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Three-dimensional regularities of distribution of air-inlet characteristic velocity in natural-draft wet cooling tower*
323
2008,20(3):323-330
THREE-DIMENSIONAL REGULARITIES OF DISTRIBUTION OF AIRINLET CHARACTERISTIC VELOCITY IN NATURAL-DRAFT WET COOLING TOWER* WANG Kai, SUN Feng-zhong, ZHAO Yuan-bin, GAO Ming, SHI Yue-tao School of Energy and Power Engineering, Shandong University, Jinan 250061, China, E-mail: [email protected]
(Received Apri 6, 2007, Revised August 10, 2007)
Abstract˖A model for heat and mass transfer in a natural-draft wet cooling tower was established. Numerical simulation with the k-İ turbulent model was conducted. Distribution rules of air inlet aerodynamic field were studied. Field experiments were done in a cooling tower in power plant, and the test data was compared with the related results. The definition of characteristic air velocity was proposed and its influencing factors, such as the cross-wind velocity and circumferential angle, were quantitatively studied. It can be used to evaluate the performance of cooling tower and to calculate the ventilation quantity and resistance of air inlet. It is also a theoretical basis for cooling tower design and performance optimization. Key words: cooling tower, flow field, numerical simulation, air inlet
1. Introduction The cooling process of circulating water is of great importance in power plants. The performance of cooling tower greatly affects the economy and safety of power plants. The critical step of thermal calculation in designing a natural-draft wet cooling tower is to figure out the resistance of air flow and ventilation quantity. Meanwhile, cooling tower performance has great dealings with cross-wind. The interior flow field of tower is unevenly distributed and spiral vortexes are incurred in windy weather. In addition, the environmental air flows around the tower, which weakens the interior air flow. As a result, the tower performance deteriorates. Wei [1] conducted model experiments in a wind tunnel and measured the water temperature and inlet air velocity of the prototype dry cooling tower, then defined a non-dimensional parameter to quantify the cross-wind effects on heat exchange efficiency of dry
* Project supported by the Natural Science Foundation of Shandong Province (Grant No. Z2003F03). Biography: WANG Kai (1982-), Male, Ph. D. Student
tower. Zhang et al.[2-8] studied the cross-wind effects on the pressure field, ventilation quantity, temperature field and heat exchange capacity of a dry cooling tower by means of numerical simulation. Zhang also performed some cold tests and used air extractor to bleed the air, in order to simulate the air buoyancy. He concluded that the interior air flow towards the leeward of tower in windy day. So huge spiral vortex is incurred in the tower, and it becomes difficult for air to flow into the tower. Besides, the original pressure and velocity distribution at the tower bottom also alter. Wind may traverse the tower bottom when strong wind occurs. All the researches mentioned above were focused on dry towers, and sparse grid was used in calculation. In addition, the formulas of ventilation quantity and heat exchange capacity are linearly fitted out and imprecise. And the effect of density variation of interior air in the tower is not taken into consideration. Rafat [9,10] analyzed some influencing factors of wet cooling efficiency, such as the water droplet diameter, inlet water temperature, nozzle number, water flux and cross-wind. Rafat concluded that the heat exchange capacity is improved when cross-wind
324
velocity is higher than 7.5 m/s. However, Rafat did not consider the cross-wind effects on ventilation quantity and the resistance of air flow. In this article, a model for the heat and mass transfer in a natural-draft wet cooling tower is established. Relative numerical simulation is conducted to figure out the distribution regularities of inlet air under various cross-wind conditions. Besides, the definition of characteristic air velocity is put forward and its influencing factors, such as cross-wind velocity and circumferential angle, are quantitatively studied. It can be used to figure out the ventilation quantity and resistance of air inlet. Hence, it is a theoretical basis for cooling tower design and performance optimization. 2. Model for heat and mass transfer Convection and evaporation are the main forms of heat exchange in the natural-draft wet cooling tower. Radiation can be ignored because of its small amount[11]. Figure 1 shows the process of heat and mass transfer in a wet tower. In order to calculate conveniently, the following assumptions are made: (1) Thermal resistance of water film can be ignored, and the saturated air enthalpy is in linear proportion to water temperature. (2) In water distribution area, filling area and raining area, water droplet or film is enveloped by a saturated air layer. The temperature of this saturated air layer is the same as water temperature. The relative humidity of this layer is 1. Heat and mass transfer is considered to be induced by the difference between the layer moisture content f s and the wet air moisture content f a , and by difference between saturated enthalpy of the air layer hs and wet air enthalpy ha . (3) If D is heat-transfer coefficient and D is mass-transfer coefficient, then the Lewis number Le = D / Dc = 1.0 .
dha NTU (ha hsw ) = dV AF
(1)
The heat balance equation can be written in the following form:
ma dha = ca mi dTa + cwTw ma dTw
(2)
Modifying the second term on the right side of Eq.(2), which represents the sensible heat taken away by evaporative water, by multiplying a coefficient j, after rearrangements, we can get
dha dhsw = jma cs dV dV mwc pw
(3)
where me represents the mass of water loss in a tower, and then j can be written as follow:
j = 1
c pw meTwo
Qa + Qe
(4)
According to heat and mass balance equations, we can get the outlet water temperature
Two = Tref +
mwi (Twi Tref )c pw ma (hao hai ) mwo c pw (5)
where the sybscript i denotes inlet, o the outlet, a the air, w the water, c the specific heat, h the enthalpy, m the mass flow rate, T the temperature, c p the constant-pressure specific heat, cs the specific heat of saturated air at its corresponding temperature, Qa is the convective heat, Qe = me R , the heat taken away by evaporation, R the water latent heat of vaporization, Tref the reference temperature when the water enthalpy is zero, AF he total area of filling, NTU DAV AF / ma , the number of transfer units, AV the surface area of droplet per unit volume.
Fig.1 Heat and mass transfer process in a wet cooling tower
According to the mass balance equation, heat balance equation and mass transfer equation of infinitesimal volumes [10], we can get
3. Application 3.1 Governing equations The governing equations for cooling tower simulation involve: the continuity equation, momentum equation, energy equation and component [12] equation . There is no need to give unnecessary
325
details. The realizable k-İ turbulent model is used to enclose the equations set. It can avoid possible negative stress which is incurred in the case of great time averaged strain ratio. Because the Reynolds number is very low at near wall areas and turbulent there is not fully developed, the effect of turbulent fluctuation is less than that of molecular viscosity. Hence, in stead of directly using the k-İ model, the [13] is opted. When control wall function method + volume node of near wall areas accord with y >11.63, the flow of this area obeys the logarithmic law, so its velocity u is
u+ =
u u 1 = = ln Ey + uW Ww N
(6a)
U y+ =
Ww =
'y U W w
P
U
=
U CP1/ 4 k 1/ 2u u+
'y
C P P
1/ 4 1/ 2
k
(6b)
(6c)
where u is the time averaged fluid velocity, uW the wall frictional velocity, W w the wall shear stress, U the air density, 'y the distance between node and wall, P the kinematical viscosity, which is related to the Prandtl number for air, k the turbulent kinetic energy at node, E a constant related to surface roughness, which is equal to 9.8 herein, CP is related to time-averaged rotational-velocity tensor, it approximates 0.09. Within computational process, the finite volume method is used to discretize the governing equations. The high-accuracy second-order upwind format is adopted. The coupled iteration adopts the SIMPLE method and uneven body-fitted stagger grid. The buoyancy caused by air density difference can be disposed according to the Boussinesq hypothesis[14], that is, all physical variables in the equation is considered as constants except density, and density merely takes the body force related terms of the momentum equation into consideration. 3.2 Investigated subject The air-inlet flow field of a 300 MW unit cooling tower of a power plant in Shandong Province, China, is numerically simulated under various cross-wind velocities. The size parameters of this tower are the bottom radius:46.646 m, the top radius 28.846 m, the throat radius 26.641 m, the tower height 125 m, the air inlet height 9 m, the raining field height 8 m, the filling height 2 m, the water trap height 12.50 m. The
environmental parameters are: the atmospheric pressure 1.01325 u 105 Pa, the dry-bulb temperature Tidry : 12ć, the wet-bulb temperature Tiwet : 8ć. The drag parameters of the tower are: the water density 1000 kg/m3, the water flux Gw=1.1375 u 104 kg/s, the water spray density q=1.75kg/(s m2), AF =6500m2, the water specific heat 4.1868 kJ/(kg K), test constant of rain area: 0.1. A rectangular coordinate system is used, as shown in Fig.2. The origin is at the circle center of air inlet top cross section. The cross-wind blows along the negative X direction, and the boundary layer effect is taken into consideration. A rectangular parallelepiped outside the tower is set up as computational domain. Six cases with different cross-wind velocities are simulated, including v2 is 1 m/s(light air),2.5 m/s(light breeze),2.8 m/s,4 m/s(third-level wind),6 m/s(fourth-level wind)and 9 m/s(fifth-level wind). v2 is cross-wind velocity at infinity at a height of 2 m above the ground. The influencing factors of inlet air velocity are studied, such as the height Z, the circumferential angle ș, the radial distance r and the cross-wind velocity v2. The range of Z is 0.5 m- 8 m, the range of r is 47 m-51 m and the values of ș are 0o,45o,Ă ,315o, with a spacing 45o. Define the windward point on X axis is ș=0o, and the counter-clockwise is the positive direction when looking down from the top Z.
Fig.2 Sketch of computational area
4. Results and analyses The inlet air flow field is analyzed, which is axi-symmetric in the non-windy condition, so the inlet air velocity is independent of circumferential angle ș. When there is cross-wind, if r and ș are determined, the difference of inlet air velocity along altitude direction is small, especially when Z ranges from 5.5 m to 2.5 m. Hence, Z= 4.5 m cross section, namely the section at a height of 1/2 air inlet height, can be taken as the characteristic section, because the velocity at this section can reflect the general distribution regularities of the flow field. Besides, the velocity variation here is gentle, so it can reduce the measurement error.
326
tangential component of velocity and small radial component. Near 180o leeward, the inlet air velocity and intake is very small. So it is adverse to cooling tower performance. Figure 3(c) indicates that when v2 is great (higher than fifth-level wind), the radial component of inlet air velocity at leeward points at the tower outside, namely the wind traverses tower bottom. In this circumstance, there is no obvious wind entering into tower at leeward. Air enters the tower almost completely at windward. It is distinctly different from what Figure3(a) shows. 4.2 Radial distance effect Figure 4 shows the relation between the radial distance r, the circumferential angle ș and the inlet air velocity at the characteristic section for various values of v2. The inlet air velocity decreases when r increases. The velocity reduction rate is gentle within zones that are no more than 2 m away from bottom wall. Only four cases, namely ș is 45o,90o,135o and 180o, are given because of the limited space. The inlet air velocity v changes intensely with r at ș=0o (windward) and ș=180o (leeward). While v changes gently with r at ș= r 45o-135ozones. As v2 increases, all the inlet air velocity increases except at near180o, where v approximately ranges from 1.5 m/s-5.5 m/s. This phenomenon shows that the effect of cross-wind variation is higher at windward than at leeward.
Fig.3 Velocity distribution of r=49m circle at characteristic section (Z= 4.5m)
4.1 Inlet air flow field at various cross-wind velocities The inlet air flow field is axi-symmetric in non-windy condition. Figure 3 shows the velocity distribution of r=49m circle at characteristic section when v2 varies. Figure 3(a) indicates that when v2 is low, the axi-symmetry of inlet air flow field is destroyed, the windward inlet air velocity is higher than the leeward one, but there is obvious air entering into the tower at leeward. From Figure3(b) it can be seen that when v2 increases, the windward inlet air velocity also increases. Although inlet air velocity value achieves its maximum near r90o zone, air intake here is not the maximum because of the large
Fig.4
Relation between radial distance and inlet air velocity at characteristic section
4.3 Characteristic velocity According to the above analyses, we define the inlet air velocity of circle at the distance 2 m away
327
from the bottom wall (namely r=49m) at characteristic section as the characteristic velocity vc, which can reflect the total distribution regularities of inlet air velocity. In addition, the measurement error can be reduced because of the gentle velocity variation there. In windy days, vc has dealings with load, atmospheric parameters, filling resistance, v2 and ș. Because X=0 is a symmetry plane for inlet air flow field, we can just study the distribution regularities of vc from ș=0o to ș=180o. From Figure 4 it is known that at ș=0o-90o (windward), vc increases along with ș. vc arrives at its maximum near ș= r 90o (but its radial component is very small). At ș=90o-180o (leeward), vc decreases along with ș. vc arrives at its minimum near ș=180o (all the vc refers to modulus of characteristic velocity). The relation between vc and ș conforms to the Lorentz distribution, that is, (7)
Table 1 gives the values of parameters in Eq.(7). On the basis of the obtained results, the ventilation quantity of the tower can be figured out as follow:
v³
air inlet surface
ȡ
ș =2ʌ
0
³
h0 =9
0
vc = a + b v2 + c v22
(9)
Table 2 gives the values of parameters in Eq.(9). Near ș=180o, the relation between vc and v2 conforms to the Gauss distribution, that is,
vc = y 0 +
A S w 2
e
2
v 2 xc 2 w2
(10)
where
2A w vc = y0 + S 4 T xc 2 + w2
G=
Only four cases, namely ș is 0 o ,45 o , 180 o and 270 o , are given, because of the limited space. From Fig.5 it can be seen that the relation between characteristic vc and v2 conforms to parabolic distribution except at leeward near ș=180 o .
vr
49
< dA
(8)
y0 = 2.22757 r 0.29436 , xc =7.34413r 0.30011,
w = 2.7886 r 1.84496 , A =10.41466 r 2.54524 The reliability index of Eq.(10) is Chi2/DOF=0.21325, R2=0.89465, where R is the correlation coefficient, DOF the degree of freedom, and Chi2 the quadratic sum of normal distribution variables. The more Chi2/DOF approaches zero, the more accurate that the Gauss fitting is.
Fig.5 Relation between vc and v2
Figure 5 shows the relation between vc and v2.
Fig.6 Distribution of v in the gale as air guide plates are fixed
328
Table1 Parameters in Eq. (7) v2(m/s)
1
2.5
2.8
4
6
9
Y0
1.647
13.92
1.05
10.06
3.04
12.29
A
4482.5
15194.2
2557.9
10225.1
5201.1
15317.4
w
546.31
504.49
236.93
368.16
237.27
381.6
xc
40.69
60.98
64.11
60.84
63.10
41.22
R2
0.98
0.95
0.92
0.92
0.97
0.90
Chi2/DOF
0.015
0.432
0.594
1.511
0.776
6.377
Table 2. Parameters in Eq.(9) ș
0o
45 o
90 o
135 o
225 o
270 o
315 o
a
2.787
1.579
0.713
2.506
4.365
2.476
1.2563
b
0.541
1.373
2.434
0.331
0.838
1.250
1.4926
c
0.0587
0
0.146
0.06
0.164
0.0102
0
R
0.997
0.996
0.972
0.998
0.862
0.995
0.992
P
0.0002
0.0001
0.0048
0.0001
0.05
0.0003
0.0001
SD
0.252
0.41
0.639
0.159
1.366
0.342
0.626
Note: SD denotes the standard variance, P the significant level, and the accuracy of the thcurve fitting increases with decreasing SD and P.
After the calculation of ventilation quantity, the inlet air resistance can be figured out. In addition, the operational efficiency of cooling tower can be quantitatively analyzed. vc is also a theoretical basis for cooling tower design and performance optimization. When there is gale, the inlet air flow field can be improved by fixing air guide plates around the air inlet of the cooling tower. The guide plates can augment the ventilation quantity and reinforce heat transfer in the cooling tower[15]. Figure 6 shows the characteristic velocity distribution in gale condition as air guide plates are fixed. Compared with Figure 3(c), the flow field is greatly improved from ș= r 120o to ș= r 170o, and there is almost no air
traverses through the tower bottom in the gale. The future work for the authors is to optimize the quantity of air guide plates and their shapes and installed positions. 4.4 Verification The field measurements of the inlet air velocity of a 300 MW unit cooling tower in a power plant in Shandong Province were performed in order to verify the numerical simulation. The inlet air velocities in four weather conditions were tested by means of vane-wheel type anemoscope, including v2=0 m/s, 2 m/s, 2.5 m/s, and 2.8 m/s. The maximum measurement error of this anemoscope is 0.1 m/s. Atmospheric parameters during the field
329
measurements were: the pressure 0.102 MPa, the dry-bulb temperature 10.4 ć , and the wet-bulb temperature 7.2ć. Only the inlet air velocity of r=49m circle at Z= 5m (near the characteristic section) is given because of limited space. Figure 7 shows the measured values of vc in various cross-wind conditions. The statistical data indicate that more than 60% data are reliable, whose errors are within 0.6 m/s as compared with the measured values, while only less than 8% data are dubious, whose errors are greater than 1.5 m/s as compared with measured values.
(3) The difference of inlet air velocity along altitude direction is small. The inlet air velocity decreases as the radial distance increases. Its reduction rate is gentle within zones that are no more than 2 m away from bottom tower wall. In windy days, the relation between the characteristic velocity vc and the circumferential angle ș conforms to the Lorentz distribution. The relation between vc and cross-wind v2 conforms to the parabolic distribution except zone near ș=180o (leeward), where the relation conforms to the Gauss distribution. The calculation method and result are also suitable for other natural-draft wet cooling towers. References [1]
Fig.7 Measured values of vc at various cross-wind conditions
5. Conclusions (1) The model for heat and mass transfer in a natural-draft wet cooling tower has been established. The inlet air aerodynamic field in windy condition is numerically simulated and its three-dimensional distribution regularities are studied. The field experiments are conducted in a cooling tower in a power plant, and the test data are compared with the simulated results. More than 60% simulated results are reliable, whose errors are within 0.6 m/s compared with measured values. Only less than 8% data are dubious, whose errors are greater than 1.5 m/s. (2) The inlet air flow field of cooling tower is not axi-symmetric when there is cross-wind. The inlet air velocity at windward is higher than that at leeward, and its minimum is near ș=180o (leeward). Air traverses the tower bottom in the gale and there is little air entering into tower at leeward. The definition of characteristic velocity is put forward. It can be used to quantitatively evaluate the cooling efficiency and to calculate the ventilation quantity and air intake resistance of the tower. It is a theoretical basis for cooling tower design and performance optimization.
WEI Qing-ding, ZHANG Bo-yin and LIU Ke-qi et al. A study of the unfavorable effects of wind on the cooling efficiency of dry cooling towers[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1995, 54-55: 633-643. [2] ZHAI Zhi-qiang, ZHU Ke-qin and FU Song. Model experiment for the influence of cross-wind on the air flow field in natural draft dry-cooling tower[J]. Journal of Experimental Mechanics, 1997, 12(2): 306-311 (in Chinese). [3] ZHANG Xiao-dong, WANG Qing-zhao. Impact of side wind on the cooling performance of natural draft air cooling tower[J]. Electric Power, 1999, 32(6): 34-36 (in Chinese). [4] XIE Zuo-tao, ZHANG Xiao-feng and TANG Guang-ming et al. Numerical simulation of 2D horizontal cooling water discharge in generalized curvilinear coordinate[J]. Journal of Hydrodynamics, Ser. B, 2006, 18(1): 91-96. [5] MA Jian-feng, SHEN Xin-rong and ZHANG Ben-zhao et al. Numerical analysis of the fluid flow in a rotating curved elliptical pipe[J]. Journal of Hydrodynamics, Ser.B, 2005, 17(2): 171-178. [6] ZHANG Xiao-dong, ZHENG Yong-gang and WANG Qing-zhao. Numerical simulation of aerodynamic field of dry cooling tower[J]. Thermal Engineering, 2000, 15(1): 52-55 (in Chinese). [7] SU M. D. , TANG G. F. and SU S. Numerical simulation of fluid flow and thermal performance of a dry-cooling tower under cross wind condition[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1999, 79(3): 289-306. [8] RAFAT Al Waked, MASUD Behnia. The performance of natural draft dry cooling towers under crosswind: CFD study [J]. International Journal of Energy Research, 2004, 28(2): 147-161. [9] LI Guang-zheng, HUANG Jian-chun. Numerical simulations of a centered conducting body on natural convection and heat transfer in an enclosure[J]. Journal of Hydrodynamics, Ser. B, 2005, 17(5): 539-545. [10] RAFAT Al Waked, MASUD Behnia. CFD simulation of wet cooling towers[J]. Applied Thermal Engineering, 2006, 26(4): 382-395.
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[11] ZHAO Zhen-guo. Cooling tower[M]. Beijing: Chinese Water Conservancy and Electric Power Press, 1996(in Chinese). [12] ZHANG Ting, WU Chao and LIAO Hua-sheng et al. 3D Numerical simulation on water and air two-phase flows of the steps and flaring gate pier[J]. Journal of Hydrodynamics, Ser. B, 2005, 17(3): 338-343. [13] WANG Fu-jun. Computational fluid dynamics analysis[M]. Beijing Tshinghua University Press, 2004 (in Chinese).
[14] SUN Liang, MA Dong-jun and SUN De-jun et al. High accuracy scheme for unsteady thermal convection flow[J]. Journal of Hydrodynamics, Ser. A, 2006, 21(3): 363-368 (in Chinese). [15] ZHANG Xia-ling, YANG Xu, LI Xiang-qun et al. Numerical simulation to heat exchange of direct air-cooled condenser in power plants[J]. Journal of Hydrodynamics, Ser. A, 2005, 20(suppl.): 874-880 (in Chinese).
2008,20(3):323-330
THREE-DIMENSIONAL REGULARITIES OF DISTRIBUTION OF AIRINLET CHARACTERISTIC VELOCITY IN NATURAL-DRAFT WET COOLING TOWER* WANG Kai, SUN Feng-zhong, ZHAO Yuan-bin, GAO Ming, SHI Yue-tao School of Energy and Power Engineering, Shandong University, Jinan 250061, China, E-mail: [email protected]
(Received Apri 6, 2007, Revised August 10, 2007)
Abstract˖A model for heat and mass transfer in a natural-draft wet cooling tower was established. Numerical simulation with the k-İ turbulent model was conducted. Distribution rules of air inlet aerodynamic field were studied. Field experiments were done in a cooling tower in power plant, and the test data was compared with the related results. The definition of characteristic air velocity was proposed and its influencing factors, such as the cross-wind velocity and circumferential angle, were quantitatively studied. It can be used to evaluate the performance of cooling tower and to calculate the ventilation quantity and resistance of air inlet. It is also a theoretical basis for cooling tower design and performance optimization. Key words: cooling tower, flow field, numerical simulation, air inlet
1. Introduction The cooling process of circulating water is of great importance in power plants. The performance of cooling tower greatly affects the economy and safety of power plants. The critical step of thermal calculation in designing a natural-draft wet cooling tower is to figure out the resistance of air flow and ventilation quantity. Meanwhile, cooling tower performance has great dealings with cross-wind. The interior flow field of tower is unevenly distributed and spiral vortexes are incurred in windy weather. In addition, the environmental air flows around the tower, which weakens the interior air flow. As a result, the tower performance deteriorates. Wei [1] conducted model experiments in a wind tunnel and measured the water temperature and inlet air velocity of the prototype dry cooling tower, then defined a non-dimensional parameter to quantify the cross-wind effects on heat exchange efficiency of dry
* Project supported by the Natural Science Foundation of Shandong Province (Grant No. Z2003F03). Biography: WANG Kai (1982-), Male, Ph. D. Student
tower. Zhang et al.[2-8] studied the cross-wind effects on the pressure field, ventilation quantity, temperature field and heat exchange capacity of a dry cooling tower by means of numerical simulation. Zhang also performed some cold tests and used air extractor to bleed the air, in order to simulate the air buoyancy. He concluded that the interior air flow towards the leeward of tower in windy day. So huge spiral vortex is incurred in the tower, and it becomes difficult for air to flow into the tower. Besides, the original pressure and velocity distribution at the tower bottom also alter. Wind may traverse the tower bottom when strong wind occurs. All the researches mentioned above were focused on dry towers, and sparse grid was used in calculation. In addition, the formulas of ventilation quantity and heat exchange capacity are linearly fitted out and imprecise. And the effect of density variation of interior air in the tower is not taken into consideration. Rafat [9,10] analyzed some influencing factors of wet cooling efficiency, such as the water droplet diameter, inlet water temperature, nozzle number, water flux and cross-wind. Rafat concluded that the heat exchange capacity is improved when cross-wind
324
velocity is higher than 7.5 m/s. However, Rafat did not consider the cross-wind effects on ventilation quantity and the resistance of air flow. In this article, a model for the heat and mass transfer in a natural-draft wet cooling tower is established. Relative numerical simulation is conducted to figure out the distribution regularities of inlet air under various cross-wind conditions. Besides, the definition of characteristic air velocity is put forward and its influencing factors, such as cross-wind velocity and circumferential angle, are quantitatively studied. It can be used to figure out the ventilation quantity and resistance of air inlet. Hence, it is a theoretical basis for cooling tower design and performance optimization. 2. Model for heat and mass transfer Convection and evaporation are the main forms of heat exchange in the natural-draft wet cooling tower. Radiation can be ignored because of its small amount[11]. Figure 1 shows the process of heat and mass transfer in a wet tower. In order to calculate conveniently, the following assumptions are made: (1) Thermal resistance of water film can be ignored, and the saturated air enthalpy is in linear proportion to water temperature. (2) In water distribution area, filling area and raining area, water droplet or film is enveloped by a saturated air layer. The temperature of this saturated air layer is the same as water temperature. The relative humidity of this layer is 1. Heat and mass transfer is considered to be induced by the difference between the layer moisture content f s and the wet air moisture content f a , and by difference between saturated enthalpy of the air layer hs and wet air enthalpy ha . (3) If D is heat-transfer coefficient and D is mass-transfer coefficient, then the Lewis number Le = D / Dc = 1.0 .
dha NTU (ha hsw ) = dV AF
(1)
The heat balance equation can be written in the following form:
ma dha = ca mi dTa + cwTw ma dTw
(2)
Modifying the second term on the right side of Eq.(2), which represents the sensible heat taken away by evaporative water, by multiplying a coefficient j, after rearrangements, we can get
dha dhsw = jma cs dV dV mwc pw
(3)
where me represents the mass of water loss in a tower, and then j can be written as follow:
j = 1
c pw meTwo
Qa + Qe
(4)
According to heat and mass balance equations, we can get the outlet water temperature
Two = Tref +
mwi (Twi Tref )c pw ma (hao hai ) mwo c pw (5)
where the sybscript i denotes inlet, o the outlet, a the air, w the water, c the specific heat, h the enthalpy, m the mass flow rate, T the temperature, c p the constant-pressure specific heat, cs the specific heat of saturated air at its corresponding temperature, Qa is the convective heat, Qe = me R , the heat taken away by evaporation, R the water latent heat of vaporization, Tref the reference temperature when the water enthalpy is zero, AF he total area of filling, NTU DAV AF / ma , the number of transfer units, AV the surface area of droplet per unit volume.
Fig.1 Heat and mass transfer process in a wet cooling tower
According to the mass balance equation, heat balance equation and mass transfer equation of infinitesimal volumes [10], we can get
3. Application 3.1 Governing equations The governing equations for cooling tower simulation involve: the continuity equation, momentum equation, energy equation and component [12] equation . There is no need to give unnecessary
325
details. The realizable k-İ turbulent model is used to enclose the equations set. It can avoid possible negative stress which is incurred in the case of great time averaged strain ratio. Because the Reynolds number is very low at near wall areas and turbulent there is not fully developed, the effect of turbulent fluctuation is less than that of molecular viscosity. Hence, in stead of directly using the k-İ model, the [13] is opted. When control wall function method + volume node of near wall areas accord with y >11.63, the flow of this area obeys the logarithmic law, so its velocity u is
u+ =
u u 1 = = ln Ey + uW Ww N
(6a)
U y+ =
Ww =
'y U W w
P
U
=
U CP1/ 4 k 1/ 2u u+
'y
C P P
1/ 4 1/ 2
k
(6b)
(6c)
where u is the time averaged fluid velocity, uW the wall frictional velocity, W w the wall shear stress, U the air density, 'y the distance between node and wall, P the kinematical viscosity, which is related to the Prandtl number for air, k the turbulent kinetic energy at node, E a constant related to surface roughness, which is equal to 9.8 herein, CP is related to time-averaged rotational-velocity tensor, it approximates 0.09. Within computational process, the finite volume method is used to discretize the governing equations. The high-accuracy second-order upwind format is adopted. The coupled iteration adopts the SIMPLE method and uneven body-fitted stagger grid. The buoyancy caused by air density difference can be disposed according to the Boussinesq hypothesis[14], that is, all physical variables in the equation is considered as constants except density, and density merely takes the body force related terms of the momentum equation into consideration. 3.2 Investigated subject The air-inlet flow field of a 300 MW unit cooling tower of a power plant in Shandong Province, China, is numerically simulated under various cross-wind velocities. The size parameters of this tower are the bottom radius:46.646 m, the top radius 28.846 m, the throat radius 26.641 m, the tower height 125 m, the air inlet height 9 m, the raining field height 8 m, the filling height 2 m, the water trap height 12.50 m. The
environmental parameters are: the atmospheric pressure 1.01325 u 105 Pa, the dry-bulb temperature Tidry : 12ć, the wet-bulb temperature Tiwet : 8ć. The drag parameters of the tower are: the water density 1000 kg/m3, the water flux Gw=1.1375 u 104 kg/s, the water spray density q=1.75kg/(s m2), AF =6500m2, the water specific heat 4.1868 kJ/(kg K), test constant of rain area: 0.1. A rectangular coordinate system is used, as shown in Fig.2. The origin is at the circle center of air inlet top cross section. The cross-wind blows along the negative X direction, and the boundary layer effect is taken into consideration. A rectangular parallelepiped outside the tower is set up as computational domain. Six cases with different cross-wind velocities are simulated, including v2 is 1 m/s(light air),2.5 m/s(light breeze),2.8 m/s,4 m/s(third-level wind),6 m/s(fourth-level wind)and 9 m/s(fifth-level wind). v2 is cross-wind velocity at infinity at a height of 2 m above the ground. The influencing factors of inlet air velocity are studied, such as the height Z, the circumferential angle ș, the radial distance r and the cross-wind velocity v2. The range of Z is 0.5 m- 8 m, the range of r is 47 m-51 m and the values of ș are 0o,45o,Ă ,315o, with a spacing 45o. Define the windward point on X axis is ș=0o, and the counter-clockwise is the positive direction when looking down from the top Z.
Fig.2 Sketch of computational area
4. Results and analyses The inlet air flow field is analyzed, which is axi-symmetric in the non-windy condition, so the inlet air velocity is independent of circumferential angle ș. When there is cross-wind, if r and ș are determined, the difference of inlet air velocity along altitude direction is small, especially when Z ranges from 5.5 m to 2.5 m. Hence, Z= 4.5 m cross section, namely the section at a height of 1/2 air inlet height, can be taken as the characteristic section, because the velocity at this section can reflect the general distribution regularities of the flow field. Besides, the velocity variation here is gentle, so it can reduce the measurement error.
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tangential component of velocity and small radial component. Near 180o leeward, the inlet air velocity and intake is very small. So it is adverse to cooling tower performance. Figure 3(c) indicates that when v2 is great (higher than fifth-level wind), the radial component of inlet air velocity at leeward points at the tower outside, namely the wind traverses tower bottom. In this circumstance, there is no obvious wind entering into tower at leeward. Air enters the tower almost completely at windward. It is distinctly different from what Figure3(a) shows. 4.2 Radial distance effect Figure 4 shows the relation between the radial distance r, the circumferential angle ș and the inlet air velocity at the characteristic section for various values of v2. The inlet air velocity decreases when r increases. The velocity reduction rate is gentle within zones that are no more than 2 m away from bottom wall. Only four cases, namely ș is 45o,90o,135o and 180o, are given because of the limited space. The inlet air velocity v changes intensely with r at ș=0o (windward) and ș=180o (leeward). While v changes gently with r at ș= r 45o-135ozones. As v2 increases, all the inlet air velocity increases except at near180o, where v approximately ranges from 1.5 m/s-5.5 m/s. This phenomenon shows that the effect of cross-wind variation is higher at windward than at leeward.
Fig.3 Velocity distribution of r=49m circle at characteristic section (Z= 4.5m)
4.1 Inlet air flow field at various cross-wind velocities The inlet air flow field is axi-symmetric in non-windy condition. Figure 3 shows the velocity distribution of r=49m circle at characteristic section when v2 varies. Figure 3(a) indicates that when v2 is low, the axi-symmetry of inlet air flow field is destroyed, the windward inlet air velocity is higher than the leeward one, but there is obvious air entering into the tower at leeward. From Figure3(b) it can be seen that when v2 increases, the windward inlet air velocity also increases. Although inlet air velocity value achieves its maximum near r90o zone, air intake here is not the maximum because of the large
Fig.4
Relation between radial distance and inlet air velocity at characteristic section
4.3 Characteristic velocity According to the above analyses, we define the inlet air velocity of circle at the distance 2 m away
327
from the bottom wall (namely r=49m) at characteristic section as the characteristic velocity vc, which can reflect the total distribution regularities of inlet air velocity. In addition, the measurement error can be reduced because of the gentle velocity variation there. In windy days, vc has dealings with load, atmospheric parameters, filling resistance, v2 and ș. Because X=0 is a symmetry plane for inlet air flow field, we can just study the distribution regularities of vc from ș=0o to ș=180o. From Figure 4 it is known that at ș=0o-90o (windward), vc increases along with ș. vc arrives at its maximum near ș= r 90o (but its radial component is very small). At ș=90o-180o (leeward), vc decreases along with ș. vc arrives at its minimum near ș=180o (all the vc refers to modulus of characteristic velocity). The relation between vc and ș conforms to the Lorentz distribution, that is, (7)
Table 1 gives the values of parameters in Eq.(7). On the basis of the obtained results, the ventilation quantity of the tower can be figured out as follow:
v³
air inlet surface
ȡ
ș =2ʌ
0
³
h0 =9
0
vc = a + b v2 + c v22
(9)
Table 2 gives the values of parameters in Eq.(9). Near ș=180o, the relation between vc and v2 conforms to the Gauss distribution, that is,
vc = y 0 +
A S w 2
e
2
v 2 xc 2 w2
(10)
where
2A w vc = y0 + S 4 T xc 2 + w2
G=
Only four cases, namely ș is 0 o ,45 o , 180 o and 270 o , are given, because of the limited space. From Fig.5 it can be seen that the relation between characteristic vc and v2 conforms to parabolic distribution except at leeward near ș=180 o .
vr
49
< dA
(8)
y0 = 2.22757 r 0.29436 , xc =7.34413r 0.30011,
w = 2.7886 r 1.84496 , A =10.41466 r 2.54524 The reliability index of Eq.(10) is Chi2/DOF=0.21325, R2=0.89465, where R is the correlation coefficient, DOF the degree of freedom, and Chi2 the quadratic sum of normal distribution variables. The more Chi2/DOF approaches zero, the more accurate that the Gauss fitting is.
Fig.5 Relation between vc and v2
Figure 5 shows the relation between vc and v2.
Fig.6 Distribution of v in the gale as air guide plates are fixed
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Table1 Parameters in Eq. (7) v2(m/s)
1
2.5
2.8
4
6
9
Y0
1.647
13.92
1.05
10.06
3.04
12.29
A
4482.5
15194.2
2557.9
10225.1
5201.1
15317.4
w
546.31
504.49
236.93
368.16
237.27
381.6
xc
40.69
60.98
64.11
60.84
63.10
41.22
R2
0.98
0.95
0.92
0.92
0.97
0.90
Chi2/DOF
0.015
0.432
0.594
1.511
0.776
6.377
Table 2. Parameters in Eq.(9) ș
0o
45 o
90 o
135 o
225 o
270 o
315 o
a
2.787
1.579
0.713
2.506
4.365
2.476
1.2563
b
0.541
1.373
2.434
0.331
0.838
1.250
1.4926
c
0.0587
0
0.146
0.06
0.164
0.0102
0
R
0.997
0.996
0.972
0.998
0.862
0.995
0.992
P
0.0002
0.0001
0.0048
0.0001
0.05
0.0003
0.0001
SD
0.252
0.41
0.639
0.159
1.366
0.342
0.626
Note: SD denotes the standard variance, P the significant level, and the accuracy of the thcurve fitting increases with decreasing SD and P.
After the calculation of ventilation quantity, the inlet air resistance can be figured out. In addition, the operational efficiency of cooling tower can be quantitatively analyzed. vc is also a theoretical basis for cooling tower design and performance optimization. When there is gale, the inlet air flow field can be improved by fixing air guide plates around the air inlet of the cooling tower. The guide plates can augment the ventilation quantity and reinforce heat transfer in the cooling tower[15]. Figure 6 shows the characteristic velocity distribution in gale condition as air guide plates are fixed. Compared with Figure 3(c), the flow field is greatly improved from ș= r 120o to ș= r 170o, and there is almost no air
traverses through the tower bottom in the gale. The future work for the authors is to optimize the quantity of air guide plates and their shapes and installed positions. 4.4 Verification The field measurements of the inlet air velocity of a 300 MW unit cooling tower in a power plant in Shandong Province were performed in order to verify the numerical simulation. The inlet air velocities in four weather conditions were tested by means of vane-wheel type anemoscope, including v2=0 m/s, 2 m/s, 2.5 m/s, and 2.8 m/s. The maximum measurement error of this anemoscope is 0.1 m/s. Atmospheric parameters during the field
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measurements were: the pressure 0.102 MPa, the dry-bulb temperature 10.4 ć , and the wet-bulb temperature 7.2ć. Only the inlet air velocity of r=49m circle at Z= 5m (near the characteristic section) is given because of limited space. Figure 7 shows the measured values of vc in various cross-wind conditions. The statistical data indicate that more than 60% data are reliable, whose errors are within 0.6 m/s as compared with the measured values, while only less than 8% data are dubious, whose errors are greater than 1.5 m/s as compared with measured values.
(3) The difference of inlet air velocity along altitude direction is small. The inlet air velocity decreases as the radial distance increases. Its reduction rate is gentle within zones that are no more than 2 m away from bottom tower wall. In windy days, the relation between the characteristic velocity vc and the circumferential angle ș conforms to the Lorentz distribution. The relation between vc and cross-wind v2 conforms to the parabolic distribution except zone near ș=180o (leeward), where the relation conforms to the Gauss distribution. The calculation method and result are also suitable for other natural-draft wet cooling towers. References [1]
Fig.7 Measured values of vc at various cross-wind conditions
5. Conclusions (1) The model for heat and mass transfer in a natural-draft wet cooling tower has been established. The inlet air aerodynamic field in windy condition is numerically simulated and its three-dimensional distribution regularities are studied. The field experiments are conducted in a cooling tower in a power plant, and the test data are compared with the simulated results. More than 60% simulated results are reliable, whose errors are within 0.6 m/s compared with measured values. Only less than 8% data are dubious, whose errors are greater than 1.5 m/s. (2) The inlet air flow field of cooling tower is not axi-symmetric when there is cross-wind. The inlet air velocity at windward is higher than that at leeward, and its minimum is near ș=180o (leeward). Air traverses the tower bottom in the gale and there is little air entering into tower at leeward. The definition of characteristic velocity is put forward. It can be used to quantitatively evaluate the cooling efficiency and to calculate the ventilation quantity and air intake resistance of the tower. It is a theoretical basis for cooling tower design and performance optimization.
WEI Qing-ding, ZHANG Bo-yin and LIU Ke-qi et al. A study of the unfavorable effects of wind on the cooling efficiency of dry cooling towers[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1995, 54-55: 633-643. [2] ZHAI Zhi-qiang, ZHU Ke-qin and FU Song. Model experiment for the influence of cross-wind on the air flow field in natural draft dry-cooling tower[J]. Journal of Experimental Mechanics, 1997, 12(2): 306-311 (in Chinese). [3] ZHANG Xiao-dong, WANG Qing-zhao. Impact of side wind on the cooling performance of natural draft air cooling tower[J]. Electric Power, 1999, 32(6): 34-36 (in Chinese). [4] XIE Zuo-tao, ZHANG Xiao-feng and TANG Guang-ming et al. Numerical simulation of 2D horizontal cooling water discharge in generalized curvilinear coordinate[J]. Journal of Hydrodynamics, Ser. B, 2006, 18(1): 91-96. [5] MA Jian-feng, SHEN Xin-rong and ZHANG Ben-zhao et al. Numerical analysis of the fluid flow in a rotating curved elliptical pipe[J]. Journal of Hydrodynamics, Ser.B, 2005, 17(2): 171-178. [6] ZHANG Xiao-dong, ZHENG Yong-gang and WANG Qing-zhao. Numerical simulation of aerodynamic field of dry cooling tower[J]. Thermal Engineering, 2000, 15(1): 52-55 (in Chinese). [7] SU M. D. , TANG G. F. and SU S. Numerical simulation of fluid flow and thermal performance of a dry-cooling tower under cross wind condition[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1999, 79(3): 289-306. [8] RAFAT Al Waked, MASUD Behnia. The performance of natural draft dry cooling towers under crosswind: CFD study [J]. International Journal of Energy Research, 2004, 28(2): 147-161. [9] LI Guang-zheng, HUANG Jian-chun. Numerical simulations of a centered conducting body on natural convection and heat transfer in an enclosure[J]. Journal of Hydrodynamics, Ser. B, 2005, 17(5): 539-545. [10] RAFAT Al Waked, MASUD Behnia. CFD simulation of wet cooling towers[J]. Applied Thermal Engineering, 2006, 26(4): 382-395.
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