Numerical simulation of laboratory tornado simulator that can produce translating tornado-like wind flow

Journal of Wind Engineering & Industrial Aerodynamics 190 (2019) 200–217

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Numerical simulation of laboratory tornado simulator that can produce translating tornado-like wind flow Fangping Yuan a, Guirong Yan b, *, Ryan Honerkamp b, Kakkattukuzhy M. Isaac a, Ming Zhao c, Xiaoyong Mao d a

Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA School of Engineering and Construction Management, Western Sydney University, Penrith, NSW, 751, Australia d School of Civil Engineering, Suzhou University of Science and Technology, Suzhou, Jiangsu Province, 215000, China b c

A R T I C L E I N F O

A B S T R A C T

Keywords: Translating tornado Tornado simulator Wind effects CFD simulations

Tornado simulators have been built to produce tornado-like vortices to investigate the characteristics of tornadic winds and their effects on civil structures. However, conducting testing in tornado simulators is expensive and time-consuming, and has limitations due to the small size of laboratory tornado simulators and the low wind speed that can be generated. To address these problems, this study is to develop an approach to numerically simulate a type of laboratory tornado simulator that can generate translating tornadoes. Different from previous numerical simulations of laboratory tornado simulators, in this study, all the major mechanical components in the tornado simulator are modeled, including the guide vanes, fan, and honeycomb section. Using the developed numerical tornado simulator, both stationary and translating tornadic wind fields will be produced. For each type of wind field, the characteristics of both the overall and near-ground wind flow will be extracted and investigated. The obtained wind flow will be compared with the data measured in the laboratory tornado simulator and the in situ radar-measured data. The numerical model developed in this study can be used to conduct more “testing” on the computer; and the simulating strategies verified here can be applied to simulate a larger-scale tornado simulator.

1. Introduction The United States has on average more tornadoes annually, over 1000, than any other countries on Earth (see Fig.1). Furthermore, statistically the variance of the number of tornadoes per tornadic event from 1954 to 2014 increased at a rate of 2.89% annually (Moore, 2017). Tornadoes have resulted in incredible amounts of property damage and significant numbers of fatalities each year (see Figs. 2 and 3). Annually, tornadoes cause 90 fatalities and 1500 injuries (Simmons et al., 2013). In 2011 only, $9.8 billion of estimated damage was generated in Tuscaloosa, Birmingham, and Huntsville, Alabama as well as Chattanooga, Tennessee as a result of tornado outbreaks occurring in major metropolitan areas (Smith and Matthews, 2015). To mitigate this wind hazard, it is imperative to conduct in-depth research on tornado dynamics and wind effects of tornadoes on civil engineering structures. To design civil structures that can survive tornadoes, in situ

measurements of tornadic winds around civil structures (near the ground) are valuable to obtain the actual wind effect. However, it is very challenging to obtain the in situ measurements, especially near-ground measurements, due to the fact that they are violent, small and shortlived with an average warning lead time of only 10–15 min and unpredictable tracks (Savory et al., 2001; Simmons and Sutter, 2005; http://www.spc.noaa.gov/faq/tornado/ef-scale.html). Therefore, researchers started to study the tornadic wind fields and wind effects on structures in laboratory tornado simulators. Apart from the historically used Ward-type tornado simulator (Chang, 1966; Ward, 1972) and its modified versions (Church et al., 1979; Leslie, 1977; Jischke and Light, 1983; Diamond and Wilkins, 1984), the recently developed versions of tornado simulator in North America are located at Iowa State University (ISU) (Haan et al., 2008), Texas Tech University (Mishra et al., 2008a) and Western University (WU) (Refan and Horia, 2016) as well as Tongji University (Cao et al., 2018). Through testing on

* Corresponding author. E-mail addresses: [email protected] (F. Yuan), [email protected] (G. Yan), [email protected] (R. Honerkamp), [email protected] (K.M. Isaac), [email protected]. au (M. Zhao), [email protected] (X. Mao). https://doi.org/10.1016/j.jweia.2019.05.001 Received 22 July 2018; Received in revised form 21 April 2019; Accepted 3 May 2019 Available online 18 May 2019 0167-6105/© 2019 Elsevier Ltd. All rights reserved.

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Journal of Wind Engineering & Industrial Aerodynamics 190 (2019) 200–217

these laboratory tornado simulators, swirling wind flow was characterized and wind effects of tornadoes on low-rise buildings were investigated (Hu et al., 2011; Haan et al., 2009; Chang, 1971; Bienkiewicz and Dudhia, 1993; Fouts et al., 2003; Mishra et al., 2008b; Sengupta et al., 2008; Natarajan and Hangan, 2012; Rajasekharan et al., 2013; Sabareesh et al., 2013). However, utilizing laboratory tornado simulators for the purpose of studying tornadic events through both experiments and numerical simulations has the limitation of not being able to replicate the full intensity and scale of naturally occurring tornadoes in terms of wind speed and impact. In addition to this, the physical tornado simulator can be expensive to construct and require much effort dedicated to maintenance and adjustment between tests. On the contrary, numerical simulations hold the advantages of flexibility for varying inflow and boundary conditions, surface roughness, and even air density and temperature; in addition, full intensity and scale of real-world tornadoes can be replicated by numerical simulation if the simulations are conducted at full scale. If the physical laboratory tornado simulator is numerically simulated using CFD simulations and verified using the data measured in a physical tornado simulator, tornadoes with different flow structures and tornadic wind effects on different civil structures can be investigated through numerical simulation in the future, eliminating the need for repeated testing in physical simulators. Therefore, this study is to develop an approach to numerically simulate a type of laboratory tornado simulator. By applying the proposed approach the real-world tornado events and their wind effects on civil structures can be potentially reproduced, and the high cost associated with repeated lab experiments and adjustments can be potentially avoided. The related research published in the literature is reviewed below. Kuai et al. modeled the tornado simulator of ISU using FLUENT and investigated the flow of air through the tornado simulator (Kuai et al., 2008). A sheared inflow boundary condition that introduces the swirling motion to the computational domain was applied to the inflow entering the bottom of the inflow cylinder, and a pressure outlet boundary condition on the top surface of the outflow cylinder was also generated. Although they built a basic shape of the physical tornado simulator, this shape did not include any sloping in the upper region where the guide vanes apply rotation to the air. It is noted that the description of their CFD simulation did not include any information regarding replicating the guide vanes, fan, or honeycomb section (Kuai et al., 2008). By using their numerical model, they simulated the flow field of full-scale tornadoes to verify the ability of their CFD models to capture the flow characteristics (Kuai et al., 2008). They found that their CFD simulation results were within an acceptable range in comparison to the physical tornado simulator, but they found several differences compared to natural tornadoes and concluded to further study the effect of floor surface roughness (Kuai et al., 2008). Besides the contribution on tornadic wind characterization using the laboratory tornado simulator, Cao et al. developed a CFD model of their laboratory tornado simulator, which followed the mechanism of generating swirling wind flow that ISU implemented (Cao et al., 2018). Instead of modelling the entire facility, they only included the lower part of the duct in the model; and they eliminated the 18 guide vanes at the top and the fan in the middle in the numerical model. The top of this partial duct included in the model was set as a velocity inlet; and the exterior wall of the computational domain between the bottom of the duct and the ground is set as a pressure outlet and the top of the inner cylinder is set as another pressure outlet. To generate the rotating downdraft flow at the periphery, they applied tangential velocity and radial velocity at the velocity inlet, to mimic the effect of turning vanes. Although they did not model most of the major mechanical components, such as the guide vanes, the fan and the upper part of the exterior wall of the duct, they did apply the porous media model to model the honeycomb section. They simplified the physical model in their numerical simulation and validated their numerical model by comparing their findings to those of Haan et al. (2008) and full-scale tornados, specifically the Mulhall and Spencer

tornados. However, the simplification will not follow the physical self-circulation of the flow in the tornado simulator and does not allow for full visualization of the mechanism of tornadic wind field generation. In addition, it may be challenging to determine the relative magnitudes of tangential velocity and radial velocity input at the velocity inlet in order to simulate a specific tornado. Ishihara et al. modeled a Ward-type laboratory tornado simulator and investigated the flow of air through this simulator (Ishihara et al., 2011). Large Eddy Simulation was applied to model turbulence. They simulated the honeycomb section and guide vanes, but they did not simulate the fan directly. In their study, the effect of the fan was modeled by applying a velocity outlet boundary condition at the outlet on the top of the simulator (Ishihara et al., 2011). Through this numerical model, they replicated numerically the wind flow patterns that the physical tornado simulator generated (Ishihara et al., 2011). In (Liu and Ishihara, 2016), Liu and Ishihara adopted a similar but simpler numerical model to simulate the Ward-type tornado simulator. In that model, they applied an empirical velocity profile at the inflow boundary and thus got rid of the complicated guided vane section. The reference velocity and reference length in the velocity profile were obtained by comparing the velocity profile with the model with the guided vane section. By doing so, they investigated the relationship between the flow structures and the swirl ratios, also the influence of the surface roughness and translating speed. Natarajan applied CFD, utilizing FLUENT, to simulate three different types of laboratory tornado simulators, which are a Ward-type Tornado Vortex Chamber, the WindEEE (Wind Engineering, Energy, and Environment) device at WU, and the Atmospheric Vortex Engine, a device created by Louis Michaud to generate tornado-like vortices for the purpose of power production by harnessing the wind field (Natarajan, 2011). In his simulations of the Ward-type Tornado Vortex Chamber, he did not model the mechanical components of the physical simulator other than the walls and input and output regions, which were needed to specify the velocity and direction of the flow. His numerical simulation results were close to those measured during the real-world tornados (Natarajan, 2011), but were not able to completely capture the characteristics of the flow generated in the laboratory tornado simulator, which may be caused by the fact that the effect of mechanical components was not properly included in the model. Although numerical models have been developed for some physical laboratory tornado simulators, the previous numerical simulation was mainly focused on the convergence region with equivalent effect, instead of modelling all the mechanical components in the tornado simulator. In this study, to simulate the laboratory tornado simulator more accurately, an approach to simulate each mechanical component will be proposed. Considering that the tornado simulator at ISU can produce tornado-like vortices that can translate, the tornado simulator numerically simulated here will follow the same mechanism of generating tornadic winds as the tornado simulator at ISU. In this type of tornado simulator, the airflow is sucked up by the fan and passes through the guide vanes to add an angular momentum to the flow, and then is up-drafted back into the honeycomb section to be straightened before entering the fan inlet. That is, the airflow self-circulates inside the chamber. To achieve a better performance than the tornado simulator at ISU, the shape of the chambers/duct is modified into a curved shape from a multi-sided shape to evaluate the simulator to be built at the Missouri University of Science and Technology (MST). The remaining of the paper is organized as follows. First, the dimensions and properties of the tornado simulator to be numerically simulated are introduced. Then, how to model each mechanical component in the tornado simulator using ANSYS FLUENT is discussed. Finally, the wind flow generated in the numerical tornado simulator is investigated. The generated overall wind flow and near-ground wind field are presented and compared with published test results and in situ radar-measured data. This study is expected to achieve in-depth insights into this type of tornado simulator, to provide a guidance on an optimal design of a tornado simulator to better simulate tornado-like wind flow in the laboratory, and to provide a guidance on parameter setup (e.g., fan 201

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airflow with the swirling motion is up-drafted back into the inner cylinder, where it is straightened by the honeycomb section before entering the fan inlet. The flow circulation in a radial-axial plane is illustrated in Fig. 4(B). The swirling wind flow is generated under the inner cylinder. In this tornado simulator, the use of the curved chambers/duct is expected to reduce energy loss due to the abrupt change of the air-flow direction, which happens to the multi-sided chambers in the tornado simulator of ISU; the guide vanes that follow the contour of the curved chambers/duct are expected to mitigate flow separation and decrease turbulence generated in the duct as the flow changes direction. Through the above modifications, it is expected to achieve better overall efficiency and higher potential circulation velocities than the tornado simulator at ISU, as proved in a previous study by the present authors (Yuan et al., 2016). The chamber can maneuver freely along a straight path using a bridge crane to simulate the translation of a tornado, as shown in Fig. 5. The floor plane can be raised or lowered to achieve variations of floor height and observe changes associated with different tornado conditions.

speed and guide vane angles) for experimental testing. 2. Tornado simualtor to Be simulated The tornado simulator at ISU has successfully generated tornado-like vortices to simulate the tornadic wind field (Haan et al., 2008), which is a great contribution to the research community of wind engineering and hazard mitigation. The tornado simulator to be numerically simulated in this study follows the same mechanism to generate tornado-like vortices as the one at ISU. The diameter of the tornado simulator considered here is smaller than the one at ISU. Different from the tornado simulator at ISU, the chambers/duct in this tornado simulator have a curved shape, and the guide vanes follow the contour of the curved duct (see Fig. 4). The schematic diagram and the corresponding solids model of this tornado simulator are presented in Fig. 4(A) and (B), respectively. As shown in Fig. 4, this tornado simulator consists of the outer and inner chambers (constituting a duct), 37 guide vanes, and the inner cylinder with a fan and honeycomb section. The dimensions of each component are listed in Table 1. The mechanism to generate the swirling wind flow is described as follows. The fan is positioned to suck the air from the bottom to the top region of the simulator, providing a driving force to establish the flow circulation. After the flow passes through the guide vanes, which have a non-zero angle with respect to the radius of the simulator, an angular momentum is added to the airflow. Then the

3. Modelling of mechancial components and Cfd simulation setup 3.1. CAD model and mesh A 3D CAD model is developed in the solids modelling software package, SOLIDWORKS. The 3D CAD model is then exported into the meshing software package, POINTWISE, to generate a high-quality mesh. A hybrid mesh strategy is adopted with tetrahedral cells in the chamber and hexahedral cells in the “near-ground domain” (the computational domain between the bottom of the chambers and the ground plane). The total number of cells of this mesh is 5.5–6.5 million, depending on the guide vanes angle around their turning axis. Because the geometric dimension of each component is widespread, from 1.6
103 m (vane thickness) to 3.76 m (diameter of the outer chamber), the mesh has a transition from very fine in the vane region to coarser away from it. A zoomed-in view of the vane region from the top of the simulator is shown in Fig. 6. In addition, since the primary objective of the simulation is to capture the wind flow near the ground, the mesh is finer near the ground plane than at higher elevations. To be specific, the inflating technique is used to generate the mesh along the height of the “near-ground domain” (dg ¼ 0.315 m), and the thickness of the first layer is 0.01 m, with the growth rate of 1.2. In particular, along the axial direction in the ‘nearground domain’, under the honeycomb section, a small circle with finer unstructured mesh is created and extruded to the honeycomb section through the inflating technique.

Fig. 1. A tornado.

3.2. Modelling the fan using the fan boundary condition The fan used in this tornado simulator generates a flow rate of 86,000 cubic feet per minute (Q  40.587 m3/s) when the guide vane angle is zero with a static pressure increase of 1.5 inches of water (ΔP373Pa) at RPM ¼ 1770. To develop a comprehensive numerical study of a fan, it requires an accurate 3D CAD model of the fan itself, including the details of the blade, hub, inlet and outlet boundary walls, a well-designed mesh which matches the topology of the fan components, and the consideration of relative motion between the fan and the surrounding fluid flow, which is beyond the scope of this work. In this study, the fan is modeled using the FLUENT fan boundary condition (Fan Boundary Condi). Herein the fan is treated as an interface, across which a static pressure jump is applied. The user can either apply a constant static pressure jump or a polynomial function of static pressure jump in terms of normal flow velocity to simulate the fan effect. According to the fan performance datasheet provided by the fan manufacturer, the pressure jump at RPM ¼ 1770 is 373 Pa. Therefore, in the present simulations, a pressure jump ΔP ¼ 373 Pa is applied. In this simulation, the volume flow rate across the fan is obtained as Q ¼ 8.92 m3/s if the guide vanes angle around their turning axis is set as 30 .

Fig. 2. Damage due to EF-5 Joplin Tornado in 2011.

Fig. 3. Collapse due to Vilonia Tornado in 2011. 202

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Fig. 4. Tornado simulator with a curved chamber. (A) Schematic diagram; and (B) 3D CAD model. Table 1 Dimensions of the CAD model. The text should go to the very left, parallel to the following lines. Height of the chamber, Hs

the text should go to the veyr left91.13 in./2.315 m

Diameter of the outer chamber, Do Diameter of the inner chamber, Di Diameter of the inner cylinder, Dc Height of the inner cylinder, Hi Thickness of the honeycomb section, th Distance between the chamber bottom and ground plane, dg Length of the vane, Lv Height of the vane, Hv Distance between the bottom of inner cylinder and the bottom of chamber, Ht Guide vane angle (from radial direction)

148.16 in./3.763 m 131.10 in./3.330 m 49.25 in./1.251 m 51.90 in./1.318 m 13.90 in./0.353 m 12.40 in./0.315 m 29.42 in./0.747 m 8.03 in./0.204 m 30.63 in./0.778 m

Fig. 5. The overview of the entire tornado simulator facility.

30 /50

detailed CFD simulation of a honeycomb section requires an actual honeycomb CAD model and a fine mesh for the interior of the honeycomb cells, which will be very expensive in terms of computational time and cost (Vinayak et al., 2011). Therefore, in this study, the honeycomb section is modeled using the porous media model in FLUENT (Porous Media manua).

3.3. Modelling the honeycomb section using the porous media model As the air flows back into the inner cylinder to complete a loop of aircirculation, in order to straighten the airflow, a honeycomb section is placed at the bottom of the inner cylinder, as shown in Fig. 4. The

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0.353 m in this study, which can be found in Table 1; C is a coefficient that takes an approximate value of 0.98 if the Reynolds number is greater than 400 and th/Dh > 1.6, where Dh is the diameter of the hole. For the tornado simulator simulated here, th/Dh ¼ 23 > 1.6, and Rer8.89
104, which is much larger than 400. Therefore, the coefficient C ¼ 0.98 is applied here. Here, it is assumed that the porosity of the honeycomb section is 0.9, thenAp =Af ¼ 1/0.9. By substituting the values of Ap =Af , t and C into Eq. (3), the inertial resistant factor in the axial direction is obtained as C2 ¼ 0.7. Previous studies (Vinayak et al., 2011) and our preliminary study have shown that with the values of C2 in the radial and azimuthal directions 10 times larger than that of C2 in the axial direction, the straightening effect is sufficient. Therefore, in this simulation, the inertial resistant factors used in the radial and azimuthal directions are C2 ¼ 70 (100 times of C2 in the axial direction) in order to ensure optimal straightening. Physically, high values of C2 in the radial and azimuthal directions mean low flow velocities in those two directions, which enhances the straightening effect in the axial direction. From Eq. (3), a high C2 can be achieved by reducing the honeycomb cell size, Af. Therefore, in the laboratory, the straightening effect can be improved by reducing the honeycomb cell size. However, reducing the honeycomb cell size may decrease the axial velocity. Therefore, an optimum balance must be maintained for maximum efficiency.

Fig. 6. Zoomed-in view of mesh in the vanes region.

In FLUENT, the porous medium is modeled by adding a momentum source term to the standard Navier-Stokes equations. The momentum source term is composed of two parts: the viscous loss term (Darcy's law) and inertial loss term. It can be written as 3 X

Si ¼ 

Dij μvj þ

3 X

j¼1

! Cij ρjvjvj

(1)

j¼1

where Si is the source term for ith (x, y or z) momentum equation, νj is the velocity component in jth direction, jνj is the magnitude of the velocity, ρ is the flow density, μ is the dynamic viscosity, and D and C are prescribed matrices. The first and second terms on the right hand side of Eq. (1) denote the viscous loss and the inertial loss, respectively. For a simple homogeneous porous medium, D and C become diagonal matrices, and then the momentum source term can be simplified as  Si ¼ 

μ 1 v þ C2 ρjvjvi 2 α i

3.4. Modelling the translation of a tornado In previous research, to numerically simulate the translation of a tornado, a moving wall boundary condition is applied to the ground while fixing the tornado simulator to create a relative motion (Natarajan and Hangan, 2012; Liu and Ishihara, 2016; Phuc et al., 2012). Unlike the previous research, this study induces the chamber to move by applying the sliding mesh technique in FLUENT (Sliding mesh manua) while leaving the ground plane unmoved, which is the same as the practical situation. Fig. 7 presents the mesh created to simulate the translation of a tornado. In the numerical model, a box with a thickness of 0.315 m is placed below the chamber to simulate the “near-ground domain” beneath the chamber with the bottom of this box representing the ground boundary. The length and width of the box are 7.1 m and 4.17 m, respectively. The chamber translates at a speed of VT on the top surface of the box in the positive x direction. Since different shapes of cells are used for the chamber and the “nearground domain” (tetrahedral cells in the chamber and hexahedral cells in the “near-ground domain”), a mesh interface is created between the top surface of the box and the bottom surface of the chamber. This mesh interface will be turned on when using the sliding mesh technique to achieve the translating motion of the tornadic wind flow in FLUENT.

 (2)

where vi is the flow velocity component, ρ is the flow density, μ is the dynamic viscosity, α is the permeability and C2 is the inertial resistant factor (namely pressure loss coefficient). Since the Reynolds number is the ratio of inertial forces to viscous forces, the viscous loss effect can be neglected if the Reynolds number is large. In this study, the definition of Radial Reynolds number, Rer ¼ Q’/ 2πν (Church et al., 1979), is adopted. Here, Q’ is the volumetric flow rate per unit axial length, which is calculated as Q/h ¼ 8.16 m2/s in this study (where Q ¼ 8.92 m3/s is the volumetric flow rate, and h ¼ 1.093 m is the distance from the ground plane to the honeycomb section), and ν is the kinetic viscosity of the air, which is 1.46
105 m2/s. Therefore, the Radial Reynolds number of this system is approximately Rer ¼ 8.89
104, which is sufficiently large to assume that the flow is highly turbulent in the system and the viscous loss effect inside the honeycomb section can be neglected. Experiments at Purdue University show that the critical swirl ratio that controls the structure of the flow is a decreasing function of radial Reynolds number and has asymptotic limit when radial Reynolds number is very large (Rer > 2
105) (Church et al., 1979). For our moderate high radial Reynolds number, we could expect our critical swirl ratio (from single vortex to double-celled vortices) is around S ¼ 0.5 or higher (Church et al., 1979). Our numerical results in the later sections also approve that. The inertial resistant factor C2 in the stream wise direction is derived from the empirical model for turbulent flow through a perforated plate (Smith and Winkle, 1958), C2 ¼

  2 1 Ap Af  1 C2 t

3.5. Boundary and initial conditions The tornado simulator is designed as a flow generator with the air circulating inside, driven by the fan. Therefore, no inflow and outflow boundary conditions are applied to this numerical model. The guide

(3)

where Ap is the area of the honeycomb section (assuming that the honeycomb cells are circular orifices); Af is the free area, which is the total area of the holes; t is the thickness of the honeycomb section and it is Fig. 7. Mesh used in the simulation when translating motion is present. 204

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vanes, inner cylinder, outer and inner chambers (duct walls), and ground plane are all setup as no-slip boundary conditions (no-slip walls), which indicates zero velocity at these walls. Since the tornado-like vortex is only generated between the bottom of the honeycomb section and the ground plane, with the outer diameter similar to the inner cylinder, it is assumed that the flow field near the outer wall of the chamber (inside the chamber) and away from the outer wall of the chamber (outside the chamber) will not be significantly affected by the generated tornado-like vortex. Therefore, the circular side wall under the circular duct in the “near-ground domain” (for the stationary case) is setup as a wall with zero shear stress, which indicates a zero gradient of all three velocity

“near-ground domain” is generated using the inflating technique along the axial direction. The thickness of the first layer is set as 0.02 m, 0.01 m and 0.005 m, respectively. For each case, the growth rate in thickness between layers is 1.2. The obtained results show that the difference in the maximum tangential velocity and core radius among the three cases with different sizes of mesh is below 5%. Therefore, in the following simulations, 0.01 m is taken as the thickness of the first layer for computational efficiency.

components along the radius on that surface (∂V∂Rtan ¼ 0; ∂V∂Rrad ¼ 0; ∂V∂axial R ¼ 0; ). Herein, Vtan , Vrad and Vaxial represent tangential, radial and axial/ vertical velocities, respectively. This is an approximation justified by the fact that the flow velocities are much smaller and more uniform at the outer chamber wall in the “near-ground domain” than the maximum tangential velocity in the tornado core region. For the translating case, since the translating velocity is much less than the maximum tangential velocity in the vortex region, the boundary conditions of the box in the “near-ground domain” are kept the same as the stationary case. In addition, the fan is treated as an interface, across which a constant static pressure drop is applied, as mentioned in Section 3.2. Initially, the velocity and gauge pressure is zero everywhere inside the simulator. It is worth noting that the key to properly simulate the wind flow is to correctly set up the reference pressure. In FLUENT, if no pressure boundaries are involved in the model, the gauge pressure field is adjusted after each iteration to keep the flow from floating, by subtracting the pressure value at the reference pressure location from the entire gauge pressure field. By default, the location of the reference pressure is the cell center at or closest to (0,0,0) (users manual. http). In this study, the entire system is driven by the fan and no pressure inlet/outlet boundary condition is applied; the location of the reference pressure point must be set up at a position that is very close to the circular sidewall under the chamber for the stationary case, instead of (0,0,0); and the value of the reference pressure is set up as standard atmospheric pressure. All these are consistent with the practical situation. For the translating case, the defaulted location of the reference pressure (0,0,0) can be applied, as this point will move far away from the vortex center during the motion.

4.1. Stationary tornadic wind field

4. Generated tornadic wind field

4.1.1. Overall flow field When the chamber does not translate, a stationary tornadic wind field will be generated. This section presents the overall flow field generated by the numerical tornado simulator. First, the simulation was run for 2 s, by which a tornado-like vortex has been developed, and then another 4 s of simulation was run. The total time elapsed for the simulation is 6 s. Figs. 8 and 9 present the mean static pressure contours and mean velocity vector distribution on the radial-axial plane at y ¼ 0. The mean quantities are ensemble-averaged from t ¼ 2–6 s. The data sample step is every 10

3.6. Simulation setup A transient, incompressible, three-dimensional CFD simulation is conducted in this work using the commercial software, ANSYS FLUENT. Since tornado-like vortices are highly turbulent, an appropriate turbulence model is required to accurately characterize the flow field. Large eddy simulation (LES), k-ε, and k-ω are the most popular turbulent models. Although k-ε, and k-ω models prevail in simulating turbulent flows due to their low computational cost, previous research has shown that they are not capable of simulating the two-cell, and multi-cell vortices (Mishra et al., 2008b; Kuai et al., 2008; Natarajan, 2011). Therefore, in this study, LES is used to model the turbulence. In LES, large eddies are resolved with filtered time-dependent Navier-Stokes equations while small eddies are modeled with a sub-grid stress model such as the Smagorinsky-Lilly model. As a result, the grid resolution directly affects the filtering of small eddies. Therefore, in order to obtain reasonable results, a fine mesh is applied in this simulation so that the eddies that are captured have a reasonable resolution. Standard sea-level atmospheric conditions (pressure ¼ 101,325 Pa, temperature ¼ 288.15 K, and dynamic viscosity ¼ 1.789
105 Pa s) are used in the simulations. The natural convection effect is ruled out by setting a constant density everywhere in the system. The finite volume-based SIMPLEC scheme is used for the numerical solution, with Δt ¼ 0.01s as the time-step size. The residual error is limited to 0.001 for continuity and all three velocity components. The mesh dependence study has been conducted with three different mesh sizes inside the “near-ground domain”. To be specific, the mesh of

Fig. 8. (A): Time-averaged static pressure contours on radial-axial plane at y ¼ 0 for the stationary case with the guide vane angle of 30 . (B): Surface pressure coefficient profiles for guide vane angles of 30 and 50 at t ¼ 6 s. The pressure coefficient is calculated with the ambient pressure as reference pressure and overall maximum tangential velocity as a reference velocity. 205

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Fig. 9. Time-averaged velocity vector distribution on radial-axial plane at y ¼ 0. Guide vane angle is 30 .

time steps. Therefore, from t ¼ 2–6 s, 40 data samples are used to calculate the mean quantities. The convergence of the mean values are investigated by means of comparing the overall mean tangential velocities if we choose the data sample steps as 10, 20 and 25. Results show that the time sampling error is below 5%. From Fig. 8(A), it can be seen that the fan interface experiences a significant pressure change, which is caused by the static pressure rise applied from the fan inlet to the fan outlet. The surface pressure coefficient profile in Fig. 8(B) shows a pressure deficit at the centerline, and the flattened profile at the centerline indicates a central downdraft along the vortex axis which had

been found in experiments with a swirl ratio>0.5 (Church et al., 1979; Haan et al., 2008). From the distribution of the velocity vector (based on the resultant velocity) in Fig. 9, it can be seen that starting at the fan interface, the flow passes through the guide vanes, where it gains angular momentum due to the non-zero guide vane angle, and then into the duct, and finally travels back into the inner cylinder, where it loses angular momentum and is straightened when passing through the honeycomb section. This self-circulating flow meets the design expectation of this type of tornado simulator. The streamlines presented in a three-dimensional (3D) view in Fig. 10 give an overview of the fluid flow

Fig. 10. 3D streamlines of the whole model. Guide vane angle is 30 . Velocity here represents the resultant velocity of the tangential, radial and axial components. 206

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inside the simulator. It shows that tornado-like vortices (rotating and going up) are generated in the region between the ground plane and the bottom of the inner cylinder. In the upper region of the tornado simulator (between the inner wall of the duct and the wall of the inner cylinder), although rotating flow is observed, it rotates at the same elevation and does not go up.

Table 3 Two length scales at different swirl ratios (compared between CFD simulations and Tornado Spencer).

Case 1 Case 2 Case 3

4.1.2. Swirl ratio and flow structure of the generated tornado-like vortices For a tornado, the most important controlling parameter is the swirl ratio (S), which is a ratio of the amount of rotational energy to the convective energy in the vortex. The value of S controls the vortex structure. Although the swirl ratio is a dominant governing parameter in determining the vortex structure, it does not have a unique expression or definition. Its expression or definition differs between different types of laboratory tornado simulators. Since a modified ISU tornado simulator is simulated here, the swirl ratio defined by ISU (Haan et al., 2008, 2009) is adopted here  S ¼ π r2c Vt;max Q

Table 2 Parameter comparison between cases with different setting angles for guide vanes. Case 2

30 17.11 m/s 0.316 m 0.2748 m 8.92 m3/s 0.60 0.127

50 14.75 m/s 0.354 m 0.2732 m 6.48 m3/s 0.89 0.118

hmax,r/hmax,s

Swirl ratio

460 498 478

0.47 0.60 0.89

4.1.3. Near-floor wind field One purpose of conducting laboratory-scale tornado simulation is to controllably produce the near-floor tornadic wind field, since the flow field in this region has the most impact on civil structures in a natural tornado event. Fig. 11 presents the time-averaged velocity and streamline on the radial-axial plane at y ¼ 0 between the ground plane and the bottom of the honeycomb section, within which the near-ground flow field is captured. The color contours represent the magnitude of the tangential velocity and the arrows/vectors represent the resultant velocity of the radial and axial components (in the x and z directions, respectively). The high resolution of the near-ground velocity vectors indicates that the induced flow field is well resolved, which demonstrates the capability of our numerical model to investigate the tornado-like vortices. Fig. 11(A) is for the case where the guide vane angle is set as 30 (with S ¼ 0.60). In these figures, a fully developed turbulent core is observed, where the breakdown bubble penetrates to the ground plane. Inside the core, a downdraft is developed around the centerline, and updrafts are developed in the surrounding areas, which is consistent with the conclusion drawn in (Davies-Jones et al., 2001). Fig. 11(B) is for the case where the guide vane angle is set as 50 (with S ¼ 0.89). From these figures, a similar vortex breakdown bubble, but with a larger core radius, can be found, which is consistent with a larger swirl ratio. Fig. 12 presents the instantaneous streamlines on both a horizontal plane and a vertical plane for the two simulated cases. From the streamlines on the horizontal plane, a single vortex is observed in Fig. 12 (A), while two subvortices are observed in Fig. 12(B). By combining the information on the steamlines on the vertical plane, it is concluded: 1) when the guide vane angle is 30 degrees (S ¼ 0.60), a double-celled single-vortex is produced; 2) when the guide vane angle is 50 (S ¼ 0.89), a multi-vortex tornado is produced. From the instantaneous streamlines on the radial-axial plane, it also shows that the downdraft touches the ground in both cases. Fig. 13 presents the time-averaged streamlines on a horizontal plane for both cases. By comparing Figs. 12(A) and 13(A), for the case with S ¼ 0.60, it suggests that the time-averaged flow structure is symmetrical around the central axis, while the instantaneous flow structure is not, and the vortex is inclined along the height. By comparing Figs. 12(B) and 13(B), for the case with S ¼ 0.89, it is worth noting that the multi-vortex flow structure is an instantaneous phenomenon, as there is only one vortex on the horizontal plane based on the time-averaged data, while there are two subvortices on the horizontal plane based on the instantaneous data. This suggests that the flow structure of tornadoes is dynamic and transient, and thus the tornadic wind loads acting on civil structures should be treated as dynamic loads in order to better predict the performance of structures under tornadoes. In addition, all the above results shows that this laboratory tornado simulator can produce tornado vortices with different flow structures. Fig. 14 presents the mean pressure, tangential, radial, and axial velocity contours on the radial-axial plane at y ¼ 0 between the ground plane and the bottom of the inner cylinder for both cases. From the static pressure contours in Fig. 14(I), it can be seen that there is a pressure deficit around the centerline (the corresponding surface pressure coefficient profile is presented in Fig. 8(B)). This pressure deficit verifies the generation of the vortex. This result is consistent with the observation in the tornado simulator at ISU (Fig. 6 in (Haan et al., 2008)). In fact, if the

(4)

Case 1

rc,max,r/rc,max,s 435 381 341

rate, which is verified in our simulations as well (see Table 3).

where rc is the core radius at which the maximum tangential velocity is reached, Vt,max is the maximum tangential velocity, and Q is the volume flow rate through the fan interface. Conventionally, the corresponding aspect ratio is defined as a ¼ h/r0, where h and r0 are the height of velocity inlet and the radius of outlet. In our numerical model, the height of velocity inlet is equal to the distance between the chamber and the ground plane, which is denoted as dg in Fig. 4(A), while the radius of outlet is equal to the radius of the inner cylinder, which is Dc/2. Therefore, the corresponding aspect ratio of our numerical simulator is a ¼ 0.504. Church et al. (1979) reported that the vortex structure generated in a Ward-type laboratory simulator is strongly affected by the swirl ratio. Experiments showed that the inflow directly moves up along the axis of the vortex at a low swirl ratio ranging between 0.1  S < 0.2. When slightly increasing the swirl ratio, a downdraft occurs around the tornado center, which is referred to as Vortex Breakdown. The position of Vortex Breakdown bubble moves downward furthermore until it touches the floor when continuously increasing the swirl ratio to S ¼ 0.5. When the swirl ratio is beyond S ¼ 0.5, double-celled vortex structures can be observed, respectively. In this paper, two cases are investigated with the guide vane angle being setup as 30 and 50 . The corresponding swirl ratio, maximum tangential velocity, the height at which the maximum tangential velocity locates and the volumetric flow rate are calculated and are presented in Table 2. From the results, it shows that by increasing the guide vane angle from 30 to 50 , the overall maximum mean tangential velocity decreases, so does the volumetric flow rate, while the core radius expands and the swirl ratio increases. The increase in the swirl ratio makes sense since increasing the guide vane angle introduces more rotational energy into the system. In previous experiment testing in the tornado simulator at ISU, it was observed that the swirl ratio of the generated vortex increased from 0.08 to 1.14 by adjusting the angle of guide vanes from 15 to 55 (Haan et al., 2008). Also note increasing the guide vane angle increases the amount of circulation but decreases the volumetric flow

Guide vane angle Overall maximum mean tangential velocity (Vt,max) Core radius (rc) Height z coordinate at which Vt,max is obtained Volume flow rate (Q) Swirl ratio (S) h/rc

Vane angle 40 30 50

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Fig. 11. Left: Mean tangential velocity magnitude contours and mean velocity vectors in radial-axial plane at y ¼ 0 between the floor and the bottom of the inner cylinder for the stationary case. The vector length indicates the magnitude of the resultant velocity of the radial and axial components. Right: Mean tangential velocity magnitude contours and the mean streamlines in radial-axial plane at y ¼ 0. (A) When the guide vane angle is 30 while S ¼ 0.60; and (B) When the guide vane angle is 50 while S ¼ 0.89.

maximum tangential velocity decreases, which may be explained by the conservation of angular momentum. Fig. 15 presents the time-averaged tangential, radial, and axial velocity profiles as a function of radial distance at different elevations above the ground for the case where the angle of guide vanes is 30 . In each subfigure, the elevation above the ground is represented by the distance between the ground plane and the height of interest, designated by “h” in the figure. (In) particular, h ¼ 0.1rc is the elevation at which the maximum tangential velocity is reached. The radial distance expressed on the horizontal axis is normalized by the core radius (rc ¼ 0.315 m), and the velocity expressed on the vertical axis is normalized by the maximum mean tangential velocity (Vt,max ¼ 17.11 m/s). From Fig. 15(A), the tangential velocity first gradually increases from zero at the centerline, and then continues to increase to the peak value of 1 at the core radius (r/rc ¼ 1), and then gradually decays in the far field along the radial distance. Also, in general the magnitude of the maximum tangential velocity decreases with the increase in elevation, although they almost have the same magnitude at high elevations of h ¼ 0.5rc and h ¼ rc. For comparison, the tangential velocity profile based on the Rankine Vortex Model is also presented in Fig. 15(A). It shows that the tangential velocity profile at lower elevations of the tornado simulator is more consistent with the Rankine Vortex Model. In addition, the above behaviors are consistent with the radar data measured in a real-world tornado event, which will be presented in Section 4.3. The radial velocity profiles in Fig. 15(B) shows that an outward flow (positive value) takes place close to the centerline, and an inward flow (negative value)

guide vanes are set as zero angle with respect to the radial direction, no significant swirling motion will be introduced into the system, except for the swirling motion introduced by the fan itself, which is not included in this simulation. As a result, the computed flow field will be analogous to the axisymmetric irrotational flow in a corner with a high pressure region located at the centerline. On the contrary, once the guide vanes are set at a non-zero angle with respect to the radial direction, a swirling motion will be added into the system, and the conservation law of angular momentum induces a low pressure region at the centerline. In general, the centrifugal force due to the swirling motion is balanced by the pressure gradient in the radial direction and the radial momentum flux (Ward, 1972). From the tangential velocity contours (see Fig. 14(II)), it is observed that the magnitudes of the tangential velocities on the two sides of the centerline are approximately identical, but with opposite directions, which verifies the generation of the swirl motion. Radial velocity contours in Fig. 14(III) indicate an inward flow far away from the centerline and outward flow close to the centerline. In this simulation, on the radialaxial plane, the positive radial velocity is in the positive x direction, which is why, in the region close to the centerline, the velocity is negative on the left side to the centerline and is positive on the right side. From Figure (IV), the flow around the centerline beneath the honeycomb section is fully downward, and the downward flow touches the floor. The observations from Fig. 14(III) and 14(IV) are consistent with the velocity vectors presented in Fig. 11. By comparing Fig. 14(AII) and 14(BII), when S increases from 0.60 to 0.89, the core radius increases, while the 208

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Fig. 12. Left: instantaneous zoomed-in streamlines on horizontal planes at z ¼ 0.1 m and z ¼ 0.4 m for two cases. Right: instantaneous streamlines of the resultant velocity of radial and axial components on vertical plane at y ¼ 0 m. (A) When guide vane angle is 30 while S ¼ 0.6; and (B) When guide vane angle is 50 while S ¼ 0.89.

toward the vortex center takes place in the far field away from the centerline. This outward radial flow around the centerline and close to the ground plane is due to the penetration of the vortex breakdown bubble to the ground plane and the inward radial flow in far field is caused by the inflow entering from the duct to the centerline. The axial velocity profiles shown in Fig. 15(C) illustrate the downward flow around the centerline and the upward flow away from the centerline. In general, the maximum axial velocities at the lower elevations are smaller than those at higher elevations for both downdraft and updraft flow. Fig. 16 presents the time-averaged tangential, radial, and axial velocity profiles as a function of vertical distance at different radial distances from the centerline for the case in which the angle of guide vanes is 30 . The velocity magnitude and vertical distance are normalized by the maximum mean tangential velocity (Vt,max ¼ 17.11 m/s) and the core radius (rc ¼ 0.315 m), respectively. From Fig. 16(A), it can be seen that the tangential velocity is relatively small inside the radius of r ¼ 0.5rc, and the magnitude does not change much along the vertical distance. However, when r ¼ rc, the graph shows that the tangential velocity increases from zero at the elevation of ground plane to a peak value at an elevation that is adjacent to the ground (h ¼ 0.1 rc), and then falls to a minimum value at approximately h ¼ 0.5rc above the ground, and finally increases again to an approximately constant value. Further moving away from the centerline at r ¼ 2rc, the tangential velocity dramatically

increases to an approximately constant value, which is always smaller than the tangential velocity at the core radius. All the above behaviors are consistent with the radar observation (Haan et al., 2008; Alexander and Wurman, 2004; Wurman and Alexander, 2005) (Fig. 12 in Reference (Haan et al., 2008) and Fig. 17 in (Alexander and Wurman, 2004)). The radial velocity profiles presented in Fig. 16(B) shows that for the flow inside the core (r ¼ 0.1rc, 0.2rc or 0.5rc), at low elevations, the flow is outward (positive values), and at high elevations, the radial velocity is almost zero, which indicates that there is a downward flow around the centerline without any significant inward or outward flow components; for the flow far away from the core (r ¼ 2rc), the flow is inward (negative values). Also, it seems that the radial velocity tends to be the strongest at low elevations and relatively far from the centerline, which makes sense since the air is flowing from the duct to the centerline. These observations are consistent with the findings from radar measurements during 2012 Russel, KS tornado (see Fig. 4 in (Kosiba and Wurman, 2013)). From Figure (C), it is clear that a downward flow takes place around the centerline (r ¼ 0.1rc, 0.2rc and 0.5rc), while an upward flow occurs at the far field away from the centerline (r ¼ rc and 2rc). 4.1.4. Comparison between the numerical simulation results in this study and previous testing results for the stationary case By adjusting the angle of guide vanes and fan speed, Haan et al. 209

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Fig. 13. Time-averaged streamlines on vertical plane at z ¼ 0.1 m for both cases. (A) When guide vane angle is 30 while S ¼ 0.60; and (B) When guide vane angle is 50 while S ¼ 0.89.

samples, and the mean quantities are averaged over these 20 data samples). In the stationary case, the mesh cells do not move during the whole simulation. In this translating case, to simulate the translation of a tornado, the chamber moves (carried by the overhead crane), while the “near-ground domain” (computational domain representing the field between the bottom of the chamber and the ground plane) is fixed and does not move along with the chamber. Accordingly, the mesh cells inside the chamber move, but those inside the “near-ground domain” (where the near-ground wind flow is generated) do not move at all. Even though the chamber and the cells inside the chamber move, the data sampling method can still correctly calculate the time-averaged flow properties of the cells in the chamber. However, the obtained timeaveraged flow properties for the mesh cells in “near-ground domain” are not associated with those calculated in the chamber, i.e., they do not represent the near-ground flow properties underneath the chamber. This is because the mesh cells in the “near-ground domain” do not move together with the cells in the chamber and the data sampling method averages the flow properties of each unmoving cell among all time instants. To address this problem, a MATLAB code is developed to calculate the time-averaged flow properties from the instantaneous flow properties obtained by FLUENT. Herein the data are extracted at a certain interval for averaging. To be specific, the data are only extracted at 16 time instants at the interval of 0.25 s, which are at ¼ 2.25 s, at t ¼ 2.5 s, at t ¼ 2.75 s, …, and at t ¼ 16 s. And the averaging is based on the extracted data at the above 16 time instants. Similar to the stationary case, at each data sample the instantaneous flow properties on the mesh grid are extracted, and finally the mean values over 16 data samples are calculated. This code has been validated by our stationary cases, and thus was applied in this translating case. Fig. 17 presents the instantaneous static pressure distribution and contours of instantaneous tangential velocity magnitude on the radialaxial plane at y ¼ 0 when the guide vane angle is set as 30 . From Fig. 17(A), we can find that the transient flow field changes dramatically over time during the translating motion. Also, the generated vortex flow in the translating case is skewed. This is because the friction on the ground plane forces the bottom of the vortex to lag behind the top (which is moving from x ¼ 0 to x ¼ 2 m over 4 s with a speed of 0.5 m/s). This is consistent with the in situ observation in Tornado Spencer, in which the tornado was observed to have a 20 incline with the ground in a vertical tilt toward north (Alexander and Wurman, 2004). The top of the vortex in

produced the tornado-like vortices with a wide range of swirl ratios in the laboratory tornado simulator (Haan et al., 2008). Two typical vortex structures were presented, a low swirl ratio of 0.08 at 15 angle of guide vanes and high swirl ratio of 1.14 at 55 angle of guide vanes. Their results showed that single-celled and double-celled single-vortex structures were developed at S ¼ 0.08 and 1.14, respectively. With the developed numerical model in this study, the double-celled single-vortex flow structure was produced at S ¼ 0.60. By comparing the velocity vectors in the case of S ¼ 1.14 in (Haan et al., 2008) and those in the case of S ¼ 0.60 in this simulation, it shows that both cases have the similar flow structure, that is, the flow moves downward along the centerline while moving upward away from the centerline. And this case is also consistent with the trends observed by Church et al. (1979). In addition, the trend of the tangential velocity profile from this numerical simulation (Fig. 15(A)) is well consistent with that extracted from the radar-measured velocity data (see Fig. 23(B)) and experimental measurements presented in (Haan et al., 2008). Haan et al. also showed that the normalized tangential velocity profile at S ¼ 1.14 collapses well with the observations of Tornadoes Spencer and Mullhall at the elevations of h ¼ 0.1rc and h ¼ 0.52rc, especially at h ¼ 0.52rc (Haan et al., 2008). It verifies the capability of the numerical model developed in this study on simulating tornado-like wind flow.

4.2. Translating tornadic wind field 4.2.1. Overall flow field When the chamber of the tornado simulator translates above the ground plane, a transient tornadic wind field will be generated. In this case, a total of 6 s of flow is simulated with a stationary state for the first 2 s, and a translating motion at the speed of 0.5 m/s during the following 4 s. The translating motion is in the positive x direction. An animation of the development of tornado-like vortices during the translation can be found in supplement materials. It should be mentioned that in the stationary case, the time-averaged flow properties are obtained by using the data sampling method in FLUENT. That is, at each time instant, the flow quantities in each individual mesh cell are first calculated, and then the obtained quantities are ensemble averaged in each individual mesh cell over a data sample set (for example, if the user defines the sample step as 10, then FLUENT will collect the data samples every 10 time steps. If the whole simulation takes total 200 time steps, then the program will collect 200/10 ¼ 20 total data 210

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Fig. 14. Contour plots of time-averaged static pressure (I), tangential velocity magnitude (II), radial velocity (III), and axial/vertical velocity (IV) on radial-vertical plane at y ¼ 0 between the floor and the bottom of the inner cylinder. Stationary case. (A) When guide vane angle is 30 with S ¼ 0.60; and (B) When guide vanes angle is 50 with S ¼ 0.89.

radius is approximately 12.7% smaller than that in the stationary case. This results in a reduction of swirl ratio from 0.60 for the stationary case to 0.44 for the translating case. In previous research, it was reported that by applying the translating motion, the mean tangential velocity slightly decreases for a lower swirl ratio, while it increases for a higher swirl ratio (Natarajan and Hangan, 2012). This suggests that the numerical simulation results in our study are consistent with the previous research findings. Fig. 19 shows that a double-celled single-vortex flow structure is generated during the translating motion although the swirl ratio is slightly reduced to a value lower than 0.5. This once again reveals the transient characteristics of tornadic wind loads. In the future, parametric study will be conducted to investigate how the translating motion affects the characteristics of the generated wind flow.

Tornado Spencer followed the main body of the upper vortex, which was above the cloud level, while the lower vortex trailed behind. The obtained results are also consistent with previous numerical studies, in which LES simulations of a laboratory tornado simulator and full-scale tornado showed that translation effect causes a slight reduction of swirl ratio, and forces the vortex to be skewed (Natarajan and Hangan, 2012; Lewellen and Lewellen, 1997). The contours of tangential velocity magnitude presented in Fig. 17(B) also demonstrates that the flow structure changes over time. The significant change of the pressure field and velocity field during the translating motion leads to a significant transient wind load change on the building structures which induces severe damage to them. 4.2.2. Near-ground wind flow Fig. 18 presents the mean tangential velocity magnitude contours and the vectors of the mean resultant velocity of the radial and vertical (axial) components on the radial-vertical plane at y ¼ 0 between the ground plane and the bottom of the inner cylinder. The axisymmetric flow field is now skewed due to the translating motion. The maximum tangential velocity occurs at rc ¼ 0.275 m at a height z ¼ 0.275 m with a magnitude of Vt,max ¼ 16.395 m/s, which is about 4.2% less than the maximum tangential velocity in the stationary case (17.11 m/s). Moreover, the core

4.2.3. Translating speed effect In this section, parametric studies are conducted to investigate the translating speed effect on the generated tornadic vortices. Three translating speeds VT ¼ 0.5 m/s, 1 m/s and 1.5 m/s are tested. The translating duration is chosen as 6s, 3s and 2s for VT ¼ 0.5 m/s, 1 m/s and 1.5 m/s respectively. In this way, the tornado-like vortex translates 3 m in all three cases. Based on the similarity theory discussed in the later section, the scaled-up time of translating duration is 8.8 min, 4.4 min and

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Fig. 15. Time-averaged velocity component profiles as a function of radial distance at different elevations above the ground. Guide vane angle is 30 . (A) Tangential velocity with Rankine Vortex Model; (B) Radial velocity; and (C) Axial velocity.

Fig. 16. Time-averaged normalized velocity component profiles as a function of vertical distance. Guide vane angle is 30 . (A) Tangential velocity; (B) Radial velocity; and (C) Axial velocity.

2.93 min, respectively. In the simulations, the total flow time lasts 8s, 5s and 4s respectively, since a 2s stationary vortex is always simulated before translation. It is clear to see that the introduction of translating motion leads to a tilt in the vortex near the ground plane from Fig. 20. As the translating speed increases from 0.5 m/s to 1.5 m/s, the vortex becomes more skewed. This

can be explained by more intense shear stress due to the higher translating speed. From the surface pressure coefficient profiles along radial axis presented in Figure 21(A), it can be found that the pressure coefficient increases as the translating speed goes up. Although the tangential velocity profiles are quite different among all three cases, the local maximum tangential velocity at h ¼ 0.1rc does not change very much (Figure 21(B)). 212

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Fig. 17. Instantaneous flow field for the translating case with the guide vane angle of 30 at t ¼ 3s, 4s, 5s and 6s. (A): Instantaneous static pressure on the radial-axial plane at y ¼ 0; (B): contours of instantaneous tangential velocity on the radial-axial plane at y ¼ 0. VT ¼ 0.5 m/s.

Also note that, for VT ¼ 0.5 m/s and 1 m/s, the tangential velocity has almost the same peak values of tangential velocity on both sides of the vortex, while for VT ¼ 1.5 m/s, the peak tangential velocity on the trailing side is larger than that on the leading side of the vortex.

real-world tornadoes, it is important to find the velocity and length scales of the tornado simulator relative to a real-world tornado. Herein, the Spencer, SD Tornado of 30 May 1998 is selected as the real-world case to compare with. For this real-world tornado, the overall maximum tangential velocity was observed as Vt,max ¼ 81 m/s at h ¼ 20 m, and the core radius at h ¼ 20 m was found to be rc ¼ 120 m (Haan et al., 2008). Dr. Hangan's research group has conducted intensive research on the similitude theory that can be applied in tornadic wind fields (Hangan and Kim, 2008; Refan et al., 2014). In their approach, the velocity scale is

4.3. Geometric, velocity and time scaling and comparison of CFD simulation results with radar-measured data In order to relate the numerically simulated tornadic vortices to the 213

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observed in Tornado Spencer. Therefore, suggested by Reference (Refan et al., 2014), the ratio of core radius related to the swirl ratio of 0.47 is used as the length scale for our numerical simulator and the value is λL ¼ 435. With the length and velocity paragraph determined, the time scale λT can be determined by the ratio of length scale and the velocity scale, which is obtained as λT ¼ 88 in this study. With this time scale, the corresponding full-scale tornado can last 5.9 min if we scale up our simulation flow time, which is 4 s in the stationary case after a tornadic flow field is generated. Considering that the averaging elapse time of a realworld tornado is about 5–10 min, the corresponding scaling time from our simulation is well consistent with real-world situations. Fig. 23 illustrates our scaled-up tangential velocity profile along the radial distance and with the associated profiles obtained from the radarmeasured data in the Spencer Tornado. The length scale (λL ¼ 435) and the velocity scale (λv ¼ 81/16.36 ¼ 4.95) are applied. Figure 23(A) presents the tangential velocity profiles at different elevations above the ground of the full-scale tornado scaled up from the tornado-like vortices produced in our tornado simulator. To obtain the profile at a certain elevation, for example at h ¼ 20 m, the length scale (λL ¼ 435) is first applied to scale the height h ¼ 20 m to our simulator height, which is 20 m/435 ¼ 0.046 m; then, the tangential velocity profile at h ¼ 0.046 m in our simulator is extracted; finally, the velocity scale (λv ¼ 4.95) is applied to obtain the corresponding full-scale tangential velocity profile by multiplying λv ¼ 4.95 to the obtained velocity profile at h ¼ 0.046 m in our simulator. It can be seen that at a lower level (h ¼ 20 m), the maximum tangential velocity is the largest, and the magnitude decreases with the increase in elevation, which is consistent with the real-world tornado shown in Figure 23(B). In addition, as shown in Figure 23(A), the tangential velocity at far field decreases to around 20 m/s; and at the higher elevations, the profiles are almost overlapped, which are also consistent with the real situation observed in Figure 23(B). The maximum tangential velocity at h ¼ 110 m was measured as 65 m/s at r ¼ 200 m in the radar observation, while our simulation results show that the maximum tangential velocity at h ¼ 110 m is slightly greater than 65 m/s at r ¼ 150 m. In general, good agreements have been achieved on the trend between our simulated tornado and this real-world tornado.

Fig. 18. Mean tangential velocity magnitude contours and mean velocity vectors on radial-vertical plane at y ¼ 0 between the ground plane and the bottom of the inner cylinder, for the translating case with the guide vane angle of 30 .

determined by the ratio of the overall maximum tangential velocity between the real-world tornado and the simulated tornadic wind fields. By implementing this approach, the velocity scale λV ¼ 81/16.36 ¼ 4.95 is obtained (the maximum tangential velocity of S ¼ 0.47 when the angle of guide vane is setup as 40 ). Dr. Hangan's group developed a systematic approach to determine the length scale out of the ratio of core radius (rc,max,r/rc,max,s) and the ratio of the height corresponding to the overall maximum tangential velocity (hmax,r/hmax,s), based on the fact that the scales of simulated vortices are dictated by the characteristics of the simulated flow (Hangan and Kim, 2008) (where subscript c stands for the core radius, max stands for the maximum tangential velocity, s and r stand for the simulation and real-world tornadoes). Based on their approach, the swirl ratio at which the rc,max,r/rc,max,s graph and the hmax,r/hmax,s graph converge/intersects represents the swirl ratio of a real tornado, and the length scale related to this swirl ratio, either rc,max,r/rc,max,s or hmax,r/hmax,s, can be taken as the length scale. To implement this approach, the ratios of rc,max,r/rc,max,s hmax,r/hmax,s and as well as the associated swirl ratios for three simulated cases are presented in Figure 22. Figure 22 shows that the length scales intersect before S ¼ 0.47 in our simulation when the angle of guide vane is setup as 40 . Although this flow structure is not shown in the previous sections, it displays a similar double-celled single-vortex structure for the swirl ratio of 0.47, which is also consistent with the flow structure

5. Conclusions and future work Tornadoes have resulted in incredible amounts of property damage and significant numbers of fatalities each year in Mainland America. To design civil structures that can survive tornadoes, it is important to

Fig. 19. Left: Instantaneous zoomed-in streamlines on horizontal planes at z ¼ 0.1 m and z ¼ 0.4 m and Right: Instantaneous streamlines on vertical plane at y ¼ 0 at t ¼ 4.5 s, for the translating case with the guide vanes angle of 30 . VT ¼ 0.5 m/s. 214

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Fig. 20. Comparison of contours of velocity magnitude in the radial-axial plane at y ¼ 0 with different translating speeds. Upper: VT ¼ 0.5 m/s, Middle: VT ¼ 1 m/s, Lower: VT ¼ 1.5 m/s. Guide vane angle is 30 for all three cases.

the characteristics of both the overall and near-ground wind flow are extracted and investigated. The obtained streamlines and vector plots have verified the designed mechanism to generate the tornado-like vortices. In addition, the obtained wind flow is compared with the measured data in the physical laboratory tornado simulator published by ISU. It demonstrates that the numerical tornado simulator is capable of reproducing the tornado-like vortices generated in the physical tornado simulator at ISU. It also demonstrates that this laboratory tornado simulator is capable of generating different types of tornado-like wind flow (single-cell single-vortex tornadoes, double-cell single-vortex tornadoes and multi-vortex tornadoes). Once this model is further validated, tornadoes with other different flow structures and tornadic wind effects on different civil structures can be investigated through numerical simulations at a low cost (the numerical model developed in this study can be used to do “testing” on the computer), which can provide an assistance in determining design tornadic wind loads. In addition, the verified numerical simulating strategies for the physical laboratory tornado simulator can be extended to simulate a larger-scale tornado simulator. This may potentially address the

understand the tornadic wind flow near ground and the induced wind pressure acting on civil structures. To achieve this, considering that the in situ measurements of tornadic wind field around the structure (near the ground) are very challenging, experimental testing facilities, tornado simulators, have been built to produce tornado-like vortices to investigate the characteristics of tornadic winds and their wind effects on civil structures. It is worth noting that it is expensive and time-consuming to conduct experimental testing. This study provides an approach to numerically simulate a type of laboratory tornado simulator to achieve both high accuracy and low computational cost. All the major mechanical components in the physical tornado simulator are modeled in the simulation. To be specific, the fan is modeled using the fan boundary condition and the honeycomb section is modeled using the porous media model in FLUENT. For the type of tornado simulator simulated here, since the tornado-like vortices are generated by self-circulating airflow inside the chamber of the simulator, no inflow/outflow boundary conditions are required to be applied. LES is applied to simulate turbulence. Using the developed numerical tornado simulator, both stationary and translating tornadic wind fields are produced. For each type of wind field, 215

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Fig. 23. Comparison of tangential velocity profile in terms of radial distance between our numerical simulation (S ¼ 0.47) and Tornado Spencer. (A) Our numerical simulation; (B): Radar-measured data (Kuai et al., 2008).

limitations of experimental testing due to the small size of existing laboratory tornado simulators and the low wind speed that can be generated. In the future, parametric studies on different setting angles of guide vanes, static pressure rises across the fan interface, porous medium model constants of the honeycomb section, translating speed, and surface roughness will be conducted systematically to better understand the working mechanism of this type of laboratory tornado simulator. Ultimately, different shapes of civil structures will be placed in the developed numerical tornado simulator to systematically investigate the wind effects of tornadoes on civil structures.

Fig. 21. (A): Comparison of surface pressure coefficient profiles along the radial axis for different translating speeds. The reference velocity is 20 m/s for all three speeds. (B): Comparison of tangential velocity profiles at h ¼ 0.1rc for different translating speed, rc is the core radius for the stationary case when the guide vane angle is 30 .

Acknowledgements The authors greatly appreciate the financial support from National Science Foundation, the Hazard Mitigation and Structural Engineering program, through the project, “Damage and Instability Detection of Civil Large-scale Space Structures under Operational and Multi-hazard Environments” (Award No.: 1455709). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jweia.2019.05.001. References Alexander, C.R., Wurman, J., 2004. The 30 may 1998 spencer, south Dakota, storm. Part I: the structural evolution and environment of the tornadoes. Mon. Weather Rev. 133, 72–96. Bienkiewicz, B., Dudhia, P., 1993. June). Physical modeling of tornado-like flow and tornado effects on building loading. In: Proceeding 7th US National Conference on Wind Engineering, pp. 95–106.

Fig. 22. Two length scales at different swirl ratios (compared between CFD simulations and Tornado Spencer).

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