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Natural ventilation of buildings due to buoyancy assisted by wind: Investigating cross ventilation with computational and laboratory simulation
Building and Environment 66 (2013) 104e119
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Natural ventilation of buildings due to buoyancy assisted by wind: Investigating cross ventilation with computational and laboratory simulation Anastasia D. Stavridou*, Panagiotis E. Prinos Division of Hydraulics and Environmental Engineering, Department of Civil Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 December 2012 Received in revised form 30 March 2013 Accepted 16 April 2013
In this paper cross natural ventilation due to buoyancy assisted by wind is investigated with computational and laboratory simulation. The impact of the outlet’s opening position is investigated, forming cross ventilation of variable distance h e namely, the vertical distance between midpoints of leeward and windward opening e, for three initial Froude numbers: (i) Fr0 ¼ 1.15, (ii) Fr0 ¼ 2.79, (iii) Fr0 ¼ 4.85. For the computational simulation a fluid dynamic software is used and the problem is solved by solving the 3D unsteady Reynolds Averaged Navier Stokes (RANS) equations in conjunction with the energy equation and the turbulence model RNG k-ε. The laboratory simulation took place in an open channel and the experimental model represents a building form of orthogonal shape. The interior of the experimental model is filled with solution of ethanol at conditions of normalized gravity, but also with salted water at conditions of inversed gravity. The time taken for the indoor space to empty is calculated numerically and experimentally. Based on Froude number dynamic similarity, the experimental and computational results are characterized by good agreement and the functional process of natural ventilation is being explicated. In addition, the suggestion of using ethanol solution for the density difference between interior and exterior fluid in laboratory simulation of natural ventilation is verified successfully, as the results with use of ethanol solution are in good agreement with those using salted water. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Natural ventilation of buildings Computational fluid dynamics Laboratory simulation Computational simulation
1. Introduction Natural ventilation of buildings constitutes a basic parameter of bioclimatic design. It aims at improving indoor air quality by achieving good air exchange rates, providing thermal comfort and healthy living conditions, as well as maintaining a convenient indoor environment. Thus natural ventilation promotes not only protection and restoration of indoor air, but also sustainability and energy saving. Awbi et al. [5] deal with ventilation of buildings, while emphasizing on themes as quantification of outdoor air flow rate to a building and distribution of this ventilation air around the space. Allard et al. [4] examine the efficient use of natural ventilation in buildings in order to decrease the energy consumption for cooling purposes, increase the indoor thermal comfort levels and improve indoor air quality.
* Corresponding author. Tel.: þ30 2310995708. E-mail addresses: [email protected] (A.D. Stavridou), [email protected] (P.E. Prinos). 0360-1323/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.buildenv.2013.04.011
The fluid mechanics of natural ventilation, as the flow generated by temperature differences and by the wind, are examined by Linden [10] aiming at giving designers rules and intuition on how air moves within a building. This research reveals a fascinating branch of fluid mechanics, dealing with two basic forms of ventilation: mixing and displacement ventilation. Previous investigations of these two types of ventilation have been carried out by Linden et al. [2], in case of a space connected to a large body of stationary ambient fluid. Hunt and Linden [1] describe the fluid mechanics of natural ventilation by the combined effects of buoyancy and wind. In particular they examine transient draining flows in a space containing buoyant fluid, when the wind and buoyancy forces reinforce one another, while connections between the enclosure and the surrounding fluid are with high-level and lowlevel openings on both leeward and windward faces. They also give conditions for the transition to a mixing flow for three initial Froude number parameter ranges (i) displacement ventilation for 0 < Fr0 < 2.5, (ii) transitional ventilation for 2.5 < Fr0 < 3.3, (iii) mixing ventilation for Fr0 > 3.3. Steady e state flows in an enclosure ventilated by buoyancy forces assisted by wind are examined by Hunt and Linden [8], while ventilation openings connecting the
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internal and external environment are at high level on the leeward facade and at low level on the windward facade. Analytical solutions are derived for calculating natural ventilation flow rates and air temperatures in a single e zone building with two openings, one at low level and one at high level of the opposite wall, when no thermal mass is present, by Li and Delsante [9]. Results of a CFD simulation of the wind e assisted stack ventilation of a single e storey enclosure with high and low-level ventilation openings are presented by Cook et al. [6] and compared with both the laboratory measurements and analytical model of the flow and thermal stratification developed by Hunt and Linden [8]. The control of naturally ventilated buildings subject to wind and buoyancy is examined by Lishman and Woods [11], while the geometry cases investigated refer to cross ventilation with one windward and one or two leeward openings. Transitions in natural ventilation flow driven by changes in the wind are examined by Lishman and Woods [12]. Cross ventilated rooms are also analysed by Visagavel and Srinivasan [7] by varying the width of the window opening using CFD. A computational approach of wind driven natural ventilation through multiple windows of a building is examined by Bangalee et al. [13]. In case of cross ventilation, the geometry investigated has two windward and two leeward openings, placed at a height relatively close to the ceiling of the space, while the flow is considered to be steady. They investigate the physical mechanism of the air movement, while the necessity of three-dimensional approach in studying natural ventilation system is emphasized. Ramponi and Blocken [14] investigate CFD simulation of crossventilation, of coupled outdoor wind flow and indoor air flow, for a generic isolated building and examine the impact of computational parameters. They present a series of coupled 3D steady RANS simulations, while the geometry studied include one middle windward and one middle - leeward opening. Geometry in building design and its influence on flow pattern of a naturally ventilated space is a major issue [24,25,27,29e31]. For better understanding of the ventilation mechanism [24], CFD simulations and experimental measurements are carried out [25,26,28], while special attention is given to the process of numerical simulation as well as the experimental one. Gan uses [15] the commercial CFD software FLUENT for simulation of buoyancy-driven natural ventilation of buildings. The steady state of air flow and heat transfer through two-dimensional ventilation cavities is examined and the impact of the computational domain is investigated. Reduced e scale building model using air as working fluid and numerical investigations to buoyancy e driven natural ventilation is carried out by Walker et al. [16]. The scaled model of the naturally ventilated prototype building is created at 1:12 scale and the steady-state buoyancydriven natural ventilation under different scenarios is examined. Rundle et al. [17] carry out a validation of CFD simulations for atria geometries. It is indicated that CFD can be used to successfully simulate the heat transfer and fluid flow in atria geometries and describe the physical phenomena. Nguyen and Reiter [18] use CFD with the RNG k-ε turbulence model and wind tunnel experiment to investigate the effect of ceiling configurations on indoor air motion and ventilation flow rates. The accuracy of the RNG k-ε turbulence model to successfully predict indoor wind motion is confirmed. Evaluation of various turbulence models for the prediction of the airflow and temperature distributions in atria is carried out by Hussain et al. [19]. The steady state governing equations are solved using the commercial CFD solver FLUENT, while relatively good agreement between experimental and CFD predictions are obtained. Van Hooff et al. [20] carry out Particle Image Velocimetry (PIV) measurements and an analysis of transitional flow in a ventilated enclosure. The experimental data and analysis are specifically intended to support the development and validation of
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numerical models for ventilation flow. It is also mentioned that there is a lack of experimental data for transitional ventilation flow. Formal calibration methodology for CFD models of naturally ventilated indoor environments is examined by Hajdukiewicz et al. [21]. The calibration process is supported by the on-site measurements performed in a normally operating building. Combined wind tunnel and CFD analysis for indoor airflow prediction of wind driven cross ventilation is investigated by Lo et al. [22]. Winddriven natural ventilation in a low-rise building is investigated by Tecle et al. [23], while the experiments are carried out in a wind tunnel. Taking into account the existing literature, it is deduced that the issue of cross ventilation with combined and assisting wind and buoyancy forces, regarding geometries that can provide information for openings’ position for different types of ventilation flows, accompanied by experimental data and numerical results, constitute a field that is valuable for research. This work examines natural ventilation in an enclosure either with low windward and high leeward opening or with low windward and middle leeward opening, for three initial Froude numbers: (i) Fr0 ¼ 1.15, (ii) Fr0 ¼ 2.79, (iii) Fr0 ¼ 4.85. Each initial Froude number corresponds to a certain type of ventilation, namely, Fr0 ¼ 1.15 is chosen for displacement ventilation, Fr0 ¼ 2.79 represents transitional ventilation, and Fr0 ¼ 4.85 corresponds to mixing ventilation. These initial Froude numbers are chosen to examine dynamic similarity between wind and buoyancy forces in the experimental model and at full-scale. Full-scale is analysed through the 3D unsteady - state using the CFD software FLUENT, while for the first time the experiments were carried out in a flow channel at conditions of normalized gravity by using ethanol solution. Experiments with salted water at conditions of inversed gravity have been also carried out to testify the results produced by the use of ethanol solution. This paper is organized as follows. Firstly the computational simulation is described, including governing equations, building design, numerical procedure, boundary conditions, and cases studied. Subsequently the laboratory simulation is examined, including experimental model and apparatus, experimental process and cases studied. Then presentation, description and discussion of the results follow. Figures from the computational and laboratory simulation are shown, and the time change of the decline rate of mean temperature is illustrated. Finally, a number of conclusions are derived, regarding outlet’s opening position, initial Froude number, dynamic similarity between small-scale (laboratory simulation) and full-scale (computational simulation), the functional process of each type of ventilation investigated, as well as the use of ethanol in laboratory simulation. 2. Computational simulation (theory/calculation) The software used for the computational simulation of this work is FLUENT 6.01. FLUENT is a Computational Fluid Dynamic (CFD) code which constitutes a state-of-the-art computer program for modelling fluid flow and heat transfer in complex geometries [3]. FLUENT provides complete mesh flexibility, solving the flow problems with unstructured meshes that can be generated about complex geometries with relative ease. The geometry and grid of the present simulation was created using Gambit [32]. For turbulent flows the programme solves conservation equations for mass and momentum (RANS, Reynolds e Averaged NaviereStokes equations). For flows involving heat transfer or compressibility, an additional equation for energy conservation is
1
In particular, version 6.0.12 of Fluent is used.
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Fig. 1. (a) Dimensions of the building form, (b) Three e dimensional digital volume. Grid.
solved. Additional transport equations are also solved when the flow is turbulent. In the present work, the 3D unsteady RANS equations in conjunction with energy equation and the turbulence model RNG k-ε are solved. For density calculation, the Ideal Gas
model is used. This model does not treat density as a constant, but computes it through the ideal gas law. The eddy viscosity is calculated through the eddy-viscosity concept (mt ¼ rCm k2/ε) after the solution of transport equations in which the RNG k-ε
Fig. 2. Two geometry types: low windward e high leeward opening, low windward e middle leeward opening (computational simulation).
A.D. Stavridou, P.E. Prinos / Building and Environment 66 (2013) 104e119 Table 1 Parameter range for the six cases of computational simulation. h (m)
DT (K)
U (m/s)
Fr0
2.1 2.1 2.1 1.05 1.05 1.05
4 4 4 4 4 4
0.62 1.5 2.6 0.62 1.5 2.6
1.15 2.79 4.85 1.15 2.79 4.85
model is based. In addition the energy equation is solved, for calculating the temperature variation within the computational domain. 2.1. Building design For the computational simulation of the building form, depicted in Fig. 1 (a), a three e dimensional digital volume is designed (scale 1:1). The digital volume and the discretization grid, presented in Fig. 1 (b), are design with Gambit, a design program that collaborates with FLUENT. The dimensions of the building form are the following: height 2.5 m, width 1.5 m, and length 2.95 m. The volume of the enclosure is 11 m3, while three windward and three leeward openings have been designed. Each opening is square e shaped and its dimensions are: height ¼ length ¼ 0.18 m. In the present work, only the low windward opening is used, while at the leeward wall either the high or the middle opening is used. The vertical distance between midpoints of the openings is: a) 2.1 m
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between low and high opening, and b) 1.05 m between low and middle opening. The discretization grid consists of 52800 hexahedral cells.
2.2. Numerical procedure For the solution of the equations, the segregated solver has been used. The flow is incompressible and the unsteady equations are solved. Using the segregated approach [3], the governing equations are solved sequentially (i.e., segregated from one another). Because the governing equations are non-linear (and coupled), several iterations of the solution loop are performed before a converged solution is obtained. Fluid properties are updated, based on the current solution. The momentum equations are each solved in turn using current values for pressure and face mass fluxes, in order to update the velocity field. Since the velocities obtained may not satisfy the continuity equation locally, a ``Poisson-type’’ equation for the pressure correction is derived from the continuity equation and the linearized momentum equations. This pressure correction equation is then solved to obtain the necessary corrections to the pressure and velocity fields and the face mass fluxes such that continuity is satisfied. Equations for turbulence characteristics and energy are solved using the previously updated values of the other variables. A check for convergence of the equation set is made. These steps are continued until the convergence criteria are met. Convergence for continuity, momentum and k and ε is of order 104, and for energy 106. For solution process control a false time step is selected equal to 0.1 s.
Fig. 3. (a) Experimental model made of plexiglass, (b) Open channel in the Laboratory of Hydraulics, Department of Civil Engineering e AUTh.
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Fig. 4. Two geometry types: low windward e high leeward opening, low windward e middle leeward opening (laboratory simulation).
2.3. Boundary conditions The boundary conditions used to simulate the ventilated enclosure here are chosen carefully, in order to describe correctly the existing conditions. For the opening that represents the inlet of the flow, the boundary type of “velocity inlet” is selected. Velocity inlet boundary condition is used to define the velocity and scalar properties of the flow at inlet boundaries. For the outlet of the flow, the “pressure outlet” is taken. Pressure outlet boundary condition is used to define the static pressure at flow outlets (and also other scalar variables, in case of backflow). In addition, for all the walls, floor and ceiling, the boundary condition type of “wall” is selected. Wall boundary condition is used to bound fluid and solid regions. 2.4. Cases Displacement, transitional and mixing ventilation are examined with computational simulation. Three initial Froude numbers are selected to represent each type of ventilation: Fr0 ¼ 1.15 for displacement ventilation, Fr0 ¼ 2.79 for transitional ventilation, Fr0 ¼ 4.85 for mixing ventilation. In the present work the initial Froude number is given by
1=2 Fr0 ¼ U= g00 h
(1)
where g0’ is the reduced gravity at t ¼ 0, U is the wind velocity and h is the vertical distance between midpoints of windward and leeward opening. The reduced gravity is given by
g0 ¼ g
DT T
¼ g
Dr r
(2)
where g is the acceleration due to gravity, DT and Dr are the temperature and density difference between the internal and external environment respectively, T and r are the temperature and density of the external environment respectively. Note that for an ideal gas Dr/r ¼ DT/T. Table 2 Parameter range and symbols for the six cases of laboratory simulation. h (m)
Dr
(kg/m3)
0.116 0.116 0.116 0.058 0.058 0.058
35 6 2 35 6 2
U (m/s)
0.23 0.23 0.23 0.23 0.23 0.23
Fr0
1.15 2.79 4.85 1.15 2.79 4.85
Symbol for lab simulation with use of ethanol solution
Symbol for lab simulation with use of salted water
1_A_1 2_A_1 3_A_1 1_A_2 2_A_2 3_A_2
1_B_1 2_B_1 3_B_1 1_B_2 2_B_2 3_B_2
It is noted that for initial Froude number’s calculation, in this work, parameter h represents a reference distance that comes from the geometry with low windward e high leeward opening. Accordingly, the initial Froude number for geometry with low windward e middle leeward opening is calculated as a reference value, in relation with the geometry of low windward e high leeward opening, and parameter h still represents a reference distance which comes from the geometry with low windward e high leeward opening. The investigation takes place for two geometry types (low windward e high leeward opening, low windward e middle leeward opening) as shown in Fig. 2, while three values of wind velocity are examined (0.62 m/s, 1.5 m/s and 2.6 m/s). The initial temperature difference between indoor and outdoor air is equal to 4 K (DT ¼ 4 K). In particular, at t ¼ 0 min, indoor and outdoor temperature are equal to 292 K and 288 K respectively. The parameter range for the six cases of computational simulation is shown in Table 1. 3. Laboratory simulation 3.1. Experimental model and apparatus For the laboratory simulation, an experimental model is designed and constructed Fig. 3(a) to represent the building form described in x 2.1. The construction material of the experimental model is plexiglass, the scale is 1:18 and the interior dimensions are: length 16.3 cm, width 8.3 cm, height 13.8 cm. Each opening is 1 cm2 in area, while the thickness of the walls, the floor and the ceiling is 1 cm. A feed hole is opened at the top of the model, sealed with a metallic valve. The laboratory simulation took place in an open channel of the Laboratory of Hydraulics in Department of Civil Engineering e Aristotle University of Thessaloniki, shown in Fig. 3(b). The channel dimensions are: 10.0 m 0.25 m 0.5 m (length width height). The open flow channel has an horizontal bottom and is connected with a pump, while the flow depth during the experiments was kept at 0.19 m. A water tank is also connected with the Table 3 Validation test of the measurement method with the use of colouring matter, by using conductivity e meter. Time t (s)
Salinity S (&)
0 60 120 210 270 330 360 390
0.3 1e4.8 1e2.2 1.1e1.3 0.4e0.6 0.3e0.4 0.3e0.4 0.3
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channel to collect the water. Rotating blades at the channel end are used to control the flow depth and the velocity of the flow. The measurements are carried out with the following instruments: conductivity e meter, thermometer, micro-propeller for measuring flow velocity and assay balance. Moreover a videocamera Olympus Camedia C-7070 Wide Zoom with timing was used.
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3.2. Experimental process and cases Displacement, transitional and mixing ventilation are also examined in the laboratory simulation, while three initial Froude numbers are selected to represent each type of ventilation. For the investigation of dynamic similarity between wind and buoyancy forces in the experimental model and at full-scale [1], the initial
Fig. 5. Laboratory simulation results for Fr0 ¼ 1.15: Ethanol solution, 1_A_1 & 1_A_2 for h ¼ 0.116 m and 0.058 m respectively. (Note: Online colour Figures accompany the BW print version.)
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Froude numbers in the laboratory simulation are taken equal with those of the computational simulation. This investigation takes place for two geometry types (low windward e high leeward opening, low windward e middle leeward opening) as shown in Fig. 4, while three values of density difference e between the fluid inside the model and the flowing water of the channel e are examined (35 kg/m3, 6 kg/m3 and 2 kg/m3). The “wind velocity” or else the flow velocity is equal to 0.23 m/s (U ¼ 0.23 m/s). The parameter range for the six cases of
laboratory simulation, as well as the symbol of each case, used at the illustrations from the laboratory simulation, are depicted in Table 2. Density difference between indoor and outdoor fluid is formed either by using ethanol solution or by using salted water. The interior of the experimental model is filled with solution of ethanol at conditions of normalized gravity, but also with salted water at conditions of inversed gravity. Ethanol (ethyl alcohol) is a colourless liquid and has a density of 0.78934 gr/cm3 at 20 C.
Fig. 6. Laboratory simulation results for Fr0 ¼ 1.15: Salted water, 1_B_1 & 1_B_2 for h ¼ 0.116 m and 0.058 m respectively.
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For the estimation of the time (t) taken for the indoor space to empty, a count is carried out through the video camera’s chronometer. This count measures the time needed for the total replacement of the indoor solution by outdoor water. For this process to be feasible, the indoor solution is coloured with red dye, Rhodamin B (C28H31ClN2O3). For the validation of this method, a validation test is carried out by using a conductivity e meter. During this test, salted water, of salinity S ¼ 16.9& and density 1010 kg/m3, is placed inside the experimental model. The experimental model is placed in the flow channel, while the measured salinity of the flowing water at the moment is S ¼ 0.3& and the flow velocity is 0.23 m/s. At t ¼ 0 s the low windward and the high leeward openings are opened. Note that in this validation test, low and high definitions refer to the physical location of openings, regardless the conditions of gravity. Subsequently, the salinity outside the high leeward opening is measured with the use of the conductivity e meter, for different moments of time as presented in Table 3. It is obvious that, at t ¼ 390 s, the outgoing fluid is of salinity equal to that of the flowing water (0.3&). Visually, the time needed for the indoor fluid to turn from red to transparent is 6 min plus 30 s, namely 390 s. Consequently, the time coming from the measurement with the conductivity e meter, coincides with the corresponding one coming from the visual observation. This fact validates the measurement method with the use of colouring matter.
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the upper part of the space, while this tone degrades by reaching the floor of the space. At the same time, for h ¼ 0.058 m, the layer mentioned has more distinct form and more firm colour tone. In addition, it is observed that, at t ¼ 4 min for h ¼ 0.116 m, the indoor liquid is characterized by an intermediate red colour (pink). At the same time, for h ¼ 0.058 m, there is an intense red colour at the part of the indoor space laying above the middle leeward opening, while an intermediate red colour (with degrading of colour tone while reaching the floor of the space) characterizes the space below the middle leeward opening. The intense stratification and the interface observed, at t ¼ 4 min for h ¼ 0.058 min, continues to exist at t ¼ 7.4 min, when there is even greater distinctness to the colour tones. The photo shoot at t ¼ 7.4 min, for h ¼ 0.116 m, shows that this moment the indoor liquid reaches totally transparent. A gradual transition of colour tones, from red to total transparent, with time evolution is observed at a great part of indoor space for h ¼ 0.116 m. An area of more intense tones is observed at the upper part of the space, which fades out by reaching the floor of the model. Thus, a type of stratification develops corresponding to a
4. Results and discussion In the following sections, computational and laboratory results are analysed and discussed for Fr0 equal to 1.15, 2.79, 4.85. The relationship between the prototype and the scaled model is also elaborated. 4.1. Effect of outlet’s opening position for Fr0 ¼ 1.15 (displacement ventilation) Laboratory simulation results for Fr0 ¼ 1.15 (displacement ventilation) are presented in Fig. 5, for h ¼ 0.116 m and 0.058 m, at conditions of normalized gravity. For h ¼ 0.116 m, the time taken for the indoor space to empty is t ¼ 7.4 min. This time refers to the time taken, for the indoor liquid’s colour to turn from red to transparent. For h ¼ 0.058 m, the corresponding time is increased significantly (t ¼ 32 min). Hence, for a 50% decrease in h there is a time increase of 332%. Analytically, four photo shoots from the video tape recording, are depicted and compared in Fig. 5, for h ¼ 0.116 m and 0.058 m and times t ¼ 0 min, t ¼ 40 s, t ¼ 4 min and t ¼ 7.4 min. The different tones of red show the density difference between the indoor liquid and the outdoor water. Namely, total red corresponds to the initial density difference, Dr ¼ 35 kg/m3, while as the red colour fades out, the density difference decreases. When the colour turns to total transparent, then density difference is equal to zero, Dr ¼ 0, and the indoor fluid is totally replaced. At t ¼ 40 s, for h ¼ 0.116 m, an area (forming a type of layer) of intense red colour tone is observed at
Table 4 Laboratory time taken for the space to empty, in case of using ethanol solution (eth.) and in case of using salted water (sal.). h (m)
Fr0
tex (eth.)
tex (sal.)
0.116 0.116 0.116 0.058 0.058 0.058
1.15 2.79 4.85 1.15 2.79 4.85
7.4 7.7 7.8 32 8.9 8.1
7.4 7.7 7.8 33.6 8.9 8.1
Fig. 7. Time change of the decline rate of mean temperature (a) Fr0 ¼ 1.15, (b) Fr0 ¼ 2.79, (c) F0 ¼ 4.85.
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certain type of interface characterized by some mixing elements. At about the midway of the phenomenon, the intense tone area is formed especially at the upper left part (just opposite the high leeward opening). The height of the interface, developed between the lighter coloured fluid and the heavier transparent fluid, increases continuously with time for h ¼ 0.058 m. Although, for a certain time period, the lighter coloured fluid accumulates to the upper part of the space and, to a certain point is trapped, while its discharge is slow, as the incoming flow channel velocity is relatively low and the mixing elements of the phenomenon are restricted. Results, at conditions of inversed gravity, are analogous and are shown in Fig. 6, for t ¼ 0 min, t ¼ 40 s, t ¼ 4 min and t ¼ 7.4 min. For
h ¼ 0.116 m, the time taken for the space to empty is t ¼ 7.4 min, while for h ¼ 0.058 m the corresponding time is t ¼ 33.6 min. Hence, for a 50% decrease in h there is a time increase of 354%. By comparing the photos shown in Figs. 5 and 6 and the time evolution of the phenomenon for each case, it is observed that laboratory simulation with use of ethanol, gives results with very good approximation to those coming from laboratory simulation with use of salted water and simultaneous inversion of gravity conditions. In both methods, the flow field, the stratification developed and the colour tones of the indoor fluids are identical, with only difference the inversed mode of depiction due to the gravity conditions. This good approximation is also verified by the final time values (t) measured for each case (Table 4). Consequently,
Fig. 8. Temperature contoures (K) : t ¼ 1,5,10,30 min (Fr0 ¼ 1.15, U ¼ 0.62 m/s, h ¼ 2.1 m, low windward e high leeward opening).
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the laboratory simulation for Fr0 ¼ 1.15 (displacement ventilation), shows that as h decreases, the time taken for the space to empty increases. Computational simulation elaborates this investigation. A part of the results of the computational simulation is presented in Fig. 7, where the diagram of the time change of the decline rate of mean temperature is depicted, for Fr0 equal to 1.15, 2.79, 4.85. In this diagram, the dependent variable is the ratio [(DTinitial-DTn)/DTinitial] 100 and the independent variable is time (t) in minutes. At the ratio of the dependent variable, the variable DTinitial is defined by the temperature difference between indoor and outdoor air at t ¼ 0 min. The variable DTn is defined by the temperature difference between the mean temperature of indoor air, at each new time selected (t ¼ n), and the temperature of outdoor air. The
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indoor mean temperature of each time selected alters with the passing of time, while the outdoor temperature is considered to be constant. From the diagram in Fig. 7 (a), for Fr0 ¼ 1.15 (displacement ventilation), it is observed that, the time taken for the space to empty e in particular at a percentage of about 95% e for h ¼ 2.1 m is t ¼ 27.5 min, while the corresponding time for h ¼ 1.05 m is t ¼ 130 min. Analytical computational simulation results, for Fr0 ¼ 1.15, for h ¼ 2.1 m and 1.05 m are shown in Figs. 8e11. The temperature profile and the velocity field for h ¼ 2.1 m, are presented in Figs. 8 and 9. In this case, an ascending interface is observed throughout the phenomenon. In the temperature contours diagram, it is observed that cold, and thus heavier, air enters from the low-windward opening. This low-tempered air flow is distinct, even
Fig. 9. Velocity vectors (m/s) : t ¼ 1,5,10,30 min (Fr0 ¼ 1.15, U ¼ 0.62 m/s, h ¼ 2.1 m, low windward e high leeward opening).
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Fig. 10. Temperature contoures (K) : t ¼ 1,5,10,30 min (Fr0 ¼ 1.15, U ¼ 0.62 m/s, h ¼ 1.05 m, low windward e middle leeward opening). (Note: The temperatures indicated into the schemes of indoor space are considered to be approximative and they intend to present colour variation.)
at t ¼ 1 min. The stratification, due to temperature fluctuation, is intense and obvious at t ¼ 5 min. With the passing of time, at t ¼ 10 min, the interface’s thickness decreases, while at t ¼ 30 min it is totally removed. Velocity vectors form courses that verify the contours of temperature observed at each moment of time. The temperature profile and the velocity field for h ¼ 1.05 m, are presented in Figs. 10 and 11. In this case, the ascending interface moves slower than the one in case with h ¼ 2.1 m, as the velocities at the upper space of the enclosure are very small and the swirls formed produce a slower movement. Here, there is also incoming cold air from the low-windward opening, while the outlet is placed in the middle of the leeward wall. From the temperature contours, a warm layer of air is observed (at t ¼ 5, 10,
30 min), laying above the middle-leeward opening, with a distinct interface of small thickness. With the passing of time, the stratification remains distinct, even when the warm air layer’s thickness decreases. The velocity vectors follow courses intending to reach the outlet of middle-leeward opening. At t ¼ 5, 10, 30 min, intense mobility of air masses, that lead warm air to the outlet, is restricted to the part of interior space below the height of the middle-leeward opening, while at the upper part, the velocity magnitudes are low. Although these velocities are small, a recirculation course is formed leading the warm air mass down to the outlet in a slow pace. It is obvious that around the interface, there is a distinct difference of velocities’ sizes and directions, which retains the horizontal form of this face.
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Fig. 11. Velocity vectors (m/s) : t ¼ 1,5,10,30 min (Fr0 ¼ 1.15, U ¼ 0.62 m/s, h ¼ 1.05 m, low windward e middle leeward opening).
Computational simulation results explicate laboratory simulation results, as temperature contours and velocity vectors explain the characteristics of the flow, the physical mechanism of the air movement and the functional process of ventilation. Thus the chromatic grade depicted in the lab results is validated. From the computational simulation, comes up that for a 50% decrease in h there is a time increase of 373%. 4.2. Effect of outlet’s opening position for Fr0 ¼ 2.79 (transitional ventilation) Laboratory simulation results for Fr0 ¼ 2.79 (transitional ventilation), are presented in Fig. 12, for h ¼ 0.116 m and 0.058 m, at conditions of normalized gravity. At t ¼ 5 min the indoor solution’s
colour is darker for h ¼ 0.058 m than that of case with h ¼ 0.116 m. This shows that for h ¼ 0.058 m, more time is needed, for the indoor fluid to reach a desired density. At the end of this laboratory simulation it is shown that for h ¼ 0.116 m, the time taken for the indoor space to empty is t ¼ 7.7 min, while for h ¼ 0.058 m the corresponding time is t ¼ 8.9 min. At conditions of inversed gravity, the results are similar (Table 4). Consequently, for Fr0 ¼ 2.79, a 50% decrease in h has an impact on the time taken for the space to empty, as it causes a time increase, of about 15,6%. By analysing the laboratory photo shoots and the time course of the phenomenon for each case, it is observed, for both cases of different h, that the solution inside the model has an intermediate red (pink) colour tone, approximately to the totality of the space (the colour at the upper part of the space is slightly darker).
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Fig. 12. Laboratory simulation results for Fr0 ¼ 2.79: Ethanol solution, 2_A_1 & 2_A_2 for h ¼ 0.116 m and h ¼ 0.058 m respectively.
Nevertheless, for h ¼ 0.058 m, the colour tone is, in general, slightly more intense than that of case with h ¼ 0.116 m. A gradual transition of colour tones of red, from darker ones to lighter ones, evolves with the passing of time, at the totality of the volume inside the model, for h ¼ 0.116 m. Nevertheless, the colour tone at the upper part of the space and especially at the upper left corner is more intense. The area of the down right corner, namely the area of the main course of the flow is the first that starts fading out in colour tone. Apart from the gradual fading out of colour tone, the configuration of a vague interface above the height of the middle opening is observed, for h ¼ 0.058 m. This vagueness is expected, as the type of ventilation investigated here is transitional ventilation, namely ventilation that alters from displacement mode to mixing mode. Consequently, in this transitional type of ventilation, the formation of a kind of interface with indefinite
boundaries is possible, as mixing elements of the flow at the boundary of the interface disrupt the stratification. Thus, through the laboratory simulation for Fr0 ¼ 2.79 (transitional ventilation), is deduced that a decrease in h causes an increase in the time taken for the space to empty. This increase is quite smaller than the corresponding one observed for Fr0 ¼ 1.15 (displacement ventilation). Through the computational simulation, for Fr0 ¼ 2.79 (transitional ventilation), it is observed that, the time taken for the space to empty e at a percentage of about 95% e for h ¼ 2.1 m is t ¼ 11.8 min, while the corresponding time for h ¼ 1.05 m is t ¼ 13.7 min (Fig.7(b)). Analytical computational simulation results, for Fr0 ¼ 2.79, for h ¼ 2.1 m and 1.05 m are shown in Fig. 13. The temperature profile and the velocity field for h ¼ 2.1 m, are depicted in Fig. 13 (a) e (b). In this case, it is not observed a
Fig. 13. (a) Temperature contours (K) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 2.79, U ¼ 1.5 m/s, h ¼ 2.1 m, low windward e high leeward opening) (b) Velocity vectors (m/s) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 2.79, U ¼ 1.5 m/s, h ¼ 2.1 m, low windward e high leeward opening) (c) Temperature contours (K) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 2.79, U ¼ 1.5 m/s, h ¼ 1.05 m, low windward e middle leeward opening) (d) Velocity vectors (m/s) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 2.79, U ¼ 1.5 m/s, h ¼ 1.05 m, low windward e middle leeward opening). (Note: The temperatures indicated into the schemes of indoor space are considered to be approximative and they intend to present colour variation.)
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stratification forming a horizontal interface, as a short circuiting flow with small swirls forms and hence, a transition to a mixing mode of ventilation occurs. This is obvious, even at t ¼ 1 min, where the warmest air mass is accumulated at the upper left side of the interior space. At t ¼ 5 min, there is a low-tempered air mass at the right part of the space, near the windward wall, and a colder one at the left part of the space, near the leeward wall and throughout the height of the indoor space. The velocity field supports and explains the temperature profile. At t ¼ 1 min, there is a formation of three swirls. At t ¼ 5 min, the swirl lying on the down internal part of the leeward wall, strengthens and takes up the larger part of the interior space, throughout the height of it, while the other two swirls vanish. The temperature profile and the velocity field for h ¼ 1.05 m, are presented in Fig. 13 (c) e (d). In this case, transition to a mixing mode of ventilation is also obvious, although the swirls formed are weaker than those in case of h ¼ 2.1 m. This is observed, even at t ¼ 1 min, where cold entering air moves to the middle leeward opening, leaving a warm air mass lying above. This flow results in accumulation of air mass of higher temperature in the upper internal corner of windward wall, at t ¼ 5 min, while the contour of temperature reaching the middle leeward opening has higher temperature value than the corresponding one in case of h ¼ 2.1 m. In the velocity field, at t ¼ 1 min, two swirls appear, while they have weaker form than the corresponding ones in case of h ¼ 2.1 m. At t ¼ 5 min, the swirl formed in the internal part of the leeward opening strengthens, but covers smaller part of the space in relation to the corresponding moment of time in case of h ¼ 2.1 m. In transitional ventilation, computational simulation results also explicate laboratory simulation results, as temperature contours and velocity vectors explain the characteristics of the transitional flow, the physical mechanism of air movement and the functional process of ventilation. It is also clear that, a 50% decrease in h causes an increase of the time taken for the space to empty, both in computational simulation (16.1%) and in laboratory simulation (15.6%). 4.3. Effect of outlet’s opening position for Fr0 ¼ 4.85 (mixing ventilation) Laboratory simulation results for Fr0 ¼ 4.85 (mixing ventilation), are presented in Fig. 14, for h ¼ 0.116 m and 0.058 m, at conditions of normalized gravity. For t ¼ 7.8 min the indoor solution’s colour is slightly darker for h ¼ 0.058 m than that of case with h ¼ 0.116 m. This shows that in case of h ¼ 0.058 m, slightly more time is needed,
117
for the indoor fluid to reach a desired density. At the end of this laboratory simulation it is shown that for h ¼ 0.116 m, the time taken for the indoor space to empty is t ¼ 7.8 min, while for h ¼ 0.058 m the corresponding time is t ¼ 8.1 min. At conditions of inversed gravity, the results are similar (Table 4). Consequently, for Fr0 ¼ 4.85, a 50% decrease in h has a small impact on the tame taken for the space to empty, as it causes a time increase, of about 3.8%. There is a small increase value (just 3.8%), due to the mixing mode of ventilation that is intense to both cases of different h (h ¼ 0.116 m and h ¼ 0.058 m). By analysing the laboratory photo shoots and the time course of the phenomenon for each case, it is observed, for both cases of different h, that the solution inside the model undergoes a colour tone decay, with the passing of time, formed to the totality of the space. This uniform distribution of the decay, comes from the mixing process that dominates the interior space, as the fluid circulation takes up the whole space, resulting in mixing the indoor “air”. Nevertheless, for h ¼ 0.058 m, the colour tone is, in general, slightly more intense e so slightly that needs high attention to be observed e than that of case with h ¼ 0.116 m. Thus, through the laboratory simulation for Fr0 ¼ 4.85 (mixing ventilation), is deduced that a decrease in distance h causes an increase in the time taken for the space to empty. However, this increase is much smaller than the corresponding one observed for Fr0 ¼ 1.15 (displacement ventilation) or for Fr0 ¼ 2.79 (transitional ventilation). Through the computational simulation, for Fr0 ¼ 4.85 (mixing ventilation), it is observed that, the time taken for the space to empty e at a percentage of about 95% e for h ¼ 2.1 m is t ¼ 7.1 min, while the corresponding time for h ¼ 1.05 m is t ¼ 7.4 min (Fig.7(c)). Analytical computational simulation results, for Fr0 ¼ 4.85, for h ¼ 2.1 m and 1.05 m are shown in Fig. 15. The temperature profile and the velocity field for h ¼ 2.1 m, are depicted in Fig. 15 (a)e(b). In this case, cold air enters the space through the low windward opening and the indoor air is well mixed, even at t ¼ 1 min. This fact, is observed by the temperature contours, while at t ¼ 5 min it is even more developed. In the velocity field, there is a swirl formed near the interior side of the leeward wall that turns out to cover the totality of the space. This swirl is obvious even at t ¼ 1 min. The temperature profile and the velocity field for h ¼ 1.05 m, are presented in Fig. 15 (c) e (d). In this case, the mixing mode of ventilation is also obvious, although there is a middle leeward opening. The reason that the form of the flow field, in mixing
Fig. 14. Laboratory simulation results for Fr0 ¼ 4.85: Ethanol solution, 3_A_1 & 3_A_2 for h ¼ 0.116 m and h ¼ 0.058 m respectively.
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Fig. 15. (a) Temperature contours (K) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 4.85, U ¼ 2.6 m/s, h ¼ 2.1 m, low windward e high leeward opening) (b) Velocity vectors (m/s) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 4.85, U ¼ 2.6 m/s, h ¼ 2.1 m, low windward e high leeward opening) (c) Temperature contours (K) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 4.85, U ¼ 2.6 m/s, h ¼ 1.05 m, low windward e middle leeward opening), (d) Velocity vectors (m/s) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 4.85, U ¼ 2.6 m/s, h ¼ 1.05 m, low windward e middle leeward opening). (Note: The temperatures indicated into the schemes of indoor space are considered to be approximative and they intend to present colour variation.)
ventilation, is similar in both cases e h ¼ 1.05 m and h ¼ 2.1 m e, is that the velocity of incoming air is high enough to cause mixture at the totality of the space, without regard to the height at which the leeward opening lies. In mixing ventilation, computational simulation results also explicate laboratory simulation results. Temperature contours and velocity vectors explain the characteristics of the mixing flow, the physical mechanism of indoor fluid’s movement and the functional process of ventilation. It is also clear that, a 50% decrease in h causes an increase of the time taken for the space to empty, both in computational simulation (4.2%) and in laboratory simulation (3.8%). 4.4. Ratio between the time of the prototype and the scaled model The relationship between the time of the prototype and the scaled model is determined by the ratio of time (lt). This ratio is defined as lt ¼ tpr/tex, where tpr and tex are time values referred to the duration of the phenomenon in the prototype and the experiment respectively. Here, prototype refers to full-scale (computational simulation) and scaled model refers to the experiment (laboratory simulation). In case of natural ventilation due to wind, with no buoyancy force, the ratio of time (lt,w) can be estimated by using the equations lL ¼ hpr/hex, lU,w ¼ Upr/Uex and lt,w ¼ lL/lU,w, where lt,w is the ratio of time for wind-induced ventilation with no buoyancy force, lL is the ratio of length, lU,w is the ratio of wind velocity, hpr and hex Table 5 Ratios of time: lt ¼ tpr/tex and lt,w ¼ lL/lU,w. Geometry 1 refers to the configuration with low windward e high leeward opening, and geometry 2 refers to the configuration with low windward e middle leeward opening. Geometry
Fr0
tpr (CFD)
tex (eth.)
lt
lt,w
1 1 1 2 2 2
1.15 2.79 4.85 1.15 2.79 4.85
27.5 11.8 7.1 130 13.7 7.4
7.4 7.7 7.8 32 8.9 8.1
3.72 1.53 0.91 4.06 1.54 0.91
6.7 2.8 1.6 6.7 2.8 1.6
refer to the vertical distance between midpoints of windward and leeward opening in the prototype and experiment respectively, Upr and Uex refer to the wind velocity in the prototype and the outdoor fluid’s velocity in the experiment respectively. Table 5 depicts the ratios of time (lt) for each case of natural ventilation, due to buoyancy assisted by wind, investigated in this work, as well as the ratios of time (lt,w) estimated in corresponding cases of natural ventilation due to wind, with no buoyancy force. In case of natural ventilation due to buoyancy assisted by wind, the ratio of time is expected to be smaller than the corresponding one of natural ventilation caused by wind with no buoyancy force, pffiffiffiffiffiffiffi 0 because of the existence of buoyancy velocity g h. Thus, in displacement, transitional and mixing ventilation due to buoyancy assisted by wind, the ratio of time is expected to be smaller than the one produced by equations for wind-induced ventilation (lL ¼ hpr/ hex, lU,w ¼ Upr/Uex, lt,w ¼ lL/lU,w) and this is verified, for both geometries examined. 5. Conclusions This paper presented the investigation of cross natural ventilation of buildings due to buoyancy assisted by wind, with computational and laboratory simulation. The effect of the outlet’s opening position is examined for three initial Froude numbers, corresponding to three different types of ventilation: displacement, transitional and mixing ventilation. Full-scale is analysed through the 3D unsteady e state using the CFD software FLUENT, while the laboratory simulation took place in an open channel and the experimental model is filled with solution of ethanol at conditions of normalized gravity and with salted water at conditions of inversed gravity. The time taken for the indoor space to empty is calculated numerically and experimentally and the functional process of natural ventilation is elaborated. The following conclusions are derived: The position of the outlet’s opening plays an important role as it affects the time taken for the indoor space to empty as well as the flow field. It is observed that as the vertical distance h
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between the midpoints of the openings decreases, the time taken for the indoor space to empty increases. For Fr0 ¼ 1.15 (displacement ventilation), a 50% decrease in h causes a time increase of 332% according to the results of laboratory simulation with ethanol solution, 354% according to the results of laboratory simulation with salted water, and 373% according to the results of computational simulation. For Fr0 ¼ 2.79 (transitional ventilation), the corresponding time increase is 15.6% in experiments with either ethanol solution or salted water, and 16.1% according to the results of computational simulation. For Fr0 ¼ 4.85 (mixing ventilation), the respective time increases are 3.8% and 4.2%. Based on the above findings, it is observed that the time increase is significantly higher in displacement ventilation than the respective one in the other two types of ventilation. The time increase in transitional ventilation is also observed to be higher than that of mixing ventilation. The Froude number, and particularly the initial Froude number (Fr0) plays an important role in natural ventilation of buildings. Fr0 determines the flow field, the type and the functional process of ventilation developed in an enclosure with a particular geometry. The experimental and computational results are characterized by good agreement, based on Froude dynamic similarity. This is obvious by the characteristics of each type of ventilation, the flow field, the physical mechanism of air movement and the functional process that are validated both experimentally (small-scale) and numerically (full-scale). The effect of changing the outlet’s opening position is also in good approximation in both laboratory and computational simulation, for the three types of ventilation (displacement, transitional, mixing). The suggestion of using ethanol solution for the density difference between interior and exterior fluid in laboratory simulation of natural ventilation is verified successfully. The results with use of ethanol solution are in good agreement with those of using salted water solution.
Acknowledgements This investigation was supported by a scholarship provided by IKY (State Scholarships Foundation) to the first author. References [1] Hunt GR, Linden PF. The fluid mechanics of natural ventilation e displacement ventilation by buoyancy e driven flows assisted by wind. Building and Environment 1999;34:707e20. [2] Linden PF, Lane-Serff GF, Smeed DA. Emptying filling boxes: the fluid mechanics of natural ventilation. Journal of Fluid Mechanics 1990;212:309e35. [3] Fluent Incorporated. Fluent 6.0 documentation 2001. [4] Allard F, Santamouris M, Alvarez S, Dascalaki E, Guarracino G, Maldonado E, Sciuto S, Vandaele L. Natural ventilation in buildings e a design handbook. London: James & James (Science Publishers) Ltd; 1998. [5] Awbi HB. Ventilation of buildings. 1st ed. London: E&FN Spon; 1991. [6] Cook MJ, Ji Y, Hunt GR. CFD modelling of natural ventilation: combined wind and buoyancy forces. International Journal of Ventilation 2003;1(3):169e79.
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[7] Visagavel K, Srinivasan PSS. Analysis of single side ventilated and cross ventilated rooms by varying the width of the window opening using CFD. Solar Energy 2009;83:2e5. [8] Hunt GR, Linden PF. Steady-state flows in an enclosure ventilated by buoyancy forces assisted by wind. Journal of Fluid Mechanics 2001;426:355e86. [9] Li Y, Delsante A. Natural ventilation induced by combined wind and thermal forces. Building and Environment 2001;36:59e71. [10] Linden PF. The fluid mechanics of natural ventilation. Annual Reviews of Fluid Mechanics 1999;31:201e38. [11] Lishman B, Woods AW. The control of naturally ventilated buildings subject to wind and buoyancy. Journal of Fluid Mechanics 2006;557:451e71. [12] Lishman B, Woods AW. On transition in natural ventilation flow driven by changes in the wind. Building and Environment 2009;44:666e73. [13] Bangalee MZI, Lin SY, Miau JJ. Wind driven natural ventilation through multiple windows of a building: a computational approach. Energy and Buildings 2012;45:317e25. [14] Ramponi R, Blocken B. CFD simulation of cross-ventilation of a generic isolated building: impact of computational parameters. Building and Environment 2012;53:34e48. [15] Gan G. Simulation of buoyancy-driven natural ventilation of buildings e impact of computational domain. Energy and Buildings 2010;42:1290e300. [16] Walker C, Tan G, Glicksman L. Reduced-scale building model and numerical investigations to buoyancy-driven natural ventilation. Energy and Buildings 2011;43:2404e13. [17] Rundle CA, Lightstone MF, Oosthuizen P, Karava P, Mouriki E. Validation of computational fluid dynamics simulations for atria geometries. Building and Environment 2011;46:1343e53. [18] Nguyen AT, Reiter S. The effect of ceiling configurations on indoor air motion and ventilation flow rates. Building and Environment 2011;46:1211e22. [19] Hussain S, Oosthuizen PH, Kalendar A. Evaluation of various turbulence models for the prediction of the airflow and temperature distributions in atria. Energy and Buildings 2012;48:18e28. [20] van Hooff T, Blocken B, Defraeye T, Carmeliet J, van Heijst GJF. PIV measurements and analysis of transitional flow in a reduced-scale model: Ventilation by a free plane jet with Coanda effect. Building and Environment 2012;56: 301e13. [21] Hajdukiewicz M, Geron M, Keane MM. Formal calibration methodology for CFD models of naturally ventilated indoor environments. Building and Environment 2013;59:290e302. [22] Lo LJ, Banks D, Novoselac A. Combined wind tunnel and CFD analysis for indoor airflow prediction of wind-driven cross ventilation. Building and Environment 2013;60:12e23. [23] Tecle A, Bitsuamlak GT, Teshome EJ. Wind-driven natural ventilation in a lowrise building: a Boundary Layer Wind Tunnel study. Building and Environment 2013;59:275e89. [24] Wu YC, Yang AS, Tseng LY, Liu CL. Myth of ecological architecture designs: comparison between design concept and computational analysis results of natural ventilation for Tjibaou Cultural Center in New Caledonia. Energy and Buildings 2011;43:2788e97. [25] Kobayashi T, Sandberg M, Kotani H, Claesson L. Experimental investigation and CFD analysis of cross-ventilated flow through single room detached house model. Building and Environment 2010;45:2723e34. [26] Larsen TS, Nikolopoulos N, Nikolopoulos A, Strotos G, Nikas KS. Characterization and prediction of the volume flow rate aerating a cross ventilated building by means of experimental techniques and numerical approaches. Energy and Buildings 2011;43:1371e81. [27] Nikas KS, Nikolopoulos N, Nikolopoulos A. Numerical study of a naturally cross-ventilated building. Energy and Buildings 2010;42:422e34. [28] van Hooff T, Blocken B. On the effect of wind direction and urban surroundings on natural ventilation of a large semi-enclosed stadium. Computers & Fluids 2010;39:1146e55. [29] Norton T, Grant J, Fallon R, Sun DW. Optimising the ventilation configuration of naturally ventilated livestock buildings for improved indoor environmental homogeneity. Building and Environment 2010;45:983e95. [30] van Hooff T, Blocken B. Coupled urban wind flow and indoor natural ventilation modelling on a high-resolution grid: a case study for the Amsterdam ArenA stadium. Environmental Modelling & Software 2010;25:51e65. [31] Tablada A, De Troyer F, Blocken B, Carmeliet J, Verschure H. On natural ventilation and thermal comfort in compact urban environments e the old Havana case. Building and Environment 2009;44:1943e58. [32] Fluent Incorporated. Gambit 1.3 documentation 2000
Contents lists available at SciVerse ScienceDirect
Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Natural ventilation of buildings due to buoyancy assisted by wind: Investigating cross ventilation with computational and laboratory simulation Anastasia D. Stavridou*, Panagiotis E. Prinos Division of Hydraulics and Environmental Engineering, Department of Civil Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 December 2012 Received in revised form 30 March 2013 Accepted 16 April 2013
In this paper cross natural ventilation due to buoyancy assisted by wind is investigated with computational and laboratory simulation. The impact of the outlet’s opening position is investigated, forming cross ventilation of variable distance h e namely, the vertical distance between midpoints of leeward and windward opening e, for three initial Froude numbers: (i) Fr0 ¼ 1.15, (ii) Fr0 ¼ 2.79, (iii) Fr0 ¼ 4.85. For the computational simulation a fluid dynamic software is used and the problem is solved by solving the 3D unsteady Reynolds Averaged Navier Stokes (RANS) equations in conjunction with the energy equation and the turbulence model RNG k-ε. The laboratory simulation took place in an open channel and the experimental model represents a building form of orthogonal shape. The interior of the experimental model is filled with solution of ethanol at conditions of normalized gravity, but also with salted water at conditions of inversed gravity. The time taken for the indoor space to empty is calculated numerically and experimentally. Based on Froude number dynamic similarity, the experimental and computational results are characterized by good agreement and the functional process of natural ventilation is being explicated. In addition, the suggestion of using ethanol solution for the density difference between interior and exterior fluid in laboratory simulation of natural ventilation is verified successfully, as the results with use of ethanol solution are in good agreement with those using salted water. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Natural ventilation of buildings Computational fluid dynamics Laboratory simulation Computational simulation
1. Introduction Natural ventilation of buildings constitutes a basic parameter of bioclimatic design. It aims at improving indoor air quality by achieving good air exchange rates, providing thermal comfort and healthy living conditions, as well as maintaining a convenient indoor environment. Thus natural ventilation promotes not only protection and restoration of indoor air, but also sustainability and energy saving. Awbi et al. [5] deal with ventilation of buildings, while emphasizing on themes as quantification of outdoor air flow rate to a building and distribution of this ventilation air around the space. Allard et al. [4] examine the efficient use of natural ventilation in buildings in order to decrease the energy consumption for cooling purposes, increase the indoor thermal comfort levels and improve indoor air quality.
* Corresponding author. Tel.: þ30 2310995708. E-mail addresses: [email protected] (A.D. Stavridou), [email protected] (P.E. Prinos). 0360-1323/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.buildenv.2013.04.011
The fluid mechanics of natural ventilation, as the flow generated by temperature differences and by the wind, are examined by Linden [10] aiming at giving designers rules and intuition on how air moves within a building. This research reveals a fascinating branch of fluid mechanics, dealing with two basic forms of ventilation: mixing and displacement ventilation. Previous investigations of these two types of ventilation have been carried out by Linden et al. [2], in case of a space connected to a large body of stationary ambient fluid. Hunt and Linden [1] describe the fluid mechanics of natural ventilation by the combined effects of buoyancy and wind. In particular they examine transient draining flows in a space containing buoyant fluid, when the wind and buoyancy forces reinforce one another, while connections between the enclosure and the surrounding fluid are with high-level and lowlevel openings on both leeward and windward faces. They also give conditions for the transition to a mixing flow for three initial Froude number parameter ranges (i) displacement ventilation for 0 < Fr0 < 2.5, (ii) transitional ventilation for 2.5 < Fr0 < 3.3, (iii) mixing ventilation for Fr0 > 3.3. Steady e state flows in an enclosure ventilated by buoyancy forces assisted by wind are examined by Hunt and Linden [8], while ventilation openings connecting the
A.D. Stavridou, P.E. Prinos / Building and Environment 66 (2013) 104e119
internal and external environment are at high level on the leeward facade and at low level on the windward facade. Analytical solutions are derived for calculating natural ventilation flow rates and air temperatures in a single e zone building with two openings, one at low level and one at high level of the opposite wall, when no thermal mass is present, by Li and Delsante [9]. Results of a CFD simulation of the wind e assisted stack ventilation of a single e storey enclosure with high and low-level ventilation openings are presented by Cook et al. [6] and compared with both the laboratory measurements and analytical model of the flow and thermal stratification developed by Hunt and Linden [8]. The control of naturally ventilated buildings subject to wind and buoyancy is examined by Lishman and Woods [11], while the geometry cases investigated refer to cross ventilation with one windward and one or two leeward openings. Transitions in natural ventilation flow driven by changes in the wind are examined by Lishman and Woods [12]. Cross ventilated rooms are also analysed by Visagavel and Srinivasan [7] by varying the width of the window opening using CFD. A computational approach of wind driven natural ventilation through multiple windows of a building is examined by Bangalee et al. [13]. In case of cross ventilation, the geometry investigated has two windward and two leeward openings, placed at a height relatively close to the ceiling of the space, while the flow is considered to be steady. They investigate the physical mechanism of the air movement, while the necessity of three-dimensional approach in studying natural ventilation system is emphasized. Ramponi and Blocken [14] investigate CFD simulation of crossventilation, of coupled outdoor wind flow and indoor air flow, for a generic isolated building and examine the impact of computational parameters. They present a series of coupled 3D steady RANS simulations, while the geometry studied include one middle windward and one middle - leeward opening. Geometry in building design and its influence on flow pattern of a naturally ventilated space is a major issue [24,25,27,29e31]. For better understanding of the ventilation mechanism [24], CFD simulations and experimental measurements are carried out [25,26,28], while special attention is given to the process of numerical simulation as well as the experimental one. Gan uses [15] the commercial CFD software FLUENT for simulation of buoyancy-driven natural ventilation of buildings. The steady state of air flow and heat transfer through two-dimensional ventilation cavities is examined and the impact of the computational domain is investigated. Reduced e scale building model using air as working fluid and numerical investigations to buoyancy e driven natural ventilation is carried out by Walker et al. [16]. The scaled model of the naturally ventilated prototype building is created at 1:12 scale and the steady-state buoyancydriven natural ventilation under different scenarios is examined. Rundle et al. [17] carry out a validation of CFD simulations for atria geometries. It is indicated that CFD can be used to successfully simulate the heat transfer and fluid flow in atria geometries and describe the physical phenomena. Nguyen and Reiter [18] use CFD with the RNG k-ε turbulence model and wind tunnel experiment to investigate the effect of ceiling configurations on indoor air motion and ventilation flow rates. The accuracy of the RNG k-ε turbulence model to successfully predict indoor wind motion is confirmed. Evaluation of various turbulence models for the prediction of the airflow and temperature distributions in atria is carried out by Hussain et al. [19]. The steady state governing equations are solved using the commercial CFD solver FLUENT, while relatively good agreement between experimental and CFD predictions are obtained. Van Hooff et al. [20] carry out Particle Image Velocimetry (PIV) measurements and an analysis of transitional flow in a ventilated enclosure. The experimental data and analysis are specifically intended to support the development and validation of
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numerical models for ventilation flow. It is also mentioned that there is a lack of experimental data for transitional ventilation flow. Formal calibration methodology for CFD models of naturally ventilated indoor environments is examined by Hajdukiewicz et al. [21]. The calibration process is supported by the on-site measurements performed in a normally operating building. Combined wind tunnel and CFD analysis for indoor airflow prediction of wind driven cross ventilation is investigated by Lo et al. [22]. Winddriven natural ventilation in a low-rise building is investigated by Tecle et al. [23], while the experiments are carried out in a wind tunnel. Taking into account the existing literature, it is deduced that the issue of cross ventilation with combined and assisting wind and buoyancy forces, regarding geometries that can provide information for openings’ position for different types of ventilation flows, accompanied by experimental data and numerical results, constitute a field that is valuable for research. This work examines natural ventilation in an enclosure either with low windward and high leeward opening or with low windward and middle leeward opening, for three initial Froude numbers: (i) Fr0 ¼ 1.15, (ii) Fr0 ¼ 2.79, (iii) Fr0 ¼ 4.85. Each initial Froude number corresponds to a certain type of ventilation, namely, Fr0 ¼ 1.15 is chosen for displacement ventilation, Fr0 ¼ 2.79 represents transitional ventilation, and Fr0 ¼ 4.85 corresponds to mixing ventilation. These initial Froude numbers are chosen to examine dynamic similarity between wind and buoyancy forces in the experimental model and at full-scale. Full-scale is analysed through the 3D unsteady - state using the CFD software FLUENT, while for the first time the experiments were carried out in a flow channel at conditions of normalized gravity by using ethanol solution. Experiments with salted water at conditions of inversed gravity have been also carried out to testify the results produced by the use of ethanol solution. This paper is organized as follows. Firstly the computational simulation is described, including governing equations, building design, numerical procedure, boundary conditions, and cases studied. Subsequently the laboratory simulation is examined, including experimental model and apparatus, experimental process and cases studied. Then presentation, description and discussion of the results follow. Figures from the computational and laboratory simulation are shown, and the time change of the decline rate of mean temperature is illustrated. Finally, a number of conclusions are derived, regarding outlet’s opening position, initial Froude number, dynamic similarity between small-scale (laboratory simulation) and full-scale (computational simulation), the functional process of each type of ventilation investigated, as well as the use of ethanol in laboratory simulation. 2. Computational simulation (theory/calculation) The software used for the computational simulation of this work is FLUENT 6.01. FLUENT is a Computational Fluid Dynamic (CFD) code which constitutes a state-of-the-art computer program for modelling fluid flow and heat transfer in complex geometries [3]. FLUENT provides complete mesh flexibility, solving the flow problems with unstructured meshes that can be generated about complex geometries with relative ease. The geometry and grid of the present simulation was created using Gambit [32]. For turbulent flows the programme solves conservation equations for mass and momentum (RANS, Reynolds e Averaged NaviereStokes equations). For flows involving heat transfer or compressibility, an additional equation for energy conservation is
1
In particular, version 6.0.12 of Fluent is used.
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Fig. 1. (a) Dimensions of the building form, (b) Three e dimensional digital volume. Grid.
solved. Additional transport equations are also solved when the flow is turbulent. In the present work, the 3D unsteady RANS equations in conjunction with energy equation and the turbulence model RNG k-ε are solved. For density calculation, the Ideal Gas
model is used. This model does not treat density as a constant, but computes it through the ideal gas law. The eddy viscosity is calculated through the eddy-viscosity concept (mt ¼ rCm k2/ε) after the solution of transport equations in which the RNG k-ε
Fig. 2. Two geometry types: low windward e high leeward opening, low windward e middle leeward opening (computational simulation).
A.D. Stavridou, P.E. Prinos / Building and Environment 66 (2013) 104e119 Table 1 Parameter range for the six cases of computational simulation. h (m)
DT (K)
U (m/s)
Fr0
2.1 2.1 2.1 1.05 1.05 1.05
4 4 4 4 4 4
0.62 1.5 2.6 0.62 1.5 2.6
1.15 2.79 4.85 1.15 2.79 4.85
model is based. In addition the energy equation is solved, for calculating the temperature variation within the computational domain. 2.1. Building design For the computational simulation of the building form, depicted in Fig. 1 (a), a three e dimensional digital volume is designed (scale 1:1). The digital volume and the discretization grid, presented in Fig. 1 (b), are design with Gambit, a design program that collaborates with FLUENT. The dimensions of the building form are the following: height 2.5 m, width 1.5 m, and length 2.95 m. The volume of the enclosure is 11 m3, while three windward and three leeward openings have been designed. Each opening is square e shaped and its dimensions are: height ¼ length ¼ 0.18 m. In the present work, only the low windward opening is used, while at the leeward wall either the high or the middle opening is used. The vertical distance between midpoints of the openings is: a) 2.1 m
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between low and high opening, and b) 1.05 m between low and middle opening. The discretization grid consists of 52800 hexahedral cells.
2.2. Numerical procedure For the solution of the equations, the segregated solver has been used. The flow is incompressible and the unsteady equations are solved. Using the segregated approach [3], the governing equations are solved sequentially (i.e., segregated from one another). Because the governing equations are non-linear (and coupled), several iterations of the solution loop are performed before a converged solution is obtained. Fluid properties are updated, based on the current solution. The momentum equations are each solved in turn using current values for pressure and face mass fluxes, in order to update the velocity field. Since the velocities obtained may not satisfy the continuity equation locally, a ``Poisson-type’’ equation for the pressure correction is derived from the continuity equation and the linearized momentum equations. This pressure correction equation is then solved to obtain the necessary corrections to the pressure and velocity fields and the face mass fluxes such that continuity is satisfied. Equations for turbulence characteristics and energy are solved using the previously updated values of the other variables. A check for convergence of the equation set is made. These steps are continued until the convergence criteria are met. Convergence for continuity, momentum and k and ε is of order 104, and for energy 106. For solution process control a false time step is selected equal to 0.1 s.
Fig. 3. (a) Experimental model made of plexiglass, (b) Open channel in the Laboratory of Hydraulics, Department of Civil Engineering e AUTh.
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Fig. 4. Two geometry types: low windward e high leeward opening, low windward e middle leeward opening (laboratory simulation).
2.3. Boundary conditions The boundary conditions used to simulate the ventilated enclosure here are chosen carefully, in order to describe correctly the existing conditions. For the opening that represents the inlet of the flow, the boundary type of “velocity inlet” is selected. Velocity inlet boundary condition is used to define the velocity and scalar properties of the flow at inlet boundaries. For the outlet of the flow, the “pressure outlet” is taken. Pressure outlet boundary condition is used to define the static pressure at flow outlets (and also other scalar variables, in case of backflow). In addition, for all the walls, floor and ceiling, the boundary condition type of “wall” is selected. Wall boundary condition is used to bound fluid and solid regions. 2.4. Cases Displacement, transitional and mixing ventilation are examined with computational simulation. Three initial Froude numbers are selected to represent each type of ventilation: Fr0 ¼ 1.15 for displacement ventilation, Fr0 ¼ 2.79 for transitional ventilation, Fr0 ¼ 4.85 for mixing ventilation. In the present work the initial Froude number is given by
1=2 Fr0 ¼ U= g00 h
(1)
where g0’ is the reduced gravity at t ¼ 0, U is the wind velocity and h is the vertical distance between midpoints of windward and leeward opening. The reduced gravity is given by
g0 ¼ g
DT T
¼ g
Dr r
(2)
where g is the acceleration due to gravity, DT and Dr are the temperature and density difference between the internal and external environment respectively, T and r are the temperature and density of the external environment respectively. Note that for an ideal gas Dr/r ¼ DT/T. Table 2 Parameter range and symbols for the six cases of laboratory simulation. h (m)
Dr
(kg/m3)
0.116 0.116 0.116 0.058 0.058 0.058
35 6 2 35 6 2
U (m/s)
0.23 0.23 0.23 0.23 0.23 0.23
Fr0
1.15 2.79 4.85 1.15 2.79 4.85
Symbol for lab simulation with use of ethanol solution
Symbol for lab simulation with use of salted water
1_A_1 2_A_1 3_A_1 1_A_2 2_A_2 3_A_2
1_B_1 2_B_1 3_B_1 1_B_2 2_B_2 3_B_2
It is noted that for initial Froude number’s calculation, in this work, parameter h represents a reference distance that comes from the geometry with low windward e high leeward opening. Accordingly, the initial Froude number for geometry with low windward e middle leeward opening is calculated as a reference value, in relation with the geometry of low windward e high leeward opening, and parameter h still represents a reference distance which comes from the geometry with low windward e high leeward opening. The investigation takes place for two geometry types (low windward e high leeward opening, low windward e middle leeward opening) as shown in Fig. 2, while three values of wind velocity are examined (0.62 m/s, 1.5 m/s and 2.6 m/s). The initial temperature difference between indoor and outdoor air is equal to 4 K (DT ¼ 4 K). In particular, at t ¼ 0 min, indoor and outdoor temperature are equal to 292 K and 288 K respectively. The parameter range for the six cases of computational simulation is shown in Table 1. 3. Laboratory simulation 3.1. Experimental model and apparatus For the laboratory simulation, an experimental model is designed and constructed Fig. 3(a) to represent the building form described in x 2.1. The construction material of the experimental model is plexiglass, the scale is 1:18 and the interior dimensions are: length 16.3 cm, width 8.3 cm, height 13.8 cm. Each opening is 1 cm2 in area, while the thickness of the walls, the floor and the ceiling is 1 cm. A feed hole is opened at the top of the model, sealed with a metallic valve. The laboratory simulation took place in an open channel of the Laboratory of Hydraulics in Department of Civil Engineering e Aristotle University of Thessaloniki, shown in Fig. 3(b). The channel dimensions are: 10.0 m 0.25 m 0.5 m (length width height). The open flow channel has an horizontal bottom and is connected with a pump, while the flow depth during the experiments was kept at 0.19 m. A water tank is also connected with the Table 3 Validation test of the measurement method with the use of colouring matter, by using conductivity e meter. Time t (s)
Salinity S (&)
0 60 120 210 270 330 360 390
0.3 1e4.8 1e2.2 1.1e1.3 0.4e0.6 0.3e0.4 0.3e0.4 0.3
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channel to collect the water. Rotating blades at the channel end are used to control the flow depth and the velocity of the flow. The measurements are carried out with the following instruments: conductivity e meter, thermometer, micro-propeller for measuring flow velocity and assay balance. Moreover a videocamera Olympus Camedia C-7070 Wide Zoom with timing was used.
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3.2. Experimental process and cases Displacement, transitional and mixing ventilation are also examined in the laboratory simulation, while three initial Froude numbers are selected to represent each type of ventilation. For the investigation of dynamic similarity between wind and buoyancy forces in the experimental model and at full-scale [1], the initial
Fig. 5. Laboratory simulation results for Fr0 ¼ 1.15: Ethanol solution, 1_A_1 & 1_A_2 for h ¼ 0.116 m and 0.058 m respectively. (Note: Online colour Figures accompany the BW print version.)
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Froude numbers in the laboratory simulation are taken equal with those of the computational simulation. This investigation takes place for two geometry types (low windward e high leeward opening, low windward e middle leeward opening) as shown in Fig. 4, while three values of density difference e between the fluid inside the model and the flowing water of the channel e are examined (35 kg/m3, 6 kg/m3 and 2 kg/m3). The “wind velocity” or else the flow velocity is equal to 0.23 m/s (U ¼ 0.23 m/s). The parameter range for the six cases of
laboratory simulation, as well as the symbol of each case, used at the illustrations from the laboratory simulation, are depicted in Table 2. Density difference between indoor and outdoor fluid is formed either by using ethanol solution or by using salted water. The interior of the experimental model is filled with solution of ethanol at conditions of normalized gravity, but also with salted water at conditions of inversed gravity. Ethanol (ethyl alcohol) is a colourless liquid and has a density of 0.78934 gr/cm3 at 20 C.
Fig. 6. Laboratory simulation results for Fr0 ¼ 1.15: Salted water, 1_B_1 & 1_B_2 for h ¼ 0.116 m and 0.058 m respectively.
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For the estimation of the time (t) taken for the indoor space to empty, a count is carried out through the video camera’s chronometer. This count measures the time needed for the total replacement of the indoor solution by outdoor water. For this process to be feasible, the indoor solution is coloured with red dye, Rhodamin B (C28H31ClN2O3). For the validation of this method, a validation test is carried out by using a conductivity e meter. During this test, salted water, of salinity S ¼ 16.9& and density 1010 kg/m3, is placed inside the experimental model. The experimental model is placed in the flow channel, while the measured salinity of the flowing water at the moment is S ¼ 0.3& and the flow velocity is 0.23 m/s. At t ¼ 0 s the low windward and the high leeward openings are opened. Note that in this validation test, low and high definitions refer to the physical location of openings, regardless the conditions of gravity. Subsequently, the salinity outside the high leeward opening is measured with the use of the conductivity e meter, for different moments of time as presented in Table 3. It is obvious that, at t ¼ 390 s, the outgoing fluid is of salinity equal to that of the flowing water (0.3&). Visually, the time needed for the indoor fluid to turn from red to transparent is 6 min plus 30 s, namely 390 s. Consequently, the time coming from the measurement with the conductivity e meter, coincides with the corresponding one coming from the visual observation. This fact validates the measurement method with the use of colouring matter.
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the upper part of the space, while this tone degrades by reaching the floor of the space. At the same time, for h ¼ 0.058 m, the layer mentioned has more distinct form and more firm colour tone. In addition, it is observed that, at t ¼ 4 min for h ¼ 0.116 m, the indoor liquid is characterized by an intermediate red colour (pink). At the same time, for h ¼ 0.058 m, there is an intense red colour at the part of the indoor space laying above the middle leeward opening, while an intermediate red colour (with degrading of colour tone while reaching the floor of the space) characterizes the space below the middle leeward opening. The intense stratification and the interface observed, at t ¼ 4 min for h ¼ 0.058 min, continues to exist at t ¼ 7.4 min, when there is even greater distinctness to the colour tones. The photo shoot at t ¼ 7.4 min, for h ¼ 0.116 m, shows that this moment the indoor liquid reaches totally transparent. A gradual transition of colour tones, from red to total transparent, with time evolution is observed at a great part of indoor space for h ¼ 0.116 m. An area of more intense tones is observed at the upper part of the space, which fades out by reaching the floor of the model. Thus, a type of stratification develops corresponding to a
4. Results and discussion In the following sections, computational and laboratory results are analysed and discussed for Fr0 equal to 1.15, 2.79, 4.85. The relationship between the prototype and the scaled model is also elaborated. 4.1. Effect of outlet’s opening position for Fr0 ¼ 1.15 (displacement ventilation) Laboratory simulation results for Fr0 ¼ 1.15 (displacement ventilation) are presented in Fig. 5, for h ¼ 0.116 m and 0.058 m, at conditions of normalized gravity. For h ¼ 0.116 m, the time taken for the indoor space to empty is t ¼ 7.4 min. This time refers to the time taken, for the indoor liquid’s colour to turn from red to transparent. For h ¼ 0.058 m, the corresponding time is increased significantly (t ¼ 32 min). Hence, for a 50% decrease in h there is a time increase of 332%. Analytically, four photo shoots from the video tape recording, are depicted and compared in Fig. 5, for h ¼ 0.116 m and 0.058 m and times t ¼ 0 min, t ¼ 40 s, t ¼ 4 min and t ¼ 7.4 min. The different tones of red show the density difference between the indoor liquid and the outdoor water. Namely, total red corresponds to the initial density difference, Dr ¼ 35 kg/m3, while as the red colour fades out, the density difference decreases. When the colour turns to total transparent, then density difference is equal to zero, Dr ¼ 0, and the indoor fluid is totally replaced. At t ¼ 40 s, for h ¼ 0.116 m, an area (forming a type of layer) of intense red colour tone is observed at
Table 4 Laboratory time taken for the space to empty, in case of using ethanol solution (eth.) and in case of using salted water (sal.). h (m)
Fr0
tex (eth.)
tex (sal.)
0.116 0.116 0.116 0.058 0.058 0.058
1.15 2.79 4.85 1.15 2.79 4.85
7.4 7.7 7.8 32 8.9 8.1
7.4 7.7 7.8 33.6 8.9 8.1
Fig. 7. Time change of the decline rate of mean temperature (a) Fr0 ¼ 1.15, (b) Fr0 ¼ 2.79, (c) F0 ¼ 4.85.
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certain type of interface characterized by some mixing elements. At about the midway of the phenomenon, the intense tone area is formed especially at the upper left part (just opposite the high leeward opening). The height of the interface, developed between the lighter coloured fluid and the heavier transparent fluid, increases continuously with time for h ¼ 0.058 m. Although, for a certain time period, the lighter coloured fluid accumulates to the upper part of the space and, to a certain point is trapped, while its discharge is slow, as the incoming flow channel velocity is relatively low and the mixing elements of the phenomenon are restricted. Results, at conditions of inversed gravity, are analogous and are shown in Fig. 6, for t ¼ 0 min, t ¼ 40 s, t ¼ 4 min and t ¼ 7.4 min. For
h ¼ 0.116 m, the time taken for the space to empty is t ¼ 7.4 min, while for h ¼ 0.058 m the corresponding time is t ¼ 33.6 min. Hence, for a 50% decrease in h there is a time increase of 354%. By comparing the photos shown in Figs. 5 and 6 and the time evolution of the phenomenon for each case, it is observed that laboratory simulation with use of ethanol, gives results with very good approximation to those coming from laboratory simulation with use of salted water and simultaneous inversion of gravity conditions. In both methods, the flow field, the stratification developed and the colour tones of the indoor fluids are identical, with only difference the inversed mode of depiction due to the gravity conditions. This good approximation is also verified by the final time values (t) measured for each case (Table 4). Consequently,
Fig. 8. Temperature contoures (K) : t ¼ 1,5,10,30 min (Fr0 ¼ 1.15, U ¼ 0.62 m/s, h ¼ 2.1 m, low windward e high leeward opening).
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the laboratory simulation for Fr0 ¼ 1.15 (displacement ventilation), shows that as h decreases, the time taken for the space to empty increases. Computational simulation elaborates this investigation. A part of the results of the computational simulation is presented in Fig. 7, where the diagram of the time change of the decline rate of mean temperature is depicted, for Fr0 equal to 1.15, 2.79, 4.85. In this diagram, the dependent variable is the ratio [(DTinitial-DTn)/DTinitial] 100 and the independent variable is time (t) in minutes. At the ratio of the dependent variable, the variable DTinitial is defined by the temperature difference between indoor and outdoor air at t ¼ 0 min. The variable DTn is defined by the temperature difference between the mean temperature of indoor air, at each new time selected (t ¼ n), and the temperature of outdoor air. The
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indoor mean temperature of each time selected alters with the passing of time, while the outdoor temperature is considered to be constant. From the diagram in Fig. 7 (a), for Fr0 ¼ 1.15 (displacement ventilation), it is observed that, the time taken for the space to empty e in particular at a percentage of about 95% e for h ¼ 2.1 m is t ¼ 27.5 min, while the corresponding time for h ¼ 1.05 m is t ¼ 130 min. Analytical computational simulation results, for Fr0 ¼ 1.15, for h ¼ 2.1 m and 1.05 m are shown in Figs. 8e11. The temperature profile and the velocity field for h ¼ 2.1 m, are presented in Figs. 8 and 9. In this case, an ascending interface is observed throughout the phenomenon. In the temperature contours diagram, it is observed that cold, and thus heavier, air enters from the low-windward opening. This low-tempered air flow is distinct, even
Fig. 9. Velocity vectors (m/s) : t ¼ 1,5,10,30 min (Fr0 ¼ 1.15, U ¼ 0.62 m/s, h ¼ 2.1 m, low windward e high leeward opening).
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Fig. 10. Temperature contoures (K) : t ¼ 1,5,10,30 min (Fr0 ¼ 1.15, U ¼ 0.62 m/s, h ¼ 1.05 m, low windward e middle leeward opening). (Note: The temperatures indicated into the schemes of indoor space are considered to be approximative and they intend to present colour variation.)
at t ¼ 1 min. The stratification, due to temperature fluctuation, is intense and obvious at t ¼ 5 min. With the passing of time, at t ¼ 10 min, the interface’s thickness decreases, while at t ¼ 30 min it is totally removed. Velocity vectors form courses that verify the contours of temperature observed at each moment of time. The temperature profile and the velocity field for h ¼ 1.05 m, are presented in Figs. 10 and 11. In this case, the ascending interface moves slower than the one in case with h ¼ 2.1 m, as the velocities at the upper space of the enclosure are very small and the swirls formed produce a slower movement. Here, there is also incoming cold air from the low-windward opening, while the outlet is placed in the middle of the leeward wall. From the temperature contours, a warm layer of air is observed (at t ¼ 5, 10,
30 min), laying above the middle-leeward opening, with a distinct interface of small thickness. With the passing of time, the stratification remains distinct, even when the warm air layer’s thickness decreases. The velocity vectors follow courses intending to reach the outlet of middle-leeward opening. At t ¼ 5, 10, 30 min, intense mobility of air masses, that lead warm air to the outlet, is restricted to the part of interior space below the height of the middle-leeward opening, while at the upper part, the velocity magnitudes are low. Although these velocities are small, a recirculation course is formed leading the warm air mass down to the outlet in a slow pace. It is obvious that around the interface, there is a distinct difference of velocities’ sizes and directions, which retains the horizontal form of this face.
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Fig. 11. Velocity vectors (m/s) : t ¼ 1,5,10,30 min (Fr0 ¼ 1.15, U ¼ 0.62 m/s, h ¼ 1.05 m, low windward e middle leeward opening).
Computational simulation results explicate laboratory simulation results, as temperature contours and velocity vectors explain the characteristics of the flow, the physical mechanism of the air movement and the functional process of ventilation. Thus the chromatic grade depicted in the lab results is validated. From the computational simulation, comes up that for a 50% decrease in h there is a time increase of 373%. 4.2. Effect of outlet’s opening position for Fr0 ¼ 2.79 (transitional ventilation) Laboratory simulation results for Fr0 ¼ 2.79 (transitional ventilation), are presented in Fig. 12, for h ¼ 0.116 m and 0.058 m, at conditions of normalized gravity. At t ¼ 5 min the indoor solution’s
colour is darker for h ¼ 0.058 m than that of case with h ¼ 0.116 m. This shows that for h ¼ 0.058 m, more time is needed, for the indoor fluid to reach a desired density. At the end of this laboratory simulation it is shown that for h ¼ 0.116 m, the time taken for the indoor space to empty is t ¼ 7.7 min, while for h ¼ 0.058 m the corresponding time is t ¼ 8.9 min. At conditions of inversed gravity, the results are similar (Table 4). Consequently, for Fr0 ¼ 2.79, a 50% decrease in h has an impact on the time taken for the space to empty, as it causes a time increase, of about 15,6%. By analysing the laboratory photo shoots and the time course of the phenomenon for each case, it is observed, for both cases of different h, that the solution inside the model has an intermediate red (pink) colour tone, approximately to the totality of the space (the colour at the upper part of the space is slightly darker).
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Fig. 12. Laboratory simulation results for Fr0 ¼ 2.79: Ethanol solution, 2_A_1 & 2_A_2 for h ¼ 0.116 m and h ¼ 0.058 m respectively.
Nevertheless, for h ¼ 0.058 m, the colour tone is, in general, slightly more intense than that of case with h ¼ 0.116 m. A gradual transition of colour tones of red, from darker ones to lighter ones, evolves with the passing of time, at the totality of the volume inside the model, for h ¼ 0.116 m. Nevertheless, the colour tone at the upper part of the space and especially at the upper left corner is more intense. The area of the down right corner, namely the area of the main course of the flow is the first that starts fading out in colour tone. Apart from the gradual fading out of colour tone, the configuration of a vague interface above the height of the middle opening is observed, for h ¼ 0.058 m. This vagueness is expected, as the type of ventilation investigated here is transitional ventilation, namely ventilation that alters from displacement mode to mixing mode. Consequently, in this transitional type of ventilation, the formation of a kind of interface with indefinite
boundaries is possible, as mixing elements of the flow at the boundary of the interface disrupt the stratification. Thus, through the laboratory simulation for Fr0 ¼ 2.79 (transitional ventilation), is deduced that a decrease in h causes an increase in the time taken for the space to empty. This increase is quite smaller than the corresponding one observed for Fr0 ¼ 1.15 (displacement ventilation). Through the computational simulation, for Fr0 ¼ 2.79 (transitional ventilation), it is observed that, the time taken for the space to empty e at a percentage of about 95% e for h ¼ 2.1 m is t ¼ 11.8 min, while the corresponding time for h ¼ 1.05 m is t ¼ 13.7 min (Fig.7(b)). Analytical computational simulation results, for Fr0 ¼ 2.79, for h ¼ 2.1 m and 1.05 m are shown in Fig. 13. The temperature profile and the velocity field for h ¼ 2.1 m, are depicted in Fig. 13 (a) e (b). In this case, it is not observed a
Fig. 13. (a) Temperature contours (K) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 2.79, U ¼ 1.5 m/s, h ¼ 2.1 m, low windward e high leeward opening) (b) Velocity vectors (m/s) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 2.79, U ¼ 1.5 m/s, h ¼ 2.1 m, low windward e high leeward opening) (c) Temperature contours (K) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 2.79, U ¼ 1.5 m/s, h ¼ 1.05 m, low windward e middle leeward opening) (d) Velocity vectors (m/s) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 2.79, U ¼ 1.5 m/s, h ¼ 1.05 m, low windward e middle leeward opening). (Note: The temperatures indicated into the schemes of indoor space are considered to be approximative and they intend to present colour variation.)
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stratification forming a horizontal interface, as a short circuiting flow with small swirls forms and hence, a transition to a mixing mode of ventilation occurs. This is obvious, even at t ¼ 1 min, where the warmest air mass is accumulated at the upper left side of the interior space. At t ¼ 5 min, there is a low-tempered air mass at the right part of the space, near the windward wall, and a colder one at the left part of the space, near the leeward wall and throughout the height of the indoor space. The velocity field supports and explains the temperature profile. At t ¼ 1 min, there is a formation of three swirls. At t ¼ 5 min, the swirl lying on the down internal part of the leeward wall, strengthens and takes up the larger part of the interior space, throughout the height of it, while the other two swirls vanish. The temperature profile and the velocity field for h ¼ 1.05 m, are presented in Fig. 13 (c) e (d). In this case, transition to a mixing mode of ventilation is also obvious, although the swirls formed are weaker than those in case of h ¼ 2.1 m. This is observed, even at t ¼ 1 min, where cold entering air moves to the middle leeward opening, leaving a warm air mass lying above. This flow results in accumulation of air mass of higher temperature in the upper internal corner of windward wall, at t ¼ 5 min, while the contour of temperature reaching the middle leeward opening has higher temperature value than the corresponding one in case of h ¼ 2.1 m. In the velocity field, at t ¼ 1 min, two swirls appear, while they have weaker form than the corresponding ones in case of h ¼ 2.1 m. At t ¼ 5 min, the swirl formed in the internal part of the leeward opening strengthens, but covers smaller part of the space in relation to the corresponding moment of time in case of h ¼ 2.1 m. In transitional ventilation, computational simulation results also explicate laboratory simulation results, as temperature contours and velocity vectors explain the characteristics of the transitional flow, the physical mechanism of air movement and the functional process of ventilation. It is also clear that, a 50% decrease in h causes an increase of the time taken for the space to empty, both in computational simulation (16.1%) and in laboratory simulation (15.6%). 4.3. Effect of outlet’s opening position for Fr0 ¼ 4.85 (mixing ventilation) Laboratory simulation results for Fr0 ¼ 4.85 (mixing ventilation), are presented in Fig. 14, for h ¼ 0.116 m and 0.058 m, at conditions of normalized gravity. For t ¼ 7.8 min the indoor solution’s colour is slightly darker for h ¼ 0.058 m than that of case with h ¼ 0.116 m. This shows that in case of h ¼ 0.058 m, slightly more time is needed,
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for the indoor fluid to reach a desired density. At the end of this laboratory simulation it is shown that for h ¼ 0.116 m, the time taken for the indoor space to empty is t ¼ 7.8 min, while for h ¼ 0.058 m the corresponding time is t ¼ 8.1 min. At conditions of inversed gravity, the results are similar (Table 4). Consequently, for Fr0 ¼ 4.85, a 50% decrease in h has a small impact on the tame taken for the space to empty, as it causes a time increase, of about 3.8%. There is a small increase value (just 3.8%), due to the mixing mode of ventilation that is intense to both cases of different h (h ¼ 0.116 m and h ¼ 0.058 m). By analysing the laboratory photo shoots and the time course of the phenomenon for each case, it is observed, for both cases of different h, that the solution inside the model undergoes a colour tone decay, with the passing of time, formed to the totality of the space. This uniform distribution of the decay, comes from the mixing process that dominates the interior space, as the fluid circulation takes up the whole space, resulting in mixing the indoor “air”. Nevertheless, for h ¼ 0.058 m, the colour tone is, in general, slightly more intense e so slightly that needs high attention to be observed e than that of case with h ¼ 0.116 m. Thus, through the laboratory simulation for Fr0 ¼ 4.85 (mixing ventilation), is deduced that a decrease in distance h causes an increase in the time taken for the space to empty. However, this increase is much smaller than the corresponding one observed for Fr0 ¼ 1.15 (displacement ventilation) or for Fr0 ¼ 2.79 (transitional ventilation). Through the computational simulation, for Fr0 ¼ 4.85 (mixing ventilation), it is observed that, the time taken for the space to empty e at a percentage of about 95% e for h ¼ 2.1 m is t ¼ 7.1 min, while the corresponding time for h ¼ 1.05 m is t ¼ 7.4 min (Fig.7(c)). Analytical computational simulation results, for Fr0 ¼ 4.85, for h ¼ 2.1 m and 1.05 m are shown in Fig. 15. The temperature profile and the velocity field for h ¼ 2.1 m, are depicted in Fig. 15 (a)e(b). In this case, cold air enters the space through the low windward opening and the indoor air is well mixed, even at t ¼ 1 min. This fact, is observed by the temperature contours, while at t ¼ 5 min it is even more developed. In the velocity field, there is a swirl formed near the interior side of the leeward wall that turns out to cover the totality of the space. This swirl is obvious even at t ¼ 1 min. The temperature profile and the velocity field for h ¼ 1.05 m, are presented in Fig. 15 (c) e (d). In this case, the mixing mode of ventilation is also obvious, although there is a middle leeward opening. The reason that the form of the flow field, in mixing
Fig. 14. Laboratory simulation results for Fr0 ¼ 4.85: Ethanol solution, 3_A_1 & 3_A_2 for h ¼ 0.116 m and h ¼ 0.058 m respectively.
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Fig. 15. (a) Temperature contours (K) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 4.85, U ¼ 2.6 m/s, h ¼ 2.1 m, low windward e high leeward opening) (b) Velocity vectors (m/s) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 4.85, U ¼ 2.6 m/s, h ¼ 2.1 m, low windward e high leeward opening) (c) Temperature contours (K) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 4.85, U ¼ 2.6 m/s, h ¼ 1.05 m, low windward e middle leeward opening), (d) Velocity vectors (m/s) for t ¼ 1 min and t ¼ 5 min (Fr0 ¼ 4.85, U ¼ 2.6 m/s, h ¼ 1.05 m, low windward e middle leeward opening). (Note: The temperatures indicated into the schemes of indoor space are considered to be approximative and they intend to present colour variation.)
ventilation, is similar in both cases e h ¼ 1.05 m and h ¼ 2.1 m e, is that the velocity of incoming air is high enough to cause mixture at the totality of the space, without regard to the height at which the leeward opening lies. In mixing ventilation, computational simulation results also explicate laboratory simulation results. Temperature contours and velocity vectors explain the characteristics of the mixing flow, the physical mechanism of indoor fluid’s movement and the functional process of ventilation. It is also clear that, a 50% decrease in h causes an increase of the time taken for the space to empty, both in computational simulation (4.2%) and in laboratory simulation (3.8%). 4.4. Ratio between the time of the prototype and the scaled model The relationship between the time of the prototype and the scaled model is determined by the ratio of time (lt). This ratio is defined as lt ¼ tpr/tex, where tpr and tex are time values referred to the duration of the phenomenon in the prototype and the experiment respectively. Here, prototype refers to full-scale (computational simulation) and scaled model refers to the experiment (laboratory simulation). In case of natural ventilation due to wind, with no buoyancy force, the ratio of time (lt,w) can be estimated by using the equations lL ¼ hpr/hex, lU,w ¼ Upr/Uex and lt,w ¼ lL/lU,w, where lt,w is the ratio of time for wind-induced ventilation with no buoyancy force, lL is the ratio of length, lU,w is the ratio of wind velocity, hpr and hex Table 5 Ratios of time: lt ¼ tpr/tex and lt,w ¼ lL/lU,w. Geometry 1 refers to the configuration with low windward e high leeward opening, and geometry 2 refers to the configuration with low windward e middle leeward opening. Geometry
Fr0
tpr (CFD)
tex (eth.)
lt
lt,w
1 1 1 2 2 2
1.15 2.79 4.85 1.15 2.79 4.85
27.5 11.8 7.1 130 13.7 7.4
7.4 7.7 7.8 32 8.9 8.1
3.72 1.53 0.91 4.06 1.54 0.91
6.7 2.8 1.6 6.7 2.8 1.6
refer to the vertical distance between midpoints of windward and leeward opening in the prototype and experiment respectively, Upr and Uex refer to the wind velocity in the prototype and the outdoor fluid’s velocity in the experiment respectively. Table 5 depicts the ratios of time (lt) for each case of natural ventilation, due to buoyancy assisted by wind, investigated in this work, as well as the ratios of time (lt,w) estimated in corresponding cases of natural ventilation due to wind, with no buoyancy force. In case of natural ventilation due to buoyancy assisted by wind, the ratio of time is expected to be smaller than the corresponding one of natural ventilation caused by wind with no buoyancy force, pffiffiffiffiffiffiffi 0 because of the existence of buoyancy velocity g h. Thus, in displacement, transitional and mixing ventilation due to buoyancy assisted by wind, the ratio of time is expected to be smaller than the one produced by equations for wind-induced ventilation (lL ¼ hpr/ hex, lU,w ¼ Upr/Uex, lt,w ¼ lL/lU,w) and this is verified, for both geometries examined. 5. Conclusions This paper presented the investigation of cross natural ventilation of buildings due to buoyancy assisted by wind, with computational and laboratory simulation. The effect of the outlet’s opening position is examined for three initial Froude numbers, corresponding to three different types of ventilation: displacement, transitional and mixing ventilation. Full-scale is analysed through the 3D unsteady e state using the CFD software FLUENT, while the laboratory simulation took place in an open channel and the experimental model is filled with solution of ethanol at conditions of normalized gravity and with salted water at conditions of inversed gravity. The time taken for the indoor space to empty is calculated numerically and experimentally and the functional process of natural ventilation is elaborated. The following conclusions are derived: The position of the outlet’s opening plays an important role as it affects the time taken for the indoor space to empty as well as the flow field. It is observed that as the vertical distance h
A.D. Stavridou, P.E. Prinos / Building and Environment 66 (2013) 104e119
between the midpoints of the openings decreases, the time taken for the indoor space to empty increases. For Fr0 ¼ 1.15 (displacement ventilation), a 50% decrease in h causes a time increase of 332% according to the results of laboratory simulation with ethanol solution, 354% according to the results of laboratory simulation with salted water, and 373% according to the results of computational simulation. For Fr0 ¼ 2.79 (transitional ventilation), the corresponding time increase is 15.6% in experiments with either ethanol solution or salted water, and 16.1% according to the results of computational simulation. For Fr0 ¼ 4.85 (mixing ventilation), the respective time increases are 3.8% and 4.2%. Based on the above findings, it is observed that the time increase is significantly higher in displacement ventilation than the respective one in the other two types of ventilation. The time increase in transitional ventilation is also observed to be higher than that of mixing ventilation. The Froude number, and particularly the initial Froude number (Fr0) plays an important role in natural ventilation of buildings. Fr0 determines the flow field, the type and the functional process of ventilation developed in an enclosure with a particular geometry. The experimental and computational results are characterized by good agreement, based on Froude dynamic similarity. This is obvious by the characteristics of each type of ventilation, the flow field, the physical mechanism of air movement and the functional process that are validated both experimentally (small-scale) and numerically (full-scale). The effect of changing the outlet’s opening position is also in good approximation in both laboratory and computational simulation, for the three types of ventilation (displacement, transitional, mixing). The suggestion of using ethanol solution for the density difference between interior and exterior fluid in laboratory simulation of natural ventilation is verified successfully. The results with use of ethanol solution are in good agreement with those of using salted water solution.
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