AIAA 91-3277 An Experimental and Computational Study of 2-D Parallel Blade-Vortex Interaction S. Lee and D. Bershader Stanford Univ., Stanford, CA M. M. Rai NASA-Ames, Moffet Field, CA

AIAA 9th Applied Aerodynamics Conference

September 23-25, 1991 / Baltimore, MD For permission to copy or republish, contact the American lnrtitute of Aeronautics and Astronautics 370 L'Enfant Promenade, S.W., Woshington, D.C. 20024

AN EXPERIMENTAL AND COMPUTATIONAL STUDY O F 2-D BLADE-VORTEX INTERACTION

Soogab Lee* and Daniel Bershadert A$L c 7 8 ( 9 Department of Aeronautics and Astronautics [ i

Stanford University, Stanford, California and

Man Mohan Rait NASA-Ames Research center,Moffet Field, California

Abstract

An experimental and computational study is car- ried out to investigate the dominant physical factors of 2-D parallel blade-vortex interaction (BVI) and its noise generation. A shock tube was used to generate a starting vortex which interacted with a target airfoil. Double-exposed holographic interferometry and airfoil surface pressure measurements were employed to ob- tain quantitative data during the BVI. As a numerical approach, thin-layer Navier-Stokes code, with a mul- tizonal grid, was also used to resolve the phenomena occuring in the BVI, especially in the head-on collision case.

I. Introduction

Rotor impulsive noise is, of all the known sources of helicopter far-field noise radiation, the one which tends to dominate the acoustic spectrum of most he- licopters. The helicopter generates a highly directional and rather unique form of impulsive noise which is thought to be generated by two source mechanisms; these are (1) high-speed impulsive noise due t o forma- tion of a shock on the advancing blade tip, and (2) blade-vortex interaction (BVI) in low-powered descend- ing flight or maneuvers, especially during an approach to a landing[Fig.l]. These sources are distinct, unre- lated and complex phenomena. Particularly, in the case of BVI noise, understanding of the noise-generating mechanism and theoretical comparison with experiment

* Research Assistant, Student Member AIAA. t Professor, Fellow AIAA. t Research Scientist, Member AIAA.

Copyright @American Institute of Aeronautics and Astronautics, Inc., 1991. All rights reserved.

are less decisive because they depend strongly on the lo- cal aerodynamic state of the rotor blade. Even though many experimental and theoretical studies have been carried out by now, there is still a fundamental ques- tion: what is the physical origin of BVI impulsive noise? To answer this question, first of all, we should know: (1) What kinds of aerodynamic phenomena dominate BVI noise? (2) What are the dominant parameters of these phenomena and their relations with one another.

Schmitz and Boxwe11*(1976) found, from their full- scale in-flight experiments, that the BVI acoustic signal propagates mostly forward and below the rotor tip-path plane whereas high speed impulsive noise does mainly forward of the plane. They also reported acoustic far- field impulsive noise patterns for a wide range of steady operating conditions. Tangle?( 1977) investigated the mechanism of helicopter noise through Schlieren flow visualization aided by full-scale blade pressure measure- ment in the wind tunnel and found that shock waves play a role in many of t,he blade-vortex interactions. Nakamura3( 1981) performed the calculation of the acous- tic far-field using the experimental data of a model Op- erational Loads Survey(0SL) blade, based on the as- sumption that only known surface pressure variations contributed to the radiated noise. However, that study was of limited success since the experimental data did not contain sufficient pressure informations for predic- tion. Recently, many r e s e a r c h e r ~ ~ * ~ s ~ have carried out wind tunnel or shock tube experiments and found that the BVI phenomenon was seen to be concentrated near the very leading edge of the airfoil. In addition, they reported that the advancing blade, in which the vortex and the blade are positioned almost parallel, is a strong conhibutor to the acoustic field.

The present goal of this rescarch is to investigate tslie influence of important factors on the two-dimensional BVI phenomenon and understand the noise generation

1

mechanism. It is evident that in flight the interaction is made more complex because of three-dimensional dis- tortion and partial randomization of the vorticity field; therefore, in general, the generic BVI problem[Fig.2] is unsteady and three-dimensional but it has two limit- ing cases according to the intersection angle( A ) be- tween the vortex axis and the airfoil span direction. When A = 90 degrees, the problem becomes steady 3-D whereas it is unsteady 2-D at A = 0 degree as can be seen in [Fig.3]. To simulate a 2-D BVI prob- lem experimentally, a shock tube was built to generate a compressible vortex which was being convected at a constant velocity in a quasi-uniform subsonic or tran- sonic stream. The vortex then interacted with a target airfoil( NACA 0012 shape in the present case).

The current phase of this work consists of a sys- tematic series of experimental and computational in- vestigations of the BVI with suitable variation of the most relavant parameters chosen from (1) the basic vortex features, such as circulation, vortex core size, and maximum tangential velocity, (2) transverse off- set of vortex path from the stagnation streamline( the miss distance), (3) freestream Mach number, (4) angle of attack, (5) shape of airfoil. Double-exposed holo- graphic interferometry and fast-response Kulite trans- ducers were used to obtain quantitative data during the BVI. As a numerical approach, a thin-layer Navier- Stokes code was used to resolve the phenomena occur- ing in the 2-D parallel BVI, especially in head-on col- lision. A fifth-order-accurate, upwind-biased scheme, based on the Osher-type of flux differencing with a mul- tizonal grid , was employed to preserve the vortex struc- ture more accurately, which is important for solving the head-on collision case.

11. Experiment

A shock tube, which has a rectangular test section, was designed to investigate two-dimensional blade-vortex interaction problem. The test section allows the shock to diffract essentially cylinderically, as illustrated in [Fig.4]; thus, the 2-D feature of the flow-field is re- tained. The diffracted shock is curved; however, the central section which interacts with the vortex gener- ator is closely planar. In this figure, the oblique solid line represents the shock speed which diminishes upon shock diffraction beginning at the area change(x=O on the horizontal scale). The dotted line which forks off the solid line represents the path of the convected vor- tex following separation from the generating airfoil. The cross section of the main shock tube is 5cm x 5cm.;

the vertical dimension increases to 50 cm at the area change. 25 cm x 36 cm plexiglass windows are mounted parallel to each other on the opposite sides of the test section. The duration time of a quasi-uniform flow af- ter a shock passes is about 4msec. To measure the speed of the shock, two Kulite transducers, which have a sensitive area of .010” in diameter, were employed -

upstream from the test section. To increase the shock speed( or induced free stream), Helium was used for a driving gas. A NACA 0018 airfoil was used as a vortex generator.

Double-pulsed holographic interferometry[Fig.5] was employed not only to determine the exact trajectory of the convecting vortex but also to measure the density distribution of the vortex. For synchronizing the laser light source discharge with the shock motion, the sig- nal from the second pressure transducer was used, af- ter delay by the digital delay generator together with the inherent delay in the Q-switch laser pulse mech- anism. The duration time of the ruby laser pulse is 10 nanoseconds. Agfa Gavart 10E75, which has a res- olution of 2800 lines/mm, was used as an emulsion plate. The emulsion plate recorded two holograms in two steps. The first exposure was made when the fluid is a t rest and the second one was made at the time of interest. These exposures produced two different in- terference patterns by phase shift of the second object beam according to the distribution of density of the flow. These image-plane holograms were reconstructed by use of the sodium lamp or He-Ne laser. The fringes in the hologram represent contours of constant density, the increment between fringes corresponding to .Of304 kg/m3, which is about 1/20 of the at,mospheric density, in accordance with the equation;

where I{ is Dale-Gladstone constant, A0 is the wave- - - length of pulsed ruby laser, prej is the density at a reference point ,and L is the span of test section. The diaphragm pressure ratio was controlled f 1 % from shot to shot by using polyester( mylar ) sheets. Aft,er the trajectory was determined, the pressure distribu- tions of the vortex were obtained by use of surface- mounted fast-response pressure gauges which provided time histories across the vortex during vortex passage.

From these measured density and pressure data, the tangential velocity can be deduced by the modified ra- dial momentum equation below by assuming that the unsteady term, the radial convection term, and normal

2

are only required in the path of the vortex and in the wake and boundary layers associated with the airfoil. The grids in all three zones were generated by using a combination of algebraic and elliptic grid generation procedures. The grids are orthogonal to the surface of the airfoil ,where zones 1 and 2 are discretized with 121 x 151 grids and zone 3 is discretized with a 273 x 573 grid, a total of approximately 193,000 grid points.

Boundary conditions and vortex embedding

The lower boundaries of all three grids correspond to the airfoil surface; hence, the no-slip condition and an adiabatic wall condition are imposed on these bound- aries. In addition, the derivative of pressure normal to the wall surface is set to be zero. All these conditions and the equations of state together yield

where n is the direction normal to the airfoil surface. These boundary conditions are implemented in an im- plicit manner by using the following equation to update the grid points on the airfoil surface.

where

1 0 0 0

.=(o 0 0 1 0 O 0)

O a P l

/ e o o o \ ~ = [ o 0 0 0 ")

o ae pe e and

6' = - J i , ~ / J i , l

0 = -uwal l /Pwal l

P = -vwaii /Pwall

Eq.( 12) is an implicit, spatially first-order-accurate im- plementation of the no slip adiabatic wall condition. A second-order-accarate, three-point, forward-difference corrector step is also implemented after each time step. In Eq.(12), @ is an approximation to Q n + l . When

p = 0,QP = @' and when the Osher scheme is iter- ated to convergence at a given timestep, @' = Qfl+l .

It should be noted that Eq.(12) requires the grid to be orthogonal at the airfoil surface and the Jacobians of the transformation, J i , l and Ji ,2 , to be independent of T .

For far-field boundaries of all three zones, the char- acteristic methods can be used to specify the condi- tions. Since the upper boundaries 51 = qmaZ are sub- sonic inlet ones, three quantities need to be specified and one quantity is extrapolated from the interiors of the zones. As we know, for the unsteady two dimen- sional case, there are four characteristics and four Rie- mann invariants. The first three conditions to be spec- ified are the generalized Riemann invariants given by

"712 - u77y R 2 = J G i j

The dependent variables p, u, v, and p in eq.(13) are taken to be the free-stream values under the following conditions: (1) the airfoil is at. zero angle of attack and (2) the grid does not contain a vortex. The fourth quantity which is necessary to update the points on this boundary is also a Riemann invariant

The right boundary of zone 1 and the left boundary of zone 2 are subsonic exit boundaries. A simple, implicit- extrapolation procedure followed by an explicit , post- update correction is used at these boundaries. The im- plicit part of the boundary condition for zone 1 is

Jimaz- 1 j (Qimaz-lj-QYmaz-lj) -p+l 0

(15) -

( @ 2 z , j -@mar, j 1 - Jim,, ,

this step is followed by the explicit correction

Pimas, j = P ,

And then, the free dream pressure P , is replaced by the pressure corresponding to the composite vortex in a free-stream solution if the grid system contains a vor- tex. The exit boundary of the zone 2 is treated in a sim- ilar way. The last boundary is the wake boundary sepa- rating zones l and 2. Although the grid lines of zones l and 2 are continuous across the wake , for convienence

4

the wake boundary is also treated as a patch boundary. For the manner in which these boundary conditions can be implemented implicitly and the method for transfer- ing the information in the time-accurate manner across the patch-boundaries; see Raigp".

In order to get the analytical structure of the vortex used in the calculation to closely resemble the experi- mental one, the maximum circulation, core radius, and peak tangential velocity must be identical in the ex- perimental and analytical vortices. The analytical ex- pression of the tangential velocity of the vortex is given by

where Q, and r are the core radius and the distance from the center of the vortex, respectively, and both are non-dimensionalized by the chord length of the airfoil. f is defined by the maximum circulation divided by freestream velocity and chord length. The sign of the vortex is defined negative in a clockwise flow direction for the isolated vortex. The pressure and density for the vortex convecting in the freestream are obtained as belows n

where the density p is obtained from

- Y P l P + 3 = YPrn/PW y - 1 2 7 - 1

Equation[l7] is integrated in conjunction with Eq.[18] using a Runge-Kutta scheme. The differential equa- tion is integrated from a large value of r , where the pressure and density are known, inward to the center of the vortex. Eqs.[16-181 represent a stationary vor- tex which satisfies the steady Euler equations. Navier- Stokes equations with appropriate boundary conditions are solved for steady state solutions, then the vortex is initialized a t the distance of 5 chord lengths ahead of the airfoil. The convection of the vortex and the interaction with the airfoil are then monitored. This calculation takes about 20 seconds per timestep and needs totally 50 hours of CPU time in CRAY-YMP for solving one case.

IV. Results and Discussions

The generation of single vortex

[Fig31 are sixteen successive holographic interfero- grams, showing the generation of shock-induced start- ing vortex and convection of this vortex to the target

5

airfoil. The holograms were taken with relative time increments of about 25 micro-seconds between expo- sures. In the stage 1, typical triple shock configura- tions are shown on both upper and lower surfaces of the vortex generator. In the lower surface, the shock has passed the entire airfoil and the Mach stem is about to diffract around the trailing edge. A reflected shock and sliplines are clearly shown in this picture. In the stage 2, the diffracted Mach stem from the lower sur- face intersects the other Mach stem on the upper sur- face and formed an attached vortex. Mach shock con- figurations exhibit conical similarity in distance/time as the time goes on. In the third stage, the shock- induced starting vortex has detached and is beginning to move to downstream. It would appear to have been knocked off the trailing edge by the advancing leeward- side shock. Although the vortex is detached, one ob- serves a residual connection to the trailing edge in the form of a periodic-structured layer with smaller-scale vorticity. After stage 4, the vortex is convecting with the freestream induced by the shock. In these holo- grams, the shock becomes almost planar and sliplines are shown between the shock and vortex. From the stage 9 to stage 16, the reflected shock from the lead- ing edge of the target airfoil is shown.. Through these stages, another vortex is growing due to the separation on the upper surface of the vortex generator, showing totally different behavior from the shock-induced start- ing vortex. One might, be able t o notice, from the stage 14 to the stage 16, that a sound wave is developing after the vortex has interacted with the reflected shock.

The vortex structure

To understand the physics of the BVI phenomenon, it is very desirable to know the precise structure of the vortex coming toward the airfoil. For the case of M , = .5,1'/Uw? = -.283 , the vortex was generated by a NACA 0018 airfoil inclined by 30 degrees. The convection velocity of the vortex was about 180 m/sec, which was measured by both holographic interferom- etry and three pressure transducers installed on the vortex trajectory. [Fig. 101 and [Fig91 show the holo- graphic interferogram and its density distribution, re- spectively. The measured pressure distribution and its curve fit are shown in [Fig.ll]. Derivatives of the pres- sure with respect to the radial distance and its curve fit are also shown in [Fig.l2]. In [Fig.l3], the tangen- tial velocity profile of the vortex, calculated from the curve-fits of these two independent measurements, are compared with the analytical vortex model of Eq.(16). In this comparison, the experimental vortex has al- most the same profile as the viscous vortex model wilh

= -.283,a, = .018. The core size of the vortex is much smaller than those of tip-trailing vortices which are typically 5 - 15% of the chord length.

Nielsen and Schwind"(l971), based on the idea of Hoffman and J o ~ b e r t ' ~ ( 1 9 6 3 ) ~ have divided the vortex into four distinct regions based on an analogy with the turbulent boundary layer: (1) Viscous core governed by viscous diffusion, (2) Logarithmic region dominated by turbulent diffusion, (3) Transition region to the outer inviscid region, (4) Irrotational region in which the cir- culation is constant. [Fig.l4] is the semi-log plot for the circulation distribution of the experimental vortex with respect to r/aol where r is the distance from the center of the vortex and a0 is the core size. The result is qualitatively very similar to the measurements of Tung et. a1.13(1983) on the rotor-tip vortices by using hot- wire anemometry even though this vortex is a start- ing vortex. The proportionality constant in the linear region, which is dominated by turbulent diffusion, is given by .43 which is close to .39 in average by Tung13, .44 reported by Cor~iglia '~(1973)~ .5 by Hoffman and Joubert"( 1963) and Phillips'5( 1981) ,even though this constant may vary with the shape of airfoil and have a weak dependence on the Reynolds number. The curve- fit result is as follows:

Core region:

Logarithmic region:

Transition region:

r/rrnuz = .~O(~/QO) ' ,

r/rrnaz = .51+ .431n(r/ao),

l?/rrnUz = 1 - .80ecp[-.65(r/ao)],

0 5 r/ao < .62

.62 5 r /ao 5 1.8

1.8 5 r/ao

The above vorbex actually experiences decay as time goes on; its location in [Fig.9-14] corresponds to a po- sition just before the leading edge of the airfoil( the travel time from the trailing edge of the vortex genem tor =500psec, and the pressure trace across the travel- ing vortex was measured without a target airfoil). For the details of the effect of compressibility on the vortex structure, see Mandella and Bershader"( 1987).

Head-on collisional BVI

Obviously, among the parallel BVIs, head-on col- lision case affects most strongly the aerodynamics and acoustics near the leading edge because it has the largest interacting area. [Fig.l5] shows the comparison be- tween the holograms and computational snapshots for head-on collision case of f = -.283,a, = .018. In the interferograms, the free-stream moves from right to left

, vice versa in the computation. At the first interfero- gram, a negative vortex( defined as a clockwise vortex in left-to-right freestream) is coming toward the airfoil. As the vortex approaches the airfoil, there is a down- ward component of the velocity across the airfoil nose. This induced velocity makes the stagnation point move upward and generates a separation on the lower surface. In the second hologram, the separation bubble grows and begins to convect with the flow. This secondary vortex is positive, different from the original one. In the third and fourth holograms, the stagnation point is moving back to its original position as the two vortices move downstream. The strength of the vortices is be- coming weak as they are annihilating each other. It is quite evident that the combination of the vortex weak- ening and separation from the airfoil surface means that such vortices have essentially no significant effect on the flow over the aft part of the airfoil. It also implies that the leading edge radius is a more important reference rather than the chord 1engt.h when we scale the vortex dimension.

.

In the computation, we also see the generation of secondary vortices due to the separation and the oscil- lation of the stagnation point during the head-on BVI. The computational snapshots are very similar to the experimental pictures qualitatively, but the quantita- tive match is not exact. The reason are: (1) vortex trajectories of experiment and computation are slightly different; (2) We still have some dissipation in the com- putation because the core size of the vortex is very small in this case. (3) The experimental vortex also showed dissipation during its convection. In [Fig. 161, the ex- perimental pressure traces at three selected positions, such as 2, 5, and 10 % of the chord length, are com- pared with the computational results. Even though the two results are not perfectly matched, they are qualita- tively very similar, except that the experimental traces show steeper slopes than the computational ones. In [Fig.l7] shows the effect of core size on the strong vari- ation of lift coefficient CL during the peak-interaction period of a head-on collision between vortex and air- foil. This result shows the importance of core size on the head-on BVI. It would be worth while to investigate experimentally the effect of core size of the vortex on the pressure fluctuation near the airfoil during head-on BVI, but it is not easy, in experiments, to make two vor- tices which have the same circulation with different core sizes. A recent experimental and computational work by Caradonna et (1989) reported that the vortex core size did not have a strong influence on BVI. In that study the authers scaled pressure variations by its vortex strength numerically.

6

[Fig.l8] represents four contour plots at t=5.16( t is non-dimensionalized by Um/c ), when the two in- coming and secondary vortices are about to merge into together. In the density, pressure, and Mach number contours, 20 lines were drawn from the minimum to the maximum at a constant increment, 200 lines were in the vorticity plot. We can notice the secondary vor- tex has a lower density and pressure at the center than the original vortex does since the incoming vortex lost its strength through the interaction with the airfoil. In Mach number contours, the existence of a super- sonic region, with subsonic one, inside the vortices is shown since the velocity of the vortices is added by the freestream on one side where it is subtracted on the op- posite side. The vorticity contours shows the vorticity field is also highly distorted during head-on collision. In [Fig.lS], twelve computational snapshots are shown for the density contour developments during head-on colli- sion BVI when Ma = . 7 , r = -.283. In these contour plots, we can notice that sound waves are generated right after the vortex hits the leading edge, and that the waves propagate upstream.

IV. Summary and Conclusions

The present study indicates: (1) A single shock- induced starting vortex was generated by a suitable vortex generator in the enlarged test section of the shock tube; (2) The independent density measurement by holographic interferometry and pressure measure- ments of the vortex enable us to obtain the tangen- tial velocity and circulation distributions of the vortex and to use these results to embed the same vortex in the calculation; (3) In a shock-induced starting vor- tex, the proportionality constant in the logarithmic re- gion of the circulation distribution was found as 0.43 , which is colse to those of typical tip-trailing vortices; (4) During the head-on collision case in BVI( the vor- tex is clockwise), the airfoil experiences separation on the lower surface and transition of the stagnation piont to the upper surface( rapid oscillation of the stagna- tion point), resulting in the rapid and severe pressure variation near the leading edge which contributes to the dipole sources of radiated noises. (5) Navier-Stokes calculation with a high-order scheme and a multizonal grid shows good qualitative agreement with experiment even in the head-on collision case. (6) Futher experi- mental work is desirable to study the core-size effect, the transonic head-on BVI with shock motion, and the noise propagation.

7

Acknowledgements

This work was sponsored by NASA-Ames and the U.S. Army Research Office under Contract Number NCA2-339. Useful comments of Dr. C. Tung and Dr. Y. H. Yu are gratefully acknowledged, as are discussions with Professor Nicholas Rott, Dr. G. R. Srinivarsan, and Dr. W. J. McCroskey. The authers are grateful to Dr. M. Mandella for some of his holograms.

REFERENCES

Schmitz, F. H . and Boxwell, D. A., ‘In-flight far fi- ield measurement of helicopter impulsive noise, ’ J. America1 Helicopter Society, Vo1.21,(4),0ct.1976

Tangler, J. L., ‘Schlieren and noise studies of rotors in forward flight,’ Paper77,33-05,33rd Annual Na- tional Forum of the American Helicopter Society, Washington, DC, 1977.

Nakamura, Y. , ‘Prediction of Blade-Vortex interac- tion noise from measured blade pressure,’ Paper 32, Seventh European Rotorcraft and Powered lift air- craft forum,

Caradonna, F. X., Strawn, R. C. and Bridgeman, J. O., ‘ An experimental and computational study of rotor-vortex interactions,’ Vertica, Vo1.12,No.4,1988

Straus, P. R. and Mayle, R. E.,‘ Airfoil pressure measurements during a blade-vortex interaction and a comparison with theory,’ AIAA Paper 88-0669, RenoJevada, Jan. 1988.

Meier, G. E. A. and Obermeier, F., ‘Noise generation and boundary layer effects in vortex-airfoil interac- tion and methods of digital hologram analysis for these flow fields,’ Final technical report, European research office of the US. Army, 1990.

’ Rai, M. M. and Chakravarthy, S. R. ‘ An Implicit form for the Osher upwind scheme,’ AIAA Journal, V01.24~No.5, 1986.

a Rail M. M. ‘Navier-Stokes simulation of blade-vortex interaction using high order accurate upwind schemes,’ AIAA-87-0543, 25th Aerospace sciences meeting, Reno, 1987.

Rai, M. M. and Chaussee, D. S. ‘New implicit bound- ary procedures: Theory and Application,’ AIAA Journal, Vol. 22, No. 8, 1984.

lo Rai, M. M. ‘Navier-Stokes simulations of rotor-stator interaction using patched and overlaid grids,’ AIAA 85-1519, 7th Computational fluid dynamics confer- ence, Cincinnati, Ohio, 1985.

l 1 Nielsen, J. N. and Schwind, R. G., ‘Decay of a vortex pair behind an aircraft,’ Aircraft wake turbulence and its detection, edited by J . Olson et. al., Plenum press, New York, 1981.

l2 Hoffman, E. R. and Joubert, P. N., ‘Turbulent line vortices,’ J. Fluid Mech., Vol. 16, Part.3, 1963.

l3 Tung, C. et al, ‘The structure of trailing vor- tices generated by model rotor blades,’ Vertica Vol.7,No. 1,1983

al, ‘Rapid scanning, three- dimensional hot wire anenonometer surveys of wing tip vortices,’ J. Aircraft,Vol.lO, No.12, 1973.

l 5 Phillips, W. R. C. ‘The turbulent trailing vortex dur- ing roll-up,’ J . Fluid Mech., P. 105, 1981.

l6 Mandella, M and Bershader, D,‘Quantitative study of the compressible vortex: generation,structure and interaction with airfoil,’ AIAA Paper 87-0328, Reno, Nevada,Jan.1987

l4 Corsiglia, V. R. et.

Appendix

For an axisymetric, compressible, viscous flow, the radial momentum equation can be expressed like be- lows:

where the first term corresponds to the unsteady accel- eration; the second term is the convective acceleration; the third term is the pressure gradient term; the fourth term is the centripetal acceleration; and the last terms are the specific radial force due to normal stress.

8

I - -

LEVEL FLIGHT

ROTOR WAKE

DESCENDING FLIGHT

[Fig.l] Interaction of tip vortices with a rotor disk for level and descending flights.

[Fig.2] Blade-vortex intersections during partial-power descent flight(from Tangle$).

n

PARALLEL BVI (Ai = 0 )

[Fig31 Typical parallel blade-vortex interaction and its parameters. ( Lines around the airfoil are density con- tuors.)

I

I Xtm)

[FigA] The x-y plot of the shock wave and vortex, su- perimposed on schematic diagram of the shock tube configuration.

Counter Gt I Pick-ups I

Digital

Genera-

I 0sci11oscope.s I I ,

Hologram

I

Ruby Laser 6943 A

Ruby Laser Power Supply

[Fig.5] Schematic top view of the experimental set-up for holographic interferometry and airfoil surface pressure measurements.

ZONE 1 (121 x 151 )

ZONE 3

ZONE 2 (121 x 151 )

[Fig.6] The computational multi-zonal, patched grid. ( Totally 193,000 grid points)

[Fig.7] Close-up of the grid near the leading edge.

STAGE 1

STAGE 2

STAGE 3

STAGE 4

STAGE 6

STAGE 7

F

STAGE 8 [Fig.8] Sixteen successive holographic interferograms at 25 micrc+second intervals, showing the generation of a shock- induced starting vortex and the convection to the target airfoil in the enlarged test section of the shock tube( Continued ).

STAGE 9

STAGE 10

STAGE 11

STAGE 12

STAGE 13

STAGE 14

STAGE 15

STAGE 16

[Fig31 Sixteen successive holographic interferograms a t 25 micro-second intervals, showing the generation of a shock- induced starting vortex and the convection to the target airfoil in the enlarged test section of the shock tube.

I2

1 0 -

[Fig.lO] Holographic Interferogram of the vortex.

- - - - - - ---- - -___ * -3

%I

Pressure data of vortex I

1 mc+8

5.mc+7 h

E 2 -k

\

o.ak+o v

\

3 -5.ooe+7

- I .ooc+8

1.0 -

0.8 - 2 . \ ' 0.6

* ;>.,+ i+ '?' ; *. i +\. ; *.-*

- t

*t-*** - .","Y9-b i * *-e++ i

'\ i t ? 9; - 'a,+,+

.-... d P l d r w e - f i t

02 4.2 4. I 0.0 0.1 0.2

rlc

08

2 . Q \ Q 0 6 -

04

02

[Fig.ll] Measured pressure profile of the vortex and its curve-fit.

--. nwc fit

-

1.5

IO

8 5

s 1 '

0.5

Tangential velocity of vortex I

+ dcduccdfromexpcnmcnt

-

0.0 ' I

42 4. I 0.0 0.1 0.2 rlc

[Fig.l3] The velocity profile calculated from measure- ments of the density and pressure distributions across the vortex and its curve-fit by the analytical model(Eq.lG).

. I I 10 T/QO

[Fig.l4] Semi-log plot of the normalized circulation (I'/FmaZ) with respect to the distance from the cen- ter of the vortex.

a,

[Fig.l5] Comparison of experimental holographic interferograms and computational snapshots during the head-on collision at M, = .5,f = -.283. ( The linea in computation represent density contoure; the holograme were taken at 25 micrwxcond intervals.)

1 . , . , . , . , . , . , . , .

4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.0

Time

1 . , . , . , . , . , . , . I .

Computation 0 -

2 -

.1 lclcs.02 2 lclem - 3 l l h . 1 0

4 4.2 4 4 4.6 4.0 5.0 5.2 5.4 5.6 5.6

* ' . ' - ' - ' . ' . ' * ' .

Time

1

0

3

u"

-1 4.2 4.4 4.0 4.8 5.0 5.2 5.4 5.6 5.8

Time

2 . , . , . , . , . . - 1 . 1 .

I - . .. t computation

4.2 4.4 4.6 4.0 5.0 5.2 5.4 5.0

Time B

[Fig.l6] Comparison of experimental and computational pressure histories of near-leading edge points during head-on BVI at M , = . 5 , f = -.283, and a0 = .OB.

3 Y

0.4

0.2

0

t

I ao = 0.018 uo = 0.160

- . . . . . . . .

"." 4 4.5 5 5.5 6 6.5 7

Non-dimensional time

[Fig.l7] The effect of the vortex core size on the lift coefficient during head-on BVI at M , = .5, f = -283.

Density contour Pressure contour

Mach number contour Vorticity contour

[Fig.l8] The density, pressure, Mach number, vorticity contours of k 5 . 1 6 during head-on BVI when M , = .5, r = -.283, and a0 = .018; t is non-dimensionalized by clUm ( t=O a tXv= -5.0 and the vortex hits the leading edge a t approximately k 5 . 0 ) ; 20 contours from the minimum to the maximum at constant increments are shown in the density, pressure, and Mach number plots, and 200 contours in the vorticity plot.

L $ - 1