Fenekos E Etal_2002_on The Calculation Of Steady Flow About Isolated Helicopter Fuselage

4 th GRACM Congress on Computational Mechanics GRACM 2002 Patra, 27-29 June, 2002 © GRACM

ON THE CALCULATION OF STEADY FLOW ABOUT ISOLATED HELICOPTER FUSELAGE Evgenios G. Fenekos 1, Andronicos E. Filios 2 , Dionissios P. Margaris1 , Anastasios P. Fragias 1, Dimitrios G. Papanikas 1 1

2

Fluid Mechanics Laboratory, Mechanical Engineering and Aeronautics Department,

University of Patras, 26500 Patras, Greece, e-mail: [email protected], web page: http://fml.mech.upatras.gr

ASETEM/SELETE., Researcher in Fluid Mechanics Lab., Mechanical Engineering and Aeronautics Department, University of Patras, 26500 Patras, Greece, e-mail: [email protected] Keywords: Panel method, Helicopter fuselage, Helicopter aerodynamics Abstract: The calculation of the pressure and velocity distribution on a helicopter fuselage is based on a panel method. The surface of the body is represented by a sufficiently large number of quadrilateral panels. The effect of thickness is accounted for by constant source density distribution on each surface panel. The lift effect is accounted for by the 'inner surface' with ring vortex lattice representing a constant strength flow problem governed by Laplace equation for the velocity potential. Compressibility effects are included applying Goethert's rule. The inviscid solution is extended for simulation of the boundary layer and the separated flow regime. The boundary layer along the fuselage streamlines is proceeded according to Rotta's integral method while the wake is modelled through a system of interacting vortex filaments produced downstream of the separation line. The developed modular computational procedure provides results that are directly compared with experimental data on a reference helicopter fuselage. 1 INTRODUCTION The aerodynamic environment of rotorcraft configurations is complex due to the nature of the inflow of rotating blade and the wake systems as well as relatively fuselage shape characteristics. Given the wide range of flight conditions in which helicopters must operate, part icularly during hovering maneuvers, and given design constraints based on internal cargo and external stores, the aerodynamic optimization of the fuselage is not always possible. However, the fuselage can significantly affect the overall performance of the helicopter in all flight conditions. Understanding and predicting the aerodynamics of helicopter fuselages will be important to rotorcraft designs, particularly when the designs require greater range and speed. Analytical methods for evaluating the aerodynamics of helicopter fuselages are available, including both potential theory and Navier-Stokes solutions. Early computational methods were based on the solution of the potential equation using a singularity method with constant -strength source panels. Sin ce that early work, the computation of flow over arbitrarily shaped bodies has advanced significantly [1,2]. The shape of most helicopter fuselages as well as the wide range of flight conditions virtually guarantees that some amount of flow separation wil l occur. A computational method could model this separation in panel methods with a boundary layer model (coupled inviscid and viscous solver). However, if separation does occur, the code must also model the wake. Shedding a wake that convects downstream the vorticity released when the boundary layer separates does this modeling. The success of this approach depends on the ability to correctly calculate both where the wake leaves the fuselage and its trajectory. One approach is to test the configuration in a wind tunnel and determine the separation location experimentally. This information can then be used in the potential code to determine the wake location [3,4] . More sophisticated approaches determine the wake separation point as part of the boundary laye r solution [5]. The objective of the present paper is to demonstrate a computational procedure for the prediction of the flow around a helicopter fuselage using a panel method. Fuselage surface is represented by a number of quadrilateral plane panels with constant source distribution. The numerical model leads to the prediction of pressure and velocity distribution around the helicopter fuselage. Applying Goethert’s rule includes compressibility effects. The potential flow solution is extended to include the boundary layer displacement effect and the influence of the separated flow regime. A two dimensional

Evgenios G. Fenekos, Andronicos E. Filios, Dionissios P. Margaris, Anastasios P. Fragias, Dimitrios G. Papanikas

integral method is applied along the fuselage streamlines for the account of the displacement of the boundary layer, while the wake is simulated by a system of interacting vortex filaments produced downstream of the separation line. The computational procedure efficiency is validated through comparison with available experimental data, including various fuselage geometries and flow conditions, allowing the assessment of the accuracy of the codes. The comparison with experimental data also helps in establishing the relative importance of un-modeled effects such as regions of flow separation from the fuselage [6]. 2 MATHEMATICAL MODELING The calculation of the pressure and velocity distribution on a helicopter fuselage is based on a panel method. The surface of the body is represented by a sufficiently large number of quadrilateral plane panels. The effect of thickness is accounted for by constant source density distribution on each surface panel. The lift effect is accounted for by paneling the "inner surface" with rinq vortex lattice each representing a constant strength flow problem governed by Laplace equation for the velocity perturbation potential f , i.e.

∇ 2φ = 0

(1)

where f is the sum of the source-panels potential (f S) and the doublet-panels potential (f D )

ϕS = −

ϕD =

1 σ(S ) dS ∫∫ 4π S r (S, p)

1 ∂ µ(S i ) 4π ∫∫ ∂ n S i

(2)

 1    dSi  r (S i , p )

(3)

The perturbation potential at the body surface must satisfy the condition

∂ϕ rr = −n U ∞ ∂n S

(4)

where n is the unit vector normal to the surface of the body. The solution to this boundary problem is derived from the following integral equation.

1 r σ(S) 1 r ∂  1 r r n∇ ∫∫ dS − n∇ ∫∫ µ(S i )   dSi = n U ∞ 4π r 4π ∂n  r  S S

(5)

i

Applying Goethert’s rule includes compressibility effects The inviscid solution is extended for simulation of the boundary layer and the separated flow regime. The boundary layer along the fuselage streamlines is proceeded according to Rotta's integral method while the wake is modeled through a system of interacting vortex filaments produced downstream of the separation line. The mechanism of the vortices formation is shown in Figure 1. U( rs)

New Front Position 2

New Vortex U ( rs )

Vort ex positio n a t t ime t - ∆t

2

P( r)

r' d Uw

r r = α ⋅∆t

Uc ⋅∆ t

d rw

Γ = 2 ωΑ w

Uc

Evgenios G. Fenekos, Andronicos E. Filios, Dionissios P. Margaris, Anastasios P. Fragias, Dimitrios G. Papanikas

Figure 1. Formation of vortices around helicopter fuselage.

r r The velocity of the vortices at the time where they are generated is u (rS ) / Ω and their circulation is r r 3 dΓ / dt = u( rS ) / z . Biot-Savart law defines the induced velocity from a vortex element at the point P (r) in the wake, i.e.

dv w

r r Γ r ′ × drw = 4π rr ′ 3

(6)

r r r r r where r ′ = U C ∆t + r , r ′ = a ∆t and U C the vortex speed and a the speed of sound. The above-described wake modeling of a helicopter fuselage gives accurate results for subsonic flow conditions and for different fuselage geometries. 3 COMPUTATIONAL PROCEDURE The physical-mathematical modeling is implemented numerically by means of a computer code, namely HEFUPA, calculating the entire flowfield around the isolated helicopter fuselage. The computational procedure is described in the flow chart shown in Figure 2. Input surfaces point coordinates S (x,y,z) Geometry module

Paneling Geometric parameters of panels

Panel optimization

Matrix formulation steady flow System solution

Main Computation Module

Pressure and velocity distribution over body surface Streamline calculation

Boundary Layer Module

2-D boundary layer solution

Separated flowwake geometry

Friction coefficient distribution Integration of pressure and friction coefficient

Output of aerodynamic coefficients

Aerodynamic Forces Module

Velocities calculation over the body

Output velocities

Flow field Module

Evgenios G. Fenekos, Andronicos E. Filios, Dionissios P. Margaris, Anastasios P. Fragias, Dimitrios G. Papanikas

Figure 2. Flow chart of the HEFUPA numerical code. The flowfield calculation around the isolated NASA Langley fuselage is performed with the numerical code utilizing quadrilateral plane panels with constant source distribution. Due to the symmetry of the fuselage in the xz-plane only the half model is considered using a number of 613 panels. The surface discretisation of the NASA Langley fuselage is shown in Figure 3. The calculations are referred in a free stream Mach number 0.09 that corresponds in an advance ratio of 0.15 and at zero incidence angle (a f) and zero yaw angle (ß f). The calculated results are given in terms of pressure coefficients at the fuselage stations x/R=0.2, 0.3, 1.34 and 1.53 as well as along the control points of the panels close to the top centerline of the fuselage that are shown in figure 4.

Figure. 3: Surface discretisation of the NASA Langley fuselage.

Figure 4: Computed pressure distribution on fuselage contour. The potential flow solution (PF) is corrected due to the boundary layer (BL) displacement effect and the wake (W) effect. The boundary layer calculation is based on a two-dimensional integral method applied along the computed friction lines that are shown in figure 5.

Figure 5: Computed friction lines on fuselage surface. The potential flow solution is corrected due to the boundary layer by adding into the local model geometry the corresponding boundary layer displacement thickness. The derived solution is considered as the viscous solution out of the wake (PF+BL). The separated flow regime downstream of the separation line (predicted with the application of the boundary layer module) is simulated by the interacting vortex filaments with their motion described in the Langrangian reference frame (Figure 6). The potential flow solution, corrected with the wake, is referred as the potential flow solution plus the wake correction (PF+W). The complete viscous solution takes into account the boundary layer and the wake development and it is noted as PF+BL+W. The boundary layer calculation on the main fuselage does not indicate any separation while a separation is predicted in the downstream portion of the pylon at the station x/R=0.995 resulting t? a wake structure shown in

Evgenios G. Fenekos, Andronicos E. Filios, Dionissios P. Margaris, Anastasios P. Fragias, Dimitrios G. Papanikas

figure 6 for a non-dimensional time tU∞ / l ref = 1.0

Figure 6: Numerical wake simulation of the NASA Langley model.

The computed data in all calculation cases are shown in Figures 7 to 11. Great differences in the calculations occur behind the pylon where the boundary layer separation starts and the wake effect strongly influences the flow around the fuselage.

Pressure coefficient, c p

-0,08

PF PF+W PF+BL PF+BL+W

-0,12

-0,16

-0,20

-80

-40

0

40

80

f, deg

Figure 7. Pressure distribution at fuselage contour station x/R=0.2. 4. CONCLUSIONS The flowfield calculation around an isolated helicopter rotor is performed with a panel method for coupling viscid-inviscid analysis utilizing quadrilateral plane panels with constant source distribution. The potential flow solution is used while corrections for the boundary layer and wake effects are included in the calculations. Computational results presented in the paper are in good agreement with those obtained by other potential flow models or by experimental data [6]. This investigation of the NASA Langley helicopter body was a preliminary investigation to determine the suitability of HEFUPA to eventually solve the flow around a helicopter fuselage without including the main rotor effects. The applied methodology simulates sufficiently the problem and clearly demonstrates HEFUPA’s potential

Evgenios G. Fenekos, Andronicos E. Filios, Dionissios P. Margaris, Anastasios P. Fragias, Dimitrios G. Papanikas

and the need for further development.

Pressure coefficient, c p

-0,08

PF PF+W PF+BL PF+BL+W

-0,12 -0,16 -0,20 -0,24 -80

-40

0

40

80

f, deg

Figure 8. Pressure distribution at fuselage contour station x/R=0.3.

0,2

Pressure coefficient, cp

0,0 -0,2 -0,4

PF PF+W PF+BL PF+BL+W

-0,6 -0,8 -1,0

-80

-40

0

40

80

f, deg

Figure 9. Pressure distribution at fuselage contour station x/R=1.34.

0,10

Pressure coefficient, cp

0,08 0,06 0,04 0,02

PF PF+W PF+BL PF+BL+W

0,00 -0,02 -80

-40

0

40

80

f, deg

Figure 10. Pressure distribution at fuselage contour station x/R=1.53.

Evgenios G. Fenekos, Andronicos E. Filios, Dionissios P. Margaris, Anastasios P. Fragias, Dimitrios G. Papanikas

1,2 PF PF+W PF+BL PF+BL+W

Pressure coefficient, cp

0,8 0,4 0,0 -0,4 -0,8 0,0

0,5

1,0

1,5

2,0

Fuselage contour station, x/R

Figure 11. Computed pressure distribution on the top centerline of the helicopter fuselage.

REFERENCES [1] Chaffin, M.S., Berry, J.D. (1994), Navier-Stokes and Potential Theory Solutions for a Helicopter Fuselage and Comparison With Experiment, NASA TM 4566. [2] Morino, L., ed. (1985), Computational Methods in Potential Aerodynamics, Springer-Verlag, New York. [3] Gleyzes, C., De Saint-Victor, X., Falempin, G. (1989), “Experimental and Numerical Study of the Flow Around an Helicopter Fuselage. Determination of Drag Coefficient”, 15 th European Rotorcraft Forum, Paper No. 5. [4] Le, T.H., Ryan, J., Falempin, G. (1987), “Wake Modeling for Helicopter Fuselage”, 13 th European Rotorcraft Forum. Paper No. 2-8. [5] Polz, G. (1982) The Calculation of Separated Flow at Helicopter Bodies, NASA TM 76715. [6] Freeman, C.E., Mineck, R.E. (1979), Fuselage Surface Pressure Measurements of Helicopter Wind-Tunnel Model With a 3.15-Meter Diameter Single Rotor, NASA TM 80051.