Uniform, Steady Jet, and Synthetic Jet Cross-Flows Across a Circular Cylinder

Rajnish N Sharma1 and Soon K Siong.2

The University of Auckland, Auckland 1142, New Zealand

This paper reports on a study of the aerodynamic behaviour of a circular cylinder in uniform, steady jet and synthetic jet flows. Both experimental and computational fluid dynamic (CFD) methods are applied in this study. An existing experimental testing rig for synthetic jet actuation was modified for this study. Synthetic jet actuation and flow field models were developed using the commercial package ANSYS-CFX. These were validated and then used to provide insight into synthetic jet interactions with a cylinder. A circular cylinder which was three times the size of the slot jet width was considered. Experimental data and CFD visualization reveal that there are significant differences in the aerodynamics of a circular cylinder when immersed in uniform, steady jet and synthetic jet flows. Large flow fluctuations around the cylinder together with transverse vortex trains obtained with a synthetic jet imply intense mixing. This might be an advantage in terms of affecting heat and mass transfer. Further studies are recommended to fully understand cylinder – synthetic jet interactions for different sizes of cylinder relative to the jet.

Nomenclature DC = drag coefficient of cylinder (dimensionless)

pC = mean surface pressure coefficient (dimensionless)

pC~ = qp /~ = standard deviation of surface pressure coefficient fluctuations (dimensionless) d = cylinder diameter (m)

od = orifice diameter (m) f = actuation cyclic frequency (Hz)

vsf = = frequency of vortex shedding (Hz) vsT/1K = a constant (dimensionless) p~ = standard deviation of surface pressure fluctuations (Pa)

q = average dynamic pressure of onset flow (Pa) Re = ν/Ud = cylinder Reynolds number (dimensionless)

jRe = ν/oj dU = jet Reynolds number (dimensionless)

S = νω /2od = Stokes number (dimensionless)

Str = jo Ud /ω = Strouhal number (dimensionless) tΔ = time step (s)

T = 1/f = period of actuation (s) vsT = = period of vortex shedding (s) vsf/1

aU = time and spatial average jet expulsion velocity (m/s)

jU = π/2 aU = average jet expulsion velocity (m/s) U = velocity (m/s) 1 Senior Lecturer, Department of Mechanical Engineering, The University of Auckland, Private Bag 92019, Auckland, NEW ZEALAND; Email r.sharma@auckland.ac.nz; Member AIAA. 2 Graduate Student, Department of Mechanical Engineering, The University of Auckland, Private Bag 92019, Auckland, NEW ZEALAND;

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39th AIAA Fluid Dynamics Conference22 - 25 June 2009, San Antonio, Texas

AIAA 2009-4170

Copyright © 2009 by R N Sharma. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

w = slot width (m) x = distance along jet from jet exit (m) Greek symbols δ = boundary layer thickness (m) ν = kinematic viscosity of air (m2/s) ω = fπ2 actuation radian frequency (rad/s)

I. Introduction he synthetic jet (SJ) is a quasi-steady jet of air generated a few diameters from the orifice of a synthetic jet actuator (SJA), as illustrated in Figure 1. Actuation involves the forcing of an oscillatory air-flow through the

orifice from a cavity with a driven flexible wall. During out-flow, an air jet is formed directly in front of the orifice, accompanied by a vortex ring around the orifice which is shed as out-flow weakens and reverts to in-flow. Since the in-flow part of the oscillatory cycle entrains air from the periphery rather than from in front of the orifice, the flow-field established directly downstream of the orifice is relatively undisturbed leading to the maintenance of a quasi-steady or synthetic jet of air. The train of vortex rings that are periodically shed are advected away from the orifice and eventually breakdown in the region of this synthetic jet, thus intermittently transporting momentum to and thereby sustaining the jet (Smith and Glezer, 1998). A major advantage of the synthetic jet over the ordinary steady jet is that it does not require a continuous supply of fluid from elsewhere for the maintenance of the jet, since the air jet is synthesised from the surrounding fluid. Consequently, the actuator has advantages of simple structure, low cost and easy installation. The synthetic jet has thus attracted much research within the last decade.

T

Forming vortex ring

Shed vortex rings

Driven wall

Synthetic jet velocity profile

Figure 1. Synthetic jet actuator

Whilst the synthetic jet actuator can be a simple device, a jet formation criterion has to be met for the formation of a synthetic jet. Utturkar et. al. (2003) have recently determined a theoretical jet formation criterion given by

KSStr

j >= 2

Re1 (1)

where jo UdStr /ω= is a Strouhal number based on the actuation frequency fπω 2= , orifice diameter or slot width do, and the average orifice exit expulsion velocity π/2 aj UU = ; in which is the time and spatial average exit velocity (i.e. average during the expulsion stage only);

aUν/Re ojj dU= is the jet Reynolds number;

νω /2odS = is a Stokes number; and constant K is 1 for 3D and 0.16 for 2D and axi-symmetric synthetic jets

respectively. Past investigations into applications of synthetic jets range from thrust vectoring of jet engines (Smith and

Glezer, 1994), through mixing enhancement (Davies and Glezer, 1999), to external flow boundary layer separation control (Cook et. al., 1999). A number of studies have also focussed upon the interaction of synthetic jets with

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boundary layer cross-flows (Mittal and Rampunggon, 2001). Synthetic jets have also been used to enhance heat and mass transfer (Amon et. al., 2001). Synthetic jet actuators can also be scaled down to small scale, and thus to micro-scale applications, by the use of piezo-oscillators to oscillate the cavity membrane. When the synthetic jet flow is positioned at a critical point on a body (e.g. a cylinder), such as on the leading edge or separation point , it can affect flow pattern around the body by suppressing the separation as well as the laminar-turbulent transition region (Amitay et. al., 1998).

With the versatility, scalability and other advantages of the synthetic jet described above, an unlimited array of applications for the technology is possible. In flow control and heat transfer applications, the synthetic jet interacts with bluff bodies of different types. In order to be able to understand the potential of the synthetic jet, it is wise to first understand the aerodynamic behaviour of different bodies in the synthetic jet flow field. This paper therefore describes a CFD and experimental study of the aerodynamics of a circular cylinder in the flow field of a synthetic jet, and compares these with the behaviour under uniform and steady jet flows across the cylinder.

II. Experimental Apparatus And Procedure The synthetic jet actuator used in this study was developed in an earlier project (Rajashekhar, 2003), and it

consists of a cavity made of 180mm diameter PVC piping of lengths ranging from 100mm to 250mm to achieve different cavity volumes. As shown in Figure 2, the face plates can be changed to alter the characteristics of the orifice. For the studies described in this paper, a 10mm wide and 160mm long slot orifice was used. The driven wall of the actuator consists of a 50Watt – 7.5ohm loudspeaker, which is driven using a sinusoidal voltage input from a signal generator. The actuator is instrumented with an accelerometer on the loudspeaker to measure its displacements and velocities, while a pressure tap to the centre of the actuator cavity allows measurement of the internal pressure using a differential pressure transducer. A hot wire anemometer was used to measure the characteristics of the flow field of the synthetic jet. All signals were low-pass filtered at 500Hz and digitised at a rate of 1000Hz.

Figure 2. Synthetic jet actuator

Figure 3. 30mm cylinder, mounted on a traversing rig on right

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In order to be able to understand and control the actuator for conducting experiments with a cylinder, it was important first to determine the characteristics of the actuator and its components. The resonance of the loudspeaker diaphragm, uncoupled from the actuator, in the rigid body mode was determined using a white noise input signal. The frequency response characteristics of the loudspeaker thus measured, from which it was readily deduced that it has a natural frequency of 44Hz, beyond which its response falls rapidly. In order to be able to drive the actuator with a reasonable level of input, it might therefore be useful to consider this response, and then choose a driving frequency close to this natural frequency.

On the other hand, as Gallas et al (2003) and Sharma (2006) have previously shown, the Helmholtz frequency of the actuator cavity is also of importance. The actuator output is maximised near the speaker diaphragm and Helmholtz resonance frequencies. Hence, a series of tests was conducted which involved ‘jamming’ of the speaker diaphragm to make for an uncoupled cavity, and the excitation of the actuator cavity with white noise signal through another speaker external to the actuator orifice. This way, the Helmholtz frequency of the actuator cavity was determined to be in the vicinity of 140Hz. Given that the speaker response is relatively low around these frequencies, it was then decided to drive the actuator nearer the diaphragm resonance frequency established earlier.

For the cylinder, a relatively long and d = 30mm diameter aluminium alloy tube was instrumented with a pressure tap at its midpoint (see Figure 2c), to which a Honeywell differential pressure transducer, model XSCL04DC was flush mounted. A rig allowed the positioning of the cylinder with respect to the synthetic jet actuator, as well as the rotation of the cylinder so as to allow measurement of surface pressures over angles of 0° to 180°. Parallel measurements were made of the surface pressures in a small wind tunnel representing uniform cross flow, and with a steady jet using the same orifice, but supply air being provided from a fan blower.

III. CFD Methodology The commercial CFD package ANSYS CFX-5.7.1 was used to perform numerical analysis of the synthetic jet

flow, as well as of uniform and steady jet flows and their interactions with the circular cylinder; see Figure 4. Two-dimensional models were created with a computational domain that was 800mm (27d) long and 500mm (17d) wide. For uniform cross flow at velocity U, the 30mm diameter cylinder was placed 172mm (5.5d) from the inlet. The maximum mesh spacing was set to 2mm, while 15 inflation layers were used for the near surface or the boundary layer region around the cylinder. The total inflation layer thickness was set according to the recommendations for a bluff body, (ANSYS, 2004) where 7/1Re035.0 −= dδ ν/Re Ud= = cylinder Reynolds number. Consequently, the total number of elements used was in the vicinity of 230,000. Six different Reynolds numbers from 60 - 50,000 were used.

17d d

27d Ua

Uniform Cross Flow

x=5d

d

27d

Ua17d

Steady Jet Flow

x

x/w=5, 10

d

27d

u 17d

u=Ua.sin(2πft)

Synthetic Jet Flow

x

x/w=5, 10 Figure 4. CFD Model setup

For the steady and synthetic jet modeling, a slot of width w = 10mm was modeled as an inlet boundary condition, with the remainder of the upstream boundary assigned as a wall with no-slip condition. In the case of a synthetic jet, a sinusoidal inlet velocity, )2sin( tfUU a π= was specified, where Ua = amplitude of velocity and f = frequency of oscillation of the velocity. A cylinder of 30mm diameter being same as the experimental cylinder was located at distances of (a) x/w = 5 and (b) x/w = 10 from the slot. Again, the maximum mesh spacing was set to 2mm and appropriate inflation layer settings were used adjacent to the cylinder surface, giving a total of about 215,000 elements in the computational flow domain.

The time-step for the transient simulations were as follows: (a) For the case of uniform cross and steady jet flows, it was set to one twentieth of period of vortex shedding Δt = Tvs/20 = 1/(20 fvs), where fvsd/U = Str = 0.21 for vortex shedding from a cylinder; and (b) For the case of synthetic jet flow, it was set to one hundredth of the period of cycle of synthetic jet actuation i.e. Δt = T/100 = 1/(100 f). The second order upwind differencing scheme was

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used for the advection terms in the Navier-Stokes equation, while the second order backward Euler differencing scheme was used for the transient term. The convergence criteria involved a RMS residual target of 1 × 10-7, and solutions were obtained for at least 25 cycles of vortex shedding and / or synthetic jet actuation. Air at 25˚C with constant density was used.

IV. Results and Discussions Figure 5 shows the streamlines of flow obtained from CFD visualization for the uniform cross flow, steady jet

flow and synthetic jet flow across the cylinder. Significant differences in flow patterns are observed depending upon the flow type, and in the case of jet flows, on the location of the cylinder relative to the slot, x/w. In the case of steady jet flow, with the cylinder diameter to slot width ratio d/w = 3 in the present study, it is clear that when the cylinder is situated at x/w = 5, vortex shedding, which is typical of uniform cross flow, does not occur. Instead, two contra-rotating vortices are evident. However when x/w = 10, jet instability is observed whereby the jet flips on either side of the cylinder in tandem with vortex shedding. This leads to vortex like structures also forming in the upstream region of the cylinder. The differences observed with x/w are likely to be related to the location of the cylinder relative to the potential core region of the jet. The potential core is known to extend to approximately x/w = 5, a illustrated in Figure 6. When the cylinder is at x/w = 5, it encounters a relatively strong non-turbulent jet core resulting in the flow remaining attached. However, when the cylinder is at x/w = 10, it is now in a turbulent and relatively weak flow region, becoming susceptible to instability as observed.

For synthetic jet flow, complex flow patterns are formed which culminate in the sideways deflection of the synthetic jet vortices as they approach the cylinder. A closer examination of the flow field near the cylinder reveals that as a boundary layer is formed, the arrival of the synthetic jet vortices leads to the destruction of the boundary layer, as secondary vortices are rolled up and then shed from the cylinder upstream surface. These are also alternately deflected sideways. A train of vortices consisting of alternate synthetic jet vortices and those shed from the cylinder result, which move transversally away from the cylinder on either side.

These result in relatively large fluctuations in pressure on the cylinder surface, as confirmed from experimental and CFD pressure coefficient. The mean pressure coefficient, , distributions around the cylinder under the three different flow scenarios, namely uniform, synthetic jet and steady jet cross flow, are shown in Figure 7. The first point to be made here is that both the computational predictions and experimentally measured data show almost exact agreement in the case of the two jet flow situations. This is not surprising since the grid including the inflation layers around the cylinder were created accurately for the CFD prediction. Secondly, it is not surprising to see that the steady jet distribution (for both

pC

pC 5/ =odx and 10/ =odx positions) are higher in magnitude than those for the synthetic jet flow situations. This is because the steady jet flow has a continuous flow and therefore has a higher velocity at and the flow still remains relatively strong at 5/ ≤odx 10/ =odx . However, the synthetic jet situations have low magnitudes (almost half the magnitudes of steady jet) because it consists of reversing flows, with smaller mean levels. On the other hand, since synthetic jet flows have large fluctuations, it might be interesting to analyze the standard deviation of the pressure coefficient fluctuations for the synthetic jet across the cylinder.

pC

The standard deviation of fluctuation is defined as pC qpC p /~~= where p~ is the standard deviation of pressure

and q is the average onset dynamic pressure. The standard deviation of pressure fluctuation in uniform flow and continuous or steady jet flow across the cylinder are expected to be relatively small and are dependent on the characteristics of turbulent shear layers and the stability of the flow. On the other hand, the synthetic jet flow is highly fluctuating, resulting in large fluctuations in surface pressure, hence a high standard deviation of pressure fluctuations is evident in Figure 8, which shows the comparison of the standard deviation of distribution around the cylinder under the three different flow situations. It is not surprising to see that for the uniform cross flow across the cylinder,

pC

pC~ are generally low due to low pressure fluctuations because the flow is relatively smooth. pC~ for the steady jet however are somewhat larger indicating it has higher pressure fluctuations, particularly at 10/ =odx position than at position, being due to the jet instability observed earlier. 5/ =odx

A comparison of cylinder drag coefficients in Table 1 shows that the mean drag levels are much smaller than those obtained with either uniform or steady jet cross flows. That this is the case while large flow fluctuations are effected around the cylinder with a synthetic jet, implies that there are minimal drag penalties with a synthetic jet if used for fluid mixing or heat transfer applications.

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(a) Uniform flow Re=6000 (b) Steady jet x/w=5

(c) Steady jet x/w=10 (at two different time steps)

End of 2nd Actuation Cycle End of 2.5 Actuation Cycles

(d) Synthetic jet x/w=5

End of 3rd Actuation Cycle End of 3.5 Actuation Cycles

(e) Synthetic jet x/w=10

Figure 5. Streamline patterns from CFD flow visualization

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Potential Core, x/w=5

Turbulent Shear Layer

(Not To Scale)

Flow Input

Figure 6. The schematic of the steady jet across a cylinder at different x/w positions

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180Deg

Mea

n C

p

SJs Cp Mean x/do=5 CFD SJs Cp Mean x/do=5 ExperimentSJs Cp Mean x/do=10 CFD SJs Cp Mean x/do=10 ExperimentSteadyJet Cp Mean x/do=5 CFD SteadyJet Cp Mean x/do=5 ExperimentSteadyJet Cp Mean x/do=10 CFD SteadyJet Cp Mean x/do=10 ExperimentUniform Flow CFD Uniform Flow Experiment

Figure 7. Mean pressure coefficient distribution around the cylinder

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180Deg

Std

Cp

SJs Std x/do=5 CFD SJs Std x/do=5 ExperimentSJs Std x/do=10 CFD SJs Std x/do=10 ExperimentSteadyJet Std x/do=5 CFD SteadyJet Std x/do=5 ExperimentSteadyJet Std x/do=10 CFD SteadyJet Std x/do=10 ExperimentUniform Flow Std CFD Uniform Flow Std Experiment

Figure 8. Standard deviation pressure coefficient distributions around the cylinder

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Table 1 Drag coefficients Uniform Flow

Across Cylinder Steady Jet Across Cylinder Synthetic Jet Across Cylinder

(Expulsion Only) CFD Exp CFD Exp CFD Exp

wx / 5 10 5 10 5 10 5 10 1.52 1.59 0.21 0.33 0.25 0.40 0.28 0.23 0.31 0.30 DC

V. Conclusions Experimental measurements and CFD visualization reveal that there are significant differences in the

aerodynamics of a circular cylinder when immersed in uniform, steady jet and synthetic jet flows. It was found that large flow fluctuations around the cylinder together with transverse vortex trains as well as low drag coefficients are obtained with a synthetic jet, as compared with uniform and steady jet cross flows. These imply the momentum, heat and mass transport enhancement potential of synthetic jets with a reduced drag penalty.

Acknowledgements The study described in this paper was funded by a University of Auckland - Vice-Chancellors University

Development Grant. This support is gratefully acknowledged.

References Amitay, M., Smith, B.L., Glezer, A., 1998. Aerodynamic flow control using synthetic jet technology, 36th Aerospace Sciences

Meeting and Exhibit, AIAA-1998-208, Reno Nevada USA, Jan. 12-15. Amon, C.H., Murthy, J., Yao, S.C., Narumanchi, S., Wu, C., Hsieh, C., 2001. MEMS enabled thermal management of high heat

flux devices (EDIFICE), Experimental Thermal and Fluid Science 25, 231-242. ANSYS, 2004. CFX 5.7.1 User manual. Crook, L., Sadri, A.M., Wood, N.J., 1999. The development and implementation of synthetic jets for the control of separated

flow. AIAA 99-3176. Davies, S.A., Glezer, A., 1999. Mixing control of fuel jets using synthetic jet technology. AIAA 99-0447. Gallas, Q., Holman, R., Nishida, T., Carrol, B., Sheplak, M., Cattafesta, L., 2003. Lumped element modeling of piezoelectric-

driven synthetic jet actuators. AIAA Journal 41 (2), 240-247. Mittal, R., Rampunggoon, P., 2001. Interaction of a Synthetic Jet with a Flat Plate Boundary Layer. 39th Aerospace Sciences

Meeting and Exhibit, AIAA 2001-2773. Rajashekhar, M., 2003. A bench-top synthetic jet actuator for research purposes. University of Auckland dissertation. Sharma, R., 2006. An analytical model for synthetic jet actuation. AIAA 2006-3035. Smith, B.L., Glezer, A., 1994. Vectoring of a High Aspect Ratio Rectangular Air Jet Using a Zero-Net-Mass-Flux Control Jet.

Bulletin of the American Physical Society 39. Smith, B.L., Glezer, A., 1998. The formation and evolution of synthetic jets. Physics of Fluids 31, 2282-2297. Utturkar, Y., Holma, R., Mittal, R., Carrol, B., Sheplak, M, Cattafesta, L., 2003. A jet formation criterion for synthetic jet

actuators. AIAA 2003-0636.

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