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### Theme 14

1. 1. SECTION 3. AERODYNAMICS OF AN AIRPLANE THEME 14. AN INTERFERENCE OF AN AIRPLANE PARTS After assembling the aircraft separate parts into the whole their streamlining andaerodynamic characteristics change. It is caused by mutual influence of these parts i.e.interference. We can distinguish the interference of three types: 1) between the liftingand poorly lifting elements (wing and fuselage, tail-plane and fuselage, nacelle andwing and others); 2) between the lifting elements (wing and tail-plane); 3) between jetsof engines or props and parts of the aircraft. Lets find out physics of the interference ofthe aircraft various parts. 14.1. Geometrical characteristics of an aircraft The external shapes of an aircraft and its parts, their sizes and mutual arrangementproviding the obtaining of necessary aerodynamic characteristics are called asaerodynamic configuration. The aircraft aerodynamic configuration is characterized by presence of someseparate parts, their mutual arrangement and geometrical features. The followingaerodynamic configurations of the aircraft are the most widespread. Aircraft are distinguished by number of wings as biplanes and monoplanes. Thebiplane configuration contains two wings located one above another. This structure waswidely used at the beginning of aircraft development. Now the majority of airplanes areconstructed by the monoplane scheme, i.e. with one wing. There distinguish the normal airplane configuration, canard configuration,configuration “tailless” and “a flying wing” by presence and location of horizontal tailunit. Horizontal tail of normal configuration is located behind the wing. Thisconfiguration provides the favorable conditions for flow about wing, however 124
2. 2. horizontal tail is in the zone of disturbed flow caused by wing and on some modes canlose the efficiency. In the canard configuration the horizontal unit is placed ahead of a wing andworks in an undisturbed flow, but it effects the flow about wing. This influence can beboth negative and positive depending on the horizontal tail shape both wing and theirmutual arrangement. The airplanes of the configuration “tailless” have no horizontal tail and theconfiguration “flying wing” besides actually has no fuselage and vertical tail. For monoplanes one differs three configurations depending on wing installationby fuselage altitude: low-wing monoplane, mid-wing monoplane and high-wingmonoplane. Vertical tail, as a rule, is installed in a tail part of the airplane. Depending on thenumber of fins the aircraft can be designed on single-finned, twice-finned and multi-finned configurations, and on the number of fuselages the aircraft can be designed onthe single-fuselage and twice-fuselage configurations. The power plant essentially influences external shape of modern aircraft. Theengines can be mounted in a wing, on a wing, under a wing, under a wing on pylons, ina fuselage, under a fuselage, on a horizontal tail unit, in a fin. In the aircraft aerodynamic configuration its separate elements (wing, fuselage,horizontal tail, vertical tail, engine nacelles etc.) influence each other. Therefore, theaerodynamic characteristics of these elements will vary in aircraft system and at theisolated streamlining. One distinguishes a positive and negative interference, depending on whethertotal aerodynamic characteristics are improved (in certain sense) or became worse. Thiscircumstance is necessary for taking into account while aerodynamic designing. Physical features of interaction of lifting surfaces (such as wing, horizontal tail)with a fuselage, engine nacelles with a wing and fuselage, wing and horizontal tail willbe considered below. There are other kinds of interaction, for example, jets of the airprop or turbo-prop engines with elements of the aircraft, influence of the cargo plane 125
3. 3. onto dropped freights, influence of ground or water surfaces onto the aircraftaerodynamic characteristics etc. 14.2. Coefficient of flow deceleration. Generally wing, horizontal and vertical tail installed a fuselage will be flown withspeed different from speed of incoming flow V∞ . It occurs due to the influence ofviscosity and to the appearance of head shock waves at M∞ > M* . Coefficient of flowdeceleration is used for the account of this effect, which is a ratio of mean dynamicpressure before a considered aircraft element to dynamic pressure of undisturbedflow q∞ : kd wing = q w q∞ ; kd h.t . = q h.t . q∞ ; kd v .t . = qv .t . q∞ , (14.1) 2 2where q∞ = 0 .5 ρ ∞V∞ = 0 .7 p∞ M ∞ is the dynamic pressure of undisturbed flow; (q w = 0 .5 ρV 2 ) w ( , q h.t . = 0 .5 ρV 2 ) h.t . ( , qv .t . = 0 .5 ρV 2 ) v .t . is the dynamic pressurebefore a wing, horizontal and vertical tail-plane. One assumes, that density ρ = ρ∞ = const and pressure p = p∞ = const , we shallrecord: 2 2 2 2 Vw ⎛ Mw ⎞ Vh .t . ⎛ M h . t . ⎞ 2 Vv2t . ⎛ M v .t . ⎞ kd wing = =⎜ ⎜ ⎟ , k d h.t . = ⎟ =⎜ ⎟ , k d v .t . = . = ⎜ ⎜ M ⎟ . ⎟ 2 V∞ ⎝ M∞ ⎠ V∞ 2 ⎜ M ⎟ V∞ 2 ⎝ ∞ ⎠ ⎝ ∞ ⎠ At known coefficient of flow deceleration the Mach number M before an aircraftelement is determined by the following formulas: M w = M ∞ k d w , M h . t . = M ∞ k d h . t . , M v . t . = M ∞ k d v .t . . These numbers M are necessary for taking into account at calculating theaerodynamic characteristics of the isolated parts. For example, lift of a wing and its drag depend on M w = M ∞ kd w Сα λ = f ⎛ ⎜ M w − 1 , λ tgχ , η ⎞ , С xв λ c 2 = f ⎛ M w − 1 , λtgχ , η ⎞ . 2 ⎟ ⎜ 2 ⎟ ya ⎝ ⎠ ⎝ ⎠ 126
4. 4. Lets consider the process of flow deceleration. At the beginning we shall studyflow about a wing (horizontal tail), located on a fuselage. In a subsonic flow( M∞ < M* ) speed deceleration before a wing for the normal configuration and beforehorizontal tail for the canard configuration occurs only in a boundary layer on a part of afuselage located ahead of a wing or horizontal tail. Taking into account that thethickness of a boundary layer δ * is much less than wing span or tail span, it is possibleto assume kd wing = 1 , kd h.t . = 1 , kd v .t . = 1 . Shock wave occurs before a fuselage nose in a supersonic flow M∞ > 1 (Fig. 14.1). Flow rate decreases behind the shock wave. The amount of flow deceleration coefficient depends on intensity of the Fig. 14.1. shock wave. In turn, intensity of theshock wave depends on wave drag of the fuselage nose and number M ∞ . Approximately it is possible to adopt that: {kd wing , kd h.t . , kd v .t .} ≈ 1 − 0 .02( M∞ − 1)C x 2 nose . It is necessary to take into account a capability of shock wave getting onto a wing surface (horizontal tail). At that the external parts will be streamlined by an undisturbed flow (Fig. 14.2). Fig. 14.2. Lets consider the case, whenthe wing and horizontal tail are located on the fuselage. For such configuration theleading lifting surface can effect flow deceleration before the trailing lifting surface. 127
5. 5. Deceleration occurs due to the viscosity (trailing lifting surface getting into theaerodynamic trail) at M∞ < M* and, in addition, behind the shock wave from thetrailing lifting surface at M∞ > M* (Fig. 14.3). Here it is necessary to distinguish theaircraft normal configuration and canard configuration. Fig. 14.3. Influence of trailing lifting surface: a) - normal configuration; b) - canard configuration; c) - field of speeds behind the wing. Lets determine thickness of a boundary layer in the aerodynamic trail behind thewing for the normal configuration ( 2 H = 0 .86 1 + 0 .2 M ∞ ) C x p w ( x 1 + 0 .5 ) b1 , x 1 = x1 b1where x1 and b1 are the geometrical parameters of the semispan of horizontal tail(Fig. 14.3). If y h.t . > H , then tail-plane (wing) does not fall into the aerodynamic trail causedby wing (horizontal tail). In this case, for the normal configuration we receive kd h.t . = 1 at M∞ ≤ M* , kd h.t . = k 2 at M∞ > M* , 128
6. 6. where k 2 is the coefficient of flow deceleration behind a system of shock waves from (the fuselage nose and wing, k 2 = f C x nose , C xw wing , M ∞ , x 1 . ) At horizontal tail falling into the aerodynamic trail from a wing ( y h.t . < H ) weshall have kd h.t . = k12 at M∞ ≤ M* , kd h.t . = k12 k 2 at M∞ ≥ M* . (k12 = f C xp wing , M ∞ , x 1 ) where k12 is the factor, which characterizes flowdeceleration in the aerodynamic trail behind the wing. In the canard configuration the coefficient of flow deceleration before a wing isdetermined under the formula kd w = k* k1 , k* = 1− (1 − k12 ) S* 12 12 Swwhere factor ( ) k12 = f C xp h.t . , M ∞ , x 1 . Multiplier k1 = 1 at M∞ < M* and ( )k1 = f C x nose , C xw h.t . , M ∞ , x 1 at M∞ > M* . 14.3. Wing downwash As it is known, the vortex sheet is formed behind a lifting surface which creates adownwash. This downwash reduces true angle of attack of a lifting surface located backthat should be taken into account at calculating its lift and moment characteristics. Lets consider the case of the normal configuration, when the tail unit is located behind the wing. The wing repels air downwards with some speed Vi at creation of lift. Due to it, flow incoming onto horizontal Fig. 14.4 Wing downwash tail downwashes downwards at some angleε ≅ Vi V∞ , which is called the angle of downwash (Fig. 14.4). The downwash behind awing influences the aerodynamic characteristics of all aircraft parts located behind the 129
7. 7. wing. First of all wing downwash influences the aerodynamic characteristics ofhorizontal tail, because downwash reduces the angle of attack of horizontal tail. If theaircraft angle of attack α , an angle of attack of horizontal tail with taking into accountan angle of downwash ε will be α г .о . = α − ε . (14.2) The value of angle of downwash depends on the wing plan form, angle of itssetting, wing and fuselage interference, angle of attack, number M ∞ , and coordinates ofthe considered point. The significant influence on the angle of downwash is paid byvortexes forming at flow about wing on its lateral and leading edges. Disturbances are distributed in all parties at subsonic speeds, therefore tail uniteffects the flow about the wing, located before it. However this influence, as a rule, isinsignificant in comparison with wing influence onto flow about tail unit locatedbehind. The wing downwash also reduces an angle of attack of that fuselage part whichis located behind a wing. Disturbances are not distributed forward against flow at supersonic speeds, thearea of their propagation is limited by cones of disturbances and shock waves. That iswhy there can be zones in which there is no downwash at supersonic speeds. The angle of downwash depends on wing lift, therefore, on an angle of attack. For linear site this dependence can be written as ε = ε0 + ε α α . (14.3) The derivative ε α of downwash by the Fig. 14.5. Dependence of derivative of angle of attack depends on number M ∞ , as it downwash ε α on number M ∞ is shown in fig. 14.5. At subsonic speeds the lifting properties of the wing grow atincreasing of number M ∞ , the derivative ε α also increases. They drop at supersonicspeeds with the increasing of number M ∞ , besides, the zones of disturbancespropagation are narrowing, therefore derivative ε α reduces. 130
8. 8. If the mean angle of downwash is known, then the angle of attack of horizontal ( )tail is calculated under the formula α h.t . = α 1 − ε α − ε 0 . For the aircraft of thenormal configuration the parameter (1 − ε α ) is called the factor of tail-planeeffectiveness. The angle of downwash ε0 is determined by aerodynamic andgeometrical twist of wing. The configuration of horse-shoe vortex is used as the basis for calculation ofdownwash that is right, because the vortex sheet is unstable and at some distance isturned off in two tip vortexes. The remarks: 1. Generally downwash is variable spanwise. However, at calculating the totalaerodynamic characteristics of the trailing lifting surface in the aerodynamicconfiguration one takes the mean value of downwash spanwise. Obviously, thedownwash before a wing will be less in the canard configuration, as wing external partsfall into the upwash. 2. In the aircraft system the components of downwash ε α and ε0 will alsodepend on mutual arrangement of the leading and trailing lifting surfaces, shape andgeometry of cross section of the leading lifting surface with a fuselage, numbers M ∞ .The fuselage influence onto downwash is taken into account by change of theconfiguration of the horse-shoe vortex. 3. The additional sources of downwash can be the jets of the air prop and jetengines which turbulent baffling and ejection properties create a field of speeds directedto jet axis. Using model of horse-shoe vortex it is possible to offer the following formula forcalculation of components of angle of downwash caused by system: lifting surface-fuselage: Cα k x k y kc k f , ε 0 = − ε α α 0 k m α ya ε = (14.4) πλ 131
9. 9. where λ and C α are aspect ratio and derivative of the lift coefficient of forward yasurface cantilevers. The multipliers k i which are included in (14.4), depend onaerodynamic configuration of the aircraft and Mach number M ∞ . The multiplier k x takes into account mutual arrangement of a wing andhorizontal tail fuselage lengthwise. The multiplier k y takes into account verticaldisplacement of horizontal tail relatively to wing. The multiplier kc is connected toaerodynamic configuration of the aircraft (for normal configuration kc = 1 ). Themultipliers k f and k m also take into account the influence of fuselage onto downwashand depend on the shape of cross section a forward lifting surface - fuselage. 14.4. Interference of the engine nacelles with parts of an airplane 14.4.1. Nacelles location on the fuselage lateral area in its tail part The convergent-dilative channel is formed between nacelle and fuselagepromoting separation of the boundary layer and growth of profile drag of the system nacelle-fuselage (Fig. 14.6). At subsonic speeds with M∞ ≈ M* in a channel it is possible to expect the appearance of shock waves that causes further growth of drag. Obviously, the additional drag caused by interference is conveniently taken into account into nacelle drag with the help of introduction of the correction factor. In particular, the nacelle profile drag in the system with Fig. 14.6. fuselage is determined with taking into account an interference factor C xp e .n .( f) = nke .n .C xp is .e .n . S e .n . ,where n is the nacelle quantity, C xp is .e .n . is the profile drag of one isolated nacellewith midsection Se .n . ( S e .n. = Se .n. S , S - characteristic area). The factor ke .n . takes into account an interference effect 132
10. 10. ke .n . = 1 + 0 .3 n , n = 1, 2 , 4 ; ke .n . = 1.8 , n = 3 . It is necessary to point to one more effect - decreasing of nacelle lift in theairplane system because of its falling in the wing downwash. This effect is increased atlifting devices deflection. 14.4.2. Nacelle installation onto wing. As well as in the previous case a source of additional drag is the formation of achannel between nacelle and wing with increased flow rate in a channel and reducedspeed in the outgoing area of nacelle. Here increasing of the boundary layer happensand the flow stalling is possible. In the channel at M∞ ≈ M* shock waves can occur. Allsaid concerns the nacelles located on pylons or directly under the wing. Other reason is connected with features of flow about swept wing at engine nacelle installation on it. Disturbance of flow on the isolated wing takes place in this case, the additional chamber of streamlines by nacelle walls (Fig. 14.7) occurs. In area 1 nearby the wing leading edge an additional rarefaction will occur due to increasing of speed. In area 2 , on the contrary, decreasing speed occurs nearby the wing leading edge with further Fig. 14.7. opportunity of increasing at the nacelle tip. Critical Machnumber M* of the nacelle-wing system decreases. Thus, the flow disturbance on thewing connected with the nacelle installation (or pylon) causes an increase of drag. The most unfavorable nacelle location is directly under a wing without offsetting.In this case areas of minimum pressure on the wing surface and nacelle coincide, due tothat the positive pressure gradients grow and the conditions for earlier stalling of theboundary layer are created. 133
11. 11. Nacelle displacement forward or back, its location on wing axis or on pyloncauses a decreasing of the interference drag. The least interference is received at nacellelocation wing chordwise. As well as in case of the nacelle installation on the fuselage, an additional drag isaccounted by a factor ke .n . in nacelle drag, which depends on nacelle location relativelyto the wing: k e .n . = k 1 k 2 k 3 , − 0 .5 ( a − 1) 2 0 .05 2 k1 = 1 + + 8 .6 h2 exp − 4 h , k 2 = 1 + 0 .8 exp , 2 6h + 1 0 .6 λ e .n . k3 = 1 + . λ e .n . + 16 x 2 2Here the factor k 1 takes into account nacelle displacement along perpendicular to thewing plane h = H d e .n . ; k 2 - mutual influence of two nacelles located on one wingcantilever a = a d e .n. ; k 3 - nacelle displacement along the wing chord x = x le .n. .If one nacelle is located on the wing cantilever, then k 2 = 1 . The geometric parametersH , a , x are shown in fig. 14.8. Fig. 14.8. Engine nacelle location on a wing The mutual influence of two nacelles installed on one wing cantilever causesgrowth of drag, mainly, in an outcome of increase of flow rate between them andgrowth of pressure gradient on the nacelles surface. It is possible to reduce the interference drag of the wing-nacelle system if nacelleaxis is disposed with taking into account the direction of local flow rate. 134
12. 12. The positive effect of nacelle interference with the wing can be received atM ∞ > 1 . In this case nacelles should be placed behind the line of wing maximumthickness. The increased pressure induced by a shock wave from the nacelle creates acomponent force of pressure directed forward (negative drag); there appears small lift. 14.4.3. Mutual influence of prop and airplane It is convenient to divide study of mutual influence of prop and airplane into twoparts: influence of airplane parts onto prop and prop influence onto plane. Axial speed component decreases under engine nacelle influence in the place ofprop installation. The flow becomes decelerated and radial speed component appears. The wing influence onto prop located before the wing is similar to engine nacelleinfluence or fuselage effect, but flow is decelerated before a wing much less, as a rule. The wing influence onto prop located above the wing can be substantial and isexhibited in increasing or reduction of flow velocity incoming on the prop, incomparison with speed of undisturbed flow. The prop influence onto the plane is shown, first of all, through a pressure risingin jet directly behind the plane of rotation, where engine nacelle, wing and other parts ofthe airplane are located. Besides, the jet behind the prop has speed exceeding speed ofthe incoming undisturbed flow and distinguished from it by direction due to twist andlack of coincidence of the prop axis with direction of the undisturbed flow or deflectionof jet from the prop by other parts of the airplane. The pressure rising in jet behind the prop causes an additional pressure increasingat nose sections of the airplane elements located in jet that is an additional drag. The increasing of speed and change of flow direction in jet behind the propcauses changes of forces of pressure and friction and their distributions. It results inoccurrence of additional drag and additional lift on parts of the airplane blown by jetfrom the prop. Influence of the prop on horizontal tail located behind the props is the same as onthe wing. However, the increasing of positive pitching moment occurs on the normal 135
13. 13. configuration airplanes at negative lift of horizontal tail which is necessary to counteractby additional deflection of elevators for diving. As the greatest effect from the airplane parts blown by props occurs at smallflight speeds , i. e. at takeoff modes, then it is necessary to take into account theinfluence of ground proximity onto the airplane aerodynamic characteristics while propsactivity. The influence of ground proximity is shown first of all in decreasing of flowdownwash caused by the prop jet. It results in increasing of wing lift, reduction of itsinduced drag, decreasing of horizontal tail negative lift and reduction of its pitchingmoment. 136