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Influence of non-uniform layout fillings on thermal performance for wet cooling tower
Accepted Manuscript Title: Influence of non-uniform layout fillings on thermal performance for wet cooling tower Author: Ming Gao, Lei Zhang, Ni-ni Wang, Yue-tao Shi, Feng-zhong Sun PII: DOI: Reference:
S1359-4311(15)00974-6 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.09.054 ATE 7046
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
12-6-2015 18-9-2015
Please cite this article as: Ming Gao, Lei Zhang, Ni-ni Wang, Yue-tao Shi, Feng-zhong Sun, Influence of non-uniform layout fillings on thermal performance for wet cooling tower, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.09.054. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Influence of Non-uniform Layout Fillings on Thermal Performance for Wet Cooling Tower Ming Gaoa, Lei Zhanga, Ni-ni Wangb,Yue-tao Shia, Feng-zhong Suna* a, School of Energy Source and Power Engineering, Shandong University, Jinan 250061, China b, Shandong Electric Power Engineering Consulting Institute, Jinan, 250014, China *Corresponding author: [email protected], Tel: 0086-531-88395691
Highlights Performance of cooling tower under non-uniform layout fillings is outstanding. Optimal layout pattern is that ra/rc is approximately 0.44 and rb/rc is around 0.71. Performance of optimal layout pattern can enhance by 30% at maximum within the scope of this test. Conclusions can lay important theoretical foundation concerning future research.
Abstract: Based on the similarity theory, thermal-state model experiment in lab is performed to investigate the thermal performance of wet cooling towers under different layout patterns of fillings, and five kinds of layout patterns, including uniform layout and four kinds of non-uniform layout patterns, are studied in this paper. Experimental results manifest that the thermal performance of wet cooling towers under non-uniform layout patterns is outstanding by calculating and analyzing five performance parameters which are ooling termperature difference, cooling efficiency, Merkel number, Lewis number and ratio of evaporative heat rejection. Additionally, research also obtained the optimal three-block layout pattern of fillings in which the radius ratio of ra/rc is approximately 0.44 and rb/rc is around 0.71, here ra, rb and rc are the radius of three blocks, respectively. What’s more, compared with the uniform 1
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layout pattern of fillings, the thermal performance of the optimal layout pattern can enhance by 30% at maximum within the scope of this test. Keywords: Wet cooling tower; Non-uniform layout fillings; Thermal performance;
Comment [U1]: AUTHOR: Two different versions of the Abstract section were provided and the one in the manuscript has been retained. Please check and confirm it is correct.
Experimental research
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Nomenclature
Qm
evaporative heat rejection [KJ]
V wind velocity [m/s]
Qa
contact heat rejection [KJ]
D
mw
circulating water rate [m3/h]
Re Renold number
0
dry bulb temperature [℃]
Fr
wo
wet air temperature at outlet[℃] airflow rate [kg/s]
the lower diameter of model tower[m]
density Froude number
L
characteristic dimension [m]
G air
r
radius of fillings [cm]
H
height of fillings [cm]
air-water ratio
Subscript
P1~P5 five layout patterns of fillings
a,b,c location of filling layout
t
1 inlet
cooling termperature difference [℃]
Le f
K
t
'
Lewis number
2/out outlet lim
ratio of evaporative heat rejection circulating water temperature [℃]
w
limited value water
K
heat coefficient
top the top of the model tower
i
air specific enthalpy [KJ/kg]
superscript
im
averaged specific enthalpy [KJ/kg]
''
saturated
c pw specific heat of water [KJ/Kg.K]
Greek symbols
v
cooling efficiency Merkel number
heat transfer coefficient [W/m2K]
V
mass transfer coefficient [Kg/m2h]
n
c pm a
specific heat of wet air [KJ/Kg.K]
Q
density of air [kg/m3]
total heat rejection rate [KJ] 3
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1 Introduction As a primary component of the cool-end system in thermal power plants or in some nuclear power plants, the wet cooling towers play an important role to cool the circulating water from the condenser, and its efficiency has a great impact on the total cycle efficiency of power plants [1]. Based on the prior studies, the influence factor of efficiency is mainly the thermal performance of filling zone because 70% of heat dissipating capacity depends on the filling zone [2]. Therefore, it is extremely important and necessary to study the heat and mass transfer performance of filling zone both from an academic as well as an industrial point of view. For a long time, many researchers focus on the thermal performance investigation of fillings for wet cooling towers, and the early research may trace back to 1940s [3-5]. Briefly, the research work in regard to fillings is divided into three aspects which are theoretical mathematical model research, model experiment in lab and numerical computation. Concerning theoretical mathematical model research to the thermal performance of fillings, one mathematical model and computer simulation program had been developed to study the thermal performance of splash fillings for counter-flow cooling tower, and the one-dimensional model adopts basic aerodynamic, hydrodynamic and heat/mass transfer information to predict the performance of the filling material without depending on cooling tower test data [6]. In order to evaluate more accurately the thermal performance of fillings, Jose [7] defined a new model parameter called as thermo-fluid dynamic efficiency. Additionally, based on 4
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one-dimensional heat and mass transfer equation, Milosabljevic [8] derived a mathematical model which can also be used to predict the thermal performance of fillings. Aiming at splash fillings, film fillings and splash-film fillings, Kloppers [9] firstly proposed a new form of empirical equation which correlates fillings loss coefficient data more effectively, compared with other forms of empirical equations, and then Kloppers [10, 11] compared and analyzed three mathematical models which are used to performance calculation of wet cooling tower, that is, Poppe model, Merkel model and e-NTU model. Research results reported that Poppe model had a comparatively high accuracy. According to Muangnoi’s study [12], an exergy analysis was used to indicate exergy and exergy destruction of water and air flowing through the cooling tower, and a mathematical model was developed to find the properties of water and air in filling zone. Research showed that the combination of two types of filling material should be chosen by placing very efficient filling material at the bottom region and placing a regular one at the top region. On the basis of one fouling model in filling zone, Khan [13] pointed out that the fouling of fillings is one of the most important factors affecting its thermal performance, which reduces cooling tower effectiveness and capability with time. Previous experiments have been mostly performed to study filling type and filling material. In recent years, a “VGA” (Vertical Grid Apparatus) type filling was adopted to conduct experimental research. Lemouari [14-17] performed a series of experimental investigation of the thermal performance for wet cooling tower filled 5
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with a VGA type filling which is 0.42m high and consists of four galvanized sheets having a zigzag form. In addition, Gharagheizi [18] presented an experimental and comparative study for two film-type fillings which are vertical corrugated fillings and horizontal corrugated fillings. The obtained results demonstrated that the thermal performance of the cooling tower is affected by the type and arrangement of fillings, and the tower with vertical corrugated fillings has higher efficiency than the one with horizontal corrugated fillings. Apart from mathematical model research, Milosabljevic [8] also carried out experimental measurements on two pilot-scale cooling towers in order to analyze the performance of different filling materials. What’s more, the performance of other elements, such as droplet separators and water spray nozzles, was investigated in the pilot experiments. Hu et al. [19, 20] conducted thermal performance experiment of fillings as well, studied the thermal performance of PVC fillings under the different height conditions, and the conclusion manifested that the thermal performance enhances by 25% and the drag coefficient increases by 6Pa if the filling height increases by 0.5m. Based on three different fillings [21] (cross-fluted film, trickle and fibre cement), the drop size distribution beneath different fillings is reported by an experimental apparatus. And the conclusions indicated that the Rosin–Rammler distribution curve generally does not fit the measured data adequately and thus should be avoided. Filling aging and blockage has great impact on the thermal performance of wet cooling towers, one model experiment was conducted to study the thermal 6
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performance of wet cooling towers under filling blockage conditons, and the results declared that the thermal performance of cooling tower decreased under filling blockage conditons [22]. A.M. Lavasani et al [23] dealt with an experimental investigation of thermal performance of a forced draft counter-flow wet cooling tower filled with a rotational splash type filling, and the tower’s performance parameters were compared when the filling had been rotated and when it does not rotate (like common existing towers). As one of the very important application methods, computational fluid dynamics (CFD) method is also used to research the thermal performance of fillings for wet cooling tower. Klimanek [24] presented a filling model of heat/mass transfer for wet cooling tower, which applied the shooting technique with self-adaptive Runge–Kutta step control, and was designed to be included in a large scale CFD calculation of cooling towers where the fillings are treated as a porous medium with prescribed distributions of mass and heat sources. Another CFD model [25] is a two-dimensional axisymmetric two-phase simulation of the heat/mass transfer inside wet cooling towers, and the heat/mass transfer in the filling zone is represented by using source terms implemented with Poppe style transfer coefficients. The results showed a largely uniform velocity profile across the tower radius with the greatest non-uniformity occurring at the outer edge of the tower. In addition, Huang et al [26] also performed the CFD research regarding arrangement of the filling material and spraying water in cooling tower. Bilal A et al [27] explained filling fouling in cooling towers as well as its modeling strategy to study performance evaluation problems, and 7
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the fouling model is put forward in terms of normalized filling performance. Additionally, N. Williamson et al [28] described a simple two-dimensional model to determine the optimal fill shape and water distribution profile to maximinze the cooling rage of a typical natural draft wet cooling tower, and the results showed that the optimal layout differs significantly from a uniform profile. According to the above-mentioned review, the previous studies for fillings inside wet cooling towers focused on filling material and shape in terms of theoretical model, experiment in lab and numerical computation, which are more valuable to wet cooling tower research. However, the prior researches failed to discuss the height difference of filling layout, and regarded fillings as the same height in different radius inside tower. What’s more, actually uniform layout pattern of fillings is unreasonable on the basis of field synergy theory because of the non-uniform air dynamic field inside tower. Thus, studies regarding the layout pattern of fillings are more crucial to the further energy-saving research for wet cooling towers. Consequently, in this paper studies are conducted regarding the layout patterns of fillings inside wet cooling towers via basic thermal-state model experiments to reveal the thermal performance under different layout patterns of fillings, and to obtain the optimal layout pattern.
2 Experimental Study Design 2.1 Experimental objectives The environmental air keeps absorbing heat and moisture during the whole course of heat/mass transfer inside tower, so the air temperature and humidity near 8
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tower center are higher than those of the outside, and the heat and humidity absorption potential of air near tower center become relatively weak. Thus it is also non-uniform for the air dynamic field inside tower, and fillings should be arranged in the non-uniform pattern based on the field synergy theory which is proposed by GUO et al [29], that is, the fillings near tower center should be higher and those of the outside should be lower, which had not so far been considered and/or discussed in previous studies. As a consequence, the corresponding inlet and outlet parameters inside wet cooling tower are measured to calculate and derive the cooling efficiency, cooling temperature difference, Merkel number, Lewis number, and so on which are adopted to evaluate the thermal performance under different payout patterns of fillings. And the ultimate objectives of this paper is to obtain the optimal layout pattern of fillings inside wet cooling tower, this conclusions can provide a significant outcome to the further energy-saving research and engineering design of filling zone as well. 2.2 Experimental setup and operating conditions The experimental setup is displayed via the schematic diagram depicted in Fig.1. The model tower adopted in this experiment is designed to simulate a typical wet cooling tower in large-scale power plants in terms of the engineering similarity theory, the similarity criteria include geometry similarity, Frounde number similarity and wind velocity scale similarity which are detailed in [30-32]. Thereinto, the relevant scale measure of model to prototype tower is 1:100. In addition, the details of the primary measurement setup and instruments are listed in Table 1. 9
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The whole experimental activity hence simulates the actual working process of a typical wet cooling tower in thermal power plants. Prior to the start up of the experiments, the circulating water is heated up to required temperature by several electric heaters, and then transported to the upper tank by the circulating water pump. During the experiments, the circulating water enters the model tower and goes through the fillings from top to bottom, while the dry air flows through the fillings from bottom to top. The heat and mass transfer are conducted in the presence of cross flow. Additionally, there is a conditioning and fresh air system device to adjust the temperature and humidity in the lab which can ensure the consistent conditions between experiments. In order to reveal qualitatively influence rules of different layout patterns on thermal performance of wet cooling tower, and obtain relative change of thermal performance parameters under different layout patterns of fillings, the operating conditions are listed below: the circulating water inlet temperature is 50℃, 55℃ and 60℃, respectively; And the circulating water rate is 4L/min, 6L/min and 8L/min, additionally, filling layout patterns which cover five kinds in this study are detailed as follows (seen in 2.3 part). 2.3 Similarity criteria The dimensions of the model cooling tower is given as 37cm×68cm×85cm (top
outlet diameter × bottom diameter × height), and the height of the tower inlet is 50mm. The test process also complies with the dynamic similarity, kinematic similarity and thermodynamic similarity, besides the geometric (scale) similarity, including the 10
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Froude number and wind velocity scale. Under actual operating conditions, it is difficult to implement Re and Fr number similarity simultaneously. The velocity in Re number varies inversely with the model scale in terms of Eq.(1,2), while the velocity in Fr number varies directly with the square root of model scale in terms of Eq.(3). Therefore, the Re and Fr number similarity cannot be satisfied simultaneously in one model experiment. In this thermal model experiment, the driving force of buoyancy and the inertial force of crosswind are the main factors to be considered, while the viscous force is less important. Therefore, the density Fr number similarity, which is defined by Eq. (3), should have the priority to be satisfied over the Re number [33]. R e out
R e top F r V out
out
Vout D out
(1)
V top D out
(2)
gL V out P
out
gL M
(3)
where subscript P represents prototype tower and subscript M denotes model tower, out is the density of the outlet air, and is the density difference between the
inlet and outlet air, and L is the characteristic size. According to the Fr similarity (as can be seen in Eq.(3)) , the ratio of proportion of experimental to actual velocity is 1:10. Besides the density Fr, the wind velocity scale between the model and prototype tower must also be equal according to kinematic similarity, is given as, v out v to p
v out P v to p
M
(4)
11
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where vout is the top outlet wind velocity and vtop is the top level wind velocity of model tower. 2.4 Filling layout patterns inside the model tower In this experiment, five kinds of layout patterns which have the same volume are designed to study the heat/mass transfer performance of wet cooling tower. The schematic plot of non-uniform layout fillings can be seen in Fig.2, and the block plan is shown in Fig.3, the details of different layout patterns are pointed out in Tab.2 which the serial number of P1~P5 represents five kinds of patterns. Additionally, this paper focused on the layout pattern, not the materials and structure of fillings, so the plastic S-wave fillings which are used widely in the real cooling tower are employed in this research.
3 Calculation models of thermal performance parameters In this paper five parameters are adopted to act as evalutation criteria of thermal performance, including cooling termperature difference t , cooling efficiency , Merkel number n , Lewis number
Le f
and ratio of evaporative
heat rejection K ' . And the specific calculating method can be seen as follows: The temperature difference t and cooling efficiency are defined as Eq.(5) and Eq.(6), t t1 t 2
t1 t 2 t1 t lim
(5) t
t1 t lim
(6)
12
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Where t1 and t2 are the circulating water inlet and outlet temperature of model tower, and tlim is the cooling limit, that is, the wet bulb temperature of inlet air. The calculation method of Merkel number refers to the enthalpy potentail method proposed by Merkel in 1925 [34], and its expression can be wirtten as, n
1 K
c pw
t1
i
t2
'' ma
im a
(7)
dt
The simpson expansion formula of Eq.(7) is given by, n
c pw t 1 4 1 '' '' '' 6 K i2 i1 im im i1 i2
'' Where i1 , i2'' and im'' are the saturated enthalpy at the temperature of
(8) t1 , t 2
and
t m t1 t 2 2 , respectively. i1 , i2 and im are the specific enthalpy of inlet air,
outlet air and the average. c pw is the specific heat of water. And the average specific enthalpy im can be written as, im
i1 i2
(9)
2
Furthermore, the K in Eq.(8) is a heat coefficient which represents the heat carried by evaporation loss, and accroding to the field test procedures of wet cooling tower, its expression is defined as, K 1
t2 5 8 6 0 .5 6 ( t 2 2 0 )
(10)
As one of the significant performance parameters, The Lewis number relates the relative rates of heat and mass transfer in wet cooling towers, which can be written as,
Le f
v c pm a V
(11)
13
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Where v is the heat transfer coefficient, V is the mass transfer coefficient, and c pm a
is the specific heat of wet air. The total heat rejection rate of circulating water Q which is composed of
evaporative heat rejection Q m and contact heat rejection Q a is given by, Q Q a Q m c pw m w t
(12)
where m w reperents circulating water rate. In this experiment, according to the heat balance theory the evaporative heat rejection Q m can be obtained by, Qm
G air c pm a
(13)
wo 0
where 0 is the environmental dry bulb temperature, w o is the wet air temperature at outlet of model tower, and G air is the airflow rate in model tower which can be given by, G a ir
mw 1
(14)
where 1 is the density of inlet air, and is the air-water ratio which can be given by,
c pw t K ( i2 i1 )
(15)
Thus, the ratio of evaporative heat rejection K ' is obtained by the combination of Eq.(12) and Eq.(13), K '
Qm Q
G air c pm a ( w o 0 ) c pw m w t
(16)
4 Experimental results and analysis 4.1 Experimental research regarding influence of different layout patterns on thermal performance 14
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The relationship curves between cooling efficiency, temperature difference, Merkel number and five kinds of layout patterns are shown in Figs.4-6 under two different operating conditons which the circulating water inlet temperature is 50℃ and 60℃, the circulating water rate is 6L/min. Fig.4 discripts the change rules of cooling efficiency under five kinds of layout patterns of fillings. It can be seen that the cooling efficiency under non-uniform layout patterns which are P2-P4 patterns is obviously higher than that under uniform layout pattern which is P1 pattern. Experimental results manifest that, compared with uniform layout pattern (P1), the cooling efficiency can enhance approximately by 24%-30% under different non-uniform layout patterns (P2-P4).
Fig.5 and Fig.6 expain the change rules of cooling temperateure difference and Merkel number under five kinds of layout patterns of fillings. Based on Figs.5-6, the almost same rules can be reported that the thermal performance is excellet under non-uniform layout patterns in terms of not only cooling temperature difference but also Merkel number. And the relative increase value of cooling temperature difference and Merkel number are around 22-28% and 21-29%, respectively.
As mentioned above, the environmental air keeps absorbing heat and moisture during the whole course of heat/mass transfer from the outside to the inside of tower, so the air temperature and humidity near tower center are higher than those of the outside. Therefore, the driving force near tower center would decrease and the air 15
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dynamic field inside tower is also non-uniform, which in turn leads to the smaller wind velocity through the fillings near the tower center. At the same time, the wet air near the tower center is close to saturated, and the heat and humidity absorption potential of air near tower center become relatively weak. Consequently, the fillings near the tower center should be thinner. In the same way, in the outer space of the tower which is near the tower wall, the driving force is comparatively larger, and the wind velocity near this zone is also higher. Meanwhile, the wet air near the tower wall is far from the saturated state. For this reason, the fillings near the tower wall should be thicker. Apparently, this model experiment indicated that the thermal performance of wet cooling tower under four kinds of non-uniform layout patterns is exceedingly predominant. And the next work is to reveal the optimal non-uniform layout pattern by this thermal-state model experiment, which is extremely indispensable for further energy-saving research of wet cooling tower. 4.2 Experimental research concerning the optimal non-uniform layout patterns Figs.7-8 illustrate the change rules of Lewis number and ratio of evaporative heat rejection under four kinds of non-uniform layout patterns (P2, P3, P4, P5) when the circulating water inlet temperature is 50℃ and 60℃, and the circulating water rate is 6L/min. It can be seen from Fig.8 that under different operating conditions, the Lewis number reaches the maximum under the P4 pattern. It means that the heat transfer coefficient is larger and the mass transfer coefficient is relatively lower under the P4 16
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pattern. What’ more, compared Fig.7 and Fig.8, it can be observed that the corresponding ratio of evaporative heat rejection become lower as long as the Lewis number is bigger under any layout patterns. According to the fundamental heat and mass transfer theory [35], the lower the mass transfer coefficient is, the less the evaporative heat rejection becomes, which in turn reduces the ratio of evaporative heat rejection. After the comprehensive comparison of Figs.4-8, under the P4 layout pattern, the thermal performance, including cooling efficiency, cooling temperature difference and Merkel number, reaches the maximum. In other words, in four non-uniform layout patterns, the thermal performance of P4 pattern is higher than that of the other three patterns. At the same time, the ratio of evaporative heat rejection of P4 pattern comes to the minimum. Consequently, experimental results infer that the P4 non-uniform layout pattern is the best plan in which the radius ratio of ra/rc is approximatly 0.44 and rb/rc is around 0.71. According to five performance parameters mentioned in this paper, the thermal performance of the optimal layout pattern can enhance by 30% at maximum within the scope of this test, compared with the uniform layout pattern.
5 Conclusions In terms of the thermal-state model experimental research and mathematical calculation, the principal results are as follows. (1) The environmental air keeps absorbing heat and moisture during the whole course of heat/mass transfer inside tower, so the air temperature and humidity near 17
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tower center are higher than those of the outside, thus the air dynamic field inside tower appears the non-uniform distribution. Based on the non-uniform air dynamic field, the fillings should be laid by means of non-uniform pattern. Experiemntal research in this paper demonstrated that compared with the uniform layout pattern of fillings, the thermal performance of wet cooling tower under non-uniform layout patterns is outstanding. (2) Concerning the four kinds of non-uniform layout patterns, the optimal layout pattern of non-uniform fillings is obtained in this paper, that is, the fillings are deivided into three blocks which are inner block, medium block and outer block. And the radius of three blocks are ra, rb and rc, respectively. Research showed that the radius ratio of ra/rc is approximately 0.44 and rb/rc is around 0.71 under the optiaml pattern. (3) Based on calculating and analyzing five performance parameters which are ooling termperature difference, cooling efficiency, Merkel number, Lewis number and ratio of evaporative heat rejection. The results can be concluded that the thermal performance under the optimal layout pattern can enhance by 30% at maximum within the scope of this test, compared with the uniform layout pattern of fillings. It should be specially explained that the 30% improvement obtained from thermal-state model experimetn should be validated by computational simulation or engineering practice which will be conducted in our future research work. But obviously, these conclusions can lay an important theoretical foundation concerning future research, and provide a siginificant outcome both at academic and applied 18
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level.
Acknowledgement This paper is supported by National Natural Science Foundation of China (No.51106092) and Ji'nan university institute innovation plan (No. 201303077).
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[34] F. Merkel. Verdunstungshuhlung. Zeitschrift des Vereines Deutscher Ingenieure (VDI) 70(1925) 123-128．
[35] P.X. Wang. Heat and mass transfer. Science press. Beijing. 1998．
22
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Fig.1 Schematic diagram of experimental cooling tower Fig.2 Schematic plot of non-uniform layout fillings
Fig.3 Block plan for non-uniform layout fillings Fig.4 Relationship cvrves between cooling efficiency and filling layout patterns OC1: Operating conditions 1,50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
Fig.5 Relationship curves between temperature difference and filling layout patterns OC1: Operating conditions 1, 50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
Fig.6 Relationship curves between Merkel number and filling layout patterns OC1: Operating conditions 1, 50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
Fig.7 the change rules of Lewis number under non-uniform layout patterns OC1: Operating conditions 1, 50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
Fig.8 the change rules of ratio of evaporative heat rejection under non-uniform layout patterns OC1: Operating conditions 1, 50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
23
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Table 1 Monitored parameters and measurement instruments Items
Measuring instruments
Accuracy
Atmospheric pressure
Hot-wire manometer (KA31)
±3 %
Inlet dry and wet bulb temperature
Psychrometer
±0.1 ℃
Outlet air temperature
Copper-constantan thermocouple
±0.3 ℃
Inlet and outlet water temperature
Mercury thermometer
±0.1 ℃
Air humidity
Hygrometer (HI8564)
±2 %
Circulating water flow rate
Rotameter
±1.5 %
Tab.2 Details for five kinds of layout patterns Item
P1 Uniform layout pattern
P2
ra (cm) rb (cm) rc (cm) ra/rc rb/rc H1 (cm) H2 (cm) H3 (cm)
29.5 29.5 29.5 8 8 8
9 24.7 29.5 0.31 0.84 4 8 10
P3 P4 Non-uniform layout patterns 11 23.2 29.5 0.37 0.79 4 8 10
13 21 29.5 0.44 0.71 4 8 10
P5 15 19 29.5 0.51 0.64 4 8 10
P1: uniform layout pattern; P2-P5: non-uniform layout patterns
24
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S1359-4311(15)00974-6 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.09.054 ATE 7046
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
12-6-2015 18-9-2015
Please cite this article as: Ming Gao, Lei Zhang, Ni-ni Wang, Yue-tao Shi, Feng-zhong Sun, Influence of non-uniform layout fillings on thermal performance for wet cooling tower, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.09.054. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Influence of Non-uniform Layout Fillings on Thermal Performance for Wet Cooling Tower Ming Gaoa, Lei Zhanga, Ni-ni Wangb,Yue-tao Shia, Feng-zhong Suna* a, School of Energy Source and Power Engineering, Shandong University, Jinan 250061, China b, Shandong Electric Power Engineering Consulting Institute, Jinan, 250014, China *Corresponding author: [email protected], Tel: 0086-531-88395691
Highlights Performance of cooling tower under non-uniform layout fillings is outstanding. Optimal layout pattern is that ra/rc is approximately 0.44 and rb/rc is around 0.71. Performance of optimal layout pattern can enhance by 30% at maximum within the scope of this test. Conclusions can lay important theoretical foundation concerning future research.
Abstract: Based on the similarity theory, thermal-state model experiment in lab is performed to investigate the thermal performance of wet cooling towers under different layout patterns of fillings, and five kinds of layout patterns, including uniform layout and four kinds of non-uniform layout patterns, are studied in this paper. Experimental results manifest that the thermal performance of wet cooling towers under non-uniform layout patterns is outstanding by calculating and analyzing five performance parameters which are ooling termperature difference, cooling efficiency, Merkel number, Lewis number and ratio of evaporative heat rejection. Additionally, research also obtained the optimal three-block layout pattern of fillings in which the radius ratio of ra/rc is approximately 0.44 and rb/rc is around 0.71, here ra, rb and rc are the radius of three blocks, respectively. What’s more, compared with the uniform 1
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layout pattern of fillings, the thermal performance of the optimal layout pattern can enhance by 30% at maximum within the scope of this test. Keywords: Wet cooling tower; Non-uniform layout fillings; Thermal performance;
Comment [U1]: AUTHOR: Two different versions of the Abstract section were provided and the one in the manuscript has been retained. Please check and confirm it is correct.
Experimental research
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Nomenclature
Qm
evaporative heat rejection [KJ]
V wind velocity [m/s]
Qa
contact heat rejection [KJ]
D
mw
circulating water rate [m3/h]
Re Renold number
0
dry bulb temperature [℃]
Fr
wo
wet air temperature at outlet[℃] airflow rate [kg/s]
the lower diameter of model tower[m]
density Froude number
L
characteristic dimension [m]
G air
r
radius of fillings [cm]
H
height of fillings [cm]
air-water ratio
Subscript
P1~P5 five layout patterns of fillings
a,b,c location of filling layout
t
1 inlet
cooling termperature difference [℃]
Le f
K
t
'
Lewis number
2/out outlet lim
ratio of evaporative heat rejection circulating water temperature [℃]
w
limited value water
K
heat coefficient
top the top of the model tower
i
air specific enthalpy [KJ/kg]
superscript
im
averaged specific enthalpy [KJ/kg]
''
saturated
c pw specific heat of water [KJ/Kg.K]
Greek symbols
v
cooling efficiency Merkel number
heat transfer coefficient [W/m2K]
V
mass transfer coefficient [Kg/m2h]
n
c pm a
specific heat of wet air [KJ/Kg.K]
Q
density of air [kg/m3]
total heat rejection rate [KJ] 3
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1 Introduction As a primary component of the cool-end system in thermal power plants or in some nuclear power plants, the wet cooling towers play an important role to cool the circulating water from the condenser, and its efficiency has a great impact on the total cycle efficiency of power plants [1]. Based on the prior studies, the influence factor of efficiency is mainly the thermal performance of filling zone because 70% of heat dissipating capacity depends on the filling zone [2]. Therefore, it is extremely important and necessary to study the heat and mass transfer performance of filling zone both from an academic as well as an industrial point of view. For a long time, many researchers focus on the thermal performance investigation of fillings for wet cooling towers, and the early research may trace back to 1940s [3-5]. Briefly, the research work in regard to fillings is divided into three aspects which are theoretical mathematical model research, model experiment in lab and numerical computation. Concerning theoretical mathematical model research to the thermal performance of fillings, one mathematical model and computer simulation program had been developed to study the thermal performance of splash fillings for counter-flow cooling tower, and the one-dimensional model adopts basic aerodynamic, hydrodynamic and heat/mass transfer information to predict the performance of the filling material without depending on cooling tower test data [6]. In order to evaluate more accurately the thermal performance of fillings, Jose [7] defined a new model parameter called as thermo-fluid dynamic efficiency. Additionally, based on 4
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one-dimensional heat and mass transfer equation, Milosabljevic [8] derived a mathematical model which can also be used to predict the thermal performance of fillings. Aiming at splash fillings, film fillings and splash-film fillings, Kloppers [9] firstly proposed a new form of empirical equation which correlates fillings loss coefficient data more effectively, compared with other forms of empirical equations, and then Kloppers [10, 11] compared and analyzed three mathematical models which are used to performance calculation of wet cooling tower, that is, Poppe model, Merkel model and e-NTU model. Research results reported that Poppe model had a comparatively high accuracy. According to Muangnoi’s study [12], an exergy analysis was used to indicate exergy and exergy destruction of water and air flowing through the cooling tower, and a mathematical model was developed to find the properties of water and air in filling zone. Research showed that the combination of two types of filling material should be chosen by placing very efficient filling material at the bottom region and placing a regular one at the top region. On the basis of one fouling model in filling zone, Khan [13] pointed out that the fouling of fillings is one of the most important factors affecting its thermal performance, which reduces cooling tower effectiveness and capability with time. Previous experiments have been mostly performed to study filling type and filling material. In recent years, a “VGA” (Vertical Grid Apparatus) type filling was adopted to conduct experimental research. Lemouari [14-17] performed a series of experimental investigation of the thermal performance for wet cooling tower filled 5
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with a VGA type filling which is 0.42m high and consists of four galvanized sheets having a zigzag form. In addition, Gharagheizi [18] presented an experimental and comparative study for two film-type fillings which are vertical corrugated fillings and horizontal corrugated fillings. The obtained results demonstrated that the thermal performance of the cooling tower is affected by the type and arrangement of fillings, and the tower with vertical corrugated fillings has higher efficiency than the one with horizontal corrugated fillings. Apart from mathematical model research, Milosabljevic [8] also carried out experimental measurements on two pilot-scale cooling towers in order to analyze the performance of different filling materials. What’s more, the performance of other elements, such as droplet separators and water spray nozzles, was investigated in the pilot experiments. Hu et al. [19, 20] conducted thermal performance experiment of fillings as well, studied the thermal performance of PVC fillings under the different height conditions, and the conclusion manifested that the thermal performance enhances by 25% and the drag coefficient increases by 6Pa if the filling height increases by 0.5m. Based on three different fillings [21] (cross-fluted film, trickle and fibre cement), the drop size distribution beneath different fillings is reported by an experimental apparatus. And the conclusions indicated that the Rosin–Rammler distribution curve generally does not fit the measured data adequately and thus should be avoided. Filling aging and blockage has great impact on the thermal performance of wet cooling towers, one model experiment was conducted to study the thermal 6
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performance of wet cooling towers under filling blockage conditons, and the results declared that the thermal performance of cooling tower decreased under filling blockage conditons [22]. A.M. Lavasani et al [23] dealt with an experimental investigation of thermal performance of a forced draft counter-flow wet cooling tower filled with a rotational splash type filling, and the tower’s performance parameters were compared when the filling had been rotated and when it does not rotate (like common existing towers). As one of the very important application methods, computational fluid dynamics (CFD) method is also used to research the thermal performance of fillings for wet cooling tower. Klimanek [24] presented a filling model of heat/mass transfer for wet cooling tower, which applied the shooting technique with self-adaptive Runge–Kutta step control, and was designed to be included in a large scale CFD calculation of cooling towers where the fillings are treated as a porous medium with prescribed distributions of mass and heat sources. Another CFD model [25] is a two-dimensional axisymmetric two-phase simulation of the heat/mass transfer inside wet cooling towers, and the heat/mass transfer in the filling zone is represented by using source terms implemented with Poppe style transfer coefficients. The results showed a largely uniform velocity profile across the tower radius with the greatest non-uniformity occurring at the outer edge of the tower. In addition, Huang et al [26] also performed the CFD research regarding arrangement of the filling material and spraying water in cooling tower. Bilal A et al [27] explained filling fouling in cooling towers as well as its modeling strategy to study performance evaluation problems, and 7
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the fouling model is put forward in terms of normalized filling performance. Additionally, N. Williamson et al [28] described a simple two-dimensional model to determine the optimal fill shape and water distribution profile to maximinze the cooling rage of a typical natural draft wet cooling tower, and the results showed that the optimal layout differs significantly from a uniform profile. According to the above-mentioned review, the previous studies for fillings inside wet cooling towers focused on filling material and shape in terms of theoretical model, experiment in lab and numerical computation, which are more valuable to wet cooling tower research. However, the prior researches failed to discuss the height difference of filling layout, and regarded fillings as the same height in different radius inside tower. What’s more, actually uniform layout pattern of fillings is unreasonable on the basis of field synergy theory because of the non-uniform air dynamic field inside tower. Thus, studies regarding the layout pattern of fillings are more crucial to the further energy-saving research for wet cooling towers. Consequently, in this paper studies are conducted regarding the layout patterns of fillings inside wet cooling towers via basic thermal-state model experiments to reveal the thermal performance under different layout patterns of fillings, and to obtain the optimal layout pattern.
2 Experimental Study Design 2.1 Experimental objectives The environmental air keeps absorbing heat and moisture during the whole course of heat/mass transfer inside tower, so the air temperature and humidity near 8
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tower center are higher than those of the outside, and the heat and humidity absorption potential of air near tower center become relatively weak. Thus it is also non-uniform for the air dynamic field inside tower, and fillings should be arranged in the non-uniform pattern based on the field synergy theory which is proposed by GUO et al [29], that is, the fillings near tower center should be higher and those of the outside should be lower, which had not so far been considered and/or discussed in previous studies. As a consequence, the corresponding inlet and outlet parameters inside wet cooling tower are measured to calculate and derive the cooling efficiency, cooling temperature difference, Merkel number, Lewis number, and so on which are adopted to evaluate the thermal performance under different payout patterns of fillings. And the ultimate objectives of this paper is to obtain the optimal layout pattern of fillings inside wet cooling tower, this conclusions can provide a significant outcome to the further energy-saving research and engineering design of filling zone as well. 2.2 Experimental setup and operating conditions The experimental setup is displayed via the schematic diagram depicted in Fig.1. The model tower adopted in this experiment is designed to simulate a typical wet cooling tower in large-scale power plants in terms of the engineering similarity theory, the similarity criteria include geometry similarity, Frounde number similarity and wind velocity scale similarity which are detailed in [30-32]. Thereinto, the relevant scale measure of model to prototype tower is 1:100. In addition, the details of the primary measurement setup and instruments are listed in Table 1. 9
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The whole experimental activity hence simulates the actual working process of a typical wet cooling tower in thermal power plants. Prior to the start up of the experiments, the circulating water is heated up to required temperature by several electric heaters, and then transported to the upper tank by the circulating water pump. During the experiments, the circulating water enters the model tower and goes through the fillings from top to bottom, while the dry air flows through the fillings from bottom to top. The heat and mass transfer are conducted in the presence of cross flow. Additionally, there is a conditioning and fresh air system device to adjust the temperature and humidity in the lab which can ensure the consistent conditions between experiments. In order to reveal qualitatively influence rules of different layout patterns on thermal performance of wet cooling tower, and obtain relative change of thermal performance parameters under different layout patterns of fillings, the operating conditions are listed below: the circulating water inlet temperature is 50℃, 55℃ and 60℃, respectively; And the circulating water rate is 4L/min, 6L/min and 8L/min, additionally, filling layout patterns which cover five kinds in this study are detailed as follows (seen in 2.3 part). 2.3 Similarity criteria The dimensions of the model cooling tower is given as 37cm×68cm×85cm (top
outlet diameter × bottom diameter × height), and the height of the tower inlet is 50mm. The test process also complies with the dynamic similarity, kinematic similarity and thermodynamic similarity, besides the geometric (scale) similarity, including the 10
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Froude number and wind velocity scale. Under actual operating conditions, it is difficult to implement Re and Fr number similarity simultaneously. The velocity in Re number varies inversely with the model scale in terms of Eq.(1,2), while the velocity in Fr number varies directly with the square root of model scale in terms of Eq.(3). Therefore, the Re and Fr number similarity cannot be satisfied simultaneously in one model experiment. In this thermal model experiment, the driving force of buoyancy and the inertial force of crosswind are the main factors to be considered, while the viscous force is less important. Therefore, the density Fr number similarity, which is defined by Eq. (3), should have the priority to be satisfied over the Re number [33]. R e out
R e top F r V out
out
Vout D out
(1)
V top D out
(2)
gL V out P
out
gL M
(3)
where subscript P represents prototype tower and subscript M denotes model tower, out is the density of the outlet air, and is the density difference between the
inlet and outlet air, and L is the characteristic size. According to the Fr similarity (as can be seen in Eq.(3)) , the ratio of proportion of experimental to actual velocity is 1:10. Besides the density Fr, the wind velocity scale between the model and prototype tower must also be equal according to kinematic similarity, is given as, v out v to p
v out P v to p
M
(4)
11
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where vout is the top outlet wind velocity and vtop is the top level wind velocity of model tower. 2.4 Filling layout patterns inside the model tower In this experiment, five kinds of layout patterns which have the same volume are designed to study the heat/mass transfer performance of wet cooling tower. The schematic plot of non-uniform layout fillings can be seen in Fig.2, and the block plan is shown in Fig.3, the details of different layout patterns are pointed out in Tab.2 which the serial number of P1~P5 represents five kinds of patterns. Additionally, this paper focused on the layout pattern, not the materials and structure of fillings, so the plastic S-wave fillings which are used widely in the real cooling tower are employed in this research.
3 Calculation models of thermal performance parameters In this paper five parameters are adopted to act as evalutation criteria of thermal performance, including cooling termperature difference t , cooling efficiency , Merkel number n , Lewis number
Le f
and ratio of evaporative
heat rejection K ' . And the specific calculating method can be seen as follows: The temperature difference t and cooling efficiency are defined as Eq.(5) and Eq.(6), t t1 t 2
t1 t 2 t1 t lim
(5) t
t1 t lim
(6)
12
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Where t1 and t2 are the circulating water inlet and outlet temperature of model tower, and tlim is the cooling limit, that is, the wet bulb temperature of inlet air. The calculation method of Merkel number refers to the enthalpy potentail method proposed by Merkel in 1925 [34], and its expression can be wirtten as, n
1 K
c pw
t1
i
t2
'' ma
im a
(7)
dt
The simpson expansion formula of Eq.(7) is given by, n
c pw t 1 4 1 '' '' '' 6 K i2 i1 im im i1 i2
'' Where i1 , i2'' and im'' are the saturated enthalpy at the temperature of
(8) t1 , t 2
and
t m t1 t 2 2 , respectively. i1 , i2 and im are the specific enthalpy of inlet air,
outlet air and the average. c pw is the specific heat of water. And the average specific enthalpy im can be written as, im
i1 i2
(9)
2
Furthermore, the K in Eq.(8) is a heat coefficient which represents the heat carried by evaporation loss, and accroding to the field test procedures of wet cooling tower, its expression is defined as, K 1
t2 5 8 6 0 .5 6 ( t 2 2 0 )
(10)
As one of the significant performance parameters, The Lewis number relates the relative rates of heat and mass transfer in wet cooling towers, which can be written as,
Le f
v c pm a V
(11)
13
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Where v is the heat transfer coefficient, V is the mass transfer coefficient, and c pm a
is the specific heat of wet air. The total heat rejection rate of circulating water Q which is composed of
evaporative heat rejection Q m and contact heat rejection Q a is given by, Q Q a Q m c pw m w t
(12)
where m w reperents circulating water rate. In this experiment, according to the heat balance theory the evaporative heat rejection Q m can be obtained by, Qm
G air c pm a
(13)
wo 0
where 0 is the environmental dry bulb temperature, w o is the wet air temperature at outlet of model tower, and G air is the airflow rate in model tower which can be given by, G a ir
mw 1
(14)
where 1 is the density of inlet air, and is the air-water ratio which can be given by,
c pw t K ( i2 i1 )
(15)
Thus, the ratio of evaporative heat rejection K ' is obtained by the combination of Eq.(12) and Eq.(13), K '
Qm Q
G air c pm a ( w o 0 ) c pw m w t
(16)
4 Experimental results and analysis 4.1 Experimental research regarding influence of different layout patterns on thermal performance 14
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The relationship curves between cooling efficiency, temperature difference, Merkel number and five kinds of layout patterns are shown in Figs.4-6 under two different operating conditons which the circulating water inlet temperature is 50℃ and 60℃, the circulating water rate is 6L/min. Fig.4 discripts the change rules of cooling efficiency under five kinds of layout patterns of fillings. It can be seen that the cooling efficiency under non-uniform layout patterns which are P2-P4 patterns is obviously higher than that under uniform layout pattern which is P1 pattern. Experimental results manifest that, compared with uniform layout pattern (P1), the cooling efficiency can enhance approximately by 24%-30% under different non-uniform layout patterns (P2-P4).
Fig.5 and Fig.6 expain the change rules of cooling temperateure difference and Merkel number under five kinds of layout patterns of fillings. Based on Figs.5-6, the almost same rules can be reported that the thermal performance is excellet under non-uniform layout patterns in terms of not only cooling temperature difference but also Merkel number. And the relative increase value of cooling temperature difference and Merkel number are around 22-28% and 21-29%, respectively.
As mentioned above, the environmental air keeps absorbing heat and moisture during the whole course of heat/mass transfer from the outside to the inside of tower, so the air temperature and humidity near tower center are higher than those of the outside. Therefore, the driving force near tower center would decrease and the air 15
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dynamic field inside tower is also non-uniform, which in turn leads to the smaller wind velocity through the fillings near the tower center. At the same time, the wet air near the tower center is close to saturated, and the heat and humidity absorption potential of air near tower center become relatively weak. Consequently, the fillings near the tower center should be thinner. In the same way, in the outer space of the tower which is near the tower wall, the driving force is comparatively larger, and the wind velocity near this zone is also higher. Meanwhile, the wet air near the tower wall is far from the saturated state. For this reason, the fillings near the tower wall should be thicker. Apparently, this model experiment indicated that the thermal performance of wet cooling tower under four kinds of non-uniform layout patterns is exceedingly predominant. And the next work is to reveal the optimal non-uniform layout pattern by this thermal-state model experiment, which is extremely indispensable for further energy-saving research of wet cooling tower. 4.2 Experimental research concerning the optimal non-uniform layout patterns Figs.7-8 illustrate the change rules of Lewis number and ratio of evaporative heat rejection under four kinds of non-uniform layout patterns (P2, P3, P4, P5) when the circulating water inlet temperature is 50℃ and 60℃, and the circulating water rate is 6L/min. It can be seen from Fig.8 that under different operating conditions, the Lewis number reaches the maximum under the P4 pattern. It means that the heat transfer coefficient is larger and the mass transfer coefficient is relatively lower under the P4 16
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pattern. What’ more, compared Fig.7 and Fig.8, it can be observed that the corresponding ratio of evaporative heat rejection become lower as long as the Lewis number is bigger under any layout patterns. According to the fundamental heat and mass transfer theory [35], the lower the mass transfer coefficient is, the less the evaporative heat rejection becomes, which in turn reduces the ratio of evaporative heat rejection. After the comprehensive comparison of Figs.4-8, under the P4 layout pattern, the thermal performance, including cooling efficiency, cooling temperature difference and Merkel number, reaches the maximum. In other words, in four non-uniform layout patterns, the thermal performance of P4 pattern is higher than that of the other three patterns. At the same time, the ratio of evaporative heat rejection of P4 pattern comes to the minimum. Consequently, experimental results infer that the P4 non-uniform layout pattern is the best plan in which the radius ratio of ra/rc is approximatly 0.44 and rb/rc is around 0.71. According to five performance parameters mentioned in this paper, the thermal performance of the optimal layout pattern can enhance by 30% at maximum within the scope of this test, compared with the uniform layout pattern.
5 Conclusions In terms of the thermal-state model experimental research and mathematical calculation, the principal results are as follows. (1) The environmental air keeps absorbing heat and moisture during the whole course of heat/mass transfer inside tower, so the air temperature and humidity near 17
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tower center are higher than those of the outside, thus the air dynamic field inside tower appears the non-uniform distribution. Based on the non-uniform air dynamic field, the fillings should be laid by means of non-uniform pattern. Experiemntal research in this paper demonstrated that compared with the uniform layout pattern of fillings, the thermal performance of wet cooling tower under non-uniform layout patterns is outstanding. (2) Concerning the four kinds of non-uniform layout patterns, the optimal layout pattern of non-uniform fillings is obtained in this paper, that is, the fillings are deivided into three blocks which are inner block, medium block and outer block. And the radius of three blocks are ra, rb and rc, respectively. Research showed that the radius ratio of ra/rc is approximately 0.44 and rb/rc is around 0.71 under the optiaml pattern. (3) Based on calculating and analyzing five performance parameters which are ooling termperature difference, cooling efficiency, Merkel number, Lewis number and ratio of evaporative heat rejection. The results can be concluded that the thermal performance under the optimal layout pattern can enhance by 30% at maximum within the scope of this test, compared with the uniform layout pattern of fillings. It should be specially explained that the 30% improvement obtained from thermal-state model experimetn should be validated by computational simulation or engineering practice which will be conducted in our future research work. But obviously, these conclusions can lay an important theoretical foundation concerning future research, and provide a siginificant outcome both at academic and applied 18
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level.
Acknowledgement This paper is supported by National Natural Science Foundation of China (No.51106092) and Ji'nan university institute innovation plan (No. 201303077).
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Fig.1 Schematic diagram of experimental cooling tower Fig.2 Schematic plot of non-uniform layout fillings
Fig.3 Block plan for non-uniform layout fillings Fig.4 Relationship cvrves between cooling efficiency and filling layout patterns OC1: Operating conditions 1,50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
Fig.5 Relationship curves between temperature difference and filling layout patterns OC1: Operating conditions 1, 50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
Fig.6 Relationship curves between Merkel number and filling layout patterns OC1: Operating conditions 1, 50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
Fig.7 the change rules of Lewis number under non-uniform layout patterns OC1: Operating conditions 1, 50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
Fig.8 the change rules of ratio of evaporative heat rejection under non-uniform layout patterns OC1: Operating conditions 1, 50℃, 6L/min OC2: Operating conditions 2, 60℃, 6L/min
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Table 1 Monitored parameters and measurement instruments Items
Measuring instruments
Accuracy
Atmospheric pressure
Hot-wire manometer (KA31)
±3 %
Inlet dry and wet bulb temperature
Psychrometer
±0.1 ℃
Outlet air temperature
Copper-constantan thermocouple
±0.3 ℃
Inlet and outlet water temperature
Mercury thermometer
±0.1 ℃
Air humidity
Hygrometer (HI8564)
±2 %
Circulating water flow rate
Rotameter
±1.5 %
Tab.2 Details for five kinds of layout patterns Item
P1 Uniform layout pattern
P2
ra (cm) rb (cm) rc (cm) ra/rc rb/rc H1 (cm) H2 (cm) H3 (cm)
29.5 29.5 29.5 8 8 8
9 24.7 29.5 0.31 0.84 4 8 10
P3 P4 Non-uniform layout patterns 11 23.2 29.5 0.37 0.79 4 8 10
13 21 29.5 0.44 0.71 4 8 10
P5 15 19 29.5 0.51 0.64 4 8 10
P1: uniform layout pattern; P2-P5: non-uniform layout patterns
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