Influences and Optimizations of Vertical Facades on the Aerodynamic Loadings for High-Rise Buildings

Abstract

The architectural facade, including balconies, vertical frames, and sunshades, is widely installed on the surfaces of high-rise buildings, and will affect the wind load and airflow around the buildings. However, current studies mainly focus on local wind pressure, with limited research on aerodynamic forces and a lack of optimization design methods for vertical facades. This paper investigates the aerodynamic effects of different vertical facade layouts on high-rise buildings through wind tunnel experiments. Subsequently, CFD simulations were performed on 120 generated models. By combining neural networks and genetic algorithms, this paper optimized the aerodynamics of the vertical facades on a high-rise building, analyzed the flow field around the building, and provided reference for the aerodynamic optimization design of vertical facades on high-rise building facades. The results show that vertical facades could reduce the base shear forces and overturning moments of tall buildings, and the mean drag coefficient can be reduced by up to 31%, and the RMS value of lateral force coefficient by 57%, through the aerodynamic optimization. Through the analysis of flow fields around tall buildings, the “chamfer” formed by the vertical facades and the building corner is attributed as the main reason for reducing the aerodynamic forces of tall buildings. Furthermore, the negative resistance on vertical facades caused by the adverse pressure gradient is another major factor for reducing the mean value of aerodynamic force.

1. Introduction

With the increasing demands for architectural aesthetics and various functions, different types of building facades, including balconies, vertical frames, and sunshades, are widely installed on the surfaces of high-rise buildings, as shown in Figure 1. Obviously, these facades would significantly influence the aerodynamic loadings on the building surface, which might jeopardize the safety margin of the wind-resistant design of main frames and envelopes of high-rise buildings. However, the wind loads provided by structural load codes (such as ASCE 7–10 [1]; GB 50009-2012 [2]; Nassiraei, 2024 [3]) are mainly based on wind tunnel load data for buildings with smooth surfaces. Therefore, it is highly important to study the impact of architectural facades on the wind-resistant design of high-rise buildings.

In the past few decades, research on the impact of architectural facades on wind loadings has been relatively limited, with a primary focus on local wind pressures of high-rise buildings through wind tunnel testing. Stathopoulos and Zhu [4,5] investigated the wind pressures on buildings with balconies or mullions on one wall. Their findings revealed that balconies can slightly reduce wind pressure, while mullions tend to produce adverse wind effects along wall edges. Maruta et al. [6] explored the influence of uniform roughness and balconies with or without mullions on local wind pressures of tall buildings. Their experimental results indicated that surface roughness significantly affects wind pressures, especially near the leading edge of the side wall, where severe peak pressures decrease with increasing roughness. Yuan et al. [7] conducted wind tunnel tests on tall buildings equipped with horizontal appurtenances on the upper part to study the impact of different sizes and spacings of these appurtenances on local wind pressures. They discovered that the area of large positive peak pressures on building models with appurtenances was substantially smaller than those without, and the largest negative peak pressure on the higher leading corner could be reduced by 42% compared to smooth surface conditions. In addition to local wind pressures, Quan et al. [8] examined the effects of the depth and spacing of vertical ribs on the base moment of a super-tall building, demonstrating a noticeable influence. Cheng et al. [9] used wind tunnel tests to study the impact of various architectural facades on both local wind pressures and aerodynamic forces of tall buildings. Their results showed that facades significantly affect local wind pressures and aerodynamic forces, with models featuring vertical facades exhibiting notably lower mean base shear forces and base moments compared to those with smooth surfaces.

As Computational Fluid Dynamics (CFD) techniques continue to advance and high-performance computing resources become more accessible, numerical simulations using CFD have gained widespread application in the field of wind engineering and the wind-resistant design of buildings and structures [10,11,12]. Due to the superior performance in reproducing the instantaneous flow field around, and fluctuating pressures on, buildings and structures, Large Eddy Simulation (LES) has been used to evaluate wind loading, including both of the mean and fluctuating components in wind engineering [13,14,15,16,17,18,19]. For the computation of the wind loading of tall buildings with architectural facades, Ai and Zhou [20,21] used LES to numerically simulate the wind pressure of an actual high-rise building with complex decorative ribs. The results show that the numerical results are safe and reliable. Liu et al. [22] employed LES to study the impact of ribs mounted on the windward face of a square tall building and discovered that local recirculation in the front corner region significantly affects flow separation and alters the behavior of the shear-layer flow. Hui et al. [23] explored the effects of vertical ribs with various arrangements on the flow field and aerodynamic characteristics using LES. Their findings indicated that ribs on the windward face and downstream ribs on the sidewall can notably influence the separated shear-layer behavior by inducing local recirculation. In addition, many scholars [24,25,26] have recently used CFD technology to study vertical ribs on the surface of building. Overall, CFD technology is now a key tool in wind engineering and is also used in this paper.

The literature review reveals that architectural facades have a substantial impact on wind loads acting on buildings, with vertical facades being particularly effective in reducing aerodynamic forces on tall buildings. Nevertheless, the majority of existing studies concentrate on how architectural facades influence local wind pressure. There are few studies on the laws of vertical facades affecting aerodynamic forces, and there is no optimal design method of vertical facades for aerodynamic forces.

To systematically and deeply study the influence of vertical facades on aerodynamic force, Section 2 of this paper conducts wind tunnel tests on models with vertical facades of different sizes and spacings to explore the change laws of aerodynamic forces. In Section 3, based on 2.5-dimensional (2.5D) LES simulations (Yan et al. [27]), the aerodynamic optimization of vertical facades is carried out by a BP (Back Propagation) neural network and the genetic algorithm (GA). Section 4 conducts the 3D LES simulations of tall buildings with vertical facades to elucidate the flow mechanism around the vertical facades that affects the aerodynamic forces on tall buildings. Finally, Section 5 gives some conclusions.

2. Aerodynamic Force Characteristics Based on Wind Tunnel Experiments

In this section, the arrangement of wind tunnel experiments and setup of vertical facade models are given. Then, base forces, including the mean and fluctuating aerodynamic forces under different wind directions from the wind tunnel experiments, are discussed.

2.1. Setup of Wind Tunnel Experiments

The wind tunnel experiments detailed in this paper were conducted in the wind tunnel facility at Beijing Jiaotong University. The test section measures 3.0 m in height, 2.0 m in width, and 15.0 m in length, with a maximum wind speed capacity of 40.0 m/s. As depicted in Figure 2, the atmospheric boundary layer wind field is simulated using traditional wedge-shaped objects and roughness elements. The building models used have dimensions of 10 cm × 10 cm × 50 cm (B × D × Z_H), corresponding to a geometric scale of 1:400. It is easy to calculate that the blocking ratio is 0.83%, which is much less than the requirement of 3%. A mean wind speed profile with a power law index α = 0.22, representing urban terrain (category C), was simulated in accordance with the Chinese building loading code (GB 50009-2012 [2]). The mean wind speed (U_z) and turbulence intensity (I_z) measured at various heights are illustrated in Figure 3a, where U_H (set as 10 m/s in this study) denotes the mean wind speed at height Z_H. It can be calculated that the Reynolds number for wind tunnel experiments is approximately 6.8 × 10⁴. Furthermore, the power spectrum of wind speed obtained from the experiment is presented in Figure 3b and shows good agreement with the Von Karman spectrum.

As shown in

Table 1. Vertical facade models.

Models

1

2a

2b

2c

3a

3b

3c

4a

4b

4c

F-1-3b

F-3c-3b

Spacing (s/B)

1

1/6

1/6

1/6

1/11

1/11

1/11

1/20

1/20

1/20

1/11 from edge

1/11

Depth (d/B)

0

4/50

2/50

1/50

4/50

2/50

1/50

4/50

2/50

1/50

1/25

1/50 (1/25, two facades near the edge)

, a total of 12 model tests were conducted in this study through using vertical facades of different sizes and spacings. Model 1 is a reference model without vertical facades, and four walls of the remaining 11 models are all affixed with vertical facades. The extensional depth of the facade is d and the spacing is s. Model F-1-3b is that 2 vertical facades are added on each wall based on Model 1, and Model F-3c-3b is that 2 vertical facades are altered on each wall based on Model 3c, as shown in Figure 4. Moreover, balsa wood is utilized in HFFB experiments to construct models that possess sufficient stiffness while maintaining a lightweight structure. Additionally, the mean wind speed at the top of the building model remains at 8 m/s, with a velocity scale of 1:5, which corresponds to a time scale of 1:80. The sampling duration for each direction is set at 150 s, equivalent to 200 min in full-scale conditions.

The coefficient of base shear force C_Fx(φ, t), the coefficient of base moment C_My(φ, t), and the coefficient of base torsion C_Tz(φ, t) (where the x-axis corresponds to the 0° direction and the y-axis to the 90° direction) at time t and under the wind direction φ are defined as follows.

$$C_{Fx}\left(\varphi ,t\right)={\displaystyle \frac{F_x\left(\varphi ,t\right)}{\frac{1}{2}\rho U_H^{2}B{Z}_H}}$$

(1)

$$C_{My}\left(\varphi ,t\right)={\displaystyle \frac{M_y\left(\varphi ,t\right)}{\frac{1}{2}\rho U_H^{2}B{Z}_H^2}}$$

(2)

$$C_{Tz}\left(\varphi ,t\right)={\displaystyle \frac{T_z\left(\varphi ,t\right)}{\frac{1}{2}\rho U_H^{2}BD{Z}_H}}$$

(3)

where F_x(φ, t), M_y(φ, t), and T_z(φ, t) are the base shear force, the base moment, and the base torsion at time t under the direction φ for HFFB model, respectively. Through Equations (1)–(3), the base shear force, base moment, and base torsion are converted into three dimensionless quantities, which can more directly reflect the changes in aerodynamic forces.

In the subsequent analysis, the mean base shear force coefficient and the mean base bending moment coefficient are represented by C_{Fx_mean} and C_{My_mean}, respectively. Additionally, the root mean square (RMS) values of the base shear force coefficient, base moment coefficient, and base torsion coefficient are denoted as C_{Fx_rms}, C_{My_rms}, and C_{Tz_rms}, respectively.

2.2. Mean Aerodynamic Force Coefficients

Figure 5 presents the mean base shear forces (C_{Fx_mean}) for different models under 0° wind direction. Obviously, the mean base shear force of models with vertical facades is smaller than that of the smooth model, which can further confirm that the vertical facade has the effect of reducing the base shear force. Comparing models 2a, 2b, and 2c (or models 3a, 3b, and 3c; or models 4a, 4b, and 4c), it can be found that the mean base shear forces of models 2a and 2c are smaller than that of model 2b (or 3a, 3c < 3b; or 4a, 4c < 4b), which can be inferred that the effect of a vertical facade to reduce the base shear force will be reduced when the depth of vertical facade is too small or too large. The reason may be that the effect of the vertical facade to reduce the base shear force is not obvious enough when the depth of vertical facade is small, or the continuous increase of the vertical facade depth will increase the base shear force when vertical facade depth is large. Comparing models 2a, 3a, and 4a (the depth of vertical facade is relatively long), the mean base shear force is as follows: 4a < 2a < 3a. While comparing models 2b, 3b, and 4b (or 2c, 3c, and 4c), the mean base shear force is: 2b > 3b > 4b (or 2c > 3c > 4c). It can be inferred that the mean base shear force decreases with the decrease of spacing when the vertical facade depth is not large; that is, the smaller the spacing, the more obvious the effect of vertical facade on reducing the base shear force.

As shown in Figure 6, vertical facades V₁ and V₂ and corner C₀ form a shape similar to a “chamfer”, which may be one of the reasons for reducing the base shear force. Then, the mean base shear force of model 3b is smaller than that of model 3c, which means that the “chamfer” shape of model 3b is better than that of model 3c. Therefore, in order to verify this inference, the vertical facade arrangement in the “chamfer” area of model 3b is directly applied to model 3c to form the model F-3c-3b. As can be seen from Figure 5, the mean base shear force of model F-3c-3b is reduced by 10.3% compared with that of model 3c, which is enough to indicate that the “chamfer” shape does play a role that cannot be ignored. The same conclusion can be illustrated with model F-1-3b and model 1. Model F-1-3b adds the vertical facade arrangement in the “chamfer” area of model 3b on the basis of model 1, resulting in a reduction of the mean base shear force of model F-1-3b by about 12.0% compared to model 1. In addition, the mean base shear force of model 3b is about 15.8% lower than that of model F-1-3b, from which it can be inferred that the vertical facades arranged in the middle area of building wall also play a role in reducing the base shear force. Moreover, it can also be explained that the different arrangements of vertical facade in the middle area of building wall lead to different effects by comparing model F-3c-3b with model F-1-3b.

In general, the vertical facade has the effect of reducing the mean base shear force, and the effect of different spacing and depth is different; moreover, both the “chamfer” shape (composed of vertical facades and corner point) and the arrangement of vertical facades in the middle area of the building wall contribute to reducing the mean base shear force.

Figure 7 shows the variation curves of mean base shear force with change of wind direction for each model. It can be seen that shape of the variation curves of the mean base shear force of each model are basically the same. Among them, the mean base shear force of each model reaches the maximum value in the wind directions of 0°~20°, and then gradually decreases, and basically tends to 0 when reaching 90°. Differences among the mean base shear forces of different models are larger when the wind direction is small, and the differences becomes smaller when the wind direction is large. As the wind direction gradually increases (the differences among the mean base shear forces of different models gradually decrease), the mean base shear force of models with vertical facades tends to exceed that of the smooth surface model. Figure 8 shows the variation curves of the mean base moment of each model with change in wind direction. Obviously, the variation law of the mean base moment of each model are basically consistent with that of the mean base shear force.

2.3. Fluctuating Aerodynamic Force Coefficients

Variation in the RMS values of base shear forces (C_{Fx_rms}) for each model under different wind directions is shown in Figure 9. Obviously, the C_{Fx_rms} values of the models with vertical facades are basically smaller than those of smooth models around the wind directions of 0° and 90°, while the C_{Fx_rms} values of some models with vertical facades exceed the smooth model near 45° wind direction. Among them, the C_{Fx_rms} values of model 4b are 18.7% and 25.2% lower than those of model 1 at wind directions of 0° and 90°, respectively. Variation curves of the RMS values of base blending moments (C_{My_rms}) under different directions are shown in Figure 10, which is close to the RMS values of base shear forces (C_{Fx_rms}). Among them, the C_{My_rms} values of model 4b are 21.1% and 24.7% lower than those of model 1 at wind directions of 0° and 90°, respectively. Figure 11 shows variation curves of the RMS values of base torque (C_{Tz_rms}) under different directions. The C_{Tz_rms} values of models with vertical facades are mostly larger than those of the smooth model. Among them, the C_{Tz_rms} values of model 3b are increased by 40.4% compared with model 1. In general, for the RMS values of base shear forces and base blending moments, the vertical facades have a significant reduction effect, which is mainly affected by the spacing and depth. On the contrary, vertical facades have an increasing effect on the RMS values of base torque.

3. Aerodynamic Optimization Based on Numerical Simulation

Currently, more and more machine learning algorithms are being used to solve scientific problems in wind engineering, such as aerodynamic optimization and wind load prediction [28,29,30,31,32,33]. In this section, the aerodynamic optimization of vertical facades will be performed by combining CFD simulations and neural network algorithm. From Section 2, it can be seen that a vertical facade has a decreasing effect on the base shear force and base moment of tall buildings, and that the spacing and depth of the vertical facade are the main influencing factors. In order to obtain the optimal vertical facade arrangement for providing reference to the design, the drag and lateral force coefficients of models with vertical facades of different spacing and depth are obtained based on 2.5D CFD simulations. Then, the computational data are used to train the BP neural network, and the genetic algorithm (GA) optimizes the vertical facade arrangement. Finally, 3D LES is implemented to simply verify the optimization results.

3.1. Setup of LES Simulations

The computational settings for LES simulations, including governing equations, computational domain and grid settings, boundary conditions, and numerical algorithms, are given in this section. Note that this section uses both 2.5D and 3D LES simulations, so they are introduced separately.

3.1.1. Governing Equations of LES

The LES turbulence model is used in this paper, and the governing equation is as follows:

$${\displaystyle \frac{\partial \overline{u_i}}{\partial x_i}}=0$$

(4)

$${\displaystyle \frac{\partial \overline{u_i}}{\partial t}}+{\displaystyle \frac{\partial (\overline{u_i}\overline{u_j})}{\partial x_j}}=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial \overline{P}}{\partial x_x}}+\nu {\displaystyle \frac{{\partial }^2\overline{u_i}}{\partial x_j\partial x_j}}-{\displaystyle \frac{\partial {\tau }_{ij}}{\partial x_j}}$$

(5)

where u_i (i = 1, 2, 3) is the velocity component; ρ, P and ν are the air density, pressure and kinematic viscosity, respectively; the over-bar denotes the spacing filtered quantities. In this study, the subgrid scale (SGS) stress, ${\tau }_{ij}=\overline{u_i{u}_j}-\overline{u_i}\overline{u_j}$, can be solved using the Smagorinsky model [34,35].

In this study, all numerical computations were conducted using parallel processing with 36 threads on the ANSYS/FLUENT 2021R1 platform. Specifically, the pressure–velocity coupling was achieved using the Semi-Implicit Method for Pressure-Linked Equations Consistent (SIMPLEC) [36]. The numerical approximation of pressure gradients was calculated using the Green–Gauss node-based method. The time derivative was discretized using a second-order difference scheme, while the time integration was performed using a fully implicit method. The convective and diffusion terms of the momentum equations were discretized using a bounded central difference scheme to ensure low diffusivity. Additionally, to improve convergence, a Reynolds-Averaged Navier–Stokes (RANS) simulation was conducted prior to each Large Eddy Simulation (LES) computation.

3.1.2. 2.5D LES Setup

The computational domain of 2.5D LES [27] is shown in Figure 12. In this study, 2.5D LES represents that in the LES numerical model, the model in the computational domain is infinitely long in the spanwise direction. The dimensions of the computational domain are 20B (width), 45B (length), and 2B (height), and the geometric ratio is 1:200. A hybrid grid with the unstructured grids near the building and the structured grids for the outer area are used for the computational domain, as shown in Figure 13. In order to ensure the numerical stability, the prismatic grid is adopted on the building surface, and the minimum grid height perpendicular to the surface is set to B/400, and the growth ratio is 1.05. For the unstructured grid, the minimum size of the near wall is set to B/80, and the growth ratio is 1.2. The total grid number of models is in the range of 4 × 10⁵ to 1.5 × 10⁶. The time step is set to 0.0032 s. The inflow is uniform flow and the speed is set to 8 m/s. Boundary conditions of the bottom, top, and lateral sides of the computational domain are set as symmetry, and the outlet is set as pressure-outlet. The drag and lateral force are saved after 900 time steps for each model, and a total of 1500 time steps are recorded, i.e., 4.8 s (equivalent to 3.2 min of actual time). Note that only 0° wind direction is focused on here.

In order to verify the numerical simulations, grid independence verification is carried out by comparing numerical simulation results using three grid sizes, respectively. Then, the mean drag coefficient and the RMS value of the lateral force coefficient of the square model without facades are computed using the most appropriate grid size.

Table 2. Comparisons of C_{l_rms} and C_{d_mean}.

	Studies	Cl_rms	Cd_mean
Experiments	Lyn et al. [37,38]	-	2.1
	Bearman and Obasaju [39]	-	2.15
CFD	Sohankar and Norberg [40]	1.5 1.23	2.22 2.03
	Pourquie et al. [41]	1.01 1.12 1.02	2.2 2.3 2.03
	Wang and Vanka [42]	1.29	2.03
	Nozawa and Tamura [43]	1.39	2.62
	Kawashima and Kawamura [44]	1.26 1.38	2.72 2.78
	Present study	1.24	2.17

gives a comparison with the results of other studies. It can be seen that the accuracy of numerical simulations is appropriate.

3.1.3. 3D LES Setup

In the 3D Large Eddy Simulation (LES) setup, the computational domain has a length of 24H and a width and height of 4H each (see Figure 14), where H represents the height of the building model. The blocking ratio, calculated to be approximately 1.25%, satisfies the requirements of computational wind engineering [45]. A structured mesh is utilized and generated using the software ICEM 2021R1. To accommodate various wind directions, the computational domain grid is divided into two sections: a cylindrical region surrounding the building model and an outer region extending away from the model (see Figure 15). To verify grid independence, two grids, G1 and G2, were generated. For G1, the first layer grid size perpendicular to the model surface was set to 0.1/(Re)^0.5, where Re = U_HB/ν (with U_H representing the inflow velocity at the height of the building model, and Re being approximately 2.7 × 10⁵). The first layer grid size parallel to the model surface was set to 1.0/(Re)^0.5. The grid size growth ratio was 1.05 in the cylindrical region and 1.2 in the outer region. For G2, the first layer grid size perpendicular to the model surface was reduced to 0.05/(Re)^0.5, and the size parallel to the model surface was set to 0.5/(Re)^0.5, with all other parameters remaining the same as in G1.

The Consistent Discrete Random Flow Generation (CDRFG) technique [46] is employed to create inflow turbulence. The velocity history data for each grid point on the inflow boundary are generated using a User-Defined Function (UDF) within the finite volume-based ANSYS/FLUENT software. For the computational domain, a symmetry boundary condition ($\partial \overline{u}/\partial n=0,\partial \overline{w}/\partial n=0,\overline{v}=0$) is applied to the lateral faces, while a slip wall with zero shear stress is used at the top. The building surface (including architectural facades) and the bottom of the domain are treated with a no-slip wall condition. Additionally, the outlet boundary is defined as an outflow condition. These boundary conditions for the computational domain are summarized in

Table 3. Boundary conditions for computational domain.

Surfaces	Boundary Conditions
Inlet	Velocity-inlet, CDRFG technique
Outlet	Outflow
Top	Slip Wall
Side face	Symmetry
Bottom and building surface	No-slip Wall

.

In order to verify the numerical simulations, grid independence verification is carried out by comparing the mean base shear forces of model 2a under different wind directions using G1 and G2, respectively. As shown in Figure 16, the numerical simulation results of grids G1 and G2 are basically consistent. Therefore, in order to improve the computational efficiency, this paper uses grid G1 for subsequent numerical simulations.

It is worth noting that all numerical computations in this paper were performed in parallel using 28 threads on the ANSYS/FLUENT platform, with the maximum turbo frequency of up to 5.8 GHz. For the 2.5D LES cases in this paper, the calculation time required for each numerical simulation is approximately 40 min. For 3D LES, the calculation time is approximately 1600 min. In addition, both numerical simulation results are close to experimental results, which will be mentioned later.

3.2. Optimization Parameters and Goals

According to the analysis of experimental data, the results under 0° wind direction are more representative, so the optimization process in this section is aimed at the 0° wind direction. In addition, since the vertical facade has different effects on the mean and RMS values of base shear force, the mean drag coefficient and the RMS value of lateral force coefficient are used as the targets for optimization in this section, respectively. The drag coefficient C_d and lateral force coefficient C_l can be respectively calculated by Equations (6) and (7). F_d and F_l are the drag and the lateral force, respectively, and U_ref is the reference velocity, which is taken as 8 m/s. Furthermore, A is the windward area of the building model.

$$C_d={\displaystyle \frac{F_d}{0.5\rho U_{ref}^{2}A}}$$

(6)

$$C_l={\displaystyle \frac{F_l}{0.5\rho U_{ref}^{2}A}}$$

(7)

Figure 17 shows the square as the basic section, and the depth of vertical facade is d, and the spacing s. Then, two variables v₁ and v₂ are defined:

$$v_1=s/B{v}_1\in [0.025,0.333]$$

(8)

$$v_2=d/B{v}_2\in [0.0125,0.075]$$

(9)

It is worth noting that the ranges of the two variables are set to consider the reasonable arrangement of vertical facades in real buildings.

In the optimization process, the aerodynamic data are used to train the BP neural network [47], and the well-trained BP neural network is taken as the objective function in the GA method for aerodynamic optimization. However, the training of neural networks requires a large amount of aerodynamic data, so LES under the 3D atmospheric boundary layer is very expensive. Tamura and Miyagi [48] have shown that 2.5D flow is sufficient to evaluate the aerodynamic behavior of tall buildings in the atmospheric boundary layer. And Elshaer et al. [49] have successfully evaluated the aerodynamic force of tall buildings in the atmospheric boundary layer using 2.5D LES. Therefore, LES results from 2.5D flow are used for BP neural network training in this section. As shown in Figure 18, 120 variable combinations are randomly generated within the ranges of v₁ and v₂, and the LES computations are performed for the models corresponding to each set of variables.

3.3. Optimization Results and Its Validation

In this section, the computational data are used to train the BP neural network, and combine the genetic algorithm (GA) to optimize the vertical facade arrangement. Finally, 3D LES is implemented to simply verify the optimization results.

3.3.1. Optimization Results

After completing the numerical computations of 120 variable combinations with 2.5D LES, BP neural network can be trained with the results. Of the total data, 70% are used for BP neural network to learn, and another 30% are used for its verification and testing. Figure 19 shows the training results with 80, 100, and 120 samples, which indicate that the BP neural network provides the accurate result. Overall, the training conclusions become better as the number of samples increases. In addition, it can be found from the error analysis of BP neural network results obtained by training 120 samples that the error of 60% the data is within 5%, which indicates that the training effect of the BP neural network here is very good and that it can be used as the objective function of the genetic optimization algorithm.

The GA optimization process is conducted when the BP neural network training is completed. Firstly, an initial population is randomly generated, and then the operations, including selection, crossover and mutation, are used to generate a new population. The operation of selection uses the roulette method to select individuals with high fitness. The operation of crossover is used to exchange genes between two individuals to produce new individuals. The mutation operation generates the new individual by mutation of one or some genes on one individual to avoid the optimization solution falling into local extrema. The number of individuals in the initial population is set to 100, and each individual contains two genes (variables v₁ and v₂) and is coded by binary with a coded number of 20 bits. The maximum genetic algebra is initially set to 100. In the genetic algorithm, selection, crossover, and mutation operations are crucial for optimization [50,51,52]. The selection probability is set to 0.9, the crossover probability to 0.7, and the mutation probability to 0.001. These parameters work together to guide the algorithm’s search process. (1) The selection operation, based on individual fitness, has a 0.9 probability of choosing fitter individuals to pass their genes to the next generation. This promotes the spread of advantageous genes and improves the overall population quality. (2) Crossover, occurring with a probability of 0.7, combines the genes of two parents to create offspring. This helps explore the solution space by generating new gene combinations and enhances the algorithm’s global search ability. (3) Mutation, with a probability of 0.001, introduces new genes by randomly altering individual genes. Despite the low probability, it provides sufficient population diversity over many iterations, helping the algorithm escape local optima. (4) Five independent genetic optimization runs are conducted to reduce the chance of the optimal solution being trapped in local optima. This ensures result stability and reliability, verifying the rationality of the parameter settings and the algorithm’s ability to consistently find high-quality solutions.

Figure 20a shows the optimization process of the genetic population for the mean drag coefficient. It can be seen that the population has been converged to the 20th generation, and the convergence value is 1.498 (v₁ = 0.111 and v₂ = 0.070), which is reduced by 31% compared with the model without facades, as shown in Figure 20a.

Figure 20b shows the optimization process of the genetic population for the RMS value of the lateral force coefficient. It can be seen that the population has been converged to the 15th generation, and the convergence value is 0.529 (v₁ = 0.200 and v₂ = 0.075), which is reduced by 57% compared with the model without facades, as shown in Figure 21.

3.3.2. Validation of Optimization Results

In order to verify the model with the smallest mean drag coefficient (M1: v₁ = 0.111, v₂ = 0.070), another typical model with vertical facades (M1c: v₁ = 0.050, v₂ = 0.015) is selected and its mean drag coefficient is 1.951 (M1 is 23% lower than M1c). Then, the LES cases under the 3D atmospheric boundary layer are performed for these two models.

Figure 22 shows the mean velocity contours with streamlines of the two models at the height z = 0.67H. It can be seen that M1 with the optimal arrangement of vertical facades has a smaller wake size than M1c, which obviously confirms that M1 has a significant reduction in drag. In addition, the mean drag coefficients of the two models computed by 3D LES are respectively 0.665 and 0.907, and the mean drag of M1 to M1c is reduced by about 27%. Comparing the drag computed by 2.5D LES (M1 is 23% lower than M1c), it can be seen that the drag computed by 2.5D LES is reasonable for evaluating the relative drag of tall buildings.

4. Result Interpretation by Flow Field

Figure 23 shows the mean velocity streamlines and mean pressure contour diagram of horizontal sections of models 1, 3b, F-1-3b, and F-3c-3b. It can be seen that the negative pressure area and negative pressure value on the side of model 1 are significantly larger than those of the other three models. Figure 24 shows the mean velocity streamline diagram of one-half of the horizontal section of models 1 and 3b for detailed observation. It can be known that there is a backflow near the side wall due to the adverse pressure gradient after the flow is separated from the leading edge of side wall, which results in a large negative pressure area on the model side. When vertical facades are present, especially in the model corner areas, the negative pressure area can be reduced to the inner area of the vertical facades on the model side (such as in model 3b). By analyzing the cross-sectional streamline diagram, a schematic diagram of flow separation at the corner of models can be drawn in Figure 25. It can be inferred that the negative pressure area and negative pressure value are mainly affected by the shape of the corner formed by vertical facades. That is, the corners of model 3b with vertical facades are similarly chamfered, thereby exhibiting the effect of reducing the aerodynamic force. It is worth noting that Mooneghi and Kargarmoakhar [53] have demonstrated, by comparing the flow fields around square and chamfered sections, that chamfered sections have less impact on the surrounding flow field and produce smaller wake sizes, resulting in lower aerodynamic force.

Figure 26 shows the mean aerodynamic force coefficients of vertical facades on the sides of Models 3b, F-1-3b, and F-3c-3b. The aerodynamic force direction on the vertical facade is opposite to the wind direction, likely due to the pressure difference caused by the wind impacting the vertical facade (see Figure 27). Moreover, the aerodynamic force on the edge vertical facade is greater than on others. This may be because the front and back of the edge vertical facades experience positive and negative pressures, respectively (see Figure 27), creating a larger pressure difference and thus a greater component force. As shown in Figure 27, the mean pressure gradually increases from the leading edge to the trailing edge of the side wall. For any vertical facade on a side wall, the pressure on the side of incoming flow is smaller than that on the wake side, which will generate a force from high pressure to low pressure on the vertical facade. As a result, the same conclusion can be drawn that the mean aerodynamic direction of the vertical facade is opposite to the wind direction.

5. Conclusions

Through the wind tunnel test, the aerodynamic forces of tall building with vertical facades are studied in depth in this paper. Then, aerodynamic optimization for a tall building and flow field analysis around a tall building are performed based on LES simulations. The main contributions and conclusions are as follows.

(1) Vertical facades have the effect of reducing the mean and the RMS values of base shear forces and base moments of tall buildings, which is mainly affected by the spacing and depth. In particular, the C_{Fx_rms} value of model 4b is 25.2% lower than that of model 1 at wind directions of 90°.

(2) The layout of vertical facades on the surfaces of tall buildings, considering the optimal aerodynamic force, can be obtained by the CFD + BP neural network + genetic algorithm optimization method. By this method, the mean drag coefficient can be reduced up to 31%, and the RMS value of the lateral force coefficient can be reduced by 57%.

(3) Through the analysis of the flow field around tall buildings, the “chamfer” formed by the vertical facades and the model corner are two of the major factors to reduce the aerodynamic force. Furthermore, the negative resistance on vertical facades caused by the adverse pressure gradient is another major factor.

This study uses a GA-based to explore the aerodynamic characteristics and optimization of buildings with vertical facades. Given the facades’ greater vertical scale than horizontal scale, 3D LES is simplified to 2.5D LES, reducing CFD simulation costs. However, when applying the GA genetic algorithm to general aerodynamic optimization problems, there are some limitations, such as the following:

(1) Genetic algorithms typically require substantial iterations and population evaluations. For problems that cannot be simplified, this incurs high computational and time costs.

(2) Improper initial population selection or parameter settings may lead GAs to converge prematurely to local optima rather than global optima, especially in complex, multimodal solution spaces.

(3) GA performance is sensitive to parameter settings (e.g., selection, crossover, and mutation probabilities). Unsuitable parameters can cause slow convergence or local optimum trapping.

In addition to genetic algorithms (GAs), other optimization algorithms, such as particle swarm optimization (PSO), ant colony optimization (ACO), and artificial bee colony (ABC) algorithms, can be explored. Comparing different optimization algorithms and surrogate models is expected to be conducted in future research to find the most effective algorithm combinations.

It should be noted that for the high-rise building models studied in this paper, 2.5D flow can be used to assess the relative magnitude of 3D flow’s aerodynamic forces, but its ability to assess the absolute magnitude remains questionable.