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A new class of airfoils with slot suction - AIAA 96-0058 A...

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Unformatted text preview: AIAA 96-0058 A New Class of Airfoils with Slot-Suction Farooq Saeed and Michael S. Selig University of Illinois at Urbana-Champaign Urbana, IL 34th Aerospace Sciences Meeting & Exhibit January 15-18, 1996 / Reno, NV For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 370 L'Enfant Promenade. S.W., Washington, 0.0. 20024 A NEW CLASS OF AIRFOILS WITH SLOT-SUCTION Farooq Saeedl and Michael S. Selig‘ Department of Aeronautical and Astronautical Engineering University of Illinois at Urbana—Champaign Urbana, Illinois 61801 ABSTRACT In a recent paper by Saeed and Selig, a gener- alized method for the multipoint inverse design of airfoils with slot-suction was proposed and success- fully implemented. The new inverse design method for slot-suction airfoils, unlike earlier design meth- ods, not only addresses key issues particular to slot- suction airfoils but is also capable of multipoint de sign. To illustrate the underlying principles of the theory behind the new inverse design method for slot-suction airfoils, the theory as applied in the de- sign of Joukowski airfoils with slot-suction is pre- sented along with a few examples. The examples illustrate important differences and improvements over the existing design methods. In light of these developments, the more generalized method of Saeed and Selig is used to design airfoils with slot-suction for a variety of aircraft ~ ~ications, such as. thick airfoils for all-wing spamuaders, airfoils for maxi- mum lift, aud airfoils with extended length of lami- nar flow. NOMENCLATURE b = location of the suction-slot, C = Re"‘9 c = airfoil chord C; = airfoil drag coefficient C: = airfoil lift coefficient 09 = slot-suction coefficient, Q, / Vooc d = location of the stagnation point down- stream of the suction-slot, C = Re“ D = airfoil drag f = front stagnation point, C = Re“ F,, F, = 1: and y components of force F(z), F (C ) = complex potential functions L = airfoil lift Mo = airfoil pitching moment R = circle radius Q, = suction strength t = rear stagnation point, C = Re“ Copyright © 1996 by Farooq Saeed and Michael S. Selig. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. t Graduate Research Assistant. Student Member AIAA. 1 Assistant Professor. Member AIAA. t /c = airfoil thickness to chord ratio 5 relative design velocity distribution across the slot-suction segment V.» = freestream velocity z(¢), y(¢) = airfoil coordinates z = airfoil-plane complex coordinate, a: + iy z" = trailing-edge location in the z—plane a0], = the angle of attack for zero-lift B = location of the suction-slot I‘ = circulation strength 6 = location of the stagnation point downstream of the suction-slot e = trailing-edge angle parameter C = initial circle-plane complex coordinate, E + in or Re“ C0 = a real constant I: = thickness control parameter 9) = camber control parameter, 2‘: - A p = fluid density INTRODUCTION The fact that large lift coefficients can be obtained from thick airfoils with active boundary-layer control (suction and/or blowing) without separation has not only been predicted through analytical models such as those of Glauert"3 but has also been confirmed through numerous experimental studies."9 An in— herent advantage of these airfoils is that large lift co- efficients can be obtained as compared to the conven- tional airfoil configurations. Moreover, very thick airfoils could also be designed that exhibit laminar flow characteristics over a greater part of the sur— face throughout a CL-range which is large enough to completely cover the normal flight range, and which are also thick enough to provide ample room for the stowage of engines, passengers and other loads with- out the possibility of flow separation. The possibilty for such efficient cruise perfor- mance and structural arrangements has revived interestm'“ in advanced concept transport air- craft with active boundary layer control (suction and/or blowing), such as the Goldschmied’s thick- wing spanloader all-freighter,m shown in Fig. 1, or a more recent high-lift system concept,11 Fig. 2, for the C-Wing configuration of the McDonnell-Douglas Fig. 1 Layout10 of the modified GLAS II 31.5%thick laminar-flaw airfoil with a 10.3 in chord. Blended Wing Body concept, shown in Fig. 3. Ow— ing to the renewed interest, it was felt necessary to design a new class of airfoils that employ slot-suction which could be used in the aircraft sizing studies to examine the potential payofi' for boundary-layer con- trol as applied to the advanced-concept wings. A common factor among the numerous aircraft sizing studies, related to the design of the advanced concept configurations with active active boundary layer control, has been the use of the classical inverse design approach of Glauertl'3 in the design of airfoil sections that employ slot-suction. In a more recent study,16 it was shown that Glauert’s airfoil did not employ suction but a step drop in the velocity and, therefore, on this basis a new inverse design method for airfoils that employ slot-suction was proposed and successfully implemented. The new method,16 which is bmed on conformal mapping, draws on the theory of first published by Epplerw'm and extended by Selig and Maughmer.19 Unlike the existing inverse design methods“3 for slot-suction airfoils, the new method16 not only ac- counts for the effect of true suction at the slot- location, i.e., the velocity increases in front of the slot and decreases behind it,20 but it is also car pable of multipoint design. This makes it a more practical and versatile tool for the design of slot- suction airfoils. Moreover, unlike earlier methods, the new method can address certain issues, for ex- ample, it can relate the amount of pressure recovery with amount of suction and vice versa. In light of the new developments, a need arose to re-evaluate the existing applications of earlier design methods for slot-suction airfoils. Therefore, the main focus of this paper is to re-evaluate existing design concepts as well as applications of slot-suction airfoils on the basis of the new design method now available. In order to illustrate the underlying theoretical ba- Fig. 2 High-Lift system concepts11 for 18% transonic Griffith air-foils. Fig. 3 The McDonnell-Douglas Blended Wing Body (BWB) concept.11 sis of the new method for a generalized multipoint inverse design of airfoils with slot-suction,14 the the- ory, as applied to the design of Joukowski airfoils with slot-suction, is presented in the next section. In the later sections, the more generalized multipoint inverse design of airfoils with slot~suction is applied in the design of airbils for various applications, such as, thick airfoils for all-wing spanloaders, airfoils for maximum lift, and airfoils with extended lengths of laminar flow, to name a few. JOUKOWSKI AIRFOILS WITH SLOT-SUCTION Theory The flow in the C-plane is modeled by the pres- ence of a uniform flow of unit velocity at an angle of attack a, a. vortex of strength I‘ at the origin and a point sink of strength Q.(Q, < 0). The sink is placed at C = b in the flow field so that when a cir- cle of radius R centered at the origin is added to the flow, using the Milne-Thomson circle theorem,”1 it falls on the boundary of the circle at C = b = Re“. The complex potential for the flow field with the circle added is given by 2 F(C) = e"" + slag;— Q: 32 - .I‘ +'2—1r (T—b)+t2—Ilnc (l) + gm“ — b) and where l":41rRsin(a- A)-Q, cot(fi 2 A) (2) is the circulation strength required to satisfy the Kutta condition by filing the rear stagnation point at C = t = Re“. Since a stagnation point must exist downstream of the suction slot, say, at C = d = Re“ on the circle, imposing this condition requires that . A — ,6 . fl — 6 A - 6 Q. -— 81rRsm( 2 )sin( 2 )cos(a—T) (3) The front stagnation point is then located at C = f: Re” where7 = 1r+2a+fi-—6—-A and the complex velocity is given by a0-2)(l-z><l-2)"(x-%)e-~ which on the circle C = Re“ becomes 77:"- Ln: “4"?) “(g-6) WE") cos(———-—¢ - fl 3- 6 + A - a) fwd/2) (5) To obtain the flow about a Joukowski airfoil in the z-plane, the flow about the circle in the C-plane is mapped via the Joukowski tranformation, z = z(C). The flow about the Joukowski airfoil in the z-plane is then determined from the following relation E = (dF/dchny. dz My. “(dz/dam.» In order to resolve the singularity at the trailing edge stagnation point, since Eq. (6) becomes inde- terminate there, L’Hospital rule is applied to Eq. (6) which yields the following result. (6) lim £-—lsin(A-6) A—fl z-z..dz ‘ R 2 c“ 2 sin (lg-Z) £4” (7) Ail-foil Lift, Drag and Moment The forces and the pitching moment acting on the airfoil are determined from the Blasius relations, which are Mo = gm” . (3—9224 (9) where Cl is any closed curve that encircles the air- foil. The resulting airfoil lift and drag components of the forces are L = pI‘, D = —pQ, (10a,b) which in coefficient form are C: = 2r/C, 04 = —2Q,/c (110,5) Substituting Eqs. (2) and (3) into the above yields C; = Eggsmw— A)- 2—Q'-cot(fi-’\) (12) c 2 Ca = 16:}: sin(fi;’\) sin(fi;6) moor-1%!) (13) where c is the airfoil chord. As mentioned in Ref. 16, the lift-curve slope is still nominally 21', with suction Q, providing an ofi'set to the lift coefficient. More- over, an expression for the angle of attack for zero- lift on can be obtained from Eq. (12) by setting 01 equal to zero. It is given by _ . -1 Q: g "‘ ’\ am, _ A+sin [—41]; cot( 2 )] (14) It shows that the angle of attack for zero-lift an], not only depends on the amount of suction Q. but also on the location of the suction slot fl. the location of the trailingvedge stagnation point A, and the radius R. Using the definition of the slot—suction coefficient, Cq and comparing it with Eq. (11b) yields the result C4 = —2qu (14) Since Q, < 0 corresponds to suction, the analy- sis indicates that suction not only results in an in— creased lift coefiicient due to the increased circula- tion around the airfoil, but *0 results in a positive value for the drag coefficient purely due to suction. The exprwsion for the pitching moment about the origin of the z-plane (positive clockwise) is given by Mo = 2pQ.{Rsin(a — H) + C. sin(a - x)} — pC.{Q, sin(a — It) + I‘cos(a — 06)} pm. (15) I + 2rpsin 2a — Implementation The results from the theory were implemented in a computer program. In the program, the angle of attack a and the suction strength Q, are kept as the control variables while the suction slot location 5, the trailing-edge stagnation point location A, the camber control parameter a: and the thickness con- trol parameter It are fixed a design variables. The location of the stagnation point downstream of the suction-slot, i.e. 6, is determined numerically for the specified value of the suction strength Q. and the de- sign variables such that either (A-21r) < 6 < 5 if the suction slot is on the upper surface, i.e. 0 < [3 < 7, or B < 6 < A if the suction slot is on the lower surface, i.e. 7 < 3 < 21. Figure 4 shows the results from a typical analy- sis run, which, illustrates the effects of varying the amount of suction Q, (Fig. 4(a)) and the angle of attack a (Fig. 4(b)) on the velocity distribution and the aerodynamic characteristics of the Joukowski airfoil. The values of the design variables in the example presented in Fig. 4 are; B = 100.5 deg, A = 355 deg, ac = 140 deg, w = 5 deg, R = 1.1207 and (o = 0.152. Interpretation of Results The results indicate that the magnitude of velocity becomes infinite at the suction-slot which is then immediately followed by a stagnation point. If the effects of true suction are accounted for, then ideally one should expect such a behaviour.20 The airfoil in Fig. 3(a) has a C; that varies from 1.209 to 1.322 and (8) {IE Fig. 4 Velocity distribution over a Joukowski airfoil: (a) with and without suction at a = 5 deg (b) with a constant suction of strength Q, = —0.1 at different angles of attack. a C; that varies from 0.000 to 0.148 as the amount of suction Q, is increased (more negative) from 0.0 to -0.3 at a constant angle of attack a = 5 deg. The airfoil in Fig. 3(b) has a C; that varies from 0.644 to 2.420 and a constant C; of 0.049 as the angle of attack is increased from 0 to 15 deg with the same amount of suction Q, = —0.1. The explanation for this high value of the drag co- efficient is as follows. If the forces of the airfoil are being measured on a balance, the measured drag co— efficient will include an amount —2Q,/c due to the removal of air; this quantity should therefore be sub- tracted to give the drag due to the wake alone.20 For this, it is assumed that the fluid removed by suction is discharged so that its static pressure and velocity are identical to the pressure and velocity at infin- ity or, in other words, there is no loss of momentum within the suction system. Thus, the suction system contributes zero drag and the wake drag is the to- tal drag which ha to be overcome by the propulsive system. In reality, the efficiency of the suction sys- tem will dictate the actual contribution of the drag due to suction to the total drag. As evident from these example, a significant amount of prwsure recovery can be achieved by em- ploying suction in the vicinity of the trailing edge. This fact alone is useful in many of the applications related to the advanced-concept wings. For exam- ple, suction could be employed over very thick wings to prevent separation of the boundary-layer, which would otherwise result in a huge drag penalty. As another example, thin airfoils could be made to op- erate at very high angles of attack without flow sep- station. To explore these interesting ideas, a method16 for the multipoint inverse design of airfoils with slot-suction was formulated and successfully applied in the design of airfoil with slot-suction. A brief overview of the method is given in the next section along with design of slot-suction airfoils for various applications. A GENERALIZED METHOD FOR SLOT-SUCTION AIRFOIL DESIGN Overview ofthe method The generalized multipoint inverse design method“ls for slot-suction airfoils is based on the the- ory first published by Epplerlma and later refined by several others but primarily draws on the work of Selig and Maughmer”. The method is based on conformal mapping. Multipoint design is achieved by dividing the airfoil into a number of segments and then specifying the desired velocity along with the desired angle of attack, the location of suction slot, and the munt of suction for each segment. Like in any inverse design method, specification of velocity is not completely arbitrary and is subject to three integral constraints and several conditions that must be satisfied in order for the multipoint inverse design problem to be well posed. Additional restric- tions result if the airfoil is to have a specified pitching moment, thickness ratio, or other constraints. The resulting system of equations is then solved partly as a linear system and partly through multidimensional Newton iteration. In the next section, the generalized multipoint in- verse design method16 for slot-suction airfoils is ap- plied to obtain airfoil sections that were designed us- ing Glauert’s approach and are being used in aircraft sizing studies of some of the advanced concept air- crafts. Apart from its multipoint design capability,"3 the new method is not only able to relate pressure recovery to the amount of suction but also is capable of predicting the component of the drag coefficient due to suction alone. 0n the basis of which, the power requirements for the suction system could be determined. Application A class of suction airfoils was designed by Glauertl-a based on the idea suggested by Dr. A. A. Griffith that an airfoil could be de- signed with a favourable pressure gradient every- where along the chord except at one location where there would be a discontinuity and a sharp pressure rise. If suction was applied just ahead of the loca~ tion of discontinuity, potential flow would exist and flow would not separate. By applying this method, Glauert designed the GLAS l-IV series of suction airfoils. GLAS stands for Griffith Laminar Airfoil (with) Suction. As mentioned earlier, Glauert’s design method for the design of slot-suction airfoils does not take into account the effects of true suction at the slot loca tion. Figure 4 clearly indicates that for slot suc- tion on an airfoil, a stagnation point must exist on the airfoil surface just downstream of the slot. Glauert’s airfoils do not exhibit this characteristic feature. Moreover, there is no specified parameter related to the amount of suction. Instead, the veloc- ity d'ntributions of Glauert-type airfoils, Fig. 5(a), show a step drop in the velocity at the location of the slot. It was shown in Ref. 16 that this type of velocity distribution can be obtained by making the pressure recovery infinitely steep at the slot location. Math- ematically, a logarithmic spiral is used to represent this discontinuity. To achieve this physically, the suction slot must be included in the treatment of the discontinuity. In Fig. 5(b), a Glauert-type air- foil was designed with suction at the slot-location. As evident from Fig. 5(b), the flow experiences a fa— vorable pressure gradient which is seen as a rise in the velocity, as the flow enters or leaves the slot. A stagnation point also exists downstream of the slot- location. Figure 6’“ shows a comparison between the theo- retical and experimental velocity distributions over a GLAS II airfoil. The figure highlights the essen- (a) 2.4 2.0 1.0 0.0 0.4 -0.2 0.0 0.2 0.4 0.0 0.0 1.0 (b) 2.4 1.0 V 1 .2 0.0 0.4 0.0 43.2 0.0 0.2 0.‘ 0.0 0.0 1 .0 ale C} Fig. 5 Velocity distribution over a Glauert- type airfoil (a) without suction at a = 15.3 deg (b) with a suction of strength Q, = -0.00001 at a = 15.5 deg. tial difference in the behaviour of the flow in the vicinity of the suction—slot between the theoretical model, that uses a step discontinuity at the slot lo- cation, and experiment. A comparison between the experiment, Fig. 6, and the theoretical velocity dis- tribution, Fig. 5(b), obtained from the new method indicates that the presence of a sink at the slot lo- cation represents a good model for the flow in the vicinity of the suction slot. Thus, slot-suction airfoils could be designed using the new method, in a man- ner similar to Glauert’s approach, for applications where a favorable pressure gradient over the whole Fig. 6 Chordwise distributions of velocity'“‘1 on a 30 per cent thick Griffith airfoil. Fig. 7 Velocity distribution over the slot- suction airfoil at a = 5 dog and a suction strength of Q, = —0.02. airfoil chord is essential. Examples of such appli- cations include thick airfoils for all-wing spanloader configurations, maximum and high-lift airfoils. Examples of thick ail-foils for all wing span-loaders are shown in Figs, 1 and 2. The multipoint inverse design method for slot-suction airfoil was used to design a slot-suction airfoil, shown in Fig. 7, which is similar to the 18% transouic Griffith airfoil in Fig. 2. The location of the suction slot was fixed at 87% chord for the design. The velocity distribution along with the airfoil geometry are shown in Fig 7 at a = 5 deg and suction strength Q, = —0.02. At these (a) 10.2 0.0 0.2 0.4 as as 1.0 (b) Fig. 8 Velocity distribution over the airfoil at a = 12 deg (a) for different values of suction strength (b) for different values of net pres- sure recovery. conditions, the airfoil lift and drag coeflicients are 0.675 and 0.0116, respectively, based on the inviscid results since transonic flow is beyond the scope of th'm paper. Slot-suction could also be employed over the trailing-edge flaps to obtain high-lift. Since the ve- locity over the upper surface of a deflected trailing- edge flap, shown in Fig. 2, reaches a maximum near the hinge a...
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