Simultaneous High Speed Stereo PIV and LDA Measurements in …ltces.dem.ist.utl.pt/lxlaser/lxlaser2012/upload/302... · 2012-06-20 · times higher than the axial flow component

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 09-12 July, 2012

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Simultaneous High Speed Stereo PIV and LDA Measurements in the

highly transient vortical wake of an axial fan

Philipp Mattern1*, Sten Sieber1*, Michael Dues2, Saban Caglar1, Martin Gabi1

1: Karlsruhe Institute of Technology (KIT), Fachgebiet Strömungsmaschinen (FSM), Germany

2: Intelligent Laser Applications GmbH (ILA), Germany * correspondent authors: [email protected], [email protected]

Abstract Simultaneous Laser Doppler Anemometry (LDA) and High-Speed Stereo Particle Image Velocimetry (HS-SPIV) measurement are carried out for a transient high speed comparison of both measurement systems. The out of plane component of the Stereo PIV is compared to the measurements of the 1D LDA in a ducted swirl flow. The flow regime is highly turbulent at a Reynolds number of 𝑅𝑒!"#$ ≅166.000 and swirl component being six times higher than the axial flow component. An axial fan without outlet guide vanes is used to serve as a swirl generator. This work describes the synchronization, the simultaneous measurement and post processing. The results are merged, analyzed and show a good correlation in time and absolute value. The systematic error is in the range of around 0.5 m/s, independent of flow velocity and turbulence intensity and could be compensated under perfect PIV seeding conditions. Consequently the authors conclude that a well-adjusted HS-SPIV system can resolve flow phenomena as accurate in time and absolute velocity as LDA. Additionally it delivers spatial information of the flow field which is not possible using a LDA system. Introduction In the last decade PIV measurement technics and equipment has developed rapidly. Nowadays PIV systems are capable to operate with high resolutions and/or very high frequencies up to several thousand Hertz. Thus High-Speed Particle Image Velocimetry (HS-PIV) tends to replace Laser Doppler Anemometry (LDA) or Hot Wire Anemometry (HWA) for investigations of turbulent flows. Receiving high spatial and temporal resolution of a turbulent flow field by HS-PIV reduces the effort of using several measurement techniques, i.e. described by N. Grosjean et. al. [1] to distinguish between unsteadiness and periodic fluctuations or by A. Cenedese et al. [2] to investigate the mixing properties of a free jet in time and space. In all these studies LDA or HWA was used for temporal and PIV for spatial resolution. Moreover a lot of work has been done validating, PIV by LDA [3], [4], respectively HWA [5]. Most of the time this is done by using averaged data or data with a recording frequency less than 50Hz. This paper presents the results of simultaneous High-Speed Stereo Particle Image Velocimetry (HS-SPIV) and LDA measurements, to make an approach to validate the transient HS-SPIV data, in particular the out of plane velocity component by 1D-LDA. As flow regime a high turbulent ducted swirl flow is chosen at a Reynolds number of 𝑅𝑒!"#$ ≅ 166.000 and swirl component being six times higher than the axial flow component. Experimental setup The following section describes the experimental installation as illustrated in Figure 1. An acrylic glass duct is used for the optical access for PIV and LDA, followed by aluminum ducts with an overall length of 20D. The flexible exhaust hose guides the flow into a test rig installation consisting of a venturi flow meter, a choke and a booster.


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List of Symbols 𝑐! [m/s] Axial velocity component

𝑐! [m/s] Circumferential velocity component

D [m] Inner diameter of the duct

IA [px²] Interrogation Area

∆𝑝 [Pa] Pressure raise

PD [s] Puls distance

PHI [-] Volume flow coefficient: 𝑃𝐻𝐼 = !!!!!!"

PSI [-] Pressure coefficient: 𝑃𝑆𝐼 = !∆!!!²

R [m] Inner Radius of the duct

Re [-] Reynolds number

U [m/s] Circumferential velocity of the impeller outer diameter

𝑈! [m/s] Averaged axial velocity in a pipe

𝑉 [m³/s] Volume flow

z [m] Axial coordinate along a pipe

𝜌 [kg/m³] Density

Figure 1: Experimental test rig, setup for measurements in x-z plane


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An axial fan, designed with r·cu=const., has been used without outlet guide vane to serve as a swirl generator. To verify the operation point during the measurements, a four point averaged wall pressure was measured in a cross section 5D downstream from the trailing edge of the blade (see operation point Figure 2). A more detailed description of the experimental setup regarding from a fluid machinery point of view can be found in [6]. Measurement system The following section describes the measurement setup for LDA, PIV and their synchronization. Seeding The seeding was produced by a DEHS Atomizer. The main challenge was to achieve a seeding density satisfying the demands of both laser optical systems LDA and PIV. The seeding density should not be too high, leading to measurement errors for the LDA system (miscounting of particles). Nor should it be too low, therefore being not recognized clearly by the PIV system anymore. The approach was too calibrate and adjust the seeding density for the LDA on the highest, still accurately und continuously measureable seeding since the LDA system offers less adjustment options. The HS-SPIV system can be adapted to seeding conditions in various ways (light sheet, focus, pre filters etc.). As common for a PIV system, the most convenient setup was found by means of trial and error. LDA measurements For the LDA setup a shifted 1D Nd:YAG based system at a wavelength of 532nm was used. The chosen focal length allowed measurements along the entire tube radius R. To carry out simultaneous LDA-PIV measurements, this profile line was aligned to the PIV measurement plane as Figure 3 shows. HS-SPIV measurements The HS-SPIV measurements were carried out in the x-y plane (cross section), at z=2D downstream of the fan’s trailing edge, as defined in Figure 3. For flow illumination, a dual oscillator-single head, diode pumped Nd:YLF laser Darwin Duo from Quantronix©, with an output wavelength of 527 nm is used. Two high speed cameras, Photron© FASTCAM SA4, with a 1024x1024 pixel resolution at 1000 fps and the corresponding Photron© FASTCAM Viewer software are used for recording. Scheimpflug Tilt

Figure2: Fan’s characteristic curve showing point of

operation during measurements

Figure 3:Position and orientation of the HS-SPIV setup

0

0.1

0.2

0.3

0.175 0.225 0.275 0.325

PSI

PHI


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Adapters and two Canon© EF 85mm f/1.8 USM lenses on automated EOS Rings from ILA© GmbH have been used. Trigger System For the LDA and PIV measurements being synchronous, it was necessary to trigger both systems with the same signal. This was realized by using a highly efficient ILA© Synchronizer with a 5ns resolution. After setting up the systems and entering a “ready state”, a continuous recording into a ring loop buffer was carried out. On the rectangle trigger event both systems ran for 2.7 s into the buffer. The start of a recording cycle is illustrated in Figure 4. Afterwards the data was collected via Ethernet to the PC. Longer continuously combined PIV-LDA measurements were not possible, because the buffers of both systems cannot be read out in real-time at the moment. Post processing LDA post processing For interpreting of the LDA Data, ILA’s LDAControlQt© was used. The raw frequency data of the LDA was recorded at 50 MHz resulting in around 130 million samples. The raw data was then transformed via FFT into, i.e. for M3, 13603 measured, single velocitiy values. These were then combined into 3719 packages (representing one particle), each with a corresponding velocity-timestamp pair. Having almost the same wavelength, the high intense double pulse of the PIV system, distorted the LDA measurement during the opening time of the Q-Switches. Nonetheless, this only affected the moment while a Q-Switch was open. At any other time the LDA measurements were valid.

Figure 5: LDA voltage raw signal (red) including detected PIV pulses (Q1,Q2)

PIV post processing Since the seeding density was a compromise between raw data quality and measurability and with the focus on accuracy and continuity of the LDA system, the PIV image quality was poorer than normally possible with this kind of setup. The PIV post processing was realized by using PIVTEC©’s PIVView Version 3.2. To combine the information of both cameras, common methods of dewarping and disparity correction were applied.

Figure 4: Timeline visualizing Trigger and synchronization

for LDA and PIV


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Although the poor seeding quality was a problem itself, the main disadvantages of the setup was that both systems had almost the exact same wavelength (PIV: 532nm vs. LDA: 527nm). This resulted in a clearly visible LDA beam in every PIV picture. By means of masking and static background subtraction this distortion could be minimized (see Figure 6).

Figure 6: PIV Background subtraction: Raw image à Mean image à

Pre filtered image (Cam1, M3, all images inverted) The mask had to be applied over the exact region were the LDA measurement took place (Figure 7, blue mask), resulting in a covered spot less than 4.7% of the interrogation area (IA) (Figure 7, center image). Although the preprocessed raw image data was capable of being correlated down to an IA of 16x16 pixels with an overlap of 50%, due to the covered spot an IA of 64x64 pixels with an overlap of 50 % was chosen. The Figure 7 shows the correlation plane (right image) of the examined area with one distinct pixel shift peak, confirming this approach.

Figure 7: PIV Masking (blue) of the LDV measurement spot and correlation plane (green) (Cam1, M3)

Cross correlation resulted in a field of 1113 active vectors. As post filtering methods, only a dynamic mean test (Mean: 2.5; Var.: 2.0) and a maximum displacement difference test of 3 were used. Due to this, less than 17 vectors had to be interpolated in single correlation, none of them anywhere near the region of interest. Figure 8 shows this for a random instantaneous picture of M3.


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Velocity extraction and data merging For the spatial merging the closest PIV vector to the LDA measurement position was extracted for comparison. Here Figure 9 shows the LDA measurement positions (M2, M3, M4) in the averaged PIV image of the out of plane component of the velocity (normalized by the inlet velocity cinlet). A pulse distance (PD) of 50 µs between both cavities of the Laser system means that every single PIV vector field is averaged over 50 µs. The recording frequency of the PIV system was set to 1000 Hz (see Figure 4). Accordingly this combination leads to a smoothing effect on the PIV data, further described in the analysis and conclusion chapter. The amount of 2728 vector fields was available for a time period of 2.7 s. To compare both datasets, it was necessary to project one dataset onto the other. With the PIV data being already smoother and the LDA data having more discrete values, but non-uniformly distributed, it was reasonable to project the LDA data onto the PIV timestamp. This was realized using a simple linear 1D-interpolation. Other methods like spline, cubic or nearest neighbor interpolation were not suitable, because they interpreted the dataset too much. Figure 10 shows the comparison between real measured values and their interpolation onto the PIV timestamp for a time span of 0.1 second. The particular segment shows one of the worst fits compared to the whole measurement time span of 2.7 seconds.

Figure 8: random 3C correlated picture of M3 (Vector: in-plane

displacement, contour: out-of -plane component)

Figure 9: LDA position (M2, M3, M4) in the averaged PIV image of the out of plane component of the velocity cm/cinlet

Figure 10:Comparison between the original LDA velocity data vs. the

onto the PIV timestamp interpolated LDA data


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For strong fluctuations the interpolation resulted in a smoothing effect (green marked areas). This can also be seen in Figure 11. Here the normal distribution of the interpolated data is narrower than the original data. Due to the difficult seeding conditions for the LDA system, it could also happen, that more than one particle passed the measurement volume. The red marked spot in Figure 10 could be interpreted as two particles (with slightly different velocities) being detected at the same time. In this case, the interpolation has a positive damping effect. The resulting overlapped time span of both methods was still around 2.7 seconds with 2680 separate values that could be compared.

Figure 11: velocity normal distribution of LDA data and interpolated LDA data

Analysis The following chapter deals with the analysis of the post processed results of the simultaneous transient HS-SPIV-LDA data. Figure 12 shows the same time segment as described in the data merging chapter (compare Figure 10), this time with the overlaid PIV data. It is clearly visible, that both signals match very well in shape and temporal run. In addition, it shows that the absolute value of the PIV data is slightly higher than the corresponding LDA point.

Figure 12: superimposed PIV and interpolated LDA data


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To illustrate the similarity furthermore, a normalized cross correlation of both signals is shown in Figure 13. Each signal is normalized so its autocorrelations at zero lag is identically to 1.0. The shift of zero proves that the trigger system was working properly and a coefficient of nearly 0.7 is sufficient enough to say that both signals are very similar.

Figure 13: Normalized cross correlation of the PIV and LDA data for M3

For the purpose of data validation and consistency, the PIV and LDA signals were analyzed separately regarding their distribution. As shown in Figure 12 on the left and middle plot, both signals show a Gaussian distribution as expected for a physical phenomenon. The comparison of the fitted normal distribution of both signals is shown on the right side of Figure 14. The tip of the bell-shaped curve and therefore the average velocity of the signals are around 7.3m/s for the LDA and 8.0m/s for the PIV. Meaning the PIV signals are on average 9% higher than the LDA. Due to the smoothening effects on the PIV signals, as described before, the PIV distribution is a little bit narrower than the one of the LDA.

Figure 14: velocity distribution of the PIV and LDA data

Summarized Table 1 shows all results of the analyzed data comparing PIV and LDA for all three measurement positions.

Comparable Points

Cross corr. coeff.

[-]

Mean Vel. PIV

[m/s]

Mean Vel. LDA [m/s]

Mean Vel.Difference [m/s]

Deviation LDA PIV

[%]

STD PIV

[m/s]

STD LDA

[m/s]

Sys. Error

[m/s]

Stoch Error

[m/s]

Tu LDA

[%]

Tu PIV

[%]

M2 2674 0.63 0.94 0.49 0.45 91.8 1.13 1.17 0.59 0.94 237 121 M3 2680 0.70 7.96 7.27 0.65 9.5 1.05 1.37 0.65 0.89 18 13 M4 2682 0.54 8.96 8.55 0.41 4.8 0.65 0.91 0.35 0.70 10 7


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Conclusion The analysis showed a clear correlation between the time resolve LDA and PIV signals for all measured positions. For this conclusion section the difference between the LDA and PIV results are of special interest. M3 and M4 are positioned in the free vortex area of a Rankine vortex like flow regime, while the M2 measurement position is in the much more unstable transition area of the forced vortex to free vortex area. Here turbulent phenomena of the transition area as well as the highly turbulent behavior of the vortex core with its backflow and its fluctuation regarding its center point are detected. For M3 and M4 the relative offset, consequently the measurement difference between PIV and LDA is less than 10% respectively less than 5% (see Table 1). The whole signal of the fluctuating deviation of M3 is shown in Figure 15.

Figure 15: Signal deviation between LDA and PIV, mean offset=systematic error (red line)

superimposed by a randomly fluctuating offset=stochastic error As illustrated the signal offset can be divided in a mean and a superimposed randomly fluctuating offset signal. The mean offset stands for the systematic error which should be possible to compensate by the PIV system adjustments. The fluctuation part of the signal difference between LDA and PIV, needs to be interpreted as the stochastic error and shows Gaussian distribution, as Figure 16 shows.

Figure 16: Gaussian distribution of the stochastic error between LDA

and PIV measurements for M2, M3 and M4

Compared to the M3 and M4 position, the average velocity deviation LDA to PIV for the M2 measurement of around 91% seems to very high. However the absolute value of the velocity is low


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and the absolute deviation of 0,45m/s is in the same range as it is for M3 and M4. Analogous results are shown for stochastic error in Table 1 (0.7 – 0.94m/s) and Figure 17. It illustrates the fitted normal distribution of fluctuation around the mean deviation between the LDA and the PIV system.

Figure 17: fitted normal distribution of fluctuation around the mean

deviation between the LDA and the PIV system

A significant difference can be found in turbulence intensity. The PIV results underestimate the turbulence intensity (here regarding the out of plane component) especially in the highly unstable area of M2 by a factor of almost two. In addition, an approach was made to only compare the data when a “perfect hit” was detected. The authors defined this “perfect hit” as the LDA signal exactly between a PIV double-pulse illustrated in Figure 19.

Figure 19: LDA voltage signal showing a “perfect hit”: LDA signal lies between a PIV double-pulse

The analyzed “perfect hit” results showed no significant improvement compared to the one already presented. However having the signal of one system (PIV) directly recorded by the other system was a quiet convenient way to validate that the trigger system worked. Like mentioned before, the authors assume that the differences between the LDA and PIV results are caused by the measurement methods themselves. PIV detects the particle shift during a defined time interval ∆𝑡!"#, in practice the time between the two pulses of a double pulse. The result is a velocity vectorfield averaged over exactly this time interval ∆𝑡!"# . LDA averages as well, in


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simplified terms, by detecting the time ∆𝑡!"# between two light scatters of the passing particle. However for the here presented work the PIV averaging time ∆𝑡!"# = 50𝜇𝑠 is more than a factor of 100 larger than the averaging time of the LDA system, ∆𝑡!"# < 0.2𝜇𝑠. To achieve the same accuracy in detecting turbulent fluctuations with a PIV system, it would be necessary to decrease the pulse distance dramatically. Increasing the recording frequency of the PIV system would increase the temporal resolution, even higher than the LDA’s resolution in time, but it still would not be better concerning the accuracy of turbulent fluctuations. Simultaneous LDA and PIV measurement have been carried out for a transient high speed comparison of both measurement systems. The out of plane components of a HS-SPIV were compared to the measurements of a 1D LDA in a ducted swirl flow. Main problems for a simultaneous measurement were the different seeding requirements of both systems and the nearly identical wavelength of the laser systems. The results show good correlation in time and magnitude. The mean offset, hence systematic error is in the range of around 0.5 m/s and independent of flow velocity and turbulence intensity. It should be possible to minimize this by fine-tune the PIV system. (However, with the biggest variable in this experiment still being the already optimized seeding, this couldn’t be proved) Consequently the authors conclude that a well-adjusted HS-SPIV system can resolve flow phenomena as accurate in time and absolute velocity as LDA. Additionally it delivers spatial information of the flow field which is not possible using a LDA system. For a measurement of characteristic turbulent parameters however, it fails since the time between pulses averages out crucial velocity fluctuations. For future approaches, it would be helpful to have 3D- LDA Data, to compare all components and their derivatives. Different wavelength of the measurement systems could reduce the effort. Finally a lager dataset with various flow regimes would help to improve the error estimation. Literature [1] N. Grosjeany, L. Graftieauxy, M. Michardy, W Hübnerz, C. Tropeaz, J. Volkertz - Combining LDA

and PIV for turbulence measurements in unsteady swirling flows, Measurement Science and Tech-nology Volume 8 Number 12, 1997

[2] A. Cenedese, G. Doglia, G. P. Romano, G. De Michele, G. Tanzini - LDA and PIV Velocity Meas-urements in Free Jets, Experimental Thermal and Fluid Science 9:125-134, 1994

[3] G. P. Romano - PIV and LDA Velocity Measurements Near Walls and in the Wake of a Delta Wing, Optics and Lasers in Engineering 16:293-309, 1992

[4] Jens Nørkær Sørensen, Igor Naumov, Robert Mikkelsen - Experimental investigation of three-dimensional flow instabilities in a rotating lid-driven cavity, Experiments in Fluids 41: 425–440, 2006

[5] P. Lavoie, G. Avallone, F. De Gregorio, G. P. Romano, R. A. Antonia - Spatial resolution of PIV for the measurement of turbulence, Experiments in Fluids 43:39–51, 2007

[6] Philipp Mattern, Sten Sieber, Đorđe Čantrak, Friedrich Fröhlig, Şaban Çaglar, Martin Gabi – Investigation on the Swirl Flow caused by an Axial Fan – A Contribution to the Revision of ISO 5801, FAN2012 Senlis, France, 2012

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Simultaneous High Speed Stereo PIV and LDA Measurements in …ltces.dem.ist.utl.pt/lxlaser/lxlaser2012/upload/302... · 2012-06-20 · times higher than the axial flow component