Cross Flow Fan. Ceiling Fan. Fan Coil Unit. All Air System. Centrifugal Fan. Axial Fan 1 Ã. V(m/s). Figure 6. The variation of β value with the mean velocity in the ...
Studies on the Fluctuation Characteristics of Airflow in the Built Environment ZHU Yingxin, OUYANG Qin, JIANG Yi Department of Building Science & Technology, Tsinghua University, Beijing 100084, China Abstract: The fluctuation characteristic of airflow is one of the important factors to influence the indoor thermal environment and human thermal comfort, which attracts researchers’ interest in these years. This paper introduces the recent researches on the fluctuation characteristics of airflow conducted in Tsinghua University. Results show that there exist obvious differences and interesting connections between the fluctuation characteristics of natural and mechanical wind in built environment, which may be main reason why people have different thermal sensations to them. The subject’s vote of thermal comfort for the imitating natural wind, sinusoidal airflow and constant airflow shows that the acceptance for imitated natural wind is the highest at the same mean velocity. Keywords: built environment; fluctuation characteristics of airflow; thermal environment; thermal comfort 1. Introduction The steady thermal environment is the goal of the conventional building thermal environment control, which is characterized by human neutral thermal sensation, airflow speed lower than 0.15 m/s and the relative humidity around 50%. Although the steady thermal environment is easy for control, it may cause two main problems in actual applications: the “air-conditioning syndrome” due to the lack of environment stimulus and the high energy cost because of keeping the constant low air temperature for human thermal comfort. Many field surveys show that the naturally-ventilated built environment has better acceptability by human bodies. In 1992, Busch et al. [1] investigated the thermal comfort of occupants in both naturally-ventilated buildings and air-conditioned buildings in Bangkok and Thailand. They found that in naturally-ventilated buildings, the comfortable air temperature is higher than that in air-conditioned buildings, and the natural wind with relatively high mean velocity is more acceptable than mechanical wind at the same velocity. Other researchers got similar conclusions from studies in some other places such as Libya and China [2, 3]. The most obvious difference between natural wind and mechanical wind in built environment is the difference of airflow generation source, which consequentially leads to the different fluctuation characteristics of the two kinds of winds. Go deep into study the fluctuation characteristics of natural wind and mechanical wind in the domain of building environment, considering human thermal sensation, is significant for improving indoor thermal environment. If the naturally-ventilated environment is
generated passively or actively, it may be able to obtain indoor environment satisfying the human health while saving energy, It may bring great innovation to the traditional air conditioning mode. Tsinghua University started the research of the fluctuation characteristics of airflow and their impact on thermal comfort since 1990s. Some recent achievements of fluctuation characteristics of airflow research are briefly introduced in this paper. 2. Typical parameters of fluctuation characteristics of airflow In the research, many parameters describing the fluctuation characteristics of airflow from stochastic analysis theory, turbulence statistical theory, chaos and fractal theory are involved, such as turbulence intensity, turbulent integral/eddy time scale & length scale, self correlation coefficient, spectral characteristics parameters, correlation dimension and phase space reconstruction map. ZHU Y. Q.[5] suggested 4 indexes for distinguishing natural wind and mechanical wind. Beside the slope of power spectral curve, the dimensionless width of phase space reconstruction map, information entropy and information dimension were proposed as well as the criteria indexes. Which among them are the typical and necessary parameters to represent the fluctuation characteristics of airflow in built thermal environment? Is it necessary to replenish some other parameters? In the viewpoint of the final purpose of this study, – control the fluctuation characteristics of airflow to improve human thermal comfort, the chosen typical parameters should firstly be closely correlative to human thermal comfort, and secondly, they should be independent from each other. Further study shows that, the skewness of probability distribution of velocity (Sk β value), turbulence intensity (Tu value) and spectral characteristics (including and e value) are not only correlative to the human thermal comfort, but also have independent physical meanings and represent some aspects of the fluctuation characteristics of airflow,, so that these parameters can be considered as the typical/necessary parameters describing the fluctuation characteristics of airflow in built thermal environment. Furthermore, the spectral characteristics are the most important parameters among them. In addition, the turbulent integral length scale (the scale of large eddy) L value can be considered as an important subsidiary analytical parameter because of its explicit physical meanings. The turbulence intensity (Tu) shows the information on the average magnitude of the velocity fluctuation over an interval of time related to the mean velocity, which is defined by:
Tu =
v′ 2 v
(1)
Where v is the mean velocity (m/s), v′ is the fluctuant velocity (m/s). The skewness (Sk) describes the difference of the probability distribution of the velocity from the normal distribution, which is defined by:
Sk =
1 N
N
∑(
vi − v
i =1
v
)3
(2)
'2
Power spectrum analysis is an important analyzing tool to study the fluctuation characteristics of airflow. The power spectral density function in spectrum analysis can give the relationship between frequency and its corresponding energy of different eddies. The power spectrum density function E(f) meets the following equation: ∞
∫
0
E( f )df = v′2
(3)
where f is the frequency (Hz). β The negative slope of logarithmic power spectrum curves ( ) in human sensitive frequency region (0.01-1 Hz) is used as the index in the spectral analysis. A β fluctuation of constant power spectrum independent of the frequency (namely =0) is β termed 1/f 0 fluctuation or white-noise. The noise with equal to 2 is named β Brown-noise, and the noise with value between 0 and 2 is named 1/f fluctuation. The 1/f fluctuations are ubiquitous in nature and have close relationship with people’s pleasure [4]. β Figure1 illustrates the and e value in the logarithmic power spectrum chart. Figure 1(a) shows a very typical 1/f fluctuation. But it is easy to find that the power spectrum curve of some mechanical air flow is far from a beeline, see Figure 1(b). Therefore, a new index e was proposed for indicating whether the wind velocity signal has 1/f fluctuations property: 1 e = N
∑ (lg E
n
2 ( f ) − lg E ( f ) )
(4)
Where E(f) is the original power spectrum density function; En(f) is the linearly fitted power spectrum density function, which meets E n ( f ) ~ f
−β
.
When e value is less than 0.4, the velocity signal of airflow can be regarded to have 1/f fluctuations property. The scale of large eddy L indicates the typical length of the large eddy and is correlative closely with the boundary conditions.
3
0
2
-1
1
-2
β -3
β = 1.1
-1
lg E(f)
lg E(f)
0
= 1.1
-4
-2
-5
-3
-6
-4 -5 -4
-3
-2
-1
-7 -4
0
-3
-2
lg f
-1
0
lg f
(a) airflow 1 （β=1.1, e=0.3） (b) airflow 2 （β=1.1, e=0.54） Figure 1 The Logarithmic power spectrum curve of the airflow 3. The fluctuation characteristics of natural and mechanical wind 3.1 Natural wind Figure 2 to Figure 5 show the statistical distribution result of the fluctuation characteristics of natural wind under various environments. Although the fluctuation characteristics of natural wind are a little different due to the difference of the sampling environments, but the similarity among them is more and greater than their individuality. The natural wind samplings with low velocity (less than 3m/s) which are acceptable to human body all have the following characters: in the power β spectrum curve, value is between 1.4~1.7; e value distributes between 0.3~0.35 (indicating the good accordance with 1/f fluctuations); Tu value is relative higher (usually larger than 0.5); the probability distribution of velocity presents obvious abnormal distribution. In addition, L value of outdoor natural wind is generally in the magnitude of 101 m while that of indoor airflow is close to the dimension of the actual room. 60%
40%
60%
percentage
Pencentage
80%
20%
40%
20%
Outdoor open area
value Around the building
25 0 .
1. 31. 2
1. 41. 3
β
1. 51. 4
1. 61. 5
1. 71. 6
0%
1. 81. 7
1. 91. 8
0%
e value
Indoors
β Figure 2. The distributions of values of natural wind
Outdoor open area
Around the building
Indoors
Figure 3. The distributions of e values of natural wind
60%
100%
40%
percentage
percentage
80% 60% 40%
20%
20%
Tu value Outdoor open area
Around the building
00. 5
0. 51. 0
1. 01. 5
1. 52. 0
2. 03. 0
2 40. 0.
0.
60.
4
6 80. 0.
1.
00.
8
0 21. 1.
3. 04. 0
0%
0%
S k value Indoors
Outdoor open area
Around the building
Indoors
Figure 4. The distributions of Tu values Figure 5. The distributions of Sk values of natural wind of natural wind But it should be noticed that, the test results of the natural wind by seashore show that the fluctuation characteristics of the natural wind near the ground change when the mean velocity increases to a higher extent. For example, when velocity is higher than 5 m/s,β value and Tu value will decrease, the probability distribution of the velocity will trend to normal distribution. 3.2 Mechanical wind The mechanical wind is produced by artificial mechanical system of high-speed rotating vanes, so the fluctuation characteristics of airflow near the air supply outlet is unavoidably influenced by this mechanical system. With the increase of jet distance, the jet flow gradually diffuses into the space and entrains the ambient air around, then the velocity descends and the scale of airflow movement increases gradually. Therefore, the fluctuation characteristics of the airflow may change obviously. The various mechanical wind environments have been tested and investigated, and it is found that: 1) The fluctuation characteristics of mechanical wind transform obviously in the space. In the position near the air supply outlet, β value of the mechanical wind is usually between 0~0.5, Tu value is relative lower, and the probability distribution of the velocity is normal. With the jet distance extending, β value，Tu value，L value gradually increase, average velocity decreases and the probability distribution of the velocity presents abnormal distribution. 2) Analysing the test results of air flow at different air supply velocity, from different kinds of fans and air diffusers, it is found that in the mechanical airflow diffusing process in the building space, both the changes in mean velocity and the large eddy’s scale (L value) are important and independent factors influencing the fluctuation characteristics transformation. The influences of these two factors are inverse. Figure 6 shows the variations of β value with mean velocity, and it is found that they variations with different kinds of wind generation sources.
2.0 1.8 1.6 1.4
ß
1.2 1.0
Ceiling Fan
0.8
Axial Fan 2
0.6
Fan Coil Unit All Air System
0.4
Axial Fan 1
0.2
Cross Flow Fan
0.0 0.0
0.5
1.0
1.5
2.0
2.5
Centrifugal Fan 3.0
3.5
4.0
V(m/s)
Figure 6. The variation of β value with the mean velocity in the diffusion of space of different kinds of mechanical wind 3.3 The differences and relations between the fluctuation characteristics of natural wind and mechanical wind Colligate the research of various cases of natural wind and mechanical wind, it can be found that between the fluctuation characteristics of natural wind and mechanical wind in built environment there exist obvious differences and interesting relations. The transformations of the fluctuation characteristics of natural wind and mechanical wind with mean velocity can be illustrated as Figure 7. When the mean velocity is less than 3 m/s, the fluctuation characteristics of natural wind keep constant in different built environments, while those of mechanical wind vary obviously with jet diffusing in the space. With the decrease of mean velocity, the fluctuation characteristics of mechanical wind tend to close to those of natural wind, but only when the mean velocity decreases to the imperceptible velocity range (less than 0.3 m/s), the fluctuation characteristics of mechanical wind will possibly reach to those of natural wind. In this case, the mean velocity is too low to affect human thermal comfort. The dynamic characteristics Natural wind
Mechanical wind
0.25 m/s
3 m/s Mean velocity
Figure 7. The differences and relations between the fluctuation characteristics of natural wind and mechanical wind
Figure 8. The spectral characteristic of natural and mechanical wind
Considering spectral characteristics as an example (as Figure 8), the spectrum of β typical natural wind (curve 4 in Figure 8) meets the rule of “1/f fluctuation”, and value keeps at 1.5 or so. For the mechanical wind around the air outlet, because of the shearing action of the vanes of fan, the energy of mechanical wind mainly concentrates in the frequency region higher than human sensitive region (0.01-1 Hz). β The spectrum (curve 1) is still “white noise” (namely =0) in human sensitive frequency region. With the diffusion and attenuation of mechanical wind in the room space, the energy of the high frequency dissipates quickly. The spectrum curves drift to the direction of natural wind (curve 1→ curve 2→ curve 3), and is close to the spectrum of natural wind (curve 4) when the mean velocity is less than some extent (about 0.3 m/s). Therefore, for mechanical wind, if only the mean velocity is in the scope of sensible velocity (higher than 0.25 m/s), the spectral characteristics are obviously differenct from those of natural wind and far from “1/f fluctuations”. Because the close relationship between the 1/f fluctuations and human comfort, it’s concluded that it is the main reason why people prefer natural wind to mechanical wind. The spectral characteristic is the most important parameter reflecting fluctuation, so it is believed that in the perceptible velocity scope, the differences in spectral β and e) can be regarded as the main criteria to characteristics (the values of distinguish the natural wind from mechanical wind. 4. The practice to imitate natural wind The main purpose of studying the fluctuation characteristics of natural wind and mechanical wind is to ameliorate the artificial air flow environment so that to improve human thermal comfort. 4.1 The practice to imitate natural wind At present, terminal throttle valve opening control and the variable frequency control of the fan motor are two main effective methods to realize the dynamic control of artificial airflows. Figure 9 and Figure 10 show the principles of these two methods respectively. Timing phase control signal
Phase current
Stepper motor
Drive Circuit
Computer
Control the motion of valve
Valve
Figure 9. The principle of terminal throttle valve opening control 0～10V voltage analog output
Computer D/A
Frequency changer
Control the rotational speed of fan
Fan
Figure 10. The principle of variable frequency control of fan However, it’s found that, due to the restriction of the response frequency of the ‘dynamic air generator’, whether in the terminal throttle valve control or variable frequency control of fan motor, there both exist ‘effective control’ part and ’ineffective control’ part in the spectrum of dynamic airflow near the outlet. It
means that under present technical level, although the ‘dynamic air generator’ can effectively change the low-frequency energy distribution of the dynamic airflow, it is hard to eliminate the high-frequency energy inherently exists in the mechanical airflow. Besides, the distribution of fluctuation characteristics of airflow in the building space is studied. It is found that the spectrum of airflow transform obviously with the airflow dissipates in the space. Figure 11 shows the transformation rules of the spectrum of dynamic airflow (generated by variable frequency control of the fan motor, and the control signal is time averaged original signal of natural wind velocity) in the space. Effective control Ineffective control
Figure 11 The transformation rule of the spectrum of dynamic wind in space The spectrum of airflow near the outlet (as curve 1 in Figure 11) differs much from that of the original natural wind signal (there exist obvious ‘effective control’ part and ‘ineffective control’ part). With the jet distance extended, the spectrum curves drift from curve 1 curve 2 curve 3. Curve 4 in Figure 11 shows the spectrum of uncontrolled steady mechanical wind near the outlet. Through of variable frequency control, it is change to curve 1. Then, with the dissipation of the airflow, the control signal’s influence on the airflow weakens gradually, so the negative slope of ‘effective control’ part of the spectrum curve decreases gradually. While the ‘ineffective control’ part of the curve shifts to low-frequency region continuously, indicating the high-frequency energy dissipates continuously during the diffusion of airflow. When the jet distance reaches to some extent, the ‘effective control’ part and ‘ineffective control’ part of the spectrum curve conjoin into a smooth oblique line, which is shown as curve 3. Through the control method above, the dynamic airflow with the mean velocity of nearly 1 m/s and having similar fluctuation characteristics as those of natural wind can be generated. While for the constant mechanical wind, generally only with sufficient mean velocity dissipation in the space to` the extent lower than 0.3 m/s, the fluctuation characteristics may close to those of natural wind. In this point of view, it is able to produce artificial airflow having the fluctuation characteristics of natural wind in the perceptible velocity scope (V>0.3 m/s) by this dynamic air generator, and
→
→
the imitation of natural wind is realized to a certain extent. 4.2 The experiment of thermal comfort vote In order to test the effect of imitating natural wind, the thermal comfort subject vote is carried out. Figure 12 to Figure 15 give the subject evaluation on the sensation to three kinds of airflow (imitating natural wind, sinusoidal airflow and constant airflow). The result shows that the subjects have the best sensation to the imitating natural wind. Table 1 gives the average value and standard deviation of TSV (Thermal Sensation Vote) and TCV (Thermal Comfort Vote), which shows that TSV of the dynamic airflow (imitating natural airflow and sinusoidal airflow) is lower than the constant airflow by 0.37 and the TCV of imitating natural airflow is close to 0 the most (which shows the subjects are the most comfortable). The above results are all passed by test of significance. 100%
87.0%
80%
80%
76.0%
71.4%
61.3%
60% 60%
50.0% 43.8%
49.0% 43.8%
40% 40%
28.6%
20%
24.0%
13.0%
31.9%
20% 6.3%
5.2%
2.1%
6.8%
0%
0%
Constant airflow
Constant airflow Imitating natural Sinusoidal airflow wind Wish to increase or keep the airflow
weak
Imitating natural wind
Normal
Sinusoidal airflow
Strong
Stronger
Wish to decrease the airflow
Figure 12. The evaluation on the demand for airflow 100%
Figure 13. The evaluation on the intensity of airflow
80%
75.5%
80%
69.3%
63.5%
60.9% 60%
60% 39.1%
40% 20%
95.8%
100%
83.3%
30.7%
40%
36.5% 24.5%
16.7%
20% 4.2% 0%
0% Constant airflow
Imitating natural wind
monotone
Sinusoidal airflow
no monotone
Constant airflow
Imitating natural wind
Sinusoidal airflow
discomfortable feeling for the wind no discomfortable feeling
Figure 14. The evaluation on the Figure.15. The evaluation on the monotonicity of the airflow sensation for the airflow The result of subjects’ favorite airflow is revealed in Figure 16 to Figure 18. In neutral-warm environment, the imitating natural airflow is preferred by more subjects. And 91% of subjects believe that imitating natural wind is better than the constant airflow. The percentage of acceptance of sinusoidal airflow comes next after the imitating natural airflow.
Table 1. The average value and standard deviation of TSV and TCV of three kinds of airflow Imitating natural Constant airflow wind Sinusoidal airflow Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. TSV 0.609 0.7207 0.239 0.5719 0.22 0.6648 TCV -0.486 0.5118 -0.297 0.3329 -0.372 0.4537 Note:1) TSV index: 3 hot, 2 warm, 1 slightly warm, 0 neutral, -1 slightly cool, -2 cool, -3 cold; 2) TCV index: 0 comfortable, -1 slightly uncomfortable, -2 uncomfortable, -3 very uncomfortable 91%
100% 80%
80%
80% 60%
54%
60%
54% 46%
60%
40%
40%
20%
20%
37%
40% 20%
9%
0%
0%
0% Constant airflow
Imitating natural wind
9%
Imitating natural wind
Sinusoidal airflow
Figure 16. Selection Figure 17. Selection proportion for proportion for imitating constant airflow and natural wind and imitating natural wind sinusoidal airflow
Constant airflow
Imitating natural wind
Sinusoidal airflow
Figure 18. Selection proportion for three kinds of airflow
5. Conclusion Generally speaking, the conclusions are drawn as the followings: 1) The skewness, turbulence intensity and spectral characteristics (including β value and e value) can be regarded as the typical parameters to describe the fluctuation characteristics of airflow, and the spectral characteristics are the most important parameters among them. 2) Compared with mechanical wind, the fluctuation characteristics of natural β β wind in different environment have the commonness include higher value ( >1.1) with smaller e value(0.3~0.35, having 1/f fluctuations property), larger L value, higher Tu value (Tu >0.4) and abnormal probability distribution of velocity. But when velocity is higher than 5 m/s,β value and Tu value will decrease, the probability distribution of the velocity will trend to normal distribution. 3) The fluctuation characteristics of mechanical wind around the air supply opening or with the relatively high mean velocity are obviously different from those of natural wind. With the jet diffusion of mechanical wind in the space, the fluctuation characteristics (especially spectral characteristics) would gradually drift to those of natural wind. But only when the mean velocity decreases to the imperceptible velocity range (lower than 0.3 m/s), the fluctuation characteristics of mechanical wind will possibly close to those of natural wind. 4) Thermal comfort vote test testify that, in the neutral-warm environments, the imitating natural airflow can improve the thermal sensation and get the most acceptance.
References: [1] Busch J F. Tale of two populations: thermal comfort in air- conditioned and naturally ventilated offices in Thailand. Energy and Buildings, 1992, 18(3-4): 235-249. [2] Ealiwa M A, Taki A H, Howarth A T, et al. An investigation into thermal comfort in the summer season of Ghadames, Libya. Building and Environment, 2001, 36 (2): 231-237. [3] Xia Y Z, Zhao R Y, Jiang Y. Thermal comfort in naturally ventilated houses in Beijing. HV & AC, 1999, 29(2):1-5. (in Chinese) [4] Yamamoto M T. “1/f fluctuations in biological systems,” Proceeding of Annual International Conference of the IEEE Engineering in Medicine and Biology, Chicago, USA, 1997. pp 2692-2697. [5] Zhu Y.Q., Research on the Fluctuant Characteristics of Natural Wind and Mechanical Wind, Thesis of Master Degree of Tsinghua University, China, 2000.5
