aeroelastic design code (aedc) for high aspect ratio wing ... · aeroelastic design code (aedc) for...

AeroElastic Design Code (AEDC) for high aspect ratio wing sizing

G. Gatta, F. Romano & M. Pecora Structural Design & Aeroelasticity Laboratory, CIRA - Italian Aerospace Research Center, Italy

Abstract

The aim of this work is to illustrate the features of an in-house developed piece of software (AEDC) to perform the aeroelastic analyses concerning the different steps of a high aspect ratio wing design. The wing is wholly made of composite material: a common high-strength graphite/epoxy is used for the spars and the facings of the skin panels in a honeycomb core sandwich. The code, written in Fortran language, is constituted of several modules: two modelling modules for the complete aeroelastic model definition and three analysis modules for divergence, flutter and gust analysis according to JAR 25 airworthiness design requirements. By means of a random gust analysis, AEDC determines/updates the external load characteristics (shear, bending and torque moment) acting on the wing and evaluates the equivalent static forces for the finite element model using a matched gust manoeuvre. Once the aerodynamic model of the wing and tail plane is constructed, a first load evaluation is obtained under the hypothesis of trimmed rigid aircraft, according to the Houbolt criteria. Using the results of preliminary wing sizing performed in a multi-level integrated procedure (MLISS), the elasticity of the structure is introduced in the aircraft trimming equations in order to update the previous loads. But if the loads change a new sizing is requested and so on. These iterations between external load updating and structural sizing run until the convergence is reached; the final structure has the minimum weight for the fixed load condition and doesn’t exhibit aeroelastic instabilities. Keywords: aspect ratio, composite honeycomb, trimming equations, flutter analysis, aeroelastic instability, random gust analysis, load characteristic, equivalent static force.

© 2005 WIT Press WIT Transactions on The Built Environment, Vol 80, www.witpress.com, ISSN 1743-3509 (on-line)

Computer Aided Optimum Design in Engineering IX 279

1 Introduction

The AeroElastic Design Code is completely developed in Fortran language and provided with a graphic interface in Matlab environment. It is composed by two modelling modules (aerodynamic and structural) for the complete aeroelastic model definition and three analysis modules (for divergence, flutter and gust analysis). The structural module allows representing the structure in a modal basis using theoretical or experimental normal modes. With the aerodynamic module the steady and unsteady Generalized Aerodynamic Forces (GAF) can be determined. In the divergence analysis module the critical divergence speed can be estimated; the flutter analysis module allows the existence of aeroelastic instabilities to be checked. Finally, in the gust response module the problem of gust loading is resolved: the mean square value of the response is calculated on the basis of the power spectrum of the excitation. It’s useful to divide the design approach in two phases: the first phase goes from the rigid aircraft hypothesis to the determination of the loads of the loop 1 on the elastic aircraft (figure 1); the second phase starts from these loads and terminates with the characterization of the best structure after a series of iterations between the structural sizing and the aeroelastic design (figure 3).

2 Wing structure and materials In order to have a high structural efficiency a profile characterised by a high thickness to chord ratio (20%) is used. The wing box has a two-spar configuration: the front and rear spar are located at 25% and 60% of the chords respectively. The span is 61 m, the area 122 m2 so the aspect ratio is 30.5; the root and tip chords are 4.0 m and 1.0 m respectively.

Figure 1: First phase scheme.


280 Computer Aided Optimum Design in Engineering IX

The wing is conceived entirely in composite materials: the spars are laminates with two different lay-ups for web and cap, while the skin is in honeycomb core sandwich panels. In particular, in the laminates of the panels (skin and web) the major part of the plies is supposed +/-45° oriented, while the caps are essentially unidirectional laminates 0° oriented (the 0° direction is along the span). For all laminates a common high-strength graphite/epoxy composite material is used, the IM7/977-2 produced by ICI Fiberite. The allowable values are opportunely knocked down to take into account the effects of moisture absorption and impact damages. According to previous experiences on the composite materials, the applied knock down factors are about 40-50%, then the design results quite conservative. The considered honeycomb core material is HRH-10-1/8-1.8 produced by Hexcel Composites.

3 Aerodynamic and structural models

The aerodynamic model of wing and tail plane is based on the Doublet Lattice Method (DLM) and constituted by 446 aerodynamic boxes; it includes 3 lifting surfaces (wing, horizontal and vertical tails) and 1 control surface (elevator). A complete interference between the aerodynamics of wing and tail plane is introduced. The structural model of the wing has 1026 nodes and uses 1 concentrated mass (to simulate the engine), 998 shell elements (spar webs and skin panels), 164 rod elements (spar caps) and 42 rigid elements (ribs) for an amount of 6156 degrees of freedom.

4 Design approach: first phase

After a first load evaluation (loop 0) under the hypothesis of rigid trimmed aircraft and a preliminary wing sizing, the elasticity of the structure is introduced in the aircraft trimming equations in order to update the loads (loop 1). The preliminary wing sizing in the scheme corresponds to the first wing sizing.

4.1 First load evaluation

To make a sizing according to JAR 25 [1] the stiffness and mass distributions for the entire aircraft must be identified, but in the preliminary design phase these distributions are not yet defined. So, at first, the aircraft is supposed rigid and represented by the only plunge mode, excited at the cruise speed (Vc) by a Random Gust with a Von Karman Power Spectral Density (PSD). From this load condition the ∆NG at centre of gravity has been evaluated (2.26) by means of a Random Gust Analysis and a Pseudo Static Manoeuvre with a load factor of 1+∆NG (3.26) has been imposed according to the approach followed by Houbolt [2]. In table the first values of the characteristics are listed:



Table 1: External load characteristics (loop 0).

--------------------------------------------------------------------------------- Span(m) Fx(N) Fy(N) Fz(N) Mx(N*m) My(N*m) Mz(N*m) 4.000 0.00 0.00 64188.62 711341.54 -224003.33 0.00 4.500 0.00 0.00 60330.66 679294.43 -210275.63 0.00 5.325 0.00 0.00 60330.66 629487.70 -210275.63 0.00 5.975 0.00 0.00 56719.59 592063.56 -198309.55 0.00 6.598 0.00 0.00 52541.41 556796.06 -184623.79 0.00 ……………… ………… ………… …………………… ……………………… ………………………… …………

------------------------------------------------------------------------------------------------- From the load characteristics AEDC extracts the equivalent static forces to use on the finite element model. To determine these forces, the equilibrium equations are written considering the derivatives relative to the rigid aircraft. In a Nastran Force File the equivalent unit forces relative to 4 different effects are linearly combined according the following factors: 1) incidence effect ∝ q*α 2) elevator effect ∝ q*δ 3) zero effect ∝ q 4) focal moment effect ∝ q where q = 1/2*ρ*V2 is the dynamic pressure. The air density at sea level is ρ=1.225 kg/m3, the cruise speed is V = 70 m/s, so the dynamic pressure is q=3001.25 N/m2. Solving the trim equations the incidence and elevator angles are calculated:

α = -5.10° ; δ = -0.41° Once determined α and δ relative to the trimmed aircraft, the load coefficients can be computed:

q*α = -266.93 N/m2 q*δ = -21.59 N/m2

The load condition includes the previous four effects and the inertia effect (engine + structure); a concentrated mass (Nastran CONM2 element [3]) of 400 kg schematises the engine.

4.2 Wing sizing (loop 0)

Once evaluated the external loads due to the previous manoeuvre a first wing sizing has been performed using the MLISS procedure [4]. The outputs of the procedure are the spar cap areas, spar web lay-ups, skin lay-ups. The weight obtained in the first sizing is 1207.8 kg.

4.3 Elastic aircraft trimming

A first structure with inertial and elastic properties has been determined, so the trimmed conditions can be evaluated taking into account the effects of the elastic deformation on the load distribution. The aerodynamic load on the wing decreases thanks to the elasticity of the structure: the resultant load due to the elasticity of the structure is shifted towards to the wing root respect to the rigid configuration.



Figure 2: Aerodynamic load comparison.

4.3.1 External load characteristics (loop 1) So the previous manoeuvre (with a load factor of 3.26) is reported to an elastic configuration: the stiffness and mass matrices of the wing box are imported in AEDC and assembled to the other structural elements. The new load characteristics are determined:


------------------------------------------------------------------------------------------------- Span(m) Fx(N) Fy(N) Fz(N) Mx(N*m) My(N*m) Mz(N*m) 4.000 0.00 0.00 57667.93 547664.74 -202988.15 0.00 4.500 0.00 0.00 57982.41 518648.56 -202583.04 0.00 5.325 0.00 0.00 53231.06 474759.02 -189464.26 0.00 5.975 0.00 0.00 49559.85 442533.28 -178463.43 0.00 6.598 0.00 0.00 48098.51 412578.86 -173506.96 0.00 ……………… ………… ………… …………………… ……………………… ………………………… …………

-------------------------------------------------------------------------------------------------

4.3.2 Equivalent static forces (loop 1) In the equilibrium equations, the elastic contribution is added to the derivatives relative to the rigid aircraft, in order to compute the new equivalent static forces. Respect to the rigid case, a fifth effect is added (the elastic one) and combined with the previous four effects by means of a multiplier proportional to the dynamic pressure. The sixth effect is always the inertial one. Moreover, the load condition contemplates an enforced displacement by means of the Nastran card SPCD [3] to take into account the elasticity of the structure of the aircraft on which the wing is attached (the wing root isn’t clamped).

5 Design approach: second phase

The loads of the loop 1 are used as input for the second phase: a new wing sizing is performed, the properties of the structural model are updated and a new



aeroelastic model is defined. The output of the phase is a new load set; if there is a consistent difference between the new and old loads a new wing sizing is necessary. The iterations between the aeroelastic design and the structural sizing run until the convergence is reached; at convergence the structure with the minimum weight and without aeroelastic instabilities is obtained. In order to avoid repeating the same procedure for two or three times, some iterations aren’t described, but only the results are reported.

5.1 Loop 2

Performing a sizing with the loads of the loop 1, a new weight of 1025.6 kg is obtained. This structure is used to determine the loads of the loop 2. After the evaluation of the normal modes with their relative representation on the aerodynamic grid, the flutter analysis and then, if there are no flutter instabilities, the atmospheric turbulence analysis are performed.

Figure 3: Second phase scheme.



The equivalent manoeuvre load factor is 2.7 and the relative load characteristics are:


------------------------------------------------------------------------------------------------- Span(m) Fx(N) Fy(N) Fz(N) Mx(N*m) My(N*m) Mz(N*m) 4.000 0.00 0.00 47783.57 438392.26 -177150.18 0.00 4.500 0.00 0.00 48467.22 414133.55 -177429.32 0.00 5.325 0.00 0.00 43865.70 377971.90 -164544.74 0.00 5.975 0.00 0.00 40627.45 351551.12 -154468.01 0.00 6.598 0.00 0.00 39408.24 327006.25 -150000.25 0.00 ……………… ………… ………… …………………… ……………………… ………………………… …………

------------------------------------------------------------------------------------------------- With the new incidence and elevator angles (–3.90° and –1.37° respectively) the new equivalent static forces are determined. The forces on the rear spar (positive along z axis) are higher than the forces on the front spar (negative along the z axis), then they generate a pitching down moment. The new sizing returns a weight of 907.9 kg for the entire wing, obtaining a reduction of 24.8% respect to the loop 0 sizing. The weight for unit wing area is 7.4 kg/m2. This weight is very close to the estimated one in the preliminary design phase (907.9 kg vs. 933.7 kg). The maximum vertical deflection at limit load passes from 1.52 m (on the loop 0 wing) to 2.09 m. The value calculated by finite element analysis is equal to the value determined in AEDC, so the assumed load distribution can be considered sufficiently accurate. The deflection seems very low if compared with that one of similar wings. For example, the wing tip deflection of the Boeing Condor is about 8.7 m at 125% of the limit load (load factor = 2.5) [5]. This difference is essentially due to the different thickness to chord ratios of the two profiles; unfortunately this ratio for the profile of the Condor wing is unknown, but if a profile of 12% is supposed, it’s possible to estimate the tip deflection of the sized wing by the inertia ratio. Indicating with I20 and I12 the inertia for a profile of 20% and 12% respectively:

78.21220 2

12

20 =

=

II

So the tip deflection at limit load is 2.07*2.78 = 5.75 m, at 125% of the limit load is 5.75*1.25 = 7.19 m, comparable with the Condor wing deflection. Moreover, the load factor of 2.7 is comparable with the Condor design load factor. The loads relative to the loop 2 are lower than the loads relative to the loop 1 so a new sizing is requested. It has been decided to stop the iterations at this stage not only because the aim of the present work is to show the potentialities of the software only but also because the loads of the loop 3 are resulted very close to the loads just calculated. So the considerations reported in the next paragraphs are referred to the loop 2 structure.



6 Normal modes evaluation

For the normal modes evaluation, the Lanczos method is applied. The structural deformations relative to the normal modes are interpolated on the aerodynamic grid by means of a spline matrix based on the Infinite Plate Spline (IPS) method [6]:

δAERO= S*δSTR

The transpose spline matrix allows passing from the aerodynamic forces to the structural ones:

FSTR= ST*FAERO As example, the first bending mode is reported; it is characterized by a frequency of 1.628 Hz. The dynamic characteristics of the structure (natural frequencies and modes, generalized masses) are used in the aerodynamic model in order to determine the Generalized Aerodynamic Forces.

7 Aeroelastic analyses

The aeroelastic model is so completed and the analyses can be performed to evaluate the new loads.

7.1 Divergence and flutter analysis

The divergence analysis gives a speed of 195.2 m/s (it was of 170.0 m/s for the loop 0 structure); this decreasing in the divergence speed is due to an increasing in the flexibility of the structure.

Figure 4: First bending mode.



Figure 5: V-g diagram.

A flutter analysis is performed in order to check the presence of aeroelastic instabilities inside the flight envelope. The diagram in figure 5 presents the results of the flutter analysis performed at Operative Empty Weight (OEW) and sea level. The highest aerodynamic load on the wing is associated to this condition and not to Maximum Zero Fuel Weight condition (the fuel contributes to reduce the load). The aerodynamic forces are calculated for 27 reduced frequencies and represented by a Roger’s Finite State Approximation. The analysis is based on 2 rigid (pitch and plunge) and 12 elastic modes. No flutter instabilities are identified inside the flight envelope. The predicted critical flutter speed is greater than 100 m/s, well beyond the maximum achievable aircraft velocity.

7.2 Atmospheric turbulence analysis

After a check on the aeroelastic instabilities inside the certification flight envelope, the response to the atmospheric turbulence according to ACJ.25.341(b) paragraph is determined. According to JAR 25 the gust loads must be determined by means of dynamic analysis using a random approach and/or pseudo-random approach (tuned gust). The inputs for a complete turbulence analysis are the Von Karman PSD and the normal modes used for the flutter analysis. The outputs are represented from the delta load characteristics relative to the gust. The delta load characteristics so calculated are added to the load characteristics relative to Nz=1 (named aeroelastic loads and calculated in the hypothesis of flexible aircraft).



The load characteristics are all medium quadratic values (Root Mean Square values). So at this stage the load correlation is essential: a calculation section is fixed (wing root), a load characteristic is fixed (bending moment) and the other load characteristics are correlated to the fixed one and determined on the entire aircraft. The correlation is performed according to Noback method [7]. With AEDC it’s not yet possible to determine the dynamic forces equivalent to the correlated load characteristics relative to a gust response. In this work to avoid the problem of the equivalent dynamic forces determination, a bending moment trend along the span deriving from an equivalent static manoeuvre and matched to the bending moment trend deriving from the global response of the atmospheric turbulence has been considered. From this pseudo static manoeuvre, the load factor and then the equivalent forces to use for the model can be determined.

8 Conclusions and future works

This work has proposed a software tool to use for the aeroelastic analyses concerning the different steps of a high aspect ratio wing design. The code is written in Fortran language and constituted by five principal modules both for the aeroelastic model definition and the aeroelastic analyses performing according to JAR 25. In AEDC the flutter analysis is used only for a check on a structure already sized. In future the value of the critical flutter speed will be an aeroelastic constraint to consider in the structural sizing, that is a minimum value for the critical flutter speed will be imposed.

References

[1] JAR 25 – Airworthiness Design Requirements, change 15. [2] John C. Houbolt, On turbulence environment and design criteria, AGARD

conference proceedings n° 140 “Flight in Turbulence”. [3] MSC/Nastran, Quick reference guide, Ver. 2001. [4] G. Gatta, F. Romano, L. Di Palma, M. Pecora, Wing Design of a High

Altitude and Long Endurance Aircraft, International Conference on Computational & Experimental Engineering and Sciences, Madeira, Portugal, 26-29 July 2004.

[5] Matthew G. Sexstone, Aircraft Structural Mass Property Prediction Using Conceptual-Level Structural Analysis, SAWE paper no. 2410, index category no. 23, pp. 13.

[6] R. L. Harder, R. N. Desmarais, Interpolation Using Surface Splines, Journal of Aircraft, Vol. 9, No. 2, pp. 189 – 191, 1972.

[7] R. Noback, The Generation of Equal Probability Design Load Conditions, Using P.S.D. Techniques, NLR TR 85014 U, National Aerospace Laboratory NLR, Amsterdam, The Netherlands, Jan 1985.



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