This paper gives an overview of drag reduction on aerofoils by means of active control of Tollmien–Schlichting (TS) waves. Wind-tunnel experiments at Mach numbers of up to Mx=0.42 and model Reynolds numbers of up to Rec=2×106, as well as in-flight experiments on a wing glove at Mach numbers of M<0.1 and at a Reynolds number of Rec=2.4×106, are presented. Surface hot wires were used to detect the linearly growing TS waves in the transitional boundary layer. Different types of voice-coil- and piezo-driven membrane actuators, as well as active-wall actuators, located between the reference and error sensors, were demonstrated to be effective in introducing counter-waves into the boundary layer to cancel the travelling TS waves. A control algorithm based on the filtered-x least mean square (FxLMS) approach was employed for in-flight and high-speed wind-tunnel experiments. A model-predictive control algorithm was tested in low-speed experiments on an active-wall actuator system. For the in-flight experiments, a reduction of up to 12 dB (75% TS amplitude) was accomplished in the TS frequency range between 200 and 600 Hz. A significant reduction of up to 20 dB (90% TS amplitude) in the flow disturbance amplitude was achieved in high-speed wind-tunnel experiments in the fundamental TS frequency range between 3 and 8 kHz. A downstream shift of the laminar–turbulent transition of up to seven TS wavelengths is presented. The cascaded sensor–actuator arrangement given by Sturzebecher & Nitsche in 2003 for low-speed wind-tunnel experiments was able to shift the transition Δx=240 mm (18% x/c) downstream by a TS amplitude reduction of 96 per cent (30 dB). By using an active-wall actuator, which is much shorter than the cascaded system, a transition delay of seven TS wavelengths (16 dB TS amplitude reduction) was reached.
Since transition on an unswept wing is initiated by Tollmien–Schlichting (TS) instabilities , friction drag can be reduced by the attenuation of these waves. The experimental approach is based on the superposition principle and was first demonstrated by Liepmann et al.  and Milling  and later by Thomas  for two-dimensional mono- and bi-frequency TS waves, as well as by Pupator & Saric  for random noise signals. The natural amplification of controlled, generated TS waves was prevented by superposition of artificially generated counter-waves, leading to a delay in the laminar–turbulent transition. The downstream shift of the transition region results in lower overall friction drag due to the improved extent of the laminar boundary layer. A real-time filter model, based on the least mean square (LMS) algorithm , was used to calculate the appropriate counter-wave for the two-dimensional case. Evert et al.  and Opfer  developed and applied control strategies for a flat-plate boundary layer with two-dimensional components. The numerical investigation of Gmelin & Rist  used the TS information upstream of an actuator for the calculation of a wall-normal velocity fluctuation (v′) for the superposition process, which is directly connected to the streamwise fluctuation (u′). For more detailed information on recent progress, the work of Bagheri  dealing with a mode analysis for controlling transition or the work of Engert  on active wave control (AWC) applications in compressible flows are recommended. This short introduction on AWC approaches will now focus on the development and application of sensor–actuator systems for AWC at TU Berlin.
A two-dimensional system based on a slot actuator was successfully applied for TS wave cancellation in wind-tunnel experiments by Baumann & Nitsche . The sensor–actuator layout and the time signals show the basic principle of a closed-loop AWC system (figure 1) . Without AWC (off, no actuator signal), the TS waves grow while travelling downstream from the reference to the error sensor. With AWC (on), the controller can calculate a counter-wave at the slot actuator’s position. The superposition of the actuator’s signal and the TS wave will attenuate the flow disturbances. The result can be found in the error sensor signal. The TS wave is almost completely cancelled. Comparing this slot actuator to a membrane actuator, Sturzebecher & Nitsche  found better cancellation results using the membrane actuator by comparing the ratio between the r.m.s.-values of the error signal with and without control (attenuation) with respect to the maximum velocity fluctuation measured for the uncontrolled case. The selected power spectra of both actuator types at their highest attenuation rates illustrate the same trend (figure 2a). Sturzebecher & Nitsche  also investigated a spanwise and a cascaded sensor–actuator arrangement. The promising single-actuator approach was verified in free-flight experiments by Peltzer et al. , which will be presented in §3a, as well as in high-speed wind-tunnel applications by Engert et al. , presented in §3b. The next evolutionary step from a cascaded system to a streamwise extended actuation subsequently led to a distributed and wall-integrated configuration . Therefore, active-wall actuator arrays consisting of oscillating surface membranes were developed, and the results will be presented in §3c.
2. Sensor–actuator systems
Based on the principle setup shown in figure 1, each configuration presented consists of reference sensors upstream and error sensors downstream of a membrane actuator. Surface-mounted hot wires with 5 μm diameter served as sensors to detect the very small velocity fluctuations of the TS waves within the boundary layer. They generate negligible surface roughness and provide a high signal-to-noise ratio, as well as a 40 kHz cut-off frequency at the overheat ratio used, which is between 1.5 and 1.7 (cf. ). The sensors were not calibrated, but were adjusted for equal sensitivity in all experiments. The flexible membrane of the actuator is prestretched and then integrated into the surface to avoid any flow-disturbing roughness. To drive the membrane via a plunger, a voice coil or piezo elements are used (figure 3). The sensor signals are captured and amplified via constant-temperature anemometry (CTA) modules with subsequent signal-conditioning units built by TU Berlin. They are processed within a real-time application on a digital signal processing (DSP) system by DSpace, which also calculates the driving signal for the actuator.
Two different control strategies are implemented, depending on the actuation setup. A filtered-x least mean square (FxLMS) closed-loop control model (figure 2b) is used for single-actuator systems (and repeated for streamwise-cascaded systems), whereas for an active-wall actuator an open-loop, model-predictive control algorithm is necessary to calculate the signals for each actuator stage. For in-flight and high-speed experiments, the closed-loop FxLMS algorithm estimates the TS wave at the position of the actuator. The linear development of the travelling TS wave between the upstream reference sensor and the downstream error sensor is estimated within the control algorithm using both sensor signals (P(q−1)). Owing to the finite distance between the actuator and the error sensor, the error sensor signal cannot be used directly for the introduction of a proper counter-wave. In addition, the electrical and mechanical behaviour of the actuator system and the introduction of the counter-wave into the flow have to be represented in the algorithm. Therefore, the secondary path S(q−1), including all these influences, has to be identified in advance. For a correct identification of S(q−1), the naturally occurring TS waves have to be counterbalanced, using the primary path P(q−1). Otherwise, the signal of the naturally developing TS wave would be swapped over the process and would interfere with the identification of the secondary path S(q−1). Finally, the linear development of the TS wave over the sensor actuator system can now be used to estimate the control path W(q−1), symbolizing the distance between the reference sensor and the actuator. The signal of the reference sensor is filtered within the controller by the secondary path estimate (filtered-x) and the error sensor signal is used within the least mean square (LMS) algorithm to adapt the filter coefficients of the control path W(q−1) in real time. When the filters are perfectly adapted, the reference signal filtered with the control and secondary path would be identical to the signal of the error sensor. By using the linearity of the process, a counter-wave at the actuator’s position can be calculated. Subsequently, the counter-wave can be used to cancel the TS wave by superposition.
3. Active wave control applications
(a) In-flight experiments
The growth of natural TS waves strongly depends on the environmental flow conditions. With respect to practical aircraft applications, the AWC experiments by Baumann & Nitsche  had to be verified by in-flight experiments under real atmospheric conditions . These in-flight experiments were carried out on a two-dimensional laminar wing glove for a two-seater sailplane/glider (Grob G103). The measuring glove has a modified E603 profile with a two-dimensional central section of 1.0 m span and 1.22 m chord length and was mounted on the right wing of the glider (figure 4). The boundary layer on the glove was investigated at flight velocities ranging from 20 to 27 m s−1 (Rec≤2.4×106). The sensor–actuator system was matched according to these flight conditions.
An extract of a 2 s time signal (figure 5) of four spanwise-arranged reference and error sensors represents the natural TS instabilities on the glove without AWC. All reference sensor signals show TS wavepackets with relatively small amplitudes. The boundary layer is laminar. However, the wavepackets are in phase (two-dimensional); only the value of the amplitude differs, as was observed in previous flight measurements (cf. ). The reference sensor RS16 detected the most amplified TS wavepacket. The amplitudes of the error sensors are increased overall (figure 5b). The error sensor ES22 has higher amplitudes than the neighbouring sensors. This sensor is located downstream of the reference sensor RS16 mentioned. Owing to these spanwise variations in flight measurements, a spanwise autonomously working sensor–actuator system is needed.
The frequency spectra of a reference and an error sensor (RS16 and ES22) are given in figure 6 for different flight velocities. In the reference sensor signal the fundamental frequencies are amplified at all velocities over the sensor noise level. The highest amplification is reached at the lowest velocity (25.2 m s−1), corresponding to a high angle of attack of the sailplane, as well as the glove. In glider flights, the flight velocity depends directly on the angle of attack. In the error sensor signal (ES22) downstream of the reference sensor, all frequencies are more amplified, but still not turbulent. In addition to the enhancement of fundamental TS frequencies, the second-mode frequencies started to increase. The laminar boundary layer achieved an advanced amplification stage close to transition. For comparison of cases without and with AWC, the flight velocity, as well as the spectra of the reference sensor, had to match in order to guarantee the same boundary conditions.
Figure 7 shows power spectra of reference and error sensors with and without AWC as one result at a flight velocity of 26.5 m s−1. The spectra of every single reference sensor are exactly the same whether the AWC is activated or not. This proves the comparison of equal boundary-layer stages. Furthermore, the actuator has an insignificant influence up to the location of the reference sensors. Focusing on the spectra of the error sensor row (figure 7b), it is obvious that the amplitudes of the second-mode frequencies (1000–1600 Hz) are cancelled almost completely. At the spanwise position (ES22, z=−20 mm), where instabilities are amplified most, an attenuation of the fundamental TS instabilities of about 12 dB is reached. This corresponds to a local amplitude reduction within the fundamental frequencies of up to 75 per cent.
Figure 8a depicts a sequence of the time signal of the reference, the error sensor and the actuator of one streamwise system. For the case without AWC, the actuator signal is zero. With AWC, an actuator signal is generated and appears similar to the time signal of the reference sensor with a phase shift. The amplitudes of the error sensor signal are decreased compared to the case without AWC. The r.m.s. value of the same error sensor (ES22) is determined in figure 8b. The high r.m.s. value of up to t≈0.65 s represents the amplification of the TS wave at this transition stage without AWC. After turning on the actuation, the r.m.s. value is decreased. This means that the amplitudes of the TS waves were damped and the AWC was successful under atmospheric conditions.
(b) High-speed experiments
The AWC concept showed its ability to cancel TS waves at moderate velocities, but the conditions in practical aircraft applications, especially the higher Mach and Reynolds numbers, are much more challenging.
The sensor–actuator system was accordingly transferred to a model for high-speed experiments, which were conducted in the transonic wind-tunnel facility at TU Berlin. The open-loop wind tunnel can be adjusted to free-stream Mach numbers ranging from 0.2 up to 0.95. The high contraction ratio of the nozzle (47 : 1) reduces the free-stream turbulence intensity to 0.15 per cent. The two-dimensional test section was equipped with fibre-glass adaptive walls, which can be adjusted to impress a pressure gradient onto the flow, enforcing or attenuating the natural transition process. This will allow shifting the transition region to the sensor and actuator position at different free-stream Mach numbers. Therefore, one model can be used for different Mach numbers.
A NACA0004 aerofoil was used for the unswept leading edge of the 30 mm thick, generic wing model (figure 9a). In addition to the fibre-glass adaptive walls of the test section, the trailing edge flap of the model allows the adjustment of the pressure gradient on the aerofoil.
For basic high-speed investigations, sensor arrays of three spanwise rows consisting of five streamwise-located sensors each were used up- and downstream of the actuator (figure 9b). The highlighted sensors were used for the control experiments. The membrane actuator itself is located at x/c=30%, where c=833 mm is the chord of the aerofoil. This results in a local Reynolds number at the actuator’s position of Rex≈2×106 for a local Mach number of Mx=0.35.
A natural development of TS waves in the high-speed, low-turbulence wind tunnel dominated the flow field and led to a typical transition process. The sensor signals of the middle row (figure 10a, AWC off) depict the rising r.m.s. level at the transitional flow stage. The TS wavepackets can be detected in the time signal, as well as in the frequency domain. The fundamental and the higher-order instabilities are selectively amplified according to stability theory. Spectra of the error sensor are presented in figure 10b and show the growth of the primary TS frequencies at rising Mach numbers.
Focusing on the time signal of the error sensor in figure 11b (AWC off), the typical TS wavepackets were apparent. These TS disturbances can be clearly found within the power spectra of the sensor (figure 11a, AWC off). The wide peak between 4 and 8 kHz can be identified as the dominating part of the TS wavepacket. This first peak is followed by a second-order one in the range of 10–15 kHz.
As mentioned before, the reference signal is used by the FxLMS algorithm to calculate the counter-wave, which is introduced into the flow by the actuator, whereas the error sensor signal is used to adapt the filter weights of the algorithm. The time signal of the error sensor shows a significant reduction in amplitude and the TS wavepackets disappear with active control in place (AWC on). Alternatively, the power spectra of the error sensor can be used for validating the cancellation success. The amplitudes of the TS fluctuations are strongly reduced, achieving a reduction of 20 dB (90% TS amplitude) at a local Mach number of 0.42 in the frequency range of the main TS peak (figure 11a, AWC on). The high-frequency components are hardly affected due to the individual actuator characteristic in this frequency range.
Comparing the r.m.s. values over the model length for the actuated and non-actuated flow (Mx=0.35) as an example, a downstream shift of the transition region by seven TS wavelengths is obvious (figure 10a). The transition process can be successfully delayed by Δx≈45 mm. The remaining disturbances will start to grow again while travelling downstream.
(c) Low-speed wind-tunnel experiments with an ‘active-wall’ actuator
Owing to this reamplification of the TS waves, which are not completely cancelled, the control scheme can be cascaded streamwise to attenuate the remaining disturbances as long as a linear development is present. The work of Sturzebecher & Nitsche  presents a streamwise repeated arrangement for TS wave control in a low-speed wind tunnel on a modified NACA0008 aerofoil with a chord length of c=1.3 m at a free-stream velocity of u∞ =17 m s−1 (figure 12a). This streamwise cascade of three independent sensor-actuator systems cancelled the TS waves by ≈30 dB (96% amplitude) and shifted the transition 18% x/c (Δx=240 mm) downstream (figure 12b), but requires sensors between the actuators, as well as computational power to calculate three control paths individually.
An alternative and promising approach lies in an extended range of actuation. The transitional boundary layer is controlled by an increased area of the ‘active compliant wall’. Actuator arrays for spatial AWC consist of several single streamwise elements that oscillate one common surface membrane (figure 3b). Each element consists of a cymbal-like piezo-polymer composite construction. By deflection at different positions, the membrane can generate a ‘travelling wave’. In experiments, the extension from one locally fixed sensor–actuator system to a sequence of five streamwise cascaded actuator elements allows for an extended delay in transition, because reamplification of TS waves is delayed across a wider area (figure 13). The five-element ‘cymbal’ actuator applied was developed in collaboration with the Department of Microsystems Engineering (IMTEK) at the University of Freiburg .
With active-wall actuation it is impossible to integrate surface sensors between single actuator elements due to the continuous, common membrane. Another requirement is the calculation of up to five actuation signals from one global reference sensor located upstream of the active wall. The closed-loop controller introduced before is only capable of calculating one actuation signal out of a single reference signal. Apart from that, it needs continuous information on the flow directly downstream of the actuator elements. Because of these restraints, a real-time open-loop model-predictive control (MPC) strategy was implemented in cooperation with our project partners from the Department of Plant and Process Technology (MRT) of TU Berlin. For more detailed information, the work of King et al.  is recommended.
Together with the active wall and 20 surface sensors, this control system was applied in wind-tunnel experiments. Low-speed experiments were conducted in a low-turbulence wind tunnel on an unswept two-dimensional wing model based on a symmetrical NACA0008 aerofoil (c=1.3 m), which was also previously used by Sturzebecher & Nitsche . Figure 14 illustrates time traces of the 20 streamwise adjacent surface sensors. In figure 14a, the actuator is inactive and TS waves are amplified by the flow in the streamwise direction. With the actuator working, amplification is stopped and velocity fluctuations on the wing’s surface downstream of the membrane are even smaller than upstream of the actuator.
Figure 15a illustrates the actuation effect on the TS amplification and transition range. Overall fluctuation amplitudes downstream of the actuator are reduced by 83 per cent. Consequently, laminar–turbulent transition on the test wing is delayed in the direction of the trailing edge by approximately 140 mm, which equals about seven average TS wavelengths. The TS cancellation in the frequency domain is shown in figure 15b. At the error sensor position, 15 mm downstream of the actuator, the first mode of unstable TS frequencies between 200 and 600 Hz is attenuated by 16 dB. Owing to mode coupling, the second-mode instabilities around 1 kHz disappear almost completely.
A snapshot of the membrane displacement of the ‘wavy wall’ actuator section is shown in figure 16 for two different time steps. These values were derived indirectly from the known actuator transfer function and the actual controller signals during AWC. The generation of a travelling counter-wave can be observed. The required displacement amplitudes go up to ±30 μm, which equals ±1% of the boundary-layer thickness δ99. As expected, the generated wavelength corresponds to the average TS wavelength of λTS=20 mm for this particular boundary-layer flow (Pätzold et al. 2010, unpublished work).
The principle of AWC by means of wave superposition was successfully transferred to an actuator system for flight experiments on a laminar wing glove. The results confirmed the sensor–actuator system, as well as the principle itself, of cancelling the TS waves by 12 dB (75% local TS amplitude). The high-speed wind-tunnel experiments used a similar membrane actuator layout on a generic wing model to transfer the promising single-actuator results to higher Mach numbers. The transition region was shifted about seven TS wavelengths (≈45 mm) downstream at a local Mach number of Mx=0.35. For Mx=0.42 at the actuators position, a TS wave amplitude reduction of 90 per cent (20 dB) was achieved. The one-stage layout of the actuator was successfully extended to a cascaded system on a modified NACA0008 profile to delay the amplification of the remaining flow disturbances at a Mach number of M≤0.1 by Sturzebecher & Nitsche . A significant shift of 18 per cent chord length was achieved, which in absolute numbers equals a transition delay of Δx=240 mm for a sensor–actuator system extending over the same range.
An active-wall actuator will cover a wider streamwise distance when compared with a single actuator. Placing the sensors up- and downstream of this spatially distributed actuator is the logical step to a ‘wavy wall’ actuator system, covering the wing surface for complete suppression of the TS waves. A five-stage piezo-driven wavy wall actuator was able to successfully delay the transition by Δx=140 mm (x/c≈11%) in low-speed wind-tunnel experiments. Referring the transition shift Δx to the sensor–actuator extension (xwavy wall=80 mm) results in a factor of Δx/xwavy wall≈1.75, showing the superiority of the wavy wall compared with the cascade, which only reaches a factor of Δx/xcasc=1.
This paper is based partly on investigations conducted within the AVERT (Aerodynamic Validation of Emission Reducing Technologies) research project funded by the European Commission and partly on research undertaken in the framework of the SPP1207 DFG-Priority Program, Nature-Inspired Fluid Mechanics (Strömungsbeeinflussung in der Natur und Technik).
One contribution of 15 to a Theme Issue ‘Flow-control approaches to drag reduction in aerodynamics: progress and prospects’.
- This journal is © 2011 The Royal Society