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Experimental investigation of tornado-like vortex dynamics with swirl ratio: The mean and turbulent flow fields
J. Wind Eng. Ind. Aerodyn. 98 (2010) 936–944
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Experimental investigation of tornado-like vortex dynamics with swirl ratio: The mean and turbulent flow fields Pooyan Hashemi Tari, Roi Gurka, Horia Hangan n The Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, 1151 Richmond St., London, Ontario N6A 5B9, Canada
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 September 2009 Received in revised form 1 October 2010 Accepted 5 October 2010 Available online 20 October 2010
An experimental simulation of tornado-like vortices is conducted in a small tornado vortex simulator in order to study the effect of swirl ratio on flow characteristics. Particle Image Velocimetry (PIV) method is employed to quantitatively determine the tornado-vortex velocity field for swirl ratios ranging from 0.08 to 1. The radial and tangential components of velocity as well as the core radius of the tornado increase with increase in swirl ratio. The location of the maximum radial and tangential velocities is adjacent to the ground where the tornado vortex interacts with the surface. The values of normal and shear turbulent stresses indicate the existence of a laminar core for small swirl. As expected the shear stresses increase with swirl ratio as the vortex becomes turbulent. The highest turbulent production corresponds to the critical case of vortex touchdown. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Tornado-like vortex Swirl ratio Particle Image Velocimetry (PIV)
1. Introduction Twisdale and Vickery (1992) reported that 52–75% of the extreme annual winds in South-Central United States were registered on thunder days, which may be associated with downburst or tornadic winds. An average of 80 deaths and 1500 injuries (Wind Hazard Reduction coalition) per year accompanied with tornadic winds in the USA prove the importance of the tornado flow investigations. Previous laboratory (e.g. Ward, 1972; Church et al., 1979; Snow, 1982) and numerical studies (e.g. Lewellen, 1962; Davies-Jones, 1973) have shown that the complex flow structure of tornado-like vortices depends primarily on the swirl ratio, i.e. the ratio between the initial tangential and radial velocities of the flow. Swirl ratio is defined as S¼roG/2Qh, where G is the background circulation, ro the characteristic radius usually corresponding to the radius of the updraft region, h the height that usually corresponds to the depth of the inflow layer and Q the volume flow rate per unit axial length. Variation in the swirl ratio results in various developments of the tornado-like vortices. This starts with a thin laminar core for very small swirls, followed by a turbulent vortex breakdown aloft for small swirls, touchdown for moderate swirls and two-celled vortex for high swirls. The other dimensionless parameters governing these laboratory tornado-like vortices are the aspect ratio, a¼ h/ro, representing the geometry of the flow and the Reynolds number, Re ¼Q/2pn. It is expected that the flow characteristics of tornado vortices on smooth surfaces do not strongly depend on
n
Corresponding author. E-mail address: [email protected] (H. Hangan).
0167-6105/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2010.10.001
the Reynolds number above a certain critical value (ReE 105; Church et al., 1979). The full scale measurements of Lee and Wurman (2005) showed that for the F4 Mulhall tornado the computed swirl ratios between 2 and 6 were consistent with the observed multiple vortex radar signatures. Hangan and Kim (2008) also showed that RANS numerical simulations of tornado-like vortices of swirl ratio S ¼2 compare well with the F4 Spencer South Dakota data. Lewellen et al. (2000) argued that for real tornadoes the correlation between swirl and flow patterns is more problematic. He emphasized that even under the same large-scale swirl ratio several physical parameters such as surface roughness, tornado translation speed and near-ground inflow distribution could strongly influence the structure of the central vortex corner flow, in which the vortex core interacts with the ground surface. For practical engineering purposes it is nevertheless important to quantitatively characterize the flow fields associated with tornado-like vortices at various swirl ratios. Laboratory simulations of tornado-like vortices have the advantage of controlled conditions and repeatability. Previously these experiments were conducted in Tornado Vortex Chambers (TVCs; Wan and Chang, 1972; Ward, 1972; Davies-Jones, 1973; Church et al., 1977; Baker and Church, 1979; Church et al., 1979; Rotunno, 1979; Lund and Snow, 1993; Wang et al., 2001; Mishar et al., 2008). These TVCs have the advantage of independently controlling the radial/axial flow rate and the tangential components by means of a fan at the top and swirling device at the bottom. However, because of the swirling device, the optic access to the flow region of interest is impossible. Quantifying dynamic characteristics of a tornado vortex in the surface region would be important from the wind engineering point of view. More recently Sarkar et al. (2005)
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derived an alternate configuration, which allows optical access at the base as well as translation of the entire system. The Doppler radar field measurements of real tornadoes are increasingly available (Wurman and Gill, 2000; Bluestein et al., 2004). Recently, detailed field data has been obtained for the Spencer, South Dakota F4 tornado of May 30, 1998 (Sarkar et al., 2005; Wurman and Alexander, 2005) and for the Mulhall F4 tornado of May 3, 1999 (Lee and Wurman, 2005). Nevertheless some limitations apply to full scale data sets as well: dangerous environment near the surface and near the core region, unpredictable path of a tornado translation. Most importantly, the characteristic of radar waves, not following the curvature of the earth, affects the accuracy of the near-ground measurements. It should also be noticed that the Radar waves are not able to measure the out of plane component (vertical component) of the velocity field directly. In order to quantitatively characterize the effects of swirl ratio on tornado-like vortex we develop a prototype Tornado Vortex Simulator (TVS) similar to the large tornado simulator at the University of Iowa, USA (Haan et al., 2007). We employ the Particle Image Velocimetry (PIV) technique to characterize the flow fields for swirl ratios ranging from 0.08 to 1. Based on simple extensions of the matching procedure used by Hangan and Kim (2008), these swirl ratios would cover real tornado situations spanning from F0 to F2 Fujita scale. Previous laboratory investigations quantified the flow field dynamics of tornado vortices for only a limited number of swirl ratios. The aim of the present work is to quantify both the mean and turbulent flow field for a range of swirl ratios. In addition the turbulent field is investigated as a function of swirl. These turbulent characteristics may play a strong role in the destructive characteristic of the tornado vortex. The results are also compared with a simple analytical model (modified Rankine vortex model) to be used in prediction and risk models. In an accompanying paper we explore the energy re-distribution with swirl ratio following a Proper Orthogonal Decomposition (POD) approach.
2. Experimental set-up 2.1. Tornado Vortex Simulator (TVS) The schematic diagram of the apparatus used to generate the tornado vortex is presented in Fig. 1a. This simulator has a new design compared with traditional ones (Ward, 1972; Snow et al., 1979). Fig. 1b displays the flow direction inside the simulator. Using a return duct in order to induce circulation through the inlet flow (shown in Fig. 1b) allows for optical (laser-based) measurements to be taken in the near-surface region, which is of highest interest for wind engineering applications (Wilson and
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Rotunno, 1986). Moreover, this design has the advantage that it can be integrated as a translating tornado generator in a wind tunnel configuration similar to the large tornado simulator at the University of Iowa, USA (Haan et al., 2007). The TVS includes 18 turning vanes at the top generating the swirl, three co-axial circular cylinders (their geometrical features appear in Fig. 1a), 9 blade axial fan used as the suction source delivering a maximum capability of 300 cm (0.1416 m3/s) flow rate and a plexiglass ground plate (91.5 cm by 91.5 cm) allowing optical access from underneath. The vane angles could be adjusted by using a linkage mechanism and consequently vary the swirl ratio. Based on preliminary tests, the inflow depth was set to 10 cm in order to have minimum effect of the fan on the near-surface region of the vortex flow. Therefore, the aspect ratio was fixed for all experiments presented herein as a¼1.34.
2.2. Velocity measurements using Particle Image Velocimetry The PIV system included a double pulsed Nd:YAG laser operating at 15 Hz, emitting 120 mJ/pulse at a wavelength of 532 nm. The CCD camera had a spatial resolution of 1 K by 1 K pixels with a dynamic range of 8 bit operating at 30 frames per –second, which enabled capture of 15 image pairs resulting in 15 velocity maps per second. Appropriate light sheet forming optics were used in order to create a light sheet with 1 mm thickness. The seeded particles used in the experiments were made of olive oil and generated by a Laskin nozzle with an average diameter of 1 mm. The Stokes velocity of the particles is 10 4 m/s, significantly smaller (four order of magnitudes) compared to the characteristic mean velocity at the tornado simulator. The Stokes velocity of the particles set the time response between the particles motion relative to the flow investigated. Using particles with these properties fulfills the condition that the particles follow adequately the flow field without having any momentum of drift. A total of 1000 two-dimensional vector maps were acquired for each run. The two planes that were investigated were axial–radial (‘‘vertical’’) and radial–tangential (‘‘horizontal’’). Fig. 2a and b shows the schematic diagram of the test set-up for both cases. For each swirl ratio, the time interval between the two laser pulses was adjusted based on the preliminary measurement of the flow rate and accordingly the mean velocity. Characteristic time intervals were between 600 and 1500 ms corresponding to a velocity magnitude of 1.7 and 0.2 m/s, respectively. The field of view for the vertical plane was 26.5 cm by 15.5 cm while for the horizontal plane 10.4 cm by 10.4 cm. TSI software was utilized to perform the image analysis and extract the velocity fields using the cross correlation technique for each interrogation window. The interrogation window was set to be 64 64 pixel with an overlap of 50%.
2r0 =h
Fig. 1. Schematic diagram of (a) the tornado vortex simulator and (b) flow direction inside the simulator.
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Fig. 2. Schematic diagram of the experimental set-up in (a) vertical measurements and (b) horizontal measurements.
The spurious vectors were removed during the post-processing by using statistical filters such as standard median and global outlier filters, which were later replaced by interpolated vectors. The amount of erroneous vectors did not exceed 5% of each vector map. The estimated velocity errors for horizontal and vertical measurements are 1.8% and 2.1%, respectively. The actual size of the interrogation window is 6.5 and 9 mm for the vertical and horizontal planes, respectively. The interrogation window, which defines the PIV resolution, is about 30 times larger compared to the Kolmogorov dissipation scale, which is in the order of 250 mm, ranging from 200 to 350 as a function of swirl ratio. In the present work, there is no attempt to resolve the smallest scales of the flow or to draw any conclusions in respect to the turbulence and its associated mechanisms at the dissipative scales. Turbulent characteristics are presented in the form of rms, Reynolds stress and production, which are the main features of large-scale motion of the flow.
3. Flow field characteristics The velocity maps were used to determine swirl ratios as well as mean velocity profiles, core radius of tornado vortex and Reynolds stresses corresponding to each swirl ratio. Detailed assessments of each parameter are presented in the following sections. 3.1. Swirl ratio The swirl ratio was determined using S ¼roG/2Qh, where G is the circulation magnitude, ro the outer radius of the inner cylinder, which is known as the updraft hole and Q represents the flow rate. Fig. 3a shows the variation in swirl ratio, circulation and Reynolds number versus vane angle. The Reynolds number was calculated based on Re¼ Q/hv, where Q is calculated based on the radial velocity profile at the inlet location where the air comes out of the return duct, h is the inflow height (h¼10 cm) and n the kinematic viscosity of air. As expected the swirl ratio and the related flow circulation increase monotonically and in a similar manner with increasing vane angle. However, the Reynolds number does not vary substantially (less than 15%) with the swirl ratio for vane
S=0.08
S=0.68
S=0.4
S=1.00
Fig. 3. (a) Variation in swirl ratio, circulation and Reynolds number versus vane angle. (b) Flow visualization for various swirl ratios (S ¼ 0.08, 0.4, 0.68 and 1).
angles 151o y o531. At larger vane angles, however, a decrease in flow rate and therefore Reynolds number is observed. It is inferred that for larger vane angles, the swirl ratio and flow rate cannot be controlled separately; in other words they affect each other, which has also been observed in the Iowa tornado simulator (Haan et al., 2007). This trend can be attributed to extra load exerted on the motor of the fan at high swirl and needs to be corrected in future TVS designs. Fig. 3b shows flow visualizations obtained for swirl ratios ranging from S ¼0.08 to S ¼1.00. The flow visualizations were performed using dry ice as the source of smoke and a high resolution, SLR digital camera. All images are snapshots captured at 0.02 s camera speed. For S ¼0.08 a thin laminar tornado-like vortex forms with a reduced stagnation area on ground plate. By imparting more swirl a turbulent vortex breakdown occurs aloft and touches down at approximately S¼ 0.4. For S40.4 (S¼0.68 and 1.00) the tornado vortex becomes turbulent. The outer portion of the vortex having helical waves surrounds the inner portion by a shear zone. This shear zone becomes thinner by increasing the swirl ratio from S ¼0.68 to S¼1.00.
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3.2. Mean flow field 3.2.1. Tangential velocity profiles Fig. 4 presents time and azimuthally averaged tangential velocities versus radius for three different swirl ratios at seven heights above the ground. The calculation of tangential velocity at each radial position was performed by averaging the values at the same radial positions over twelve azimuth angles. All the results are obtained using the velocity measurements from the horizontal plane measurements and normalized by the maximum tangential velocities corresponding to each height at each given swirl ratio. Data corresponding to various heights tend to collapse using this normalization. The collapse improves with increase in swirl and is best toward the core region (r/Ro2), far from the influence of the external cylindrical boundary of the apparatus. These results are also compared to a modified Rankine vortex model shown with lines in Fig. 4 and defined as v¼
2G1 R2 þ r 2
ð1Þ
where GN, R and r are circulation input, core radius of the tornado vortex and radial position, respectively. 3.2.2. Core radii and maximum tangential velocities Fig. 5a displays the core radius (R) of the tornado-like vortex versus height for three swirl ratios: S¼ 0.08, 0.4 and 0.68. Core radii at each height were determined based on the maximum tangential
velocity. It can be observed that the core radius enlarges with increase in swirl ratio as previously observed (e.g. Ward, 1972; Davies-Jones, 1973; Baker and Church, 1979; Church and Snow, 1993). At S ¼0.08, where a low swirl jet occurs, the core radius is small with an average radius of approximately 1.5 cm. At intermediate swirl (S¼0.4), the vortex core radius is almost constant with height ( 2.5 cm) corresponding to a columnar type vortex. With the increase in swirl (S¼0.68) the core radius presents a local maximum and becomes asymptotically constant aloft (average radius of 2.7 cm). This corresponds to a conical vortex pattern near the surface and a columnar vortex aloft. Fig. 5b shows the distribution of maximum tangential velocity with respect to height for the three cases of swirl ratios, normalized by average axial velocity for each swirl.
3.2.3. Radial velocity profiles Fig. 6 presents the time averaged radial velocity profiles normalized by average axial velocity, computed at a region immediately above the inflow depth (z 10 cm), versus nondimensional height at three radial positions for the same three swirl ratios. Results based on both horizontal and vertical plane PIV measurements are presented. The lines show the calculated mean velocities from measurements in vertical planes and the results shown with symbols are obtained from horizontal measurements at seven heights and azimuthally averaged. Overall the velocity
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z/rO=0.07 z/rO=0.14 z/rO=0.21 z/rO=0.28 z/rO=0.41 z/rO=0.66 z/rO=0.94 Rankine
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Fig. 4. Tangential velocity versus radius. For S¼ 0.08, 0.4 and 0.68, velocities are normalized by the maximum tangential velocities at every horizontal plane. The radius is normalized by the core radius, R, corresponding to the maximum velocity in each plane. The results are compared with a Rankine vortex model.
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Fig. 5. (a) Core radius versus height for three swirl ratios (S ¼0.08, 0.4 and 0.68; the core radius of the tornado vortex is the radial position at which maximum tangential velocity occurs). (b) Maximum tangential velocity distribution versus height for three swirl ratios (S¼ 0.08, 0.4 and 0.68).
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Fig. 6. Radial velocity profiles versus height for different swirl ratios and radial positions. Velocities are normalized by the average axial velocity between r ¼0 and r¼ ro (the radius of the inner cylinder). Symbols correspond to vertical plane measurements and lines correspond to horizontal plane measurements.
profiles obtained from the vertical planes are in good agreement with the ones calculated based on the horizontal plane PIV measurements. The discrepancies at S¼ 0.68 arise due to significant out of plane motion in the horizontal plane where axial velocity becomes dominant close to the ground. In the outer region, the inward radial inflow is impelled due to the favorable
radial pressure gradient resulting from significant swirl velocity aloft as well as the decrease in tangential velocity close to the surface because of surface friction. Closer to the core region, the radial velocity decreases and changes to axial velocity. Each radial velocity profile has a maximum value close to the surface. The height at which this is maximum corresponds to the limit between
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the surface flow and the updraft flow regions and is almost constant with varying radii. For S¼ 0.08, the maximum radial velocity happens at z/ro ¼ 0.28. With the increase in swirl, the position of the maximum radial velocity moves closer to the surface due to the reduction in the boundary layer thickness. This height could not be properly captured for S¼0.68. The increase in radial velocity with increase in swirl is attributed to the reduction in radial boundary layer depth for higher swirls as well as the intensified swirl velocity at the core region above the surface. 3.2.4. Axial velocity profiles Mean axial velocity profiles versus non-dimensional height at three radial positions for four cases of swirl ratios are depicted in Fig. 7. The profiles are normalized by the average axial velocity for each swirl ratio. It is observed that for each swirl ratio the elevation of maximum axial velocity is above the position of the maximum radial and tangential velocity for which laminar vortex is in accordance with the results obtained by Baker (1981); however, for high swirls this observation is in contrast with the numerical results of Lewellen et al. (2000). This effect is attributed to the influence of the fan on the upper-region of the vortex flow. According to Fig. 7, axial velocity at the same height decreases with increase in radial distance for swirl ratios, S¼0.08 and 0.4. This is expected as the axial flux feeds from the radial one. The trend has also been observed by previous investigations (e.g. Church and Snow, 1993; Baker, 1981). For the third case (S ¼0.68) the highest axial velocity still occurs near the centre line of the tornado-like
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vortex up to a certain height. However, for z/ro ¼0.55 the axial velocity near the core gradually decreases and becomes smaller compared to the outer values. The adverse pressure gradient that develops may explain the early drop in the axial velocity aloft. This might indicate the existence of a two-celled structure above this height penetrating toward the surface with excess swirl. It is also interesting to note that for this case (S ¼0.68), levels of high axial and tangential velocities (Fig. 5b) correlate to the minimum core radii (Fig. 5a). This is indicative of vortex stretch occurring at the interface between the near-surface conical vortex and the aloft columnar vortex. For the last case (S ¼1.00) axial velocity at the centre line has the lowest magnitude most probably due to the two-celled structure of the tornado vortex. The axial velocity has the maximum magnitude and lowest radial gradient inside the annulus region located in the region of maximum tangential velocity. The down flow close to the tornado axis, observed in previous investigations (Lewellen et al., 2000; Church et al., 1979; Church and Snow, 1993), does not appear in present measurements and this is attributed to the close presence of the fan at the top of the simulator. This influence is aimed to be eliminated for future versions of the TVS. 3.3. Turbulent characteristics In order to characterize the turbulent aspects of the flow, in particular, the coupling between swirl ratio (which controls the
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Fig. 7. Axial velocity profiles versus height for four cases of swirl ratios at three radial positions (r/ro ¼ 0.12, 0.6 and 0.84). Velocities are normalized by the average axial velocity.
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amount of energy that is distributed within the flow) and turbulent effects, we present and analyze the turbulent characteristics of the flow for five different swirl ratios: 0.08, 0.15, 0.25, 0.4 and 0.68. The profiles are plotted as a function of height above the ground at two chosen radial locations r/ro ¼0.18 and 0.375. First radial location resides inside the core region while the second one is in the outer region of the tornado vortex for all swirl ratios studied herein (see also Fig. 5a). The turbulent quantities analyzed here are root mean square (rms) of the axial fluctuating velocity (w0 rms), rms of the radial fluctuating velocity (u0 rms), rms of the tangential fluctuating velocity (v0 rms), Reynolds Stress (/u0 w0 S) and the production term in the turbulent kinetic energy balance equation. The results are normalized based on the maximum value of axial velocity for every swirl ratio. For each set of data, the maximum value was extracted over all the heights and radii. The choice of an average value for normalization might be misleading, since axial velocity changes significantly along its axial direction. Fig. 8 presents the root mean square of the turbulent component of axial velocity at two radial locations 0.18ro and 0.375ro. It is clearly shown that with increase in swirl ratio, the turbulent vortex descends toward the surface as the rms values increase toward the base. For both the inner (r/ro ¼ 0.18) and outer (r/ro ¼0.375) regions, the axial stresses are small and almost constant with height near the surface for swirl ratios o0.4. Wilson and Rotunno (1986) showed that at low swirl (S¼ 0.28 in their case), the viscid core is relatively thin. There is a sudden jump in axial stresses for S¼0.4. This indicates a touchdown of the turbulent vortex formed aloft. For S¼0.68, the axial stresses increase further and present a maximum at z/ro ¼0.625 and z/ro ¼0.875 in inner and outer regions, respectively. This is attributed to the effect of the two-celled structure of the tornado vortex. The high axial stresses at these heights are most probably related to the increase in the mean axial velocity component observed before (Fig. 7). Far from the core region the location of the peak values moves up from 0.625ro to 0.875ro due to the attenuation of axial velocity at the out-core region. Fig. 9 represents the radial stresses at the core. Similar to the axial stresses the amplitude and variation with height are less
Fig. 8. RMS of axial velocity at (a) r ¼0.18ro and (b) r¼ 0.375ro.
Fig. 9. RMS of radial velocity at r ¼0.18ro.
Fig. 10. RMS of tangential velocity at r ¼0.18ro.
significant for So0.4. As the swirl increases the maximum radial stresses occur close to the surface. This is a result of (i) vortex strengthening and (ii) touching down. Fig. 10 presents the tangential stresses inside the core region. Since the tangential velocity component can only be determined from horizontal PIV plane measurements, there are fewer points (7 horizontal planes only) available on these profiles compared to the other two components resulting in increased scatter of the data points. Therefore, in order to emphasize the trends of these profiles as function of swirl ratio and its relation to the other two velocity component, curve fitting to the data points is also shown (as solid lines). Similar to the radial and axial stresses, the tangential stress values increase by increasing the swirl ratio. As the swirl ratio increases, the vertical position of the maximum tangential stress descends toward the surface since the vortex touches down. For So0.4 the stresses are smaller and the maximum stress occurs at z/ ro ¼0.94. For S ¼0.08, the appearance of maximum is due to the formation of the tornado vortex aloft. Similar trend in vertical variation of rms values can be seen for S¼0.16 where a thin laminar vortex is represented. For S¼0.25, the rms values increase gradually with height. This can be attributed to the presence of the two-cell structure of the tornado vortex aloft. For S 40.4, the variation in the tangential stresses with height is very similar to the variation in the maximum tangential velocity with height (see Fig. 5b). The highest values of all normal stresses occur at the limit of the surface layer and at the core of the viscous region where highest values of velocity gradients are observed (Lewellen et al., 2000). The comparison of normal stress values shows that the main part of the turbulent energy is generated by radial normal straining. Fig. 11 presents the variation in Reynolds shear stress (/u0 w0 S) at the same two radial locations. The shear stresses exhibit a distinct pattern for So0.4 compared to large swirls. For S¼ 0.08 and 0.15, the Reynolds stresses are almost zero, which indicates a
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Reynolds stress at r=0.375r0
Fig. 12. Turbulent kinetic energy production term at (a) r ¼0.18ro and (b) r ¼0.375ro.
Fig. 11. Reynolds stress at (a) r ¼0.18ro and (b) r¼ 0.375ro.
laminar core similar to the one proposed by Snow (1982). For S ¼0.25 the shear stresses are almost zero in the outer region (Fig. 11)b, while at the core, they increase gradually with height similar to the variation in the tangential stresses (Fig. 11a). The Reynolds stresses present a quasi-symmetrical behavior across the core for S¼0.4, while for S¼0.68, it seems that there is no symmetry. It can be assumed that the vortex at S¼0.68 is not symmetric anymore and exhibits a pattern similar to the one suggested by Church et al. (1979) as shown in Fig. 4d where the tornado core is turbulent. For both cases (0.4 and 0.68), the Reynolds stress features a similar behavior as in jets, where at the entrainment region between the jet and the surrounding fluid, a zone of relatively high shear emerges at the interface between the surface layer. The maximum values at the core are two times larger compared to the outer region. For the outer region, the surface shear stresses increase and eventually dominate over the aloft interface stresses. These wall friction effects increase with swirl ratio. It can also be observed that for S¼0.4 and 0.68, shear stress values become negative after a certain height in both core and outer region. A plausible answer for this change of sign can be the presence of downward direction in fluctuating part of the axial components due to the two-cell structure of the tornado at high swirls. The location of this change is closer to the ground in the core region where the viscous core plays a dominant role compared to the outer region. The Reynolds shear stresses based on tangential and radial fluctuating velocities (/u0 v0 S) have also been computed. They show similar behavior to other turbulence characteristics with respect to the swirl ratio and therefore are not presented here for the sake of brevity. An important parameter that characterizes the amount of turbulence generated in a given flow is the production term in the turbulent kinetic energy equation (/ui0 uj0 SSij). A PIV system enables the direct measurement of this term in a plane using four terms out of nine, /u0 u0 4Sxx, /w0 w0 SSzz and 2/u0 w0 SSxz.
Assuming that the flow field is axisymetric, the measured turbulent production captures most of the energy generated in the flow. Fig. 12 shows that for So0.4, the turbulent production is small both in the core and the outer region. This is in formal agreement with the stress behavior being low for low swirls. Therefore for low swirls, the conceptual model proposed by Snow et al. (1979) is valid with a laminar organized vortex flow at the core. The fact that turbulence production shows larger values aloft is associated with both the presence of an aloft vortex and the effect of the fan rotation. A remarkable result is obtained for S¼0.4, where the turbulent vortex touches down and the production approaches maximum values. The turbulent production term has higher values in the core region in comparison with the outer region. It appears that at relative high swirl ratios, most of the energy is created in the corner region flow where the vortex interacts with the ground. A similar behavior is obtained for S ¼0.68, but the production values are smaller. In accordance with Lewellen et al. (2000), it can be concluded that the swirl ratio plays a dominant role in the dynamics of the flow and there exists a critical swirl ratio above which the tornado flow interacts with the surface, creating a region where the flow produces energy and momentum in an order of magnitude higher compared to low swirl flows. This may lead to the conclusion that close to the ground, the turbulent rather than the mean flow field is responsible for the damage associated to tornado events.
4. Concluding Remarks The sensitivity of tornado-like vortex flow to swirl ratio is experimentally studied using a small tornado vortex simulator. The investigation employs the Particle Image Velocimetry (PIV) technique to characterize the mean and turbulent flow components.
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It is found that the radial and tangential mean velocity components increase with increase in swirl. The location of the maximum velocities is close to the surface and descends toward the surface with increase in swirl. The vortex core widens with swirl with small laminar cores for So0.4 and larger turbulent cores for S40.4. The turbulent flow characteristics show that both normal stresses and shear stresses increase with increase in swirl, noticeably close to the surface. The radial normal stresses are higher compared to axial, tangential and shear stresses, that is the turbulent energy is mainly generated by radial straining. The location of the maximum turbulent production is close to the ground inside the core region of the tornado vortex. Most importantly, the maximum turbulent kinetic energy is produced at S¼0.4, which corresponds to the tornado vortex touchdown. This leads to the possibility that turbulent energy rather than mean velocity relates to the intense destruction that tornadoes produce at the ground level. References Baker, G.L., 1981. Boundary layers in a laminar vortex flows. PhD Thesis, 143 pp., Purdue University, West Lafayette, IN, USA. Baker, G.L., Church, C.R., 1979. Measurements of core radii and peak velocities in modeled atmospheric vortices. J. Atmos. Sci. 36, 2413–2424. Bluestein, H.B., Weiss, C.C., Pazmany, A.L., 2004. The vertical structure of a tornado near Happy, Texas on 5 May 2002: high-resolution mobile W-band Doppler radar observations. Mon. Weather Rev. 132 (10), 2325–2337. Church, C.R., Snow, J.T., 1993. Laboratory models of tornadoes. Geophys. Monogr. 79, 284–295. Church, C.R., Snow, J.T., Baker, G.L., Agee, E.M., 1979. Characteristics of tornado-like vortices as a function of swirl ratio: a laboratory investigation. J. Atmos. Sci. 36, 1755–1766. Church, C.R., Snow, J.T., Agee, E.M., 1977. Tornado vortex simulation at Purdue University. Bull. Am. Meteorol. Soc. 58, 900–908. Davies-Jones, R.P., 1973. The dependence of core radius on swirl ratio in a tornado simulator. J. Atmos. Sci 30, 1427–1430. Haan, F.L., Sarkar, P.P., Gallus, W.A., 2007. Design, construction and performance of a large tornado simulator for wind engineering applications. Eng. Struct. J. Earthquake Wind Ocean Eng. 30, 1146–1159.
Hangan, H., Kim, J.-D., 2008. Swirl ratio effects on tornado vortices in relation to Fujita scale. J. Wind Struct. 11, 291–302. Lee, W.C., Wurman, J., 2005. The diagnosed structure of the Mulhall tornado. J. Atmos. Sci. 62, 2373–2393. Lewellen, W.S., 1962. A solution of three dimensional vortex flows with strong circulation. J. Fluid Mech. 14, 420–432. Lewellen, D.C., Lewellen, W.S., Xia., J., 2000. The influence of a local swirl ratio on tornado intensification near the surface. J. Atmos. Sci. 57, 527–544. Lund., D.E., Snow, J.T., 1993. Laser Doppler velocimetry measurements in tornado like vortices. In: Church, C., Burgess, D., Doswell., C., Daxies-Jones., R. (Eds.), The Tornado: Its Structure, Dynamics, Prediction, and Hazards. Geophysical Monograph Series, vol. 79. American Geophysics Union Press, pp. 297–306. Mishar, A.R., James, D.J., Letchford, C.W., 2008. Physical simulation of a single-celled tornado-like vortex, part A. Flow field characterization. J. Wind Eng. Ind. Aerodyn. 96, 1243–1257. Rotunno, R., 1979. A study in tornado-like vortex dynamics. J. Atmos. Sci. 36, 140–155. Sarkar, P., F. Haan, W. Gallus Jr.K. le, 2005. Velocity measurements in a laboratory tornado simulator and their comparison with numerical and full scale data. In: Proceedings of the 37th Joint Meeting Panel on Wind and Seismic Effects, Tsukuba, Japan, May 2005. Snow, J.T., Church, C.R., Barnhart, B.J., 1979. An investigation of the surface pressure fields beneath simulated tornado cyclones. J. Atmos. Sci. 37, 1013–1026. Snow, J.T., 1982. A review of recent advances in tornado vortex dynamics. Rev. Geophys. 20, 953–964. Twisdale, L.A., Vickery, P.1., 1992. Research on thunderstorm wind design parameters. J. Wind Eng. Ind. Aerodyn. 41 (44), 545–556. Wan, C.A., Chang, C.C., 1972. Measurement of the velocity field in a simulated tornado-like vortex using three-dimensional velocity probe. J. Atmos. Sci. 29, 116–127. Wang Fl., James D., Letchford C., Peterson R., Snow J., 2001. Development of a prototype tornado simulator for the assessment of fluid structure interaction. In: Proceedings of the First Americas Conference on Wind Engineering, Clemson, SC. Ward, N.B., 1972. The exploration of certain features of tornado dynamics using a laboratory model. J. Atmos. Sci 29, 1194–1204. Wilson, T., Rotunno, R., 1986. A numerical simulation of a laminar end-wall vortex and boundary layer. Phys. Fluids 24, 3993–4005. Wind Hazard Coalition, 01/31/2006 /http://www.windhazards.orgS. Wurman, J., Gill, S., 2000. Fine scale radar observations of the Dimmitt, Texas (2 June 1995), tornado. AMS Monthly Weather Review 2000 128, 2135–2164. Wurman, J., Alexander, C.R., 2005. The 30 May 1998 Spencer, South Dakota, storm, part II. Comparison of observed damage and radar-derived winds in the tornadoes. AMS Mon. Weather Rev. 2005 (133), 97–118.
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Experimental investigation of tornado-like vortex dynamics with swirl ratio: The mean and turbulent flow fields Pooyan Hashemi Tari, Roi Gurka, Horia Hangan n The Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, 1151 Richmond St., London, Ontario N6A 5B9, Canada
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 September 2009 Received in revised form 1 October 2010 Accepted 5 October 2010 Available online 20 October 2010
An experimental simulation of tornado-like vortices is conducted in a small tornado vortex simulator in order to study the effect of swirl ratio on flow characteristics. Particle Image Velocimetry (PIV) method is employed to quantitatively determine the tornado-vortex velocity field for swirl ratios ranging from 0.08 to 1. The radial and tangential components of velocity as well as the core radius of the tornado increase with increase in swirl ratio. The location of the maximum radial and tangential velocities is adjacent to the ground where the tornado vortex interacts with the surface. The values of normal and shear turbulent stresses indicate the existence of a laminar core for small swirl. As expected the shear stresses increase with swirl ratio as the vortex becomes turbulent. The highest turbulent production corresponds to the critical case of vortex touchdown. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Tornado-like vortex Swirl ratio Particle Image Velocimetry (PIV)
1. Introduction Twisdale and Vickery (1992) reported that 52–75% of the extreme annual winds in South-Central United States were registered on thunder days, which may be associated with downburst or tornadic winds. An average of 80 deaths and 1500 injuries (Wind Hazard Reduction coalition) per year accompanied with tornadic winds in the USA prove the importance of the tornado flow investigations. Previous laboratory (e.g. Ward, 1972; Church et al., 1979; Snow, 1982) and numerical studies (e.g. Lewellen, 1962; Davies-Jones, 1973) have shown that the complex flow structure of tornado-like vortices depends primarily on the swirl ratio, i.e. the ratio between the initial tangential and radial velocities of the flow. Swirl ratio is defined as S¼roG/2Qh, where G is the background circulation, ro the characteristic radius usually corresponding to the radius of the updraft region, h the height that usually corresponds to the depth of the inflow layer and Q the volume flow rate per unit axial length. Variation in the swirl ratio results in various developments of the tornado-like vortices. This starts with a thin laminar core for very small swirls, followed by a turbulent vortex breakdown aloft for small swirls, touchdown for moderate swirls and two-celled vortex for high swirls. The other dimensionless parameters governing these laboratory tornado-like vortices are the aspect ratio, a¼ h/ro, representing the geometry of the flow and the Reynolds number, Re ¼Q/2pn. It is expected that the flow characteristics of tornado vortices on smooth surfaces do not strongly depend on
n
Corresponding author. E-mail address: [email protected] (H. Hangan).
0167-6105/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2010.10.001
the Reynolds number above a certain critical value (ReE 105; Church et al., 1979). The full scale measurements of Lee and Wurman (2005) showed that for the F4 Mulhall tornado the computed swirl ratios between 2 and 6 were consistent with the observed multiple vortex radar signatures. Hangan and Kim (2008) also showed that RANS numerical simulations of tornado-like vortices of swirl ratio S ¼2 compare well with the F4 Spencer South Dakota data. Lewellen et al. (2000) argued that for real tornadoes the correlation between swirl and flow patterns is more problematic. He emphasized that even under the same large-scale swirl ratio several physical parameters such as surface roughness, tornado translation speed and near-ground inflow distribution could strongly influence the structure of the central vortex corner flow, in which the vortex core interacts with the ground surface. For practical engineering purposes it is nevertheless important to quantitatively characterize the flow fields associated with tornado-like vortices at various swirl ratios. Laboratory simulations of tornado-like vortices have the advantage of controlled conditions and repeatability. Previously these experiments were conducted in Tornado Vortex Chambers (TVCs; Wan and Chang, 1972; Ward, 1972; Davies-Jones, 1973; Church et al., 1977; Baker and Church, 1979; Church et al., 1979; Rotunno, 1979; Lund and Snow, 1993; Wang et al., 2001; Mishar et al., 2008). These TVCs have the advantage of independently controlling the radial/axial flow rate and the tangential components by means of a fan at the top and swirling device at the bottom. However, because of the swirling device, the optic access to the flow region of interest is impossible. Quantifying dynamic characteristics of a tornado vortex in the surface region would be important from the wind engineering point of view. More recently Sarkar et al. (2005)
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derived an alternate configuration, which allows optical access at the base as well as translation of the entire system. The Doppler radar field measurements of real tornadoes are increasingly available (Wurman and Gill, 2000; Bluestein et al., 2004). Recently, detailed field data has been obtained for the Spencer, South Dakota F4 tornado of May 30, 1998 (Sarkar et al., 2005; Wurman and Alexander, 2005) and for the Mulhall F4 tornado of May 3, 1999 (Lee and Wurman, 2005). Nevertheless some limitations apply to full scale data sets as well: dangerous environment near the surface and near the core region, unpredictable path of a tornado translation. Most importantly, the characteristic of radar waves, not following the curvature of the earth, affects the accuracy of the near-ground measurements. It should also be noticed that the Radar waves are not able to measure the out of plane component (vertical component) of the velocity field directly. In order to quantitatively characterize the effects of swirl ratio on tornado-like vortex we develop a prototype Tornado Vortex Simulator (TVS) similar to the large tornado simulator at the University of Iowa, USA (Haan et al., 2007). We employ the Particle Image Velocimetry (PIV) technique to characterize the flow fields for swirl ratios ranging from 0.08 to 1. Based on simple extensions of the matching procedure used by Hangan and Kim (2008), these swirl ratios would cover real tornado situations spanning from F0 to F2 Fujita scale. Previous laboratory investigations quantified the flow field dynamics of tornado vortices for only a limited number of swirl ratios. The aim of the present work is to quantify both the mean and turbulent flow field for a range of swirl ratios. In addition the turbulent field is investigated as a function of swirl. These turbulent characteristics may play a strong role in the destructive characteristic of the tornado vortex. The results are also compared with a simple analytical model (modified Rankine vortex model) to be used in prediction and risk models. In an accompanying paper we explore the energy re-distribution with swirl ratio following a Proper Orthogonal Decomposition (POD) approach.
2. Experimental set-up 2.1. Tornado Vortex Simulator (TVS) The schematic diagram of the apparatus used to generate the tornado vortex is presented in Fig. 1a. This simulator has a new design compared with traditional ones (Ward, 1972; Snow et al., 1979). Fig. 1b displays the flow direction inside the simulator. Using a return duct in order to induce circulation through the inlet flow (shown in Fig. 1b) allows for optical (laser-based) measurements to be taken in the near-surface region, which is of highest interest for wind engineering applications (Wilson and
937
Rotunno, 1986). Moreover, this design has the advantage that it can be integrated as a translating tornado generator in a wind tunnel configuration similar to the large tornado simulator at the University of Iowa, USA (Haan et al., 2007). The TVS includes 18 turning vanes at the top generating the swirl, three co-axial circular cylinders (their geometrical features appear in Fig. 1a), 9 blade axial fan used as the suction source delivering a maximum capability of 300 cm (0.1416 m3/s) flow rate and a plexiglass ground plate (91.5 cm by 91.5 cm) allowing optical access from underneath. The vane angles could be adjusted by using a linkage mechanism and consequently vary the swirl ratio. Based on preliminary tests, the inflow depth was set to 10 cm in order to have minimum effect of the fan on the near-surface region of the vortex flow. Therefore, the aspect ratio was fixed for all experiments presented herein as a¼1.34.
2.2. Velocity measurements using Particle Image Velocimetry The PIV system included a double pulsed Nd:YAG laser operating at 15 Hz, emitting 120 mJ/pulse at a wavelength of 532 nm. The CCD camera had a spatial resolution of 1 K by 1 K pixels with a dynamic range of 8 bit operating at 30 frames per –second, which enabled capture of 15 image pairs resulting in 15 velocity maps per second. Appropriate light sheet forming optics were used in order to create a light sheet with 1 mm thickness. The seeded particles used in the experiments were made of olive oil and generated by a Laskin nozzle with an average diameter of 1 mm. The Stokes velocity of the particles is 10 4 m/s, significantly smaller (four order of magnitudes) compared to the characteristic mean velocity at the tornado simulator. The Stokes velocity of the particles set the time response between the particles motion relative to the flow investigated. Using particles with these properties fulfills the condition that the particles follow adequately the flow field without having any momentum of drift. A total of 1000 two-dimensional vector maps were acquired for each run. The two planes that were investigated were axial–radial (‘‘vertical’’) and radial–tangential (‘‘horizontal’’). Fig. 2a and b shows the schematic diagram of the test set-up for both cases. For each swirl ratio, the time interval between the two laser pulses was adjusted based on the preliminary measurement of the flow rate and accordingly the mean velocity. Characteristic time intervals were between 600 and 1500 ms corresponding to a velocity magnitude of 1.7 and 0.2 m/s, respectively. The field of view for the vertical plane was 26.5 cm by 15.5 cm while for the horizontal plane 10.4 cm by 10.4 cm. TSI software was utilized to perform the image analysis and extract the velocity fields using the cross correlation technique for each interrogation window. The interrogation window was set to be 64 64 pixel with an overlap of 50%.
2r0 =h
Fig. 1. Schematic diagram of (a) the tornado vortex simulator and (b) flow direction inside the simulator.
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0.5
5
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4
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0.2 0.1 0 20
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3
2
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1
0
0
4
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Re x 10
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60
Fig. 2. Schematic diagram of the experimental set-up in (a) vertical measurements and (b) horizontal measurements.
The spurious vectors were removed during the post-processing by using statistical filters such as standard median and global outlier filters, which were later replaced by interpolated vectors. The amount of erroneous vectors did not exceed 5% of each vector map. The estimated velocity errors for horizontal and vertical measurements are 1.8% and 2.1%, respectively. The actual size of the interrogation window is 6.5 and 9 mm for the vertical and horizontal planes, respectively. The interrogation window, which defines the PIV resolution, is about 30 times larger compared to the Kolmogorov dissipation scale, which is in the order of 250 mm, ranging from 200 to 350 as a function of swirl ratio. In the present work, there is no attempt to resolve the smallest scales of the flow or to draw any conclusions in respect to the turbulence and its associated mechanisms at the dissipative scales. Turbulent characteristics are presented in the form of rms, Reynolds stress and production, which are the main features of large-scale motion of the flow.
3. Flow field characteristics The velocity maps were used to determine swirl ratios as well as mean velocity profiles, core radius of tornado vortex and Reynolds stresses corresponding to each swirl ratio. Detailed assessments of each parameter are presented in the following sections. 3.1. Swirl ratio The swirl ratio was determined using S ¼roG/2Qh, where G is the circulation magnitude, ro the outer radius of the inner cylinder, which is known as the updraft hole and Q represents the flow rate. Fig. 3a shows the variation in swirl ratio, circulation and Reynolds number versus vane angle. The Reynolds number was calculated based on Re¼ Q/hv, where Q is calculated based on the radial velocity profile at the inlet location where the air comes out of the return duct, h is the inflow height (h¼10 cm) and n the kinematic viscosity of air. As expected the swirl ratio and the related flow circulation increase monotonically and in a similar manner with increasing vane angle. However, the Reynolds number does not vary substantially (less than 15%) with the swirl ratio for vane
S=0.08
S=0.68
S=0.4
S=1.00
Fig. 3. (a) Variation in swirl ratio, circulation and Reynolds number versus vane angle. (b) Flow visualization for various swirl ratios (S ¼ 0.08, 0.4, 0.68 and 1).
angles 151o y o531. At larger vane angles, however, a decrease in flow rate and therefore Reynolds number is observed. It is inferred that for larger vane angles, the swirl ratio and flow rate cannot be controlled separately; in other words they affect each other, which has also been observed in the Iowa tornado simulator (Haan et al., 2007). This trend can be attributed to extra load exerted on the motor of the fan at high swirl and needs to be corrected in future TVS designs. Fig. 3b shows flow visualizations obtained for swirl ratios ranging from S ¼0.08 to S ¼1.00. The flow visualizations were performed using dry ice as the source of smoke and a high resolution, SLR digital camera. All images are snapshots captured at 0.02 s camera speed. For S ¼0.08 a thin laminar tornado-like vortex forms with a reduced stagnation area on ground plate. By imparting more swirl a turbulent vortex breakdown occurs aloft and touches down at approximately S¼ 0.4. For S40.4 (S¼0.68 and 1.00) the tornado vortex becomes turbulent. The outer portion of the vortex having helical waves surrounds the inner portion by a shear zone. This shear zone becomes thinner by increasing the swirl ratio from S ¼0.68 to S¼1.00.
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3.2. Mean flow field 3.2.1. Tangential velocity profiles Fig. 4 presents time and azimuthally averaged tangential velocities versus radius for three different swirl ratios at seven heights above the ground. The calculation of tangential velocity at each radial position was performed by averaging the values at the same radial positions over twelve azimuth angles. All the results are obtained using the velocity measurements from the horizontal plane measurements and normalized by the maximum tangential velocities corresponding to each height at each given swirl ratio. Data corresponding to various heights tend to collapse using this normalization. The collapse improves with increase in swirl and is best toward the core region (r/Ro2), far from the influence of the external cylindrical boundary of the apparatus. These results are also compared to a modified Rankine vortex model shown with lines in Fig. 4 and defined as v¼
2G1 R2 þ r 2
ð1Þ
where GN, R and r are circulation input, core radius of the tornado vortex and radial position, respectively. 3.2.2. Core radii and maximum tangential velocities Fig. 5a displays the core radius (R) of the tornado-like vortex versus height for three swirl ratios: S¼ 0.08, 0.4 and 0.68. Core radii at each height were determined based on the maximum tangential
velocity. It can be observed that the core radius enlarges with increase in swirl ratio as previously observed (e.g. Ward, 1972; Davies-Jones, 1973; Baker and Church, 1979; Church and Snow, 1993). At S ¼0.08, where a low swirl jet occurs, the core radius is small with an average radius of approximately 1.5 cm. At intermediate swirl (S¼0.4), the vortex core radius is almost constant with height ( 2.5 cm) corresponding to a columnar type vortex. With the increase in swirl (S¼0.68) the core radius presents a local maximum and becomes asymptotically constant aloft (average radius of 2.7 cm). This corresponds to a conical vortex pattern near the surface and a columnar vortex aloft. Fig. 5b shows the distribution of maximum tangential velocity with respect to height for the three cases of swirl ratios, normalized by average axial velocity for each swirl.
3.2.3. Radial velocity profiles Fig. 6 presents the time averaged radial velocity profiles normalized by average axial velocity, computed at a region immediately above the inflow depth (z 10 cm), versus nondimensional height at three radial positions for the same three swirl ratios. Results based on both horizontal and vertical plane PIV measurements are presented. The lines show the calculated mean velocities from measurements in vertical planes and the results shown with symbols are obtained from horizontal measurements at seven heights and azimuthally averaged. Overall the velocity
1.1
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939
z/rO=0.07 z/rO=0.14 z/rO=0.21 z/rO=0.28 z/rO=0.41 z/rO=0.66 z/rO=0.94 Rankine
0.6 0.5
z/rO=0.07 z/rO=0.14 z/rO=0.21 z/rO=0.28 z/rO=0.41 z/rO=0.66 z/rO=0.94 Rankine
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0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 r/R S=0.08
0
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z/rO=0.07 z/rO=0.14 z/rO=0.21 z/rO=0.28 z/rO=0.41 z/rO=0.66 z/rO=0.94 Rankine
0.4 0.3 0.2 0.1 0 0
0.5
1
1.5 2 r/R S=0.68
2.5
3
Fig. 4. Tangential velocity versus radius. For S¼ 0.08, 0.4 and 0.68, velocities are normalized by the maximum tangential velocities at every horizontal plane. The radius is normalized by the core radius, R, corresponding to the maximum velocity in each plane. The results are compared with a Rankine vortex model.
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1
1
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0.8
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940
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0.3 0.35 R/rO
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0
1
2
3
4 5 vmax/wO
6
7
8
9
Fig. 5. (a) Core radius versus height for three swirl ratios (S ¼0.08, 0.4 and 0.68; the core radius of the tornado vortex is the radial position at which maximum tangential velocity occurs). (b) Maximum tangential velocity distribution versus height for three swirl ratios (S¼ 0.08, 0.4 and 0.68).
1
r/rO=0.12 r/rO=0.6 r/rO=0.84 r/rO=0.12 r/rO=0.6 r/rO=0.84
1
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S=0.08
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Fig. 6. Radial velocity profiles versus height for different swirl ratios and radial positions. Velocities are normalized by the average axial velocity between r ¼0 and r¼ ro (the radius of the inner cylinder). Symbols correspond to vertical plane measurements and lines correspond to horizontal plane measurements.
profiles obtained from the vertical planes are in good agreement with the ones calculated based on the horizontal plane PIV measurements. The discrepancies at S¼ 0.68 arise due to significant out of plane motion in the horizontal plane where axial velocity becomes dominant close to the ground. In the outer region, the inward radial inflow is impelled due to the favorable
radial pressure gradient resulting from significant swirl velocity aloft as well as the decrease in tangential velocity close to the surface because of surface friction. Closer to the core region, the radial velocity decreases and changes to axial velocity. Each radial velocity profile has a maximum value close to the surface. The height at which this is maximum corresponds to the limit between
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the surface flow and the updraft flow regions and is almost constant with varying radii. For S¼ 0.08, the maximum radial velocity happens at z/ro ¼ 0.28. With the increase in swirl, the position of the maximum radial velocity moves closer to the surface due to the reduction in the boundary layer thickness. This height could not be properly captured for S¼0.68. The increase in radial velocity with increase in swirl is attributed to the reduction in radial boundary layer depth for higher swirls as well as the intensified swirl velocity at the core region above the surface. 3.2.4. Axial velocity profiles Mean axial velocity profiles versus non-dimensional height at three radial positions for four cases of swirl ratios are depicted in Fig. 7. The profiles are normalized by the average axial velocity for each swirl ratio. It is observed that for each swirl ratio the elevation of maximum axial velocity is above the position of the maximum radial and tangential velocity for which laminar vortex is in accordance with the results obtained by Baker (1981); however, for high swirls this observation is in contrast with the numerical results of Lewellen et al. (2000). This effect is attributed to the influence of the fan on the upper-region of the vortex flow. According to Fig. 7, axial velocity at the same height decreases with increase in radial distance for swirl ratios, S¼0.08 and 0.4. This is expected as the axial flux feeds from the radial one. The trend has also been observed by previous investigations (e.g. Church and Snow, 1993; Baker, 1981). For the third case (S ¼0.68) the highest axial velocity still occurs near the centre line of the tornado-like
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vortex up to a certain height. However, for z/ro ¼0.55 the axial velocity near the core gradually decreases and becomes smaller compared to the outer values. The adverse pressure gradient that develops may explain the early drop in the axial velocity aloft. This might indicate the existence of a two-celled structure above this height penetrating toward the surface with excess swirl. It is also interesting to note that for this case (S ¼0.68), levels of high axial and tangential velocities (Fig. 5b) correlate to the minimum core radii (Fig. 5a). This is indicative of vortex stretch occurring at the interface between the near-surface conical vortex and the aloft columnar vortex. For the last case (S ¼1.00) axial velocity at the centre line has the lowest magnitude most probably due to the two-celled structure of the tornado vortex. The axial velocity has the maximum magnitude and lowest radial gradient inside the annulus region located in the region of maximum tangential velocity. The down flow close to the tornado axis, observed in previous investigations (Lewellen et al., 2000; Church et al., 1979; Church and Snow, 1993), does not appear in present measurements and this is attributed to the close presence of the fan at the top of the simulator. This influence is aimed to be eliminated for future versions of the TVS. 3.3. Turbulent characteristics In order to characterize the turbulent aspects of the flow, in particular, the coupling between swirl ratio (which controls the
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Fig. 7. Axial velocity profiles versus height for four cases of swirl ratios at three radial positions (r/ro ¼ 0.12, 0.6 and 0.84). Velocities are normalized by the average axial velocity.
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amount of energy that is distributed within the flow) and turbulent effects, we present and analyze the turbulent characteristics of the flow for five different swirl ratios: 0.08, 0.15, 0.25, 0.4 and 0.68. The profiles are plotted as a function of height above the ground at two chosen radial locations r/ro ¼0.18 and 0.375. First radial location resides inside the core region while the second one is in the outer region of the tornado vortex for all swirl ratios studied herein (see also Fig. 5a). The turbulent quantities analyzed here are root mean square (rms) of the axial fluctuating velocity (w0 rms), rms of the radial fluctuating velocity (u0 rms), rms of the tangential fluctuating velocity (v0 rms), Reynolds Stress (/u0 w0 S) and the production term in the turbulent kinetic energy balance equation. The results are normalized based on the maximum value of axial velocity for every swirl ratio. For each set of data, the maximum value was extracted over all the heights and radii. The choice of an average value for normalization might be misleading, since axial velocity changes significantly along its axial direction. Fig. 8 presents the root mean square of the turbulent component of axial velocity at two radial locations 0.18ro and 0.375ro. It is clearly shown that with increase in swirl ratio, the turbulent vortex descends toward the surface as the rms values increase toward the base. For both the inner (r/ro ¼ 0.18) and outer (r/ro ¼0.375) regions, the axial stresses are small and almost constant with height near the surface for swirl ratios o0.4. Wilson and Rotunno (1986) showed that at low swirl (S¼ 0.28 in their case), the viscid core is relatively thin. There is a sudden jump in axial stresses for S¼0.4. This indicates a touchdown of the turbulent vortex formed aloft. For S¼0.68, the axial stresses increase further and present a maximum at z/ro ¼0.625 and z/ro ¼0.875 in inner and outer regions, respectively. This is attributed to the effect of the two-celled structure of the tornado vortex. The high axial stresses at these heights are most probably related to the increase in the mean axial velocity component observed before (Fig. 7). Far from the core region the location of the peak values moves up from 0.625ro to 0.875ro due to the attenuation of axial velocity at the out-core region. Fig. 9 represents the radial stresses at the core. Similar to the axial stresses the amplitude and variation with height are less
Fig. 8. RMS of axial velocity at (a) r ¼0.18ro and (b) r¼ 0.375ro.
Fig. 9. RMS of radial velocity at r ¼0.18ro.
Fig. 10. RMS of tangential velocity at r ¼0.18ro.
significant for So0.4. As the swirl increases the maximum radial stresses occur close to the surface. This is a result of (i) vortex strengthening and (ii) touching down. Fig. 10 presents the tangential stresses inside the core region. Since the tangential velocity component can only be determined from horizontal PIV plane measurements, there are fewer points (7 horizontal planes only) available on these profiles compared to the other two components resulting in increased scatter of the data points. Therefore, in order to emphasize the trends of these profiles as function of swirl ratio and its relation to the other two velocity component, curve fitting to the data points is also shown (as solid lines). Similar to the radial and axial stresses, the tangential stress values increase by increasing the swirl ratio. As the swirl ratio increases, the vertical position of the maximum tangential stress descends toward the surface since the vortex touches down. For So0.4 the stresses are smaller and the maximum stress occurs at z/ ro ¼0.94. For S ¼0.08, the appearance of maximum is due to the formation of the tornado vortex aloft. Similar trend in vertical variation of rms values can be seen for S¼0.16 where a thin laminar vortex is represented. For S¼0.25, the rms values increase gradually with height. This can be attributed to the presence of the two-cell structure of the tornado vortex aloft. For S 40.4, the variation in the tangential stresses with height is very similar to the variation in the maximum tangential velocity with height (see Fig. 5b). The highest values of all normal stresses occur at the limit of the surface layer and at the core of the viscous region where highest values of velocity gradients are observed (Lewellen et al., 2000). The comparison of normal stress values shows that the main part of the turbulent energy is generated by radial normal straining. Fig. 11 presents the variation in Reynolds shear stress (/u0 w0 S) at the same two radial locations. The shear stresses exhibit a distinct pattern for So0.4 compared to large swirls. For S¼ 0.08 and 0.15, the Reynolds stresses are almost zero, which indicates a
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Fig. 12. Turbulent kinetic energy production term at (a) r ¼0.18ro and (b) r ¼0.375ro.
Fig. 11. Reynolds stress at (a) r ¼0.18ro and (b) r¼ 0.375ro.
laminar core similar to the one proposed by Snow (1982). For S ¼0.25 the shear stresses are almost zero in the outer region (Fig. 11)b, while at the core, they increase gradually with height similar to the variation in the tangential stresses (Fig. 11a). The Reynolds stresses present a quasi-symmetrical behavior across the core for S¼0.4, while for S¼0.68, it seems that there is no symmetry. It can be assumed that the vortex at S¼0.68 is not symmetric anymore and exhibits a pattern similar to the one suggested by Church et al. (1979) as shown in Fig. 4d where the tornado core is turbulent. For both cases (0.4 and 0.68), the Reynolds stress features a similar behavior as in jets, where at the entrainment region between the jet and the surrounding fluid, a zone of relatively high shear emerges at the interface between the surface layer. The maximum values at the core are two times larger compared to the outer region. For the outer region, the surface shear stresses increase and eventually dominate over the aloft interface stresses. These wall friction effects increase with swirl ratio. It can also be observed that for S¼0.4 and 0.68, shear stress values become negative after a certain height in both core and outer region. A plausible answer for this change of sign can be the presence of downward direction in fluctuating part of the axial components due to the two-cell structure of the tornado at high swirls. The location of this change is closer to the ground in the core region where the viscous core plays a dominant role compared to the outer region. The Reynolds shear stresses based on tangential and radial fluctuating velocities (/u0 v0 S) have also been computed. They show similar behavior to other turbulence characteristics with respect to the swirl ratio and therefore are not presented here for the sake of brevity. An important parameter that characterizes the amount of turbulence generated in a given flow is the production term in the turbulent kinetic energy equation (/ui0 uj0 SSij). A PIV system enables the direct measurement of this term in a plane using four terms out of nine, /u0 u0 4Sxx, /w0 w0 SSzz and 2/u0 w0 SSxz.
Assuming that the flow field is axisymetric, the measured turbulent production captures most of the energy generated in the flow. Fig. 12 shows that for So0.4, the turbulent production is small both in the core and the outer region. This is in formal agreement with the stress behavior being low for low swirls. Therefore for low swirls, the conceptual model proposed by Snow et al. (1979) is valid with a laminar organized vortex flow at the core. The fact that turbulence production shows larger values aloft is associated with both the presence of an aloft vortex and the effect of the fan rotation. A remarkable result is obtained for S¼0.4, where the turbulent vortex touches down and the production approaches maximum values. The turbulent production term has higher values in the core region in comparison with the outer region. It appears that at relative high swirl ratios, most of the energy is created in the corner region flow where the vortex interacts with the ground. A similar behavior is obtained for S ¼0.68, but the production values are smaller. In accordance with Lewellen et al. (2000), it can be concluded that the swirl ratio plays a dominant role in the dynamics of the flow and there exists a critical swirl ratio above which the tornado flow interacts with the surface, creating a region where the flow produces energy and momentum in an order of magnitude higher compared to low swirl flows. This may lead to the conclusion that close to the ground, the turbulent rather than the mean flow field is responsible for the damage associated to tornado events.
4. Concluding Remarks The sensitivity of tornado-like vortex flow to swirl ratio is experimentally studied using a small tornado vortex simulator. The investigation employs the Particle Image Velocimetry (PIV) technique to characterize the mean and turbulent flow components.
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It is found that the radial and tangential mean velocity components increase with increase in swirl. The location of the maximum velocities is close to the surface and descends toward the surface with increase in swirl. The vortex core widens with swirl with small laminar cores for So0.4 and larger turbulent cores for S40.4. The turbulent flow characteristics show that both normal stresses and shear stresses increase with increase in swirl, noticeably close to the surface. The radial normal stresses are higher compared to axial, tangential and shear stresses, that is the turbulent energy is mainly generated by radial straining. The location of the maximum turbulent production is close to the ground inside the core region of the tornado vortex. Most importantly, the maximum turbulent kinetic energy is produced at S¼0.4, which corresponds to the tornado vortex touchdown. This leads to the possibility that turbulent energy rather than mean velocity relates to the intense destruction that tornadoes produce at the ground level. References Baker, G.L., 1981. Boundary layers in a laminar vortex flows. PhD Thesis, 143 pp., Purdue University, West Lafayette, IN, USA. Baker, G.L., Church, C.R., 1979. Measurements of core radii and peak velocities in modeled atmospheric vortices. J. Atmos. Sci. 36, 2413–2424. Bluestein, H.B., Weiss, C.C., Pazmany, A.L., 2004. The vertical structure of a tornado near Happy, Texas on 5 May 2002: high-resolution mobile W-band Doppler radar observations. Mon. Weather Rev. 132 (10), 2325–2337. Church, C.R., Snow, J.T., 1993. Laboratory models of tornadoes. Geophys. Monogr. 79, 284–295. Church, C.R., Snow, J.T., Baker, G.L., Agee, E.M., 1979. Characteristics of tornado-like vortices as a function of swirl ratio: a laboratory investigation. J. Atmos. Sci. 36, 1755–1766. Church, C.R., Snow, J.T., Agee, E.M., 1977. Tornado vortex simulation at Purdue University. Bull. Am. Meteorol. Soc. 58, 900–908. Davies-Jones, R.P., 1973. The dependence of core radius on swirl ratio in a tornado simulator. J. Atmos. Sci 30, 1427–1430. Haan, F.L., Sarkar, P.P., Gallus, W.A., 2007. Design, construction and performance of a large tornado simulator for wind engineering applications. Eng. Struct. J. Earthquake Wind Ocean Eng. 30, 1146–1159.
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