Jf

f/

// ./

C+-/g/;//J "

7/-c/'a

A PARAMETRIC STUDY OF TRANSONIC BLADE-VORTEX INTERACTIONNOISE

A. S. Lyrintzis, Assistant ProfessorY. Xue, Research Assistant

Aerospace Engineering and MechanicsUniversity of Minnesota

Minneapolis, MN 55455-0153

Principal Investigator: A. S. Lyrintzis

Final Report, Contract No. NAG 6-626 (7/1/90-6/30D 1)

(NASA-CR-188811) A PARAMETRIC STUOY OF

TRANSF)NIC _LAOe-VO_TEX INTERACTION NOISE

Fin+l Technical Report, 1 dul. !9o0 - 30

Jun. [991 (_innesota Univ.) 5g p CSCL 20A

S]17]

N91-31928

Unclas

00401

f

/

fJ

ff

fJ

JJ

Abstract

Several parameters of transonic blade-vortex interactions (BVI) are being studied and someideas for noise reduction are introduced and tested using numerical simulation. The model used isthe two-dimensional high frequency transonic small disturbance equation with regions ofdistributed vorticity (VTRAN2 code). The far-field noise signals are obtained by using theKirchhoff method which extends the numerical two-dimensional near-field aerodynamic results tothe linear acoustic three-dimensional far-field. The BVI noise mechanisms are explained and the

effects of vortex type and strength, and angle of attack are studied. Particularly, airfoil shapemodifications which lead to noise reduction are investigated here. The results presented areexpected to be helpful for better understanding of the nature of the BVI noise and better bladedesign.

.£

ff

ff

jJ

J

Introduction

In recent years, helicopters have proved to be convenient and reliable means of

transportation, because of their ability to take off, land and maneuver in areas inaccessible to fixedwing aircraft. Helicopter aerodynamics are very complex, because three-dimensional, unsteady,transonic, viscous, aerodynamic phenomena are involved. (An excellent survey of helicopter

aerodynamics can be found in a recent review paper by Johnson [1].) The increasing use ofhelicopters in both military and civilian applications has drawn attention to the noise that theygenerate. In civilian applications this noise can be very annoying and in military applicationsprovides early warning of a helicopter's approach. Internal noise problems make helicoptersunattractive to prospective civilian passengers and in the military often substantially exceedacceptable limits. Noise in the design of new or modified helicopters is today a matter of greatconcern. The helicopter noise rules (Appendix H to Federation Aviation Regulations (FAR) Part36) contain the helicopter noise levels for which compliance must be shown for actual flight tests.Depending on the maximum certified weight of the helicopter, the maximum allowable noise levelsare between 88 and 108 EPNdB(Effective Perceived Noise Lever) for flyover, 90 and 110 EPNdBt'or approach, and 89 and 109 for the takeoff condition. It should be reiterated that these standardsare applicable to all type certification applications received on or after March 6, 1986 [2]. In orderto comply with these rules, the designer must have very good estimates of the detailed noisecharacteristics of the proposed rotorcraft.

Among the several types of helicopter noise [3], that due to Blade Vortex-Interactions (BVI)is one of the most important. When present, BVI leads to high levels of vibration and to intensenoise radiation. A great deal of computational and experimental effort is being expended tominimize the adverse effects of BVI, so that structural fatigue and acoustic detectability can be

reduced, and crew and passenger comfort and noise abatement can be improved. Advances inthose areas will lead to significant increases in productivity, public acceptance, and thecompetitiveness of the U. S. rotorcraft industry.

BVI is the aerodynamic interaction of a rotor blade with the trailing vortex system generated

by preceding blades as shown in figure 1 (from reference [4]). In level steady-state flight theinduced velocity of the rotor disk tends to make all the tip vortices pass under the rotor disk.However, during steady descending flight or maneux, ers the tip vortices are forced into the rotordisk plane causing strong blade-vortex interactions. The occurrence of BVI is very sensitive torotor design parameters and helicopter operating conditions and has a profound impact onhelicopter performance. When it occurs BVI is loud, impulsive in character, and tends to dominatethe other noise sources, as shown experimentally (e.g. Schmitz and Yu [5]).

The newly developed tilt rotor aircraft also have some complicated three-dimensional BVIgeometries that generate far-field noise [6]. The design characteristics of the tilt rotor aircraft makeit a suitable candidate for short-to-medium range commercial transport applications. One of theimportant issues though, is the effect of the generated noise on the community and the passengers.Tilt rotor aircraft have additional operational options. For example, descent can be accomplishedwith high or low nacelle tilt, high or low glide slope, different airspeeds, etc. Even for a givennacelle tilt and flight path, lift can be distributed differently between rotors and wing. Thus, anoptimization study of tilt rotor operations for noise reduction should be carried out. Also, tilt rotoraircraft have more complicated acoustic mechanisms than helicopters for various reasons.Previous experimental studies show that one of the dominating mechanisms during descent isblade-vortex interaction.

The noise reduction and prediction capabilities are often achievable through experimentalprograms directed at understanding the noise source mcchanisms and the effects of design andflight parameters on noise. Flight test or wind tunnel test programs can be used, but in either case

/

ff

ff

JJ

there are certain problems such as high expense, safety risks, atmospheric variability as well as

reflection problems for wind tunnel tests. Therefore, numerical simulations with a proper modelare being employed for the prediction of BVI noise because they are cheap and efficient, although avery accurate model for BVI noise has not yet been found for practical applications.

Interactions generate the most significant noise when they are intrinsically unsteady, as whenthe vortex is exactly or nearly parallel to the blade. Incompressible BVI have been successfullytreated in the past [7]. For typical helicopter cases it was shown in references [8] and [9] that theaerodynamics and aeroacoustics of the interactions are transonic. In such cases the flow can beinitially modeled by two-dimensional unsteady transonic flow (figure 2).

Unsteady transonic flow problems have been solved numerically in the past. The lowfrequency approximation of the unsteady two-dimensional Transonic Small Disturbance (TSD)equation was first solved by Ballhaus and Goorjian [10] and the LTRAN2 code was created.Since then the code has been updated to include high frequency effects [11], viscosity [12],monotone switches [13] and second order effects [14]. However, the acoustic waves resultingfrom the unsteady motion have not been adequately studied.

Two-dimensional transonic BVI was first studied computationally in the near- and mid-fieldby George and Chang [8, 9] who used the high frequency transonic small disturbance equation,including regions of convected vorticity. References [8, 9] also contain detailed discussions of thebackground and formulation of the transonic BVI problem. A comprehensive code, VTRAN2was developed [15, 16]. The vorticity is bilinearly distributed inside a vortex core and branch cutsare introduced in the x-direction. The vortex can either follow a prescribed path, or be convected

with the free stream. A new look at the physics of the acoustics of unsteady transonic flow,especially around an oscillating flap, was given in reference [17].

In references [18-24] the two-dimensional transonic BVI problem is also solved using thesmall disturbance theory and the more complex Euler and thin-layer Navier Stokes equations. AlsoBaeder et aL [24, 25] presented some near- and mid-field results. A direct comparison of theresults obtained from the different methods (from small disturbance to Navier Stokes equations)shows that the results are very similar [9]. In fact the results tend to coincide the further away wemove from the airfoil surface. At great distances from the airfoil though, the waves become verydifficult to follow because of numerical diffusion and dispersion errors, which led us to use theKirchhoff method.

The Kirchhoff method was introduced [16, 27-32] to extend the numerically calculatednonlinear aerodynamic near-field results to the linear acoustic far-field. This method uses aGreen's function for the linearized governing equation to derive a representation for the solution interms of its values and derivatives on a closed surface S in space, which is assumed to include allthe nonlinear flow effects and noise sources. The potential and its derivatives can be numericallycalculated from a nonlinear aerodynamic code (e.g. VTRAN2). The Kirchhoff method has the

advantage of including the full diffraction effects and eliminates the erroneous propagation of thereactive near-field.

In this report we first present some discussion of the BVI noise source mechanisms, whichleads to ideas for noise reduction on transonic BVI noise. Typical results for types A, B and Cshock motions are shown. Some typical results are shown in comparison to other methods.Directivity is shown for different coordinate systems. Then ideas and numerical tests for noisereduction are introduced. The results are shown for the airfoil (NACA64A0(O) shape modification

achieved through the addition to various portions of the airfoil lower surface of cosine or NACA 4-digit shapes of different maximum thickness. These results give us ideas of how to modify theshape of the airfoil for noise reduction. An example of a modified airfoil (SC1095rn) is alsodemonstrated. Then, we show results for the splitting vortex model, variations of vortex strengthand increasing angle of attack, parameters that could be adjusted for noise reduction. Finally,

3

F

.I

/-

some results for fu:_ure experimental BVI cases are shown. Some of those results were also

reported in reference [32], but a more detailed discussion is given here.

The Numerical Method (VTRAN2)

VTRAN2 is a code [ 15, 16] developed for analyzing the interactions of convected regions ofvorticity with airfoils using transonic small disturbance theory. It is based on the ADI implicitscheme of the LTRAN2 code [10] with the inclusion of the high frequency term as described inreference [11] and the addition of regions of convected vorticity using the cloud-in-cell andmultiple branch-cut approach. The code was modified to include viscosity [12] and monotoneswitches [ 13].

The equation for the unsteady transonic small-disturbance potential _ is:

A@t t + 2B_x t = C@x x + t_,y (1)

where

k2M '2 kM 2 1-M 2

A-82/3' B- 82/3, C- 82/3 -('f+l)M re@x,

is the disturbance-velocity potential, M is the free-stream Mach number, 8 is the airfoil thickness

ratio and k is the reduced frequency 0x:/U o where m is the characteristic frequency of the unsteady

motion, c is the airfoil chordlength and U o is the free stream velocity. The quantifies x, y, t, _ in

equation 1 have been scaled by c, c/81/3, m -1, and c82/3 U o, respectively. The exponent m in the

nonlinear term is chosen as m = 2, which is suitable for stronger shocks as it locates the shocks

more accurately [33].

For BVI the characteristic frequency of the motion depends on the lateral distance between

the airfoil and the vortex path. For large miss distances Yv the characteristic frequency m is Uo/Y v

and thus k=c/yv<<l. Therefore, the k 2 term in A ifnplies that the ftrst term (i. e. high frequency

term) in equation (1) can be dropped giving the low frequency small disturbance theory, which

was used in the LTRAN2 code. However, for BVI cases of interest yv=C, and thus k-- I and the

full small disturbance equation (1) (including the high frequency term) is needed. Since time t isnondimensionalized, the choice of k for the case of BVI is irrelevant and was taken as k=l

(m=Uo/c), meaning that one time unit corresponds to a free stream convection of one chord.

The boundary conditions are:

1. Upstream outer boundary condition:

_x = t_y = 0 as x->-,,,, (2)

2. Lateral outerboundary condition:

_x = _y = 0 as

3. Downstream outer boundary condition:

y -> + ,_, (3)

4

f,/

t/

.J_-5.-

Ox + k Ot = 0 as x -> + oo (4)

4. Airfoil surface boundary condition (applied at y=0):

Oy+ aY+___Y- ax +k at as 0<x<c (5)

where Y+ defines the airfoil surface. The boundary conditions are summarized in figure 3.

For the viscosity calculations the viscous ramp method (wedge) is used. The viscous rampmodel simulates the shock/boundary layer interaction by placing a wedge-nosed ramp at the base ofthe shock to obtain the reduced shock pressure rise. The surface geometry must be augmented bythe ramp model by adding an extra viscous term in the boundary condition of equation (5). Detailsof the calculation of that viscous term can be found in reference [34]. The ramp model was derivedfor steady-state computations. However, it can be incorporated into unsteady computations in aquasi-steady fashion. Thus, the model is valid for low frequencies, and its use in high frequencyproblems such as BVI can only give some qualitative information about the effect of viscosity withalmost no additional CPU time. The more complicated and CPU time-consuming lag-entrainmentmethod which was also incorporated in our code was not used, because it was not superior to thewedge model for unsteady cases [34].

The classical Kutta condition is satisfied by this small disturbance formulation. We areinterested in cases for which the reduced frequency range is less than 4, which is the limit for theapplication of the Kutta condition [35].

The pressure coefficient Cp in the unsteady small-disturbance theory is:

Cp = -282/3( _x+ k _t) (6)

In addition, the wake condition

Fx + kl-'t = 0 (7)

implies that a branch cut exists between the trailing edge and the downstream outer boundary,

across which the potential jump is, A_ = 1-', where F is the circulation.

A finite vortex core is used (cloud-in-cell method) for reasons of computational stability.-ZI'hecore has a finite square shape limited by gridlines and the vorticity is bilinearly distributed inside.Thus, several branch cuts (in the x-direction) are introduced. The vortex can have a free path(convected by the flow) or a prescribed path (miss distance Yv = constant, vortex velocity=Uo).

Details of the theoretical formulation were given by Chang [36] and Lyrintzis [16].

An alternating direction implicit (ADD method is used for the solution of the equation, wherethe high frequency term is added in the y-sweep. An approximate factorizafion technique withmonotone switches [13] is used for the steady calculation, which provides a start-up solution.Special care is taken for the conservative differentiation along the uneven mesh.

A (213x199) mesh is used for the calculations. The computational mesh points are clusteredmore densely near and in front of the airfoil and then are stretched exponentially from the nearairfoil region to about 200 chords from the airfoil in x and 400 in y-direction. More mesh pointsare added in the y-direction for the more accurate evaluation of the normal derivatives on theKirchhoff surface. It was shown in the past that the (213x199) mesh leads to smoother results than

5

f

ff

fJ

J.J

the (213xl 19) mesh_ The code has a high vectorization level and the CPU time for each two-dimensional case on a Cray-2 computer is about 4 minutes for 800 time-marching steps.

The numerical simulation method (VTRAN2 code) introduced above is simple and efficient.Also, it is able to catch the main features of transonic BVI, which are the shock motions around

airfoils. The code was shown to agree well with other, more complex approaches including Eulerand thin-layer Navier-Stokes computations [9]. Thus, we expect that our conclusions will alsohold if more accurate Euler/Navier-Stokes predictions are used. Three-dimensionality will, ofcourse, influence the results. Some of the presented results will hold for three-dimensional cases,but only actual three-dimensional calculations (e. g. [37]) can show that. However, at greatdistances from the airfoil the waves become very difficult to follow because of numerical diffusionand dispersion errors. Thus, in order to study the far-field a more accurate method is neededwhich must also include three-dimensional effects. First, we will examine the different methodsused in acoustic studies.

Methods of Acoustic Analysis

Sound can be considered as the propagating part of the full solution of some fluid-flow

problems. In a few cases the radiated sound can be found this way. However, in most cases ofpractical interest one cannot find a full numerical solution everywhere in the flow, because ofdiffusion and dispersion errors caused by increasing mesh size in the far-field. Thus, it is oftenadvantageous, or even necessary, to develop ways of determining the far-field noise from near-field solutions. The various approaches used to find the far-field noise, as explained by George[38], can be classified as follows:

1) Full Flow Field Solution: This is a calculation of the full nonlinear flow field including far-fieldwaves. An example of an application of this technique for the calculation of radiating wavesin the mid-field from transonic blade-vortex interactions is given by Baeder et al. [25, 26].However, in order to numerically resolve the details of the acoustic three-dimensional far-

field very, fine mesh should be used which makes these computations impractical fortechnically significant problems even with today's powerful supercomputers.

2) Acoustic Analogy: This is a nonlinear near-field solution plus the Ffowcs Williams and

Hawkings equation. This approach starts from the calculation of the nonlinear near- andmid-field and the far-field is found from a linear Green's function formulation evaluated in

terms of surface and volume integrals over the retarded time transformations of the near- andmid-field flow and body surfaces. We would note that there are substantial difficulties in

including the nonlinear quadrupole term (which requires second derivatives) in the volujaaeintegrals, especially around shock surfaces. Thus, many investigators use near-field dataonly on the blade surface, which is less accurate since the effect of shocks is not accountedfor. For a review of the applications of acoustic analogy the reader is referred to Farassat andBrentner [39].

3) Nonlinear Near-field Plus KirchhoffMethod: This is a calculation of the nonlinear near- andmid-field with the far-field solutions found from a linear Kirchhoff formulation evaluated on

a surface surrounding the nonlinear-field. The full nonlinear equations are solved in the fh-stregion (near-field), usually numerically, and a surface integral of the solution over the controlsurface gives enough information for the analytical calculation in the second region (far-field). This method provides an adequate matching between the aerodynamic nonlinear near-field and the acoustic linear far-field. An advantage of the method is that the surface integralsand the first derivatives needed can be easily evaluated from the near-field CFD data; fulldiffraction and focusing effects are included while eliminating the propagation of the reactivenear-field. The method is simple and accurate as it accounts for the shock-related noise in thefar-field. This technique is the basis of this research.

6

ff

fJ

JJ

Kirchhoff's Method

Kirchhoffs method is an innovative approach to the rotorcrafl noise problem which takesadvantage of the mathematical similarities between the aeroacoustic equations and the equations ofclassical electrodynamics. We propose to apply the considerable body of theoretical knowledgeregarding electrodynamic field solutions to arrive at a creative and novel solution to a difficultproblem of technological importance.

Kirchhoffs formula was first published in 1882. Morgans [40] derived a Kirchhoff formulafor a moving surface using a lengthy and complicated analysis. Hawkings [41] and Morino [42-44] rederived that formula for some special cases using the Green's function approach. Recently,Farassat and Myers [45] rederived the general Kirchhoff formula for a moving deformablepiecewise smooth surface using generalized derivatives.

Kirchhoff's formula has also been used in the theory of light diffraction and other

electromagnetic problems (Jones [46], Stratton [47]), as well as in problems of wave propagationin acoustics (Pierce [48]). Hawkings [4I] used this formula to predict the noise from high speedpropellers and helicopter rotors. Korkan et at. [49, 50] calculated high speed propeller noise usingthe Kirchhoff formulation of Hawkings [51]. Morino [52, 53] used a Kirchhoff formulation forthe development of boundary element methods. Purcel et aI. [51, 52] and Baeder [53] used amodified Kirchhoff method including also some nonlinear effects to calculate high speedcompressibility noise. Some examples of Kirchhoff method implementations are also given inreference [28]. The Kirchhoff method was also used in BVI [16, 27, 29-32] to extend thenumerically calculated nonlinear aerodynamic BVI results to the linear acoustic far-field.

The Green's function approach pioneered by Morino [42-44] was chosen for its simplicityand because the coordinate system used is suitable for BVI calculations. The method uses aGreen's function for the linearized governing equation to derive a representation for the solution interms of its values and normal and time derivatives on a closed surface S in space, which isassumed to include all the nonlinear flow effects and noise sources. A full three-dimensional,

compressible formulation is used, because in this case the Green's function is simpler and becausethe method is easily extended to include spanwise variations to model three-dimensional BVI. Abrief discussion of the Kirchhoff formulation is given in the following paragraphs; for more detailsthe reader is referred to the above references.

A Green's function for the linearized governing equation is used to derive a representation forthe solution in terms of its values and derivatives on a closed surface S in space, which is assumedto include all the nonlinear flow effects and noise sources. A full three-dimensional formulation is

used, because the Green's function is simpler in this case, and because the method can be easilyextended to include spanwise variations to model three-dimensional BVI.

The Green's function G for the linear unsteady potential flow is the solution of the equation:

1 U ¢3 o_V2G - _ ( o _--_+ _ )G= _i(x-x 1,Y'Yl,Z'Zl,t-tl)

? (8)

where co is the speed of sound, U o is the free stream velocity, subscript 1 implies the acoustic

source, and here 8 is the well known Dirac delta function. We should note that equation (2) is the

same as equation (1) without the nonlinear terms. The Green's function G must satisfy thecausality condition for hyperbolic equations

ff

f/

//

/

OG

G= _]-=0 fort<t 1

The solution of equation (2) for the subsonic case is given by

where

8(tl-t+z)G = -

4rtrl3

ro = {(x_x,)2+132[(y_y,)2+(z_z,)2]} I/2

[ro-M(x-x')]"C=

CO[32

= (1-M2)1/2

(9)

This result is well known (see, for example, Morino [42]). If we assume that all the acousticsources are enclosed by an imaginary closed rigid surface S, then we can prove (Green's theorem)that the pressure distribution outside this surface S is given by:

j(_ 3r° ax' o ar o1 _p __..._1 _ ( n____oo_ M_____o ) ___

P(x°'Y°'Z°) =- 4---_ ano + Corot2 + ro2 3--_o_dS' o (10)

where ..... denotes a point on the Kirchhoff surface, M is the free stream Mach number, c o is the

speed of sound, subscript o denotes the transformed values using the well known Prandtl-Glauerttransformation:

x o = x, Yo = 13Y, Zo = l3z

n is the outward vector normal to the surface S, and subscript '_ implies the evaluation at the

retarded time tl= t-z.

Thus, the values of the pressure and its normal derivatives on an arbitrary surface around.thespanwise extent of an arbitrary flow are enough to give the far-field radiation at any arbi_?aryexternal point. In our work we use a rectangular box coinciding with mesh points in order tosimplify the computation. The control volume is shown in figure 4. The pressure and itsderivatives can be numerically calculated from an aerodynamic near-field code.

Since Kirchhoff's method assumes that linear equations hold outside this control surface S, itmust be chosen large enough to include the region of nonlinear behavior. However, due toincreasing mesh spacing the accuracy of the numerical solution is limited to the region immediatelysurrounding the moving blade. As a result S cannot be so large as to lose accuracy in thenumerical solution for the mid-field. Therefore, a judicious choice of S is required for theeffectiveness of the Kirchhoff method. A rectangular box-shaped surface (figure 4) is used for thecalculations. The VTRAN2 code is used to calculate the solutions on the surface S. The x-limits

for S were varied between 0.15 and 0.50 chords and values of 0.25 chords upstream anddownstream of the leading and trailing edges are chosen. The y limits of S for our calculations arevaried over a range from Ys = 0.25 to 4.00 chords distance from the airfoil. Higher Mach numbers

yield higher optimum values for Ys because of the stronger nonlinearities in the larger lateral extent

ff

ff

fJ

Jof the flow region, a_ expected from the scaling laws of transonic flow. The similarity parameter

K (K=(1-M2)/52/3 , where d is the airfoil maximum thickness) can be used for the scaling of

transonic flow. Figure 5 shows the dependance of Ys on the value of K and was derived from

numerical experiments with our code for a (213x 199) mesh.

Strip theory approximation is used, that is, the two-dimensional VTRAN2 solution is appliedon different segments of the blade in a stripwise manner. Blade segments ranging from two tosixteen in aspect ratio are used. Usually mesh limitations keep the Kirchhoff surface close enoughto the blade where the two-dimensional strip theory solution is still valid. It can be shown that thewake does not need to be included in S, since the pressure is continuous across it. The distributedvortex, being a region where the homogeneous equation is invalid, should be included within thesurface S. However, the effect of including or not including the vortex is comparatively small,

particularly as it is nearly unaccelerated while it is outside S. We verified this by tryingcalculations with surfaces which included and excluded the vortex when it was near the airfoil. Bymaking calculations with or without the inclusion of the tip surfaces we found [28] that they haveonly a small effect; thus they were neglected for most of the calculations.

Finally, some effects for non-parallel blade-vortex interactions were studied in the pastutilizing the Kirchhoff method formulation and strip theory [29]. We can simulate a vortex ofarbitrary shape or sweep interacting with a blade using VTRAN2 results for a paralIel BVI, varyingthe delay time for the different chordwise strips. This technique is limited to small intersection

angles k, as the three-dimensional effects become large in higher angles. However, it is expected

to provide adequate information in small intersection angles. The same technique of delaying timescan be used for any arbitrarily shaped vortex (i.e. circular vortex).

Types of Unsteady Shock Motion

Tijdeman [54] showed experimentally, using an oscillating flap, that varying airfoil surfaceboundary conditions can give three different types of unsteady shock motion: (figure 6)

Type A shock motion, where the shock at the rear of the supersonic region merely moves back andforth with concurrent changes in strength.

Type B shock motion, where the shock moves similarly to type A, but disappears temporarilyduring the unsteady motion.

Type C shock motion, where the supersonic region disappears, but a shock wave leaves the airfoiland propagates forward to the far-field. ":

The above three types of unsteady shock motions heavily affect the characteristics (e. g. lift, drag)of all unsteady transonic flows. The type of shock motion that occurs in a given situation dependson the flow characteristics (e. g. free stream Mach number, airfoil shape, amplitude and frequencyof the unsteady motion). These types of shock motion can even be observed in steady airfoils withsevere flow separation downstream of the shock waves. Their existence in BVI has been verifiedby different experiments and calculations (e. g. Tangler's experiments [55]).

Results and Discussion

Some mid-field calculations for BVI are performed using VTRAN2 with a refined mesh tofollow the waves of interest. Then the Kirchhoff method is used to examine the noise at the far-

field. The viscous shock/boundary layer interaction is used, although the effect of this term isweak, as shown in reference [3 I].

9

ff

ff

fJ

J

We use a NACA 64A006 airfoil; the vortex strength was Clv = 0.4 (Clv is a nondimensional

measure of the vortex strength: Clv = 2F/cUo) and the vortex miss-distance Yo = -0.5 chords, for a

fixed vortex path. The initial vortex position is Xo = -9.51 chords and the free stream velocity is

one (arbitrary units) so the vortex passes below the airfoil leading edge at time T = 9.51. TheMach numbers of 0.875, 0.854, and 0.822 correspond to shock wave motions of types A, B, andC, respectively, as also shown in references [9, 27]. The three different types of the unsteadyshock motion are thus studied. For the Kirchhoff surface (figure 4) we used a span of 8 chords,Xs = 0.25 chords and Ys = 3.5, 2.5 and 1.9 chords for the three types A, B and C, respectively. Ys

is chosen from figure 5, as explained before.

Initially, we run a couple of cases for verification purposes. Figure 7 shows the liftcoefficient variation with instantaneous x-location of the vortex: VTRAN2 solution, NACA

64A006 airfoil, /vioo=0.85, ot = 0°, Clv=0.4, and yo=-0.26 chords. The result of the same for

Euler solution can be found in reference [21]. The comparison shows that the two solutions arevery close except the same difference on the trailing edge of airfoil, which is believed to be causedby the finer meshis used by VTRAN2 on the trailing edge region. We also run the case:

NACA0012 airfoil, Moo=0.80, o_ = 0 °, Clv=0.4, and yo=-0.26. The comparison with Euler and

Navier Stokes equations and other small disturbance formulations (from reference 56) is shown infigure 8 and is very satisfactory.

1. Noise Source Mechanisms of BVI

Figure 9 shows the Cp(T) signal of the three types of unsteady shock motion in the far-field

(point O, r=20 chords, 0=30o), as shown in figure 4, using Kirchhoff's method. The signal for

the higher Mach number (type A) propagates upstream slower, so it takes a longer time to arrive atthe same point. The signal consists of two disturbances (I, II) as also shown in references [27,28]. The primary disturbance I is the main BVI noise and it originates at the airfoil when the

vortex passes below the leading edge. The secondary disturbance II corresponds to the unsteadyshock motion and depends on the motion of the shock wave, or even the entire supersonic regionmotion induced by the vortex passage. It originates at the airfoil at a later time, (when the vortex is6-8 chords behind the airfoil), and depends heavily on the type of shock motion. The time delayof disturbance II decreases with decreasing Mach number and disappears in subcritical cases. Thedirectivity of the two disturbances is very different as will be shown later. The existence of thesecond disturbance was observed computationally by George and Chang [6] and was also verifiedexperimentally by Caradonna et al. [57] and Shenoy [58] and Lent et al. [59], and computation_.llyby George and Lyrintzis [27, 28], Owen and Shenoy [22] and Liu et al. [26]. For example,Shenoy [58] performed some Schlieren experiments for a rotor and a second disturbance was seen

to propagate in the far-field as postulated by computational results.

From figure 9 we can see that disturbance I increases slightly with increasing Mach number.

We should also bear in mind that the definition of Cp includes division by M 2, so the effect of theMach number is stronger than it appears in the above figures. Disturbance II also exists for type Aand B shock motions, because it is caused by the movement of the entire supersonic pocket. It

also appears to be decreasing as we move from type C to type A. However, if we measure it frompeak to peak (instead of just reading the max value) it still increases, but at a lower rate thandisturbance I.

Figure 10 shows the lift coefficient C1 (T) for a suberitical case (M=0.6) and types A, B and

C of shock motion. We can see that the total change of C1 is higher at higher Mach numbers.

10

ff

fJ

J..5:

The drag coefficient Cd will be discussed next. It is well known that in uniform subcriticaI

inviscid flow Cd is zero. It should be noted though, that Cd is not zero for subcritical inviscid BVI

because of acceleration due to the vortex. When the flow becomes supercritical, the inviscid Cd

is higher because of the formation of supersonic pockets. This was verified by running the codefor subcritical and supercritical cases. Cd can be easily calculated in terms of the pressure

distribution. Figure 11 shows Cd (T) for a subcritical case (M=0.6) and types A, B and C of

shock motion. The change in the Cd signal is much lower than the change in the C1. However,

there is a significant increase as we move from subcritical to supercritical cases. Also the signal ispositive when a shock wave is always present (e. g. type A). Finally, the Cd signal seems to catch

some part of the second disturbance whereas C1 does not. This was also detected by Liu et al.[26] for some BVI cases using a thin layer Navier Stokes code, but is easier to see in the case of an

oscillating flap [ 17], because there the periodicity of the motion is well-defined.

The directivity of the noise signal in the far-field is very complicated, as has been shown byexperimental studies. Most of these experiments are also three-dimensional, which makes them

very difficult to compare. For example, in reference 60 it was shown for a model helicopter rotor

that the maximum signal can have a different direction if the advance ratio I-t is varied.

Directivity is studied in a vortex (or fluid) fixed coordinate system keeping the distance from

the vortex rv constant (rv = 50 chords). The relationship between the angles 0 and 0v in an airfoil

fixed and a vortex f'axed coordinate system is shown in figure 12. The observer is, however, fixedwith the airfoil. Both ways of looking at the waves produced by BVI are effective in following thenoise produced when the vortex meets the leading edge of the airfoil and, in principle, all theirresults can be transformed into each other. However, the second, fluid-fixed way is not aseffective in following any waves which originate at the airfoil when the vortex has been convected

a chord length or more behind the airfoil. Such waves typically are associated with unsteady shockmotion on the airfoil, which typically originates when the vortex is 6 to 8 chord lengths behind theairfoil. The vortex-oriented, or fluid-fixed, viewpoint is closer to the case of a helicopter flyover.However, forward-radiated disturbances in the mid-field which are emitted at times after the vortex

passage are sometimes difficult to observe. Some further discussion on the coordinate systems canbe found in reference [27].

The Cp(t) signal for different directions is plotted in figures 12 and 13 for a subcritical case(M=0.6) and type C shock motion, respectively (note that span = 4 chords for this case). Fromfigure 12 (M=0.6) we can see that we have only one disturbance. The amplitude of that

disturbance is increasing as the direction angle 0 increases from 0 o to 90 ° (downward directiv[ty).

In figure 13 we can see two disturbances. Disturbance I is getting weaker as the direction angle 0

increases from 0° to 90 ° (forward directivity). Disturbance II is getting stronger as the direction

angle 0 increases from 00 to 90 ° (downward directivity). The two disturbances also move closer

as the angle 0 is increased, and finally almost merge at 0 =120 °. This implies a different point of

origin.

In figures 12 and 13 the observer is still fixed with respect to the airfoil. The observer can beeasily made to move with the vortex, as is implied by the use of the vortex-fixed coordinatesystem. If we do that, the results for type C are shown in figure 14. The BVI signals are slightly

modified. For example, for 0=30 ° (0v=5.73 °) the second disturbance is larger and is closer to

the first one, because the observer is moving closer to the airfoil after the first disturbance. (If thesecond disturbance is emitted when the vortex is 7 chordlengths downstream, then with moving

observer 0 is increased to 76.8 ° and r is almost half.) Figure 15 shows frequency spectra for the

11

f

ff

fJ

Jf ._. "°

above case with moving observer using Fast Fourier Transform _). However, these resultsdo not seem to be very accurate probably due to descretization errors. Since in most experiments avortex-fixed coordinate system is used, a moving observer should be used for verification of futureexperimental results.

We propose to regard the noise due to transonic BVI as being composed of the following twoparts: (1) linear acoustic source (dipole); (2) non-linear acoustic source (quadrupole).

The linear acoustic source, is associated with oscillating drag and lift, (21 and Cd signals as

shown in figures 10 and 11, and the corresponding noise directivity presents dipole patterns in thesame way as does linear acoustic analysis. This behavior can be observed if we look at thesubsonic case (e. g. M--0.6) directivity in figure 12. In this case there is only disturbance I whichhis a downward directivity, since the C1 variation is much stronger than the Cd, it is expected that

the C1 does dominate the linear signal.

The non-linear acoustic source is related to the shock wave variations on the airfoil lower

surface during a BVI. The noise is related to shock strength variations and the amplitude of theshock wave motion. Shock strength variations occur as the vortex passes below the airfoil and canbe detected by the significant increase in the Cd signal for the supercritical cases. They generate a

strong portion of disturbance I that dominates the signals, especially at the horizontal direction andhas a Cd dipole directivity. Thus we can see from figure 13, which shows the directivity of the

type C shock motion, that disturbance I now has a forward directivity. Abrupt shock wavemotions cause variations of the entire supersonic pocket. These variations usually take place muchlater and generate disturbance II, which can also be detected from the Cd signal. Disturbance II has

a more complicated directivity. Trying different Mach numbers and different airfoil shapes (see for

example reference 31), we found that disturbance II becomes maximum at an an angle between 60 °

and 90 o, depending on the flow parameters.

Thus, disturbance I depends on the shock strength and the C1 variations as the vortex passes

below the airfoil. In subcritical cases only the CI variations are relevant, and in supercritical cases

the Shock noise dominates, especially near the horizontal. Disturbance II depends on the shockmotion that is generated when the vortex is farther downstream (6-8 chords). The twodisturbances can have a different point of origin, which changes their relative distance, as shown infigure 13. Disturbance I can be reduced by weakening the shock formation on airfoil, anddisturbance II can be reduced by stabilizing the shock wave motion on airfoil.

3. Some Cases for Future BVI Experiments -:

Some test cases for future BVI experiments are shown here. For all test cases we have aNACA 0012 airfoil, vortex strength C1v=0.65, a fixed vortex path, initial vortex position -9.51chords.

Case 1:

Case 2:

Case 3:

Case 4:

The cases are:

M--0.70, yo=-0.26,

M--0.71, yo=-0.26,

M--0.70, yo=-0.26,

M--0.70, yo=-0.26,

a=O o

a=O o

a= 0.2345 ° (corresponding C1 without a vortex=O.04)

a= -0.2345 ° (corresponding Cl without a vortex=-O.04)

For all the cases C1, Cd, and far-field directivity signals are shown in figures 16-26. From figure

16 we can see that the slight increase for the Mach number between cases 1 and does not influenceC1 and Cd very much. Directivity signals (figures 17-20) for both fixed and moving observer

show that the signal is max when 0 is between 60 ° and 70 ° which corresponds to 0v=22°-28 ° .

Finally (as will also be shown in section 4c of the results) for cases 3 and 4 we can see from

12

./f

fJ

JJ

/"

figures 21-26, that _n increase of the angle of attack (i. e. from 0 to 0.2345) decreases the resultingBVI noise, whereas a decrease in the angle of attack increases the resulting BVI noise. Fromfigures 23-26 we can see that the directivity patterns remain almost unchanged.

4. Noise Reduction Techniques

Several ideas for noise reduction of transonic BVI are introduced as follows:

a) Airfoil shape modifications:

The transonic BVI shock motions are mainly generated on the lower airfoil surface. Thus thelower surface of the airfoil needs to be modified, particularly near the leading edge, becausedisturbance I is generated as the vortex passes below the airfoil leading edge and disturbance IIdepends on the shock wave motion which is influenced by changes near the leading edge.Initially, as a theoretical test, we used a simple cosine function (l-cosx) as the shape added to asection of the airfoil (NACA64A006) that gives the continuous slope for the modified airfoil. Thenthe more practical NACA 4-digit airfoil shape is added to the airfoil.

Figure 27 shows the modified airfoil shape in comparison with original one. The maximumthickness added is 0.4% and 0.8% and the total distance of the modification is 38% from leadingedge. It should noted here that all shapes are shown three times fatter, so that the modification can

be detected easier. The 0.8% modified airfoil was given a small angle of attack ct=0.028 °, so that

the C1 stays the same, but our conclusions are also valid at 0t=0 °. The 0.4% modified airfoil was

run at ix=0 °, since the changes in the C1 are very small in this case. Figure 27 shows the

corresponding far-field noise signals at 0=30 ° and 0=90 ° . We can see from these figures that both

disturbances are reduced. However, another small disturbance is generated in between, and ismainly due to shape irregularities near the end of the modification interval. The 0.4% modificationproduces less noise.

Then we moved the modification interval from 38% to 26%, and used the smaller maximumthickness (i. e. 0.4%). Figure 28 shows the modified airfoil and the corresponding far-field noise

signals at 0=30 ° and 0=90 ° . The 38% modification is also included in the figure for comparison

purposes. We can see that the 26% modification interval gives somewhat better results.

We also modified the airfoil by adding a NACA 4-digit thickness line, with the s_tmemaximum thickness as before (i. e. 0.4%) on 38% region of the airfoil. The disadvantag;_ of

adding such a shape is that the slope of the airfoil surface is no longer continuous. Figure 29

shows the airfoil modification and the corresponding far-field noise signals at 0=30 ° and 0=90 o,

respectively. For this case, we used the angle of attack it=.04 o in order to get same lift with the

unmodified airfoil. In comparison with result from cosine modification, disturbance I/decreasedsubstantiNIy, which means that the shock motion was stabilized to some degree. The additionalsmall disturbance that appeared in the previous cosine-shaped triodificadon has almost disappeared.From figure 29 we can see that the NACA 4-digit shape produces less noise than the cosine-shaped modification.

The above results showed us that a small (e. g. 0.4% maximum thickness) modification closeto the leading edge (e. g. 25% modification section) can lower substantially the BVI noise. Theshape of the modification is important and should be adjusted using trial and error, so thataerodynamic performance does not deteriorate.

13

Jf

ff

ff

JJ

J .-5,-

A modified airfoil SC1095rn was developed by Sikorsky Aircraft Co. to improve the

aerodynamic characteristics of the SC1095 airfoil. Figures 30-32 show the time history of the CIand Cd with the comparisonbetween airfoils SC1095 and SC1095rn for the cases of free stream

Mach number M_=0.6, 0.7, and 0.8 accordingly. For all cases, the vortex strength was Clv=0.4

the vortex miss-distance yo=-0.5 chords, for a fixed vortex path, the initial vortex position is -9.51chords. The following things should be noted that there are two pulses found in Cd(T) and onepulse in CI(T), as in previous cases. The pulses for SC1095rn seemed to appear weaker than the

ones for SC 1095, especially when the Mach number increases from Mo,,--0.6 to 0.8. As the free

steam velocity increase, the second pulse in Cd(T) becomes stronger, which is because strongershock waves are being generated.

The corresponding far-field acoustic signal Cp(T) is shown in figures 33-37 at 30 ° below the

airfoil. The first pulse in Cp(T), the difference between SC1095 and SC1095rn airfoils remains

about the same when the free stream Mach number increases from Moo---0.6 to 0.8, and the pulse

for SC1095 is stronger. This could be because SC1095rn airfoil enlarges the radius of leading

edge which reduces the effects of the vortex passage. The second pulse, is stronger for SCI095compared to SC1095rn and the difference increases when the free stream Mach number increases

from Moo=0.6 to 0.8. It is believed that this increase is related to the shock wave which is

generated on the airfoil lower surface. The shock wave generated in SC1095rn is stronger, but itdoes not move as much, generating less noise.

The corresponding far-field directivity of the acoustic signals showed in figures 38-43, for a

fixed observer. For M_---0.6, the first pulse reaches the maximum value at 0--90 °, and there are

no significant differences between the directivity for SC1095 and SC1095rn airfoil. Starting from

Moo---O.7, there are two pulses appeared in the far-field directivity acoustic signals. The first pulse

reaches the maximum value at 0=0 ° and the second pulse reaches its maximum value at 0=70 °,

while the two pulses become equally significant at 0=30 °, starting at Moo--0.7 to 0.8. In general,

the noise directivity patterns are the same between the two airfoil, but the pulse amplitudes forSC1095 are stronger than the ones for SC1095rn and the differences increase when free stream

Mach number increases from M,,o--0.6 to 0.8. As a concluding remark we can say that, although

SC1095rn airfoil was developed to improve aerodynamics, it also generated less far-field .BVInoise. "

Finally, from a study of 4-digit NACA airfoil shapes we found [31] that symmetric airfoils,and airfoils with a point of maximum camber further upstream, seem to give less BVI noise forconditions producing the same lift.

b) Splitting one vortex into two vortices:

This idea can be realized by splitting the trailing vortex using a small airfoil slat in front of themain airfoil. Some exploratory experiments [61] are currently conducted with such aconfiguration. Figure 44 shows the idea behind the two-vortex model. In order to simplify theproblem we have assumed that the distance between the vortices remains constam. Figure 44 alsoshows the effectof splitting the vortex in BVI far-field noise. We varied the distance between thetwo vortices from d=.25 to .5. It is shown from figure 44 that the longer the distance between thesplitting vortices, the more the noise can be reduced, although the noise is not reduced as much aswith airfoil shape modification.

14

if

f

,/J

J

c) Changing Otfier Parameters

The vortex strength is a very important parameter. If we can reduce the vortex strength by onehalf by designing a better blade tip, for example, then the corresponding far-field noise will bereduced greatly as shown in figure 45. However, the vortex miss distance does not have a verystrong effect (for distances 0.25 to 0.5 chords), as shown elsewhere [28].

When we want larger lift (thrust), the'a_ngle of attack should be increased. In such case, figure46 shows one example where both disturbances are reduced significantly. This explains why themaximum BVI noise always occurs in a certain helicopter descent region. BVI noise can bereduced by a proper combination of advance ratio and descent rate during approach into a noisesensitive area (Schmitz and Yu [5]).

Conclusions

An existing numerical finite difference code VTRAN2 was used to analyze noise due totransonic BVI. The two-dimensional unsteady transonic small disturbance equation was solvednumerically using ADI techniques with monotone switches, including viscous effects due toshock-boundary interactions and the cloud-in-cell method for the simulation of the vortex. TheKirchhoff's method was used to extend the numerica_lly calculated two-dimensional near-fieldaerodynamic results to the three-dimensional linear acoustic far-field.

The effect of the three types of unsteady shock motion (A, B and C) was investigated. The

unsteady pressure coefficients Cp(t) showed the existence of two main disturbances. The first one(I) is believed to be associated with the fluctuating lift coefficient (C1) (linear noise) and the shock

strength variations generated when the vortex passes below the airfoil (nonlinear noise);disturbance I has a strong forward directivity. The second (I1) is believed to be associated with themovement of the shock wave generated at a later time (the vortex is 6-8 chordlengths behind theairfoil) and has a strong downward directivity (nonlinear noise). The maximum radiation occurs at

an angle 0 between 60 ° and 90 ° below the horizontal for an airfoil-fixed coordinate system; it

depends on both disturbances I and II and the details of the airfoil shape.

Modified airfoiIdesigns can be very effective in reducing the BVI noise under the same liftand Math number conditions. In particular, a small (e. g. 0.4% maximum thickness) modificationclose to the leading edge (e. g. 25% modification section) can Iower substantially the BVI noise.

The overall BVI noise can be reduced by utilizing the modified airfoil SC1095m in comparisonwith airfoil SC1095, especially for the higher Mach number cases. Thus, although SC1095rn

airfoil was developed to improve aerodynamics, it also reduced the BVI noise. Experimentsshould be conducted to verify the prediction, as well as to cover evaluation of other noise sourceeffects. The shape of the modification is also very important, and should be investigated further.

It was shown that splitting the vortex into two can reduce the noise significantly. In fact,both disturbances are reduced. Also, the longer the distance between the two vortices the lowerwill be the noise produced. It is shown that BVI noise will be greatly reduced by reducing thevortex strength which can be achieved with a better blade tip design. Also, BVI noise will be_eatly reduced by increasing the angle of the attack, which it explains why thrust can have aneffect on BVI noise. BVI noise can be reduced by a proper combination of advance ratio anddescent rate during approach into a noise sensitive area.

I5

if

ff

fJ

S ./

Acknowledgements

C. Kitaplioglu from NASA Ames Research Center was the technical monitor and his

suggestions during the course of the research are greatly appreciated by the authors. Thecalculations were performed at the computational facilities of Minnesota Supercomputer Institute

(MSI).

References

.

,

.

4.

Johnson, W. R., "Recent Developments in Rotary-Wing Aerodynamic Theory," AIAA

Journal, Vol. 24, No. 8, Aug. 1986.

Bries, E., Barbini, W., and Honaker J., "Current Issues Affecting the Civil Industry"

Vertiflite Journal, Jan. 1991 pp. 20-23:

George, A. R_, "Helicopter Noise: State-of-the-Art," Journal Aircraft, Vol. 15, No. 11,November 1978, pp. 707-715.

Schlinker, R. H., and Amiet, R. K., "Rotor-Vortex Interaction Noise," NASA CR-3744,Oct. 1983.

5. Schmitz, F. H., and Yu, Y. H., "Helicopter Impulsive Noise: Theoretical and ExperimentalStatus," in Recent Advances in Aeroacoustics, A. Krothapalli and C. A. Smith, editors,

Springer-Verlag, NY, 1986.

6. George, A. R., Smith, C. A., Maisel, M. D. and Brieger, J. T., "Tilt Rotor Aircraft Aero-acoustics,"Proceedings of the 45th Annual Forum of the American Helicopter Society,

Boston, MA., May 1989.

7. Poling, D. R., Dadone, L., Telionis, D. P., "Blade-Vortex Interaction," AIAA Journal, Vol.27, No. 6, June 1989, pp. 694-699.

8. George, A. R. and Chang, S. B., "Noise Due to Transonic Blade-Vortex Interactions,"Proceedings of the 39th Annual National Forum of the American Helicopter Society, PaperA-83-39-50-D000, 1983.

w_ '"

9. George, A. R. and Chang, S. B., "Flow Field and Acoustics of Two-dimensional TransonicBlade-Vortex Interactions," AIAA Paper 84-2309, AIAA 9th Aeroacoustics Conference,

Williamsburg, VA, October 15-17, 1984.

10. Ballhaus, W. F. and Goorjian P. M. "Implicit Finite-Difference Computations of UnsteadyTransonic Flows about Airfoil," AIAA JournaL, Vol. 15, No. 12, Dec. 1977, pp. 1728-

1735.

11. Rizzetta D. P., and Chin, W. C., "Effect of Frequency in Unsteady Transonic Flow," AIAAJournal, Vol. 17, No. 7, July 1979, pp. 779-781.

12. Guruswamy P. and Goorjian P. M."Effects of Viscosity on Transonic Aerodynamic andAeroelasfic Characteristics of Oscillating Airfoils" AIAA Journal, Vol. 21, No. 9, Sept.

1984, pp. 700-707.

16

ff

ff

fJ

J13. Goorjian, P. M_:, Meagher, M. E., and Van Buskirk, R. D., "Monotone Switches in Implicit

Algorithms for Potential Equations Applied to Transonic Flows" AIAA Journal, Vol 23,No. 4, Apr. 1985, pp. 492-498.

14. Goorjian, P. M., and Van Buskirk, R. D., "Second-Order-Accurate Spatial Differencing forthe Transonic Small-Disturbance Equation" AIAA Journal, Vol. 23, No. i I, Nov. 1985,pp. I693-1699.

15. Lyrintzis, A. S., and George, A. R., "VTRAN2: Computation of Two-dimensional Blade-

Vortex Interactions Using the Unsteady Small Disturbance Equation, (User's Manual)"Cornell University, Ithaca NY, March 1986.

16. Lyrintzis, A. S. "Transonic Blade-Vortex Interactions," Ph.D. Dissertation, Mechanical andAerospace Engineering Department, Cornell University, Ithaca NY, Jan. 1988.

17. Lyrintzis, A. S., and Xue, Y., "Acoustics of Transonic Flow Around an Oscillating Flap," toappear in Journal of Fluids Engineering; also University of Minnesota SupercomputerInstitute Research Report, UMS191/169, Minneapolis, MN, June 1991.

18. McCroskey, W. J. and Goorjian, P. M., "Interactions of Airfoils with Gusts andConcentrated Vortices in Unsteady Transonic Flow," AIAA Paper 83-1691, AIAA 16thFluid and Plasma Dynamics Conference, Danvers, MA, July 1983.

19. Srinivasan, G. R., McCroskey, W. J., and Kutler, P., "Numerical Simulation of theInteraction of a Vortex with Stationary Airfoil in Transonic Flow," AIAA Paper 84-0254,

, AIAA 22nd Aerospace Sciences Meeting, Reno, Nevada, Jan., 1984.

20. Sankar, N. L., and Tang, W., "Numerical Solution of Unsteady Viscous Flow Past RotorSections," AIAA Paper 85-129, Jan. 1985.

21. Srinivasan, G. R., McCroskey, W. J., and Baeder J. D., "Aerodynamics of two-dimensionalBlade-Vortex Interaction," AIAA Journal, Vol. 24 No. 10, Oct. 1986, pp. 1569-1576.

22. Owen S. T., and Shenoy R. K., "Numerical Investigation of Two-Dimensional Blade-VortexInteraction," Proceedings of the AHS National Specialists" Meeting on Aerodynamics and

Aeroacoustics, Arlington, Texas, Feb. 1987.

23. Damodaran, M., and Caughey, D. A., "A Finite Volume Euler Calculation of theAerodynamics of Transonic Airfoil-Vortex Interaction," AIAA Journal, Vol. 26, No-::l 1,

Nov. 1988, pp.1346-1353.

24. Baeder, J. D., McCroskey, W. J., and Srinivasan, G. R., "Acoustic Propagation UsingComputational Fluid Dynamics," Proceedings of the 42nd Annual Forum of the AmericanHelicopter Society, Washington, DC, June, 1986, Vol. 1, pp. 551-562.

25. Baeder, J. D., "Computation of Non-Linear Acoustics in Two-Dimensional Blade-VortexInteractions," 13th European Rotorcraft Forum, Arles, France, Sept. 1987.

26. Liu, N. S. Davoudzadeh, F., Briley, W. R., and Shamroth, S. J., "Navier Stokes Simulationof Transonic Blade-Vortex Interactions," Proceedings of the International Symposium onNonsteady Fluid Dynamics (ASME), Miller, J. A., and Telionis, D. P., editors, Toronto,Canada, June 1990, pp 177-186.

27. George, A. R., and Lyrintzis, A. S., "Acoustics of Transonic Blade-Vortex Interactions,"AIAA Journal, Vol. 26, No. 7, July 1988, pp. 769-776.

17

ff

ff

fJ

28. Lyrintzis, A. S., and George, A. R., "Far-Field Noise of Transonic Blade-VortexInteractions,"American Helicopter Society Journal, Vol. 34, No.3, July 1989, pp.30-39.

29. Lyrintzis, A. S., and George, A. R., "The Use of Kirchhoff Method in Acoustics," AIAAJournal, Vol. 27, No. I0, Oct. 1989, pp. 1451-1453.

30. Lyrintzis, A. S., and George, A. R., "Study of Transonic Blade-Vortex InteractionNoise,"Noise Control Engineering Journal, Vol. 32, No. 3, May-June 1989, pp. 105-109.

31. Lyrintzis, A. S., and Xue, Y., "A Study of the Noise Mechanisms of Transonic Blade-VortexInteractions", to appear in Oct. 1991 issue of AIAA Journal; also University of MinnesotaSupercomputer Institute Research Report, UMS190/141, Minneapolis, MN, July 1990.

32. Xue, Y., and Lyrintzis, A. S., "Noise Reduction for Transonic Blade-Vortex Interactions,"to be presented at the American Helicopter Technical Specialists meeting on RotorcraftAcoustics and Fluid Dynamics, Philadelphia, PA, Oct. 1991; also University of MinnesotaSupercomputer Institute Research Report, UMS191/205, Minneapolis, MN, August 1991.

33. Ballhaus, W. F., "Some Recent Progress in Transonic Flow Computations," in NumericalMethods in Fluid Dynamics, ed. Wirz H. J., and Smolderen J. J., McGraw Hill, NY1978, pp. 155-235.

34. Rizzetta, D. P., "Procedures for the Computation of Unsteady Transonic Flow IncludingViscous Effects," NASA CR-166249, 1982.

35. Poling, D. R., Telionis, D. P., "The Response of Airfoils to Periodic Disturbances-TheUnsteady Kutta Condition," AIAA Journal, Vol.24, No.2, Feb. 1986, pp. 193-199.

36. Chang, S. B., "Aerodynamics and Acoustics of Transonic Two-Dimensional Blade-VortexInteractions," Ph.D. Dissertation, Mechanical and Aerospace Engineering Department,Cornell University, Ithaca N-Y, Jan. 1985.

37. Tadghighi, H., Hassan, A. A., and Charles, B., "Prediction of Blade-Vortex InteractionNoise Using Airloads Generated by a Finite-Difference Technique," Proceedings of the46th Annual Forwn of the American Helicopter Society, Washington DC, May 1990, Vol.I, pp. 367-378.

38. George, A. R., "Noise from High Speed Surfaces," in Aero- and Hydro-Acoustics IUTAMSymposium Lyon 1985, G. Compte-Bellot and J. E. Ffowcs Williams editors, Springer,Berlin, Heidelberg 1986.

39. Farassat, F., and Brentner, K. S., "The Uses and Abuses of the Acoustic Analogy inHelicopter Rotor Prediction," Proceedings of the American Helicopter Society NationalSpecialists" Meeting on Aerodynamics and Aeroacoustics, Arlington, TX, Feb. 1987.

40. Morgans, R. P., "The Kirchhoff Formula Extended to a Moving Surface," PhilosophicalMagazine, 9, s.7, No. 55, 1930, pp. 141-161.

41. Hawkings, D.L., "Noise Generation by Transonic Open Rotors," Westland Research Paper599, 1979.

42. Morino, L., "A General Theory of Unsteady Compressible Potential Aerodynamics," NASAContractor Report CR-2464, December 1974.

18

i

//

/ 43. Morino, L., "St_eady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics -

Production Version 1.1 (SOUSSA-P, 1.1), Vol. 1, Theoretical Manual," NASA ContractorReport CR- 159130, 1980.

44. Morino, L., "Mathematical Foundations of Integral Methods," in Computational Methods inPotential Aerodynamics, Morino L. editor, Springer-Verlag, 1985, pp. 270-291.

45. Farassat, F., and Myers, M. K., "Extension of Kirchhoff's Formula to Radiation from

Moving Surfaces," Journal of Sound and Vibration, Vol. 123, No. 3, June 1988, pp.451-460.

46. Jones, D. S., The Theory of Electromagnetism, Pergamon Press, 1964.

47. Stratton, J. A., Electromagnetic Theory, McGraw-Hill, 1941.

48. Pierce, A. D., Acoustics-An Introduction to its Physical Principles and Applications, NewYork, McGraw-Hill, 1941.

49. Forsyth, D. W., and Korkan, K. D., "Computational Aeroacoustics of Propeller Noise in theNear- and the Far-field," AIAA paper 87-0254, AIAA 25th Aerospace Science MeetingReno, Nevada, Jan. 1987.

50. Jaeger, S., and Korkan, K. D., "On the Prediction of Far-Field Computational Aeroacousticsof Advanced Propellers," AIAA paper 90-3996, AIAA 13th Aeroacoustics Conference,Oct. 1990.

5 i. Purcell, T. W., Strawn, R. C., and Yu, Y. H., "prediction of High-Speed Rotor Noise Witha Kirchhoff Formula," Proceedings of the American Helicopter Society NationalSpecialists' Meeting on Aerodynamics and Aeroacoustics, Arlington, TX, Feb. 1987.

52. Purcell, T. W., "CFD and Transonic Helicopter Sound," Paper No. 2, I4th EuropeanRotorcraft Forum, Sept. 1988.

53. Baeder, J. D., "Euler Solutions to Nonlinear Acoustics of Non-Lifting Hovering RotorBlades," 16th European Rotorcraft Forum, Glascow, Scotland, Sept. 1990.

54. Tijdeman, H., "Investigations of the Transonic Flow Around Oscillating Airfoils," NLR TR77090- U, NLR The Netherlands, 1977.

-£

55. Tangler, J.L., "Schlieren and Noise Studies of Rotors in Forward Flight," Paper 77, 33-05, Presented at the 33rd Annual National Forum of the American Helicopter Society,Washington, D. C., May 1977.

56. Baeder, J.D., "The Computation and Analysis of Acoustic Waves in Transonic Airfoil-Vortex Interactions", Ph.D. Dissertation, Dept. of Aeronautical and AstronauticalEngineering, Stanford University, Sept. 1989.

57. Caradonna, F. X., Laub, G. H., and Tung, C., "An Experimental investigation of theParallel Blade-Vortex Interaction," 10th European Rotorcraft Forum, The Hague,Netherlands, August 1984.

58. Shenoy, R. K. "Aeroacoustic Flowfield and Acoustics of a Model Helicopter Tail Rotor at aHigh Advance Ratio," Proceedings of the 45th Annual Forum of the American HelicopterSociety, Boston, MA., May 1989.

19

ff

fI"

ti

59. Lent, K., Lqt_r, K., Meier, G., Miller, K., Schievelbusch, O., Schurmann O., andSzumowski,A., "Noise Mechanismsof TransonicBlade-Vortex Interaction," AIAApaper90-3972,AIAA 13thAeroacousticsConference,Oct. 1990.

60. Martin, M. R., andSplettstoesser,W. R., "AcousticResultsof the Blade-VortexInteractionAcousticTestof a40 PercentModel Rotor in theDMW," Proceedings of the American

Helicopter Society National Specialists" Meeting on Aerodynamics and Aeroacoustics,Arlington, Texas, Feb. 1987.

61. Telionis, D. P., private communication.

20

if

//

i,-/

/./

/

Figure 1. Formulation of BVI for a four blade rotor (from Schlinker and Amiet [4]).

vORTEX PARt_LLEL TO BLADE

( TWO- OIMENSiO,";:'.L C.",SE )+

+<.

r¢:-,,( tv ,Yv I

TWO - DIMENSIONAL

SIDE VIEW

yi

][

CASE :

Figure 2. Two-dimensional BVI.

21

ORIGINAL

OF POOR

PAGE IS

QUALITY

ff

ff

//

/'{'x = U,

II

\

II

J

%Wake Vx+kE t--O

_1_ !_l_ !

i I I 1

[_ianch cuts

II

C

+

Cx = 0, _y=¢,)

Figure 3. Domain and boundary conditions for VTRAN2.

Y z

Meo

x

o

re

[

I

II

------------1--

°

ZS

t-

J ___..2

!

t!

1

Pigure 4. Kirchhoffs surface for the calculation of the far-field.

22ORIGiNaL PAGE IS "

OF POO_ QUALITY

ff

ff.

fJ

f

Ys

3.5

2.5

2

1.5

Jk\

\

\

\

\

\

\

"lt\

\

1 1.1 1.2 1.3 1.4 _.5 1.6

K

Figure 5. Empirical relationship of Kirchhoff surface length Ys vs transonic similarity parameterK.

Type A

Type B

Type C

C

f/

Figure 6. The three types of unsteady shock motion.

23

I

f

ff

//-

/EULER SOLUTION

269 X 67 GRID

181X 45 GRID

.1

0

-.2

-.3

w .

-- - ,a

°|

..... VTRAN2

AIRFOIL, . I , I h_...-..-, ' t , I

-5 -3 -1 1 3 5

X V

Figure 7. Comparison of VTRAN2 with Euler solution (from [21]); 64A006, M=0.85, Clv---0.4,

yo=-0.26.

10

05

0.00

-.05

O

-.10

-.15

-.20

/ ,.*"_"

r_[j---"

; .

.... "I-SD (VTRAN2)

"X.\ ,f:"_.\ _t -- Euler

"_XX._XJ// ............... TSD (CAVIAT)_._f' LinoarLt ed TSD

,l

-.25 1 t i I I z I I

-2. -1. O. 1. 2. 3. 4. 5. 6. 7.

lqme, t

_ Figure 8. Comparison of VTRAN2 results wi_ other codes (from [561); 0012, M=0.S, Clv=0.41 [

yo=-0.26. ................... ,. _ !

,

24

/f

ff

//

o

0.003

0.002

0.001

0.000 l_

-0.001

-0.002

-0.003

I II

,i iii:

.: .: ._",,: - i

i "i

°°

"?

"C"

!

._ II

!i .i;

; i :':

i

'.. .:.t : ii

.}

L-"I"

"B"

i .

-A o

''' ''''' I'"'''"'I' "'''" 'I'"'' '''' I'" ',, ,,,

80 90 1O0 1 10 120 1-30 140 i 50 1 60

--%

Figure 9. Comparison of the far-field BVI noise for types A, B, C; point O (r '-- 20 chords,

0=30 o, span = 8 chords).

25

!f-

/_,.,_

/./

//

/

0,1

0.05

-0.05

-0.1

-0.i5

-0.2

--M=.875

-- - -M=.854

- -',_"'/'q= 82Z

• • ","" M=.6

1 0 20 30 40 50T

Figure 10. Comparison of the C1 (T) signal for BVI; M---0.6, types A, B, C.

0.01

0.008 -

0.006 -

cd 0.004

0.002

-0.002

--M:.875-- - - M=.854

.... M= e?,2.

, ,.,,-. M=.6

- r.t.i ' #l

.... I .... I .... I .... I .... I

0 10 20 30 40 50T

Figure 11. Comparison of the Cd (T) signal for BVI; M=0.6, types A, B, C.

-%

26

.

ff

ff

/

J0.0015

6-0, ev=-O

0.(!,010

0.0005

0.0000 ........... " _ :"" ..................

cr -0.0005

-0.0010

-0.0015 T-, , , I .... I .... : .... I .... -

20 30 40 50 60 70T

0.0015

0.0010

0.0OO5

0.0000

-O.OO05

-0.0010

-0.0015

0=30, 0".'=12.54

r

: I

i

20 30 40 50 60 70

0.0015

0.0010

0.0005

0.0000

-0.0O05

-0.0010

-0.0015

20

8=,60, 8v=20.69

J

,,

1

' ' ' ' i ' ' ' ' I ' ' ' ' I ' ' ' ' I ....

30 40 50 60 70

0.0015

0.0010

0.00O5

0.0000

-0.0005

43.0010

-0.0015

20

0=70, 0v=35,68

' ' ' ' I .... I ' ' ' ' I .... I ' ' ''

30 40 50 60 70

0=90, _=-53.I30.0015

o,oolo .,'_

0.0005 i i

-0,0005 I-0.0010

-0.0015

20

' ' ' ' I ' ' ' ' I .... I .... ! ....

30 40 50 60 70

7e5:-° vof, ,

Figure 12. BVI noise directivity for M=0.6; rv = 50 chords, span = 4 chords.

i

27

ff

ff

f/

//

0.003

0_0, Ov--O

0.002 '

0.001

(3-

o

0.000

II

J ::.

. . .,

....

"_:-0.001 _ :

v-0.002 .... i .... i .... J .... i .... I ....

40 45 50 55 60 65

T

0.003

0.002

0.001

Q..

o0.000 '

-0.0Ol

-0.002

0=60, 0v=14.61

II

A, i°&-'% ;

-"'; i

_': i.... __..t,e,_I__--L__ _.__...J

: ": .

IL., i,..illl..l .I.1

40 45 50 55 60 65 70

0.003

0=30, 0v=5.73

i.

0.002 "i /-

, i

-0.001 ', ;11

-0.002 .... , .... t .... i .... _ .... _ ....40 45 50 55 60 65

0.001

CL

c)0.000

T

0.003 -

0=90, 0_-34.71

0.002

0.001

0

0.000

-0.001

-0.002

3"z;:

;U

0 45 50 55 60 65 70

T

0.0036=-120, 0v=64.61

-%

0.002

0.001

0

0.000

4i!

,t

•.._-.,=_-r_-".--_- ---

-0.00;

-0.002 .... , ...... ', • , .... , .... , ....40 45 50 55 60 65 70

Figure 13. BVI noise directivity for type C; rv = 50 chords, span = 4 chords, fixed observer.

28

.

//

/

J

J

0.005

0.003 -

0.001 -

-0.001 -

-0.003 -

0v=5.73

-0.005 , , , , i .... a .... , .... = ....

20 25 30 35 40 45T

0.005

0.003

0.001

-0.001

-0.003

-0.005

0v=14.61

i i _ m = i * , | I * m , | , m o i i I i * . *

20 25 30 35 40 45

0.005

0.003

0.001

-0.001

-0.003

-0.005

0v=34.71

,,, i |,, |. |,.u,i,,,li i | iml , , | I

20 25 30 35 40 45 50

0.005

0.003

0.001

.-0.001

-0.003

-0.005

0x---74.61

,,,,i,,,,i,**,1,,,,i,,,,I,,,,

20 25 30 35 40 45 50

Hg_re 14. BVI noise directivity for type C; rv = 50 chords, span = 4 chords, moving observer.2

29

_

ff

ff

Jt_--I/

O3

fSO

160

140

120

10o

80

0v=5.73

! ! I ! ! e

0 1 106 2 1063 1064 10.6 5 1066 106 7 106

frequence (Hz}

180

160

140

120

lOO

8o

0_'=14.61

! I I I I 1 J

1 10 6 2 10 6 3 10 6 4 10 6 5 10 6 6 10 6 7 10 6

f80

160

140

120

100

80

ev=34.71

'! ' ! i | i ! e

0 1 10_ 2 10 s 3 106 4 106 5 106 6 10 s 7 106

fSO

160

140

120

100

8O

0"v=74,61

i I I I I I

1 10 s 2 10 s 3 106 4 106 5 10 s 6 106 7 10 s

Figure 15. Noise :spectra using FFF; type C, rv = 50 chords, span = 4 chords, moving observer.

/;

30

i

.J11-

CI

0.2

0.1

o

-o.1

-0.2

-0.3

-0.4

0

_M=.7

.... M=.71

I I I I I I I I

5 10 15 20 25 30 35 40T

Figure 16.

0.015

0.01

o.oo5

CA 0

-0.005

_M=.7

..... M=.71

-0.01 I I I I I l I I

0 5 10 15 20 25 30 35 40T

CI(T) and Cd(T) signal for NACA 0012, Clv--0.65, yo=-0.26, M=0.70, 0.71

31

//

f.,I

i/../

/0.006

0.004

0.002

cp 0

-0.002

-0.004

e=0, ev---0

.... I .... [ .... I .... I .... I ....

20 30 40 50 60 70 80T

0.006

0.004

0.002

-0.002

-0.004

0=30, _.'=9.51

''''I''''I''''I''''I''''I .... i

20 30 40 50 60 70 80

0.006

0=60, 0v=22.68

0.006

0=70, 6".'=-28.87

0.004

0.002

-0.002

-0.004 |lllllllll.llll.lllll|l.lll,l

20 30 40 50 60 70 80

0.004

0.002

-0.002

-0.004.... I .... I'' ' 'I '''' I''' ' I '" ""

20 30 40 50 60 70 80

0.006

0.004

0.002

-0.002

-0.004

8=90, 0v---45.57

,,,,l..,,l,,,.l,,,il..,,l,,,,

20 30 40 50 60 70 80

0=120, e_-82.68

0.006

0.004 --_

0.002

0 --,,,--_

-0.002

" I-0.004 , . , , .... , .... , .... , .... , ....

20 30 40 50 60 70 80

Figure 17. BVI noise directivity for NACA 0012, Clv=0.65, yo=-0.26, M=0.70, rv = 50 chords,

span = 4 chords.

32

f

ff

ff

JJ

J

q_

0.005

0.004

0.003

0.002

0.001

0

-0.001

-0.002

-0.003

0v=9.51

''' ' I'''' I'''' I'''' I'''

20 25 30 35 40

T

0.005

0.004

0.003

0.002

0.001

°-0.001

-0.002

...... 0.003

45 5O

0v=22.68

2O

.... ! .... 1,,,,1,.,,i,.,,1,,i,

25 30 35 40 45 50

0.005

0v=45.57

0.004

O.0O3

0.002

0.001

0

-0.001

-0.002 -

-0.003 I ' ' ' ' I '' I ' I ' ' _' I '' ' ' I ' ' ' ' I '' ' '

20 25 30 35 40 45 50

0v=82.68

0.005

0.004 -

0.003 -

0.002 -

0.001 -

0-

-0.001 -

-0.002 -

-0.003 ' : I I I I I I ' I I i ' I I I i I i I I I I I I I I ' I I I

20 25 30 35 40 45 50

Figure 18. BVI noise directivity for NACA 0012, C1v=0.65, yo=-0.26, M---0.70, rv = 50 chords,

span = 4 chords, moving observer.

33

f/

//

/-J

J

0.006

0.004

0.002

Cp 0

-0.002

-0.004

e--O, Ov=O

,,,,I,,''1''''i''''1''''1''''

20 30 40 50 60 70 80T

0.006

0.004

0.002

-0.002

-0.004

0=60, 0v=22.06

20

.,,,l''''l''''l''''t''''l''''

30 40 50 60 70 80

0.006

0.004

0.002

-0.002

-0.004

6=30, ev=-_.21

i,v'-

I I I I | I 1 I I I I I I I | I I I I illt I I I I ' !

20 30 40 50 60 70 80

0.006

8=70, e%_:_. 15

0.004

0.002

o ;-0.002

-0.004 .... _ ........ i ..........

20 30 40 50 60... 70 80

0.006

0.004

0.002

-0.002

-0.004

0=90, 0v--44.770=-120, 0_ I06

0.006 " ;

iiiiiiiillilllllllllllllllll!

0.004

0.002

-0.002

-0.004 *l,,|,,,,|,,,l|_|l,|,'''| '''"

20 30 40- 50 60 70 8020 30 40 50 60 70 60

Figure 19. BVI noise dircctivity for NACA 0012, C]v=0.65, yo=-0.26, M--0.?], rv = 50 chords, "

span = 4 chords.

34

ff

//

/J

J

cp

0.005

0.004

0.003

0.002

0o001

0

-0.001

-0.002

-0.003

0v=9.21

0.005

0.004

0.003

0.002

0.001

0

-0.001

-0.002

-0.003

25 30 35 40 45 50T

'' ' " I'''' I''' ' I'''' i" ''' I ....

20

0v=22.06

¢.____.

20 25 30 35 40 45 50

0.005

0.004

0.003

0.002

0.001

0

-0.001

-0.002

-0.003

0v=44.77

WW"-

• " " • I ' " " = I ' ' ' * I "" * ' I " " "" I " " ' "

20 25 30 35 40 45

0.005I

0.004

0.003

0.002

0.001

0

-0.001 -

-0.002 -

-0.003

50

0v--82.06

20 25 30 35 40 45 50

Figure 20. BVI noise directivity for NACA 0012, Clv--0.65, yo=-0.26, M--0.71, rv = 50 chords,

span = 4 chords, moving observer.

35

_

ff

fJ

J

J

Cl

0.2

0.1

-0.I

-0.2

-0.3

-0.4

i

11

-- _ ......... __--

--angle of attack=.2345 deg

..... angle of attack=O deg

5 10 15 20 25 30 35 40T

0.01

0.005

OJ 0

-0.005 -

--angle of attack=.2345 deg

..... angle of attack=O deg

i,r

5 10 15 20 25 30 35 40T

-.%

Figure 21. CI(T) and Cd(T) signal for NACA 0012, Clv--0.65, yo=-0.26, M=0.70, C1 (without

vortex)= 0.04, 0.0.

36

ff

ff

fJ

J

0.2

0.1

c_ 0

-0.3

-0.4

angle of attack=-.2345 deg

..... angle of attack-----O deg

_I_I_''tHHI''HI_H'I

10 15 20 25 30 35 40T

0.015

0.01

0.005

Od 0

-0.005

"0.01

_angle of attack=-.2345 deg

..... angle of attack=0 deg

,,,.,.i,,,,i,,_,1_,,i,,_1,,,,i,,,,i,,,,i

5 10 15 20 25 30 35 40T

Figure 22. CI(T) and Cd(T) sign,'d for NACA 0012, C1v=0.65, yo=-0.26, M=0.70, CI (withoutvortex)= -0.04, 0.0.

37

ff

ff

fJ

JJ

co

0.006

0.004

0.002

-0.002

-0.004

0.006

0.004

0.002

-0.002

-0.004

0=0, Ov=O

_,1,,,,i,,,,i,,,,1,,,_1,,

20 50 40 50 60 70T

6==60, _=22.68

8O

0.006

0.004

0.002

-0.002

-0.004

0.006

0.004

0.002

-0.002

e:30, 0v=9.51

.... I .... I .... I .... t .... I '_

20 30 40 50 60 - 70 80

_=70, O','=28.87

V

_'' I .... I .... I .... I .... I .... -0.004 .... _ .... _ .... , .... _ .... i ....

20 30 40 50 60 70 8020 30 40 50 60 70 80

0.006

0.004

0.002

-0.002

-0.004

0=90, 0"._-45.57 0_-120, 0v--gZ68

0.006

0.004

0.002

-0.002

-4,

.... _ .... J .... a .... _ .... : .... -0.004 .... i .... i .... i .... t .... _ ....

20 30 40 50 60 70 80 20 30 40 50 60 70 80

Figure 23. BVI noise directivity for NACA 0012, Clv--0.65, yo=-0.26, M=0.70, CI (with_outvortex)= 0.04, rv = 50 chords, span = 4 chords.

38

Jf

ff

fJ

J

0.006

0.004

0.002

Cp 0

-0.002

-0.004

0--0, Ov--O

0.006

0.004

0.002

-0.002

-0.004

0=30. 0",._9.51

1,,,i,,,,i,_,,i,,,,i,,,,I,,,,20 30 40 50 60 70 80

20 39 40 50 60 70 80T

0.006

0.004

0.002

-0.002

-0.004

0.006

0.004

0.002

-0.002

i , i " i i .... I .... I .... t .... i i i I l

-0.004 .... i .... , .... : .... _ .... , ....

20 30 40 50 60 70 80 20 30 40 50 60 70 80

0.006

6=90. 0v_5.57 _1_, _---g2_68

0.006 _-_ ....

0.004

0.002

-0.002

0.004

0.002

-0.002

-0.004 .... I .... I .... 4 .... I .... I ....-0.004 .... = .... , .... i .... , .... I ....

20 "30 40 50 60 70 80 20 30 40 50 60 70 80

Figure 24. BVI noise directivity for NACA 0012, Clv---0.65, yo=-0.26, M=0.70, CI (withoui

vortex)=-0.04, rv = 50 chords, span = 4 chords.

39

ff

ff

fJ

J

co

0.005

0.004

0.003

0.002

0.001

0

-0.001

-0.002

-0.003

0v=9.5 ]

-. ¢,_...

20 25 30 35 ,40 45

T

5O

0.005 _

0.004

0.003

0.002

0.001

0

-0.001

-0.002

-0.003

{,v=e_.6S

1--T , , ! .... 1 .... I ' ' ' ' t ' ' ' ' I ' ' ' '

20 25 30 35 4O 45 50

0.005

0.004

0.003

0.002

0.001

0

-0.001

-0.002

-0.003

0_.'-=45.57

' ' ' ' I ' ' ' ' I i , , , ! , , , , I ' ' ' ' J I 1 ' I

20 25 30 35 4C 45 50

0.005

0,004

0.003

0.002

0.001

0

-0,001

-0.002

-0.003

Ov=-g2.6g

) ' ' ' I ' ' ) ' I ' , , ' 1 ) ' ' ' I ' ' ' ' I ' ' ; '

20 25 30 35 40 45 50

Figure 25. BVI noise directivity for NACA 0012, C1v--0.65, yo=-0.26, M=0.70, Cl (withoutvortex)= 0.04, rv = 50 chords, span = 4 chords, moving observer.

4O

.

ff

ff

J

J

0.005

0.004

0.003

0.002

0.001

0

-0.001

-0. 002

-0.003

0v=9,51

_ -'n--r-'r't-

20 25 30 35 40 45 50

T

0.005

0.004

0.003

0.002

0.001

0

-0,001

-0.002

-0.003

0v=22.68

20 25 30 35 40 45 50

0.005

0.004

0,003

0.002

0.001

0

-0.001

-0.00:2

-0.003

2O

ev---45.57

, , , , i , , , , i , , , , i , , , , i , , • , i , , , ,

25 30 35 40 45 50

0.005

0.004

0.003

0.002

0.001

0

-0.001

-0.00"2

-0.003 i , , , I i = i i | , , , ' t ' ' ' i I i i , i I i = g i

20 25 30 35, 40 45 50

Figure 26. BVI noise directivity for NACA 0012, Clv--0.65, yo=-0.26, M--0.70, C1 (withoUtvortex)= -0.04, rv = 50 chords, span = 4 chords, moving observer.

41

r

//

/

jf

J

c_

0.001

OO008

0 0006

0.0004

00002

-0 0002

-0.0004

-0.0006

_64A006

__. -÷ 4_/oCt)SX

:',t ....."co"

.... i • , , • ! • , , , i .... i , , , F1

80 go 100 110 120 130

T

0.0025

0.002

0.0015

0.001

0.0005

0

-0.0005

-0.001

-0.0015

-- - -+.4%cosx

_ , , i .... i .... i .... ! .... i .... i

GO 70 80 gO 100 110 120

f

Figure 27. Cosine curve modification of 64A006 and far-field BVI noise (rv=50, 0=30 °, 900);thickness: 0.4%, 0.8%, modificadon"interval: 38%.

42

//

/I/

/-J

JJ

0.0006

0,00O4

0,0002

-0.0002

-0.0004

a138%+ .4 %cosx

..... at26%+ .45_-.o sx

,, , , l , , , , |',',1, 1, , ,' I ' ' ''1 " ' ' '1

80 90 100 110 120 130 140

T

//

0.0015

0.001

0.0005

Cp 0

-0.0005

-0.001

..... at26%+,4%cosx

-n771,, ,,I, ,, I I, I, ,I,,,' I' ''' I

60 70 80 gO 100 110 120

T

Figure 28. Cosine curve modification of 64A006 and far-field BVI noise (rv=50, 0=30 °, 900);thickness: 0.4%, modificati6n intervals: 26%, 38%.

43

_

ff

fJ

JJ

/

0.0006

0.0004

0.0002

Co 0

-0.0002

-0.0004

..... at38%+.4%cosx

I

i I

_at38%+.4%NACA4dig_

80 90 100 110 120 130 140

T

0.001 5

0,001

0.0005

ce 0

-0.0005

..... at38%+.4°/.Cosx

--at38%+.4%NACA4dlglt

-o.ool .... I'''"l''''l''''l''''l''''l

60 70 80 90 100 110 120

T

Figure 29. Cosine and NACA 4-digit Sickness curve modification of 64A006 and fa_field BVI

noise (rv=50, 0=30O, 90o); thickness: 0.4%, modification interval: 38%.

44

f_

ff

ff

JJ

J

Cd

0.0!5

0,01

0.005

-0.005

-0.01

J

__ _ .Cr

^:

)

-0"

I i , , _ I i 1 i , 1 _ ' i , I _ ' _ i 1

10 20 30 4O 50T

CI

0.3

0.2

0.1

-0.1

-0.2

I

I

i,

---_--sc 1 __,_ _

-- o--SCl09Srn

,,,,i,,,_I,,''I''''I .... I

. 0 10 20 30T

Figure 30. Cd(T) and C](T) for SCI095 and SCI095m at Moo=&&

40 50

45

r

ff

fJ

/

/

Cd

0.015

O.O'i

0005

-0.005

-0.01

. ""#!

_ v

f l;

0 10 20 30 405_

CI

Figure 3 l.

0.3

0.2

0_1

-0.!

-0.2

!

_scl _9:5

.... sclOgSrn

0 10 20 30 40

T

Cd(T) and CI(T) for 5C1095 and SC1095rn at Moo=0.7.

5,2

46

ff

f/-

//

//

0.02

00_5

0005

-0.005

(

r:

I'

i!

i!:

m

r _

- ~ o _

! i i

10 2O 30 _C 5O

Figure 32.

0.3

Cl

0.2

.0.1

-0.1

-0.2

\1'

1:

i6!

JI

---_--sclO_5

--_-SC1095rn

0 _0 20 30

T

Cd(T) and CI(T) for SC1095 and SC1095m at M_,=0.8.

50

47

ff

ff

// 0.002

/-

0.0015

0.001

0.0005

Cp 0

-0.0005

-0.001

-0.001 5

!i--E--s c i 09 5rn

i _ I _ i _ '--' I i

6020 30 40 50

Figure 33.

(r=20 chords, 0=30 °, span=8 chords)

0.003 -

BVI noise Cp(T) signal for SCI095 and SC1095m at Moo=0.6

0.002

0.001

Cp 0

-0.001

i

-0.002

t r _

..... sci095

---_--s c _ 095rn

Figure 34.

20 30 4O 50 60T

BVI noise Cp(T) signal for SC1095 and SC1095rn at M,,_---0.65

(r=-20 chords, 0=30 °, span=8 chords)

70

I

7O

48

ff

ff 0004

0.002

Cp 0

-0.002

-0.004

-0.006

_..j

- I I i

30 40 50 60 _,_ 80

Figure 35. BVI noise Cp(T) signal for SC1095 and SC1095rn at M_=0.7

(r=-20 chords, 0=30 °, span=8 chords)

c_

0.005

0.004

0.003

O.O02

0.00I

0

-0.001

-O.O02

-0.003

-0.004

-0.005 i ' i ' ' ' I ' '

..... sc1095

---a--s c 1095rn

t 1 i : i j ' I

40 50 60 70 80 90T

Figure 36. BVI noise Cp(T) signal for SC1095 and SC1095m at M_,--0..75

(r=-20 chords, 0=30 °, span=8 chords)

49

f

f

0.005

0.004

0.003

O.O02 "

0.001

-0.001

-0.002

-0.003 ' ' I ' ' ' I '

q

a

1,

b/"

t{ f

t

V

...... sc;095

---E_-- s c ;095rn

60 70 80 90 1O0 1 10

T

Figure 37. BVI noise Cp(T) signal for SC1095 and SC1095m at Moo=0.8

(r=-20 chords, 0=30 °, span=8 chords)

5O

ff

ff

ff

J

f 0.003

0.002

0.001

CO 0

-0.001

-0.002

0 _0, _'=0

............................... ................................................

j .........................................................................................

i | I I I

20 30 40 50 60 70T

0.003

0.002

0.001

0

-0.001

-0.002

0=30, 0-,'= 12.54

.................... 1!! .................: ............. ._ht ...................

i I _ l_'-:----q

20 30 40 50 60 70T

0.003

O.002

0.001

0

-0.001

-0.002

(_-60, 0v=28 69

° •° .

• ,• ,

.................. ,.; .!_..-,...............................

I I I l

20 30 40 50 60 70T

6=70, _.'=35.6S0.003

0.002 .......................................................................................,*

0.001 .................................::_- .......:...........................................t --

..................................i l.................................................................. _':v','- ...........................

.................................• .................................................

.................................. _ ....................................................

,.......................................................................................

I i I I

20 30 40 50 60 70T

0

-0.001

-0.002

,.."e

0.003

0.002

0.001

-0.001

-0.002

2

0=9O, 0v=53.13

,°

...................................fl ....................................................

................... ,-;- i-i-'<...............................

................................:...iI..................................................

' ' '' ' I ' ' ' ' | ' ' ' '="I ' ' ' ' [ " ' ' '

0 30 40 50 60 70T

0.003

0.002

0.001

c_ o

-0.001

-0_002

O= 120, 0V=8S.69

' " ' ' ] ' " " " I .... I " ' ' ' l ' ' '-'r-

20 30 a$ 50 60 70T

:/_

Figure 38 BVI noise directivity for airfoil SC1095 at Moo--0.6; r,,=50 chords, span--4 chords

51

ff

ff

ff

JJ

004v

0.002

C__ 0

-0.002

-0.304

0 =0, Ov:O

t ........................... ! ....................................................iiiiiiiiiiiiiiiiiiiiiiii ii iii ii

.............................. i ..........................................................

.... I ' ' ' ' I .... I .... I ' ' _ ""

30 40 50 60 70 80T

Cp

0.004

0.002

-0.002

-0.004

0=30. 0',':7.9S

,.t

........ j,**',; f". ................

i,,j

-1'''1 .... I .... |''''1 ....

30 40 50 60 70T

8O

0:60, 0v:19.49

I0_004 .................................. _ ........................................................

0.002 t................................ ¢_ ........................................................

_ct °

Co 0 ............. ,_'"t','_ ....... _", .......................--,_PO I •

l,',,I, _ ........................................... =c...._. ..............................

............................... ,_ ..........................................................-0.002 -

-8.004 _r--'r'--_ I • ' ' ' I ' ' ' ' I .... | ....

30 40 50 60 70 80T

0.004

0.002

CO 0

-0.002

-0.004

0=70, 0v:25.19

",; ; _.,.........................i ;_....,..........................................

3O

' ' ' ' I ' ' ' " I ' ' ' ' 1 ' ' ' ' I ' ' ' '

40 5O 60 70T

8O

0.004

0.002

CO 0

-0.002

-0,004

0:90, 0v:41.41

_" " ' I ' ' ' ' I ' ' ' ' I ' ' ' '

30 40 50 60 70T

8O

0.004

0.002

Cp 0

-0.002

-0.004

6=]20, 0v=79.49

__" ;_. ..............................

I

_ ' ' I ' ' ' ' | " " ' ' ! ' ' ' ' I ' ' ' '

30 40 50 60 70 80T

Figure 39. BVI noise directivity for airfoil SC1095 at Moo--0.7; rv=50 chords, span=4 chords

52

ff

f/

f,/

/./

O.OOG

.O04

3_002

C_ 0

- 0 002

0:0, Ov=O

...................... i ..................................................

0

:!

.: :;............................. _I :_ .............................................

• ,', ;:

............'> ....."ii:,. ...........

• ] l l I : i , i | i , ] _ i * ' ' 1 | _ , * i

30 40 50 60 70 8T

O.OOG0:33. 0v=6.42

0.004

0.002

Cp 0

-0.002

3O

I

................. 4 ¸ _, ..........

:: ,,

": !i.....................!i T*i.......................................

...........................i_- ?-_.........................................,,j _,

40 50 60 70 81-

0.006

0.004

0.002

QP o

-0.002

3

0:60, Ov=l 6.15

..................................tii.................................................

.................................I[7"T ...............................................

..................._;..|.:--1...._......=_._._.-.=.;.,.,_ ..

....................................q.....;,,..........................................., ,'_, ,'i , ,, .... i

0 4O 50 6O 70 8T.

0.0060=70. On'=21,26

0.004 ............................................................................................ b'v

....................................... -i ...................................................f

0.002 ....................................................................................

' _:..3.................................................................................. J

":; ,.............. " _-',;."-¢I .'"_ ......... i-_,r_-,c_;_ .__ -_" • ........

] ii _ -.................................. It--'I'_ .............................................

,t,O 50 60 70 80i"

Cp 0

-0.002

3

0.0060=90, 0v:36.87

O.00.-¢"

0.002

Co. 0

...................................... t ....................................................

!.

(• I I I | I I -i I I I I I I ! t I , I '| _ , 1 ,

0 40 50 60 " 70 8T

Figure.40. BVI noise directivity for airfoil

0.0_,_8=120. 0V=76.15

0.004

0.002 ............................. l, ..................................................

_-°c_ 0 ................. ._: _-,_:.......................

1

-0.002 t .... , .... , .... _ , ' ' ' , ....

0 30 40 59 60 70 _ _OT

SC1095 at Mog---0.8; r,,=50 chords, span--4 chords

53

ff

/f

//

// O 003

/

0 002

0 001

0

-0 001

-0002

O-_L Ov-O

t I , ' { 1 l 1 I [ 1 ] l-- I I I ' _ ' { ' I ' 1 _

3O 40 50 60 70T

@

Q003

0 002

0.001

0

.0001

-0.002

.......................... ,,. ..................................

............ _, _'.................

-i .............

20 30 _0 50 60 70T

0 003

0 002

0.001

0

-0.001

-0.002

0=60. 0v=28.69

ZZIIIIIIIIIIIZ]I/ /!ZZ/IIIIIZIII/IIIIIIIZIIIIII

.... I .... I .... ! .... I ....

20 30 40 50 60 70T

qo

O.003

0.002

0.001

0

-0.001

-0.002

6=7O, e',=35.6g

°.

i ,

................ . .-;..',.,........................

iiiiiiiiiiiiiiil/iZiiiiiii!'iii!/i17111111111111/iii/iiiii171111

0 30 "0 50 60 70T

0.001

0

-0001

-0002

0=90, _'=53.13

0.003

...........................................................................................

,I0.002 .................................... ,'5,....................................................

ii

................. ,-_-4-i_.......................

..................................-..].!...................................................

u u i .... , ....

20 30 40 50 60 70T

0.003

0.002

0.001

cp o

-0.001

-0.002

£'------"20, 6_----_&69

............................ i .......................................

20 30 40 50 60T

7O

Figure 41. BVI noise directivity for airfoil SC1095m at M_---0.6; rv=50 chords, span--4 chords

54

ff

//

//

//

O O04

0=0, Ov=O

0.003

0002

0001

Cp 0

-0.001

-0002

.......................... 4 ......................................................

.......................... 4 ......................................................

i i i i I , , II I i i i , I I , w i I ' m J i

30 40 50 60 70 80T

0004

0003

0,002

0001

0

-0001

-0002

5=30, 0_'=7.95

I

' ' ' ' I ' ' ' ' | . , _ . i _ , , , I ' ' = '

30 40 50 60 70 80

ooo4(1=60, _,,= 19.49

0.003 ..................................................................................

°°iiiooooiiiiiiiiiiiiiiiiiiiiiiiiiiiiii-0.001

-0.002 .... = .... i .... t .... i ....

30 40 50 60 70 80

0.004

('*= ._. ev=23.t 9

0

-0.001

-0.002

0.003 ..........................................................................

0.002 .........................................................................

0.001 ............................................................................

.... I .... I .... I .... I ....

30 40 5_ 60 70 80

0.004

0=90, 0v-_41.41

0.003 ...................................................................................

oooi iiiiiili0,001

0

-0,001

-0.002 .... i .... i .... i .... i ....

30 40 SO 60 70 80

0 004

0=12'5,, £r_=7949

0.003

0.002

0.001

0

Ii

-0.001 " ........................................................

-0.002 .... , .... , - - - , .... , ....

30 40 50 60 70 80

I

Figure 42. BVI noise directivity for airfoil SC1095m at Moo=0.7; r,,=50 chords, s2an--4 chords

55

ff

ff

ff

JJ

" 004

" 0O2

0:0. Ov:0

........................ t ...................

:I

................ -i ii

............ ': :::,_ , ,, ,,_

............................... _ .t. J .....................

I I I I I 1 l I I I I I ' ' I I ' I T i I ; I I

40 50 60 70 8OT

.0:._9. Ov :&42

O.00-"

0.002

C_'_ 0

-0.002

30

!:'," : ',

/'-.. ;i :"

% , _ •

...... _,; ,: ..............................J

'i• = 1 ; i _ , , i , _ . , I , ) ) i _, .

40 SO 60 70 80T

0=60, 0",'=1615 0=70, t.'K':21.26

0.004

0.002

C-p 0

-0.002

3O

..................................."!

.......... , .... ._._f',,' .-: ....._ :.-_,.,-,-_-,-;_-,--" ....._,.) cl • "

l) ),.

.................................... _ ._ -,_: ..........................................

_0 50 60 70 807

0--90, (X,=36.87 0=120, 9.-=-76.15

0.004

0.002

Ca 0

". 002

30

i

,i11

.....................................i..!.................................................

.'_ i

.................................. I ........ •.................................................

40 50 60 70T

0.004

0.002

Cp 0

-0.002

30

• • ;t'.................... _.._,_: ._ ....................

_-, I " ' i i I , • : I , ) i , I _

,40 50 60 70 80T

Figure 43. BVI noise directivity for airfoil SC1095rn at M_=0.8; rv=50 chords, span=4 chords

56

if

ff

ff

JJ

J

.... ,, L !

2- Vortex

Cp

Figure 44.

0.003

0.002

o.ooi

-0.001

-0.002

---I-- 1- Vort

t ..... d-.25 (2.volt.)

5 (2 voct

I I I I I

90 100 110 120 t30 140

Vortex splitting model and far-field BVI noise (rv=50, 0=30°).

57

_

fI" 0.001 -

,I

/ 0.0008 -/

0.0006

0.0004

0.0002

Op0

-0.0002

-0.0004

-0.0006

--CIv=.4

..... CIv=.2

' ' I .... i ' ' ' ' I .... I ' '"_

80 90 100 110 120 130

T

Figure 45. Effect of vortex strength on far-field BVI noise (rv=50, e=30o).

0.001 -

°0.0008 -

0.0006

0.0004

0.0002

0

-0.0002

-0.0004 -

-0.0006

--..-.,, .it;

I I I I i I I I

80 90

--angle of attack = 0 deg

..... angle of attack = 1 dog

' ''''1''''t''''1

100 110 120 130

T

Figure 46. Effect of angle of attack on far-field BVI noise (rv=50, 0=30°).

58