AI AA-9 I - 066 2 Numerical Study of the Effects of Icing on Fixed and Rotary Wing Performance 0. J. Kwon and L. N. Sankar Georgia Institute of Technology Atlanta, GA

29th Aerospace Sciences Meeting January 7-10, 1991/Reno, Nevada

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Numerical Study of the Effects of Icing on Fixed and Rotary Wing Performance

Oh J. Kwon' Lakshmi N. Sankart

Georgia Institute of Technology Atlanta, Georgia 30332

ABSTRACT

The sectional and total aerodynamic load character- istics and performance degradation of swept wings and helicopter rotors have been studied using a three- dimensional, compressible Navier-Stokes solver. Cor- relations of predictions with experimental data for swept wings with and without leading-edge ice for- mation show the ability of the present computational technique t o accurately predict both the distributed surface pressures and integrated sectional loads. The leading-edge flow separation and reattachment on the wing surface associated with the leading-edge ice are also captured well showing a vortex formation and the spanwise migration of the flow inside the separated flow region. In the case of the helicopter rotors in hover, the rotor thrust loss and the torque penalties due to the leading-edge ice formation are numerically demonstrated.

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INTRODUCTION

The adverse effects of ice formation a t the leading edge on aerodynamic characteristics are well known not only for the fixed wing aircraft but also for he- licopters [I , 21. Ice accretion on the leading edge of the wings and rotor blades causes premature flow sep- aration, and can result in detrimental effects on aer- dynamic performance by severely reducing the lift, increasing the drag, and changing the aerodynamic moment characteristics. The changes in aerodynamic forces and moment can also affect the aeroelastic be- havior ofwings and helicopter rotors so that the struc- tural system may be damaged. In the case of heli- copters, since the rotor provides both lift and propul- sive thrust, the performance degradation due to the ice

'Post-Doctoral Fellow. School of Aerospace Engineering. Member AIAA.

IAssociate Proiessor, School 01 Aerospace Engineering. Member AIAA.

Copyright 01991 by Oh J. Kwon and Lakshmi N . S a n k . Published by the American Institute of Aeronautics and Astrc- nautics, Inc., with permission.

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accretion has significant effects on the overall perfor- mance. Reliable techniques for quantitative prediction of leading edge ice formation for different atmospheric conditions and for the prediction of the effects of icing on the aerodynamic performance of wings and rotors are urgently needed, so that next generation aircraft and rotorcraft may be designed to cope with icing.

There has been active research [3-101 at NASA, uni- versity, and industry sites t o develop techniques for the prediction of ice accretion and to evaluate the perfor- mance of wings and helicopter rotors due to icing both analytically and experimentally. The work covers ar- eas such as i) first principle-based numerical modeling of the leading edge ice accretion on 2-D airfoil sections, ii) experimental determination of ice shape on fixed wings and helicopter rotors, ii) experimental studies of the effects of icing on the aerodynamic characteristics of 2-D and 3-D fixed wings and helicopter rotors, and iv) development of research tools based on 2-D and 3- D Navier-Stokes equations to study the pre- and post stall aerodynamic characteristics of finite wings.

Computational studies of the aerodynamic charac- teristics and performance degradation of wings and r- tors are very demanding because they require state- of-the-art computational tools and an adequate tur- bulence model to properly catch complicated flow fea- tures, such as leading-edge flaw separation, flow reat- tachment, vortex formation and shedding, associated with the ice formation. This is particularly true for 3-D flow simulations which require several hundred thousand grid points and several hours of CPU time on modern high-speed computers. In the case of heli- copter rotors, a separate wake model is also required to take into account the tip vortex and the inner vortex sheet from preceding blades and from previous blade turns underneath the rotor disk plane, not captured by the computational domain for the primary blade. Since the inclusion of an accurate wake eKect on the rotor blade is essential to accurately estimate the rw tor performance and an accurate calculation of helical rotor wakes is sometimes as difficult as numerically solving the flow over the helicopter blade itself, the calculation of helicopter performance degradation due

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to the leading-edge ice formation is more complex than for k e d wing configurations.

In the past, computational studies for predicting the aerodynamic performance degradation due to leading- edge ice formation focused on 2-D airfoils [9] and 3-D fixed wings with a rectangular planformshape [lo]. In these studies, the surface pressure distributions, the integrated sectional lift and drag were compared with experimental data, and the leading-edge flow separa tion and vortex shedding were also studied in detail.

The present work is an extension of the previous efforts and deals with the aerodynamic characteristics and performance degradation of fixed swept wings and helicopter rotors in hover for both clean and iced con- ditions. An untwisted, untapered NACA 0012 airfoil based wing with 30' leading-edge sweep angle is chn- sen for the fixed wing studies. Where possible, de- tailed surface pressures and sectional airloads are com- pared with experiments [ll]. For helicopter rotors, a generic rotor configuration is chosen. The detailed computational procedure to account for the wake ef- fects is described, and the performance degradation of the helicopter rotors due to icing is qualitatively demonstrated.

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MATHEMATICAL AND NUMERICAL FORMULATION

- Governing Equations: The equations governing unsteady, compressible,

three-dimensional flow are the full Navier-Stokes equa- tions, and may be written in a Cartesian coordinate system as:

41 + Fz + Gp + Hz = Rz +Sr +Tz (1)

Here, q is the unknown flow properties vector, and z, y , and z are the axes of the Cartesian coordinate system The freestream is directed parallel to x-axis as shown in Fig. 1. F,G and H are the inviscid flux vectors and R, S, and T are the viscous terms for each 2, y, and I axes. To facilitate treatment of arbitrary plan- forms and airfoil shapes, the equations are solved in a body-fitted coordinate system. The following general curvilinear coordinate system is used:

E = E ( r , y , : , t )

0 = v ( z , Y > z > q

C = C ( t , y , z , t ) (2) r = t

In such a coordinate system, the governing equa- tions may be written i n the following strong conserva- tion form:

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q, + F( + G, + H ( = R, + S, + T< (3)

The quantities q, F, G, H,R, S , T are related to their Cartesian counterparts through the metrics of transformation.

In such a general coordinate system, the wing sur- face maps onto a < = Constant surface. The span direction is associated with the 7 coordinate, and the direction normal to the flow maps onto E = Constant lines or planes. For a detailed description of the flow and flux vectors in the Cartesian and transformed co- ordinate systems, the reader is referred t o Ref. 12.

For a turbulence closure, a two layer Baldwin- Lomax eddy viscosity model patterned after the Cebeci-Smith model has been used in this work. Even though use of such a simple model in massively sepa- rated flows may be considered questionable, the study of 2-D stalled flows using two other models, one based on Johnson-King ODE formulation and the second based on the classical two equation ~ - 6 model, did not show any appreciable improvements with the higher- order models when identical grids were used with all the three turbulence models [l3]. In order t o keep the computer time resources small, the Baldwin-Lomax model has been used in all the 3-D calculations pre- sented here.

Solution Procedure: The governing equations are parabolic in time, and

may be advanced in time using a suitable stable, dissi- pative scheme. In the present work, st.andard second- order accurate central differences were used to ap- proximate the spatial derivatives, and to compute the metrics of transformation. The highly non-linear flux terms F and H , which are unknown at a given time level 'n+ 1' were linearized about their values a t a pre- vious time level 'n'. The spanwise flux vector deriva- tive was treated semi-implicitly, and requires no time linearization. The time derivative was approximated as a first-order accurate, twopo in t backward differ- ence. The resulting equations were reexpressed ac a penta-diagonal matrix system of simultaneous equa- tions for the 'delta' quantity (q"+' - q") . The penta- diagonal matrix system was approximately factored into a product of tridiagorial matrices using the Beam- Warming approximate factorization scheme, as d i s cussed in Ref. 14.

The use of standard central differences to approxi- mate the spatial derivatives can give rise to growth of high frequency errors in the numerical solution with time. To control this growth, a set of artificial dissi- pation terms were added to the discretized equations. These dissipation terms used a combination of second and fourth order differences of the flow properties, in a manner discussed by Jameson et al. [15].

Grid Generation: An algebraic Cgr id generator has been built into

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the computer code, and can generate computational grids around arbitrary planforms and arbitrary airfoil sections. The grid generation methodology is based on the sheared parabolic coordinate scheme. The user needs to prescribe the leading edge coordinates and the section chord and twist at chosen stations. The grid generation routines perform the necessary interpola tion (linear along the span and cubic in the chordwise direction) to enrich the input wing shape. After the sheared parabolic grid is generated, the points along the grid lines in the direction approximately normal t o the wing surface are redistributed so that the first point off the wall is a t a user specified distance off the surface, and an adequate number of points are placed within the boundary layer. A typical grid for a swept wing is presented in Fig. 2 which shows the upper half of the computational domain at the wing root sym- metric plane and on the surface of the wing.

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Boundary Conditions: In the present numerical procedure, for the sake of

simplicity, all the boundary conditions are applied ex- plicitly after each time step. Since the cases included in the present paper deal with low subsonic Mach nnm- bers, the flow quantities at the far-field are set to he the undisturbed freestream conditions. To satisfy this condition, the far-field boundaries are stretched far enough, and placed at least 6 to 7 chord lengths from the surface of the wing or helicopter rotor blade. At the downstream boundary, the pressure is assumed to recover to freestream values and all the other flow quantities including the density and velocity are ex- trapolated from the interior. The Ggrid generated by the present algebraic transformation created a cut that originates from the trailing edge. On this cut the flow quantities are averaged from above and below.

At the inboard station of the helicopter blade, the spanwise flux is turned off, and a quasi-two- dimensional flow is simulated. In the case of swept wings, this plane is the wing root plane and the span- wise symmetric boundary condition should be applied. The experiment to be compared with the present re- sults [ l l ] had a semispan wing with a splitter plate a t the wing root to minimize the effects of the wind tun - nel wall boundary layer on the flow over the wing. The splitter plate had its own thin boundary layer which interacts with the flow on the wing. Also, the splitter plate allows vorticity to shed into the flow and reduces the effective angle of attack at the wing root sections. Thus, the flow at the wing-splitter plate junction is different from that at a wing symmetric plane. In our studies, a n c 4 p boundary condition is applied at the wing root-splitter plate junction, and an ade- quate number of nodes are used to capture the Row i n this region.

On the surface of the wing and helicopter blade, a

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nc-slip boundary condition was applied. In the case of helicopter rotor blades, one must take into account the t ip vortex and inner wake sheet from preceding blades and from previous blade turns, which exist un- derneath the rotor disk plane out side of the compu- tational domain. This was accomplished by changing the blade sectional effective angle of attack based on the magnitude of downwash velocity obtained from a separate wake code. For this purpose, a prescribed- wake/lifting-line code [16] was used which calculates the helicopter hover performance by repeatedly apply- ing the Biot-Savart law between the blade bound VOE

tex and the wake vortex lines. Here, the blade was modeled as a lifting line at the blade quarter chord. The tip vortex was represented by a single vortex line and its geometry w a s obtained from a generalized c- ordinate which was predetermined experimentally [17]. The inner vortex sheet was modeled as trailing vortex lines, and their geometries were determined iteratively by relaxing the axial location after each iteration. A detailed description of this wake code can be found in Ref. 16.

RESULTS AND DISCUSSION

Fixed Swept Wings: An untwisted, untapered wing with 30° leading-edge

sweep angle and an aspect ratio of4.06 is taken as the baseline clean wing configuration. The airfoil section for this clean wing is a NACA 0012 airfoil in a plane normal to the wing leading-edge. The same wing, with the leading edge modified with an simulated glaze ice shape is studied in the iced wing calculations. It is assumed that the ice formationstretches from the wing root to the tip maintaining the same shape. The wing configuration and assumed ice shape are identical to that used by Bragg et al. [ l l ] in their wind tunnel studies, facilitating a direct one-twone comparison of computed and measured data. The leading-edge ice shape is shown in Fig. 3 for a section normal to the wing leading edge. The freestream Mach number is 0.12 and the Reynolds number is 1.5 x IO6 based on the wing chord length normal to tlie wing leading edge.

The computational C-grid consists of 151 stream- wise points ( 105 on the wing surface), 42 spanwise points (36 on the wing). and 4 4 points in t l i e normal direction as shown in Fig. 2. The grid points ar? c l u s tered on the wing leading edge in streamnis? direction and near the wing surface i n normal direction so that the leading-edge suction. the boundary layer charac- teristics, and the separation patterns can be captured accurately. As described earlier, the wing root plane was treated as a solid wall allowing a no-sliii bound- ary condition. Thus, the spanwise grid points are also clustered at this plane and stretched toward the tip so

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that the growth of the boundary layer on the splitter plate and its interaction with the flow over the wing can be captured more accurately.

For the purpose of comparison, two angles of at- tack equal to 4 O and are chosen for the numerical simulation. The chordwise pressure distribution and the spanwise section loads have been compared with the experiment [ll]. The chordwise pressures are pre- sented in a direction normal to the wing leading-edge, rather than along the freestream, as in the experiment. The spanwise sectional lift coefficients are normalized by the wing chord length normal to the wing leading edge for o n e - b o n e direct correlations.

In Fig. 4, the computed surface pressures for the clean, swept wing a t 8 degree angle of attack are shown at several spanwise stations. Correlation with experi- ment shows excellent agreement over the chord a t all spanwise stations except that the predicted suction peaks at the mid span stations are slightly lower than the experiment. The flow remains attached to the sur- face of the wing at this angle of attack.

Fig. 5 shows the spanwise distribution of the com- puted and measured airloads (i.e. measured surface pressures integrated over the chord) a t 8 degree an- gle of attack. The computed airloads are in good agreement with the measured loads over the span both at the inboard stations and at the tip. The three- dimensional tip effect is also accurately predicted with a rapid drop of the sectional loads at the tip.

Fig. 6 shows the surface pressures of the swept wing with simulated glaze ice a t 4 degree angle of attack. The sharp curvature of the assumed ice shape leads to vcry high local suction peaks in the Navier-Stokes simulations and appears as spikes in the C, plots. The experimental data are relatively smooth. At this low degree angle of attack, the overall agreement between the experiment and theory is fairly good. The pressure distribution on the surface of the wing leading edge shows a relatively flat region which is associated with the locally separated flow at the leading edge.

A numerical flow visualization technique was applied to the flow over the wing and the streamline patterns on the wing upper surface and the particle trajectory simulations were obtained. Fig. 7 shows a simulation of the surface oil flow on the iced wing upper surface at 4 degree angle of attack. It is seen that there is a strong spanwise velocity component of the flow, which is typical for a wing with finite leading-edge sweep an- gle. It also appears that the flow separated right a t the wing leading edge reattaches at about 20 % of the wing chord as demonstrated by a clear dividing streamline pattern. A locally separated flow exists be- tween the wing leading edge and the flow reattachment line which causes the plateau region of pressure distri-

In Fig. 8, a particle trajectory simulation of the flow

-

-

.- bution in Fig. 6.

is shown on the iced wing upper surface a t 4 degree angle of attack. Inside the separated flow region, a strong vortical flow exists which originates from the wing leading edge at the root and travels toward the tip and eventually merges into the wing tip vortex. The center of the vortex inside the separated region is located approximately a t the middle of the separated region. Once the flow reattaches, the flow particles fol- low the surface of the wing smoothly and travel toward the wing trailing edge and the tip.

The chordwise pressure distributions for the iced wing at 8 degree angle of attack are compared with the experimental results in Fig. 9. Again, a good cor- relation with the experiment is observed both inside the leading-edge separation region and on the attached flow region afterward. The approximate magnitude of separation and flow reattachment points are predicted well. Unlike the 4 degree angle of attack case, the sep- arated flow region at 8 degree angle of attack becomes bigger as the flow travels toward the tip and finally separates fully a t the tip.

The above observation is clearly demonstrated on the surface oil flow simulation in Fig. 10 showing the flow reattachment line as a dividing streamline which extends from the leading-edge a t the wing root to the wing trailing edge near the tip. The flow on the sur- face is directed toward the wing leading edge before the reattachment and toward the trailing edge after. Fig. 10 also shows a thin and narrow secondary vor- tex region and the flow separation and reattachment lines associated with this secondary separation region near the wing leading edge for most of the rnidspan stations.

Fig. 11 shows the particle trajectories of the iced wing upper surface at 8 degrees angle of attack. The flow inside the separation region forms a strong vorti- cal flow with its core originates from the wing leading edge at the root and travels toward the wing tip and finally merges into the tip vortex. The flow particles inside the separated flow region are trapped and moves in a helical path around the vortex core. The particles outside the separated region show a nice and smooth behavior and follow the boundaries of separated flow region and the wing surface after the ROUP reattach- ment.

Fig. 12 shows comparisons of the computed and measured sectional loads for the iced wing. The corn- puted load distributions along the span for both 1 and 8 degree angles of attack are in good agreement with the experiments. At 4 degree angk of attack, the flow separation is confined near the wing leading edge for all spanwise stations and thus does not affect the inte- grated sectional load behavior severely. In the 8 degree angle of attack case, the relatively flat pressure distri- bution inside the leading-edge separation region and the reduction of leading-edge suction create a loss of

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the sectional load along the span, the magnitude of which is approximately proportional to the length of the separation region. A t the outboard stations it is observed that the loss of sectional load associated with leading-edge separation is approximately 15 % or more than that of the clean wing at the same flight condi- tion.

Helicopter Rotors in Hover: A typical two-bladed helicopter rotor with the solid-

ity of 0.05964 was chosen as the baseline clean rotor. The rotor blade has a rectangular planform and uses NACA 0012 airfoil sections. The same rotor with a simulated glaze ice on the blade leading-edge was con- sidered t o be an iced rotor. It is assumed that the ice formation stretches from the blade root to the tip maintaining the same shape. The sectional generic ice shape is shown in Fig. 13. For the present work, the tip Mach number w a s 0.34 and the tip Reynolds num- ber was 2.1 x lo6 based on the blade chord length. The computational C-grid consisted of 115 streamwise points ( 95 on the wing surface), 38 spanwise points (33 on the wing), and 41 points in the normal direc- tion. A sectional view of the grid near the leading edge is also shown in Fig. 13.

For the numerical calculations, three blade collec- tive pitch angles of 5, 7 and 9 degrees are chosen for both the clean and the iced rotors. The loading vari- ations in terms of the collective pitch angle have been compared with a lifting-line hover analysis [I61 and also with classical blade-elementfannular-momentum results. Finally, the torque vs. thrust variation for both clean and iced rotors has been computed to as- sess the performance degradation penalty due to the leading-edge ice formation on the helicopter rotors in hover. The tw-dimensional section aerodynamic char- acteristics of lift and drag needed in the hover analysis for both with and without the simulated glaze ice are obtained from experiments [SI as a function of angle of attack and Reynolds number.

In Fig. 14 the thrust loading coefficients for clean rotors are presented at the above three collective pitch angles and compared with lifting-line and blade- elementfmomentum methods. The present Navier- Stokes predictions compare with the other two poten- tial methods well except a t the higher collective pitch angle. Since the present Navier-Stokes calculations rely on the wake information separately provided, the accuracy of load predictions at high collective pitch angles is strongly dependent on the accuracy of the wake code, especially at high collective pitch angles.

In Fig. 15 a similar comparison of thrust loading coefficients is shown for the iced rotors. Since the sim- ulated glaze ice and the associated flow separation at the leading edge for the rotors is much smaller in scale than that of fixed wings, the penalty due to the icing

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on the rotor thrust is not severe at least for the cases presented here. Thus, the magnitude of thrust loading and its slope for the collective pitch angle is similar to those of clean rotors. A typical section particle trajec- tories around the leading edge for the iced rotor are shown in Fig. 16 at 90 % of span.

Fig. 17 shows the comparison of rotor torque re- quired in terms of total thrust required. I t clearly demonstrates the adverse effects of leading edge ice accretion on the helicopter main rotor by increasing the required torque equal to 25 to 30 % over that of a clean rotor a t the same thrust settings.

CONCLUDING REMARKS

A three-dimensional Navier-Stokes solver has been used to study the performance of swept wings and he- licopter main rotors in hover, both with and without simulated glaze ice a t the leading edge. The calculated chordwise pressure distribution and the integrated sec- tional loads of both clean and iced wings are in good agreement with experiments, The locally separated flow region and the flow reattachment under icing are well predicted. Numerical flow visualization and par- ticle trajectory simulations also show features such as flow separation, reattachment, and the formation and spanwise migration of vortical flow inside the sepa- rated region. In the case of helicopter rotors in hover, the leading-edge ice did not affect the total th rus t load- ing of rotors significantly, a t least for the collective pitch angles studies here. I t is observed that there is approximately a 25 to 30 % torque penalty associated with the ice formation on the leading edge.

ACKNOWLEDGMENT

This work was sponsored by NASA Lewis Research Center under grant NAG-3-768. The authors would like to thank Dr. M . G . Potapczuk, for his guidance and support for this effort.

REFERENCES

1. Preston, G . hl . and Blackman, C. C., "CFlects of Ice Formations on Airplane Performancr i n h v e l Cruising Flight," NACA Th'-159P. htay 19.16

2. Korkan, K . D., Dadone, L . , and Shaw, R. J . , "Per- formance Degradation of Helicopters due to Icing - A Review," Presented ai the 4 I s t Annual Forum of the American Helicopier Socieiy, F t . Worth, Texas, May 15-17, 1985.

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3. Hansman, R. I . , Yamaguchi, K., Berkowitz, B., and Potapczuk, M., “ Modeling of Surface Rough- ness Effects on Glaze Ice Accretion,” Jan. 1989, A I A A Paper 89-0734.

4. Cebeci, T., Chen, H., and Alemdaroglu, N., “For- tified LEWICE with Viscous Effects,” Presenied ai ihe A I A A 28ih Aerospace Sciences Meeting, Reno, Nevada, Jan. 8-11, 1990, A I A A Paper 90- 0754.

5. Lee, J. D., “Documentation of Ice Shapes on the Mail Rotor of a UH-IH Helicopter in Hover,’’ Aeronautical Research Laboratory, The Ohio State University, 1983.

6. Korkan, K. D., Cross, E. J., Jr., and Cornell, C. C., “Experimental Study of Performance Degra- dation of a Model Helicopter Main Rotor with Simulated Ice Shapes,” Presenied ai ihe A I A A 22th Aerospnce Sciences Meeting, Reno, Nevada, Jan. 9-12, 1987, A I A A Paper 84-0184.

7. Bragg, M. B. and Spring, S. A,, “An Experimen- tal Study of the Flow Field about an Airfoil with Glazelce,” Presenied ai the A I A A 25th Aerospace Sciences Meeting, Reno, Nevada, Jan. 12-15, 1987, A I A A Paper 87-0100.

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8. Bragr. M. B. and Khodadoust, A., “Effect ofSim-

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ulated Glaze Ice on a Rectangular Wing,” Pre- sented a1 the A I A A 27th Aerospace Sciences Meei- ing, Reno, Nevada, Jan. 9-12, 1989, A I A A Paper 89-0750.

9. Potapczuk, M. G., “Numerical Analysis of a NACA 0012 Airfoil with Leading Edge Ice Accre- tions,” Presenied at t h e A I A A 25ih Aerospace Sci- ences Meefing, Reno, Nevada, Jan . 12-15, 1987, A l A A Paper 87-0101.

14. Wake, B. E., “Solution Procedure for the Navier- Stokes Equations Applied to Rotors,” Ph. D. Dissertation, Georgia Institute of Technology, At- lanta, GA, 1987.

15. Jameson, A. and Baker, T . J., “Solution of the Euler Equations for Complex Configurations,” A I A A Paper 83-1919, 1983.

16. Samant, S. S. , and Gray, R. B., “A Semi- Empirical Correction for the Vortex Core Effect on Hovering Rotor Wake Geometries,” Proceed- ings of ihe 3 r d Annual Forum of ihe American Helicopter Society, Washington, D.C., May 1977, pp. 02-1 - 02-10.

17. Kocurek, J. D., and Tangier, J . L., “A Prescribed Wake Lifting Surface Hover Performance Analy- sis,” Journal of the American Helicopier Society, Val. 22, ( l ) , Jan. 1977, pp. 24 ~ 35.

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10. K w o n , 0. J . and Sankar, L. N. , “NumericalStudy of the Effects of Icing on Finite Wing Aerodynam-

Fig. 1: Perspective view of a fixed swept wing with leadine-edee ice accretion. - -

its," Presenied at i k e A I A A 26th Aerospace Sci- ences Mee t ing , Reno, Nevada, Jan. 8-11, 1990, A I A A Paper 90-0757

11. Khodadoust, A. and Bragg, M. B., “Measured Aerodynamic Performance of a Swept Wing with a Simulated Ice Accretion,” Presenied at the A I A A 28th Aerospace Sciences Meeitng, Reno, Nevada, Jan . 8-11, 1989, A l A A Paper 90-0490.

12. Wake, B. E. and Sankar, L . N . , “Solution of the Navier-Stokes Equations for the Flow About a b tor Blade,” Journa l of the American Helicopter Socrety, Vol. 34, No. 2, April 1989.

13. Wu. J.-C.. “A Study of Unsteady Turbulent Flow

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1 Past Airfoils,” PI~: D. DissertGion, Georgia In- stitute of Technology, Atlanta, GA, 1988.

Fig. 2: Typical C-grid around the wing

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1 .o I

0 Experiment 1 0.8 1 - Calculation

0 . 2 1 . , * , , , , , , I 0.0 0.0 0.2 0.4 0.6 0.8 1 .o

S p a n

Fig. 3: Simulated glaze ice accretion for fixed wing simulations [Ill.

Fig. 5: Spanwise load distribution for the clean swept wing at 8' angle of attack.

2 I

2 9 I

27 % SPAN 42 % SPAN 56 %SPAN 71

9 9 N N

9 N I I I

0 0

0";' o"f no u;

9 9 0

0 0 0

9 c

9 c

9 L

0.00.2 0.4 0.6 0.8 1.0 0.00.2 0.4 0.6 0.8 1.0 0.00.2 0.4 0.6 0.8 1.0

CHORD CHORD CHORD

; -, 72 % SPAN 89 %SPAN

9 0 N N , 0 O Calculation -

0"f a; V I

9 0 9 0 Experiment 0

9 9 0.00.2 0.4 0.6 0.8 1.0 0.00.2 0.4 0.6 0.8 1.0

- L

CHORD CHORD

Fig. 4: Surface pressure distribution for the clean swept wing at 8" angle of attack.

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Y

9

Y

r

27 % SPAN I 42 % SPAN 56 % SPAN I -

I

0

n' 0 9

0

u?

9

0

- 0

CHORD ?

9

Y

- 72 % SPAN I 89 %SPAN

- I

0 Calculation - n' 0 9

0

Experiment 0 Y

9 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0

.- CHORD CHORD

Fig. 6: Surface pressure distribution for the iced swept wing at 4' angle of attack.

__ Fig. 7: Surface oil flow simulation for the iced swept wing at 4" angle of attack.

Fig. 8: Particle trajectories for the iced swept wing at 4' angle of attack.

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*! I 56 % SPAN 9

- - I

2 n 1 0 9

0

Y

9

0

- 0.0 0.2 0.4 0.6 0 . 8 1.0 0.00.2 0.4 0.6 0 . 8 1.0 0 . 0 0 2 0.4 0.6 0 . 8 1.0

CHORD CHORD CHORD

Y

9

- Y 72 Z SPAN I 89 %SPAN

- I

Calculation - 2 n' 0 9

Y

9

0

Experiment 0 0

- 0.0 0.2 0.4 0 .6 0.8 1.0 0.0 0.2 0.4 0.6 0 . 8 1.0

CHORD CHORD

Fig. 9: Surface pressure distribution for the iced swept wing at 8' angle of attack

L Fig. 10: Surface oil flow simulation for the iced swept wing at 8" angle of attack.

Fig. 11: Particle trajectories for the iced swept wing at 8" angle of attack.

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1 .o I I I I

n Experiment

Calculaiion 0.8 - -

- 0 .

0.4 -

0.2 -

0.0 I I I 8

0.0 0.2 0.4 0.6 0.8 1.0 Span

Fig. 12: Spanwise load distributions for the iced swept wing a t 4’ and 8’ angles of attack

- NAVIER-STOKES --I- LIFTING-LINE

2 1 . . . ~ ~ ~ ~ BLADE ELEMENT/MOM

4.0 6.0 8.0 COLLECTlVl PITCH (DEG.)

Fig. 14: Thrust loading vs. collective pitch angle for the clean rotor.

- NAVIER-STOKES

W 0 ....’.. BLADE ELEMENT/MOM J _ _ _ _ LIFTING-LINE

X I 4.0 6.0 8.0

COLLECTIVI PITCH (DEG.) .O

- Fig. 13: Close-up view of the grid and the generic ice shape near the leading edge of the rotor blade.

Fig. 15: Thrust loading vs. collective pitch angle for the iced rotor.

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Fig. 16: Details of flow separation a t 90 % of the rotor blade.

0

0; 0.0 2.0 1.0

.

0

o CLEAN ROTOR 0 ICED ROTOR P

- Fig. 17: Effect of icing on the thrust vs. torque char- acteristics of the iced rotor.

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