Synthetic jets

It is well known that active flow control through continuous or pulsed blowing requires large values of the mass flow rate which are incompatible with a practical use on a civil aircraft.

This is the reason why following promising early studies in 1940s and 1950s, the topic of active flow control has lost some interest before a come-back in the mid-1990s with the appearance of a new type of actuator: the synthetic jets. They are also called zero-net-mass-flux actuators since they do not require any compressed air feeding but just an electrical supply. This is the reason why they have received a great interest since they solved the problem of mass flow rate from the previous technical solutions. Despite having a time-averaged mass flow rate equal to zero, they have a positive momentum flux. However, the main problem of synthetic jets in the literature is that they have maximum peak velocities of the order of 170 m.s^-1 and moreover with very small orifice areas (1 mm²). So, there is a need to develop more powerful synthetic jet actuators with peak velocities close to the speed of sound and for large orifice areas. A research project, for which I was project leader, has been launched in 2012 at ONERA and ended in 2015 aiming at developing a high performance synthetic jet actuator.

Assuming adiabatic compression/expansion, it is possible to define a simple model of the synthetic jet flow from the ideal gas law:

𝑑𝑑𝑑𝑑

where P is pressure inside the synthetic jet cavity, P0 is the initial pressure, γ is the specific heat ratio and V is the cavity volume. The temporal variation of the cavity volume can be decomposed in two terms. The first one is the volume variation and the second one is the mass flow through the orifice. Using the conservation of mass in the cavity, it is possible to write:

1 stroke. The first term is incompressible and corresponds to the mass conservation, dxp/dt corre-sponds to the piston velocity so, in the incompressible case, the second term is equal to zero and the exit velocity is just the ratio of piston and orifice areas multiplied by the piston velocity. The second term gives the compressible contribution and decreases the synthetic jet velocity as ex-pected. Practically, the compressibility has a very important effect close to the speed of sound which leads to a reduction of the peak velocity by 40% compared to an the incompressible

as-sumption. If the piston has a sinusoidal movement xp = S sin(ωt) where S is the piston stroke and ω is the pulsation, eq. (2) becomes:

𝑈𝑈 =𝐴𝐴𝑝𝑝

𝐴𝐴𝑜𝑜𝑆𝑆𝑆𝑆 cos 𝑆𝑆𝑑𝑑 − 𝑑𝑑 𝛾𝛾𝑑𝑑0

𝑑𝑑𝑑𝑑

𝑑𝑑𝑑𝑑 (3)

So, for a given piston stroke, the first term increases linearly with the actuation frequency.

Aside from this very simple model, another model has been developed to help to the de-sign of synthetic jet actuators. This model follows the one explained in [18] which consists in computing at each time step, the cavity volume and then, assuming the compression/expansion is adiabatic and the time to reach equilibrium in the cavity is negligible, it is possible to compute the cavity pressure and temperature. Knowing the external pressure, it is possible to compute the jet velocity and consequently the mass loss in the cavity volume. It is also possible to take into ac-count the pressure losses in the orifice for example. Although very simple, this model allows studying the effect of parameters like orifice area, piston movement shape and so on. This model is available in Excel sheet and Python format to be easily usable by the ONERA model shop in Lille for example. It has been validated by comparing the cavity pressure with a Kulite sensor mounted on the actuator (see picture Fig. I.4). Fig. I.1 shows the comparison of the model (in red) with the measurements (in black). Despite its simplicity, a very good agreement has been ob-tained. Interesting observations can be done: for example, the pressure signal is not symmetric with respect to a pressure ratio equal to 1 and secondly, the blowing phase has a shorter duration than the suction one. This is due to the fact that the density of the air coming from outside is low (1 bar) compared to the internal cavity pressure (3.9 bar in the present case). So, it takes more time to fill the cavity with air coming from the outside than to empty it. Moreover, if one looks at the mass of air in the cavity as function of time (not shown here), one can remark that this mass does not come back to its original values when jet velocities are close to the speed of sound be-cause there is not enough time to fill the cavity. And if the cavity is not fully filled, the following blowing phase will have a reduced peak velocity. A not so well-known conclusion is that close to sonic exit velocities, the suction phase limits the synthetic jet performance. Nevertheless, the suc-tion phase is the most effective one because sucsuc-tion is more effective than blowing (see ref. [44]).

This has been verified in wind tunnel tests with control by continuous suction or blowing (see Chapter V, section 2.2).

Fig. I.1: Comparison of actuator internal pressure ratio between model (in red) and measurements (in black).

Fig. I.2 shows the momentum coefficient of a given actuator (stroke, piston and orifice are-as) as function of the actuation frequency (for M∞ = 0.2, c = 0.5 m). The jet momentum flux in-creases with frequency as expected from eq. (3) but seems to reach a plateau which value depends on the orifice area. This saturation is due to the suction phase which limits the actuator

perfor-mance. A sonic velocity corresponds to the inflection point on the curves. Compared to a pulsed blowing actuator (purple curve in Fig. I.3) which is not limited in terms of performance because the higher the air feeding pressure, the higher the momentum coefficient, a synthetic jet is limited in performance because of its suction phase.

Fig. I.2: Momentum coefficient of a synthetic jet as function of frequency for two slot widths.

Fig. I.3: Momentum coefficient as function of internal pressure for a synthetic jet (in black) and a pulsed jet (in purple).

A simple and cheap way to have a high-performance is to use a RC model engine (see Fig.

I.4). The engine is coupled with an electric motor and a Kulite sensor has been added to measure the cavity pressure. The advantage of this technical solution, in addition to his cost, is that a RC engine has a large stroke (8.5 mm) compared to a piezoelectric actuator (0.2 mm for the same volume) or a loudspeaker. Since the stroke S is one order of magnitude higher, the peak velocity is also higher following eq. (3). Fig. I.4 shows a Schlieren visualisation of the synthetic jet. Shock cells classical of an underexpanded jet can be observed. The estimated peak Mach number is equal to two.

0 0.5 1 1.5 2 2.5 3 3.5

0 100 200 300 400 500 600

f (Hz)

Cmu (%) fente 0.25mm

fente 0.5mm

0 0.5 1 1.5 2 2.5 3

1 1.5 2 2.5 3 3.5 4 4.5

Pch (bars)

Cmu (%)

Jet synthétique Jet pulsé DC=0.5

slot width 0.25mm slot width 0.5mm

synthetic jet pulsed jet DC = 0.5

Fig. I.4: Pictures of the synthetic jet actuator (top) and Schlieren visualisation (bottom).

This crankshaft mechanism has then been integrated into a model leading edge (see Fig. I.5) and tested in a wind tunnel (see Chapter V, section 2.2). Fig. I.5 (right) shows the measured cavity pressure ratio as function of time for different actuation frequencies. As said before, the jet veloci-ty and consequently the pressure ratio increase with the actuation frequency. A maximum pressure ratio of 1.7 has been measured which corresponds to a peak jet velocity of around 300 m.s^-1 which is much larger than any other synthetic jet actuator in the literature. Moreover, the orifice area corresponds to a slot of 150×0.1 mm² and not a small hole of 1 mm². Often, the synthetic jet per-formances are compared in terms of peak velocity but it is easy to increase the peak velocity by reducing the orifice area Ao as shown by eq. (3). A more fair comparison should be done in terms of momentum flux instead of velocity since it is the numerator of the momentum coefficient which will be defined more precisely in Chapter V, section 1.2.

Fig. I.5: Synthetic jet actuator with constant flap oscillation amplitude (left) and internal pressure ratio as function of non-dimensionalised time for several frequency (right).

electric motor

RC model engine

RC model engine

Kulite sensor

The drawback of this technical solution is that the synthetic jet velocity depends on the ac-tuator frequency. So, it is not possible to study the effect of the forcing frequency on the separated flow with a constant synthetic jet velocity. To solve this issue, one has to change the piston stroke with the actuation frequency. Unfortunately, this is not possible with a crankshaft mechanism for which the stroke is fixed. This is the reason why a variable stroke actuator has been developed (with ONERA’s model shop in Lille) to solve this issue. The advantage of this technical solution is that the large piston stroke and high jet velocity are kept and it is now possible to study inde-pendently the effect of the forcing frequency and the jet velocity. This work has led to the deposit of an “Enveloppe Soleau” with a colleague. A prototype has been manufactured and characterised by hot-wire anemometry on the actuator test bench in Lille (see Fig. I.6). Fig. I.6 (bottom) shows the peak velocity as function of the frequency for different piston amplitudes (rotating flap). First, one can remark that the peak velocity increases with the frequency as shown previously. Second-ly, the larger the piston oscillation amplitude, the larger the peak velocity. One can also remark a saturation around 150 m.s^-1 which is maybe due to a too low power of the electric motor. Unfor-tunately, by lack of time to improve the present actuator performance (the objective was to have 300 m.s^-1), the previous constant stroke actuator which had better performance has been chosen.

Fig. I.6: Synthetic jet actuator with variable flap oscillation amplitude (top left), actuator on the characterization bench (top right) and exit velocity as function of velocity for different flap

ampli-tude (bottom).

After this first project, a new project has been launched in 2015 for four years with the SME Cedrat Technologies specialised in piezoelectric actuators. Compared to classical piezoelectric based synthetic jet actuators in the literature which have small strokes (< 0.1 mm), Cedrat Tech-nologies has developed Amplified Piezoelectric Actuators (APA®). Strokes up to 2 mm can be reached. Moreover, during the current project, a new amplification mechanism has been proposed which multiplies the stroke by a factor of 17. Fig. I.7 (top) shows a picture of the prototype with

the APA below and the piston and actuator cavity above. Fig. I.7 (below) shows two instantane-ous velocity flowfields at the peak suction and at the peak blowing times obtained from a URANS simulation with a deformable mesh to take into account the piston movement. The difference in cavity volume can be seen on the left field and the exit velocity signal on the top right plot. Peak blowing velocities of 310 m.s^-1 are obtained which satisfies the objective.

Fig. I.7: Prototype of piezoelectric synthetic jet actuator (top), numerical simulation of synthetic jet at peak suction (middle) and at peak blowing (bottom).