Acoustic PIV: Measurements of the acoustic particle velocity using synchronized PIV-technique André Fischer, Emilie Sauvage, Ingo Röhle Department of Engine Acoustics, Institute of Propulsion Technology German Aerospace Center (DLR), Berlin, Germany, andre.fischer@dlr.de Abstract: Synchronized particle image velocimetry (PIV) technique has been adopted for directly measuring the acoustic particle velocity in an acoustically excited flow field. To demonstrate this technique the acoustic filed was measured in an empty test section as well as in front of a perforated plate. The plate was chosen as a pre-experiment for the investigation of liners which are perforated plates used as acoustic dampers. The test rig is made of acrylic glass and is excited by a loudspeaker. In the test section the velocity fields were acquired at a certain phase of the sinusoidal excitation frequency and the measured velocity vectors were obtained by standard a PIV procedure using cross-correlation of two subsequent raw images. Due to synchronized recording the acoustic particle velocity can be extracted in post processing by the subtraction of two specific flow filed configurations. There the second velocity field was recorded at a 180 phase shift of the excitation frequency. The results show a good agreement with theoretical considerations and demonstrate that using this method both, the acoustic particle and the mean flow velocity of a flow field can be measured simultaneously. To point out the constraints of this method a variation in the excitation amplitude was performed using an empty test section. Furthermore the influence of a superposed turbulence flow generated by PC cooling fan was investigated. Finally prospective improvements of this method via sophisticated post processing are discussed. 1. Introduction In most cases, investigations of acoustic fields are achieved by the measurement of the acoustic pressure using microphones. Then the acoustic particle velocity can be derived from the acoustic pressure due to the conjugated equations for pressure and velocity. The acoustic field can be used to determine the impedance of flow ducts, perforated liners, nozzles etc. nevertheless the acoustic pressure respectively the acoustic particle velocity are required as functions of time and spatial location. Since a localized measurement technique only yields data for a single point a PIV system is preferred because, velocity data is obtained over a large area and measurement time is reduced. Additional this non-intrusive measurement technique offers the possibility to measure in regions therein the environmental conditions precludes classical techniques or therein the sensor itself can disturb the measurement. PIV itself becomes a more commonly used tool in research and industry, due to advances in computer and camera technology. Applying PIV to measure the acoustic particle velocity or celerity was shown in literature by Hann and Greated [1], developing a correlation method which allows the measurement of the amplitude of oscillation of a sinusoidal sound field by using the spectrum of multiply exposed images. Celerity measurements in an impedance tube were realized by Blackshire [2] and Humphreys et al. [3] for a variety of pure tone sound fields. Parallel measurements of acoustic streaming and particle velocities are demonstrated by Nabavi et al.[4]. Berson et al. [5] has applied PIV in the stack of a thermoacoustic refrigerator to measure acoustic velocities also in presence of standing waves. This paper mainly focuses on measurement of the acoustic particle velocity and the flow field in absence of standing waves, so this method is applicable for flow configurations where a superposition of the flow and the acoustic field exists. - 1 -
2. Theory PIV measures a velocity field in a laser induced light sheet and derives a velocity vector expression of the flow field by dividing the particle displacement of two successive PIV images by the pulse distance. Hereby the particle displacement is demined via cross correlation in subdivided image areas specified by the resolution of the vector map. When a sound wave is propagating into a homogeneous gas medium it creates small local disturbances in density, pressure and velocity. The fluctuations depending on spatial location and time are considered to be small compared to the mean values. The velocity fluctuations can be interpreted as the acoustic particle velocity. It is the perturbation velocity of a particle moving back and forth in the direction of the sound wave propagation. It is not the velocity of the wave propagation itself, which is called speed of sound. In the test section an additional non-negligible turbulence term exists, so the measured velocity is assumed as triple composition that allows writing the measured total velocity u in the following form: total u = u + u + u. (1) total mean turbulence ' acoustic Whereas u mean presents the mean flow component and u turbulence the turbulence term of the flow field ' and u acoustic describes the acoustic that varies depending on the phase of excitation. In order to extract the acoustic particle velocity a synchronized image acquisition and an appropriated post data processing is necessary. The image acquisition based on circuit device that admits an 180 phase shift between two following vector images regarding to the acoustic excitation. One vector image consists of two exposed single images as known from the standard PIV procedure. Figure 1 visualizes the principle of recording for two sets of PIV images. Figure 1: Two sets of PIV images having 180 phase shift and the vector representation of the total measured velocity. The first raw image of the first set is acquired when the particle displacement due to the excitation frequency is deflected regarding the zero-crossing, here exemplary at 90 the maximum positive displacement. The second raw image is taken at the second maximum displacement at 270 located at the negative site of zero-crossing. Out of both raw images a vector field can be calculated. The second set of raw images is acquired in the same way but switched in the image order. Since the maxima of the second set are inversed, both vector fields consisting of an opposed acoustic particle velocity vector which can be described by Equation.1. Additional an arrow representation of the total measured velocity is included under the graphs in Figure 1. A subtraction - 2 -
of both equations representing vector field one and two ends up in: u utotal = u u + 2u (2) total 1 2 turbulence 1 turbulence 2 ' acoustic Thereby the constant velocity fraction u mean vanishes and the calculated acoustic particle velocity is supplementary expressed by the turbulence term uturbulence 1 uturbulence 2. This turbulence term is a stochastic term, so there is nearly no correlation neither in time nor in spatial location between these two successive vector maps. Due to the randomness of this turbulence term in a large number of measurements the term tends to disappear. Now it is possible to calculate the acoustic particle velocity by subtracting and averaging. If 2N represents a large number of images Equation (2) can be written as: N N 1 2 i= 1 u u i i+ 1 = 2u' acoustic. (3) To obtain the best results the phase shift between the two raw images of one vector map has to be taken into consideration. Figure 2 shows the sinusoidal displacement for one particle caused by the excitation frequency. Since the measured velocity is calculated by dividing the displacement between two images by the pulse distance, the proportional measured acoustic particle velocity can be interpreted as the slope between two points representing the time of image acquisition. Accordingly there exists a maximum measurable velocity depending on the time delay between these two images. On the other hand there also exists a pulse distance, where the acoustic particle velocity is measured as zero, because both images are taken when the particle has the same spatial location. This occurs when both images are taken at zero-crossing and the displacements due to excitation in both images are zero. Consequently both images need to be taken symmetrically around the zero crossing to get the measurable celerity amplitude. The maximum celerity can be measured if the two pictures are taken within the linear zone of the sine wave. Additionally the optimum pulse distance is influenced by the magnitude of the mean flow because the conditions needs to be suitable for image cross correlation. Figure 2: Phase shift between two images to get maximum acoustic particle velocity. - 3 -
3. Experimental procedure The squared test section made of acrylic glass allows an optical access into the region of interest, as shown in Figure 3. The dimensions of the test section are 155mm in length and 140mm in height as well as 140mm in depth. On one side a loudspeaker is connected via a speaker horn, which is conical inside allowing a smoother transition from the loudspeaker cross section into the test section. Figure 3: Photo of the test section. The excitation signal emitted by the loudspeaker is generated by a frequency generator and can be adjusted via an amplifier up to 140dB sound pressure inside the test section. The amplitude of excitation is measured by a wall-flushed mounted ¼ inch microphone inside the upper wall of the test section. An additional PC cooling fan can be installed at the upper wall, to generate a turbulent flow field depending on the rotation speed level of the fan. Furthermore, a small plate can be inserted inside the chamber aligned parallel or perpendicular to the transmitted wave. The side of the test section opposite to the speaker is terminated by acoustic foam that allows the sound wave propagation outside the test section and minimizes the seeding leakage. The inlet for the oil based liquid seeding is located at the lower wall side of the test section. The enlightenment of the around 2µm seeding particles is done by a two-pulsed Nd-YAG laser system working at 532nm wavelength. The two laser beams are focused and expand by a set of four lenses to span the beam into a laser sheet of 2mm thickness inside the horizontal plane of middle section. The CCD camera featuring a focal length of 85 mm is mounted perpendicular to the laser sheet looking from bottom to top. A region of 4x3cm can be observed containing a resolution of 1600x1200 pixels. The synchronization between laser and camera is realized by a trigger box as commonly used for PIV and can be seen as an autarkic independent system. The synchronizer box owns a trigger input which is used to synchronize the laser-camera system to the excitation signal of the loudspeaker. This is realized by a self made circuit device that is mainly based on two components, a synchronous binary counter to reduce the signal frequency by a factor of 2 and an exclusive OR gate which generates the 180 angle shifting by comparing two signals (see Figure 4) - 4 -
Figure 4: Scheme of the 180 phase shift circuit device. Since the recoding speed of the system is limited by the CCD camera their acquisition frequency is used as the time base for the laser-camera system. So the first input of the 180 shift circuit is connected to the camera output having an acquisition frequency of 2Hz. Passing the synchronous binary counter the signal is halved in frequency. In Figure 4 it can be seen as signal b arriving the OR gate. As second input of the circuit device the excitation frequency of the loudspeaker is connected, that is generated by a frequency generator (signal a). If a raising or falling edge of the halved camera signal is detected by the OR-gate, it will shift the generator signal by 180. Now the output signal of the circuit device is connected to the trigger box that is able to adjust itself to the incoming triggering signal. So the trigger input frequency of synchronizer is equal to the excitation frequency but shifted by 180 in phase if the image acquisition of two raw images has been passed. The input frequency of the synchronizer is now the time base for the laser camera system. Using the trigger input the synchronizer box is able to adjust the internal program that drives the laser-camera system. Since the trigger input frequency is much higher than the camera frequency, the synchronizer box has enough time to adjust to the new time base if a phase-switch occurs. Finally for each phase reversal, only one set of two raw images are taken. As the phase shifting is a periodic phenomenon, all taken sets are exactly recorded at the same time for each period having a 180 phase shift between the previous and following sets. To adjust the phase within the period the trigger box can be additionally off-set in phase, which allows moving in 0.5 step size. This way of synchronizing was chosen; because the set-up needs to be variable to experiments thereby the driven frequency is provided by the experiment itself (e.g. periodic or oscillating flows having acoustic feedbacks). Otherwise the 180 phase shift can be done directly at the loudspeaker signal. - 5 -
4. Results For investigations of the amplitude sensitivity the excitation of the loudspeaker was set to a single constant frequency varying in the amplitude inside the empty test section. A successful implementation of this acquisition and data processing technique is exemplary shown in Figure 5 excited with 104dB at 211Hz. Figure 5: Calculated acoustic particle velocity (2u ) for sinusoidal excitation (211Hz, 104dB) in empty test section. The calculated acoustic field propagates from right to left with higher acoustic particle velocity near the loudspeaker. At the connection point between speaker horn and test section acoustic source can be assumed as a linear source. This may explain the relatively constant velocity distribution along the y-coordinate near the loudspeaker. Since a 3D phenomenon is existent the linear source changes to a point source characteristic. This can be seen along the abscissa where the velocity distribution along y-coordinate has a maximum at nearly 15mm height and is spherical shaped. The result of the complete variation in amplitude, ranging from 65 to 104dB can be seen in Figure 6. The low frequency of 211Hz has been selected because at this frequency the acoustic velocity is slow but the displacement is high. Figure 6: Mean acoustic particle velocity versus the sound pressure level of the excitation. - 6 -
As expected higher acoustic particle velocities have been measured by increasing the amplitude of the loudspeaker. The number of averaged image sets decreases from 100 at lower amplitude levels to 20 image sets at higher amplitudes. In the shown double logarithmic scale, a linear trend between increasing sound pressure level and acoustic velocity can be identified. The trend is constant for amplitudes higher than 80dB and reasonable vector field can be achieved. At lower amplitudes, the amount of averaged images may not be enough so that the background noise may be too high. In order to investigate the turbulence sensitivity an additional PC cooling fan was installed inside the test section for measuring the celerity in presence of turbulent flow. Figure 7: Calculated acoustic fields for various levels of turbulence inside the test section at 211Hz and 104dB. Results for varying the turbulence level inside the test section can be seen in Figure 7. The top left picture shows the initial state there the fan is switched off. The higher calculated acoustic particle velocities compared to Figure 5 can be explained by the changed view field of the camera closer to the loudspeaker. Additional to the initial state the development of the calculated velocity field with increasing turbulence level are shown in Figure 7 plus the associated standard deviation. It can be seen that up to 14 percent rotation speed the initial state can be calculated. At higher levels the calculated acoustic filed is still overlapped by the turbulence field. Even though the averaged images are increased up to 1000 at 30 percent rotation speed the turbulence was not eliminated as shown bottom right. Up to now the turbulence can be quantified only by the rotation speed of the PC fan in percent as well as by the standard deviation of the averaged vector images but some statements can be done. The acoustic particle can be computed applying this method at the present of turbulent flow. Reasonable results recording few images can be obtained up to approximately 10 percent in standard deviation of the maximum measured velocity. With rising standard deviation the amount of images has to be increased. In the near future the minimum number of needed images has to be expressed by mathematical formulations. Applying this image acquisition, the next experiment observes the interaction between a sound wave and a perforated plate featuring a hole with a 2mm diameter in the center of the plate. The plate is installed perpendicular to the wave propagation direction dividing the test section so - 7 -
that the acoustic field is disturbed by the plate and both sides are connected only through the hole. This pre-experiment is a simplified application of a sound wave interaction with a perforated wall zoomed to one single hole. Two different excitation levels were adjusted at the opposite side of the loudspeaker to 104 and 130dB. Results are given in Figure 8 wherein a flow field induced by the acoustic can be seen. Due to the fact that the induced flow field is periodic, the mean flow did not vanish after averaging and still remains as residual. Depending on the excitation amplitude a different flow field configuration occurs. For higher amplitudes (lower picture) a periodic vortex generation can be observed with higher flow velocities. For lower amplitudes only a periodic flow through the hole without vortex generation can be seen (see Figure 8-top). Similar results can be found in literature by Ahuja [6] who investigated the acoustic behavior of a rectangular slit orifice. Figure 8: Interaction between acoustic field and flow field through a perforated plate for different excitation amplitudes (top: 211Hz, 104dB bottom: 211Hz, 130dB). Nevertheless, in both cases the acoustic particle velocity could not be extracted in the vicinity of the hole because a secondary flow with high mean flow values is induced by the acoustics. That induced mean flow is superposed on the acoustic field in the same periodic manner and did not vanish applying this method. But the acoustic particle velocity still remains as a part of the measured vector and can maybe extracted via vector decomposition. Since the dynamic range of a PIV system is limited by a factor of 200 [7] the minimum measurable acoustic particle velocity depends on the strength of the induced flow. For the second measurement this leads to minimal measureable particle velocity of around 5 mm/s. That is still in the expected range of the celerity and indicates that decomposition can be successfully. One possible splitting technique may be the Helmholtz-Hodge decomposition that decomposes a vector field into a curl free, a divergence free component, and a harmonic part as shown by Polthier and Preuß [8] or Tong et al.[9]. For low Mach-number aero-acoustic applications it can be expected that the acoustic field is irrotational which allows the application of this technique. Other approaches using energy distributions for separating the acoustic may be found in applying POD methods (proper orthogonal decomposition). Since the velocity field is more energetic than the acoustic it appears to be useful. Of course filter techniques provide wide range of tools to enhance important features of vector fields but should be used with caution parallel to other methods. - 8 -
5. Conclusion and Outlook This paper presents a synchronized PIV recording technique combined with an individual data post processing that is able to determine simultaneously the acoustic particle velocity respectively the mean flow velocity of a flow field. A circuit device was developed that allows the recording of raw images in the required order at the desired phase angle. Thus the proposed post processing can be done straightforwardly. With this technique reasonable results for the acoustic field are achieved for excitation amplitudes larger than 80dB. The influence of the excitation frequency has to be performed in further work to find the maximum measureable frequency. Additional the capability of measuring with multi-sine excitation instead of pure tone excitation are the subject of current research. The presented method was successfully applied to measure the celerity of a sinusoidal excited flow filed superposed by turbulent flow pattern. The influence by the turbulence can be countered by averaging over a larger number of images, but needs to be proved mathematically in the future. Limits of this method have been found if a periodic excited flow field exists as shown for the perforated plate. For this case several decomposition techniques are proposed which needs to be implemented and tested. Standard investigations of the acoustic field are mainly performed by microphones which need to have a mechanical access to the flow field. If the environmental conditions preclude classical measurements methods and an optical access is available a non intrusive technique is profitable. The presented method called acoustic PIV seems to be a promising non intrusive technique, which will be developed for research applications on liners to determine their impedance properties. 6. Acknowledgements The authors wish to gratefully acknowledge the financial support by the Helmholtz Association (HGF) supporting the Helmholtz-University Young Investigators Group. Thanks are also extended to Henrik Birke for his assistance during the experimental work. References [1] D.B. Hann and C.A. Greated, The measurement of flow velocity and acoustic particle velocity using particle image velocimetry, Meas. Sci. Technol., 8(12):1517-1522, December 1997. [2] J.L. Blackshire, Analysis of Particle Image Velocimetry (PIV) Data for Acoustic Particle Velocity Measurements, NASA Contractor Report 201664, January 1997. [3] W.M. Humphreys Jr., S. M. Bartram, T.L. Parrott and M.G.Jones, Digital PIV measurements of acoustic particle Displacements in normal incidence impedance tube, AIAA-1998-2611 Advanced Measurement and Ground Testing Technology Conference, 20th, Albuquerque, NM, June 15-18, 1998 [4] M Nabavi, M. H. K. Siddiqui and J. Dargahi, Simultaneous measurement of acoustic and streaming velocities using synchronized PIV technique, Meas. Sci. Technol., 18(7):1811-1817, May 2007. [5] A. Berson, M. Michard and P. Blanc-Benon, Measurement of acoustic velocity in the stack of a thermoacoustic refrigerator using particle image velocimetry, Heat Mass Transfer., DOI: 10.1007/s00231-007-0316-x, July 2007. [6] K.K. Ahuja, R.J. Gaeta Jr and M. D Agostino, High Amplitude Acoustic Behaviour of a Slit-Orifice Backed by a Cavity, NASA Contractor Report 210635, December 2000. [7] M. RAFFEL, C. WILLERT, J. KOMPENHANS, Particle Image Velocimetry: A Practical Guide (Experimental Fluid Mechanics) Springer-Verlag, Berlin, Heidelberg, 1998 [8] K. Polthier and E. Preuß, Variational Approach to Vector Field Decomposition, Scientific Visualization, Springer- Verlag (Proc. of Eurographics Workshop on Scientific Visualization, Amsterdam 2000) [9] Y.Tong, S. Lombeyda, A. N. Hirani and M. Desbrun, Discrete multiscale vector field decomposition Proc.of ACM SIGGRAPH, Vol. 22 (3):445-452, July 2003-9 -