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The air conditioning of indoor environments requires compliance with the thermohygrometric conditions of comfort which also includes the air distribution. This work deals with the thermofluid dynamics of the main components of airconditioning systems, namely primary air systems with fan coils and displacement systems examined in winter and summer conditions. The study highlights the problems of each typology and identifies some best plant solutions. The air distribution systems by means of fan coils allow to reach thermal comfort even at very low speeds, which results also in reduced noise in the environment.
The displacement system allows to work with lower air mass flow rate especially in summer cooling (the reduction is around 60%), whereas slightly different situation occurs in winter conditions. It has been found that it is possible to obtain a flow rate reduction of about 50% by combining together heating and cooling, with a considerable energy savings. The paper shows also that further advantages of the displacement systems compared to an allair system, has to do with the air velocity values in the occupied space.
Mixing air Distribution, Fan coil, Displacement Systems, Thermal comfort, CFD analysis.
The air distribution in airconditioned environments is an important issue for thermal comfort. The primary air with fan coil systems and the displacement systems are among the most widely used airconditioning schemes. Usually the assessment of air distribution requires the use of CFD codes that require a lot of time and computing resources. These tools are justified only in important plant applications such as theaters, museums, exhibition rooms, surgery rooms, etc.
Aim of this paper is to discuss a CFD simulation for the most usual type environments (for example offices) with the two types of systems mentioned above in order to obtain simple practical rules for the system design.
The reference room is of 5 x 4 x 3 m, with thick walls of 0,31 m, openings of 1 x 2.5 m, as shown in Figure 1. Furniture is typical of an office with a chair, a desk and a computer, see Figure 2 and Figure 3.
Figure 1. The reference room
Figure 2. Chair and desk
Figure 3. The reference room with chair and desk inside
The Transfer Function Method (TFM) gives a winter and summer thermal loads which for climatic conditions typical of Sicily for winter and summer respectively is 670 W and 1350 W.
The total air mass flow to be introduced by means of the fan coil is 0.056 m³/s in winter and 0.109 m³/s in the summer. The ventilation flow rate is equal to 11.7 L/s or 42 m³/h.
The primary air is fed with a nozzle of 0.2x0.65 m in size, as shown in Figure 4.
Figure 4. Size and shape of the inlet air nozzle and the fan coil
The wall transmittance is 0.441 W/(m².K) and the windows transmittance is 2.937 W/(m².K). The multiphysical problem involves solution of the conservation laws for mass, momentum, energy and concentration. Under assumptions of Newtonian fluid and uncompressible turbulent flow, the averaged NavierStokes equations read as:
$\rho \frac{\partial \mathbf{u}}{\partial t}+\rho(u \square \nabla) \mathbf{u}=\nabla \cdot\left[p l+\mu\left(\nabla \mathbf{u}+(\nabla \mathbf{u})^{T}\right)\frac{2}{3} m(\nabla \cdot \mathbf{u}) l\right]+\mathbf{F}$
$\frac{\partial \rho}{\partial t}+\nabla \cdot(\rho \mathbf{u})=0$
$\rho C_{p} \frac{\partial T}{\partial t}+\rho C_{p} \mathbf{u} \cdot \nabla T=Q+k \nabla^{2} T$
The COMSOL Multiphysics® CFD simulation code was utilized. The air and other material properties are shown in table 2.
Figure 5. The mesh of the model
Continuous equations have been spatially discretized by a finite element approach based on the Galerkin method on nonuniform and nonstructured computational grids made of triangular Lagrange elements of order 2. Influence of spatial discretization has been preliminary studied in order to assure meshindependent results, figure 5.
The global flux across the walls in winter is 750 W, the air temperature from the fan coil is 30 °C, the primary air temperature is 20 °C (neutral conditions), the body temperature of the man inside the room is 36 °C and the computer temperature is supposed to be 50 °C. In summer conditions the wall flux is 1000 W, the air temperature from the fan coil is 18 °C, the primary air temperature is 26 °C (neutral conditions).
The simulation was carried out under the hypothesis that the external temperature is sinusoidal with a period of 24 h. The attenuation and phase factor are calculated according ISO EN 13786 for the type of wall used in the model. The parameters for the simulation are summarized in the following tables:
Table 1. Dynamic parameters wallinnner air for the calculation
Parameter 
Value 
T_{m} winter 
5 °C 
T winter 
10 °C 
T_{m} summer 
25 °C 
T summer 
13 °C 
Material 
(kg/m³) 
C_{p }(J/(kgK)) 
k (W/(m K)) 
Air 
^{p}_{atm}/RT 
1005 
0.028 
Chair 
30 
1400 
0.04 
Body 
985 
3550 
0.60 
Equation 
Inlet 
Outlet 
fluid/solid 
External walls 
1 
u=U_{in} 
p=p_{atm} 
U=0 
U=0 
3 
T=T_{in} 
$\mathbf{n} \cdot(k \vec{\nabla} T)=0$ 
 
$\mathbf{n} \cdot(k \vec{\nabla} T)$$=h\left(TT_{e x t}\right)$ 
Parameter 
Value 
Units 
Thermal flux to the floor 
200 
W 
Thermal flux for internal wall 
150 
W 
Fan coil air temperature 
30 
°C 
Primary air temperature 
20 
°C 
Man temperature 
36 
°C 
Computer temperature 
50 
°C 
Parameter 
Value 
Units 
Thermal flux to the floor 
200 
W 
Thermal flux for internal wall 
150 
W 
Fan coil air temperature 
18 
°C 
Primary air temperature 
26 
°C 
Man temperature 
36 
°C 
Computer temperature 
50 
°C 
4.1 Fan coil system with primary air
The results for the case of primary air with fan coil system, are summarized in the following figures.
Figures 6 to 9 refer to winter condition, whereas figures 10 to 11 refer to summer conditions.
Figure 6. Air Velocity distribution in winter
Figure 7. Air Velocity distribution nearby the human body in winter
Figure 8. Air Velocity distribution in summer
Figure 9. Temperature distribution nearby the human body in winter
Figure 10. Air Velocity distribution nearby the human body in summer
Figure 11. Temperature distribution nearby the human body in summer
The temperature distribution at the head and at the feet of the occupant for winter and summer condition are given in figures 12 and 13.
Figure 12. Air temperature at head and feet in winter
Figure 13. Air temperature at head and feet in summer
On the basis of these results, one can make the following remarks. The primary air and fan coil systems are very simple and reliable. They allow optimal air distribution inside the rooms and make to reach easily the thermal comfort conditions, even at very low speeds. The low speed in turn reduces the noise in the environment.
The use of thicker walls (from 0.331 m to 0.443 m) may allow an easier management of the plant, reducing the energy consumption.
4.1 Displacement system
The second type of plant is the displacement system. The equations to be solved are similar to those already shown. A standard k ε − turbulence model (Launder and Spalding 1974; Ignat et al. 2000) has been applied to solve the momentum equations. Logarithmic wall functions were applied in the near wall flow and considered parallel to the wall. The geometrical position of the components can be seen from Figure 14.
Figure 14. Displacement and inlet grille position
To optimize the meshing grid many calculations were performed, as summarized in the following table 5.
Table 5. Mesh optimization
Mesh 
M_{1} 
M_{2} 
M_{3} 
M_{4} 
Elements number 
26982 
41238 
64814 
85688 
Mean Temperature (°C) 
28.035 
27.696 
27.035 
26.864 
Difference (°C) 
0.339 
0.661 
0.171 

Percentage (%) 
1.22 
2.44 
0.64 

Mean Speed (m/s) 
0.011 
0.017 
0.014 
0.012 
Difference (m/s) 
0.006 
0.003 
0.002 

Percentage (%) 
33.58 
22.14 
14.19 

The dynamic data for the calculation are reported in table 6.
The results of the simulation are shown in the following figures and tables.
Table 6. Dynamic parameters wallinnner air for the calculation
Flow rate at the displacement in winter 
250 
m³/h 
Flow rate at the displacement in summer 
236 
m³/h 
T_{m} winter 
28 
°C 
T_{m} summer 
12 
°C 
Figure 15. Mesh grid of the model and particular view near the displacement
Figure 16. Temperature distribution al the plane of the body in summer
Table 7. Calculated parameters in summer
Parameter 
Head 
Feet 
Difference 
Temperature (°C) 
26.505 
22.867 
3.738 
Speed (m/s) 
0.01217 
0.10791 
0.094 
Figure 17. Temperature distribution al the plane of the body in winter
Table 8. Calculated th parameters in winter
Parameter 
Head 
Feet 
Difference 
Temperature (°C) 
19.063 
16.880 
2.190 
Speed (m/s) 
0.0096 
0.0159 
0.009 
Figure 18. Air flux in winter
Figure 19. Air flux in summer
The simulations were performed in various scenarios, as summarized in the following table 9.
Table 9. Simulation at various scenarios
Parameters 
Seated body 
Seated body and PC off 
Standing body 
Standing body and PC off 

Temperature [°C] 
Head 
26,864 
26,693 
27,223 
26,972 

Feet 
22,41 
22,119 
22,234 
22,019 
Speed [m/s] 
Head 
0,01127 
0,00311 
0,02204 
0,02127 
Feet 
0,13569 
0,13009 
0,16345 
0,16155 
The vertical distribution of the temperature is given in table 10 for the summer and table 11 for the winter.
Table 10. Vertical distribution of the temperature in summer
Point 
Temperature [°C] 

Head 
Feet 

1 
19,081 
16,928 
2 
19,076 
16,868 
3 
19,078 
16,853 
4 
19,063 
16,873 
Mean 
19,075 
16,88 
Table 11. Vertical distribution of the air speed in winter
Point 
Speed [m/s] 

Head 
Feet 

1 
0,0117 
0,0062 
2 
0,0091 
0,0103 
3 
0,0101 
0,0214 
4 
0,0075 
0,0259 
Mean 
0,0096 
0,0159 
Simulations were carried, but not shown here, in transient condition. From the obtained outputs it’s possible to observe that the displacement system allows to reduce considerably the air flow rate during summer cooling (reduction compared to primary air is around 60%). On the contrary, in winter there is an increase of approximately 12% in the air flow.
A further advantage represented by the displacement systems, compared to an allair system, concerns the air speed values in correspondence of the occupants; in fact, because of the characteristics of the mixing systems, traditional air systems promote the air at velocity higher than that of the displacement system.
High air speeds could cause considerable discomfort for occupants.
Other simulations with the airflow vent at the other side of the wall are not presented here but give comparable outcomes.
The CFD simulations of air conditioning systems allow to get a lot of information on fluiddynamic distribution inside the occupied spaces. Simulations for a typical office room showed that displacement systems have higher efficiency and make indoor air quality good. The use of primary air and fan coil systems allows to cover easily the thermal or cooling load and rapidly reach design conditions. External walls (specifically their mass and their transmittance) may play an important role in thermal transients and in HVAC control.
C_{p} specific heat at constant pressure (J/(kg·K))
F magnitude of buoyancy force (N/m3)
h convective coefficient (W/(m^{2}·K))
k thermal conductivity (W/(m·K))
p pressure (Pa)
u magnitude of speed vector (m/s)
Q metabolic heat (W)
t time (s)
T temperature (K)
η ventilation effectiveness
μ dynamic viscosity (Pa·s)
ρ density (kg/m3)
Subscripts
atm atmospheric
ext external
in Inlet
out outlet
T turbulent
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