Aeroelastic Characteristics Analysis of Helicopter Rotor s

The 2nd Asian/Australian Rotorcraft Forum and The 4th International Basic Research Conference on Rotorcraft Technology

Tianjin, China, September 08-11, 2013

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Aeroelastic Characteristics Analysis of Helicopter Rotors Based on

CFD/CSD Coupling Method

Wang Junyi Zhao Qijun Xiao Yu Master Candidate Professor Doctoral Candidate

National Key Laboratory of Rotorcraft Aeromechanics College of Aerospace Engineering

Nanjing University of Aeronautics and Astronautics Nanjing, China

(Tele: +086-025-84893753) (E-mail: [email protected], [email protected], [email protected])

ABSTRACT

Aeroelastic analysis of helicopter rotors is a challenging multidisciplinary problem. For accurate aeroelastic characteristics analysis, the unsteady rotor flowfield is solved by Computational Fluid Dynamics (CFD) module based on N-S/Euler equations and overset grid, while Computational Structural Dynamics (CSD) module is introduced to handle blade flexibility. In the CFD module, dual time-stepping algorithm is employed in temporal discretization with 4-stage Runge-Kutta scheme applied at each physical step, Jameson’s second-order cell-centered scheme is adopted in spatial discretization and B-L turbulent model is used to simulate the viscous effect in the vicinity of blade with minimized computational cost. The CSD module is developed based on Hamilton’s variational principles and modified to obtain advanced blade-tip analysis ability by deriving the finite element equations for multiple tip elements and integrating into the original code. Grid deformation is implemented using algebraic method through coordinate transformations to achieve deflections with high quality and efficiency. A loose CFD/CSD coupling strategy is developed to transfer information between fluid and structure. The CFD module is validated by analyzing the flowfield of 7A rotor while the CSD module is checked through calculating the natural frequencies of Maryland rotating beam. The advantage of advanced blade-tip modification is demonstrated through calculating the dynamics characteristics of UH-60A rotor. Then loose coupling is established and adopted in SA349/2 and UH-60A rotor airloads prediction and the calculated results are compared with test data. Finally, conclusions about rotor aeroelastic characteristics (such as natural frequencies, swept angle variations, airloads and vorticity) are drawn, which are important to high-fidelity airloads prediction and further aeroelastic analysis. 1 INTRODUCTION

In order to obtain accurate airloads, the unsteady, three-dimensional flowfield details are required, such as advancing blade shock, reverse flow region, dynamic stall, etc. The lifting line aerodynamics used in the CSD module lack accuracy and become a considerable shortcoming compared to high-fidelity CFD method. On the other hand, rotor blades are highly flexible, structural deformations have significant influences on rotor aerodynamic

characteristics. Therefore, CSD module is required for precise CFD analysis. Hence, the CFD and CSD codes are mutually dependent in rotor airloads prediction as well as aeroelastic characteristics analysis.

Nowadays, advanced blade-tip shapes, such as swept and anhedral, are widely employed in modern helicopter rotor design to acquire desired aerodynamic performance. This unconventional rotor blade design increases the difficulty in aerodynamics characteristics analysis and makes CFD/CSD coupling a necessary tool in

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high-fidelity airloads prediction. CFD/CSD coupling can also provide better understanding for the flowfield around advanced blade-tip. In 1986, Tung and Caradonna[1] carried out CFD/CSD coupling for the first time and coupled the transonic small-disturbance code with comprehensive code CAMRAD to analyze lifting rotor in forward flight. In 2006, Potsdam, Yeo and Johnson[2] studied the UH-60A airloads under different conditions using loosely coupled OVERFLOW-D and CAMRAD II and obtained better results over the lifting line aerodynamics used in CSD. Nygaard, Saberi et al.[3] coupled OVERFLOW-2 with RCAS to investigate the parameter sensitivity of loose coupling in forward flight, and then studied transient maneuver using tight coupling. In 2011, Yeo, Potsdam and Ormiston[4] analyzed the aeroelastic stability of ADM rotor adopting tight CFD/CSD coupling, and the OVERFLOW-2/RCAS captures better key features in the damping trends. In 2012, Bhagwat, Ormiston et al.[5] tightly coupled OVERFLOW-2 and RCAS to improve airloads prediction as well as control load predictions. Hence, accurate airloads prediction and aeroelastic characteristics analysis require coupled CFD/CSD method. The subject of this paper is to develop and validate the advanced blade-tip modification of the CSD module, and then investigate the SA349/2 and UH-60A rotor flowfield in high speed forward flight condition using CFD/CSD loose coupling in order to predict the aerodynamic airloads accurately.

2 NUMERICAL METHODOLOGY

2.1 CFD Methodology

2.1.1 Grid Generation MethodIn the present work, the C-H body-fitting blade grid is used in spatial discretization. Firstly, the 2D grid around rotor airfoil is generated;

then, geometric twist distributions, chord length variations and quarter-chord positions are imposed with the tip approximated to be a bevel tip; finally, the grid is extended at root to cover the rootcut portion and tip region to capture the tip vortex generated at this region, see Fig.1.

Figure 1 C-H body-fitting blade grid

Thereafter, the Cartesian background grid is generated around blade grid and extended into farfield. The central region is refined to accurately capture the rotor wake generated from rotor blades. The inflow farfield boundary is 3R, while the wake farfield boundary is 4R.

2.1.2 Overset Grid Method In the flowfield calculation considering the elastic deformation, the hole boundary needs to be determined at every azimuth since the relative positions between blade grid cells and background grid cells are varying. The ‘Top-Map’ hole cutting method[6] is adopted to determine the spatial relationship between the body-fitting deformable grid and the Cartesian background grid. The minimum hole boundary can be determined through searching the blade surface grids and assigning the corresponding Cartesian grid number. The maximum hole boundary can be found in a similar manner, and the overset grid system is shown in Fig.2.



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Figure 2 Overset grid system

In this paper, the overset grid includes several individual C-H blade grids and one Cartesian background grid. The blade grids are identical with dimensions of 153×57×27 (chordwise, spanwise, and normal) for SA349/2 blade and 149×81×31 for UH-60A blade. The Cartesian grid has dimensions of 131×143×131 (longitudinal, vertical, and lateral) for SA349/2 rotor and 142×164×121 for UH-60A rotor.

2.1.3 Grid Deformation Method

The blade deformation is carried out based on the algebraic method[7]. Deformations are given as functions of radius and azimuth in the form of [ ( , )u r ψ , ( , )v r ψ , ( , )w r ψ ,

( , )v r ψ′ , ( , )w r ψ′ , ( , )rφ ψ ]T, where u , v and w is linear axial, lag and flap deformation, v′ and w′ is lagging and flapping derivatives while φ is elastic torsion. The given rotor geometry is deformed in accordance with the corresponding quarter-chord motion. And at any section, a rotation matrix DUT is defined to represents the transformation relationship between deformed and undeform coordinate system. The deformed

grid coordinates are given by:

( )TDU lin

x xy T y xz z

′ ′ = + ′

(1)

where the vector linx represents the linear

deflections given by , , Tu v w . The blade deformations are shown in Fig.3, it can be seen that the deform algorithm achieves grid deformation and maintain good grid quality at the same time.

Figure 3 Deformable blade grid

2.1.4 Flowfield Solver

The flowfield solver is developed based on N-S and Euler equations for blade body-fitting grids and Cartesian background grid, respectively. The governing equations[8] in conservative form are:

( )c vWd F F dS Qdt Ω ∂Ω Ω

∂Ω+ − = Ω

∂ ∫ ∫ ∫

(2) [ , , , , ]

0

,

T

r

x xx y xy z xzr x

c r y v x yx y yy z yz

r z x zx y zy z zz

r t x x y y z z

W u v w E

Vn n nuV n p

F vV n p F n n nwV n p n n nHV V p n n n

ρ ρ ρ ρ ρ

ρτ τ τρ

ρ τ τ τ

ρ τ τ τρ θ θ θ

=

+ ++ = + = + + + + + + + +

where Ω is the control volume at any spatial station, ∂Ω is the boundary of Ω ,



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dS is a face element on ∂Ω . The equations are computed using Jameson’s second-order cell-centered spatial discretization with second and fourth order artificial dissipation. Dual time-stepping algorithm is adopted to simulate the unsteady flowfield, and the calculation can be considered to be quasi-steady at each physical step so that 4-stage Runge-Kutta scheme is employed. The viscous blade region is computed using B-L turbulent model in that the calculation expense is relatively small and is capable of capturing small regional separation flow. The farfield boundary condition is determined according to Riemann invariant while the inner boundary is no-slip condition for N-S equations. Only pressure components of the forces calculated in the present work are introduced into the coupling procedure since viscous effects are negligible for normal force and pitching moment prediction[2].

2.2 CSD Methodology

The CSD module is developed based on Hamilton’s variational principle[9], see Eq.(3):

2

1

( ) 0t

tU T W dtδ δ δ− − =∫ (3)

The finite element model has 14 degrees of freedom (DOFs) without warping and transverse shear, and the end nodes have six DOFs while the middle node has two DOFs (see Fig.4).

Figure 4 Nodal degrees of freedom

For the blades employed in this study, the

sectional properties are obtained from experimental data. Then, these sectional properties are introduced to mass, damping and stiffness matrix assembly procedure. The assembled dynamic equations are solved iteratively by using Newmark-beta method.

2.2.1 Advanced Blade-Tip Modification

To analyze advanced rotor blade-tip with swept or anhedral or combined tip variations, the CSD module is modified to include complex blade-tip[9][10][11]. For advanced blade-tip analysis with combined forward-backward swept such as BERP and highly nonlinear twist like UH-60A, several tip elements rather than one are required to simulate tip configuration details. Firstly, the basic transformation for a single tip element is presented:

[ ]L Gq q= Λ (4)

The translational transformation is linear:

[ ]

L G

eb

u uv T vw w

=

(5)

The angular relationship between the blade-tip and the straight portion at the junction is preserved after deformation, and it yields nonlinear transformation matrix:

, ,

, ,

([ ] [ ])

L G

Kx eb x

x x

w T T wv v

φ φ − = + −

, ,

, ,

([ ] [ ])

L G

Cx eb x

x x

w T T wv v

φ φ − = + −

(6)

, , ,

, , ,

([ ] [ ]) [ ]

L G G

C Mx eb x x

x x x

w T T w T wv v v

φ φ φ − = + − + −

Then, the global to local transformation



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matrix can be established: [ ] 0 0

0 [ ] 00 [ ] [ ]

L GLK

LC

M LC

q qq qq q

Λ = Λ

Λ Λ

(7)

Finally, the global to local transformation matrix for multi-tip element is derived:

[ ]

1

1

n n i

nq qq qq q

− −

− = Λ

(8)

where [ ] [ ] [ ]1

_ 1 _ 1...n

J n J n i

−

− − +Λ = Λ Λ in

Eq.(8) is the transformation matrix for element (n-1). And the transformation from local to global coordinate system is similar and can be expressed as Eq.(9).

[ ][ ][ ]

[ ]([ ][ ] [ ][ ])

[ ][ ][ ] 0

L LC Gi

L M LC Gi i

L LK G Gi i

M qM C q

K q F

Λ Λ +

Λ Λ + Λ +

Λ Λ + =

(9)

2.3 CFD/CSD Coupling Strategy

After the CFD and CSD module are established, coupling strategy is required to transfer fluid and structural information between the two modules. There are two basic method of coupling[12]: loose coupling (LC) and tight coupling (TC). LC exchanges information on a per revolutionary basis and is adopted in airloads prediction in level steady flight condition. Fig.5(a) shows a typical CFD/CSD loose coupling strategy, the structure module calculates the structural motions and transfers to fluid module, the fluid module then computes the flowfield with provided information and returns forces back to the structure module.

Figure 5(a) A typical loose coupling strategy

In this paper, only LC is carried out in rotor airloads prediction and investigated in details, and the flowchart of LC is shown in Fig.5(b).

Start

Input overset grid system

CSD solver per revolution

CSD information to CFDdeformation, control, etc.

Blade grid deformation

LC converge ?

FinishYes

No

Transfer CFD airloads to CSD through interpolation

2D airfoil C gird

Distribute C grid along spanwise to form C-H grid

Generate Cartesian background grid

Construct matrix M,C,K and Vector F

Solve dynamic equations iteratively

Converge ?

Rotor operation parameters

CFD solver per revolution

Search hole boundary and donor cells

Flowfield variable interpolation at donor cells

Spatial discretization + Dual time-stepping algorithm

Yes

No

Initialization

Converge ?Yes

No

Trim ?Yes

No

Delta load correction

Figure 5(b) The CFD/CSD loose coupling flowchart

3 MODULAR Validation

3.1 CFD Module Validation

The CFD module is validated by calculating the pressure distributions of the Helishape 7A rotor[13][14] using rigid blade assumption. The operating condition in hover is

0 7.46θ = and 0.617tipM = , and the results are as shown in Fig.6(a) and (b). It can be seen that the CFD module employed is capable of capturing accurate airloads and can be used in CFD/CSD coupling.

Figure 6(a) 7A rotor pressure distributions



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Figure 6(b) 7A rotor pressure distributions

3.2 CSD Module Validation

The CSD module is validated through two different blade models: the Maryland rotating beam[15] and the UH-60A[16][17] rotor. The Maryland rotating beam with 45 degree swept is analyzed and compared with experimental data in Fig 7. In this analysis, 18 elements are used for the straight portion while 5 elements are employed to simulate the swept tip. The first five order flapping frequencies agree well with test data while there is discrepancy for the first torsional frequency which might be the result of the nonlinear torsion poorly captured with existing finite element model.

Figure 7 45-degree swept natural frequencies

Fig.8 is the variation of frequencies along with swept angle. The model used here is the same as in the former case and the calculated frequencies agree well with the test data. Both flapping and torsional frequencies are accurately computed and it demonstrates the validity of the modified advanced blade-tip ability over a wide range of tip angle variation.

Figure 8 Validation for swept angle variations

The UH-60A natural frequencies in Fig.9 show that the developed advanced blade-tip modification is able to analyze highly nonlinear blade-tip shapes and can obtain better results compared with single-tip element. The solid line is calculated by using UMARC with first hand sectional properties, therefore it is taken as reference values for comparison. Since the UH-60A sectional properties found in published papers[16][17] are not detailed enough, the blade natural frequencies can be considered to be reasonable. Furthermore, the improvement in the present analysis scenario is not obvious enough as a result of limited input parameters, but it enables the CSD module to analyze advanced blade-tip with swept combination such as the CLOR serious in the further studies.



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Figure 9 UH-60A blade natural frequencies

Therefore, the modified CSD module is proven to be reliable for CFD/CSD coupling and is used in the present work.

4 CFD/CSD COUPLING RESULTS

Results for both SA349/2 rotor and UH-60A rotor are presented for high speed level steady flight. The flight conditions are tabulated in Table 1.

Table 1 Operation Conduitions µ

0θ 1cθ 1sθ SA349/2 0.378 14.42 2.22 -9.46 UH-60A 0.368 12.55 3.39 -8.62

The airloads comparison of SA349/2 rotor at 0.97r is shown in Fig.10. As can be seen, the CFD/CSD coupling normal force coefficient agrees with the test data[18] and shows significant enhancement compared to lifting line aerodynamics used in CSD module. Hence, CFD/CSD coupling shows its advantages over analysis using comprehensive analysis code.

Figure 10 SA349/2 airloads comparison

And the pressure distribution in Fig.11 is obtained at azimuth 180 and close to the experimental data. It indicates that the CFD/CSD coupling method captures accurate pressure distributions on blade surface and forms the basis of high-fidelity normal force prediction over all azimuths.

Figure 11 SA349/2 pressure distributions

The airloads of UH-60A rotor in high speed forward flight condition C8534 is calculated and compared with test data[2] in Fig.12. The general shape and peak position are well captured, but the magnitude of normal force does not agree well with experimental values, probably because the pitching moment is not accurately captured.

Figure 12 UH-60A airloads comparison

As shown in Fig.13 is the pressure distribution of UH-60A rotor at azimuth 225 compared with test data[19][20]. Similar to the



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SA349/2 case, it shows good agreement between calculated results and measured values and demonstrates that the present coupling method is valid for surface pressure distribution calculation as well as normal force prediction.

Figure 13 UH-60A pressure distributions

Fig.14 shows the vorticity magnitude of UH-60A rotor in C8534. Since the forward flight speed is high, the rotor wake is quickly convected into the farfield without obvious blade vortex interaction. The tip vortex is not clearly isolated from the wake of the inboard portion and suggests more refined Cartesian background grid is required. It demonstrates that the flowfield details are captured and proves the effectiveness of the present CFD/CSD coupling method.

Figure 14 UH-60A vorticity magnitude

5 CONCLUSIONs

A Navier-Stokes CFD solver has been loosely coupled with a moderate deformation beam based CSD solver. The CSD module is modified and validated for CFD/CSD loose coupling. The SA349/2 and UH-60A rotor flowfield is simulated and the airloads are predicted using the developed method. The following conclusions are summarized from the presented results: (1) The rotor airloads obtained using CFD/CSD coupling is more precise than that of the lifting line aerodynamics used in comprehensive code. (2) The CSD module computes better structural characteristics with more tip elements used and verifies the validity of the modified CSD module in this paper, so that it can be used to analyze more complex blade-tip. (3) The present CFD/CSD loose coupling is efficient in predicting rotor airloads and can be coupled with all force and moment components without convergence problems. (4) The grid deformation method used in the present work can not only achieve grid deflection with high quality, but also reduce the computational time occupied by dynamically updated body-fitting grid at every azimuth position. The present aeroelastic characteristics analysis provides foundations for further aeroelastic analysis such as investigation of aeroelastic stability about helicopter rotor.

REFERENCES

[1] Tung, C., Caradonna, F.X., Johnson W, The prediction of transonic flows on an advancing rotor, Journal of the American Helicopter Society, vol.32, no.3, p.4-9, 1986.

[2] Potsdam, M., Yeo, H., Johnson, W., Rotor airloads prediction using loose aerodynamic/structural coupling, Journal of Aircraft, vol.43, no.3, p.732-742, 2006.

[3] Nygaard, T.A., Saberi, H., Ormiston, R.A., Strawn, R.C., Potsdam, M. CFD and CSD



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coupling algorithms and fluid structure interface for rotorcraft aeromechanics in steady and transient flight condition, American Helicopter Society 62nd Annual Forum, Phoenix, AZ, May 9-11, 2006.

[4] Yeo, H., Potsdam, M., Ormiston, R.A., Rotor aeroelastic stability analysis using coupled computational fluid dynamics/computational structure dynamics, Journal of the American Helicopter Society, vol.56, no.4, p.1-16, 2011.

[5] Bhagwat, M.J., Ormiston, R.A., Saberi, H.A., Xin, H., Application of computational fluid dynamics/computational structural dynamics coupling for analysis of rotorcraft airloads and blade loads in maneuvering flight, Journal of the American Helicopter Society, vol.57, no.3, p.1-21, 2012.

[6] Wang, B., Zhao, Q.J., Xu, G., Xu, G.H., A new moving-embedded grid method for numerical simulation of unsteady flow-field of the helicopter rotor in forward flight, Acta Aerodynamica Sinica, vol.30, no.1, p.14-21, 2012.

[7] Datta, A., Sitaraman, J., Chopra, I., Baeder, J.D., CFD/CSD prediction of rotor vibratory loads in high-speed flight, Journal of Aircraft, vol.43, no.6, p.1698-1709, 2006.

[8] Blazek, J., Computational fluid dynamics: principles and applications, second edition, Elsevier Ltd, 2005.

[9] Yuan, K.A., Friedmann, P.P., Aeroelasticity and structural optimization of composite helicopter rotor blades with swept tips, NASA CR 4665, 1995.

[10] Bir, G., Chopra, I., et al. University of Maryland Advanced Rotor Code (UMARC) theory manual, Technical Report UM-AERO 94-18, Center for Rotorcraft Education and Research, University of Maryland, College Park, July 1994.

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[16] Davis, S.J., Predesign study for a modern 4-bladed rotor for the RSRA, NASA CR 166155, 1981.

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Documents

Aeroelastic Characteristics Analysis of Helicopter Rotor s