- Email: [email protected]
Piv experimental research of instantaneous flow characteristics of circular orifice synthetic jet
453
Ser.B, 2007,19(4):453-458
PIV EXPERIMENTAL RESEARCH OF INSTANTANEOUS FLOW CHARACTERISTICS OF CIRCULAR ORIFICE SYNTHETIC JET* XU Jing-lei, SHA Jiang, LIN Chun-feng, ZHANG Kun-yuan School of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China, E-mail: [email protected] (Received May 17, 2006; Revised September 15, 2006) ABSTRACT: The instantaneous flow characteristics of circular orifice synthetic jet was experimentally studied by a phase-locked Particle Image Velocimetry (PIV) system. The instantaneous flowfields, including the forming, developing and breaking down of the vortex for the jet were clearly shown by the PIV experimental results. As the basis of the study of the instantaneous flow, 36 images were taken and phase-averaged for each condition. The PIV experiment was mainly focused on the time evolution of the vortex pairs formed in the push cycle, the saddle point existing in the suck cycle, the variation of the centerline velocity in the whole cycle and the cross-stream velocity profiles and their self-similarity. Finally, the orifice depth was changed from 1.5 mm to 2 mm and 3.5 mm in order to study the effect of different orifice depths on the flow structure, which shows that at all stream wise sections, the peak of the mass flux and momentum flux increases as the orifice depth increases. Furthermore, the nondimensional distance of the mass flux from the exit is the maximum, while the nondimensional distance of the centerline velocity peak from the exit is the minimum, and nondimensional distance of the momentum flux from the exit section is between them. KEY WORDS: circular synthetic Velocimetry (PIV) , phase-locked
jet,
Particle
Image
1. INTRODUCTION The synthetic jet is a mean fluid motion generated by large-amplitude oscillatory flow through an orifice or a nozzle. Since its first use in 1994[1], the synthetic jet has become popular in laboratory flow-control. The primary advantage of the synthetic jet is its zero-net-mass nature, which needs no plumbing, and, when applied to a base
flow, results in unique effects that are not possible with steady or pulsed suction or blowing. These effects include the creation of closed recirculation regions and low-pressure regions, and the introduction of arbitrary scales to the base flow [1-3]. Synthetic Jet Actuator (SJA) has been quickly developed and become a hot spot of research in the world recently, because of its great potential in the active control of flowfields [1-13]. With the development and refinement of the Particle Image Velocimetry (PIV) technology [14,15], the detailed flow field structure, especially in different phases, of the SJA can be studied instantaneously with the help of the phase lock technology, which is important to study the essence of the SJA. In this article, a PIV system with the phase-locked technology is used to study instantaneously the detailed flowfield structure. And the time evolution of the vortex pairs formed in the push cycle, the saddle point existing in the suck cycle, the variation of the centerline velocity in the whole cycle and the cross-stream velocity profiles and their self-similarity are mainly concerned. Finally, the orifice depths have been changed from 1.5 mm to 2 mm and 3.5 mm in order to study the effect of different orifice depths on the flow structure. Some useful conclusions can be drawn.
2. EXPERIMENTAL SETUP The piston actuator and the coordinate of the
* Project supported by the Chinese Aeronautics Science Foundation (Grant No. 0 3 A 5 2 0 0 5 ) . Biography: XU Jing-lei (1971-),Male, Ph. D., Associate Professor
454
flow field is shown in Fig.1, in which d and h are the diameter and the depth of the circular orifice respectively, and x and y are the coordinate in the streamwise direction and the direction perpendicular to it respectively. In the experiment, the depth of the circular orifice h varies from 1.5 mm to 2 mm and 3.5 mm.
Fig.1 The experimental piston actuator
The PIV is used to obtain whole-field velocity data. The primary zero net mass air jet and the ambient air are seeded with smoke particles. A schematic of the experimental arrangement of the PIV system is shown in Fig.2 and a very brief description of this technique is provided in the following.
This arrangement makes it possible to acquire up to 15 image pairs per second. The image is acquired from the camera using a PCI board, which resides on a single slot of the PCI bus of a personal computer. The input to the synthetic jet actuator was supplied by a signal generator with the forcing frequency held constant at f=100HZ. After amplified by the power amplifier with the out voltage at V=8v, the input signal went into the exciter and made it move up and down. Because of screw connection with the exciter, the piston moved as the same pattern as the exciter, and then the synthetic jet was produced. On the other hand, the same input signal from the generator went into the synchronizer to make the phases of synthetic jet and the PIV measurement harmony to fulfill phase-locked. Finally, the flowfield would be computed on the basis of image pairs captured by the CCD camera by the professional software insight 6.0.
Fig.3 The instant vectors and streamlines of push cycle
Fig.2 The schematic of the experimental devices
A primary feature of the PIV used here is the ability to record two images in quick succession, from which the velocity field is derived using a cross-correlation algorithm. This is possible by integrating its two main hardware components: the TSI Power View 2M CCD and a double-pulsed Nd:YAG laser (produced by the New Wave Co., Gemini, 200 mJ) for flowfield illumination. A light sheet, about 1.0 mm thick, is created using a combination of spherical and cylindrical lenses. At the heart of camera is the CCD, with a resolution of 1660(H) × 1220(V) pixels. The camera is also equipped with a fast electronic shutter and outputs ten bit digital images, via a progressive scan readout system, at a rate of 30 frames per second.
3.
EXPERIMENTAL RESULT AND ANALYSIS Figures 3 and 4 are the instant vectors and streamlines of the push cycle and suck cycle of the SJA measured by the PIV for d=1mm and h=1.5mm (the same geometry is kept below unless with a special statement). The following characteristics of the SJA flowfield are evident. Firstly, in the suck cycle of the SJA, there exist clearly different structure zones in the flowfield, which are much different from those in the traditional jet and have been numerically studied in Ref.[9]. The flowfield is separated by the “saddle point” as shown in Fig.4. From the orifice exit section to the “saddle point”, the ambient flow is absorbed into the actuator cavity along the surface, while the fluid flow at downstream of the “saddle point” develops
455
downstream and has not been affected by the suck cycle, Secondly, as the synthetic jet develops downstream, the ambient fluid is entrained into it continuously, and consequently the mass flow and the boundary thickness of the synthetic jet increase. Finally, the synthetic jet is mixed with ambient fluid because of its viscosity and cannot be distinguished at last.
center, the ambient fluid flows into the actuator cavity and then the “saddle point” appears. Moreover, the distance of the “saddle point” from the exit increases to the maximum as the piston moves from the top dead center to the balance position, where the variation rate of cavity volume is the largest. After passing the balance point, the variation rate decreases, and the distance of the “saddle point” from the exit decreases as well to the minimum. Although the tendency can be clearly shown in Fig.6, the minimum position of the “saddle point” has not been captured because of the somewhat coarse time step in this experiment, which needs further research in the future.
Fig.4 The instant vectors and streamlines of suck cycle
The time evolution of the nondimensional distance of the vortex core from the orifice exit and the velocity peak of the flowfield are shown in Fig. 5, where both of them increase with time. It should be noticed that the two curves almost coincide with each other when t/T<0.1, which means the vortex core is almost at the same position as the centerline velocity peak. But with the time increased, the vortex core is located downstream of the centerline velocity peak, which means the self-induced velocity of the vortex pair is greater than the convective velocity of the fluid itself.
Fig.6 The trajectory of “saddle” point
Fig.7 The self-similarity at t/T=0.417
Fig.5 The trajectory of vortex core and velocity peak
Figure 6 shows the variation of “saddle point” position with time during the suck cycle. It can be seen that the nondimensional distance of the “saddle point” from the exit increases with time at first, till it reaches the maximum at t/T=0.75, and then it decreases gradually. It is mainly because the signal varies sinusoidally, and therefore the piston of the SJA moves cosinoidally. When the piston moves from the top dead center to the bottom dead
From Ref.[8] we know that the mean mainstream velocity profiles of the SJA at the different downstream sections have the self-similarity. In order to find out whether it is also true for the instantaneous flowfield, 36 images of three cycles are used to obtain the phase-averaged results, which are used to study the similarity of the instant mainstream velocity profiles of the SJA at the different downstream sections. Figures 7 and 8 show the similarity during the whole cycle, where U is the velocity at any position and Umax is the centerline velocity at the same downstream section. Y and Y0.5 are the y coordinate value of the same position and the y coordinate value of the point whose velocity is equal to the half of the centerline velocity at the same downstream section.
456
X/d=25 at the different instants during a full cycle. From the experimental results it can be seen that the self-similarity is still work under this condition. Like the push cycle, all the curves in the region of Y/Y0.5 ≤ 2 , of the suck cycle agree with those
Fig.8 The self-similarity at t/T=0.750
given by the self-similarity equation U/Umax=exp[-(Y/Y0.5)2] very well. So the conclusion can be drawn that the self-similarity of the main stream velocity at the different sections is still work for the instantaneous flowfield as well as the mean flowfield, except the region of upstream of the “saddle point” in the suck cycle.
The self-similarity velocity curves at the different downstream sections at t/T=0.417 in the push cycle are shown in Fig.7, from which one can see that all the curves almost coincide with each other in the region of Y/Y0.5 ≤ 2, and agree with the self-similarity equation U/Umax=exp[-(Y/Y0.5)2][6] very well. But in the region of 2 ≤ Y/Y0.5 ≤ 10 the agreement with the self-similarity equation U/Umax=exp[-(Y/Y0.5)2] is a little poor with the maximum relative error of 10%, which means that the self-similarity equation is more suitable in the center region of instantaneous synthetic jet. Furthermore, the self-similarity velocity curves at the same downstream sections as in Fig.7 at t/T=0.75 in the suck cycle are shown in Fig.8, and it is notable that only the curves of the downstream sections of the “saddle point” have the self-similarity as shown in Fig.8. For the curves of the upstream sections of the “saddle point”, they hardly have the self-similarity. So they are not shown in Fig.8. That means the self-similarity equation is workable only in the region downstream of the “saddle point” for the suck cycle.
Fig.9 The velocity profiles at X/d=25
Through the experiment, it is found that the self-similarity appears not only at different positions at the same instant, but also at different instants at the same position. Figures 9 and 10 show the main stream velocity and its self-similarity at
Fig.10 The self-similarity at X/d=25
Finally, the effect of the orifice depth h on the SJA flowfield has also been experimentally studied with h varying from 1.5 mm to 2 mm and 3.5 mm. With the limitation of the experimental condition, only the mean flowfield for the three depths are obtained and compared. Figure 11 shows the centerline velocity distribution of the mean flowfield along the downstream direction. Because h=1.5mm and h=2.0mm are not far from with each other, the two curves are almost the same and much different from the curve for h=3.5mm.
Fig.11 Centerline velocity of the mean flowfield
From Fig.11 one can see that the peak of the centerline velocity of the SJA increases as the depth increases, and the nondimensional distance of the centerline velocity peak from the exit increases a little as well. It can be explained that under the same flow condition, the wall boundary layer
457
develops more for h=3.5mm than for the other two cases. In order to expel the same amount of fluid, the centerline velocity of the h=3.5mm must increase. During the push cycle of the SJA, a pair of counter-rotating vortex forms and develops downstream by their self-induced velocity. As the vortex pair moves, more and more ambient fluid is entrained into the SJA, and makes the mass flow rate at the different sections increases, till it reaches the maximum. After that, the mass flow rate decreases gradually because of the viscous dissipation, and will decrease to zero at unlimited faraway, as shown in Fig.12.
44.76, respectively. Figure 14 shows the orifice depth effect on the synthetic jet boundary development, which is very little as shown in the figure. And the expansion angle of the jet is about 26o.
Fig.14 Jet boundary development of different depths
Fig.12 Centerline mass flux of the mean flowfield
Fig.13 h=3.5mm, nondimensional distribution of centerline velocity, momentum flux and mass flux
Because the centerline velocity may stand for the entrainment strength of the ambient fluid by the SJA, the centerline velocity peak is accordant with the position where the strongest entrainment takes place, which means that the peak of the mass flux should be downstream of the peak of the centerline velocity. Figure 13 shows the distribution of nondimensional centerline velocity, momentum flux and mass flux. They are normalized by their maximum respectively. From Fig.13 one can see that the position of the momentum flux peak is between the centerline velocity peak and the mass flux peak. For example, for h=3.5mm, the nondimensional distance from the exit x/d for centerline velocity peak, the momentum flux peak and the mass flow rate peak are 6.72, 20.60 and
4. CONCLUSIONS The instantaneous flow characteristics of circular orifice synthetic jet has been experimentally studied by a phase-locked PIV system. The PIV experiment is mainly concerned with the time evolution of the vortex pairs formed in the push cycle, the “saddle point” which exists in the suck cycle, the cross-stream velocity profiles and their self-similarity. Finally, the orifice depths have been changed from 1.5 mm to 2 mm and 3.5 mm in order to study the effect of different orifice depths on the flow structure. And the following conclusion can be drawn: (1) Both of the nondimensional distance of the vortex core from the exit and the velocity peak of the flowfield increase with time. And the two curves almost coincide with each other as t/T<0.1. But with the time increased, the vortex core is situated downstream of the centerline velocity peak. (2) The nondimensional distance of the “saddle point” from the exit of the SJA increases with time at first, till it reaches the peak, and then it decreases gradually. The position of the maximum distance of the “saddle point” is accordant with the balance position of the piston. (3) The self-similarity of the main stream velocity at the different downstream sections is still work for instant flowfield as well, except in the region of upstream of the “saddle point” in the suck cycle. All the curves almost coincide with each other in the region of Y/Y0.5 ≤ 2, and agree with that given by the self-similarity equation U/Umax=exp[-(Y/Y0.5)2] very well. (4) The peak of the centerline velocity of the SJA increases with the depth, and the nondimensional distance of the centerline velocity
458
peak from the exit increases a little as well. (5) At all streamwise sections, the peak value of the mass flux and momentum flux increases with the orifice depth. And the nondimensional distance of the mass flux from the exit is the maximum, while the nondimensional distance of the centerline velocity peak from the exit is the minimum, and nondimensional distance of the momentum flux from the exit section is between them.
REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
SMITH B. L., SWIFT G. W. Synthetic jets at large Reynolds number and comparison to continuous jets[R]. AIAA-2001-3030, 2001. HONOHAN A. M., AMITAY M. and GLEZER A. Aerodynamic control using synthetic jets[R]. AIAA -2000-2401, 2000. BETTRIDGE M. W., SPALL R. E., SMITH B. L. Aerodynamic jet vectoring using steady blowing and suction[R]. AIAA-2004-921, 2004. SMITH B. L., GLEZER A. The formation and evolution of synthetic jets [J]. Physics of Fluids, 1998, 10(9):2281-2297. CHEN F. J. Development of synthetic jet actuators for active flow control at NASA Langley[R]. AIAA-2000-2405, 2000. UTTURKAR Y., HOLMAN R., MITTAL R. et al. Jet formation criterion for synthetic jet actuators[R]. AIAA-2003-0636, 2003.
[7] SMITH B. L. , GLEZER A. Jet vectoring using synthetic jets[J]. J. Fluid Mech. ,2002, 458: 1-34. [8] SMITH B. L., SWIFT G. W. A comparison between synthetic jets and continuous jets [J]. Experiments in Fluids, 2003, 34(4): 467-472. [9] LUO Zhen-bing, XIA Zhi-xun. Advances in synthetic jet technology and applications in flow control [J]. Advances in Mechanics, 2005, 35(2):221-234(in Chinese). [10] LI Nian, ZHANG Kun-yuan, XU Jing-lei. Experimental investigation for primary flow vectoring using parallel synthetic jets [J]. Journal of Propulsion Technology. 2005, 26(3):248-251(in Chinese). [11] GAO Feng, WANG Liang. Numerical study of the effectiveness of using a single micro-jet actuator to vector primary flow [J]. Journal of Northwestern Polytechnical University. 2003, 21(5):528-531(in Chinese). [12] YAO Chung-Sheng, CHEN Fang Jenq, NEUHART Dan. Synthetic jet flow field database for CFD validation [R]. AIAA-2004-2218, 2004. [13] MUELLER M. O., BERNAL L. P., MISKA P. K. et al. Flow structure and performance of axisymmetric synthetic jets [R]. AIAA-2001-1008, 2001. [14] LIU Ying-zheng, CAO Zhao-min. Recnt progress in particle image velocimetry in China [J]. Journal of Hydrodynamics, Ser. B, 2006,18(1):11-19. [15] ZHANG Jun, XU Jie, HONG Fang-wen et al. PIV Technique and its application in ship hydrodynamics[J]. Journal of Hydrodynamics, Ser. B, 1999, 11(4): 118-126.
Ser.B, 2007,19(4):453-458
PIV EXPERIMENTAL RESEARCH OF INSTANTANEOUS FLOW CHARACTERISTICS OF CIRCULAR ORIFICE SYNTHETIC JET* XU Jing-lei, SHA Jiang, LIN Chun-feng, ZHANG Kun-yuan School of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China, E-mail: [email protected] (Received May 17, 2006; Revised September 15, 2006) ABSTRACT: The instantaneous flow characteristics of circular orifice synthetic jet was experimentally studied by a phase-locked Particle Image Velocimetry (PIV) system. The instantaneous flowfields, including the forming, developing and breaking down of the vortex for the jet were clearly shown by the PIV experimental results. As the basis of the study of the instantaneous flow, 36 images were taken and phase-averaged for each condition. The PIV experiment was mainly focused on the time evolution of the vortex pairs formed in the push cycle, the saddle point existing in the suck cycle, the variation of the centerline velocity in the whole cycle and the cross-stream velocity profiles and their self-similarity. Finally, the orifice depth was changed from 1.5 mm to 2 mm and 3.5 mm in order to study the effect of different orifice depths on the flow structure, which shows that at all stream wise sections, the peak of the mass flux and momentum flux increases as the orifice depth increases. Furthermore, the nondimensional distance of the mass flux from the exit is the maximum, while the nondimensional distance of the centerline velocity peak from the exit is the minimum, and nondimensional distance of the momentum flux from the exit section is between them. KEY WORDS: circular synthetic Velocimetry (PIV) , phase-locked
jet,
Particle
Image
1. INTRODUCTION The synthetic jet is a mean fluid motion generated by large-amplitude oscillatory flow through an orifice or a nozzle. Since its first use in 1994[1], the synthetic jet has become popular in laboratory flow-control. The primary advantage of the synthetic jet is its zero-net-mass nature, which needs no plumbing, and, when applied to a base
flow, results in unique effects that are not possible with steady or pulsed suction or blowing. These effects include the creation of closed recirculation regions and low-pressure regions, and the introduction of arbitrary scales to the base flow [1-3]. Synthetic Jet Actuator (SJA) has been quickly developed and become a hot spot of research in the world recently, because of its great potential in the active control of flowfields [1-13]. With the development and refinement of the Particle Image Velocimetry (PIV) technology [14,15], the detailed flow field structure, especially in different phases, of the SJA can be studied instantaneously with the help of the phase lock technology, which is important to study the essence of the SJA. In this article, a PIV system with the phase-locked technology is used to study instantaneously the detailed flowfield structure. And the time evolution of the vortex pairs formed in the push cycle, the saddle point existing in the suck cycle, the variation of the centerline velocity in the whole cycle and the cross-stream velocity profiles and their self-similarity are mainly concerned. Finally, the orifice depths have been changed from 1.5 mm to 2 mm and 3.5 mm in order to study the effect of different orifice depths on the flow structure. Some useful conclusions can be drawn.
2. EXPERIMENTAL SETUP The piston actuator and the coordinate of the
* Project supported by the Chinese Aeronautics Science Foundation (Grant No. 0 3 A 5 2 0 0 5 ) . Biography: XU Jing-lei (1971-),Male, Ph. D., Associate Professor
454
flow field is shown in Fig.1, in which d and h are the diameter and the depth of the circular orifice respectively, and x and y are the coordinate in the streamwise direction and the direction perpendicular to it respectively. In the experiment, the depth of the circular orifice h varies from 1.5 mm to 2 mm and 3.5 mm.
Fig.1 The experimental piston actuator
The PIV is used to obtain whole-field velocity data. The primary zero net mass air jet and the ambient air are seeded with smoke particles. A schematic of the experimental arrangement of the PIV system is shown in Fig.2 and a very brief description of this technique is provided in the following.
This arrangement makes it possible to acquire up to 15 image pairs per second. The image is acquired from the camera using a PCI board, which resides on a single slot of the PCI bus of a personal computer. The input to the synthetic jet actuator was supplied by a signal generator with the forcing frequency held constant at f=100HZ. After amplified by the power amplifier with the out voltage at V=8v, the input signal went into the exciter and made it move up and down. Because of screw connection with the exciter, the piston moved as the same pattern as the exciter, and then the synthetic jet was produced. On the other hand, the same input signal from the generator went into the synchronizer to make the phases of synthetic jet and the PIV measurement harmony to fulfill phase-locked. Finally, the flowfield would be computed on the basis of image pairs captured by the CCD camera by the professional software insight 6.0.
Fig.3 The instant vectors and streamlines of push cycle
Fig.2 The schematic of the experimental devices
A primary feature of the PIV used here is the ability to record two images in quick succession, from which the velocity field is derived using a cross-correlation algorithm. This is possible by integrating its two main hardware components: the TSI Power View 2M CCD and a double-pulsed Nd:YAG laser (produced by the New Wave Co., Gemini, 200 mJ) for flowfield illumination. A light sheet, about 1.0 mm thick, is created using a combination of spherical and cylindrical lenses. At the heart of camera is the CCD, with a resolution of 1660(H) × 1220(V) pixels. The camera is also equipped with a fast electronic shutter and outputs ten bit digital images, via a progressive scan readout system, at a rate of 30 frames per second.
3.
EXPERIMENTAL RESULT AND ANALYSIS Figures 3 and 4 are the instant vectors and streamlines of the push cycle and suck cycle of the SJA measured by the PIV for d=1mm and h=1.5mm (the same geometry is kept below unless with a special statement). The following characteristics of the SJA flowfield are evident. Firstly, in the suck cycle of the SJA, there exist clearly different structure zones in the flowfield, which are much different from those in the traditional jet and have been numerically studied in Ref.[9]. The flowfield is separated by the “saddle point” as shown in Fig.4. From the orifice exit section to the “saddle point”, the ambient flow is absorbed into the actuator cavity along the surface, while the fluid flow at downstream of the “saddle point” develops
455
downstream and has not been affected by the suck cycle, Secondly, as the synthetic jet develops downstream, the ambient fluid is entrained into it continuously, and consequently the mass flow and the boundary thickness of the synthetic jet increase. Finally, the synthetic jet is mixed with ambient fluid because of its viscosity and cannot be distinguished at last.
center, the ambient fluid flows into the actuator cavity and then the “saddle point” appears. Moreover, the distance of the “saddle point” from the exit increases to the maximum as the piston moves from the top dead center to the balance position, where the variation rate of cavity volume is the largest. After passing the balance point, the variation rate decreases, and the distance of the “saddle point” from the exit decreases as well to the minimum. Although the tendency can be clearly shown in Fig.6, the minimum position of the “saddle point” has not been captured because of the somewhat coarse time step in this experiment, which needs further research in the future.
Fig.4 The instant vectors and streamlines of suck cycle
The time evolution of the nondimensional distance of the vortex core from the orifice exit and the velocity peak of the flowfield are shown in Fig. 5, where both of them increase with time. It should be noticed that the two curves almost coincide with each other when t/T<0.1, which means the vortex core is almost at the same position as the centerline velocity peak. But with the time increased, the vortex core is located downstream of the centerline velocity peak, which means the self-induced velocity of the vortex pair is greater than the convective velocity of the fluid itself.
Fig.6 The trajectory of “saddle” point
Fig.7 The self-similarity at t/T=0.417
Fig.5 The trajectory of vortex core and velocity peak
Figure 6 shows the variation of “saddle point” position with time during the suck cycle. It can be seen that the nondimensional distance of the “saddle point” from the exit increases with time at first, till it reaches the maximum at t/T=0.75, and then it decreases gradually. It is mainly because the signal varies sinusoidally, and therefore the piston of the SJA moves cosinoidally. When the piston moves from the top dead center to the bottom dead
From Ref.[8] we know that the mean mainstream velocity profiles of the SJA at the different downstream sections have the self-similarity. In order to find out whether it is also true for the instantaneous flowfield, 36 images of three cycles are used to obtain the phase-averaged results, which are used to study the similarity of the instant mainstream velocity profiles of the SJA at the different downstream sections. Figures 7 and 8 show the similarity during the whole cycle, where U is the velocity at any position and Umax is the centerline velocity at the same downstream section. Y and Y0.5 are the y coordinate value of the same position and the y coordinate value of the point whose velocity is equal to the half of the centerline velocity at the same downstream section.
456
X/d=25 at the different instants during a full cycle. From the experimental results it can be seen that the self-similarity is still work under this condition. Like the push cycle, all the curves in the region of Y/Y0.5 ≤ 2 , of the suck cycle agree with those
Fig.8 The self-similarity at t/T=0.750
given by the self-similarity equation U/Umax=exp[-(Y/Y0.5)2] very well. So the conclusion can be drawn that the self-similarity of the main stream velocity at the different sections is still work for the instantaneous flowfield as well as the mean flowfield, except the region of upstream of the “saddle point” in the suck cycle.
The self-similarity velocity curves at the different downstream sections at t/T=0.417 in the push cycle are shown in Fig.7, from which one can see that all the curves almost coincide with each other in the region of Y/Y0.5 ≤ 2, and agree with the self-similarity equation U/Umax=exp[-(Y/Y0.5)2][6] very well. But in the region of 2 ≤ Y/Y0.5 ≤ 10 the agreement with the self-similarity equation U/Umax=exp[-(Y/Y0.5)2] is a little poor with the maximum relative error of 10%, which means that the self-similarity equation is more suitable in the center region of instantaneous synthetic jet. Furthermore, the self-similarity velocity curves at the same downstream sections as in Fig.7 at t/T=0.75 in the suck cycle are shown in Fig.8, and it is notable that only the curves of the downstream sections of the “saddle point” have the self-similarity as shown in Fig.8. For the curves of the upstream sections of the “saddle point”, they hardly have the self-similarity. So they are not shown in Fig.8. That means the self-similarity equation is workable only in the region downstream of the “saddle point” for the suck cycle.
Fig.9 The velocity profiles at X/d=25
Through the experiment, it is found that the self-similarity appears not only at different positions at the same instant, but also at different instants at the same position. Figures 9 and 10 show the main stream velocity and its self-similarity at
Fig.10 The self-similarity at X/d=25
Finally, the effect of the orifice depth h on the SJA flowfield has also been experimentally studied with h varying from 1.5 mm to 2 mm and 3.5 mm. With the limitation of the experimental condition, only the mean flowfield for the three depths are obtained and compared. Figure 11 shows the centerline velocity distribution of the mean flowfield along the downstream direction. Because h=1.5mm and h=2.0mm are not far from with each other, the two curves are almost the same and much different from the curve for h=3.5mm.
Fig.11 Centerline velocity of the mean flowfield
From Fig.11 one can see that the peak of the centerline velocity of the SJA increases as the depth increases, and the nondimensional distance of the centerline velocity peak from the exit increases a little as well. It can be explained that under the same flow condition, the wall boundary layer
457
develops more for h=3.5mm than for the other two cases. In order to expel the same amount of fluid, the centerline velocity of the h=3.5mm must increase. During the push cycle of the SJA, a pair of counter-rotating vortex forms and develops downstream by their self-induced velocity. As the vortex pair moves, more and more ambient fluid is entrained into the SJA, and makes the mass flow rate at the different sections increases, till it reaches the maximum. After that, the mass flow rate decreases gradually because of the viscous dissipation, and will decrease to zero at unlimited faraway, as shown in Fig.12.
44.76, respectively. Figure 14 shows the orifice depth effect on the synthetic jet boundary development, which is very little as shown in the figure. And the expansion angle of the jet is about 26o.
Fig.14 Jet boundary development of different depths
Fig.12 Centerline mass flux of the mean flowfield
Fig.13 h=3.5mm, nondimensional distribution of centerline velocity, momentum flux and mass flux
Because the centerline velocity may stand for the entrainment strength of the ambient fluid by the SJA, the centerline velocity peak is accordant with the position where the strongest entrainment takes place, which means that the peak of the mass flux should be downstream of the peak of the centerline velocity. Figure 13 shows the distribution of nondimensional centerline velocity, momentum flux and mass flux. They are normalized by their maximum respectively. From Fig.13 one can see that the position of the momentum flux peak is between the centerline velocity peak and the mass flux peak. For example, for h=3.5mm, the nondimensional distance from the exit x/d for centerline velocity peak, the momentum flux peak and the mass flow rate peak are 6.72, 20.60 and
4. CONCLUSIONS The instantaneous flow characteristics of circular orifice synthetic jet has been experimentally studied by a phase-locked PIV system. The PIV experiment is mainly concerned with the time evolution of the vortex pairs formed in the push cycle, the “saddle point” which exists in the suck cycle, the cross-stream velocity profiles and their self-similarity. Finally, the orifice depths have been changed from 1.5 mm to 2 mm and 3.5 mm in order to study the effect of different orifice depths on the flow structure. And the following conclusion can be drawn: (1) Both of the nondimensional distance of the vortex core from the exit and the velocity peak of the flowfield increase with time. And the two curves almost coincide with each other as t/T<0.1. But with the time increased, the vortex core is situated downstream of the centerline velocity peak. (2) The nondimensional distance of the “saddle point” from the exit of the SJA increases with time at first, till it reaches the peak, and then it decreases gradually. The position of the maximum distance of the “saddle point” is accordant with the balance position of the piston. (3) The self-similarity of the main stream velocity at the different downstream sections is still work for instant flowfield as well, except in the region of upstream of the “saddle point” in the suck cycle. All the curves almost coincide with each other in the region of Y/Y0.5 ≤ 2, and agree with that given by the self-similarity equation U/Umax=exp[-(Y/Y0.5)2] very well. (4) The peak of the centerline velocity of the SJA increases with the depth, and the nondimensional distance of the centerline velocity
458
peak from the exit increases a little as well. (5) At all streamwise sections, the peak value of the mass flux and momentum flux increases with the orifice depth. And the nondimensional distance of the mass flux from the exit is the maximum, while the nondimensional distance of the centerline velocity peak from the exit is the minimum, and nondimensional distance of the momentum flux from the exit section is between them.
REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
SMITH B. L., SWIFT G. W. Synthetic jets at large Reynolds number and comparison to continuous jets[R]. AIAA-2001-3030, 2001. HONOHAN A. M., AMITAY M. and GLEZER A. Aerodynamic control using synthetic jets[R]. AIAA -2000-2401, 2000. BETTRIDGE M. W., SPALL R. E., SMITH B. L. Aerodynamic jet vectoring using steady blowing and suction[R]. AIAA-2004-921, 2004. SMITH B. L., GLEZER A. The formation and evolution of synthetic jets [J]. Physics of Fluids, 1998, 10(9):2281-2297. CHEN F. J. Development of synthetic jet actuators for active flow control at NASA Langley[R]. AIAA-2000-2405, 2000. UTTURKAR Y., HOLMAN R., MITTAL R. et al. Jet formation criterion for synthetic jet actuators[R]. AIAA-2003-0636, 2003.
[7] SMITH B. L. , GLEZER A. Jet vectoring using synthetic jets[J]. J. Fluid Mech. ,2002, 458: 1-34. [8] SMITH B. L., SWIFT G. W. A comparison between synthetic jets and continuous jets [J]. Experiments in Fluids, 2003, 34(4): 467-472. [9] LUO Zhen-bing, XIA Zhi-xun. Advances in synthetic jet technology and applications in flow control [J]. Advances in Mechanics, 2005, 35(2):221-234(in Chinese). [10] LI Nian, ZHANG Kun-yuan, XU Jing-lei. Experimental investigation for primary flow vectoring using parallel synthetic jets [J]. Journal of Propulsion Technology. 2005, 26(3):248-251(in Chinese). [11] GAO Feng, WANG Liang. Numerical study of the effectiveness of using a single micro-jet actuator to vector primary flow [J]. Journal of Northwestern Polytechnical University. 2003, 21(5):528-531(in Chinese). [12] YAO Chung-Sheng, CHEN Fang Jenq, NEUHART Dan. Synthetic jet flow field database for CFD validation [R]. AIAA-2004-2218, 2004. [13] MUELLER M. O., BERNAL L. P., MISKA P. K. et al. Flow structure and performance of axisymmetric synthetic jets [R]. AIAA-2001-1008, 2001. [14] LIU Ying-zheng, CAO Zhao-min. Recnt progress in particle image velocimetry in China [J]. Journal of Hydrodynamics, Ser. B, 2006,18(1):11-19. [15] ZHANG Jun, XU Jie, HONG Fang-wen et al. PIV Technique and its application in ship hydrodynamics[J]. Journal of Hydrodynamics, Ser. B, 1999, 11(4): 118-126.