WO2015024601A1

WO2015024601A1 - Boundary layer control via nanosecond dielectric/resistive barrier discharge

Info

Publication number: WO2015024601A1
Application number: PCT/EP2013/067532
Authority: WO
Inventors: Giuseppe CORREALE; Ilya Popov
Original assignee: Correale Giuseppe; Ilya Popov
Priority date: 2013-08-23
Filing date: 2013-08-23
Publication date: 2015-02-26
Also published as: WO2015024601A8; EP3036977A1

Abstract

A System for controlling boundary layer of a fluid flowing over the surface of a body (2) is described. The system comprises at least one nanosecond- dielectric/resistive barrier discharge plasma actuator (1) disposed on said surface of said body (2) at a specific location according to the task to be performed, at least one probe (8), placed on the surface of said body (2) at a specific location according to the task to be performed by said actuator (1), to measure characteristics of the flow and to emit signals corresponding to said characteristics, a highvoltage nanosecond pulse generator (6) to apply at least one specific high voltage nanosecond pulse to said at least one actuator (1) and a controller (9) connected to said probe (8) to drive said highvoltage nanosecond pulse generator (6) according to said signals emitted by said probe (8). Different application scenario of the system are described.

Description

BOUNDARY LAYER CONTROL VIA NANOSECOND DIELECTRIC/RESISTIVE BARRIER DISCHARGE

Field of the invention

The present invention relates to devices, systems and methods for controlling shear and boundary layers of a fluid flowing over a surface of a body by dielectric/resistive barrier discharge plasma actuators.

Background art

It is well known in aerodynamics that a body having an aerodynamic profile that moves within a fluid experiences the formation of a boundary layer (BL) over its surfaces. This is because the layer of fluid particles that directly touches the surfaces have no relative motion with respect to that surfaces. Considering the various layers of fluid particles in the outward orthogonal direction from the surfaces, each fluid layer has a velocity a bit higher than the one closer to the solid wall until the upper layer whose velocity equals the relative velocity of the free stream with respect to the aerodynamic body, creating in this way a velocity gradient in the direction perpendicular to the solid wall. This phenomenon is due to the viscosity interaction between the fluid layers. The BL is, by definition, a thin region of a wall bounded flow where viscosity is not negligible. The height of the BL is defined by the location of the fluid layer having a velocity equal to the 99% of the free stream velocity. The BL can be classified in three main categories: 1 ) laminar, 2) transitional and 3) turbulent, depending upon the state of motion of the fluid layers. Aerodynamics performances of moving bodies, such as aircrafts, are directly dependent upon the properties of the BL that they develop. As a matter of fact, the BL increases the effective thickness of the body on which it is formed, in turn increasing the thickness of the wake that the body generates. During motion, a negative pressure gradient can separate the BL from the surface, forming a shear layer (SL), thus increasing the size of the wake that the aerodynamic body generates during its motion, in turn increasing drag and reducing the efficiency of the vehicle itself. On an air vehicle, such as an aircraft, BL separation, i.e. due to negative pressure gradient or side and/or vertical gusts, causes a loss of lift giving rise to a high risk for the people on board. In order to increase efficiency and safety of vehicles, devices, systems and methods for flow control were designed. With flow control it is meant the ability to alter favourably the natural characteristic or disposition of a flow. Regarding wall bounded flows in particular, flow control means BL control: it includes any mechanism or process through which the BL of a fluid flow is caused to behave differently than it naturally would, while developing along a smooth straight surface. The flow control techniques can be divided into two main categories: 1 ) Passive and 2) Active. Passive techniques refer to systems mounted on the external surfaces of a body that actuate mechanically the flow at any moment, even when it is not required. The main drawback of this kind of techniques is that they cannot be "switched off," so they produce additional drag at any time. In order to solve problems of passive techniques, active techniques have been made. An active flow control is a system that can be activated by a user, or by an automatic or semi-automatic control loop, only when it is required. More specifically with active flow control it is meant the possibility to control actively the flow, i.e. any system or device that operates only when flow control is required. They have a characteristic higher efficiency than passive flow control techniques. On the other hand, active flow control techniques have the drawbacks of being expensive, in terms of required energy and constructive costs, and are highly complex due to their kinematic mechanisms and moving elements. In order to overcome the drawbacks due to mechanical moving components new non- mechanical active control techniques have been developed. An ideal system would be a system able to actively control the flow without using kinematic mechanisms and moving elements, and thus have all the positive effects of an active technique without its drawbacks. Currently, there is a strong interest for using dielectric barrier discharge (DBD) plasma actuators for active flow control. This technology is believed to be very promising. Appealing aspects of these devices are a cheap and simple layout combined, being fully electronic, with no moving parts and fast response time, besides energy consumption is rather low. These devices ionize the air close to the surface of the aerodynamic body in such a way to influence the flow adjacent to said surface. A DBD plasma actuator, see Fig.2, consists of two electrodes 4, 5, one normally exposed to the flow and the other embedded in a dielectric barrier layer. The two electrodes 4, 5 are activated by a high voltage generator 6. Different type of actuators have been studied and proposed based on the type of high voltage generator driver. The first type of actuator being proposed is the AC-DBD plasma actuator that is driven by a high voltage alternating current (AC) power generator with a discharge time of the order of milliseconds. In this type of actuator the ionized air, i.e. the plasma produced, results in a vectorial body force that acts on the neutrally charged air surrounding the discharge. AC-DBD plasma actuators have shown a low control authority, limiting its applicability. The low control authority of the AC-DBD plasma actuator comes from the fact that said body force can modify flow field but its effectiveness is reduced with increased velocity of the flow under control. So for high velocities the AC-DBD plasma actuator cannot operate effectively. Moreover, it has been demonstrated that the nature of AC discharge is a self-limiting process since the direction of the body force produced by an AC-DBD plasma actuator depends upon the phase of the AC waveform. Therefore, researchers have pushed the envelope in order to overcome the limitations of the AC-DBD plasma actuator. To overcome these limitations researchers have studied the possibility of creating discharges by using waveforms other than AC. The Nanosecond variant of DBD (NS-DBD) plasma actuators has shown higher control authority with respect to AC-DBD plasma actuators. NS-DBD plasma actuators are actuated by a high voltage nanosecond (NS) pulse current signal, giving rise to a different plasma phenomenology when compared with AC-DBD plasma actuators. NS-DBD plasma actuator relies mainly on thermal effect and not only on the creation of a body force, but their working principle is not yet completely known. Several studies demonstrated the capability of the NS-DBD plasma actuators to actively control the flow in condition of leading edge separation. NS-DBD plasma actuators are able to overcome the limitations of the AC-DBD plasma actuators: they have much lower energy consumption, increased lifetime and the actuation mechanism is not self-limiting. NS-DBD plasma actuators can work within a much wider range of velocities and fly conditions with a reaction time in the order of 0,1 milliseconds. They have also the capability of noise reduction and de-icing. One of the problems of the NS-DBD plasma actuators is that they do not work reliably for every scenario. This is because their efficiency is strictly dependent on the location where they are placed and on their geometry. On the other hand, not knowing exactly the working principle of the thermal effect produced by the NS-DBD plasma actuator, does not allow to determine where to place it in order to achieve a specific flow control task. There are many cases where flow control might not only be beneficial but also necessary: it could be used for reducing drag, enhancing lift, increasing safety as well as for designing super manoeuvrable fighter planes, longer-range-more-precise missiles, or faster and quieter underwater vehicles, till hypersonic transportation and spacecraft launcher. Thus, an improvement in the efficiency and reliability of the NS-DBD plasma actuator is highly needed.

Brief Description of the Invention

The main object of this invention is to solve the problems of the low efficiency/effectiveness of NS-DBD plasma actuators and to provide devices, systems and methods, based on this kind of actuators, that can perform different tasks of active flow control. These objects are achieved by a system for controlling, according to claim 1 , boundary layer of a fluid flowing over the surface of a body, according to the task to be performed, comprising:

a) at least one nanosecond dielectric/resistive barrier discharge (NS-D/RBD) plasma actuator located on said surface at a predefined location;

b) at least one probe, placed over said surface at a predefined location for measuring characteristics of the flow and to emit signals corresponding to said characteristics;

c) a high voltage nanosecond pulse generator for applying at least one specific high voltage nanosecond pulse to said at least one nanosecond dielectric/resistive barrier discharge plasma actuator;

d) a controller connected to said probe for driving said high voltage nanosecond pulse generator according to said signals emitted by said probe;

wherein said at least one nanosecond dielectric/resistive barrier discharge plasma actuator comprises:

- a dielectric or resistive barrier layer defining two major parallel surfaces opposed one to the other having the longest extension in a direction transverse to the incoming flow defining a "z" axis of a Cartesian coordinate system where the thickness of said barrier layer is parallel to the "y" axis and the width of said barrier layer is parallel to the "x" axis.

- two electrodes each of them micromachined or printed directly on one of said two major parallel surfaces of said barrier layer, being perfectly flushed to said surfaces, the first electrode being laterally shifted with respect to the second electrode forming a gap of zero millimetres in the x- direction.

The NS-D/RBD plasma actuator of the invention introduces into the BL under control a thermal disturbance that changes locally the thermodynamics proprieties of the air within the discharge volume. The invention is based on the fact that such thermal disturbance can be manipulated and then be used for controlling SL and BL. The invention aims to an NS-D/RBD plasma actuator that optimizes this thermal effect. The required manipulation is designed taking into account the flow field to be controlled and the kind of task that is desired to achieve.

Among the tasks that can be performed by an NS-D/RBD plasma actuator of the invention, there are the ones related to: 1 ) delay/advance transition, 2) suppress/enhance turbulence, 3) prevent/provoke/delay flow separation, 4) reduce noises or 5) melt ice formed during flight.

The position of the NS-D/RBD plasma actuator on the surface so as the voltage amplitude, pulse width and repetition rate are function of the specific application. The barrier layer can be either resistive, e.g. made out of silicon based foam or rubber, either dielectric, e.g. made out of a polyimide. As it will be explained below in the detailed description of the invention, using a resistive barrier layer instead of a dielectric one enables manipulation of said thermal effect to widen the range of applications. Advantageously, the electrodes have the shape of a parallelepiped with the longest side having a direction transverse to the flow direction, i.e. the z- direction. The actuator works as a transmission line where the signal enters the short side parallel to the x-y plane and is reflected at the open end on the opposite side. In a preferred embodiment of the nanosecond dielectric/resistive barrier discharge (NS-D/RBD) plasma actuator the parts of the electrodes at the open end, on the side where the electrodes face each other, are rounded. The length and the width of the NS-D/RBD plasma actuator are functions of the specific application and the high voltage nanosecond pulse generator used. Advantageously, one of the electrodes is exposed to the flow and the other one is embedded into said barrier layer. Advantageously, the length of the embedded electrode is higher than the length of the electrode exposed to the flow.

Brief description of figures

Further characteristics and advantages of the invention will become more apparent in light of a detailed description of a preferred embodiment, but not exclusive, of an NS-D/RBD plasma actuator, illustrated by way of example and not limited, with the aid of the accompanying figures in which:

Fig. 1 represents a diagram showing the physical principle of NS-D/RBD actuation. Fig. 2 represents a schematic drawing of the NS-D/RBD plasma actuator according to the invention.

Fig. 3 represents the NS-D/RBD plasma actuator as a transmission line with a preferred embodiment of the shape of the electrodes.

Fig. 4 represents the same NS-D/RBD plasma actuator of Fig. 3 in a 3- dimensional representation.

Fig. 5 represents an array of NS-D/RBD plasma actuators disposed on the wing of an aircraft.

Fig. 6 represents different application scenarios of the NS-D/RBD plasma actuator according to the invention.

The same reference numbers in the figures identify the same elements or components.

Detailed description of a preferred embodiment of the invention

The NS-D/RBD plasma actuator 1 introduces into the field of motion a discontinuity into the viscosity field. The intensity of the jump into the viscosity field is the key parameter. Such disturbance, travelling during the flow motion, develops in space and time. It could get naturally amplified or dumped down. The location where the disturbance is introduced, its amplitude and its frequency range are crucial parameters, and a proper design should be such to make the smallest possible disturbance, i.e. lowest energy expense, to grow big enough in order to drive a laminar to turbulent transition of the boundary layer under control. Thus, the efficiency η of a NS-D/RBD plasma actuator, depends on its location on the surface of the moving body 2. Moreover, the efficiency η of a NS-D/RBD plasma actuator also depends on its geometry. The location of the NS-D/RBD plasma actuator, the applied voltage, pulse duration and repetition rate depend also on the specific task. For example, on an aircraft the system can be designed such to increase lift during take-off. However, if a vertical gust happens it will change boundary conditions, so changing the values of voltage amplitude and repetition frequency required for achieving the designed task.

Figure 1 shows the physical principle of a NS-D/RBD actuation. The plot represents "the stability diagram" of a wall bounded flow. On the x-axis the Reynolds Number based on the displacement thickness (Re₈*) of the BL, defined as:

_ U8* (x)

^{Ke *} -— ^~ V— where U is the free stream velocity, v is the kinematic viscosity and δ*(χ) is the displacement thickness of the BL. This equation defines the relation between Reynolds number and position on the x-axis. On the y-axis the non-dimensional frequency (cog*) defined as:

2n *(x)f_r

ω*· =—— where δ*(χ) is the displacement thickness of the BL, fr is the frequency in Hz and U is the free stream velocity in meter/sec. The plot is calculated solving the Orr- Sommerfeld equation. In the derivation of the Orr-Sommerfeld equation a disturbance stream function ψ is defined as:

Where ψ is the stream function, φ is the amplitude of the fluctuation, a is the wavenumber, x is space, ω is frequency, t is time and i is the complex coefficient. In the so-called spatial mode of stability analysis the circular frequency ω is assumed to be real and the wave number a to be complex, so: a = a_r + ia_t Where (¾. is the real part of the wave number and ¾ is the imaginary part of the wave number. Combining the last two equations it is possible to obtain an equation that represents the evolution in space of any disturbance introduced into a BL:

It follows that a disturbance grows, remains constant or decays with x for ¾ < 0, ¾ = 0, (¾ > 0 respectively. The contours in the stability diagram depict (¾ levels, labeled on the contours lines in the figure. The contour line indicated with the reference A represents the neutral curve ((¾ = 0). The dashed contour lines represent the stable region of the BL (¾ > 0), solid contour lines represent the unstable region (¾ < 0). So we can define -¾ as the amplification rate of the given disturbance. Moreover, in the plot a dashed black vertical line represents the frequencies triggered by the NS-D/RBD plasma actuator at the location where it is placed and where the thermal disturbance is introduced. The y value of the intersection point (square symbol in the plot) between this line and the contour represents the least stable non-dimensional frequency triggered by the NS-D/RBD plasma actuator, i.e. the frequency that is most excited naturally. If the NS-D/RBD plasma actuator, as it is represented in the figure, is placed in the stable region of the BL, the amplitude of the thermal disturbance introduced will always decay downstream. In order to make the NS-D/RBD plasma actuator work, the amplitude of the disturbance that it is produced has to be big enough in order to reach the unstable region with an amplitude that is in the same order of magnitude of the smallest fluctuation present into the flow at that location (about the 1 % of the free stream velocity). The amplitude of the disturbance can be calculated, according the linear stability theory, as:

„ +■ da p-«t( +dx)

' ϊ

And after integrating the latter equation, we obtain: In (— J = j —a_tdx

\<½/ J where x₀ is the station where the disturbance with frequency ω and amplitude a₀ first becomes unstable (circle symbol in the plot). So the optimal location for NS- D/RBD plasma actuator 1 can be determined knowing: 1 ) a i.e. the amplitude of the disturbance given by the NS-D/RBD plasma actuator, which depend upon the supplied high voltage nanosecond pulse amplitude and upon the geometrical properties of the NS-D/RBD plasma actuator, 2) a₀ i.e. the amplitude of a minimum fluctuation in the unstable region that is usually about 1 % of the free stream velocity, and 3) i.e. the amplification rate. In turn, the NS-D/RBD plasma actuator, depending on the amplitude of the disturbance that it is able to introduce into the field of motion, has to be placed in a location such that said thermal disturbance, growing thinner developing downstream, does reach the unstable region of the BL under control with an amplitude still comparable to the smallest fluctuation present into the flow at that location. Once the thermal disturbance gets into the unstable region the natural selected amplified frequency will depend on the flow case under consideration, according to linear stability theory. For instance, in the figure the two solid lines B and C represent respectively the most amplified frequency naturally selected by the flow itself at the location where the disturbance get introduced and at the first unstable point in the field of motion respectively.

Fig. 2 represents the NS-D/RBD plasma actuator 1 according to the invention, showing the dimensions (not in scale) of the most important elements. The NS- D/RBD plasma actuator 1 comprises one electrode 4 made for example of copper, micro-machined or printed directly on the barrier layer 3, being perfectly flushed. Said barrier layer 3, is dielectric is preferably made out of polyimide, if resistive is preferably made out of silicon based foam or rubber. The thickness of said dielectric or resistive barrier layer 3 depends upon the specific task for which the system is designed. A second electrode 5, that can also be made out of copper, is also micro-machined or printed directly on the other side of the barrier layer 3, being perfectly flushed, and is laterally shifted with respect to the first electrode 4 forming a gap gD of zero millimetres in x-direction. Length in z-direction of said first electrode 4 is designed upon the specific application and on the high voltage nanosecond pulse generator used, while said second electrode 5 is between 1 to 5 % longer with respect the first electrode 4 and with a width depending upon the specific application and on the high voltage nanosecond pulse generator used. The thickness of both electrodes should be as small as possible. Said flow control device is perfectly flush mounted on the surface exposed to a fluid flow of said aerodynamics body 2, with said first electrode 4 exposed to the flow. The electrodes 4, 5 are coupled with a high voltage nanosecond pulse generator 6. Said high voltage nanosecond pulse generator 6 can be furnished with batteries package 10, Fig.6, designed according to the specific application. A controller 9, see Fig. 6, is coupled with said high voltage nanosecond pulse generator 6. The controller 9 is programmed to activate the system maximizing the efficiency based on the feedback received through a feedback loop that comprises at least a probe 8 that measures the flow characteristics downstream the NS-D/RDB plasma actuator 1 . A high voltage nanosecond pulsed electrical input is applied to the said electrodes 4, 5 such that an electrical field is built up between them. Said applied high voltage nanosecond pulse is in the order of various kilovolts, with a length in time of several tens of nanoseconds. The rising time of said high voltage nanosecond pulse is an important parameter; in general the smaller the better. It does affect the actual shape of the high voltage nanosecond pulse so changing the amount of energy releasable into the flow. Moreover, the rising time affects the uniformity of the discharge and the velocity of propagation of the high voltage nanosecond pulse throughout the NS-D/RBD plasma actuator 1 , ultimately affecting the upward scalability limit of the length of the electrodes 4, 5. The applied voltage is much higher than the threshold of air for electrical breakdown so a glow discharge takes place between the electrodes 4, 5. The upper limit of the applied high voltage nanosecond pulse has been found experimentally to be of the order of 10 kV. Electrons leave the exposed electrode 4 trying to reach the other one 5. The discharge cannot reach the second electrode 5 in the case of a dielectric barrier 3, or only partially in the case of a resistive barrier 3, so electrons get accumulated on the surface of the barrier 3. Few nanoseconds after the energy input, when potential voltage of the applied pulse drops to zero, a new voltage potential is created between the exposed electrode 4 and the electrons accumulated on the barrier layer 3, these electrons move backwards into the exposed electrode 4, producing a second discharge. The time between the two discharges is called "silent period" of the discharge. Being the electrical field several times higher than the breakdown threshold for air, the energy discharged is such that electrons, travelling from an electrode towards the other one, are able to hit and dissociate the flow molecules exciting their translation degrees of freedom. The dissociated particles then translate towards the external edges of the discharge volume, expanding adiabatically for the first microsecond, in turn, increasing temperature and pressure within the discharge volume. The formerly discussed thermal phenomenology produces several effects listed hereafter. A small body force develops in the perpendicular direction with respect to the plane where NS-D/RBD plasma actuator 1 is applied. Such small body force generates a velocity change of about 0,3 m/s. This momentum produces a fluctuation of the vertical component of the velocity from a flow point of view. As well as momentum, also a fluctuation into the pressure field is created. Such discontinuity travels downstream as any discontinuity would, moving along specific paths related to the specific hydrodynamics flow case. In case the fluid is a gas, e.g. air, within the discharge volume a viscosity rise to a temperature rise corresponds. Such viscosity rise creates a gradient of viscosity related to the temperature gradient. It does affect the velocity gradient to which it is overlapped. As well as gradient of viscosity, together with gradient of temperature, also a gradient of density is formed. One microsecond after the discharge the gas starts expanding. A shock wave is then formed, such shock wave moves for the first few micrometres with a speed about 1 ,5 times the speed of sound. The shock wave speed propagation decays very rapidly to the speed of sound within few microseconds, becoming a sound wave while propagating downstream. Moreover, within the discharge volume, weak compression takes place after the shock wave when it is still supersonic, so a tiny increase of the heat capacity of the fluid mass behind it in turn. The shock wave, having a velocity dependent on the velocity of the mean in which it is travelling and considering that it is created in a region where a velocity gradient exists, in turn induces a small pressure gradient throughout the shear or boundary layer thickness in which it is propagating. Briefly: about one microsecond after the discharge, with voltage peak in the order of several kilovolts, rising time in the order of nanoseconds and width in the order of tens of nanoseconds, pressure and temperature rise within the discharge volume because of the energy released into the flow by the discharge, (such energy activates translation degrees of freedom of dissociated particles). Rises in temperature and pressure produce a small body force, pressure and velocity fluctuations, viscosity and density gradients and two shock waves (one for each period of the discharge). From an energetic point of view, a very fast and sharp input, independently from its nature i.e. momentum/ viscosity/ pressure fluctuation/gradient, or any combination of them, even if very small, results to be still in the same order of magnitude with respect to the region of the field of motion where it is introduced. This very fast and sharp electrical input, which can be approximated by a Dirac delta function, excites the flow with its own typical gasdynamics time scales. Such impulsive reaction represents the actual input of the NS-D/RBD plasma actuator into the flow. Such input, in a bounded flow case, produces as output a hydrodynamic instability called "wave packet". This wave packet is basically composed by a train of waves within a specific frequency range, depending upon the sharpness of the impulsive flow reaction to the energy input of the NS-D/RBD plasma actuator 1 . Those waves, depending upon the frequency they have and the location where they are inputted, have different growth rates, according to Linear Stability Theory. While developing in space and time, they are able to interact with flow structures such as any specific hydrodynamic instability depending on the considered flow case. So, active flow control is achievable as long as the energy input of the NS-D/RBD plasma actuator 1 can be manipulated in such a way to produce as an output an impulsive flow-input with a frequency range comparable to the one of the natural hydrodynamic instability relative to the specific flow case under control. This means that for each specific flow case different strategies are to be taken in order to achieve active flow control. Parameters that will affect the control of the flow are: location of the plasma actuator 1 , high voltage nanosecond pulse shape, frequency of discharge, direction of the momentum input with respect to the direction of the free stream, strength of pressure gradients. All these terms have to be taken into consideration while designing a flow control strategy, since they all contribute to the formation of a wave packet capable of affecting the specific hydrodynamic instability for the specific flow case under control. Manipulation of said wave packet is then necessary in order to carry out any flow control task. In order to do so embodiments of methods are sought. Coming back to the geometrical configuration of the actuator 1 , the dimensions in the x- direction of W1 and t_u of the electrode 4 exposed to the flow are not so relevant for the final goal of flow control since the energy given with the discharge is not stored into the conductive material of the electrode itself. The discharge length is depending on the shape of the high voltage nanosecond pulse, the thickness of the barrier tu and the gap ge between the electrodes 4, 5. Electrons leave the exposed electrode 4 and propagate along the covered electrode 5. If this electrode 5 is not wide enough, the length of the discharge will be shorter than one expected, thus thermalizing a smaller portion of air, and reducing the NS-D/RBD plasma actuator effectiveness. It is found experimentally that for a voltage of 10 kilovolt, a barrier thickness of 198 μιτι and a gap ge between electrodes 4, 5 of 0 mm, the optimal width W2 for the covered electrode is about 5mm. The thickness tr of the barrier layer 3 interposed between the electrodes 4, 5 is depending on the kind of barrier i.e. if it is resistive or dielectric and on the amplitude of the maximum voltage applied. It might also be dimensioned in order to increase the lifetime of the NS- D/RBD plasma actuator 1 . Thermal effect of the NS-D/RBD plasma actuator 1 also depends on this parameter, i.e. on tr. The thicker the barrier is, the smaller the electrical field between the two electrodes 4, 5, and in turn a smaller thermal disturbance is introduced. Theoretically it is possible to calculate the barrier dimension taking into account its dielectric constant ε, knowing the value of the electrical field necessary for obtaining a wanted effect. Nevertheless, optimal dimensioning requires tests. Electrodes 4, 5 must be printed or micromachined with a thickness tu as small as possible, preferably in the order of nanometers, in order to obtain a more evenly distributed energy input all along the length of the NS-D/RBD plasma actuator 1 . The distance ge between the electrodes 4, 5 is a very important parameter that affects the effectiveness and the efficiency of the plasma actuator 1 . If the two electrodes 4, 5 are overlapped, i.e. if ge is negative, they work as a capacitor, storing energy between them and not inputting that energy into the flow, so the efficiency is reduced. On the other hand, if they are displaced at a certain distance, i.e. ge is positive, the electrical field drops, and the discharge is shorter, thermalizing a smaller portion of air, so reducing its effectiveness. The gap ge between the electrodes 4, 5 must be zero millimeters. In order to ensure this optimal gap ge=0, the electrodes 4, 5 must be printed or micromachined. The length of NS-D/RBD plasma actuator 1 in the third dimension, i.e. in the span direction, that is the z-direction in Fig. 4, is dimensioned upon the length in time of the given electrical pulse and its velocity of propagation. Another important detail to notice in figure 2 is that the plasma actuator is perfectly flushed to the surface 2 where it is applied, in order not to trip mechanically the BL under control.

FIG. 3 and 4 show the NS-D/RBD plasma actuator 1 seen from different prospective. In Fig. 3 the NS-D/RBD plasma actuator 1 seen from the top, with the longest dimension perpendicular to the flow direction. Experiments have shown that a NS-D/RBD plasma actuator 1 acts as transmission line. High voltage nanosecond pulse travels within the NS-D/RBD plasma actuator 1 with a speed equal to 0,5 times the speed of light. Experimentally it is possible to determine the velocity of propagation of the high voltage nanosecond pulse within the given actuator geometry, where the velocity of propagation depends on the electrical impedance of the NS-D/RBD plasma actuator 1 , that depends upon the thickness of barrier tr, and the electrical impedance of the high voltage cable used for feeding the NS-D/RBD plasma actuator 1 with the high voltage nanosecond pulse given by the high voltage nanosecond pulse generator 6. Thus, knowing the velocity of propagation and the length in time of the high voltage nanosecond pulse, it is possible to scale upwards the NS-D/RBD plasma actuator 1 . For a given high voltage nanosecond pulse of about 23 nanoseconds, the maximum length obtainable is calculated as: maximum length [m] = (Velocity of the pulse[m/s]) * (width of the pulsels]) In our case maximum, length = ^1.5 * 10⁸ — * (23 * 10 ⁹ [≤·]) ¾ 3.5 [?n]

Impedance is dependent on the parameters of the NS-D/RBD plasma actuator 1 such as geometrical dimensions and dielectric constant of materials used, and in experiments it was found to be in the range Z = 50-1 00 Ohms. This effect has the following consequences:

1 ) for the best performance the impedance of the feeding cable should match the impedance of the NS-D/RBD plasma actuator 1 .

2) at the end of the NS-D/RBD plasma actuator 1 reflection occurs.

Reflection from the open end of the transmission line has the same polarity as the incident high voltage nanosecond pulse, which sums up producing a doubled voltage at the open end of the electrodes 4, 5. Since a uniform barrier thickness t_r is used along the whole NS-D/RBD plasma actuator 1 , the said thickness t_r of the barrier layer 3 should be dimensioned based on two times the voltage of the inputted high voltage nanosecond pulse. An excessive increase of the thickness t_r of the barrier leads to a lower electric field strength resulting in suboptimal performance. To mitigate this negative effect, the magnitude of the reflection can be lowered by making the electrodes 4, 5 of different lengths. Additionally, at the sharp corners of the electrodes 4, 5, the electric field is stronger, increasing the risk of the barrier layer 3 breakdown. As a workaround, the corners of the electrodes 4, 5 facing each other are made rounded 7 at the open end of the NS- D/RBD plasma actuator 1 . Fig. 4 shows a three dimensional prospective of the NS-D/RBD plasma actuator 1 , where the x-direction is roughly the direction of the incoming flow. It is possible to note the longer dimension of the embedded electrode 5 and the rounded corners 7.

Fig. 5 shows a wing 200 with a linear array of NS-D/RBD plasma actuators 1 , each one or group of them having different tasks. In the figure are represented also different pressure probes 8, implemented on the surface of the wing 200, to read the pressure fluctuations within the pressure field around the wing 200 and aimed to determine whether flow is attached on the surface or separated. Pressure probe 8 can be substituted with any other kind of aerodynamic diagnostic probe e.g. Pitot probes, pressure transducers, hot wires, etc. References 6, 9, 10 indicate forms of hardware comprising a high voltage nanosecond pulse generator 6, a controller ( micro On Board Computer) 9 and a battery package 10

Fig. 6 shows some application scenarios of NS-D/RBD actuators 1 . Promising applications of plasma devices, such as NS-D/RBD plasma actuators 1 , involve laminar-to-turbulent BL and SL transition control; flow separation delay or elimination with the consequent lift over drag enhancement; NS-D/RBD plasma actuator can also be used as shock wave patterns control as well as shockwave- BL interaction. Moreover, an active de-icing system can be designed capable of melting ice on flow stagnation points and it can also be used for designing a noise reduction/destruction system. Position of the NS-D/RBD plasma actuator 1 , applied voltage, pulse duration and frequency rate depend, as we have described, on the specific task. Fig. 6A shows an application of the actuator related to leading edge laminar separation control. The NS-D/RBD plasma actuator 1 is placed in the neighbourhood of the leading edge of the airfoil 2. A probe 8, for example a pressure trasducer, measures the status of the airflow downstream, then the signal from the probe 8 is fed into the controller 9 which governs the operation of the high voltage nanosecond pulse generator 6. Depending of the flight conditions, a pulsed discharge with voltage amplitude of at least 2500 V is applied to the electrodes 4, 5 of NS-D/RBD plasma actuator 1 . The repetition frequency F of the high voltage nanosecond pulses can be calculated according to the formula:

(F x L)/U=2

where L represents length of flow separated , U is free stream velocity and 2 is a coefficient found experimentally. The Voltage V is determined such that the electric field created E, accounting for the dielectric constant ε of the barrier layer 3, is higher than the threshold E_t of molecolar dissociation of the flow and lower than the E_b breakdown voltage of the barrier layer 3:

E,< E <E_b

The system can react quickly to any sudden lateral or vertical gust, forcing the flow to reattach thereby reducing flight turbulence and at the same time reducing the drag due to the wake generated by the separated flow. In turn, at the same time the system increases flight safety, increases the efficiency of the aircraft, reduces fuel consumption and increases range of manoeuvrability of the aircraft. Moreover, it is possible to have the wing more inclined with respect to the free stream flow direction such to produce a higher lift while producing a low wake drag, so allowing shorter strokes for landing and taking-off, with an increase of the safety.

Fig. 6B shows the application of the control system to flow laminar separation delay and laminar separation bubble elimination. The NS-D/RBD plasma actuator 1 in this case can be placed upstream in the neighbourhood of the separation line and aligned parallel to the leading edge of the aerodynamic surface. Depending on the free stream velocity conditions, a pulsed discharge with voltage amplitude and repetition frequency according to the previous formulas can be used in order to force flow separation delay or elimination and/or cancelling laminar bubble separation. A wave packet will be introduced into the BL and the flow structures responsible for the natural laminar-to-turbulent transition of the flow will be triggered and amplified so turning the natural laminar flow into a forced turbulent one. In case of laminar separation delay or elimination, the said turbulent BL will force the free separated laminar SL to turn turbulent, so in turn moving the separation line downstream its original location. In case of laminar bubble separation the mechanism is similar: the forced turbulent BL will burst the bubble, eliminating it. In this way it is possible to reduce the drag due to the wake generated by the separated flow or the bubble, to increase flight safety, efficiency of the aircraft, range of manoeuvrability of the aircraft and to reduce fuel consumption.

Fig.6C shows a system for de-icing and noise control. In the method of de-icing control at least one NS-D/RBD plasma actuator 1 can be placed in the neighbourhood of the region where ice is formed, that normally is the stagnation point on the nose of the airfoil 2. Depending of the boundary conditions, a pulsed discharge with specific voltage amplitude and repetition frequency can be used in order to melt the formed ice. The portion of fluid flow heated up by the discharge, interacting with the ice crystals, will transfer heat according to thermodynamics, melting the formed ice. The ice formed on the airfoil 2 changes its aerodynamics characteristics and represents a risk for the user. The method reduces and/or cancels the formation of ice, increasing flight safety. This method could allow installation of wind turbines in polar regions.

In the method of noise control at least one NS-D/RBD plasma actuator 1 can be placed in the neighbourhood of the region where noise is produced, normally at trailing edge of the airfoil 2. Depending on the free stream velocity conditions, a pulsed discharge with specific voltage amplitude and repetition frequency can be used in order to destroy fluid structures responsible for the production of the noise. In turn, the wave packet introduced into the BL interacts with said fluid structures affecting their size and frequency. This method reduces and/or cancels out the noise generated, for instance, during landing or take-off, making aircrafts and airports close to towns more user-friendly and less sound-pollutant.

Other scenarios, not represented in the figure 6, refer to method of Laminar-To- Turbulent Transition control and to method of load control.

In the method of laminar-to-turbulent transition control at least one NS-D/RBD plasma actuator 1 according to the invention, can be placed in the neighbourhood of the receptivity region of the boudary layer under control. Depending on the free stream velocity conditions, a pulsed discharge with specific voltage amplitude and repetition frequency can be used in order to force laminar-to-turbulent transition of the BL under control. Doing so, a wave packet will be introduced into the BL and the flow structure responsible for the natural laminar-to-turbulent transition of the flow will be triggered and amplified so turning the natural laminar flow into a forced turbulent one. The forced turbulent BL will have a smaller height with respect to a laminar one and be much more resistant to negative pressure gradients. At the same time this method reduces the drag due to the wake by reducing the height of the BL and increases safety and range of manoeuvrability of the aerodynamics device under control by producing a BL much more stable and resistant to separation.

In the method of load control at least one NS-D/RBD plasma actuator 1 can be placed on at least one rotor blade. Depending on the free stream velocity and boundary conditions, a pulsed discharge with specific voltage amplitude and repetition frequency can be used in order to control the portion of the flow acting on the blade so, in turn, controlling the load. Doing so a wave packet will be introduced into the BL and the flow structures responsible for the natural transition of the flow will be triggered and amplified so turning the natural laminar flow in a forced turbulent one. Using multiple systems, like in Fig. 5, located in different places along the span of a warped blade, and with proper program of the controller 9, it is possible to activate cyclically each system in order to produce a region of attached flow and regions of separated flow all along the warped blade. In turn the method allows to design a wide range of load distributions, so achieving load control. With this method it is possible to design, for instance, an aero-braking system for the rotor, thus increasing efficiency and lifetime of the rotor itself. Moreover, vertical axis wind turbine can be designed such to have a much higher efficiency and effectiveness with respect to the present state of art of that technology.

The described NS-D/RBD plasma actuator could also be used for producing micro jet thrusts. Depending on the application, a pulsed discharge with specific voltage amplitude and repetition frequency could be used in order to produce a micro jet within a pressurised chamber. Such micro jet, in turn, can be used, for instance, in order to make small orbital adjustments on micro satellites, so substituting complex and expensive payloads such as micro-magneto torques and reaction wheels.

Flow control can be achieved also by using multiple NS-D/RBD plasma actuator systems 1 like the one represented in Fig 5 with groups of NS-D/RBD plasma actuators 1 performing each a different task.

We have described a NS-D/RBD plasma actuator making special reference to one having a dielectric barrier, but what has been described can be applied also to a resistive barrier actuator. Both kinds of plasma actuators work in the same way: they both introduce a thermal disturbance. Nevertheless, there is a difference on the disturbance that is produced. In case of dielectric barrier the thermal disturbance is introduced completely into the flow and it moves like a discontinuity within the field of motion. On the other hand, in case of resistive barrier the produced thermal disturbance is mainly distributed within the resistive layer which rises its temperature much more with respect to the dielectric barrier since more current is produced, and then the heat into the barrier gets transferred into the flow more smoothly. This intrinsic difference makes them able to accomplish different flow control tasks. For instance, the dielectric barrier will always trigger transition of the BL from laminar to turbulent, while the resistive barrier will be able to delay transition.

The described NS-D/RBD plasma actuator 1 can be used in order to improve efficiency and safety of existing systems as well as new designed ones. The NS- D/RBD plasma actuator 1 described could be applied for example, to airplane's wings, tails, rudders, fuselages, nacelles, intakes, nozzles; to blades for wind turbine, to racing cars or trucks or trains as well as bridges and high buildings.

Claims

1 . System for controlling a boundary layer of a fluid flowing over the surface of a body (2), according to the task to be performed, comprising:

a) at least one nanosecond dielectric/resistive barrier discharge plasma actuator (1 ) located on said surface at a predefined location;

b) at least one probe (8), placed over said surface at a predefined location for measuring characteristics of the flow and to emit signals corresponding to said characteristics;

c) a high voltage nanosecond pulse generator (6) for applying at least one specific high voltage nanosecond pulse to said at least one nanosecond dielectric/resistive barrier discharge plasma actuator (1 );

d) a controller (9) connected to said probe (8) for driving said high voltage nanosecond pulse generator (6) according to said signals emitted by said probe(8);

wherein said at least one nanosecond dielectric/resistive barrier discharge plasma actuator (1 ) comprises:

- a dielectric or resistive barrier layer (3) defining two major parallel surfaces opposed one to the other having the longest extension in a direction transverse to the incoming flow defining a "z" axis of a Cartesian coordinate system where the thickness of said barrier layer (3) is parallel to the "y" axis and the width of said barrier layer is parallel to the "x" axis.

- two electrodes (4, 5) each of them micromachined or printed directly on one of said two major parallel surfaces of said barrier layer (3), being perfectly flushed to said surfaces, the first electrode (4) being laterally shifted with respect to the second electrode (5) forming a gap (ge) of zero millimetres in the x- direction.

2. System according to Claim 1 , wherein the dielectric or resistive barrier layer (3) is embedded in said body (2), one of the two major surfaces of the barrier layer (3) being at the same level of the surface of said body (2) being exposed to the flow.

3. System according to Claim 2, wherein either the first (4) or the second (5) electrode has a surface exposed to the flow and flushed to the surface of the dielectric layer (3) exposed to the flow.

4. System according to claim 3, wherein the first (4) and second (5) electrodes, have a major dimension in the z-direction, said major dimension being calculated according to the formula:

L=Vv*W

where L= Maximum length in meters, V_v=Velocity of propagation of the pulse in meters/seconds and W= width of the pulse in seconds.

5. System according to claim 4, wherein the dimension in the z-direction of the first electrode (4) is smaller than the corresponding dimension of the second electrode (5).

6. System according to claim 5, wherein the first (4) and second (5) electrodes are connected to the high voltage nanosecond pulse generator (6) through the same sides parallel to the x-y plane.

7. System according to claim 6, wherein the corners of the first (4) and second (5) electrodes facing each other at the open end opposite to the sides connected to the high voltage nanosecond pulse generator (6), are rounded (7).

8. System according to the preceding claims, comprising more than one nanosecond dielectric/resistive barrier discharge plasma actuator (1 ), each nanosecond dielectric/resistive barrier discharge plasma actuator (1 ) being connected to a high voltage nanosecond pulse generator (6) connected to a said controller (9), said controller (9) being connected to said at least one probe (8) and wherein, each nanosecond dielectric/resistive barrier discharge plasma actuator (1 ) or groups of nanosecond dielectric/resistive barrier discharge plasma actuators (1 ), perform a different task.

9. Method for controlling the system according to the preceding claims, wherein said high voltage nanosecond pulse is in the range 2500-10.000 Volt and duration comprised between 5 and 100 nanoseconds and has a rising time in the range of 1 -10 nanoseconds.

10. Method according to claim 9, wherein a series of pulses can be applied to said nanosecond dielectric/resistive barrier discharge plasma actuator(1 ).

1 1 . Method according to claim 9, wherein a series of bursts each containing a number of single high voltage nanosecond pulses can be applied to said nanosecond dielectric/resistive barrier discharge plasma actuator(1 ).

12. Method according to claim 10 or 1 1 , wherein the repetition frequency F of said series of high voltage nanosecond pulses or bursts can be calculated according to the formula:

(F x L)/U=2

where L represents length of flow separated on said surface , U is free stream velocity and 2 is a coefficient found experimentally.

13. Method for controlling the system according to claim 8, wherein said controller (9) can actuate all nanosecond dielectric/resistive barrier discharge plasma actuators (1 ) at the same time or addressing them independently.

14. Device for controlling the boundary layer of a fluid flowing over a surface of a body (2), comprising:

a) a dielectric or resistive barrier layer (3) defining two major parallel surfaces opposed one to the other having the longest extension defining a "z" axis of a Cartesian coordinate system where a thickness of the barrier layer (3) is parallel to the "y" axis and the width of the barrier layer (3) is parallel to the "x" axis of said Cartesian coordinate system;

b) first and second electrodes (4, 5) each of them micromachined or printed directly on one of said two major parallel surfaces of said barrier layer (3), being perfectly flushed to said surfaces, the first electrode (4) being laterally shifted with respect to the second electrode (5) forming a gap (ge) of zero millimetres in the x- direction

wherein :

- wherein each of the first and second electrodes (4, 5) has two major surfaces parallel to the "x-z" plane, one surface exposed and one surface inside the resistive/dielectric barrier layer (3), the surface exposed is flushed to the surface of said barrier layer (3),

- wherein one of the first and second electrodes (4, 5) has dimensions in the "z"- direction smaller than the corresponding dimension of the other electrode,

- wherein the first and second electrodes (4, 5) are connected through the same sides parallel to the "x-y" plane to a high voltage nanosecond pulse generator (6), - wherein the first and second electrodes (4, 5) have toe rounded corners (7) facing each other along the "z" direction at the open end side opposite to the side connected to said high voltage nanosecond pulse generator (6),

- wherein the maximum length of one of the first and second electrodes (4, 5) in the z-direction is calculated according to the formula:

L=V_V ^*W

15. A system for controlling laminar flow separation from an aerodynamic surface, comprising:

a) at least one device according to claim 14,

b) at least one probe (8) to measure characteristics of the flow and to emit signals corresponding to said characteristics,

c) a high voltage nanosecond pulse generator (6) to apply at least one specific high voltage nanosecond pulse to said at least one device between 2500 and

10000 Volt and duration comprised between 5 and 100 nanoseconds with rising time in the range 1 -10 nanoseconds,

d) a controller (9) connected to said probe (8) to drive said high voltage nanosecond pulse generator (6) according to said signals emitted by said probe(8);

wherein said device is aligned parallel to the leading edge of the said aerodynamic surface and placed upstream of or at the separation line or in the receptivity region of the boundary layer.

16. A system for controlling laminar to turbulent transition of a boundary layer on an aerodynamic surface, comprising:

a) at least one device according to claim 14,

b) at least one probe (8) to measure the characteristics of the flow and to emit signals corresponding to said characteristics,

10000 Volt and duration comprised between 5 and 100 nanoseconds with rising time in the range 1 -10 nanoseconds, d) a controller (9) connected to said probe (8) to drive said high voltage nanosecond pulse generator (6) according to said signals emitted by said probe(8);

wherein said device is aligned parallel to the leading edge of said aerodynamic surface and placed upstream of or at the separation line or in the receptivity region of the boundary layer.

17. A system for noise reduction on aerodynamic surfaces, comprising:

a) at least one device according to claim 14,

c) a high voltage nanosecond pulse generator (6) for applying at least one specific high voltage nanosecond pulse to said at least one device between 2500 and 10000 Volt and duration comprised between 5 and 100 nanoseconds with rising time in the range of 1 -10 nanoseconds,

d) a controller (9) connected to said probe (8) to drive said high voltage nanosecond pulse generator (6) according to said signals emitted by said probe (8);

wherein said device is placed on said aerodynamic surface near to the location where noise reduction is desired.

18. A system for active de-icing on aerodynamic surfaces, comprising:

a) at least one device according to claim 14,

c) a high voltage nanosecond pulse generator (6) for applying at least one specific high voltage nanosecond pulse to said at least one device between 2500 and

10000 Volt and duration comprised between 5 and 100 nanoseconds with rising time in the range of 1 -10 nanoseconds,

d) a controller (9) connected to said probe (8) to drive said high voltage nanosecond pulse generator (6) according to said signals emitted by said probe (8),

wherein said device is placed on said aerodynamic surface near to the location where ice is formed, normally close to flow stagnation points.