Particle Image Velocimetry Measurement of Tornado...

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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Particle Image Velocimetry Measurement of Tornado-like Vortices

Compared with Doppler Radar Data

Maryam Refan1,*, Horia Hangan1, Kamran Siddiqui1

1: WindEEE Research Institute, Western University, Canada

* correspondent author: [email protected] Abstract Particle Image Velocimetry (PIV) technique was employed to characterize the flow field of simulated tornado vortices and to establish a relationship between laboratory generated tornadoes and the field ones. Field data collected by mobile Doppler radars were analyzed using a mathematical method namely the Ground-based Velocity Track Display (GBVTD) and the velocity fields were extracted. The horizontal velocity field of tornado vortices, simulated in Model WindEEE Dome, was measured using PIV for a wide range of vortex intensity. The substantial mismatch between the averaging time of the full-scale data and the laboratory data which is originated in the very small length scale of the simulation and the low sampling rate of the PIV system, was addressed and corrected using the Durst curve. Once modified, the velocity field of the simulated vortex was compared with that of the full-scale tornado and the swirl ratio of the field tornado as well as the length and velocity scales of the simulation were identified. This practice, for the first time, provided an opportunity to compare the velocity field of tornado vortices obtained through PIV and radar measurements using proper scaling. 1. Introduction Tornadoes in nature are characterized by Fujita Scale (F-Scale) or Enhanced Fujita Scale (EF-Scale), which are forensic parameters based on damage. On the other hand, simulated tornadoes are mainly characterized by the swirl ratio (S) which is the ratio between the far field tangential to radial velocities. This non-dimensional parameter (S) is defined based on a tornado simulator geometry and therefore, it is very challenging to identify the swirl ratio of a real tornado since the inlet and outlet boundaries are not clear in nature. As a result, to simulate tornado-like vortices either numerically or experimentally and, study the damage associated with them, it is necessary to search and establish a relationship between the laboratory swirl ratio and the full-scale Fujita/Enhanced Fujita Scale. This way, scaling parameters may be identified for each simulator (and simulation) and can be used for modeling different types of tornadic winds. Full-scale measurements of tornadic flows using Doppler radars have been limited due to safety issues and uncertainties in forecasting. In recent years, advances with portable Doppler radars and development of mathematical models, such as the Ground-Based Velocity Track Display (GBVTD) [1], have enabled scientists to investigate three-dimensional axisymmetric velocity fields of tornadoes in nature. On the other hand, Particle Image Velocimetry (PIV) measurements of laboratory simulated tornadoes are increasingly available. PIV measurements along with the GBVTD method can be used to fill the current gap in the experimental and numerical investigations of tornado flow field which is the relationship between the simulated and field tornadoes. However, the first step is to recognize limitations of each method and then establish a baseline for relating the two measurement techniques: Doppler radar and PIV. Ultimately, the laboratory data can be compared with the full-scale data in order to identify the velocity and length scale of the simulations. Herein, an exploratory research attempt is made to compare the velocity field of tornadic flows obtained through PIV and Doppler radar measurements. To achieve this, experimental data of tornado-like vortices simulated in Model WindEEE Dome, over a wide range of swirl ratios, are obtained. In addition, a large dataset of GBVTD-retrieved full-scale velocities from tornadoes of various intensities is created. After considering the limits of each measurement method, this complete set of experimental and full-scale data is then implemented for comparison purposes. 2. Experimental data


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The 1/11 scaled model of the WindEEE Dome (MWD) was used to simulate tornado-like vortices and characterize their flow field [2]. WindEEE is a three-dimensional and time dependent wind testing chamber of 25 m inner diameter and 40 m outer diameter. The Model WindEEE Dome was designed, constructed and commissioned in 2010 at Western to validate the conceptual design of WindEEE. By using a system of 100 dynamic fans on the six peripheral walls coupled with 18 larger fans at the ceiling level, MWD can produce any type of wind systems including translating tornadoes and downbursts as well as a variety of time dependent shear flows (see Fig. 1). Tornado-like vortices can be generated in this simulator using top fans as the source of suction and the adjustable periphery vanes at the lower chamber to control the swirl. A 120 mJ/pulse Nd:YAG laser along with a CCD camera with a spatial resolution of 2336 × 1752 pixels were used to perform PIV measurements. The camera was connected to a frame grabber that acquires 8-bit images. The field of view of the camera was set to 23.4 cm by 17.5 cm. A four-channel digital delay generator was used to control the timing of the laser light pulses. For each experimental run, images were captured at a rate of 30 Hz resulting in 15 vector maps per second. A combination of cylindrical and spherical lenses was used to obtain a light sheet with a uniform thickness of 2 mm. The tornado chamber was seeded with Di-Ethyl-Hexyl-Sebacate (C26H50O4) particles, with an average diameter of 1 µm. These particles have the Stokes velocity of 2.5×10-5 m/s which is five orders of magnitude smaller than the mean speed of the simulated tornado flow. Therefore, the seeding particles are sufficiently small to follow the fluid motion accurately and not alter the fluid properties or flow characteristics. The horizontal velocity field (radial-tangential) was measured at the center of the simulator and at 8 different heights. The experimental setup for horizontal plane measurements is illustrated in Fig. 2. The vertical velocity field (axial-radial) was only investigated at the updraft region to calculate the flow rate. The time interval between the two laser pulses was selected based on the mean velocity of the flow. These time intervals varied between 100 µsec and 550 µsec depending on the swirl ratio and the height at which measurements were performed. The adjustments were made to have a peak to noise ratio of 1.5 or higher in all experimental runs.

Fig. 1 Schematic drawing of the Model WindEEE Dome, showing the inner and outer chambers as well as the inflow

and updraft regions

Fig. 2 PIV setup for horizontal plane measurements illustrating the simulator as well as camera, laser unit and optics


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X (m)

Y(m)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.220

0.02

0.04

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0.08

0.1

0.12

0.14

0.16

a)

X (m)

Y(m)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.220

0.02

0.04

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b)

X (m)

Y(m)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.220

0.02

0.04

0.06

0.08

0.1

0.12

0.14

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c)

Fig. 3 Instantaneous horizontal velocity vector maps obtained from PIV measurements at z=3.5 cm for a) S=0.22, b) S=0.57 and c) S=0.96

The captured images were processed using the TSI software to extract vector maps. Cross-correlations were performed over 64 by 64 pixels interrogation windows with 50% overlap. Spurious vectors, which did not exceed 1% of the total vectors in each vector map, were identified and then replaced by interpolated vectors. The maximum estimated error is 7.2% for horizontal velocity measurements. The spatial resolution of PIV measurements is 3.2 mm. This resolution is 1-2 orders of magnitude larger than the Kolmogorov dissipation scale, depending on the swirl ratio. As a result, no attempt was made to resolve the smallest scales of the tornado-like flow. The swirl ratio can be defines as S = r0Γ∞/2Qh where, r0 is the updraft radius, Γ∞=2πrcVtan,max is the


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maximum circulation, Q is the flow rate and h is the inflow height and rc is the core radius. Using the vector maps of the tangential velocity inside the chamber, obtained through PIV measurements, it was concluded that MWD can produce tornado-like vortices with swirl ratios ranging between 0.12 and 1.29. To perform statistical analysis of the flow properties, determination of an appropriate sample size of PIV recordings is essential. The sample size in PIV measurements, with 95% confidence interval, can be calculated based on the equation given by Hamburg [3]: n=(3σx/e)2 where n is the sample size, σx is the standard deviation and e is the maximum allowed error (e= ±0.08 m/s) with 99.7% probability. The azimuthally averaged velocity value at a certain radial position (z/r0=0.35) in the outer region of the vortex flow for S=0.57 was considered to calculate an appropriate sample size. The average of tangential velocity in horizontal plane measurements was 8.74 m/s with the standard deviation of 0.82 m/s. After substituting all the values in the equation, the sample size found to be n=946, i.e. statistical analyses converge for measurement of 946 or higher vector maps. Therefore, 2000 images were acquired for each experimental run, resulting in 1000 vector maps. A sample of measurements is presented in Fig. 3. In this figure, instantaneous velocity fields obtained from the horizontal plane measurement for three values of swirl ratio and 3.5 cm above the ground are displayed. It is observed that as the swirl ratio increases, the vortex core expands. Also, at S=0.96 a two-celled vortex is observed which implies that the vortex break down bubble formed aloft, has already touched the ground and the flow regime is fully turbulent. This conclusion was further investigated and confirmed through flow visualizations and surface static pressure measurements [2]. Fig. 4 shows time and azimuthally averaged tangential velocities (herein after called tangential velocities) variation with radius at various heights and for S=0.57. The maximum tangential velocity and the corresponding radius (i.e. core radius) at each height are used to normalize the velocity and radius, respectively. Results are also compared with the Rankine vortex model. Clear variation in the experimental values with height is observed. Also, the Rankine vortex model shows agreement with only the upper level measurements. These observations can be explained by the increased surface friction at and after the touch-down.

r/rc

Vtan/V

tan,max

0 1 2 30

0.2

0.4

0.6

0.8

1

Z/r0=0.175Z/r0=0.2Z/r0=0.225Z/r0=0.25Z/r0=0.35Z/r0=0.4Z/r0=0.675Z/r0=0.75Rankine

Fig. 4 Radial profiles of the normalized tangential velocity at various heights for S=0.57

3. Full-scale data The GBVTD method was employed to extract axisymmetric three-dimensional structure of the parent vortex, mainly tangential velocity profiles at various heights from single-Doppler radar data of the Spencer, SD 1998 (F4), Stockton, KS 2005 (F1), Clairemont, TX 2005 (F0), Happy, TX 2007 (EF0) and Goshen County (LaGrange), WY 2009 (EF2) tornadoes. Each tornado was studied at various instants of its life cycle. In total, nine volumes of data were analyzed with this mathematical method. The term “volume” refers to one complete radar scan of the tornado from regions very close to the ground to hundreds of meters aloft. As an example, Fig. 5 displays Doppler velocity contour maps of the Happy, TX 2007 tornado. The GBVTD analysis was performed to reconstruct the flow field of this tornado from 0203:20 to 0204:17 UTC. This


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volume consisted of 13 radar sweeps with elevation angle increments ranging from 0.3˚ to 3˚.

Fig. 5 Doppler velocity contours of Happy, TX 2007 tornado from 0203:20 to 0204:17 UTC

R (m)

z(m)

0 200 400 600 8000

200

400

600

800

1000

Vtan (m/s)3836343230282624222018161412

5

Fig. 6 Vertical velocity vectors superimposed on tangential velocity contours for Happy, TX 2007 tornado from

0203:20 to 0204:17 UTC A sample of full-scale data analysis is provided here. Fig. 6 illustrates vertical velocity vectors along with the contour map of tangential velocities for one volume in Happy, TX 2007 tornado, extracted by the GBVTD method. Maximum tangential velocity of 37.9 m/s is observed at regions very close to the ground with corresponding core radius of 160 m. The strong central downdraft aloft is weakening as reaching the ground. The overall vertical flow pattern suggests that the vortex break-down bubble formed aloft is approaching the ground surface. 4. Comparison considerations The experimentally measured tangential velocities reported in here are averaged over azimuthal angle and time. The averaging time of the PIV measurements equals to the number of vector maps (1000) times the duration of acquiring one vector map (2/30Hz) which equals to 66 sec. The length scale of simulating mid-range EF1 to low-end EF3 rated tornadoes in MWD is estimated to be λl=1/1500 [4] and the typical velocity scale of tornado simulations, based on F2 tornado wind speeds, is equal to λv=1/7.7 [5]. These result in a time scale of λt=0.005 which means, averaging time of 66 sec of PIV


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velocity measurements scales up to an averaging time of 13200 sec (3.6 hrs) of full-scale velocity data. This scaled up averaging time is far from reality as tornadoes usually last less than 30 min. Moreover, full-scale velocity data are instantaneous measurements even though it takes approximately 3 sec for a Doppler radar to scan the flow at a given beam angle. Therefore, direct comparison of current PIV measurements with full-scale velocity data is not possible. Two factors attribute to this issue: first, the low sampling rate of the PIV system and second, the small length scale of the simulation. In order to compare the PIV results with the full-scale data, it is necessary to account for the effect of averaging time on velocity values. The Durst curve [6] serves this purpose. This curve relates wind velocities averaged over t sec to wind velocities, from the same storm, averaged over 3600 sec (one hour). The velocity ratio between one second to 3600 sec averaging time determined from the Durst curve (V1/V3600=1.57) can be used to adjust instantaneous wind velocities of full–scale data to equivalent wind velocities averaged over one hour. Note that Durst curve was developed for atmospheric boundary layer flows and there is a need to develop a similar curve for non-synoptic winds. In the meantime, the Durst curve provides an opportunity to compare velocity data from a 30 Hz PIV system to Doppler radar measured wind velocities as the velocity adjustment ratio is 1 for an averaging time of one hour or higher. Future work in the WindEEE Dome facility will benefit from larger simulation scale as well as time resolved PIV measurements. This will alleviate the velocity scaling issues raised herein. 5. Similarity analysis There are various geometric lengths in a simulator such as updraft, core radius, inflow and inner chamber height as well as the core radius (rc) and the height corresponding the maximum tangential wind speed (Zmax). Among these lengths, only the two latter ones are measureable in a real tornado; rc and Zmax. Therefore two length scale ratios can be defined as the ratios between full-scale Doppler radar (index D) and Simulation (index S) data: rc,D/rc,S and Zmax,D/Zmax,S. Radial Reynolds numbers (Rer) that can be achieved in simulators are orders of magnitude smaller than the one estimated for a real tornado. As a result, there is a mismatch in the dynamic scaling. However, previous studies [7-10] have shown that the dynamic similarity can be violated given that the radial Reynolds number is above a critical value. This critical Reynolds number (Rer,c) can be identified for each simulator. For simulations above Rer,c, the flow characteristics, such as the core radius and the transition from a single vortex to multiple vortices, are independent of the radial Reynolds number and are strongly a function of swirl ratio. Since the dynamic similarity is not satisfied in tornado simulations, the velocity scale needs to be determined independent of the radial Reynolds number condition. Tangential, axial and radial velocity components of an actual tornado can be deducted using GBVTD technique. However, as addressed by Nolan [11], radial and axial components calculated by this method are questionable, especially for weaker tornadoes. As a result, the ratio between the overall maximum tangential velocity of a real tornado and that of a simulated one (Vtan,max,D/Vtan,max,S) are used here to determine the velocity length scales for each simulated tornado. The velocity scale was estimated through identifying the overall maximum tangential velocity, Vtan,max = Vtan(rc,max, zmax), of the simulated tornado over various heights for a given swirl ratio and then comparing it with that of the full-scale measurements. Next, the core radius and the height corresponding the overall maximum tangential velocity for the simulated vortex (rc,max,S and zmax,S, respectively) at each swirl ratios were compared to their counterparts in the natural tornado (rc,max,D and zmax,D) which resulted in two length scale ratios. Since the length scale of simulations must be a single value, it is expected that the two length scale ratios converge towards one value at a certain swirl ratio. This is a key condition that, if satisfied, may then be used to relate swirl Ratio to Fujita scale and therefore modeled tornado-like vortices (experimentally or numerically) to full-scale tornadoes. These analyses are explained in detail by Refan and Hangan [4]. 6. Results The scaling approach explained above was applied to the experimental and full-scale data collected. Fig. 7 displays the two length scales variation with swirl ratio for one volume of Happy, TX 2007 tornado from 0203:20 to 0204:17 UTC. It is observed that as the swirl ratio increases, the two length scales demonstrate a convergence behavior over a range of swirl ratios. Based on the GBVTD-retrieved velocity fields, this


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volume of the Happy, TX 2007 tornado is at the touch-down stage. As a result, the length scale associated with S=0.57 was chosen for this event. The velocity scale (λv=1/2.75) and the length scale (λl=1/2627) for volume 4 of Happy, TX 2007 tornado can be used to scale up the experimental tangential velocity profiles and then compare them with the full-scale data. Fig. 8 shows that overall, radial profiles of the tangential velocity obtained through PIV measurements match very well with the full-scale measurements at different heights. The agreement is observed inside and outside of the tornado core region as well as for the core radius and the maximum tangential velocity. This practice was performed for other volumes of data and resulted in a good agreement between simulations full-scale data.

Swirl ratio

LengthScale

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

2000

4000

6000

8000

10000 rc,max,D/rc,max,Szmax,D/zmax,S

Fig. 7 Geometric scaling ratio as a function of swirl ratio for Happy, TX 2007 tornado from 0203:20 to 0204:17 UTC

r (m)

Vtan(m/s)

0 200 400 600 800 10000

5

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z=100mz=105mz=150mz=131mz=200mz=210m

Fig. 8 Comparison between simulated (solid lines) and full-scale (symbols) tangential velocity profiles at various heights for Happy, TX 2007 tornado (from 0203:20 to 0204:17 UTC) after applying the velocity and length scales

6. Conclusions The application of PIV measurements in characterizing the tornado-like flows and their relationship with the full-scale phenomenon was investigated. The very small length scale of the simulation along with the low sampling rate of the PIV system resulted in a significant mismatch between the averaging time of the full-scale data and the scaled up laboratory data. Durst curve was implemented to adjust for this averaging time. The swirl ratio of a certain volume of the Happy, TX 2007 tornado was approximated and the velocity and length scales of the simulation were determined. At the end, the scaled up tangential velocity profiles


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obtained from PIV measurements were compared with the adjusted (using Durst curve) tangential velocity field of the Happy, TX 2007 tornado which resulted in a good agreement. To better address the issue of averaging time mismatch, the next set of experiments will be performed in WindEEE Dome which will result in a geometric scaling 11 times larger than the MWD. In addition, a high-speed PIV system will be used to carry out experiments which allows for lower sampling time. References [1] Lee W C, Jou J D, Chang P L (1999) Tropical cyclone kinematic structure retrieved from single-Doppler radar observations. Part I: interpretation of Doppler velocity patterns and the GBVTD technique. Monthly Weather Review 127:2419-2439. [2] Refan M, Hangan H (2013) Qualitative and quantitative characterization of the tornado-like flow field in a new model scale wind dome. Unpublished results. [3] Hamburg M (1970) Statistical analysis for decision making. Harcourt, Brace and Worl, Incorporated, The University of California. [4] Refan M, Hangan H, Wurman J (2013) Reproducing Tornadoes in Laboratory using Proper Scaling. The 12th Americas Conference on Wind Engineering (12ACWE), Seattle, Washington, USA, June 2013, Nominated for review for possible inclusion in the special issue of the J. of Wind Eng. and Ind. Aerodyn. [5] Haan Jr F L, Sarkar P P, Gallus W A (2008) Design, construction and performance of a large tornado simulator for wind engineering applications. Engineering Structures 30:1146-1159. [6] Durst C S (1960) Wind speed over short periods of time. Meteorological Magazine 89:181-187. [7] Ward N B (1972) The exploration of certain features of tornado dynamics using a laboratory model. J. Atmos. Sci. 29:1194-1204. [8] Jischke M C, Parang M (1974) Properties of simulated tornado-like vortices. J. Atmos. Sci. 31:506-512. [9] Church C R, Snow J T, Baker G L (1979) Characteristics of tornado-like vortices as a function of swirl ratio: a laboratory investigation. J. Atmos. Sci. 36:1155-1776. [10] Davies-Jones R P (1973) The dependence of core radius on swirl ratio in a tornado simulator. J. Atmos. Sci. 30:1427-1430. [11] Nolan D S (2012) On the use of Doppler-radar-derived wind fields to diagnose the secondary circulation of tornadoes. J. Atmos. Sci. 70:1160-1171.

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