Bulletin of the JSME Journal of Fluid Science and Technology

1

Bulletin of the JSME

Journal of Fluid Science and TechnologyVol.9, No.1, 2014

Japanese Original : Trans. Jpn. Soc. Mech. Eng., Vol.77, No.783, B (2011), pp.2093-2104 (Received 15 Aug., 2011)Paper No.T2-2011-JBR-0681(13-00181)

© 2014 The Japan Society of Mechanical Engineers[DOI: 10.1299/jfst.2014jfst0007]

Study on the fundamental flow characteristics of synthetic jets

(Behavior of free synthetic jets)

Koichi NISHIBE*, Yuki FUJITA**, Kotaro SATO*** and Kazuhiko YOKOTA****

Received 13 August 2013

Abstract

Jet flows have been applied in numerous fields to control flow separation. Over the last decade, several studies

on the production of synthetic jets have been performed. However, little information is available about a number

of aspects concerning synthetic jets, including details of the structure and the formation mechanism of such jets.

The present study attempts to clarify some of the fundamental flow characteristics of free synthetic jets on the

basis of experiments and numerical simulations. Experimental velocity measurements and flow visualizations

are performed using the hot-wire anemometer and the smoke wire method, respectively. It is found that both the

temporal change in the flow pattern and the time-averaged velocity distribution at the centerline depend on K =

ReU̅ /S2(the ratio of the Reynolds number to the square of the Stokes number). The unsteady downstream flow

characteristics are discussed in addition to the relation between the formative point of the synthetic jet and the

value of K. Furthermore, the flow pattern and the unsteady flow characteristics of the synthetic jet are compared

with those of a continuous jet.

1. Introduction

In recent years, jet flows have found use in an increasingly broad range of applications, and thus studies on the

application of two-dimensional jets for flow control have been conducted actively (Joslin and Jones, 1996). In particular,

numerous studies have been performed on the boundary layer and stall control, and some of the research findings are in

the process of being implemented for practical use. Recently, attempts have been made to apply flow control methods

that use jet flow more actively than in the past for the development of a circulation control wing (CCW) or to reduce the

drag of a bluff body. To generate a continuous jet, it is necessary to use a turbo machine consisting of many metallic

parts, including a rotor, stator, casing, bearing, among others, as well as a driving source. Flow control using a continuous

jet is inappropriate for a more compact and lighter design; therefore, the entire system becomes complicated.

As an alternative to a continuous jet, a flow control method that uses synthetic jets is being suggested (Amity et. al.,

2001; Duvugneau et.al., 2007; Shuster and Smith, 2007; Tensi et. al., 2002; Whitehead and Gursul, 2006; You and Moin,

2007). Synthetic jets that repeat the blowing and suction alternately form vortex pairs or vortex rings near the exit and

generate a velocity distribution and actual flow similar to those of a continuous jet by entrainment downstream, even

though the time-averaged velocity and flow rate are zero at a nozzle exit. As for actuators, plasma and piezo-driven as

well as speaker-type actuators have already been invented, which are suitable for more compact and lighter designs

Key words : Synthetic jet, Continuous jet, Free jet, Velocity distribution, Jet formation, Smoke wire method, Unsteady flow, Turbulence

*Department of Mechanical Engineering, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan

E-mail: [email protected] **DMW Corporation,

1-5-1 Omorikita, Ota-ku, Tokyo 143-8558, Japan ***Department of Innovative Mechanical Engineering, Kogakuin University,

1-24-2 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677, Japan ****Department of Mechanical Engineering, Aoyamagakuin University,

5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa 252-5258, Japan

22

Nishibe, Fujita, Sato and Yokota, Journal of Fluid Science and Technology, Vol.9, No.1 (2014)


because they do not have a rotating part and have few mechanically driven parts. A diversified drive source is one of the

main characteristics of synthetic jets, and a noncontact energy supply will be available in the future. Therefore, synthetic

jets are expected to be used for the flow control of micro air vehicles or in high-lift devices and medical fluid machines.

In previous studies, synthetic jet actuators were attached to the suction surfaces of airfoils to control the flow separation

(Duvugneau et. al., 2007; Joslin and Jones, 1996). Studies on the fundamental flow characteristics of synthetic jets have

also been conducted, and the jet flow structure and unsteady characteristics have been discussed in recent studies (Koso

and Kinoshita, 2006; Zhang and Wang, 2007). Specifically, Holman et. al. (2005) described the conditions and

mechanism for the generation of synthetic jets by investigating the geometric shape of the exit.

To use synthetic jets as an alternative to continuous jets, however, many issues need to be resolved, including high-

speed flow or high flow rate generation and noise reduction. Moreover, further discussions are required on the basic

properties of the flow and the application conditions. In particular, several points remain unclear pertaining to the details

of the synthetic jet formation mechanism and flow structure, as well as its unsteady characteristics. Further, insufficient

data are available on the similarities and differences between synthetic and continuous jets. To the best of our knowledge,

there has been no study that has focused on the formative point of synthetic jets.

In this study, an attempt is made to identify the basic characteristics of two-dimensional synthetic jets on the basis of an

experiment and a numerical analysis under the free jet flow (infinite synthetic jets) condition. The flow patterns of synthetic

jets are compared by using the results of a smoke wire visualization experiment and the results of a numerical simulation.

Then, the effect of K (a parameter for nondimensional stroke that is defined as K = ReU̅/S2 (Holman et. al., 2005), where

ReU̅ = U̅b0/ν denotes the Reynolds number, S is the number of strokes S = [2πfb02/ν]1/2, f is the frequency, and ν is the

kinetic viscosity) is investigated on the flow formation mechanism and unsteady characteristics. Furthermore, the

similarities and differences between continuous and synthetic jets are discussed on the basis of the time-averaged velocity

distribution and velocity fluctuation along the jet centerline, and the formative point of the jet is identified on the basis

of the flow direction and spectrum analysis along the jet centerline.

2. Nomenclature

b0 ： slot width = 5.0 × 10-3 [m]

f ： frequency [1/s]

H1 ： step height [m]

H2 ： distance from slot to upper boundary [m]

K ： corresponding non-dimensional stroke = Re𝑈/S2 [ - ]

l ： slot length = 1.0 × 10-1 [m]

L0 ： stroke length [m]

ReU0 ： reynolds number based on U0 = U0b0/ν [ - ]

ReU̅ ： reynolds number based on U̅ = U̅b0/ν [ - ]

RMS ： turbulence intensity at center of the jet [m/s]

S ：

St ： strouhal number = f b0 /Us0

t ： time [s]

T ： cycle of the velocity fluctuation at the outlet of the slot [s]

U0 ： downstream-directed average exit nozzle velocity of jet [m/s]

U̅ ： time-averaged jet velocity during the expulsion stroke [m/s]

Uｍ： maximum time-averaged jet velocity in arbitrary x position [m/s]

Usa ： velocity amplitude for synthetic jets [m/s]

| u | ： absolute value of the jet velocity = [u2 + v2]1/2

u ： velocity in the x direction [m/s]

v ： velocity in the y direction [m/s]

XPJ ： formative point of pulsating jet from the slot [m]

XQC ： formative point of jet with quasi unsteady characteristic of continuous jet

from the slot [m]

ν ： kinematic viscosity [m2/s]

Subscripts

c ： continuous jet

s ： synthetic jet

stokes number = [2πf b02/ν]1/2 [ - ]

33



3. Experimental setup

3.1 Experimental apparatus

A schematic view of the experimental apparatus is shown in Figure 1(a). The working fluid is air. The rectangular

cylinder of the nozzle is supported at each end by an acrylic plate, and a two-dimensional jet is induced downstream of

the two-dimensional slot. The plenum tank in the present experimental apparatus was designed on the assumption that

the Helmholtz resonance frequency is approximately 30 Hz (in this report, the experiment was conducted from 10 to 50

Hz). The synthetic jet is generated by a loudspeaker (Diecook D-15L) driven by a signal generator (MCPLG1100D) that

sends signals through a power amplifier (Classic Pro V3000). In this experimental setup, the output sound pressure level

is 91 dB/1 m/1 w, and the reproducible exit velocity amplitude for synthetic jets Usa is 23.5 m/s at 50 Hz. Meanwhile, a

continuous jet is generated by the blower (Showa Denki CO., LTD. U75-2-R313). The synthetic and continuous jet

velocities at the outlet of the slot are controlled by the signal generator and inverter (TOSHIBA CO., LTD. VFNC1 -

2007P), respectively. Figure 1 (b) shows a magnified view of the test section, including the slot part in Figure 1 (a). Inside

the rectangular cylinder, the slot has a nozzle shape that combines a circular arc R = 30 mm and the length of the

rectangular cylinder span direction l = 100 mm. Air is guided to the inside of the rectangular cylinder (Figure 1 (b)) from

the plenum tank, where it changes direction and is ejected from the slot through the nozzle during the expulsion period

for the continuous jet and synthetic jet. The slot width b0 can be varied by changing the spacer thickness (in this report,

b0 = 5 mm, aspect ratio l/b0 = 20).

3.2 Experimental method

The velocity measurements for both jets are performed using a pitot tube and hot-wire anemometer (Kanomax

IHW100) with an I-type probe (0251R-75), a probe support (7A0103), and a traverser (Chuo Precision Industrial ALS-

230-C2P). However, the measurements of the flow velocities with a hot-wire anemometer are vulnerable to large errors

in the regions prone to local backflow, such as the complicated flow field near the slot.

In this report, it is noted that the velocity in the x direction is expediently set as u = | u | on the assumption that the

velocity in the y direction v ≈ 0, since v (m/s) is relatively smaller than u (m/s). Therefore, if a reverse flow or a large

eddy occurs, it is not possible to interpret the absolute value of the velocity u.

A flow visualization experiment for observing the behavior of the jet is performed using the smoke wire method. The

wire is established at the position of the spanwise center and 25 mm downstream from the outlet slot (x/b0 = 5) in the

flow visualization, and the smoke is generated. A nichrome wire with a diameter of 0.35 mm and liquid paraffin are used

as the smoke wire and smoke agent, respectively. The visualization is recorded using a digital camera (300 fps, CASIO

EX-F1) with a light source (PHOTRON HVC-SL) placed at the measurement section downstream. However, the

Reynolds number is set as ReU0 ≈ 990，ReU̅ ≈ 1980 to ensure the quality of the streamline in the visualization

experiment.

b0

Slot

l

(b) Magnified view of test section (a) Speaker-driven synthetic jet actuator

Fig. 1 Schematic of experimental apparatus.

PowerAmplifier

Inverter

Rectangular CylinderAcrylic plate

Speaker

Flow meter

Blower

Cavityb0

Slot l

SignalGenerator

44



4. Numerical simulation

A commercially available computer code (SCRYU/Tetra, Software Cradle Co., Ltd) is used for the numerical

simulations. The simulations are conducted by applying the k–ε turbulent model with approximately 200,000 grid points.

The flow conditions correspond to a two-dimensional incompressible viscous flow.

Figure 2 depicts a typical numerical domain as well as typical boundary conditions. For simplification, the velocity

at the inlet, u0 = Usa sinωt, is applied to the slot instead of the moving boundary condition. In this study, uniform velocities

vw = 0.01US0 and vw = – 0.01US0 were applied at H1 = 380b0 and H2 = 380b0, respectively, which correspond to the

infinite boundary. In the case of the continuous jet, vw = 0.01Uc0 at H1 = 380b0 and vw = – 0.01UC0 at H2 = 380b0 were

set as the infinite boundary condition. In addition, a constant static pressure was specified for the outlet with no-slip

conditions at the wall surface for the continuous jet and synthetic jet.

5. Results and discussion

5.1 Definitions of Reynolds number, representative velocity, and K

Holman et. al. (2005) defined the typical velocity and Reynolds number for synthetic jets. First, the time-averaged

exit velocity, Us0, which evaluates the values during the expulsion cycle only, is expressed by the following equation:

Us0 = fL0 = 1T

∫ u0T/2

0(t)dt (1)

where u0 is the slot exit velocity, T is the cycle, f is the frequency, and L0 is the stroke (length of the fluid body that is

blown out in one cycle). A flow with momentum is generated during the blowing phase, and the flow during the suction

cycle is almost similar to the sink flow of the potential flow; hence, Us0 which ignores the flow rate during the suction

phase and evaluates the jet velocity during the blowing cycle only is proposed as the primary approximation of the

velocity to determine momentum. In addition, the Reynolds number is defined as ReU0 = U0b0/ν, where the exit velocity

of the synthetic jets, Us0, and the exit velocity of the continuous jets, Uc0, are characteristic flow velocities. When a

comparison of the flow characteristics of the synthetic and continuous jets is conducted for the same ReU0 = 2430 and

ReU̅ = 4860 condition, these characteristic flow velocities are described as Us0 and Uc0, respectively, but exclude the

results from the flow visualizations using the smoke-wire method. The time averaged jet velocity during the expulsion

stroke toward the downstream, U̅, is expressed by the following equation:

U̅ = 2T

∫ u0(t)dtT/2

0 = 2Us0 (2)

In addition, the Reynolds number when velocity U̅ is the typical velocity is defined as ReU̅ = U̅b0/ν, which is written

as a reference. As a parameter for the non-dimensional stroke L0/b0, we use K, which can be expressed by using the

Reynolds number ReU̅ and the stroke number S. K is defined as follows:

K = ReU̅

S2 =

L0

πb0=

Us0

πfb0 (3)

As mentioned above, the effect of K on the flow characteristics with the same Reynolds number Re𝑈0 is discussed except

for some cases.

Fig. 2 Numerical simulation domain and boundary conditions.

55



5.2 Synthetic jet behavior

Figure 3 shows a behavior observation example of two-dimensional synthetic jets for the case of K = 9.55. Figure 3

(a) shows the result of visualization experiments using the smoke-wire method (ReU0 ≈ 990), Figure 3 (b) is a velocity

vector diagram obtained from a numerical simulation (ReU0 = 2430), and Figure 3 (c) is the vorticity distribution obtained

from the numerical simulations. The vorticity scale in Figure 3 (c) is between – 2500 and 2500 [1/s], and the out-of-range

values are shown in white and black. For all cases, Figure 3 (i)–(v) shows the temporal change in the flow patterns

corresponding to one cycle of slot exit velocity change. A vortex pair is formed near the slot in the case of Figure 3 (ii)

at the time of the maximum blow (maximum exit velocity) by the (a) experiment and (b) from the vector diagram obtained

from the numerical simulation. Then, in Figure 3 (iii) and (iv), it can be observed that the vortex pair moves downstream

while maintaining symmetry (toward the right in the figure). Because Figure 3 (a) is a visualization using the smoke-

(i) t/T = 0,

us0 = 0 m/s

(ii) t/T = 0.25,

us0 = 23.5 m/s

(iii) t/T = 0.50,

us0 = 0 m/s

(iv) t/T = 0.75,

us0 = -23.5 m/s

(v) t/T = 1.0,

us0 = 0 m/s

(a) Flow pattern from EXP (b) Velocity field from CFD (c) Vorticity field from CFD

Fig. 3 Flow pattern of synthetic jet from EXP and CFD results (K = 9.55)

(EXP: Experiment, CFD: Numerical simulation).

0 10 20 30 40 50x/b0

Smoke wire

-20

-10

0

10

20

y/b

0

10 (m/s)-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

vorticity ω (1/s)

-2500 2500-20

-10

0

10

20

y/b

0

0 10 20 30 40 50x/b0

Smoke wire

66



wire method, a vortex pair is treated as a fluid body of smoke, and the density of the smoke does not correspond to the

velocity vector. Thus, it is not possible to simply compare (a) and (b). Figure 3 (iv) shows the case where the exit velocity

is us0 = – 23.5（negative）m/s, where a vortex pair moves downstream even during the suction cycle. A vortex pair

generated during the blowing cycle t/T = 0 – 0.5）develops and moves downstream, away from the slot. Then, even after

the exit velocity changes to the suction phase, the induced velocity of a developed vortex pair exceeds the suction

velocity, and the vortex pair is expected to continue moving downstream even though the translational velocity is not

constant. Furthermore, the vector diagram in Figure 3 (b) (iv) shows that over a wide range, excluding the slot

neighborhood, the velocity in the x direction, u, is positive. When focusing on the velocity u on the jet centerline y/b0 =

0, x/b0 ＞ 3 at K = 9.55 and the velocity u is always positive, which means that although velocity fluctuation is present

at x/b0 ＞ 3, a flow similar to continuous jets is formed, and the suction does not cause the flow direction to move toward

the slot side. For Figure 3 (i), (ii), (iii), and (v) excluding (iv), which shows the suction case the velocity u is positive at

any point on the jet centerline. Incidentally, Holman et. al. (2005) reported that synthetic jets are not generated in the case

of K < 1, and authors also confirmed in a preliminary study that a jet is not developed when K is extremely small, because

a vortex pair formed near the slot during the blowing cycle is pulled back to the slot during the suction cycle. In other

words, the formation of synthetic jets is thought to be determined by whether or not the vortex pair that is repeatedly

generated is able to move downstream. In the vorticity distribution shown in Figure 3 (c), a vortex pair formed near the

slot is observed more clearly than in Figure 3 (a) or (b), and it moves almost linearly while maintaining symmetry as time

passes. This shows that a vortex pair is formed near the slot between Figure 3 (i) and (ii), or when the slot exists, the

velocity changes from zero to maximum. In Figure 3 (ii), in addition to the vortex pair formed near the slot, another

vortex pair that formed one cycle before at x/b0 ≈ 21 is shown. The vorticity distribution series shows that the x-direction

interval of a periodically formed vortex pair becomes smaller as it moves downstream. As with the vorticity scale in

Figure 3 (c), it is hard to identify a vortex pair given x/b0 ＞ 35, but it is observed from the vorticity distribution, vector

diagram and visualization pictures that the synthetic jet at K = 9.55 is a highly symmetric flow within the range shown

in the above figure.

Figure 4 shows the time-averaged velocity at the jet center (y/b0 = 0). The horizontal axis is x/b0, and the vertical axis

is the velocity in the nondimensional x direction based on the characteristic velocity Us0 of the synthetic jet and the typical

velocity Uc0 of the continuous jet. The parameter is K. The open symbols indicate the results of the numerical simulation,

and the filled symbols indicate the experiment results. For reference, the value of an experimental equation against a

continuous jet (Rajaratnam, 1976) is shown as a solid line. It is known that with a continuous jet, the slot exit velocity is

u/Uc0 ≈ 1 in a potential core at the maximum, and then it starts to decay as it moves downstream. Under the conditions

used for the experiments and calculations in this study, the calculation results tend to exceed the experimental results.

When focusing on the results of a numerical simulation of a synthetic jet, the time-averaged velocity is u/Uc0 ≈ 0 at the

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60 70 80

u/U

c0, u

/Us0

x/b0

Fig. 4 Dimensionless maximum streamwise velocities along centerline varied with x/b0


CFD EXP

Conti. Jet ○ ●

K =9.55 △ ▲

K =15.92 □ ■

K =47.76 ◇ ◆

— : EXP Formula (Conti. Jet)–：EXP Formula (Conti. Jet) (Rajaratnam, 1976)

77



slot exit, and the average flow is formed downstream (in the experiment, no results around the slot neighborhood are

shown where the flow direction changes significantly). In this figure, for any K, the time-averaged velocities to reach the

maximum time-averaged velocity of u/Us0 ≈ 0.84 from the slot exit with x/b0 ≈ 4.0 are mostly distributed in a curved

line. In other words, under the conditions of this study, the maximum velocity and the point where the maximum velocity

is reached are nearly independent of K. However, an oscillatory flow with directional change is observed from the slot

exit to x/b0 ≈ 4.0, indicating that the characteristics are completely different from those of a continuous jet. On the other

hand, the velocity decay process after the maximum velocity is reached depends on K, and, especially for K = 9.55 and

15.92, the velocity starts to decay with fluctuation. The experimental results and numerical simulation results mostly

show the same tendency, and the velocity fluctuation over the maximum velocity at K = 9.55 and 15.92 is thought to

show a behavior unique to synthetic jets, and not seen in continuous jets. Under the conditions of this study, a simple

decay of the jet center velocity is observed, as in a continuous jet in the case of K = 47.76. However, what causes the

velocity to increase or decrease and the difference in the results when K is changed are not known yet, and further study

is required. It is thought that the reason why numerical analysis results tend to exceed the experimental results and not

match quantitatively is that although a flow in an experiment is mixed or diffused three-dimensionally, a flow in a

numerical analysis is assumed to be two-dimensional and, the k–ε model is used. Therefore, one of the reasons is that the

rate of vortex decay is gradual in the numerical analysis and, for both a continuous jet and synthetic jet, a two-dimensional

jet structure is maintained more toward the downstream side as compared to the experimental results. While this

numerical analysis has the problems of two models, or a two-dimensional calculation and turbulence model, the results

match the experimental results qualitatively, and the study is thought to be reliable for understanding the synthetic jet

characteristics.

5.3 Jet formation

Figure 5 (a) shows the velocity vector diagram, and Figure 5 (b) shows the vorticity distribution at the time of

maximum suction. Figure 5 (i), (ii), and (iii) shows the results when K = 9.55, 15.92, and 47.76, respectively. The vorticity

scale is different from that of Figure 3, and the scale for vorticities between – 500 and 500 [1/s] is shown, with the out-

of-range values indicated in white or black. Figures 5 (i) and 3 (iv) show the same conditions, the only difference being

the vorticity scale. In the vector diagram in Figure 5 (i) (a) for K = 9.55, the jet center velocity of y/b0 = 0 is u = 0 near

x/b0 = 4, and the jet center velocity is positive when x/b0 ≧ 4, even though it is during the suction phase. Similarly, in

Figure 5 (ii) (a) for K = 15.92 and in Figure 5 (iii) (a) for K = 47.76, the jet center velocity becomes positive when x/b0

≧ 4.7 and x/b0 ≧ 9, respectively, and the sign change of the velocity u, which is a characteristic of synthetic jets, is not

observed. On the scale in Figure 5 (i) (b), the existence of a vortex pair is clearly identified when x/b0 ≈ 17 and 28. In

addition, a vortex pair is observed when x/b0 ≈ 37, but in the vector diagram in Figure 5 (i) (a), because of viscous

diffusion, the vortex is expected to decay to the point where it is hard to identify the vortex-induced local reverse flow

zone. Therefore, when x/b0 ≧ 28, the velocity fluctuation amplitude, which is a characteristic of synthetic jets, is low,

and it is assumed to become close to the unsteady flow characteristics of a continuous flow as it moves downstream. The

same tendency can be seen for K = 47.76 around x/b0 ≧ 50. In (i) K = 9.55 and (iii) K = 47.76, nearly symmetrical flow

fields are observed as the vortex pair maintains its translational motion against the x-axis, but in (ii) K = 15.92, the

symmetry of the flow field is no longer maintained downstream, and the vortex becomes the staggered arrangement of a

reverse Karman vortex. The conditions and mechanism with which this asymmetric flow is formed are unknown, and

there is a need for discussions on synthetic jets, including the relationship between the vibration characteristics and the

vortex configuration, as well as stability.

Figure 6 shows the velocity waveform of an absolute value |u| along the centerline (y/b0 = 0) against K = 9.55 (f = 50

Hz) obtained using a hot-wire anemometer. Figure 6 (a), (b), and (c) shows the measurement results for x/b0 = 0.4, 3.4,

and 13.4, respectively. As u fluctuates between positive and negative in (a) x/b0 = 0.4, which is immediately after the slot

exit, the number of peaks is equal to twice the specified frequency of 50 Hz. A large peak appears during blowing, and a

small peak appears during the suction cycle. On the other hand, in (c) x/b0 = 13.4, u remains positive at all times as the

average flow is developed, and there is no directional change. Under the conditions of this study, no directional change

in flow is observed downstream of x/b0 = 3.4 in (b), and the minimum value of the velocity waveform is nearly zero at

around x/b0 = 3.4. For x/b0 ＜ 3.4, the velocity becomes negative at some time period, and for x/b0 ＞ 3.4, the velocity

is always positive. This point is defined as the formative point of a pulsating jet from the slot XPJ in this study.

88



Figure 7 shows the relationship between the non-dimensional formative point of pulsating jet XPJ/b0 and K, in which

the jet formation point is defined as the point where the positive/negative reversal in velocity is no longer observed along

the centerline during the suction phase, or the point after which the flow is always positive in the downstream direction.

The experimental and numerical results show the same tendency, indicating that XPJ/b0 increases almost linearly when K

is increased and that the jet formative point moves downstream. According to the definition for this figure, synthetic jets

with lower K values have characteristics similar to those of continuous jets formed upstream. In Figure 4, the point where

the time-averaged velocity becomes maximum along the centerline is nearly independent of K, but under the definition

10 20 30 40 50 60 70 80x/b0

0

10 [m/s]

0

y/b0

10

20

-10

-20

(a) Velocity vector (b) Vorticity field



Fig. 5 Velocity vector fields in maximum suction cycle from simulations.

(i) Synthetic jet (K = 9.55, f = 50 Hz)

(ii) Synthetic jet (K = 15.92, f = 30 Hz)

(iii) Synthetic jet (K = 47.76, f = 10 Hz)

10 [m/s]

10 20 30 40 50 60 70 80x/b0

0

0

y/b0

10

20

-10

-20

0

y/b0

10

20

-10

-2010 20 30 40 50 60 70 80

x/b00

vorticity ω [1/s]

-500 5000

0

y/b0

10

20

-10

-2010 20 30 40 50 60 70 80

x/b00

vorticity ω [1/s]

-500 5000

0

y/b0

10

20

-10

-2010 20 30 40 50 60 70 80

x/b00

vorticity ω [1/s]

-500 5000

10 20 30 40 50 60 70 80x/b0

0

10 [m/s]

0

y/b0

10

20

-10

-20

0

5

10

15

20

25

30

0 0.02 0.04 0.06 0.08 0.1

|u| [

m/s

]

t [s]

0

5

10

15

20

25

30

0 0.02 0.04 0.06 0.08 0.1

|u| [

m/s

]

t [s]

0

5

10

15

20

25

30

0 0.02 0.04 0.06 0.08 0.1

|u|

[m/s

]

t [s]

Fig. 6 Velocity waveform variation along centerline from hot-wire anemometer (K = 9.55).

(a) x/b0 = 0.4 (b) x/b0 = 3.4 (c) x/b0 = 13.4

99



of the jet formative point in this figure, which focuses on one of the major characteristics of synthetic jets, or the

positive/negative reversal of velocity, XPJ/b0 depends on K, and XPJ/b0 becomes higher as K increases.

5.4 Unsteady characteristics of synthetic jet

Figure 8 shows the non-dimensional turbulence intensity, root-mean-square (RMS) values of the velocity fluctuation

RMS/um at the centerline for K = 9.55, 15.92, and 47.76. The filled symbols indicate the experimental values, and the

open symbols indicate numerical analysis values. The results for the continuous jet and the experimental results for the

continuous jet from Heskestadt (1965) are also shown with a dashed line. For the numerical simulations using the k–ε

model, however, the fluctuation velocity RMS values are the same in the x and y directions, and k cannot be broken down

to u' and v', where u' and v' indicate the velocity fluctuation elements in the x and y directions, respectively, expressed as

a turbulence model. For this reason, although it is a rather wild assumption, we assumed u' ≈ v' as the primary

approximation (and thus k = (u'2+v'2)/2 ≈ u'2), and evaluated as u' = √𝑘 for convenience. In this study, the RMS value

is obtained by adding the above u' to the fluctuation element of the x-direction velocity at a certain point in time, as

obtained from the numerical simulation, and assuming that this value is the real velocity fluctuation element. Therefore,

the numerical simulation results in this figure are shown as a reference, and even though the experimental results and

numerical simulation results cannot be simply compared, the approximate outlines of these results are similar. The

subsequent passages primarily discuss the experiment results. The RMS/um value of a continuous jet increases almost

monotonically as x/b0 increases. On the other hand, in the case of a synthetic jet, the RMS/um value is high near the slot

as the jet is formed by oscillatory flow but decreases as x/b0 increases. However, the RMS/um value starts to increase

downstream of x/b0 ≈ 25 for K = 9.55, x/b0 ≈ 30 for K = 15.92, and x/b0 ≈ 50 for K = 47.76. Therefore, it is assumed

that downstream of the above points, unsteady characteristics similar to those of the continuous jet are maintained.

The x-direction velocity fluctuation spectrum distributions at the centerline for K = 9.55 and 47.76 are shown in Figure

9 (i) and (ii), respectively, where (a) shows the experimental results, and (b) shows the numerical simulation results. In

all of these figures, the predominant frequency component appears near the Strouhal number St, which is the equivalent

of the excitation frequency in the slot neighborhood (for K = 9.55, St ≈ 0.033 and for K = 47.76, St ≈ 0.007), and the

predominant frequency component decays on the downstream side. In Figure 9 (i), for K = 9.55, the predominant

frequency component remains on the downstream side according to the experimental results, but its value becomes very

low, whereas in the numerical simulation, it is difficult to substantially identify the predominant frequency component

downstream. The experimental result (a) shows that at x/b0 = 25, where RMS/um starts to increase, the peak value of the

0

2.5

5

7.5

10

12.5

15

0 10 20 30 40 50 60 70 80 90 100

XP

J /b

0

K

EXP

CFD

Fig. 7 Formative point of pulsating jet at centerline for various values of K


1010



predominant frequency component becomes 1/5 of the peak value at x/b0 = 5, whereas with the numerical simulation in

(b), it becomes 1/60. In Figure 9 (ii), for K = 47.76, the experimental and numerical simulation results both show the

harmonic components. The experimental results in (a) show that the peak value of the dominant frequency component at

x/b0 = 50 becomes 1/7 of the peak value at x/b0 = 5. In the numerical simulation results in (b), it becomes 1/15 at x/b0 =

50. This shows that at a point where RMS/um starts to increase, the peak value of the predominant frequency is

substantially lower than the value at the slot exit. Hence, downstream of this point, the pulsation caused by the

suction/blowing at the slot exit and the translational motion of a vortex pair, which is the main characteristic of the

synthetic jet, almost disappears, and it becomes hard to determine whether the flow originates with the continuous jet or

the synthetic jet.

In Figure 10, the formation point XQC of the flow having the same unsteady characteristics as the continuous jet is

defined as the point in the experiment results where RMS/um starts to increase and the point in the numerical simulation

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70 80

RM

S/u

m

x/b0

EXP Conti.Jet

(Heskestadt, 1965)

CFD EXP

Conti.Jet ○ ●

K =9.55 △ ▲

K =15.92 □ ■

K =47.76 ◇ ◆

Fig. 8 Variation in RMS values in streamwise direction along centerline


0

0.15

0.3

0.45

0.6

0.75

0.9

1.05

0.000 0.007 0.013 0.020 0.027

0.033 0.040

0.047 0.053

0.060 0.067

x/b0

Sp

ectr

al

den

sity

St

0

4

8

12

16

20

0.000 0.007 0.013 0.020 0.027

0.033 0.040

0.047 0.053

0.060 0.067

x/b0

Sp

ectr

al

den

sity

St

(i) Synthetic jet (K = 9.55, f = 50 Hz)

(a) Experiment (b) Numerical Simulation

(ii) Synthetic jet (K = 47.76, f = 10 Hz)

Fig. 9 Power spectrum of velocity at centerline from experiment and numerical simulation.

(a) Experiment (b) Numerical Simulation

0

6

12

18

24

30

0.000 0.007 0.013 0.020 0.027 0.033

0.040 0.047

0.053 0.060

0.067

x/b0

Sp

ectr

al

den

sity

St

5

10

15

2025

3035

4045505560

0.000 0.007 0.013 0.020 0.027 0.033

0.040 0.047

0.053 0.060

0.067

x/b0

Sp

ectr

al

den

sity

St

1111



results where the peak value of the predominant frequency component of the velocity fluctuation spectrum distribution

becomes 1/5 of the peak value of x/b0 = 5 and RMS/um takes the minimum value for the first time; the relationship between

K and XQC/b0 is shown in Figure 10. Here, in the numerical simulation, the results are omitted K ≈ 15 because an

unexplained asymmetric flow is formed K ≈ 15, as mentioned above, which shows unique unsteady characteristics. For

both the experimental and the numerical simulation results, the XQC/b0 value increases as K increases, except for one

experimental value. Therefore, when focusing on the unsteady characteristics, the flow characteristics of synthetic jets

become similar to those of continuous jets when K is lower and further upstream. K and XQC/b0 are not directly

proportional, however, and it is assumed that the XQC/b0 value is higher than the directly proportional value when K =

9.55, because the velocity fluctuation at the slot exit cannot be disregarded when K is low. The details are still unknown

and remain issues to be tackled by further study.

6. Conclusions

In this study, experiments and numerical simulations were conducted to investigate the fundamental flow

characteristics of infinite two-dimensional synthetic jets, and we reached the following conclusions:

1. The typical flow patterns, which included flow visualizations using the smoke-wire method, velocity vector diagrams

obtained using a numerical simulation, vorticity distribution, and vortex pair behavior, showed that the experimental

results and numerical simulation results matched qualitatively. In addition to a symmetric flow, in which the vortex

pair undergoes translational motion caused by their mutually induced velocity, we have indicated the possibility of

asymmetric flow, in which the vortex has a staggered arrangement.

2. It was found that the time-averaged velocity of the synthetic jet along the centerline is zero at the slot exit but

reaches a maximum at x/b0 ≈ 4.0, and the average velocity decreases from this point downstream, although it

fluctuates slightly. In addition, the time-averaged velocity along the centerline increases almost irrespective of K

until it reaches the maximum, whereas in the decaying process, it is dependent on K.

3. The point where the velocity sign change caused by the blowing/suction at the slot on the jet centerline no longer

occurs was identified and defined as the jet formative point, which showed the relationship between the non-

dimensional jet formation point XPJ/b0 and K. This also showed that XPJ/b0 is essentially directly proportional to K.

0

10

20

30

40

50

60

0 10 20 30 40 50

XQ

C /b

0

K

EXP

CFD

Fig. 10 Formative point of quasi-continuous jet at centerline with various values of K


1212


© 2014 The Japan Society of Mechanical Engineers[DOI: 10.1299/jfst.2014jfst000 ]7

4. In the case of synthetic jets, RMS/um is at the maximum near the slot and decreases as x/b0 increases, but from a

certain point, it starts to increase. In addition, the change in RMS/um depends on K.

5. The point where the tendency of RMS/um changes and the point where the predominant frequency component in the

velocity fluctuation spectrum distribution almost disappears are basically the same.

6. We found the point on the jet centerline where the unsteady characteristics of the synthetic jet become equal to those

of the continuous jet; the point was defined as XQC. Furthermore, we showed the relationship between K and XQC/b0.

The value of XQC/b0 was found to essentially be directly proportional to K.

Acknowledgements

The authors would like to thank Professor Toshihiko Shakouchi of Mie University and Associate Professor Toru Koso

of Kyushu University for their advice, along with Mr. Shunichi Fujiki, the president of the Beltek International

Corporation, for his assistance in the design and construction of the experimental apparatus. This work was carried out

with the support of a Grant-in-Aid for Scientific Research (21560187) from the Research Center for Urban Disaster

Mitigation (UDM) of Kogakuin University.

References

Amitay, M. Smith, D., Kibens, V., Parekh, D., and Glezer, A., Aerodynamic flow control over an unconventional airfoil

using synthetic jet actuators, AIAA Journal, Vol. 39, No.3 (2001), pp.361-370.

Duvigeneau, R., Hay, A., and Visonneau, M., Optimal location of a synthetic jet on an airfoil for stall control, Journal of

Fluid Engineering, Vol.129 (2007), pp.825-833.

Heskestadt, G., Hot-wire measurements in a plane turbulent jet, Transactions of the ASME, Journal of Applied Mechanics,

Vol.32 (1965), pp.721-734.

Holman, R., Utturkar, Y., Mittal, R., Smith, B., and Cattafesta, L., Formation criterion for synthetic jets, AIAA Journal,

Vol. 43, No.10 (2005), pp.2110-2116.

Joslin, R.D., and Jones, G.S., Applications of circulation control technology (Progress in astronautics and aeronautics,

AIAA Inc., Vol.214 (2006).

Koso, T., and Kinoshita, T., Jet flow formation using an annular synthetic jet actuator, Proceeding of JSME annual

meeting, pp.211-212 (2006) (in Japanese).

Rajaratnam, N., Turbulent jets, Elsevier Scientific Publishing Company (1976), Equation (1.93).

Shuster, J.M., and Smith, D.R., An experimental study of the formation and scaling of a round synthetic jet, Physics of

Fluids, Vol.19-045109 (2007), pp.1-21.

Tensi, J., Boué, I., Paillé, F., and Dury, G., Modification of the wake behind a circular cylinder by using synthetic jets,

Journal of Visualization, Vol.5, No.1 (2002), pp.37-44.

Whitehead, J. and Gursul, I., Interaction of synthetic jet propulsion with airfoil aerodynamics at low reynolds numbers,

AIAA Journal, Vol. 44, No.8 (2006), pp.1753-1766.

You, D., and Moin, P., Study of flow separation over an airfoil with synthetic jet control using large-eddy simulation,

Annual Research Briefs, Center for Turbulence Research (2007), pp.311-321.

Zhang, P.F., and Wang, J.J., Novel signal wave pattern for efficient synthetic jet generation, AIAA Journal, Vol. 45, No.5

(2007), pp.1058-1065.

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