- Email: [email protected]
Airflow analysis in an air conditioning room
ARTICLE IN PRESS
Building and Environment 42 (2007) 1531–1537 www.elsevier.com/locate/buildenv
Airflow analysis in an air conditioning room Ooi Yongsona, Irfan Anjum Badruddina,, Z.A. Zainala, P.A. Aswatha Narayanab a
School of Mechanical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Malaysia MS Ramaiah School of Advanced Studies, Gnanagangothri Campus, New BEL Road, MSR Nagar, Bangalore 560 054, India
b
Received 16 September 2005; received in revised form 30 November 2005; accepted 16 January 2006
Abstract The aim of superior air conditioning system is no longer constrained to advancing the efficiency of cooling machine, but includes the study of airflow with the assistance of the distribution of several significant parameters. A simple numerical study of the turbulent flow over an enclosed air conditioning system was not practicable a few decades ago since the computer facilities were not sufficient. In this paper, a standard office room was taken up for simulation. Temperature and velocity distribution over various virtual planes for different locations of the air conditioner blower were analyzed to achieve the maximum comfort for the occupant. With Fluent, as solution tool, k–epsilon and Reynolds stress models for turbulence flow were used for the analysis. The different locations of blower placement are analyzed for better comfort of occupant in the room and it is found that the occupant will experience most comfort if the air conditioner blower is placed on location II compared to the other two locations. This work can also be extended to a more complex air conditioning system like in the industries, hospitals as well as the gigantic shopping malls. r 2006 Elsevier Ltd. All rights reserved. Keywords: Temperature distribution; Velocity distribution; Virtual planes; k–epsilon; Reynolds stress; Maximum comfort
1. Introduction As the standard of living is increasing, more and more people are seeking for a comfortable living whether in work or at rest. Air conditioner has become a popular comfortproviding device since two decades. It has become a need for everyone, whether in an office or home especially for warm and wet climate countries like Malaysia. People are seeking for more comfortable working environment in order to perform their duties well. Main objective of an air conditioning system, in general, is to provide the maximum comfort to the entire air conditioning area. To achieve this objective, an analysis of performance of the cooling machine will be subsequently insufficient. Scope should be widening to an analysis of airflow over the entire air conditioning system [1]. Therefore, the design of air conditioning system no longer focuses on the effectiveness of cooling machine alone. Much research has been carried Corresponding author. Tel.: +604 5995999 x 6369; fax: +604 5941025. E-mail address: [email protected] (I.A. Badruddin).
0360-1323/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2006.01.002
out in this field. Using computational fluid dynamics (CFD) will probably not replace physical experiments completely but it can significantly reduce the amount of experimental work. This tool is capable for analyzing the flow pattern of the air conditioning system in short span of time, which was previously impossible from experimental and theoretical methods [2]. Moreover, CFD gives virtual distribution of airflow, temperature, etc. in entire domain which is highly difficult to get from experiments because of time and cost involved. Unfortunately, there is no universal flow model to represent the entire flow pattern for the air conditioning system [3]. Recently, research has been carried out in relation to airflow in an air conditioning room. Heating, ventilating and air conditioning (HVAC) have been analyzed by Mathews et al. [4] for the use of human science building (HSB) at the University of Pretoria wherein there is a saving of 60% in power consumption. Besides, indoor humidity behaviors associated with decoupled cooling in hot and humid climates have been analyzed by Zhang and Niu [5]. Cheong et al. [6] have carried out a research on the dispersion of contaminants in an office environment using
ARTICLE IN PRESS O. Yongson et al. / Building and Environment 42 (2007) 1531–1537
1532
Nomenclature N a n r t u v w t P e k e mt Gk Gb YM
number of hexahedron cells grid spacing number of nodes density of fluid time velocity magnitude in x direction velocity magnitude in y direction velocity magnitude in z direction shear stress pressure internal energy turbulent kinetic energy rate of dissipation turbulent viscosity generation of turbulent kinetic energy due to the mean velocity gradients generation of turbulent kinetic energy due to buoyancy contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate
empirical and modeling techniques. Thermal comfort parameters were measured at predetermined grid points within a virtual plane to predict the airflow pattern of supply air jet, as well as to determine the occurrence of thermal stratification in office space by Sekhar and Ching [7]. In the present paper, the analysis is carried out for an air conditioning system for a single room using CFD. The distribution of various parameters like temperature and velocity has been studied to determine the best placement location for air conditioner blower and also the area which is suitable for the occupant. 2. Modeling 2.1. Interior design A standard room model of a single office room, which contains information of floor plans, has been taken from a standard reference book [8]. The width (y-direction); length (x-direction) and height (z-direction) are 2.7; 3.7 and 3.0 m, respectively, which is shown in Fig. 1(a). Formally there is no fixed arrangement for the furniture. It will depend on the style and the favorites of the occupant of the room itself. Subsequently, an idea of the furniture arrangement including the placement location of cabinet or shelf, table and chair is generated as given in the book [9] of interior design, which is shown in Fig. 1(a).
Prandtl number Prt C1e , C2e, C3e constants used in turbulent model sk turbulent Prandtl numbers for k se turbulent Prandtl numbers for e E total energy (tij)eff deviatoric stress tensor T temperature cp specific heat capacity at constant pressure Cij convection term in Reynolds stress transportation equation DTij turbulent diffusion term in Reynolds stress transportation equation (RSTE) DLij molecular diffusion term in RSTE Pij stress production term in RSTE Gij buoyancy production term in RSTE fij pressure strain term in RSTE eij dissipation term in RSTE Fij production by system rotation term in RSTE m dynamic viscosity I number of iterations
locations, which have been named as locations I, II and III as shown in Fig. 1(b)–(d), respectively.
2.3. Governing equations There are three groups of basic equations, which are derived from three basic physics laws of conservation. The mass conservation, momentum conservation and energy conservation results in the continuity equation, Navier– Stokes equation and energy equation, respectively. Since the flow in an air conditioning room is turbulent flow [10], the k–epsilon and the Reynolds stress viscous models have been chosen for investigation. The standard k–epsilon model is a semi-empirical model based on model transport equations for the turbulent kinetic energy (k) and its dissipation rate (e). The transport equation for k is derived from the exact equation, while the transport equation for e is obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart. The turbulent kinetic energy, k, and its rate of dissipation, e, are obtained from the following transport equations: Dk q mt qk r ¼ mþ (1) þ G k þ G b re Y M , Dt qxi sk qxi
2.2. Blower placement r For a single office room, normally a split unit will be used. There are three most suitable blower placement
De q ¼ Dt qxi
m qe e e2 mþ t þ C 1e ðG k þ C 3e Gb Þ C 2e r . k se qxi k (2)
ARTICLE IN PRESS O. Yongson et al. / Building and Environment 42 (2007) 1531–1537
1533
Fig. 1. The sketch of the room model: (a) coordinate system for the entire room; (b) blower placement in location I; (c) blower placement in location II and (d) blower placement in location III.
Convective heat and mass transfer modeling in the k–epsilon models is given by the following: q q ðrEÞ þ ½ui ðrE þ pÞ qt qxi cp mt qT q ¼ kþ þ uj ðtij Þeff þ S h . qxi Prt qxi
r
De q ¼ Dt qxj
mþ
mt qe 1 e e2 þ C e1 ½Pii þ C e3 G ii C e2 r . se qxj k 2 k
(6) ð3Þ
Abandoning the isotropic eddy-viscosity hypothesis, the Reynolds stress model (RSM) closes the Reynolds-averaged Navier–Stokes equations by solving transport equations for the Reynolds stresses, together with an equation for the dissipation rate. This means that four additional transport equations are required in two-dimensional flows and seven additional transport equations must be solved in three-dimensional flows. Since the RSM accounts for the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate in a more rigorous manner than oneequation and two-equation models, it has greater potential to give accurate predictions for complex flows. The exact transport equations for the transport of the Reynolds stresses, rui uj , may be written as follows: q ðrui uj Þ þ C ij ¼ DTij þ DLij þ Pij þ Gij þ fij þ eij þ F ij . qt (4) The turbulent kinetic energy, k, and its rate of dissipation, e, are obtained from the following transport equations: Dk q m qk 1 ¼ r mþ t þ ðPii þ G ii Þ reð1 þ 2M 2t Þ, Dt qxj 2 sk qxi (5)
The convective heat and mass transfer modeling in the Reynolds stress models will be same as k–epsilon model, which is given by the following relation: q q ðrEÞ þ ½ui ðrE þ pÞ qt qxi cp mt qT q ¼ kþ þ uj ðtij Þeff þ Sh . qxi Prt qxi
ð7Þ
To solve these equations, initial and boundary condition must be specified around the boundary of system (domain). Because the equations are highly nonlinear, they are not solvable by explicit, closed-form analytical methods. The numerical finite volume method as used in Fluent has been used for solving the equations. The domain is discretized into cells or elements and nodal points are defined. Upon solution of the equations, the values of the dependent variables are known at the nodal points. The values of some constants in the differential equations are given in Table 1. All slandered values have been used for simulation purpose. 2.4. Boundary conditions Fig. 2 shows the circulation of air through the blower. Hot air enters surface (ABCD) and cool air flows out from the blower at surface (CDEF).
ARTICLE IN PRESS O. Yongson et al. / Building and Environment 42 (2007) 1531–1537
1534 Table 1 Default values for some constants
Table 2 Number of hexahedron cells and nodes
Model constants
k–e
RSM
Grid spacing, a (cm)
15
10
7.5
Cm C 1e C 2e Cs C1 C2 C10 C20 sk se
0.09 1.44 1.92 – – – – – 1 1.3
0.09 1.44 1.92 0.22 1.8 0.6 0.5 0.3 1 1.3
Number of hexahedron cell, N Number of node, n
7988 9453
26 706 29 934
64 440 70 196
Table 3 The location of virtual planes Surface name
Plane equation (cm)
z-top z-central z-bottom x-central x-front y-left x-back y-right
z ¼ 210 z ¼ 100 z ¼ 40 x ¼ 130 x ¼ 310 y ¼ 80 x ¼ 70 y ¼ 220
2.6. Virtual planes
Fig. 2. The airflow in and out at the blower.
The boundary condition of each surface is as follows.
Inlet (surface CDEF) J Velocity magnitude ¼ 5 m/s Velocity direction at xcomponent ¼ 1 ycomponent ¼ 0
) For location I:
zcomponent ¼ 1
For locations II and III, cool air flows in the direction same as location I (451 down from surface CDEF relative to the blower). J Temperature ¼ 295 K. Outlet (surface ABCD) J Gauge pressure ¼ 0 Pa. J Temperature ¼ 300 K. Other walls (including surface at blower, surface of furniture and wall of the room) J Temperature ¼ 300 K.
2.5. Grid spacing There are various types of cells, which can be used for meshing purpose. The available three-dimensional cell types are tetrahedron, hexahedron, prism as well as pyramid. The hexahedron cell has been chosen due to its homogeneity with the room model. The three types of grid spacing are 15 cm (coarse), 10 cm (medium) and 7.5 cm (fine). Table 2 shows the number of hexahedron cells with respect to their grid spacing or mesh size.
The simulated description will contain parameters such as temperature, velocity, pressure, etc. in every location point in the entire flow volume, which is in three dimensions. Present method gives a general picture for the comfort in room. For swing attached, the analysis will be complicated and is a function of time. Thus, it is assumed that the air flows at 451 from blower. For presenting the results in a simple way, eight planes have been designated which can be in horizontal and vertical directions in order to view the information clearly on entire volume. Table 3 shows the location of the virtual planes that have been created. 2.7. Residual The accuracy in the CFD simulation is obtained in terms of residual. Residual is the measurement of the error. The smaller the residual, the smaller is the error. Fig. 3 shows the plot of residuals versus number of iterations for model (RSM 10-1) with the Reynolds stress viscous model; grid spacing of 10 cm and the blower location at location I. While observing the variation of residual with respect to number of iterations, the residual keeps on decreasing from the start to around 800 iterations. Then, the residual remains same although the numbers of iterations have increased. The iteration has been stopped since there is no variation in the result. This has been applied to all the simulated models. 3. Results and discussion 3.1. Comparison of viscous models There are two types of viscous models to be considered, which are k–epsilon and Reynolds stress model. It is important to make sure that the suitable viscous model is
ARTICLE IN PRESS O. Yongson et al. / Building and Environment 42 (2007) 1531–1537
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Fig. 3. Residual plotting for RSM 10-1 model.
applied to the model to be simulated. So, a model where the blower is placed in location I is chosen for investigating the variation of temperature over a selective virtual surface, z-top. It is seen from Fig. 4 that all the contours are different from each other except for Figs. 4(e) and (f), which are nearly the same. Therefore, Reynolds stress model for grid spacing of 10 and 7.5 cm gives almost identical results. Based on the independence of grid spacing, Reynolds stress model is considered as a better viscous model and has been chosen for simulation of airflow for other blower placement locations. The computational time also is another factor to be considered while dealing with the long time simulation. The simulation times for all models are shown in Table 4. Even though simulation time for Reynolds stress models is nearly twice simulation time of k–epsilon models, Reynolds stress model is chosen for further analysis, as it is grid independent. The computational time of Reynolds stress model for grid spacing 7.5 cm (10.0 h) is 4.5 times more than the spacing of 10 cm (2.2 h). There is not much difference with respect to their temperature contours between mesh spacing of 10 and 7.5 cm for Reynolds stress model. Hence, the 10 cm mesh spacing has been chosen for further simulation.
3.2. Suitable blower placement location To observe the suitable position of blower placement, analysis of eight virtual planes has been carried out for locations I, II and III. Among the planes, the z-center plane is the most important plane since it represents the condition of the room well. The suitable blower location also can be found out by investigating the various parameter distributions over the various planes. Parameters like velocity magnitude and temperature have been analyzed as done by Ladeinde and Nearon [11]. Among the planes that have been studied, z-center is the best plane to view the temperature as well as velocity magnitude distribution in horizontal direction near the occupant. It
Fig. 4. Comparison between k–epsilon and Reynolds stress for temperature distribution at specified z–top plane with grid spacing. All values are in degree Kelvin.
Table 4 Computational time for various models Viscous model k–epsilon Grid spacing (cm) Computational time (h) Number of iterations, I
15 0.2 600
10 1.0 700
Reynolds stress 7.5 4.5 1100
15 0.4 700
10 2.2 1000
7.5 10.0 1400
is also suitable to predict the temperature and velocity magnitude distribution over the entire room. By observing the velocity magnitude over various planes for blower placement in locations I, II and III, as in Fig. 5 the air velocity around the occupant and table are in the range of 0.4–1.5 m/s (highlighted with dotted outline square in indicator bar). This is the criterion for ‘weak wind’, which is the most comfortable velocity magnitude to the occupant. The distribution of velocity magnitude over the entire z-center plane for locations I, II and III are shown in Fig. 5(a)–(c), respectively. From Fig. 5(a), it is seen that the occupant experience about 1.0 m/s velocity. Besides, in Fig. 5(b), the occupant experience 1.25 m/s wind while the blower is placed in location II. For Fig. 5(c), the occupant experience 1.0 m/s wind. Locations I–III are acceptable from velocity magnitude criteria. In order to get a better visualization of the circulation of airflow in the room, vectors have been plotted over the three important planes, which are perpendicular to the z-axis. The vector
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O. Yongson et al. / Building and Environment 42 (2007) 1531–1537
Fig. 7. Velocity vectors when air passing through occupant (plane at centre of z-axis). Fig. 5. Velocity magnitude distribution over a virtual surface z-center for blower: (a) location I; (b) location II and (c) location III. All values are in meter per second.
Fig. 8. Temperature distribution over a virtual surface z-center for blower: (a) location I; (b) location II and (c) location III. All values are in degree Kelvin. Fig. 6. Three-dimensional view of velocity vectors for three horizontal plane perpendicular to z-axis.
shows the direction of the airflow on the particular plane in three dimensions as well as the magnitude. As shown in Fig. 6, the air is flowing almost downward near the area where occupant sits. The directions of the airflow slowly change to horizontal component while moving further away from the occupant. The magnitude of the air velocity is high on the top plane and getting reduced when it flows downward to the occupant as shown in Fig. 6. Components of vectors are also plotted on the most critical center plane, when air is passing through the body of the occupant (Fig. 7). The components vectors are small in magnitude close to the occupant, whereas the vector magnitude increases while getting further away from the occupant. It can be seen from this figure that the occupant area is a comfortable zone to sit since smaller vector magnitude are desirable to avoid disturbance due to wind. As shown in Fig. 7, the air is flowing back to the blower on the right-hand side of the occupant. For temperature criteria, the temperature for comfort should be in the range of 20–25 1C. All the three-blower
placement locations fulfill this criterion. But to reduce the size of compressor, it seems to choose a location that will provide the coolest region near the occupant. It saves cost with smaller compressor and consumes lower power, at the same time provides comfort to the occupant. If the blower is placed in location I, the temperature is distributed more or less uniformly over the entire room as shown in Fig. 8(a), but the occupant is not sitting in the coolest region of the entire room. So, a better position of the blower should be found since this is not the best position. By referring to Fig. 8(b) where the blower is placed in location II, although the temperature is not uniformly distributed over the entire room, but it satisfies the requirement of air conditioning office room. Basically, the room can be divided into two portions, which are the hot region (right-hand side of Fig. 8(b)) and cool region (left-hand side of Fig. 8(b)). The hot region is located in a space that is seldom used by occupant while the cool region is the space that always is occupied by the occupant. Basically, the occupant will experience about 296.3 K (23.3 1C). On the other hand, the occupant is sitting near the coolest region in the entire room as in Fig. 8(b). So, this will be the best position to place the air conditioner blower.
ARTICLE IN PRESS O. Yongson et al. / Building and Environment 42 (2007) 1531–1537
Next, the location III is analyzed. The occupant is sitting in the hottest region of the entire room as shown in the Fig. 8(c). So, this location is totally not effective and is the worst among the three possible locations that have been discussed. Since this is a three-dimensional case, the temperature distributions for other virtual planes have also been investigated. It is observed that placement in location II will provide the maximum comfort for the occupant or in other words, occupant experience the coolest temperature when the blower is located in location II. Hence, location II will be the suitable location for the blower placement. 3.3. Comfort region Previously, the furniture arrangement is fixed and the problem is to find the suitable blower placement location. Now is the other way around. The same models stated in previous sections are used to locate the comfort region or coolest region for energy saving as stated before. As shown in the plan view in Fig. 6, the dotted outline square covers the cool region (contours are blue in color) for the entire room for three possible blower placement locations. This is applicable to help the furniture arrangement of an air conditioning room. While the blower is placed in location I, almost the entire room is in blue color contours. It is seen that almost the whole area has cool condition while the occupant can be located center left by referring to Fig. 8(a). This will be the suitable location when this room is used for living room or multiple functional hall while there is a need to cool the entire room. For location II, the cool region is smaller compared to the location I. The cool air is just concentrated at the left side of the plan as shown in Fig. 8(b). The rest of the room is not cooled. The location III manages to keep the upper center region cool as shown in Fig. 8(c). By this way, the position of the occupant can be determined which is the right place to sit on while the air conditioner blower is already fixed. With CFD method, the flows characteristics can easily be predicted and can be compared with the experimental method, where the sophisticated measurement instrumentation must be provided.
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4. Conclusion 1. Between Reynolds stress model and k–epsilon model, Reynolds stress model seem to be grid independent than k–epsilon model for the three-grid spacing investigated. Although simulation of Reynolds stress model takes a longer time compared to the k–epsilon model, but mesh spacing independency seem to be more significant. 2. Location II is found to be the most suitable location to place the air conditioner blower. The temperature distribution shows that the occupant is seated in the cool region. 3. The occupant will experience most cool region if the air conditioner blower is placed on location II compared to the other two locations. 4. This work can also be extended to a more complex air conditioning system like in the industries, hospitals as well as the gigantic shopping malls. References [1] Haines RW. Control system for heating, ventilating and air conditioning. 2nd ed. New York: Van Nostrand Reinhold; 1977. [2] Anderson JD. Computational fluid dynamics. International Edition. New York: McGraw-Hill; 1995. [3] Baker AJ, Richard MK, Eliott BG, Subrata Roy, Edward GS. Computational fluid dynamics: a two-edged sword. ASHRAE Journal 1997:51–8. [4] Mathews EH, Botha CP, Malan A. HVAC control strategies to enhance comfort and minimise energy usage. Energy and Buildings 2001;33:853–63. [5] Zhang LZ, Niu JL. Indoor humidity behaviors associated with decoupled cooling in hot and humid climates. Building and Environment 2003;38:99–107. [6] Cheong KWD, Djunaedy E, Poh TK, Tham KW, Sekhar SC, Wong NH, et al. Measurements and computations contaminant’s distribution in an office room. Building and Environment 2003;38:135–45. [7] Sekhar SC, Ching CS. Indoor air quality and thermal comfort studies of an under-floor air-conditioning system in the tropics. Energy and Buildings 2002;34:431–44. [8] Jerold LA. Architectural plan for adding on or remodeling. TAB Books; 1992. [9] Wong J. The modern design for living. Taiwan: Wanibooks/ Sharppoint; 1995. [10] Su M, Chen Q, Chiang C-M. Comparison of different subgrid-scale models of large Eddy simulation for indoor airflow modeling. Journal of Fluids Engineering Transactions of the ASME 2001;123:628–39. [11] Ladeinde F, Michelle DN. CFD applications in the HVAC & R Industry. ASHRAE Journal 1997;1:44–8.
Building and Environment 42 (2007) 1531–1537 www.elsevier.com/locate/buildenv
Airflow analysis in an air conditioning room Ooi Yongsona, Irfan Anjum Badruddina,, Z.A. Zainala, P.A. Aswatha Narayanab a
School of Mechanical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Malaysia MS Ramaiah School of Advanced Studies, Gnanagangothri Campus, New BEL Road, MSR Nagar, Bangalore 560 054, India
b
Received 16 September 2005; received in revised form 30 November 2005; accepted 16 January 2006
Abstract The aim of superior air conditioning system is no longer constrained to advancing the efficiency of cooling machine, but includes the study of airflow with the assistance of the distribution of several significant parameters. A simple numerical study of the turbulent flow over an enclosed air conditioning system was not practicable a few decades ago since the computer facilities were not sufficient. In this paper, a standard office room was taken up for simulation. Temperature and velocity distribution over various virtual planes for different locations of the air conditioner blower were analyzed to achieve the maximum comfort for the occupant. With Fluent, as solution tool, k–epsilon and Reynolds stress models for turbulence flow were used for the analysis. The different locations of blower placement are analyzed for better comfort of occupant in the room and it is found that the occupant will experience most comfort if the air conditioner blower is placed on location II compared to the other two locations. This work can also be extended to a more complex air conditioning system like in the industries, hospitals as well as the gigantic shopping malls. r 2006 Elsevier Ltd. All rights reserved. Keywords: Temperature distribution; Velocity distribution; Virtual planes; k–epsilon; Reynolds stress; Maximum comfort
1. Introduction As the standard of living is increasing, more and more people are seeking for a comfortable living whether in work or at rest. Air conditioner has become a popular comfortproviding device since two decades. It has become a need for everyone, whether in an office or home especially for warm and wet climate countries like Malaysia. People are seeking for more comfortable working environment in order to perform their duties well. Main objective of an air conditioning system, in general, is to provide the maximum comfort to the entire air conditioning area. To achieve this objective, an analysis of performance of the cooling machine will be subsequently insufficient. Scope should be widening to an analysis of airflow over the entire air conditioning system [1]. Therefore, the design of air conditioning system no longer focuses on the effectiveness of cooling machine alone. Much research has been carried Corresponding author. Tel.: +604 5995999 x 6369; fax: +604 5941025. E-mail address: [email protected] (I.A. Badruddin).
0360-1323/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2006.01.002
out in this field. Using computational fluid dynamics (CFD) will probably not replace physical experiments completely but it can significantly reduce the amount of experimental work. This tool is capable for analyzing the flow pattern of the air conditioning system in short span of time, which was previously impossible from experimental and theoretical methods [2]. Moreover, CFD gives virtual distribution of airflow, temperature, etc. in entire domain which is highly difficult to get from experiments because of time and cost involved. Unfortunately, there is no universal flow model to represent the entire flow pattern for the air conditioning system [3]. Recently, research has been carried out in relation to airflow in an air conditioning room. Heating, ventilating and air conditioning (HVAC) have been analyzed by Mathews et al. [4] for the use of human science building (HSB) at the University of Pretoria wherein there is a saving of 60% in power consumption. Besides, indoor humidity behaviors associated with decoupled cooling in hot and humid climates have been analyzed by Zhang and Niu [5]. Cheong et al. [6] have carried out a research on the dispersion of contaminants in an office environment using
ARTICLE IN PRESS O. Yongson et al. / Building and Environment 42 (2007) 1531–1537
1532
Nomenclature N a n r t u v w t P e k e mt Gk Gb YM
number of hexahedron cells grid spacing number of nodes density of fluid time velocity magnitude in x direction velocity magnitude in y direction velocity magnitude in z direction shear stress pressure internal energy turbulent kinetic energy rate of dissipation turbulent viscosity generation of turbulent kinetic energy due to the mean velocity gradients generation of turbulent kinetic energy due to buoyancy contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate
empirical and modeling techniques. Thermal comfort parameters were measured at predetermined grid points within a virtual plane to predict the airflow pattern of supply air jet, as well as to determine the occurrence of thermal stratification in office space by Sekhar and Ching [7]. In the present paper, the analysis is carried out for an air conditioning system for a single room using CFD. The distribution of various parameters like temperature and velocity has been studied to determine the best placement location for air conditioner blower and also the area which is suitable for the occupant. 2. Modeling 2.1. Interior design A standard room model of a single office room, which contains information of floor plans, has been taken from a standard reference book [8]. The width (y-direction); length (x-direction) and height (z-direction) are 2.7; 3.7 and 3.0 m, respectively, which is shown in Fig. 1(a). Formally there is no fixed arrangement for the furniture. It will depend on the style and the favorites of the occupant of the room itself. Subsequently, an idea of the furniture arrangement including the placement location of cabinet or shelf, table and chair is generated as given in the book [9] of interior design, which is shown in Fig. 1(a).
Prandtl number Prt C1e , C2e, C3e constants used in turbulent model sk turbulent Prandtl numbers for k se turbulent Prandtl numbers for e E total energy (tij)eff deviatoric stress tensor T temperature cp specific heat capacity at constant pressure Cij convection term in Reynolds stress transportation equation DTij turbulent diffusion term in Reynolds stress transportation equation (RSTE) DLij molecular diffusion term in RSTE Pij stress production term in RSTE Gij buoyancy production term in RSTE fij pressure strain term in RSTE eij dissipation term in RSTE Fij production by system rotation term in RSTE m dynamic viscosity I number of iterations
locations, which have been named as locations I, II and III as shown in Fig. 1(b)–(d), respectively.
2.3. Governing equations There are three groups of basic equations, which are derived from three basic physics laws of conservation. The mass conservation, momentum conservation and energy conservation results in the continuity equation, Navier– Stokes equation and energy equation, respectively. Since the flow in an air conditioning room is turbulent flow [10], the k–epsilon and the Reynolds stress viscous models have been chosen for investigation. The standard k–epsilon model is a semi-empirical model based on model transport equations for the turbulent kinetic energy (k) and its dissipation rate (e). The transport equation for k is derived from the exact equation, while the transport equation for e is obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart. The turbulent kinetic energy, k, and its rate of dissipation, e, are obtained from the following transport equations: Dk q mt qk r ¼ mþ (1) þ G k þ G b re Y M , Dt qxi sk qxi
2.2. Blower placement r For a single office room, normally a split unit will be used. There are three most suitable blower placement
De q ¼ Dt qxi
m qe e e2 mþ t þ C 1e ðG k þ C 3e Gb Þ C 2e r . k se qxi k (2)
ARTICLE IN PRESS O. Yongson et al. / Building and Environment 42 (2007) 1531–1537
1533
Fig. 1. The sketch of the room model: (a) coordinate system for the entire room; (b) blower placement in location I; (c) blower placement in location II and (d) blower placement in location III.
Convective heat and mass transfer modeling in the k–epsilon models is given by the following: q q ðrEÞ þ ½ui ðrE þ pÞ qt qxi cp mt qT q ¼ kþ þ uj ðtij Þeff þ S h . qxi Prt qxi
r
De q ¼ Dt qxj
mþ
mt qe 1 e e2 þ C e1 ½Pii þ C e3 G ii C e2 r . se qxj k 2 k
(6) ð3Þ
Abandoning the isotropic eddy-viscosity hypothesis, the Reynolds stress model (RSM) closes the Reynolds-averaged Navier–Stokes equations by solving transport equations for the Reynolds stresses, together with an equation for the dissipation rate. This means that four additional transport equations are required in two-dimensional flows and seven additional transport equations must be solved in three-dimensional flows. Since the RSM accounts for the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate in a more rigorous manner than oneequation and two-equation models, it has greater potential to give accurate predictions for complex flows. The exact transport equations for the transport of the Reynolds stresses, rui uj , may be written as follows: q ðrui uj Þ þ C ij ¼ DTij þ DLij þ Pij þ Gij þ fij þ eij þ F ij . qt (4) The turbulent kinetic energy, k, and its rate of dissipation, e, are obtained from the following transport equations: Dk q m qk 1 ¼ r mþ t þ ðPii þ G ii Þ reð1 þ 2M 2t Þ, Dt qxj 2 sk qxi (5)
The convective heat and mass transfer modeling in the Reynolds stress models will be same as k–epsilon model, which is given by the following relation: q q ðrEÞ þ ½ui ðrE þ pÞ qt qxi cp mt qT q ¼ kþ þ uj ðtij Þeff þ Sh . qxi Prt qxi
ð7Þ
To solve these equations, initial and boundary condition must be specified around the boundary of system (domain). Because the equations are highly nonlinear, they are not solvable by explicit, closed-form analytical methods. The numerical finite volume method as used in Fluent has been used for solving the equations. The domain is discretized into cells or elements and nodal points are defined. Upon solution of the equations, the values of the dependent variables are known at the nodal points. The values of some constants in the differential equations are given in Table 1. All slandered values have been used for simulation purpose. 2.4. Boundary conditions Fig. 2 shows the circulation of air through the blower. Hot air enters surface (ABCD) and cool air flows out from the blower at surface (CDEF).
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1534 Table 1 Default values for some constants
Table 2 Number of hexahedron cells and nodes
Model constants
k–e
RSM
Grid spacing, a (cm)
15
10
7.5
Cm C 1e C 2e Cs C1 C2 C10 C20 sk se
0.09 1.44 1.92 – – – – – 1 1.3
0.09 1.44 1.92 0.22 1.8 0.6 0.5 0.3 1 1.3
Number of hexahedron cell, N Number of node, n
7988 9453
26 706 29 934
64 440 70 196
Table 3 The location of virtual planes Surface name
Plane equation (cm)
z-top z-central z-bottom x-central x-front y-left x-back y-right
z ¼ 210 z ¼ 100 z ¼ 40 x ¼ 130 x ¼ 310 y ¼ 80 x ¼ 70 y ¼ 220
2.6. Virtual planes
Fig. 2. The airflow in and out at the blower.
The boundary condition of each surface is as follows.
Inlet (surface CDEF) J Velocity magnitude ¼ 5 m/s Velocity direction at xcomponent ¼ 1 ycomponent ¼ 0
) For location I:
zcomponent ¼ 1
For locations II and III, cool air flows in the direction same as location I (451 down from surface CDEF relative to the blower). J Temperature ¼ 295 K. Outlet (surface ABCD) J Gauge pressure ¼ 0 Pa. J Temperature ¼ 300 K. Other walls (including surface at blower, surface of furniture and wall of the room) J Temperature ¼ 300 K.
2.5. Grid spacing There are various types of cells, which can be used for meshing purpose. The available three-dimensional cell types are tetrahedron, hexahedron, prism as well as pyramid. The hexahedron cell has been chosen due to its homogeneity with the room model. The three types of grid spacing are 15 cm (coarse), 10 cm (medium) and 7.5 cm (fine). Table 2 shows the number of hexahedron cells with respect to their grid spacing or mesh size.
The simulated description will contain parameters such as temperature, velocity, pressure, etc. in every location point in the entire flow volume, which is in three dimensions. Present method gives a general picture for the comfort in room. For swing attached, the analysis will be complicated and is a function of time. Thus, it is assumed that the air flows at 451 from blower. For presenting the results in a simple way, eight planes have been designated which can be in horizontal and vertical directions in order to view the information clearly on entire volume. Table 3 shows the location of the virtual planes that have been created. 2.7. Residual The accuracy in the CFD simulation is obtained in terms of residual. Residual is the measurement of the error. The smaller the residual, the smaller is the error. Fig. 3 shows the plot of residuals versus number of iterations for model (RSM 10-1) with the Reynolds stress viscous model; grid spacing of 10 cm and the blower location at location I. While observing the variation of residual with respect to number of iterations, the residual keeps on decreasing from the start to around 800 iterations. Then, the residual remains same although the numbers of iterations have increased. The iteration has been stopped since there is no variation in the result. This has been applied to all the simulated models. 3. Results and discussion 3.1. Comparison of viscous models There are two types of viscous models to be considered, which are k–epsilon and Reynolds stress model. It is important to make sure that the suitable viscous model is
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Fig. 3. Residual plotting for RSM 10-1 model.
applied to the model to be simulated. So, a model where the blower is placed in location I is chosen for investigating the variation of temperature over a selective virtual surface, z-top. It is seen from Fig. 4 that all the contours are different from each other except for Figs. 4(e) and (f), which are nearly the same. Therefore, Reynolds stress model for grid spacing of 10 and 7.5 cm gives almost identical results. Based on the independence of grid spacing, Reynolds stress model is considered as a better viscous model and has been chosen for simulation of airflow for other blower placement locations. The computational time also is another factor to be considered while dealing with the long time simulation. The simulation times for all models are shown in Table 4. Even though simulation time for Reynolds stress models is nearly twice simulation time of k–epsilon models, Reynolds stress model is chosen for further analysis, as it is grid independent. The computational time of Reynolds stress model for grid spacing 7.5 cm (10.0 h) is 4.5 times more than the spacing of 10 cm (2.2 h). There is not much difference with respect to their temperature contours between mesh spacing of 10 and 7.5 cm for Reynolds stress model. Hence, the 10 cm mesh spacing has been chosen for further simulation.
3.2. Suitable blower placement location To observe the suitable position of blower placement, analysis of eight virtual planes has been carried out for locations I, II and III. Among the planes, the z-center plane is the most important plane since it represents the condition of the room well. The suitable blower location also can be found out by investigating the various parameter distributions over the various planes. Parameters like velocity magnitude and temperature have been analyzed as done by Ladeinde and Nearon [11]. Among the planes that have been studied, z-center is the best plane to view the temperature as well as velocity magnitude distribution in horizontal direction near the occupant. It
Fig. 4. Comparison between k–epsilon and Reynolds stress for temperature distribution at specified z–top plane with grid spacing. All values are in degree Kelvin.
Table 4 Computational time for various models Viscous model k–epsilon Grid spacing (cm) Computational time (h) Number of iterations, I
15 0.2 600
10 1.0 700
Reynolds stress 7.5 4.5 1100
15 0.4 700
10 2.2 1000
7.5 10.0 1400
is also suitable to predict the temperature and velocity magnitude distribution over the entire room. By observing the velocity magnitude over various planes for blower placement in locations I, II and III, as in Fig. 5 the air velocity around the occupant and table are in the range of 0.4–1.5 m/s (highlighted with dotted outline square in indicator bar). This is the criterion for ‘weak wind’, which is the most comfortable velocity magnitude to the occupant. The distribution of velocity magnitude over the entire z-center plane for locations I, II and III are shown in Fig. 5(a)–(c), respectively. From Fig. 5(a), it is seen that the occupant experience about 1.0 m/s velocity. Besides, in Fig. 5(b), the occupant experience 1.25 m/s wind while the blower is placed in location II. For Fig. 5(c), the occupant experience 1.0 m/s wind. Locations I–III are acceptable from velocity magnitude criteria. In order to get a better visualization of the circulation of airflow in the room, vectors have been plotted over the three important planes, which are perpendicular to the z-axis. The vector
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Fig. 7. Velocity vectors when air passing through occupant (plane at centre of z-axis). Fig. 5. Velocity magnitude distribution over a virtual surface z-center for blower: (a) location I; (b) location II and (c) location III. All values are in meter per second.
Fig. 8. Temperature distribution over a virtual surface z-center for blower: (a) location I; (b) location II and (c) location III. All values are in degree Kelvin. Fig. 6. Three-dimensional view of velocity vectors for three horizontal plane perpendicular to z-axis.
shows the direction of the airflow on the particular plane in three dimensions as well as the magnitude. As shown in Fig. 6, the air is flowing almost downward near the area where occupant sits. The directions of the airflow slowly change to horizontal component while moving further away from the occupant. The magnitude of the air velocity is high on the top plane and getting reduced when it flows downward to the occupant as shown in Fig. 6. Components of vectors are also plotted on the most critical center plane, when air is passing through the body of the occupant (Fig. 7). The components vectors are small in magnitude close to the occupant, whereas the vector magnitude increases while getting further away from the occupant. It can be seen from this figure that the occupant area is a comfortable zone to sit since smaller vector magnitude are desirable to avoid disturbance due to wind. As shown in Fig. 7, the air is flowing back to the blower on the right-hand side of the occupant. For temperature criteria, the temperature for comfort should be in the range of 20–25 1C. All the three-blower
placement locations fulfill this criterion. But to reduce the size of compressor, it seems to choose a location that will provide the coolest region near the occupant. It saves cost with smaller compressor and consumes lower power, at the same time provides comfort to the occupant. If the blower is placed in location I, the temperature is distributed more or less uniformly over the entire room as shown in Fig. 8(a), but the occupant is not sitting in the coolest region of the entire room. So, a better position of the blower should be found since this is not the best position. By referring to Fig. 8(b) where the blower is placed in location II, although the temperature is not uniformly distributed over the entire room, but it satisfies the requirement of air conditioning office room. Basically, the room can be divided into two portions, which are the hot region (right-hand side of Fig. 8(b)) and cool region (left-hand side of Fig. 8(b)). The hot region is located in a space that is seldom used by occupant while the cool region is the space that always is occupied by the occupant. Basically, the occupant will experience about 296.3 K (23.3 1C). On the other hand, the occupant is sitting near the coolest region in the entire room as in Fig. 8(b). So, this will be the best position to place the air conditioner blower.
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Next, the location III is analyzed. The occupant is sitting in the hottest region of the entire room as shown in the Fig. 8(c). So, this location is totally not effective and is the worst among the three possible locations that have been discussed. Since this is a three-dimensional case, the temperature distributions for other virtual planes have also been investigated. It is observed that placement in location II will provide the maximum comfort for the occupant or in other words, occupant experience the coolest temperature when the blower is located in location II. Hence, location II will be the suitable location for the blower placement. 3.3. Comfort region Previously, the furniture arrangement is fixed and the problem is to find the suitable blower placement location. Now is the other way around. The same models stated in previous sections are used to locate the comfort region or coolest region for energy saving as stated before. As shown in the plan view in Fig. 6, the dotted outline square covers the cool region (contours are blue in color) for the entire room for three possible blower placement locations. This is applicable to help the furniture arrangement of an air conditioning room. While the blower is placed in location I, almost the entire room is in blue color contours. It is seen that almost the whole area has cool condition while the occupant can be located center left by referring to Fig. 8(a). This will be the suitable location when this room is used for living room or multiple functional hall while there is a need to cool the entire room. For location II, the cool region is smaller compared to the location I. The cool air is just concentrated at the left side of the plan as shown in Fig. 8(b). The rest of the room is not cooled. The location III manages to keep the upper center region cool as shown in Fig. 8(c). By this way, the position of the occupant can be determined which is the right place to sit on while the air conditioner blower is already fixed. With CFD method, the flows characteristics can easily be predicted and can be compared with the experimental method, where the sophisticated measurement instrumentation must be provided.
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4. Conclusion 1. Between Reynolds stress model and k–epsilon model, Reynolds stress model seem to be grid independent than k–epsilon model for the three-grid spacing investigated. Although simulation of Reynolds stress model takes a longer time compared to the k–epsilon model, but mesh spacing independency seem to be more significant. 2. Location II is found to be the most suitable location to place the air conditioner blower. The temperature distribution shows that the occupant is seated in the cool region. 3. The occupant will experience most cool region if the air conditioner blower is placed on location II compared to the other two locations. 4. This work can also be extended to a more complex air conditioning system like in the industries, hospitals as well as the gigantic shopping malls. References [1] Haines RW. Control system for heating, ventilating and air conditioning. 2nd ed. New York: Van Nostrand Reinhold; 1977. [2] Anderson JD. Computational fluid dynamics. International Edition. New York: McGraw-Hill; 1995. [3] Baker AJ, Richard MK, Eliott BG, Subrata Roy, Edward GS. Computational fluid dynamics: a two-edged sword. ASHRAE Journal 1997:51–8. [4] Mathews EH, Botha CP, Malan A. HVAC control strategies to enhance comfort and minimise energy usage. Energy and Buildings 2001;33:853–63. [5] Zhang LZ, Niu JL. Indoor humidity behaviors associated with decoupled cooling in hot and humid climates. Building and Environment 2003;38:99–107. [6] Cheong KWD, Djunaedy E, Poh TK, Tham KW, Sekhar SC, Wong NH, et al. Measurements and computations contaminant’s distribution in an office room. Building and Environment 2003;38:135–45. [7] Sekhar SC, Ching CS. Indoor air quality and thermal comfort studies of an under-floor air-conditioning system in the tropics. Energy and Buildings 2002;34:431–44. [8] Jerold LA. Architectural plan for adding on or remodeling. TAB Books; 1992. [9] Wong J. The modern design for living. Taiwan: Wanibooks/ Sharppoint; 1995. [10] Su M, Chen Q, Chiang C-M. Comparison of different subgrid-scale models of large Eddy simulation for indoor airflow modeling. Journal of Fluids Engineering Transactions of the ASME 2001;123:628–39. [11] Ladeinde F, Michelle DN. CFD applications in the HVAC & R Industry. ASHRAE Journal 1997;1:44–8.