A numerical investigation of effects of cavity and orifice parameters on the characteristics of a synthetic jet flow

Sensors and Actuators A 165 (2011) 351–366

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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

A numerical investigation of effects of cavity and orifice parameters on the characteristics of a synthetic jet flow Manu Jain, Bhalchandra Puranik, Amit Agrawal ∗ Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

a r t i c l e

i n f o

Article history: Received 7 May 2010 Received in revised form 25 September 2010 Accepted 2 November 2010 Available online 16 November 2010 Keywords: Synthetic jet Acoustic actuator Cavity design Computational fluid dynamics (CFD)

a b s t r a c t A synthetic jet is a quasi-steady jet of fluid generated from the periodic motion of a diaphragm enclosed in a cavity with opening/s on one or more walls. In this study, numerical simulations are performed to investigate the effect of various cavity parameters and orifice/cavity shapes on the ensuing synthetic jet flow. A circular orifice synthetic jet is simulated assuming axisymmetric behaviour. The quality of results is verified by time, grid, and domain independence studies, and the results are validated against existing experimental and numerical data. The moving diaphragm is modelled with a velocity boundary condition, with a moving piston boundary condition as well as with a moving wall boundary condition. The results obtained using these approaches are compared and it is concluded that the moving wall boundary condition provides the most realistic representation of the motion of the diaphragm. The simulation results show that synthetic jets are more affected by changes in the geometric parameters of the orifice than those of the cavity. The most significant parameters are determined to be the orifice and cavity radii and the orifice length. Two new parameters – volumetric efficiency and orifice utilization factor, are introduced; different types of diaphragms can be compared with the help of these parameters. The results obtained in this study are significant because they provide basic design guidelines for cavity and orifice, and can be used for optimization of the cavity and orifice shape for maximum velocity or mass flow rate. © 2010 Elsevier B.V. All rights reserved.

1. Introduction A synthetic jet is generated by the periodic motion of a piston or a vibrating membrane inside a cavity, with one or more openings in its other walls. The primary advantage of a synthetic jet over a continuous jet is that the former is synthesized from the surrounding fluid and therefore does not require a continual supply of external fluid unlike for a continuous jet [1]. In a cycle of operation, the total mass flow from the cavity is zero but the net momentum flux is non-zero. When applied to a base flow, a synthetic jet produces unique effects such as closed recirculation and low-pressure regions. Potential applications of a synthetic jet are in flow control, propulsion, mixing of fluids, and thermal management of electronic devices [2–10]. Synthetic jets have attracted a large number of researchers from various fields during the last decade. Production of a time-averaged net fluid motion using mechanical or acoustic means has been tried for many decades. Ingard and Labate [11] and Dauphinee [12] used standing waves in an acoustically driven circular tube to obtain an oscillating velocity field and thus generated a zero net mass flux jet with opposing trains of vor-

∗ Corresponding author. Tel.: +91 22 2576 7516; fax: +91 22 2576 6875. E-mail address: [email protected] (A. Agrawal). 0924-4247/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2010.11.001

tex rings on both sides of the orifice. Smith and Glezer [1] present an overview of such early-time investigations. Recently, Trávníˇcek et al. [13] and Tesaˇr et al. [14] have proposed promising alternate designs capable of giving synthetic jet like flow but with a mean component. Synthetic jet and these alternate designs can be used for cooling/drying applications [15–17]. Smith and Glezer [1] studied the synthetic jet formation and evolution from a rectangular slot. Schlieren imaging and velocity measurements using hotwire anemometry were used to visualize and describe the flow features. They also compared this jet with a conventional two-dimensional jet and found that a synthetic jet entrains more fluid from the surrounding; synthetic jet however loses momentum more rapidly as compared to a continuous jet. Cater and Soria [18] used water as the working fluid instead of air. A piston cylinder assembly was used as the actuator, with a circular orifice on the opposite wall. Using flow visualization images, they categorized the observed flow patterns based on Reynolds number (Re) and Strouhal number (St). They suggested that zero net mass flux jet is formed when vorticity is advected away from a generator at a rate faster than the vorticity is diffused by viscosity. By using dimensional analysis, experiments as well as numerical simulations, Utturkar et al. [19] proposed a jet formation criteria for relatively thick orifice plates (width to hydraulic diameter ratio greater than two) based on Reynolds and Stokes (S) numbers, as

352

M. Jain et al. / Sensors and Actuators A 165 (2011) 351–366

Fig. 1. (a) Geometry and boundary conditions of the computational domain employed in the simulations and (b) cavity and orifice, showing the relevant geometric parameters.

Re/S2 > 2 for a two-dimensional jet and Re/S2 > 0.16 for an axisymmetric jet. Holman et al. [20] provide the jet formation criterion for orifices of different shapes. Agrawal and Verma [21] have provided a similarity analysis of flow in the far field. Although experimental studies have provided a good understanding of flow physics in both near and far fields of a synthetic jet, some important flow features such as flow inside the cavity or mass flow rate through the orifice are difficult to measure experimentally. Numerous numerical studies covering different aspects of the synthetic jet formation and applications have been carried out. The primary challenge in a numerical study is the modelling of the moving diaphragm. To simplify the simulation, the earlier studies have employed one of the following:  a wall normal velocity boundary condition at the orifice exit plane [22–25], or  a moving piston condition [26], or  a moving membrane condition [27–29]. Note that only the last of these may accurately represent the physical situation. Furthermore, for simplicity only the region outside the cavity was modelled by some of the authors [22,25]; however, Rizzetta et al. [23] and Mallinson et al. [27] have modelled the entire flow field (including cavity and orifice). These latter researchers have pointed out that it is essential to model the cavity flow even at the cost of restricting the simulations to only a few cycles. The literature survey suggests that the details of the flow inside the cavity need to be better documented. In addition, the cavity/orifice design has not been studied in sufficient detail. These facts motivated the authors to undertake the present study. We also note that some of the studies [22,25,28] have used incompressible flow solver in their simulations because the frequencies employed were relatively small; this assumption may not apply at high frequencies because the rapid oscillations in the flow at high frequencies can give rise to compressible flow behaviour. Most of the numerical studies in the past have simulated only a single

case, over a limited frequency range, with variation of one or two parameters such as cavity or orifice dimensions. There is therefore a need to study the effect of individual parameters separately and compare them with a baseline case; such results can be used for maximization of synthetic jet flow. In order to address these issues, a comprehensive analysis of the different parameters that affect the formation and evolution of a synthetic jet, including cavity and orifice dimensions, has been carried out in this study. Ways to increase the Reynolds number or the maximum velocity from the orifice exit in order to obtain an enhanced performance of the synthetic jet have also been explored in this work. Therefore, mass flow rate from orifices of different shapes and dimensions is analyzed in sufficient detail. The specific objectives of the present work are: to study the effect of various parameters such as amplitude, frequency, geometry/shape of cavity and orifice on the ensuing flow from the cavity, and to compare the effect of various parameters against the baseline case and suggest ways to achieve the best performance for a synthetic jet. 2. Numerical simulation procedure This section provides the details of the numerical simulation such as geometry, mesh, and other solution parameters. Time, grid and domain independence study results are also presented. The most challenging part in the simulation is the handling of the vibrating diaphragm. Different approximations to simulate the vibrating diaphragm are tested and presented in this section. 2.1. Software The commercial package Fluent 6.2 is used for simulations while Gambit 2.1 is used for geometry creation and grid generation. The equations solved are conservation of mass and momentum for a two-dimensional axisymmetric geometry. The flow is assumed to be compressible and laminar. The compressibility effects come into picture because of the rapid change in pressure/density due to the

M. Jain et al. / Sensors and Actuators A 165 (2011) 351–366

353

40

movement of the diaphragm. In other words, the (1/)D/Dt term in the continuity equation can no longer be neglected. The justification for assuming the flow to be laminar is provided later.

35

piston vibrating membrane velocity inlet

30 25

The synthetic jet cavity is divided into two regions: the first includes the cavity and orifice, and the second comprises the ambient air into which the jet exits (Fig. 1(a)). Boundary conditions are specified at the cavity end and the ambient fluid (air) into which the jet is expelled. The diaphragm and cavity surfaces are considered as impermeable walls as shown in Fig. 1(a); the ambient air is specified with a pressure outlet. Details of cavity and orifice are shown in Fig. 1(b). The diaphragm is defined separately from the other walls so that a user-defined function can be used to describe its movement. The geometry shown in Fig. 1(a) has been meshed with unstructured mesh (triangular elements) for the cavity (up to the orifice exit). The tri-pave unstructured scheme is chosen to allow for relative displacement among the nodes on the diaphragm. The relative displacement among the nodes on the diaphragm is necessary which is not possible with the structured quadrilateral scheme. The outer field is meshed with structured quadrilaterals. Combining the unstructured and structured grids significantly reduces the simulation time by restricting the number of grid points to be re-meshed after each time step and still allows usage of the dynamic mesh feature of the software, which is applied at the vibrating diaphragm and cavity. This combination does not affect the quality of results and brings the simulation time within manageable limits. A sample grid showing every alternate point is presented in Fig. 2.

20

velocity (m/s)

2.2. Geometry and mesh

15 10 5 0 -5 -10 0

0.25

0.5

0.75

1

t/T Fig. 3. Velocity versus time curves for the diaphragm moving as a piston, modelled as a vibrating membrane, and modelled as a velocity inlet.

The velocity inlet boundary condition is given by U = Uo sin(2ft)

(1)

The time-varying geometry of a diaphragm moving as a piston is expressed as X = a sin(2ft)

(2)

The time-varying geometry of the vibrating diaphragm is given

2.3. Diaphragm boundary conditions

by

As already mentioned, the most crucial part of the numerical simulation of the synthetic jet is the modelling of the vibrating diaphragm. Several approximations have been employed in the past to achieve this. These include using a velocity inlet boundary condition with an assumed profile at the location of the diaphragm/orifice exit (Eq. (1)) or using a moving piston boundary condition (Eq. (2)). The swept volume is maintained identical to that in the case of an actually vibrating diaphragm. In the present simulations, a wall boundary condition with the diaphragm vibrating sinusoidally in time such that the geometry of the wall is parabolic at any instant has been employed to simulate the vibrating diaphragm (Eq. (3)). Additionally, the boundary conditions given by Eq. (1) and Eq. (2) have also been tested.



X =a 1−

 r 2  rc

sin(2ft)

(3)

Here U is the instantaneous velocity, Uo is the forcing velocity, f is the frequency, t is the time, a is the amplitude of vibration, X is the displacement, and rc is the radius of the cavity. Eq. (3) is expected to represent a vibrating diaphragm more realistically than either Eq. (1) or Eq. (2). Here we provide a direct comparison of velocity at the exit of the orifice as a function of time, over an actuation cycle, for the three cases. Fig. 3 shows that the velocity versus time curves for piston and velocity inlet boundary conditions are substantially different from those for the case of a moving membrane. (Note that the swept

Fig. 2. Sample grid depicting only the alternate grid points.

M. Jain et al. / Sensors and Actuators A 165 (2011) 351–366

volume is kept constant for the three cases.) In particular, the velocity inlet boundary condition predicts smaller velocities but gives qualitatively the same behaviour as that obtained from a vibrating membrane. Simulations using this condition require only about half of the computational time as that taken with the use of a vibrating membrane. Therefore, the velocity inlet boundary condition can be used as a first approximation. Fig. 3 also shows that approximating the diaphragm as a moving piston predicts higher values of velocity when compared to those predicted using a vibrating membrane boundary condition. This is because the movement of a piston is unidirectional, which increases the velocity component along the axial direction. The above result suggests that the temporal variation of pressure inside the cavity and at the exit of orifice differs for the three cases. Fig. 3 shows that despite the restriction on the swept volume, the velocity profiles for the three cases are sufficiently different. This is because the flow inside the cavity is compressible, due to which the movement of the diaphragm does not translate into a corresponding motion of the cavity fluid. The mass of the fluid ejected is less by 10% for the velocity inlet boundary condition and higher by 24% for the moving piston boundary condition, when compared with the case of a moving membrane. This suggests that boundary conditions for piston and velocity inlet might not represent the situation realistically enough. All the further simulations in this work are performed with the moving membrane boundary condition. The computational time required with the moving boundary is however relatively large due to re-meshing required after each time step. In addition, the requirement of data storage is higher in this case.

16 laminar turbulent Experimental

14 12 10 8

velocity (m/s)

354

6 4 2 0 -2 -4 -6

0

0.25

0.5

0.75

t/T Fig. 4. Velocity versus time curve at centre-line and 1 mm from the orifice exit.

scale defined as



T/2

Lo =

uo (t)dt

(4)

0

Uo = Lo f

(5)

Uo do 

2.4. Time, grid and domain independence studies

ReU0 =

To ensure that the simulation results are adequately resolved, a systematic time and grid independence study was undertaken. The time step varies from 1 to 10 ms for a diaphragm vibrating at f = 500 Hz, which is equivalent to 1/(2000f) to 1/(200f). The maximum difference between the different time steps is 3.75% during the ejection phase [30], but increases to 12.5% during the suction phase (not shown). The time step of 1/(1000f) is found to capture both the positive and negative peaks correctly, and this time step is employed for all calculations [30]. The grid independence studies showed that the results are most sensitive to the number of grid points near the orifice. As a result, it is ensured that the maximum concentration of grid points is along the orifice or near the orifice exit. A 0.1 mm resolution at the orifice exit is found adequate for an orifice with a diameter of 3 mm. Inside the cavity, the grid is uniform while an exponentially varying grid is applied in the outer domain to obtain adequate grid concentration in the vortex built-up area. In domain independence studies for the near field of the jet, it is found that a domain size of 20 orifice diameters (along the axis) and 10 orifice diameters (in the lateral direction) is sufficient. For this domain size, jet near field parameters are not affected by pressure outlet boundary condition applied at the end of the outer region. We find that the first two cycle results are affected by numerical transient and are therefore discarded. Note that Tesaˇr and Zhong [36] found that variations continue over many more cycles. Here, the final data is analyzed only when the monitored results show stabilization over at least 3 cycles.

Uo is the average velocity at the orifice exit during the expulsion stroke, do is the orifice diameter, and T is the period of oscillation. A Strouhal number based on the frequency of oscillation f, the velocity scale Uo , and the stroke length Lo is defined as

2.5. Data reduction

ı(y, t) =

2.5.1. Reynolds number To compare a synthetic jet with a continuous jet, Smith and Glezer [1] proposed the use of Reynolds number based on a velocity

In Eq. (8), ı is the instantaneous position of diaphragm, ımax is the amplitude of vibration, y is the radial distance from the centre of diaphragm, dc is the diameter of diaphragm, and t is the

Sto =

(6)

fDo . Uo

(7)

3. Validation of simulation results This section presents the validation results. As observed from Fig. 4, the expulsion stroke agrees well with our experimental results; however, the velocity during the suction stroke is somewhat underpredicted. Limited turbulent flow simulations were also undertaken using the standard k–ε model. The velocity build up is faster and the maximum velocity is slightly higher in the turbulent case as compared to that in the laminar case. The Reynolds numbers from experimental data, laminar and turbulent numerical simulations are 737, 723 and 747 respectively. The experimental results obtained in our laboratory [31,32] indicate that the flow is laminar close to the orifice although in the far-field it may be turbulent. We conclude that close to the orifice laminar to turbulent transition does not occur, and laminar calculations are considered appropriate. Accordingly, all the further calculations in this work are performed assuming the flow to be laminar. Mane et al. [29] have performed a synthetic jet simulation for a bimorph actuator with a logarithmic approximation for the motion of diaphragm: ımax 2



1−

4y2 dc2

+

8y2 dc2

ln

 2y  dc

cos(2ft)

(8)

M. Jain et al. / Sensors and Actuators A 165 (2011) 351–366

a

10 1

4 Numerical Mane et al. [29] (Numerical) Mane et al. [29] (Experimental)

3.5

(b)

Smith and Glezer [1] (rectangular orifice) Gaetano and Gaetano [26] (circular orifice) numerical

10 0

3 2.5

Ucl/Uo

absolute velocity (m/s)

355

2

10 -1

1.5 10 -2

1 0.5 0

0

0.25

0.5

0.75

10 -3

1

t/T

b

2

3

4

5 6 7 8 910

x/do Numerical Mane et al. [29] (Numerical) Mane et al. [29] (Experimental)

5.5 5

absolute velocity (m/s)

1

6

Fig. 6. Comparison of non-dimensional centreline velocity with that reported in the literature.

4.5

axial distance is compared with the experimental results of Gaetano and Gaetano [33] (for a circular orifice) and that of Smith and Glezer [1] (for a planar orifice). Fig. 6 suggests that the numerical results are in excellent agreement with the circular orifice result. Also notice that Ucl /Uo can become greater than unity for circular orifice while it is just less than unity for the planar orifice. This indicates that the centreline velocity (Ucl ) takes less axial distance to build up in the case of circular orifice. The results in this section help to validate the numerical calculations.

4 3.5 3 2.5 2 1.5 1

4. Parametric studies

0.5 0

0

0.25

0.5

0.75

1

t/T Fig. 5. Velocity versus time curves for bimorph actuator at different frequencies of excitation: (a) 32 Hz and (b) 50 Hz.

time. Using identical numerical conditions, simulation results are compared with those of Mane et al. [29] (experimental and numerical data) in Fig. 5. For the purpose of this comparison, a moving membrane boundary condition with identical deflection of the diaphragm, amplitude of deflection, etc. as used earlier is employed here for a meaningful comparison. While there are certain differences between the present work and that reported by Mane et al., the overall agreement is reasonable. Further validation tests are undertaken for streamwise variation of the centreline velocity. The change in the average velocity with

Performance of a synthetic jet actuator is expected to be sensitive to the parameters related to the cavity and orifice geometry. Experimental determination of the effect of individual parameters is time consuming and expensive; nontheless, it has been attempted by Chaudhari et al. [31,32]. In addition, it is rather difTable 1 Simulation parameters for the baseline case. See Fig. 1(b) for definition of the various parameters. Simulation parameter

Symbol

Value

Cavity height Cavity radius Orifice diameter Orifice length Amplitude of diaphragm Frequency

hc rc = dc /2 do ho a f

7.0 mm 22.5 mm 3.0 mm 2.5 mm 0.2 mm 250 Hz

Table 2 Values of different parameters employed in the parametric study. Parameter

Range

Diaphragm

Amplitude Frequency

0.1–0.2 mm (0.1, 0.11, 0.12, 0.14, 0.16, and 0.2 mm) 200–1100 Hz (200, 250, 500–1100 Hz in step of 100 Hz)

Cavity dimensions

Radius Height

10–60 mm (10, 12.5, 15, 17.5, 20, 22.5, 25, 30, 40, 50, and 60 mm) 1.5–18 mm (1.5, 2.5, 5, 7, 9.5, 12, and 18 mm)

Orifice dimensions

Radius Length

1–8 mm (1, 2, 3, 4, and 8 mm) 0.5–3 mm (0.5, 1.5, 2.5 and 3 mm)

Cavity shape

Cylindrical, Conical, Parabolic

Orifice shape

Bevel, Round edges

a

M. Jain et al. / Sensors and Actuators A 165 (2011) 351–366

1200

1100

1000

24

2900

23

2800

22

2700

21

2600

20

2500

19

2400

Re

18 17 800

16 Re max velocity

15

700

600

500 0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

50 Re Maximum velocity average velocity

40

35

2300 2200 30

2100 2000

14

1900

13

1800

12

1700

11

1600

10 0.18

1500 400

25

20

500

600

700

800

amplitude (mm)

b

900

1000

1100

15 1200

f

20

Fig. 8. Re/maximum velocity/average velocity versus frequency.

a = 0.1 mm a = 0.11 mm a = 0.12 mm a = 0.14 mm a = 0.16 mm

15

the orifice exit. Fig. 7(b) suggests that the velocity versus time curve is qualitatively similar in nature for all amplitudes. At higher amplitudes, the peak velocity is achieved earlier because the velocity builds up faster. The shape of the curve is more symmetric at lower amplitude.

10

velocity (m/s)

45

velocity (m/s)

3000

velocity (m/s)

900

25

Re

356

4.2. Effect of diaphragm excitation frequency (f) 5

From an analysis of flow in the cavity, Gallas et al. [34] have suggested occurrence of two resonance frequencies: the Helmholtz frequency of the orifice and the diaphragm natural frequency. The Helmholtz frequency (fH ) is given by

0

fH =

-5

0

0.25

0.5

0.75

1

t/T Fig. 7. Effect of amplitude of vibration (a) Re/Maximum velocity versus amplitude. (b) Velocity versus time curves at 1 mm from the orifice exit.

ficult to gather precise flow field information inside the cavity. Individual control over interlinked parameters such as cavity radius and amplitude of vibration is also difficult and prone to misleading conclusions. Numerical simulations can provide results over a wide range of parameters with reasonable computational time and adequate flow resolution inside the cavity. For comparison between different shapes and sizes, a baseline case with parameters as given in Table 1 is defined. Parameters varied in this study are summarized in Table 2. 4.1. Effect of amplitude of vibration of diaphragm (a) To study the effect of change in the amplitude of vibration of the diaphragm on the velocity and Reynolds number, the peak-to-peak displacement of the diaphragm is varied from 0.1 mm to 0.2 mm. As the amplitude increases, the volume swept by the diaphragm in a cycle also increases. This causes more fluid to exit the cavity. Variation of Reynolds number and maximum velocity with respect to the amplitude is approximately linear as observed from Fig. 7(a). Fig. 7(b) shows the velocity versus time plot at 1 mm distance from

 1   4h o 2

3r02

+

8 32 ro



Vc c 2

−0.5

(9)

where c is the speed of sound in the fluid, ho is the thickness of the orifice, ro is the radius of orifice, and Vc is the volume of the cavity. A typical plot for frequency response for a cavity volume of 1.113 × 10−5 m3 is shown in Fig. 8. The Helmholtz frequency suggested by the simulations is between 600 Hz and 700 Hz, which agrees with the value of fH calculated from Eq. (9). The diaphragm natural frequency (fD ) depends on the material (elasticity), mass, dimensions of diaphragm, and amplitude of vibration. It is given by fD =

 1   m   r 6 (1 − ˛2 ) −0.5 c 2

62 rc4

16E3

(10)

where rc is the radius of diaphragm, E is the elastic modulus of diaphragm, ˛ is the Poisson ratio,  is the thickness of diaphragm, and m is the mass of the diaphragm. In the present simulation study, the natural frequency by itself cannot be determined, due to the assumption of zero thickness and mass-less wall. Chaudhari et al. [32] found that the diaphragm frequency obtained from the experiments compare favourably with that calculated from Eq. (10), while the Helmholtz frequency compares within ±30%. 4.3. Effect of cavity height (hc ) Simulations are performed by varying the cavity height from 0.5 × do to 6 × do while keeping all other parameters constant. Fig. 9(a) shows the phase angle between the diaphragm motion

M. Jain et al. / Sensors and Actuators A 165 (2011) 351–366

a

the flow peaks, the diaphragm may start moving away from the orifice thus reducing the pressure inside the cavity, which results in a decrease in the velocity. Variation in the shape of a velocity curve results in higher Reynolds numbers for a shorter cavity height. Re variation is from 1544 (0.5 × do ) to 1430 (12 × do ) which is about 6% change. If the phase difference between the diaphragm and the flow increases beyond 90◦ , the peak velocity reduces and the velocity versus time curve is much sharper as observed for the case of 6 × do (phase angle 99◦ ). The Reynolds number is reduced by 15% for this case. Care should be taken while designing the cavity so that the phase difference at any time remains small (below 90◦ ) so that the performance is not adversely affected.

100 T/2 0 or T 80

phase angle (degree)

357

60

40

4.4. Effect of Radius of the cavity (rc ) 20

0

0

5

10

15

20

cavity height (mm)

b

30

4.4.1. Case 1. Amplitude constant In this series of simulations, the amplitude of vibration was held constant. Because of this, the volume swept by the diaphragm varies with the change in cavity radius. In particular, the radius of cavity was reduced while keeping the amplitude of vibration constant. Maximum velocity of fluid reduces with a decrease in the swept volume. Positive part of velocity curve over a cycle keeps on increasing for radius smaller than 15 mm (Fig. 10(a)) which shows reduced size of the suction zone. Reynolds number reduces from 1450 (swept volume = 3 mm3 , rc = 22.5 mm) to 167 (swept volume = 1.33 mm3 , rc =10 mm). Thus, a reduction by a factor of 2.25 in the swept volume results in a reduction by a factor of approximately 8 in Reynolds number. Below this, there is no flow from the cavity as the ejected fluid is sucked back in. The variation in Reynolds number and maximum velocity is approximately quadratic with respect to swept volume Fig. 10(b). Synthetic jet formation ceases when 1/St is 0.19, this critical value is close to the limit of 0.16 given by Utturkar et al. [19]

hc= 0.5do hc=0.83do hc=1.66do hc=2.33do hc=3.17do hc=4do hc=6do

25

20

velocity (m/s)

Any change in the radius of the cavity changes the diaphragm radius since the diaphragm bounds one end of the cavity. Change in the diaphragm radius affects the volume swept by the diphragm and the amplitude of the vibration (peak-to-peak displacement of the diaphragm). Since other parameters also change, the comparison between different cavity radii cannot be done directly. To overcome this difficulty, two different cases were simulated.

15

10

5

0

-5

-10

0

0.25

0.5

0.75

1

t/T Fig. 9. Effect of cavity height: (a) phase angle versus cavity height curve and (b) velocity versus time curves.

and the velocity at the orifice exit at the commencement of suction stroke and at the commencement of ejection stroke. A cycle of operation of synthetic jet is assumed to be 360◦ where 0◦ is when the diaphragm is farthest from the orifice. Phase difference is determined as the angle between the diaphragm movement and the flow reversal at the orifice exit. Fig. 9(a) suggests that phase difference increases linearly with increase in the cavity height. Phase-neutral velocity profiles at the orifice exit are plotted in Fig. 9(b) for comparison. Changing the cavity height from 0.5 × do to 4 × do reduces the peak velocity by only 8%. In addition, the velocity build up is similar in all cases, but at smaller cavity heights, this build up is sustained for a longer period, leading to the formation of a plateau at the top of the velocity profile curve. This is attributed to the lesser phase difference between the diaphragm motion and velocity cycle at smaller cavity heights (when the flow peaks at the orifice exit, the diaphragm motion is still towards the orifice). Thus, the peak velocity is sustained for a longer period. (The plateau can also be due to vortices getting trapped inside the cavity and later getting expelled with the fluid.) For large cavity heights, by the time

4.4.2. Case 2. Swept volume constant In this series of simulations, the swept volume was held constant. The amplitude of vibration varies appropriately with the change in cavity radius. As observed from Fig. 11, at a certain cavity radius, maxima for Reynolds number and velocity are found to exist. This can be attributed to the fact that with higher amplitude at a lower radius of cavity, the acceleration of diaphragm is higher and the flow does not get enough time to adjust to the rapid diaphragm motion. At higher values of radius of cavity, the flow from inside the cavity does not reach the orifice while the diaphragm starts reversing, which weakens the pressure field inside the cavity and results in lower mass flow rate. It can be deduced that there is an optimum radius of diaphragm at which the momentum transfer is highest between the diaphragm and the fluid. This indicates that the radius of the cavity is an important parameter for optimizing the synthetic jet. To maximize the performance of a synthetic jet, it is necessary to find the optimum radius for a particular swept volume 4.5. Effect of Orifice length (ho ) Four cases with orifice length variation from 0.17 × do to 1 × do (i.e., 0.5 mm to 3 mm) were simulated to find the effect of orifice length on the flow. Changes in the shape of the curve depicting

358

a

M. Jain et al. / Sensors and Actuators A 165 (2011) 351–366

rc= 22.5 mm rc = 20 mm rc = 17.5 mm rc = 15 mm rc = 12.5 mm rc = 10 mm

25 20

Re Maximum velocity

1800

35 1600 30

1400

15

1200

Re

25

1000

10

20

800

velocity (m/s)

velocity(m/s)

40

2000

30

5 600

15

0 400 10

-5

200 0

-10 0

0.25

0.5

0.75

1

t/T

b 1500

20

30

40

50

60

5 70

cavity radius (mm) Fig. 11. Velocity variation: Re and maximum velocity versus cavity radius with swept volume being constant.

30 Re Maximum velocity

1400 1300

cycles, the jet does not form as the mass ejected in ejection stroke is sucked back inside the cavity during suction stroke. Mass flow rate keeps on increasing until the orifice diameter is 3 mm, after which it remains almost constant (Fig. 13(b)).

25

1200 1100 1000

20

800

15

700 600 500

velocity (m/s)

900

Re

10

10

5. Effect of orifice and cavity shape In the previous section, the dimensions were varied while the geometry of the cavity and the orifice were left unchanged. In the present section, a few alternate geometries are simulated.

400

5.1. Orifice with smooth edges

300

5

200 100 0

1

1.5

2

2.5

3

0

3

swept volume (mm ) Fig. 10. Effect of cavity radius with amplitude being constant. (a) Velocity versus time curves and (b) Re/maximum velocity versus swept volume ratio.

velocity versus time, over a cycle were observed (Fig. 12(a)). From 0.17 × do to 0.5 × do , the maximum velocity increases slightly and remains stagnant until 0.83 × do and then it decreases. Reynolds number increases slightly from 0.167 × do to 0.5 × do , and decreases afterwards (Fig. 12(b)). The decrease in Re between 0.5 × do and 0.84 × do even while the maximum velocity remaining constant is due to a change in shape of the velocity versus time curve. This indicates that there is an optimum orifice length where the maximum flow is obtained. Velocity variation at the orifice exit is about 4 m/s, which is about 14% of the maximum velocity of the baseline case. 4.6. Effect of Diameter of the orifice (do ) To find out the effect of orifice diameter on the flow parameters, five cases with variation in orifice diameter (from 1 to 8 mm) were simulated. The Reynolds number and maximum velocity were plotted against orifice diameter (Fig. 13(a)). The maximum Reynolds number is attained at 2 mm orifice diameter even though the maximum velocity is attained at 1 mm orifice diameter. When orifice diameter is 8 mm, even though there are positive and negative

To study the effect of a smooth edge orifice, its corners are rounded with a 0.5 mm arc. The rounding is tested for three cases: inner edge, outer edge, and both the edges; such cases are relevant from the viewpoint of engineering applications [37]. As shown in the velocity versus time plot (Fig. 14), there is a 25% reduction in the peak velocity but the nature of the curve is approximately the same as a ‘normal cavity’. This compares well with the two-dimensional simulations of Lee and Goldestin [24] who found a 20% reduction for a round orifice as compared to their baseline case. Reduction in velocity is due to the reduced separation at the entrance due to smooth flow passage and nozzle-like effect of the rounded edges. A careful study of the flow revealed that the smooth edge reduces the vortex formation inside the orifice and allows more fluid to be drawn from the sides of the orifice as compared to the normal orifice. Fig. 14 shows that the smooth edged orifice has a slightly higher velocity in the initial stages because the resistance to outgoing fluid is less. Using rounded edges on either inner or outer side of orifice produces higher velocities than using rounded edges on both the sides. With an orifice with only outer edges rounded, the same peak velocity as that from a normal orifice is obtained. Mass flow rate comparison shows that the highest mass flow rate is obtained from the orifice with both edges rounded, followed by the orifice with rounded edges on the outer side and normal orifice. There is a 10% increase in mass flow rate from orifice with both edges rounded and 5% increase from only the outer edges rounded. It is therefore recommended to use smooth edges on the outer side, which gives higher mass flow rate without reduction in peak velocity.

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5.2. Shape of the orifice A bevel-shaped orifice with varying angle was simulated to find out the effect of shape change. All bevel-shaped orifices have a fixed diameter (of 3 mm) at the centre of the converging section (Fig. 15(a)) to facilitate comparison. In the case of unidirectional flow (a normal jet with Mach number less than 1), converging nozzles provide acceleration to the flow. However, the effect of the orifice geometry in synthetic jets is not clear. As a synthetic jet has a bidirectional (ejection and suction) flow, convergence would help during ejection part but might have an adverse effect during suction. The simulations show that in a synthetic jet, slightly less velocity of a jet is obtained (Fig. 15(b)) as the velocity reduces due to the effect of diverging nozzle during suction stroke, which decelerates the flow during suction. This effect reduces the total mass flow in and out of the system, and hence, the ejection velocities tend to be on the lower side. Maximum exit velocity at 1 mm from the orifice exit is reduced initially up to a nozzle angle of 15◦ due to

4

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a higher distance travelled by fluid along the orifice length, which implies more resistance to the fluid flow. After 15◦ flow separation from the nozzle walls and during suction stroke, a vortex begins to form right inside the length of the nozzle. We obtain higher ejection velocities as the resistance to flow by the nozzle walls is less in this case and the effect of a small-sized outlet comes in picture. Reynolds number based on the orifice exit diameter, as shown in Fig. 16(a), shows a sharp decline up to about 5◦ , and then a slow decrease up to 15◦ after which it again falls rapidly. If the Reynolds number is calculated based on the midsection diameter equal to 3 mm, it shows a decline up to 5◦ followed by a rise. However, it never reaches the value of a straight orifice. Mass flow rate initially increases with angle before reducing and is up to 5% more than the normal orifice (Fig. 16(b)). After 15◦ , as the angle increases, the orifice exit diameter is reduced further. This gives higher exit velocity but the mass flow rate falls below the normal orifice again. 5.3. Shape of the cavity To find out the effect of change in the shape of the cavity, conical and parabolic cavities as shown in Fig. 17(a) and (b) were simulated.

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Fig. 15. Effect of orifice shape: (a) Bevel-shaped orifice and (b) velocity versus time curve.

It was expected that such shapes with smaller dead zone may help eject a larger amount of the fluid. The velocity at the exit and mass ejected during the ejection stroke are considered as parameters to evaluate the design. The results are compared against a ‘normal’ cavity. Velocity profiles over a cycle for different cavity shapes are plotted in Fig. 17(c). Conical and parabolic cavities give almost the same peak velocity as the normal cylindrical cavity. Velocity versus time curve for a cylindrical cavity has a plateau at the top, which is not present in the other two shapes. This difference in shape can be attributed to higher resistance offered by flow-restricting cavity walls since the cavity walls are nearer to the diaphragm in the case of conical and parabolic shapes. Due to this, the velocity increases gradually and the formation of vortices at the orifice exit slows down. These shapes also reduce the vortex build-up inside the cavity and orifice, and smoothens the velocity curve. Mass flow from conical and parabolic cavity is about 4% less than that from the cylindrical cavity. Reynolds number is slightly less for conical and

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parabolic cavities as the shape of the curve depicting velocity versus time is different. The far-field flow parameters for all the cavity shapes were also found to be almost identical. The shape of cavity therefore does not seem to affect the synthetic jet substantially. 6. Discussion Some explanation for the flow behaviour observed above is offered in this section. A discussion on the definition of Reynolds number is also provided along with definition of two new parameters. 6.1. Exit velocity In this section, different shapes of the velocity-versus-time curve observed in the previous sections are analyzed. At small values of frequency, the shape of the exit-velocity-versus-time curve is perfectly sinusoidal. Variation in velocity corresponds to the cross-

ing of vortex pair at the point of observation (Fig. 4). As the size and strength of the vortex pair generated reduces, fluctuations in velocity reduce. At the start of the expulsion cycle, the fluid near the side of the orifice moves out first increasing the velocity (see Fig. 18(a)). However, along the centerline inside the cavity, the fluid continues to move towards the diaphragm. When the diaphragm moves further out, more fluid is expelled. But the fluid coming from inside the cavity faces resistance from the fluid moving in the opposite direction. Therefore, the velocity dips momenterially. When the velocity reaches its peak value, the formation of a small region with two peaks is noticeable. At the first peak, the vortices that form near the edge of the orifice are fully grown. These vortices get detached from the orifice exit surface and start moving downstream (Fig. 18(b)). When they reach the point at which the velocity measurements are sampled, the diaphragm continues to move towards the orifice. As a result, the fluid continuouly comes out from the orifice somewhat like a slug and follows the vortex pair (Fig. 18(c)). The velocity drops by a small amount as the vortex

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Fig. 18. Velocity vectors and pressure contours for different times in a cylce of operation. Colour map for velocity vector showing magnitude in m/s. Pressure contours are for gauge pressure and unit used is Pa.

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Fig. 18. (Continued).

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pair crosses the point of observation (Fig. 18(d)). The crossing over of the vortex pair corresponds to the secondary peak. After crossing over of the vortex pair, the veocity starts decreasing when the diaphragm reverses. This shows similarity to the trends in Smith and Swift [35] where at a higher Reynolds number, both plateau at the top of the velocity curve and the two peaks are observed. The strength of the second peak depends on the phase difference between the diaphragm movement and the fluid expelled from the orifice exit. At lower orifice length (see Fig. 12 (0.17 × do )), the time required by the fluid to traverse the orifice is small so that the vortex formation is rapid. As the vortex ring gets bigger and detaches, the diaphragm continues to move towards the orifice (expulsion stroke) and the phase differecne is small. The fluid which comes out from the orifice pushes the vortex pair, and as a result, the second peak of velocity curve is higher. At a medium orifice length (0.5 × do ), time required for vortex formation is more, and consequently, phase difference is more. The two peaks observed in velocity curve have the same height and correspond to the passing of the vortex pair through the point of observation. At a higher orifice length (0.83 × do ), phase difference increase further and by the time the vortex ring is formed, the diaphragm starts moving in the opposite direction (suction stroke). Near the wall, fluid starts coming towards the orifice thus creating resistance to the fluid ejected. This reduces the speed which results in a lower second peak. Similar behaviour is observed with a change in orifice height. The negative portion of the velocity versus time curve also shows variation. As the suction phase starts, flow is sucked in from near the walls (Fig. 18(e)). As time progresses, and suction pressure lowers further, the flow is sucked in from a wider area in front of the orifice. The flow gets detached from the walls and fills the full orifice. Velocity increases and reaches its peak with the formation of vortex pair inside the cavity (Fig. 18(f)). The vortex pair moves forward and as it reaches the diaphragm (Fig. 18(g)), it slows down thus increasing the pressure, reducing the suction effect, and slowing the flow temporarily. As this vortex pair starts moving along the diaphragm (Fig. 18(h)), velocity increases again thus forming the second peak. Strength of the second peak depends on the phase difference between the incoming flow and the diaphragm motion. The shape of the velocity versus time curve is altered upon changing the shape and size of orifice or cavity. This, in turn, changes the size of the vortices or the phase angle between the diaphragm

motion and velocity at observed point reducing the plateau at the top. This behaviour was not reported in previous numerical simulations because time resolution is better in this study than in the previous studies. A better time resolution enables more detailed flow evolution study. In addition, most of the earlier simulations have used turbulent model to predict the time-averaged behaviour which suppresses the instantaneous variations. 6.2. Use of centre-line velocity for calculations In almost all the experimental studies, the velocity is measured at the centreline of the orifice exit. This velocity is normally used as the characteristic velocity and employed to calculate different flow quantities. For a large orifice with continuous flow, a top hat profile at the orifice exit gives reasonably good results, this is however not the case with a synthetic jet. For a synthetic jet, normally the orifice size is small and the velocity profile at the orifice exit is not constant (Fig. 19(a) and (b)). The velocity variation across the radial direction of orifice is large. To assess the use of the centreline velocity for calculations, 30 data points across the radial direction of a 1.5 mm radius orifice, each representing a circular ring of 0.05 mm, were taken and velocity versus time graph was plotted. Average velocity from these points was then used to calculate the flow rate from their respective rings. If only centreline velocity is taken as a representative for the full orifice flow, mass flow rate is higher by 37%. Therefore, we conclude that the use of only the centreline velocity over-predicts the flow rate in the case of a synthetic jet. A parameter that gives the actual orifice utilization can be defined as the ratio of average velocity across orifice to the centreline velocity of the orifice as ˇo =

Uavg . Uo

(11)

Here, ˇo is the newly defined utilization factor of orifice, Uavg is the average velocity at the orifice exit, and Uo is the average centreline velocity at the orifice exit. For this study, ˇo is approximately 0.72 for the case of a vibrating membrane and 0.83 for the case of a piston. A higher value of ˇo indicates a flatter profile with fewer variations. Estimation of this new parameter gives a better accuracy in predicting various flow parameters like mass flow rate and momentum flux.

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6.3. Radial variation in velocity at the orifice exit

forward stroke:

A synthetic jet does not have a continuous unidirectional flow at the orifice exit rather the velocity varies with time. As reviewed in the Introduction, several studies have neglected the flow inside the cavity and performed simulations with a prescribed velocity profile at the inlet. The purpose of this subsection is to present the velocity profiles as a function of time at the orifice exit, and examine if some such simplification is possible. In ejection stroke (Fig. 19(a)), as the diaphragm starts moving from its bottom position towards the orifice (t/T = 0.025), some flow continues to come inside the cavity from the previous suction stroke. Owing to the phase difference between the diaphragm motion and the fluid flow at the orifice exit, a small bump in velocity is observed near the wall of the orifice. As the diaphragm advances (t/T = 0.175), the flow direction reverses in the core but the velocity remains higher near the wall of the orifice. From t/T = 0.225 to 0.25, development of core flow can be seen. The velocity profile shows a higher velocity in the centre portion of the orifice while the velocity along the orifice wall becomes lower. This velocity profile remains valid until t/T = 0.5 other than near the wall. Because of a small recirculation zone, negative velocity is seen near the orifice walls for t/T = 0.325–0.5. During suction stroke (Fig. 19(b)), as the diaphragm starts moving away from the orifice (t/T = 0.525 and 0.625), the flow starts reversing near the orifice centre as well. A reverse flow with a large negative velocity at the centre of the orifice is observed from t/T = 0.65 to 0.725. Between t/T = 0.75 and 0.925, the velocity profile is almost flat but the maximum velocity first decreases (up to t/T = 0.825) before increasing slightly (t/T = 0.925). Velocity decreases as the diaphragm nears its farthest position from the orifice at t/T = 0.975. At t/T = 1, a sharp drop in velocity is seen as the diaphragm reverses its direction, after reaching its end position. Several different shapes of the velocity profile are observed for expulsion and suction strokes. The shape of the velocity profile is complex in both suction and ejection strokes because flow reversal starts near the orifice wall and eventually a core flow develops. Velocity first increases rapidly near the wall and then decreases even though the velocity at the central portion keeps on increasing. In ejection stroke, the bulk of the flow occurs at the centre portion of the orifice (r/ro = 0.7) whereas the flow is more evenly spread in suction stroke (up to r/ro = 0.9). Thus, the maximum velocity is lower in suction stroke. Top hat velocity profile can be used as an approximation only after the core flow develops at centre portion of the orifice. Core flow condition is valid for 0.275 times of the total period in ejection and 0.325T in suction stroke, i.e., for about 55% and 65% of the total time, respectively. Maximum velocity during ejection is at t/T = 0.275 when the diaphragm has moved about 1/20 of the peak-to-peak amplitude from its neutral position towards the orifice while it is at t/T = 0.75 for suction stroke when the diaphragm is at its neutral position. It indicates that a top hat velocity profile is a relatively better approximation for suction stroke although the top hat assumption may not work satisfactorily in either stroke. Use of a boundary condition for velocity profile requires a data bank by which the profile used can be updated frequently. It is obvious from the above result that the velocity does not vary sinusoidally with time and application of Eq. (1) will lead to erroneous results, as already mentioned.

v =

6.4. Introduction of a new parameter (Volumetric efficiency, v ) We propose to define another new parameter called volumetric efficiency v to quantify the performance of a synthetic jet cavity. Volumetric efficiency is defined as the ratio of the volume flow during the ejection stroke to the swept volume of a diaphragm in

Vm Vs

365

(12)

The parameter is similar to that defined in the literature on internal combustion engine but differs from that defined by Trávnícek et al. [38]. For this study, v is approximately 0.8 for a membrane vibrating with a parabolic profile and 0.85 for a membrane vibrating with a logarithmic profile. Thus, at displacing a fluid, a diaphragm vibration with a logarithmic shape is more efficient than the one with a parabolic one. For a piston-type motion of diaphragm, this parameter is 0.9. This parameter can be used to compare between different types of diaphragm motions like sinusoidal and logarithmic. Design of the diaphragm should be based on this parameter to give the desired displacement. 6.5. Summary of parameters affecting synthetic jet Frequency and amplitude are crucial parameters that affect the synthetic jet performance and can be varied by changing the signal and power input to the diaphragm. Shorter cavity height reduces the resistance to flow and decreses the phase difference between the diaphragm motion and velocity at the orifice exit. This increases the speed of vortex thus allowing vortices to grow and travel faster, which in turn increases both the Reynolds number and the mass ejected from the cavity. Thus, it is recommended to have as small a cavity height as possible. Cavity radius is the most improtant parameter as it affects both amplitude and swept volume of a diaphragm. Finding the optimum radius (i.e., the one that yields a maxima for Re and mass flow) is critical. The orifice diameter has the highest effect on jet parameters, as the pressure field strength is dependent on it. For a given setting of amplitude and frequency, there exists an optimum diameter with which a maximum flow is obtained. The Reynolds number for this diameter is either maximum or close to the maximum. The orifice height is found to have a higher effect on maximum velocity. An optimum orifice height ensures the highest possible velocity and mass flow. Cavity shape and size do not seem to affect the flow parameters significantly. Use of rounded edges in the orifice exit gives a smaller peak velocity but a better performance in terms of mass flow. For optimization, it is required to consider the end use of the actuator thus enabling maximum velocity or maximum flow. Bevel-shaped orifice gives higher velocities only after an inclination angle of 15◦ . The use of converging nozzle as orifice with smaller angles is found to be detrimental for both mass flow rate and maximum ejection velocity. Use of higher angle beyond separation limits can increase the jet ejection velocity but reduces the mass flow rate. The best angle to operate is found just after the separation takes place. It is about 15◦ . It gives almost the same velocity as that of the normal orifice and a slightly higher mass flow rate. 7. Conclusions This study provides a detailed numerical simulation of an axisymmetric synthetic jet. The simulation results are compared with the existing experimental and numerical results for the purpose of validation. A vibrating diaphragm is simulated as a moving boundary and is compared with other boundary conditions employed in the literature. It is observed that the approximations of the boundary condition in terms of a velocity inlet with top hat profile or in terms of a sinusoidal moving piston do not simulate the actual behaviour of a vibrating diaphragm. The Helmholtz frequency could be accurately determined from these simulations. A detailed description of near flow field is provided with the help of vector plots and pressure contours. A moderate comparison between laminar and turbulent flow fields has also been performed.

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To find the effect of parameters of diaphragm, cavity and orifice on the flow, different cases were designed and compared with a baseline case. With an increase in amplitude, a monotonic rise in Reynolds number and maximum velocity is observed. The simulation results show that cavity and orifice height do not affect the maximum velocity appreciably; these however change the velocity versus time behaviour. Orifice height has more effect than the cavity height on the maximum velocity. Changing the cavity radius has more effect on the maximum velcity and Reynolds number even when the amplitude of vibration is constant. There is an optimum cavity radius for a given swept volume at which both maximum velocity and Reynolds number are achieved. By changing the orifice and cavity shape, maximum velocity can be increased but it does not necessarily mean an increase in Reynolds number or mass flow rate. A detailed discussion on the shape of velocity versus time curve is presented. Use of centre-line velocity for calculating the jet parameters is investigated. Two new parameters–orifice utilization and volumetric efficiency are defined. These parameters can be used for comparing different cavity shapes and diaphragm motions, which will help in designing the cavity and choosing the diaphragm. An alternate method to calculate the phase difference between diaphragm and flow is presented; this can be used to get phaselocked data with diaphragm motion in experiments. Acknowledgement We are grateful to Mr. Max Liese for the experimental data in Fig. 4. References [1] B.L. Smith, A. Glezer, The formation and evolution of synthetic jets, Phys. Fluids 10 (1998) 2281. [2] B.L. Smith, A. Glezer, Jet vectoring using synthetic jets, J. Fluid Mech. 458 (2002) 1–34. [3] M. Amitay, V. Kibens, D. Parekh, A. Glezer, The dynamics of flow reattachment over a thick airfoil controlled by synthetic jet actuators, in: AIAA, 37th Aerospace Sciences Meeting and Exhibit, 1999. [4] A. Crook, M. Sadri, N.J. Wood, The development and implementation of synthetic jets for control of separated flow, AIAA Paper 3176 (1999). [5] A. Seifert, L.G. Pack, Oscillatory control of separation at high Reynolds number, AIAA J. 37 (1999) 1062. [6] Y. Chen, S. Liang, K. Anug, A. Glezer, J. Jagoda, Enhanced mixing in a simulated combustor using synthetic jet actuators, in: AIAA, 37th Aerospace Sciences Meeting and Exhibit, 1999. [7] J.S. Campbell, W.Z. Black, A. Glezer, J.G. Hartley, Thermal management of a laptop computer with synthetic air microjets, in: Sixth intersociety Conference on Thermal and Thermomechanical Phenomenon in Electronic System, Institute of Electrical and Electronics Engineers, 1998. [8] N. Beratlis, M.K. Smith, Optimization of synthetic jet cooling for microelectronics applications, in: Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2003. [9] M. Chaudhari, B. Puranik, S.V. Prabhu, A. Agrawal, Heat transfer enhancement with synthetic jet impingement, in: International conference on Advances in Mechanical Engineering (IC-ICAME), Bangalore, 2008. [10] M. Chaudhari, B. Puranik, A. Agrawal, Heat transfer characteristics of synthetic jet impingement cooling, Int. J. Heat Mass Transfer 53 (2010) 1057. [11] U. Ingard, S. Labate, Acoustic circulation effects and the nonlinear impedance of orifices, J. Acoustic Soc. Am. 22 (1950) 211. [12] T.M. Dauphinee, Acoustic air pump, Rev. Sci. Instrum. 28 (1957) 452. [13] Z. Trávníˇcek, V. Tesaˇr, A.-B. Wang, Enhancement of synthetic jets by means of an integrated valve-less pump: Part II. Numerical and experimental studies, Sens. Actuators A 125 (2006) 50. [14] V. Tesaˇr, C.-H. Hung, W.B. Zimmerman, No-moving-part hybrid-synthetic jet actuator, Sens. Actuators A 125 (2006) 159.

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Biographies Manu Jain obtained his B. Tech (hons) from R.E.C. Hamirpur in 2002 and M. Tech (TFE) from IIT Bombay in 2009. He is currently working as Scientist in Aeronautical Development Establishment, Defence Research and Development Organization, Bangalore, India. His field of interests are: launch and tow body dynamics and aerodynamics. Bhalchandra Puranik is an assistant professor in the Department of Mechanical Engineering at the Indian Institute of Technology Bombay since 2004. He obtained his BE in 1994, MS in1997 and PhD in 2000, all in Mechanical Engineering. His research interests include gas dynamics and flows with shock waves, electronics cooling, and solar thermal engineering. Amit Agrawal obtained his B.Tech from IIT Kanpur in 1996. He worked at Tata Motors, Pune for two years, before joining graduate studies at the University of Delaware, USA. After obtaining his PhD in 2002, he spent about 2 years as postdoctoral fellow at the University of Newcastle, Australia. He is currently an Associate Professor at IIT Bombay. His areas of interest are experimental, numerical and theoretical investigation of turbulent flows and flow at the microscales.