Heat load capability matching principle and its applications to anti-freezing of air-cooled condenser

Applied Energy 127 (2014) 34–43

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Heat load capability matching principle and its applications to anti-freezing of air-cooled condenser Lijun Yang ⇑, Xiaoli Zhao, Xiaoze Du ⇑, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipments of Ministry of Education, China School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China

h i g h l i g h t s  It is of use to propose anti-freezing measures for air-cooled condenser.  Heat load capacity matching principle for the anti-freezing is suggested.  Anti-freezing steam flow rate increases with decreasing ambient temperature.  Anti-freezing fan flow rate increases with increasing exhaust steam flow rate.  Back pressure can be much more reduced at secure steam flow rates.

a r t i c l e

i n f o

Article history: Received 21 January 2014 Received in revised form 1 April 2014 Accepted 9 April 2014 Available online 3 May 2014 Keywords: Air-cooled condenser Heat load capability Anti-freezing Back pressure Ambient temperature Axial flow fan

a b s t r a c t Air-cooled condenser in power plants takes a risk of freezing in extremely cold days, so it is of benefit to the safe and economical operation of direct dry cooling system to propose the anti-freezing principles and take measures. On the basis of the heat load balance between the exhaust steam and cooling air, the heat load capacity matching principle for the anti-freezing of air-cooled condenser is proposed with reference to the freezing point of water. By applying heat exchanger model to the finned tube bundles of air-cooled condenser, the thermo-aerodynamic behavior of cooling air, the condensation of exhaust steam and the sensible heat rejection of condensate in a representative air-cooled condenser cell are synchronously modeled and resolved. The correlations among the ambient temperature, flow rate of cooling air, exhaust steam flow rate and quality, and back pressure of turbine that prevent the air-cooled condenser from freezing are discussed, and the anti-freezing flow rate of exhaust steam, back pressure of turbine and flow rate of axial flow fan are obtained. The results show that the anti-freezing flow rate of exhaust steam and back pressure both increase with decreasing the ambient temperature and increasing the flow rate of axial flow fan, from which derive the secure steam flow rate that can reduce the back pressure as much as possible to improve thermal efficiency. The anti-freezing fan flow rate increases with increasing the exhaust steam flow rate and ambient temperature, but varies little with back pressure. The increased steam quality will result in a higher heat load at the steam side, which allows a higher rotational speed of fan to be free of freezing for air-cooled condenser. The application of heat load capacity matching principle to the anti-freezing of air-cooled condenser contributes to the secure and optimal operation of dry cooling system in power plants. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Dry cooling system has been increasingly developed in the condenser heat rejection of power plants in the past years due to urgent water resource issues all over the world. As one of the dry cooling technologies, direct dry cooling system makes use of air-cooled condenser to reject the exhaust steam heat to the ⇑ Corresponding authors. Tel.: +86 10 61773373; fax: +86 10 61773877. E-mail addresses: [email protected] (L. Yang), [email protected] (X. Du). http://dx.doi.org/10.1016/j.apenergy.2014.04.025 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.

ambient atmosphere, so the ambient temperature, ambient wind speed and direction, and the like play important roles in the operation of air-cooled condensers. In extremely cold days, air-cooled condenser is even faced with the freezing risk that the finned tube bundles may encounter damage. It is helpful for the safe and economical operation of air-cooled condenser in power plants to propose anti-freezing approaches. With regard to the freezing mechanism for water and other working media, many investigations have been thoroughly carried out. Smith and Meeks [1] considered the effects of a thick wall on

L. Yang et al. / Applied Energy 127 (2014) 34–43

35

Nomenclature a A b cp f fn gn h k kn K m n p qv Q r R Re S t u v x xj

core friction coefficient heat transfer surface area (m2) core friction exponent specific heat (J kg1 K1) flow friction factor polynomial coefficient for the pressure rise of axial flow fan polynomial coefficient for the tangential velocity of axial flow fan specific enthalpy (J kg1) overall heat transfer coefficient (W m2 K1) turbulence kinetic energy (m2 s2) loss coefficient mass flow rate (kg s1) rotational speed (r min1) pressure (Pa) volumetric flow rate (m3 s1) heat rejection (W) latent heat of condensation (kJ kg1) radius of fan (m) Reynolds number source term in generic equation temperature (K) velocity (m s1) specific volume (m3 kg1) steam quality x-coordinate (m)

Greek symbols U diffusion coefficient (m2 s1) e heat exchanger effectiveness

the freezing process occurring inside a cylindrical container, finding that the wall temperature and thermal diffusivity play roles in the freezing rate and the shape of interface between the solid and liquid. Seeniraj and Hari [2] studied the solidification characteristics of a liquid flowing through a convectively cooled pipe under different flow situations, and obtained the limiting conditions for the commencement of the solidification. Tay et al. [3] investigated the phase change thermal energy storage performances for the pinned and finned tubes in freezing process, finding that the finned tube design performed 20–40% better in effectiveness and took 25% lesser time for the phase change process. Amin et al. [4] carried out freezing and melting tests in a tank filled with PCM encapsulated spheres, proving that the effectiveness–NTU method is applicable for PCM freezing and melting. Tan et al. [5] numerically studied the two-dimensional transient freezing problem for recovery and storage of the cryogenic gas cold energy by using Solidification and Melting model, pointing out that dimensionless numbers, such as Biot number and Stefan number of PCM, and the Stanton number of the coolant flowing in the tube, have remarkable effects on the characteristics of the freezing. Habeebullah [6] studied the growth rate of ice on the outside of cooled copper tubes by experimental measurement, discovering conspicuous axial growth rate of ice at low coolant Reynolds numbers and short freezing times. The slope of the ice thickness with axial distance showed moderate dependency on time, but varied with coolant flow rate, Stanton and Biot numbers. Lamberg and Siren [7] proposed a simplified analytical model to predict the solid–liquid interface location and temperature distribution of the fin in the solidification process with a constant end-wall temperature in the two dimensional PCM storage. A factor called the

ep l q r rp u w

turbulence dissipation rate (m2 s3) dynamic viscosity (kg m1 s1) density (kg m3) minimum flow to face area ratio turbulent Prandtl number scalar variable correction factor for the log mean temperature difference

Subscripts 0 rated 1 inlet 2 outlet a air ab ambient c core e exit f face i inlet m mean min minimum o outlet s steam T turbulence w water wa water-air z axial direction h tangential direction u scalar variable

fraction of solidified PCM is also introduced, by which the solidification picture at a given time can be predicted. Conde et al. [8] developed a two-dimensional model of heat transfer and solidification of a laminar flow inside a tube, and obtained a correlation to predict the blocking lengths of different fluids and operating conditions such as pipe diameter, mean velocity, wall and liquid temperatures. Emphases are placed on the liquid/solid phase change process in the aforementioned literatures. Moreover, Barigozzi et al. [9] investigated the variations of the net power output, fan load and exhaust steam pressure with ambient temperature and flow rate of district heating water for combined wet and dry cooling system in coldest months, and obtained the optimized running parameters free of freezing, but unfortunately, the freezing mechanism and anti-freezing measures for air-cooled condenser are hardly mentioned. Air-cooled condenser generally consists of tens of A-frame condenser cells with the finned tube bundles and the axial flow fan below [10]. The particular A-frame finned tube bundle configuration and turbulent aerodynamic behavior at the exit of axial flow fan result in the bad-proportioned flow and temperature fields across the finned tube bundles, so the freezing inside the tube of the finned tube bundles becomes more complicated. And moreover, the freezing process for the air-cooled condenser is composed of two unlike courses, first of which is the condensation of the exhaust steam from turbine, and second is the sensible heat rejection from the condensate to the liquid water at the freezing point. But unfortunately, no research work can be found concerning the freezing process of air-cooled condenser and the antifreezing measures taken by the direct dry cooling system in power plants.

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L. Yang et al. / Applied Energy 127 (2014) 34–43

As the key issues to the freezing of air-cooled condenser, the ambient temperature, flow rate of axial flow fan, back pressure of turbine, exhaust steam flow rate and quality will be investigated in this paper. The heat load capacity matching principle for antifreezing will be proposed. By introducing the heat exchanger model to the finned tube bundles, the cooling capability of ambient air and the heat rejection from the exhaust steam can be simultaneously modeled, thus the anti-freezing parameters can be obtained. It can contribute to the safe and economical operation of air-cooled condensers in power plants at extremely cold regions. 2. Heat load capability matching principle Considering that the freezing point of water varies little with the pressure near the atmospheric pressure, so the freezing point is regarded as 0 °C approximately in this research. The anti-freezing of air-cooled condenser should guarantee that the outlet water temperature of the finned tube bundles is not below the freezing point of 0 °C. The heat rejection of the exhaust steam consisting of the latent heat of the condensation and the sensible heat of water from the condensation temperature to the freezing point should not be lower than the heat load capacity of cooling air, in order that the air-cooled condenser can be free from freezing, which constitutes the heat load capacity matching principle for the anti-freezing of air-cooled condenser. The heat rejection of the exhaust steam Qs takes the following form.

Q s ¼ ms ðhs  hw Þ ¼ ms ðxr þ cpw ðts  t 0 ÞÞ ¼ ms ðxr þ cpw ts Þ

ð1Þ

where ms is the mass flow rate of exhaust steam, hs and hw are the enthalpies of exhaust steam and water at freezing point respectively. x is exhaust steam quality and r is condensation latent heat. cpw is the specific heat of water. ts is the condensation temperature and t0 is the freezing point, which is zero in the unit of °C. For the cooling air, the energy balance equation satisfies

Q a ¼ ma cpa ðta2  t a1 Þ ¼ qa Af uf cpa ðta2  t a1 Þ

ð2Þ

where Qa is the heat load of cooling air, ma is the mass flow rate, qa is the density, Af, uf are the face area and face velocity of the finned tube bundles of air-cooled condenser. cpa is the specific heat of cooling air. ta1 and ta2 are the inlet and outlet temperature of cooling air. According to the temperature profiles of exhaust steam, condensate and cooling air for air-cooled condenser as shown in Fig. 1, the heat transfer equation of air-cooled condenser takes the following form.

Q ¼ kADt ¼ ksa Asa

t 0a2  ta1 t s  t 00a2  ðt0  t a1 Þ t s t a1 þ kwa Awa w ts t00 ln ts ta2 0 ln a2

ð3Þ

t 0 t a1

where Q, k, A, Dt are the heat transfer rate, overall heat transfer coefficient, gas-side surface area and log mean temperature difference for the condenser. ksa, kwa are the heat transfer coefficient between the exhaust steam and cooling air, and heat transfer coefficient between the water and cooling air. Asa, Awa are the gas-side surface areas for the condensation and sensible heat rejection respectively. t0a2 and t00a2 are the outlet air temperatures at the condensation part and the sensible heat rejection part of finned tube bundles respectively. w is the correction factor of log mean temperature difference for the actual cross-flow finned tube bundles [11]. 3. Air-cooled condenser modeling The fluid and heat flows across the fin-tube bundles should be solved synchronously with the aerodynamic behavior of the axial flow fan for the condenser, but the flow complication and physical modeling troubles related to the fan blade passages and fin-tube

Fig. 1. Temperature profiles of exhaust steam, condensate and cooling air for aircooled condenser.

bundles issue a great computational challenge [12], so only one isolated condenser cell is taken into account in this work to investigate the aerodynamic behavior inside the A-frame and the thermo-flow performances of the fin-tube bundles, based on which the fan regulation and exhaust steam control are proposed to prevent air-cooled condenser cell from freezing. According to the actual configuration of the condenser cell for a typical 600 MW direct dry cooling generating unit, the physical model is developed as shown in Fig. 2, in which the heat exchanger model is used to characterize the finned tube bundles and the porous jump surface is adopted to simulate the axial flow fan. For the heat exchanger model, heat exchanger cores introduce a pressure drop to the gas stream, also termed the primary fluid, and transfer heat to or from a second fluid, referred to as the auxiliary fluid. The model can be used to compute auxiliary fluid inlet temperature for a fixed heat rejection or total heat rejection for a fixed auxiliary fluid inlet temperature. The auxiliary fluid properties can be a function of the pressure and temperature, thus allowing that the auxiliary fluid may be single-phase or two-phase. In this work, the cooling air is taken as the primary fluid, and the exhaust steam and condensate are regarded as the auxiliary fluid. In heat exchanger model, the flow loss is processed by using the porous media hypothesis and the streamwise pressure drop Dp [13] is expressed as

1 Dp ¼ f qam u2Amin 2

ð4Þ

where qam is the mean air density, uAmin is the air velocity at the minimum flow area. f is the streamwise pressure loss coefficient, which can be computed from the following Equation [13].

f ¼ K c þ 1  r2  ð1  r2  K e Þ



ve ve þ2 1 vi vi



þ fc

A Ac

vm vi

ð5Þ

where r is the minimum flow to face area ratio, Kc and Ke are entrance and exit loss coefficients, Ac is the minimum cross-sectional flow area, ve and vi are specific volumes at the exit and inlet, vm is the mean specific volume, fc is the core friction factor, which is defined as

fc ¼ aRebmin

ð6Þ

where a and b are core friction coefficient and exponent [13]. Remin is the Reynolds number for the velocity at the minimum flow area. To obtain the parameters in the streamwise pressure loss coefficient, the flow experiments were conducted in the wind tunnel for the cooling air flowing through the wave-finned flat-tube bundles that are commonly adopted by the Single Row Condenser (SRC) design of a 600 MW generating unit. The variations of the

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L. Yang et al. / Applied Energy 127 (2014) 34–43

Fig. 2. Schematic of air-cooled condenser and computational model. (a) air-cooled condenser cell, (b) computational domain and boundary conditions.

Table 1 Parameters in heat exchanger model of air-cooled condenser.

r

Kc

Ke

a

b

0.597

0.494

0.115

3.8533

0.64

pressure drop with the air velocity at the minimum flow area were achieved thus the coefficients in Eqs. (5) and (6) can be calculated as listed in Table 1. Inside the finned tube bundles of condenser, the temperatures of exhaust steam and condensate are stratified in the direction of the fluid flow. As a result, the heat rejection is not constant over the entire finned tube bundles. The fluid zone representing the heat exchanger core is subdivided into macroscopic cells or macros along the auxiliary fluid path. Heat rejection is computed for each cell within a macro and added as a source term to the energy equation for the cooling air flow. The heat transfer for a given cell Qcell is computed from

  Q cell ¼ ema cpa t in;auxiliaryfluid  t cell

ð7Þ

where e is air-cooled condenser effectiveness, tin,auxiliaryfluid and tcell are the auxiliary fluid inlet temperature of macro containing the cell and the cell temperature. The heat rejection from a macro Qmacro is calculated by summing the heat transfer of all the cells contained within the macro.

X

Q macro ¼

Q cell

ð8Þ

all cells in macro

The total heat rejection from the finned tube bundles of aircooled condenser Qtotal is computed as the sum of the heat rejection from all the macros:

X

Q total ¼

Q macro

ð9Þ

all macros

For the fan model, the pressure rise Dp is expressed as the polynomial form of the axial velocity uz [14].

Dp ¼

N X fn un1 z

ð10Þ

n¼1

where fn is the polynomial coefficient. N is the term number of the polynomial, which takes 3 in this work. By fitting the performance curve at the rated rotational speed of the typical fan adopted in

air-cooled condensers, the polynomial coefficients are obtained. f1 = 195.596, f2 = 19.998, f3 = 3.967, f4 = 0.570, f5 = 0.022. Owing to the three-dimensional flow complexities caused by fan blades, the tangential velocity should be imposed on the fan surface, however the radial velocity can be neglected [15,16]. The tangential velocity uh is specified by the following empirical equation.

uh ¼

N X

g n Rn

ð11Þ

n¼1

where gn is the polynomial coefficient, R is the radius of axial flow fan. When the geometric details of the fan blade are known, the tangential velocity at various radial distances can be obtained, so the polynomial coefficients that fit the tangential velocity at the rated rotational speed are acquired. g1 = 15.1, g0 = 25.76, g1 = 11.791, g2 = 4.321, g3 = 0.354. The axial flow fan used in air-cooled condenser usually operates in the frequency conversion mode, so the rotational speed can be easily regulated to alter the flow rate and pressure rise of the fan. The operation performance of the axial flow fan obeys the similarity principle as follows.

For the volumetric flow rate; qv ¼ qv0

For the total pressure; pt ¼ pt0

 2 n n0

n n0

ð12Þ

ð13Þ

where n is the rotational speed of axial flow fan, n0 is the rated rotational speed. qv0, and pt0 are the volumetric flow rate and total pressure at the rated rotational speed. The rated rotational speed, volumetric flow rate and total pressure as well as the designed parameters of air-cooled condenser are listed in Table 2. By fitting the performance curve of axial flow fan at various rotational speeds, the coefficients in Eqs. (10) and (11) can be obtained as listed in Table 3 and 4. Besides the finned tube bundles and axial flow fan setup in the boundary conditions, the inlet and outlet of the computational domain take the pressure boundary conditions. Other surfaces at the computational domain are set the symmetry boundary conditions as shown in Fig. 2(b). The wind-break walls and the ground are appointed adiabatic condition and the exhaust steam duct is given the constant temperature. Other surfaces inside the computational domain are internal assistant surfaces, through which the cooling air can flow.

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L. Yang et al. / Applied Energy 127 (2014) 34–43

Table 2 Designed parameters of axial flow fan and finned tube bundles for air-cooled condenser. Rated rotational speed (r min1)

Rated volumetric flow rate (m3s1)

Rated pressure rise (Pa)

Finned tube bundles type

Face velocity of finned tube bundles (ms1)

Surface area of finned tube bundles (m2)

80

480

92

Single row wave-finned flat tube bundles

2.2

14,559

Table 3 Polynomial coefficients for the correlation between the pressure and normal velocity of axial flow fan at various rotational speeds. Rotational speed (r min1)

f1

f2

f3

f4

f5

16 32 48 64

12.53631 28.20645 72.20834 132.4133

5.06293 7.59434 12.1509 16.4544

3.96681 3.96681 3.96681 3.96681

2 1.50034 0.93771 0.69247

0.3417 0.15186 0.05932 0.03235

Table 4 Polynomial coefficients for the correlation between the tangential velocity and distance from the fan center at various rotational speeds. Rotational speed (r min1)

g1

g0

g1

g2

g3

16 32 48 64

1.9114 3.8228 5.7342 9.557

3.2608 6.5215 9.7823 16.3038

1.4925 2.9851 4.4776 7.4627

0.547 1.0939 1.6409 2.7348

0.0448 0.0896 0.1344 0.2241

The conservation equations take the following generic form to characterize the flow and heat transfer of cooling air.

  @ quj u @ @u þ Su ¼ Cu @xj @xj @xj

ðj ¼ 1; 2; 3Þ

ð14Þ

where uj is the velocity in the xj direction. u, C/, S/ are the variable, its diffusion coefficient and source term respectively as listed in Table 5. In this work, the RNG k-e turbulence model is adopted to characterize the air turbulent flows due to its higher accuracy in rapidly strained and swirling flows. With the purpose of the validation of the numerical results, the volumetric flow rates of axial flow fan at the rated rotational speed for various ambient temperatures and exhaust steam flow rates were calculated by numerical simulations, to which the aforementioned fan and heat exchanger models were applied. The calculated average flow rate is about 483 m3/s, which agrees well with the design data of 480 m3/s for the axial flow fan adopted by air-cooled condensers. It shows that the fan and heat exchanger models, as well as the computational methods proposed in this paper are reliable enough to study the anti-freezing of air-cooled condenser. During the process of simulation, the exhaust steam flow rate and quality are primarily specified. The pressure drop from the turbine to the condenser is ignored in this study, so the condensation

pressure is regarded as the back pressure of turbine. Once the back pressure is known, the exhaust steam inlet temperature of the aircooled condenser can be obtained. The maximum allowed heat rejection of the exhaust steam that prevents the condensate from freezing is thus figured out according to Eq. (1). Following the heat load capacity matching principle, the thermal load of the cooling air should not exceed this maximum allowed heat rejection. By means of the rotational speed adjustment of the axial flow fan and the change of the ambient temperature, the thermal loads at both the exhaust steam side and cooling air side can accord with each other, so the anti-freezing exhaust steam flow rate and quality, anti-freezing back pressure, anti-freezing flow rate of cooling air and anti-freezing ambient temperature are obtained.

4. Results and discussion 4.1. Anti-freezing steam flow rate In terms of the heat load capacity matching principle, the exhaust steam flow rate should be more than one certain value to prevent the condensate from freezing at a given ambient temperature and a fixed rotational speed of fan, which is defined as the anti-freezing exhaust steam flow rate. It depends on the back pressure and exhaust steam quality besides the ambient temperature and running mode of fan. Fig. 3 shows the variation of anti-freezing exhaust steam flow rate with the ambient temperature, first of which is at various flow rates of the fan, second is at different back pressures of turbine and last is at various steam qualities. It can be seen from all figures that the anti-freezing exhaust steam flow rate becomes lower with increasing the ambient temperature, as a result of the heat load capacity matching principle that the allowed steam flow rate can decrease to match the reduced heat load of cooling air due to the increased ambient temperature. From Fig. 3(a) can also be observed that the anti-freezing exhaust steam flow rate increases with increasing the flow rate of cooling air through the fan, resulting from that the increased flow rate of fan will lead to a higher heat load of cooling air, thus requires a higher exhaust steam flow rate in terms of the heat load capacity matching principle. At high flow rates of fan, the antifreezing steam flow rate can be found dropped conspicuously as the ambient temperature increases due to the combined effects of the cooling air flow rate and ambient temperature that play dominant roles in the heat load capacity of cooling air.

Table 5 Summery of the generic governing equation. Equations

u

Cu

Su

Continuity x-momentum

1 ui

0

0

l

@p  @x þ @x@ i i

y-momentum

uj

l

@p  @x þ @x@ i j































@uj @uk @ @ i l @u @xj þ @xj l @xj þ @xk l @xj



z-momentum

uk

l

@p  @x þ @x@ i k

Energy Turbulence kinetic energy Turbulence dissipation rate

cpt kn

l/rpT l + lT/rpk l + lT/rpe

Sh GK + Gb – qep

ep



@uj @uk @ @ i l @u @xi þ @xj l @xi þ @xk l @xi



@u @ui k l @x þ @x@ j l @xkj þ @x@ k l @u @xk k

e2

ep ffi qC 1 Sep  qC 2 kþppffiffiffiffiffi mep þ C 1e kn C 3e Gb

L. Yang et al. / Applied Energy 127 (2014) 34–43

39

Fig. 3. Variation of anti-freezing exhaust steam flow rate with ambient temperature. (a) at various flow rates of fan, (b) at various back pressures, (c) at various steam qualities.

Table 6 Contrast between anti-freezing and secure exhaust steam flow rates. Ambient temperature (°C)

Flow rate of fan (kg/s) 100

200

300

400

500

0.59 0.65 0.73 0.79 0.87 0.94 1.02 1.08 1.15

1.23 1.37 1.52 1.66 1.84 1.97 2.12 2.23 2.38

1.76 1.99 2.20 2.42 2.65 2.86 3.08 3.30 3.51

2.33 2.62 2.91 3.21 3.49 3.80 4.10 4.38 4.68

2.90 3.26 3.64 4.05 4.42 4.78 5.14 5.50 5.83

(b) Anti-freezing steam flow rate 0 0.58 5 0.64 10 0.72 15 0.78 20 0.86 25 0.92 30 1.00 35 1.06 40 1.12

1.21 1.34 1.49 1.63 1.80 1.93 2.08 2.18 2.33

1.73 1.95 2.16 2.38 2.59 2.80 3.02 3.23 3.45

2.29 2.57 2.85 3.14 3.42 3.72 4.01 4.29 4.58

2.84 3.19 3.56 3.97 4.32 4.68 5.03 5.38 5.72

(a) Secure steam flow rate 0 5 10 15 20 25 30 35 40

The anti-freezing exhaust steam flow rate versus the ambient temperature at various back pressures is shown in Fig. 3(b), in which the fan operates at the rated rotational speed of 80 r/min

with the flow rate of 500 kg/s. It can be seen that the anti-freezing steam flow rate varies little with the back pressure, showing that the back pressure can be adjusted to a low level as much as possible when the exhaust steam flow rate goes beyond the limit of anti-freezing flow rate. The latent heat of exhaust steam is related to the condensation pressure, but this correlativity is very weak, so the condensation heat transfer and sensible heat of condensate from the condensation temperature to freezing point are less concerned with the back pressure, and the anti-freezing exhaust steam flow rate changes little with the back pressure. At the rated rotational speed of fan and constant back pressure of turbine, the variation of anti-freezing exhaust steam flow rate with the steam quality and ambient temperature is shown in Fig. 3(c). As the steam quality increases, the anti-freezing steam flow rate decreases due to the inverse proportion between them as demonstrated in Eq. (1), so the higher the steam quality is, the lower the anti-freezing exhaust steam flow rate is. From the aforementioned discussions can be drawn that, the reduced back pressure of turbine cannot bring to a freezing risk for air-cooled condenser any more when the exhaust steam flow rate arrives at a high enough value at a certain ambient temperature and a flow rate of cooling air. This exhaust steam flow rate is safe for the operation of air-cooled condenser in extremely cold days, so called the secure exhaust steam flow rate. The back pressure can be reduced as much as possible when the exhaust steam flow rate exceeds the secure one, so the thermal efficiency of the power plant can be improved and the coal consumption will

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L. Yang et al. / Applied Energy 127 (2014) 34–43

Fig. 4. Anti-freezing protective exhaust steam flow rate at various ambient temperatures and flow rates of fan. (a) fan flow rate of 100 kg/s, (b) fan flow rate of 200 kg/s, (c) fan flow rate of 300 kg/s, (d) fan flow rate of 400 kg/s, (e) fan flow rate of 500 kg/s.

become lower. Table 6(a) lists the secure exhaust steam flow rate at various ambient temperatures and fan flow rates for the designed back pressure of 15.6 kPa, which is a little higher than the anti-freezing steam flow rate as listed in Table 6(b). It decreases as the ambient temperature increases and fan flow rate decreases as a result of the heat load capacity matching principle. When the flow rate is less than the secure steam flow rate, but exceeds the anti-freezing steam flow rate, the back pressure can also be reduced to improve the thermal efficiency, so this exhaust steam flow rate range from the anti-freezing steam flow rate to the secure one is called the protective steam flow rate. But it should be cautious in case the back pressure becomes lower than the one corresponding to the anti-freezing exhaust steam flow rate. Fig. 4 shows the protective exhaust steam flow rate at various ambient temperatures and fan flow rates. It can be found that the range of protective exhaust steam flow rate varies widely as the ambient temperature decreases, showing that the lower the ambient temperature is, the wider the range of the protective exhaust steam flow rate by back pressure adjustment. In terms of the heat load capacity matching principle, the low ambient temperature will result in a high heat load at the air-side, so the increased matching heat load at the steam side requires that the exhaust steam flow rate should increase, and the range of the protective steam flow

rate will become wider. Similar to the ambient temperature, the increased fan flow rate will also result in the wider range of protective steam flow rate as shown in Fig. 4, and meanwhile, the range of protective steam flow rate shifts to high steam flow rates with increasing the fan flow rate due to the increased heat load. 4.2. Anti-freezing fan flow rate As the key issue to the anti-freezing of air-cooled condenser, the flow rate of cooling air plays important roles, so it is helpful to investigate the variation of anti-freezing flow rate of fan with other parameters. Fig. 5 shows the anti-freezing flow rate of fan versus the ambient temperature at various steam-side parameters, first of which is for the exhaust steam flow rate, second is for the back pressure, and third is for the steam quality. As the ambient temperature increases, the anti-freezing fan flow rate can also go up as a result of the energy conservation at the air side, by which the heat load is equal to the fan flow rate multiplied by the temperature difference between the outlet air temperature of air-cooled condenser and the ambient temperature. From Fig. 5(a) can be seen that, the anti-freezing fan flow rate increases with increasing the exhaust steam flow rate at the same ambient temperature, which is as a result of the heat load capacity

L. Yang et al. / Applied Energy 127 (2014) 34–43

41

Fig. 5. Variation of anti-freezing fan flow rate with ambient temperature. (a) at various steam flow rates, (b) at various back pressures, (c) at various steam qualities.

matching principle that the increased exhaust steam flow rate will bring on a higher heat load at the exhaust steam side, so the matching heat load at the air side can also be increased, leading to the increased fan flow rate. As illustrative cases, the anti-freezing fan flow rate is only about 100 kg/s at the exhaust steam flow rate of 1.0 kg/s and ambient temperature of 25 °C, but it arrives at about 480 kg/s at the exhaust steam flow rate of 4.5 kg/s and the same ambient temperature. The rotational speed of axial flow fan should be regulated according to the exhaust steam flow rate and ambient temperature. The anti-freezing fan flow rate versus the ambient temperature at various back pressures is shown in Fig. 5(b). It can be seen that the anti-freezing fan flow rate has a little bit increase as the back pressure goes up, but this change can almost be negligible. As pointed out in Eq. (1), the increased back pressure will lead to a higher heat load at the steam side, which allows that the rotational speed of fan can be raised to match the increased heat load. Though the sensible heat rejection of the condensate from the condensation temperature to freezing point can go up conspicuously with increasing the back pressure, the latent heat of condensation varies little with the back pressure, moreover, the sensible heat is far less than the latent heat, so the impact of back pressure on the antifreezing flow rate of fan is so weak that it can be ignored in practical engineering. Fig. 5(c) gives the variation of anti-freezing fan flow rate with ambient temperature at various steam qualities, in which the increase of the anti-freezing fan flow rate can be clearly observed

as the steam quality increases. According to the heat load capacity matching principle, the increased steam quality results in a higher heat load at the steam side, which allows a higher rotational speed of fan to be free of freezing for air-cooled condenser. 4.3. Anti-freezing back pressure The back pressure of turbine is commonly used to prevent aircooled condenser from freezing in practical engineering, so it needs to investigate the impacts of back pressure upon the freezing issue in power plants. Fig. 6 shows the variation of anti-freezing back pressure with the exhaust steam flow rate at various ambient temperatures, fan flow rates and steam qualities. From all the figures can be seen that, the anti-freezing back pressure decreases with increasing the exhaust steam flow rate, showing that the back pressure can be adjusted to a low threshold for an improved thermal efficiency if the exhaust steam flow rate is high enough, which can contribute to the efficient operation of air-cooled condenser. From Fig. 6(a), it can be observed that the exhaust steam flow rate corresponding to the anti-freezing back pressure changes to the higher value with decreasing the ambient temperature at the rated rotational speed of axial flow fan, showing that the antifreezing back pressure can be conspicuously reduced even at extremely low ambient temperatures when a great quantity of exhaust steam flows into the air-cooled condenser. However, the antifreezing of air-cooled condenser cannot be realized by means of back pressure increase any way if the exhaust steam flow rate is

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Fig. 6. Variation of anti-freezing back pressure with exhaust steam flow rate. (a) at various ambient temperatures, (b) at various flow rates of fan, (c) at various steam qualities.

too small in cold days, only by the slowdown of the rotational speed of fan can prevent the condensate from freezing. Fig. 6(b) shows the anti-freezing back pressure versus the exhaust steam flow rate at various flow rates of cooling air and at ambient temperature of 5 °C. As the rotational speed increases, the exhaust steam flow rate related to the anti-freezing back pressure becomes high as a result of the heat load capacity matching principle. The anti-freezing back pressure can be conspicuously reduced even at the rated rotational speed of axial flow fan when a great quantity of exhaust steam flows through the finned tube bundles. But when the exhaust steam flow rate lessens to a low value, the back pressure cannot perform any function in the antifreezing of condensate if much more cooling air flows across the finned tube bundles. In this instance, the increased exhaust steam flow rate or the reduced rotational speed of fan is needed to be free of freezing for the air-cooled condenser. At the rated rotational speed of fan and ambient temperature of 5 °C, the variation of anti-freezing back pressure with the exhaust steam flow rate and steam quality is shown in Fig. 6(c). As the wet steam, the higher the exhaust steam quality is, the stronger the heat load capacity at the steam-side, so the allowed exhaust steam flow rate can become lower at the same matching heat load capacity of cooling air, therefore, the exhaust steam flow rate related to the anti-freezing back pressure can be reduced at high steam qualities. It is of benefit to the anti-freezing of air-cooled condenser when the exhaust steam takes a high steam quality.

5. Conclusions The impacts of ambient temperature, fan flow rate, exhaust steam flow rate and quality, and back pressure upon anti-freezing of air-cooled condenser are discussed on the basis of the heat load capacity matching principle. The anti-freezing exhaust steam flow rate can be reduced with increasing the ambient temperature, but should increase with increasing the flow rate of cooling air. The anti-freezing steam flow rate varies little with the back pressure, showing that the back pressure can be adjusted to a low level as much as possible when the exhaust steam flow rate goes beyond the limit of anti-freezing flow rate. As the ambient temperature increases, the anti-freezing fan flow rate increases also as a result that the heat load is equal to the fan flow rate multiplied by the temperature difference between the outlet air temperature and ambient temperature. The antifreezing fan flow rate increases with increasing the exhaust steam flow rate, but varies little with back pressure. The increased steam quality will result in a higher heat load at the steam side, which allows a higher rotational speed of fan. The exhaust steam flow rate corresponding to the anti-freezing back pressure changes to the higher value with increasing the ambient temperature at the rated rotational speed of fan. As the rotational speed increases, the exhaust steam flow rate related to the anti-freezing back pressure becomes high. The exhaust steam

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flow rate related to the anti-freezing back pressure can be reduced at high steam qualities, showing that high steam quality is of benefit to the anti-freezing. The heat load capacity matching principle can be applied to the anti-freezing of air-cooled condenser, which contributes to the safe and efficient operation of dry cooling system in power plants. Acknowledgements The financial supports for this research, from the National Natural Science Foundation of China and Shenhua Group Corporation Limited (Grant No. U1261108) and the National Scientific and Technical Supporting Program of China (Grant No. 2011BAA04B02), are gratefully acknowledged. References [1] Smith RN, Meeks E. Experimental investigation of freezing inside a thickwalled cylinder. Exp Therm Fluid Sci 1993;7:22–9. [2] Seeniraj RV, Hari GS. Transient freezing of liquids in forced flow inside convectively cooled tubes. Int Commun Heat Mass 2008;35:786–92. [3] Tay NHS, Bruno F, Belusko M. Comparison of pinned and finned tubes in a phase change thermal energy storage system using CFD. Appl Energy 2013;104:79–86. [4] Amin NAM, Bruno F, Belusko M. Effectiveness–NTU correlation for low temperature PCM encapsulated in spheres. Appl Energy 2012;93:549–55.

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