CFD analysis of the generic isolated indoor stadium: Impact of wind direction and roof configuration for wind drift in badminton

. Indoor stadiums are built to minimise the effects of the environment and weather on sporting events. The shuttlecock in badminton is extremely vulnerable to a slight wind gust caused by ventilation in the indoor stadium. It is critical in elite tournaments to design the driftless court area stadium without compromising player and spectator ventilation comfort. CFD simulation is used to study two roof structures widely used in indoor stadium construction: barrel and gable roofs with two ventilation openings in opposite directions for lateral and longitudinal airflow. The simulation is carried out in 3D steady Reynolds-averaged Navier-Stokes (RANS) using the Shear-Stress Transport (SST) k-⍵ model. Grid independency is carried out to compare the results with wind tunnel measurement data from the literature. The non-dimensional velocity and coefficient of pressure contour are obtained in the vertical centre plane and horizontal plane (H=0.06m and 0.02m) from the ground. Finally, the gable roof configuration with longitudinal wind direction volume flow rate increased to 26% and the average velocity in the horizontal (H=0.02m) is 0.19 leading to low wind drift near the ground. There is no huge impact on the roof configuration (barrel and gable) compared to the wind direction (longitudinal and lateral) of the opening in the model.


Introduction
Badminton is a racket sport played with a shuttlecock made up of feathers surrounded by a hemispherical cork.Due to its lightweight and bluff body shape, it will easily deviate from the actual trajectory even for small wind gusts known as wind drift.The indoor stadium is built to avoid environmental or weather disturbance in sports but in the case of badminton, the indoor ventilation (natural or air-conditioning) wind alters the actual trajectory of the shuttlecock in the tournament [1][2][3].This problem is a huge challenge because the reduction of wind drift needs to be achieved without compromising the ventilation for the player and spectator.The lack of ventilation leads to dehydration for the player and discomfort for the spectator.Most of the International tournaments are conducted in a Multi-purpose arena / indoor where no special attention is given to badminton drift [4].The elite player started complaining about the drift which became a huge controversy during the tournaments [1][2][3][4][5][6].There were a lot of studies that have been carried out on the cross ventilation effect in lowrise buildings like the effect of roof types, inlet-outlet openings ratios, opening location and building size ratios.The research works in the cross ventilation set up trends in both generic and real-time stadium studies [7][8][9][10][11][12][13][14][15][16].In the case of cross ventilation on generic buildings [7][8][9][10], the effect of grid generation, opening size and location, sheltered and unsheltered, numerical and geometrical parameters has been carried out by the researcher through field measurement [11][12][13][14][15][16], wind tunnel and CFD.From the literature of review, it's evident that almost no studies have been conducted in the generic stadium to understand the influence of wind drift related to ventilation for badminton stadium construction or design.In this paper, we are going to study the impact of roof configuration and opening wind direction in the different roof stadium configurations through Computational Fluid Dynamics (CFD) to understand the best design for less wind drift near the ground and effective ventilation in the stadium.From the ventilation point of view, this paper is not only trying to understand the volume flow rate, but also the mean velocity on the given area of the flow of the indoor air to eliminate the drift.This paper deals with a couple of approaches to understanding indoor and outdoor interaction.The simulation results are validated with a literature paper [17] which provides detailed wind tunnel PIV data for an isolated building with a flat roof with opposite openings.

Wind Tunnel Experiment
The wind tunnel experiment is conducted by Karava et al [17] for the isolated generic wind-induced cross-ventilation building model for a flat roof for different configurations of opening location and size.The experiment is conducted in the boundary layer wind tunnel with a test section 180 X 308 X 96m 3 at Concordia University, Canada.The experiment is conducted in the nine-configuration model with three different porosity (opening area-towall area) of 5%, 10% and 20% respectively.In the experiment, a reference velocity of 6.6m/s at the building height.In this paper, the CFD investigation is carried out on the rectangle opening located on the opposite side (top region) at a height of 57mm from the ground at 10% porosity for validation purposes.For more detail on the experiment refer [17].

Indoor stadium and CAD development
The indoor stadium generally uses two types of roof configurations:-Barrel roof and Gable roof.The flat roof configuration is developed as per the dimensions of Karava et al to compare the CFD simulation results with the wind tunnel data.The validating model is developed for the dimensions 100 X 100 X 180 mm 3 which is a reduced model of the 20 X 20 X 16 m 3 full-scale dimension at a 1:200 ratio.The models are with top opposite rectangle opening configurations with 10% porosity (18 X 46 mm 2 ).The same dimension as the validating model with a barrel and gable roof is designed for the CFD simulation.For the roof dimension for all configurations refers to Figure 1.

CFD simulation
CFD gains importance in urban physics research like aerodynamics studies for buildings and stadium infrastructures.CFD is used in studying natural ventilation, wind loads, pedestrian comfort, and pollution dispersion.Also, play a huge role in designing the sports stadium with ventilation efficiency and low wind disturbance in the play area.In this paper, CFD is going to be employed based on the literature research carried out by Blocken et al for the cross-ventilation studies for generic isolated buildings.Isometric view of gable roof with longitudinal wind direction opening at the top (in mm).(e).Isometric view of gable roof with lateral wind direction opening at the top (in mm).

Domain and grid generation
The cuboidal computational domain is constructed at the ratio 1:200 scale of the wind tunnel.The domain size and the grid generation technique are adopted based on the work carried out by Perén et al.The distance between the front of the building and a domain is three times the height of the building, the distance between the side and top wall is five times the height of the building and the rear to the domain is fifteen times the building height as shown in Figure 2a.The mesh generation is focused on all directions of the building and concentrated meshing in the building and surroundings shown in Figure 2b.The grid sensitivity study is carried out for the validating simulation and is shown in Figure 3 -(a).Course mesh with 2,09,796 elements, (b).Reference mesh with 4,31,796 elements and (c).Fine mesh with 6,92,521 elements.This analysis is carried out to improve the simulation accuracy and optimize computational timing.For grid analysis results refer to section 4.4.

Boundary Condition
In the domain the front wall is the inlet plane and the rear is the outlet plane.Symmetry condition is applied to the top and both lateral walls of the domain.In the inlet, ABL is imposed based on the wind tunnel measurement.The inlet wind velocity profile is defined based on the logarithmic law given in Eq. ( 1) below.
Where, Z0 is from the experiment [17], U*ABL= 0.35m/s, ḱ is von Karman constant (0.42) and Z is the height of the domain.The turbulent kinetic energy [k], turbulence dissipation rate [] and specific dissipation rate [⍵] is calculated based on the reference [7,8].In the outlet pressure, zero static pressure is applied and in the symmetry condition, zero normal velocity and gradient are imposed.

Solver setting
The ANSYS-Fluent commercial CFD code is used, 3D steady Reynolds-Averaged Navier-Stroke (RANS) solved with shear-stress transport (SST) k-⍵ model as per the recommendation of Perén, Ramponi and Blocken.The second order is used for the discretization scheme, pressure interpolation and pressure coupling with the SIMPLE algorithm.The convergence is obtained in scaled residuals with a minimum of 10 -6 for x and y momentum, 10 -5 for z momentum, 10 -4 for k, ⍵ and continuity [7][8][9][10].To obtain a reliable value, the iteration is monitored till 10,000 iterations to reach a stationary solution.

Grid independence analysis and Validation
The non-dimensional length (X/D) horizontal measurement line is created between the inlet and outlet opening to measure the non-dimensional velocity for grid analysis and validation.In all three mesh cases, the simulation is carried out on a flat roof and mean velocity (V/Uref) is compared along the measurement line between the opening.The reference mesh results argue to be a better choice of selection over a course mesh due to the large deviation from the actual and fine mesh compared to the reference mesh model shows almost the same result by costing high computational timing.We conclude that the reference mesh model is suitable for this study and same is used for the remaining model in this paper.The obtained CFD results of the reference mesh model are compared with the Karava et al V/Uref measurement along the horizontal line between the opening which shows the agreeable result of accuracy, refer to Figure 5.

Impact of the roof configuration and wind direction opening type
To understand the roof impact on the ventilation and wind drift in badminton stadiums, two roof configuration with two wind directions (Longitudinal and Lateral) is considered in the study.To understand the influence, the same inlet and outlet opening type with the same dimension is used in all models.The non-dimensional velocity and coefficient of pressure contour are obtained in the vertical centre side plane and the horizontal plane at heights 0.06m and 0.02m from the ground as shown in Figure 6.The high Cp is found on the leeward side (inside the rooftop) of both roofs in the lateral wind direction.The longitudinal wind direction holds a high Cp inside compared to the lateral wind direction in both roof cases (barrel and gable).In the longitudinal direction, the roof can only accommodate low volume on the top side between the opening for the exchange of airflow but in the lateral direction having a uniform volume at the top between the opening gains the advantage.From non-dimensional velocity (V/Uref) measurement along the horizontal line between the inlet and outlet opening refer to Figure 3, for both roofs lateral wind nondimensional velocity drops largely in the centre compared to the longitudinal wind opening location which impacts the volume flow rate and wind drift.   1 shows the non-dimensional average velocity on the different planes in flat and other roof configurations.The non-dimensional average velocity ranges from 0.18 to 0.46, the 0.46 is highest found in the barrel roof configuration in the longitudinal wind opening at the horizontal plane (H=0.06m).and 0.19 is lowest in the gable roof configuration in the longitudinal wind opening at the horizontal plane (H= 0.02m).To understand the wind drift, the horizontal plane (H=0.02m) is studied in all roof configurations, the gable roof in the longitudinal direction has a lower average non-dimensional velocity of 0.19 among other roof configurations and followed by the barrel roof in the lateral direction is 0.20.Both barrel longitudinal and gable lateral directions account for the same average nondimensional velocity of 0.22.It can be concluded that the Gable roof in the longitudinal direction accounts for the best ventilation with low wind drift in the ground for a badminton stadium.We have found that rather than a roof type (Gable or Barrel), the wind direction opening in the stadium will contribute more impact on ventilation and wind drift effect in the stadium.

Limitations and future study
Our main goal in this paper are to understand the influence of ventilation and wind velocity flow pattern near the ground.Based on the obtained results, we could suggest the roof configuration and wind direction opening for the stadium with less wind drift near the ground but without compromising the ventilation.There is some limitation based on other parameters and external factors in our study but can be addressed in future research.
• In all configurations internal building layout is not considered (like stadium gallery) but must be studied.• All CFD analyses done in the isolation environment, surrounding buildings and other surroundings infrastructure will affect the obtained results.• Only two majorly used roof configuration for the indoor stadium is taken into account for the study, maybe other new configuration can perform better than an obtained conclusion.• Parameters like ABL, thermal effect, buoyancy, building height, ventilation opening size, the internal volume of the stadium and other inclined wind direction in the opening will have a huge impact on the ventilation and wind drift in the stadium.

Conclusion
The paper presents the CFD simulation results of cross ventilation study for the flat, barrel and gable roof with longitudinal and lateral wind direction.A grid independency study is performed on a flat roof validated with wind tunnel data.Based on the non-dimensional velocity in the horizontal centreline between the opening, non-dimensional velocity contour and Coefficient of pressure contour.We found that the gable roof configuration in a longitudinal direction and barrel roof configuration in a lateral direction is better than other models with efficient ventilation with less wind drift area for badminton.
(a).Isometric view of the Karava et al[17] reduced-scale model with an opposite opening at the top (in mm).(b).Isometric view of barrel roof with longitudinal wind direction opening at the top (in mm).(c).Isometric view of barrel roof with lateral wind direction opening at the top (in mm).(d).

Fig 4 .
Fig 4. Indication of the horizontal measurement line in the model to measure the non-dimensional velocity between the inlet and outlet opening.

Fig 5 .
Fig 5. Comparison of mean velocity across the horizontal line between the opening for Reference Case, Course Mesh, Fine Mesh and PIV Measurement.

Fig 6 .
Fig 6.Contour measurement plane (a).Side plane at the model centre (b).Top plane at height from the ground is 0.06m and (c).Top plane at height from the ground is 0.02m

Fig 13 .
Fig 13.Comparison of mean velocity across the horizontal line between the opening (a) Barrel roof -longitudinal and lateral wind flow (b).Gable roof -longitudinal and lateral wind flow.