(c)l999 American Institute of Aeronautics & Astronautics

\ A99-33384 AIAA-99-3146

b bt B C CL

G

C ma

CN

C%

d D f g h hi I L

B S

The Interactions Between a Canard and Thick Bodies Part II: Analysis of the Interactions

Asher SigaI*

Faculty of Aerospace Engineering Technion - Israel Institute of Technology

Haifa 32000, Israel

A modular model, consisting of cruciform canard controls mounted on a thin forebody and five interchangeable thick main bodies, was tested at a Mach number of 0.8. The canard was installed at the + and x positions, and at deflection angles of 0,6, and 12 deg. The model was equipped with two sting balances, in a setup that enabled the extraction of the loads acting on the canard unit and those acting on the bodies. Four interactions are identified and quantified in this part: effects of the canard on the thickening of the main bodies and on the boattails, at angle of attack and due to canard deflection. These interactions are analyzed using a methodology that estimates the effect of change of diameter of the main bodies on the lateral position of the trailing canard vortices and on their images. The results of the analysis are in good agreement with the test data for the main bodies, and in fair agreement for the boattails.

Nomenclature

forebody boattail main body canard controls lift coefficient pitching-moment coefficient pitching-moment curve slope normal-force coefficient normal-force curve slope reference length, diameter of the forebody diameter of main body lateral position of a trailing vortex lateral position of an image vortex vertical position of a trailing vortex vertical position of an image vortex influence factor lift force radial coordinate in the transverse plan body radius body cross-section area

*Associate Fellow. ALAA. Presently: Adiunct Professor, Dept. of Aerospace Engineering, SDSU,. San- Diego, CA. E-mail: sigal@kahuna.sdsu.edu

Copyright 0 1999 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

SR reference area, (rt/4)d2 XcP center of pressure location % radial velocity component in the transverse

plane U free stream velocity Greek

; angle of attack canard deflection

CJ strength of source P air density l- circulation Subscript 1 thickening of main body

C canard bt boattail f front balance m main balance

Introduction

Part I of this article, Ref. 1, describes a wind-tunnel investigation of a modular model, consisting of a canard unit mounted on a thin forebody and five interchangeable thick main bodies. Ref. 1 gives the geometry of the model, the test conditions, and the measurement system. It emphasizes the aerodynamic characteristics of the bodies alone and of the canard unit. It also identifies the effects of the

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main bodies on the canards: a slight decrease of the normal-force curve slope and of the normal-force due to canard deflection, as main body thickness increases.

The present part identifies the effects of the canards on the thickenings of the main bodies (the ogives connecting the forebody to the main bodies) and on the boattails, and analyzes these effects.

The Interactions

The Models and the Tests A schematic of the test model and designation of the modules are depicted in Fig.1. The main body was mounted on a six-component sting balance, as can be seen in Fig. 2. The forebody was mounted on a short five-component balance (no axial-force). This arrangement provided the canard unit (forebody and canards) loads and the entire configuration loads, thus enabling the extraction of the canard-main-body interactions. Mach number of the tests was 0.8 and angle of attack was varied between -6 and 14 deg. The canards were tested in the + and x positions, and at deflection angles of 0, 6, and 12 deg.

Characteristics of Canard-Body Configurations Test results of the canard unit, mounted on body b- B20, and of the total configuration are presented in Figs. 3 and 4, for the + and the x positions, respectively. The normal-force coefficients obtained by each balance are presented as a function of the appropriate angle of attack. However, the differences between forebody and main body angles of attack, which results from the bending of the front balance, are small. The normal-force curve slopes of the configurations are slightly larger than those of the canard units. The non-linear components of the normal-force curves of the configuration are larger than those of the canard unit, indicating the contribution of the body. When the canards are deflected, the normal-force coefficients of the configuration, at zero angle of attack, are lower than those of the canard unit. AS angle of attack increases, the normal-force curves of the configuration cross over those of the canard unit, and increase without saturation. For undeflected canards, the initial slopes of the pitching-moment curves (C, vs. CN) are smaller than those of the canard unit, indicating a more rearward center of pressure location, due to the

contribution of the bodies. The pitching-moment curves of the canard unit cluster, indicating that the center of pressure of this unit is practically independent of deflection or roll position (detailed analysis of this issue is given in Ref. 1). For deflected canards there are positive total pitching- moments at zero normal-force, indicating the existence of moment couples. As normal-force coefficient increases, the center of pressure location of the configuration, indicated by the ratio C,/CN, moves rearward due the nonlinear contribution of the body.

Similar results were obtained with the other bodies. The above mentioned effects are more pronounced as D/d increases.

Canard on Main Body Influences The contributions of the plain main bodies to the stability derivatives were obtained by applying Eqn. (1) to the data of the configurations with undeflected canard.

CNa 1 = CNu. m-CNa f

C = c, m-c, f

xc;;d = C, ,/CN , (1)

The results are plotted in Fig. 5, together with those obtained for the bodies alone. It is apparent that the normal-force curve slopes of the thickenings of the main bodies are reduced by the presence of the canard. The center of pressure locations of this contribution is more forward? relative to the case of bodies alone. This indicates that the down load, that reduces cNa ,, acts more aft than the center of pressure of the thickenings of the bodies alone.

Define canard on main body influence factor by

I, = cNa i(b-C-B*&, ,(b-B*)-1 (2)

The average value, based on the data presented in Fig. 5, (one irregular datum excluded) is

I, = -0.25

As mentioned above, the total normal-force coefficients at zero angle of attack, obtained by the main balance are smaller than those obtained by the front balance. The negative differences are shown in Fig. 6. Define a second influence factor by:

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Is = AC,., ,/CN f (3.a)

where ACN i = CN ,,, -CN f at a--O. (3.b)

Dividing A& i by CNa i of the matching isolated body yields that the induced loads correspond to the effect of a downwash of 1.8 or 4.0 deg., for canard deflection of 6 or 12 deg, respectively. The dependence of Is on diameter ratio and canard position is discussed in the next chapter and is shown in Fig. 8.

Canard on Boattail Influences The contributions of the boattails to the normal- force curve slopes, in the presence of the canard, were obtained by subtracting the stability derivatives of configurations having plain bodies from those of matching configurations having boattails. The findings are summarized in Table 1.

Table 1 The characteristics of the boattails in the presence of the canard

CNab( \ coxllig. b-C-B20bt bGB25bt With canard at + -2.13 -4.63 With canard at x -2.45 -4.75 Bodies alone -4.14 -7.80

The presence of the canard considerably reduces, in absolute value, the contribution of the boattails to the normal-force curve slopes. Similar to the first interaction, define a boattail influence factor by

I a bt = Ga b,(b-C-B *bt)/CN, b,(b-B *bt)- 1 (4)

The average value, based on the data given in Table 1, is

I, bl = -0.42.

The total normal-force coefficients of configurations with boattails, at zero angle of attack and with deflected canards, are larger than those of the matching plain configurations. Similar to the second influence factor, define

16 bt = ACN b&N f (54

where ACN br = CN ,(b-C-B*bt)-C, ,(b-C-B*) at a=O. (5.b)

The experimentally obtained average values (between 6 and 12 deg deflections) are given in Table 2.

Table 2 The boattail influence factor due to canard deflection

&jbt \ config. b-C-B20bt b-GB25bt canard at + 0.040 0.070 canard at x 0.046 0.102

Analysis

Review of the P-N-K Methodology Analysis of the effect of vortex system on afterbodies is included in Pitts, Nielsen and Kaattary’s classic NACA Rep. 1307 (Ref. 2). They modeled each lifting surface by a horseshoe vortex, whose bound section produces lift L’ = puT per unit span. The external trailing vortex is a free vortex, while the internal vortex is an image of the external one, which satisfies the tangency conditions on the body.

The relationship between the circulation and the lift produced by the canard unit is

r = %US& &f-g), (6)

For slender fins, the source of the trailing vortex is at

f, = r,+(x/4)(s-r), (7)

The location of the image vortices is given by

g = fr2/(f2+h2) hi = hr2/(f2+h2)

(8)

The net lift carried on a body section, located downstream of the canards, is

AL = -2puTA(f-g) (9)

where A(f-g) is the change of (f-g) along that body section. The non-dimensional form of Eqn. (9) is

ACL = -(4TAJSa)A(f-g) (10)

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With regard to the location of the free vortices, the authors of Ref. 2 refer to the “step by step” analysis (vortex tracking) of Rogers3 However, their own analysis assumes that the free vortices are convected in the direction of the free flow.

The Present Methodology In order to apply Eqn. (10) there is a need to know the trajectories of the free vortices downstream of the canard trailing edge. Vortex tracking was explored for the study of vortex roll-up (e. g. Rogers3 or Spreiter and Sacks4) and for the analysis of wing-tail interaction (e. g. Edwards and H&do’). Their analysis considered two contributions to the displacement of the vortices: the cross-flow over the body at angle of attack, and the mutual induction of the vortices. Slender-body theory was used for the former and two-dimensional vortex theory for the later. Nielsen6 (in Chapter 6) and Hemsch’ provide additional details and references. More advanced vortex trackers are being used in several component buildup codes, e. g. Portnoy’ or Lesieuire et a1.9 These trackers require numerical integration along the body.

The emphasis of this work is on the effect of variable body diameter at small angles of attack. It is expected that in this case the changing diameter will dominate the lateral displacement of the vortices. Thus, an approximate approach was sought, that will yield an analytical solution, rather than a need for numerical integration.

According to subsonic slender body theory, i. e. Ashley and Landahl” or Katz and Plotkin,” the local source strength, representing a slender body at zero angle of attack, is

o/U; = dS(x)/dx = 2xRdR/dx (14)

The radial velocity component induced by it, at small distances from the axis, is approximately

q,N = (1/2m)dS/dx = R/r (15.a)

Since free vortices are aligned with streamlines

q,N = drfdx = Iur (15.b)

Integration yields:

r2-R2 = r,2-R2 (a constant) (16)

The physical interpretation of Eqn. (16) is that at zero angle of attack, the free vortices coincide with the outer surface of an incompressible hollow stream tube, whose inner surface is the body.

Validation The application of the present analysis to the test data is done for zero angle of attack, in compliance with the definitions of the influence factors. Only the radial displacement of the canard vortices, as described by Eqn. (16), is being considered. Substituting Eqn. (6) into Eqn. (10) yield

ACL = CL c A(f-@/(f-g), (17.a) A% = C, c WgY(f-g), (17.b)

Ignoring the small differences between CL and CN, the above influence coefficients become

Ia = CNa&Na l(b-B) Nf-g)l/(f-g)c (184 I6 = A(f-g),/(f-g)c (18.b) Ia bt = CNa&Na b&B> A(fig)bd(f-g)c (18.~)

1s bt = A@-&b&f-Ed, (18.d)

The ratio A(f-g)/(f-g),, which is the normalized change of the lateral distance between the trailing vortices and their images, is summarized in Table 3. For near zero angles of attack and weak vortices, the influence coefficients are independent of the roll position.

Table 3 Vortex lateral distance parameter

D/d 1.5 2.0 2.5 A(f-g),/(f-g)c -0.052 -0.110 -0.176 A(f-g)&f-g), - - 0.060 0.124

A similar analysis, assuming that the free canard vortices trail in the direction of the free stream, gave values that are 2 to 3 times larger than those given in Table 3. This shows the importance of tracking the vortices for the analysis of the interactions.

Ia

&e experimental data was obtained by applying Eqn. (2) to the data presented in Fig. 5. The analytical prediction was obtained using Eqn. (18.a), experimental data for the normal-force curve slopes of the canard unit and of the thickening of the main bodies, and the calculated vortex lateral

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distance parameter given in Table 3. A comparison between test data and analysis in presented in Fig. 7. The analysis overestimates, in absolute value, the data. The average analytical value is -0.31, namely 2 1% larger than the average experimental value.

The experimental data was obtained using Eqn. 3, the data summarized in Fig. 6 and experimentally obtained characteristics of the canard unit. The analytical values, according to Eqn. (18.b), are taken from Table 3. Fig. 8 compares the results of the analysis with those of the test. It is apparent that the analytical curve is in the middle of the test data.

-LB.l The test data was obtained by applying Eqn. (3) to the data given in Table 1. The analysis uses Eqn. (18.~) and experimental data for the characteristics of the canard unit and the isolated boattails. The average analytical value is -0.34, namely 19% smaller, in absolute value, than the experimentally obtained average value.

Comparison of Table 2 and the bottom line of Table 3 show that the analysis overestimates the experimentally obtained data by an average of 4 1%.

Summary and Conclusions

The wind-tunnel test data of Ref. 1 were processed and four interactions between a canard and thick bodies were identified: effects of the canard on the thickenings of the main bodies and on the boattails, at angle of attack and due to canard deflection.

An approximate vortex tracker, which is based on slender body theory, is used to estimate the change of the radial location of the canard trailing vortices along the body, at zero angle of attack.

The canard on body interactions were analyzed, using the concept of Pitts, Nielsen and Kaattary, coupled with the present estimate of the vortex positions. The calculated results agree well with the experimentally obtained data for the main bodies, and are in fair agreement for the boattails.

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References

&gal, A., and Victor, M., “The Interactions between a Canard and Thick Bodies, Part I: Characteristics of the Components,” AIAA-97- 2249, June 1997. Pit& W. C., Nielsen, J. N., and Kaattari, G. E., “Lift and Center of Pressure of Wing-Body- Tail Combinations at Subsonic, Transonic, and Supersonic Speeds,” NACA report 1307, 1957. Rogers, A. W., “Application of Two- Dimensional Vortex Theory to the Prediction of Flow Behind Wings of Wing-Body Combinations at Subsonic and Supersonic Speeds,” NACA TN 3227,1954. Spreiter, J. R., and Sacks, A. H., “A Theoretical Study of the Aerodynamics of Slender Cruciform-Wing Arrangements and their Wakes,” NACA Rep. 1296, 1957. Edwards, S., and Hikido, A., “ A Method for Estimating the Rolling Moment Caused by Wing-Tail Interference for Missiles at Supersonic Speeds,” NACA RM A53H18, 1953. Nielsen, J. N., “Missile Aerodynamics,” MC Graw-Hill, Inc., New York, 1960. Hernsch, M. J., Component Build-Up Method for Engineering Analysis of Missiles at Low-to- High Angles of Attack,” Chapter 4 in “Tactical Missile Aerodynamics: Prediction Methodology,” Progress in Astonautics and Aeronautics, Vol. 142, AIAA Publication, 1992. Portnoy, H., “Calculation of the Aerodynamic Forces and Moments on Complex Cruciformed-Winged Missile Configurations up to Intermediate Angle of Attack,” Israel Journal of Technology, Vol. 23, Nos. l-2, 1986, pp. 33-46. Lesieutre, D. J., Mendenhall, M. R., Nazario, S. M., and Hemsch, M. J., “Aerodynamic Characteristics of Cruciform Missiles at High Angles of Attack,” AIAA-87-0212, Jan. 1987. Ashley L., and Landahl, M., “Aerodynamics of Wings and Bodies,” Addison-Wesley Publishing Co., Inc., Reading, MA, 1965. Katz, J., and Plotkin, A., “Low-Speed Aerodynamics, ” McGraw-Hill, Inc., New York. 1991.

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025 --------- .- -.- - - - - - -.-

_ -0 Gq;

625-bl ______- -23”

Fig. 1 Schematic of the model and designation of the modules.

LFROt4T BALANCE h4AlN BALANCE

Fig. 2 General assembly of configuration b-COO-B15

b-COO+-820. main. Y10.6 0 b-COO+-820. front. bk0.B

A b-Cob+-820. moln, Y=O.B 2 V b-C06+-820. front. YsO.8

q b-C12+-B20. maln. ikO.8 0 b- Cl2+-BZO. front. YrO.6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-8 0 8 16 -4 0 4 8 12 a CN

b-COO+-820. main. Y=O.

b-COO+-820. front. Y=O. b-COB+-BZO. moln. Mz0.i

b,C06+-B20. front. Y=O.,

b,C12+-B20, moln. Y=O.C b,C12+-820. front. Y10.e

E o 0”

B

B 6 1 B I

I . .

,...

Fig. 3 Test results of the canard unit and the total configuration at the + position: a) normal-force coeffLzient vs. angle of attack, and b) pitching-moment coeffbzient vs. normal-force coeftlcient.

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0 b-COOX-820. maln. U=O.8

0 b-COOX-820. front. Y=O.,kl

A b-COSX-B20, maIn. UsO.8 V b~CO6X~B20. front. Y=O.B

0 b-C12XJ20. main. Y=O.8 & b-C12XJ20. front. Y=O.8

0 a 16 a

:: 0 b-COOXJ20. maln. Y=O.B 0 b-COOX-620. tront. Moo.8

A s

beCObX-B20. maln. U=O.8

V b-C06XmB20. front. Y=O.8

0 b-C12X-820. maln, Y-O.11

D b-C12Xe820. tront. Y=O.8

4 CN

a -4

Fig. 4 Test results of the canard unit and the total configuration at the x position: a) normal-force coefficient vs. angle of attack, and b) pitching-moment coefficient vs. normal-force coefficient.

‘a zm u

1 i E$JiJ+j

. . . ..i.......................... : 0”““““’

fi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..I............ 0 ;

i . . . . . . . 8. ; . . . . . . . . . . . . P

0

1.5 2.5

00

m I

0 bodies alone 0 rlth canard +

0 with canard X

-...........1.............1............:,..........

8 ; ;

; B

A 6 -...........__....__...................~..........

4 , ,

1.5 2.5

Fig. 5 The stability derivatives of the plain main bodies in presence of the canard: a) normal-force curve slope, and b) center of pressure location.

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s 0

0

m d I

h! i

0 0 b-COB+-B b-COB+-B

A A b-Cl2+-8 b-Cl2+-8 . L-J . L-J 0 0 b-COIX-E b-COIX-E V V b-CUX-B b-CUX-B

-........... + . . . . . . . . . . ..i . . . . . 0 . . . . . . . . . . -........... + . . . . . . . . . . ..i . . . . . 0 . . . . . . . . . .

z z

-...........I.............:............I........... -...........I.............:............I...........

1 I I

1.5 1.5 2.5 2.5

1 Fig. 6 The aerodynamic loads induced by canard / deflection on the plain main bodies.

Fig. 7 The influence coeffkient on the main bodies at angle of attack.

I 1.5 2.5

N

9 0

-? ‘:

1 : ~I2J

~...........~..........................~............. 4 0 I

6 $

I ! I 1.5

Did

2.5

( Fig. 8 The inthence coefficient on the main I bodies due to canard deflection.

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