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A simplified numerical study on the energy performance and thermal environment of a bedroom TAC system
Accepted Manuscript
A simplified numerical study on the energy performance and thermal environment of a bedroom TAC system Mao Ning , Zhang Bin , Song Mengjie , Deng Shiming PII: DOI: Reference:
S0378-7788(17)33600-9 10.1016/j.enbuild.2018.02.018 ENB 8334
To appear in:
Energy & Buildings
Received date: Revised date: Accepted date:
2 November 2017 20 January 2018 2 February 2018
Please cite this article as: Mao Ning , Zhang Bin , Song Mengjie , Deng Shiming , A simplified numerical study on the energy performance and thermal environment of a bedroom TAC system, Energy & Buildings (2018), doi: 10.1016/j.enbuild.2018.02.018
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Highlights A simplified numerical study was carried out The thermal and energy performance of TAC in bedrooms were evaluated RSM method was used to build predictive models of indoor thermal environment
The predicted results using CFD and RSM methods were compared
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A simplified numerical study on the energy performance and thermal environment of a bedroom TAC system Mao Ning1, Zhang Bin2, Song Mengjie3*, Deng Shiming4 1
Department of Gas Engineering, College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao, China 2
School of Civil Engineering & Architecture, Linyi University, Linyi, China
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Department of Human and Engineered Environmental Studies, Graduate School of Frontier
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Sciences, The University of Tokyo, Chiba, Japan 4
Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China
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Abstract
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In subtropics, the higher energy consumption of air conditioning system in summer period brought about the application of task/ambient air conditioning (TAC) systems,
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not only in commercial buildings, but also in residential buildings. To better assess the
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performance of the TAC system, a numerical study was carried out to predict the
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energy and thermal performance of a bedroom TAC system in a bedroom in
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subtropical area. To conveniently predict the indoor thermal environment, response surface methodology (RSM) was applied to simplify the procedure of numerical simulation. Firstly, CFD study was carried out to evaluate the thermal and energy performance of the TAC system. Secondly, RSM method was used to establish the predictive models of important index of indoor thermal environment to form the simplified numerical method. Thirdly, these two methods were used and the predicted 2
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values were compared. It was found that the energy consumption was reduced from 260 W to 160 W when the ts was increased from 19 ºC to 23 ºC, and the averaged draft risk (DRoz) reached at 20% when the Qs was set at 110 l/s. The significant
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vertical non-uniformity of air temperature, air velocity and relative humidity were also reported. Besides, the CFD method was compared with the simplified numerical method (RSM method). It was found that the maximum deviation between using the
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RSM and CFD methods was less than 5% in predicting energy consumption, draft risk, thermal parameters in the occupied zone, stratified air temperature and stratified air relative humidity. Overall, the simplified numerical method (CFD based RSM method)
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can predict the indoor thermal environment accurately.
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Keywords
Task/ambient air conditioning (TAC) systems, Response surface methodology (RSM),
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Indoor thermal environment, Energy consumption, Stratified thermal parameter, CFD
Corresponding author: Dr. SONG Mengjie (JSPS Researcher) Department of Human and Engineered Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan E-mail: [email protected]
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Nomenclature
Specific heat at constant pressure Draft risk Averaged DR in the occupied zone Metabolic heat production Energy consumption
Qs RHoz RH0.1 RH0.6 RH1.1 RH1.7 t toz tr
Supply air flow rate Averaged relative humidity in the occupied zone Averaged relative humidity at height of 0.1 m Averaged relative humidity at height of 0.6 m Averaged relative humidity at height of 1.1 m Averaged relative humidity at height of 1.7 m Air temperature at a measurement position Average air temperature in an occupied zone Return air temperature
l/s % % % % % ºC ºC ºC
ts tsk t0.1 t0.6 t1.1 t1.7 voz
Supply air temperature Mean skin temperature Averaged air temperature at height of 0.1 m Averaged air temperature at height of 0.6 m Averaged air temperature at height of 1.1 m Averaged air temperature at height of 1.7 m Air velocity in an occupied zone
ºC ºC ºC ºC ºC ºC m/s
v0.1 v0.6
Averaged air velocity at height of 0.1 m Averaged air velocity at height of 0.6 m
m/s m/s
v1.1 v1.7 ρ Tu
Averaged air velocity at height of 1.1 m Averaged air velocity at height of 1.7 m Air density Turbulence intensity
m/s m/s kg/m3 -
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Abbreviation ADPI
Air Diffusion Performance Index
CFD DR PMV
Computational fluid dynamics Draft risk Predicted Mean Vote 4
J/(kg·K) % % W/m2 W
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Cp DR DRoz M Qc
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RSM TAC
Response surface methodology Task/ambient air conditioning
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1 Introduction
Bedrooms in residential buildings are important places for human beings’ relaxation and body recovery, which are critically affected by the indoor thermal environment.
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Therefore, investigations into the indoor thermal environment inside residential buildings have attracted more and more researchers recently [1, 2, 3, 4]. For the last two decades, to provide a suitable thermal environment, task/ambient air conditioning (TAC) systems, due to their better performance in terms of energy saving and flexible
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control over thermal environments [5, 6], had attracted continuous attentions.
The indoor thermal environment mainly includes parameters: air temperature, air
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velocity and relative humidity in the room [7]. Parts of these previous studies are related to the thermal parameters in the occupied zone around the people. Ho et al. [8]
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investigated the occupied zone in an office with an underfloor air distribution systems.
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The moderate temperature zones around the person and suitable relative humidity were found. Corgnati et al. [9] carried out experiments to study the jet flow in the occupied zone, and studied the maximum DR in the occupied zone. Ye et al. [10] investigated the energy consumption of impinging jet ventilation. At different supply conditions, the averaged air temperature in the occupied zone was calculated, and heat loss rate of the occupied zone was computed. Cheng [11] studied the temperature distribution of the clothing surface of a thermal manikin in an office with different 5
ACCEPTED MANUSCRIPT ventilation systems: mixing and displacement. It is revealed that the decreased temperature may benefit to the thermal comfort of human body. Other than these studies on thermal environment in a ventilated room, some researchers investigated some specified space equipped with task/ambient conditioning (TAC) system. Mao et al. [12] investigated a bed based TAC system through experiments and numerical
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simulation. The air temperature, air velocity and relative humidity distribution in the occupied zone were calculated to evaluate the thermal performance of the TAC system. Pan et al. also [13] used PMV in the occupied zone to evaluate the thermal comfort of a novel bedroom TAC system compared with a full volume air
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conditioning system. Those researches indicate the importance of thermal environment in a room with ventilation or TAC system.
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About the studies on the indoor thermal environment, Computational fluid dynamics (CFD) is an important tool, which can simultaneously predict airflow and heat
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transfer in buildings [14, 15]. The information provided by CFD can be used to
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evaluate the thermal environment and energy saving performance of air conditioning systems in buildings. A lot of works has been conducted on velocity, temperature and
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humidity distributions using CFD methods [16, 17, 12]. On the other hand, the energy consumption and thermal comfort were also investigated using CFD method
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[ 18 , 19 ]. Those previous researches showed good agreements between the computational results and the experimental data. Although CFD method is the most suitable solution save time compared with the experiments, it still cost a lot of time if many factors need to be studied. For example, Mao et al. [20] carried out numerical study on the influence of envelope heat gain on indoor thermal environment in a bedroom. In this study, 90 simulation cases were designed and investigated. Pan et al. 6
ACCEPTED MANUSCRIPT [13] carried out 28 CFD simulation cases to investigate the task ambient air conditioning system, and evaluate the thermal comfort and energy saving performance of the system. The conduction on the large number of simulation cases cost lots of time and need complicated computation system. Therefore, it’s necessary
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to develop new method to simplify the study on indoor thermal environment.
In some previously studies on space cooling, Response surface methodology (RSM) as a regression method was used to simplify the study process. RSM is a mathematical and statistical technique which builds a polynomial equation based on
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the experimental data and helps to describe the behavior of a data set. Its objective is to make statistical previsions. RSM method can be well applied to the conditions which are influenced by several variables [21]. In statistics, RSM method predicts the
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relationships between several explanatory parameters and one or more response variable [22]. RSM method has been effectively used in area related to refrigeration,
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fluid dynamics and building environment. Geppert and Stamminger [23] studied the
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factors influencing energy consumption of a domestic refrigerators using RSM method. A second-order polynomial equation was established for the energy
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consumption. The results show that the RSM method was effective for understanding the effects of factors. Ng et al. [24] studied the air diffusion in a displacement
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ventilated office, and used RSM method to build the model of ADPI to investigate the effect of exhaust position, diffuser and supply temperature on air diffusion. In these studies, RSM gives a good prediction conveniently and describes behavior of a response variable when two or more design variables are varied simultaneously.
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ACCEPTED MANUSCRIPT As mentioned above, using the CFD method to investigate the energy utilization and thermal performance of a bedroom TAC system may require lots of time and high computing capacity. Therefore, the aim of this study was to develop a simplified numerical method based on the traditional CFD method. The key problem of the simplified numerical method was to establish relationship between the thermal
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performance variables and the operating parameters. Firstly, a TAC system in bedrooms in a typical residential building of Hong Kong was developed. Secondly, CFD method was used to evaluate the thermal and energy performance of the TAC system. Thirdly, RSM method was used to develop a simplified numerical method to
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evaluate the performance of TAC system. Finally, the two methods were compared and analyzed.
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2 Methodology
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The methodology used in this study is schematically shown in Fig. 1. The objective of
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the current study is to propose a simple method to predict the indoor thermal environment inside residential buildings. To validate this method, more CFD
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simulation cases were carried out and compared with the results predicted by the simple prediction method. In this study, firstly, a CFD model to simulate a bedroom
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thermal environment was developed, and validated by the previous experimental data. Secondly, according to the ranges of supply air temperature and supply air flow rate [25, 26, 27], simulation cases used to build prediction models were determined through a full-factorial design approach. And then, the air flow characteristics inside the bedroom were calculated using a CFD method. The energy consumption (Qc) and thermal comfort (draft risk), thermal parameters (air temperature, air velocity and 8
ACCEPTED MANUSCRIPT relative humidity) in the occupied zone, and stratified thermal parameters inside the bedroom were obtained at different cases. Thirdly, based on these simulation results, the relationship between the PMV, Qc, DR, thermal parameters and operating parameters (Qs, ts) were established, and prediction equations obtained. Fourthly, to validate these prediction equations, more simulation cases were carried out with
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different Qs and Ts. The simulation results in aspects of energy consumption, thermal comfort and thermal parameters were compared with the results obtained by the
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prediction equations.
CFD method
Validation
Factorial Design
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Simulation cases
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Experimental data
Ts (19, 19.5, 20, 20.5, 21, 22, 22.5, 23 ºC)
Simulation cases
Qs (50, 60, 70, 80, 90, 100, 110 l/s)
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(2 parameters, 3 levels)
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RSM method
Predictive models
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Qc comparison DR toz , voz , RHoz t0.1 , t0.6 , t1.1 , t1.7 v0.1 , v0.6 , v1.1 , v1.7 RH0.1 , RH0.6 , RH1.1 , RH1.7
• • • •
Energy consumption Draft risk Thermal parameters (occupied zone) Stratified thermal parameters
Simplified numerical method
Fig. 1 Schematic of the methodology 9
ACCEPTED MANUSCRIPT 2.1 CFD method and numerical study
Computational fluid dynamics (CFD) has been widely used in building HVAC related studies to simulate indoor air flow, indoor air temperatures and indoor air quality, etc. [28, 29, 30, 31, 32]. Different from experiments, which only get limited data on
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temperature and velocity inside an experimental space, CFD can simultaneously predict more detailed information of airflow and heat transfer in buildings.
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2.1.1 Geometry model
A bedroom was built and investigated in this study. Experiments were carried out in the bedroom for validation of the CFD results. A task ambient air conditioning system
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was located in the bedroom. The system consists of a supply air outlet, a return air inlet, a bed and a thermal manikin. The supply air outlet (0.57 × 0.21 m) was placed at
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1.1 m above the floor level, and the return air inlet (0.37 × 0.16 m) at 0.32 m, as
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shown in Fig. 2. A cuboid was designated as an occupied zone according to previous studies [33, 34], and the rest of the space inside the bedroom an unoccupied zone, as
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shown in Fig. 2. A thermal manikin consisting of 16 different body parts was placed on the bed to assemble a sleeping person [33]. The surface temperature and heat loss
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of different body parts were measured. Seven measurement locations in the unoccupied zone and six in the occupied zone were identified, as shown in Fig. 2(b). In the unoccupied zone, air dry-bulb temperature, wet-bulb temperature and air velocity were measured at four heights, 0.1 m, 0.6 m, 1.1 m and 1.7 m above floor level, at each of these locations [35]. Inside the occupied zone, the above parameters were measured at 0.8 m and 1.0 m above floor level in each of the six locations. To 10
ACCEPTED MANUSCRIPT simulate the bedroom, a geometry model was established and the corresponding grids was generated using ANSYS ICEM [36], as shown in Fig. 2 [12]. Mesh was respectively generated for the occupied zone and the unoccupied zone, as shown in Fig. 2(c). Prism mesh was generated on the surface of the thermal manikin, as shown
620 External wall
Unoccupied zone
Front wall
400
Occupied zone
Supply air outlet
1250
900
L
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(a) Geometry
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425 N
100
K
900
3600 mm
475
460
Return air inlet
580 mm
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F
E
D
Bed
600 mm
500
1250
475
Thermal manikin
2530 mm
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in Fig. 2(d). More related detailed information can be found in reference [37].
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1840
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A
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(b) Measurement locations
(c) Sectional view of the mesh
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(d) Detailed mesh structure
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Fig. 2 The simulated bedroom with TAC system
2.1.2 CFD model
A commercial CFD code ANSYS Fluent [38] was used to compute the thermal environment inside the bedroom. The air flow field was calculated by the three-dimensional and steady-state Reynolds averaged Navier-Stokes (RANS) 11
ACCEPTED MANUSCRIPT equations, combined with continuity and energy equations. The SIMPLE algorithm was used to compute the convective terms with a second order scheme. The SST turbulence model [39] was used for modeling the turbulent flow due to its best performance for predicting air velocity and temperature distributions inside a room [40, 41]. To predict the moisture transfer between the surface of the thermal manikin
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and its surrounding environments, a species transport model was used. The surface-to-surface (S2S) radiation model was used to compute the radiation heat exchange among the surfaces in the bedroom [12, 42].
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2.1.3 Boundary conditions
The CFD model was solved using boundary conditions including temperature,
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velocity and radiation values at the supply air outlet, return air inlet and bedroom wall, which were detailed in previous studies [43], and thermal manikin skin temperature,
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and moisture concentration. Mean skin surface temperature, tsk, was an important
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factor influencing human’s thermal sensation. Fanger [ 44 ] proposed a linear regression equation to evaluate the value of tsk, as shown in Equation (1). According
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to ASHRAE Standard [45], the metabolic rate (M) of a sleeping person is 40 W/m2,
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and the workload (W) is zero, therefore, the mean skin temperature would be 34.6 ºC.
tsk 35.7 0.0275(M W )
(1)
To predict the moisture transfer between the surface of the thermal manikin and the surrounding environment, air moisture content was taken as 10 g/kg air at the surfaces of the thermal manikin according a previous study [46]. The gradient of air moisture 12
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Table 1 Boundary conditions of the CFD method Item Boundary Conditions 1 Supply outlet Air velocity (0.43 - 0.94 m/s), air temperatures (19 - 23 ºC) 2 Return inlet Pressure outlet 3 Thermal manikin 16 body parts with fixed temperature, emissivity 0.07 [37] 4 External wall Outdoor surface temperature 30 ºC, emissivity 0.1, 5 Window Outdoor surface temperature 30 ºC, emissivity 0.94 6 Bed Adiabatic wall, emissivity of 0.77 7 Floor Adiabatic wall, emissivity of 0.2 8 Other walls Adiabatic wall, emissivity of 0.07
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2.1.4 Mesh independence
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Different mesh numbers were used to verify the independence of grids. Fig. 3 shows the predicted tuz for grid numbers of 0.8 million, 1.2 million, 1.6 million, 2 million
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and 2.4 million mesh elements. As seen, the obtained results varied with the increase
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in mesh number till 2.0 million. And then the computed tuz at 2.0 million
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approximates to that at 2.4 million. Therefore, the CFD simulation using mesh
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number of 2.0 million can be considered to be mesh independent.
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26.1 26.0 25.9
tuz (C)
25.8 25.7 25.6 25.5
25.3 25.2 0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Mesh elements (million)
2.2
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25.4
2.4
2.6
2.1.5 Validation of the CFD method
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Fig. 3 Computed tuz at different mesh numbers
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The CFD method was evaluated using previous experimental data [37]. Fig. 4 shows
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the comparisons of air temperature, air velocity values and relative humidity between the CFD and the experimental data, respectively. As seen in Fig. 4, the averaged
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absolute temperature differences between the measured and the simulated ones were 0.01 ºC at Location D and 0.02 ºC at Location L, and the averaged absolute velocity
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differences between the measured and the predicted ones were -0.03 m/s in the
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unoccupied zone and 0.09 m/s in the occupied zone, respectively. At location D, the numerically simulated relative humidity values were close to the measured ones. At location L, the measured relative humidity values were slightly lower than the numerically predicted ones. The maximum deviation of the relative humidity ratio is about 3%, which is acceptable for comparisons in this study. According to the suggestions in a previous study [47], the CFD method in this study was validated.
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2.0
2.0
2.0
Location D 1.8
1.6
1.6
1.6
1.4
1.4
1.4
1.2
1.2
1.2
0.8
0.4
Experiment CFD
0.2
1.0 0.8
0.6
0.4
0.4 0.2 0.0
0.0 24
25
26
27
28
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0.0 0.1 0.2 0.3 0.4 0.5 0.6
o
1.2
1.2
Location L
Location L
1.0
0.9
0.9
0.8
0.7
0.7
0.6
1.0
0.7
0.6
0.6
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23 24 25 26 27 28 29 30 o
Temperature ( C)
0.9
0.8
M
0.8
1.1
Height (m)
1.0
Location L
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1.1
Height (m)
1.1
0 10 20 30 40 50 60
Relative humidiy (%)
Velocity (m/s)
Temperature ( C)
1.2
0.8
0.6
0.2
0.0
1.0
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1.0
Height (m)
1.8
0.6
Height (m)
Location D
1.8
Height (m)
Height (m)
Location D
0.0
0.2
0.4
0.6
Velocity (m/s)
0.8
0 10 20 30 40 50 60
Relative humidity (%)
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Fig. 4 The comparison between numerically predicted and experimentally measured
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air temperature, velocity and relative humidity
2.1.6 Simulation cases
According to previous related studies, simulation cases at different supply air temperatures and supply air flow rates were designed and carried out. There were 15 cases designed. When the ts was set at 22 ºC, the Qs was set at from 50 to 110 l/s, with 15
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an interval of 10 l/s. When the Qs was set at 60 l/s, the ts was set at from 19 to 23 ºC, with an interval of 0.5 ºC. These cases were used to evaluate the energy and thermal performance of the TAC system.
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2.2 Simplified numerical study
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Response surface methodology (RSM) is a mathematical and statistical technique which builds a polynomial equation and helps to describe the behavior of a data set. The RSM method includes three steps: (1) design of experiment, (2) data collection
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on operating parameters.
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using CFD approach, (3) establishing predictive models of response variables based
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2.2.1 Factorial design
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A two-parameter three-level full-factorial approach for simulation was used to determine simulation cases, as shown in Table 2. The operating parameters, supply air temperature, supply air flow rate and envelope exterior wall temperature, were designated as the three parameters where using the full-factorial approach. Each of these parameters was studied at three levels: a low, middle and a high level. The range
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of the parameters was given based on previously related studies [37, 25]. The minimum number of simulation cases for the three-level two-parameter approach was
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therefore 32 or 9, as shown in Table 3.
Table 2 Design parameters and their three levels used in the study Parameters
Low level
Middle level
High level
19 50
21 80
23 110
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ts (ºC) Qs (l/s)
Table 3 Simulation matrix for the factorial design
Qs (l/s)
19 21 23 21 21 19 19 23
50 50 50 80 110 80 110 80
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110
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T23Q110
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T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80 T19Q110 T23Q80
ts (ºC)
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Case No.
2.2.2 Response variables
The objective of this study was to build predictive models using RSM method to predict the indoor thermal environment simply. The thermal environment can be
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represented using two types of variables: macroscopical and microcosmic types. The former includes energy consumption and thermal comfort, and the latter includes occupied zone thermal parameters (air temperature, air velocity and relative humidity)
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and stratified thermal parameters.
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(1) Energy consumption
In this study, cooling air was delivered into the bedroom, and flow back to return air inlet after being heated. Therefore, the energy consumed on cooling the indoor
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the bedroom, as follows:
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environment can be calculated using the energy variation of air entering and exiting
(2)
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Qc QsC p (ts tr )
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(2) Thermal comfort
Draft is an unwanted local cooling for a human body caused by air movement. Draft risk (DR) is a draft rating index used to predict the percentage of occupants feeling draft: DR=(34-t )(v-0.05)0.62 (0.37vTu +3.14)
(For v 0.05 m/s, use v=0.05m/s; For DR>100%, use DR=100%) [45, 48] 18
(3)
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ASHRAE Standard 55 [45] suggests that the value of DR in each measurement position should not be greater than a permissible value of 20%. The DR values
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obtained in the occupied zone were averaged to get the mean DR values represented using DRoz.
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(3) Indoor thermal parameters
As stated in Section of Introduction, the prediction of air temperature, air velocity and
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relative humidity in the occupied zone is very important to assess the thermal comfort
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level and energy consumption inside a room. In this study, the air temperatures in the
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occupied zone were computed using CFD model and averaged to get the averaged air temperature in the occupied zone (toz). The toz reflects the cooling effect of the task
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ambient air conditioning system [37]. At the same time, the computed air velocities
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were averaged to get the averaged air velocity in the occupied zone (voz). The computed relative humidity were averaged to get the averaged relative humidity in the occupied zone (RHoz).
Due to the effect of stratified thermal parameters on indoor thermal comfort, it’s 19
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necessary to investigate the air temperature, air velocity and relative humidity at different heights inside the bedroom. According to ASHRAE Standard and previous related studies [37], these parameters were calculated at heights of 0.1m, 0.6m, 1.1m
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and 1.7m above the floor level. The air temperatures, air velocities and relative humidity at each height were averaged to obtain the values at each height and were labeled using t0.1, t0.6, t1.1, t1.7, v0.1, v0.6, v1.1, v1.7, RH0.1, RH0.6, RH1.1 and RH1.7,
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respectively.
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3 Results and analysis
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3.1 Establishment of predictive model using the RSM method
Using the simulation cases in Table 3, the energy consumption, DR values are
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calculated according to Equations (2) and (3), and listed in Table 4. Besides, the air
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temperature, air velocity and relative humidity in the occupied zone and at different heights were averaged and summarized in Table 5-7.
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Table 4 Energy consumption and DR values Qc
DRoz
T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80
232.60 192.32 152.69 245.34 293.03 297.32
7.78 7.40 6.67 15.40 20.61 17.47
T19Q110 T23Q80 T23Q110
355.92 196.48 235.85
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Case No.
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23.42 13.45 17.89
Table 5 Air temperature in the occupied zone and at different heights toz (ºC)
t0.1 (ºC)
t0.6 (ºC)
t1.1 (ºC)
t1.7 (ºC)
T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80 T19Q110 T23Q80 T23Q110
23.03 23.99 25.11 22.64 22.23 21.14 20.56 24.21 23.89
22.22 23.63 25.10 23.13 22.86 21.55 21.26 24.72 24.50
23.09 24.20 25.47 23.26 22.91 21.78 21.33 24.76 24.55
24.99 25.70 26.34 24.09 23.56 22.87 22.18 25.36 24.95
26.73 27.24 27.69 26.08 23.55 25.35 24.17 26.85 25.68
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PT
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Case No.
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Table 6 Air velocity in the occupied zone and at different heights voz (m/s)
v0.1 (m/s)
v0.6 (m/s)
v1.1 (m/s)
v1.7 (m/s)
T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80
0.1440 0.1596 0.1689 0.3321 0.4767 0.3287
0.0640 0.0515 0.0487 0.0830 0.1261 0.0745
0.0394 0.0550 0.0538 0.1207 0.1910 0.1109
0.0135 0.0182 0.0218 0.0613 0.0864 0.0531
0.0067 0.0090 0.0113 0.0322 0.0556 0.0271
T19Q110 T23Q80 T23Q110
0.4720 0.3393 0.4849
0.1300 0.0950 0.1354
0.1938 0.1333 0.1959
0.0856 0.0637 0.0970
0.0648 0.0363 0.0567
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Case No.
Table 7 Relative humidity in the occupied zone and at different heights RHoz
RH0.1
T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80 T19Q110 T23Q80 T23Q110
54.78 60.04 66.11 59.11 58.89 53.40 53.14 65.53 65.32
54.67 60.21 66.41 59.75 59.53 54.15 53.95 65.94 65.70
RH0.6
RH1.1
RH1.7
55.58 60.93 66.87 59.97 59.56 54.52 53.99 66.14 65.75
54.78 60.36 66.40 59.65 59.21 54.16 53.59 65.87 65.47
53.70 59.29 65.46 58.72 58.66 53.07 52.85 65.11 65.14
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Case No.
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The aim of this study is to establish relationship between the response variables and the operating parameters. Therefore, considering the main effects of parameters and their two-parameter interactions, a second-order model was chosen. The model can be expressed as follows:
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Y X 0 X1ts X 2Qs X11ts 2 X 22Qs 2 X12tsQs
(4)
Where X1, X2… are regression coefficients.
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Analysis of variance (ANOVA) was performed and the significance of parameters were obtained based on the calculated P-values. The predictive models were obtained
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as follows:
Energy consumption
(5)
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Thermal comfort
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Qc 336.430 11.6844ts 5.6898Qs 0.002936Qs 2 0.1673tsQs
(6)
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DRoz 25.1665 0.585ts 0.8722Qs 0.001643Qs 2 0.01842tsQs
Thermal parameters in the occupied zone
toz 22.3496 0.29ts 0.2235Qs 5.24110 4 Qs 2 5.208 103 tsQs
voz 0.29 4.033 103 ts 8.128 103 Qs 1.7426 105 Qs 2
23
(7)
(8)
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RH oz 47.3057 1.1633ts 0.1594Qs 0.09167ts 2 4.074 10 4 Qs 2 3.542 103 tsQs
(9)
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Thermal parameters at different heights
(10)
t0.6 18.1899 0.4354ts 0.1529Qs 3.595 10 4 Qs 2 3.493 103 tsQs
(11)
t1.1 28.8989 0.07912ts 0.2500Qs 5.683 10 4 Qs 2 5.898 103 tsQs
(12)
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t0.1 11.2948 0.6561ts 0.06664Qs 1.415 10 4 Qs 2 1.480 103 tsQs
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t1.7 22.6464 0.3310ts 0.04589Qs
v0.6 0.1387 0.003238ts 0.002403Qs
(14)
(15)
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v0.1 0.6518 0.05222ts 0.002051Qs 0.0011ts 2 9.3889 106 Qs 2 8.625 105 tsQs
(13)
v1.1 0.1294 0.002525ts 0.002196Qs 6.2407 106 Qs 2
v1.7 0.1184 0.004708ts 0.001563Qs 2.3889 106 Qs 2 5.2917 105 tsQs
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(16)
(17)
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RH 0.1 33.8471 0.2957ts 0.03501Qs 0.07704ts 2 1.454 10 4 Qs 2
(18)
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RH0.6 41.5731 0.645ts 0.1059Qs 0.08042ts 2 2.630 10 4 Qs 2 1.958 103 tsQs (19)
(20)
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RH1.1 35.5054 0.355ts 0.05425Qs 0.07625ts 2 8.3333 105 Qs 2 0.001083tsQs
RH1.7 38.2050 0.6517ts 0.09489Qs 0.08292ts 2 0.0002407Qs 2 0.002208tsQs (21)
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3.2 Evaluation of energy performance
The energy consumption (Qc) were calculated and shown in Fig. 5. It was found that
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the energy consumption was decreased from 260 W to 160 W when the ts was
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increased from 19 ºC to 23 ºC, and was decreased from 259 W to 168 W when the Qs
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was decreased from 110 l/s t 50 l/s. At the same time, under the same operating conditions, Equation (5) established using RSM method was used to compute Qc values. The comparisons of the Qc values predicted by RSM and CFD methods were shown in Fig. 5. It can be found that the profiles by the two methods have the similar trend. The comparison shows that the maximum difference between using the two
25
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methods was 8.90 or 8.21 W, accounting for about 4% of the Qc value, and the averaged difference was 5.55 or 5.29 W, accounting for about 2% of the Qc value. This indicates that the RSM method agrees well with the CFD method for predicting
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Qc values.
300
CFD RSM
250
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Qc (W)
200
150
100
Difference Max: 8.90 Min: 2.24 Ave: 5.55
0 18
19
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50
20
21
22
23
24
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ts (C)
(a) at different ts values (Qs=60 l/s)
PT
300
250
CFD RSM
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Qc (W)
CE
200
150
100
Difference Max: 8.21 Min: 1.87 Ave: 5.29
50
0 40
50
60
70
80
90
100
110
120
Qs (l/s)
(b) at different Qs values (ts=22 ºC) Fig. 5 Comparison of predicted Qc between using RSM and CFD methods 26
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3.3 Evaluation of thermal performance
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3.3.1 Draft risk
The DRoz values were calculated based on the CFD results and shown in Fig. 6. As
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seen, the DRoz values were effectively reduced through increasing ts and decreasing Qs. Fig. 6(b) shows the variation of DRoz with increase in Qs. It was found that when the Qs was set at 110 l/s the DR reached at 20% which was much higher may cause
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thermal discomfort. This suggests that a higher supply air temperature and a lower
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supply air flow rate can guarantee a suitable thermally comfortable environment. Besides, DRoz values were also predicted using Equation (6) established by RSM
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method and compared with that using CFD method. It can be found that these curves
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have the same trend. The comparison shows that the maximum difference between the
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two methods was 0.56 in Fig. 6(a) or 0.47 in Fig. 6(b), accounting for about 5% of the DRoz value, and the averaged difference was 0.33 or 0.20, accounting for around 3% of the DRoz value. This suggests that the RSM method agrees well with the CFD method for predicting thermal comfort.
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20
CFD RSM
18 16
DRoz (%)
14 12 10 8 6
Difference Max: 0.56 Min: 0.08 Ave: 0.33
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4 2 0 18
19
20
21
22
23
ts (C)
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(a) at different ts values (Qs=60 l/s) 30
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CFD RSM
25
DRoz (%)
20
15
Difference Max: 0.47 Min: 0.03 Ave: 0.20
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10
5
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0 40
50
60
70
80
90
100
110
120
Qs (l/s)
PT
(b) at different Qs values (ts=22 ºC)
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Fig. 6 Comparison of predicted DRoz between using RSM and CFD methods
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3.3.2 Averaged thermal parameters in the occupied zone
The air temperature, air velocity and relative humidity at different ts and Qs were calculated using the CFD methods and shown in Figs. 7, 8 and 9, respectively.
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As shown in Fig. 7, the toz values were raised when the ts was increased, and the increase of ts by 4 ºC resulted in 2.5 ºC of increase in toz. Different from ts, the increase in Qs resulted in the decrease in toz. As seen, when the Qs was at a high level,
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the decrease in toz was slowed down. To evaluate the accuracy of the RSM in predicting air temperature, the toz values were compared with that calculated using Equation (7) established by RSM method. It was found that the maximum difference
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between using the two methods was 0.29 ºC where ts = 22 ºC and Qs = 50 l/s, accounting for about 1% of toz value. Furthermore, the profile of toz predicted using RSM method has the similar trend as that using CFD method, even no matter it’s
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linear in Fig. 7(a) or it’s curved in Fig. 7(b). This is due to the term of Q2 in Equation
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(7) that makes RSM method display curved profile. Considering trend of profile and
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zone.
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values of toz, RSM performs well in predicting the air temperature in the occupied
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25.0
CFD RSM
24.5 24.0
toz (C)
23.5 23.0
Difference Max: 0.17 Min: 0.06 Ave: 0.11
22.5
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22.0 21.5 18
19
20
21
22
23
ts (C)
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(a) at different ts values (Qs=60 l/s) 25.0
CFD RSM
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24.5
toz (C)
24.0 23.5 23.0
Difference Max: 0.29 Min: 0.00 Ave: 0.07
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22.5 22.0
ED
21.5 40
50
60
70
80
90
100
110
120
Qs (l/s)
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(b) at different Qs values (ts=22 ºC)
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Fig. 7 Comparison of predicted toz between using RSM and CFD methods
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The prediction of air velocity in the occupied zone (voz) was shown in Fig. 8. It was found that the ts had little effect on voz while Qs had significant effect. As seen, an increase of 4 ºC in ts just resulted in an increase of 0.03 m/s in voz, while an increase of 60 l/s in Qs resulted in an increase of 0.33 m/s in voz. This suggested that changing Qs can effectively improve the air velocity in the occupied zone. To compare the RSM 30
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method with the CFD method, the voz values were calculated using Equation (8), and shown in Fig. 8. As seen, at ts from 19 to 23 ºC, the maximum voz difference was 0.0092 m/s, accounting for around 4% of voz value, the minimum voz difference was
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0.0003 m/s, accounting for around 0.2% of voz value, and the average voz difference was 0.0040 m/s, accounting for around 2% of voz value. On the other hand, when the Qs was raised from 50 l/s to 110 l/s, the maximum, minimum and average difference
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were lower than those shown in Fig. 8(a). Hence, RSM method can give a good
0.50
CFD RSM
0.45
0.30 0.25
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voz (m/s)
0.35
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0.40
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prediction for the averaged air velocity in the occupied zone.
0.20 0.15
Difference Max: 0.0092 Min: 0.0003 Ave: 0.0040
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0.10 0.05
AC
0.00 18
19
20
21
22
23
ts (C)
(a) at different ts values (Qs=60 l/s)
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0.50 0.45
CFD RSM
0.40
0.30 0.25 0.20
Difference Max: 0.0080 Min: 0.0001 Ave: 0.0023
0.15 0.10 0.05 0.00 40
50
60
70
80
Qs (l/s)
90
100
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voz (m/s)
0.35
110
120
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(b) at different Qs values (ts=22 ºC)
Fig. 8 Comparison of predicted voz between using RSM and CFD methods
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Fig. 9 shows the comparison of RSM and CFD methods in predicting averaged
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relative humidity in the occupied zone. As seen, the increase in ts caused significant increase in relative humidity in the occupied zone (RHoz), while the increase in Qs
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resulted in the slight decrease in RHoz. The highest RHoz exceeded 60%, which
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suggested a suitable ts and Qs should be selected. The comparisons between using
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CFD and RSM showed that the maximum difference was 0.41% with varied ts or 0.2% with varied Qs, accounting for lower than 1% of the RHoz value. The averaged difference was 0.20% or 0.13%, which accounted for around 0.3% of the RHoz value. This suggests the values predicted by the RSM method agree well with the CFD results.
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70
CFD RSM
68 66
62 60 58 56
Difference Max: 0.41 Min: 0.01 Ave: 0.20
54 52
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RHoz (%)
64
50 18
19
20
21
22
23
ts (C)
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(a) at different ts values (Qs=60 l/s) 68
CFD RSM
66
RHoz (%)
64 62 60 58
Difference Max: 0.2 Min: 0.06 Ave: 0.13
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56
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70
54 52
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50 40
50
60
70
80
90
100
110
120
Qs (l/s)
PT
(b) at different Qs values (ts=22 ºC)
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Fig. 9 Comparison of predicted RHoz between using RSM and CFD methods
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3.3.3 Stratified thermal parameters
The stratified distributions of thermal parameters were also investigated previously. In a conditioned and ventilated room, due to the insufficient mixing of room air and the conditioned air, stratified temperature differences along the height were observed [49, 50, 51,
52]. According to the ASHRAE standard, thermal stratification that results 33
ACCEPTED MANUSCRIPT in the air temperature at the head level being warmer than at the ankle level may cause thermal discomfort. Therefore, it’s necessary to study the stratified thermal parameters distributions in the bedroom with the TAC.
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The air temperatures at different heights from the floor level were calculated and shown in Fig. 10. It was found that the air temperature was increased significantly with the increase in height, suggesting significant stratified air temperature
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non-uniformity. Besides, the increase in ts caused the increase in air temperature at different heights. To compare the two methods, detailed operating parameters were selected and more CFD cases conducted. The air temperature was determined from 19
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ºC to 23 ºC with an interval of 0.5 ºC. A clearer investigation on the difference
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between using these two methods at heights of 0.6 m, 1.1 m and 1.7 m showed that
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the largest deviation occurred at height of 1.7 m. The maximum difference was 0.19
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ºC, which accounts for 1% of the t1.7 value. The averaged difference at 0.6 m, 1.1 m and 1.7 m were 0.03 ºC, 0.08 ºC and 0.09 ºC, respectively. This indicates that RSM
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can predict the stratified air temperature distribution inside the bedroom as the same as the CFD method.
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1.8 CFD: T19Q60 T19.5Q60 T20Q60 T20.5Q60 T21Q60 T21.5Q60 T22Q60 T22.5Q60 T23Q60
1.6 1.4
Height (m)
1.2 1.0 0.8
RSM:
0.6
0.2
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0.4
0.0 21.6 22.0 22.4 22.8 23.2 23.6 24.0 24.4 24.8 25.2 25.6 26.0 26.4 26.8 27.2 27.6
Air temperature (C)
T19Q60 T19.5Q60 T20Q60 T20.5Q60 T21Q60 T21.5Q60 T22Q60 T22.5Q60 T23Q60
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Fig. 10 Prediction of stratified air temperature at different ts using RSM and CFD methods
Fig. 11 shows the stratified air velocity distributions predicted by the CFD and RSM
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methods at different Qs. Different from the curves of air temperature, the velocity
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decreased at higher height due to the lower location of supply air outlet. Meanwhile,
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the air velocity would be influenced by the increase in Qs, as seen in Fig. 11. When the Qs was at a high level, the air velocity at height of 0.6 m was increased
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significantly to the highest value due to that this height was near the location of
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supply air outlet. The comparisons between using CFD and RSM showed that at heights of 0.6 m and 1.1 m, the air velocity using the two methods were close to each other, as seen in Fig. 11. However, large deviations were found at heights of 0.1 m and 1.7 m. The maximum v1.7 difference was 0.0096 m/s, accounting for 19% of the v1.7 value, and maximum v0.1 difference was 0.0095 m/s, accounting for 14.6% of the v0.1 35
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value. In a conclusion, the deviation between using RSM and CFD methods to predict the velocity at different ts or Qs is obvious. The proportion of maximum difference is lower than 20% which can be seen acceptable. Moreover, the relations between the air
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velocity and height, ts, Qs were well predicted. 1.8 1.6
CFD:
T22Q50 T22Q60 T22Q70 T22Q80 T22Q90 T22Q100 T22Q110
1.4
1.0
RSM:
0.8 0.6 0.4 0.2 0.0 0.00
0.02
0.04
0.06
0.08
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Height (m)
1.2
0.10
0.12
0.14
0.16
0.18
T22Q50 T22Q60 T22Q70 T22Q80 T22Q90 T22Q100 T22Q110
0.20
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Air velocity (m/s)
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Fig. 11 Prediction of stratified air velocity at different Qs using RSM and CFD methods
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The relative humidity values along the height at different Qs were shown in Fig. 12. It was found that the highest RH value occurred at height of 0.6 m. This was caused by
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the highest air velocity and lower air temperature. The former reduced the moisture
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produced by the thermal manikin, and the latter resulted in the higher RH value. Afterwards, the relative humidity values were calculated using RSM method and compared with that calculated using CFD method, as shown in Figs. 12. It was found that, at different Qs, the RSM method described similar variations of RH to the CFD method with the increase in height. At height of 0.6 m and 1.1 m, the deviations 36
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seemed obvious. The maximum differences of RH1.1 and RH0.6 between using RSM and CFD methods were 0.14 and 0.11 respectively, accounting for less than 0.2% of the RH value. It can be concluded that the RSM method can give a correct prediction
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on RH distribution along the height. 1.8 1.6
CFD:
T22Q50 T22Q60 T22Q70 T22Q80 T22Q90 T22Q100 T22Q110
1.4
1.0
RSM:
0.8 0.6 0.4 0.2 0.0 61.0
61.5
62.0
62.5
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Height (m)
1.2
63.0
63.5
64.0
64.5
T22Q50 T22Q60 T22Q70 T22Q80 T22Q90 T22Q100 T22Q110
65.0
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RH (%)
PT
ED
Fig. 12 Prediction of stratified RH at different Qs using RSM and CFD methods
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4 Conclusions
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A simplified numerical study was carried out to evaluate the thermal and energy performance of the bedroom TAC system. The numerical study includes three steps: (1) CFD study, (2) establishment of predictive model, and (3) performance evaluation and comparisons. The CFD method was firstly used for performance evaluation. In this step, 15 cases were carried out. Secondly, the RSM method was used as a 37
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simplified numerical method. In this step, 9 CFD simulation cases were carried out for establishment of predictive model. The models involved energy consumption of the task ambient air conditioning system, draft risk in the occupied zone, thermal
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parameters in the occupied zone and stratified thermal parameters inside the bedroom. It can be found that, less cases were used in the simplified numerical method,
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suggesting that computing cost was obviously saved.
The following comparison showed that, for energy consumption, draft risk, thermal parameters in the occupied zone, and stratified thermal parameters (except for air
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velocity), the maximum difference between using RSM and CFD methods were found
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at less than or equal to 5%. For the stratified air velocity, although the maximum
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difference was calculated between 10% and 20%, and the average difference was controlled at around 10%. Therefore, the RSM method can be seen have a good
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prediction in energy consumption, draft risk, air temperature, air velocity and relative
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humidity. Therefore, using CFD based RSM method is a simple and accurate methodology to predict the indoor thermal environment.
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Acknowledgements
The study was supported by “Research Foundation for Talents of China University of
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Petroleum (East China)” (Project No.: YJ201501018), “the Fundamental Research Funds for the Central Universities” (Project No.: 18CX02077A), and “National
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Natural Science Foundation of China” (Grant No.: 51606044).
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AIAA J 1994; 32: 1598-1605. [40] Stamou A, Katsiris I. Verification of a CFD model for indoor airflow and heat transfer. Build Environ 2006; 41: 1171-1181. [41] Zhai ZQ, Zhang Z, Zhang W, Chen QY. Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD: Part-1: summary of prevalent turbulence models. HVAC&R Res 2005; 13: 853-870. [42] Raithby GD, Chui EH. A finite-volume method for predicting a radiant heat transfer in enclosures with participating media. J Heat Transf 1990; 112: 415-423. [43] Mao N, Pan DM, Chan MY, Deng SM. Experimental and numerical studies on the performance evaluation of a bed-based task\ambient air conditioning (TAC) system. Appl Energ 2014; 136: 956-967. [44] Fanger PO. Thermal comfort. Copenhagen: Danish Technical Press; 1970. [45] ASHRAE, ASHRAE Standard 55-2010, Thermal Environmental Conditions for Human Occupancy, 2010. [46] Sevilgen G, Kilic M. Numerical analysis of air flow, heat transfer, moisture transport and thermal comfort in a room heated by two-panel radiators. Energ Buildings 2011; 43: 137-146. [47 ] Chen Q, Srebric J. A procedure for verification, validation and reporting of indoor environment CFD analyses. HVAC&R Res 2002; 8: 201-216. [48] ISO Standard 7730, Ergonomics of the thermal environment - Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria, 2005. [49] Mao N, Song M, Pan D, Deng S. Comparative studies on using RSM and TOPSIS methods to optimize residential air conditioning systems. Energ 2018; 144: 98-109. [50] Halvonova B, Melikov A. Performance of “ductless” personalized ventilation in conjunction with displacement ventilation: Impact of disturbances due to walking person(s). Build Environ 2010; 45: 427-436. [51] Mao N, Song M, Pan D, Li Z, Deng S. Numerical investigations on the effects of envelope thermal loads on energy utilization potential and thermal non-uniformity in sleeping environments. Building Environ 2017; 124: 232-244. [52] Halvonova B, Melikov A. Performance of “ductless” personalized ventilation in conjunction with displacement ventilation: Impact of disturbances due to walking person(s). Build Environ 2010; 45: 427-436.
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A simplified numerical study on the energy performance and thermal environment of a bedroom TAC system Mao Ning , Zhang Bin , Song Mengjie , Deng Shiming PII: DOI: Reference:
S0378-7788(17)33600-9 10.1016/j.enbuild.2018.02.018 ENB 8334
To appear in:
Energy & Buildings
Received date: Revised date: Accepted date:
2 November 2017 20 January 2018 2 February 2018
Please cite this article as: Mao Ning , Zhang Bin , Song Mengjie , Deng Shiming , A simplified numerical study on the energy performance and thermal environment of a bedroom TAC system, Energy & Buildings (2018), doi: 10.1016/j.enbuild.2018.02.018
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Highlights A simplified numerical study was carried out The thermal and energy performance of TAC in bedrooms were evaluated RSM method was used to build predictive models of indoor thermal environment
The predicted results using CFD and RSM methods were compared
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A simplified numerical study on the energy performance and thermal environment of a bedroom TAC system Mao Ning1, Zhang Bin2, Song Mengjie3*, Deng Shiming4 1
Department of Gas Engineering, College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao, China 2
School of Civil Engineering & Architecture, Linyi University, Linyi, China
3
Department of Human and Engineered Environmental Studies, Graduate School of Frontier
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Sciences, The University of Tokyo, Chiba, Japan 4
Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China
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Abstract
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In subtropics, the higher energy consumption of air conditioning system in summer period brought about the application of task/ambient air conditioning (TAC) systems,
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not only in commercial buildings, but also in residential buildings. To better assess the
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performance of the TAC system, a numerical study was carried out to predict the
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energy and thermal performance of a bedroom TAC system in a bedroom in
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subtropical area. To conveniently predict the indoor thermal environment, response surface methodology (RSM) was applied to simplify the procedure of numerical simulation. Firstly, CFD study was carried out to evaluate the thermal and energy performance of the TAC system. Secondly, RSM method was used to establish the predictive models of important index of indoor thermal environment to form the simplified numerical method. Thirdly, these two methods were used and the predicted 2
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values were compared. It was found that the energy consumption was reduced from 260 W to 160 W when the ts was increased from 19 ºC to 23 ºC, and the averaged draft risk (DRoz) reached at 20% when the Qs was set at 110 l/s. The significant
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vertical non-uniformity of air temperature, air velocity and relative humidity were also reported. Besides, the CFD method was compared with the simplified numerical method (RSM method). It was found that the maximum deviation between using the
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RSM and CFD methods was less than 5% in predicting energy consumption, draft risk, thermal parameters in the occupied zone, stratified air temperature and stratified air relative humidity. Overall, the simplified numerical method (CFD based RSM method)
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can predict the indoor thermal environment accurately.
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Keywords
Task/ambient air conditioning (TAC) systems, Response surface methodology (RSM),
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Indoor thermal environment, Energy consumption, Stratified thermal parameter, CFD
Corresponding author: Dr. SONG Mengjie (JSPS Researcher) Department of Human and Engineered Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan E-mail: [email protected]
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Nomenclature
Specific heat at constant pressure Draft risk Averaged DR in the occupied zone Metabolic heat production Energy consumption
Qs RHoz RH0.1 RH0.6 RH1.1 RH1.7 t toz tr
Supply air flow rate Averaged relative humidity in the occupied zone Averaged relative humidity at height of 0.1 m Averaged relative humidity at height of 0.6 m Averaged relative humidity at height of 1.1 m Averaged relative humidity at height of 1.7 m Air temperature at a measurement position Average air temperature in an occupied zone Return air temperature
l/s % % % % % ºC ºC ºC
ts tsk t0.1 t0.6 t1.1 t1.7 voz
Supply air temperature Mean skin temperature Averaged air temperature at height of 0.1 m Averaged air temperature at height of 0.6 m Averaged air temperature at height of 1.1 m Averaged air temperature at height of 1.7 m Air velocity in an occupied zone
ºC ºC ºC ºC ºC ºC m/s
v0.1 v0.6
Averaged air velocity at height of 0.1 m Averaged air velocity at height of 0.6 m
m/s m/s
v1.1 v1.7 ρ Tu
Averaged air velocity at height of 1.1 m Averaged air velocity at height of 1.7 m Air density Turbulence intensity
m/s m/s kg/m3 -
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PT
CE
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Abbreviation ADPI
Air Diffusion Performance Index
CFD DR PMV
Computational fluid dynamics Draft risk Predicted Mean Vote 4
J/(kg·K) % % W/m2 W
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Cp DR DRoz M Qc
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RSM TAC
Response surface methodology Task/ambient air conditioning
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1 Introduction
Bedrooms in residential buildings are important places for human beings’ relaxation and body recovery, which are critically affected by the indoor thermal environment.
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Therefore, investigations into the indoor thermal environment inside residential buildings have attracted more and more researchers recently [1, 2, 3, 4]. For the last two decades, to provide a suitable thermal environment, task/ambient air conditioning (TAC) systems, due to their better performance in terms of energy saving and flexible
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control over thermal environments [5, 6], had attracted continuous attentions.
The indoor thermal environment mainly includes parameters: air temperature, air
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velocity and relative humidity in the room [7]. Parts of these previous studies are related to the thermal parameters in the occupied zone around the people. Ho et al. [8]
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investigated the occupied zone in an office with an underfloor air distribution systems.
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The moderate temperature zones around the person and suitable relative humidity were found. Corgnati et al. [9] carried out experiments to study the jet flow in the occupied zone, and studied the maximum DR in the occupied zone. Ye et al. [10] investigated the energy consumption of impinging jet ventilation. At different supply conditions, the averaged air temperature in the occupied zone was calculated, and heat loss rate of the occupied zone was computed. Cheng [11] studied the temperature distribution of the clothing surface of a thermal manikin in an office with different 5
ACCEPTED MANUSCRIPT ventilation systems: mixing and displacement. It is revealed that the decreased temperature may benefit to the thermal comfort of human body. Other than these studies on thermal environment in a ventilated room, some researchers investigated some specified space equipped with task/ambient conditioning (TAC) system. Mao et al. [12] investigated a bed based TAC system through experiments and numerical
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simulation. The air temperature, air velocity and relative humidity distribution in the occupied zone were calculated to evaluate the thermal performance of the TAC system. Pan et al. also [13] used PMV in the occupied zone to evaluate the thermal comfort of a novel bedroom TAC system compared with a full volume air
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conditioning system. Those researches indicate the importance of thermal environment in a room with ventilation or TAC system.
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About the studies on the indoor thermal environment, Computational fluid dynamics (CFD) is an important tool, which can simultaneously predict airflow and heat
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transfer in buildings [14, 15]. The information provided by CFD can be used to
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evaluate the thermal environment and energy saving performance of air conditioning systems in buildings. A lot of works has been conducted on velocity, temperature and
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humidity distributions using CFD methods [16, 17, 12]. On the other hand, the energy consumption and thermal comfort were also investigated using CFD method
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[ 18 , 19 ]. Those previous researches showed good agreements between the computational results and the experimental data. Although CFD method is the most suitable solution save time compared with the experiments, it still cost a lot of time if many factors need to be studied. For example, Mao et al. [20] carried out numerical study on the influence of envelope heat gain on indoor thermal environment in a bedroom. In this study, 90 simulation cases were designed and investigated. Pan et al. 6
ACCEPTED MANUSCRIPT [13] carried out 28 CFD simulation cases to investigate the task ambient air conditioning system, and evaluate the thermal comfort and energy saving performance of the system. The conduction on the large number of simulation cases cost lots of time and need complicated computation system. Therefore, it’s necessary
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to develop new method to simplify the study on indoor thermal environment.
In some previously studies on space cooling, Response surface methodology (RSM) as a regression method was used to simplify the study process. RSM is a mathematical and statistical technique which builds a polynomial equation based on
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the experimental data and helps to describe the behavior of a data set. Its objective is to make statistical previsions. RSM method can be well applied to the conditions which are influenced by several variables [21]. In statistics, RSM method predicts the
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relationships between several explanatory parameters and one or more response variable [22]. RSM method has been effectively used in area related to refrigeration,
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fluid dynamics and building environment. Geppert and Stamminger [23] studied the
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factors influencing energy consumption of a domestic refrigerators using RSM method. A second-order polynomial equation was established for the energy
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consumption. The results show that the RSM method was effective for understanding the effects of factors. Ng et al. [24] studied the air diffusion in a displacement
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ventilated office, and used RSM method to build the model of ADPI to investigate the effect of exhaust position, diffuser and supply temperature on air diffusion. In these studies, RSM gives a good prediction conveniently and describes behavior of a response variable when two or more design variables are varied simultaneously.
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ACCEPTED MANUSCRIPT As mentioned above, using the CFD method to investigate the energy utilization and thermal performance of a bedroom TAC system may require lots of time and high computing capacity. Therefore, the aim of this study was to develop a simplified numerical method based on the traditional CFD method. The key problem of the simplified numerical method was to establish relationship between the thermal
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performance variables and the operating parameters. Firstly, a TAC system in bedrooms in a typical residential building of Hong Kong was developed. Secondly, CFD method was used to evaluate the thermal and energy performance of the TAC system. Thirdly, RSM method was used to develop a simplified numerical method to
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evaluate the performance of TAC system. Finally, the two methods were compared and analyzed.
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2 Methodology
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The methodology used in this study is schematically shown in Fig. 1. The objective of
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the current study is to propose a simple method to predict the indoor thermal environment inside residential buildings. To validate this method, more CFD
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simulation cases were carried out and compared with the results predicted by the simple prediction method. In this study, firstly, a CFD model to simulate a bedroom
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thermal environment was developed, and validated by the previous experimental data. Secondly, according to the ranges of supply air temperature and supply air flow rate [25, 26, 27], simulation cases used to build prediction models were determined through a full-factorial design approach. And then, the air flow characteristics inside the bedroom were calculated using a CFD method. The energy consumption (Qc) and thermal comfort (draft risk), thermal parameters (air temperature, air velocity and 8
ACCEPTED MANUSCRIPT relative humidity) in the occupied zone, and stratified thermal parameters inside the bedroom were obtained at different cases. Thirdly, based on these simulation results, the relationship between the PMV, Qc, DR, thermal parameters and operating parameters (Qs, ts) were established, and prediction equations obtained. Fourthly, to validate these prediction equations, more simulation cases were carried out with
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different Qs and Ts. The simulation results in aspects of energy consumption, thermal comfort and thermal parameters were compared with the results obtained by the
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prediction equations.
CFD method
Validation
Factorial Design
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Simulation cases
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Experimental data
Ts (19, 19.5, 20, 20.5, 21, 22, 22.5, 23 ºC)
Simulation cases
Qs (50, 60, 70, 80, 90, 100, 110 l/s)
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(2 parameters, 3 levels)
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RSM method
Predictive models
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Qc comparison DR toz , voz , RHoz t0.1 , t0.6 , t1.1 , t1.7 v0.1 , v0.6 , v1.1 , v1.7 RH0.1 , RH0.6 , RH1.1 , RH1.7
• • • •
Energy consumption Draft risk Thermal parameters (occupied zone) Stratified thermal parameters
Simplified numerical method
Fig. 1 Schematic of the methodology 9
ACCEPTED MANUSCRIPT 2.1 CFD method and numerical study
Computational fluid dynamics (CFD) has been widely used in building HVAC related studies to simulate indoor air flow, indoor air temperatures and indoor air quality, etc. [28, 29, 30, 31, 32]. Different from experiments, which only get limited data on
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temperature and velocity inside an experimental space, CFD can simultaneously predict more detailed information of airflow and heat transfer in buildings.
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2.1.1 Geometry model
A bedroom was built and investigated in this study. Experiments were carried out in the bedroom for validation of the CFD results. A task ambient air conditioning system
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was located in the bedroom. The system consists of a supply air outlet, a return air inlet, a bed and a thermal manikin. The supply air outlet (0.57 × 0.21 m) was placed at
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1.1 m above the floor level, and the return air inlet (0.37 × 0.16 m) at 0.32 m, as
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shown in Fig. 2. A cuboid was designated as an occupied zone according to previous studies [33, 34], and the rest of the space inside the bedroom an unoccupied zone, as
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shown in Fig. 2. A thermal manikin consisting of 16 different body parts was placed on the bed to assemble a sleeping person [33]. The surface temperature and heat loss
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of different body parts were measured. Seven measurement locations in the unoccupied zone and six in the occupied zone were identified, as shown in Fig. 2(b). In the unoccupied zone, air dry-bulb temperature, wet-bulb temperature and air velocity were measured at four heights, 0.1 m, 0.6 m, 1.1 m and 1.7 m above floor level, at each of these locations [35]. Inside the occupied zone, the above parameters were measured at 0.8 m and 1.0 m above floor level in each of the six locations. To 10
ACCEPTED MANUSCRIPT simulate the bedroom, a geometry model was established and the corresponding grids was generated using ANSYS ICEM [36], as shown in Fig. 2 [12]. Mesh was respectively generated for the occupied zone and the unoccupied zone, as shown in Fig. 2(c). Prism mesh was generated on the surface of the thermal manikin, as shown
620 External wall
Unoccupied zone
Front wall
400
Occupied zone
Supply air outlet
1250
900
L
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(a) Geometry
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425 N
100
K
900
3600 mm
475
460
Return air inlet
580 mm
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F
E
D
Bed
600 mm
500
1250
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Thermal manikin
2530 mm
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in Fig. 2(d). More related detailed information can be found in reference [37].
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1840
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A
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(b) Measurement locations
(c) Sectional view of the mesh
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(d) Detailed mesh structure
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Fig. 2 The simulated bedroom with TAC system
2.1.2 CFD model
A commercial CFD code ANSYS Fluent [38] was used to compute the thermal environment inside the bedroom. The air flow field was calculated by the three-dimensional and steady-state Reynolds averaged Navier-Stokes (RANS) 11
ACCEPTED MANUSCRIPT equations, combined with continuity and energy equations. The SIMPLE algorithm was used to compute the convective terms with a second order scheme. The SST turbulence model [39] was used for modeling the turbulent flow due to its best performance for predicting air velocity and temperature distributions inside a room [40, 41]. To predict the moisture transfer between the surface of the thermal manikin
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and its surrounding environments, a species transport model was used. The surface-to-surface (S2S) radiation model was used to compute the radiation heat exchange among the surfaces in the bedroom [12, 42].
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2.1.3 Boundary conditions
The CFD model was solved using boundary conditions including temperature,
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velocity and radiation values at the supply air outlet, return air inlet and bedroom wall, which were detailed in previous studies [43], and thermal manikin skin temperature,
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and moisture concentration. Mean skin surface temperature, tsk, was an important
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factor influencing human’s thermal sensation. Fanger [ 44 ] proposed a linear regression equation to evaluate the value of tsk, as shown in Equation (1). According
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to ASHRAE Standard [45], the metabolic rate (M) of a sleeping person is 40 W/m2,
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and the workload (W) is zero, therefore, the mean skin temperature would be 34.6 ºC.
tsk 35.7 0.0275(M W )
(1)
To predict the moisture transfer between the surface of the thermal manikin and the surrounding environment, air moisture content was taken as 10 g/kg air at the surfaces of the thermal manikin according a previous study [46]. The gradient of air moisture 12
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Table 1 Boundary conditions of the CFD method Item Boundary Conditions 1 Supply outlet Air velocity (0.43 - 0.94 m/s), air temperatures (19 - 23 ºC) 2 Return inlet Pressure outlet 3 Thermal manikin 16 body parts with fixed temperature, emissivity 0.07 [37] 4 External wall Outdoor surface temperature 30 ºC, emissivity 0.1, 5 Window Outdoor surface temperature 30 ºC, emissivity 0.94 6 Bed Adiabatic wall, emissivity of 0.77 7 Floor Adiabatic wall, emissivity of 0.2 8 Other walls Adiabatic wall, emissivity of 0.07
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2.1.4 Mesh independence
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Different mesh numbers were used to verify the independence of grids. Fig. 3 shows the predicted tuz for grid numbers of 0.8 million, 1.2 million, 1.6 million, 2 million
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and 2.4 million mesh elements. As seen, the obtained results varied with the increase
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in mesh number till 2.0 million. And then the computed tuz at 2.0 million
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approximates to that at 2.4 million. Therefore, the CFD simulation using mesh
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number of 2.0 million can be considered to be mesh independent.
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26.1 26.0 25.9
tuz (C)
25.8 25.7 25.6 25.5
25.3 25.2 0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Mesh elements (million)
2.2
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25.4
2.4
2.6
2.1.5 Validation of the CFD method
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Fig. 3 Computed tuz at different mesh numbers
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The CFD method was evaluated using previous experimental data [37]. Fig. 4 shows
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the comparisons of air temperature, air velocity values and relative humidity between the CFD and the experimental data, respectively. As seen in Fig. 4, the averaged
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absolute temperature differences between the measured and the simulated ones were 0.01 ºC at Location D and 0.02 ºC at Location L, and the averaged absolute velocity
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differences between the measured and the predicted ones were -0.03 m/s in the
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unoccupied zone and 0.09 m/s in the occupied zone, respectively. At location D, the numerically simulated relative humidity values were close to the measured ones. At location L, the measured relative humidity values were slightly lower than the numerically predicted ones. The maximum deviation of the relative humidity ratio is about 3%, which is acceptable for comparisons in this study. According to the suggestions in a previous study [47], the CFD method in this study was validated.
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2.0
2.0
2.0
Location D 1.8
1.6
1.6
1.6
1.4
1.4
1.4
1.2
1.2
1.2
0.8
0.4
Experiment CFD
0.2
1.0 0.8
0.6
0.4
0.4 0.2 0.0
0.0 24
25
26
27
28
29
0.0 0.1 0.2 0.3 0.4 0.5 0.6
o
1.2
1.2
Location L
Location L
1.0
0.9
0.9
0.8
0.7
0.7
0.6
1.0
0.7
0.6
0.6
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23 24 25 26 27 28 29 30 o
Temperature ( C)
0.9
0.8
M
0.8
1.1
Height (m)
1.0
Location L
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1.1
Height (m)
1.1
0 10 20 30 40 50 60
Relative humidiy (%)
Velocity (m/s)
Temperature ( C)
1.2
0.8
0.6
0.2
0.0
1.0
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1.0
Height (m)
1.8
0.6
Height (m)
Location D
1.8
Height (m)
Height (m)
Location D
0.0
0.2
0.4
0.6
Velocity (m/s)
0.8
0 10 20 30 40 50 60
Relative humidity (%)
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Fig. 4 The comparison between numerically predicted and experimentally measured
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air temperature, velocity and relative humidity
2.1.6 Simulation cases
According to previous related studies, simulation cases at different supply air temperatures and supply air flow rates were designed and carried out. There were 15 cases designed. When the ts was set at 22 ºC, the Qs was set at from 50 to 110 l/s, with 15
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an interval of 10 l/s. When the Qs was set at 60 l/s, the ts was set at from 19 to 23 ºC, with an interval of 0.5 ºC. These cases were used to evaluate the energy and thermal performance of the TAC system.
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2.2 Simplified numerical study
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Response surface methodology (RSM) is a mathematical and statistical technique which builds a polynomial equation and helps to describe the behavior of a data set. The RSM method includes three steps: (1) design of experiment, (2) data collection
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on operating parameters.
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using CFD approach, (3) establishing predictive models of response variables based
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2.2.1 Factorial design
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A two-parameter three-level full-factorial approach for simulation was used to determine simulation cases, as shown in Table 2. The operating parameters, supply air temperature, supply air flow rate and envelope exterior wall temperature, were designated as the three parameters where using the full-factorial approach. Each of these parameters was studied at three levels: a low, middle and a high level. The range
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of the parameters was given based on previously related studies [37, 25]. The minimum number of simulation cases for the three-level two-parameter approach was
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therefore 32 or 9, as shown in Table 3.
Table 2 Design parameters and their three levels used in the study Parameters
Low level
Middle level
High level
19 50
21 80
23 110
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ts (ºC) Qs (l/s)
Table 3 Simulation matrix for the factorial design
Qs (l/s)
19 21 23 21 21 19 19 23
50 50 50 80 110 80 110 80
23
110
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T23Q110
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T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80 T19Q110 T23Q80
ts (ºC)
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Case No.
2.2.2 Response variables
The objective of this study was to build predictive models using RSM method to predict the indoor thermal environment simply. The thermal environment can be
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represented using two types of variables: macroscopical and microcosmic types. The former includes energy consumption and thermal comfort, and the latter includes occupied zone thermal parameters (air temperature, air velocity and relative humidity)
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and stratified thermal parameters.
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(1) Energy consumption
In this study, cooling air was delivered into the bedroom, and flow back to return air inlet after being heated. Therefore, the energy consumed on cooling the indoor
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the bedroom, as follows:
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environment can be calculated using the energy variation of air entering and exiting
(2)
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Qc QsC p (ts tr )
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(2) Thermal comfort
Draft is an unwanted local cooling for a human body caused by air movement. Draft risk (DR) is a draft rating index used to predict the percentage of occupants feeling draft: DR=(34-t )(v-0.05)0.62 (0.37vTu +3.14)
(For v 0.05 m/s, use v=0.05m/s; For DR>100%, use DR=100%) [45, 48] 18
(3)
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ASHRAE Standard 55 [45] suggests that the value of DR in each measurement position should not be greater than a permissible value of 20%. The DR values
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obtained in the occupied zone were averaged to get the mean DR values represented using DRoz.
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(3) Indoor thermal parameters
As stated in Section of Introduction, the prediction of air temperature, air velocity and
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relative humidity in the occupied zone is very important to assess the thermal comfort
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level and energy consumption inside a room. In this study, the air temperatures in the
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occupied zone were computed using CFD model and averaged to get the averaged air temperature in the occupied zone (toz). The toz reflects the cooling effect of the task
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ambient air conditioning system [37]. At the same time, the computed air velocities
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were averaged to get the averaged air velocity in the occupied zone (voz). The computed relative humidity were averaged to get the averaged relative humidity in the occupied zone (RHoz).
Due to the effect of stratified thermal parameters on indoor thermal comfort, it’s 19
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necessary to investigate the air temperature, air velocity and relative humidity at different heights inside the bedroom. According to ASHRAE Standard and previous related studies [37], these parameters were calculated at heights of 0.1m, 0.6m, 1.1m
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and 1.7m above the floor level. The air temperatures, air velocities and relative humidity at each height were averaged to obtain the values at each height and were labeled using t0.1, t0.6, t1.1, t1.7, v0.1, v0.6, v1.1, v1.7, RH0.1, RH0.6, RH1.1 and RH1.7,
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respectively.
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3 Results and analysis
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3.1 Establishment of predictive model using the RSM method
Using the simulation cases in Table 3, the energy consumption, DR values are
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calculated according to Equations (2) and (3), and listed in Table 4. Besides, the air
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temperature, air velocity and relative humidity in the occupied zone and at different heights were averaged and summarized in Table 5-7.
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Table 4 Energy consumption and DR values Qc
DRoz
T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80
232.60 192.32 152.69 245.34 293.03 297.32
7.78 7.40 6.67 15.40 20.61 17.47
T19Q110 T23Q80 T23Q110
355.92 196.48 235.85
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Case No.
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23.42 13.45 17.89
Table 5 Air temperature in the occupied zone and at different heights toz (ºC)
t0.1 (ºC)
t0.6 (ºC)
t1.1 (ºC)
t1.7 (ºC)
T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80 T19Q110 T23Q80 T23Q110
23.03 23.99 25.11 22.64 22.23 21.14 20.56 24.21 23.89
22.22 23.63 25.10 23.13 22.86 21.55 21.26 24.72 24.50
23.09 24.20 25.47 23.26 22.91 21.78 21.33 24.76 24.55
24.99 25.70 26.34 24.09 23.56 22.87 22.18 25.36 24.95
26.73 27.24 27.69 26.08 23.55 25.35 24.17 26.85 25.68
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Case No.
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Table 6 Air velocity in the occupied zone and at different heights voz (m/s)
v0.1 (m/s)
v0.6 (m/s)
v1.1 (m/s)
v1.7 (m/s)
T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80
0.1440 0.1596 0.1689 0.3321 0.4767 0.3287
0.0640 0.0515 0.0487 0.0830 0.1261 0.0745
0.0394 0.0550 0.0538 0.1207 0.1910 0.1109
0.0135 0.0182 0.0218 0.0613 0.0864 0.0531
0.0067 0.0090 0.0113 0.0322 0.0556 0.0271
T19Q110 T23Q80 T23Q110
0.4720 0.3393 0.4849
0.1300 0.0950 0.1354
0.1938 0.1333 0.1959
0.0856 0.0637 0.0970
0.0648 0.0363 0.0567
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Case No.
Table 7 Relative humidity in the occupied zone and at different heights RHoz
RH0.1
T19Q50 T21Q50 T23Q50 T21Q80 T21Q110 T19Q80 T19Q110 T23Q80 T23Q110
54.78 60.04 66.11 59.11 58.89 53.40 53.14 65.53 65.32
54.67 60.21 66.41 59.75 59.53 54.15 53.95 65.94 65.70
RH0.6
RH1.1
RH1.7
55.58 60.93 66.87 59.97 59.56 54.52 53.99 66.14 65.75
54.78 60.36 66.40 59.65 59.21 54.16 53.59 65.87 65.47
53.70 59.29 65.46 58.72 58.66 53.07 52.85 65.11 65.14
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Case No.
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The aim of this study is to establish relationship between the response variables and the operating parameters. Therefore, considering the main effects of parameters and their two-parameter interactions, a second-order model was chosen. The model can be expressed as follows:
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Y X 0 X1ts X 2Qs X11ts 2 X 22Qs 2 X12tsQs
(4)
Where X1, X2… are regression coefficients.
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Analysis of variance (ANOVA) was performed and the significance of parameters were obtained based on the calculated P-values. The predictive models were obtained
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as follows:
Energy consumption
(5)
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Thermal comfort
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Qc 336.430 11.6844ts 5.6898Qs 0.002936Qs 2 0.1673tsQs
(6)
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DRoz 25.1665 0.585ts 0.8722Qs 0.001643Qs 2 0.01842tsQs
Thermal parameters in the occupied zone
toz 22.3496 0.29ts 0.2235Qs 5.24110 4 Qs 2 5.208 103 tsQs
voz 0.29 4.033 103 ts 8.128 103 Qs 1.7426 105 Qs 2
23
(7)
(8)
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RH oz 47.3057 1.1633ts 0.1594Qs 0.09167ts 2 4.074 10 4 Qs 2 3.542 103 tsQs
(9)
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Thermal parameters at different heights
(10)
t0.6 18.1899 0.4354ts 0.1529Qs 3.595 10 4 Qs 2 3.493 103 tsQs
(11)
t1.1 28.8989 0.07912ts 0.2500Qs 5.683 10 4 Qs 2 5.898 103 tsQs
(12)
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t0.1 11.2948 0.6561ts 0.06664Qs 1.415 10 4 Qs 2 1.480 103 tsQs
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t1.7 22.6464 0.3310ts 0.04589Qs
v0.6 0.1387 0.003238ts 0.002403Qs
(14)
(15)
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v0.1 0.6518 0.05222ts 0.002051Qs 0.0011ts 2 9.3889 106 Qs 2 8.625 105 tsQs
(13)
v1.1 0.1294 0.002525ts 0.002196Qs 6.2407 106 Qs 2
v1.7 0.1184 0.004708ts 0.001563Qs 2.3889 106 Qs 2 5.2917 105 tsQs
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(16)
(17)
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RH 0.1 33.8471 0.2957ts 0.03501Qs 0.07704ts 2 1.454 10 4 Qs 2
(18)
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RH0.6 41.5731 0.645ts 0.1059Qs 0.08042ts 2 2.630 10 4 Qs 2 1.958 103 tsQs (19)
(20)
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RH1.1 35.5054 0.355ts 0.05425Qs 0.07625ts 2 8.3333 105 Qs 2 0.001083tsQs
RH1.7 38.2050 0.6517ts 0.09489Qs 0.08292ts 2 0.0002407Qs 2 0.002208tsQs (21)
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3.2 Evaluation of energy performance
The energy consumption (Qc) were calculated and shown in Fig. 5. It was found that
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the energy consumption was decreased from 260 W to 160 W when the ts was
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increased from 19 ºC to 23 ºC, and was decreased from 259 W to 168 W when the Qs
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was decreased from 110 l/s t 50 l/s. At the same time, under the same operating conditions, Equation (5) established using RSM method was used to compute Qc values. The comparisons of the Qc values predicted by RSM and CFD methods were shown in Fig. 5. It can be found that the profiles by the two methods have the similar trend. The comparison shows that the maximum difference between using the two
25
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methods was 8.90 or 8.21 W, accounting for about 4% of the Qc value, and the averaged difference was 5.55 or 5.29 W, accounting for about 2% of the Qc value. This indicates that the RSM method agrees well with the CFD method for predicting
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Qc values.
300
CFD RSM
250
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Qc (W)
200
150
100
Difference Max: 8.90 Min: 2.24 Ave: 5.55
0 18
19
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50
20
21
22
23
24
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ts (C)
(a) at different ts values (Qs=60 l/s)
PT
300
250
CFD RSM
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Qc (W)
CE
200
150
100
Difference Max: 8.21 Min: 1.87 Ave: 5.29
50
0 40
50
60
70
80
90
100
110
120
Qs (l/s)
(b) at different Qs values (ts=22 ºC) Fig. 5 Comparison of predicted Qc between using RSM and CFD methods 26
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3.3 Evaluation of thermal performance
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3.3.1 Draft risk
The DRoz values were calculated based on the CFD results and shown in Fig. 6. As
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seen, the DRoz values were effectively reduced through increasing ts and decreasing Qs. Fig. 6(b) shows the variation of DRoz with increase in Qs. It was found that when the Qs was set at 110 l/s the DR reached at 20% which was much higher may cause
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thermal discomfort. This suggests that a higher supply air temperature and a lower
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supply air flow rate can guarantee a suitable thermally comfortable environment. Besides, DRoz values were also predicted using Equation (6) established by RSM
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method and compared with that using CFD method. It can be found that these curves
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have the same trend. The comparison shows that the maximum difference between the
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two methods was 0.56 in Fig. 6(a) or 0.47 in Fig. 6(b), accounting for about 5% of the DRoz value, and the averaged difference was 0.33 or 0.20, accounting for around 3% of the DRoz value. This suggests that the RSM method agrees well with the CFD method for predicting thermal comfort.
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20
CFD RSM
18 16
DRoz (%)
14 12 10 8 6
Difference Max: 0.56 Min: 0.08 Ave: 0.33
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4 2 0 18
19
20
21
22
23
ts (C)
24
(a) at different ts values (Qs=60 l/s) 30
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CFD RSM
25
DRoz (%)
20
15
Difference Max: 0.47 Min: 0.03 Ave: 0.20
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10
5
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0 40
50
60
70
80
90
100
110
120
Qs (l/s)
PT
(b) at different Qs values (ts=22 ºC)
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Fig. 6 Comparison of predicted DRoz between using RSM and CFD methods
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3.3.2 Averaged thermal parameters in the occupied zone
The air temperature, air velocity and relative humidity at different ts and Qs were calculated using the CFD methods and shown in Figs. 7, 8 and 9, respectively.
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As shown in Fig. 7, the toz values were raised when the ts was increased, and the increase of ts by 4 ºC resulted in 2.5 ºC of increase in toz. Different from ts, the increase in Qs resulted in the decrease in toz. As seen, when the Qs was at a high level,
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the decrease in toz was slowed down. To evaluate the accuracy of the RSM in predicting air temperature, the toz values were compared with that calculated using Equation (7) established by RSM method. It was found that the maximum difference
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between using the two methods was 0.29 ºC where ts = 22 ºC and Qs = 50 l/s, accounting for about 1% of toz value. Furthermore, the profile of toz predicted using RSM method has the similar trend as that using CFD method, even no matter it’s
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linear in Fig. 7(a) or it’s curved in Fig. 7(b). This is due to the term of Q2 in Equation
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(7) that makes RSM method display curved profile. Considering trend of profile and
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zone.
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values of toz, RSM performs well in predicting the air temperature in the occupied
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25.0
CFD RSM
24.5 24.0
toz (C)
23.5 23.0
Difference Max: 0.17 Min: 0.06 Ave: 0.11
22.5
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22.0 21.5 18
19
20
21
22
23
ts (C)
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(a) at different ts values (Qs=60 l/s) 25.0
CFD RSM
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24.5
toz (C)
24.0 23.5 23.0
Difference Max: 0.29 Min: 0.00 Ave: 0.07
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22.5 22.0
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21.5 40
50
60
70
80
90
100
110
120
Qs (l/s)
PT
(b) at different Qs values (ts=22 ºC)
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Fig. 7 Comparison of predicted toz between using RSM and CFD methods
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The prediction of air velocity in the occupied zone (voz) was shown in Fig. 8. It was found that the ts had little effect on voz while Qs had significant effect. As seen, an increase of 4 ºC in ts just resulted in an increase of 0.03 m/s in voz, while an increase of 60 l/s in Qs resulted in an increase of 0.33 m/s in voz. This suggested that changing Qs can effectively improve the air velocity in the occupied zone. To compare the RSM 30
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method with the CFD method, the voz values were calculated using Equation (8), and shown in Fig. 8. As seen, at ts from 19 to 23 ºC, the maximum voz difference was 0.0092 m/s, accounting for around 4% of voz value, the minimum voz difference was
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0.0003 m/s, accounting for around 0.2% of voz value, and the average voz difference was 0.0040 m/s, accounting for around 2% of voz value. On the other hand, when the Qs was raised from 50 l/s to 110 l/s, the maximum, minimum and average difference
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were lower than those shown in Fig. 8(a). Hence, RSM method can give a good
0.50
CFD RSM
0.45
0.30 0.25
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voz (m/s)
0.35
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0.40
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prediction for the averaged air velocity in the occupied zone.
0.20 0.15
Difference Max: 0.0092 Min: 0.0003 Ave: 0.0040
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0.10 0.05
AC
0.00 18
19
20
21
22
23
ts (C)
(a) at different ts values (Qs=60 l/s)
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0.50 0.45
CFD RSM
0.40
0.30 0.25 0.20
Difference Max: 0.0080 Min: 0.0001 Ave: 0.0023
0.15 0.10 0.05 0.00 40
50
60
70
80
Qs (l/s)
90
100
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voz (m/s)
0.35
110
120
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(b) at different Qs values (ts=22 ºC)
Fig. 8 Comparison of predicted voz between using RSM and CFD methods
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Fig. 9 shows the comparison of RSM and CFD methods in predicting averaged
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relative humidity in the occupied zone. As seen, the increase in ts caused significant increase in relative humidity in the occupied zone (RHoz), while the increase in Qs
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resulted in the slight decrease in RHoz. The highest RHoz exceeded 60%, which
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suggested a suitable ts and Qs should be selected. The comparisons between using
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CFD and RSM showed that the maximum difference was 0.41% with varied ts or 0.2% with varied Qs, accounting for lower than 1% of the RHoz value. The averaged difference was 0.20% or 0.13%, which accounted for around 0.3% of the RHoz value. This suggests the values predicted by the RSM method agree well with the CFD results.
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70
CFD RSM
68 66
62 60 58 56
Difference Max: 0.41 Min: 0.01 Ave: 0.20
54 52
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RHoz (%)
64
50 18
19
20
21
22
23
ts (C)
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(a) at different ts values (Qs=60 l/s) 68
CFD RSM
66
RHoz (%)
64 62 60 58
Difference Max: 0.2 Min: 0.06 Ave: 0.13
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56
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70
54 52
ED
50 40
50
60
70
80
90
100
110
120
Qs (l/s)
PT
(b) at different Qs values (ts=22 ºC)
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Fig. 9 Comparison of predicted RHoz between using RSM and CFD methods
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3.3.3 Stratified thermal parameters
The stratified distributions of thermal parameters were also investigated previously. In a conditioned and ventilated room, due to the insufficient mixing of room air and the conditioned air, stratified temperature differences along the height were observed [49, 50, 51,
52]. According to the ASHRAE standard, thermal stratification that results 33
ACCEPTED MANUSCRIPT in the air temperature at the head level being warmer than at the ankle level may cause thermal discomfort. Therefore, it’s necessary to study the stratified thermal parameters distributions in the bedroom with the TAC.
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The air temperatures at different heights from the floor level were calculated and shown in Fig. 10. It was found that the air temperature was increased significantly with the increase in height, suggesting significant stratified air temperature
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non-uniformity. Besides, the increase in ts caused the increase in air temperature at different heights. To compare the two methods, detailed operating parameters were selected and more CFD cases conducted. The air temperature was determined from 19
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ºC to 23 ºC with an interval of 0.5 ºC. A clearer investigation on the difference
ED
between using these two methods at heights of 0.6 m, 1.1 m and 1.7 m showed that
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the largest deviation occurred at height of 1.7 m. The maximum difference was 0.19
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ºC, which accounts for 1% of the t1.7 value. The averaged difference at 0.6 m, 1.1 m and 1.7 m were 0.03 ºC, 0.08 ºC and 0.09 ºC, respectively. This indicates that RSM
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can predict the stratified air temperature distribution inside the bedroom as the same as the CFD method.
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1.8 CFD: T19Q60 T19.5Q60 T20Q60 T20.5Q60 T21Q60 T21.5Q60 T22Q60 T22.5Q60 T23Q60
1.6 1.4
Height (m)
1.2 1.0 0.8
RSM:
0.6
0.2
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0.4
0.0 21.6 22.0 22.4 22.8 23.2 23.6 24.0 24.4 24.8 25.2 25.6 26.0 26.4 26.8 27.2 27.6
Air temperature (C)
T19Q60 T19.5Q60 T20Q60 T20.5Q60 T21Q60 T21.5Q60 T22Q60 T22.5Q60 T23Q60
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Fig. 10 Prediction of stratified air temperature at different ts using RSM and CFD methods
Fig. 11 shows the stratified air velocity distributions predicted by the CFD and RSM
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methods at different Qs. Different from the curves of air temperature, the velocity
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decreased at higher height due to the lower location of supply air outlet. Meanwhile,
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the air velocity would be influenced by the increase in Qs, as seen in Fig. 11. When the Qs was at a high level, the air velocity at height of 0.6 m was increased
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significantly to the highest value due to that this height was near the location of
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supply air outlet. The comparisons between using CFD and RSM showed that at heights of 0.6 m and 1.1 m, the air velocity using the two methods were close to each other, as seen in Fig. 11. However, large deviations were found at heights of 0.1 m and 1.7 m. The maximum v1.7 difference was 0.0096 m/s, accounting for 19% of the v1.7 value, and maximum v0.1 difference was 0.0095 m/s, accounting for 14.6% of the v0.1 35
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value. In a conclusion, the deviation between using RSM and CFD methods to predict the velocity at different ts or Qs is obvious. The proportion of maximum difference is lower than 20% which can be seen acceptable. Moreover, the relations between the air
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velocity and height, ts, Qs were well predicted. 1.8 1.6
CFD:
T22Q50 T22Q60 T22Q70 T22Q80 T22Q90 T22Q100 T22Q110
1.4
1.0
RSM:
0.8 0.6 0.4 0.2 0.0 0.00
0.02
0.04
0.06
0.08
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Height (m)
1.2
0.10
0.12
0.14
0.16
0.18
T22Q50 T22Q60 T22Q70 T22Q80 T22Q90 T22Q100 T22Q110
0.20
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Air velocity (m/s)
ED
Fig. 11 Prediction of stratified air velocity at different Qs using RSM and CFD methods
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The relative humidity values along the height at different Qs were shown in Fig. 12. It was found that the highest RH value occurred at height of 0.6 m. This was caused by
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the highest air velocity and lower air temperature. The former reduced the moisture
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produced by the thermal manikin, and the latter resulted in the higher RH value. Afterwards, the relative humidity values were calculated using RSM method and compared with that calculated using CFD method, as shown in Figs. 12. It was found that, at different Qs, the RSM method described similar variations of RH to the CFD method with the increase in height. At height of 0.6 m and 1.1 m, the deviations 36
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seemed obvious. The maximum differences of RH1.1 and RH0.6 between using RSM and CFD methods were 0.14 and 0.11 respectively, accounting for less than 0.2% of the RH value. It can be concluded that the RSM method can give a correct prediction
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on RH distribution along the height. 1.8 1.6
CFD:
T22Q50 T22Q60 T22Q70 T22Q80 T22Q90 T22Q100 T22Q110
1.4
1.0
RSM:
0.8 0.6 0.4 0.2 0.0 61.0
61.5
62.0
62.5
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Height (m)
1.2
63.0
63.5
64.0
64.5
T22Q50 T22Q60 T22Q70 T22Q80 T22Q90 T22Q100 T22Q110
65.0
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RH (%)
PT
ED
Fig. 12 Prediction of stratified RH at different Qs using RSM and CFD methods
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4 Conclusions
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A simplified numerical study was carried out to evaluate the thermal and energy performance of the bedroom TAC system. The numerical study includes three steps: (1) CFD study, (2) establishment of predictive model, and (3) performance evaluation and comparisons. The CFD method was firstly used for performance evaluation. In this step, 15 cases were carried out. Secondly, the RSM method was used as a 37
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simplified numerical method. In this step, 9 CFD simulation cases were carried out for establishment of predictive model. The models involved energy consumption of the task ambient air conditioning system, draft risk in the occupied zone, thermal
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parameters in the occupied zone and stratified thermal parameters inside the bedroom. It can be found that, less cases were used in the simplified numerical method,
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suggesting that computing cost was obviously saved.
The following comparison showed that, for energy consumption, draft risk, thermal parameters in the occupied zone, and stratified thermal parameters (except for air
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velocity), the maximum difference between using RSM and CFD methods were found
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at less than or equal to 5%. For the stratified air velocity, although the maximum
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difference was calculated between 10% and 20%, and the average difference was controlled at around 10%. Therefore, the RSM method can be seen have a good
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prediction in energy consumption, draft risk, air temperature, air velocity and relative
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humidity. Therefore, using CFD based RSM method is a simple and accurate methodology to predict the indoor thermal environment.
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Acknowledgements
The study was supported by “Research Foundation for Talents of China University of
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Petroleum (East China)” (Project No.: YJ201501018), “the Fundamental Research Funds for the Central Universities” (Project No.: 18CX02077A), and “National
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Natural Science Foundation of China” (Grant No.: 51606044).
References
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