Modelling of Wind Pressure Coefficients on C-Shaped Building Models

Designs of buildings are changing with emerging demands of several aesthetical features and efficient design based on geometry. Development of new building materials and construction techniques have enabled us to build new buildings which are tall and unsymmetrical, but unfortunately such structures are more susceptible to wind loads. %us it becomes necessary to estimate wind loads with higher degree of confidence. Although ample information regarding wind load on symmetrical and regular structure is available in various international codes, they lack the study of effect of wind forces on unsymmetrical structures. %is paper presents experimental and numerical studies of the wind effect on commonly used C-shaped buildings with varying aspect ratio and its optimization caused by the alteration of angle of incidence. Furthermore, results obtained by numerical analysis have been validated with the experimental one. For this study, numerical analysis has been carried out using ANSYS Fluent with k-εmodel of turbulence. Computational fluid dynamics (CFD) techniques is used to evaluate the surface pressure on various faces of the model for angle of attack of 0° to 180° at an interval of 30° in a subsonic open circuit wind tunnel. %e results found by CFD technique are well compared with the experimental results which suggest the feasibility of using this technique of predicting wind pressures on building efficiently and accurately.


Introduction
Gradual increase of demand of tall and unsymmetrical buildings with efficient geometric design and planning needs futuristic visionary and scientific estimates of various kinds of forces.Wind force is one of them, which plays a crucial role in case of unsymmetrical buildings.Shortage of land and demand of good aesthetical view have forced us to construct nonconventional plan-shaped building.Although ample information regarding wind load on symmetrical structure (conventional plan-shaped structure) is available in various international codes, for example, IS: 875 (Part 3): 1987(code of practice for wind loads for buildings and structures) [1], no such direct reference is available for irregular planshaped structures.e effect is even more critical for unsymmetrical and tall structures due to dynamic response arising from vortex shedding and galloping.Among the loads which act on buildings, the wind load is quite difficult to predict.However, the evolution of computer programs for structural analysis has made the prediction of wind pressure relatively easy to design a building to suit any given set of applied loads.
ough now a days nonconventional plan shapes are very common building configurations, experimental as well as numerical data for such shapes for different wind directions are very limited.Various literatures provide the study of effect of wind pressure on tall and irregular shape of buildings.Paterson and Apelt [2] first presented the research on computation of wind flows over threedimensional buildings by numerical analysis and found accurate results for some wind flows over simple threedimensional buildings.Kwok [3] conducted the wind tunnel model test to analyse the effect of building shape on the wind-induced response of a tall building with a rectangular cross section.Afterwards, Stathopoulos and Zhou [4] presented the paper which shows the numerical prediction of turbulent wind pressures on the building surfaces with sharp corners of right angles for different wind incidence angle.Miyashita et al. [5] presented effects of corner cuts and openings in high-rise square buildings.Li et al. [6] have described the results obtained from the measurements of wind effects on two high-rise buildings with 70 storeys and 30 storeys, respectively.Gomes et al. [7] investigated pressure distributions on L-type and U-type building models under varying wind incidence angle.Chakraborty et al. [8] showed that pressure induced on a "+" plan-shaped tall building is widely different from that of a square plan-shaped tall building.Amin and Ahuja [9] presented the effects of side ratio on wind pressure distribution on rectangular buildings.Dagnew et al. [10] focused on numerical analysis of wind pressures on high-rise buildings by using the Commonwealth Advisory Aeronautical Council (CAARC) building model.
e authors applied CFD techniques to predict wind load on CAARC irregular-shaped model.Chakraborty et al. [11] presented a study that showed irregular plan-shaped buildings are subjected to different pressure distributions, as compared to regular plan-shaped buildings after distribution.Yi and Li [12] conducted experiment in a tall building at Hong Kong as well as wind tunnel model test to explain force and pressure coefficients and high-frequency balance.e wind tunnel test result was seen to be fairly equivalent with a full model test.Li et al. [13] also conducted the wind tunnel test on L-plan-shaped tall building to quantify dynamic load across the wind.ey proposed an empirical formulation by considering the side ratio and territory of the building to express wind load.Bhattacharyya and Dalui [14] investigated mean wind pressures on E-plan-shaped tall building and compared experimental results with numerical analysis using CFD.ey compared their results by plotting pressure contours on all the surfaces using experimental as well as predicted values using CFD analysis.For better comparison of the results, the Fourier series expansion was obtained using the experimental data and compared with both the experimental data and CFD analysis.Li et al. [15] studied some recent efforts for credible computational fluid dynamics simulations in China.Chow et al. [16] investigated to simulate smoke filling in big halls by CFD.Mohanta and Patra [17] used CFD simulation for studying the flow field distribution in converging compound channel by the LES turbulence model.
In present study, numerical as well as experimental analysis has been carried out on irregular shape, i.e., Cshaped of the building for wind incidence angle of 0 °to 180 °at the interval of 30 °. ANSYS FLUENT is used to numerically model the domain and study the wind flow, and experimental data were obtained by using wind tunnel.e main purpose of this paper is to assess the change in wind pressure on different faces of C-shaped model due to change in wind angle and aspect ratio (height) of the building by experimental analysis and numerical analysis, and then those results were validated.Validation of results is necessary because there is no such direct reference from where wind pressure on the irregular shape of the building could be calculated.So, it becomes necessary to compare the experimental and numerical data.e wind speed is kept constant at 12.9 m/s.e wind tunnel with a bottom surface made up of plywood, a test section is 1.83 m long, and cross-sectional dimensions of 0.61 m × 0.61 m.Models are placed within the boundary layer zone, centrally in the test section at a distance of 1.2 m from the beginning of the test section.To ascertain models within the boundary layer zone, wooden cubic blocks of 25 mm size, and clear spacing of 50 mm in all directions are fixed on a 4 mm thick plywood sheet as shown in Figure 1.

Experimental Setup
e experimental models are made of transparent Perspex sheet of 3 mm thickness.Details of the two C-shaped models, as C-1 and C-2 of varying height ratios configurations, are shown in Figures 2(a)-2(c) and given in Table 1. Figure 3 represents the photograph of the C-shaped building model placed in the test section.
e models are fitted with 90 to 120 numbers of pressure-tapping points in 4-5 rows and 3-5 columns on the surfaces.e pressure-tapping points are kept at less spacing near the wall boundaries to tap the sharp pressure variation due to flow separation and at larger spacing in the middle of the surfaces.
Free stream velocity during the experiment is measured with the help of the pitot tube.e models are fitted with 90 to 120 numbers of pressure-tapping points in 4-5 rows and 3-5 columns on the surfaces.e pressure-tapping points are kept at less spacing near the wall boundaries to tap the sharp pressure variation due to flow separation and at a larger spacing in the middle of the surfaces.e free ends of tubes are connected to Digital Sensor Array (DSA) to record the fluctuating wind pressure at the corresponding tapping points.All data are measured by a DSA scan valve corporation, model DSA 3217/16 pox, USA. is DSA device is set to give an average pressure of 5 s duration.At the same time, for greater accuracy, a pressure measurement at each tapping point is repeated for three times, and the mean of three pressure data are obtained.e pressure coefficient (C P ) for each tapping point is calculated by putting the pressure data in the following equation as follows: where p � mean pressure data obtained experimentally, P ∞ � the static pressure in the reference tube, and P 0 � total pressure in the settling chamber. 2 Modelling and Simulation in Engineering

Numerical Modelling
Numerical simulations have been carried out in this study using ANSYS Fluent using the computational fluid dynamic (CFD) technique, based on the control volume method.e RNG k − ε model is used to simulate the turbulence effects.e RNG model is developed using renormalization group (RNG) methods to solve the Navier-Stokes equations, to account for the effects of smaller scales of motion.e RNG approach is a mathematical technique that can be used to derive a turbulence model similar to the k − ε model.Bhattacharyya and Dalui [18] studied wind force and pressure coefficients on the surfaces of an unsymmetrical E-shaped building using CFD ANSYS CFX software.ey used two equations k-ε turbulence model for modelling their works which offers a good compromise between numerical  Modelling and Simulation in Engineering effort and computational accuracy.Jena et.al [19] presented numerical studies on the interference effect on pentagonshaped tall buildings and analysis performed with the realizable k − ε model.Swaddiwudhipong and Khan [20] investigated wind-induced dynamic response of tall buildings using CFD.A comparative study between two widely used turbulence models, i.e., LES and k-ε Reynolds-average Navier-Stokes models have been made by Cheng et al. [21].Villalpando et al. [22] studied the flow simulation of turbulence models around a wind turbine NACA 63-415 airfoil at various angles of attack.e RNG (renormalization group) model incorporates modifications over the standard k-ε [22] model, which improves its performance.Uchida [23] presented a new evaluation technique for wind turbine generators design using a CFD model-based unsteady flow simulation with changes of wind direction.
It is advantageous to use the (k − ε) turbulence model as most commonly used in computational fluid dynamics (CFD).It simulates mean flow characteristics for turbulent flow conditions.It is a two-equation model which gives a general description of turbulence by means of two transport equations.
(i) e first transported variable determines the energy in the turbulence and is called turbulent kinetic energy (k).(ii) e second transported variable is the turbulent dissipation (ε) which determines the rate of dissipation of the turbulent kinetic energy.
e k − ε turbulence model is limited to the fully developed turbulent and nonseparated flows.It can have stability issues due to numerical stiffness.is model is still used widely despite its disadvantages. is performs poorly for complex flows involving severe pressure gradient, separation, and strong streamline curvature.e RNG produces lower turbulence levels and can underestimate the value of k.
is produces a less viscous flow that creates more realistic flow features with the complex geometry.

Numerical Analysis.
For numerical analysis, the models of C-shaped buildings of different aspect ratios have been created in ANSYS and then analysed by using the k − ε model of turbulence.ANSYS (Fluent) uses the finite element method to solve the governing equations, i.e., the region of interest is divided into the finite number of cells (the mesh or grid).
Data considered in numerical analysis:  [24].e upstream side is considered as 5H from the face of the building, downstream side is taken as 15H from the face of the building, two side clearance of the domain is taken as 5H from the face of the building, and top clearance is also taken as 5H from the top surface of the building.Such large size of the domain helps in vortex generation at the leeward side of the building, and backflow of wind can also be prevented.
e finite volume discretization approach is used to discretize the whole domain so that separation of wind flow, upwash, and downwash mechanisms can happen similar to the experimental study.e discretization (meshing) of the C-shaped model is shown in Figure 5.

Boundary Conditions.
For completing numerical modelling and simulation, there are several boundary conditions which are considered.
e flow parameter at inlet, outlet wall, and surface are needed to be considered.At inlet, the velocity of flow is 12.9 m/s, and the same velocity is provided for experimental procedure so that the result could be compared.e flow velocity at inlet is along the positive X direction.Wind is directly affecting Face C for wind incidence angle 0 °to 180 °, respectively, so the pressure distribution is symmetrical about vertical axis, and vortices generated at the wake region are also symmetrical for both the cases (Figure 6).

Variation of Pressure Coefficients.
e study of pressure coefficient is necessary in every unconventional-shaped building which is designed under wind excitation.Chakraborty et al. [11] and Mukherjee et al. [25] analysed that the critical pressure coefficients may not be found perpendicular to wind incidence angles only.For this reason, a detailed study on wind pressure variation is required with respect to wind incidence angles.

Experimental Results
. Pressure contour on different faces are plotted for every angle of incidence.Some pressure contours are shown in Figures 7 and 8, respectively, for all the faces.Also, mean pressure coefficients of all the faces are shown in Figures 9(a         -

Error Analysis.
Error analysis is also performed by obtaining mean percentage error (ME), standard deviation (SD), coe cient of determination (R 2 ), mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) [26,27].e percentage of mean error for prediction of C p by various models and their standard deviation is shown in Figure 11.Tables 2 and 3 show the error analysis of the present experimental dataset with di erent faces of C-1 and C-2 models.All the predicted R 2 values nearly 0.99 which is very good for tting other data and also the RMSE values are within the permissible limit for   Modelling and Simulation in Engineering all the faces.e better results regarding error analysis show the acceptability of the C-shaped model for the practical application.

Conclusions
e current study shows that pressure induced on the model building is significantly affected by the model geometry, configuration, aspect ratios, and angle of incidence.e significant outcomes of the present study are summarized as follows: (i) Mean pressure coefficients are the main objective of this study.Maximum positive mean pressure coefficients occur at the front face of C, and maximum negative pressure occurs at the inner face of the model.(ii) e study has been conducted with a C-shaped model experimentally as well as numerically using the wind tunnel test and CFD technique, respectively.(iii) Pressure variation on the building is directly influenced by wind flow pattern.(iv) Vortex generation and different types of mechanism such as separation of flow, upwash, and downwash are happened due to dynamic behavior of wind flow.(v) e predicted values of the error analysis are measured by four accuracy measurement procedures such as R 2 value, mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE).It is observed that all the errors are within the permissible limit.

Figure 2 :Figure 1 :
Figure 2: (a-c) Isometric view of C-1-and C-2-shaped building model and pressure-tapping locations along the periphery of models.

Table 1 :Figure 3 :
Figure 3: Photograph of C-shaped building model in the test section.

( i )
Types of fluid: air (ii) Density of air: 1.225 Kg/m 3 (iii) Viscosity of air: 1.789 × 10 −5 kg•s/m (iv) Turbulence model: k − ε model (v) Solver: pressure-based 3.2.Domain and Meshing.e domain size as shown in Figures 4(a) and 4(b) is considered as mentioned in Franke et al.

4. 1 .
Wind Flow Pattern.Pressure variation on the building is directly influenced by wind flow pattern.Vortex generation and different types of mechanism such as separation of flow, upwind, and downwind happen due to dynamic behavior of wind flow.To investigate such mechanisms more accurately, wind flow patterns around the C-shaped building are being studied for different angle of incidences varying from 0 °to 180 °at an interval of 30 °using the CFD technique.Flow pattern for different angles of incidences are shown in Figures 6(a)-6(e).

Figure 9 :
Figure 9: Mean pressure coe cients for all the faces of the C-1 model.(a) Experimental study.(b) Numerical study.

Figure 7 (
b) indicates that the maximum pressure occurs in the left side and minimum in the right side of the curvature portion (Face B) due to ow separation of wind ow.In Figure7(c), Face C is perpendicular to the wind ow, and the maximum positive pressure occurs at the central part of the face and minimum pressure at both edge sides due to curvature and edge e ect as well.Inner windward Faces G and I have similar ow pattern (Figures7(d) and 7(e)).Negative pressure decreases towards the edge.Similarly, the mean pressure coe cient contours of the C-2 shaped model are show in Figure8.4.4.Numerical Results.Pressure variation and mean pressure coe cients of all the faces of C-1 and C-2 models are also studied numerically in detail by CFD for di erent wind incidence angles.It can be seen clearly that numerically predicted pressure contours are converged well with the experimentally predicted results.But, very less variation in mean pressure coe cients are observed with respect to the experimental results (Figures9 and 10).

Figure 10 :Figure 11 :
Figure 10: Mean pressure coe cients for all the faces of the C-2 model.(a) Experimental study.(b) Numerical study.

Table 2 :
Error analysis of predicted C p for model of C-1.