparable. However, this is not the case for the propulsive case. The comparison of noise in the vicinity of the propeller plane showed that using the propellers in negative thrust conditions allows for a steeper and quieter descent compared to a conventional descent; as long as the magnitude of the negative torque produced is equal to or less than the torque required to operate the propeller in a conventional landing.


Introduction
The increasing need for sustainable aviation has triggered many new technologies in the field of aviation.The use of fuel cells, hydrogen combustion, and electric architectures are a few examples of these technologies.These technologies are generally coupled with open rotors because of their high propulsive efficiency (up to moderate Mach number and at low cruise altitudes) [1] to increase the system's overall performance.One additional benefit of electric propulsion is that propellers can be operated at a negative thrust settings that can be beneficial for achieving steeper descent, reduced landing run, better  .Velocity triangles at a fixed-pitch propeller blade section in positive and negative thrust modes [6].

𝐵
aerodynamic brakes [2,3], the concept did not gain much attention.It became relevant again with the advent of electric flight and its potential as a control device for the descent/landing phase.For a typical aircraft configuration, the propeller design is expected to be dominated by the propulsive phases, i.e., climb and cruise.Therefore, operation in the negative thrust mode will represent an off-design condition.In previous papers [6][7][8], the aerodynamic phenomena of a conventional unducted propeller in the negative thrust regime have been investigated using RANS simulations and experiments.These studies have shown that negative thrust conditions lead to almost fully separated flow around the blades of a conventional propeller.Due to limi-tations in terms of the extent of instrumentation, the experiments give limited information about the flow characteristics near the propeller blades and in the slipstream.Also, RANS simulations face difficulty in accurately predicting the flow separation due to the limitations of turbulence modeling [9,10].Therefore, higher-fidelity numerical simulations are needed to overcome these challenges.Such simulations can also provide information about the unsteadiness of the flowfield, which is expected to be relevant for aerodynamic and aeroacoustic interaction with a lifting surface immersed in the propeller slipstream.
Further, the literature on the aeroacoustics of propellers operating in the negative thrust regime is almost nonexistent.To the authors' best knowledge, only two studies [4,7] exist that investigated the aeroacoustics of negative thrust propellers.In the ref.[4], the rotor aeroacoustics were not investigated in detail; instead, the main focus was the potential impact on community noise.In the ref.[7], only tonal noise characteristics were investigated using an analytical model (Hanson's model [11]), and no assessment was made for the broadband noise.As the propeller operates in the stall or near stall conditions in the negative thrust regime, it is expected that the relative importance of the tonal and broadband noise will change along with noise directivity and noise level compared to the propulsive regime.The flow separation on the blades could lead to a dominant broadband noise and even structural vibrations and associated structure-borne noise.However, no paper on these research gaps can be found in the literature.
This paper aims to investigate the aerodynamics and far-field acoustic characteristics of a conventional propeller operating in the negative thrust regime using lattice-Boltzmann (LB) very large-eddy simulations (VLES) coupled with the Ffowcs Williams and Hawkings (FWH) integral solution based on Farassat's formulation 1A [12].The numerical setup has been validated using experimental data from ref. [8].An analysis has been done at a constant freestream and tip rotation Mach number by varying propeller pitch to characterize the aerodynamics and aeroacoustics of the propeller at equal Mach number and Reynolds number in both positive and negative thrust regimes.

Computational setup
The numerical setup was validated with the experimental data from ref. [8].The data available from the experiments dictated the geometry and operating conditions used during the validation.For the subsequent analyses, the operational conditions were modified to be more similar to those experienced in free flight.The rotor geometry is given here first.Then, the methodology is explained, along with the computational setup.

Rotor geometry
The rotor used in this study is TUD-XPROP, which is a scaled version of a propeller for a previous-generation regional turboprop aircraft.The rotor has a diameter of 0.4064 m and a hub diameter of 0.092 m.The nacelle of the rotor extended up to approximately 1.6 downstream.Originally, the propeller had six blades; however, only three blades were used for this study due to limitations of the experimental facility [8].The propeller can be seen in Fig. 2a along with its geometry parameters in Fig. 2b.

Methodology
LB-VLES simulations have been chosen for this study for two main reasons.The first reason is the method's past proven record for capturing the tonal and broadband noise in similar applications [13,14].Secondly, due to the low dissipation and dispersion [15,16], the LB-VLES simulations were deemed suitable for this study.A detailed description of the LBM can be found in the refs.[17] and [18].For the simulations, the beta version of the commercial solver PowerFLOW 6-2021 by 3DS Simulia has been used, which has been introduced in ref. [19].This beta version is especially suitable for the current application as it does not require a zig-zag trip to switch to the scale-resolving solver.Using a zig-zag trip can modify the flow separation and the broadband noise behavior [20,21], which is relevant for this research and, therefore, a change in behavior due to the artificial introduction of turbulence is not desired.The volume of the domain is discretized using a Cartesian mesh.In total, 19 discrete velocities are used in three dimensions (D3Q19) for this study, including a third-order truncation of the Chapman-Enskog expansion.An explicit time integration approach is used to solve the equations at the Courant-Friedrichs-Lewy (CFL) number of 1 for stability.The particle distribution is obtained using a collision term based on a unique Galilean invariant [22], and equilibrium distribution of Maxwell-Boltzmann [23].A very-large eddy simulation (VLES) model is implemented in PowerFLOW to take into account the effect of the subgrid unresolved scales of turbulence, which uses  −  renormalization equations [24] to compute the turbulent relaxation time.The no-slip boundary condition on walls is approximated using a pressure-gradient extended wall model [25,26].The model is based on an extension of the generalized law-of-the-wall model [27] to take into account the effect of the pressure gradient on the boundary layer development.
A hybrid CFD/CAA approach has been used in this study to compute the far-field noise.Such an approach is an ideal solution to avoid excessive computational costs related to resolving the propagation of acoustic waves to the far field.The FWH analogy was solved based on the forward-time solution [28] of Farassat's formulation 1A [12] using the post-processing software SIMULIA PowerACOUSTIC.This formulation includes surface integrals, i.e., acoustic monopoles (thickness noise) and dipoles (loading noise) terms.The volume integral, i.e., quadrupole term, is neglected in this formulation which accounts for the non-linear effects in the volume surrounding the integration surface.The quadrupole term was assumed to be negligible for the operating conditions considered in this paper as the convective Mach number of the propeller wake is less than 0.3 [29].

Computational volume and boundary conditions
The computational domain is a cube with a domain size of 128 in all three directions (Fig. 3a).The boundary conditions were specified as a velocity inlet combined with a pressure outlet and slip walls.It was made sure that the total pressure profile was uniform at the inlet.Due to the large size of the domain, the impact of the boundary conditions on the solution is expected to be minimal.The no-slip condition was used for the propeller blades, spinner, and nacelle.For sliding mesh, a volume of revolution was defined around the propeller blades and spinner.In the radial direction, a clearance of 0.1 was defined between the blade tip and the outer edge of the rotating domain.Similarly, in the axial direction, a clearance of 0.05 was defined between the spinner edge and the edge of the rotating domain.In total, 13 variable resolution (VR) regions were used based on the ref.[30].The cell volume changes by a factor of 8 between different VR regions.The finest three VR regions (VR13-11) were used around the propeller to accurately capture the flow around the propeller blades, as marked in Fig. 3b.VR10 was used in the sliding domain and downstream of the sliding domain up to 0.5.Further downstream, VR10 is used in a hollow cylinder to capture the strong gradients of tip vortices.VR9 was used in the cylinder encapsulating the propeller blades, spinner, and blade with a radius of 1.2 and extended 1 upstream and 3.5 downstream of the propeller.Other VR regions (1)(2)(3)(4)(5)(6)(7)(8) were there to ensure that the domain was large enough to minimize any spurious acoustic reflections from the boundaries of the domain.Further, an acoustic sponge was used to absorb any remaining acoustic reflections coming from the boundaries by exponentially varying the kinematic viscosity per unit temperature from 0.005  2 ∕(.) at 15 up to 0.5  2 ∕(.) at 30 as shown in Fig. 3a.As the acoustic sponge starts at a 15 distance from the propeller, its effect on the aerodynamic results is assumed to be minimal.

Grid dependence study and comparison with experiments
For the grid dependence study, two operating conditions have been chosen with a pitch angle of 15 • at 0.7 of the blade, for which extensive experimental data were available for validation [8].The two conditions were chosen as the most challenging ones to reproduce numerically.The first one is a positive thrust condition with a moderate thrust at an advance ratio ( ) of 0.60.The given pitch angle is not optimal for propulsive operation and leads to separation near the trailing edge [7].Therefore, if the grid results are converged for such an operating condition, it can be safely assumed to be converged for other positive thrust conditions with fully attached flow.However, the grid convergence in the positive thrust regime does not ensure the convergence in the negative thrust regime because of significant flow separation around the blades in that condition [6,7].The second condition is the negative thrust condition at  = 1.10, close to the maximum power output point.The details of these operating conditions can be found in Table 1.
Five different grids were compared for the grid dependence study with fine equivalent voxels varying from 1 million to 100 million, based on the previous study by Avallone et al. [30].The fine equivalent elements represent the number of elements (N) weighted by the time stepping rate, which is proportional to the mesh resolution level (VR level) and is calculated as follows: The details of the grids can be found in Table 2, where resolution is defined as the number of fine equivalent voxels per characteristic length.
The characteristic length is chosen to be chord at 0.7 blade span, which is approximately 31 mm.The setup was defined such that the blade-passing period of the propeller was an integral multiple of the time-step, which helps to avoid interpolation error in phase-locked and per-rotation averaged measurements.As the rotational speeds of the propeller are different at the chosen operating conditions, the chosen time-step is also different, resulting in a different resolution and mesh sizes.The flow was simulated for twelve revolutions for the medium grid (Grid 3) and used for seeding all the other resolutions.All the other resolutions were simulated for ten revolutions.For all the grids, the last eight revolutions were used for the measurements after ensuring that the transient period was over.

Convergence and validation study of aerodynamic properties
The integrated performance parameters, thrust coefficient   and power coefficient   , were used to verify the convergence of the in-   tegrated performance of the propeller and were compared with the experimental values.Further, the radial distributions of the time-averaged total pressure coefficient have been used to verify the convergence of the slipstream flowfield.Additional validation of the setup has been performed by comparing the phase-locked axial and tangential velocity fields in the slipstream with the experimental data.

Integral performance parameters
The Fig. 4 shows the   and   time-averaged over the last eight revolutions for the different grids compared to the experimental value.
The uncertainty of the experimental data is indicated using the shaded areas around the mean results.The standard deviation of the simulated thrust values is also shown using the shaded areas with an averaging period of six revolutions to provide a measure of the load fluctuations over the averaged rotations.The trends of the grid-dependence study have been supported with the help of skin friction contours and shearlines along the blade surface shown in Fig. 5 for the fine grid (Grid 2).The streamlines are also shown around three blade sections at radial coordinates of 0.3, 0.6, and 0.9, respectively.
In the positive thrust condition shown in Fig. 4a, the experimental thrust coefficient has an uncertainty of 2.5%, and the power coefficient has an uncertainty of 1.5%.The standard deviation of the simulated values is almost negligible, indicating the steadiness of the loads on the propeller blades.It is observed that   stays almost constant for Grid 4, Grid 3, and Grid 2 (coarse, medium, and fine, respectively).However, for Grid 1 (very fine), the thrust coefficient is increased by approxi-Fig.6. Radial distributions of time-averaged total pressure coefficient at 0.15 downstream of the propeller center.mately 4% compared to Grid 2, 3, and 4.This trend can be explained as follows.As the propeller is operating at a comparatively low Reynolds number (3.5 × 10 5 based on the propeller chord at 0.7), a leading-edge separation bubble exists on both sides of the propeller blade as can be seen in Fig. 5a.The blade sections between 0.4 -0.7 radial coordinate are on the verge of the trailing-edge separation on the pressure side, as indicated by the outward motion of shearlines at these locations.However, the prediction of the location of the separation bubble along the chord is very sensitive to the resolution of the boundary layer ( + ) besides the other parameters, such as incoming turbulence, surface roughness, and subgrid-scale modeling [31][32][33][34].For such cases, having  + ≤ 1 would be the ideal solution.However, as octree meshes are used in PowerFLOW, it becomes practically challenging to reach such  + values.Upto Grid 2, the  + values are greater than 20 on almost the whole blade surface on the suction side (front), see Table 2.However, the  + values are below 20 for Grid 1, which improves the prediction of laminar to turbulence transition [19], leading to a better thrust match with the experimental value for Grid 1 (very fine).The differences in the predicted trailing and leading edge separations along the blade span between different grids result in fluctuations in power coefficient (  ) values between Grid 3, 2, and 1.The   predictions by LBM simulations are in good agreement with the experimental thrust for all the grids except Grid 5.However, the prediction of   is off by 10-11%., indicating that the drag is underpredicted by the LBM simulation leading to a low power value.
For the negative thrust condition shown in Fig. 4b, the uncertainty in experimental measurements and the standard deviation of simulation values are less than 1%.The convergence of thrust and power is achieved for the fine grid (Grid 2) with 10% underprediction in thrust and 10% overprediction in power compared to the experiment.The significant difference in the simulated integrated performance compared to the experimental data comes from the fact that there is a leadingedge separation bubble on the suction side (back) around the blade sections starting from the root until the radial coordinate of 0.85, see Fig. 5b.Further outboard, the blade sections are fully separated.It is known from literature [31][32][33][34] that even the separation-bubble length is very sensitive to subgrid-scale modeling and grid quality, making it extremely difficult to capture this condition accurately in the numerical simulation.Moreover, the low Reynolds number in this operating condition (2.0 × 10 5 based on the propeller chord at 0.7) results in a trailing-edge separation on the pressure side (front) of the propeller blade.As there is a significant difference in the extent of flow separation between the two regimes (Fig. 5), Grid 2 was considered good enough to understand the relative change in aerodynamic and aeroacoustic characteristics between the positive and negative thrust regimes.
The slipstream characteristics have been compared with the experimental data in the next subsection to scrutinize further the results obtained from LBM simulations.The very coarse grid (Grid 5) has been omitted in further comparisons to keep the discussion clear and concise.

Slipstream
The radial distributions of the time-averaged total pressure coefficient obtained from LBM simulations in the slipstream at 0.15 downstream of the propeller (Fig. 6) have been compared with the experimental data [8] to evaluate the validity of LBM simulations.For  = 0.60 in Fig. 6a, the total pressure coefficient profile is similar for different grids except between the radial coordinate of 0.5 -0.7.Besides the fluctuating peak values at the radial coordinate of 0.6 between different grids, the medium grid shows different radial gradients between 0.5 to 0.6.This is expected to be a consequence of the presence of a leading-edge separation bubble along with the trailing-edge separation onset as shown in Fig. 5a.At this operating condition, the blade tip is negatively loaded due to local negative angles of attack (Fig. 6a), as explained by ref. [8].The experimental data shows a negative total pressure coefficient for 0.92 ≤ ∕ ≤ 1.However, in the simulations, the total pressure coefficient is negative only between 0.98 ≤ ∕ ≤ 1, resulting in a lower power requirement for a given thrust.The simulations underestimate the maximum value of the total pressure distribution, which is offset by overestimation in the outboard sections, resulting in a thrust value close to the experimental value.Thus the blade loading distribution obtained from the simulations is expected to differ from that obtained in the experiments.Fig. 6b shows the time-averaged total pressure profile for the negative thrust condition ( = 1.10).Looking at the convergence behavior, it is evident that the slipstream converges to a similar profile for fine and very fine grids.Except near the root (below the radial coordinate of 0.4), the total pressure distributions are similar in terms of gradients in the radial direction between simulations and experiments.Quantitatively, the total pressure distribution over the 10% most outboard blade radius matches with the experiment.At 40%-90% of blade radius, there is an overprediction of the total pressure, which agrees with the underprediction of the negative thrust observed in Fig. 4b.As the blade tip is completely separated (Fig. 5b), it is comparatively easier to predict in numerical simulations than a separated region with reattachment.It results in a good agreement for the outboard blade span for all the grids.However, the blade span between the root and the radial coordinate of 0.85 has separation at the leading edge with reattachment near the trailing edge.As the reattachment location is sensitive to the grid, it results in differences between the simulation and the experiment [31][32][33][34].
The gradients of total pressure coefficient profiles in the radial direction are almost insensitive to the choice of the considered grids for both positive and negative thrust regimes, except for the medium grid between 0.5 -0.6 for the positive thrust condition.Based on these compar- In Figs.8a and 8b, the velocity gradients near the tip vortices are larger in LBM simulations compared to the PIV data, and the tip vortices are shifted slightly outwards in the LBM results compared to the PIV data.These differences could originate from the slightly different blade loading.Such differences would lead to a difference in the local velocity in the slipstream, which means that the flow structures would also convect downstream at different velocities.Since the contours are shown at a fixed streamwise position in Figs.8a and 8b, their position relative to the flow structures would differ, resulting in a relatively large offset in induced velocities.Other reasons could be a possible uncertainty in the blade position or minor inaccuracies in the calibration of the PIV setup leading to a slight displacement of the data with respect to the actual physical coordinates.The line plots show that the gradients in the radial direction are adequately captured by LBM simulations, though the peak is slightly underpredicted, which is consistent with observations from Fig. 6.
Fig. 9 shows the same comparison for the negative thrust condition.The edge of the slipstream is at a higher radial coordinate in the LBM results compared to the PIV data, as seen in the contours and the left-down corner line plot (∕ = 0.7).Again the gradients in the radial direction from the LBM data are in agreement with the PIV data.LBM simulations overpredict the peak of phase-locked axial velocity compared to experiments at ∕ = 0.1 (Fig. 9a), which contradicts the time-averaged total pressure profile seen in Fig. 6b and the time-averaged axial velocity results shown in Fig. 10a.This apparent inconsistency is suspected to be a consequence of uncertainty in the phase-locked blade position in the experiment.To validate this hypothesis, a new comparison with the phase-locked PIV data at ∕ = 0.1 is shown with arbitrary phase angles of 1 • , 2 • , and 5 • in Fig. 10b.The LBM simulation no longer overpredicts the peak at ∕ = 0.1; instead, there is an underprediction that agrees with Fig. 10a, supporting the validity of the hypothesis.
Based on the comparison of the total pressure coefficient and axial and tangential velocities in the propeller slipstream, it has been proven that the fine grid (Grid 2) is able to predict the slipstream characteristics in terms of gradients in the radial and axial direction.Thus the fine grid is deemed suitable for the further comparison of the aerodynamic characteristics of the positive and negative thrust regimes.

Convergence study of far-field aeroacoustics
As the dominant noise sources are anticipated to be within the first 10 BPFs [35], the aeroacoustic convergence has been determined by comparing the directivity patterns of overall sound pressure level (OSPL) for the range of 0.5 -10 BPF.As LBM simulations work with a cartesian mesh, the three blades of the propeller have different discretization resulting in a different blade loading.This difference was up to ±4% for the positive thrust condition ( = 0.60) compared to the blade-averaged loading and up to ±1% for the negative thrust condition ( = 1.10).This difference in the blade loading leads to tonal noise at a frequency of (1/3) times the BPF in the power spectrum density (Fig. 12b); therefore, the lowest frequency is chosen to be 0.5 BPF to eliminate the contribution from this numerical noise source.The OSPL was calculated using the FWH analogy on a ring with a radius of 20, with the axis aligned with the propeller plane and the center coinciding with the propeller center to ensure that the observer is in the far field.The OSPL directivity patterns for both configurations are shown in Fig. 11.The trends are shown for half of the ring ( = 0 • − 180 • ) because of the axisymmetric inflow condition, where  = 0 • lies along the propeller axis in front of the propeller and  = 90 • lies in the propeller plane.Additionally, the power spectrum density (PSD) is shown for the fine grid (Grid 2) in Fig. 12 for two locations -propeller plane ( = 90 • ) and propeller axis ( = 0 • ).
For the positive thrust condition (Fig. 11a), the OSPL between 45 • and 150 • is almost identical between the different grids with differences below 1 dB as a consequence of similar blade loading along the blade span.For the negative thrust condition (Fig. 11b), the difference in OSPL for different grids is below 1 dB at all the directivity angles except the coarse grid.In the propeller plane, tonal noise is the most dominant noise source, as seen in Fig. 12b.Since there are minute differences in blade loading between different grids, as previously shown in Fig. 6, the match of OSPL levels in the propeller plane between different grids is an expected trend.In the propeller plane, the first three BPFs are dominant for the positive thrust condition compared to only the first BPF in the negative thrust condition; see Fig. 12b.The 1/3 BPF caused by the different meshing of the three blades of the propeller is about 25-30 dB lower than the first BPF and thus did not affect the interpretation of the aeroacoustic results.
The broadband noise is expected to be the most dominant source along the propeller axis [35], which is indeed the case (Fig. 12a) for the given operating conditions.In the positive thrust condition, the main sources of broadband noise are expected to be trailing-edge noise and vortex shedding due to flow separation (Fig. 5a).The prediction of broadband noise levels is sensitive to the resolution of the relevant turbulent scales.The coarse grid does not sufficiently resolve these turbulent scales, resulting in low (broadband) noise along the propeller axis.However, the medium and the other grids are fine enough to capture these effects, as visible in OSPL levels.The OSPL increases from the medium to the fine grid due to the better resolution of the turbulence on the latter.A further refinement in the grid results in a decrease of 3 dB along the propeller axis from the fine grid to the very fine grid.Therefore, there is an oscillatory convergence.For noise along the propeller axis, prediction within 3 dB is considered enough for this study.Flow separation is the main source of broadband noise for the negative thrust condition.Due to strong flow separation in this condition (Fig. 5b), the turbulent scales are expected to be larger than for the positive thrust    case.The medium and finer grids predict similar noise levels along the propeller axis with differences below 1 dB.
In the positive thrust condition, the noise in the propeller plane is about 12 dB higher than the noise along the propeller axis, which is an expected trend for conventional operation.However, the trend is reversed for the negative thrust condition, i.e., the noise along the propeller axis is 11-12 dB higher than the noise in the propeller plane.This change in directivity is because of two reasons: a) the flow separation in the negative thrust condition significantly increases the broadband noise compared to the positive thrust condition (4-7 dB along the propeller axis); b) lower tonal noise in the negative thrust condition compared to the positive thrust condition (20 dB in the propeller plane), because of the lower blade-tip rotational Mach number and the lower absolute blade loading.
From the above comparisons, it is observed that the fine grid (Grid 2) is able to determine the changes in the noise source characteristics between the positive and negative thrust regimes.Hence, it is considered good enough for further analysis.

Results
A propeller operating at a constant speed was used to study the far-field aeroacoustics of the negative thrust regime compared to the conventional positive thrust regime.Given the constant helical tip Mach number, the thickness noise does not change between the operational modes; therefore, it is easier to identify the changes in various noise sources due to the change in thrust and power (both direction and magnitude).The operational conditions were chosen based on a preliminary mission analysis of an ATR-42 aircraft with a relatively steep descent

Table 3
Operating conditions used for the analysis.
0.29 0.74 (5.5 • ) and are listed in Table 3.The resulting chosen freestream Mach number was 0.29 and the helicoidal tip Mach number was set to 0.74 to achieve reasonable similarity with a full-scale turboprop propeller.
For this study, the simulations were performed at 0 • angle of attack with respect to the propeller so that there was no periodic unsteady loading on the blades.In a realistic configuration, this would be an additional noise source.However, it was decided to eliminate this noise source in this study for ease of interpretation of the results.The pitch angle of the blade was changed from 10 • to 45 • with a step of 5 • to vary the propeller loading.As the propeller is operated at a fixed advance ratio ( = 1.34), there was only a single operating point at which the propeller operated at its peak efficiency for the selected advance ratio.However, this was deemed acceptable because a difference in tip Mach number would affect the comparison more significantly than the obtained differences in propeller efficiency.An additional pitch setting with  0.7 = 37.57 • was evaluated to match the absolute thrust obtained at  0.7 = 20 • , which has been used to evaluate the changes in noise sources due to the change in the operating regime (negative to positive thrust condition).The choice of  0.7 = 20 • as the reference for comparing the two regimes at an absolute thrust level was based on the earlier-mentioned preliminary mission analysis of an ATR-42 aircraft.

Aerodynamic performance
Fig. 13 shows the differences in the instantaneous flow features around the propeller blades between the positive and negative thrust regimes for   = ±0.08 at 37.57 • and 20 • pitch settings respectively.These figures show the skin friction coefficient contours and shearlines at the blade surface for the two conditions.In addition, streamlines are shown around three blade sections located at 0.3, 0.6, and 0.9.
Fig. 13a shows that the flow is attached along the whole blade span on the back side of the propeller for   = +0.08,except for the inboard sections that exhibit the presence of a separation bubble.The front side of the propeller shows a separation bubble at the mid-chord position, which can also be seen in the streamlines around the 0.3 blade section.This separation bubble is present from the root until around 0.35 and moves towards the trailing edge with increasing radial coordinate.
For the blade sections present outboard of 0.35, the separation bubble extends up to the trailing edge resulting in trailing-edge separation as seen in the streamlines around the blade sections at 0.6 and 0.9.
For the negative thrust condition (  = −0.08), the flow is attached the front (pressure) side of the propeller, except near the trailing on the inboard sections (around 0.8), Fig. 13b.There a trailing edge separation at these blade sections, as also indicated by the streamlines around the 0.6 blade section.the back side of the propeller, the flow is attached only for a small portion of the chord near the leading edge, as indicated by the separation line.This leading-edge separation is a consequence of the operation of the blade sections at high negative angles of attack (as shown using streamlines around 0.3, 0.6 and 0.9).This trend is consistent with previous studies [6,7].

Time-averaged performance analysis
Fig. 14 shows the effect of the varying pitch on the propeller performance.As the advance ratio and freestream Mach number are constant for the analysis, the inflow angle is also constant (31.4 • at ∕ = 0.7, ignoring induction), see Fig. 15.Therefore, the lower the pitch angle, the more negative the angle of attack (AoA).Similarly, the higher the pitch angle, the higher the AoA.For the pitch angles up to 30 • , the blade section at ∕ = 0.7 operates at negative angles of attack.As the pitch angle is increased from 10 • to 30 • , the negative angles of attack at blade sections are reduced, which in turn reduces drag and negative lift.As both lift and drag contribute to the negative thrust, a monotonic trend of   is seen in Fig. 14a.On the other hand, the negative power magnitude is reduced by reducing the negative lift and increased by reducing the drag.The opposite nature of these effects results in a maximum power obtainable at a certain pitch for a given operating condition, around 15 • in this case, as shown in Fig. 14a.The transition from neg-ative to positive power occurs around 27.5 • (Fig. 14a).In the positive thrust regime, the drag component opposes the lift component in the thrust direction, whereas both components contribute positively to the power.As the pitch is increased from 30 • to 45 • , the positive angles of attack increase at the blade sections, increasing lift and drag.Therefore, a monotonic trend is obtained for power in the positive thrust regime.As the flow is still attached around most of the blade for the considered operating conditions (Fig. 13a), the increase in lift is more than the increase in drag, resulting in an increase of   with the increase in pitch angle.Fig. 14b shows the variation in the efficiency of the propeller as a function of the pitch setting.Different definitions of efficiency are used for the positive and negative power regimes.The turbine efficiency (  ), the inverse of the propeller efficiency, has been used for the negative thrust regime.It relates to the shaft power regenerated per unit of negative-propulsive power (  ∞ ) produced, while the propeller efficiency (  ) relates to the propulsive power (  ∞ ) produced per unit of shaft power consumed.A higher turbine efficiency does not necessarily mean higher absolute power regeneration, which can be observed in the current case.The 25 • pitch setting gives the highest turbine efficiency (Fig. 14b), while the 15 • pitch setting results in maximum negative power magnitude (Fig. 14a).At the 25 • pitch setting, the flow is still attached on the inboard part of the blade and is separated only on the outboard part.However, as the pitch angle is reduced to 20 • , the flow is separated around a larger part of the blade span, resulting in a larger drag increase compared to the lift increase.This results in a larger increase in the negative thrust magnitude compared to the increase in the negative power magnitude resulting in reduced turbine efficiency.As the pitch angle is reduced even further, there is no increase in the regenerated power; however, there is a significant increase in the negative thrust, further steepening the turbine efficiency slope.At 30 • pitch, the propeller operates at a very inefficient positive thrust condition due to inboard sections operating in the negative thrust regime (Fig. 14c).
As the pitch angle is increased to 35 • , the propeller efficiency increases significantly (80%).With the further increase of pitch angle, the blade sections operate at higher loading and a sub-optimal L/D ratio, especially at 45 • pitch, where the efficiency drops to 69%.
The thrust distribution along the blade span in Fig. 14c shows that the inboard part of the blade has a higher loading in the negative thrust regime than the positive thrust regime.The higher loading near the root is a consequence of higher absolute AoA at negative thrust conditions leading to higher lift and drag.The loading peak is around a radial coordinate of 0.7 in the negative thrust operations, in contrast to the positive thrust regime, where the maximum is around 0.85.The flow separation around the blade tip shifts the peak inwards in the negative thrust regime; that is why the loading peak is located around 0.8 at

25
• pitch, which shifts to 0.7 at 10 • with the increase in flow separation.A local maximum is observed in the thrust distribution around 0.45 for the 10 • and 15 • pitch settings.The local lift magnitude in the negative thrust cases is negatively influenced by the flow separation (reduced Cl) and positively influenced by the increasing dynamic pressure with the increasing radial coordinate.Around 0.45, the decrease in the lift due to the flow separation is more than the corresponding increase in dynamic pressure due to the increasing rotational speed with the increasing radial coordinate.Though the drag also adds to the negative thrust magnitude, the major contribution comes from the lift (around 80%).Therefore, the local decrease in the lift magnitude results in a local maximum in the thrust distribution at the radial coordinate of 0.45 for 10 • and 15 • deg pitch settings seen in the Fig. 14c.The loading distribution for the 30 • pitch setting shows that the inboard part of the blade operates in the negative thrust regime with AoA lower than the zero lift AoA.In contrast, the outboard part of the blade operates in the positive thrust regime with AoA higher than the zero lift AoA, resulting in a small positive thrust and power overall.
Fig. 14d shows the power distribution along the blade span for different pitch settings.For the positive thrust conditions, the radial loading distribution resembles that of a minimum-induced loss design, with a peak around a radial coordinate of 0.85.For the negative thrust conditions, a completely different distribution is obtained where most of the contribution comes from the inboard section with a relatively flat distribution up to the radial coordinate of 0.6.The power at outboard sections drops to zero and even goes to positive values at the tip.The positive power at the tip, along with the negative thrust, indicates that the tip is separated to the extent that the power is consumed by that specific part of the blade (instead of being extracted from the flow) to drag the tip along with the rest of the blade.As the pitch angle is decreased from 25 • to 10 • , the increased flow separation around the blade tip increases the fraction of the span operating at positive power.The negative power magnitude increases along the whole span from 25 • to 20 • pitch.The further decrease in pitch from 20 • to 15 • only redistributes the power along the blade span.The power contribution from the inboard part of the blade increases and from the outboard part decreases with the decrease of the pitch angle, resulting in almost similar power levels at 15 • and 20 • pitch settings as already seen in Fig. 14a.A further decrease from 15 • to 10 • results in a decrease in negative power magnitude from the outboard sections; however, there is a negligible increase in power from the inboard sections, resulting in a lower negative power magnitude overall.The local maxima around 0.45 can also be seen in the power distribution of the 10 • pitch setting, which results from a decrease in local lift magnitude, as explained before.

Unsteady aerodynamic performance analysis
As the propeller is operating at 0 • inflow angle, the blade loading is expected to be axisymmetric.That is indeed the case for the positive thrust regime as shown in Fig. 16a, in which the radial distribution of instantaneous thrust coefficient ( ′  ) along the blade span is shown as a function of circumferential position.However, the same is not true for the negative thrust regime, as shown in Fig. 16b.It should be noted that the sign of the instantaneous thrust coefficient ( ′  ) has been reversed in Fig. 16b to make the comparison easier with Fig. 16a.The thrust distribution for the 20 • pitch angle shows significant fluctuations over the rotation (amplitude of up to 18% for inboard sections and up to 30% for the blade tip compared to the time-averaged loads).These fluctuations are the result of the flow separation on the back side (suction) of the propeller (Fig. 13b).The high amplitude and frequency of these fluctuations in the negative thrust regime make the blade loads dynamic rather than static.These changes in the loading may have an impact on the structural integrity of the propeller blades in the negative thrust regime.
The effect of the load fluctuations on the integrated thrust performance (from all blades together) is shown in Fig. 17a for a total of six rotations.In the positive thrust regime, the fluctuations in the integrated thrust coefficient are below ±1% of time-averaged thrust coefficient, in contrast to the negative thrust regime fluctuations, which are up to ±3%.The fluctuation in the integrated thrust might lead to additional requirements in the power train due to the excitation of the shaft.The amplitude of these fluctuations depends upon the negative thrust level (or the pitch setting in this case).As the negative thrust level increases (i.e., a decrease in pitch angle in this case), the flow separation around the blades increases, leading to an increase in load fluctuations.Fig. 17b shows the standard deviation of the integrated thrust normalized with the time-averaged thrust value.The average fluctuation amplitude increases from 0.7% to 1.5% as the negative   increases from −0.04 to −0.14.In the positive thrust regime, the sudden increase of the average fluctuation amplitude to 1.2% for   = 0.01 results from the low normalizing value (  ).In contrast to the negative thrust regime, the amplitude of fluctuation is below 0.5% for all the positive thrust conditions.Eventually, the fluctuations in the positive thrust regime would increase once significant flow separation is encountered (at higher pitch settings); however, those settings are considered irrelevant in the current study.

Slipstream
The slipstream in a negative thrust condition is expected to have sigdifferent characteristics than in a conventional positive thrust condition.The time-accurate data in the slipstream was available from simulations with a 5 • resolution for one propeller rotation leading to 72 time instances.From each time instance, three slices aligned with the three propeller blades were extracted.The resulting 216 slices were averaged (given their expected symmetry for uniform inflow) to obtain the final phase-locked results.The phase-locked axial and tangential velocity contours in the propeller slipstream have been compared in Figs.18   As expected, the operation at negative thrust results in decreased axial velocity in the slipstream compared to the freestream condition, whereas the positive thrust results in increased axial velocity.This difference in the axial velocity causes an axial shift of the tip vortex between the two conditions; see Fig. 18a.Also, the radial gradients where the tip vortex cuts the measurement plane are much higher in the positive thrust case than in the negative thrust condition.As the radial gradients due to the tip vortex at ∕ ≈ 1.0 are diffused over a larger region in the negative thrust case, the region with a higher standard deviation is also spread over a larger region compared to the positive thrust case, as can be seen in Fig. 18b.These plots also highlight the difference in the shape of the blade wake and tip vortex between the two thrust conditions.In the positive thrust condition, the blade wake is downstream of the tip vortex due to the increased axial velocity.However, the axial velocity is reduced in the negative thrust condition, leading to the tip vortex being downstream of the blade wake.
From the results shown in Fig. 18, three main inferences can be drawn regarding the nature of fluctuations experienced by a wing surface immersed in such a slipstream.Firstly, an aerodynamic surface immersed in a slipstream at a negative thrust setting would experience reduced dynamic pressure resulting in a reduction in local lift.In contrast, an aerodynamic surface immersed in a slipstream at a positive thrust would experience an increase in local lift.Secondly, as the vortices in the negative thrust regime are expected to be closer to each other due to reduced pitch between the tip vortices (Fig. 18a), this results in more pressure fluctuations over a wing immersed in a slipstream with negative thrust condition than the positive thrust condition over a given axial distance.Lastly, as can be noticed in Fig. 18b, the fluctuations due to the tip vortex are concentrated over a small region compared to the negative thrust condition.Therefore, a wing immersed in a slipstream at a positive thrust condition would experience highamplitude periodic impingement of the tip vortex.On the other hand, a wing immersed in a slipstream at a negative thrust condition would experience comparatively low-amplitude periodic impingement scattered over a comparatively larger area.These inferences will be tested in the follow-up work with the installed configuration.
Fig. 19 shows the tangential velocity in the slipstream.This study defines the tangential velocity as positive in the clockwise direction.As expected, the direction of the propeller-induced swirl is in the direction of the rotation of the propeller (anti-clockwise) in the conventional positive thrust regime, see Fig. 19a.In contrast, as the direction of the torque is reversed in the negative thrust condition, the direction of the propeller-induced swirl is also reversed, i.e., opposite to the propeller rotation.Therefore, the interaction effects with a body immersed in the propeller slipstream operating at negative thrust would be reversed compared to the effects in the positive thrust condition.Moreover, the gradients in the axial direction near the propeller plane are stronger in the negative thrust condition compared to the positive thrust condition.These differences between the two regimes originate from the differences in blade loading distribution resulting in a different vortex system leading to different inductions in the slipstream.Fig. 19b shows the contours of the standard deviation of the phase-locked tangential velocity in the propeller slipstream.The trends are similar to those shown in Fig. 18b, i.e., the strong fluctuations in the tangential velocity are concentrated in the region where the tip vortex cuts the measurement plane.Similar to Fig. 18b, Fig. 19b also shows that the high fluctuation region (around ∕ = 1.0) is spread over a larger region in the negative thrust condition compared to the positive thrust condition.
Fig. 20 shows the radial distributions of time-averaged axial and tangential velocity in the slipstream at 1 downstream of the propeller center.The axial location for the comparison was based on its relevance for an installed case.The radial distributions of axial velocity in Fig. 20a display the expected increase in velocity with the increase in thrust for the positive thrust conditions with pitch settings between 30 • and 45 • .
Similarly, the negative thrust conditions show an expected decrease in axial velocity with the increasingly negative thrust value.The radial distributions of axial velocity for 10 • and 15 • show a local maximum similar to the one seen in the blade loading distributions in Fig. 14c.
In the positive thrust regime, the strong radial gradients of the axial velocity near ∕ = 1 result from the high spanwise gradients of the loading distribution seen in Fig. 14c.In contrast, as the spanwise loading gradients are comparatively lower in the negative thrust regime near ∕ = 1, the corresponding radial gradients of the axial velocity are also lower.The slope steepens with an increase in the magnitude of the negative thrust due to the increase in the corresponding spanwise loading gradients.The increasing blade loading at the inboard sections with the decreasing pitch settings results in decreasing axial velocities in the wake at the corresponding radial coordinates in Fig. 20a.As expected, the tangential velocities are opposite in negative thrust conditions compared to the positive thrust condition due to the opposite direction of torque, see Fig. 20b.High loading at the inboard blade sections in the negative thrust regime results in high tangential velocities at the corresponding radial coordinates in the wake.With the increasing radial coordinate, though the dynamic pressure increases, the power coefficient stays almost constant (Fig. 14d), resulting in decreasing tangential velocities in the wake.Hence explaining the large radial gradients observed in the negative thrust conditions in Fig. 20b.In contrast, in positive thrust conditions, the power coefficient increases with the increasing radial coordinate resulting in almost constant tangential velocities in the wake at a given axial location, as can be seen in Fig. 20b.At the radial coordinate of 0.9, the power coefficient becomes positive in the negative thrust conditions resulting in negative tangential velocities.From these trends, it becomes clear that a wing immersed in the slipstream of a negative thrust condition will perceive a changed effective angle of attack compared to a positive thrust condition.

Far-field acoustic characteristics
The changes in the aerodynamics of the negative thrust regime compared to the conventional positive thrust regime are expected to modify the resulting acoustic emissions.The tonal noise is sensitive to both blade loading and thickness, making it difficult to isolate the changes in the noise sources between the two regimes (positive and negative thrust).Building upon the previous section's discussion, the current section also analyzes the cases with the fixed tip Mach number (different thrust settings achieved through variation in blade pitch setting).This strategy allows studying the changes in the noise characteristics solely due to the change in the blade loading characteristics and not due to a change in thickness noise.The convection effects have been neglected in this analysis as the main interest is in the change of noise mechanism.

Far-field noise directivity and power spectrum density (PSD)
Fig. 21a shows the resulting far-field noise directivity at a distance of 20.The noise directivity has been calculated in two ways.The dash lines with markers are obtained by propagating the pressure signal captured at the blade surface to the far field using the FWH analogy.Therefore, these lines represent the total noise generated by the propeller blades, i.e., the sum of tonal and broadband noise.The solid lines (without markers) are obtained by feeding the time-averaged blade loading shown in Figs.14c and 14d to Hanson's model [11] to calculate the tonal noise due to time-averaged blade loading.The noise  can be decomposed into two components using the FWH analogy: loading noise and thickness noise, based on their respective integral terms [36].The advantage of using Hanson's model is that it further decomposes the loading noise into the noise due to the thrust and torque.The source code of the Hanson's model used in this study can be found on 4TU.ResearchData repository [37].The dashed black line shows the thickness noise obtained from the FWH analogy, whereas the dotted black line shows the thickness noise obtained using Hanson's model.The FWH analogy gives the total noise obtained from the high-fidelity simulations, whereas Hanson's model gives further insight into the loading noise sources.Comparing the noise levels obtained from the two approaches shows that Hanson's model overpredicts the tonal noise by 2-3 dB for both positive and negative thrust conditions, which originates from the simplifications inherent in Hanson's model [11].The thickness noise is also overpredicted by 3 dB in the propeller plane.As broadband noise is the primary source of the noise near the propeller axis, the total noise level (predicted by FWH analogy) is higher than the tonal noise levels (predicted by Hanson's model) for 0 • ≤  < 30 • and 150 • <  ≤ 180 • .For approximately 30 • ≤  ≤ 150 • , Hansons's model agrees qualitatively with the FWH analogy and can be used to understand the relative importance of different tonal noise sources.Therefore, this analysis with the Hanson model has been used to gain more insight into these noise sources.
The positive thrust condition has 10 dB higher noise in the propeller plane than the negative thrust condition, which is also reflected in the power spectrum density plot shown in Fig. 22b.This difference in the tonal noise is expected to originate from two sources: a) higher noise due to torque in the positive thrust condition (due to higher torque, see Fig. 14d); b) differences in blade loading distribution between the two conditions as seen in Fig. 14c.These sources of difference between the loading noise at positive and negative thrust have been analyzed further by decomposing the loading noise into noise produced by thrust and torque using Hanson's model, see Fig. 21b.Though the absolute thrust level is the same for both conditions, the more outboard loading in the positive thrust condition leads to a 4 dB higher noise due to thrust.Despite the constant absolute thrust level, the magnitude of the torque is approximately three times higher in the positive thrust condition than in the negative thrust condition.The higher torque amplitude results in up to 12 dB higher noise in the positive thrust condition than in the negative thrust condition.As evident from Fig. 21b, noise due to torque is the dominant noise for the positive thrust condition for the given operating condition.In contrast, the noise produced by thrust and torque is comparable in the negative thrust condition.For both regimes, the noise due to thrust has two lobes, with the front lobe interfering destructively with the noise due to torque and the back lobe interfering constructively with the noise due to torque, irrespective of thrust direction.This interference trend between noise produced by thrust and torque agrees with the previous studies [7,35].As noise levels produced by thrust and torque are comparable in the negative thrust condition, the destructive interference results in a decreased loading noise in front of the propeller plane, as can also be seen in the FWH analogy results in Fig. 21a.In the positive thrust condition, the noise due to thrust has a small effect on the overall loading noise.Along the propeller axis (0 • ≤  ≤ 30 • and 150 • ≤  ≤ 180 • ), the negative thrust condition results in 13-15 dB higher noise than the positive thrust condition along the propeller axis; see the FWH analogy results in Fig. 21a.This is an expected result of the increased flow separation in the negative thrust condition compared to the positive thrust condition, as seen in Fig. 13.The increased broadband noise can also be seen in the power spectrum density plot shown in Fig. 22a.

Noise source map
To further understand the difference between the noise sources in positive and negative thrust conditions, a post-processing tool from 3DS named OptydB-PFNOISESCAN was used.This tool calculates the noise contribution per unit surface area emitted towards a given microphone at every time step, and then Fourier transforms the unsteady surface field to provide output for a given frequency range.The noise contribution of the surfels is calculated in terms of power density, i.e., Pa 2 /m 2 and then the resulting value is converted into dB by taking the log, resulting in the units of dB/m 2 .It should be noted that this tool uses the assumption of a compact source, which is a reasonable assumption for the first two BPFs (  ∕ < 0.1) for the given operating conditions ( ∞ = 0.29,  ℎ = 0.74).Nine time instances of the obtained results are shown for one of the blades in Fig. 23 and Fig. 24 for  = 0 • and 90 • respectively.For  = 0 • , the frequency range was chosen to be 1 -2 BPF, given the considerable difference in PSD between the two operating conditions seen in Fig. 22a and constraints imposed by the assumption of a compact source.Similarly, for  = 90 • , the first BPF was chosen to compare the location of tonal noise sources at the given operating conditions based on Fig. 22b.
Fig. 23a and 23c show the noise source maps of the front and back sides of the propeller respectively for a microphone located along the propeller axis ( = 0 • ) for   = +0.08 ( 0.7 = 37.57 • ).Similarly, Figs.23b and 23d show the noise source maps of the front and back sides of the propeller respectively for the same microphone location for   = −0.08 ( 0.7 = 20 • ).As the microphone is located along the propeller axis, the noise source contribution is independent of the circumferential position in Fig. 23.As can be noticed from the figure, broadband noise is dominant for this observer location (Fig. 22a).Since the inflow turbulence is negligible, the two main sources of broadband noise are trailing-edge noise and flow separation.For the front side of the propeller (Fig. 23a), the noise mainly comes from the trailing edge.The strong noise sources near the trailing edge can be related to the trailing-edge separation seen in Fig. 13a.Similarly, on the back side of the propeller, the noise sources are observed at the inboard sections corresponding to the separation bubble seen in Fig. 13a along with trailing-edge noise sources located relatively outboard.
In contrast, the extensive flow separation on the back side of the propeller in the negative thrust condition (as shown in Fig. 13b) leads to a dominant broadband noise contribution from the whole back surface of the blade, see Fig. 23d.Again the inboard region with the attached flow in Fig. 13b features negligible noise generation radiated to the given microphone.With the increase in local Mach number and pressure amplitude (due to the increased dynamic pressure) in the radial direction, the extent of flow separation also increases from the root to the tip, enhancing the strength of the broadband noise source.For the conventional regime, i.e., positive thrust condition, the front side is the dominant source of broadband noise.In contrast, the back side is the dominant broadband noise source in the negative thrust condition.
To compare the distribution of tonal noise source for the two operating conditions, the noise source map for  = 90 • at the first BPF is shown in Fig. 24.Because the microphone is located in the propeller plane along the 0 • line depicted in the figure, the source contribution varies with the circumferential position.This is a consequence of the varying distance between the blade surface and the microphone due to the rotation of the blade surface.Due to the increase in local Mach number and pressure amplitude (due to the increased dynamic pressure) in the radial direction, the outboard part of the blade has the most dominant contribution to the noise in the propeller plane in the conventional positive thrust regime on both the front and the back side of the propeller (Figs.24a and 24c).In the negative thrust case as well, a clear dominant noise source can be seen on the outboard part of the blade on the front side of the propeller (Fig. 24b) contributing to the tonal noise.However, on the back side of the propeller, random fluctuations are superimposed on a circumferential variation of the source amplitude (Fig. 24d).This indicates the presence of a combination of tonal and broadband noise.The tonal noise in the positive thrust condition is higher than in the negative thrust case in Fig. 24 because of higher torque in the positive thrust case, as explained previously.

Effect of thrust coefficient on OSPL
This section evaluates the effect of the thrust setting on the OSPL.Fig. 25a shows the variation of OSPL with the absolute thrust coefficient for both positive and negative thrust regimes using the FWH analogy along the propeller axis ( = 0 • ) and in the vicinity of the propeller plane (75 • ≤  ≤ 105 • ).The tonal noise in the vicinity of the propeller plane has been decomposed further by using Hanson's model into thrust, torque, and thickness noise, see Fig. 25b.In Fig. 25a, the dash-dotted lines show the noise levels along the propeller axis ( = 0 • ), where the main contribution comes from the broadband noise sources.The solid lines show the maximum OSPL level between 75 • -105 • , where the OSPL is expected to be dominated by tonal noise (see Fig. 22b).The dashed-black line shows the level of thickness noise for the given operating condition.The OSPL for the positive thrust condition increases from 71 dB to 80 dB along the propeller axis (dash-dot orange line) when the thrust coefficient increases from 0.01 to approximately 0.12.This is a result of the increase in the broadband noise caused by an increase in trailing-edge separation (Fig. 13a) with the Fig. 25.Effect of thrust coefficient on the noise sources in positive and negative thrust regimes for a propeller operating at a constant rotational speed ( = 1.34).
increase in   .Even with the trailing-edge separation, the broadbanddominated noise of the positive thrust regime is considerably lower than that of the negative thrust regime (dash-dot blue line) at all the thrust levels (as expected).The noise along the propeller axis for the negative thrust conditions has a higher positive slope than the positive thrust regime.After a certain thrust level, the broadband-dominated noise level exceeds the tonal-dominated noise levels and becomes the dominant source of the noise.This is a consequence of the significant increase in the broadband noise levels caused by the increasing separation as the magnitude of negative thrust increases.
On the other hand, the tonal-dominated noise for the positive thrust regime (solid orange line) is considerably higher than the tonaldominated noise for the negative thrust regime (solid blue line).In the vicinity of the propeller plane, the negative thrust condition with a thrust coefficient of   = −0.04produces approximately similar noise as produced in the positive thrust regime at   = +0.01.The positive thrust regime has a much steeper slope along the whole range of thrust levels than the negative thrust regime (Fig. 25).In contrast, there is a little increase in the noise near the propeller plane for |  | ≥ 0.08 in the negative thrust regime.These trends can be explained by decomposing the tonal noise into thrust, torque, and thickness noise using Hanson's model is shown in Fig. 25b.Hanson's model predicts similar trends as the FWH analogy for the noise in the given directivity range.In the vicinity of the propeller plane, the noise due to torque (dotted orange line) is the dominant noise source for the whole thrust range in the positive thrust regime.The same is true for the negative thrust regime up to the maximum regeneration point.As a result, even though the absolute thrust magnitude in the negative thrust condition (  = −0.04) is approximately four times higher than the positive thrust condition (  = +0.01), the tonal noise levels are similar due to the similar magnitude of   (|  | = 0.02), see Fig. 14a.As in the positive thrust regime, the torque increases with the increasing thrust magnitude, and the tonal noise levels also increase.However, in the negative thrust regime, the operating conditions with   = −0.08 and −0.11 have similar values of   (Fig. 14a), resulting in similar tonal noise levels.After the maximum regeneration point, the magnitude of the negative torque starts to decrease, whereas the magnitude of the negative thrust continues to increase.As a result, noise due to thrust becomes the dominant noise source after a certain point; see Fig. 25b.However, such an operating condition probably would not be relevant for an aircraft due to the high magnitude of the negative thrust coefficient.

Main inferences for landing using negative thrust settings
Three main inferences can be drawn from the trends observed in Fig. 25.Firstly, it can be concluded that for a given absolute thrust level, the negative thrust regime can be expected to have lower noise in the propeller plane than the positive thrust regime based on two facts: a) For a given thrust level, the noise due to thrust in positive thrust condition can be expected to be always higher than the noise due to negative thrust due to more outboard loading; b) As concluded in the earlier work [7] as well, the torque required to generate a given thrust level can be expected to be always higher than the torque regenerated at the same absolute thrust level in the negative thrust regime (for a conventional propeller design).As a result, the sum of the noise due to both thrust and torque is expected to be lower in the negative thrust regime compared to the positive thrust regime for a given absolute thrust; therefore, the resulting tonal noise is also expected to be lower.Secondly, it can be concluded that for a conventional propeller, the negative thrust regime is expected to be noisier along the propeller axis than the positive thrust regime, irrespective of the thrust or torque level.Lastly, the noise due to torque is expected to be the dominant noise source in the operating conditions (moderate thrust levels) relevant for a landing using negative thrust.When the negative torque is below the torque required to operate the propeller in a conventional landing, the noise near the propeller plane can be expected to be either lower or similar to the noise generated by the propeller in a conventional landing.A similar torque level in the two regimes is achieved at a higher absolute thrust in the negative thrust regime compared to the conventional positive thrust regime.It essentially means that a steeper descent is possible without increasing the tonal noise (without considering the effects of inflow angle on the tonal noise).Moreover, the steeper descent means that the vicinity of the airport is exposed to the noise for a shorter time and generally at larger distances.This would lead to reduced noise hindrance even at a constant source noise level.

Conclusions
A numerical investigation has been carried out using the Lattice-Boltzmann method coupled with a very large-eddy model to understand the aerodynamics and far-field noise characteristics of an isolated propeller operating in positive and negative thrust regimes.The setup has been validated by comparison against experimental data for two operating conditions ( = 0.60, and 1.10).In the case of the positive thrust condition ( = 0.60), the LBM simulations are able to predict the thrust accurately (within 1%).However, the power prediction is off by about 10% due to the underprediction of the drag.The underprediction of drag is expected to occur because of a separation bubble on the blade surface, which makes the prediction of the reattachment location difficult and thus leads to higher uncertainty on the drag.Due to the limitations in simulating separated flow, the negative thrust regime ( = 1.10) simulations underpredict the power and overpredict the thrust by 10%.The comparison of the radial distribution of total pressure, and axial and tangential velocity distributions in the slipstream showed that LBM-VLES simulations are able to capture the gradients in the radial and axial directions despite the differences in the predicted integrated performance.As the LBM-VLES simulations performed in this paper tend to underpredict and overpredict the power for positive and negative thrust regimes, respectively, it can be concluded that the simulations tend to be conservative in the prediction of tonal noise for the positive thrust conditions and overpredict the tonal noise for the negative thrust regime given that the noise due to the torque is dominant at low to moderate thrust settings.
A propeller operating at a constant rotational speed but varying pitch angle was used to investigate the far-field noise characteristics with a freestream Mach number of 0.29 and helicoidal tip rotational Mach number of 0.74, resulting in an advance ratio of 1.34.Such a configuration ensures that the thickness noise stays constant as the loading is changed with the variation of pitch setting.The resulting absolute thrust coefficient lies in the range of 0.01 -0.12 for the positive thrust regime and between 0.04 -0.14 for the negative thrust regime.As expected, thrust shows a monotonic decreasing trend with the increase in pitch angle in the negative thrust regime.Power reaches a maximum at a unique pitch setting (for the studied propeller at 15 • ).The blade loading distributions show that the peak in the radial distribution of thrust is located inboard (0.7R) compared to the spanwise location of maximum loading (0.85R) for the positive thrust regime.Moreover, most of the negative power comes from the inboard part of the blade (up to 0.6R) compared to the positive thrust regime, where the maximum power loading is around 0.85R.The flow separation around the blades in the negative thrust regime increases average fluctuations from 0.7% at   ≈ −0.04 to 1.5% at   ≈ −0.14 in the integrated thrust.
In comparison, the fluctuations are below 0.5% for all thrust settings in the positive thrust regime.Further, the blade loading in the negative thrust regime shows the amplitude of fluctuations of up to 18% for inboard sections and up to 30% near the blade tip compared to the timeaveraged loads.The analysis of the slipstream flowfields shows that an aerodynamic body immersed in a slipstream at a negative thrust setting will experience reduced dynamic pressure and opposite tangential velocity compared to those experienced at a positive thrust setting.
The analysis of the far-field noise characteristics shows that a conventional propeller operating in the negative thrust regime can be expected to produce more broadband noise than in positive thrust conditions at all practical thrust settings.The tonal noise in the positive thrust regime is higher than in the negative thrust regime for a given absolute thrust.This difference arises from two sources.Firstly, the higher torque leads to higher noise due to torque in the positive thrust regime.Secondly, the higher absolute loading on the inboard blade segments results in a lower noise due to thrust in the negative thrust regime, even though the absolute thrust level is the same.As the noise due to torque is the dominant noise source for low to moderate thrust settings, a steeper and quieter descent compared to a conventional descent is possible using negative thrust as long as the negative torque produced is equal to or lower than the torque required to operate the propeller in a conventional landing (without considering the effect of inflow angle on propeller noise).Additional reduction in noise hindrance is expected due to the steeper descent leading to shorter exposure time to the community noise.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1
Fig.1.Velocity triangles at a fixed-pitch propeller blade section in positive and negative thrust modes[6].

Fig. 3 .
Fig. 3. Computational domain and boundary conditions along with the VR regions.

Fig. 4 .
Fig. 4. Effect of mesh refinement on the predicted integrated thrust and power.

Fig. 5 .
Fig. 5. Visualization of flow around the propeller blade using skin friction coefficient and shear lines (fine grid).(For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

Fig. 8 .
Fig. 8.Comparison of the phase-locked slipstream from PIV data and LBM simulations for the positive thrust condition at  = 0 • ( = 0.60, fine grid).

Fig. 13 .
Fig. 13.Visualization of instantaneous flow around the propeller blade using skin friction coefficient and shear lines for   = ±0.08 at  = 1.34.

Fig. 16 .
Fig. 16.Radial distribution of instantaneous thrust coefficient ( ′  ) along the propeller blade span over a rotation as a function of circumferential position for   = ±0.08 at  = 1.34.

Fig. 18a and
Fig.18a and 19ashow the contours of the mean of the phase-locked velocities and Figs.18b and 19bshow contours of the standard deviation of the phase-locked velocities.In these figures, the slipstream contours on the top side of the nacelle show the negative thrust condition, and the slipstream in the positive thrust condition is shown on the bottom side.As expected, the operation at negative thrust results in decreased axial velocity in the slipstream compared to the freestream condition, whereas the positive thrust results in increased axial velocity.This difference in the axial velocity causes an axial shift of the tip vortex between the two conditions; see Fig.18a.Also, the radial gradients where the tip vortex cuts the measurement plane are much higher in the positive thrust case than in the negative thrust condition.As the radial

Fig. 20 .
Fig. 20.Radial distributions of time-averaged axial and tangential velocity in the propeller slipstream at 1 downstream of the propeller center at  = 1.34.

Fig. 21 .
Fig. 21.Far-field noise directivity of the propeller in positive and negative thrust regimes at absolute thrust level of |  | = 0.08 at  = 1.34.

Fig. 23 .
Fig. 23.Noise source map (1 -2 BPF) on a single propeller blade for an observer located along the propeller axis ( = 0 • ) at positive and negative thrust conditions at  = 1.34.

Fig. 24 .
Fig. 24.Noise source map (1st BPF) on a single propeller blade for an observer located in the propeller plane ( = 90 • ) at positive and negative thrust conditions at  = 1.34.

Table 1
Operating conditions for grid dependence study.

Table 2
Grids used for the grid dependence study.