Boundary-Layer Control on the Wing

A change of the flow in the very thin wall boundary layer may, under certain conditions, alter considerably the entire flow pattern around the body. A number of methods have been developed for boundary-layer control that, in some instances, have obtained importance for the aerodynamics of the airplane. The basic principles of boundary-layer control will be explained briefly in this section. In most cases, boundary-layer control is considered in the following contexts: elimination of separation for drag reduction or lift increase, or only change of the flow from laminar to turbulent, or maintaining of laminar flow. The various methods that have been investigated mainly experimentally, but also theoretically in some instances, can be highlighted as follows: boundary-layer acceleration (blowing into the boundary layer), boundary-layer suction, maintaining of laminar flow through proper profile shaping (laminar profile). A comprehensive survey of this field is given by Lachmann [36].

Boundary-layer acceleration A first possibility of avoiding separation is given by introducing new energy into the slowed-down fluid of the friction layer. This can be done either by discharging fluid from the body interior (Fig. 2-52a) or, in a simpler way, by taking the energy directly from the main flow. This method consists of injecting fluid of high pressure into the decelerated boundary layer through a slot (slotted wing, Fig. 2-52b). In either case, the velocity in the wall layer increases through energy addition and thus the danger of separation is removed. For practical applications of the method of fluid ejection as in Fig. 2-52a, particular care is required in designing the slot. Otherwise, the jet may disintegrate into vortices shortly after its discharge. More recently, extensive tests [46] have led to the method of discharging a jet at the trailing edge of the wing, which has proved to be

Figure 2-52 Various arrangements for boundary-layer control, (a) Blowing. (b) Slotted wing, (c) Suction.

very successful in raising the maximum lift (jet flap). The same benefit has been gained from blowing into the slot of a slotted wing.

A slotted wing (see Fig. 2-52Ъ) functions in the following way: On the front wing (slat) A-В, a boundary layer forms. The flow through the slot carries this layer out in the free stream before it separates. At large angles of attack, the steepest pressure rise and hence the greatest danger of separation occurs on the suction side of the slat. Starting at C, a new boundary layer is formed that may reach the trailing edge without separation. Hence, by means of wing slats, separation can be prevented up to much larger angles of attack, so that much larger lift coefficients can be obtained. In Fig. 2-53, polar diagrams (lift coefficient cL vs. drag coefficient Ci)) are given of a wing without and with a wing slat and with a rear flap. In the slot between main wing and rear flap (Fig. 2-52b), the processes are the same, in principle, as those in the front slot. The lift gain from a front slat and a rear flap is considerable. Further information on this item will be given in Chap. 8.

Boundary-layer suction Boundary-layer suction is applied for two purposes: to avoid separation and to maintain laminar flow (see Schlichting [53] and Eppler [15]). In the first case, the slowed-down portions of the boundary layer in a region of rising pressure are removed by suction through a slot (Fig. 2-52c) before they can cause flow separation. Behind the suction slot, a new boundary layer is formed that, again, can overcome a certain pressure rise. Separation may never take place if the slots are suitably arranged. This principle of boundary-layer removal by suction

v Figure 2-54 Drag (friction) coefficients of flat plate in parallel flow with homogeneous suction; cq = (—u0 )/£/«, = suction coefficient; —u0 = constant suction velocity. Curves 1, 2, and 3 without suction. 1, Laminar; 2, transition laminar-turbulent; 3, fully turbulent; 4, most effective suction.

was checked out for a circular cylinder by Prandtl as early as 1904 and has been investigated by Schrenk [58] for wing profiles.

In the second case, suction is applied for the reduction of friction drag of wings (see Goldstein [20]). This is. accomplished if suction causes a downstream shift of the laminar-turbulent transition point. For this purpose, it turned out to be more favorable to apply areawise-distributed (continuous) suction, for example, through porous walls rather than through slots. In this way the disturbances by the slots were avoided, which could have led to premature transition. That the flow can be kept laminar through suction may be seen from the fact that the friction layer becomes thinner when suction is applied and, therefore, has less of a tendency to turn turbulent. Also, the velocity profile of a laminar boundary layer with suction has a shape, compared with that of a layer without suction, that makes transition to turbulence less likely even when the boundary-layer thickness is equal in both cases.

Of particular interest is the drag law of the plate with homogeneous suction, as given in Fig. 2-54, because it is characteristic for the drag savings gained through suction-maintained laminar flow. In comparison, the drag law of the plate with a turbulent boundary layer (without suction) is added as curve (3). The drag savings that may actually be achieved cannot yet be derived. First, the limiting suction coefficient must be known, which is necessary to keep the boundary layer laminar—even for large Reynolds numbers. This minimum suction coefficient was determined as

CQcr = 1-2 • 10-4

up to the highest Reynolds numbers. This remarkably small value is included in Fig. 2-54 as “most favorable suction” (curve 4). The difference between curves 3 “turbulent” and 4 “most favorable” suction represents the optimum drag savings, In the Reynolds number range Re = 106 to 10s, they amount to about 70-80% of the fully turbulent drag.

It should be understood, however, that this saving does not take into account the power needed for the suction. Even when taking this power into account, however, the drag savings are still considerable.

Ackeret et al. [2] were the first investigators to prove experimentally that it is possible to hold the boundary layer laminar by suction. Some of their test results on a wing profile are given in Fig. 2-55. This wing profile was provided with a large number of slots. The considerable savings in drag, even including the blower power needed for the suction, is obvious. The favorable theoretical results about drag savings by maintaining laminar flow have been confirmed completely through investigations of Jones and Head [20] on wings with porous surface.

Boundary layer with blowing Another very efficient means of influencing the boundary layer is the tangential ejection of a thin jet at a separation point. This method has been applied very successfully to wings with trailing-edge flaps. By ejecting a thin jet at high speed at the nose of the deflected flap, flow separation from the flap can be avoided and hence lift can be increased considerably. The underlying physical principles are demonstrated in Fig. 2-56. At large deflections, the effectiveness of the flap as a lift-producing element is markedly reduced by flow separation (Fig. 2-56a). The lift of a wing with deflected flap does not reach at all the value that is predicted by the theory of inviscid flow. Flow separation from the flap and a resulting loss in lift may be avoided, however, by supplying the boundary layer with sufficient momentum. This is accomplished by a thin jet of high speed, tangential to the flap, introduced near the flap nose into the boundary layer (Fig.

2- 56b). The lift gain that can be realized through blowing is shown in Fig. 2-56c as

Figure 2-55 Reduction of drag coefficient of wing profiles by suction through slots, after Pfenninger [2]. (a) Optimum drag coefficient of wing with suction vs. Reynolds number, (b) Profile-drag polar.

Figure 2-56 Flap wing with blowing at the flap nose for increased maximum lift. (a) Flap airfoil without blowing, separated flow. (b) Flap airfoil with blowing, attached flow, (c) Pressure distribution.

the difference between the two pressure distributions. The effect of blow jets and jet flaps is discussed in more detail in Sec. 8-2-3. A synopsis of the increase of maximum lift of wings through boundary-layer control has been written by Schlichting [54].

Maintaining laminar flow through shaping Closely related to maintaining laminar flow through suction is maintaining a laminar boundary layer through proper shaping of the body. The goal is the same, namely, to reduce the friction drag by shifting the transition point downstream. Doetsch [12] was the first to demonstrate experimentally that considerable drag reductions can be obtained in the case of a wing profile whose maximum thickness is sufficiently far downstream (laminar profile). By shifting the maximum thickness downstream, the pressure minimum, and thus the laminar-turbulent transition point of the boundary layer, is also shifted downstream because, in general, the boundary layer remains laminar in the range of decreasing pressure. Only after the pressure rises does the flow turn turbulent. These conditions are shown in Fig. 2-57 by comparing a “normal wing” of a maximum thickness position of 0.3c and a laminar profile with a maximum thickness position of 0.45c. In the former case the pressure minimum lies at 0.1c, in the latter case at 0.65c. The drag diagram indicates that, in the Reynolds number range from 3 • 106

to 107, the drag of the laminar profile is only about one-half that of the normal profile. The aerodynamic properties of such laminar profiles have been investigated in much detail in the United States [1]. Practical application of laminar profiles is impeded particularly by the extraordinarily high demand on surface smoothness necessary to ensure that the conditions for maintaining laminar flow are not lost with surface roughness. The studies of Wortmann [75] and Eppler [14, 15] on the development of laminar profiles for glider planes should be men­tioned.