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Airflow Patterns around Buildings: Wind Tunnel Measurements and Direct Numerical Simulation G.K. Ntinas1,2, G. Zhang1, V.P. Fragos2, 1 Department of Engineering, Faculty of Sciences and Technology, University of Aarhus, Blichers Allé 20,

8830 Tjele, Denmark 2 Department of Hydraulics, Soil Sciences and Agricultural Engineering, Faculty of Agriculture, Aristotle

University of Thessaloniki, 54124, Thessaloniki, Greece *Corresponding author. E-mail address: Guoqiang.zhang@agrsci.dk (G. Zhang)

Keywords: Computational Fluid Dynamics (CFD), Direct Numerical Simulation (DNS),

scale models, wind tunnel, Navier-Stokes equations, finite element method Abstract

Accurate numerical simulations of airflow around buildings is challenging due to the dynamic characteristics of the wind. A time-dependent model has been applied for the prediction of the turbulent airflow around scale model buildings with different roof geometry in a wind tunnel. The model is based on the direct solution of transient Navier-Stokes and continuity equations using the Galerkin finite element method. To verify the model an experiment in wind tunnel was conducted and the air velocity and turbulence were measured around two building models with arched-roof and pitched-roof respectively. The velocity components and the turbulences were used to demonstrate a dynamic and statistical analysis of this complex flow. The wind tunnel tests presented good agreement with the numerical simulations with respect to airflow patterns. The building roof geometry affected the instantaneous and time-mean averaged parameters of the flow. The time-dependent simulation of the flow parameters can provide important information on instantaneous fluctuations of the complex flow phenomena around buildings which cannot be obtained by the time-mean averaged approach. INTRODUCTION

The local air motion around buildings is composed of many elements and can affect both indoor air quality in the ventilated building space and exhaust air dispersion from the buildings. Clarification of the airflow field around buildings is necessary in order to proceed in estimations of dispersion (Blocken et al., 2010), outdoor air quality and thermal environment (Li et al., 2005; Hadavand et al., 2008) and wind driven ventilation (Ohba et al., 2001; van Hooff et al., 2011). The airflow around a building is turbulent and complex due to sudden changes in flow field owing to the building. It is composed of stagnation in front of it, separation at the frontal corner and recirculating flow behind it (Murakami et al., 1990). The phenomena of airflow separation and reattachment can play an important role in the design of buildings, heating and ventilation system (Moosavi etal., 2008).

The study can be in full scale measurements, but it will be expensive, time consuming, and hard to control the experimental conditions. An alternative is to use

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small-scale models in a wind tunnel with fully controlled conditions. This approach is also usually used to verify of numerical simulations.

Using Computational Fluid Dynamics (CFD) to study airflow around buildings can be found in literature (e.g., Jiang et al., 2003; Yanaoka et al., 2007; Tominaga & Stathopoulos, 2010). Reynold Average Navier-Stokes (RANS) modelling has difficulties in simulation of the airflow around buildings and especially at separation regions. Large Eddy Simulation (LES) method uses a low-pass filter, often defined as a convolution product, to the Navier-Stokes equations (N-S). This way LES resolve larger-scale eddies, but they model (or filter) the smaller ones (Rumsey 2009).

Direct numerical simulation (DNS) can be used to analyse turbulent flows without any approximating assumption (Friedrich, 2001). A solution of two-dimensional (2D) Navier-Stokes equations for incompressible fluid was proposed by Psychoudaki et al. (2005) and Fragos et al. (2007; 2012) on separating and reattaching flows around an obstacle in a wind tunnel (WT). The focus of the DNS approach till now is on the simulation of the various, in size, formed vortices around a building due to the building’s roof geometry. Only qualitative comparisons of the proposed code have been presented.

The objectives of this investigation are a) to apply DNS method for the prediction of the external airflow around building model placed inside a wind tunnel, b) to validate the numerical predictions using measured data with quantitative comparisons. Two types of buildings models were used: one with arched-type and another with pitched-type roof. MATERIALS AND METHODS Experiments 1. The wind tunnel. Wind tunnel (WT) used for experiments is 6.91 m long and 0.5 m  0.5 m in cross section (Fig. 1). The working section of the WT was 0.6 m long. A side of the section was made of transparent glass to enable velocity measurement using Laser Doppler Anemometer (LDA) (2D FlowExplorer System, Dantec Dynamics A/S, Skovlunde, Denmark) and for visual inspection using smoke and laser sheet. 2. Air velocity. The airflow was driven by negative pressure via a variable speed air exhaust fan. The air velocity in WT was tested without building models to make sure that the air velocity was following the selected value of 0.32 m/s. The working section was started 1.82 m downwind from the WT inlet. 3. Building models. Models with arched-roof and pitched-roof (Fig. 2) were used two experiments respectively. The models were 1:60 and dimensions of H×L×H were 0.118m × 0.50m × 0.063m. The Reynolds number (Re = 10200) was calculated using the height of the WT (0.5 m) and the inlet free stream velocity (Uref = 0.32 m/s). 4. Measurements. The profiles of air velocity, at 11 distances relative to the building model, were measured. Horizontal (u) and vertical (v) velocity components were measured by the 2D LDA at a central plan of the WT. The measurement positions are showed in Fig. 3. The measurements were taken continuously at each position for 150 s before being moved to another position. Numerical Model

The DNS code using the Galerkin finite element method to solve the Navier-Stokes and continuity equations in 2D dimensions was applied (Fragos et al., 2007). 1. Governing equations The dimensionless Navier-Stokes and continuity equations used may be expressed in Eqs. (1) and (2) respectively:

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2U 1U U p U

t Re

, (1)

U 0 , (2)

where U=(u, v) is the velocity vector of the fluid with stream-wise velocity (u) and cross-wise velocity (v), its components in x and y direction respectively, t is the time, p is the pressure and Re is the Reynolds number. 2. Numerical method. Eqs. (1) & (2) were solved with the finite element method (FEM). The main characteristic of this method is the discretization of the solution region in many subregions or elements, which are united internal and cover entirely and uniquely the whole solution area. The variables of equations, describing the physical problem, were approached in the nodes of each element of the computational grid. The solution of the problem was given as a set of discrete values in the nodes of the computing field. Numerical solution

1. Boundary conditions. The building models were considered to occupy the entire width of the wind tunnel. Uniform flow conditions were set at inlet of the WT, u = Uref (in dimensionless units, u = 1). After the entrance of the WT the velocity profile follows a logarithmic law as configured from the solution of the mathematical model (Fig. 4). No-slip conditions were set at the wind tunnel walls, u = 0, v = 0 (in dimensionless units, u = 0, v = 0). At the output of the wind tunnel, free boundary condition were set, which was mathematically imposed on the finite element code (Malamataris 1991). 2. Initial condition. The initial condition was set to be similar to the initial condition of the WT experiment. Considering that in a laboratory experiment the flow is variable until it becomes stabilized, the initial condition of the flow field was chosen to be, Re = 1 (Fragos et al., 2007). 3. Computational mesh. The mesh was designed to approximate the flow variables and to reduce the computational time. The number of elements, nodes and unknowns for each structure are listed in Table 1. Further densification of the mesh, in both studied cases, resulted in no significant change in the solution. Each mesh independence control was performed in accordance with the study of Fragos et al. (2007), Fig. 5. 4. Finite element method. The solution of Eqs. (1) & (2) for the two roof forms involves dividing the region into triangular and quadrangle elements. At the top of the pitched-roof model triangular elements were used, while for the arched-roof model triangular elements with curvilinear sides were used to fit the local geometry. 5. Finite element code. Two new codes were developed in the FORTRAN for the structures of arched-roof and the pitched-type roof respectively to satisfy the specific geometries and flow conditions.

The dimensionless time step was equal to 0.01, in both cases and a total of 15000 measurements of the variables of Eqs. (1) & (2) were obtained, in each point of the computational field. The check of the time step showed that further reduction did not contributed to the accuracy of the solution. RESULTS Time-depended flow patterns

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1. Instantaneous streamlines of airflow. Fig. 6 shows the instantaneous stream-lines of airflow around the arched-roof building, at selected time units (t = 90, 100, 110, 120, 130, and 140). Fig. 7 shows the instantaneous stream-lines of airflow around the pitched-roof building, at the same time units. In both cases, an intense production of vortices is observed at downstream of the models due to the separation of the flow. A continuous change of the number and the size of the vortices is also observed due to the fluctuation of the downstream reattachment point position. At the roof of both buildings the vortices initiate on the upper edge of the roof affecting the airflow downstream of the buildings. Unlike the intense variation of the flow downstream of the buildings, a relatively invariable vortex is formed at the upstream sides. The formed vortex upstream of both buildings presents a slight variation in time due to insignificant fluctuation of the positions of separation and reattachment points. John and Liakos (2006) also observed vortex shedding in their numerical experiment using a slip with friction boundary condition at Re = 500. The differences in the flow structure can cause large gradients in the distributions of the local heat transfer coefficient.

2. Contours of instantaneous velocities. Fig. 8 shows a few examples of the contours of instantaneous u- and v-velocity around the arched-roof building at the time units t =100 and t =130. As it can be observed in the depicted contours in Fig. 8(a), the u-velocity at the downstream of the building are either negative or positive in various time units due to the rapid evolution of the flow. Fluctuations of stream-wise velocity between the two time units were predicted at the top of the roof. No significant fluctuations of u-velocity were occurred at the upstream side. Steady values of v-velocity were also observed at the upstream and near the edge of the roof, Fig. 8(b). At the downstream side of the building, the v-velocity presented similar behaviour with the u-velocity having a continuous fluctuation of values with regard to time and position. Validation of numerical simulations

In both buildings cases, the mean and fluctuating velocities along the stream-wise and cross-wise directions were predicted along the centre section of the building models. The average values of the velocity components were deduced, at each point of the computational field, by processing the computed instantaneous values. The comparison of the predicted averaged velocity components results with the measured data from the wind tunnel experiment, for Re = 10200, (Figs. 11-14) are in good agreement, with small discrepancies. The accuracy with which the predicted values of the model match with that of experimental data was statistically evaluated (Figs 15, 16) using the coefficient of determination (R2) and the root mean square error (RMSE).

1. Velocity profiles. The profiles of horizontal velocity component (u ) and vertical velocity component (v) around the arched-roof building and pitched-roof building are presented in Fig. 9 and 10 respectively. DNS results agree well with the experimental data for velocity (u ), at both upstream and downstream edges and also on the top of the building’s roof (X = 5H, 6.88H, and 5.9H).

For the arched-roof building, very small differences are shown at X = 3H before the building and at X = 7.5H, 8.8H after the building, where the vortices are developed, but both numerical and experimental data are following the same trend (Fig. 9). R2 - values of experimental and simulated u-velocities for X of 5H, 6.88H and 5.9H are 0.94, 0.99, and 0.94 respectively; and the RMSE of 0.02, 0.06, and 0.03, respectively.

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For the Pitched-roof building, minor differences are shown at X = 3H before the building and at X = 10.7H after the building. R2 - values of experimental and simulated u-velocities at X of 5H, 6.88H, and 5.9H are 0.90, 0.95, and 0.90 respectively; and the RMSE of 0.02, 0.11, and 0.01, respectively. CONCLUSIONS

A direct simulation model was applied for simulation of 2D turbulent airflow around two buildings models with different roof geometry in a WT. The agreement between the numerical simulation and measurements in both flow patterns and air velocity profiles validates the DNS code used.

It is the first time that the DNS code is validated by experimental data of a WT. The influence of the roof geometry is obvious in the airflow patterns above the roof and at downstream of the models. Intense variations were presented in streamlines and in velocity components for both building types, starting at the upstream corner of the roof and the top of the roof respectively.

The time-dependent simulation of the flow parameters can contribute in fundamental studies, which are typically conducted for isolated or successive buildings configurations to obtain insight in the flow behaviour and for parametric studies. In addition, it can provide important information on instantaneous fluctuations of the complex flow phenomena around buildings. References Blocken B, Stathopoulos T, Carmeliet J, Hensen JLM. 2010. Application of

computational fluid dynamics in building performance simulation for the outdoor environment: an overview. J Build Perform Simulat, 4(2):157-84.

Fragos VP, Psychoudaki SP, Malamataris NA. 2007. Direct simulation of two-dimensional turbulent flow over a surface-mounted obstacle. Int J Numer Method Fluids, 55(10):985-1018.

Fragos VP, Psychoudaki SP, Malamataris NA. 2012. Two-dimensional numerical simulation of vortex shedding and flapping motion of turbulent flow around a rib. Comput Fluids, 69(0):108-21.

Friedrich R, Hüttl TJ, Manhart M, Wagner C. Direct numerical simulation of incompressible turbulent flows. Comput Fluids 2001;30(5):555-79.

Hadavand M, Yaghoubi M. 2008.Thermal behavior of curved roof buildings exposed to solar radiation and wind flow for various orientations. Appl Energ., 85(8):663-79.

Jiang Y, Alexander D, Jenkins H, Arthur R, Chen Q. 2003. Natural ventilation in buildings: measurement in a wind tunnel and numerical simulation with large-eddy simulation. J Wind Eng Ind Aerod, 91(3):331-53.

John V, Liakos A. 2006. Time-dependent flow across a step: the slip with friction boundary condition. Int J Numer Method Fluids, 50(6):713-31.

Li X, Yu Z, Zhao B, Li Y. 2005. Numerical analysis of outdoor thermal environment around buildings. Build Environ, 40(6):853-66.

Malamataris NA. 1991. Computed-aided analysis of flows on moving and unbounded domains: phase-change fronts and liquid leveling. PhD Thesis, Univ of Mich, Ann Arbor, (USA);

Moosavi R, Gandjalikhan Nassab SA. 2008.Turbulent forced convection over a single inclined forward step in a duct: Part 1- flow field. Eng Appl Comp Fluid., 2(3):366-74.

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Murakami S, Mochida A, Hayashi Y, Hibi K. 1990. Numerical simulation of velocity field and diffusion field in an urban area. Energy Build, 15(3–4):345-56.

Ohba M, Irie K, Kurabuchi T. 2001. Study on airflow characteristics inside and outside a cross-ventilation model, and ventilation flow rates using wind tunnel experiments. J Wind Eng Ind Aerod, 89(14–15):1513-24.

Psychoudaki SP, Fragos VP, Malamataris NA. 2005. Computational study of a separating and reattaching flow. IASME Trans, 2(7):1120-31.

Rumsey CL. 2009. Successes and challenges for flow control simulations. Int J Flow Control, 1(1):1-27.

Tominaga Y, Stathopoulos T. 2010. Numerical simulation of dispersion around an isolated cubic building: Model evaluation of RANS and LES. Build Environ, 45(10):2231-9.

van Hooff T, Blocken B, Aanen L, Bronsema B. 2011. A venturi-shaped roof for wind-induced natural ventilation of buildings: Wind tunnel and CFD evaluation of different design configurations. Build Environ, 46(9):1797-807.

Yanaoka H, Inamura T, Kobayashi R. 2007. Numerical simulation of separated flow transition and heat transfer around a two-dimensional rib. Heat Tran Asian Res, 36(8):513-28.

 

Tables  

 

Table 1. Data of computational mesh.

Building Number of

elements

Number of

nodes

Number of

unknowns

Arched-type roof 9958 40311 90833

Pitched-type roof 11444 46219 104123  

Figures

Fig. 1. The wind tunnel.

 

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(a). with Arched-roof models

(b). with Pitched-roof models

Fig. 2. Building models in the wind tunnel

(a) (b)

Fig. 3. Air velocity measurement positions in the wind tunnel, with building models of (a), arched-roof, and (b), pitched-roof.

u=Uref&v=0

x

y

u=0v=0

u=0v=0

Free boundary condition

7H

1H

3H 0 5H 1.88H 43.12H

Wind tunnelentrance

Wind tunnel exit

 

Fig. 4. Computational domain with the arched-roof building.

 

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(a) (b)

Fig. 5. Computational mesh, a. arched-type, and b. pitched-type roof building.

 

Fig. 6. Instantaneous streamlines around an arched-type building (for Re = 10200). 

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Fig. 7. Instantaneous streamlines around a pitched-type building (for Re = 10200).

 

(a)

(b)

Fig. 8. Contours of instantaneous stream-wise (a) and cross-wise (b) velocity around an arched-type building (Re = 10200).

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Fig. 9. Profiles of averaged velocity u for the arched-type building, ---, measurements;

▬, simulations.

Fig. 10. Profiles of averaged velocity u for the pitched-type building, ▪▪▪, measurements;

▬, simulations.