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| FDIB Scientific E-Zine @ 1-2001 | ||
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THE Boundary Layer Flow ControlS to Delay Laminar-Turbulent Transition for REDUCING SKIN FRICTION Drag
Uyung Gatot S. Dinata
1. Introduction Reducing drag on the surface of an aircraft is an exciting area in aerodynamic researches. This could result in aircraft performance in terms of fuel savings as well as decrease of emissions and noise and reduced aircraft size following fuel reductions. These benefits could lead to reductions in total aircraft operating costs (Joslin [1998]). It is known that skin friction drag may be the largest portion of the total drag of an aircraft, with an amount of about 50% (Thibert et al. [1990]). At the same Reynolds numbers, laminar boundary layer has significantly lower skin friction than turbulent flow. Therefore, reducing considerable skin-friction drag could be made with longer runs of laminar boundary layer flows on the aircraft surface. A laminar boundary layer flow at low Reynolds numbers is stable. However, with increasing Reynolds number, flow instabilities termed Tollmien-Schlichting (TS) waves can lead to a transition to turbulent flow. In this case, the laminar flow can be maintained by an artificial stabilization. Various direct and indirect influence techniques for attenuating such an instability wave are available in the field of flow control. Principally, an indirect stabilizing control aims to reduce the undesired wave by modifying (structurally, mechanically, thermally, etc.) the characteristic of a boundary layer, in which the disturbance travels. In contrast, a direct control (here called active wave cancellation) performs a wave attenuation using a canceling wave in order to delay a laminar-turbulent transition. The potential of the implementation of the active cancellation of TS instabilities for delaying transition is that the energy requirement of the direct control may be significantly lower than that of indirect ones. In addition, the indirect techniques commonly necessitate much size and mass. The direct wave control with the possible profitable advantage could therefore act as the complement of the indirect ones. The concept of actively controlling instability waves as described in much expert literature on the subject is realized using the principle of wave superposition between an occurring TS wave and an artificially excited canceling wave. Canceling the unwanted wave by using an active control is performed with the “antiwave” of equal amplitude but 180° out of phase. This is similar to the active noise control (ANC) principle, which performs a noise cancellation with opposite “antinoise” (patented by Lueg, 1936). Primarily, the cancellation works out well since the TS wave is linear, and so the superposition holds when adding two waves. Active wave control systems commonly use a sensor-actuator channel, which is placed on a surface, where the TS wave is still in the linear stage to be damped. Such a sensor-actuator system consists of a reference sensor to measure an impending wave as a reference signal for driving the control to generate a proper actuating signal, an actuator downstream to introduce an actuating wave to cancel the disturbance as well as an error sensor further downstream to monitor a residual wave. The actuating signal for driving the actuator can be optimally generated with an adaptive filter control, which is operated with a specific signal-processing algorithm executed by an electronic unit. Most adaptive filter controls for canceling TS instabilities reported have employed an adaptive algorithm also called filtered-x LMS (least mean square) [Widrow et al., 1981, Burgess, 1981], which is also widely applied in the field of active noise control. Wind tunnel experiments on an active wave control using this adaptive filter algorithm have been carried out at the Technical University of Berlin for several years. The algorithm was applied previously in a single-channel system to effectively attenuate a 2-dimensional TS wave on an unswept wing by Baumann & Nitsche [1996, 1997].
2. Tollmien-Schlichting Wave The mechanism of laminar-turbulent boundary layer transition has been investigated theoretically and experimentally in fluid mechanics. Among others, W. Tollmien in 1926 and H. Schlichting in 1932 made the first major contributions to the study of transitional boundary layers. They reported that, at certain Reynolds numbers, a disturbance wave occurs. This amplifies with increasing Reynolds numbers. Today, the flow process with such convective disturbances is generally known as Tollmien-Schlichting (TS) instability. Liepmann [1943] and Schubauer & Skramstad [1948] used experiments to obtain evidence of a TS instability wave. Schubauer et al. carried out hot wire measurements at several downstream positions in a flat plate boundary layer. These were their proof of the existence of such a wave. At low Reynolds numbers, the laminar boundary layer is stable. If the Reynolds number exceeds a certain value, the boundary layer becomes unstable, whereby the signal of a weak velocity fluctuation appears. The harmonic wave amplifies as it propagates downstream. At a further downstream position, the wave encounters some irregular fluctuations as bursts of very large amplitudes. With increasing distance, they occur for a longer period of time in the signal and later break into a turbulent flow. Some reports about the physical mechanisms of laminar-turbulent transition can also be found in Schubauer & Klebanoff [1956], Kachanov [1994], and Schlichting et al. [2000]. TS waves mainly cause a transitional flow in an unswept wing. A swept wing has leading and trailing edges, which are slanted backward or forward. The effect of sweep angles (up to 50°) and wind speeds (up to about 400 ft/s) on transition on a swept wing (4-ft chord) was reported by Anscombe & Illingworth [1956]. Their result showed that, at sweep angles up to 30°, the distance of transition line was constant. With an increase in the flow speed at these sweep angles, the transition moved forward from 65% to 45% chord. At a constant speed of 200 ft/s and as the sweep angles were further increased from 35° to 50°, the transition also moved forward from 60% to 30% chord. At large sweep angles, the laminar boundary layer flow on wings can be dominantly influenced by a crossflow (CF) disturbance. The spanwise velocity component in the boundary layer causes that the flow becomes unstable. Joslin [1998] reported that, on wings with sweep angles of 0°...25°, TS waves dominate, amplify and cause a natural transition. For wing sweeps above 25°, CF disturbances are present and together with TS disturbances lead to a transition. At sweeps of 30°...35°, CF disturbances are dominant and commonly cause a transition near the leading edge region. Also, high sweep angles and large leading-edge radius of a wing can cause another boundary layer instability on the leading edge, namely attachment-line instability.
3. Indirect Wave Reduction Maintaining a laminar boundary layer on all parts of the surface could be done if instability disturbances, which lead to transition, could be avoided. Boundary-layer flow controls to prevent the instability process are prominent today, because they can be applied to aerodynamic laminar flow control techniques and thereby realize aircraft drag reduction. Based on boundary layer controls, TS instabilities could be canceled by some stabilizing influence and, thus, the turbulent boundary layer would be delayed in a downstream region (Gad-el-Hak, [1989]). Recent research works are primarily focused on the “indirect” stabilizing of instabilities by changing mean velocity profiles of the laminar boundary layer. Indirect control devices such as wing shaping and steady suction could be used for controlling the flow instabilities. Schubauer & Skramstad [1948] showed that attenuating or destabilizing a TS wave could be carried out with a favorable or adverse pressure gradient in a laminar boundary layer, respectively. A favorable boundary layer could be realized with the wing shaping, which is actually implemented to postpone transition process on NLF (natural laminar flow) airfoils. Furthermore, distributed boundary layer suctions through perforated wing surface areas can decrease the boundary layer thickness that also has a stabilizing effect. By using this method, longer runs of laminar flows can be made on a large areas of the aircraft surface (Joslin [1998]).
4. Direct Wave Cancellation In contrast to the preceding wave reducing method for extending the Reynolds numbers of laminar flows, the technique of a “direct” cancellation of TS waves aims to change the fluctuating velocity profiles of the laminar boundary layer. Experimental and numerical investigations to date for this technique have used the principle of wave superposition. This means that a secondary antiwave with similar amplitude but opposite phase is introduced into the flow to realize a destructive interference of the primary instability wave. Therefore, TS-type instabilities can be reduced directly resulting in a delayed transition. The direct wave cancellation technique was already demonstrated in some experimental works of Milling [1981], Liepmann et al. [1982a, b], Thomas [1983], Biringen [1984], Pupator & Saric [1989], Ladd & Hendricks [1988], Ladd [1990] as well as Grosche & Yong-Guang [1990]. Milling & Liepmann et al. used vibrating wires and heating wires respectively to show a successful superposition technique between a single-frequency wave and artificial antiwave in water tunnels. They also reported that, using the superposition technique, the second wave could force the boundary layer into a state of turbulence. Liepmann et al. carried out experiments on this technique with spanwise flush-mounted heating wires at two streamwise positions in a flat plate boundary layer. A TS wave was generated by the first heating wire upstream. This wave was damped downstream by the second wire, which generated a canceling wave at the same frequency but opposite in phase. Meanwhile, Thomas conducted experiments involving the superposition of the wave on an axisymmetric body in a wind tunnel. He used spanwise oscillation ribbons which carried alternating currents to generate a TS wave upstream and to cancel it downstream. The cancellation was carried out with alternating currents in different phases. Several years later, Pupator et al. showed the direct control of random waves in a flat plate boundary layer by using a periodic suction-and-blowing actuator in a wind tunnel. Some numerical investigations of a laminar-turbulent transition and its control by periodic disturbances were reported, e.g., by Kleiser et al. [1985], Joslin et al. [1996] and Mughal [1998]. Joslin et al. used fully unsteady Navier-Stokes equations in their numerical works for reducing TS instability waves. They suggested that the best cancellation result with the superposition technique is obtained when the disturbance is still primarily two-dimensional. Mughal reported an active wave control in a swept wing boundary layer. Some of the numerical works by Gmelin et al. [2000a, b] performed an open-loop feedforward control using an optimal, fixed filter to compute an appropriate canceling wave based on a reference wave upstream. The wave was, then, introduced into the flow by an actuator downstream to cancel the amplified reference wave propagating over the actuator location. It is clear that the experimental and numerical investigations described above had established the principle of transition delay to extend downstream region of laminar flow by a direct wave cancellation.
5. Adaptively Active Wave Cancellation The direct technique to reduce disturbance levels is adopted by active wave controls for canceling an unwanted propagating primary wave with a second set of electronically generated antiwave. This canceling wave is emitted into the flow by an actuator. A feedforward controller manipulates a signal from a reference sensor upstream in order to obtain an appropriate actuating signal delivered to the actuator. Due to randomly occurring disturbances or the variability in the physical system being controlled, the controller can generate the actuating signal optimally using an adaptive filter as conducted by Ladd et al. [1988]. A residual wave downstream is continuously sensed by an error sensor delivering a control feedback for an optimal adaptive wave cancellation. The adaptive filter is performed in a processor executing an algorithm, which improves its filter weights based on the signals of both sensors. Recently, Baumann et al. [1996, 1997, 1999, 2000] reported a considerable attenuation of TS waves in an unswept wing boundary layer by using such an adaptive filter with a digital signal processor. This system was able to damp mainly 2D waves up to 90% amplitude reduction and to delay transition over one tenth of the cord length. In [Baumann, 1999], complete basic wind tunnel investigations and performance range of the single-channel system are presented. Meanwhile, Enghardt [1996] reported the investigation result of adaptively suppressing Kelvin-Helmholtz instabilities of a 2D shear layer in a water tunnel. In addition, Raguse [1998] showed the similar adaptive technique for damping TS instability waves in a flat plate boundary layer with a single-channel active wave control system. Sturzebecher & Nitsche [2000] have shown a well attenuation of TS wave in the boundary layer on the upper surface of a wing with independent multi-channel sensor actuator systems.
6. Summary Summarizing the above research results, TS waves could be reduced indirectly by changing the characteristic of TS wave path and directly by emitting appropriate antiwaves in order to delay their development to the transition. The adaptive cancellation method has been applied in actively reducing such disturbances. One of future challenges may be an efficient global reduction of spatial TS waves. 7. References
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