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Available online at www.sciencedirect.com Procedia Engineering 00 (2017) 000–000
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Procedia Engineering 205 (2017) 2553–2560
10th International Symposium on Heating, Ventilation and Air Conditioning, ISHVAC2017, 1922 October 2017, Jinan, China
A Study of the Temperature Characteristics of Low Speed Curved Surface Jet in the Lower Air Supply Area Ruibin Lia, Chen Huanga,*, Xuelei Gaob, Xin Wanga a
School of environment and architecture, University of Shanghai for Science and Technology, Shanghai and 200093, China b Shenzhen Institute of Building Research Co. Ltd
Abstract Semi-cylindrical diffusers are widely popular in displacement ventilation and lower air supply systems. The big point of the air flow characteristics of the curved surface jet is the “Cold Lake Effect”, arounding the ground. In this paper, we derive a theoretical model of this “Cold Lake Effect” to investigate semi-cylindrical diffusers. The temperature distribution of the air supply in the main section was calculated with different air flow rate and initial air supply temperature. The temperature distribution model was experimentally verified. It is a good agreement with the calculated results, whereby the maximum deviation is 0.812°C. The study of the temperature characteristics, is a reference for making indoor thermal environment comfort better, and it can provide technical measures for designing air distribution systems in displacement ventilation and lower air supply systems. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Conditioning. Air Conditioning. Keywords: Semi-cylindrical diffusers; Low speed curved surface jet; Mathematical model; Cold lake effect; Temperature distribution
1. Introduction Low sidewall air supply of air conditioning can improve indoor air quality and shorten energy consumption, especially in large space. The tuyeres arranged on the ground surface are generally provided with semi-cylindrical diffusers to enlarge the air supply area. As known, the density of the cold air supply is less than that of the indoor * Corresponding author. Tel.: +86-021-55273409. E-mail address:
[email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning. 10.1016/j.proeng.2017.10.231
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airflow of the working zone. The colder air can slow down to the floor by the density difference, and make a lower temperature region, named as “Cold Lake Effect” around the floor. This phenomenon is a burden on the thermal comfort and also on the energy consumption. The cold air supply from the air column is a lower speed curved surface jet. In present, few research has been directed on the underlying facets of this lower speed curved surface jet. A lot of research on the lower air supply systems focused on the application of the system, or the overall indoor wind speed and temperature environment. There is little research on the “Cold Lake Effect”. Therefore, it is necessary to study the “Cold Lake Effect” through a combination of theoretical and experimental approaches. Reports by N. P. V. from a large number of experiments on the flat and column-shaped air outlets arranged on the wall, showed that the ground air speed distribution is affected not only by the air flow but also the temperature difference between the air supply (or the number of Archimedes) and the type of tuyere [1]. Furthermore, a theoretical derivation by M. Sandberg and C. Blomqvist on the airflow movement near the tuyere in the office displacement ventilator laboratory study, obtained an expression representing the air flow speed on the descending point of the initial section of the air outlet and also uncovered a relationship between the air supply temperature and the ambient temperature [2]. Dedicated research into the low speed curved surface tuyere started in the 90's. Characteristic experiments on the curved surface were conducted by R. Ma, describing in detail the air flow characteristics in the curved surface of the displacement ventilation [3]. The influence of the tuyere characteristics on the surface speed field were also analyzed in his paper. Further to this, P. Zhou and Q. Li illustrated a unique system design idea which incorporates thermal comfort standards by using typical displacement ventilation cases [4]. The temperature and speed field of the room were analyzed and measured by different terminal devices. While several theoretical and experimental studies on the characteristics of the air supply jet in a limited space has been carried out by the scholars, the mathematical modeling and experimental studies on the speed and temperature of the airflow in the low speed curved surface are rare. In this paper, we carried out theoretical and experimental research on the characteristics of the airflow under the curved surface air supply in large space, and meanwhile the model of temperature distribution in the main section and its key parameters of the surface airflow were experimentally verified. 2. Methods 2.1. Experiment summary In this paper, an experimental study on the temperature characteristics of the semi-cylindrical air outlets installed in a large space thermal environment laboratory was conducted. The space covers an area of 20 × 14.8 m2. The top height of the roof is 8.75 m, and the lowest point of the roof is 6.5 m. Fig. 1 shows the appearance of the air supply system. The cooling air is supplied by eight semi-cylindrical supply air outlets of 600 mm diameter, which were laid symmetrically on low-side of the north and south wall. The air is returned by eight return air louvers of 400 mm diameter arranged symmetrically at a height of 4 m above. 2.2. The method for determination of the related parameters In order to study the temperature characteristics of the lower speed curved surface jet in the lower air supply area, the ground temperature was measured by an Infrared Thermal Camera. The distribution of the floor temperature measurement points is shown in Fig. 2. The airflow speed and temperature were measured by a hot air-type wind speed transmitter (Universal anemometer). This anemometer is equipped with a wind speed probe and a temperature probe on a short spindle, therefore we can measure the wind speed and temperature simultaneously.
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Fig. 1. The appearance of the air supply system.
Fig. 2. The layout of the floor temperature measuring points.
2.3. Establishment of the length model of the air flow in the initial section Fig. 3 shows a schematic diagram of the curved surface air flow. The surrounding air is sucked in by the air flow via an action of negative buoyancy, assuming the entrainment coefficient is e. It is also assumed that the air flow is insulated from the floor during the process of movement, and the heat transfer due to temperature difference between the air flow and the environment is ignored. As shown in Fig. 3, the surface of the air inlet is section 1, and the end of initial section is section 2. Assuming that the mass flow rate of section 1 is m0, and the mass flow rate of the surrounding air is me. Therefore, by the conservation of energy:
m0 c pT0 + me c pTe = ( m0 + me )c pTa
(1)
Where T0 is the air supply temperature, °C; Te is the environment temperature, °C; Ta is the airflow temperature at the end of initial section, °C; Cp is the air specific heat capacity at constant pressure, J·kg−1·K−1. As entrainment coefficient is e=(m0+me)/m0, can be obtained by substituting e into equation (1) resulting in:
Li /etProcedia al. / Procedia Engineering 205 (2017) 2553–2560 RuibinRuibin Li et al. Engineering 00 (2017) 000–000
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Fig. 3. Schematic diagram of curved surface air flow.
e=
Te − T0 Te − Ta
(2)
The length of the initial section is a, taking a micro-air flow at the top of the tuyere as the analysis object. There is a temperature difference between the airflow and the surrounding air, and this particle has a downward acceleration. As the surrounding air is sucked in by the air flow entraiment in the initial section, the air temperature can be forced to change, so the micro-air flow has a varying downward acceleration caused by this difference in temperature. Alongside this, the horizontal speed component is constant, which is the initial speed of the outlet. Assuming that the downward acceleration of the airflow is linear from the surface of the air outlet to the end of the initial section. Therefore, the acceleration at a certain moment is:
g ′ = g 0′ −
g′ = g
g 0′ − g a′
(3)
τ0
ΔT Δρ =g T ρ
(4)
Where τ 0 is the time required for the small airflow to move from the top to the drop point.
The equation in the horizontal direction is: The equation in the vertical direction is:
a = u0τ 0
τ0
H − ha =
Substituting equation (3) into (6), we can find:
0
0
H − ha =
Where, substituting it into equation (7) we can find:
1 1− g 0′τ 02 e) H - ha = (1 − 6 3
From equation (8) we can find: τ 0
τ
(5)
g ′dτdτ
(6)
g 0′τ 02 g′ (2 + a ) 6 g 0′
(7)
(8)
=
6e( H − ha ) g 0′ (2e + 1)
(9)
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Substituting equation (9) into equation (5), we can find:
a = u0
6e( H − ha ) g 0′ (2e + 1)
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(10)
2.4. Establishment the temperature model of air flow in the main section The cooling airflow moves radially from the initial section. We assume that there is no airflow entrainment along the flow path. The flow rate is eq0, and the convective heat transfer coefficient between the airflow and the floor is hf, whose value takes 8.72 W·m−2·K−1. Heat transfer coefficient of temperature difference between the airflow and the upper air is he, its value to take 2.3 W·m−2·K−1. The average temperature in the vertical direction is Tr, as shown in Fig. 3, the floor temperature is Tf, the environment temperature is Te and the initial temperature of main section is Ta. Along the direction of r, the temperature rise caused by heat transfer is dTr in a micro-body, so the heatobtaining quantity is:
QdT = c p ρql dTr = c p ρeq0 dTr
(11)
r
The heat transfer between air flow and the floor is: QdT = h f (T f − Tr )πrdr
(12)
The heat transfer between airflow and surrounding air is: QdT = he (Te − T f )πrdr
(13)
rf
re
By the conservation of energy QdT = QdT + QdT , as shown in the following equation: r
rf
re
cρql dTr = h f (T f − Tr )πrdr + he (Te − Tr )πrdr
(14)
Introducing the boundary conditions: Tr=Ta at r=r0+a, and neglecting the variation of the air density of the curved surface jet. So we can obtain:
Tr =
h f T f + heTe − c1e
Where c1 =
−
( h f + he )πr 2 2 cρeq0
h f + he h f T f + heTe − Ta ( h f + he ) e
−
π ( r0 + a ) 2 ( h f + he ) 2 cρeq0
(15)
(16)
3. Results 3.1. Analysis of temperature distribution characteristics The characteristic parameters in the initial section are shown in Table 1. There is the heat transfer between the cold air and the surrounding air during movement. The line of the minimum temperature point in the vertical direction corresponds to the trajectory of the air flow. Fig. 4 is the distribution of the minimum temperature in the vertical direction of the single tuyere in different operating conditions. In Table 1, the air flow rate of CASE 1 is 1726 m3·h−1, the air flow rate of CASE 2 is 1225 m3·h−1 and the air flow rate of CASE 3 is 1001 m3·h−1. And the calculated number of Archimedes are also shown in Table 1. From the Fig. 4, with the increase of air flow rate, the location of the minimum temperature point is higher. But at about r=1.1m the minimum temperature remains at the lowest point, at this point, the air flow rate has no effection on the location of the minimum temperature point.
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Fig. 4. The height of the lowest temperature point for a single air outlet. Table 1. Archimedes number and the three parameters in initial. Parameter
CASE 1
CASE 2
1726
1225
1001
Ar
3.13
5.99
9.85
a
1.00
0.80
0.60
ha
0.18
0.23
0.30
Outlet air speed [m·s−1]
0.41
0.29
0.24
Initial section end air speed [m·s−1] Wind speed difference [m·s−1]
0.57 0.16
0.52 0.23
0.59 0.35
Cooling air flow rate [m3·h−1]
CASE 3
3.2. Experimental verification of the length model of airflow and the temperature distribution model In this paper, we establish a mathematical model of the jet flow in a lower speed curved surface, and obtain the correlation expressions of the initial air speed and the temperature distribution of the main section. The model of airflow temperature and the lower speed curved surface jet are experimentally verify. The experimental conditions in this study are shown in Table 2. The entrainment coefficient e is calculated by equation (2). Table 2. Experimental verification conditions. Parameter
CASE 1
Tuyere operation
CASE 2
CASE 3
Single open
Cooling air flow rate [m3·h−1]
1726
1225
1001
Air supply temperature [°C]
17.5
19
19.4
Environment temperature [°C]
29.8
30.92
32.5
Airflow terminal temperature [°C]
21.46
24.75
26.74
Floor temperature [°C] Entrainment coefficient
29.6 1.47
31.22 1.93
32.31 2.27
The initial length of the theoretical value a is calculated by equation (10), and a comparison of experimental and theoretical values are shown in Table 3. The maximum deviation between theoretical and experimental values is 0.1m. So the results conduct that the theoretical values can be verify by the experimental ones. The air specific heat capacity is 1004 J·kg−1·K−3. The air density is taken as 1.2 kg·m−3, c1 is determined by equation (16), and other parameters are taken as the experimental values. CASE1, CASE2 and CASE3 determined the airflow temperature of the Cold Lake along the jet direction on the center line of the air outlet. The comparison between theoretical values of Tr and experimental values are shown in Fig. 5, Fig. 6 and Fig. 7.
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Table 3. The differences between experimental and theoretical values. Parameter
CASE 1
CASE 2
CASE 3
1726
1225
1001
3.13
5.99
9.85
a Measured value [m]
1.00
0.80
0.60
a Theoretical value [m] Deviation [m]
1.12 0.12
0.81 0.01
0.63 0.03
Relative deviation
3.13
5.99
9.85
Cooling air flow rate [m ·h ] 3
−1
Ar
Fig. 5. The comparison between theoretical values and experimental values of CASE 1.
Fig. 6. The comparison between theoretical values and experimental values of CASE 2
Fig. 7. The comparison between theoretical values and experimental values of CASE 3
4. Discussion From Fig. 5, the temperature Tr along the r direction shows approximate linear growth at the outset, and thereafter growth slows down until eventually stabilization. Below 4.1m, the experimental values are slightly larger than the theoretical ones, and after 4.1m, the theoretical values are slightly larger than the experimental values and the maximum deviation is 0.768°C. It can be seen from Fig. 6 that the theoretical and experimental values are consistent. In particular, the experimental values are higher than the theoretical values before 6.1m, with a maximum deviation of 0.812°C and after 6.1m, the experimental values agree well with the theoretical values. Similarly we can see from Fig. 7 that, the experimental values are higher than the theoretical values before 10.1m, with a maximum deviation of 0.72°C and after 10.1m, the experimental values agree well with the theoretical values. In
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conclusion, the experimental values of the average temperature of the air flow in the main section are in good agreement with the theoretical values, so the theoretical values are deemed acceptable by the experiments. 5. Conclusions In this paper, a theoretical model of the “Cold Lake Effect” in the area of the lower air supply by lower speed curved surface diffuser was derived. The temperature distribution of air flow in the main section of the surface air supply was calculated at the conditions of different air volume and air supply temperature. We established a length model of air flow in the initial section and a temperature model of air flow in the main section, and these models were verified by experiments. The results shows that the considerable good agreement between the calculated and measured values. The maximum deviation between the theoretical and experimental values of the initial length was 0.1m. The maximum deviation between the experimental and the theoretical values of the average temperature in the main section was less than 0.812°C. This study is a reference for the improvement of indoor thermal environment comfort, and it is helpful for the design of the air distribution systems in the displacement ventilation and lower air supply systems. Acknowledgements This work is financially supported by the National Natural Science Foundation of China (51278302). References [1] N. P. V, Stratified flow in a room with displacement ventilation and wall-mounted air terminal devices, ASHRAE Trans. J, 1994,100 (pt. 1) 1163-1169. [2] M. Sandberg. C, Blomqvist. Displacement ventilation systems in office rooms, ASHRAE Transactions J, 1989, 95 (2) 1041-1049. [3] R. Ma, Influence of the characteristics of air supply terminal devices on velocity field and temperature gradient in occupied zone with displacement ventilation, HV&AC, 2003, 33 (3) 12-16. [4] P. Zhou, Q. Li, Study on performance and application of displacement ventilation terminal device, Tongji University, (1998 ) 1-112. [5] C. Fan, Air conditioning design and engineering record of large space building, China Architecture & Building Press, 2001. [6] N. P. V, Velocity distribution in a room ventilated by displacement ventilation and wall-mounted air terminal devices, Energy and Building J, 2003, 31 (3) 179-187. [7] C. Y.H. Chao, M.P. Wan, Air flow and air temperature distribution in the occupied region of an under floor ventilation system, Building and Environment J, 2004, 39 (7) 749-762. [8] H. Martin Mathisen, Displacement ventilation - The influence of the characteristics of the supportive air terminal device and the airflow pattern. Indoor Air, 1991, 1 (1) 47-64. [9] R. Ma, Z. Lian, Comprehensive Study on Calculation Method of Thermal Distribution Coefficient in Working Area of Floor, HV&AC, 1994 (1) 11-13.
