HYBRID-SYNTHETIC JET ACTUATOR
2. The actuator model
2.3. Feedback loop
3.1. Oscillation frequency
3.2. Modified Strouhal number
3.3. Constant Strouhal number regime
3.4. Constant propagation velocity regime
Actuators based on the synthetic jet idea are currently becoming of increasing importance for a number of applications, especially involving control of flow separation and/or transition to turbulence in internal or external aerodynamics. They are much more practical and less sensitive to mechanical damage than the initially proposed actuators influencing the flow by mechanical tabs or vanes extended from the wall into the flow. They are also finding use in applications aimed at extremely high power density convective heat and mass transfer between fluid and walls
Synthetic jets are formed by a periodically alternating inflow into and outflow
from a nozzle., mainly with the perspective of using their rectification properties in fluidic pumping. They were called synthetic jets the term suggesting their being synthesised from individual vortex rings, although this character is there only in a certain range of operating conditions. Synthetic jet actuators are a particularly attractive idea in the context of small scale, microelectromechanical systems (MEMS)â€œ because scaling down is usually associated with decreasing Reynolds number, which decreases efficiency of mixing as well as of convective heat transfer in steady flows. The pulsation associated with of the synthetic jet flows agitates the flowfield and produces effects similar to those of turbulent convection. There are, in fact, some experimental data suggesting that synthetic jets are capable of achieving extreme magnitudes of the thermal power transfer density, unobtainable by any other means, because the pulsation can destroy or reduce the thin insulating layer of stagnant fluid, held at the wall in steady flows. In spite of its minute thickness, this layer has the essential limiting influence on the achievable heat transfer rate, because heat has to cross it by the very ineffective conduction mechanism
A serious disadvantage of the pure synthetic jets, especially in the impingement
cooling (or heating) applications, is their re-ingestion of fluid that has already passed over
the cooled (or heated) surface. Supply of external, not yet heated (or cooled) fluid is
demanded. This is also needed for improvement in the flow manipulation applications,
especially beneficial being the additional momentum of the supplied fluid. Recently it
became obvious that in several important engineering applications there are definite
reasons for using synthetic jets with non-zero nozzle flow rate balance. Usually the
balance is positive (more fluid leaving the nozzle per cycle than sucked into it). The fluid jets with this type of periodic unsteadiness are called hybrid-synthetic jet. Simplified cases of harmonic time dependence of the nozzle flow (real wave shapes are usually more complex) for the re-ingesting cases of the periodic jet flow are compared with the mere pulsation in Fig. 1. The word synthetic is retained in the term for the hybrid-synthetic jets because, due to the sign reversal of the flow in the nozzle in each cycle, these flows may retain the typical character of the succession of vortex rings. The actuator generated the hybrid-synthetic jet by superimposing on the alternating flow a steady flow component, produced locally by a flow rectification effect using no-moving-part fluidic diodes. If removal of the heat absorbed by the fluid is required, this localized generation may be unsuitable. It may be necessary to bring a replacement fluid to the nozzle by ducts or cavities from more distant locations, even though this eliminates one of the characteristic advantages of synthetic jets, the absence of the ducting and saving the volume (e.g. in an aircraft wing) the duct occupy. However, in the hybrid-synthetic jets this volume may be much smaller than required in the cases of steady flow or the pulsation (Fig. 1) without the re-ingestion.
Fig. 1. The present hybrid-synthetic jet case compared with the zero-mean synthetic jet and pulsed flows:
time dependences of nozzle flow rates with harmonic oscillation.
In spite of the advantages, a problematic side of current synthetic as well as the
newly proposed hybrid-synthetic jets is the generally impractical character of the actuators used to generate the flow. They are now built with moving components like
pistons or diaphragms. This complicates both manufacturing and assembly. The moving
devices are delicate and easily damaged, and generally exhibit a limited life span. They
cannot operate at high temperatures required in some high thermal power density
applications. Electromagnetic drivers used to move the pistons are heavy. Electrostriction
and piezoelectric principles have difficulties in producing sufficient volume changes.
Flow control using no-moving-part fluidic oscillators, without the problems associated with of mechanical oscillation generators, has been known since 1970s. However, the fluidic oscillators have been always intended as mere distributors of the supplied flow alternatively into two exit nozzlesâ€or more often without the exit nozzles as devices superimposing pulsation (Fig. 1) on an otherwise steady flow, thereby. There was never an idea of utilising the jetpumping effect inside the fluidic oscillator for generating the suction into the exit nozzle for a part of the oscillation cycle. This novel way of generating the hybrid-synthetic jets is the subject of the present paper.
2. The actuator model
The basic idea of the described actuator is shown schematically in Fig. 2. The alternating flow in two exit nozzles A and B is generated by a no-moving-part actuator driven by supplied air flow. The actuator is extremely simple, consisting of a specially shaped cavity in which the periodic aerodynamic processes take place. Essentially, the actuator consists of two components: (a) a small fluidic flow control valve of the type described and (b) feedback loop channel, the flow in which de-stabilizes the valve and produces self-excited oscillation . To be able to activate the feedback flow, the valve has to exhibit amplification propertiesâ€a higher than unity flow and/or pressure gain between its input control terminals X and the output terminals Y. The output flow is provided from the supplied steady flow, brought into the supply nozzle through the supply terminal S. In the present case, the fluidic amplifier valve is of the diverter type. The supplied flow is not turned down by the control action, but diverted into one of the two output terminals, Y1 and Y2. Each of them is connected to one of the two exit nozzles, A and B. The time-mean flow rate in each nozzle is positive: more flow issues in the outflow phase than is sucked in during the following inflow suction phase of the cycle. The actuator drives not a single nozzle but two nozzles operating in opposing phasesâ€œsuction in nozzle A is simultaneous with outflow from the other nozzle B. Availability of two phase-shifted exit flows is an advantage for some applications.
Fig. 2. Schematic representation of the fluidic oscillator: a jet-deflection diverter type fluidic bistable
amplifier is provided with feedback loop connecting the two control terminals X1 and X2. Black triangles:
nozzles, white triangles: diffusers.
The oscillating-flow valve under investigation is actually a scaled-up laboratory
model of the proposed future final device. The scaling up in the present case is intended
not only to simplify the study of the actuator properties but also to make possible use of
the model in wind tunnel experiments scaled up to make easier a smoke visualisation and
PIV measurements of the controlled external near-wall flows. The model was designed to
operate with dn = 6 mm dia exit nozzles (A and B), while the future final version of the
actuators used in flight vehicles are to have five times smaller exit diameter dn = 1.2 mm.
The hybrid-synthetic jet to be generated by the flight vehicle version of the actuator is
required to operate at a frequency of f = 150 Hz. Conditions in periodic unsteady flows
are governed by the Stokes number similarity: if the scaled up model is to behave in a
hydrodynamically similar manner, its operating Stokes number:
where v is the (kinematic) fluid viscosity â€œ is to be the same. For air at the usual
laboratory conditions, the above-mentioned actuator is to operate at Sk = 13.76. For the
five times scaled up model, the same value of Sk requires the operating frequency to be
very low, at only f = 6 Hz. Experimental results prove (cf. Fig. 13) that the model is
actually capable of operating in sustained oscillation across a wide frequency spectrum,
from 1 to 200 Hz, which (with some caution) may be interpreted as the range from
25 Hz to 5 kHz in the five times smaller unit.
The amplification property is due to the capability of diverting the jet leaving the
supply nozzle by the action of much weaker control flows, brought into the control
terminals X1 and X2. In the tested model the steady state flow amplification gain is
approximately 14.5. This means that for deflecting the flow from one output terminal to
the other it is sufficient to apply a control flow of approximately 7% of the supplied air
flow. In actual operation, the flow in the valve is switched by incoming pulses, which â€œ
owing to their sudden shock character â€œ may be even weaker.
The amplifier exhibits bistability: if there is no acting control signal, it remains in
one of two alternative stable states. This is achieved by using the Coanda effect of jet
attachment to walls. There are two attachment walls, W1 and W2 (Fig. 2) placed
symmetrically on both sides of the path of the main jet, which is formed by the supply
flow issuing from the supply nozzle. The jet may attach equally well to either one of the
two walls, which keep it deflected and guide it into one of the two collectors, connected
to the output terminals Y1 and Y2. Shown in Fig. 3 there are computed pathlines in the
valve for the state with the jet guided into the output terminal Y2. The jet-pumping effect
of the entrainment into the jet should be noted: the output mass flow rate passing
through the output terminal Y1 is negative. It is useful to relate its value to the magnitude
of the supplied mass flow rate ; in the particular case of the valve geometry shown in
Fig. 4 the steady-state computed relative value:
a small value (suction flow maxima in oscillation regime are actually higher) but enough
to terminate the previous positive outflow and generate a vortex ring downstream from
the nozzle A. A short flow pulse admitted into the control terminal X2 then suffices for
switching the jet so that it is directed into the other output terminal Y1.
Fig. 3. The entrainment into the jet directed towards the nozzle B in the amplifier generates a return flow
into the exit nozzle A â€œ changing their role in the next half-cycle. This way, the flows from the nozzles
generate the desired hybrid-synthetic jets. In the oscillatory regime, the relative return flows are much
larger than the values shown here obtained by steady-state computation.
Fig. 4. Geometry of the amplifier, derived from the successful geometry [A] used by Tesar  and later
Perera and Syred .
The geometry specified in Fig. 4 is symmetric and planarâ€all cavities forming the amplifier are of the same depth.. Remarkable detail is the positive internal feedback created by the concave bi-cuspid shape of the splitter between the two collectors. The amplifier was made by laser cutting the contour shape in polymethylmetacrylate (Perspex) sheets, of 1.2 mm thickness. To obtain a higher nozzle aspect ratio as well as an exit cross-section compatible with the required 6 mm dia exits, the valve body was made by stacking five sheets. The stack was clamped between thick Perspex top and bottom cover plates, as shown in Fig. 5. The output terminals of the same 6 mm diameter as well as the supply terminal of the same size, together with the smaller 5 mm dia control terminals, were all made as drilled holes in the bottom cover plate.
Fig. 5. Photograph of the assembled amplifier as used in the experimental investigations. The stack of
sheets with laser-cut cavities was clamped between thick transparent cover plates.
The performance of the amplifier valve was investigated by a series of numerical
flow field computations using a standard commercial CFD software FLUENT 6. The
Computation domain, fully three-dimensional, corresponded to the test model. It was
discretised using an unstructured grid of 69,501 tetrahedral finite volumes (18,715
triangular wall faces). The computations used standard 2-equation turbulence model with
RNG handling of low turbulence Reynolds numbers. The investigations were focused on
ascertaining the controllability, which was the only problem encountered earlier with the
geometry [A] (which required narrowing the control nozzle exit during its development). It should be perhaps mentioned that the rather small, 0.5 mm control nozzle width of the present model were initially considered too small for reproducible manufacturing by the laser cutters. A possibility of increasing the width to 0.7 mm was investigated, but the results of this change were disappointing, indicating again advisability of small control nozzle widths. Steady-state computational results (with the 0.5 mm control nozzle width) in Fig. 6, Fig. 7, Fig. 8 and Fig. 9 show details of the flow control by switching. In Fig. 6, the switching process is presented (symbols denoting individual computed states) in terms of the flow transfer characteristicâ€the dependence of the relative output flow Ã‚ÂµY1 (Eq. (2) in the terminal Y1 on the relative control flow rate in the terminal X1):
which is first increasing and then decreasing, maintaining constant supply mass flow rate (and hence constant Reynolds number Re). The two exit nozzles issue into the same
space so that the pressure difference _PY between the amplifier outputs is constant and
equal to zero. In the state A, with at the beginning zero control flow and the supplied air
flow directed into the output terminal Y1 the computed flowfield is shown in Fig. 7. Note
that in this state the relative output flow rate in Fig. 6 is
larger than 1.0 because of the added inflow from Y2 given (its magnitude given by Eq. (3)
â€ note, however, the opposite position of the jet). Subsequent increase of the control
flow has little effect, just slightly decreasing the jet pumping into Y2. The small
influence is mainly because any tendency towards deflection of the jet into Y2 is
countered by the positive internal feedback, provided by the standing vortex trapped
between the cusps of the splitter. This is shown in the state B immediately before the
switching in Fig. 8. The switching takes place when the further increase of the control
flow rate to Ã‚ÂµY1 = -0.17 overcomes the combined action of the Coanda effect and the
stabilizing internal feedback. In the next computed state C, Fig. 9, the jet from the supply
nozzle is already attached to the other attachment wall. The flow through the output
terminal Y1 is now negative and it should be noted that its magnitude is due to additional
jet-pumping effect of the control flow â€ larger than the value given by Eq. (3). Subsequent further increase of the control flow rate brings no qualitative changes. The jet
pumping effect is seen in Fig. 6 to grow, up to about Ã‚ÂµY1 = -0.3. This is an important fact:
in the oscillatory regime, with large control flows, the effective return (suction) flow in
the exit nozzles are substantially higher than what might be expected by considering the
zero control flow values in Fig. 3.
Fig. 6. Flow transfer characteristic of the amplifier in relative co-ordinates: the response to the control
signal admitted to only one control terminal X1. Switching takes place when the control flow reaches
7% of the supply mass flow rate .
Fig. 7. Computed velocity distribution in the midplane (at h/2 = 3 mm from the bottom of the cavities) with
no control flow-state A in Fig. 6. Lighter shades of grey (rendering of the original colour coding)
correspond to higher absolute velocity.
Fig. 8. Pathlines of flow in the state B of Fig. 6. The cusped splitter nose generates an internal positive
feedback loop resisting the switching.
Fig. 9. Numerically computed pathlines in the state C of Fig. 6. The control flow has overcome the internal
feedback and the jet is switched to the other attachment wall.
When the control flow is then decreased, there is, of course, no return to the state
C. Instead, the state D shown already in Fig. 3, with the smaller suction rate Ã‚ÂµY1 = -0.17,
is finally reached when the control flow returns to zero.
2.3. Feedback loop
To produce the oscillation, the amplifying valve is provided with negative feedback loop arranged to be more powerful than the stabilising positive internal feedback. There is no classical connecting of the output and control terminals. The disadvantage in the case of the present amplifier with two input as well as two output terminals would be the necessity of providing two such loops. A simpler version of feedback actually used, as shown in Fig. 10, uses the single feedback loop connecting the two control terminals X1 and X2. The feedback loop has to introduce a delay into the feedback signal path. With the simple connecting tube (without accumulation in a chambers), the cause of the delay is mostly the fluid inertia. Another mechanism is a delay due to the finite propagation time of acoustic waves in the tube. In the present case, the results indicate the presence of both mechanisms.
Fig. 10. The feedback loop converts the amplifier into an oscillator by connecting its two control terminal
with the feedback loop tube. The trombone frequency adjustment may be useful for fine tuning; in the
present experiments the tube length was adjusted by gradual cutting.
The feedback action is based on the pressure difference between the two control
nozzle terminals X1 and X2 caused by the entrainment into the jet. This is the cause of the
Coanda effect that keeps the jet at its attachment wall. The pressure is lower at the side
where the attachment wall prevents a flow of additional outer fluid into the entrainment
region. If connected by the feedback loop, the difference gives rise to a fluid flow in the
loop towards the lower-pressure control nozzle. This flow gradually gains a momentum
sufficient for driving a substantial control flow into this nozzle. Because of the
amplification properties of the valve, this control flow suffices to switch the jet to the
opposite attachment wall. The pressure difference between the control terminals X1 and
X2 caused by the entrainment into the jet then changes sign, tending to reverse the flow
direction in the loop. Because of fluid inertia, however, it takes some time for the fluid in
the loop channel to come to a stop and to begin flowing back. This provides the phase
delay. The jet remains for a certain short time attached to the opposite attachment wall,
sufficiently long to produce the inversed pressure levels in the control nozzles. Then,
however, the reverse flow in the feedback loop increases and when it reaches the 7%
limit, switches the jet back to its original position. The oscillation cycle then can start
Because of the decisive importance of the duration of the cycle of the delay in the
feedback loop, it is easy to adjust the frequency of generated oscillation by changing the
loop length. One possibility is shown in Fig. 10. In the present case, however, the
requirement of the very low frequency led to very large feedback loop tube lengths of the
order of metres. The trombone change of length would be impractical. Instead, in the
laboratory experiments, a Tygon tube of original full 52 m length obtained from supplier
was gradually cut to shorter lengths, ending at 1 m. To investigate the effect of tube
diameter, the procedure was repeated with four tubes, of 2.5, 4, 5, and 10 mm i.d. The
cross-sectional areas of these tubes were f-times larger than the control nozzle exit crosssection, according to the accompanying table. Most results presented here are for d = 10, but effect of d was interestingâ€its size can influence substantially the signal propagation velocity in the loop.
3.1. Oscillation frequency
The oscillator was found to generate the oscillations reliably across a wide range of conditions. The output was picked up by piezoelectric pressure transducer and monitored on an oscilloscope. Fig. 11 and Fig. 12 present typical example of oscilloscope traces obtained in the experiment with the largest, 10 mm i.d. feedback loop tube. As seen in Fig. 11, the waveshapes at low frequencies were nearly rectangular and very regular. The rectangularity is due to the jet in the valve remaining attached at one of the attachment walls until the switching occurs. However, as the frequency increased with shortening the tube length l, the high-frequency components of the spectrum became progressively more damped until the waveshapes approached (but never reached) the simple harmonic oscillation as shown schematically in Fig. 1. The scatter superimposed on the rectangular shape in Fig. 11 was partly due to transition phenomena (after each switching) in the sensors and signal processing devices and partly caused by flow turbulence. Comparison with Fig. 12 provides a useful idea about what is obtained with a decreasing supply flow rate. Apart from the smaller oscillation frequency, there was a recognisably lower level of high-frequency turbulence. The relative magnitude of the low-frequency noise is, however, roughly the same. The noise visible in Fig. 11 and Fig. 12 made the measurement of the main variable of interest, the oscillation frequency f, somewhat imprecise. It was hence decided to evaluate the frequency f as the inverse of the mean oscillation period _t measured in the oscilloscope records.
Fig. 11. An example of a typical oscilloscope record of generated oscillation with 10 mm i.d. tube loop.
Fig. 12. Another example of the oscilloscope traceâ€with the same 10 mm i.d. loop at a lower Reynolds
number. Absolute magnitude of the noise is lower, but also the pulsation is weaker (requiring increased
oscilloscope magnification). Resultant signal/noise ratio is nearly the same as in Fig. 11.
The experiments were performed with air. At each of the four tube diameters d,
the tube length l was gradually decreased. With each length l, the oscillator was supplied
by gradually increased volume flow rate in eight steps from 10 to 80 l/min. This
corresponded to the supply nozzle exit Reynolds numbers from Re = 1790 (at the very
beginning of transition into turbulence in the issuing jet) to Re = 14,340 (fully turbulent
jet). Fig. 13 shows that oscillation frequency f increased in inverse proportion to the
decreased length l of the feedback loop. The dependence on flow rate was found more
complicated. The usual property of many self-excited aerodynamic oscillations is a
constant, Reynolds number independent value of Strouhal number Sh; which in fluidics is
usually evaluated as
(b is the supply nozzle width and w is the supply nozzle bulk exit velocity). The value is
plotted in Fig. 14 (for the data from Fig. 13) as a function of the supply nozzle Reynolds
number. Somewhat disappointingly, this non-dimensionalisation did not lead to a simple
Fig. 13. The frequency vs. loop length dependences obtained with the 10 mm dia loop tube at different
supply flow rates. The power law fit exponent near to 1.0 suggest that the frequency is simply inversely
proportional to the feedback loop length l.
Fig. 14. The experimental results obtained with the 10 mm dia loop tube at different supply flow rates replotted in terms of the Strouhal number Sh as a function of Reynolds number Re.
3.2. Modified Strouhal number
As a step towards finding an invariant of the investigated phenomenon, it seemed
reasonable to multiply Sh defined in Eq. (6) by the length l to utilise the inverse
proportionality f 1/l of Fig. 13. To retain the non-dimensionality, Sh was multiplied by
the relative length l/b, leading to modified Strouhal number evaluated from the tube
length l as the characteristic dimension. Indeed, the result in Fig. 15, re-plotting the data
from Fig. 14, is a welcome simplification. It should be noted that the modified Strouhal
number in Fig. 15 is actually multiplied by a factor of 2.0. This has no effect on the
character of the dependence, but brings an interesting interpretation possibility. This is
based on an observation that the jet switching in the valve is a fast process so that the
oscillation period _t = 1/f measured in the oscilloscope records (Fig. 11 and Fig. 12) is
almost equal to two propagation times of the switching signal in the feedback loop. The
available frequency and length data make possible the following rough estimation of the
propagation velocity wa:
of the signal in the tube. The modified Strouhal number using the length l as the
characteristic dimension may be therefore interpreted (Fig. 15) as the ratio of this
propagation velocity and the nozzle exit velocity. The result is an inverse to the common
definition of Mach number:
w is the exit velocity and wa is the acoustic propagation velocity. Of course, taking the
velocities from different locations has nothing to do with standard Mach numbers and the
quantity serves here merely as a short-hand notation extending the Ma concept beyond
the boundaries of its standard usage.
Fig. 15. Another re-plotting of the results from Fig. 13 using the modified Strouhal number. The data
suggest there are two different regimes: one at low Re < 3000 and the other at high Re.
Considering the overall picture obtained with the area ratio f = 26.18 feedback
tube in Fig. 15 â€œ with the other tube diameters the overall character is analogous â€œ it is
apparent that the results conform to the usual idea of Reynolds number independent
Strouhal number only at very low Re end. The modified Strouhal number there still
recognisably depends on the tube length l.
On the other hand, there is a distinctly different regime at the high Re end of the
investigations. Here, the dependence on the length l disappears. The data there admit a
power-law fit, in Fig. 15 made for tube length l = 7 m. The value of the exponent very
near to 1.0 suggests that neglecting the experimental inaccuracy, there is
which by cancellation of w, means a constant propagation velocity:
3.3. Constant Strouhal number regime
At the low Re, perhaps approximately Re < 3500, which may be plausibly
interpreted as the regime of laminar character of the jet issuing from the supply nozzle, at
least in the vicinity of the control nozzles, the modified Strouhal number is apparently
independent of Re. The extent of Reynolds numbers in Fig. 16 is too short to make this
fully convincing, but the constancy is supported by measurements with different area
ratio f feedback tubes, as may be seen from the linear growth of frequency with the
supply mass flow rate in Fig. 20. For long tubes, l > 5 m, the modified Strouhal number is
also practically independent of the loop length l. This is documented in Fig. 17. For
shorter lengths (l < 5 m) the low Re values exhibit a weak growth with lengths l, the
modified Strouhal number being there roughly proportional to . This,
however, is the region of short signal propagation times where the switching time inside
the valve may become a non-negligible part of the overall delay in the feedback that
governs the oscillation frequency. As a result, the dependence in Fig. 17 may be an
apparent effect caused by the simplification in deriving Eq. (7).
Fig. 16. The data for low Re (here Re < 4000) from Fig. 15 show the modified Strouhal number practically
independent of loop length l, for long tubes l > 5 m. For short lengths (l < 5 m) there is a recognisable
growth roughly proportional to l1/4.
Fig. 17. Velocity of the signal propagation wa (approximately evaluated) in the feedback loop is near to the
speed of sound. In the high Reynolds number regime wa is constantâ€here seen to be practically
independent of the loop length l.
3.4. Constant propagation velocity regime
In this regime, the propagation velocity wa evaluated by the approximate Eq. (7) is
a constant not only independent of the flow rate through the valve (Fig. 17 and Fig. 18)
but also of the other varied parameter, the feedback loop length l (Fig. 17). The transition
into this regime, plotted in terms of the flow rate in Fig. 18 or in terms of Re in Fig. 19,
resembles similar dependences found in aeroelastic phenomena with lock-in to elastic
resonance. A typical example may be, e.g. fluid flow driven vibration of an elastically
supported cylinder in cross-flow, which oscillates at the vortex shedding frequency
increasing with flow velocity unless the frequency is near to the resonant frequency
determined by the cylinder mass and elastic constant of the support, which then becomes
dominant causing the oscillation to be, in a certain range, insensitive to velocity changes.
This analogy suggests quite strongly that there is a similar cause, a resonant phenomenon,
behind the observed range of insensitivity to the flow rate changes. The propagation
velocity values of wa in this insensitive region in Fig. 17 and Fig. 19 are so near to the
speed of sound:
r (J/kgK) is the gas constant of air and T (K) temperature, that there is little doubt about
the resonance is an acoustic one. Eq. (11), of course, is valid for adiabatic propagation in
unbounded space. In a tube, the temperature changes associated with the compression in
the propagating sound wave do not affect a thin thermal boundary layer at the tube wall.
The temperature in the layer is remains near to the original temperature of the wall. A
very simple model of the compression process Pvk = const may assume adiabatic core
with polytropic exponent k = and the isothermal layer with k = 1. Alternatively, one
may introduce a global polytropic exponent for the whole tube, involving the combined
effect of these two components and having there fore values between 1 and .
Obviously, if the tube diameter d is smaller, the relative magnitude of the isothermal
layer volume is larger and the overall exponent decreases, in turn decreasing the
Fig. 18. Constant Sh linear growth of oscillation frequency f with flow rate at low Re is replaced at
higher flow rates by constantâ€œfrequency resonance. Some data suggest continuation of the linear growth
beyond the resonant lock-in.
Fig. 19. The propagation velocity (again evaluated approximately, neglecting the switching time in the
amplifier) for different feedback tube diameters show the similar transition into the regime B, locked-in to
what is apparently an acoustic resonance.
Indeed, the propagation velocity in Fig. 19 is seen to be smaller. It is plotted in
Fig. 20 in nondimensional presentation, as a dependence on the feedback loop tube
showing how the heat transfer phenomena (thermal boundary layer) in the small diameter
tubes can substantially decrease the propagation speed below the adiabatic value. The
results, despite the approximative nature of Eq. (7), are in remarkable agreement with
values obtained by much more sophisticated propagation measurement methods.
Fig. 20. Dependence of the propagation velocity in resonant conditions in the feedback loop tube on Stokes
number for different tube diameters d.
Control of flow and/or heat and mass transfer by the hybrid-synthetic jets operates
with flow pulses of higher magnitude than the supplied time-mean flow rateâ€thus
reducing the requirements placed on the supply ducting, while character of succession of
ring vortices is the same as in the standard zero time-mean synthetic jets . The
continuous exchange of fluid is a particular advantage for synthetic jet operations in
stagnant or low velocity outer conditions, especially if these involve increased
In this paper, the idea of generating the hybrid-synthetic jets by the no-movingpart
fluidic oscillator was experimentally verified on a laboratory model and proved to be
a sound one. The actuator eliminates the problems associated with bringing to it the
driving electric current. It is easy and inexpensive to manufacture, lightweight and yet
robust and resistant to adverse conditions. It lends itself to modern manufacturing
methods (laser cutting the present model form, etching in the intended small scale). It
needs no maintenance and when made from suitable materials may resist even extremely
high temperatures, acceleration and radiation environment.
From theoretical point of view, it was surprising to find that in the operating range
of interest the processes are apparently undergoing a transition between two different
regimes, revealing quite complex underlying aerodynamic mechanisms taking place
inside what is a simple constant cross-section feedback loop tube.
 C.E. Spyropoulos, A Sonic Oscillator, in: Proceedings of the Fluid Amplification
Sympozium, vol. III, Harry Diamond Laboratories, Washington, D.C., 1964, pp. 27â€œ
 V. Tesar, A mosaic of experiences and results from development of high-performance
bistable flow-control elements, Proceedings of the Conference on Process Control
by Power Fluidics Sheffield, UK (1975).
 H. Viets, Flip-flop jet design, AIAA J. 13 (1975), pp. 1375â€œ1379.
 V. Tesar, Pump or blower, in particular for transporting difficult-to-pump fluids-in
Czech, Czechoslovak Certificate of Authorship No. 192 082, April 1976.
 M. Favre-Marinet and G. Binder, Structure des jets pulsants, J. MÃƒÂ©canique, ThÃƒÂ©orique
Appl. 18 (1979), p. 357.