Reduction of Skin Friction Drag
The contribution to the drag of a streamlined shape from skin friction can be reduced appreciably if transition from laminar to turbulent flow can be delayed. An estimate of the gains to be realized can be seen from Figure 4.40. This flgurd has befen prepared based on Figure 4.1 and the methods outlined earlier for calculating the drag of a flat plate over which the boundary layer is partly laminar and partly turbulent. In this case, the total CF is calculated from
Cf = CFt(R) ~ x,[CPT(Rt) — CpL(R,)] (4.55)
In this equation, a subscript T refers to turbulent flow and a subscript L to a laminar flow. R, is the transition Reynolds number based on the transition length, /,, shown in Figure 4.40. x, is the relative distance from the leading edge to the transition point expressed as a fraction of the total length. The notation CFt(R,), for example, does not indicate a product but, instead, shows that Cft is to be evaluated at the Reynolds number R,.
From Figure 4.40, it is obvious that the skin friction can be reduced significantly if some means can be found to stabilize the laminar layer so as to prevent or delay transition to a turbulent layer. Such a procedure is known as boundary layer control (BLC) or laminar flow control (LFC). BLC is the more
Figure 4.40 Skin friction coefficient for a flat plate as a function of Reynolds number for constant transition lengths. |
general term and encompasses other purposes such as controlling the boundary layer, laminar or turbulent, in order to delay separation. LFC is therefore preferred when reference is made to stabilizing the laminar boundary layer.
‘It is not the purpose of this textbook to consider in detail the fluid mechanics involved with stabilizing the laminar layer. Generally, the problem is that of maintaining a boundary layer that is thin with a full velocity profile. This latter statement is clarified in Figure 4.41.
A passive method of maintaining laminar flow is by shape alone. A good example of this is the family of airfoils, the NACA 6-series airfoils discussed briefly in Chapter Three. One of these, the NACA 662-015 airfoil, is pictured in Figure 4.42 along with its chordwise pressure distribution. Note that because
of its shape, the pressure decreases with distance all the way back to the 65% chord position. This favorable pressure gradient is conducive to maintaining a thin boundary layer with a stable velocity profile. One might assume, as a first estimate, that its transition point is close to the 65% chord position.
For comparison, consider the NACA0015 airfoil having the same thickness ratio but with its maximum thickness located further forward than the 662-OI5 airfoil. This airfoil, together with its pressure distribution, is shown in Figure 4.43. For this airfoil, one might expect transition to occur at around the 20% chorck where*the flow first encounters an adverse pressure gradient.
Both the 662-OI5 and 0015 airfoils lie within the families of airfoils considered in Figure 4.44. For rough surfaces, Cd is approximately the same for both airfoil families. The roughness causes transition in both cases to occur near the leading edge. The picture is different in the case of smooth surfaces. Here Cd equals 0.0064 for the 0015 airfoil but only 0.0036 for the laminar flow airfoil. These correspond to Q values of approximately 0.0032 and 0.0018 for the respective airfoils. Using Figure 4.40 and the transition points of 0.2C and 0.65C, values of Q of 0.0026 and 0.0014, respectively, are obtained corresponding to Cd values of 0.0052 and 0.0028. The difference between these values and the experimental results may be attributable to errors in the estimated transition locations. Most likely, however, the difference is attributable to form drag. For both airfoils, the differences are
Figure 4.44 Variation of Section Cdmln with thickness ratio for conventional and laminar flow NACA airfoils, (a) NACA four and five-digit series, (b) NACA 66- series.
close to the estimates of form drag that one obtains from examining the increase in total Cd with thickness ratio.
The favorable pressure distribution of the series-66 airfoils undoubtedly delays transition, thereby reducing the skin friction drag. For a particular airfoil, however, extensive laminar flow can only be maintained over a limited range of Q values and for Reynolds numbers that are not too large. The Cd
versus C, curve, known as the drag polar, for a laminar flow airfoil has the rather unusual shape typified by Figure 4.45 (or earlier by Figure 3.8). This drag bucket results from the fact that for C, values between approximately + or -0.2, the chordwise pressure distribution is sufficiently favorable to maintain laminar flow over most of the airfoil. Without this “bucket,!’ the drag curve extrapolates to a Cd value at a zero C, close to that for a more conventiopal airfoil having this same thickness.
With careful attention to surface waviness and roughness, appreciable laminar flow can be achieved with airfoils up to Reynolds numbers in excess of 20 million, as shown by Figure 4.46 (Ref. 3.1). This same figure emphasizes the importance of surface finish. Unimproved paint is seen to be rough. enough to cause premature transition at a Reynolds number of approximately 20 x 106. The result is a doubling in the drag coefficient for this particular airfoil.
One has to be somewhat careful in interpreting this figure. At first glance, it might appear that transition is being significantly delayed up to a Reynolds number of 60 x 106, since the drag coefficient is nearly constant up to this Reynolds number. A closer look shows the Cd to decrease up to an R of approximately 32 x Ю6. It then increases up until an R of approximately 54 x 106. Above this value of R, it appears that Cd is tending to decrease.
Obviously, from Figure 4.40, a constant Cd as R increases requires that the transition point move forward. This is assuming that the form drag is not dependent on R. This is a valid assumption; if anything, the form Cd tends to decrease with R.
It is difficult to divide the total drag into form and skin friction drag because of the dependence of the skin friction drag on the transition location. However, based on the potential flow pressure distribution, it is reasonable to assume that transition occurs at around the 50% chord point at the lower Reynolds numbers. With this assumption, the same form drag coefficient is obtained at R values of 12 x 106 and 30 x 106, that is, a form Cd, of 0.0013. For the same transition location and form Cd, Figure 4.40 leads to a predicted Cd of
0. 0036. This is close to what one might expect if the data for Figure 4.46 a are extrapolated beyond an R of 32 million.
Using the form Cd of 0.0013 and Figure 4.40, the peak Cd of 0.0050 at an R of 54 x 106 leads to a transition location at this higher Reynolds number of 18% of the chord. Thus, it is concluded that the shape of the 65(42i)-420 airfoil is able to stabilize the laminar boundary layer up to the midchord point for Reynolds numbers as high as 30 million. For higher Reynolds numbers, the transition point moves progressively forward.
The size of roughness that can be tolerated without causing transition can be estimated from Figure 4.47 (Ref. 3.1). It is somewhat surprising to find that the results do not depend significantly on the chordwise position of the roughness. In fact, it appears that the downstream positions are less tolerant to roughness height than positions near the leading edge.
. Section lift coefficient, Cj Figure 4.45 Characteristics of the NACA laminar flow 65г-015 airfoil. |
Figure 4.47 Variation of boundary layer Reynolds number with projection fineness ratio for two low drag airfoils. [Як, = transition Reynolds number based on height (which will cause transition) of protuberance, к, and local velocity outside transition of boundary layer.] (I. H. Abbott and A. E. VonDoenhoff, Theory of Wing Sections, Dover Publications, Inc., 1959. Reprinted by permission of Dover Publications, Inc.)
Since one can never be sure of the shape of a particle, based on Figure 4.47, a value of Rkt of 1400 is recommended as being reasonable. In the case of Figure 4.46, this criterion leads to a roughness as small as 0.004 in. in height as the cause of the drag rise at an R value of 20 million.
Figure 4.48 is a convenient graph for quickly determining Reynolds numbers at a given speed and altitude. For example, a typical light airplane operating at 10,000 ft at a speed of 150 mph has a unit Reynolds number of
1.1 x 10* or, for a chord of 5.5 ft, a Reynolds number of 6.05 x Ю6. A jet transport cruising at 35,000 ft at 500 mph las a unit R of 1.8 x Ю6. This results in an R of 27 x 106 for a chord length of 15 ft.
For the light plane, an Rof 1400 gives an allowable roughness height of
0. 015 in. A height of 0.009 in. or less should not cause transition on the jet transport’s wing. These may not be difficult criteria to meet for a wind tunnel model’or an isolated panel. On an operational, full-scale aircraft with rivets, access panels, deicers, gas caps, wheel-well covers, and the like, the achievement of this degree of smoothness is a real challenge. Even if such smoothness is attained, a few bugs smashed on the leading edge can easily destroy the aerodynamic cleanliness.
An active method of providing LFC involves removing the boundary layer as it develops so as to keep it thin with a stable velocity profile. This requires that power be expended to apply suction to the boundary layer either through a porous surface or across closely spaced thin slots transverse to the flow, as shown in Figure 4.49. The latter method has received the most attention. One of the earliest investigations of LFC using discrete spanwise slots was reported in Reference 4.18. Here, laminar flow was achieved up to a Reynolds number of 7.0 x 106 on NACA 18-212, 27-215, and 0007-34 airfoils. This result is not very impressive in comparison to Figure 4.46, where transition is apparently delayed up to R values of 30 x Ю6 for a smooth surface and 20 x 106 for the painted surface. However, the airfoils tested by Reference 4.18 were prior to the series-6 airfoils and had pressure gradients less favorable than the laminar flow series developed later. It was found that, with only a small expenditure of power, the boundary layer could be stabilized over an extensive region having an Adverse pressure gradient. Somewhat discouraging was the fact that the use of suction did not reduce the sensitivity of transition to roughness.
Flight testing performed in the mid-1960s provided more encouraging results, as reported in Reference 4.19. Two WB-66 airplanes were modified and redesignated X-21A. These airplanes had 30° swept wings with an aspect ratio of 7. The boundary layer was removed by approximately 120 slots on each surface. The slots varied in width from about 0.0035 to 0.01 in.
I Difficulties were encountered with instabilities in the skewed boundary layer along the swept leading edge produced by the spanwise flow. However, the use of fences and chorwise suction slots spaced along the leading edge
V fps
Figure 4.48 Reynolds number as a function of velocity and altitude.
Figure 4.49 Laminar flow control by suction through thin slots transverse to the flow. |
alleviated this problem. The final result was the attainment of full-chord laminar flow at a Reynolds number of 45.7 x 106.
The adoption of a powered LFC system represents a challenging exercise in systems analysis and design. The saving in drag must be measured against the weight and initial cost of the ducting, pumps, and double skin required to remove the boundary layer. According to Reference 4.19, performance analyses showed that the required engine size for a jet transport in the 300,000-lb class is smaller than that for the turbulent counterpart. This smaller engine results in a weight saving that offsets the weight penalty of the pumping equipment. With both the inner and outer skins contributing to the
Figure 4.50 Performance gains from laminar flow control. (R. E. Kosin, “Laminar Flow Control by Suction as Applied to X-21A Airplane”, AIAA Journal of Aircraft, 1965. Reprinted from the Journal of Aircraft by permission of the American Institute of Aeronautics and Astronautics.) |
wing’s structural integrity, the weight of all of the pumping equipment is estimated at between 1.3 and 1.4 psf. Considering the weight, drag, and specific fuel consumption, an optimized design incorporating LFC shows an increase of one-third in the range for a fixed payload or in the payload for a fixed range at a design range of 5000 nmi. These predicted performance gains are shown in Figure 4.50 (taken from Ref. 4.19).