1. Introduction and Literature Review
After winning the bid of the 2022 FIFA Men’s World Cup, Qatar has become the first country in the Middle East to host such a mega event [
1]. The World Cup not only provides significant opportunities for the country but also brings great challenges in terms of minimizing the total energy consumption for cooling the stadiums during the event and providing thermal comfort for both spectators and players. As required by the FIFA’s Green Goal policy [
2], a neutral-carbon world cup should be delivered by Qatar. However, Qatar is a country where 14.7 TWh, 36% of the annual electricity usage in 2016, is attributed to air-conditioning [
3]. On the other hand, FIFA indicates that a comfort temperature range of 20 to 25.5 °C is required for spectator tiers [
4]. Although the event has been announced to be hosted in winter, November and December [
5], the highest design temperature still reaches 34.2 °C and the average relative humidity for the two months is approximately 70% [
6]. Thus, to deliver energy-saving and thermally comfortable stadiums for the event, the country should seek solutions from energy-efficient cooling systems [
7,
8,
9,
10] or passive cooling techniques for stadiums.
Current existing stadium studies mainly focus on assessing the wind flow inside or around the stadium bowl. These studies were mainly conducted by using Computational Fluid Dynamics (CFD) and atmospheric boundary layer (ABL) wind tunnels. Van Hooff and Blocken [
11] evaluated the indoor natural ventilation of a case study stadium in Amsterdam under five ventilation configurations by employing a coupled CFD modelling method for the urban wind flow and indoor air flow. It was found that the air change rate per hour (ACH) can be improved by up to 43% by expanding the opening sizes near the roof. Based on the same coupled modelling method, the authors [
12] investigated the effect of the surrounding buildings around the same case study stadium and the wind direction on the ACH of the stadium. The maximum deviations in ACH between different wind directions can reach 75% and 152% for the cases without and with surrounding buildings, respectively. In addition, the ACH in the case without considering the surrounding environment can result in a maximum positive deviation of 96% from that with a surrounding environment, which emphasizes the necessity of modelling the surrounding environment in the wind flow studies of stadiums. For the purpose of validating the CFD models of the case study stadium, the authors [
13] also presented a series of full-scale field measurements, including the solar irradiance, air temperature, humidity, natural ventilation rate and wind velocity. The data for the wind velocity was used for the validation of their further work [
11,
12]. Apart from the field measurements, the ABL wind tunnel experiments were performed by Sofotasiou [
14] to evaluate the aerodynamic performance of semi-enclosed stadiums and to also validate the CFD simulations.
To the best knowledge of the authors, only a few of existing literatures focused on the estimation of the cooling energy load for stadiums using a limited number of Building Energy Simulation (BES) tools and the evaluations of thermal conditions inside the stadium and the stadium cooling performance. Sofotasiou et al. [
15] estimated the cooling load for the case study stadium, used by van Hooff and Blocken [
11,
12,
13], by using a dynamic thermal simulation tool. The cooling energy demand for each match was at a minimum of 47 MWh and 115 MWh for maintaining the thermal comfort in the indoor environment and semi-open spaces of the stadium. Sofotasiou et al. [
16] also conducted a study on the influence of the stadium orientation on the cooling load and found that the monthly cooling load could be reduced by up to 1.48 MWh with a modification in the orientation of the stadium. Ghani et al. [
17] studied the thermal performance of the playing field in a case study stadium in Doha numerically and experimentally. The temperature measurements of grass, subsoil, ambient air and running track surface were used to validate the numerical simulation results by using Direct Numerical Simulation (DNS) and ENVI-met models. These measurements could also be used in estimating the boundary conditions for further CFD simulations. Khalil and Ashmawy [
18] explored the effect of different locations of cooling jets and employing radiant cooling at the spectator tiers on the indoor flow condition and ambient temperature at the spectator tiers. The study showed an optimum temperature distribution and air circulation pattern for the scenario using cooling jets with a supply velocity of 5 to 25 m/s and supply temperature of 18 °C above the tiers and radiant cooling pipes. Zhong et al. [
19] explored the temperature distributions and wind flow conditions for a case study stadium without and with cooling jets under the hot-humid climate of Qatar and presented comparisons of three cooling jets configurations: (1) vertical jets above the upper tiers only, (2) combined vertical and horizontal jets at tiers with only an array of jets around the pitch, (3) combined vertical and horizontal jets at tiers with three arrays of jets around the pitch. The results showed that the third configuration performed best among the three configurations. It was also observed in this study that the cooling supply air is exhausted out of the stadium through the roof, due to the negative pressure difference between the wind flow scouring over the roof and the air inside the stadium. In addition, the penetration of outside air through gates into the stadium resulted in higher temperatures of at least 35.3 °C at some local regions on the pitch. To provide a solution to this limitation, the use of mechanical ventilation technique(s) at gates of the stadium is recommended to explore.
The air curtain, defined as a continuous air stream projected over the entire envelop openings, which prevents the penetration of unconditioned air to the indoor conditioned spaces [
20], has the potential to solve the limitation presented in the previous study of Zhong et al. [
19]. It is typically used to block smoke from fires for buildings [
21] and to provide heat and moisture insulation for refrigerated storages [
22,
23]. In addition, air curtains have been used in confining heat inside traffic tunnels [
24] and reducing infiltration of outdoor air into train stations in winter [
25]. Currently, many studies have investigated the airflow characteristics of air curtains. Hayes and Stoecker [
26] defined the “optimum operation condition” of air curtains as the condition where the air curtain flow reaches the floor and the “break-through condition” as the condition where the air curtain flow does not reach the floor. On the basis of the work of Hayes and Stoecker [
26], Wang and Zhong [
27] explored and defined three air curtain flow conditions: “the optimum condition”, “the inflow break-through condition” and “the outflow break-through condition”. The infiltration models for doors equipped with air curtains were also developed by [
27] in the light of pressure differences across doors, flow coefficients and discharge modifiers. An experiment was carried out by Goubran et al. [
28] to validate the CFD modelling method of the air curtain in the previous studies and to verify the infiltration models of the air curtain doors proposed by [
27]. Qi et al. [
29] performed a parametric analysis on the influence of the supply speed and supply angle as well as the presence of people on the aerodynamics performance of the air curtain. It was found that the larger supply speed could reduce infiltration/exfiltration under the inflow and outflow break-through conditions and the larger supply angle could enhance the air curtain performance during the optimum and inflow break-through conditions but degrade its performance under the outflow break-through condition. To the authors’ best knowledge, the effect of air curtains at the gates of semi-outdoor stadiums on preventing the infiltration of outside air has not yet been studied. In addition, the analysis about the influence of a cooling system, which combines cooling jets over/at tiers of semi-outdoor stadiums and air curtains at gates, on the cooling performance of entire stadium has not yet been performed.
This research aims to evaluate and compare the thermal and wind environment of a semi-outdoor stadium under three different cooling configurations and a baseline configuration without cooling using CFD simulations. The three cooling configurations are: (1) vertical jets only above upper tiers (2) vertical jets above upper tiers and horizontal jets at the back of lower tiers and around the pitch (3) integrated vertical jets above upper tiers, horizontal jets at the back of lower tiers and air curtains at gates. Under each cooling configuration, three different scenarios are proposed to assess the influence of supply velocities of vertical jets above the tiers, horizontal jets around the pitch and air curtain supply slots at gates on the pitch thermal performance of the stadium. A full-size stadium model is developed on the basis of previous studies [
11,
12,
13] and validated by the field measurement results presented in [
11]. The cooling jets are used on the basis of the previous work of Zhong et al. [
19] which also provides the validation of the cooling jets characteristics. The air curtain modelling method is also verified by the previous results of an air curtain study [
28]. To take into account the influence of solar irradiance on the thermal boundary conditions of surfaces of ground, stadium and its surrounding buildings, de-coupled solar radiation simulation is conducted in order to calculate the radiative heat flux on these surfaces. The results are used as thermal boundary conditions for simulations assessing the thermal and wind conditions of the stadium. Three-dimensional (3D) steady Reynolds-averaged Navier–Stokes (RANS) equations and the realizable k-ε model are used to solve the thermal and wind flow conditions. The thermal comfort levels on the spectator tiers and pitch of the stadium are estimated and regarded as one of the criteria for the performance of each cooling scenario. The energy consumption per match required by each scenario is also assessed. The results of the present study provide a solution to the limitations of previous studies, where the local poor thermal performance on the pitch of a stadium with cooling jets is caused by the infiltration of hot outside air through gates of the stadium and will be useful not only for future design and retrofits of stadiums in hot climates but also for stadiums that incorporate mechanical cooling.
2. Methods
In the present study, a CFD model of a case study stadium with its surrounding buildings was developed using ANSYS Fluent 18.2 and also validated on the basis of the measured wind velocities in a wind direction of 350°, according to previous studies [
11]. The cooling jets were used on the basis of the previous work of Zhong et al. [
19] which also provided the validation of the cooling jet characteristics. The air curtains were modelled at four gates and the modelling method was verified by the previous experimental and numerical results of [
28]. The influence of solar irradiance on heat fluxes emitted from the surfaces of the ground, stadium and its surrounding buildings was considered by performing de-coupled solar radiation simulations in order to reduce relatively high computational cost of combined simulations. The radiative heat fluxes from these surfaces were calculated on the basis of the simulation results and used as thermal boundary conditions for simulations assessing the thermal and wind conditions of the stadium. The thermal and wind environment of the stadium were evaluated under three different cooling configurations and a baseline configuration.
Section 2.1 introduces the development of the model geometry and computational domain. The details of the computational grid used for the CFD simulations were described in
Section 2.2. The results of a grid independence analysis for the cell sizes of the computational grid were also presented in this subsection.
Section 2.3 presents the boundary conditions used for the de-coupled solar radiation simulations and the simulations which assess the thermal and wind conditions of the stadium. The setup of the CFD tool, Fluent, is provided in
Section 2.4 for both sets of simulations.
2.1. Development of Model Geometry and Computational Domain
The stadium model presented in this work was developed according to the studies on a case study stadium performed by van Hooff and Blocken [
11]. The surrounding buildings around the stadium (
Figure 1a) were also incorporated into the stadium model in order to consider the impact of the surrounding environment on the temperature distributions and wind flow patterns inside the stadium [
12]. The stadium and its surrounding environment (
Figure 1b) were modelled in full size on the basis of [
30]. The size of the stadium (L × W × H) is 226 m × 190 m × 72 m (
Figure 2a–c) and its interior volume is 1.2 × 10
6 m
3 [
11]. The roof (
Figure 2e), as the largest opening, has the size of 110 m × 40 m and the second largest openings are the four gates of the stadium (four arrows in
Figure 2a pointing to the gates in the corners of the stadium) [
11]. The dimensions of each gate (W
g × H
g) are 6.2 m × 6.7 m. The pitch is estimated at a height of 2.1 m over the ArenA deck (
Figure 2d). The dimensions of the urban microclimate (L
urban × W
urban × H
urban) are 626 m × 742 m × 95 m, which results in a computational domain of 1896 m × 1461 m × 432 m (L
domain × W
domain × H
domain), considering the best practice guidelines for the CFD simulations of flows in the urban microclimate recommended by Franke et al. [
31], Bartzis et al. [
32], Cowan et al. [
33], Blocken et al. [
34] and Casey and Wintergerste [
35]. Five times the stadium height H is applied to the vertical and lateral domain extensions as well as the domain extension in the flow direction between the domain inlet and the urban microclimate (
Figure 1c,d) [
31,
32,
33]. The extension in the flow direction between the urban microclimate and the domain outlet is set to 10H instead of 15H (
Figure 1d) to reduce the relatively high computational cost, which is verified to be acceptable because the reverse flow was not observed near the domain outlet in the simulations.
2.2. Details of Computational Grid
The quality of the computational grid has a significant influence on the time consumed by simulations and the accuracy of simulation results [
36]. With regards to the CFD models used for simultaneously simulating the outdoor and indoor flow in a same computational domain, a large and high-resolution grid will be caused by the large differences between the length scales of the stadium and the urban environment [
11]. Therefore, the local cell size control over the entire grid is necessary for not only improving the grid quality but also reducing unnecessary cells to save computational cost. The cell sizes of the stadium (including air curtains and cooling jets), surrounding buildings and the remaining domain were selected as 1 m, 2.5 m and 8 m, respectively, resulting in a grid with 13.2 million cells. A grid sensitivity analysis was carried out by producing two new meshes, a coarser mesh with 10.0 million cells and a finer mesh with 15.9 million cells. The most relevant variables of this research, temperature and air velocity on the cross section of the stadium and pitch, were measured by 9 data points on the cross section (
Figure 3a) and 9 data points on the pitch (
Figure 3b). The absolute mean errors in the temperature and air velocity between each two meshes were determined by:
where
,
and
are the air velocities at data point
for the coarse, medium and fine meshes, respectively;
,
and
are the temperatures at data point
for the coarse, medium and fine meshes, respectively. The absolute mean errors in air velocities between coarse and medium mesh and between medium and fine mesh
and
are 91.40% and 33.29% and those in temperatures between coarse and medium mesh and between medium and fine mesh
and
are 2.70% and 1.63%. The results of the temperature and air velocity obtained from the medium mesh are closer to those obtained from the fine mesh compared with those obtained from the coarse mesh. However, the error between the medium mesh and the fine mesh is still large, since the air velocities, which were measured close to the spectator tiers and the pitch on the cross section, are relatively small. According to Equations (1) and (2), the small values of air velocities cause the errors between each two meshes to be larger. Overall, the medium mesh is used to have a balance between the accuracy of simulation results and the computational cost required by simulations.
2.3. Boundary Conditions
The inlet wind direction used for the validation of the stadium model was φ = 350°. The prevailing wind direction of west-north-west (WNW) in Doha for the two months (
Figure 4a) [
37], represented by φ = 292.5° in
Figure 4b, was used for simulating the thermal and wind performance of the stadium. The wind profiles used for the domain inlet for both wind directions were determined by the aerodynamic roughness length y
0 [
38]. The temperatures for the flow inlet and outlet were both set up to 34.2 °C, the highest outdoor design temperature for the two months [
6]. A pressure outlet with a gauge pressure of 0 Pa was employed for the domain outlet. The turbulent kinetic energy k and the turbulent dissipation rate ε for the inlet and outlet were given by
Figure 4c. For all the walls, the standard wall functions [
39] with the sand-grain roughness modification [
40] were applied for the wall roughness. The sand-grain roughness height k
s and the roughness constant C
s were set as 0.59 m and 0.5 for the ground and 0 m and 0.5 for the stadium and surrounding buildings. According to the radiative heat fluxes calculated from the solar radiation simulations, the thermal boundary conditions for the ground, stadium and surrounding buildings were defined as the heat fluxes of 36.40 W/m
2, 11.25 W/m
2 and 3.10 W/m
2, respectively. The material for the ground was set as soil and that for the stadium and surrounding buildings was concrete. The cooling jets and air curtains were modelled as velocity-inlets with constant supply speeds and temperatures. The details of boundary conditions for the domain are listed in
Table 1.
2.4. Fluent Setup
All the simulations were solved by 3D steady-state RANS equations and the realizable k-ε turbulence model [
42]. In comparison with the standard k-ε model [
43,
44], the realizable k-ε model was selected due to its relatively high accuracy in simulating the wind flow around buildings, particularly in predicting the results in wake regions. Standard wall functions and full buoyancy effect were used for all the simulations. As for the de-coupled solar radiation simulations only, the discrete ordinates (DO) model was applied for the radiation model with the solar ray tracing method for calculating the solar load. The governing equations are not presented here but fully available in the Fluent guide [
36]. The solar calculator was set with the longitude and the latitude as well as the time zone of Doha. The influence of solar radiation on the radiative heat fluxes of the surfaces in Doha was assessed under four proposed kick-off times, i.e., 13:00, 16:00, 19:00 and 22:00 GMT+3 (Doha time) on November 21st, the opening day of the World Cup [
45]. Fair weather conditions [
36] were selected for the solar irradiance method. The sunshine factor of 0.3 was used, since the maximum values of corresponding direct normal irradiance and diffuse horizontal irradiance among the four kick-off times are verified to be close to the highest solar irradiances in Doha from limited measurement data [
46]. For both sets of simulations, pressure-velocity coupling was implemented with the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) scheme. The second order discretization method was employed to all the viscous terms and the convection terms of the governing equations. The Fluent calculations were implemented using parallel processing on a HP Z620 Workstation which contains dual Octa-Core Intel Xeon E5-2690 2.90 GHz processors and 64 GB DDR3 memory. The end of the calculation was controlled by monitoring the residuals of the governing equations and relevant variables. The solution was completed when no changes occurred between iterations and the average computational time was 24 h per simulation. The details of the Fluent setup for the simulations were summarised in
Table 2.
2.5. Building Energy Simulation (BES) Modelling
The commercial BES tool, Integrated Environmental Solutions Virtual Environment (IESVE), was used to estimate the energy consumption per match for under each cooling configuration. The IESVE is a dynamic thermal simulation software which models the heat transfer processes between a building and its ambient environment. A stadium model of the equivalent interior volume as the developed CFD model was developed in IESVE. The weather profile used in simulations is based on the data from the Doha international airport. The U-values of the stadium walls, roof and the ground were 0.26, 0.18 and 1.14 W/m
2K, according to [
41]. The supply air temperature and the cooling system outside air supply flow rate were both set to those defined in each cooling scenario. The duration of a match was estimated to be 3 h, which includes a precooling period of 1 h before the match. The heat transfer processes of conduction, convection and radiation between stadium fabric, ground surface, ambient air and surrounding environment were modelled within the tool. The governing equations used to model these processes are summarized here and are also fully available in the IESVE theory guide [
47]. The time-dependent spatial temperature distribution inside a solid without internal heat sources is described by the following partial differential equations:
where
T is the temperature,
W is the heat flux vector,
λ is the conductivity,
ρ is the density,
is the specific heat capacity and
t is the time. The heat storage in air masses or net heat flow into the air masses
Q is given by the following equation:
where
V is the air volume,
is the air density and
is the air temperature.
For the discretization method, the finite difference approach is used by the tool for the solution of the heat diffusion equation. The element is first replaced by a finite number of discrete nodes, where the temperature at each node will be calculated. The nodes are then distributed within the layers for the modelling of the heat transfer and storage characteristics for the defined time step. Then, the time step is discretized and a combined method between explicit and implicit time-stepping scheme is used to alternate nodes of the construction.
The convective heat transfer is modelled by the following equation:
where
is the heat flux from the air to the surface,
is the mean surface temperature and
K and
n are coefficients.
The heat transfer rate associated with an air stream entering a space is given by the following equation:
where
m is the air mass flow rate,
is the supply air temperature and
is the room mean air temperature.
As for the interior long-wave radiation, the net radiant exchange between a surface and the rest of the enclosure is modelled by the following equation:
where
is the net radiative loss from the surface,
is the surface heat transfer coefficient for exchange with the MRT node and
is the mean radiant temperature of the enclosure.
With regards to the exterior long-wave radiation, the net long-wave gain for an external surface of inclination
β (º) is described by the following equation:
where
is the emissivity of the exterior surface,
is the long-wave radiation received directly from the sky,
is the long-wave radiation received from the ground and
is the absolute temperature of the exterior surface. The solar flux incident on every external building surface is calculated at each time-step by this tool.
The energy calculations of this tool are based on the room and building heat balance. The sensible heat balance for heat flows of air in each room includes the following components:
Heat storage in the air (Equation (7)).
Convection from the room surfaces (Equation (8)).
Heat transfer by air movement (Equation (9)).
The convective portion of casual heat gains.
The convective portion of any plant (heating, ventilation, air-conditioning (HVAC) systems) input.
The sensible heat balance for each interior room surface is established by the following components:
Heat conduction out of the building element (Equations (5) and (6)).
Convection to the surface from the room air (Equation (8)).
Thermal radiation exchanged with the radiant temperature node (Equation (10)).
Solar gain absorbed by the surface.
The radiant portion of casual heat gains to the surface.
The radiant portion of plant (HVAC systems) input to the surface.
The sensible heat balance for each exterior building surface involves the following components:
Heat conduction out of the building element (Equations (5) and (6)).
Convection to the surface from the outside air (Equation (8)).
Thermal radiation exchanged with the external environment (Equation (11)).
Solar gain absorbed by the surface.
The latent heat balance for water vapour flows contains the following components:
Water vapour transfer by the air movement.
The latent portion of casual heat gains.
The dynamics of water vapour storage in the air.
Any plant humidification or dehumidification from HVAC systems.
The above heat balances are therefore established by equating the sum of the components under each balance to zero. The linear equations of these balances are solved by linear algebra techniques and the non-linear equations are solved by iterations until a convergence for a global solution is achieved.
4. Conclusions and Future Work
The present study aims to assess the thermal and wind environment of a semi-outdoor stadium under three different cooling configurations and a baseline configuration without cooling using Computational Fluid Dynamics (CFD) simulations. The three cooling configurations are: (1) vertical jets only above upper tiers, (2) vertical jets above upper tiers and horizontal jets at the back of lower tiers and around the pitch, and (3) integrated vertical jets above upper tiers, horizontal jets at the back of lower tiers and air curtains at gates. Under each cooling configuration, three different scenarios are proposed to evaluate the effect of supply speeds of vertical jets above the tiers, horizontal jets around the pitch and air curtains at gates on the pitch thermal conditions. A full-size stadium model was developed and validated on the basis of previous studies. The characteristics of cooling jets and air curtains were validated by previous experimental and CFD simulation results. De-coupled solar radiation simulations were implemented using the solar irradiance data in Doha under the fair weather conditions method in ANSYS Fluent in order to predict radiative heat fluxes emitted from the surfaces of the ground, stadium and surrounding buildings. The results were used as thermal boundary conditions for simulations assessing the thermal and wind conditions in the stadium. The approach wind was based on the atmospheric boundary layer (ABL) flow profile. Three-dimensional steady Reynolds-averaged Navier–Stokes (RANS) equations and the realizable k-ε model were used to solve the thermal and wind flow conditions. The thermal comfort levels on the spectator tiers and pitch of the stadium were estimated using the ASHRAE PMV method (Standard 55–2017). The energy consumption per match required by each scenario was also evaluated.
On the basis of the evaluations for the influence of supply speeds for (1) vertical jets above the tiers, (2) horizontal jets around the pitch and (3) air curtains at gates on the pitch thermal conditions, the temperature distributions on the pitch for configurations 1 and 2 are both affected by the infiltration of hot outside air of 34.2 °C and approximately 5 m/s entering from one of the gates. Configuration 3 demonstrates that the issue caused by the infiltration of hot outside air can be solved by the use of air curtains. In particular, the penetration of hot outside air into the stadium can be sufficiently blocked by the air curtains with a supply speed of 20 m/s for scenario 9. However, the lowest value of PPD of 27% under configuration 3 is still higher than that of 8% under configuration 2, since air velocities on the pitch under configuration 3 are lower. The wind environment on the pitch under configuration 3 should be improved to provide more active air movements.
Comparing the cooling configurations with the baseline configuration without cooling, the temperature at spectator tiers is reduced by at least 15.0 °C. The pitch temperature is decreased by a minimum of 4.8 °C, 9.8 °C and 15.2 °C by configurations 1–3, respectively. Consequently, the values of PMV on the pitch is improved from 5.90 (extremely hot) of the baseline to 0.35 and 1.02 of configurations 2 and 3, respectively. However, the energy consumption per match required by configuration 3 is only 54.0 MWh, which is considerably lower than that of 76.6 MWh for configuration 2. Therefore, for countries in hot climates, such as Qatar, which is required to deliver a carbon-neutral World Cup, the use of air curtains can be regarded as an energy-efficient alternative to the typical use of cooling jets for stadiums.
Further research is still required to be conducted in order to investigate the operation conditions of air curtains for stadiums and analyse the influence of air curtain parameters on its performance. The wind environment needs to be improved by applying other ventilation techniques in future studies. The sensitivity of supply air temperature and supply angle of air curtains on the pitch thermal conditions is not considered in this study and can be focused on in future. Further study can also focus on optimizing the synchronized operation of the cooling jets and air curtains by designing a control system which can adapt to the indoor requirements and the outdoor conditions.