Numerical investigation on aerodynamic noise of rigid coaxial rotor in forward flight with lift-offset

Abstract

A computational fluid dynamics (CFD) solver based on Reynolds-averaged Navier–Stokes (RANS) equations and high-efficiency trim model is used to simulate the unsteady aerodynamics of coaxial rotor. Farassat 1 A equations are adopted for predicting rotor far-field aerodynamic noise. Forward flight cases of a two-bladed rigid coaxial rotor in different advance ratios and lift-offsets (LOS) are conducted. Sound pressure histories of different observation points and noise radiation maps are analyzed. Results indicate that, the intensity of rotor thickness noise moves towards the advancing side in the rotor disk plane, with the increase of advance ratio. Due to the superposition effect, the thickness noise of coaxial rotor is symmetrical, which is different with the single rotor. At low advance ratio, loading noise of the rigid coaxial rotor is enhanced near the blade-crossing azimuths caused by the unsteady interaction of the twin rotors. The enhancement turns weak with the increase of advance ratio. At high advance ratio, increasing LOS tends to enhance the rotor-self BVI noise, while weakening the inter-rotor interaction noise. At certain flight states, appropriate LOS can reduce the overall noise radiation intensity of rigid coaxial rotor.

Keywords

Helicopter coaxial rotor aerodynamic noise forward flight computational fluid dynamics lift-offset

Introduction

Flight speed of conventional single-rotor helicopter is restricted by the compressibility on the advancing side and stalling on the retreating side of the main rotor. Rigid coaxial rotor compound helicopter adopting advancing blade concept (ABC)¹ technology has been proven to effectively improve the high-speed capability. Based on the ABC technology, a series of compound helicopters have been developed by Sikorsky Aircraft Corporation for high-speed flight, such as XH-59A, X-2 TD, and S-97. X2 TD aircraft has achieved a speed of 463 km/h in steady level flight,² which is rather higher than the conventional single-rotor helicopter.

For a lift-offset rotor in forward flight, the advancing blade is given a larger pitch than the conventional rotor to fully utilize the high dynamic pressure and improve the rotor lift. Meanwhile, the retreating blade is given a smaller pitch to reduce its drag, and avoid the potential problem of blade stall. The rolling moments generated by the two counter-rotating rotors can be balanced with each other. This leads to the total lift of the upper (lower) rotor deviating from the rotor center, which is called as lift offset (LOS),² as shown in Figure 1. LOS is a unique aerodynamic characteristic of rigid coaxial rotor. This configuration usually has small rotor space to reduce the drag in high-speed flight. Correspondingly, there are severe aerodynamic interactions, which would lead to special interaction noise.

Figure 1.

The basic ABC concept.

Over the past decade, a series of studies on the aerodynamic interaction of coaxial rotor have emerged. In some researches, the load of coaxial rotor was simulated by blade element theory (BET)^3–5 or vorticity method.^6–9 Among these, different comprehensive analysis software was applied, such as RCAS,^10,11 UMARC,^12,13 and CAMRAD II.^14–16 Those methods were usually built based on empirical formulas, which had low numerical diffusion and high computational efficiency. However, the accuracy could not be guaranteed,^17,18 especially for the complex unsteady interaction flow field around a coaxial rotor. Recently, CFD method^19–23 has been widely used for aerodynamic analysis of coaxial rotor, as it can provide more details of the interaction flow field. In 2008, Lakshminarayan et al.¹⁹ analyzed the interaction of a coaxial rotor in hover, using a compressible RANS solver OVERTURNS and sliding mesh. The impulsive loads caused by the interaction in hover were initially explained in terms of the blade thickness and loading effects. In 2019, Qi et al.,^24,25 conducted a further study of the interaction mechanism of coaxial with high-efficiency trim model. The interactions of coaxial rotor were summarized as different types according to its causes. Such as the complex rotor wake interaction, blade-crossing interaction, and blade-vortex-interaction (BVI). The rotor wake interaction is typically shown on the lower rotor affected by the wake of upper rotor. The blade-crossing interaction induces severe impulsive loads in hover and low-speed forward flight, which would lead to significantly impulsive loading noise. The BVI events can be divided into two types. One is the rotor-self BVI in forward flight. It is caused by the tip vortex detached from one blade, and acting on another blade of the rotor itself, which is similar to a single rotor. Another is the inter-rotor BVI. It is caused by the tip vortex of the upper rotor acting on the lower rotor at certain flight states, such as hover and low-speed forward flight. Understanding of coaxial-rotor interaction characteristics can provide critical guidance for the analysis of aerodynamic noise.

FW-H equations are widely used for predicting the far-field noise of rotor.^26,27 At present, researches about the aerodynamic noise of coaxial rotor with LOS are still limited. Zhu and Wang et al.^28,29 analyzed the noise characteristics of a coaxial rotor based on Farassat 1A equations and RANS equations. The effect of blade shape was studied. From 2020, Jia et al.^30–32 used the CFD/CSD coupling method and PSU-WOPWOP program conducted a series of studies about coaxial-rotor noise. Impulsive loading noises caused by the blade-crossover interaction and self-BVI were analyzed, but the thickness noise and influence of LOS were not discussed in detail. In 2022, Qi et al.³³ studied the noise characteristics of a two-bladed coaxial rotor in hover, using an unsteady RANS solver and Farassat 1A equations. Results showed that the special noise characteristics of hovering coaxial rotor were mainly caused by the noise superposition of the twin rotors and unsteady interaction loads. There were significant differences between single and coaxial rotors in terms of their noise frequency spectra and radiation directionality. However, the research was limited to the hover state.

With the increase of forward flight speed, the interaction between the twin rotors turns weak and significant rotor-self BVI events appear, which is rather different with the hover state. Correspondingly, the noise characteristics also change. Meanwhile, the magnitude of LOS also has important effect on the unsteady loads and noise of rigid coaxial rotor. This paper is a further study of the previous research.^24,33 The main purpose is to investigate the far-field noise characteristics and generation mechanisms of rigid coaxial rotor with different forward flight speeds and lift-offsets.

Numerical method

CFD solver and trim model

The cases in this paper are conducted using an unsteady CFD solver.²⁴ In the solver, Navier–Stokes equations are employed for flow-field simulation, which can be written as

\frac{\partial}{\partial t} \underset{\partial V}{∭} W d V + \underset{\partial S}{∯} (F_{c} - F_{v}) \cdot n d S = 0

(1)

where,

W

represents the vector of conservative variables.

F_{c}

and

F_{v}

are the vectors of convective and viscous fluxes.

The governing equations are spatially discretized by finite volume method. Third-order Roe-MUSCL scheme^34,35 is employed to calculate the inviscid flux terms. Second-order central differencing is used to compute the viscous terms. The Spalart-Allmaras turbulence model³⁶ is used to simulate the turbulent viscosity. Dual-time stepping approach³⁷ is adopted for temporal discretization, in which the second-order implicit backward difference scheme is used for computing the physical time step. The lower-upper symmetric Gauss-Seidel (LUSGS)³⁸ scheme is used for the convergence in pseudo-time.

In this paper, the physical time step corresponds to 0.5° azimuth, corresponding to 720 steps per revolution. Moving overset mesh is adopted to simulate the rotating and pitching movements of the coaxial rotor. Blade and background mesh is refined around the regions of blade tip and rotor wake, as shown in Figure 2. Based on previous computational experience,^31,39 the background and blade meth are refined to about 0.05c near the region of rotor tip path, which has been proven to meet the requirement of grid independence. Each blade mesh has 221 × 85 × 101 points in the streamwise, normal and spanwise directions. The background mesh has 245 × 195 × 217 points in x, y and z directions. The total number of mesh is about 17.9 million.

Figure 2.

Moving overset mesh system for the coaxial rotor.

The research is conducted with a two-bladed model rotor the parameters are listed in Table 1. The blade is untwisted, and its airfoil is NACA0012. The rotor hovering tip Mach number (Ma_tip) is 0.588 for

μ

<0.4, and reduces to 0.47 for

μ \geq

0.4, referring to the design principle of rigid coaxial rotor.¹⁸ The upper rotor rotates anti-clockwise (right-hand), while the lower rotor rotates clockwise (left-hand).

Table 1.

Parameters of the model coaxial rotor.

Parameter	Values
Rotor radius	2.0 m
Rotor cutout	0.212 R
Chord	0.22 m
Number of blades	2 + 2
Blade tip mach number	0.588 (0.470)

A high-efficiency hybrid trim model built in the previous research³⁹ is adopted for trimming. In the trim model, the BET method and the CFD solver were coupled. The Jacobian matrix was solved by high-efficiency BET method, and CFD solver was used for modifying at each trim step, which can obviously improve the trimming efficiency. Detailed description of the CFD/BET hybrid trim model can be found in the reference.³⁹

The control settings (x) and target variables (y) for trimming are shown below.

x = {θ_{0 U}, θ_{1 s U}, θ_{1 c U}, θ_{0 L}, θ_{1 s L}, θ_{1 c L}}, y = {C_{T}, C_{Q}, L O S, C_{M U}, C_{L}, C_{M L}}

(2)

LOS = | C_{L U} - C_{L L} | / C_{T}, C_{L} = C_{L U} + C_{L L}

(3)

where,

θ_{0}

is collective pitch angle,

θ_{1 s U}

and

θ_{1 c U}

are longitudinal and lateral cyclic pitches. Subscripts of U and L indicate the upper and lower rotors. C_T and C_Q are the thrust and torque coefficients. C_L and C_M are the coefficients of rolling and pitching moments.

Cases at different advance ratios are trimmed for certain LOS states. The target thrust coefficient is C_T = 0.001. Other four target variables are all set as 0. The trimmed rotor pitches for different cases conducted in this paper are given in Table 2. The CFD solver with high-efficiency trim model has been validated with various experimental cases in hover and forward flight,^24,25,39 which has been proven to have reasonable accuracy in predicting the aerodynamic performance of coaxial rotor.

Table 2.

Trimmed rotor pitches for different cases.

Rotor pitches (deg)	$θ_{0 U}$	$θ_{1 s U}$	$θ_{1 c U}$	$θ_{0 L}$	$θ_{1 s L}$	$θ_{1 c L}$
μ = 0.15, LOS = 0.0, Ma_tip = 0.588	8.67	2.70	−2.98	8.64	3.23	−2.71
μ = 0.4, LOS = 0.3, Ma_tip = 0.470	5.64	0.96	−0.64	5.47	1.09	−0.50
μ = 0.5, LOS = 0.1, Ma_tip = 0.470	10.11	1.54	−8.99	10.01	1.46	−8.67
μ = 0.5, LOS = 0.2, Ma_tip = 0.470	8.30	1.36	−5.92	8.46	1.43	−5.75
μ = 0.5, LOS = 0.3, Ma_tip = 0.470	6.41	1.10	−2.78	6.58	1.23	−2.63
μ = 0.5, LOS = 0.4, Ma_tip = 0.470	4.58	0.88	0.28	4.72	1.12	0.40

Acoustic prediction method

The rotor linear noise is predicted by Farassat 1A equations.⁴⁰ For an impermeable data surface, such as the blade surface, the acoustic pressure time history is given by

p^{'} (x, t) = p_{T}^{'} (x, t) + p_{L}^{'} (x, t)

(4)

4 π p_{T}^{'} (x, t) = \int_{f = 0} {[\frac{ρ_{0} {\dot{v}}_{n}}{r {(1 - M_{r})}^{2}} + \frac{ρ_{0} v_{n} {\hat{r}}_{i} {\dot{M}}_{i}}{r {(1 - M_{r})}^{3}}]}_{r e t} d S + \int_{f = 0} {[\frac{ρ_{0} c_{0} v_{n} (M_{r} - M^{2})}{r^{2} {(1 - M_{r})}^{3}}]}_{r e t} d S

(5)

4 π p_{L}^{'} (x, t) = \frac{1}{c_{0}} \int_{f = 0} {[\frac{\dot{p} \cos θ}{r {(1 - M_{r})}^{2}} + \frac{{\hat{r}}_{i} {\dot{M}}_{i} p c o s θ}{r {(1 - M_{r})}^{3}}]}_{r e t} d S + \int_{f = 0} {[\frac{p (\cos θ - M_{i} n_{i})}{r^{2} {(1 - M_{r})}^{2}} + \frac{p c o s θ (M_{r} - M^{2})}{r^{2} {(1 - M_{r})}^{3}}]}_{r e t} d S

(6)

where,

p_{L}^{'}

and

p_{T}^{'}

are the thickness and loading noise components. r is the distance between the source and the observer.

M_{r}

is the component of surface source Mach number in the radiation direction.

\cos θ = {n_{i} \hat{r}}_{i}

ρ_{0}

and

c_{0}

are the density and sound speed in the far field.

p

is the blade surface gauge pressure. The subscript ‘ret’ means the quantities are evaluated at the retarded time.

Considering that there is little experimental acoustic data for coaxial rotor, validation cases of AH-1/OLS⁴¹ model rotor are conducted in this paper. The radius of AH-1/OLS rotor is 0.958 m and the chord is 0.1039 m. The state of Ma_tip = .664, μ = 0.164 (10,014 test state) is a typical state of BVI. The locations and coordinates of observation points are given in Figure 3.

Figure 3.

Locations of observation points.

In calculation, the number of blade mesh is 221 × 79 × 115 in streamwise, normal and spanwise directions. The background mesh number is 235 × 211 × 193 in x-y-z directions. The background and blade meth are also refined to about 0.05 c near the rotor tip. Figure 4 shows the comparison of sound pressure results at four observation points. The main sound pressure fluctuations are well predicted indicating that the acoustic method built in this paper has reasonable accuracy. Some errors are expected, as the predicting of complex loads caused by BVI is the most challenging state of helicopter rotor. This is similar to the calculated results of other researchers.^42,43

Figure 4.

Sound pressure history validation of AH-1/OLS rotor. (a) #2 point, (b) #3 point, (c) #7 point, (d) #9 point.

The acoustic radiation hemisphere and its Lambert projection map are shown in Figure 5. The rotor disk, longitudinal, and lateral planes are marked in Figure 5(a), which will be used in the following section. The radius of the hemisphere is 10m (5R). The center is set at the center of the coaxial-rotor hub. Positions of five observation points used in this paper are marked in Figure 5(b). #1 to #3 points are set in the rotor disk plane. #1 to #5 points are set in the longitudinal plane. The angle between each adjacent two points is 22.5°.

Figure 5.

Schematic diagram of acoustic radiation hemisphere and Lambert projection. (a) Acoustic radiation hemisphere, (b) Lambert projection map.

Results and discussion

Thickness noise

In forward flight, the change of LOS corresponds to the change of rotor control pitches and load distributions, which has little influence on the thickness noise. Therefore, the influence of advance ratio and rotor tip Mach number are studied in this section, rather than LOS. The thickness noise of a rotor mainly radiates in the rotor disk plane. Figure 6 illustrates the effect of advance ratio on the radiation characteristics of thickness noise in the disk plane of a coaxial rotor. As the advance ratio increases, the intensity of thickness noise in the disk plane gradually moves towards the front-right of the rotor. With the increase of advance ratio, the noise distribution line changes from an approximate concentric circle to eccentric circles. This is mainly due to the relative velocity on the advancing side increases, while it decreases on the retreating side. A higher rotor tip Mach number reduces stronger thickness noise.

Figure 6.

SPL distributions of single-rotor thickness noise in rotor disk plane. (a) Ma_tip = .470, (b) Ma_tip = .588.

Figure 7 presents the influence of advance ratio on the coaxial rotor. It can be observed that the thickness noise distributions of the upper and lower rotors in the disk plane are symmetrical about the longitudinal plane (along 0-180° azimuths). This is because the twin rotors rotate in opposite directions. Changes in the relative velocity of blades at different azimuths caused by forward speed are symmetrical. The thickness noise of coaxial rotor is the superposition of the twin rotors. With the increase of advance ratio, the noise intensity behind the disk decreases slightly, and increases significantly in front of the disk. The increase in the longitudinal direction is greater than that in the lateral direction.

Figure 7.

SPL distributions of coaxial-rotor thickness noise in rotor disk plane (Ma_tip = .588). (a) Upper and lower rotors, (b) Coaxial rotor.

Figure 8 shows the thickness noise SPL contour of the coaxial rotor for μ = 0.15. The SPL distributions of the upper and lower rotors are symmetrical about the longitudinal plane throughout the entire hemispherical sound radiation surface. This leads to the symmetrical distribution of the rigid coaxial rotor. Due to the noise superposition of the twin rotors, there is an enhanced region at every 90° azimuth. Among them, the SPL in the front of the rotor (at 180° azimuth) is the highest, caused by the superposition effect.

Figure 8.

Thickness noise SPL contour maps (μ = 0.15, Ma_tip = .588). (a) Upper rotor, (b) Lower rotor, (c) Coaxial rotor.

The time histories of the thickness noise pressure at observation points in the rotor disk plane of the coaxial rotor at different advance ratios are shown in Figure 9. For μ = 0.4, the Ma_tip is reduced to 0.470. Due to the superposition effect, there are four troughs in the noise pressure of #2 and #3 points. Forward flight speed biases the noise intensity towards the advancing side. Coupled with the opposite rotation directions of the twin rotors, the trough amplitudes of the adjacent fluctuations caused by the upper and lower rotors are different. With the increase of advance ratio, the difference in amplitudes turns greater. This is marked in the figures. Both #2 and #3 points are located at left front of the rotor, so the thickness noise pressure fluctuations caused by the lower rotor (left-hand rotating) are greater than those caused by the upper rotor (right-hand rotating).

Figure 9.

Coaxial rotor sound pressure histories of thickness noise for points in the rotor disk plane. (a) μ = 0.15, Matip = .588, (b) μ = 0.4, Ma_tip = .470.

Loading noise

Figure 10 shows the SPL distributions of loading noise of single and coaxial rotors for μ = 0.15, LOS = 0.0. The single rotor means the isolated upper rotor, which is calculated for comparison. It adopts same control pitches with the upper rotor. The coaxial-rotor loading noise exhibits a periodic enhancement phenomenon at every other 90° azimuth, which is mainly caused by the blade-crossing interaction.²⁴ The enhancement is more evident near the longitudinal direction (at 90° and 270° azimuths), while it is relatively weaker behind the rotor disk (near 0°azimuth). There is a low SPL region along the meridian of the sound radiation sphere towards the right front of the rotor disk (at 180° azimuth). As shown in Figure 10(c) and (d), the upper rotor has a greater impact on the loading noise distribution of the coaxial rotor than the lower rotor. The distribution of lower rotor is closer to the single rotor.

Figure 10.

Loading noise SPL contour maps (μ = 0.15). (a) Single rotor, (b) Coaxial rotor, (c) Upper rotor, (d) Lower rotor.

Figure 11 displays the SPL distributions of total noise. Combined with Figure 10, the total noises of single and coaxial rotors outside the rotor disk plane are dominated by the loading noise. Near the rotor disk, the total noises are slightly enhanced due to the addition of thickness noise. For the single rotor, the SPL in the region near the rotor disk at 45° azimuth decreases. This may be due to the cancellation of sound pressure fluctuations caused by thickness noise and loading noise at certain times.

Figure 11.

Total noise SPL contour maps (μ = 0.15). (a) Single rotor, (b) Coaxial rotor.

Figures 12 and 13 present the SPL distributions of single and coaxial rotors for μ = 0.4, LOS = 0.3. At this advance ratio, the periodic enhancement of loading noise caused by coaxial rotor interaction almost disappears. The fluctuation of SPL with azimuth angle is rather gentle, especially for the loading noise of the lower rotor. As shown in Figure 12(b), the loading noise of coaxial rotor tends to be symmetrical about the longitudinal plane. According to the previous analysis, the thickness noise of coaxial rotor is also symmetrical, so its total noise also exhibits a symmetrical distribution feature overall (see Figure 13(b)).

Figure 12.

Loading noise SPL contour maps (μ = 0.4). (a) Single rotor, (b) Coaxial rotor, (c) Upper rotor, (d) Lower rotor.

Figure 13.

Total noise SPL contour maps (μ = 0.4) (a) Single rotor, (b) Coaxial rotor.

There are still significant differences between the SPL distributions of the lower rotor and single rotor at μ = 0.15. At a higher advance ratio (μ = 0.4), the coaxial rotor interaction is weakened. And the SPL distribution of lower rotor is similar to the single rotor. It should be noted that the SPL distribution of the upper rotor is still significantly different from the single rotor. It indicates that the noise components caused by the blade-crossing interaction are still obvious for the upper rotor, compared with the lower rotor. This is consistent with the analysis of the aerodynamic interaction of coaxial rotor in the previous research.²⁴ With the increase of advance ratio, the unsteady loads of the lower rotor caused by blade-crossing interaction decrease more significantly than the upper rotor. This is also reflected on the SPL distribution of loading noise, as shown in Figure 12(c) and (d). The distribution of the coaxial-rotor total noise is mainly dominated by the loading noise of upper rotor.

Figure 14 shows the time histories of loading noise pressure at different observation points for μ = 0.15. The loading noise pressure caused by the single rotor at each observation point in forward flight has strong fluctuations. The loading noise of the points at different azimuths in the rotor disk plane differs in waveform and amplitude. Among the three points, the loading noise pressure at #1 point is the most intense one. As the observation point moves downward from the rotor disk plane, the sound pressure amplitude gradually increases from #1 to #5 points.

Figure 14.

Time histories of loading noise at different observation points (μ = 0.15). (a) Single-rotor disk plane points, (b) Coaxial-rotor disk plane points, (c) Single-rotor longitudinal plane points, (d) Coaxial-rotor longitudinal plane points.

Figure 15 presents the time histories of loading-noise pressure for μ = 0.4. The changing trends of observation points in longitudinal and rotor disk planes are similar to μ = 0.15. The sound pressure amplitude gradually increases from #1 to #5 points in the longitudinal plane. Compared with μ = 0.15 state, the fluctuations of single and coaxial rotors at #1 and #3 points both decrease. At #5 point, strong blade-vortex interaction (BVI) noise is presented. The sound pressure caused by BVI are two positive fluctuations, which have larger amplitudes than #1 and #3 points. There are fewer small fluctuations between the two main fluctuations.

Figure 15.

Time histories of loading noise at different observation points (μ = 0.4). (a) Single-rotor disk plane points, (b) Coaxial-rotor disk plane points, (c) Single-rotor longitudinal plane points, (d) Coaxial-rotor longitudinal plane points.

To analyze the frequency spectra of single and coaxial rotors in forward flight, #1, #3, and #5 observation points are selected, as shown in Figures 16 and 17. The base frequency (f₀) corresponds to the rotor rotation speed, which is Ω/2π. As the rotors are two-bladed, the blade-pass frequency (BPF) is twice of based frequency (BPF = 2f₀). At the two forward flight ratios, the high-magnitude frequencies are integer multiples of BPF. The total noises at points #1 and #3 in the low frequency range (within the 15th harmonic) are dominated by thickness noise, while loading noise dominates in the higher frequency range. At point #5, the total noise is mainly dominated by loading noise.

Figure 16.

Frequency spectra of noise at different observation points (μ = 0.15).

Figure 17.

Frequency spectra of coaxial-rotor noise at different observation points (μ = 0.4).

For μ = 0.15, the loading noise of single rotor still has a large amplitude in the high-frequency range. At #1 and #3 points the highest amplitude is located at the 2nd harmonic and gradually decreases with the harmonic order. The distributions of single and coaxial rotors are similar. At #5 point, the noises of single and coaxial rotors in the high-frequency range maintain a relatively large SPL in the range of the 10th to 30th harmonics, and even exceed the SPL in the low-frequency range (below the 10th harmonic). For μ = 0.4, the frequency spectra at #1 and #3 points are similar to μ = 0.15. The variation of noise intensity with frequency at #5 point is relatively gradual. And the highest SPL occurs at the 2nd harmonic.

Influence of LOS on loading noise

Considering that LOS is designed for high-speed forward flight, cases of Ma_tip = .47, μ = 0.5 are conducted to analyze the influence of LOS on the rotational noise of coaxial rotor. The maximum Mach number of the forward side blade tip is 0.705, which is lower than the Mach number level that generates high-speed impulse (HSI) noise. The influence of LOS on the noise is mainly due to the change of rotor load distributions and aerodynamic interactions. Therefore, this section focuses on the influence of LOS on loading noise.

Figure 18 shows the Loading noise SPL contours of single and coaxial rotors with different LOS. For the single rotor, as LOS increases from 0.1 to 0.4, the maximum SPL moves from 45° to 180° azimuths. The overall noise intensity decreases and then increases, reaching maximum at LOS = 0.4. The maximum is located at the oblique below of rotor disk, along the meridian of 180° azimuth.

Figure 18.

Loading noise SPL contour maps of different LOS (μ = 0.5). (a) Single rotor, (b) Coaxial rotor.

For the coaxial rotor at LOS = 0.1, the maximum SPL point is located directly below the rotor disk center. There are prominent high SPL areas at 45° and 180° azimuths. For LOS = 0.4, the noise intensity of coaxial rotor decreases. The maximum value deviates from the direct below of the rotor, located at the oblique below of the rotor disk. This is a comprehensive result of the change of unsteady load distributions caused by the increase of LOS. The loading noise distributions of the upper and lower rotors tend to be similar to the single rotor, ignoring the difference in rotating direction. For the single rotor, the overall loading noise on the radiation hemisphere is strongest at LOS = 0.4 and weakest at LOS = 0.2. For the coaxial rotor, the strongest is LOS = 0.1, the weakest is LOS = 0.3. This indicates that adopting appropriate LOS can reduce the overall loading noise of rigid coaxial rotor.

Figure 19 shows the loading-noise radiation characteristics in three different planes of single and coaxial rotors, with different LOS states. For the single rotor, LOS has a great effect on the noise radiation directionality in the rotor disk plane. With the increase of LOS, the noise in front of the rotor (around 180° azimuth) gradually increases, while the noise behind the rotor decreases. However, LOS has little effect on the radiation directionality of the lateral plane. As LOS increases from 0.1 to 0.4, the overall intensity decreases first and then increases. In the longitudinal plane, the noise gradually increases in front of the rotor and decreases behind the rotor.

Figure 19.

SPL distributions of loading noise with different LOS (μ = 0.5). (a) Rotor disk plane, (b) Lateral plane, (c) Longitudinal plane.

For the coaxial rotor, the noise intensity of the rotor disk plane is almost symmetrical about the longitudinal plane. This is different from the single rotor, as the noise of coaxial rotor is the superposition of twin rotors. Near the blade-crossing azimuths, the aerodynamic interaction still leads to obvious load fluctuations. Thus, stronger noises are generated, especially around 90° and 270° azimuths. The interaction is weakened with the increase of LOS. Correspondingly, the interaction noise near blade-crossing azimuth is also weakened. For the lateral and longitudinal planes, the change of LOS mainly affects the noise intensity and has little impact on its radiation directionality. In the longitudinal plane, the noise intensity in the forward of the rotor disk is also slightly enhanced, but the change is not as significant as the single rotor.

Figure 20 shows the sound pressure time histories of loading noise at #5 point with different LOS. As marked in the figure, the two main noise fluctuations are caused by rotor-self BVI and inter-rotor interaction. The BVI is formed by the upper (lower) rotor itself. The inter-rotor interaction is formed by the twin rotors, which mainly includes the blade-crossing effect and the rotor wake interaction acting on the lower rotor. With the increase of LOS, the BVI is enhanced, so the amplitude caused by it increases. The inter-rotor interaction is weakened. Its corresponding amplitude decreases. For the upper rotor, LOS has no influence on its noise waveform. For the lower rotor, the BVI noise waveform has no change, while the waveform of inter-rotor interaction noise changes with LOS. That is because LOS has an influence on the wake shape of the upper rotor, which can change the characteristics of the wake-vortex interaction caused by the upper rotor acting on the lower rotor.

Figure 20.

Time histories of loading noise at #5 point with different LOS (μ = 0.5). (a) Upper rotor, (b) Lower rotor.

Conclusions

The acoustic characteristics of a rigid coaxial rotor with different advance ratios and LOS are analyzed. Rotor unsteady loads are simulated by adopting a RANS CFD solver. Rotating and pitching movements of the twin rotors are realized through overset mesh method. Control pitches of different flight states are trimmed by a high-efficiency trim model. The rotor far-field noise is calculated by Farassat 1A formulations. The noise characteristics of rigid coaxial rotor in forward flight are mainly determined by the noise superposition effect, inter-rotor unsteady interaction, and rotor-self BVI. The following conclusions can be drawn.

(1) In forward flight, as the advance ratio increases, the intensity of single-rotor thickness noise in the disk plane gradually moves towards the front-right of rotor disk. The right-rotating (upper) rotor exhibits noise enhancement in the right front, while the left-rotating (lower) rotor corresponds to the left front. The thickness noise of coaxial rotor is the superposition of counter-rotating twin rotors. The result is that the thickness noise of coaxial rotor is symmetrical about the longitudinal plane. The highest SPL lies right in front of the rotor disk. As the advance ratio and rotor speed increase, the thickness noise of coaxial rotor is evidently intensified.

(2) At a low advance ratio (such as μ = 0.15), loading noise of rigid coaxial rotor is still obviously enhanced near blade-crossing azimuths (every other 90°) due to the unsteady interaction of the twin rotors. The noise fluctuations of upper rotor are more pronounced than the lower rotor. With the increase of advance ratio, the interaction turns weak. This kind of interaction noise is gradually weakened, while rotor-self BVI noise is enhanced. At high advance ratio, due to the superposition of the twin rotors, the noise radiation intensity of the rigid coaxial rotor is roughly symmetrically distributed along the longitudinal plane.

(3) At a high advance ratio (such as μ = 0.5), increasing LOS enhances the rotor-self BVI noise, while weakening the inter-rotor interaction noise. This leads to larger BVI noise amplitude but has little influence on its waveform. For the upper rotor, the noise waveform caused by inter-rotor interaction has little change. For the lower rotor it has some changes, as LOS affects the wake shape of the upper rotor. With the increase of LOS, the overall noise level of the rigid coaxial rotor decreases first and then increases. Adopting appropriate LOS can reduce its overall noise intensity.

Nomenclature

$π R^{2}$ , rotor disk area (m²)

chord (m)

C _T

$T / ρ A Ω^{2} R^{2}$ , rotor thrust coefficient

C _Q

$Q / ρ A Ω^{2} R^{2}$ , rotor torque coefficient

C _L

$L / ρ A Ω^{2} R^{3}$ , rotor rolling moment coefficient

C _M

$M / ρ A Ω^{2} R^{3}$ , rotor pitching moment coefficient

Ma _tip

rotor tip Mach number

rotor radius

azimuth angle

θ ₀

collective pitch angle

θ_{1 s}

longitudinal cyclic pitch angle

θ_{1 c}

lateral cyclic pitch angle

Ω

rotor angular velocity

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (No. 12102154), the Foundation of State Key Laboratory of Aerodynamics of China Aerodynamics Research and Development Center (No. ANCL20230203), and the Nature Science Foundation of Yangzhou (No. YZ2024164).

ORCID iD

Haotian Qi

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