Integrated Analysis about Aerodynamic and Stealth ......with CEM method to co the nduct multi-objective optimization design of airfoil. At present, some integrated researches of wing

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

Tianjin, China, September 08-11, 2013

485

Integrated Analyses about Aerodynamic and Stealth Characteristics of

Airfoil Based on CFD/CEM Coupling Method

Jiang Xiang-wen Zhao Qi-Jun Zhao Guo-Qing Doctoral candidate Professor Doctoral candidate

National Key Laboratory of Rotorcraft Aeromechanics Nanjing University of Aeronautics and Astronautics

Nanjing, 210016, China (Tele: 86-025-84893573 Fax: 86-025-84891892)

(e-mail: [email protected], [email protected], [email protected])

ABSTRACT

The integrated analyses about aerodynamic and stealth characteristics of rotor airfoil are a challenging Multidisciplinary Design Optimization (MDO) issue. Based on Computational Fluid Dynamics (CFD)/Computational Electromagnetics Method (CEM) coupling method and surrogate model optimization techniques, an integration design method about aerodynamic/stealth is established. Firstly, the O-type body-fitted and orthogonal mesh around airfoil is generated using Poisson equation, the points per wave and the normal range satisfy aerodynamic and electromagnetic calculation accuracy requirement. Secondly, aerodynamic performances of airfoil are calculated by saving Navier-Stokes equations with Baldwin-Lomax (B-L) turbulence model. The stealth characteristics of airfoil are simulated by using Finite Volume Time Domain (FVTD) method based on Maxwell’s equations, Steger-Warming flux splitting and third-order MUSCL scheme. Thirdly, Based upon the surrogate model with Full Factorial Design (FFD) and Radial Basis Function (RBF), an integration design about CFD/CEM coupling method of rotor airfoil is conducted. Then comparing the calculated results of NACA0012 airfoil with the experimental and theoretical values, it is demonstrated that CFD and FVTD methods are effective to simulate the aerodynamic and stealth of airfoil. Then the aerodynamic/stealth characteristics of NACA series airfoils with different maximum thickness and camber combinations are discussed. At last, by choosing suitable object function and constraint condition about amplitudes of rotor airfoil at four important scattering regions, the compromised airfoil with high lift-to-drag ratio and low scattering characteristics is designed through systemic and comprehensive analyses.

1 INTRODUCTION

In recent years, the survival and penetration ability requirements of the armed helicopters become more and more important in the high-tech war. The

integrated analyses about aerodynamic/ stealth design of advanced helicopter rotor are an important trend. The selection of rotor airfoil not only affects the helicopter’s aerodynamic characteristics directly, but also is the key to reduce RCS of the armed helicopter rotor. Therefore the

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mailto:[email protected]



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integration analyses about aerodynamic/ stealth characteristics of rotor airfoil have a significant practical value. With the great improvements in CFD method, CEM method and optimization algorithms, integrated analyses about aerodynamic/stealth characteristics of airfoil is becoming more and more feasible in modern MDO rotor design. The CFD technology has been widely used in rotor airfoil aerodynamic design during the past several years [1]. Based on CFD technology, the FVTD method was established for solving scattering problem. FVTD method was first applied to calculate electromagnetic characteristics by Shankar[2] in the 1980s, Camberos [3] developed COBRA software by Steger-Warming flux discretization combined with Runge-Kutta time integration scheme, which can handle some simple electromagnetic targets. In recent years, high precision FVTD method has been preliminarily used in some complex targets[4-6] and other fields[7-8]. In the integrated investigation of airfoil, Hoang Vinh[9] and ZHU Ziqiang[10-11] coupled CFD ( full-potential or Euler equations) with CEM method to conduct the multi-objective optimization design of airfoil. At present, some integrated researches of wing airfoil were mainly focused on calculating aerodynamic characteristics with low accuracy and precision model, and then find the optimal airfoil with single constraint condition(RCS of airfoil leading edge) in optimization method. Therefore, considering blade rotating, pitching and flapping complicated motions of helicopter, the electromagnetic scattering

characteristics about leading edge, upside, downside and trailing edge are all important for the rotor airfoil. So the integrated analyses about aerodynamic and stealth must take into account four important scattering regions, which are conducive to rotor design of armed helicopter. To develop a high precision computational method that can be used in MDO design of rotor airfoil, an integration design based CFD/CEM coupling method is proposed to predict aerodynamics/stealth characteristics of airfoil in this paper. In order to satisfy practice needs, NACA airfoils which are widely used in aviation are select as baseline airfoils. The O-type aerodynamic/RCS computational girds are generated by solving Poisson equations, which improve gird generating quality and efficiency. The airfoil aerodynamics/stealth characteristics are simulated by high precision and accuracy CFD/FVTD methods. Then an integration design about CFD/CEM coupling method is developed by optimization surrogate model. Additionally, the aerodynamic/stealth characteristics of NACA series airfoils with different maximum thickness and camber combinations are discussed. At last, Choosing suitable object function and constraint condition about amplitudes of rotor airfoil at four important scattering regions, the rotor airfoil with high lift-to-drag ratio and low scattering characteristics is designed through comprehensive analyses. To develop a high precision computational method that can be used in MDO design of rotor airfoil, an integration design based CFD/CEM coupling method is proposed to



487

predict aerodynamics/stealth characteristics of airfoil in this paper. In order to satisfy practice needs, NACA airfoils which are widely used in aviation are select as baseline airfoils. The O-type aerodynamic/RCS computational girds are generated by solving Poisson equations, which improve gird generating quality and efficiency. The airfoil aerodynamics/stealth characteristics are simulated by high precision and accuracy CFD/FVTD methods. Then an integration design about CFD/CEM coupling method is developed by optimization surrogate model. Additionally, the aerodynamic/stealth characteristics of NACA series airfoils with different maximum thickness and camber combinations are discussed. At last, Choosing suitable object function and constraint condition about amplitudes of rotor airfoil at four important scattering regions, the rotor airfoil with high lift-to-drag ratio and low scattering characteristics is designed through comprehensive analyses.

2 COMPUTATIONAL METHOD

2.1 GIRD GENERATION TECHNIQUES

The O-type body-fitted and orthogonal grid around rotor airfoil is generated using Poisson equations. The grids around airfoil are shown in Fig.1. The aerodynamic/stealth computational gird contains 300 70× , there are 150 points on the lower and upper surfaces of the airfoil respectively, 70 points in the direction normal to the airfoil’s surface, and the four important scattering regions of rotor airfoil are leading edge ( 150 210≤ Ψ ≤ ), upside

( 60 120≤ Ψ ≤ ), downside ( 240 300≤ Ψ ≤ ) and trailing edge ( 30 30− ≤ Ψ ≤ ).The schematic of TM/TE wave incidence on airfoil are shown in Fig.2.

Fig.1 Computational gird around NACA0012

airfoil

Fig.2. TM/TE wave 90 incidence on NACA0012

airfoil

2.2 CFD METHOD

The airfoil flowfield characteristics are calculated by Navier-Stokes equations with B-L turbulence model. The N-S equations in integral form can be written as

( ) ( ) 0v vF GW F Gd d dt x y x yΩ Ω Ω

∂ ∂∂ ∂ ∂Ω+ + Ω− + Ω =

∂ ∂ ∂ ∂ ∂∫ ∫ ∫

(1)

where x and y are Cartesian coordinates,

W is the vector of conserved variables,

,F G are the inviscid flux, ,v vF G are the

viscous flux.



488

uW

vE

ρρρρ

=

2

( )

uu P

Fuv

E P u

ρρρ

ρ

+ =

+

2

( )

vvu

Gv PE P v

ρρ

ρρ

= +

+

0

xx

v xy

xx xy

F

Tu v kx

ττ

τ τ

=

∂ + + ∂

0

xy

v yy

xy yy

GTu v ky

ττ

τ τ

=

∂ + + ∂

(2)

where ρ , P , H and E are the density, pressure, total enthalpy per unit mass and total energy per unit mass, k is air heat transmission factor, τ is viscous related items, l tµ µ µ= + , µ is coefficient of viscosity, µl and µt are laminar flow and turbulent flow coefficient of viscosity respectively. Spatial discretization is conducted by central scheme, and temporal discretization is conducted used by the four-step Runge-Kutta method. Boundary conditions are the no reflection[12]. The viscous effect is captured by the B-L turbulent model[13] with strong robustness and high reliability, and can simulate effectively the attached flow and small separation flow.

2.3 CEM METHOD

Maxwell’s equations of electromagnetism and Euler equations of fluid mechanics belong to the same hyperbolic partial differential equations.

2.3.1 GOVERNING EQUATIONS

Maxwell’s equations in the differential form for wave propagation in free space can be expressed as

0

0

B Et

D Ht

∂ +∇× = ∂∂ −∇× = ∂

(3)

where B is the magnetic induction, E is the electric field vector, D is the electric

field displacement, and H is the magnetic

field vector. B Hµ= , µ is the magnetic

permeability, D Eε= , ε is the electric permittivity. The above equations are applied to every finite-volume cell in the grid system. The divergence theorem can be recast in total field form as

0Q F Gd dt x yΩ Ω

∂ ∂ ∂Ω + + Ω = ∂ ∂ ∂

∫ ∫ (4)

2.3.2 EQUATIONS DISCRETIZATION

Maxwell’s equations are divided into Spatial and temporal discretization. The integral form is applied to each cell. The combination of third-order MUSCL scheme and Steger-Warming flux-vector splitting algorithm are derived to solve Maxwell’s equations in conservative form. The spatial discretized formulation for the cell is

( ) ( )

4

1

1 1 1 12 2 2 2

1 ( )

y xk

i i j jj i

Q F Gt S

F F G G

=

+ − + −

∂= − ∆ + ∆

∂ ∆

= − − + −

∑

(5)

where Q is the flux average value of the

cell, ( yx ∆∆ , )is tangent vector at line

d . 1 1

1/2 1/22 21 1

1/2 1/22 2

( ) ( ) ( )

( ) ( ) ( )

L Ri i i i

L Rj j j j

F A A Q F Q F Q

G B B Q G Q G Q

+ − + −+ + + +

+ − + −+ + + +

= + = +

= + = +

(6) And

1/2 1

1/2 1 1 2

1 [(1 ) (1 ) ]4

1 [(1 ) (1 ) ]4

i i i i

i i i i

Q Q Q Q

Q Q Q Q

κ κ

κ κ

++ +

−+ + + +

= + − ∆ + + ∆ = − + ∆ + − ∆

(7) The four-stage Runge-Kutta method is used for the temporal discretization.



489

(0) n

( ) (0) ( 1)

n 1 4

1 2 3 4

1, ,4

1 / 4 1 / 3 1 / 2 1

m mm

Q QQ Q tR mQ Q

α

α α α α

−

+

=

= + ∆ = •••

= = = = =

（）

，，，

(8) where n is the present level, 1n + is the new time level, R represents the residual which is formed from the cell fluxes,

max

xt CFLλ∆

∆ ≤ ⋅, t∆ is time step, x∆ is

the minimum of the grid size, CFL represents the Courant number. In order to satisfies the requirements of calculation efficiency and stability theory, CFL must be less than 1.745, so CFL=1.5.

2.3.3 BOUNDARY CONDITIONS

For a Perfect Electrically Conducting (PEC) body, the boundary conditions[14] of the electric and magnetic fields are required respectively as

0( ) 0

t

t

n Dn n B

= ×

∇ × = => 1 0 1

1 0 1

2

2

s s s

s s s

D D DB B B

−

−

= × −

= × −

(9) where superscript t denotes sum of the incident and scattered fields, i denotes the incident field, superscript s denotes the scattered field, subscript 0 denotes the boundary of body, subscript 1 denotes the first layer of grid, subscript -1 denotes the first layer of ghost gird. The nonreflecting boundary of electromagnetic field is required as

0F G− −= = (10)

2.3.4 RCS EVALUATION

The frequency-domain field can be transformed from the time-domain electromagnetic field by Fourier transform, and the RCS is presented from near-far

field conversion to solving, radar scattering is calculated as

2 2

2 22 2lim 4 lim 4

R RR Rσ π π

→∞ →∞= =

s s

i i

E H

E H (11)

2.4 SURROGATE MODEL

Surrogate model is created with experiment design methods and approximation approaches. FFD has advantages of being able to analyze interactions among factors and effects of each factor on system. RBF is a kind of good flexibility, simple structure, and efficiency calculation model. The basic form is

1

( ) ( )n

ii

if x w rφ

=

= ∑ = ϕTw (12)

where =w 1 2 wT

pw w • • • , iw is weight

coefficient, ir is Euclidean distance of the

measured point X and sample

point iX , =ϕ 1 2( ) ( ) ( )pr r rφ φ φ • •• ,

( )rφ is radial function, The radial basis

function choose Multi-Quadric function

which has extensive estimated

characteristics.

2.5 CFD/CEM COUPLING METHOD

Based upon CFD, FVTD and Surrogate

model method, an integration design about

aerodynamic/stealth of rotor airfoil is

developed. Fig.3 shows flow chart of

CFD/CEM coupling strategy. The

CFD/CEM coupling method consists of

three modules: grid generation, solver and

integrated design.

(1) Grid generation



490

Based upon density and orthogonality of the source term adjustment, the airfoil O-type body-fitted and orthogonal grids are generated by Poisson equations. The points, area and vector of computational grid data are obtained by conversion program. (2) Solver Based upon finite volume method and B-L turbulence model, Navier-Stokes equations are chosen to solve the flowfield and aerodynamics characteristics. Based upon FVTD method, Maxwell’s equations are chosen to solve the

electromagnetic field and RCS characteristics. (3) Integrated design An optimization systematical methodology is developed based on FFD and RBF. By choosing suitable object function and constraint condition, an integration design about aerodynamic/stealth of airfoil is conducted. If optimized airfoil satisfies high lift-to-drag ratio and low scattering characteristics, the method can provide airfoil geometric parameters, if not, recalculate.

Start

Geometric parameters of airfoil

O-type body-Fitted grid generation by algebraic

method

Topological data of grid CEM simulation (FVTD)

CFD Simulation (B-L turbulence model)

RCS frequency distribution

RCS time-domain distribution

Cl, Cd and lift-drag ratio

Pressure distribution

Flow field distribution

Design of experiment

Approximation method

FFD...

RBF...

Electromagnetic field distribution

Object function Constraint condition

Optimized airfoil

SatisfySatisfy Yes

No

Solver module

Gird generation module

Integrated design module

End

Yes

No

Fig.3. Flow chart of CFD/CEM coupling strategy

3 RESULTS AND DISCUSSIONS

3.1 TEST CASE

In this section, the calculated grid density, aerodynamic and stealth characteristics of NACA0012 airfoil are compared with the experimental and theoretical values. The grid density case: as shown in Fig.4, when grid point per wave is larger than 40 (ppw 40≥ ), the waveforms are identical to the theoretical values, so ppw 40= is selected in this paper. The normal range of airfoil surface is 51.0 10 L−× , where L indicates the airfoil chord length. So the ppw and normal distribution of grids are satisfied electromagnetic and aerodynamic

viscous calculation accuracy requirement.

Fig.4. Electrical field distributions with

different grid density

The aerodynamic case: NACA0012 airfoil

at 0.7Ma = and 69 10Re = × . As shown in

Fig.5, the calculated lift, pressure distributions and polar curve are in good agreements with the experimental data[15]. It



491

has been demonstrated that the method is effective to simulate the aerodynamic characteristics of rotor airfoil.

(a) Lift and pressure distributions

(b) Polar curve Fig.5. Comparisons of aerodynamic

characteristics about NACA0012 airfoil between numerical and experimental data

The RCS case: NACA0012 airfoil at TM and TE wave, 10L λ= , incident angle

90φ = . As shown in Fig.6, the computed

results are in excellent agreements with the reference data[16]. It suggests that the method is effective in simulating the stealth characteristics of airfoil.

(a) TM wave

(b) TE wave

(c) Time domain changes of electrical field

Ez with10λ grids

(d) Electrical field Ez distribution

Fig.6.Comparisons of RCS characteristics about NACA0012 airfoil between numerical and

reference data

3.2 AERODYNAMIC AND RCS RESPONDS OF AIRFOIL PARAMETERS

The parameters of airfoil are maximum thickness, maximum camber and different maximum thickness and camber combinations. The calculated

status: 0.4Ma = , 69 10Re = × , attack angle

0α = , TM wave, incident angle 0φ = .

3.2.1. RESPONDS OF MAXIMUM THICKNESS

Fig.7 shows aerodynamic and RCS characteristics of NACA airfoils with different maximum thicknesses. The lift



492

coefficient of NACA24T changes relatively flat and the drag coefficient increases rapidly (see Fig.7(a)). The surface pressure coefficient distributions of the three airfoils are compared shown in Fig.7(b). The upper part distribution of Fig.7(c) is five airfoil bistatic RCS, and the lower part is the difference about RCS of NACA2410 with the other airfoils. The lower surface of trailing edge

( 330 ~ 360ψ = ) is more fluctuant than

that of the upper surface ( 0 ~ 30ψ = ).

With the increase of the maximum thickness, the leading edge scattering characteristics are more and more stronger，but oscillation of RCS amplitudes decrease obviously.

(a) Cl and Cd of NACA24T

(b) Cp

(c) RCS Fig.7. Aerodynamic and RCS characteristics of

NACA airfoils with different maximum thicknesses

3.2.2 RESPONDS OF MAXIMUM CAMBER

Fig.8 shows aerodynamic and RCS characteristics of NACA airfoils with different maximum cambers. The lift and drag coefficient of NACAC412 increases rapidly shown in Fig.8(a). The surface pressure coefficient distributions of the three airfoils are shown in Fig.8(b). The upper part distribution of Fig.8(c) is five airfoil bistatic RCS, and the lower part is the difference about RCS of NACA1412 with the other airfoils. The upper surface

( 0 ~ 30ψ = ) of the trailing edge is gradual

and steady than the lower surface

( 330 ~ 360ψ = ). With the increase of the

maximum camber, the RCS changes of other parts are not significant, except at the trailing edge of airfoil.



493

(a) Cl and Cd of NACAC412

(b) Cp

(c) RCS

Fig.8. Aerodynamic and RCS characteristics of NACA airfoils with different maximum cambers

3.2.3 RESPONDS OF MAXIMUM

THICKNESS AND CAMBER COMBINATIONS

Fig.9 shows aerodynamic and RCS characteristics of NACA airfoils with different maximum thickness and camber combinations. For integration design, we hope K (the lift-to-drag ratio) is higher and RCS mean value is lower. As can be seen, the RCS distributions about leading edge, upside, downside and trailing edge of airfoils are different. The lift-to-drag ratio

of upper part is higher which are beneficial to the aerodynamic characteristics, but not conducive to reduce RCS. The RCS of lower part is smaller which are beneficial to the stealth characteristics, but not conducive to aerodynamic performances. So choosing the optimal airfoil with better aerodynamic and low scattering characteristics is a compromised process.

(a) 0 30ψ = ±

(b) 90 30ψ = ±

(c) 180 30ψ = ±



494

(d) 270 30ψ = ± Fig.9. K and RCS characteristics distribution

(four receiving azimuthal angles)

3.4 INTERATED DESIGN ABOUT AERODYNAMIC AND STEALTH

The integrated analyses about aerodynamic and stealth characteristics is a MDO issue, and the shapes of airfoil that can improve aerodynamic performance and reduce RCS are usually inconsistent, so the key is to find the aerodynamic/stealth compromised conditions which can be described as Pareto front efficiently and accurately. The multi-objective problem can be transformed into a single objective problem by the linear weighted sum method. NACAC4T series airfoils are selected for research, where C denotes maximum camber and T denotes maximum thickness. The samples about different thickness and camber combinations of NACA series airfoils are selected by FFD, then the aerodynamic and stealth characteristics of airfoils are calculated by CFD and FVTD methods respectively, and the fitting characteristics are obtained by the RBF.

Fig.10(a) shows 25( 5 5× ) samples

( 1 ~ 5, C=1; T=10~18, T=2C = ∆ ∆ ) in

design place. Fig.10(b) shows 4000

( 50 80× ) fitting Samples

( 1 ~ 5, C=0.1; T=10~18, T=0.1C = ∆ ∆ ) in

design space.

(a) Samples(FFD)

(b) Fitting samples(RBF)

Fig.10. Samples in design space

Fig.11 shows K and RCS characteristics of NACA airfoil with different maximum thickness and camber combinations

( 180 30ψ = ±

). As can be seen, a Pareto

front which denoting the increase of lift-to-drag ratio and decrease of the mean RCS has been calculated in Fig.11(b). The fitting 3D curved surface and 2D plane about K and RCS characteristic of different NACA airfoils are shown in Fig.11(c)~(f). As a result, designers can choose the Pareto front or objective function with suitable constraints to find the optimized airfoil that satisfies the aerodynamic/stealth requirements in fitting curved surface.



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(a) K and RCS samples

(b) Fitting K and RCS samples

(c) Fitting 3D K curved surface

(d) Fitting 2D K plane

(e)Fitting 3D RCS curved surface

(f) Fitting 2D RCS plane

Fig.11. K and RCS characteristics of different maximum thickness and camber

combinations( 180 30ψ = ± )

Fig.12 shows RCS characteristics about four receiving azimuthal angles (leading edge, upside, downside and trailing edge ) of NACA C4T series airfoils with different maximum thickness and camber combinations. As can be seen, four receiving azimuthal angles of NACA airfoils have different Pareto fronts. Every one of four regions has its corresponding K/RCS Pareto front, and the RCS responses about four important scattering regions are all important for a rotating blade.



496

Fig.12. RCS characteristics of NACA airfoils with different max thickness and camber combinations

Based on influence factors about aerodynamic and four scattering regions of rotor airfoil, the optimized airfoil can be evaluated by appropriate objective function and constraint condition. Design status: The Mach number 0.4Ma = ,

69 10Re = × , attack of angle 0α =

, TM

wave incident angel 0φ =

, 10L λ= .

The lift-to-drag ratio and RCS about leading edge, upside, downside, trailing edge of airfoil are normalized:

Leading edge UpsideLeading edge Upside

Leading edge max Upside max

Trailing edgeDownsideDownside Downside

Downside max maxTrailing edge max

, ,( ) ( )

, , ( ) ( )

KKK

σ σσ σ

σ σ

σσσ σσ σ

= =

= = =

(13) Object function:

Leading edge Upside Downside

Trailing edge

1 1 18 8 8

1 1 8 2

:min

K

f σ σ σ

σ

= + +

+ +

(14)

Leading edge Upside Downside Trailing edge

1 1 1 10.04

8 8 8 8

S.T.: 0.9

K

σ σ σ σ+ + + ≤

≥

(15)

Table 1 shows the comparisons of weighted

sum between baseline and optimized airfoil. The aerodynamic characteristics of NACA5410 airfoil are the best, but RCS weighted sum is not the minimum. The stealthy characteristics of NACA1410 airfoil are the best, but aerodynamic performances are not optimum. When maximum thickness T=10% and maximum camber C=4.3%, the compromised NACA4.3410 airfoil satisfies the object function and constraint condition. The weighted sum error between calculated and fitting sample from surrogate model is small, the optimal method can satisfy the requirements of practical applications. Fig.13 shows the comparisons of aerodynamic and RCS characteristics between baseline and optimized airfoil. Although the compromised goal NACA4.3410 airfoil is not the optimal aerodynamic solution, aerodynamic and stealth comprehensive performances are the best. Comparing on the RCS of NACA1410 and NACA5410 airfoil

(especially trailing edge 320 340≤ Ψ ≤ ),



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the RCS of NACA4.3410 airfoil decreases significantly. Comparing on aerodynamic

pressure distributions of NACA1410, NACA4.3410 airfoil improved obviously.

Table 1 The comparisons of weighted sum between baseline and optimized airfoil

Objectives

Airfoils K

Leading edge Upside

Downside Trailing edge

1 18 81 18 8

σ σ

σ σ

+ +

+

f

NACA1410 0.30202 0.00579 0.15684

NACA5410 1.00000 0.04523 0.54523 NACA4.3410

(Fitting) 0.91114 0.03999 0.49556

NACA4.3410 (computed) 0.94733 0.03644 0.51011

(a) Airfoil geometries

(b) Cp distribution

(c) RCS characteristics

Fig.13. The comparisons of aerodynamic and RCS characteristics between baseline and

optimized airfoil 4. CONCLUSIONS An integration design method about aerodynamic/stealth is developed in this work for rotor airfoils. The solver is

applied to investigate the effects of NACA series airfoils with different thicknesses and cambers combinations. Furthermore, the optimization method which can find high lift-to-drag ratio and low scattering airfoil is developed. From the results presented in this paper, the following conclusions can be drawn: (1) The highly-accurate numerical method utilizing the Navier-Stokes and Maxwell’s equations can effectively simulate the characteristics about aerodynamic/stealth of rotor airfoils. (2) Based upon surrogate optimization model, an integration design of rotor airfoil about CFD/CEM coupling method is established, and it can be used to design the rotor airfoil which efficiently satisfies the low electromagnetic and high aerodynamic performance. (3) The aerodynamic characteristics are significantly influenced by maximum camber of airfoil, and the stealth performances are greatly influenced by maximum thickness of airfoil. The selection of rotor airfoil with high lift-to-drag ratio and low scattering characteristics is a process seeking compromised requirements, and the optimal airfoil can be found through comprehensive analyses.



498

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Integrated Analysis about Aerodynamic and Stealth ......with CEM method to co the nduct multi-objective optimization design of airfoil. At present, some integrated researches of wing