optimization on indoor air diffusion of floor-standing type room air-conditioners
TRANSCRIPT
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Energy and Buildings 40 (2008) 59–70
Optimization on indoor air diffusion of floor-standing
type room air-conditioners
Weiwei Liu, Zhiwei Lian *, Ye Yao
Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China
Received 24 November 2006; received in revised form 25 December 2006; accepted 14 January 2007
Abstract
The indoor air diffusion of a typical office equipped with a floor-standing type air-conditioner (FSAC) in summer was evaluated and optimized.
Two existing evaluation indexes, the air diffusion performance index and the energy utilization coefficient, were modified for their more reasonable
application in the evaluation on air diffusion performance of a FSAC. And also, a new index, fast cooling effect index, was presented to evaluate the
fast-cooling effect. Based on the indoor airflow simulation using computational fluid dynamics, the three indexes were applied to evaluate the air
diffusion performance of the FSAC. As a result, the optimal indoor air diffusion types with best thermal feelings, fine energy utilization efficiency
and excellent fast-cooling effect were obtained, and also, a control scheme was suggested.
# 2007 Elsevier B.V. All rights reserved.
Keywords: Thermal comfort; Energy utilization efficiency; Air diffusion; Room air-conditioner; Computational fluid dynamics
1. Introduction
Currently, more and more room air-conditioners are being
used in residential apartments, offices and even some super-
marts. They operate during several months of hot weather in a
year. In this period, most of a person’s time is spent indoors.
People, therefore, expect the indoor environment to be as
comfortable as possible.
Effective indoor air diffusion is essential to good thermal
comfort as well as minimum energy use [1]. So far, a large
amount of studies have been done for air diffusion and thermal
comfort in occupied spaces [2–7]. However, among these
studies, relatively little was devoted to room air-conditioners.
Considering the wide using, it is significant to study air
diffusion performance of room air-conditioners for a desirable
indoor environment.
In Ref. [7], for three positions of a window-type air-condi-
tioner (one type of room air-conditioner), the performance of
Abbreviations: ADPI, air diffusion performance index; CFD, computa-
tional fluid dynamics; EUC, energy utilization coefficient; FCEI, fast cooling
effect index; FSAC, floor-standing type air-conditioner; SIMPLEC, semi-
implicit method for pressure-linked equations consistent
* Corresponding author. Tel.: +86 21 34204263; fax: +86 21 34206814.
E-mail address: [email protected] (Z. Lian).
0378-7788/$ – see front matter # 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.enbuild.2007.01.010
different air distribution types was determined and compared. A
floor-standing type air-conditioner (FSAC) is also a main type
of room air-conditioner, which is shown in Fig. 1. However,
compared with a window-type air-conditioner, a FSAC has
different configuration and operating characteristics. Therefore,
the research conclusions on air diffusion of window-type air-
conditioners cannot be applied to a FSAC.
In the present work, air diffusion performance of a FSAC
was studied. Different kinds of indoor air diffusion types can be
obtained by changing directions of air outflow from the outlet
(adjust the movable guide vanes in the outlet). That means
different inclination angles of the vanes conduce different air
diffusion types. Thus, the purpose of this study is to determine
the optimal indoor air diffusion type with the maximum benefit
in terms of indoor thermal comfort and energy utilization, by
evaluating air diffusion performance of a FSAC.
2. Floor-standing type air-conditioner
A FSAC consists of two units. One (outdoor unit) is installed
outside the building, which mainly comprises a compressor, a
condenser and a fan. Another (indoor unit) is placed in the
occupied space. It contains an evaporator, a fan, an air outlet
and one (or two) inlet. The two units are connected by copper
tubes.
Nomenclature
act actual time for cooling air (s)
c specific heat of air (kJ/kg K)
C1, C2, C3, cm empirical constants of turbulence equations
Ei,j mean strain rate (s-1)
Gb production item of turbulent kinetic energy due to
buoyancy (m2/s3)
Gk production item of turbulent kinetic energy due to
mean velocity gradients (m2/s3)
ict ideal time for cooling air (s)
k turbulence kinetic energy (m2/s2)
m total quality of air in a room (kg)
mi quality of a cell (kg)
M total quality of cells (kg)
p local static pressure (Pa)
pt pressure due to fluctuating velocity (Pa)
R2 correlation coefficient
S source item in energy equation
Si source item in momentum equations
t0 temperature of supply air (8C)
tc room control dry-bulb temperature (8C)
ti air temperature of a cell (8C)
tin outflow temperature of a floor-standing type air-
conditioner (8C)
tout inflow temperature of a floor-standing type air-
conditioner (8C)
tp local air-stream dry-bulb temperature (8C)
t̄ average air temperature (8C)
t̄iz average air temperature in occupied zone (8C)
t̄oz average air temperature out occupied zone (8C)
T mean temperature (K)
Ti indoor temperature (K)
Ts set temperature of an air-conditioner (K)
T0 fluctuating temperature (K)
ui, uj mean velocities along coordinate axes (m/s)
up local air-stream velocity (m/s)
u0i, u0j fluctuating velocities along coordinate axes (m/s)
x value of inclination angle
xi, xj distances along coordinate axes (m)
y fit value of evaluation indexes
W rated refrigerating effect (kW)
Dt range of temperature lowering (8C)
Dti�o temperature difference between inflow and
outflow of a floor-standing type air-conditioner
(8C)
Greek letters
r density of air (kg/m3)
t time (s)
h molecular viscosity of air (m2/s)
ht turbulent viscosity (m2/s)
G molecular diffusivity (kg/m/s)
Gt turbulent diffusivity (kg/m/s)
di,j Kronecker delta
e turbulence dissipation rate (m2/s3)
s turbulent Prandtl number
sk turbulent Prandtl number of k
se turbulent Prandtl number of en kinematic viscosity (m2/s)
u difference in effective draft temperature (K)
Subscripts
b buoyancy
i, j spatial coordinates
in inflow
iz in occupied zone
k turbulence kinetic energy
out outflow
oz out occupied zone
s set
t turbulence
e turbulence dissipation rate
W. Liu et al. / Energy and Buildings 40 (2008) 59–7060
As shown in Fig. 1, there are two inlets in the indoor unit of a
FSAC.
In summer, indoor air flows into the indoor unit via the two
inlets (inflow) and is cooled when passing through the
evaporator in the indoor unit. Afterwards, the cooled air is
supplied to the indoor space from the outlet (outflow). Because
of continuously cooling the indoor air, the required indoor
temperature is obtained. Therefore, the FSAC handles the
whole heat load. In an occupied space equipped with a FSAC,
gaps between doors (or windows) and walls are the sole areas
for air exchange between the indoors and outdoors. Usually, the
quantity of fresh air entering the room is small.
Fig. 1. The indoor unit of a floor-standing type air-conditioner.
Table 1
Control mode of a floor-standing type air-conditioner
Control conditions Compressor Outdoor fan Indoor fan
Ti � Ts Off Off On
Ti > Ts + 1 On On On
W. Liu et al. / Energy and Buildings 40 (2008) 59–70 61
Under most circumstances, refrigerating capacity of a FSAC
is larger than the actual cooling load, so its operation has to be
intermittent, meaning that a FSAC will start when indoor
temperature is above a set temperature and stop when indoor
temperature is below the set value. The control mode of the
FSAC studied in this paper is depicted in Table 1, where Ti
stands for indoor temperature and Ts for set temperature.
Table 2 lists some technical parameters of the FSAC.
3. Evaluation method and indexes of air diffusion
performance
Up to now, almost no special methods were established to
evaluate the air diffusion performance of room air-conditioners.
Thus, an evaluation method was proposed in the present work.
3.1. Evaluation method
First, following aspects should be taken into account when
evaluating the air diffusion performance.
(1) T
Tabl
Tech
Mod
KFR
hermal comfort due to the combined effect of air
temperature and velocity.
(2) E
nergy utilization efficiency of air diffusion.(3) R
ate of indoor air temperature lowering to the settemperature. This is hardly considered in a central air
conditioning system. However, for a room air-conditioner,
it can be used as an important index to reflect the fast-
cooling effect of indoor air diffusion.
Appropriate indexes are very important for exact evaluation
on air diffusion performance. Among the existing evaluation
indexes, the air diffusion performance index (ADPI) is
appropriate to assess thermal comfort level considering the
presence of draft [6–8], and the energy utilization coefficient
(EUC) can reflect the energy utilization efficiency of air
diffusion [8,9].
However, ADPI and EUC are initially proposed to assess air
diffusion of central air conditioning systems. Moreover,
calculations of the two indexes are usually based on
experimental values, not numerical simulation. (Here, the
evaluation on air diffusion performance of the FSAC was
performed based on results of indoor airflow simulation.)
e 2
nical parameters of a floor-standing type air-conditioner
el Rated refrigerating
effect (W)
Rate
pow
-72LW/DRUYB-Q2 7200 265
Therefore, for their more reasonable application in evaluating
the air diffusion performance of room air-conditioners,
appropriate modification is required.
In addition, none of the existing indexes can be used to
evaluate the fast-cooling effect of air diffusion. Thus, a new
index, fast cooling effect index (FCEI), was proposed.
As a whole, the modified indexes ADPI and EUC, together
with the index FCEI, were adopted in the evaluation method for
room air-conditioners.
3.2. Modification on air diffusion performance index
Considering quality of all calculation cells in airflow
simulation, here, ADPI is defined as the percentage of quality of
airflow meeting following specifications for effective draft
temperature and air velocity in the occupied zone, which is
given as
ADPI ¼
quality of air meeting � 1:5 K< u< 1:0 K
and up < 0:35 m=s
total air quality of indoor occupied zone� 100%
(1)
The difference in effective draft temperature u between any
point in the indoor environment and the control condition was
defined as [10,11]
u ¼ ðtp � tcÞ � 8:0ðup � 0:15Þ (2)
When the difference in effective draft temperature u is between
�1.5 and +1.0 K and the air velocity less than 0.35 m/s, a high
percentage of people feel comfortable.
By the modification, ADPI can reflect the size of airflow zone
where people feel comfortable in an air conditioning room.
3.3. Modification on energy utilization coefficient
Under most circumstances, for the FSAC, temperature of
exhaust air (inflow of the FSAC) is close to average temperature
of the air in the occupied zone, because the inlets of the FSAC
are in the occupied zone. Therefore, according to its definition
[8,9], EUC is always near the value of 1, which is not sensitive
enough to distinguish energy utilization efficiency of different
air diffusion.
Virtually, the energy utilization efficiency of air diffusion
can be indicated by the temperature difference between air in
and out the occupied zone. Thus, here the average temperature
of air out the occupied zone is used instead of the temperature
of exhaust air. By doing so, the modified EUC is written as,
EUC ¼ t̄oz � t0
t̄iz � t0
� 100% (3)
d
er (W)
Air circulation
rate (m3/h)
Dimension of indoor
unit (mm3)
0 1100 895 � 1735 � 335
W. Liu et al. / Energy and Buildings 40 (2008) 59–7062
In summer, if the average temperature of air in the occupied
zone is lower than that out the occupied zone, EUC will be
bigger than 1.0, which indicates that most energy is used to cool
air in the occupied zone. That is people expected.
Considering the quality of cells, the average air temperature
can be calculated as,
t̄ ¼X�
timi
M
�(4)
3.4. Fast cooling effect index for fast-cooling effect
In this paper, a time ratio for fast cooling effect index, FCEI,
is proposed to evaluate the fast-cooling effect of air diffusion,
which is expressed as,
FCEI ¼ act
ict(5)
Where the act is the actual time consumed in the process of
average air temperature of the occupied zone dropping to a set
value, and the ict is an ideal time spent on cooling air of the
whole room to the same set temperature, provided that, in the
room considered, no heat and humidity load exist. According to
the definition of ict, it can be expressed as,
ict ¼ mcDt
W(6)
For a specific air-conditioner and a room, the value of ict
is a constant, if the range of temperature lowering, Dt, does
not change. Therefore, the value of FCEI depends on the size
of act. It is obvious that value of FCEI is always higher than
1.0.
The smaller the value of FCEI, the better the fast-cooling
effect of air diffusion is.
4. Modeling and experiment
As a reliable tool, computational fluid dynamics (CFD) was
increasingly employed to predict the indoor airflow in recent
years [12–15]. Here, the CFD software FLUENT 6.0 was used
to simulate airflow field in a typical office [16]. In order to
validate the simulation results, an experiment was performed to
measure the actual airflow field.
Fig. 2. Schematic representation of the office equip
For an exact airflow simulation, following factors were
considered in the model:
(1) u
ped
nsteady state of airflow because of the intermittent
operation of the FSAC;
(2) e
ffect of the movable guide vanes in the outlet of the FSACon direction of outflow;
(3) e
ffect of barriers (such as desks and computers) on indoorairflow;
(4) b
uoyancy due to density difference between airflow withdifferent temperature.
4.1. Geometry and mesh generation
The office equipped with the FSAC is on the second floor of
an office building.
The office is 5.7 m long, 4.7 m wide, and 2.85 m high. As
shown in Fig. 2, it has one external wall, two external windows,
three internal walls, floor and ceiling.
The office and objects in it were created with the pre-processor
Gambit, version 2.0.4 [17]. In the office shown in Fig. 3, one can
identify one door, four tables, three computers, three beams and,
of course, the FSAC. This ambiance has been replicated as a full
3D geometric model. Among the various objects, the geometry of
the movable guide vanes in the outlet of the FSAC was
distinguished, which played a key role in air distribution.
Within the current pre-processor both structured and
unstructured meshes can be created. The unstructured meshes
are ideally suited for the discretization of complicated geo-
metrical domains. Considering the internal structure of the
office was complex, the tetrahedron was applied.
For the outlet of the FSAC, it’s a cube, so a hexahedral
(structure) mesh was used. Compared with the whole office, the
size of the outlet and the movable guide vanes was very small.
Therefore, a smaller mesh size was adopted.
The tables and the computers were meshed by means of
hexahedron. The beams used a tetrahedral grid.
The mesh was formed by approx. 900,000.
4.2. Turbulence model
In real situation the indoor flow field changes with time.
Thus, the simulations are carried for an unsteady indoor
with a floor-standing type air-conditioner.
Fig. 3. Geometry of the office equipped with a floor-standing type air-condi-
tioner.
W. Liu et al. / Energy and Buildings 40 (2008) 59–70 63
environment. The governing equations for an unsteady buoyant
airflow consist of the Reynolds-averaging equations, expressed
as follows [18]:
Continuity :@r
@tþ @
@xiðruiÞ ¼ 0 (7)
Momentum :@
@tðruiÞ þ
@
@x jðruiu jÞ
¼ � @ p
@xiþ @
@x j
�h
@ui
@x j� ru0iu
0j
�þ Si (8)
Energy :@
@tðrTÞ þ @
@x jðru jTÞ ¼
@
@x j
�G
@T
@x j� ru0jT
0�þ S
(9)
In the momentum equations, (�ru0iu0j) are the Reynolds
stresses. Introducing the Boussinesq assumption, the items can
be given as:
�ru0iu0j ¼ � ptdi; j þ ht
�@ui
@x jþ @u j
@xi
�� 2
3htdi; j (10)
In the energy equations, item �ru0jT0 can be expressed as:
�ru0jT0 ¼ G t
@T
@x j(11)
The turbulent viscosity (ht) and the turbulent diffusivity (Gt)
are not physical property parameters of the air, which lie on the
turbulence properties. Researches indicated that, generally, the
Table 3
Boundary conditions for inlet/outlet
Location Type
Air outlet of the floor-standing type air-conditioner Mass-flow-inlet
Air inlet of the floor-standing type air-conditioner Pressure-outlet
ratio of ht to Gt can be approximatively treated as a constant:
s ¼ ht
G t
(12)
Thus, the key to calculate turbulent is to determine ht. Here, the
Realizable k � e turbulence model is employed [13,18]. In this
model, the turbulence kinetic energy (k) and its dissipation rate
(e) are determined from the following transport equations:
@
@tðrkÞ þ @
@xiðruikÞ ¼
@
@x j
��hþ ht
sk
�@k
@x j
�þ Gk þ Gb � re
(13)
@
@tðreÞ þ @
@xiðruieÞ
¼ @
@x j
��hþ ht
se
�@e@x j
�þ rC1ð2Ei; jEi; jÞ1=2e
� rC2
e2
k þffiffiffiffiffivep þ C1
ek
C3Gb (14)
ht can be obtained as:
ht ¼cmrk2
e(15)
where C1, C2, C3, cm, sk and se are constants.
For the calculation of near-wall airflow, the standard wall
functions were employed.
The airflow equations were solved using the well-known
SIMPLEC pressures–velocity coupling algorithm. Conver-
gence was reached when the normalized residual measured
less than 10�3. It is noted that temperature reaches 10�6 of
convergence.
A computer with 1 GB memory and an Intel PIII 1.8 GHz
processor was used for computations. Usually, for an unsteady
calculation, it takes about 72 h to complete.
4.3. Boundary conditions, discretization scheme and
materials
The airflow model is solved with the conditions for air outlet,
inlet and solid boundaries. These boundary conditions are
depicted in Tables 3 and 4, respectively.
The discretization scheme affects the precision of the
simulation. Table 5 illustrates the discretization scheme
adopted in this simulation.
Materials used in the simulation are listed in Table 6.
Number Dimensions
(mm2)
Hydraulic
diameter
Turbulence
intensity (%)
1 424.7 � 248.0 0.1566 4
2 600.0 � 64.0 0.0578 3
Table 4
Boundary conditions for solid walls
Internal wall External wall Floor Ceiling Window Door
Number 3 1 1 1 2 1
Thickness (mm) 280 280 145 125 45 45
Thermal conditions Convection Temperature Convection Convection Temperature Convection
Convection coefficient (W/m2 K) 8.72 – 8.72 8.72 – 8.72
Table 5
Discretization scheme
Pressure Momentum Turbulence dissipation
rate
Turbulence kinetic
energy
Energy Unsteady
formulation
Diffusion
term
Standard 2nd-order upwind 2nd-order upwind 2nd-order upwind 2nd-order upwind 1st-order implicit 2nd-order central-
difference
Table 6
Materials properties
Type Density
(kg/m3)
Specific heat
(J/(kg K))
Viscosity
(kg/(m s))
Thermal conductivity
(W/(m K))
Air Fluid Piecewise-linear 1006.43 1.7894e�5 0.0242
Beam Solid 2500 840 – 1.63
Internal wall Solid 1800 880 – 0.828
External wall Solid 1800 880 – 0.813
Floor Solid 2500 840 – 0.70
Ceiling Solid 2500 840 – 1.404
Window Solid 2500 840 – 0.68
Desk Solid 700 2310 – 0.173
Computer Solid 1170 1465 – 0.167
W. Liu et al. / Energy and Buildings 40 (2008) 59–7064
4.4. Airflow measure experiment
4.4.1. Air inlet/outlet temperature measurement
For determination on the temperature difference between
the inflow and outflow of the FSAC, temperature of outflow
and inflow of the FSAC were tested, respectively. In this
measurement, two copper–constantan thermocouples were
used, one of which was placed in the center of the outlet of
the FSAC for the outflow temperature, and the other in a
location close to the fan behind one inlet for the inflow
temperature. Both were linked to a multi-channel data collector
(KEITHLEY 2700, Keithley Instruments, USA), and tempera-
tures were recorded at 0.2 s intervals.
Fig. 4. Temperature difference between the inflow and outflow of the floor-
standing type air-conditioner.
The measurement was carried out at a summer night. Air in
the office was cooled from 26 8C to 23 8C by the FSAC. Fig. 4
shows the real-time test results.
In Fig. 4, the temperature-lowering phase means the process
of cooling indoor air from an initial temperature to an air
conditioning set value, and the temperature-preserving phase
the process of keeping the indoor air temperature at the set
value (fluctuation less than 1 8C).
4.4.2. Airflow field measurement
In order to provide experimental data for validation of the
airflow simulation, measurements of airflow temperature and
velocity at some locations in the office were needed. Because
the office was not a full-scale test room (here the experimental
results were only used for validation of the simulation), 20
measurement points were arranged in the office, as shown in
Fig. 5. At these measurement points, the velocity of airflow was
measured by an anemoscope (TSI Compuflow 8585, E & E
Process Instrumentation, Canada). Table 7 gives the locations
of the 20 measurement points. The temperatures of airflow were
tested using copper–constantan thermocouples, which were
collected by the multi-channel data collector at 1-s intervals.
The measuring instruments were listed in Table 8. Before the
measurement, all the thermocouples were calibrated in a water
bath against a standard mercury thermometer with precision of
0.1 8C (Shanghai Huo er Co., China).
Fig. 5. Schematic representation of locations of the measurement points.
Table 7
Locations of 20 measurement points
Number and locations
No. 1 2 3 4 5 6 7 8 9 10
X (m) 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2
Y (m) 1.5 3.2 1.5 3.2 1.5 3.2 1.5 3.2 1.5 3.2
Z (m) 0.1 0.1 0.6 0.6 1.4 1.4 1.8 1.8 2.2 2.2
No. 11 12 13 14 15 16 17 18 19 20
X (m) 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
Y (m) 1.5 3.2 1.5 3.2 1.5 3.2 1.5 3.2 1.5 3.2
Z (m) 0.1 0.1 0.6 0.6 1.4 1.4 1.8 1.8 2.2 2.2
W. Liu et al. / Energy and Buildings 40 (2008) 59–70 65
The accuracy of the instruments meets the requirements in
ASHRAE Standard 55-1992 and ISO 7726 [19,20].
4.5. Validation of airflow numerical simulation
4.5.1. Calculation conditions
The unsteady simulation was done on the airflow field in the
office, due to 08 angle (horizontal) of the guide vanes in the
outlet of the FSAC.
In the simulation, as to the inlet boundary condition of the
office, temperature of the outflow of the FSAC can be obtained
as
tin ¼ tout � Dti�o (16)
Table 8
Instruments used in the experiment
Instrument Model
Thermocouple Copper–constantan
Standard mercury thermometer –
Anemoscope TSI Compuflow 8585
Multi-channel data collector KEITHLEY 2700
The temperature of the inflow of the FSAC, tout, was given
by the simulation. The temperature difference between the
inflow and outflow, Dti�o, was obtained by the inlet and outlet
temperature measurement depicted in Section 4.4.1.
Table 9 illustrates the fit result of Dti�o based on the test data.
The thermal boundary temperatures of walls (air tempera-
tures out the office) were measured using copper–constantan
thermocouples, which are listed in Table 10. The lower
boundary temperatures of internal wall 3 and ceiling were the
air conditioning temperature of the next offices, respectively.
During the measurement, the temperatures almost kept
steady.
The windows and the door closed during the experiment,
therefore, the office can be treated as air-tightness. Before the
FSAC worked, the indoor air did not move, and the initial air
velocity was taken as 0 m/s. The initial air temperature in the
office was 27 8C and the set value of the FSAC 20 8C. Mass
flow rate of outflow was 0.386 kg/s. The time step size was set
as 1 s. Height of the occupied zone was 1.8 m.
In addition, there was no solar radiation entering the office
through the windows, and no computers worked, meaning that
there were no internal heat sources.
4.5.2. Comparison between simulation and experimental
results
Considering that the optimization was done based on the
steady air diffusion of the temperature-preserving phase, Fig. 6
shows the comparison between the simulated and experimental
values of the 20 indoor measurement points during this phase.
The experimental data were the average value in 1 min, and so
did the simulated data.
From Fig. 6(a), it was noted that an excellent agreement was
achieved between the measured and simulated value of air
temperature. The maximum absolute error of temperature was
1.39 K (at measurement point 15), with the maximum relative
error 0.47%.
According to Fig. 6(b), the simulated air velocity distribu-
tion (relative magnitude of velocity) at the whole measured
points yielded a good match with the measured results, though
the maximum relative error at point 13 reached 67.03%. The air
velocity was usually very low (the lowest value was 0.085 m/s
at point 13) and always fluctuated, which induced that the
accurate measurement of velocity was almost impossible. Thus,
the well-matched velocity distribution is more important and
creditable to verify the simulation, compared to the relative
error at a single point.
Consequently, the simulated results can well reflect the
actual airflow field in the office equipped with the FSAC, which
Precision Purpose
0.2 8C Measuring temperature
0.1 8C Calibration
�3% of reading Measuring velocity
– Collecting data from thermocouples
Table 10
Boundary temperatures of walls (8C)
Internal wall 1 Internal wall 2 Internal wall 3 External wall Ceiling Floor Windows Door
29 29 26.5 31 23 29 31 29
Table 9
Fit results of temperature difference between inflow and outflow (8C)
Temperature-lowering phase Temperature-preserving phase
Phase t � 53 s t > 53 s I II
Compressor off Compressor on
Fit values 0.0002t3 � 0.023t2 + 0.8658t � 0.5086 0.0094t + 10.5207 4.66 13.38
W. Liu et al. / Energy and Buildings 40 (2008) 59–7066
shows that the airflow simulation model was reasonable and
applicable.
The reasons to the errors between the simulation and the
experiment are as follows:
(1) t
Fig.
poin
he physical model of the office was simplified based on the
actual structure;
(2) t
he numerical model had some errors, such as round-offerror and discretization error;
(3) t
here were small differences between the calculationconditions and the actual conditions.
4.5.3. Variety in average air temperature during the
temperature-lowering phase
In fact, the operation of the compressor is controlled
according to the inflow temperature of the FSAC. Therefore,
specifically, the temperature-lowering phase is defined as the
process of the inflow temperature dropping from an initial value
to a set value.
Fig. 7 depicts the variety in the average air temperature of
the occupied zone and the inflow temperature during the whole
6. Comparison between the simulated and the measured values of the test
ts.
temperature-lowering phase based on the airflow simulated
result.
As shown in Fig. 7, the average air temperature had a faster
decreasing trend than that of the inflow during the whole
temperature-lowering phase. Therefore, when the inflow tempe-
rature dropped to 20 8C (the set value), the average temperature
was about 0.6 8C lower than the set value, which meant the latter
reached the set value of the FSAC more rapidly. In this
simulation, the actual time consumed in the process of average
air temperature of the occupied zone dropping to the set value
was 1942 s, while the temperature-lowering phase lasted 2270 s.
5. Determination of optimal air diffusion of the FSAC
Theverified airflow simulation model was used to calculate air
diffusion of the office conduced by different inclination angles of
the vanes in the outlet of the FSAC. Based on the simulated
results, performance of these air diffusion types in the occupied
zone were evaluated employing the three indexes, ADPI, EUC
and FCEI, respectively. By comparing and analyzing the
evaluated results, the optimal air diffusion type can be obtained.
In the simulation, the calculation conditions were the same
as those in Section 4.5, except for the initial temperature of the
office and the set value of the FSAC. Here, the two values were
separately 30 8C and 26 8C.
5.1. Inclination angle of the vanes
Theoretically, the vanes in the outlet of the FSAC can rotate
1808 (from +908 to �908), as shown in Fig. 8.
Fig. 7. Variety in the average air temperature of the occupied zone and the
inflow temperature during the temperature-lowering phase.
Fig. 8. Range of inclination angles and corresponding values of Pia.
Fig. 9. Variation of ADPI and EUC with time in the temperature-preserving
phase.
Fig. 10. ADPI of air diffusion for different inclination angles.
W. Liu et al. / Energy and Buildings 40 (2008) 59–70 67
Here, a dimensionless parameter is used to denote an
inclination angle of a vane, defined as,
Pia ¼ � inclination angle ð�Þ90�
(19)
where ‘‘+’’ means up-inclination, ‘‘�’’ down-inclination and 0
a horizontal angle.
Correspondingly, the value of Pia can change from +1.0
(+908) to �1.0 (�908).
5.2. Values of ADPI and EUC
As mentioned before, the indoor airflow is unsteady because
of the intermittent operation of the FSAC. As a result, the values
of ADPI and EUC change with time. However, considering
variation of the airflow field was small in the temperature-
preserving phase, both values can achieve stabilization (vary
slightly) at one time. Here, this time is titled as ‘‘stabilization
time’’.
For a better evaluation on air diffusion, the stable value of
ADPI and EUC should be applied. Thus, first the stabilization
time was determined.
5.2.1. Stabilization time
Fig. 9 gives the variation of ADPI and EUC during the early
10 min of the temperature-preserving phase for four inclination
angles.
In the calculation of ADPI, the indoor control temperature
(thermal comfort temperature) in Eq. (2) was taken as 26 8C in
summer [21,22].
In Fig. 9, 0 means the initial time of the temperature-
preserving phase when the inflow temperature of the FSAC
reached the set temperature for the fist time. According to the
trend shown in Fig. 9, it revealed clearly that the 8th min was
the stabilization time in this study.
5.2.2. Value of air diffusion performance index
For 10 inclination angles, values of ADPI and EUC were
calculated and compared based on the airflow simulation,
respectively. The 10 angles were�408,�108, 08, 108, 208, 308,358, 408, 458 and 608. The corresponding values of Pia can be
found in Fig. 8.
Fig. 10 shows the values of ADPI at the 8th min in the
temperature-preserving phase (the stabilization time). Figs. 11–
13 show the air temperature distribution on a middle section of
the office (Y = 2.72 m) when the inclination angle is �408, 208and 608, separately.
As illustrated in Fig. 10, when the inclination angle was
�408 or 608, the ADPI had a smaller value. As the angle was
between 20 and 458, it had a bigger value. In detail, for the
calculated 10 inclination angles, the ADPI reached its
maximum value of 0.69 at the angles of 208 and 358, and
minimum value of 0.4 at the angle of 608.It can be noted that values of ADPI for up-inclination
(except 608) were higher than those for down-inclination. This
was explained as follows.
The simulated results indicated that the average temperature
of the occupied zone (25.3–25.7 8C) was lower than the thermal
comfort temperature (26 8C) for any inclination angle, which
meant that air temperatures at most locations were smaller
than 26 8C. Thus, for these locations, the effective draft
temperature difference has the possibility of meeting the
Fig. 11. Air temperature distribution (K) on the section Y = 2.72 m when the
inclination angle is �408.
Fig. 12. Air temperature distribution (K) on the section Y = 2.72 m when the
inclination angle is 208.
Fig. 14. A fit curve of ADPI.
W. Liu et al. / Energy and Buildings 40 (2008) 59–7068
comfort specifications, only if the air velocity is low enough,
according to its definition in Section 3.2. When the vanes
inclined down, the outflow from the outlet of the FSAC was
fully developed in the occupied zone, as shown in Fig. 11,
which led to higher air velocity at most locations. Conse-
quently, the value of ADPI was lower. Compared with down-
inclination, as depicted in Fig. 12, only part of the outflow
entered the occupied zone when up-inclination, resulting in
lower air velocity at most locations, so higher value of ADPI.
Fig. 13. Air temperature distribution (K) on the section Y = 2.72 m when the
inclination angle is 608.
As to the inclination angle of 608, the main reason to the
minimum value of ADPI is that the ceiling and the beam
restricted the development of the outflow in the office, which
led to the bad performance of the air diffusion. This can be seen
in Fig. 13.
In order to obtain the air diffusion having the highest value
of ADPI, a polynomials fit on the data provided by Fig. 10 is
needed. It is known the value of ADPI is higher as the vanes
incline up. Taking into account this, here the fit was done on the
up-inclination (Pia � 0), result of which is shown in Fig. 14.
According to Fig. 14, at the Pia of 0.37 (338), the air
diffusion had a maximum ADPI of 0.69. In fact, when the
inclination angle varied between 208 and 458, the value of ADPI
changed slightly (0.68–0.69).
5.2.3. Value of energy utilization coefficient
Fig. 15 gives the values of EUC at the stabilization time.
Fig. 15 reveals the following facts.
(1) V
Fig.
alues of EUC were always higher than 1.0. This is
reasonable considering that the cooler air goes down due to
the buoyant flow, which induces a lower average air tempe-
rature in the occupied zone than out the occupied zone.
(2) T
he value of EUC had a decreasing trend with the value ofPia increasing from �0.11 to 0.67, because only part of the
cooler outflow entered the occupied zone when the vanes
incline upwards, and the bigger the up-inclination angle, the
less the outflow entered the occupied zone.
(3) U
nexpectedly, the value of EUC was not the biggest whenthe Pia had a value of �0.44. It can be seen in Fig. 11 that
the outflow directly flowed to the floor, which meant more
cold was consumed in removing the heat flux from the floor.
Therefore, the average temperature difference between the
occupied zone and the non-occupied zone was not the
maximum, so did the value of EUC.
15. EUC of air diffusion for different inclination angles and its fit curve.
Fig. 16. FCEI of air diffusion for different inclination angles and its fit curve.
Table 11
Comparison of air diffusion performance between two installation locations
Location 08 208
ADPI EUC FCEI ADPI EUC FCEI
Middle 0.61 1.195 18.34 0.69 1.105 19.26
Corner 0.38 1.201 16.70 0.54 1.080 20.14
W. Liu et al. / Energy and Buildings 40 (2008) 59–70 69
A polynomials fit on the calculated data of EUC is also
described in Fig. 15. The fit result indicated when the
inclination angle is �208 (Pia is �0.22), the corresponding air
diffusion had a maximum EUC of 1.241.
5.3. Values of fast-cooling effect index
The index FCEI was used to evaluate the fast-cooling effect
of air diffusion. Here, the value of ict was 50 s. Seven
inclination angles were chosen for comparing the values of
FCEI. The result is plotted in Fig. 16.
When the value of Pia was 0, the FCEI reached the smallest
value of 18.34. When the vanes inclined upwards, part of the
cooler outflow, not the whole, entered the occupied zone to cool
the air, so the values of FCEI were bigger. When the vanes
inclined downwards, more cold of the outflow was consumed in
removing the heat flux from the floor and the desks, resulting in
the bigger values of FCEI, too.
A polynomials fit on the calculated results of the FCEI is
given. According to the fit curve, the air diffusion due to the
inclination angle of 48 (Pia is 0.03) had a minimum FCEI of
18.33, which means the least value of act was 916 s.
5.4. Comparison between two installation locations
Besides the installation location of the FSAC in the previous
simulation (shown in Fig. 3), a corner of the office is also a
familiar installation location, which is plotted in Fig. 17.
Here, for two inclination angles of 08 and 208, the
comparison between both locations was done. The results
Fig. 17. Geometry of the office as the floor-standing type air-conditioner in the
corner.
are illustrated in Table 11. For ADPI, the air diffusion had a
larger value when the FSAC was in the middle. However, the
values of EUC were almost the same. As to the FCEI, when the
inclination angle was 08, this value for the middle location was
more than that for the corner location, whereas when the
inclination angle was 208, the result was inverse.
5.5. Discussion
Among the three evaluation indexes in the present study,
ADPI and EUC are applied for the temperature-preserving
phase, and FCEI for the temperature-lowering phase.
Here, ADPI is prior to EUC when evaluating the
performance of the air diffusion. There are two reasons. On
one hand, thermal comfort is the emphasis of this study. On the
other hand, the value of EUC was higher than 1 for any
inclination angle of the FSAC, which indicates a fine energy
utilization efficiency.
Based on the results in Sections 5.2–5.4, it is preferable to
install the FSAC in the middle close to one internal wall of the
office (as shown in Fig. 3), and the inclination angles of the
vanes corresponding to the optimal air diffusion are given in
Table 12.
According to Table 12, a control scheme of the FSAC was
suggested. When the FSAC starts, regulate the inclination angle
of the vanes to 48 for fast cooling. After about 916 s, set the
vanes to incline up 338 for best thermal feelings and good
energy utilization efficiency.
In this work, the office can be regarded as a typical room
equipped with a FSAC, with its size matching the rated
refrigerating effect of the FSAC. In addition, the indoor air
diffusion mainly depends on the airflow from the outlet of the
FSAC, and the effect of outdoor conditions was less. Therefore,
for most instances, the optimization results are applicable.
And, the evaluation method presented in this paper can almost
be used for various air diffusion conduced by room air-
conditioners.
Table 12
Optimal inclination angles of the vanes for the floor-standing type air-condi-
tioner
Location of the
floor-standing type
air-conditioner
Temperature-lowering
phase
Temperature-preserving
phase
Inclination
angle (8)FCEI/
act (s)
Inclination
angle (8)ADPI EUC
Middle close to
an internal wall
4 18.33/916 33 0.69 1.075
W. Liu et al. / Energy and Buildings 40 (2008) 59–7070
6. Conclusions
The performance of indoor air diffusion of the FSAC was
evaluated and optimized, based on the results of airflow
simulation. Following conclusions can be obtained.
The simulated results can well reflect the actual airflow field
in the office equipped with the FSAC. The airflow simulation
model built in the paper is reasonable and applicable.
Traditional evaluation indexes, such as air diffusion perfor-
mance index and energy utilization coefficient, should be
modified before employing to the air diffusion of room air-
conditioners. By appropriate modification, both indexes can be
used to obtain more reasonable results in the evaluation on air
diffusion performance of room air-conditioners.
In the temperature-lowering phase, the optimal air diffusion
is due to the inclination angle of 48 (the best value I), which has
a minimum value of fast cooling effect index.
In the temperature-preserving phase, the optimal air diffu-
sion is induced by the inclination angle of 338 (the best value
II), which has a maximum value of air diffusion performance
index and fine energy utilization coefficient.
It is suggested that when the FSAC starts, regulate the
inclination angle of the vanes to the best value I for fast
cooling. After the average air temperature of the occupied
zone reaches the set value, set the inclination angle to the best
value II for best thermal feelings and good energy utilization
efficiency.
It is preferable to install the FSAC in the middle close to one
internal wall of the office for higher thermal comfort level.
Acknowledgements
The project was financially supported by National Natural
Science Foundation of China (no. 50478018). The authors
wish to acknowledge Zhijian Hou and Zhengping Zhou for
their assistance during the experiment. And also, the authors
want to express thanks to Ms. A.L. Lian for her translation of
the paper.
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