Proceedings of 3rd International Workshop on PIV, Santa Barbara, USA, Sep.16-18, 1999

A Comparative Study of the PIV and LDV Measurements on a Self-induced Sloshing Flow

Tetsuo SAGA, Hui HU, Toshio KOBAYASHI, Shigeki SEGAWA and Nobuyuki TANIGUCHI Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Tokyo 106, Japan E-mail: saga@.iis.u-tokyo.ac.jp or huhui@cc.iis.u-tokyo.ac.jp Masaho NAGOSHI and Taizo HIGASHIYAMA Fluid Measuring Instrument Division, KANOMAX JAPAN,INC. 3-18-20 Nishishinjyuku, Tokyo160, Japan Koji OKAMOTO Nuclear Engineering Research Laboratory, University of Tokyo, Tokai-mura, Ibaraki, 319-11, Japan

ABSTRACT

Particle Imaging Velocimetry (PIV) and Laser Doppler Velocimetry (LDV) measurements on a self-induced sloshing flow in a rectangular tank had been conducted in the present study. The PIV measurement result was compared with LDV measurement result quantitatively in order to evaluate the PIV system. The comparison results show that the PIV and LDV measurement results agree with each other well in general for both the mean velocity and turbulence intensity. The disagreement level of the mean velocity between the PIV and LDV results found to be within 3% of the target velocity for PIV parameters selection. Bigger disagreement were found to concentrate at the high turbulence intensity region. The space and time resolution difference and the limited frame number of the PIV result were suggested to be the main reasons for such disagreement.

INTRODUCTION As a non-intrusive whole field measuring technique, Particle Imaging Velocimetry (PIV) can offer many advantages for the studying of fluid mechanics over other conventional one-point experimental techniques like Laser Doppler Velocimetry (LDV) or Hot Wire Anemometer (FWA). For example, PIV can reveal the global structures in a two-dimensional or three-dimensional flow field instantaneously and quantitatively without disturbing the flow, which are very useful and necessary for the research of flow mechanism, in particular for the study of unsteady flow. In order to evaluate the effectiveness and accuracy level of PIV result, many studies had been conducted based on the image processing result of artificial images, which were generated artificially with a pre-set velocity distribution, by using various PIV image processing methods or algorithms. By comparison of the velocity distribution obtained through PIV image processing and the pre-set velocity data of the artificial images, the accuracy level of the PIV result was evaluated. Many important results had been got through these studies. However, it should be noted that the artificial images used in those researches always have very good image quality, i.e. much better signal to noise ratio (SNR) than the PIV images obtained from a real PIV experiment. Besides PIV image processing, PIV experiment also includes illumination and image capturing, which may affect the PIV result

accuracy as well. So, the accuracy level can be got in a real PIV experiment still can not be fully predicted just based on the PIV image processing result of those artificial images. In order to evaluate the accuracy level of a PIV system can be got in a real PIV experiment, a comparative study of PIV and LDV measurements on a same flow field had been conducted in the present study. The measurement target flow is a self-induced sloshing flow field in a rectangular tank (Fig. 1). The free surface of the water in the rectangular tank oscillated periodically with a constant frequency which is decided by the eigenvalue of the water in the test tank. The results of the PIV measurement and LDV measurement were compared quantitatively to evaluate the PIV measurement. The compared parameters used in the present study included the freqency of the self-induced sloshing, the time average velocity and turbulence intensity, phase average velocity and turbulence intensity values. The effect of the sample number of the PIV instantaneous frames and the space resolution of the PIV images on the accuracy level of the PIV result were also discussed in the present study.

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Figure 1. The schematic of the test tank

EXPERIMENT SETUP 1. The target flow and experiment setup The measurement target flow is a self-induced sloshing flow field in a rectangular tank. Figure 1 shows the schematic

view of the thin rectangular test tank. Working fluid (water) flowed horizontally into the test tank and flowed out at a bottom centered vertical outlet. It was found that under certain condition of water level and inlet jet velocity, the free surface of the fluid (water) in the rectangular tank might oscillate periodically at a constant frequency decided by the eigenvalue of the fluid in the test tank. This phenomenon was called as "self-induced sloshing". The characteristics of the self-induced sloshing had been studied by many researches (Okamoto et al. 1991, Fukuya et al. 1996, Saeki et al. 1998 and Hu et al. 1999). The excitation of the self-induced sloshing was considered to be the non-linear interaction between the jet instability and the sloshing motion.

PC computer

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Figure 2. The schematic of the experiment setup Figure 2 shows the experimental setup system used in the present research. The flow in the test loop was supplied from a head tank, which was continuously pump-filled from a lower tank. The water level in the head tank was maintained in constant by an overflow system in order to eliminate the effect of the pump vibration on the inlet condition of the test tank. The flow rate of the loop, which was used to calculate the representative velocity and Reynolds numbers, was measured by a flow meter. A convergent unit and Honeycomb structures were installed in the upstream of the inlet of the test tank to insure the uniform flow entrance. The flow rate and the water level of the free surface in the test tank can be adjustable by changing the position of the valves installed in the flow loop.

During the experiment, the water level in the test tank was set at about H=160mm. The flow rate of the test loop was about 20 liter/min, which corresponded to the average velocity at the inlet of the test tank being about 0.333 m/s, and Reynolds number about 6,700 based on the height of the inlet (b=20mm). Since the test tank was designed to have the flow field in the test tank to be two dimensional, our measurement result showed that the flow field in the test tank was almost two-dimensional except the regions near the two walls. The comparative measurement of the PIV and LDV were conducted at the middle section of the test tank (Z=25mm section) in the present study.

2. PIV system For the PIV measurement, twin pulsed Nd:YAG Lasers were used to supply pulsed laser sheet (thickness of the sheet is about 1.0 mm) with the frequency of 7.5 Hz and power of 20 mJ/pulse to illuminated the measured flow field. Polystyrene particles (diameter of the particles is about 20-50μm, density is 1.02kg/l) were used as PIV tracers in the flow

field. A 1008 by 1016 pixels Cross-Correlation CCD array camera (PIVCAM 10-30) was used to capture the images. The twin Nd:YAG Lasers and the CCD camera were controlled by a Synchronizer Control System. The PIV images captured by the CCD camera were digitized by an image processing board, then transferred to a workstation (host computer, CPU450MHz, RAM 1024MB, HD20GB) for image processing and displayed on a PC monitor. In the present PIV measurement, two kinds of the PIV images were captured with different space resolution. One is the 0.16mm/pixel (high resolution) and another is 0.32mm/pixel (low resolution). In the present study, rather than tracking individual particle, the cross correlation method (Willert et al., 1991) was used to obtain the average displacement of the ensemble particles. The images were divided into 32 by 32 pixel interrogation windows, and 50% overlap grids were employed for the PIV image processing. The time interviel between the two pulses was set at 2-4ms to have the average displacement of the particles in the inlet jet is about 4 to 6 pixels. The post-processing procedures which including sub-pixel interpolation (Hu et al., 1998) and velocity outliner deletion (Westerweel, 1994) were used to improve the accuracy of the PIV result. Since the cross-correlation method was used for PIV image processing, the obtained velocity is the average velocity of the particles in the interrogation window. So, the space resolution ability should be the size of the interrogation windows. Therefore the space resolution of the PIV measurement is 5mm×5mm×1mm for the high resolution case and 10mm×10mm×1mm for the low resolution case by using 32 by 32 pixel interrogation windows. Since the frequency of the pulsed Nd:Yag lasers were set at 7.5 Hz, the time resolution of the present PIV measurement is 3.75Hz according to the Nyquist critical principle. 3. LDV system

The LDV system used in the present study was composed by an Argon Laser (1.5W), a LDV optical unit (TSI TRCF2), a signal processing system (TSI IFA750) and a Synchronizer Control System (TSI Datalink DL4). Polystyrene particles with the diameter of 1μm and density of 1.02 kg/l were used as tracers for the LDV measurement. 30,000 data obtained at about 30 seconds were used for the time average velocity and turbulence intensity calculation at every point. The space resolution of the LDV system is about 65.3μm (volume diameter)×0.68mm (volume lenght). Since the sample rate of the LDV measurement is set as 1000Hz, the time resolution of the LDV measurement is 500 Hz according to the Nyquist critical principle. RESULTS AND DISCUSSIONS 1. Oscillation frequency of the self-induced sloshing Figure 3 shows the oscillation of the free surface of the water in the test tank with time at three positions, i. e., left side (inlet side), center and left side of the test tank. The frequency of the self-induced sloshing can be calculated from these signals, which is 1.6Hz.

According to the research of Fukaya et al.(1996), the self-induced sloshing mode of the present study is 1st mode. Okamoto et al. (1991) had suggested that the frequency of the self-induced sloshing equal to the eigenvalue of the water in the test tank, which can be expressed as:

)tanh(21

WHn

Wgnf n ππ

π= (1)

By using above equation, the 1st mode eigenvalue of the water in the test tank for the present study case can be calculated, which is 1.56Hz. The difference between the frequency of the self-induced sloshing measured by present study (f=1.6Hz) and the 1st mode eigenvalue of the water in the test tank is within the 3% range, which verified the propose of Okamoto et al.(1991).

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Figure 3. The oscillating water level of the free surface

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Figure 4 shows the two typical instantaneous PIV velocity fields. 1000 frames of such instantaneous velocity fields were captured in the present PIV measurement with the rate of 7.5Hz. Besides the two large vortices at the right side and left lower corner of the test tank (which are almost steady vortices), a smaller vortex (which is unsteady) also can be found in the flow field, which shed from the inlet plane jet. The whole flow pattern in the test tank, such as the path of the inlet plane jet to the oulet, the size of the two steady vortices, and the flow direction at the exit of the test tank, changed very drastically with the evolution of this unsteady vortex. By using these instantaneous velocity fields, the power spectrum of the velocity can be calculated through FFT transformation, which was shown on the Figure 5(a). The power spectrum of the velocity at the same point by LDV measurement was shown on Figure 5(b). It can be seen that both PIV and LDV measurements can identify the oscillation frequency of the self-induced sloshing well with an obvious peak at the 1.6 Hz in the power spectrum profiles.

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Figure 5. The power spectrum of PIV and LDV measurements at point (X=100mm, Y=110mm, Z=25mm)

2. Time average results As mentioned above, 1000 frames of the instantaneous PIV velocity frames obtained by the PIV system at the rate of 7.5 Hz and 30,000 samples at each points got by LDV system at the data rate of 1000Hz were used to calculate the time average values of the flow field. Figure 6 shows the time avevrage velocity fields and turbulence intensity distributions of PIV and LDV

measurement results. From the figures it can be seen that only two large-scale vortices can be found at the right side and the left lower corner of the test tank from the time average result. The unsteady vortex revealed in the above instantaneous flow fields, which shed periodically from the inlet plane jet, cannot be found in the time average results. However, the high turbulence intensity region can be found along the shedding path of the unsteady vortex.

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Figure 6. Time average results by PIV and LDV measurementes

It can also be seen that the flow pattern in the test tank

revealed by PIV and LDV measurement is similar with each other very well. In order to give a more quantitatively comparison of the PIV and LDV measurement results, the time average velocity and turbulence intensity of the PIV and LDV measurements along the inlet central line of the test tank were shown on Figure 7.

Since the parameter selection of the present PIV measurement was based on the velocity of the inlet jet flow (target velocity), which is about 0.4m/s, the 3% region of the target velocity (0.4m/s) was also shown on the Fig.7(a) for the PIV measurement results. It can be seen that, the PIV result agreed with LDV result well in general for both the time average velocity and turbulence intensity. The disagreement of the PIV and LDV results for the time average velocity is within 3% of the target velocity. However,

some local disagreement (always in the high shear region) between the PIV and LDV result can also be found in the profiles. This may be explained by that since the PIV and LDV measurements have different space and time resolution, the disagreement between them was expected to exist, especially in the high intensity regions where the effect of the resolution will be more serious. As the resolution of the PIV images improving, this disagreement is expected to be decreased, which can be verified from the figure 8. It should also be noted that the disagreement between the PIV and LDV results is more serious in the turbulent velocity intensity (STD(u) and STD(v)) profiles (Fig.7(b)) than that in the mean velocity (U and V) profiles (Fig.7(a)). This may be explained by that, according to the research of Ullum et al. (1997), the necessary sampling number to calculate the mean turbulence intensity should be the square of the number to calculate the mean velocity in order to get the same level of the standard deviation. So, the standard deviation by using the same sample number (1000 instantaneous velocity fields) to calculate the time average turbulence intensity was expected to be bigger than that to calculate the time average velocity.

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Figure 7. The comparison of the time average values of PIV and LDV measurement along the inlet central line

3 The effect of the PIV image resolution

As mentioned above, two resolution levels of the PIV images had been captured in the present study. Figure 8 shows the disagreement distributions of the LDV result and PIV results by using these two kinds of images with different space resolution.

From the figures, It can be seen that the average disagreement level of LDV and PIV in the whloe flow field is within 3% of the target velocity. The bigger disagrement

between LDV and PIV results were found to concentrate at the high turbulence intensity region. It also can be seen that

as the PIV image resolution increasing, the disagreement between the LDV and PIV measurement decreasd

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Figure 8 The effect of the image resolution on the PIV measurement results.

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Figure 9. The phase average flow field of PIV result

4. Phase average results Since the free surface of the water in the test tank oscillated periodically with frequency of 1.6Hz, the phase average measurement by using PIV and LDV had also been conducted in the present research. For the phase average measurement, the free surface water level at the left side (inlet side) was detected by a water-level detecting sensor, which can send a signal to the Synchronizer Control System to trigger the laser pulses and CCD camera. The phase average results in 250 cycle of self-induced sloshing ossilation at four phase angles ( 0=θ , π/2, π and 3π/2) were shown on Figure 9. The free surface water levels at the left side (inlet side) of the test tank were at its highest position, middle level (the free surface level is decreasing), lowest position and middle level (the free surface level is increasing) corresponding to these four phase angles. Unlike the above time average result which can just reveal two steady vortices in the flow field, the unsteady vortices can also be visulized clearly in the flow field from the phase average measurement results. Besides the two steady vortices at the left lower corner and right side of the test tank, the unsteady vortex was found to change its position with the changing of the phase angle. When the phase angle increased from 0 toπ, i.e., the free surface water level at the left side of the test tank decreased from its highest position to its lowest position (from Fig.9(a), Fig.9(b) to Fig.9(c)). The unsteady vortex shed from the inlet plane jet and moved downstream. When the phase angle increased from π to 2π, i.e, the free surface water level at the left side of the test tank began to increased from its lowerst position to its highest position (from Fig. 9(c), Fig. 9(d) to Fig. 9(a)). The unsteady vortex was engulfed by the large steady vortex at the right side of the test tank, and another new vortex was found to roll up from the inlet of the test tank. Then, another new self-induced sloshing cycle began.

Figure 10 shows the phase average velocity and turbulence intensity of the PIV and LDV measurement results along the inlet central line of the test tank at the phase angle of π/2. Just as the time average results shown on Fig.7, the PIV and LDV results agreed with each other well in general. For The phase average velocity, the disagreement of PIV and LDV was also found within 3% of the target velocity. However, the disagreement of the turbulence intensity (in the high shear region) between the PIV and LDV results was found to be more serious than its time average counterpart (Fig.7(b)), these may becasue that the fewer sample number for the phase average (250 frames) than that for the time average (1000 frames). CONCLUSIONS A comparative study of Particle Imaging Velocimetry (PIV) and Laser Doppler Velocimetry (LDV) measurements on a self-induced sloshing flow in a rectangular tank had been conducted in the present study. The PIV measurement result was compared with LDV measurement result quantitatively in order to evaluate the PIV system. The comparison results show that the PIV and LDV results agree with each other well in general for both the mean velocity and turbulence intensity. The disagreement level of the mean velocity between the PIV and LDV results is within 3% of the target velocity. Bigger disagreement regions were found to concentrate at the high turbulence intensity region. The

space and time resolution difference and the limited frame number of the PIV result were suggested to be the main reasons for such disagreement.

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Figure.10 The phase average results along the inlet central line of the PIV and LDV measueremnt (phase angleπ/2)

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Growth Mechanism of Self-Induced Sloshing Caused by Jet in Rectangular Tank.Trans. of JSME, (B), Vol.62, No.599. pp64 -71

Hu, H., Saga, T., Kobayashi, T., Okamoto, K. and Taniguchi, N. (1998). Evaluation of the Cross Correlation Method by Using PIV Standard Images. Journal of Visualization, Vol.1, No.1, pp87-94.

Hu, H., Kobayashi T., Saga, T., Segawa S., Taniguchi, S. Nagoshi M. and Okamoto K. (1999) A PIV Study on the Self-induced Sloshing in a Tank with Circulating Flow. Processing of The 2nd Pacific Symposium on Flow Visualization and Image Processing.

Okamoto, K., Madrarame, H. and Hagiwara, T. (1991). Self-induced Oscillation of Free Surface in a Tank with Circulating Flow. C416/092, IMechE, pp539-545

Saeki, S., Madarame, H., Okamoto, K, and Tanaka, N., 1998. Numerical Study on the Growth Mechanism of Self-Induced Sloshing Caused by Horizontal Plane Jet FEDSM98-5208, ASME FED Summer Meeting.

Ullum, U., Schmidt, J. J., Larsen P. S., and McClusky, D. R. (1997) Statistical Analysis And Accuracy of PIV Data. Proc. of 2nd Int. Workshop on PIV.

Willert, C. E. and Gharib, M. (1991) Digital Particle Image Velocimetry. Experiments in Fluids, Vol.l0, ppl8l-l99

Westerweel, J. (1994) "Efficient Detection of Spurious Vectors in Particle Image Velocimetry Data", Exp. In Fluids, Vol.16, pp236-247.