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Wind-driven cross ventilation in long buildings
Accepted Manuscript Wind-Driven Cross Ventilation in Long Buildings Chia-Ren Chu , Bo-Fan Chiang PII:
S0360-1323(14)00167-X
DOI:
10.1016/j.buildenv.2014.05.017
Reference:
BAE 3713
To appear in:
Building and Environment
Received Date: 5 November 2013 Revised Date:
24 April 2014
Accepted Date: 6 May 2014
Please cite this article as: Chu C-R, Chiang B-F, Wind-Driven Cross Ventilation in Long Buildings, Building and Environment (2014), doi: 10.1016/j.buildenv.2014.05.017. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Wind-Driven Cross Ventilation in Long Buildings
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Chia-Ren Chu* and Bo-Fan Chiang
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Department of Civil Engineering, National Central University, Taiwan, R.O.C.
Abstract
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The rule of thumb for effective wind-driven cross ventilation suggests that the
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building length L should be less than five times of ceiling height H. This study uses a
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Large Eddy Simulation model and wind tunnel experiments to investigate the
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mechanism behind this rule of thumb. The numerical results reveal that the ventilation
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rate decreases as the building length increases. This is partly due to the pressure
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difference between the windward and leeward façades of long buildings (aspect ratio
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L/H ≥ 2.5) is smaller than that of a short building (L/H = 1.25). The other reason is
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owing to the internal friction, which can produce a sluggish zone with a low-wind speed
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inside the building. For buildings with aspect ratio L/H ≥ 5, the ventilation rate will be
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over-estimated, as much as about 20%, by ventilation models that do not consider the
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internal resistance. The location of the external openings can also influence the
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ventilation rate. When the openings are located in the opposite corners of the windward
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and leeward walls, also due to the internal friction, the ventilation was 15.5% less than
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that of openings on the centerline of the building. The mitigation effect of internal
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resistance on the ventilation rate can be quantified by a resistance model.
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Keywords: Wind-driven cross ventilation; Computational Fluid Dynamics; Large Eddy *
corresponding author: Chia-Ren Chu Mailing address: Department of Civil Engineering National Central University 300 Jhong-Da Road Jhong-Li, Taoyuan Taiwan 32001, R.O.C. E-mail address: [email protected] 1
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Simulation; Wind tunnel experiment, Building length.
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1. Introduction Wind-driven natural ventilation is an effective way to maintain a comfortable
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indoor environment in residential and commercial buildings, as well as to reduce the
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energy consumption required for mechanical ventilation [1, 2]. However, wind-driven
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ventilation is dependent on the external wind speed, direction, openings and building
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configurations [2, 3]. Building designers need a simple and accurate method for
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assessing the effectiveness of wind-driven ventilation. The most widely used method to
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calculate the ventilation rate, Q, through a building opening, is the orifice equation
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[4-5]:
2∆P ρ
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(1)
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where A is the cross-sectional area of the opening, ∆P = Pe − Pi is the difference in the
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external and internal pressures, ρ is the density of the air and Cd is the discharge
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coefficient. Typical discharge coefficients given in the literature are in the range of 0.60
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~ 0.65 for sharp-edged openings [3-5]. Eq. (1) is derived from Bernoulli’s assumption of
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inviscid, incompressible flows, which has been widely used in network airflow models
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and multi-zone models [6-8].
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For a building with only two openings, one on the windward façade and another
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on the leeward façade, the dimensionless ventilation rate through the openings can be
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found by using Eq. (1) and the continuity equation Q1 = Q2 [7, 8]:
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r 2C 2 Q Q = = Cd1 a 2 dr 2 C p1 − C p2 U H A1 1 + ra Cdr *
2
1/2
(2)
ACCEPTED MANUSCRIPT where A1 is the opening area of the windward opening, UH is the external wind velocity
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at the building height and Cp is the pressure coefficient on the external wall. The
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pressure coefficient is defined as the pressure difference between the wall and the free
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stream flow divided by the dynamic pressure of the approaching flow at the building
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height z = H. The ratio of opening areas is defined as ra = A2/A1 and the ratio of
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discharge coefficients is Cdr = Cd2/Cd1, with subscripts 1 and 2 representing the
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windward and leeward façades, respectively. Eq. (2) can be used to calculate the flow
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rate of cross ventilation [8]. However, it does not take into consideration the flow
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resistance caused by the furniture or the wall friction [9].
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Chu et al. [10] used wind tunnel experiments to investigate the wind-driven cross
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ventilation of partitioned buildings. They found that, due to the extra resistance caused
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by the internal partition, the ventilation rate of a partitioned building is always lower
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than that of a single-zone building. Chu & Wang [11] and Chu & Chiang [12] used the
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energy equation to derive a resistance model to predict the dimensionless ventilation
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rate Q* when there are obstacles in the buildings:
Q1*
1 C p1 − C p2 = A1 ζ 1 + ζ i + ζ 2
1/ 2
(3)
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where ζ1 and ζ 2 are the resistance factors of the external openings and ζi is the
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internal resistance factor of the obstacle. The resistance factors of external openings can
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be calculated as follows:
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ζ1 =
1 C A12 2 d
ζ2 =
1 C A 22 2 d
(4)
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The unit of the resistance factor is [m-4] and Eq. (3) is consistent in dimension. This
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model considers the pressure difference between the windward and leeward openings as
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resistance factor, ζ , the smaller the ventilation rate, Q, will be. This model can be used
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for buildings with no internal obstacles (ζi = 0). The extra resistance caused by the
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partition wall and furniture can be expressed in terms of internal resistance factor ζi.
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For wind-driven cross ventilation, the rule of thumb [13, 14] is that the building length L should be less than five times the ceiling height H (see Figure 1). For long
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buildings with length L/H > 5, the wind-driven ventilation will not be effective. But
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these references do not explain the reason behind this limitation. Is the ventilation rate
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reduced because of the obstacles in the building or because the wall friction increases as
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the building gets longer? Or is it because the pressure difference between the windward
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and leeward façades (driving force) decreases as the building gets longer?
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This study used a Large Eddy Simulation (LES) model to investigate the influences of building length on the flow rate of cross ventilation. The simulation results
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were verified by wind tunnel experiments and then were used to develop a predictive
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model for the ventilation rate and resistance factor of long buildings. This model can be
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used to assess the wind-driven cross ventilation in residential and commercial buildings.
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2. Numerical Model In recent years, turbulence models have been successfully applied to building
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ventilation simulations [15-18]. The numerical results can reveal the flow parameters
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that are difficult to measure in experiments. Kobayashi et al. [19] employed a standard
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k- model and the Reynolds stress model to study the transported power and power
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loss of cross ventilation in pitched roof and rectangular buildings. Hu et al. [20] used a
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Large Eddy Simulation model to study shear-driven and wind-driven cross ventilation. 4
ACCEPTED MANUSCRIPT Tominaga et al. [21] and Ramponi & Blocken [22] discussed the application of
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computational fluid dynamics (CFD) models to simulate the wind environment around
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buildings. They found that the computational domain, mesh size, boundary conditions,
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numerical scheme and convergence criterion could influence the simulation results, and
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they concluded that the numerical setup should be carefully checked.
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The Large Eddy Simulation (LES) model used in this study to investigate the cross ventilation of long buildings was the same as that used in Chu & Chiang [12]. The
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governing equations are:
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∂ui =0 ∂ xi
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∂ui ∂ui u j 1 ∂P ∂ 2 u ∂τij + =− + ν 2i − ∂t ∂x j ρ ∂ xi ∂x j ∂x j
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(6)
(7)
where the subscripts i, j = 1, 2, 3 represent the x, y and z directions, respectively; t
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represents the time; u and P are the velocity and pressure, the over-bar represents these
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quantities as spatially averaged values [23], ρ is the air density, ν is the kinematic
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viscosity of the air and τij ar and τij are the sub-grid scale stresses:
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1 τij = τkk δ ij −2µ t Sij 3
(8)
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where µt is the viscosity of the sub-grid scale turbulence, defined as:
µ t = ρ(Cs ∆ s ) 2 2Sij Sij
(9)
where Cs is the Smagorinsky coefficient [24] and Sij is the rate of strain:
1 ∂u ∂u j Sij = i + 2 ∂x j ∂x i
(10)
where ∆s is the mixing length of the sub-grid scales, which can be calculated as:
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(11)
where κ (= 0.41) is the von Karman constant, d is the distance to the closest wall and V is the volume of the computational cell. The value of the Smagorinsky coefficient Cs is dependent on the flow types [25]. In this study, Cs = 0.15 was chosen by
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comparing the simulation results with the experimental data, as described in the next
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section. The velocity near the ground and solid wall was calculated by the wall function
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[26]:
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u(z) 1 ρu*z = ln E( ) u* κ µ
(12)
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where z is the distance from the wall, u∗ is the shear velocity, E (= 9.793) is a constant
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and µ is the dynamic viscosity of the air.
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The no-slip and no-penetration boundary conditions were specified on the ground and on the building walls, and the free-slip boundary condition was specified on the
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upper and two lateral boundaries. At the outlet boundary, the zero stream-wise gradient
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condition was used for the velocities and pressure on the cell faces. The governing equations were solved using a finite volume method. The
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second-order upwind scheme was employed to solve the momentum equations, and the
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PISO (Pressure Implicit with Splitting of Operators) scheme was adopted for the
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pressure-velocity coupling. For the unsteady flow calculation, the time derivative terms
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were discretized using the second-order implicit scheme. The convergence criterion for
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the continuity and momentum equations was set as 10-5 after several tests.
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3. Wind Tunnel Experiments The simulation results of the present LES model were first compared with the 6
ACCEPTED MANUSCRIPT results of two wind tunnel experiments to demonstrate the accuracy of the numerical
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model. The first experiment was conducted by in a suction, open-type wind tunnel. The
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total length of the wind tunnel is 30 m long, the test section was 18.5 m long, 3.0 m
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wide and 2.1 m high. The rectangular building models (height H = 0.6 m and width W =
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0.3 m) of different lengths L = 0.3 m, 0.6 m, 1.20 m, 1.50 m and 1.80 m were mounted
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on the centerline of the test section. The blockage ratio of the model was 2.86%. The
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surfaces of the model were made of smooth acrylic plate without opening.
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There were pressure taps (flush to the external wall) on the roof, windward and leeward sides of the building model. All of the pressure taps were connected to a
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multi-channel high-speed pressure scanner (ZOC33/64PX, Scanivalve Inc.). The
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measuring range of the pressure sensor was ± 2758 Pa, with a resolution of ±2.2 Pa. The
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sampling frequency was 100 Hz, the sampling duration was 163.84 sec. The pressure
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module was placed inside the building model with short pneumatic tubing to the
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pressure taps.
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stream-wise velocity U(z) follow the power law function:
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The approaching flow was a boundary layer flow and the vertical profile of
U(z) z = Uo δ
α
(13)
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where Uo is the free stream velocity outside the boundary layer, z is the height from the
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ground, δ is the thickness of the boundary layer and α is the exponent of the velocity
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profile. In this experiment, δ = 1.45 m, α = 0.21, Uo = 10 m/s, and the wind speed at
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the building height UH = 8.30 m/s. The wind direction ( θ = 0o) was normal to the
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windward façade.
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Figure 2 compares the simulated and measured pressure coefficients Cp on the 7
ACCEPTED MANUSCRIPT centerlines of building surfaces. The pressure coefficients Cp1 on the windward façades
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are in the range of 0.55 ~ 0.80, and the profiles of pressure coefficients for building
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lengths L/H = 0.5 and 1.0 agree very well. This indicated that the windward pressure is
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independent of the building length. The pressure coefficient Cp1 near the leading edge of
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building roof decreased to some extent because the air flow accelerated as it pass
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through the roof. For the leeward pressure coefficients, the value Cp2 ≈ -0.2 of building
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length L/H = 0.5 is smaller than the leeward pressure coefficients (Cp2 ≈ -0.1) of other
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building lengths (L/H = 1.0, 2.0, 2.5 and 3.0). Also, the agreement between the
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measured and predicted results validates the capability of the present LES model to
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predict the pressure coefficients on building surface.
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The second experiment was conducted by Karava et al. [8]. They used particle
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image velocimetry (PIV) to measure the velocity field inside a single-zone building
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model, and investigated the influence of the opening configurations on the flow field
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and ventilation rate of the building. In their model, the building height was H = 0.08 m,
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the width W = 0.10 m and the length L = 0.10 m. The windward and leeward façades
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each has one opening at the center of the façades. The areas of the inlet and outlet
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openings were the same: A1 = A2 = 0.046 m x 0.018 m, and the wall porosity is r1 =
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A1/AF = 10.35%.
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The wind direction was normal to the windward façade ( θ = 0o). The approaching
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flow was a turbulent boundary layer flow with the boundary layer thickness δ = 0.6 m,
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the exponent α = 0.15. The wind speed at the building height is UH = 6.97 m/s. The
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Reynolds number based on the wind speed UH and building height is Re = HUH /ν =
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37,200. The vertical profile of the time-averaged velocity U(z) and stream-wise
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turbulence intensity Iu(z) (= σu(z)/U(z)) are shown in Figure 3, where σu is the standard
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deviation of the stream-wise velocity. Based on the experimental results of Karava et al.
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[8], the vertical profile of the turbulence intensity is set at the inlet boundary: z Iu ( z ) = A δ
B
(14)
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where the empirical coefficients are A = 6.33, B = -0.29. The spectral synthesizer and
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the vortex method [27, 28] were used to generate the fluctuating turbulence velocity at
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the inlet boundary for the same turbulence intensity profile described by Eq. (14).
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The requirements as suggested by Tominaga et al. [21] and Ramponi & Blocken
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[22] for the boundary conditions, computational domain and mesh were followed in this
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study. The computational domain (height 6H = 0.48 m, width 10.5H = 0.84 m and
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length 22.5H = 1.8 m) and mesh layout are shown in Figure 4. The blockage ratio of the
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cross section of the building to the computational domain was 2.0%. The wall thickness
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was set as 2.0 mm.
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The grid resolution plays an essential role in the accuracy of the LES simulation
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[25]. In this study, the areas inside and around the building were discretized by a
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uniform grid. For the area far away from the building, non-uniform grids with a
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stretching ratio of 1.10 ~ 1.25 were adopted. The grid sensitivity was checked by
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comparing the simulation results of three different grids, and it was found that the grid
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235 × 68 × 59 with the smallest grid size of ∆x = 1.0 mm, ∆y = 3.0 mm, ∆z = 3.0 mm
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had the best agreement with the experimental results of Karava et al. [8]. Therefore, it
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was used for the rest of the simulation.
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The simulated stream-wise velocities U(x)/UH along the centerline of the openings
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are shown in Figure 5 as dash lines. The velocity at the building height is UH = 6 m/s.
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The solid symbols represent the experimental results of Karava et al. [8], and the dotted
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ACCEPTED MANUSCRIPT line the simulation results of Ramponi and Blocken [22] by the shear-stress transport
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(SST) k-ω model (their reference case). Although the simulated velocities deviated from
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the measured velocities near the inlet and outlet openings, the agreement between the
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numerical and the experimental results in the region x/L = 0.5 ~ 0.8 was satisfactory.
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The discrepancy between the simulated and the measured velocities near the inlet and
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outlet openings was due to the edge reflections and shadows of the laser light sheet [8,
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21]. By comparing the simulated velocities and the experimental results of Karava et al.
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[8], it was concluded that the results of the spectral synthesizer were better than those of
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the vortex method. Therefore, the spectral synthesizer was used for the rest of this study.
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Figure 6 illustrates the simulated velocity vectors on the mid-plane of the building.
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There was a standing vortex upstream of the building. Inside the building, the air flow
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was deflected downward to the building floor as it passed through the inlet opening. The
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flow patterns inside the building and on the building roof were very similar to the
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experimental results of Ohba et al. [29], Karava et al. [8] and the numerical simulation
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of Hu et al. [20].
The ventilation rate Q into the building can be calculated by two different methods.
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The first method is to integrate the simulated time-averaged horizontal velocities at the
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openings. The ventilation rates at the inlet and outlet openings are represented by Q1
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and Q2, respectively. The second method is to substitute the opening areas, discharge
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coefficients and the predicted windward and leeward pressure coefficients into Eq. (2)
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to obtain the ventilation rate Qmodel. The time-averaged velocities and pressure
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coefficients are computed from the simulation results in between 30 ~ 40 sec.
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The dimensionless ventilation rates through the inlet and outlet openings,
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computed by the integration method, were: Q*1 = 0.423 and Q*2 = 0.414. The relative
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ACCEPTED MANUSCRIPT difference 2.1% indicated that the mass conservation between the inflow and outflow
230
was satisfactory. The ventilation rate predicted by Eq. (2) was Q*model = 0.419, with the
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simulated external pressure coefficients right above the windward and leeward openings
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Cp1 = 0.66, Cp2 = -0.17 and discharge coefficients Cd1 = 0.65, Cd2 = 0.65. In other words,
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the ventilation rates calculated by the integration model were very close to the
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prediction of Eq. (2). The good agreement between the computed ventilation rates by
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the two different methods validated the capability of the present LES model to simulate
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the wind-driven cross ventilation.
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4. Computational Setup
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The present LES model was used to investigate the wind-driven cross ventilation through a single isolated low-rise building. The external height and width of the
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building were fixed as height H = 4 m and width W = 10 m (see Figure 7). The length of
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the building was varied in the range of L = 5.0 ~ 44.0 m (the aspect ratio L/H = 1.25 ~
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11). The reference case was set as the building length L = 10 m (L/H = 2.50). For all the
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cases, the windward and leeward façades each had one opening on the centerline of the
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façades. The cross-sectional areas of inlet and outlet openings were identical A1 = A2 =
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2 m x 2 m, and the wall porosity was r1 = r2 = 10%. The thickness of the building wall
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was 0.1 m.
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The approaching flow followed Eq. (13) with the value of δ = 400 m and the
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free-stream wind speed was Uo = 12 m/s. Therefore, the wind speed at the building
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height was UH = 6.0 m/s. The Reynolds number based on the wind speed UH and
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building height was Re = HUH /ν = 1.6 × 106. The turbulence intensity profile followed
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Eq. (14), and the turbulence intensity at the building height was Iu = 23.9%. The wind 11
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direction was normal to the windward façade ( θ = 0°) of the building for all the
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simulation cases. The computational domain was 24 m (= 6H) in height and 70 m (= 7W) in width.
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The length of the computational domain varied according to the building length, the
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distance from the leeward façade to the outlet boundary was 63 m (= 15.75H). The
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blockage ratio of the building to the computational domain was 2.38%. The
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computational grid was adjusted from the grid used in the model verification. For all the
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simulation cases, the grid size inside the building was the same: ∆x/H = 0025, ∆y/H =
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0.05, ∆z/H = 0.05. The area far away from the building employed a non-uniform grid
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with the stretching ratio 1.25. For the reference case (building length L/H = 2.5), the
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grid number inside the building was 87,952 cells and the total grid number was
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1,064,770 cells (= 245 × 82 × 53 cells).
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5. Results and Discussion
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5.1 Building Length
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Figure 8(a) shows a comparison of the predicted pressure coefficients on the
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centerlines of the windward façades for different building lengths. The windward
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pressure coefficient Cp1 above the inlet opening was in the range of Cp1 = 0.60 ~ 0.75,
271
and independent of the building length. This phenomenon is similar to the results of
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wind tunnel experiments. Furthermore, the values of windward pressure coefficient are
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in the same range of experimental results. The pressure coefficient Cp1 right above the
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windward opening (z/H = 0.6) decreased slightly because the air accelerated as it flow
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into the opening.
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On the other hand, Figure 8(b) shows that the leeward pressure coefficient Cp2 ≈ 12
ACCEPTED MANUSCRIPT -0.60 for L/H = 1.25 was much smaller than the leeward pressure Cp2 = -0.15 ~ -0.20 for
278
longer buildings (L/H ≥ 2.5). It also illustrated that the leeward pressure was
279
independent of the building length when L/H ≥ 2.5. Again, this is similar to the
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experimental results of building length L/H longer than 1.0 (see Figure 2(b)). Altogether,
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Figures 2 and 8 imply that the pressure difference between the windward and leeward
282
façades (the driving force for cross ventilation) of short buildings was higher than that
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for long buildings. In other words, the ventilation rate of short buildings will be larger
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than that of long buildings.
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The contours of time-averaged pressure coefficient Cp on the mid-plane of the
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building for building lengths L/H = 1.25, 2.5, 5.0 and 8.0 are illustrated in Figure 9. Due
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to the separated shear layer on the building roof, the pressure at the leeward region of
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building length L/H = 1.25 was lower than for the other building lengths. For building
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length L/H ≥ 2.5, because the length of separated shear layer was less the building
290
length and the reattachment of eddies on the building roof, the leeward pressure was
291
much alike. Also the pressure distribution inside the building was comparable.
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It is also noteworthy that, both the experimental and numerical results show that
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the aspect ratio L/H of buildings is more influential to the leeward pressures than to the
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windward pressures. This information is important to those choosing pressure
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coefficients for ventilation design [30]. It can be explained by the separation bubble at
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the building roof. However, the critical building length is L/H > 1.0 for the wind tunnel
297
experiment, the critical building length is L/H > 2.5 for the numerical simulation. This
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difference is believed due to the aspect ratio H/W of the building. The aspect ratio H/W
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= 0.4 for the wind tunnel experiments, while H/W = 2.0 for the numerical simulation.
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The time-averaged velocity vectors on the mid-plane of the building for L/H =
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ACCEPTED MANUSCRIPT 1.25 and 2.5 are compared in Figure 10. The separated shear flows around the leading
302
corner on the building roof look very much alike, but there was reattachment toward the
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trailing corner of the building for L/H = 2.5, while no reattachment for L/H = 1.25
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because the separation bubble was longer than the building length. Also, there was a
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standing vortex inside the building between the ceiling and outlet opening, and the
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counter-clockwise rotating vortex generated resistance for the air flow passing through
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the building.
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The dimensionless ventilation rates Q*, computed by the integration method, are shown in Figure 11. The values of Q* were normalized by the dimensionless ventilation
310
rate of reference case Q*r = 0.448. When building length L/H 2.5, Eq. (2) predicted the
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ventilation rates very well. But for longer buildings (L/H ≥ 5.0), the ventilation rate
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decreased as the building length increased and Eq. (2) over-predicted the ventilation
313
rates Q*. The ventilation rate of L/H = 11 was only 80% of the ventilation rate of L/H =
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2.5. This suggested that the diminishing effect of the internal friction on the ventilation
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rate cannot be neglected when the building length L/H ≥ 5.0.
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The extra resistances caused by the friction inside the building are expressed in
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terms of the internal resistance factor ζi in Eq. (3). The value of ζi can be computed by
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substituting the simulated pressure coefficients Cp1 and Cp2 from LES into Eq. (3). The
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resistance factors of the external openings ζ1 = ζ2 = 0.148 m-4 were computed by setting
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the discharge coefficient Cd = 0.65 and the opening area A1 = A2 = 4 m2. Figure 12
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displays a non-linear relation between the dimensionless resistance factor ζi/ζ1 and the
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building length L/H. The internal resistance was negligible when L/H < 2.5, but
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increased drastically when L/H > 5. This led to the decline in the ventilation rate of long
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buildings.
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Because the building floors are smooth surfaces, the skin friction estimated by the boundary layer theory [31] is quite small. The energy loss is mainly due to the
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circulating, turbulent flow in the building. When building length L/H ≥ 5, the internal
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friction caused by the turbulent flow increased almost linearly with the building length.
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Figure 12 also infers that the resistance factors ζ1 and ζ2 of the external openings are the
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dominant parameters for short buildings without any internal obstacle (furniture and
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partition). However, the resistance factor ξi cannot be neglected for buildings with large
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aspect ratio L/H.
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Figure 13 displays the time-averaged stream-wise velocity along the centerline of
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the openings at height z/H = 0.25 (z = 1 m). The stream-wise velocities were normalized
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by the wind speed UH. For building length L/H = 1.25, the internal velocity was the
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highest due to the large pressure difference across the building, but it decreased as the
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building length increased. For short buildings, the air flow past thought the windward
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and leeward openings resembling a strong jet flow, without much energy loss. However,
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the air flow in long buildings like a diffused jet, velocity decrease as it goes further into
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the building. For L/H ≥ 5.0, the internal velocity became u/UH < 0.4 in the region near
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the leeward opening. The velocity rise near the outlet is due to the suction at the leeward
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façade. The region with a low internal velocity is called the sluggish zone. The length of
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the sluggish zone was about x/L = 0.65 ~ 0.95 for L/H = 5, but increased to x/L = 0.25 ~
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0.95 for L/H = 11. Designing cross ventilation in long spaces should pay attention to
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this phenomenon.
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5.2 Diagonal Openings Besides the building length, the opening configurations can generate additional
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the wind-driven cross ventilation of different opening configurations. However, they did
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not quantify the influences of the location of the openings on the ventilation rate. The
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purpose of this simulation was to compare the ventilation rates of openings located on
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the diagonal of the building (see Figure 14) with that of the reference case (openings at
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the center of the building façades). The size of the building (height H = 4.0 m, width W
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= 10.0 m and length L = 10.0 m), opening areas (A1 = A2 = 2 m x 2 m), wind direction
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( θ = 0°) and velocity profile at the inlet boundary were identical to those of the
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reference case. But the openings were placed in opposite corners of the windward and
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leeward facades, along the diagonal of the building.
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Figures 15(a) and 15(b) illustrate the pressure coefficients above the windward and leeward openings, respectively. The location of the pressure profile was on the
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centerline (y = 0) for the reference case, while the pressure profile was taken at y/W =
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±0.40 for the diagonal case. The windward pressures were very similar for openings
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located on the centerline and on the diagonal direction. However, the leeward pressures
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were slightly different for the reference and diagonal cases.
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The pressure difference ∆P between the windward and leeward openings was the driving force for wind-driven cross ventilation. As listed in Table 1, the pressure
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coefficient difference ∆CP = Cp1 - Cp2 above the opening (z/H = 0.7) of the reference
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and diagonal cases was 0.925 and 0.911, respectively. However, the dimensionless
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ventilation rate of diagonal case Q* = 0.368, as computed by the integration method,
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was much lower than that of reference case Q*r = 0.448. This disparity was attributed to
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the internal resistance as the air flow passed through the diagonal openings. In other
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words, the ventilation models that did not consider internal resistance, such as Eq. (2),
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over-estimated the ventilation rate for openings not on a straight line. The additional resistance for the air flow through diagonal openings could be
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quantified using the internal resistance factor ζi. Similar to the calculation used for the
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resistance factors of long buildings, the dimensionless resistance factor of the diagonal
377
openings was obtained as ζi / ζ1 = 0.856. For the same opening size and similar pressure
378
difference, the ventilation rate (calculated by integration method) through the building
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with diagonal openings was 15.5% less than that of the reference case (openings on the
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centerline of the building). For long buildings or buildings with furniture inside, the
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wind-driven cross ventilation will be further reduced.
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6. Conclusions
The rule of thumb for effective wind-driven cross ventilation suggests that the
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building length should be less than five times the ceiling height. This study used a Large
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Eddy Simulation model and wind tunnel experiments to investigate the mechanism
387
behind this rule of thumb in a single-zone, low-rise building. The numerical and
388
experimental results both revealed that the windward pressure was independent of the
389
aspect ratio of the building, but the leeward pressures of short buildings were lower than
390
that of long buildings. This is due to the separation bubbles on the building roof can
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reach the leeward sides of short buildings. In other words, the ventilation rate of a short
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building is higher owing to the larger pressure difference between the windward and
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leeward façades.
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Furthermore, it was found that the ventilation rate of building length L/H = 11 is
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20% less than that of building length L/H = 2.5, even when the pressure difference
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across the building and the opening size were the same. Plus, there was a sluggish zone 17
ACCEPTED MANUSCRIPT with low wind speed inside the building when the building length was L/H ≥ 5.0. It is
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the internal friction that caused the sluggish zone and the decline in ventilation rate. The
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conventional ventilation models that do not consider the internal resistance will
400
over-estimate the ventilation rate of long buildings.
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The location of the openings also affected the ventilation process. The simulation
402
results indicated that the ventilation rate for building with openings in opposite corners
403
of the windward and leeward façades was 15.5% lower than that of openings on the
404
centerline of the building, even though the pressure differences between the windward
405
and leeward façades of the building were very close. This was attributed to the
406
additional resistance for air flow to pass through the diagonal openings. The resistance
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model of Chu and Chiang [12] can be used to quantify the internal friction of different
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building lengths and opening configurations.
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Acknowledgement
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The authors thank the Architecture and Building Research Institute, Ministry of
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The Interior (Grant no. 10162B001), and National Science Council of Taiwan (Grant no.
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102-2221-E-008-055) for their support of this study.
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References
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[1] Allard F. Natural ventilation in buildings: a design handbook, James and James Ltd., London, England; 1998.
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[2] Aynsley R. Estimating summer wind driven natural ventilation potential for indoor
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thermal comfort. J Wind Eng Ind Aerodyn 1999; 83 (1-3):515-25. [3] Linden PF. The fluid mechanics of natural ventilation. Annual Review of Fluid Mechanics 1999; 31:201-38. [4] Etheridge D. Natural ventilation of buildings: Theory and measurement and design. 18
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John Wiley and Sons, Chichester, England, 2012.
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[5] Awbi HB. Ventilation of Buildings. 2nd ed. Taylor and Francis, London, England,
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[6] Etheridge D, Sandberg M. Building ventilation: Theory and Measurement. John
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Wiley and Sons, Chichester, England, 1996. [7] Chu CR, Chiu YH, Chen YJ, Wang YW, Chou CP. Turbulence effects on the
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discharge coefficient and mean flow rate of wind-driven cross ventilation. Build Environ 2009; 44: 2064-72. doi:10.1016/j.buildenv.2009.02.012.
[8] Karava P, Stathopoulos T, Athienitis AK. Airflow assessment in cross-ventilated
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buildings with operable façade elements. Build Environ 2011; 46(1): 266-79.
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[9] Johnson M-H, Zhai Z, Krarti M. Performance evaluation of network airflow models for natural ventilation. HVAC&R Research 2012; 18(3): 349-365. [10] Chu CR, Chiu YH, Wang YW. An experimental study of wind-driven cross
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ventilation in partitioned buildings. Energy Build 2010; 42(5): 667-73. doi:10.1016/j.enbuild.2009.11.004.
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[11] Chu CR, Wang YW. The loss factors of building openings for wind-driven ventilation. Build Environ 2010; 45(10): 2273-79. doi:10.1016/j.buildenv. 2010.04.010.
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[12] Chu CR, Chiang BF. Wind-driven cross ventilation with internal obstacles. Energy Build 2013; 67,:01-09. doi:10.1016/j.enbuild.2013.07.086.
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[13] CIBSE. Natural ventilation in non-domestic buildings: Applications Manual 10, AM10: Chartered Institution of Building Services Engineers (CIBSE), London, 1997.
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[14] Mumovic D, Santamouris M. A Handbook of Sustainable Building Design and
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Engineering: An integrated approach to energy, health and operational performance, Earthscan, England, 2009.
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[15] Evola G, Popov V. Computational analysis of wind driven natural ventilation in buildings. Energy Build 2006; 38:491-501.
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[16] Kato S, Murakami S, Mochida A, Akabashi S, Tominaga Y. Velocity-pressure field of cross-ventilation with open windows analyzed by wind tunnel and numerical simulation. J Wind Eng Ind Aerodyn 1992; 41-44: 2575-86.
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[17] Jiang Y, Chen Q. Effect of fluctuating wind direction on cross natural ventilation in buildings from large eddy simulation. Build Environ 2002; 37(4): 379-86.
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[18] Ramponi R, Blocken B. CFD simulation of cross-ventilation flow for different isolated building configurations: validation with wind tunnel measurements and 19
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analysis of physical and numerical diffusion effects. J Wind Eng Ind Aerodyn 2012; 104-106: 408-18.
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[19] Kobayashi T, Sagara K, Yamanaka T, Kotani H, Sandberg M. Power transportation
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inside stream tube of cross-ventilated simple shaped model and pitched roof house. Build Environ 2009; 44(7):1440-51. [20] Hu CH, Ohba M, Yoshie R. CFD modelling of unsteady cross ventilation flows using LES. J Wind Eng Ind Aerodyn 2008; 96(10-11):1692-706.
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[21] Tominaga Y, Mochida A, Yoshie R, Kataoka H, Nozu T, Masaru Y, Shirasawa T. AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J Wind Eng Ind Aerodyn 2008; 96:1749-61.
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[22] Ramponi R, Blocken B. CFD simulation of cross-ventilation for a generic isolated building: Impact of computational parameters. Build Environ 2012; 53:34-48.
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[23] Germano M, Piomelli U, Moin P, Cabot WH. A dynamic subgrid scale eddy
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viscosity model. Physics of Fluids A 1991; 3(7): 1760-65.
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[24] Smagorinsky J. General circulation experiments with the primitive equations. I. The basic experiment. Monthly Weather Review 1963; 91(3): 99-164.
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[25] Chen Q. Ventilation performance prediction for buildings: A method overview and recent applications. Build Environ 2009;44:848-58. doi:10.1016/ j.buildenv.2008.05.025.
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[26] Launder BE, Spalding DB. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 1974; 3:269-89.
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[27] Meroney RN. CFD prediction of dense gas clouds spreading in a mock urban
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environment. In: The Fifth International Symposium on Computational Wind Engineering, 2010. Chapel Hill, North Caroline, USA.
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[28] Huang SH, Li QS, Wu JR. A general inflow turbulence generator for large eddy simulation. J Wind Eng Ind Aerodyn 2010; 98 (10-11): 600-617.
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[29] Ohba M, Irie K, Kurabuchi T. Study on airflow characteristics inside and outside a
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cross-ventilation model, and ventilation flow rates using wind tunnel experiments. J Wind Eng Ind Aerodyn 2001; 89:1513-24.
487 488 489 490
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[30] Costola D, Blocken B, Hensen JLM. Overview of pressure coefficient data in building energy simulation and airflow network programs Build Environ 2009; 44:2027-2036. [31] Schlichting H. Boundary-Layer Theory. New York: McGraw-Hill; 1979.
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Notation
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A1, A2
cross-section area of external opening (m2)
494
A2/A1
opening ratio (dimensionless)
495
Aw
cross-section area of building interior (m2)
496
AF
area of the windward facade (m2)
497
Cd
discharge coefficient of opening (dimensionless)
498
Cp = (P-Po)/0.5ñU2
external pressure coefficient (dimensionless)
499
H
height of building (m)
500
L
length of building (m)
501
Po
reference pressure (Pa)
502
Q
ventilation rate (m3/s)
503
Q*
dimensionless ventilation rate
504
r1, r2 = A/AF
external wall porosity (dimensionless)
505
Uo
free stream wind speed (m/s)
506
UH
wind speed at the building height (m/s)
507
W
width of building exterior (m)
508
z
509
ρ
510
g
511
α
512
δ
513
θ
514
ζi
515
æ1 , æ2
516
Subscripts
517
1
windward side
518
2
leeward side
519
i
internal
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elevation (m)
air density (kg/m3)
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gravitational acceleration (m/s2) exponent of the velocity profile
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thickness of boundary layer (m) wind direction (degree)
internal resistance factor (m-4) external resistance factor (m-4)
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1
Table Caption:
2
Table 1. Simulation results of diagonal openings.
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Case
ΔCP
Q*
Reference
0.925
0.448
Diagonal
0.915
ζi (m-4)
ζi/ζ1
0
0
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Table 1. Simulation results of diagonal openings.
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0.368
0.127
0.856
ΔCP is the difference between the windward and leeward pressure coefficients above the opening (z/H = 0.7).
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1
ACCEPTED MANUSCRIPT Figure Caption: Figure 1. Schematic diagram of wind-driven cross ventilation in long buildings. Figure 2. Comparison of simulated and measured pressure coefficient on the centerlines of building surface. (a) windward façades of building height L/H = 0.5 and 1.0. (b) leeward façades of L/H = 0.5, 1.0, 2.0, 2.5 and 3.0. The symbols are
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the measured pressure coefficients, the lines are the numerical predictions.
Figure 3. Vertical profiles of time-averaged velocity U(z) and stream-wise turbulence intensity Iu(z) (= σu(z)/U(z)) of the approaching flow.
Figure 4. Computational domain and mesh layout for the numerical simulation.
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Figure 5. Comparison of predicted stream-wise velocity U(x)/UH along the centerline of boundary.
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the openings by different schemes to generate velocity fluctuation at the inlet
Figure 6. Time-averaged velocity vectors on the mid-plane of the building. The flow condition followed the experiment of Karava et al. [8]. Figure 7. Schematic diagram of the full-scale building for the numerical simulation. The openings are on the centerlines of windward and leeward walls, opening
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area A1 = A2 = 2 m x 2 m.
Figure 8. Pressure coefficients on the centerlines of building external walls: (a) above windward opening; (b) above leeward opening. Figure 9. Time-averaged pressure distribution on the mid-plane of the building for
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different building lengths. (a) L/H = 1.25; (b) L/H = 2.5; (c) L/H = 5.0; (d) L/H = 8.0.
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Figure 10. Time-averaged velocity vectors on the mid-plane of the building for different building length. (a) L/H = 1.25; (b) L/H = 2.5.
Figure 11. Effect of building length on the ventilation rate, Q*r is the dimensionless ventilation rate of reference case (L/H = 2.5).
Figure 12. Dimensionless internal resistance ζi/ζ1 as a function of building length. Figure 13. Time-averaged streamwise velocity along the centerline of the openings at height z/H = 0.25. Figure 14. Schematic diagram of a full-scale building with openings on the diagonal corners of the windward and leeward walls. The opening area A1 = A2 = 2 m x 2 m. 1
ACCEPTED MANUSCRIPT Figure 15. Pressure coefficients on the building external walls: (a) above windward opening (x/L = 0, y/W = -0.4); (b) above leeward opening (x/L = 1.0, y/W =
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0.4).
Wind
L
P1
H
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Q1
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A1
P2 Q2 A2
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Figure 1. Schematic diagram of wind-driven cross ventilation in long buildings.
2
ACCEPTED MANUSCRIPT (a) 1.0 LES, L/H=0.5 Exp. L/H=0.5
0.8
Exp. L/H=1.0
0.4 0.2
0.2
(b) 1.0
0.6
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Z/H
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Cp
LES, L/H = 0.5 Exp. L/H = 0.5 Exp. L/H = 1.0 Exp. L/H = 2.0 Exp. L/H = 2.5 Exp. L/H = 3.0
0.8
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0.0 0.0
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Z/H
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0.6
0.0 -0.8
-0.6
-0.4
-0.2
0.0
Cp
Figure 2. Comparison of simulated and measured pressure coefficient on the centerlines of building surface. (a) windward façades of building height L/H = 0.5 and 1.0. (b) leeward façades of L/H = 0.5, 1.0, 2.0, 2.5 and 3.0. The symbols are the measured pressure coefficients, the lines are the numerical predictions. 3
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0.48
0
5
10
Iu (%)
15
20
25
Exp., Karava et al. (2011) Inlet Velocity Profile
0.40
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Exp., Karava et al. (2011)
z (m)
0.32
Inlet turbulence intensity
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0.00
0
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0.08
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U (m/s)
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Figure 3. Vertical profiles of time-averaged velocity U(z) and stream-wise turbulence
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intensity Iu(z) (= σu(z)/U(z)) of the approaching flow.
4
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Wind
4.25H L+1.5H
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15H
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Figure 4. Computational domain and mesh layout for the numerical simulation.
5
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1.2 LES, vortex method LES, spectral synthesizer k-ω, Ramponi and Blocken (2012) Exp., Karava et al. (2011)
1.0
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U(x) / UH
0.8 0.6
0.2 0.0 -0.35
0.5
1.0
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0.0
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0.4
1.5
x/L
Figure 5. Comparison of predicted stream-wise velocity U(x)/UH along the centerline of the openings by different schemes to generate velocity fluctuation at the inlet boundary.
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The flow condition followed the experiment of Karava et al. [8].
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Figure 6. Time-averaged velocity vectors on the mid-plane of the building. The flow
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condition followed the experiment of Karava et al. [8].
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A2
4.0 m A1 z
x
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2.0 m
2.0 m
10 m
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y
U
L
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Figure 7. Schematic diagram of the full-scale building for the numerical simulation. The openings are on the centerlines of windward and leeward façades, opening area A1 = A2
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= 2 m x 2 m.
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ACCEPTED MANUSCRIPT (a) Windward facade
1.0 0.8
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z/H
0.6 0.4
L/H = 1.25 L/H = 2.5 L/H = 5.0 L/H = 8.0 L/H = 11.0
0.0 0.0
0.4
0.6
0.8
1.0
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0.2
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0.2
Cp
(b) Leeward facade
1.0
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0.8
0.4
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L/H = 1.25 L/H = 2.5 L/H = 5.0 L/H = 8.0 L/H = 11.0
EP
z/H
0.6
0.0 -0.8
-0.6
-0.4
Cp
-0.2
0.0
0.2
Figure 8. Pressure coefficients on the centerlines of building external walls: (a) above windward opening; (b) above leeward opening.
9
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z (m)
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x (m)
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(a) L/H = 1.25
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z (m)
(b) L/H = 2.5
x (m)
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x (m)
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(d) L/H = 8.0
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z (m)
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(c) L/H = 5.0
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z (m)
EP
x (m)
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Figure 9. Time-averaged pressure distribution on the mid-plane of the building for different building lengths. (a) L/H = 1.25; (b) L/H = 2.5; (c) L/H = 5.0; (d) L/H = 8.0.
11
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(a) L/H = 1.25
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(b) L/H = 2.5
Figure 10. Time-averaged velocity vectors on the mid-plane of the building for different building length. (a) L/H = 1.25; (b) L/H = 2.5.
12
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125
75
*
*
Q / Qr (%)
100
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50
Integration method Eq. (2)
0
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8
10
12
14
L/H
Figure 11. Effect of building length on ventilation rate, Q*r is the dimensionless
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ventilation rate of reference case (L/H = 2.5).
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1.0
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ζi / ζ1
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0.4
0.0
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L/H
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Figure 12. Dimensionless internal resistance ζi/ζ1 as a function of building length.
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Openings on the centerlines of the windward and leeward façades.
14
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2.0
L/H = 1.25 L/H = 2.50 L/H = 5.00 L/H = 8.00 L/H = 11.0
1.6
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0.2
0.4
0.6
0.8
1.0
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x/L
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u / UH
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Figure 13. Time-averaged streamwise velocity along the centerline of the openings at
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height z/H = 0.25.
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Figure 14. Schematic diagram of a full-scale building with openings on the diagonal
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corners of the windward and leeward façades. The opening area A1 = A2 = 2 m x 2 m.
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Reference case Diagonal case
0.0 0.0
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z/H
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Reference case Diagonal case
-0.3
-0.2
-0.1
0.0
Cp
Figure 15. Pressure coefficients on the building external walls: (a) above windward opening (x/L = 0, y/W = -0.4); (b) above leeward opening (x/L = 1.0, y/W = 0.4).
17
ACCEPTED MANUSCRIPT Title: Wind-driven cross ventilation in long buildings
* This study used numerical model to investigate the ventilation of long buildings.
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* The ventilation rate decreased as the building length increased. * The rule of thumb for wind-driven cross ventilation is clarified.
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* The location of the building openings also influenced the ventilation rate.
S0360-1323(14)00167-X
DOI:
10.1016/j.buildenv.2014.05.017
Reference:
BAE 3713
To appear in:
Building and Environment
Received Date: 5 November 2013 Revised Date:
24 April 2014
Accepted Date: 6 May 2014
Please cite this article as: Chu C-R, Chiang B-F, Wind-Driven Cross Ventilation in Long Buildings, Building and Environment (2014), doi: 10.1016/j.buildenv.2014.05.017. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Wind-Driven Cross Ventilation in Long Buildings
1 2 3
Chia-Ren Chu* and Bo-Fan Chiang
4
Department of Civil Engineering, National Central University, Taiwan, R.O.C.
Abstract
6
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The rule of thumb for effective wind-driven cross ventilation suggests that the
8
building length L should be less than five times of ceiling height H. This study uses a
9
Large Eddy Simulation model and wind tunnel experiments to investigate the
10
mechanism behind this rule of thumb. The numerical results reveal that the ventilation
11
rate decreases as the building length increases. This is partly due to the pressure
12
difference between the windward and leeward façades of long buildings (aspect ratio
13
L/H ≥ 2.5) is smaller than that of a short building (L/H = 1.25). The other reason is
14
owing to the internal friction, which can produce a sluggish zone with a low-wind speed
15
inside the building. For buildings with aspect ratio L/H ≥ 5, the ventilation rate will be
16
over-estimated, as much as about 20%, by ventilation models that do not consider the
17
internal resistance. The location of the external openings can also influence the
18
ventilation rate. When the openings are located in the opposite corners of the windward
19
and leeward walls, also due to the internal friction, the ventilation was 15.5% less than
20
that of openings on the centerline of the building. The mitigation effect of internal
21
resistance on the ventilation rate can be quantified by a resistance model.
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Keywords: Wind-driven cross ventilation; Computational Fluid Dynamics; Large Eddy *
corresponding author: Chia-Ren Chu Mailing address: Department of Civil Engineering National Central University 300 Jhong-Da Road Jhong-Li, Taoyuan Taiwan 32001, R.O.C. E-mail address: [email protected] 1
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Simulation; Wind tunnel experiment, Building length.
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1. Introduction Wind-driven natural ventilation is an effective way to maintain a comfortable
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indoor environment in residential and commercial buildings, as well as to reduce the
29
energy consumption required for mechanical ventilation [1, 2]. However, wind-driven
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ventilation is dependent on the external wind speed, direction, openings and building
31
configurations [2, 3]. Building designers need a simple and accurate method for
32
assessing the effectiveness of wind-driven ventilation. The most widely used method to
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calculate the ventilation rate, Q, through a building opening, is the orifice equation
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[4-5]:
2∆P ρ
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(1)
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where A is the cross-sectional area of the opening, ∆P = Pe − Pi is the difference in the
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external and internal pressures, ρ is the density of the air and Cd is the discharge
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coefficient. Typical discharge coefficients given in the literature are in the range of 0.60
39
~ 0.65 for sharp-edged openings [3-5]. Eq. (1) is derived from Bernoulli’s assumption of
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inviscid, incompressible flows, which has been widely used in network airflow models
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and multi-zone models [6-8].
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For a building with only two openings, one on the windward façade and another
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on the leeward façade, the dimensionless ventilation rate through the openings can be
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found by using Eq. (1) and the continuity equation Q1 = Q2 [7, 8]:
45
r 2C 2 Q Q = = Cd1 a 2 dr 2 C p1 − C p2 U H A1 1 + ra Cdr *
2
1/2
(2)
ACCEPTED MANUSCRIPT where A1 is the opening area of the windward opening, UH is the external wind velocity
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at the building height and Cp is the pressure coefficient on the external wall. The
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pressure coefficient is defined as the pressure difference between the wall and the free
49
stream flow divided by the dynamic pressure of the approaching flow at the building
50
height z = H. The ratio of opening areas is defined as ra = A2/A1 and the ratio of
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discharge coefficients is Cdr = Cd2/Cd1, with subscripts 1 and 2 representing the
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windward and leeward façades, respectively. Eq. (2) can be used to calculate the flow
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rate of cross ventilation [8]. However, it does not take into consideration the flow
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resistance caused by the furniture or the wall friction [9].
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Chu et al. [10] used wind tunnel experiments to investigate the wind-driven cross
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ventilation of partitioned buildings. They found that, due to the extra resistance caused
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by the internal partition, the ventilation rate of a partitioned building is always lower
58
than that of a single-zone building. Chu & Wang [11] and Chu & Chiang [12] used the
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energy equation to derive a resistance model to predict the dimensionless ventilation
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rate Q* when there are obstacles in the buildings:
Q1*
1 C p1 − C p2 = A1 ζ 1 + ζ i + ζ 2
1/ 2
(3)
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where ζ1 and ζ 2 are the resistance factors of the external openings and ζi is the
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internal resistance factor of the obstacle. The resistance factors of external openings can
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be calculated as follows:
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ζ1 =
1 C A12 2 d
ζ2 =
1 C A 22 2 d
(4)
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The unit of the resistance factor is [m-4] and Eq. (3) is consistent in dimension. This
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model considers the pressure difference between the windward and leeward openings as
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resistance factor, ζ , the smaller the ventilation rate, Q, will be. This model can be used
70
for buildings with no internal obstacles (ζi = 0). The extra resistance caused by the
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partition wall and furniture can be expressed in terms of internal resistance factor ζi.
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For wind-driven cross ventilation, the rule of thumb [13, 14] is that the building length L should be less than five times the ceiling height H (see Figure 1). For long
74
buildings with length L/H > 5, the wind-driven ventilation will not be effective. But
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these references do not explain the reason behind this limitation. Is the ventilation rate
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reduced because of the obstacles in the building or because the wall friction increases as
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the building gets longer? Or is it because the pressure difference between the windward
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and leeward façades (driving force) decreases as the building gets longer?
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This study used a Large Eddy Simulation (LES) model to investigate the influences of building length on the flow rate of cross ventilation. The simulation results
81
were verified by wind tunnel experiments and then were used to develop a predictive
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model for the ventilation rate and resistance factor of long buildings. This model can be
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used to assess the wind-driven cross ventilation in residential and commercial buildings.
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2. Numerical Model In recent years, turbulence models have been successfully applied to building
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ventilation simulations [15-18]. The numerical results can reveal the flow parameters
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that are difficult to measure in experiments. Kobayashi et al. [19] employed a standard
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k- model and the Reynolds stress model to study the transported power and power
90
loss of cross ventilation in pitched roof and rectangular buildings. Hu et al. [20] used a
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Large Eddy Simulation model to study shear-driven and wind-driven cross ventilation. 4
ACCEPTED MANUSCRIPT Tominaga et al. [21] and Ramponi & Blocken [22] discussed the application of
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computational fluid dynamics (CFD) models to simulate the wind environment around
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buildings. They found that the computational domain, mesh size, boundary conditions,
95
numerical scheme and convergence criterion could influence the simulation results, and
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they concluded that the numerical setup should be carefully checked.
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The Large Eddy Simulation (LES) model used in this study to investigate the cross ventilation of long buildings was the same as that used in Chu & Chiang [12]. The
99
governing equations are:
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∂ui =0 ∂ xi
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∂ui ∂ui u j 1 ∂P ∂ 2 u ∂τij + =− + ν 2i − ∂t ∂x j ρ ∂ xi ∂x j ∂x j
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(6)
(7)
where the subscripts i, j = 1, 2, 3 represent the x, y and z directions, respectively; t
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represents the time; u and P are the velocity and pressure, the over-bar represents these
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quantities as spatially averaged values [23], ρ is the air density, ν is the kinematic
105
viscosity of the air and τij ar and τij are the sub-grid scale stresses:
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1 τij = τkk δ ij −2µ t Sij 3
(8)
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where µt is the viscosity of the sub-grid scale turbulence, defined as:
µ t = ρ(Cs ∆ s ) 2 2Sij Sij
(9)
where Cs is the Smagorinsky coefficient [24] and Sij is the rate of strain:
1 ∂u ∂u j Sij = i + 2 ∂x j ∂x i
(10)
where ∆s is the mixing length of the sub-grid scales, which can be calculated as:
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112 113 114
(11)
where κ (= 0.41) is the von Karman constant, d is the distance to the closest wall and V is the volume of the computational cell. The value of the Smagorinsky coefficient Cs is dependent on the flow types [25]. In this study, Cs = 0.15 was chosen by
116
comparing the simulation results with the experimental data, as described in the next
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section. The velocity near the ground and solid wall was calculated by the wall function
118
[26]:
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u(z) 1 ρu*z = ln E( ) u* κ µ
(12)
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where z is the distance from the wall, u∗ is the shear velocity, E (= 9.793) is a constant
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and µ is the dynamic viscosity of the air.
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The no-slip and no-penetration boundary conditions were specified on the ground and on the building walls, and the free-slip boundary condition was specified on the
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upper and two lateral boundaries. At the outlet boundary, the zero stream-wise gradient
125
condition was used for the velocities and pressure on the cell faces. The governing equations were solved using a finite volume method. The
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second-order upwind scheme was employed to solve the momentum equations, and the
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PISO (Pressure Implicit with Splitting of Operators) scheme was adopted for the
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pressure-velocity coupling. For the unsteady flow calculation, the time derivative terms
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were discretized using the second-order implicit scheme. The convergence criterion for
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the continuity and momentum equations was set as 10-5 after several tests.
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3. Wind Tunnel Experiments The simulation results of the present LES model were first compared with the 6
ACCEPTED MANUSCRIPT results of two wind tunnel experiments to demonstrate the accuracy of the numerical
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model. The first experiment was conducted by in a suction, open-type wind tunnel. The
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total length of the wind tunnel is 30 m long, the test section was 18.5 m long, 3.0 m
138
wide and 2.1 m high. The rectangular building models (height H = 0.6 m and width W =
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0.3 m) of different lengths L = 0.3 m, 0.6 m, 1.20 m, 1.50 m and 1.80 m were mounted
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on the centerline of the test section. The blockage ratio of the model was 2.86%. The
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surfaces of the model were made of smooth acrylic plate without opening.
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There were pressure taps (flush to the external wall) on the roof, windward and leeward sides of the building model. All of the pressure taps were connected to a
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multi-channel high-speed pressure scanner (ZOC33/64PX, Scanivalve Inc.). The
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measuring range of the pressure sensor was ± 2758 Pa, with a resolution of ±2.2 Pa. The
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sampling frequency was 100 Hz, the sampling duration was 163.84 sec. The pressure
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module was placed inside the building model with short pneumatic tubing to the
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pressure taps.
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stream-wise velocity U(z) follow the power law function:
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The approaching flow was a boundary layer flow and the vertical profile of
U(z) z = Uo δ
α
(13)
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where Uo is the free stream velocity outside the boundary layer, z is the height from the
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ground, δ is the thickness of the boundary layer and α is the exponent of the velocity
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profile. In this experiment, δ = 1.45 m, α = 0.21, Uo = 10 m/s, and the wind speed at
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the building height UH = 8.30 m/s. The wind direction ( θ = 0o) was normal to the
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windward façade.
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Figure 2 compares the simulated and measured pressure coefficients Cp on the 7
ACCEPTED MANUSCRIPT centerlines of building surfaces. The pressure coefficients Cp1 on the windward façades
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are in the range of 0.55 ~ 0.80, and the profiles of pressure coefficients for building
160
lengths L/H = 0.5 and 1.0 agree very well. This indicated that the windward pressure is
161
independent of the building length. The pressure coefficient Cp1 near the leading edge of
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building roof decreased to some extent because the air flow accelerated as it pass
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through the roof. For the leeward pressure coefficients, the value Cp2 ≈ -0.2 of building
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length L/H = 0.5 is smaller than the leeward pressure coefficients (Cp2 ≈ -0.1) of other
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building lengths (L/H = 1.0, 2.0, 2.5 and 3.0). Also, the agreement between the
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measured and predicted results validates the capability of the present LES model to
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predict the pressure coefficients on building surface.
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The second experiment was conducted by Karava et al. [8]. They used particle
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image velocimetry (PIV) to measure the velocity field inside a single-zone building
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model, and investigated the influence of the opening configurations on the flow field
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and ventilation rate of the building. In their model, the building height was H = 0.08 m,
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the width W = 0.10 m and the length L = 0.10 m. The windward and leeward façades
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each has one opening at the center of the façades. The areas of the inlet and outlet
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openings were the same: A1 = A2 = 0.046 m x 0.018 m, and the wall porosity is r1 =
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A1/AF = 10.35%.
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The wind direction was normal to the windward façade ( θ = 0o). The approaching
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flow was a turbulent boundary layer flow with the boundary layer thickness δ = 0.6 m,
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the exponent α = 0.15. The wind speed at the building height is UH = 6.97 m/s. The
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Reynolds number based on the wind speed UH and building height is Re = HUH /ν =
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37,200. The vertical profile of the time-averaged velocity U(z) and stream-wise
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turbulence intensity Iu(z) (= σu(z)/U(z)) are shown in Figure 3, where σu is the standard
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deviation of the stream-wise velocity. Based on the experimental results of Karava et al.
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[8], the vertical profile of the turbulence intensity is set at the inlet boundary: z Iu ( z ) = A δ
B
(14)
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where the empirical coefficients are A = 6.33, B = -0.29. The spectral synthesizer and
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the vortex method [27, 28] were used to generate the fluctuating turbulence velocity at
187
the inlet boundary for the same turbulence intensity profile described by Eq. (14).
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The requirements as suggested by Tominaga et al. [21] and Ramponi & Blocken
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[22] for the boundary conditions, computational domain and mesh were followed in this
190
study. The computational domain (height 6H = 0.48 m, width 10.5H = 0.84 m and
191
length 22.5H = 1.8 m) and mesh layout are shown in Figure 4. The blockage ratio of the
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cross section of the building to the computational domain was 2.0%. The wall thickness
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was set as 2.0 mm.
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The grid resolution plays an essential role in the accuracy of the LES simulation
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[25]. In this study, the areas inside and around the building were discretized by a
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uniform grid. For the area far away from the building, non-uniform grids with a
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stretching ratio of 1.10 ~ 1.25 were adopted. The grid sensitivity was checked by
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comparing the simulation results of three different grids, and it was found that the grid
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235 × 68 × 59 with the smallest grid size of ∆x = 1.0 mm, ∆y = 3.0 mm, ∆z = 3.0 mm
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had the best agreement with the experimental results of Karava et al. [8]. Therefore, it
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was used for the rest of the simulation.
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The simulated stream-wise velocities U(x)/UH along the centerline of the openings
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are shown in Figure 5 as dash lines. The velocity at the building height is UH = 6 m/s.
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The solid symbols represent the experimental results of Karava et al. [8], and the dotted
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206
(SST) k-ω model (their reference case). Although the simulated velocities deviated from
207
the measured velocities near the inlet and outlet openings, the agreement between the
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numerical and the experimental results in the region x/L = 0.5 ~ 0.8 was satisfactory.
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The discrepancy between the simulated and the measured velocities near the inlet and
210
outlet openings was due to the edge reflections and shadows of the laser light sheet [8,
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21]. By comparing the simulated velocities and the experimental results of Karava et al.
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[8], it was concluded that the results of the spectral synthesizer were better than those of
213
the vortex method. Therefore, the spectral synthesizer was used for the rest of this study.
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Figure 6 illustrates the simulated velocity vectors on the mid-plane of the building.
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There was a standing vortex upstream of the building. Inside the building, the air flow
216
was deflected downward to the building floor as it passed through the inlet opening. The
217
flow patterns inside the building and on the building roof were very similar to the
218
experimental results of Ohba et al. [29], Karava et al. [8] and the numerical simulation
219
of Hu et al. [20].
The ventilation rate Q into the building can be calculated by two different methods.
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The first method is to integrate the simulated time-averaged horizontal velocities at the
222
openings. The ventilation rates at the inlet and outlet openings are represented by Q1
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and Q2, respectively. The second method is to substitute the opening areas, discharge
224
coefficients and the predicted windward and leeward pressure coefficients into Eq. (2)
225
to obtain the ventilation rate Qmodel. The time-averaged velocities and pressure
226
coefficients are computed from the simulation results in between 30 ~ 40 sec.
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The dimensionless ventilation rates through the inlet and outlet openings,
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computed by the integration method, were: Q*1 = 0.423 and Q*2 = 0.414. The relative
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ACCEPTED MANUSCRIPT difference 2.1% indicated that the mass conservation between the inflow and outflow
230
was satisfactory. The ventilation rate predicted by Eq. (2) was Q*model = 0.419, with the
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simulated external pressure coefficients right above the windward and leeward openings
232
Cp1 = 0.66, Cp2 = -0.17 and discharge coefficients Cd1 = 0.65, Cd2 = 0.65. In other words,
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the ventilation rates calculated by the integration model were very close to the
234
prediction of Eq. (2). The good agreement between the computed ventilation rates by
235
the two different methods validated the capability of the present LES model to simulate
236
the wind-driven cross ventilation.
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238 239
4. Computational Setup
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The present LES model was used to investigate the wind-driven cross ventilation through a single isolated low-rise building. The external height and width of the
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building were fixed as height H = 4 m and width W = 10 m (see Figure 7). The length of
242
the building was varied in the range of L = 5.0 ~ 44.0 m (the aspect ratio L/H = 1.25 ~
243
11). The reference case was set as the building length L = 10 m (L/H = 2.50). For all the
244
cases, the windward and leeward façades each had one opening on the centerline of the
245
façades. The cross-sectional areas of inlet and outlet openings were identical A1 = A2 =
246
2 m x 2 m, and the wall porosity was r1 = r2 = 10%. The thickness of the building wall
247
was 0.1 m.
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The approaching flow followed Eq. (13) with the value of δ = 400 m and the
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free-stream wind speed was Uo = 12 m/s. Therefore, the wind speed at the building
250
height was UH = 6.0 m/s. The Reynolds number based on the wind speed UH and
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building height was Re = HUH /ν = 1.6 × 106. The turbulence intensity profile followed
252
Eq. (14), and the turbulence intensity at the building height was Iu = 23.9%. The wind 11
ACCEPTED MANUSCRIPT 253
direction was normal to the windward façade ( θ = 0°) of the building for all the
254
simulation cases. The computational domain was 24 m (= 6H) in height and 70 m (= 7W) in width.
256
The length of the computational domain varied according to the building length, the
257
distance from the leeward façade to the outlet boundary was 63 m (= 15.75H). The
258
blockage ratio of the building to the computational domain was 2.38%. The
259
computational grid was adjusted from the grid used in the model verification. For all the
260
simulation cases, the grid size inside the building was the same: ∆x/H = 0025, ∆y/H =
261
0.05, ∆z/H = 0.05. The area far away from the building employed a non-uniform grid
262
with the stretching ratio 1.25. For the reference case (building length L/H = 2.5), the
263
grid number inside the building was 87,952 cells and the total grid number was
264
1,064,770 cells (= 245 × 82 × 53 cells).
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5. Results and Discussion
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5.1 Building Length
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Figure 8(a) shows a comparison of the predicted pressure coefficients on the
269
centerlines of the windward façades for different building lengths. The windward
270
pressure coefficient Cp1 above the inlet opening was in the range of Cp1 = 0.60 ~ 0.75,
271
and independent of the building length. This phenomenon is similar to the results of
272
wind tunnel experiments. Furthermore, the values of windward pressure coefficient are
273
in the same range of experimental results. The pressure coefficient Cp1 right above the
274
windward opening (z/H = 0.6) decreased slightly because the air accelerated as it flow
275
into the opening.
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On the other hand, Figure 8(b) shows that the leeward pressure coefficient Cp2 ≈ 12
ACCEPTED MANUSCRIPT -0.60 for L/H = 1.25 was much smaller than the leeward pressure Cp2 = -0.15 ~ -0.20 for
278
longer buildings (L/H ≥ 2.5). It also illustrated that the leeward pressure was
279
independent of the building length when L/H ≥ 2.5. Again, this is similar to the
280
experimental results of building length L/H longer than 1.0 (see Figure 2(b)). Altogether,
281
Figures 2 and 8 imply that the pressure difference between the windward and leeward
282
façades (the driving force for cross ventilation) of short buildings was higher than that
283
for long buildings. In other words, the ventilation rate of short buildings will be larger
284
than that of long buildings.
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The contours of time-averaged pressure coefficient Cp on the mid-plane of the
286
building for building lengths L/H = 1.25, 2.5, 5.0 and 8.0 are illustrated in Figure 9. Due
287
to the separated shear layer on the building roof, the pressure at the leeward region of
288
building length L/H = 1.25 was lower than for the other building lengths. For building
289
length L/H ≥ 2.5, because the length of separated shear layer was less the building
290
length and the reattachment of eddies on the building roof, the leeward pressure was
291
much alike. Also the pressure distribution inside the building was comparable.
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It is also noteworthy that, both the experimental and numerical results show that
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the aspect ratio L/H of buildings is more influential to the leeward pressures than to the
294
windward pressures. This information is important to those choosing pressure
295
coefficients for ventilation design [30]. It can be explained by the separation bubble at
296
the building roof. However, the critical building length is L/H > 1.0 for the wind tunnel
297
experiment, the critical building length is L/H > 2.5 for the numerical simulation. This
298
difference is believed due to the aspect ratio H/W of the building. The aspect ratio H/W
299
= 0.4 for the wind tunnel experiments, while H/W = 2.0 for the numerical simulation.
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The time-averaged velocity vectors on the mid-plane of the building for L/H =
13
ACCEPTED MANUSCRIPT 1.25 and 2.5 are compared in Figure 10. The separated shear flows around the leading
302
corner on the building roof look very much alike, but there was reattachment toward the
303
trailing corner of the building for L/H = 2.5, while no reattachment for L/H = 1.25
304
because the separation bubble was longer than the building length. Also, there was a
305
standing vortex inside the building between the ceiling and outlet opening, and the
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counter-clockwise rotating vortex generated resistance for the air flow passing through
307
the building.
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The dimensionless ventilation rates Q*, computed by the integration method, are shown in Figure 11. The values of Q* were normalized by the dimensionless ventilation
310
rate of reference case Q*r = 0.448. When building length L/H 2.5, Eq. (2) predicted the
311
ventilation rates very well. But for longer buildings (L/H ≥ 5.0), the ventilation rate
312
decreased as the building length increased and Eq. (2) over-predicted the ventilation
313
rates Q*. The ventilation rate of L/H = 11 was only 80% of the ventilation rate of L/H =
314
2.5. This suggested that the diminishing effect of the internal friction on the ventilation
315
rate cannot be neglected when the building length L/H ≥ 5.0.
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terms of the internal resistance factor ζi in Eq. (3). The value of ζi can be computed by
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substituting the simulated pressure coefficients Cp1 and Cp2 from LES into Eq. (3). The
319
resistance factors of the external openings ζ1 = ζ2 = 0.148 m-4 were computed by setting
320
the discharge coefficient Cd = 0.65 and the opening area A1 = A2 = 4 m2. Figure 12
321
displays a non-linear relation between the dimensionless resistance factor ζi/ζ1 and the
322
building length L/H. The internal resistance was negligible when L/H < 2.5, but
323
increased drastically when L/H > 5. This led to the decline in the ventilation rate of long
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buildings.
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Because the building floors are smooth surfaces, the skin friction estimated by the boundary layer theory [31] is quite small. The energy loss is mainly due to the
327
circulating, turbulent flow in the building. When building length L/H ≥ 5, the internal
328
friction caused by the turbulent flow increased almost linearly with the building length.
329
Figure 12 also infers that the resistance factors ζ1 and ζ2 of the external openings are the
330
dominant parameters for short buildings without any internal obstacle (furniture and
331
partition). However, the resistance factor ξi cannot be neglected for buildings with large
332
aspect ratio L/H.
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Figure 13 displays the time-averaged stream-wise velocity along the centerline of
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the openings at height z/H = 0.25 (z = 1 m). The stream-wise velocities were normalized
335
by the wind speed UH. For building length L/H = 1.25, the internal velocity was the
336
highest due to the large pressure difference across the building, but it decreased as the
337
building length increased. For short buildings, the air flow past thought the windward
338
and leeward openings resembling a strong jet flow, without much energy loss. However,
339
the air flow in long buildings like a diffused jet, velocity decrease as it goes further into
340
the building. For L/H ≥ 5.0, the internal velocity became u/UH < 0.4 in the region near
341
the leeward opening. The velocity rise near the outlet is due to the suction at the leeward
342
façade. The region with a low internal velocity is called the sluggish zone. The length of
343
the sluggish zone was about x/L = 0.65 ~ 0.95 for L/H = 5, but increased to x/L = 0.25 ~
344
0.95 for L/H = 11. Designing cross ventilation in long spaces should pay attention to
345
this phenomenon.
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5.2 Diagonal Openings Besides the building length, the opening configurations can generate additional
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ACCEPTED MANUSCRIPT resistance for cross ventilation. Karava et al. [8] and Ramponi & Blocken [18] studied
350
the wind-driven cross ventilation of different opening configurations. However, they did
351
not quantify the influences of the location of the openings on the ventilation rate. The
352
purpose of this simulation was to compare the ventilation rates of openings located on
353
the diagonal of the building (see Figure 14) with that of the reference case (openings at
354
the center of the building façades). The size of the building (height H = 4.0 m, width W
355
= 10.0 m and length L = 10.0 m), opening areas (A1 = A2 = 2 m x 2 m), wind direction
356
( θ = 0°) and velocity profile at the inlet boundary were identical to those of the
357
reference case. But the openings were placed in opposite corners of the windward and
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leeward facades, along the diagonal of the building.
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Figures 15(a) and 15(b) illustrate the pressure coefficients above the windward and leeward openings, respectively. The location of the pressure profile was on the
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centerline (y = 0) for the reference case, while the pressure profile was taken at y/W =
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±0.40 for the diagonal case. The windward pressures were very similar for openings
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located on the centerline and on the diagonal direction. However, the leeward pressures
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were slightly different for the reference and diagonal cases.
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The pressure difference ∆P between the windward and leeward openings was the driving force for wind-driven cross ventilation. As listed in Table 1, the pressure
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coefficient difference ∆CP = Cp1 - Cp2 above the opening (z/H = 0.7) of the reference
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and diagonal cases was 0.925 and 0.911, respectively. However, the dimensionless
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ventilation rate of diagonal case Q* = 0.368, as computed by the integration method,
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was much lower than that of reference case Q*r = 0.448. This disparity was attributed to
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the internal resistance as the air flow passed through the diagonal openings. In other
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words, the ventilation models that did not consider internal resistance, such as Eq. (2),
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over-estimated the ventilation rate for openings not on a straight line. The additional resistance for the air flow through diagonal openings could be
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quantified using the internal resistance factor ζi. Similar to the calculation used for the
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resistance factors of long buildings, the dimensionless resistance factor of the diagonal
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openings was obtained as ζi / ζ1 = 0.856. For the same opening size and similar pressure
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difference, the ventilation rate (calculated by integration method) through the building
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with diagonal openings was 15.5% less than that of the reference case (openings on the
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centerline of the building). For long buildings or buildings with furniture inside, the
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wind-driven cross ventilation will be further reduced.
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6. Conclusions
The rule of thumb for effective wind-driven cross ventilation suggests that the
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building length should be less than five times the ceiling height. This study used a Large
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Eddy Simulation model and wind tunnel experiments to investigate the mechanism
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behind this rule of thumb in a single-zone, low-rise building. The numerical and
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experimental results both revealed that the windward pressure was independent of the
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aspect ratio of the building, but the leeward pressures of short buildings were lower than
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that of long buildings. This is due to the separation bubbles on the building roof can
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reach the leeward sides of short buildings. In other words, the ventilation rate of a short
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building is higher owing to the larger pressure difference between the windward and
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leeward façades.
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Furthermore, it was found that the ventilation rate of building length L/H = 11 is
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20% less than that of building length L/H = 2.5, even when the pressure difference
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across the building and the opening size were the same. Plus, there was a sluggish zone 17
ACCEPTED MANUSCRIPT with low wind speed inside the building when the building length was L/H ≥ 5.0. It is
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the internal friction that caused the sluggish zone and the decline in ventilation rate. The
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conventional ventilation models that do not consider the internal resistance will
400
over-estimate the ventilation rate of long buildings.
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The location of the openings also affected the ventilation process. The simulation
402
results indicated that the ventilation rate for building with openings in opposite corners
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of the windward and leeward façades was 15.5% lower than that of openings on the
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centerline of the building, even though the pressure differences between the windward
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and leeward façades of the building were very close. This was attributed to the
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additional resistance for air flow to pass through the diagonal openings. The resistance
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model of Chu and Chiang [12] can be used to quantify the internal friction of different
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building lengths and opening configurations.
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Acknowledgement
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The authors thank the Architecture and Building Research Institute, Ministry of
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The Interior (Grant no. 10162B001), and National Science Council of Taiwan (Grant no.
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102-2221-E-008-055) for their support of this study.
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References
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[1] Allard F. Natural ventilation in buildings: a design handbook, James and James Ltd., London, England; 1998.
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[2] Aynsley R. Estimating summer wind driven natural ventilation potential for indoor
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thermal comfort. J Wind Eng Ind Aerodyn 1999; 83 (1-3):515-25. [3] Linden PF. The fluid mechanics of natural ventilation. Annual Review of Fluid Mechanics 1999; 31:201-38. [4] Etheridge D. Natural ventilation of buildings: Theory and measurement and design. 18
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John Wiley and Sons, Chichester, England, 2012.
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[5] Awbi HB. Ventilation of Buildings. 2nd ed. Taylor and Francis, London, England,
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[6] Etheridge D, Sandberg M. Building ventilation: Theory and Measurement. John
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Wiley and Sons, Chichester, England, 1996. [7] Chu CR, Chiu YH, Chen YJ, Wang YW, Chou CP. Turbulence effects on the
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discharge coefficient and mean flow rate of wind-driven cross ventilation. Build Environ 2009; 44: 2064-72. doi:10.1016/j.buildenv.2009.02.012.
[8] Karava P, Stathopoulos T, Athienitis AK. Airflow assessment in cross-ventilated
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buildings with operable façade elements. Build Environ 2011; 46(1): 266-79.
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[9] Johnson M-H, Zhai Z, Krarti M. Performance evaluation of network airflow models for natural ventilation. HVAC&R Research 2012; 18(3): 349-365. [10] Chu CR, Chiu YH, Wang YW. An experimental study of wind-driven cross
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ventilation in partitioned buildings. Energy Build 2010; 42(5): 667-73. doi:10.1016/j.enbuild.2009.11.004.
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[11] Chu CR, Wang YW. The loss factors of building openings for wind-driven ventilation. Build Environ 2010; 45(10): 2273-79. doi:10.1016/j.buildenv. 2010.04.010.
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[12] Chu CR, Chiang BF. Wind-driven cross ventilation with internal obstacles. Energy Build 2013; 67,:01-09. doi:10.1016/j.enbuild.2013.07.086.
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[13] CIBSE. Natural ventilation in non-domestic buildings: Applications Manual 10, AM10: Chartered Institution of Building Services Engineers (CIBSE), London, 1997.
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[14] Mumovic D, Santamouris M. A Handbook of Sustainable Building Design and
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Engineering: An integrated approach to energy, health and operational performance, Earthscan, England, 2009.
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[15] Evola G, Popov V. Computational analysis of wind driven natural ventilation in buildings. Energy Build 2006; 38:491-501.
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[16] Kato S, Murakami S, Mochida A, Akabashi S, Tominaga Y. Velocity-pressure field of cross-ventilation with open windows analyzed by wind tunnel and numerical simulation. J Wind Eng Ind Aerodyn 1992; 41-44: 2575-86.
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[17] Jiang Y, Chen Q. Effect of fluctuating wind direction on cross natural ventilation in buildings from large eddy simulation. Build Environ 2002; 37(4): 379-86.
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[18] Ramponi R, Blocken B. CFD simulation of cross-ventilation flow for different isolated building configurations: validation with wind tunnel measurements and 19
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analysis of physical and numerical diffusion effects. J Wind Eng Ind Aerodyn 2012; 104-106: 408-18.
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[19] Kobayashi T, Sagara K, Yamanaka T, Kotani H, Sandberg M. Power transportation
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inside stream tube of cross-ventilated simple shaped model and pitched roof house. Build Environ 2009; 44(7):1440-51. [20] Hu CH, Ohba M, Yoshie R. CFD modelling of unsteady cross ventilation flows using LES. J Wind Eng Ind Aerodyn 2008; 96(10-11):1692-706.
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[21] Tominaga Y, Mochida A, Yoshie R, Kataoka H, Nozu T, Masaru Y, Shirasawa T. AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J Wind Eng Ind Aerodyn 2008; 96:1749-61.
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[22] Ramponi R, Blocken B. CFD simulation of cross-ventilation for a generic isolated building: Impact of computational parameters. Build Environ 2012; 53:34-48.
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[23] Germano M, Piomelli U, Moin P, Cabot WH. A dynamic subgrid scale eddy
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viscosity model. Physics of Fluids A 1991; 3(7): 1760-65.
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[24] Smagorinsky J. General circulation experiments with the primitive equations. I. The basic experiment. Monthly Weather Review 1963; 91(3): 99-164.
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[25] Chen Q. Ventilation performance prediction for buildings: A method overview and recent applications. Build Environ 2009;44:848-58. doi:10.1016/ j.buildenv.2008.05.025.
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[26] Launder BE, Spalding DB. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 1974; 3:269-89.
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[27] Meroney RN. CFD prediction of dense gas clouds spreading in a mock urban
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environment. In: The Fifth International Symposium on Computational Wind Engineering, 2010. Chapel Hill, North Caroline, USA.
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[28] Huang SH, Li QS, Wu JR. A general inflow turbulence generator for large eddy simulation. J Wind Eng Ind Aerodyn 2010; 98 (10-11): 600-617.
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[29] Ohba M, Irie K, Kurabuchi T. Study on airflow characteristics inside and outside a
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cross-ventilation model, and ventilation flow rates using wind tunnel experiments. J Wind Eng Ind Aerodyn 2001; 89:1513-24.
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[30] Costola D, Blocken B, Hensen JLM. Overview of pressure coefficient data in building energy simulation and airflow network programs Build Environ 2009; 44:2027-2036. [31] Schlichting H. Boundary-Layer Theory. New York: McGraw-Hill; 1979.
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Notation
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A1, A2
cross-section area of external opening (m2)
494
A2/A1
opening ratio (dimensionless)
495
Aw
cross-section area of building interior (m2)
496
AF
area of the windward facade (m2)
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Cd
discharge coefficient of opening (dimensionless)
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Cp = (P-Po)/0.5ñU2
external pressure coefficient (dimensionless)
499
H
height of building (m)
500
L
length of building (m)
501
Po
reference pressure (Pa)
502
Q
ventilation rate (m3/s)
503
Q*
dimensionless ventilation rate
504
r1, r2 = A/AF
external wall porosity (dimensionless)
505
Uo
free stream wind speed (m/s)
506
UH
wind speed at the building height (m/s)
507
W
width of building exterior (m)
508
z
509
ρ
510
g
511
α
512
δ
513
θ
514
ζi
515
æ1 , æ2
516
Subscripts
517
1
windward side
518
2
leeward side
519
i
internal
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elevation (m)
air density (kg/m3)
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gravitational acceleration (m/s2) exponent of the velocity profile
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thickness of boundary layer (m) wind direction (degree)
internal resistance factor (m-4) external resistance factor (m-4)
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1
Table Caption:
2
Table 1. Simulation results of diagonal openings.
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5 6 7
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Case
ΔCP
Q*
Reference
0.925
0.448
Diagonal
0.915
ζi (m-4)
ζi/ζ1
0
0
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Table 1. Simulation results of diagonal openings.
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0.368
0.127
0.856
ΔCP is the difference between the windward and leeward pressure coefficients above the opening (z/H = 0.7).
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1
ACCEPTED MANUSCRIPT Figure Caption: Figure 1. Schematic diagram of wind-driven cross ventilation in long buildings. Figure 2. Comparison of simulated and measured pressure coefficient on the centerlines of building surface. (a) windward façades of building height L/H = 0.5 and 1.0. (b) leeward façades of L/H = 0.5, 1.0, 2.0, 2.5 and 3.0. The symbols are
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the measured pressure coefficients, the lines are the numerical predictions.
Figure 3. Vertical profiles of time-averaged velocity U(z) and stream-wise turbulence intensity Iu(z) (= σu(z)/U(z)) of the approaching flow.
Figure 4. Computational domain and mesh layout for the numerical simulation.
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Figure 5. Comparison of predicted stream-wise velocity U(x)/UH along the centerline of boundary.
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the openings by different schemes to generate velocity fluctuation at the inlet
Figure 6. Time-averaged velocity vectors on the mid-plane of the building. The flow condition followed the experiment of Karava et al. [8]. Figure 7. Schematic diagram of the full-scale building for the numerical simulation. The openings are on the centerlines of windward and leeward walls, opening
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area A1 = A2 = 2 m x 2 m.
Figure 8. Pressure coefficients on the centerlines of building external walls: (a) above windward opening; (b) above leeward opening. Figure 9. Time-averaged pressure distribution on the mid-plane of the building for
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different building lengths. (a) L/H = 1.25; (b) L/H = 2.5; (c) L/H = 5.0; (d) L/H = 8.0.
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Figure 10. Time-averaged velocity vectors on the mid-plane of the building for different building length. (a) L/H = 1.25; (b) L/H = 2.5.
Figure 11. Effect of building length on the ventilation rate, Q*r is the dimensionless ventilation rate of reference case (L/H = 2.5).
Figure 12. Dimensionless internal resistance ζi/ζ1 as a function of building length. Figure 13. Time-averaged streamwise velocity along the centerline of the openings at height z/H = 0.25. Figure 14. Schematic diagram of a full-scale building with openings on the diagonal corners of the windward and leeward walls. The opening area A1 = A2 = 2 m x 2 m. 1
ACCEPTED MANUSCRIPT Figure 15. Pressure coefficients on the building external walls: (a) above windward opening (x/L = 0, y/W = -0.4); (b) above leeward opening (x/L = 1.0, y/W =
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0.4).
Wind
L
P1
H
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Q1
EP
A1
P2 Q2 A2
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Figure 1. Schematic diagram of wind-driven cross ventilation in long buildings.
2
ACCEPTED MANUSCRIPT (a) 1.0 LES, L/H=0.5 Exp. L/H=0.5
0.8
Exp. L/H=1.0
0.4 0.2
0.2
(b) 1.0
0.6
0.8
1.0
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Z/H
0.6
0.2
Cp
LES, L/H = 0.5 Exp. L/H = 0.5 Exp. L/H = 1.0 Exp. L/H = 2.0 Exp. L/H = 2.5 Exp. L/H = 3.0
0.8
0.4
0.4
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0.0 0.0
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Z/H
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0.6
0.0 -0.8
-0.6
-0.4
-0.2
0.0
Cp
Figure 2. Comparison of simulated and measured pressure coefficient on the centerlines of building surface. (a) windward façades of building height L/H = 0.5 and 1.0. (b) leeward façades of L/H = 0.5, 1.0, 2.0, 2.5 and 3.0. The symbols are the measured pressure coefficients, the lines are the numerical predictions. 3
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0.48
0
5
10
Iu (%)
15
20
25
Exp., Karava et al. (2011) Inlet Velocity Profile
0.40
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Exp., Karava et al. (2011)
z (m)
0.32
Inlet turbulence intensity
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0.16
0.00
0
4
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0.08
8
12
16
20
U (m/s)
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Figure 3. Vertical profiles of time-averaged velocity U(z) and stream-wise turbulence
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intensity Iu(z) (= σu(z)/U(z)) of the approaching flow.
4
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Wind
4.25H L+1.5H
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15H
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Figure 4. Computational domain and mesh layout for the numerical simulation.
5
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1.2 LES, vortex method LES, spectral synthesizer k-ω, Ramponi and Blocken (2012) Exp., Karava et al. (2011)
1.0
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U(x) / UH
0.8 0.6
0.2 0.0 -0.35
0.5
1.0
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0.0
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0.4
1.5
x/L
Figure 5. Comparison of predicted stream-wise velocity U(x)/UH along the centerline of the openings by different schemes to generate velocity fluctuation at the inlet boundary.
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The flow condition followed the experiment of Karava et al. [8].
6
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Figure 6. Time-averaged velocity vectors on the mid-plane of the building. The flow
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condition followed the experiment of Karava et al. [8].
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A2
4.0 m A1 z
x
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2.0 m
2.0 m
10 m
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y
U
L
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Figure 7. Schematic diagram of the full-scale building for the numerical simulation. The openings are on the centerlines of windward and leeward façades, opening area A1 = A2
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= 2 m x 2 m.
8
ACCEPTED MANUSCRIPT (a) Windward facade
1.0 0.8
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z/H
0.6 0.4
L/H = 1.25 L/H = 2.5 L/H = 5.0 L/H = 8.0 L/H = 11.0
0.0 0.0
0.4
0.6
0.8
1.0
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0.2
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0.2
Cp
(b) Leeward facade
1.0
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0.8
0.4
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0.2
L/H = 1.25 L/H = 2.5 L/H = 5.0 L/H = 8.0 L/H = 11.0
EP
z/H
0.6
0.0 -0.8
-0.6
-0.4
Cp
-0.2
0.0
0.2
Figure 8. Pressure coefficients on the centerlines of building external walls: (a) above windward opening; (b) above leeward opening.
9
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z (m)
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x (m)
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(a) L/H = 1.25
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z (m)
(b) L/H = 2.5
x (m)
10
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p
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x (m)
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(d) L/H = 8.0
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z (m)
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(c) L/H = 5.0
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z (m)
EP
x (m)
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Figure 9. Time-averaged pressure distribution on the mid-plane of the building for different building lengths. (a) L/H = 1.25; (b) L/H = 2.5; (c) L/H = 5.0; (d) L/H = 8.0.
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(a) L/H = 1.25
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(b) L/H = 2.5
Figure 10. Time-averaged velocity vectors on the mid-plane of the building for different building length. (a) L/H = 1.25; (b) L/H = 2.5.
12
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150
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125
75
*
*
Q / Qr (%)
100
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50
Integration method Eq. (2)
0
0
2
4
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6
8
10
12
14
L/H
Figure 11. Effect of building length on ventilation rate, Q*r is the dimensionless
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ventilation rate of reference case (L/H = 2.5).
13
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1.0
0.8
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ζi / ζ1
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0.4
0.0
0
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4
6
8
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14
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L/H
10
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0.2
Figure 12. Dimensionless internal resistance ζi/ζ1 as a function of building length.
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Openings on the centerlines of the windward and leeward façades.
14
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2.0
L/H = 1.25 L/H = 2.50 L/H = 5.00 L/H = 8.00 L/H = 11.0
1.6
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0.8 0.4 0.0 0.0
0.2
0.4
0.6
0.8
1.0
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x/L
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u / UH
1.2
Figure 13. Time-averaged streamwise velocity along the centerline of the openings at
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height z/H = 0.25.
15
4.0 m
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2.0 m
A2
2.0 m
z
A1
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x
10 m
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y
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Figure 14. Schematic diagram of a full-scale building with openings on the diagonal
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corners of the windward and leeward façades. The opening area A1 = A2 = 2 m x 2 m.
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ACCEPTED MANUSCRIPT (a) Windward facade
1.0 0.8
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z/H
0.6 0.4
Reference case Diagonal case
0.0 0.0
0.2
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(b) Leeward facade
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EP
z/H
0.6
0.0 -0.4
Reference case Diagonal case
-0.3
-0.2
-0.1
0.0
Cp
Figure 15. Pressure coefficients on the building external walls: (a) above windward opening (x/L = 0, y/W = -0.4); (b) above leeward opening (x/L = 1.0, y/W = 0.4).
17
ACCEPTED MANUSCRIPT Title: Wind-driven cross ventilation in long buildings
* This study used numerical model to investigate the ventilation of long buildings.
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* The ventilation rate decreased as the building length increased. * The rule of thumb for wind-driven cross ventilation is clarified.
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* The location of the building openings also influenced the ventilation rate.