CFD MODELLING OF FLOOR HEATING SYSTEM IN DOME SHAPE ROOMS ACCORDING TO THE THERMAL
COMFORT CONDITION
T. Khademinejad1, S. Rahimzadeh2, P. Talebizadeh1, H. Rahimzadeh1,3, H. Sarkardeh4
1 Department of Mechanical Engineering, Amirkabir University of Technology, Tehran,
Iran. 2 School of design, Creative Industry Faculty, Queensland University of Technology,
Brisbane, Australia. 3 Member of energy and control, center of excellence, Amirkabir Univercity of
Technology, Tehran, Iran. 4 Civil Engineering Division, Department of Engineering, Hakim Sabzevari University,
Sabzevar, Iran.
Abstract Population increase, loss of energy resources and consequently high energy demand in recent years has caused countries to change their energy consumption policies. One of the most important energy consumers in rural and urban areas are buildings. Therefore, the role of heating and cooling systems is considerable in buildings with high level of energy usage. Floor heating system is a form of central heating system which achieves indoor climate control for thermal comfort using conduction, radiation and convection heat transfer. The terms radiant heating is commonly used to describe this approach regarding to the role of radiation in this system according to its significant portion of the resulting thermal comfort. Radiant heating has much more advantages compared to conventional heating systems not only in the case of energy efficiency, but also in preparing thermal comfort for settlements. In addition, floor heating systems generate lower temperature gradients in compare with other convective heating systems. In the present study, the CFD simulation is performed to analyse floor heating system in a dome shape room to reach the thermal comfort condition in the standard height of 1.8 meter above the floor. Moreover, the obtained results are
Chapter 9 In: Computational Fluid Dynamics Applications in Green Design. pp.277-294
can be translated into the architecture world in the form of new generation homes. The dome configuration applies nature’s principles of forming a highly efficient system [9]. The aim of this research is to analyse the energy consumption of a dome house, as an example of designing sustainable buildings by learning from the optimum biological forms existing in nature, since energy consumption is an important indicator on the sustainability of buildings. Only a few thermal models have been presented for dome shape homes. More attention has been given to the structural configuration than to the thermal performance of dome-like homes. Nara [10] presented a 2D CFD model for calculating the air velocity and temperature distribution due to thermal convection inside a reduced-model of a farm building under adiabatic boundary condition. The Boussinesq approximation is combined with the Navier-Stokes equation to describe the natural convection. Boulard et al. [11] used a reduced-scale model of a greenhouse with high temperature of floors to simulate the impact of solar radiation on the greenhouse. The k-ε model was added to simulate the turbulent flow. Grashof number (Gr) was used in these two papers to ensure the similarity between the full scale model and reduced scale experimental model. Luttmann-Valencia [12] developed a single node model that predicts the air temperature inside Biosphere II, located in Arizona (US). T. Nishioka et al. [13] evaluated the indoor thermal environments in a large domed stadium during the summer. To satisfy such purposes, they take into account various intelligent mechanical systems to control and create a suitable space and environment without consuming excessive energy. Their measurements included temperature distribution, humidity, air flow and outdoor weather conditions for three seasons. Shklyar and Arbel [14] examined the wind-driven isothermal flow patterns and mass fluxes in a full-scaled, pitched-roof, single span glasshouse using standard and high-Reynolds-number k-ε models. Lin and Zmeureanu [15] presented a three-dimensional thermal and airflow (3D-TAF) model that predicts the impact of large domes on the heating load of the protected house. They focused on the airflow model and made a comparison between their simulation and CFD model. Faghih and Bahadori [16] studied the thermal performance of domed roofs in order to determine how they can be helpful in reducing the maximum inside air temperature in buildings during the warm seasons of the year. They considered various parameters such as air flow around dome roofs, solar radiation, radiation heat transfer with the sky and the ground and openings on the building. They concluded that the thermal performance of the investigated domed roof is better than the building with flat roof. Moreover, they found that openings cause passive air flow inside building, which is helpful for establishing thermal comfort Croome and Moseley [17], Sharma et al. [18], Singh et al. [19] and Jain [20] presented numerical models that predict the air temperature inside a dome with lots of simplifying assumption. As an example, they considered the convective heat transfer coefficient to be constant and neglected the air movement inside the dome. Glazed domes have become increasingly popular in modern building designs. These kinds of domes are used to bring daylight and solar heat into the indoor space. Faghih and Bahadori [21] estimated the solar radiation received by several domed roofs, and determined the effect of glazed tiles covering these domes on the total solar radiation absorbed by such roofs. The results of this study can be useful in the thermal performance evaluation of domed roofs, and particularly for determining their passive cooling effects for
Chapter 9 In: Computational Fluid Dynamics Applications in Green Design. pp.277-294
the buildings they serve. For domes with multiple spaced layers of glazing, there is little information available on natural convection heat transfer within these layers. Laouadi and Atif [22] presented a numerical study on heat transfer by laminar natural convection within multi-layer domes with uniform spacing heated from the outside. They also obtained flow and temperature fields within the domed enclosure using the control volume approach combined with the fully implicit scheme. During the last two decades, application of floor heating systems in building sector have increased significantly [23, 24] as one of the most efficient systems to achieve thermal comfort in buildings with low-energy requirement. Instead of warming air and circulating it throughout the building, floor heating system heats the objects, atmosphere and occupants directly. In comparison to the conventional forced warm air circulation systems, radiant heating system needs lower energy [25]. In the recent years, there has been considerable attention to floor heating system and their thermal performance in the literatures. In addition of different investigation with respect to thermal properties [26], and dynamical behaviour [27], there are extensive studies have been devoted to energy savings of this system [28-30]. Buckley [31] studied the energy saving of floor heating systems and concluded that these systems can reduce energy costs by 30% or more with equal comfort condition compared to other conventional convective heating systems. In the present study, the CFD simulation of a three dimensional dome room coupled with a floor heating system has been developed and compared to a regular cubic room with the same volume to predict the energy consumption of two different kinds of rooms. The boundary conditions, heat transfer coefficients through building envelope and heat source outputs are considered to be similar for both rooms. Thermal comforts at comfort height in both rooms have been calculated by modelling the velocity and temperature fields using the Fluent software. 2. Model description In this study, floor heating system is simulated for a dome house by means of Computational Fluid Dynamic (CFD) and results are compared to the regular cubic room in order to indicate the energy saving capabilities and the comfort conditions of dome shape houses. The simulated dome and cubic shape rooms are graphically presented in Figure 1. In order to have a better definition of 3D rooms, two main sections that covered the entire room are defined which are called door-mid-section and window-mid-section. Door-mid-section is the plane of the 3D rooms which contains the effect of door on the temperature and velocity profiles. And also the effect of window on the flow and thermal behaviour of rooms can be seen in window-mid-section. Furthermore, at the middle of the room, a reference line is defined in order to have a better understanding of temperature and velocity gradients in the room. Door and window-mid-sections are graphically illustrated in Figures 2 and 3. Note that for the dome room, the mid sections are selected at the middle of the window and door; however, for the cubic room, the mid sections are selected at the middle of the walls. Boundary conditions, material and thermodynamic properties of the problem for both dome shape and cubic rooms are represented in Table 1. As tabulated in this table, the boundary condition of walls, roof, window and door are the same; however, constant heat flux is assumed for the floor.
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The simulation is performed in the climate condition of Tehran, the capital city of Iran. According to this consideration, the outdoor design temperatures is considered to be C°0 .
Figure 1. Perspective view of (a) dome room and (b) cubic room with dimensions in meter.
Figure 2. (a) door-mid-section and (b) window-mid-section of the 3D dome shape room.
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Absorption Coefficient ( m/1 ) 0.1 0 0.04 0 3. Numerical procedure In this research, a finite-volume approach has been used to solve flow and heat transfer equations of a floor heating system in two different room types. Numerical solutions were obtained iteratively for each of cells to produce a solution that satisfies the conservation laws for mass, momentum, and energy. For incompressible, steady state and three-dimensional flow, the governing mass, momentum and energy equations are as follow.
mS)v.(t
=∇+∂∂ ρρ (1)
Fg.p)vv.()v(t
++⎟⎠⎞
⎜⎝⎛∇+∇−=∇+
∂∂ ρτρρ (2)
hj
effjjeff Sv.JhTk.))pE(v.()E(t
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎠⎞
⎜⎝⎛+−∇∇=+∇+
∂∂ ∑ τρρ (3)
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Eq. (1) is the general form of the mass conservation equation where ρ is density, v is the velocity vector and mS is the mass added to the continuous phase from the dispersed second phase (e.g., due to vaporization of liquid droplets). Eq. (2) is momentum conservation equation where p is the static pressure, τ is the stress tensor (described below), and gρ and F are the gravitational body force and external body forces (e.g., that arise from interaction with the dispersed phase), respectively. The stress tensor τ is given by
( ) ⎥⎦⎤
⎢⎣⎡ ∇−∇+∇= Iv.vv T
32µτ (4)
where µ is the molecular viscosity, I is the unit tensor and the second term on the right hand side is the effect of volume dilation. In the energy equation (Eq. (3)), E is the total energy, effk is the effective conductivity
( teff kkk += , where tk is the turbulent thermal conductivity, defined according to the
turbulence model being used), and jJ is the diffusion flux of species j. The first three terms on the right-hand side of Eq. (3) represent the energy transfer due to the conduction, species diffusion, and viscous dissipation, respectively. hS includes the heat of chemical reaction, and any other volumetric heat sources. In Eq. (3), the total energy (E) is equal to
2
2vphE +−=ρ
(5)
where h is the sensible enthalpy. 3.1 Turbulence model To get a correct vision of the flow field, the ω−k turbulence model is chosen due to its extensive use in various engineering applications. This model is a semi-empirical model based on model transport equations for the turbulence kinetic energy ( k ) and its specific dissipation rate (ω ) which are obtained from the following transport equations:
( ) ( ) kkj
kj
ii
YGxk
xku
xk
t−++⎟
⎟⎠
⎞⎜⎜⎝
⎛
∂∂
Γ∂∂
=∂∂
+∂∂ ρρ (6)
( ) ( ) ωωωω
ρωρω YGxx
uxt jj
ii
−++⎟⎟⎠
⎞⎜⎜⎝
⎛
∂∂
Γ∂∂
=∂∂
+∂∂ (7)
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where kΓ and ωΓ represent the effective diffusivity of k and ω , respectively. kG represents the generation of turbulence kinetic energy due to mean velocity gradients and ωG represents the generation of ω . kY and ωY represent the dissipation of k and ω , respectively due to the turbulence. The effective diffusivities of ω−k turbulence model are given by
k
tk σ
µµ +=Γ (8)
ωω σ
µµ t+=Γ (9)
where kσ and ωσ are the turbulent Prandtl numbers for k and ω , respectively. The turbulent viscosity ( tµ ) is computed by combining k and ω as follows:
ωραµ k*
t = (10)
The coefficient *α damps the turbulent viscosity causing a low-Reynolds-number correction. It is given by
⎥⎥⎦
⎤
⎢⎢⎣
⎡
++
= ∞kt
kt*
**
RReRRe
10ααα (11)
where
07203
6 0 .,,R,kRe ii*
kt ==== ββ
αµωρ (12)
It is noteworthy to mention that, in the high-Reynolds-number form of the ω−k model, 1== ∞
** αα . 3.2 Radiation model In this problem, the effect of radiation heat transfer is not negligible in comparison to convection and conduction heat transfer due to determining role of radiation in the floor heating systems. In this case, Discrete Ordinate (DO) model have been chosen in order to simulate the radiation phenomena inside the rooms. The DO governing equation for an absorbing, emitting and scattering grey medium can be written as [32]:
∫ Ω′′Φ′+=++∇π
πσ
πσσ
4
42
4d)s,s()s,r(ITan)s,r(I)a()s)s,r(I.( s
s (13)
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which sσ is the scattering coefficient, a is the absorption coefficient, n is the refractive index, )s,s( ′Φ is the scattering phase function for the radiation from incoming direction s ′ and confined within the solid angle Ω′d to scattered direction s confined within the solid angle Ωd . )s,r(I is the total radiation intensity function and T is the air temperature. In this study, the wall surfaces are assumed opaque. Furthermore, for considering the buoyancy effect and the relation between the flow and energy equations, Boussinesq model is used. 3.3 mesh structure To obtain a physical pressure field, a non-uniform grid for the three dimensional model of both dome shape and cubic shape rooms is generated. Figure 4. shows the meshed midsection of the rooms. As it is clear from Figure 4, the cells near the walls are finer due to the importance of these regions. For grid independence test, three different resolutions shown in Table 2 are considered to compare the obtained numerical results. When the temperature at the height of 1.8 meter above the floor reaches to 295.15 K, the thermal comfort condition is established. The results obtained from the different grids show that an increasing the grid numbers by 41% (case II to case III) has a small influence ( %. 41016 −× ) on the temperature in thermal comfort height. According to this refinement study, all further simulations are performed with considering case II. Finally, it should be declared that the maximum error of the residuals to reach to the steady state solution is assumed to be of the order of 6101 −× .
Table 2. Grid independency test for two modelled rooms.
Dome room Cubic room Case Number of grids
Temperature in thermal comfort height (K)
Number of grids
Temperature in thermal comfort height (K)
I 295608 291.83 40257 291.35 II 404898 294.93 52801 294.88 III 681926 295.11 89072 295.08
4. Results and discussion As mentioned, the velocity and temperature distributions in a dome shape room heated by a floor heating system are investigated. The results are compared to the velocity and temperature profiles of a regular cubic room with the same heating method. The comfort temperature (295.15 K) is determined at location 1.8m above the floor according to ASHRER handbook as the comfort height [33]. As the comfort condition is achieved in the room, it means that the steady state condition is established and the numerical simulation has been converged. Then, the dissipated heat fluxes of all surfaces to the environment have been calculated for both the dome and cubic shape rooms. First, for the validation of the code, a cubic room with the dimension of
m.m.m. 819162 ×× is simulated and the results are compared with the experimental data
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[34, 35]. By selecting the same condition between the simulation and the experimental setup and also considering unsteady flow, the simulation is performed. Figure 3 shows the temperature at the height of 1m above the floor for both the experimental data and the present study. As shown in this figure, the results are in good agreement with each other.
Figure 4. Mesh structure on the midsection of (a) dome room and (b) cubic room.
Figure 5. The comparison of CFD simulation and experimental data. Figure 6a and b illustrate the temperature profiles in the door-mid-section and window-mid-section of dome shape room. It can be seen from this figure that temperature distribution in room is clearly uniform both in door-mid-section and window-mid-section. Furthermore, the temperature near window is relatively low which is due to high thermal conductivity of glass in comparison to other parts of the room such as walls and floor. Velocity vectors in the door-mid-section and window-mid-section of dome shape room can be seen in Figure 7a and b, respectively. As shown, there is a big vortex approximately in the center of the window-mid-section, while there are several smaller vortices in door-mid-section due to the temperature difference between different parts of the room. It is important that higher temperature difference will cause higher pressure difference and consequently bigger vortices can be produced.
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Figure 6. temperature profiles in (a) door-mid-section and (b) window-mid-section of dome shape room.
Figure 7. Velocity contours in (a) door-mid-section and (b) window-mid-section of dome shape room.
For better understanding of flow patterns, three different mid-sections of the room in the form of velocity vectors and velocity contours are graphically illustrated in Figure 8a and b, respectively.
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Figures 9 and 10 display the velocity contour in the mid-sections of the cubic shape room. As displayed in these figures, two big vortices are generated near the wall in both window mid-section and door mid-section, expectedly [35]. The difference between the flow patterns in the produced vortices is due to the existence of window and door.
Figure 8. (a) velocity vectors and (b) velocity contours for three different mid-sections of dome shape room.
Figure 9. Velocity vectors for door-mid-section of cubic room.
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Figure 10. Velocity vectors for window-mid-section of cubic room.
Figure 11 display the air temperature at the reference line for the dome and cubic shape rooms and Figure 12 display the air speed at the reference line for the dome and cubic shape rooms. As displayed in Figure 11, in both systems, small temperature changes could be seen along reference line due to the usage of floor heating system [36]. However, in the dome type room, at the comfort height, the air temperature is higher than the ait temperature in the cubic room. As shown in Figure 12, the air speed at the comfort height is smaller in the dome room than the cubic room. Having a higher air temperature and a lower air speed at the comfort height is an advantage of dome type room related to the cubic type room.
Figure 11. Air temperature at reference line for (a) dome room and (b) cubic room.
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Figure 12. air velocity at reference line for (a) dome room and (b) cubic room. Table 3 and Table 4 list the total heat transfer from each surface of the dome type room and cubic type room, respectively. As schematized in these tables, the total heat transfer from the floor to the room is almost 6.5% higher in the dome type room than regular cubic type room. However, the area of the floor is bigger in the dome shape room than the cubic room so that the total heat transfer per surface area from the floor to the room is 23% smaller in the dome type room than the cubic room.
Table 3. Total heat transfer for each surface of the dome type room.
Surface type Surface area (m2)
Total heat transfer (W)
Total heat transfer per surface area (W/m2)
Floor 28.23 1954.1 69.23 Dome surface 52 -1104.2 -21.23 Window 1.6 -712.4 -445.52 Door 1.8 -50.3 -27.94 Door and window connecting walls
5.39 -87.2 -16.18
Total 89.02 0 -
Table 4. Total heat transfer for each surface of the cubic type room.
5. Conclusion In the present study, the CFD simulation has been done to analyse the velocity and temperature distribution of a dome type room in comparison with the regular cubic type room with the same volume using the Fluent software. The floor heating system is employed in order to reach the thermal comfort condition in the rooms. The results show that in the dome type room, the air temperature and speed is more suitable according to the comfort conditions. However, the average of air speed is higher in the dome shape room than the cubic shape room. Furthermore, the total heat transfer from the floor is 6.5% more in the dome shape room than the cubic shape room since the area of the dome room’s floor is higher than the cubic room so that the total heat transfer per surface area is 23% smaller in the dome shape room than the cubic shape room. Moreover, in both rooms, due to the usage of floor heating system, the temperature gradients are low. References [1] WCED. Wolrd Comission on Environment and Development. Our common future.
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Taha Khademinejad received B.Sc. degree in mechanical engineering minoring inthermo fluid from University of Guilan, Rasht, Iran in 2011. He is currently pursuing the M.Sc. degree with the school mechanical engineering, Amirkabir University ofTechnology, Tehran, Iran. His current research interests include sustainable andrenewable energies, desalination, heat and mass transfer and thermodynamics.
Shahab Din Rahimzadeh completed his Bachelor degree of Architect in 2010, at IUCin Iran. He is currently a master research student in school of design (Creative IndustryFaculty) at Queensland University of Technology in Brisbane, Australia. Shahab’sMaster research focuses on parametric modeling, Climate –based Daylight Metrics, Complex Geometry and sustainability. His research aims to analysis and modeling“Use of parametric modeling and climate-based metric for the efficient design of daylight strategies in buildings with complex geometries”.
Pouyan Talebizadeh received B.Sc. and M.Sc. degree in mechanical engineering fromShahid Bahonar University of Kerman, Kerman, Iran in 2008 and 2011, respectively.He is currently pursuing the Ph.D. degree with the school mechanical engineering, Amirkabir University of Technology, Tehran, Iran. He is a lecturer in mechanicalEngineering Department, Graduate University of advanced Technology, Kerman, Iran.His current research interests include two phase flow, environmental pollution control, emission reduction, Non-thermal plasma technology, HVAC systems, optimization,and numerical modeling. E-mail address: [email protected]; [email protected]
Chapter 9 In: Computational Fluid Dynamics Applications in Green Design. pp.277-294
Hassan Rahimzadeh received the B.Sc. and M.Sc. degrees in mechanical engineering from the West Virginia Institute of Technology, Montgomery, WV, USA, and WestVirginia State University, Morgantown, WV, USA, and the Ph.D. degree ininstrumentation measurement from New South Wales University, Sydney, Australia, in 1977, 1978, and 1986, respectively. He has been with the Department of MechanicalEngineering, Amirkabir University of Technology, Tehran, Iran. His current researchinterests include two phase flow (physical and numerical modeling), hydraulics structures, environmental pollution control, renewable energy, and instrumentation.
Hamed Sarkardeh received B.Sc. degree in civil engineering from FerdowsiUniversity of Mashhad, Mashhad, Iran, and M.Sc. from Amirkabir University ofTechnology (Tehran Polytechnic) Tehran, Iran, and Ph.D. from Iran University ofScience and Technology, Tehran, Iran, in 2006, 2009 and 2013 respectively. He is alecturer in Civil Engineering Division, Department of Engineering, Hakim SabzevariUniversity, Sabzevar, Iran and also senior researcher in the Hydraulic StructuresDivision, Water Research Institute, Tehran, Iran.
