Powered-Uft Systems

Figure 3.45 (taken from Ref. 3.26) presents the growth of over the years since the Wright Brothers’ success. The two points labeled К and L are somewhat misleading, since these two aircraft were experimental in nature and used distributed suction over the wing to delay separation. From this figure and the preceding information on flapped and plain airfoils, C, ^ of

Figure 3.42 Pressure distributions for Liebeck airfoils, (a) Optimum airfoil pres­sure distribution according to variational analysis. (b) Modified form of optimum pressure distribution for airfoil upper and lower surfaces (not to scale). (R. H. Liebeck and A. I. Ormsbee, "Optimization of Airfoils for Maximum Lift”, AIAA Journal of Aircraft, 1970. Reprinted from the Journal of Aircraft by permission of the American Institute of Aeronautics and Astronautics.)

slightly over 3 is probably the best that can be achieved without the addition of power. Although two-dimensional airfoils with double-slotted flaps can do better than this, as will be seen later, their full potential cannot be achieved when applied to an airplane. Generally, the flaps cannot be applied over the entire span of the wing. In addition to this loss in СУ1[[ц. an added penalty results from the fuselage and tail download required for trim.

‘ values considerably above those achievable with flap systems dis­

cussed so far are possible by the expenditure of power. Most of the powered – flap systems presently under consideration bear a resemblance, or can be

Figure 3.43 Liebeck airfoil with its pressure distribution. (R. H. Liebeck, “Class of Airfoils Designed for High Lift”, AIAA Journal of Aircraft, 1973. Reprinted from the Journal of Aircraft by permission of the American Institute of Aeronautics and Astronautics.)

related in their performance, to the jet flap. Thus, in order to understand better the performance of systems such as upper surface blowing (USB), – externally blown flaps (EBF), augmentor wing, and circulation control, we will begin with the jet flap shown in Figure 3.46. A thin sheet of air exits the trailing edge at a downward angle of S relative to the airfoil zero lift line. This line is shown at an angle of attack a. If Гс is the total circulation around the airfoil then, assuming a and S to be small, the total lift on the airfoil will be

where itij is the mass flux in the jet and r, is the jet velocity.

As the jet leaves the airfoil, it gets turned in the direction of the free-stream velocity. In order to redirect the flux of jet momentum, it follows that a pressure difference must exist across the jet. This pressure difference, Др, can be related to mjVj and the radius of curvature R by the use of Figure 3.46b. Applying the momentum theorem in the direction of curvature,

Д pR6 = mjVj6 or

Figure 3.44b Effect of transition location on the lift and drag of a Liebeck airfoil. (R. H. Liebeck, “Class of Airfoils Designed for High Lift", AIAA Journal of Aircraft, 1973. Reprinted from the Journal of Aircraft by permission of the American Institute of Aeronautics and Astronautics.)

Since the jet exerts a force on the fluid, it can be replaced by an equivalent continuous vortex sheet that exerts the same force. Letting – y, be the strength per unit length of the sheet,

A pRO = pVyRO or

A p

VI = ф (3.54)

Measuring the position of the jet, y, positively downward, the radius of curvature and у for a nearly horizontal jet are related by

1 d2y

R dx2

Combining Equations 3.53, 3.54, and 3.55 gives

mjVj d2y pV ~d?

Equation 3.56 relates the jet vortex strength to the shape of the sheet and the jet momentum flux.

The total circulation of the jet vortex sheet can be obtained by integrating Equation 3.56 from x = 0 to °°.

Г,= Г у, d,

Jo

– _ mivi dy l” pV dx о

= ^(a + 5) (3.57)

Combining Equations 3.52 and 3.57 shows that the Kutta-Joukowski rela­tionship holds for the jet-flapped airfoil if the circulation is taken around both the airfoil and the jet.

L = PV( Гс + Гу) (3.58)

The boundary value problem is then posed where the airfoil and jet sheet are each replaced by an unknown vortex distribution. Distributions must then be found that will induce a velocity at each point on the airfoil and combining with the free-stream velocity to give a resultant velocity tangent to the airfoil. Along the sheet the following must hold.

w(x)_ dy V ~ dx

The details of the solution are beyond the scope of this text and can be found in Reference 3.19.

Although the solution of Reference 3.19 is not in closed form, the results

can be expressed in a relatively simple way. As with a physical flap, the increment in Ci because of a change in angle of attack and-flap angle can be expressed as a linear combination of the two angles.

Ci = Ci a + C,,8 (3.59)

where

^ – dC,

C|“ da

r _ dC,

С,°~І8

The derivatives Cta and Ct, are a function of the ratio of the jet momentum flux to the product of the free-stream dynamic pressure and a reference area. This ratio, known as the momentum coefficient, C„, is defined for a two-dimensional airfoil by

(3.60)

If, in addition, the jet exits ahead of the trailing edge and blows over and is deflected by a physical flap having a chord of cf (see the blown flap of Figure 3.24), then Ct, is also a function of cflc. For a pure jet flap (Q/C = 0), Cta and Q, are given by

Ci, = [4ТТ-СД1 + 0.151С/2 + 0.139См)]1/2 (3.61)

Cia = 2тг(1 + 0.151Q1/2 + 0.219Q) (3.62)

For c^c values other than zero, Q, is given in Figure 3.47. The curve ^labeled Cf/c = 1.0 in this figure corresponds to Equation 3.62 since, for this case, Ci, = Cia.

Data concerning C/max for jet-flapped airfoils is sparse. Generally, the jet flap follows the predictions of Figure 3.41 fairly closely, since the jet fixes the Kutta condition and provides some control over the boundary layer to prevent separation. As a preliminary estimate for Cu- Reference 3.3 recommends the use of the relationship presented in Figure 3.48. Here the difference in the angle of attack for stall, with and without blowing, is presented as a function of C„.

The negative pitching moment of the jet flaps is higher than the moment for conventional flaps for two reasons. First, the jet reaction acts at the trailing edge; second, the jet-flapped airfoil maintains lift all the way back to the trailing edge. As with the lift, CM can be written as a linear combination of a and S.

См = См„а + См,8

or

In this equation dC^dCi can be obtained from Figure 3.49.

cM Figure 3.49 Effect of on pitching moments for blown flaps. (B. W. McCormick, Aerodynamics of V/STOL Flight, Academic Press, Inc. 1967. Reprinted by per­mission of Academic Press, Inc.)

To illustrate the use of the foregoing relationship for the jet-flapped airfoil, consider the prediction of for the NACA 63,4-421 airfoil (Figure 3.30) equipped with a 25% blown flap deflected 50°. The jet expands isen – tropically from a reservoir pressure of 25 psia and a temperature of 70 °F. The airfoil is operating at 50 mph at SSL conditions. It has a chord of 5 ft and the jet thickness is 0.2 in.

We begin by calculating the jet velocity from the compressible Bernoulli equation (Equation 2.31).

or, with the use of Equation 2.30,

(т-о/щ У2

Цу – l)po L W From the equation of state (Equation 2.1),

Po/po= RT0

Thus,

p(1.4)(1716)(529.7) ^ 14/7^ 0 286Jj1,2

= 946.9 fps

The mass density of the expanded jet will be

p0 is calculated from the equation of state.

25(144)

p0 1716(529.7)

= 0.00396 slugs/ft3

Thus,

Pi = 0.00271 slugs/ft3

The jet mass flux will be equal to

Щ = PAvi

= 0.00271(0.2/12)(946.9)

= 0.0428 slugs/s

The free-stream dynamic pressure is

q = I pV2

= 0.002378(50 x 1.467)2/2 = 6.397 psf

Thus,

(0.0428)(946.9)

6.397(5)

= 1.27

From Figures 3.47 and 3.48,

C, a = 9.09/rad C, s = 6.5/rad

<*171M — <*max(CM = 0) = — 2

From Figure 3.30, for the unblown airfoil without a flap is equal approximately to 1.4. Using Figures 3.33 and 3.34, AC, due to the plain flap (CM = 0) is estimated as

ДС, = 2тг(0.6)(.41)(^) = 1.35 so that, using Figure 3.34

~ (0.72) (1.35) = 0.97

Thus, for Q, = 0 with the flap deflected, C(max is estimated to be 2.37. At a = 0, Q is estimated to be 1.5. Thus, with Cla = 0.109 (from Figure 3.30),

or, relative to the zero lift line, flaps up,

«ШИ = 9.7°

For the operating CM, the angle of attack for the zero lift line at stall is – estimated to equal 7.1°.

Thus,

CU = Cl«amax + C|, S

= 6.8

The preceding answer must, of course, be further corrected, using Figure 3.43 and Equation 3.46, to account for trimming tail loads. Also, it should be emphasized that the preceding is, at best, an estimate for preliminary design purposes or relative parametric design studies. In the final analysis, model and prototype component testing of the blowing system must be performed.

Credit for the practical application of the jet flap must be given to John Attinello. Prior to 1951, all blown systems utilized pressure ratios less than critical in order to avoid supersonic flow in the jet. Such systems required large and heavy ducting. For his honors thesis at Lafayette College, Attinello demonstrated with “homemade” equipment that a supersonic jet would adhere to a deflected flap. This was contrary to the thinking of the day that not only would a supersonic jet separate from a blown flap, but the losses associated with the shock wave system downstream of the nozzle would be prohibitive. Later, more sophisticated testing performed by the David Taylor Model Basin confirmed Attinello’s predictions (Ref. 3.38) of high lift coefficients for supersonic jet flaps. This led to the development of compact, lightweight systems using bleed air from the turbojet engine compressor section. The Attinello flap system was flight tested on an F9F-4 and produced a significant decrease in the stalling speed for an added weight of only 50 lb. Following this success, the Attinello flap went into production on the F-109, F-4, F8K, A5, and other aircraft, including several foreign models.