Document
The Effects of Ambient Conditions on
Helicopter Rotor Source Noise Modeling
∗ † Eric Greenwood Fredric H. Schmitz NASA Langley Research Center University of Maryland A new physics-based method called “Fundamental Rotorcraft Acoustic Modeling from Experiments” (FRAME) is used to demonstrate the change in rotor harmonic noise of a helicopter operating at dif- ferent ambient conditions. FRAME is based upon a non-dimensional representation of the governing acoustic and performance equations of a single rotor helicopter. Measured external noise is used to- gether with parameter identification techniques to develop a model of helicopter external noise that is a hybrid between theory and experiment. The FRAME method is used to evaluate the main rotor har- monic noise of a Bell 206B3 helicopter operating at different altitudes. The variation with altitude of Blade-Vortex Interaction (BVI) noise, known to be a strong function of the helicopter’s advance ratio, is dependent upon which definition of airspeed is flown by the pilot. If normal flight procedures are fol- lowed and indicated airspeed (IAS) is held constant, the true airspeed (TAS) of the helicopter increases with altitude. This causes an increase in advance ratio and a decrease in the speed of sound which results in large changes to BVI noise levels. Results also show that thickness noise on this helicopter becomes more intense at high altitudes where advancing tip Mach number increases because the speed of sound is decreasing and advance ratio increasing for the same indicated airspeed. These results suggest that existing measurement-based empirically derived helicopter rotor noise source models may give incorrect noise estimates when they are used at conditions where data were not measured and may need to be corrected for mission land-use planning purposes.
Notation Q Lighthill Stress Tensor r Propagation Distance A Rotor Disk Area ¯ r Non-Dimensional Propagation Distance a Ambient Speed of Sound r Non-Dimensional Radial Station a Longitudinal Acceleration of Aircraft R Rotor Radius x R Molar Mass of Air b Number of Rotor Blades ∗ S Blade Surface Area c Blade Element Profile Drag Coefficient d t Time of Observation C Thrust Coefficient T ¯ ′ t Non-Dimensional Time of Observation C Acoustic Pressure Coefficient p C Blade Surface Pressure Coefficient T Ambient Temperature p 0 i j ¯ U Blade Section Velocity relative to Medium C Mean Blade Section Lift Coefficient L V Aircraft Velocity Relative to Medium D Fuselage Parasite Drag f v Mean Induced Velocity f Effective Flag Plate Drag Area i e V Indicated Airspeed g Gravitational Acceleration IAS v Velocity of Medium Normal to Blade Surface H Rotor Longitudinal “H-Force” n W Vehicle Gross Weight M Section Mach Number x Cartesian Coordinate Vector M Advancing Tip Mach Number AT ¯ x Non-Dimensional Cartesian Coordinate Vector M Hover Tip Mach Number H M Mach Number along Propagation Direction r n Surface Normal Direction α Tip-Path-Plane Angle of Attack P Surface Pressure T PP ′ Γ Tip Vortex Circulation Strength p Acoustic Perturbation Pressure γ Flight Path Angle ∗ Research Aerospace Engineer, eric.greenwood@nasa.gov γ Adiabatic Coefficient of Air ∗ † Senior Research Professor, fschmitz@eng.umd.edu λ Inflow Ratio Presented at the American Helicopter Society 67th Annual Forum, μ Advance Ratio Virginia Beach, VA, May 3-5, 2011. This is a work of the U.S. ξ Airfoil Surface Slope Government and is not subject to copyright protection in the U.S. ρ Ambient Density ρ Ambient Density at Sea Level ating condition. Estimating the noise radiation of this he- SL σ Rotor Solidity licopter flying under the measured operating conditions re- τ Time of Emission verses this process and should result in the reproduction of ¯ τ Non-Dimensional Time of Emission the measured data used to construct the noise source model χ Wake Skew Ratio at that condition.
ψ Rotor Azimuth Several empirical helicopter source noise modeling Ω Rotor Rotational Speed methods are currently in use. The simplest is derived from simple noise-power-distance extrapolations of mea- sured data at a few microphone locations in order to capture Introduction some information about the directivity of helicopter noise.
(Refs. 1, 2) More complex modeling methods are based on Helicopter acoustic land-use and mission planning tools are a linear (Refs. 3–5) or planar (Refs. 6, 7) grid of ground gaining favor for both military and commercial applica- based microphones—with the most complex of these meth- tions. For the military, reducing the detection distance (the ods measuring the radiated noise from maneuvering heli- distance when an observer first notices the vehicle) is nor- copter in many directions simultaneously using a dense ar- mally the focus. In commercial applications, there is also ray of microphone positions on the ground. (Ref. 7) All of interest in the detection or noticeability of rotorcraft noise, these modeling approaches have one thing in common— especially in areas with low ambient noise levels such as they are based upon acoustic measurements at one ambient rural parks; however, the primary civil focus is designing operating condition. Changes in that ambient condition are helicopter operations which reduce community annoyance either not considered or are accounted for indirectly (and caused by exposure to helicopter noise. For any of these perhaps incorrectly) through changes in the other dependent applications, accurate noise models are needed in order to parameters.
estimate the acoustic impact of helicopter operations on the Existing land-use and mission planning tools, such as observers.
the widely used Rotorcraft Noise Model (RNM), (Refs. 3,4) Noise modeling in land-use and mission planning tools also neglect the effects of ambient conditions on the he- is composed of three distinct components: a noise source licopter source noise models. The Federal Aviation Ad- model, a propagation model, and a receiver model. The ministration’s Integrated Noise Model (INM) (Refs. 1, 2) noise source model characterizes the far-field noise radia- does include an empirical correction to data measured dur- tion of the helicopter. The magnitude and direction of ro- ing the reference flyover flight condition based on the non- tor noise is strongly dependent on the operating condition dimensional advancing tip Mach number; this is used to ad- of the helicopter, so the external noise radiation must be a just the source noise level of the measured flight condition function of the helicopter operating state. The propagation for airspeeds other than that measured, but since the cor- model estimates how the sound radiated by the helicopter rection is formulated in terms of the non-dimensional ad- will propagate through the atmosphere and around terrain vancing tip Mach number, it also includes the effect of tem- to the locations of the observers, and is a strong function perature changes by way of changes in the ambient speed of the environmental conditions and terrain. The observer of sound. However, the simple 2nd order polynomial curve model characterizes the observer characteristics that are im- fit used by the INM method does not fully account for the portant for detection or annoyance.
changes in rotorcraft noise sources due to both flight and ambient condition changes, nor can the integrated model- The focus of this paper is on improving helicopter noise ing method capture changes in the directivity of noise due source modeling. Without an accurate description of noise to changes in operating condition. (Ref. 8) radiated at the source, the acoustic impact of helicopter op- erations on observers cannot be accurately predicted. Exist- ing empirical noise models are normally based upon acous- Objective tic measurements of specific helicopters that are flown in steady-state conditions over a ground-based microphone measurement array. The measured acoustic data are then The main objective of this paper is to improve the under- back-propagated to an assumed point of radiation in order to standing of the effects of ambient conditions on helicopter form a compact helicopter source noise model that is valid external noise radiation using a non-dimensional analyti- at the chosen operating condition of the specific helicopter. cal model of main rotor harmonic noise. A new physics- This measurement and modeling process is repeated for a based experimental method called “Fundamental Rotorcraft number of steady operating conditions, with the acoustic Acoustic Modeling from Experiments” (FRAME) is used data stored as a function of the specific operating condition. to assess the acoustic radiation of an example helicopter An empirical helicopter noise source model is constructed operating at altitude. The operational, land-use and mis- from this data set which describes the magnitude and direc- sion planning implications of ambient conditions on source tion of radiated noise as a function of the helicopter oper- noise modeling are also briefly addressed.
Operations at Altitude and the Standard Atmosphere Helicopters are strongly influenced by ambient conditions Density and those conditions are strongly affected by increases in Speed of Sound operating altitude. Temperature, density, and ambient pres- Ambient Pressure sure all decrease with increasing altitude—this is shown in 0 5000 10000 15000 the top plot of Figure 1, in accordance with the International Standard Atmosphere (ISA) model. (Ref. 9) These changes affect helicopter performance and noise, usually in an ad- μ χ verse manner.
At altitude, the air is thinner and the temperature de- creases. Lower air density forces the helicopter to operate at high blade lift coefficients that can decrease performance 0 5000 10000 15000 Percent of Sea Level Value and increase the likelihood the blade will stall. The lower temperature also increases the operating Mach number of C the rotor—again decreasing performance. The aerodynam- T ics of the rotor influence noise radiation. Although the pilot M H may maintain the same flight condition, as indicated by the aircraft’s instruments, the aerodynamic and acoustic state of the rotor will change.
0 5000 10000 15000 Altitude, ft Dimensionally-Defined Flight Conditions Fig. 1. (top) The variation in atmospheric and govern- ing parameters for the ISA model. (mid/bottom) Cor- Flight conditions are typically defined by pilots using di- responding variations in the non-dimensional governing mensional parameters, i.e. indicated airspeed (IAS) and ◦ parameters for a constant 60 kts IAS -6 FPA approach.
flight path angle. Likewise, these parameters are often used to define the operating condition of the helicopter during the construction and usage of empirical helicopter source noise models. However, for a given indicated airspeed and flight advance ratios associated with 60 kts IAS flight under sea path angle, the non-dimensional parameters that are known level and at 15,000 ft ISA altitude conditions. While safety to govern rotor harmonic noise vary with ambient density of flight considerations dictate that pilots fly the helicopter and speed of sound. In this paper, the governing parameters with respect to indicated airspeed, for noise modeling pur- used to define the rotor operating condition are the advance poses, true airspeed could be used to define the helicopter ratio ( μ ), wake skew ratio ( χ ), thrust coefficient ( C ), and T flight condition. This is equivalent to holding advanced ra- hover tip Mach number ( M ). The definition and physi- H tio fixed. The effects of this approach are considered in cal relevance of these parameters is explained in Appendix Appendix II.
I. The effect of this variation in ambient conditions on the non-dimensional operating condition of a helicopter rotor is The increase in the rotor induced inflow with altitude illustrated in lower two plots of Figure 1 for a flight condi- due to the decrease in ambient air density is matched by the tion defined by a constant set of dimensional parameters— increase in advance ratio for the same indicated airspeed.
◦ in particular, for a Bell 206B3 operating at a -6.0 flight path Therefore, the wake skew ratio remains unchanged with al- angle and 60 kts IAS at a variety of ISA altitude conditions.
titude for a flight condition maintaining constant indicated The variation in governing parameters with ambient airspeed. However, the wake skew ratio will vary with alti- conditions leads to a changes in the aerodynamic and acous- tude for a constant true airspeed flight condition. The wake tic state of the rotor. As air density decreases with in- skew ratio is related to the average “miss-distance” between creasing altitude, the non-dimensional thrust coefficient in- the vortices and blades, and is consequently a significant pa- creases, bringing the rotor blades closer to stall and increas- rameter governing Blade-Vortex Interactions (BVI). Lastly, ing the circulation strength of the trailed tip vortices which due to the decrease in ambient temperature with altitude, form the rotor wake. This also leads to an increase in the the speed of sound decreases, leading to an increase in the induced inflow through the rotor. In addition, the decreased rotor tip Mach number. Altogether, these effects result in a air density causes the rotor advance ratio with respect to the significant change in the rotor acoustic state with variation medium to increase as true airspeed increases for the same in altitude that is not accounted for in any of the empirical indicated airspeed. This change in advance ratio results in a rotor noise modeling methods currently in use, all of which change in the epicycloidal pattern of the wake; for example are developed on the basis of dimensional performance pa- Figure 2 shows the “top-view” geometry of the wake for the rameters.
1 Defi ne Operating Conditions by Flight Test Non-Dimensional Wind Tunnel 0.8 Vehicle Governing Rotor Measurments Parameters of Measurements 0.6 Each T ype of Noise Source Main, T ail and Non- 0.4 Rotor Harmonic Noise Separation 0.2 Identifi cation of Identifi cation of y/R Non- Dependent Dependent Dimensional − 0.2 Modeling Modeling Analytical Parameters for Parameters for Model Each Condition each Condition − 0.4 − 0.6 Relate Dependent Modeling Sea Level Parameters to Governing − 0.8 ISA 15,000 ft Parameters (Neural Network) − 1 − 1 − 0.5 0 0.5 1 x/R Fig. 3. A flowchart describing the FRAME method for developing rotorcraft source noise models.
Fig. 2. “Top-view” epicycloidal wake geometry for sea sults in a set of dependent modeling parameters associated level and ISA 15,000 ft advance ratios at 60 kts IAS.
with the non-dimensional governing parameters of the ro- Fundamental Rotorcraft Acoustic Modeling tor noise sources. Using the dependent modeling param- from Experiments eters developed from both flight test measurements of full vehicles and wind tunnel measurements of isolated rotors, The Fundamental Rotorcraft Acoustic Modeling from Ex- a neural network model is employed to develop a func- periments (FRAME) methodology (Ref. 10), previously de- tional relationship between the non-dimensional governing veloped by the authors, is used in this paper to describe and dependent modeling parameters over the entire range the external noise radiation of the Bell 206B3 helicopter.
of operating conditions. By combining the neural network FRAME develops non-dimensional semi-empirical noise parameter estimator with the associated analytical model, source models for specific helicopters from measured data.
estimates of noise at other operating conditions than those A flowchart of the method is shown in Figure 3. Both wind measured may be made. In this paper a FRAME model is tunnel and flight test measurements are used in the model- constructed for the Bell 206B3 helicopter using a combina- ing building process. Wind tunnel measurements allow for tion of flight test data of the Bell 206B3 (Ref. 12) and wind more careful control of the operating state of the rotor over tunnel data from the similar Operational Loads Survey rotor a wide range of operating conditions, but are usually limited tested in the German-Dutch Windtunnel (DNW). (Ref. 13) to scale models of isolated rotors. Flight test measurements The underlying analytical framework used in the are necessary to acquire noise data for the entire full-size FRAME model employs a Ffowcs Williams – Hawkings vehicle, but for practical reasons the variations in operating (FW-H) acoustic analogy method. Aerodynamic inputs are condition are limited.
provided for each condition using a tunable prescribed wake In the FRAME method, both types of experimental model combined with an incompressible indicial unsteady measurements of rotor noise are first classified by oper- aerodynamics model. The non-dimensionalized form of the ating condition in terms of the non-dimensional govern- equation (Eq. 2 in Appendix I) is solved numerically using ing parameters of rotor harmonic noise. For flight test Farassat Formulation 1A. (Ref. 14) Acoustic sources off the measurements of an entire vehicle, the acoustic signals blade surfaces, such as those causing High Speed Impul- are transformed to a wind-tunnel reference frame using a sive (HSI) noise, are neglected for the moderate advanc- time-domain de-Dopplerization technique. (Ref. 11) Peri- ing tip Mach number range examined in this paper. Thick- odic averaging is then used to separate the contributions ness noise is directly computed from the blade geometry of main rotor, tail rotor, and non-rotor harmonic noise and rotor operating condition. Loading noise, both lower sources from the transformed signal. Using a parame- harmonic and BVI noise, are determined from an assumed ter identification technique, analytical models of the rotor aerodynamic model adapted to measured data using param- noise sources are then adapted to the acoustic measure- eter identification techniques. The lower harmonic loading ments by adjusting a set of physics-based dependent mod- variations required to match the measured data are deter- eling parameters to match the noise radiated for each set mined directly, but the higher harmonic loading responsible of non-dimensional governing parameters. Application of for impulsive BVI noise is found by fitting an adjustable the method across a wide range of operating conditions re- wake model.
o The wake model is based on a modified Beddoes pre- scribed wake (Refs. 15, 16) , where the dependent param- eters adjusted by the FRAME method are used to describe the non-uniform longitudinal and lateral inflow variations across the rotor disk, the initial vortex core size and its rate 105 o of growth (Ref. 17), the tip vortex rollup radius and the rate o of wake contraction (Ref. 18), and the harmonic variation of vortex circulation strength about the rotor azimuth. The ve- locities induced by the wake onto the rotor blades are then corrected using the Beddoes-Leishman indicial aerodynam- − OASPL, dB ics model (Refs. 19,20) to account for the delayed response o of the shed wake on the rapidly changing aerodynamic load- − o ing felt by the blade elements. This is similar to the analyti- − cal modeling used in previous theoretical research into BVI o o o noise, (Ref. 21) but with additional physics-based wake dis- 0 75 0 o tortion terms to allow the model to be accurately fitted to the measured acoustic data.
Fig. 4. Hovering flight steady loading noise OASPL Once the fitting process is completed for the entire set hemisphere at ISA sea level conditions.
of measured data from both the wind tunnel and flight tests, ( C = 0 . 0029 , M = 0 . 66 ) T H the variations of the dependent parameters with respect to loading noise hemisphere estimated for the 15,000 ft ISA the governing parameters are incorporated into a single ar- altitude condition, where thrust coefficient has increased for tificial neural network model. The result is a single semi- the same vehicle gross weight, due to a decrease in density, empirical model of the Bell 206B3 which is applicable over and hover tip Mach number has increased for the same ro- a wide range of operating conditions defined in terms of the tor rotational rate, due to the decrease in the speed of sound.
four non-dimensional governing parameters. This model In addition, the ambient pressure decreases as a function of can then be used to generate acoustic hemispheres repre- both ambient speed of sound and density, as per Equation 5 senting the noise radiated by the rotor for various non- in Appendix I. There is a slight increase in OASPL with al- dimensionally defined operating conditions, including the titude, but no change in directivity. The changes in ambient effects of ambient condition variations. In this paper noise conditions, hover tip Mach number and thrust coefficient radiation is described using acoustic hemispheres which are the same in the hover condition as those shown in Fig- show the far-field noise levels normalized to a fixed dis- ure 1 for forward flight.
tance of 30 ft from the main rotor hub. For BVI noise, the levels shown are calculated using the BVISPL metric, Having a non-dimensional analytical model of the ro- which is the unweighted sound pressure level of all main tor harmonic noise sources allows the governing parameter rotor harmonic noise from the 6th through 40th harmonics variations to be assessed in isolation from one another, pro- of the blade passage frequency. For lower harmonic noise, both steady loading and thickness, the unweighted OASPL o across the entire audible frequency range is calculated. The resulting acoustic hemispheres are plotted using a Lambert conformal conic projection. (Ref. 22) o Results o Steady Loading Noise First, consider the simple case of a hovering helicopter, − 90 OASPL, dB where the constant aerodynamic lift is distributed linearly o along the blade span, and the corresponding induced drag − calculated under the assumption of uniform inflow. Figure o − 4 shows the OASPL hemisphere representation of the noise o o radiated by the helicopter at sea level–as expected for steady o 0 0 75 0 o loading noise in hover, there is no azimuthal directional- ity to the noise. The OASPL noise metric is used because Fig. 5. Hovering flight steady loading noise OASPL this noise source is known to be dominated by the funda- hemisphere at ISA 15,000 ft altitude conditions.
mental frequency, with noise levels decaying rapidly with ( C = 0 . 0046 , M = 0 . 70 ) higher frequency harmonics. Figure 5 shows the steady T H 101 ( O ver a ll &&" #&$' ′ C p C T M H &'" ( #)!'
( ##%' %"# 95 OASPL, dB ## !
OASPL, dB %' ( ## 93 $"# !
*' ( ## !
+' ( 91 ( ####' ###' 0 5000 10000 15000 ( !"# ( ###' Altitude, ft Fig. 6. (a) Variation in steady loading noise OASPL Fig. 7. 60kts IAS OASPL hemisphere of thickness noise (blue) with ISA altitude conditions. (b) OASPL vari- at ISA sea level conditions.
ations associated with individual governing parameter ( μ = 0 . 14 , M = 0 . 66 , M = 0 . 66 ) H AT variations with ISA altitude conditions.
viding some physical insight into the mechanisms which airspeed (IAS) is chosen as an independent parameter in this lead to changes in noise radiation. Figure 6 plots in blue the analysis because it is the airspeed that is normally flown by variations in the maximum steady loading noise OASPL ra- pilots in order to keep the helicopter within flight safety lim- diated in any direction with altitude, for ISA ambient con- its. Thickness noise radiates in-plane ahead of and toward ditions from those associated with sea level to 15,000 ft al- the advancing side of the rotor for any forward flight con- titude. In addition, the variations in OASPL are shown for dition. Likewise, Figure 8 shows the thickness noise hemi- cases where only one parameter is allowed to vary accord- sphere predicted for the same dimensionally defined flight ing to ISA conditions, and the rest held fixed at their sea condition at an ISA 15,000 ft altitude ambient conditions.
level values. The change in ambient pressure leads to a sig- Predictably, the directivity has not changed substantially, nificant reduction in noise levels when the other parameters, but noise levels have increased. Figure 9 shows the trend in including C , are held fixed. Of course, this is not a phys- T peak thickness noise OASPL with altitude for standard ISA ically realizable situation, because the reduction in density conditions for several different indicated airspeeds. Thick- leads to a reduction in dynamic pressure, and hence lift; C T ness noise increases more rapidly with increasing altitude must be increased to provide the same thrust at altitude. The for conditions at higher airspeeds.
increase in C associated leads to an increase in noise which T cancels much of the effect of the reduction in ambient pres- ( sure. The increase in hover tip Mach number with altitude &&" leads to a moderate increase in noise levels. In total, there is #&$' a small increase in noise with altitude for this simple steady loading source.
&'" ( #)!'
( ##%' Thickness Noise %"# Thickness noise, like all other rotor harmonic noise sources, is also affected by changes in ambient conditions. From the ## !
%' OASPL, dB non-dimensionalized FW-H equation (Eq. 2 in Appendix I), ( it is apparent that thickness noise is not governed by param- $"# ## !
*' eters that only affect rotor loading, like thrust coefficient ( ## !
and inflow ratio. Therefore, given a description of the rotor +' ( ( ####' ###' geometry, thickness noise can be predicted knowing only ( !"# ( ###' the ambient pressure and blade motion through the medium, which is effectively described by the hover tip Mach num- Fig. 8. 60kts IAS OASPL hemisphere of thickness noise ber and advance ratio. Figure 7 shows the predicted OASPL at ISA 15,000 ft altitude conditions.
acoustic hemisphere for thickness noise produced by the ( μ = 0 . 18 , M = 0 . 70 , M = 0 . 89 ) H AT Bell 206B3 main rotor during 60kts IAS flight. Indicated 125 112 100 kts IAS 100 kts IAS 80 kts IAS 80 kts IAS 60 kts IAS 60 kts IAS 110 OASPL, dB OASPL, dB 100 100 0 5000 10000 15000 0 5000 10000 15000 Altitude, ft Altitude, ft Fig. 9. Peak OASPL thickness noise level variation for Fig. 11. Thickness noise OASPL trend for hover tip ISA altitude conditions for constant IAS flight. Mach number variation with temperature at altitude.
100 kts IAS 100 kts IAS 116 80 kts IAS 80 kts IAS 60 kts IAS 60 kts IAS OASPL, dB OASPL, dB 0 5000 10000 15000 0 5000 10000 15000 Altitude, ft Altitude, ft Fig. 12. Thickness noise OASPL trend for advance ratio Fig. 10. OASPL variation in thickness noise for ambient variation to maintain constant IAS at altitude.
pressure variation per ISA altitude conditions.
An increase in the advance ratio for the same hover tip As for the steady loading case, the contributions of the Mach number corresponds to an increase in the advanc- governing parameters to variation in noise levels can be as- ing tip Mach number. (See Equation 11 in Appendix I.)
sessed independently. Figure 10 illustrates the variation in The increase in advancing tip Mach number leads to a sub- thickness noise due to a decrease in ambient pressure due to stantial increase in thickness noise levels. The increase in altitude, with the sea level values of the advance ratio and noise levels with altitude is greater for higher indicated air- hover tip Mach number held fixed. The decrease in ambient speeds. The simple monopole thickness noise calculation pressure leads to a decrease in noise levels, and the effect used in the FRAME analytical model is known to under- is proportionate for all cases. (This variation is described predict noise levels at high advancing tip Mach numbers; by Equation 5 in Appendix I.) The variation in thickness the increase in noise with altitude when flying constant in- noise with only hover tip Mach number varying in accor- dicated airspeed is likely to be even higher in reality than dance to the ISA altitude conditions is shown in Figure 11.
predicted in this paper for high flight speeds.
As should be expected, the increase in hover tip Mach num- ber with altitude causes a similar increase in thickness noise for all three indicated airspeeds.
Blade-Vortex Interaction Noise Figure 12 shows the variation in thickness noise with only the advance ratio varying in order to maintain the same Blade-vortex interaction noise is a special case of load- indicated airspeed (IAS) as density decreases with altitude. ing noise, and is much more complex. The full FRAME ( ( &&" &&" #&$' #&$' &'" &'" ( ( #)!' #)!'
( ( ##%' ##%' %"# %"# ## ## ! !
BVISPL, dB BVISPL, dB %' %' ( ( $"# ## $"# ## ! !
*' *' ( ( ## ## ! !
+' +' ( ( ( ####' ( ####' ###' ###' ( ( !"# !"# ( ( ###' ###' ◦ ◦ Fig. 13. 60kts IAS -6 descent BVISPL hemisphere at Fig. 14. 60kts IAS -6 descent BVISPL hemisphere at ISA sea level conditions. ISA 5,000 ft conditions.
( μ = 0 . 14 , χ = 0 . 046 , C = 0 . 0029 , M = 0 . 66 ) ( μ = 0 . 16 , χ = 0 . 046 , C = 0 . 0034 , M = 0 . 67 ) T H T H model described previously is used to show effects of am- 20,000 ft ISA altitude prediction—in this condition, the re- bient condition variations on BVI noise. Figure 13 shows treating side BVI “hotspot” has disappeared, but a third ad- the BVISPL contours on the surface of a 30 ft radius vancing side hotspot begins to form ahead of and toward the acoustic hemisphere produced by the Bell 206B3 main ro- advancing side of the rotor.
tor FRAME model for a typical 60 kts indicated airspeed Figure 18 shows the variation of the peak and average ◦ (IAS), -6 flight path angle approach condition, known for BVISPL levels radiated over all directions across the en- high levels of BVI noise in standard sea level conditions.
tire range of ISA altitudes. Initially, BVISPL levels de- Two BVI radiate towards the advancing side: the dominant crease with altitude reaching a minimum at about 5,000 ft ◦ one radiates towards 120 azimuth and the weaker one to- ISA altitude—after this point, BVISPL see significant in- ◦ wards 160 azimuth. In addition, a weak BVISPL “hotspot” creases with altitude throughout the practical range of oper- ◦ can be observed on the retreating side of the rotor at 290 ating conditions.
azimuth.
Using the non-dimensional model, it is possible to ex- Figure 14 shows a similar BVISPL hemisphere for the amine in isolation the effect of each of the governing param- same flight condition at ambient conditions corresponding eter variations with altitude on BVI noise radiation. First, to a 5,000 ft ISA altitude. While all three BVI ”hotspots” the case is considered where all four non-dimensional gov- are still present, the magnitude of the BVI hotspots has increased. The increase in noise levels is not uniform; ( the noise radiated by the foremost advancing side BVISPL &&" #&$' hotspot has increased more rapidly than the others. In addi- tion, the advancing side BVISPL “hotspots” have shifted in direction further towards the advancing side of the rotor.
&'" ( #)!'
Figure 15 shows the hemisphere predicted by the model ( ##%' for the same dimensionally defined flight condition at a 10,000 ft ISA altitude. The BVI “hotspot” closer to the %"# retreating side has increased further in level. On the ad- ## vancing side the foremost “hotspot” has increased even !
%' BVISPL, dB ( more in BVISPL, dominating the rearmost advancing side $"# ## “hotspot.” !
*' ( ## The 15,000 ft ISA altitude BVISPL hemisphere pre- !
+' ( dicted by the FRAME model is shown in Figure 16.
( ####' ###' ( !"# ( BVISPL levels increase even further, but this time it is the ###' advancing side level which increases the most. Both the ◦ advancing and retreating side “hotspots” shift rearward.
Fig. 15. 60kts IAS -6 descent BVISPL hemisphere at ISA 10,000 ft conditions.
The retreating side BVISPL levels continue to decrease ( μ = 0 . 16 , χ = 0 . 046 , C = 0 . 0039 , M = 0 . 68 ) T H with further increases in altitude. Figure 17 shows the ( &&" 110 #&$' Peak Average &'" ( #)!'
( ##%' %"# BVISPL, dB ## !
BVISPL, dB %' ( ## $"# !
*' ( ## 98 !
+' ( ( ####' ###' ( 96 !"# ( 0 5000 10000 15000 ###' Altitude, ft ◦ Fig. 16. 60kts IAS -6 descent BVISPL hemisphere at Fig. 18. Variation of BVISPL values with ISA altitude ISA 15,000 ft conditions.
◦ conditions for 60 kts IAS, -6 descent flight.
( μ = 0 . 18 , χ = 0 . 046 , C = 0 . 0046 , M = 0 . 70 ) T H ( &&" #&$' erning parameters are held fixed at their ISA sea level val- ues, but ambient pressure is allowed to change. The pre- dicted hemisphere for the 15,000 ft ISA altitude is shown &'" in Figure 19. The directivity of the radiated noise remains ( #)!'
unchanged from the sea level case, but the levels have de- ( ##%' creased, as would be expected from Equation 5 in Appendix I.
%"# Figure 20 shows the BVISPL hemisphere contours pro- ## !
%' BVISPL, dB duced for the case where the thrust coefficient ( C ) is in- T ( ## creased to the value corresponding to a 15,000 ft ISA al- $"# !
*' titude (as in Figure 1), but the other three governing pa- ( ## !
+' rameters, as well as the ambient pressure, are held fixed at ( ( ###' ####' their standard sea level values. This has the direct effect of ( !"# ###' ( increasing the circulation strength of the trailed vortices in the model, as described in Equation 13. Consequently, the Fig. 19. BVISPL hemisphere at 15,000 ft ISA altitude ( ambient pressure with μ , χ , C and M held at ISA sea T H &&" level values.
#&$' noise resulting from each BVI is increased equally resulting in a uniform increase in BVISPL levels in all directions.
&'" Advance ratio increases with increasing altitude for the ( #)!'
( ##%' same indicated airspeed, due to the decrease in air density.
Figure 21 shows the resulting BVISPL hemisphere for a %"# change in advance ratio corresponding to 15,000 ft ISA al- titude, with the other three governing parameters and am- ## !
%' BVISPL, dB bient pressure held fixed. Compared to BVI noise radia- ( tion at standard sea level condition, shown in Figure 13, the $"# ## !
*' increased advance ratio results in an increase in BVISPL ( ## !
+' noise levels on the advancing side, due in part to an in- ( ( ####' ###' crease in advancing tip Mach number. In addition, there ( !"# ( ###' is a significant change in the directivity of the BVI noise towards the advancing side of the rotor. The increased ad- ◦ Fig. 17. 60kts IAS -6 descent BVISPL hemisphere at vance ratio at altitude substantially changes the geometry ISA 20,000 ft conditions.
of the BVI, moving the vortices rearward relative to the ( μ = 0 . 22 , χ = 0 . 046 , C = 0 . 0054 , M = 0 . 71 ) T H blades and changing the interaction angles for the same in- ( ( &&" &&" #&$' #&$' &'" &'" ( ( #)!' #)!'
( ( ##%' ##%' %"# %"# ## ## ! !
BVISPL, dB BVISPL, dB %' %' ( ( ## ## $"# $"# ! !
*' *' ( ( ## ## ! !
+' +' ( ( ( ( ####' ####' ###' ###' ( ( !"# !"# ( ( ###' ###' ◦ ◦ Fig. 20. 60kts IAS -6 descent BVISPL hemisphere for Fig. 22. 60kts IAS -6 descent BVISPL hemisphere for C only at ISA 15,000 ft altitude conditions. M only at ISA 15,000 ft altitude conditions.
T H ( μ = 0 . 14 , χ = 0 . 046 , C = 0 . 0046 , M = 0 . 66 ) ( μ = 0 . 14 , χ = 0 . 046 , C = 0 . 0029 , M = 0 . 71 ) T H T H fects all interactions similarly, so that there is no significant dicated airspeed, as shown in Figure 2. The change in wake change in directivity.
geometry influences how the acoustic disturbances of BVI phase in the medium, as explained in Appendix I, and con- Figure 23 shows the overall trends in BVISPL for varia- sequently leads to a change in the azimuthal directivity of tions in each of the governing parameter variations with al- radiated BVI noise.
titude in isolation. As might be expected, BVISPL levels in- crease uniformly with the variations in thrust coefficient and As altitude increases, temperature tends to decrease, hover tip Mach number with ISA altitude conditions. Like- leading to a reduction in the speed of sound and an increase wise, the decrease in ambient pressure alone results in a pre- in all Mach numbers, including the hover tip Mach num- dictable decrease in BVI noise levels. Most notable is the ber. Figure 22 shows the BVISPL hemisphere contours pre- change in BVISPL with advance ratio—initially, BVISPL dicted by the model for the 15,000 ft ISA hover tip Mach levels decrease as advance ratio increases. However, after number, with the other governing parameters and ambient 5,000 ft ISA altitude BVISPL increase with increasing al- pressure held at their sea level values. In general, the in- titude and advance ratio. This is because the change in ad- crease in blade section Mach numbers results in an increase vance ratio leads to a change the epicyclodial wake geome- in noise levels. The change in hover tip Mach number af- try. As the BVI locations move aft, the rearmost BVI on the advancing side weakens while the next interaction forward ( in the wake becomes stronger, as indicated by the difference &&" #&$' in BVI noise directivity between BVISPL hemispheres for the sea level (Figure 13) and 15,000 ft ISA (Figure 21) ad- vance ratio operating conditions. At 5,000 ISA altitude, nei- &'" ther interaction is at its strongest and so the overall BVISPL ( #)!'
( minima is reached. There is no change in the wake skew ra- ##%' tio with altitude for constant indicated airspeed, since the inflow increases in proportion to increases in advance ra- %"# tio, and so this parameter does not contribute to changes ## ! in noise with altitude for this dimensionally-defined flight %' BVISPL, dB ( condition. More details are provided in Appendix I.
$"# ## !
*' Three of the four governing parameters contribute to ( ## !
+' BVI noise variations with altitude for this flight condition.
( ( ####' ###' Variations in hover tip Mach number and thrust coefficient ( !"# ( ###' lead to significant increases in BVI noise with increasing altitude, but no significant changes in directivity. This in- ◦ Fig. 21. 60kts IAS -6 descent BVISPL hemisphere for crease is moderated by the reduction in ambient pressure μ only at ISA 15,000 ft altitude conditions.
with altitude. Significant changes in the levels and directiv- ( μ = 0 . 18 , χ = 0 . 046 , C = 0 . 0029 , M = 0 . 66 ) T H ity of BVI noise are caused by the variation in advance ratio 110 111 o ′ C p 60 kts IAS, − 6 110 o C 80 kts IAS, − 6 T o 60 kts IAS, − 3 M H 109 o 60 kts IAS, − 9 μ 106 108 χ Peak BVISPL, dB Peak BVISPL, dB 102 105 98 102 0 5000 10000 15000 0 5000 10000 15000 Altitude, ft Altitude, ft Fig. 23. Peak BVISPL trends for individual governing Fig. 24. Peak BVISPL trend for varying ISA altitude parameter variations with altitude. conditions at different dimensionally-defined flight con- ditions.
with altitude when indicated airspeed is held constant, due ( to the corresponding variation in the wake geometry. As &&" #&$' different BVI are strengthened or weakened by changes in advance ratio, the peak BVISPL can increase or decrease.
Thus far, the results shown have all been for the same &'" ◦ ( dimensionally defined 60 kts IAS, -6 flight path angle ap- #)!'
( ##%' proach condition. The trends shown for this flight condi- tion are not necessarily applicable to other flight conditions, %"# where the advance ratio and wake skew ratio define differ- ## ent wake geometries and may result in different variations !
BVISPL, dB %' in noise levels with ambient conditions. Figure 24 shows ( $"# ## the trends in peak BVISPL levels with altitude for several !
*' ( different flight conditions. For the faster 80 kts IAS ap- ## !
+' proach, the lowest peak BVISPL levels occur at a higher ( ( ####' ###' ( altitude, due to the change in the epicycloidal wake geome- !"# ( ###' try at a different advance ratio. In addition, because of the initially higher advancing tip Mach number, the rate of in- ◦ Fig. 25. 60kts IAS -6 descent BVISPL hemisphere at crease of BVISPL after this minimum is higher than for the ◦ ISA sea level +50 F conditions.
◦ 60 kts IAS case. For the shallower -3 flight path angle ◦ ◦ path angle approach at sea level ISA -50 F and +50 F, re- approach, the BVISPL initially increases with altitude— spectively. Directivity changes only slightly, with changes because of the greater inflow through the rotor for the in hover tip Mach number having slightly more effect on the shallower descent condition, the wake skew ratio is larger advancing side of the rotor. Overall, BVISPL noise levels and the BVI near the front of the rotor remains dominant increase with decreasing temperature and vice versa. Fig- for longer—consequently, the minimum BVISPL point is ◦ ure 27 shows the overall trend in BVISPL noise levels with reached at a higher altitude. For the steeper -9 descent, the changing temperature for this flight condition.
reduced inflow reduces the wake skew ratio, which keeps the wake near the rotor blades towards the rear of the rotor disk, and the second BVISPL peak occurs earlier as the in- True Airspeed (TAS) as an Independent Parameter teraction near the rear of the rotor grows stronger and then weaker with increasing advance ratio.
Advance ratio does not vary with altitude for a fixed true air- In addition to changes in ambient conditions due to al- speed, but the the wake skew ratio now varies with changing titude, temperature changes occurring independently of a ambient density—this case is examined in more detail in change in density result in a change in the speed of sound. Appendix II. Overall, there are smaller, but still significant This variation causes changes in the hover tip Mach num- increases in BVISPL with altitude, due to changes in hover ber as well as ambient pressure. Figures 25 and 26 show tip Mach number, thrust coefficient, and wake skew ratio.
◦ the BVISPL hemisphere contours for the 60 kts -6 flight However, because advance ratio remains fixed for a con- ( ical helicopter source noise modeling methods, the effects &&" on each noise source on the overall external noise radiation #&$' need to be considered separately. For this reason, no simple approach is likely to provide an accurate and complete cor- &'" rection of existing helicopter noise source models. Current ( #)!'
empirical helicopter noise source models generally classify ( ##%' flight conditions in terms of indicated airspeed and flight path angle—under a single known ambient condition, this %"# corresponds to variations in advance ratio and wake skew ## ratio. Variations in hover tip Mach numbers and thrust coef- !
BVISPL, dB %' ( ficients captured during typical test programs are small and ## $"# ! unintentional, but variations in these parameters can be sig- *' ( ## nificant over the practical range of helicopter operating con- !
+' ditions. The physics-based and non-dimensional FRAME ( ( ####' ###' ( method offers one solution to this problem, allowing rotor !"# ( ###' noise models to be constructed for each noise source us- ing both measured flight test data of a full scale vehicle ◦ Fig. 26. 60kts IAS -6 descent BVISPL hemisphere at under a practical range of operating conditions and wind ◦ ISA sea level -50 F conditions.
tunnel data of similar rotors under a much wider and more carefully controlled range of operating conditions than can Peak be achieved in flight. However, the FRAME method will Average require validation against measurements of full scale heli- copters operating across a range of ambient conditions be- fore it is ready for routine use.
Conclusions The parameters that govern helicopter external harmonic Peak BVISPL, dB noise radiation have been analyzed using a non-dimensional form of semi-empirical theory and parameter identification techniques. Although the approach was applied to the Bell 206B3 two-bladed helicopter in this paper, the findings are thought to be representative of other single main rotor he- − 50 − 40 − 30 − 20 − 10 0 10 20 30 40 50 o licopters. Based upon this modeling, the noise produced ∆ ISA Sea Level Temperature, F by a helicopter operating at several different altitudes was estimated. Based upon these results, it was found that: Fig. 27. Variation of BVISPL values for ISA sea level ◦ temperature variations at 60 kts IAS, -6 descent flight.
• In hover, lower frequency noise due to steady loading stant true airspeed, the directivity of the BVI is not changed increases slightly with altitude. Decreases in ambient significantly. There is a moderate increase in thickness pressure with altitude reduce the radiated noise but are noise levels with altitude for high true airspeed flight condi- mitigated by increasing hover Mach numbers. In for- tions and a moderate decrease in levels with altitude for low ward flight, the lower harmonics of loading will con- true airspeed flight conditions. This is because thickness tribute as well and noise will also vary with advance noise is more sensitive to changes in the speed of sound at ratio.
higher advancing tip Mach numbers.
• Thickness noise levels increase with increasing alti- tude when flying constant indicated airspeed because Implications for Mission Planning Tools of the dependency of thickness noise on advancing The implications for the development of land-use and mis- tip Mach number. It is mitigated slightly because of sion planning tools are clear; helicopter source noise mod- decreasing atmospheric pressures, but the strong de- els must incorporate the effects of ambient conditions on pendency on advancing tip Mach number dominates the rotor noise sources in order to avoid significant errors in (8 dB OASPL/10,000 ft). In practice, increases in ad- the estimation of ground noise and detectability contours. vancing tip Mach number may cause HSI noise to de- The effects of ambient condition variations are somewhat velop at altitude, leading to further increases in noise different for each rotor harmonic noise source; if correc- levels and changes in the frequency spectrum of radi- tions for ambient conditions are to be developed for empir- ated noise.
• When flying true airspeed, the change in thickness Appendix I: Non-Dimensionalization and Development noise levels with increasing altitude is more mod- of the Governing Parameters of Rotor Harmonic Noise erate. The increase in hover tip Mach number in- Non-Dimensionalization creases thickness noise levels, but is counteracted by the decrease in ambient pressure. At high true air- In most cases, physical relationships among variables speeds, the net effect is an increase in thickness noise can be discovered by formulating problems using non- (3/4 dB OASPL/10,000 ft at 100 kts TAS), but at dimensional analysis. Buckingham’s Π theorem, formal- low airspeeds, thickness noise decreases with altitude ized one century ago, provides a systematic procedure for (-1 dB OASPL/10,000 ft at 60 kts TAS).
determining a set of non-dimensional parameters governing a physical process. When a problem is correctly formulated on a non-dimensional basis, key relationships between the • BVI noise can change markedly with altitude for flight variables become defined in a way which makes their phys- operations at constant indicated airspeed. Indicated ical significance more clear.
airspeed compensates for decreasing density at alti- tude by increasing the forward airspeed of the heli- Consider the Ffowcs Williams – Hawkings (Ref. 23) copter. This changes the helicopters true airspeed, equation, Eq. 1, which describes the sound generated by which changes the epicycloidal BVI intersection pat- arbitrary surfaces in motion: terns, thus changing the directivity and magnitude of [ ] ∫ 1 ∂ ρ v 0 n the resulting noise. The decrease in air density with ′ p ( x , t ) = dS − (monopole) (1) 4 π ∂ t r | 1 − M | altitude also increases the circulation strength of the S r τ [ ] ∫ tip vortices trailed from each blade, causing increases 1 ∂ P n i j j dS + (dipole) in BVI noise levels. In addition, decreasing tempera- 4 π ∂ x r | 1 − M | S i r τ ture with altitude increases BVI noise radiation levels [ ] ∫ 1 ∂ Q i j due to increasing Mach numbers. Changes of up to dS (quadrupole) 4 π ∂ x x r | 1 − M | i j S r 7 dB BVISPL per 10,000 feet altitude were estimated. τ The monopole term models thickness noise by consider- ing the rotor blade as a set of monopole mass sources and • Flying true airspeed tends to maintain BVI noise sinks which describe how the blades displace the medium.
radiation patterns and noise levels. Advance ratio The dipole term models the mechanisms of loading noise, is constant with altitude explaining the similarity of including BVI, as a set of aerodynamic dipole sources on the radiation patterns. Noise levels increase slightly the surface of the blades that describe the forces the blades (1 dB BVISPL/10,000 ft) with altitude because of in- exert on the medium. The quadrupole term includes the ef- creasing tip vortex strength and increasing Mach num- fects of complex noise sources inside a fluid volume sur- bers, but the increase is mitigated to some degree by rounding the rotor blades—this is how the effect of the the decrease in atmospheric pressure.
transonic flow field that causes HSI noise is modeled. In this paper, the quadrupole term is neglected and the mod- • Formulating the problem in non-dimensional terms eling restricted to lower tip Mach number operating condi- is helpful in interpreting the variations in the acous- tions where HSI noise does not occur. The FW-H equa- tic state of the rotor with variation in the operating tion for the monopole and dipole terms can be rewritten condition. The sensitivity of the radiated noise each in non-dimensional form (Eq. 2), following the approach non-dimensional governing parameter has been clearly of Reference 13, where all all geometric terms are non- shown.
dimensionalized by the rotor radius, and all temporal terms by the rotor rotational rate.
These results show that it is important to consider how mea- ∫ 1 ∂ ξ M sured helicopter acoustic data taken under a given set of ¯ ¯ C ′ ( ¯ x , t ) = d S − (2) p conditions might be used to predict noise under different ¯ 4 π ∂ t ¯ r ( 1 − M ) S r ∫ operational conditions. It is obvious that Mach number is an 2 C n M 1 ∂ p j i j ¯ important parameter that will strongly govern radiated noise d S 4 π ∂ ¯ x ¯ r ( 1 − M ) i S r and should be carefully accounted for. For BVI noise, if the helicopter is flown so that true airspeed (TAS) is constant, where the acoustic pressure has been non-dimensionalized then the measured noise patterns that have been gathered with respect to the ambient pressure (expressed as a func- at one altitude can approximate the noise that is radiated at tion of ambient density and speed of sound): other altitudes. However, if indicated airspeed (IAS) is held ′ ¯ at these different altitudes, then significant changes in the p ( ¯ x , t ) ′ ¯ C ( ¯ x , t ) = (3) p patterns and levels of BVI noise are to be expected.
ρ a and the blade surface pressures are non-dimensionalized by For example, equation 10 can be used to relate the hover the dynamic pressure at the respective blade element: and advancing tip Mach numbers: p i j M = M ( 1 + μ ) (11) AT H C = (4) p i j ρ U ( r , ψ ) The advance ratio and hover tip Mach number also set This non-dimensionalization indicates that for an other- the epicycloidal pattern of the wake formed by the trailed wise identical non-dimensional operating condition of the tip vortices responsible for BVI, as shown in Figure 28. In rotor, the acoustic pressure amplitudes will vary in propor- combination, these two governing parameters set the num- tion to the ambient pressure ratio, as expressed in Eq. 5.
ber of potential BVI occurring on the advancing and retreat- ing sides of the rotor, as well as the interaction angles be- ( ρ a ) 0 1 ′ 0 ′ tween the rotor blades and the vortices during BVI events.
¯ ¯ p ( ¯ x , t ) = p ( ¯ x , t ) (5) 1 2 ( ρ a ) 0 2 0 The interaction angle of BVI controls how the acoustic dis- turbance accumulates in phase through the medium, and therefore contributes to the amplitude of BVI impulses and Governing Parameters of Rotor Harmonic Noise determines the azimuthal directivity of BVI noise. Figures 29 and 30 use 2D Huygens’ wavelets to illustrate how the The non-dimensional rotor operating condition is defined BVI phasing process causes the radiation of noise towards by a set of four independent parameters which are known specific azimuths for oblique and parallel BVI, respectively.
(Refs. 13, 24) to govern the rotor harmonic noise sources, The thrust coefficient is the non-dimensionalization of and these parameters can be expressed as the wake skew ra- rotor thrust with respect to a reference dynamic pressure, tio ( χ ), advance ratio ( μ ), thrust coefficient ( C ), and hover T calculated from the rotor tip speed and ambient air density, tip Mach number ( M ). This set of four non-dimensional H and a reference area taken as the rotor disk area.
governing parameters is derived from the physical pro- cesses of rotor harmonic noise generation, including thick- T ness and BVI noise. C = (12) T ρ A ( Ω R ) For a fixed hover tip speed, hover tip Mach number is defined by the ambient speed of sound: For steady flight conditions, the rotor thrust is approx- imately equal to the vehicle weight. Therefore, the ambi- Ω R M = (6) ent air density determines thrust coefficient for a particu- H a lar rotorcraft with fixed gross weight and rotor tip speed.
The thrust coefficient relates to the blade section loading, where ambient speed of sound can be estimated in air with and hence influences lower harmonic loading noise. In ad- a function of ambient temperature: dition, the trailed tip vortex circulation strength is directly √ proportional to rotor thrust coefficient, which influences the a = γ R T (7) 0 ∗ ∗ 0 strength and acoustic impact of BVI events. For instance, the analytical solution for the non-dimensionalized trailed Likewise, the rotor advance ratio is determined by the tip vortex circulation strength due to an idealized triangular true airspeed at which the rotor moves through the medium.
spanwise lift distribution is shown in Eq. 13.
V Γ 2 π C T μ = (8) = (13) Ω R Ω R b This can be related to the indicated airspeed, which is The thrust coefficient is also directly related to the blade a function of dynamic pressure, through air density using loading coefficient, C / σ , which has a similar form to the T the following expression valid for the range of rotorcraft non-dimensionalized blade surface pressure term, C , of p i j airspeeds and altitudes: Equation 2. Through Equation 14, provided in Reference 26, the blade loading coefficient can also be related to the √ ρ mean lift coefficient of the rotor blade sections. In hovering V = V (9) IAS ρ SL flight, rotor stall occurs for C / σ ∼ 0 . 13, and decreases T with increasing advance ratio due to asymmetry in local lift coefficient. Consequently, as altitude increases so does the The combination of hover tip Mach number and advance blade loading coefficient, bringing the rotor closer to stall.
ratio therefore specify the Mach number of all blade sec- Not only does this impose limits on the operation of the tions at all azimuths.
helicopter in high altitude conditions, it will also change M = M ( r , ψ ) = M ( r + μ sin ψ ) (10) rotor’s aerodynamic and acoustic state.
H where the rotor inflow ratio is the mean inflow velocity through the rotor disk non-dimensionalized by the rotor tip speed, and is defined: − V sin α + v T PP i λ = (16) Ω R The inflow ratio is determined by both the freestream ve- locity through the rotor and the velocity induced by thrust.
The contribution of the induced velocity can be estimated using simple momentum theory, resulting in Eq. 17.
C T √ λ = − μ tan α + (17) T PP 2 2 2 λ + μ The component of the freestream velocity which passes through the rotor and contributes to the inflow ratio is de- Fig. 28. The top-view geometry of the wake is set by the termined by the angle of attack between the rotor tip-path- rotor advance ratio and hover tip Mach number and de- plane and the free stream velocity. This angle of attack termines the BVI locations and interaction angles. From can be determined to first order using a simple longitudi- Reference 25.
nal force balance: D + H a f x α = − − γ − (18) T PP W g The tip-path-plane angle of attack depends on the flight path angle and longitudinal acceleration of the helicopter.
In addition, the fuselage parasite drag and rotor H-force contribute to the tip-path-plane angle of attack. For steady flight conditions where thrust and weight can be assumed equal, both the drag-to-weight (Eq. 19) and H-force-to- weight (Eq. 20) ratios can be estimated in terms of advance Fig. 29. Huygens’ wavelet diagram of an oblique BVI, ratio and thrust coefficient.
as in interaction #2 of Figure 28.
D f f e ( ) = μ (19) 2 4 ¯ C C 1 − μ + 9 μ / 4 T L W 2 AC T = (14) σ 6 1 + 3 μ / 2 H σ c 1 + 4 . 6 μ d 0 = (20) W 8 μ C T The wake skew ratio, χ , is defined in this paper to be the ratio of net rotor inflow perpendicular to the rotor tip- The wake skew ratio generally determines how at which path-plane to flow parallel to the tip-path-path. The can be angle the the trailed tip vortices composing the rotor wake expressed as the ratio of the non-dimensional inflow ratio to will convect from the front of the rotor tip-path-plane, and the advance ratio: consequently governs the average “miss distance” between λ the blades and vortices during BVI events, as shown in χ = (15) μ Figure 31. This average “miss distance” is an aggregate measure of the separation of the rotor wake from the rotor blades, and is not directly associated with any single vortex; for instance, when the average ”miss distance” is small (i.e.
the wake is near the rotor) changes in the mean inflow ratio may result in the separation between the blades and the vor- tices at some locations on the rotor to increase while at other locations the separation distance decreases. As the separa- tion distance between the vortices and blades decreases, the effect of the trailed vortex on the blade loading increases; consequently, the “miss distance” has a significant effect on BVI noise. In general, “miss distances” are at a minimum, and BVI at a maximum, when the wake skew ratio is near Fig. 30. Huygens’ wavelet diagram of a parallel BVI, as zero, and the vortices stay near the rotor tip-path-plane as in interaction #3 of Figure 28.
they convect to the rear of the rotor.
μ χ 80 Percent of MSL Value 0 5000 10000 15000 Altitude above MSL, ft C T M H Percent of MSL Value 0 5000 10000 15000 Altitude above MSL, ft Fig. 32. The relative variation in non-dimensional gov- Fig. 31. The side-view geometry of the wake is set by erning parameters with ISA altitude for a Bell 206B3 in the rotor inflow and determines the “miss-distance” be- ◦ 60 kts TAS -6.0 descending flight.
tween the vorticies and blades during BVI. From Refer- ence 25.
Sea Level 10,000 ft Appendix II: Flight Conditions 20,000 ft Defined by True Airspeed − 5 While flight conditions are typically defined in terms of in- ), degrees γ dicated airspeed (IAS), which varies with dynamic pres- sure, another option is to define flight conditions with re- spect to true air speed (TAS). Figure 32 shows the varia- − 10 tion in non-dimensional governing parameter values with changing ISA altitude conditions for the case where true Flight Path Angle ( airspeed is held constant, similar to Figure 1 for the typical indicated airspeed case. In this situation, the advance ra- tio does not vary, such that the freestream dynamic pressure − 15 30 40 50 60 70 80 90 100 decreases with altitude. This leads to a decreasing fuselage True Airspeed, kts parasite drag and rotor H-force, causing the rotor tip-path- plane to tilt backwards and reducing the inflow through the Fig. 33. A plot of the dimensionally-defined zero wake rotor. On the other hand, the reduction in air density leads skew ratio flight conditions at various altitudes.
to a substantial increase in induced inflow—overall, there is and directivity with changing ambient conditions are some- a greater increase in inflow for constant true airspeed (TAS) what less pronounced and are more predictable when defin- than when flying constant indicated airspeed (IAS). Since ing flight conditions by true airspeed instead of indicated inflow increases relative to the constant true airspeed, the airspeed, because the advance ratio remains fixed.
wake skew ratio varies with altitude. This results in the de- scent angle required for zero wake skew (and hence near The variation in thickness noise with altitude is likewise maximum BVI noise) varying with altitude, as shown in different for flight conditions defined by true airspeed than Figure 33. Depending on the true airspeed flow, the sensi- for those defined by indicated airspeed. Since advance ra- tivity of BVI to flight condition will change. The BVISPL tio remains fixed, the advancing tip Mach number only in- ◦ hemisphere contours for a 60 kts TAS -6 flight path angle creases in proportion to the increase in hover tip Mach num- approach condition at ISA altitudes of 5,000, 10,000 and ber with altitude. In addition, the reduction in ambient pres- 15,000 ft are shown in Figures 34, 35 and 36, respectively. sure with altitude reduces the amplitude of thickness noise.
The retreating side BVI “hotspot” location remains fixed Figure 38 plots the peak thickness noise level variation with with altitude, since advance ratio remains unchanged. The altitude in OASPL for several different true airspeeds. De- increase in the wake skew ratio causes a small increase in pending on the true airspeed of the vehicle, thickness noise the “miss-distances” of the BVI, but this is mitigated by the may either increase or decrease with increasing altitude.
increase in thrust coefficient and Mach numbers with alti- Higher true airspeeds correspond to higher advancing tip tude. The overall increase in BVISPL with altitude is shown Mach numbers, where the thickness noise is more sensitive in Figure 37. In general, the changes in BVISPL magnitude to further increases in advancing tip Mach number due to ( ( &&" &&" #&$' #&$' &'" &'" ( ( #)!' #)!'
( ( ##%' ##%' %"# %"# ## ## ! !
BVISPL, dB BVISPL, dB %' %' ( ( ## ## $"# $"# ! !
*' *' ( ( ## ## ! !
+' +' ( ( ( ( ####' ####' ###' ###' ( ( !"# !"# ( ( ###' ###' ◦ ◦ Fig. 34. 60kts TAS -6 descent BVISPL hemisphere at Fig. 36. 60kts TAS -6 descent BVISPL hemisphere at ISA 5,000 ft conditions. ISA 15,000 ft conditions.
( μ = 0 . 14 , χ = 0 . 048 , C = 0 . 0034 , M = 0 . 67 ) ( μ = 0 . 14 , χ = 0 . 064 , C = 0 . 0046 , M = 0 . 70 ) T H T H the decrease in ambient temperature. In practice, further in- Peak Average creases in advancing tip Mach number at high flight speeds may yield even higher increases in noise than predicted as local transonic flow allows HSI noise to develop.
In practice, helicopters must be flown according to the indicated airspeed, because the aerodynamic forces and hence vehicle performance parameters are tied to the dy- namic pressure, which varies with air density. However, 100 Peak BVISPL, dB so long as vehicle performance at altitude is taken into account when designing helicopter trajectories, helicopter noise modeling might be conducted more accurately on the basis of flight conditions defined by true airspeed than on the basis of indicated airspeed; in conjunction with the 0 5000 10000 15000 20000 flight path angle, this is equivalent to specifying flight con- Altitude, ft ditions on a non-dimensional basis of advance ratio and ( Fig. 37. Variation of BVISPL values for ISA altitude ◦ &&" conditions at 60 kts TAS, -6 descent flight.
#&$' wake skew ratio for steady flight conditions. Due to the strong effect of advance ratio on rotor harmonic noise, it &'" is also cautioned that flight conditions should not be de- ( #)!'
( fined on the basis of ground speed in helicopter source noise ##%' models, since ground speed is not equivalent to true air- %"# speed except in the absence of wind.
!
%' BVISPL, dB Acknowledgements ( $"# ## !
*' The authors would like to thank Dr. Ben Wel-C Sim and ( ## !
Michael E. Watts for helpful discussions during the prepa- +' ( ( ####' ration of this paper. In addition, the authors would like to ###' ( !"# ( ###' thank Richard D. Sickenberger, David A. Conner, Charles D. Smith, Ernesto Moralez, and William A. Decker for their ◦ Fig. 35. 60kts TAS -6 descent BVISPL hemisphere at important roles in the 2006 flight test of the Bell 206B3 he- ISA 10,000 ft conditions. licopter at Moffett Field, CA.
( μ = 0 . 14 , χ = 0 . 054 , C = 0 . 0039 , M = 0 . 68 ) T H International Organization for Standardization, “Stan- dard Atmosphere,” Technical Report 2533:1975, ISO, 100 kts TAS 109 1975.
80 kts TAS 60 kts TAS Greenwood, E. and Schmitz, F. H., “A Parameter Identi- fication Method for Helicopter Noise Source Identification and Physics-Based Semi-Empirical Modeling,” American Helicopter Society 66th Annual Forum, May 2010.
104 OASPL, dB Greenwood, E. and Schmitz, F. H., “Separation of Main and Tail Rotor noise Ground-Based Acoustic Measure- ments using Time-Domain De-Dopplerization,” 35th Euro- pean Rotorcraft Forum, September 2009.
Schmitz, F. H., Greenwood, E., Sickenberger, R. D., 0 5000 10000 15000 Gopalan, G., Sim, B. W.-C., Conner, D. A., Moralez, E., Altitude, ft and Decker, W., “Measurement and Characterization of He- licopter Noise in Steady-State and Maneuvering Flight,” Fig. 38. Peak OASPL thickness noise level variation for American Helicopter Society 63rd Annual Forum, May ISA altitude conditions for constant TAS flight.
2007.
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