Towards a Computational Fluid Dynamics-Based Fuzzy Logic Controller of the Optimum Windcatcher Internal Design for Efficient Natural Ventilation in Buildings

Recently, increased attention has been given to the coupling of computational fluid dynamics (CFD) with the fuzzy logic control system for obtaining the optimum prediction of many complex engineering problems. 'e data provided to the fuzzy system can be obtained from the accurate computational fluid dynamics of such engineering problems. Windcatcher performance to achieve thermal comfort conditions in buildings, especially in hot climate regions, is considered as one such complex problem. Windcatchers can be used as natural ventilation and passive cooling systems in arid and windy regions in Saudi Arabia. Such systems can be considered as the optimum solution for energy-saving and obtaining thermal comfort in residential buildings in such regions. In the present paper, three-dimensional numerical simulations for a newly-developed windcatcher model have been performed using ANSYS FLUENT-14 software. 'e adopted numerical algorithm is first validated against previous experimental measurements for pressure coefficient distribution. Different turbulence models have been firstly applied in the numerical simulations, namely, standard k-epsilon model (1st and 2nd order), standardWilcox k-omega model (1st and 2nd order), and SST k-omega model. In order to assess the accuracy of each turbulence model in obtaining the performance of the proposed model of the windcatcher system, it is found that the second order k-epsilon turbulence model gave the best results when compared with the previous experimental measurements. A new windcatcher internal design is proposed to enhance the ventilation performance. 'e fluid dynamics characteristics of the proposed model are presented, and the ventilation performance of the present model is estimated.'e numerical velocity profiles showed good agreement with the experimental measurements for the turbulencemodel. 'e obtained results have shown that the second order k-epsilon turbulence can predict the different important parameters of the windcatcher model. Moreover, the coupling algorithm of CFD and the fuzzy system for obtaining the optimum operating parameters of the windcatcher design are described.


Introduction
In windy and arid regions of different countries worldwide and especially in Saudi Arabia, windcatchers can be considered as the optimum solution for energy-saving and obtaining indoor thermal comfort in a natural way. Previously, different shape designs of windcatchers have been proposed and tested either numerically or experimentally, and their ventilation performance has been evaluated. Extended reviews of different theoretical and experimental methods employed to evaluate the performance characteristics of windcatchers can be found in [1]. Recently, a comprehensive review to describe the heat recovery systems that are potentially combined with natural ventilation windcatchers has been carried out [2]. More recently, the effects on the windcatcher performance of different internal factors, such as geometry and design, and the external building features and the surrounding environment have been reviewed [3].
Computational fluid dynamics has recently received great attention in the numerical simulation of the windcatcher model design and performance. Different parameters have been found to have important effects on the obtained results, such as the resolution of the computational grid, the order of discretization scheme, and the turbulence model adopted. Most of the previous studies have been performed for 3D steady RANS for traditional two-sided windcatcher models [4]. Recently, the analysis of the internal flow characteristics of the traditional two-sided windcatcher model has been performed for a better understanding of the external flow condition effects on ventilation performance [5]. e numerical simulation has been carried out using the standard k-ε turbulence model. It is concluded that other turbulence models should be applied instead of the standard k-epsilon model, e.g., the SST model. More recently, sensitivity analysis of the traditional two-sided windcatcher model has been performed in order to improve the thermal comfort conditions [6]. A 3D steady CFD simulation along with a shear-stress-transport k-ω turbulence model is applied for obtaining the windcatcher performance. e effect of introducing an internal windcatcher nozzle on the increased mass flow rate has been estimated.
Generally, it can be concluded from the previous literature that no investigations have been performed to study the effect of the internal design of the windcatcher model on the ventilation performance. Moreover, most of the previous CFD simulation has considered the known standard turbulence models. In our previous paper [7], an innovative modern design of the internal section of a four-sided windcatcher for natural ventilation in Saudi Arabia's buildings has been presented. e proposed model of the windcatcher can avoid most of the shortcomings of previous models presented in the literature in such a manner that the proposed model can harvest the incident wind from any direction. However, an estimation of the performance of the proposed model is required. It should be pointed out that the commercial ANSYS software has been applied previously in many important papers that investigated the performance of windcatcher in different flow regimes [5,[8][9][10][11][12].
In the present paper, computational fluid dynamics (CFD) for the proposed design of the windcatcher using ANSYS FLUENT-14 software is performed. Different turbulence models have been used firstly for validation of the numerical scheme. e verified model is then used for the following prediction of the windcatcher performance.

The New Internal Design of Windcatcher
e new design of the internal section of the windcatcher is illustrated in Figure 1. e illustrated design is assumed to overcome the limitations of the previous conventional windcatchers and improve their performance. e foursided wind tower is assumed to be exposed to the wind from all directions through four fixed openings. e internal design of each separated section is shown in Figure 1. Many limitations of the other models found in the literature can be eliminated by using the proposed design [13]. Moreover, this internal section is designed to increase the ventilation efficiency by using the known characteristics of aerodynamics in variable cross-section areas. e Reynolds number of the incoming air is calculated according to the relation: Re � ρVD h /μ, where ρ is the air density, V is the wind speed, µ is the dynamic viscosity, and D h is the hydraulic diameter of the cross-section (D h � 4 * area/perimeter).
In the described design shown above, it is assumed that interior of the windcatcher is divided into four separated sections. Each section has a square opening with width D in in the normal direction of the incident wind. An inclined wall with an angle θ to the horizontal direction is used to direct the incoming wind to the interior space of the windcatcher. A horizontal flat plate with a one-side opening is fixed in the downstream of the wind direction. is flat plate can be adjusted according to the ratio of L 1 /L 2 (see Figure 1).
is innovative design of the internal section of the windcatcher that receives the incident wind can lead to an increase of the wind velocity due to the convergent nozzle shape applied. After the streaming of the incoming air flow through the opening with width L 2 , air pressure will increase due to the cross-section area expansion. Consequently, the air flow is directed to the building interior with high pressure, enabling uniform air distribution in a natural way.
e model parameters, such as (L 1 /L 2 , θ) should be investigated along with the incoming wind Reynolds number to find out the optimum values of such parameters. e problem will be addressed in this study using CFD techniques. e four-sided windcatcher, previously proposed by the authors in an earlier study [7] to harvest the wind flowing in any direction, is applied. In these ventilation setups, the air enters from suitable opening and flows through the building and lastly leaves through windows, doors, or other exhaust segments. In the present study, one side of the windcatcher is numerically simulated, which is a scaled model of the proposed setup. In this study, several modifications of the windcatcher will be explored and the effect of these alterations on the pressure recovery coefficient will be studied. In the present study, only one side of the windcatcher is modelled with the view that wind would be flowing in one direction with significant velocity at a given time.

Computational Fluid Dynamics
e three-dimensional computational model is set up to simulate the considered windcatcher geometry. Also, the boundary conditions and the model operating conditions are also defined. e solution is carried out using the commercial software ANSYS FLUENT-14.
e computational domain along with the boundary conditions has been described as shown in Figure 2. A combination of structured and unstructured mesh was used for various sections of the model with approximately 450414 total nodes and 429300 elements. e model used very fine mesh near the wall and around the plate near the opening to capture the important flow behavior near the wall (i.e., y + < 5 in the viscous sublayer). e upstream velocity was imposed to the inlet section of the model.

Governing Equations
e flow characteristics inside the proposed design of the windcatcher can be predicted by solving a set of the governing equations in the form of Reynolds-averaged Navier-Stokes equations, as follows:

Reynolds-Averaged Navier-Stokes Equations.
e continuity and momentum equations for incompressible and steady turbulent flow, known as RANS equations, at each grid point of the flow field can be described by the following equations after omitting the body force: In the above system of equations, p denotes the pressure, u is the velocity vector, and ρ, µ are the flow density and the molecular viscosity, respectively. e strain rate tensor is given by S, where the turbulent stress tensor is defined as where δ ij is the Kronecker delta and is the average of the velocity fluctuations. e turbulent viscosity is defined as e turbulent kinetic energy k and its dissipation rate ε can be calculated by solving the governing equations of the standard k-epsilon model, standard Wilcox k-omega model, and SST k-omega model. More descriptions about such models and their standards constants can be found in [14][15][16].

Boundary Conditions
For the problem under consideration, as it can be shown in Figure 2, three different boundary conditions have been described according to the options available in the commercial code used. e inlet boundary conditions describe the different characteristics of the incident wind, e.g., wind speed (V), according to the Reynolds number considered. Moreover, the other relevant scalar properties of the flow are described according to the default values given in the commercial code. e pressure outlet boundary conditions require the value of the static atmospheric pressure at outlet boundary. For all walls in the geometry described in the computational domain, no slip boundary conditions have been assumed.

Model Validation
In order to validate the proposed numerical algorithm, a three-dimensional model was setup to replicate the experimental model of the one-sided windcatcher of Montazeri and Azizian [17]. e computational model was solved using commercial software, ANSYS FLUENT-14, imposing the same boundary and operating conditions as in the experimental study. Pressure recovery coefficient (Cp) was calculated on the back and side wall of the model. Different turbulence models were tried to get a comparative study to find out the best suited model for the windcatcher. e results on variation of Cp along the walls of the windcatcher using different models are illustrated in Figure 3. It is clearly seen in the figure that the second order k-ε model gives the best results when compared with the experimental data. It was therefore decided that the second order k-ε turbulent model will be used for further study on the windcatcher model.

Results and Discussion
e new model with the proposed modifications was tested numerically and pressure recovery coefficient was compared along the length of the windcatcher. e effect of changing the slab length, opening of the windcatcher, and Reynolds number was explored. For all cases, velocity contours, velocity streamlines, and velocity vectors were also compared.

Effect of Slab Length (L 1 ).
e slab length for the proposed windcatcher model was varied as 1/3, ½, and 2/3 of the side of the square cross-section of the windcatcher. e baseline case of without slab was also included in the study. Figure 4 shows the variation of pressure coefficient (Cp) at the middle of the back and side walls of the windcatcher. e Cp values are plotted along the length of the windcatcher where Y � 0 represents the entry and Y � 0.1 as the exit of the windcatcher. e pressure coefficient was high near the entry of the windcatcher and decreased along the length downward towards the exit. High value of Cp near the inlet indicates high pressure due to the presence of the slab which reduces the flow area, causing the nozzle effect. A similar phenomenon was observed at the side wall also, where Cp was also high near the inlet and remained nearly constant for most of the length of the windcatcher and slightly increased near the exit. Figure 5 shows the velocity contours for different slab lengths.

Effect of Windcatcher Opening (θ).
e opening of the proposed windcatcher model to atmosphere was varied in terms of the slant angle as θ � 30°, 45°, and 60°. e slab length as L 1 /L 2 � 0.5 was selected for this analysis. Figure 6 shows the variation of pressure coefficient (Cp) at the middle of the back and side walls of the windcatcher. e Cp values are plotted along the length of the windcatcher where Y � 0 represents the entry and Y � 0.1 is the exit of the windcatcher. e pressure coefficient, as expected, was high near the entry of the windcatcher and decreased along the length downward towards the exit. It was interesting to note that the Cp value near the inlet increased when increasing the opening of the windcatcher. Increasing value of Cp with increasing opening indicates higher pressure which can be attributed to greater mass flow of air through increased windcatcher opening. A similar phenomenon was observed at the side wall also, where Cp was also high near the inlet and remained nearly constant for most of the length of windcatcher for all values of θ. Figure 7 also shows the velocity contours for different slab lengths.

Effect of Reynolds Number (Re).
e effect of Reynolds number was investigated by imposing three different inlet velocities viz. 5 m/s, 10 m/s, and 15 m/s in the windcatcher model. e slab length was L 1 /L 2 � 0.5 and inlet opening was taken as θ � 45°for this analysis. e corresponding Reynolds numbers were 25,131, 50,262, and 75,393. Figure 8 shows the variation of pressure coefficient (Cp) at the middle of the back and side wall of the windcatcher for different values of Re. e Cp values are plotted along the length of the windcatcher where Y � 0 represents the entry and Y � 0.1 as the exit of the windcatcher. e pressure coefficient, as expected, was high near the entry of the windcatcher and decreased along the length downward towards the exit. It was worth noting that the Cp variation along the length was not significantly changed when inlet velocity was increased from 10 m/s to 15 m/s. A similar phenomenon was observed at the side wall also, where Cp was also high near the inlet and remained nearly constant for most of the length of the windcatcher for all values of Reynolds number. Figure 9 also shows the velocity contours for different slab lengths.

CFD-Based Fuzzy Logic Controller.
As seen in the previous section, the numerical results obtained from the computational fluid dynamics of the proposed internal design of a windcatcher model are dependent on a number of operating parameters, namely, L 1 /L 2 ratio, the angle (θ), and the Reynolds number (Re). ree different defined values of such operating parameters have been tested in order to show their effects on the windcatcher model performance. However, it is believed that a wide range of these operating parameters should be tested to obtain a group of values for these operating parameters. e fuzzy logic  Mathematical Problems in Engineering control system can do such a job easily and in an accurate manner [18]. e computational fluid dynamics can provide the fuzzy system with the required dataset after the required validation of the CFD models [19]. erefore, a wide range of numerical simulations using the computational fluid dynamics should be performed. e fuzzy logic system can be fed with such data in order to decide intelligently the optimum values of such operating conditions. e higher the  number of the CFD simulations, the more the correct and optimal decisions from the fuzzy system are obtained. e complete system diagram can be seen in Figure 10. Figure 11 shows the normalized output of the proposed fuzzy logic system as a function of other operating parameters. It should be pointed out that the proposed fuzzy logic system will be considered in the future work of the problem, as the present work is dedicated for the validation of the numerical procedure and the effectiveness of the proposed internal design of the windcatcher.     Figure 9: Velocity contours at different Reynolds number (Re).

Conclusions
In this study, a novel model of windcatcher was proposed to employ in passive cooling of living spaces. e suggested four-way model has openings on four sides that lead the incoming air to the duct downstream. In the present study, only one side of the system is modelled. A slab near the inlet opening was placed to create a nozzle effect to enhance the pressure recovery downstream. e model was studied numerically for the variation of slab length, Reynolds number of incoming wind velocity, and inlet opening to the atmosphere. e data analysis revealed that the introduction of a slab near the inlet improved pressure recovery, which increased with the length of the slab. Higher value of pressure recovery was also observed with increasing opening of inlet section. e effect of Reynolds number on pressure recovery was seen up to a moderate value of Re, after which it did not change significantly. e new model can help in optimizing the design parameters of windcatcher for given local atmospheric conditions. In the future work, the fuzzy logic system will be applied for obtaining the optimum values of the operating parameters.

Data Availability
No data were used to support this study.  Mathematical Problems in Engineering 9