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ADPO10512TITLE: Aerodynamics for MDO of an Innovative

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TITLE: Aerodynamic Design and Optimisation ofFlight Vehicles in a Concurrent

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16-1

Aerodynamics for MDO of an innovative configuration

G. Bernardini, A. FredianiDipartimento di Ingegneria Aerospaziale

Universitý degli Studi di PisaVia Diotisalvi 2, 56126 Pisa, Italy

L. MorinoDipartimento di Ingegneria Meccanica e Industriale

Universita degli Studi Roma TreVia della Vasca Navale 79, 00146 Roma, Italy

Abstract planes, which shows that these configurations have

A numerical methodology for the evaluation of aero- certain aerodynamic advantages (outlined in the fol-

dynamic loads acting on a complex lifting config- lowing sentences) with respect to isolated wings.

uration is presented. The work is limited to the First, the induced drag of a multiplane with elliptic

case of attached high-Reynolds number flows. A vis- distribution of circulation is lower than the induced

cous/potential interaction technique is utilized to take drag of the equivalent monoplane (i.e., of the mono-

into account the effects of the viscosity. For the plane having the same span and generating the same

potential-flow analysis, a boundary element formula- lift as the multiplane considered). In addition, the ra-

tion is used; for simplicity, only incompressible flows tio, K, between the induced drag of a multiplane and

are examined. The theoretical basis of the present that of the equivalent monoplane, decreases as the

methodology is briefly described. Comparisons with number of wings of the multiplane increases (with

available, numerical and experimental results are in- global height and lift kept constant). In the limit

cluded. as the number of wings tends to infinity ("infinity-

plane", according to the Prandtl [25] definition), K1. Introduction has the minimum value. Finally, there exists a box-

The present work is an overview paper on recent re- wing type configuration that has the same distribu-

sults on viscous-flow analysis of innovative configu- tion of circulation (and hence the same K) as the

rations (low-induced drag lifting configurations), ob- "infinity-plane"; such configuration is therefore des-

tained by the authors within the objective of de- ignated, still by Prandtl [25], at the 'Best Wing Sys-

veloping an MDO methodology. The aerodynamic tem' (BWS).

methodology is based on a boundary element formu- After the work of Prandtl [25], valid only for the lim-

lation for the velocity potential introduced by Morino ited case of multiplanes with elliptic distribution of

[16]; the effects of viscosity are taken into account by circulation, several numerical and experimental stud-

a classical viscous/inviscid coupling technique; a tech- ies have been published. Of particular interest here is,

nique for extending this approach beyond the limits the work of Nenadovitch [23] on the efficiency of bidi-

of the boundary-layer approach is also indicated. mensional biplanes. Also, an experimental analysis of

In order to put this work in the paper context, note joined wing aircraft is presented by Wolkovitch [32],

that, the increased request for low-cost air trans- whereas experimental as well as numerical/empirical

portation has generated considerable interest for non- studies on biplanes and box-wing configurations are

conventional configurations, such as biplanes with proposed by Gall and Smith [6].

wing tips connected to each other directly (joined In this paper, the attention is focused on an innova-

wing configuration) or through a vertical surface tive configuration for a new large dimension aircraft

(box-wing configuration). These configurations are (usually indicated as New Large Airplanes or NLA)

related to the early work of Prandtl [25] on multi-

Paper presented at the RTO AVT Symposium on "Aerodynamic Design and Optimisation of Flight Vehicles in aConcurrent Multi-Disciplinary Environment", held in Ottawa, Canada, 18-21 October 1999, and published in RTO MP-35.

16-2

proposed by Frediani et at. [4], [5]. This configura- Ref. [29]). The relatively recent state of our work in

tion is a biplane, with counter-swept wings (positive this context was presented in Bernardini et al. [1],

sweep for the front lower wing and negative sweep which is based on the classical viscous-potential in-

for the back upper wing, which acts as a horizon- teraction, with the viscous flow (in boundary layer

tal tail as well) connected to each other by aerody- and wake) solved by using the strip-theory approach,

namic surfaces (Figures 1 and 2). Following Frediani with an integral two-dimensional boundary layer; the

et al. [4], [5] we will refer to this configuration as viscous/inviscid coupling technique is based upon the

the Prandtl-plane. Preliminary numerical and exper- Lighthill [12] equivalent-sources approach. Match-

imental studies (Frediani et al. [4], [5]) have shown ing of the boundary-layer solution with the corrected

that the induced drag of this configuration is lower potential-flow solution is obtained by direct iteration.

than the induced drag of an equivalent monoplane. Here, the emphasis is on the most recent improve-

This fact allows one to reduce the wingspan of this ments with respect to that paper. First, we present

configuration without drag penalties and introduces an extension to higher order of the direct boundary

the possibility of respecting the maximum span-wise element formulation used in the past by the authors

dimensions (critical for the NLA with classical wing for incompressible potential flows around lifting ob-

configuration), which would allow compatibility with jects of arbitrary shape in uniform translation; this

the existing airport regulations, provides also an opportunity to clarify certain the-

Still to in order to put the work in the paper context, oretical issues connected with the trailing edge con-

note that through an unrelated activity, the authors ditions. Second, we discuss a three-dimensional in-

have been involved in the developement of an MDO tegral boundary-layer formulation, which is based

code. The weakest module in this code is the aerody- essentially on the algorithm of Nishida [24] and

namic one. In fact, the aerodynamic module in such Milewski [15]. The solution is obtained through the

a code is limited to potential flows around simply- simultaneous coupling technique introduced by Drela

connected domains; on the contrary, the Prandtl- [3].

plane configuration is multiply-connected. In addi- 2. Formulation of Ref. (1]tion, a key for this configurations (and MDO in gen-

eral) is the drag, induced and viscous. The formulation of Bernardini et al. [1] is outlined

These issues are addressed in this paper, as a first here in order to emphasize the differences of the new

step towards generating a suitable viscous aerody- formulation and also because, some new results pre-

namic module around multiply-connected configu- sented here are based on this formulation. For a de-

rations, to be incorporated in the above mentioned tailed discussion, see Ref. [18], where a review is also

MDO code. Specifically, because of the complexity presented.

and novelty of the configurations discussed above, Potential-Flow Formulation: an inviscid, incompress-

it is desirable to develop an aerodynamic methodol- ible, initially-irrotational flow remains at all times

ogy for multiply-connected configurations capable of quasi-potential (i.e., potential everywhere except for

yielding accurate predictions with a relatively small the wake surface, which is the locus of the points em-

computational effort (hence, not a CFD approach), anating from the trailing-edge). In this case, the ve-

which takes into account the effects of viscosity and locity field, v, may be expressed as v = Výo (where

of the wake roll-up (the geometry of the rolled-up p is the velocity potential). Combining with the con-

wake is evaluated through the free-wake analysis of tinuity equation for incompressible flows, V7. v = 0,

16-3

yields wake may be expressed in terms of o over the body

(1 0.at preceding times.

In Bernardini et al. [1], the boundary integral equa-The boundary conditions for this equation are as fol- tion for p based on Eq. 3 is solved numerically by

lows. The surface of the body, SB, is assumed to be discretizing the body and wake surfaces in quadrilat-

impermeable; this yields (v - vB) -n = 0, i.e., eral elements, assuming p, X and A•p to be piecewise

0__ = VB • n for x c S8, (2) constant, and imposing that the equation be satis-fied at the center of each body element (zeroth-order

where vB is the velocity of a point x E SB, whereas boundary-element collocation method).n is the outward unit normal to SB. At infinity, in a I should be noted that the geometry of the wake is

frame of reference fixed with the unperturbed fluid, not known a priori. For the case of isolated wings

we have ý= 0. The boundary condition on the wake in uniform translation, a flat wake with vortical lines

surface, S,'; are: (i) the wake surface is impermeable, parallel to the unperturbed streamlines is typically

and (ii) the pressure, p, is continuous across it. These used (prescribed-wake analysis). In the configura-imply that A(O•/8n) =0 (where A denotes discon- tion of interest here, such a priori assumptions aretinuity across Sw), and that A• remains constant in not justified by past experience. Still in Bernardinitime following a wake point x, (whose velocity is the et al. [1], the wake geometry is either prescribedaverage of the fluid velocity on the two sides of the (undisturbed) or obtained through a free-wake anal-

wake), and equals the value it had when x, left the ysis, i.e., the boundary integral equation is used to

trailing edge. This value is obtained by imposing the compute, at each time step t, the flow velocity attrailing-edge condition that, at the trailing edge, Ap nodes xi of the discretized wake surface (free-wake

on the wake equals p,. - •o on the body (subscripts analysis); the locations of x, at t.+, is then obtained

u and I denote, respectively, upper and lower sides of analysis) the loc ation of = at ( is the edthe ody urfae),by integrating the equation * • =v v(xv) by the ex-

plicit Euler method (in other words, in the case ofIn this paper, the above problem for the velocity po- free-wake analysis the shape of the wake and the flow-

tential is solved by a boundary element formulation. field solution are obtained step-by-step, as part ofThe boundary integral representation for the above the solution). For the steady-state cases of interestproblem is given by here, the solution is obtained in the limit as the solu-

Gx J ( OG ) dS (y) (3) tion for t -- oo of a transient flow due to an impul-S sive start. Incidentally, this procedure resolves also

- j A•ndS(y), the non-uniquess issue connected with steady-statew flows around multiply-connected region; indeed, inwith X :=vB -n, and G =-1/4irl]y-xII. Note that,

the case of unsteady flow the solution is unique, be-in the absence of the wake, Eq. 3, in the limit as x cause Kelvin's theorem allows one to obtain the cir-tends to SB, represents a boundary integral equation culation on the wing from the vorticity shed in thefor Wo on S, with X on 8B known from the bound-

wake (see Ref. [20]).ary condition. Once so on the body is known, Wo (and

hence v and, by using Bernoulli's theorem, p) may Boundary Layer: the viscous flow analysis is limited

be evaluated everywhere in the field. The situation is to attached steady high-Reynolds number flows. Un-

similar in the presence of the wake, since, by apply- der these assumptions, a classical integral boundary-

ing the wake and trailing-edge conditions, Aso on the layer formulation may be used. Specifically, Bernar-

16-4

dini et al. [1] use a 2D integral boundary-layer formu- •o, through suitable finite-difference approximations.

lation used as 'strip-theory'. The laminar portion is Only steady flows are considered here; then, the wake

computed by using the Thwaites collocation method geometry at the trailing-edge (typically tangents to

[30]. The transition from laminar to turbulent flow is one of the sides of the body surface at the trailing-

detected by the Michel method [14]. The turbulent edge) may be determined by the results of Mangler

portion of the boundary layer and wake are studied and Smith [13].

by the 'lag-entrainment' method of Green et al. [9]. The above formulation generates new issues con-

Viscous/Juviscid Coupling: once the boundary-layer nected to the trailing-edge. The first one, is relatedto the existence of the trailing-edge potential discon-

equations are solved, the viscous correction to the

potential flow is obtained as a transpiration velocity tinuity which implies that at any trailing-edge node

through SB and Sw (equivalent source method by there exist two unknowns, but only one collocation

Lighthill [12]). The boundary condition for ýp over point. Gennaretti et al. [8] use two collocation points

the body surface is modified as follows suitably located slightly ahead of the trailing edge

(otherwise the collocation points coincide with the

a/oan = v, • n + Xv, nodes).

where the transpiration velocity X, is given by In order to avoid ill-conditioned matrix here, as men-

tioned above, we use the approach introduced in Ref.

- (u, - u) dz, (4) [20], who, at the trailing-edge, use only one controla as, 0 point but two different integral equations: the first iswhere s denotes the arclength in the 2D boundary- the potential equation while the second is its deriva-

layer and wake, and P* is the displacement thickness. tive in the direction of the wake normal at trailing-In addition, u and ue denote, respectively, the veloc- edge.

ity within the vortical layer and at its outer edge (in a An additional issue stemming from the third-order

frame of reference fixed with the body). On the wake formulation is that of the evaluation of the derivativessurfaceni tatofth vaoneo o hehasvtie

surface one has of so at the trailing edge. These may be obtained by

A (ar/an) = (x,), + (X,),, imposing the two conditions of stagnation point andsmooth flow (see Ref. [20] for details).

where the subscripts u and I denote, respectively, the

4. Three-dimensional boundary layerupper and lower sides of the wake surface. In order to take into account the three-dimensional

3. Third-order extension effects, the viscous flow in the boundary layer and

wake, is modelled using the three-dimensional in-The specific formulation used here is based upon a

high-order formulation introduced by Gennaretti et tegral boundary-layer equations on non-ortogonal

al. [8], and extended in Refs. [20] and [21], to which grids. Specifically, the integral method uses two equa-tions for momentum (extention of von K(4rn~n equa-

the reader is referred for details (here the emphasis tion to 3 o ws) coup ed by t o auxi ia equat

is on the applications). This consists of using bicubicThe first is the kinetic energy equation and the sec-

quadrilateral elements and the Hermite interpolation ond is the tr ns t equation axm shear

for ýp in both directions. This yields a bicubic repre-

stess coefficient ('lag' equation). In order to com-sentation ind termsof the nodal derivalu ves of e thn aplete the problem, we use, following Nishida [24] and

expr/esse, and tr/mo; the nodal derivatives are then Milewski [15], the streamwise closure relations pro-expressed in terms of the unknowns of the problem,

16-5

posed by Drela [3] in his 2D integral boundary-layer lar biplane; (ii) a rectangular biplane with facing tip

method, along with the crosswise relations of John- winglets on the two wings and (iii) a box-wing. For,

ston [11]. The Mughal [22] finite-volume scheme is this show the graduality of the reduction (in the sense

used for the solution. that the biplane corresponds to the zero winglet-

Also in this case, the viscosity correction to the po- length case and the wing-box to the full length case);

tential flow is evaluated as a transpiration velocity this is apparent from Figure 3 (from Ref. [1]), which

through SB and Sw (equivalent source method by depicts a comparison of the curves K = K(G/b) for a

Lighthill [12]). However, as mentioned above, in biplane without winglets, for the corresponding box-

contrast with the formulation of Bernardini et al. wing body, and for a biplane with winglets (winglet

[1], the matching of the thin-layer solution with the length 0.4c, where c is the root chord).

potential-flow solution, is obtained by the fully simul- It should be observed that the above results have been

taneous coupling method of Drela [3], which solves obtained using a prescribed-wake approach, in or-

the viscous and inviscid equations simultaneously and der to be consistent with the Prandtl model which is

is stable even for separated flows, based on the lifting-line theory. However, the present

methodology is able to capture the effects of the wake5. Numerical results and comments

roll-up on the airloads by using a free-wake approach,

The results presented here fall into three groups. In as described above. Figure 4 (also from Ref. [1]) de-

the first group are some new results obtained with picts the Prandtl factor K as a function of G/b, for

the formulation outlined in Section 2 (some of the free-wake and prescribed-wake analysis. The results

results of Ref. [1] are included here for the sake of obtained by a free-wake approach show that the wake

clarity). The second and third group are based on roll-up effect is to reduce the value of K. For the

the formulations of Sections 3 and 4. range of G/b of practical interest in aeronautical ap-

For all the potential flow results, the airloads are de- plications (i.e., 0.1 < G/b < 0.2), we have that the

termined by using the formulation of Ref. [7], which reduction of K is about 6% for the case of a box-

is an exact generalization of the Trefftz-plane theory wing. This demonstrates the importance of including

[31] for the evaluation of aerodynamic loads around a rolled-up wake in the analysis.

objects of arbitrary shapes. The viscous drag is eval- Next, consider new potential-flow results obtained

uated by using the classical formula by Squire and with the formulation of Ref. [1]. In particular, Fig. 5

Young [28]. present a parametric study of the effects of the sweep

First, a few results obtained by Bernardini et al. [1] angle (of the front and rear wing) on the Prandtl fac-

are discussed as they help in putting the paper in the tor K of the Prandtl-plane shown in Figures 1 and

proper context. First of all, the potential flow for- 2. Here, we have considered three different config-

mulation of Section 2 has been validated in Ref. [1] urations characterized by: (a) Mid-chord front wing

by a comparison with analytical results by Prandtl sweep angle AF = 350 and mid-chord rear wing sweep

[25] either in the case of biplanes and box-wing con- angle AR -40', (b) mid-chord front wing sweep

figuration; this comparison has shown nearly perfect angle AF 370 and mid-chord rear wing sweep an-

agreement between our numerical results and the an- gle AR = -370 and, (c) mid-chord front wing sweep

alytical results of Prandtl. Also, in order to analyze angle AF = 400 and mid-chord rear wing sweep an-

the mechanism of induced-drag reduction, it is inter- gle AR = -35'. We can note that the Prandtl factor

esting to compare the efficiency K of: (i) a rectangu- of all three configuration are hardly distinguishable,

16-6

and are very close to the value of the Prandtl factor and N 2 = 24 and those obtained with the method of

of the Best Wing System (continuous line). This is Rubbert and Saaris [27] with N1 = 28 and N2 = 12.

very important because it shows that, even for the The agreement among the three formulations is good,

Prandtl-plane, we have a reduction of induced drag, except at the trailing-edge, where the pressure pre-

with respect to a traditional wing configuration. dicted in our case is higher (see also Ref. [21] which

Next, consider some preliminary results for attached shows why our results appear to be more reliable).

high-Reynolds viscous flows. The two-dimensional Finally, we present some preliminary results of the

integral boundary-layer formulation, used a 'strip- three-dimensional boundary layer formulation. In

theory' in three-dimensional application, has been particular, Figs. 11 and 12 show respectively the

validated in Ref. [1], by comparison with experimen- chordwise distribution (at 7/= 0.5 and for the upper

tal results available in literature, in the case of: (i) surface of the wing) of the streamwise displacement

isolated wing, (ii) biplane, and (iii) box-wing config- thickness, 6*, and the shape factor, H, for a RAE

uration. For the sake of completeness the results for wing with mid-chord sweep angle A = 450, RAE

the third case are presented here in Fig. 6 (also from 101 airfoil secton at Re = 2.1 • 106 and angle of at-

Ref. [1]) which depicts the polar at Re = 5.1 . 105 tack a = 6.30. Our numerical results, obtained using

of a box-wing configuration with aspect ratio 5, gap N1 = 60 and N 2 = 10, have been compared with

G = c, stagger S = c and section profiles NACA 0012. the numerical results of Milewski [15] (obtained us-

The numerical results are in good agreement, also in ing N1 = 64 and N2 = 10), and experimental results

this case, with the experimental results by Gall and of Brebner and Wyatt [2]. The transition location,

Smith [6]. Next consider new results. The formula- in this case, is fixed using experimental data. We

tion of Ref. [1] has been used for a parametric study have also included in the figure the two-dimensional

of the effect of sweep angle on the polar of a Prandtl- boundary layer formulation (unfortunately with tran-

plane. This is shown in Fig. 7 which depicts a po- sition obtained by Michel method [14]). Our three-

lar for the same three configuration of Prandtl-plane dimensional numerical results are in good agreement

used in Fig. 5. We can note that their difference is with both the Milewski [15] and with experimental

very small. data. On the contrary, the 2D formulation shows, at

Next consider the validation of third-order formula- the trailing edge, a great difference. This could find a

tion. Some results have been presented in Morino and justification in the fact that, at the trailing edge, the

Bernardini [21] for the case of simply (RAE wing) and 3D effects are higher.

multiply connected (nacelle) configurations. Here, we To conclude the paper we wish to mention a tech-

consider the particularly challanging case of a wing nique that allows us to overcome the boundary layer

with strake (see Fig. 8), at angle of attack a = 50 and limitations. This is based on a decomposition in-

having symmetric NACA 0002 airfoil sections. Fig. troduced by Morino [17] for the velocity field as

9 depicts the circulation F A= A as a function v = Vc+w, where w (obtained by direct integration

of 2y/b, while Fig. 10 shows the chordwise distri- of V x w = C := V x v) has the property that w = 0

bution of the pressure coefficient (at 2y/b = .219). where C = 0. This decomposition has been success-

The present results are obtained with a chordwise fully applied to 2D steady full potential flows with

discretization N1 = 20 and a spanwise discretization boundary-layer correction (see Morino et al. [19])

N 2 = 12, and are compared with those obtained with and to 2D steady Euler flows, obtained as an exact

the method of Roberts and Rundle [26] with N, 1 = 39 correction to the full-potential solver (see lemma et

16-7

al. [10]). The coupling of Euler with the boundary [8] Gennaretti, M., Calcagno G., Zamboni A. and

layer is now under investigation. Morino L., 'A high order boundary element for-

mulation for potential incompressible aerody-

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16-8

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Paris, 1936.

16-9

Fig. 1. Isometric view of Prandtl plane. Fig. 2. Isometric view of wing of Prandtl-plane.

1.0 1.0

" Ellitic bplane0.6

0.78

0.8.

0.5

0.61______________________________-0.0 0.1 0.2 0.3 0.4

Cib0.0 0.1 0.2 Gb 0.3 0.4 0.5

Fig. 3. Effect of winglets on Prandtl factor: rectangular Fig. 4. Effect of wake roll-up on Prandtl factor: box-wing

biplane (b/c =10, c = 5', unstaggered). body (b/c =10, ce 50, unstaggered).

1.0 0.150

-Prandtl BWS0.9 +-±Prandtl plane (i) 0.125 - Numerical (Gall and Smith)

**Prantl plane (b 0 Experimental-ePrandl plane (c) ~ rsn omltoPa"" 'WS0.100

0.8

c)0.075

0.7

0.050

0.00.025

0.5 ______________________________0.00 0,10 0.20 0.30 0.000

Gb-0.2 0.0 0.2 0.4 0.0 0.0 1.0G/b CI

Fig. 5. Effect of sweep anglc on Prandtl factor: Praurdtl- Fig. 6. Polar of box-wing body (aspect ratio 5, G/c =1,

plane. stagger = c, sectioin: NACA 0012) at Re = 5.1 i105.

16-10

0.055 7 5*y

-Prandti-plane (a)

0,045 Prandtl-plarre (b)-Prandll-plane (c)

in

'00.035 .25

0.025

9.

0.015 1.0-0.1 0.0 0.1 0.2 0.3 0.4 0.5

Cl2<

Fig. 7. Effect of sweep angle on polar of a Prandtl-plane at Fig. 8. Planform of wing with strakeRe = 2.7 - 10' .

0.125 1.0

0100

0.0

0.075

do Cp

0.050-Third-ordler (2012) 1-Thr-rdr)2x*Ref. [251 (39x24) 1.0Thr-de 2x2

+ Ref. 1r20] (38x 12) Ref. (25] (39x24)

0.025 +01.[26] (38x12)

0.000 -2.0-0.0) 02 04 2b 0.6 08 10 00 0.2 0.4 XC 06 0.63 1.0

Fig. 9. Spanwise distribution of the circu~lation, a =50, Fig. 10. Chordwise distribution Of tloe C',, a1 5'70.2109.

0012. 3.5

000 3D lornriualion

002 Milew~ski -3D formulation0 Experimental 30 Milewski

0.00420 formulation

2.5

0 0.06

200004

0.002 ._.. 15.......

00 0.2 04 00 . 0.0 0.2 0.4 06 0 8 1.05./C 5.'C

Fig. 11. Clicreiwise dlistributioin of 3* at Pe 2. 1 .toe, Fig. 12. C hoidwis c distribution of shiape factor 11 at Jr,

ar =6.3', 20//b =0.5. 2.1 lt10r,a =t6.302 2y/b =0.5.

16-11

DISCUSSION

Session II, Paper #16

Herr Sacher (DASA, Germany) asked how the engine would be represented in the potentialapproach.

Prof Morino noted that in the past, the engine has been represented by a prescribed flowat the inlet with a rigid surface. As this rigid surface should be coincident with the actualstream surface, iteration is required to determine this shape. In this present work, theapproach is to model the jet with a prescribed uniform flow plus a wake (doublet layer) tomodel the velocity discontinuity between the jet and the surrounding flow. It was notedthat this would be an ideal application of the viscous flow extension discussed during thepresentation.