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Methodology for evaluation of cooling tower performance – Part 2: Application of the methodology and computational aspects of Poppe equations
Energy Conversion and Management 52 (2011) 3282–3289
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Methodology for evaluation of cooling tower performance – Part 2: Application of the methodology and computational aspects of Poppe equations J. Smrekar a,⇑, A. Senegacˇnik b, C. Führer c a
Department of Mechanical and Structural Engineering and Materials Science, University of Stavanger, 4036 Stavanger, Norway Department of Power Engineering, University of Ljubljana, Aškercˇeva 6, SI-1000 Ljubljana, Slovenia c Department of Numerical Analysis, Lund University, P.O. Box 118, SE 22100 Lund, Sweden b
a r t i c l e
i n f o
Article history: Received 26 April 2010 Received in revised form 4 May 2011 Accepted 11 May 2011 Available online 22 July 2011 Keywords: Cooling tower Power plant Poppe model Cooling tower performance Methodology Real data
a b s t r a c t A methodology for evaluation of natural draft cooling tower (CT) performance and its application is presented. The study establishes the connection between CT performance and power output. It can estimate a change in a CT’s efficiency as well as an increase in power output as a function of cooling water temperature and load to the plant. The methodology consists of three subparts, i.e. Cooling Tower Profiler (CTP) method, CT model and a model of the power plant that are described in the first part of the paper. The second part focuses on application of the methodology in a way that minimizes error of the CT model. One week of data from the power plant were acquired for the analysis. In the CT a small area with irregularities was examined, and increased efficiency and power output are estimated by the methodology. Furthermore, another aspect of solving Poppe equations is examined resulting in reduced computational effort by approximately a half without losing any computational accuracy. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Growing consumption of fossil fuels presents a rising concern related to global warming issues. Scientists and politicians have been trying to mitigate greenhouse gases in many different ways. One of the biggest pollutants is power plants using fossil fuels for production of electricity and/or heat, for which demands are still growing. Increasing efficiency of such energy systems is one of the solutions that can considerably reduce environmental pollution. In order to continuously mitigate greenhouse gases, constant improvements of energy systems and their monitoring are necessary. As power plants are complex systems, an optimization of local parts as well as their tuning on a system level must be considered. In this paper the focus is given to a power plant with a natural draft cooling tower (CT). CTs remain widely used in power producing industry and air conditioning systems for cooling circulating water [1,2]. In conventional power plants approximately a half of the energy delivered by fuel is rejected from a cooling system. Even though this energy is low with exergy, improvements in heat rejection may significantly contribute to fuel savings as the energy flows through cooling system are huge. In this respect an explanation of the CT performance from an exergy point of view and its ⇑ Corresponding author. Tel.: +47 51832164; fax: +47 51831050. E-mail address: [email protected] (J. Smrekar). 0196-8904/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2011.05.004
trends for optimization can be found in [3,4]. This leads to a desire to better understand the operation of the CT and to optimize its design parameters [5]. Gan et al. [6] applied CFD code to predict the performance of a closed CT by using a two-phase flow of air and water droplets on the outside tube. The predicted thermal performance is compared with experimental measurements. Kloppers and Kröger [7] found out that exactly the same definition of Lewis factor must be applied in fill performance analysis and subsequent CT performance analysis. Kranc [8] looked into design of spray patterns for counterflow CTs and concluded that for a particular nozzle manifold and packing arrangement, a performance limitation exists due to the inherently non-uniform pattern of water flow. CTs have been in operation for more than five decades and proper attention in terms of monitoring and maintenance has not been given to them. Overhauls of turbines and boilers are conducted on regular bases while degradation of CTs is usually not considered. Broken packing, plugged nozzles, growing algae, broken eliminators, etc. [9] are some of the common problems in CT operation which deteriorate the CT and thence system efficiency. In 1990s Mortensen and Conley [10] put an effort to understand and reproduce the primary fouling mechanism in a controlled and accelerated laboratory regimen on a number of fill configurations to optimize geometry. Qureshi and Zubair [11] worked on modeling strategy of fouling in CT fills and incorporated it in the CT model to study performance evaluation problems. Khan and Zubair [12] validated similar model on experimental data.
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Nomenclature
e g a, b CT CTP F Pgen Q T T 0w2 m N w
computational accuracy efficiency/% coefficients cooling tower Cooling Tower Profiler function power on generator/MW heat flow/MW temperature/°C or K numerical solution of the outlet water temperature from the CT/°C mass flow rate/(kg/s) number of intervals humidity ratio/(kgwater vapor/kgdry air)
Performance of a cooling system has an important impact reflecting in corresponding back pressure in condensator and hence plant’s power output. Not many studies have been reported where the impact of the CT on power output is investigated. Barigozzi et al. [14] studied wet and dry cooling systems optimization at a CHP plant. Parametric analysis showed the significance of the cooling systems’ operation on the power output and the generated data were further used for optimization of the processes. Gañán et al. [13] presented a study showing the relation between the power output and the water temperature to condenser based on different cooling sources. However, all mentioned studies involve power plant with a CT analysis as a standalone component. Anomalies in CT are usually reflected on a local basis and are thus hard to identify. As the plane area of a natural draft CT is huge, the local irregularities can significantly affect the CT performance. The Cooling Tower Profiler (CTP) measuring technique [15] can be used for identification of such irregularities. The CTP is based on a mobile unit measuring the air temperature and velocity profiles across the plane area of CTs and it is a part of the methodology presented in this paper. The measured data on a local basis can thus be used to improve the thermodynamic performance of a CT [16]. However, the studies deal mainly with the identification of irregularities and thermodynamic improvements of CT operation whereas the impact of the local irregularities on existing CT performance and furthermore on the plant’s power output have not been investigated so far. In general, usual obstacle is that extensive measurements with suitable measuring technique and compatible method for CT analysis on a local basis are required. Nevertheless, the CTP measuring technique established a good base to evaluate the magnitude of local irregularities and their effect on power output as presented in this paper. The measured profiles are used in a CT model that presents the second part of the methodology. Its base is the Poppe model that does not require information about the constructional characteristics of a CT. These are practically impossible to measure in practice on a degraded CT. The Poppe model in conjunction with measured profiles can estimate an influence of irregularities on outlet cooling water temperature. The latter parameter is the input parameter to the empirical model of the power plant developed as the third part of the methodology. Hence, an estimation of power increase as a function of cooling water temperature and plant’s load is possible. The three subparts of the presented methodology are described in more detail in the first part of this paper [17]. In the second part of the paper, focus is given to application of the methodology covering several aspects:
x, y
length/m
Subscripts 1 inlet 2 outlet a air atm atmosphere CT cooling tower gen generator i denotation of the local scale PP power plant p initial guess w water wb wet bulb
Demonstration of the proposed methodology which has established the bridge between CT performance and plant’s power output. By application of the methodology, the impact of local irregularities in the CT on the power output and system’s efficiency can be studied. Minimization of systematic error of the methodology. It is practically impossible to measure the changes in constructional characteristics across the plane area of a real natural draft CT. Hence, the modeling on the local basis of the CT has to be done as a ‘‘black-box’’ modeling. A calculation procedure is proposed where the methodology is applied in a way that subtracts systematic errors of the models. Examination of numerical integration of Poppe equations. The modeling presented in this work is of large scale demanding a large amount of computational effort. In this respect faster calculation with practically no loss in computational accuracy is reported. The application of the methodology was done on 1 week of measured data from a power plant and a natural draft CT. The significance of efficient CT operation and its impact on power output are depicted. 2. Motivation and base for the analysis Focus is given to application of the proposed methodology the intention of which is to yield minimal error in predicted parameters. As a natural draft CT is a huge construction its evaluation is a challenging task. There are many practical issues related to measurements from the feasibility as well as the measuring point of view. CTs are huge constructions with relatively harsh environment in it. These make it practically impossible to measure changes in the CT’s characteristics, especially in its concealed parts (e.g. packing, nozzles). Measuring inlet air conditions to the packing is also not practical. Moreover, today there is no commercially available measuring instrument of air humidity that would enable reliable measurements in the CT where the air is normally supersaturated. Hence, these constraints necessitate a different approach accompanied by assumptions. For the presented methodology, these constraints and assumptions are discussed in the first part of the paper [17]. In the second part of the paper the motivation was to apply the methodology in a way that alleviates those assumptions and reduces the error of the applied models. An example of an application of the methodology is presented on real measured data from a natural draft CT and 345 MWe power plant. The analysis focuses on a part of the CT with irregularities. The base is air velocity and temperature profiles, presented in Fig. 1, which were measured above the drift eliminators. The effect
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Fig. 1. Air velocity and temperature profiles measured above the drift eliminators in the CT.
of reparation of the irregularities on power output was studied for a 1-week period covering the broad range of the plant’s operational as well as ambient conditions. 3. Application of the methodology for evaluation of CT performance The irregularities, which can be clearly identified in both air temperature and velocity profiles (Fig. 1), were the object of analysis in this study. Fig. 2 shows the selection of the area with irregularities (full square) and the condition in the CT after reparation. The Poppe model does not consider CT characteristics; instead it is based on empirical formulation of Lewis factor [18] and (measured) conditions. Hence, the symmetrical area of the same size with respect to the x-axis was used (dashed square) to represent the state after reparation. As such conditions do not reflect the state that would be achieved by new constructional elements, the analysis can be considered on the ‘‘safe-side’’. If the characteristics of new CT elements are available, the data representing operation with the new elements can be simulated and applied instead. On the basis of the measured profiles, it is possible to predict what kinds of irregularities are taking place. From Fig. 1 high air temperatures and low air velocities can be detected in the analyzed region. The measurements indicate that pressure losses, which led
to decreased velocity, could emerge due to damaged packing and/ or eliminators. High air temperatures still signify that the heat and mass transfer is high which, on the other hand, indicates that the water distribution system is working properly. By visual inspection of the investigated region, it was confirmed that the packings are the cause of irregularities in the analyzed CT. 3.1. Calculation procedure One of the most important parts of the methodology is the way of applying it. The goal is to minimize the systematic error of the CT model as it is not known for the particular CT. The solution is in calculating the differences which subtract the model’s systematic error. This is feasible by application of the CT model and the profiles in a way that yields the measured outlet water temperature presenting the original performance of the CT. Then, by applying the modified profiles (representing the conditions after reparation) and the CT model on the local basis, a new outlet water temperature is predicted reflecting the reparation. Fig. 3 shows a flow chart of the calculation procedure. It is outlined as follows: 1. Determination of CT efficiency on the basis of the measured inlet and outlet CT water temperatures and the ambient wet bulb temperature.
Fig. 2. Detection of the irregularities in the CT operation and the state after reparation.
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In Step 3, the Poppe model with measured integral CT parameters is used to calculate the average state of the air in the CT which changes with the operational condition of the plant as well as with ambient conditions. Then, in Step 4, the air velocity and temperature profiles are adapted to the new state in the CT according to the two criteria. Since the average state is calculated with the Poppe model, its application on a local scale yields the same measured outlet water temperature from the CT as was used in Step 3. Later on in Step 6, the Poppe model is applied on the local basis for calculation of the modified state in the CT. Operating with the differences subtracts the systematic error of the Poppe model and similarly of the empirical model of the plant in Step 7 (for more on the systematic error of the empirical model of the plant refer to Section 3.1.2 in the first part of the paper [17]).
3.2. Results of the CT analysis
Hence, the Poppe model is adapted to the integral measured inlet and outlet water temperatures to and from the CT respectively. This means that backward calculation on the local scale results in the same value as the measured outlet water temperature from CT. At the same time, the energy balance equation Qw = Qa is preserved according to the control volume of the CT (Fig. 6 in the first part of the paper [17]). 1. Providing conditions presenting the repaired CT. In this study, the area of the same size (symmetrical with respect to the xaxis) was used as denoted by the dashed line in Fig. 2. It did not represent the modifications that would be achieved by installing new packing, but nevertheless it sufficed for approximation of potential improvements. By known characteristics of new CT elements, the simulated data can be applied instead. 2. The modified profiles, representing a new state in the CT, are used as the boundary conditions to the Poppe model. The estimation of new conditions, i.e. calculation of the local outlet water temperatures from packing and the air humidities above eliminators across the CT, are determined. On the basis of these, the new outlet water temperature from the CT is calculated. 3. In the final step, the empirical model of the plant is employed and the increase in power output is estimated on the basis of the measured outlet water temperature and the estimated one.
50
40
/%
1. Using the Poppe method for the CT analysis, the average air temperature and humidity in the CT are calculated. 2. Discretization and superposition of the air temperature and mass flow rate profiles in order to match an operational condition of the CT. The superposition fulfills the two criteria: (i) the sum of the local air mass flow rates equals the total air mass flow rate, determined in Step 2; (ii) the average value of the local air temperatures equals the average value of the air temperature in the CT, determined in Step 3.
4
30
CT
ð1Þ
Δη
i
/%
h
gCT ¼ 1 exp 0:8696ðmw =ma Þ1:061
CT
2. Estimation of the total air mass flow rate through the CT on the basis of the measured total water mass flow rate, CT efficiency and CT characteristic. In this study, the CT characteristic used was determined according to Hampe’s model [20] and for the analyzed CT is [21]:
Analysis comprehended 1 week’s data from the plant which were also used for the validation of the empirical model of the plant (Section 3.1.2, first part of the paper [17]). As mentioned, the data were previously examined and the measurements deviating from the normal operation were eliminated from the database. For the analysis of the CT performance, a 30 min interval was used and 331 operational points throughout 1 week were examined. For each operational point the analysis related to the region with irregularities in the CT was conducted according to the flow chart in Fig. 3. Fig. 4 shows the CT efficiency on the left axis and its increase due to the reparation of irregularities on the right axis. The average CT efficiency in the 1-week analysis was 41% and its average increase 2.95%. The increase in CT efficiency resulted in a power increase as shown in the following figure. Fig. 5 shows the power output on the left axis and the power increase on the right axis. The average power output in the analyzed period was 295.590 MW and the average power increase due to reparation of the region with irregularities was 0.765 MW which correspond to 0.26%. The average power increase is relatively low, but it should be considered that the modified region comprehended only 16% of the total plane area of the CT. For the period of 1 week the difference of the average local air mass flow rates and temperatures of the two symmetrical regions are 0.29 kg/s and 1.1 °C respectively. Looking at the air mass flow rate, which defines the efficiency of the CT (Eq. (1)), the 0.29 kg/s difference represents 26% decrease with respect to the reference (symmetrical) region. Therefore, the irregularities can be considered of the low-scale magnitude.
η
Fig. 3. Flow chart for the evaluation of CT performance.
3
2 0
1
2
3
4
5
6
7
time / days Fig. 4. CT efficiency and its increase due to reparation of irregularities.
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300
250
1,1
200
0,9 0,7 0,5
0
1
2
3
4
5
6
7
ΔPgen / MW
Pgen / MW
340
0,3
wp2 ¼ watm þ 0:01mw =ma
time / days Fig. 5. Operation of the power plant and the power increase due to reparation of irregularities.
ηPP / %
40,4 40 39,6 39,2 0.14 38,8
0.1
ΔηPP / %
0.12
0.08
0
1
2
3
4
sive computational effort. In this respect the Poppe equations were examined in order to find a faster computational solution whilst, if possible, keeping the accuracy unchanged. The original Poppe equations [15], of which computational procedure has not been evaluated, were solved by the shooting method [22] and unknown variables were computed iteratively as presented schematically in Fig. 7. Left flow chart in Fig. 7 shows that if the difference between the initial guess of the humidity ratio and the computed humidity at the outlet of the CT is not within a given accuracy threshold e, then the calculated humidity ratio is used as an initial guess in the next iteration. This procedure usually converges in up to three iterations with accuracy of 104 and by using the following equation for the initial guess [19]:
5
6
7
0.06
time / days Fig. 6. Power plant efficiency and its increase due to reparation of irregularities.
Fig. 6 shows power plant efficiency and its increase due to the reparation of irregularities. The average thermal power plant efficiency was 40.08% and its increase due to reparation of irregularities in the CT was 0.11%. The increase in efficiency is expectedly low corresponding to the relatively small examined area and low-scale irregularities in the CT. The above figures show high correlation among them which is dictated by the plant’s operation. By comparing Figs. 4 and 5, it can be noticed that the CT efficiency is strongly influenced by the plant’s operation. The operational condition is determined by the thermal load to the plant and hence a higher load results in higher efficiencies of both the plant and CT. Considering the plant, this is due to operation closer to the nominal one while looking at the CT, a higher rejected heat rate from the condenser consequently results in a higher draft through the natural draft CT. An analogical explanation applies for the increments in power and both efficiencies. Hence, the plant’s operation closer to the nominal yields a higher increase in the power and efficiency of the plant as the result of CT reparation. 4. Computational aspects of Poppe equations The methodology for evaluation of CT performance is based on measurements on the local basis of a CT. In this study the plane area of the CT was discretized and 3177 nodes were used for calculation in each operational condition. Throughout 1 week of data 331 different conditions were analyzed, resulting in a comprehen-
ð2Þ
A closer look at the computation procedure reveals that iterations are not needed as the result is rather insensitive on the initial guess as long as the guess is within reasonable boundaries. A sufficiently good guess can already be achieved by Eq. (2). Moreover, the estimate is required to be computed only once for each operational condition as each node in the discretized plane area of the CT is calculated sequentially and a solution from the adjacent node can be used as initial guesses in the next node. The computation of Poppe equations without iteration means that only one good shot of initial guess suffices and the loop, which is denoted by a dashed line in the left flow chart of Fig. 7, is not needed. Hence, the proposed solution looks as depicted in the right flow chart of Fig. 7. When the integration is finished, the calculated humidity at the outlet is used in energy and mass balance equation, denoted by F, which yields the outlet water temperature. As there is no iteration applied, this simplifies the computational procedure and makes the numerical code much faster. Fig. 8 shows the humidity ratio above eliminators and corresponding outlet water temperature from packing as functions of the initial guess at different numbers of intervals and for the case where air gets supersaturated. In the left plot an initial guess, applying Eq. (2), is denoted with the red asterisk. The dashed line represents the equations that are being solved:
w2 ¼ Fðwp2 Þ
ð3Þ
where F represents Poppe equations and w2 the solution. From the left plot in Fig. 8, it can be seen that the calculated humidity ratio is practically independent of its initial guess and that the number of intervals does not significantly influence the accuracy of calculation. From approximately 10 intervals on, the difference in the solution is marginal. The independent solution indicates that the iterative procedure is not required for the case where air gets supersaturated and hence only one relatively good shot of initial guess is needed. This can be confirmed by the corresponding right plot showing practically constant outlet water temperature (second unknown variable) from the packing as a function of the initial guess. Looking at the biggest difference of calculated humidity ratio in the left plot, i.e. 1.38 105 kg/kg, the corresponding outlet water temperature difference is 104 °C. In the case of unsaturated air above the eliminators, a similar conclusion to the supersaturated state can be drawn, as can be seen from Fig. 9. The relationship between calculated humidity ration and its initial guess is also practically independent and therefore the iterations are not needed. The difference in the calculated humidity ratio with changing initial guess from 5.0 103 to 3.5 102 kg/kg is 1.1 105 kg/ kg. A small change of less than 0.01 °C by applying 15 intervals can be noticed for the outlet water temperature in the right plot. In the case of unsaturated air the number of intervals plays a higher role than in the case where air gets supersaturated. From the
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Fig. 7. Scheme of the conventional and proposed computational approach.
17.74
0.035
w2=F(wp2) 0.03
17.736 17.734
/ °C
17.732
w2
0.02
17.73
T
w2 / (kg/kg)
0.025
5 intervals 10 intervals 15 intervals 20 intervals 25 intervals
17.738
5 intervals 10 intervals 15 intervals 20 intervals 25 intervals Eq. (2)
17.728 0.015 17.726 17.724 0.01 17.722 0.005 0.01
0.02
0.03
initial guess wp2 / (kg/kg)
17.72
0.01
0.02
0.03
initial guess wp2 / (kg/kg)
Fig. 8. Humidity ratio above packing and outlet water temperature from packing (unknown variables) as functions of initial guess for the supersaturated air.
right plot it can also be seen that from approximately 10 intervals on, the solution becomes practically independent of the initial guess and also reaches a good accuracy. The example corresponds to air with a relative humidity of 0.83 above the packing. It was confirmed that approaching the saturated state, the already small non-linearity diminishes further. 4.1. Examination and comparison of the computational approaches on the analyzed data The two examples in the previous section are presented for two different boundary conditions with respect to saturation of air above eliminators. To validate the non-iterative code, it has to be tested in a broad range examining different boundary conditions. In this regard the 1-week data proved to be suitable for the task.
The plant’s operational conditions varied in the wide operational range as can be seen in Fig. 5. Consequently these variations resulted in even more intensified differences with respect to waterto-air mass flow rates and air temperatures above the eliminators on the local basis of the CT (Fig. 1). The ambient conditions in the analyzed week also varied quite extensively, i.e. ambient temperature varied from 3 to 12.5 °C and relative humidity from 36% to 100%. In the analysis the iterative code presented the reference case as an arbitrary accuracy can be achieved. For this task the accuracy was set to 104. On the other hand, the accuracy for the non-iterative code does not need to be specified since there is no loop. In the following, the two codes are compared looking at the discretized area in the CT. The case with the highest average difference in the outlet water temperature from the 1-week analysis is re-
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0.035
2
p2
5 intervals 10 intervals 15 intervals 20 intervals 25 intervals Eq. (2)
0.03
17.9
17.85
Tw2 / °C
0.025
w2 / (kg/kg)
17.95
w =F(w )
0.02
5 intervals 10 intervals 15 intervals 20 intervals 25 intervals
17.8
17.75
0.015 17.7 0.01
0.005
17.65
0.01
0.02
0.03
initial guess wp2 / (kg/kg)
17.6
0.01
0.02
0.03
initial guess wp2 / (kg/kg)
Fig. 9. Humidity ratio above packing and outlet water temperature from packing (unknown variables) as functions of initial guess for the unsaturated air.
Fig. 10. Difference in outlet water temperatures computed with the two codes.
ported. Fig. 10 shows the difference between the outlet water temperatures computed with the two codes.
From a numerical point of view, the profile change in the figure indicates that the initial guess has an influence on the solution accuracy. On the other hand, the difference varying from 0.023 to 0.014 °C is negligible from an engineering point of view. When applying Eq. (2) for estimation of the initial guess, average absolute difference was 0.0064 °C and maximum difference 0.0231 °C. When applying the solution from the adjacent node for the initial guess, the average value dropped to 0.0017 °C. When conducting extensive analysis as the one in this study, the calculation time is of high importance. When applying the iterative integration the average number of iterations for 1 week of analysis was 2.1 when setting 15 intervals and accuracy of 104. This also means that the calculation time was 2.1 times longer in comparison with the simplified code without a significant decrease in accuracy. Using the solution from the adjacent node for the initial guess reduced the average number of iterations by approximately 15% to 1.8 iterations. Optimal operation of natural draft CTs requires that cooling air gets saturated in order to use the whole potential of evaporative cooling. Usually the saturation point is met. In the case of analyzed data the air above the eliminators was calculated to be supersaturated in all cases. However, since there is a possibility that the air does not meet saturation point and can thus be unsaturated above
Fig. 11. Relative humidity above eliminators and difference between the iterative and non-iterative code in computed outlet water temperature from the packing.
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eliminators, the non-iterative code was also examined under such conditions. For demonstrational purposes an operational condition was simulated where the air does not meet saturation point. This usually happens at the circumference of a CT where the air flow is the highest and at its driest state. The result is presented in Fig. 11 showing the relative humidity above eliminators and the difference between the codes in computed outlet water temperature from the packing. The left plot shows, as expected, that the unsaturated air appears at the circumference of the CT. Relative humidity is the lowest, i.e. 0.76, at left side of the CT as can be noticed from Fig. 11. The corresponding right plot shows the biggest difference between the two codes exactly in that region with the highest air flow. However, it was still negligible with the average absolute difference being 0.0077 °C and a maximum difference of 0.0248 °C (the case with application of Eq. (2)). In comparison with the case where air gets supersaturated (Fig. 10), the conclusion can be rather similar and the performance of the non-iterative code is also acceptable. The non-iterative approach was tested in a wide range with respect to boundary conditions showing that the accuracy was preserved with significant reduction in computational time. Thus, the simplified approach appears to be an improved solution in comparison with the original one. It should be also pointed out that to make a CT analysis consistent, only one approach should be used. 5. Conclusions In the second part of the paper the application of the developed methodology is demonstrated. Modeling on the local basis of a CT was done as a ‘‘black-box’’ modeling, since changes in characteristics of a CT’s components are hard to assess. In this respect the Poppe model for CT analysis, which does not require information about CT characteristics, was applied. A calculation procedure is proposed that minimizes the error of the methodology. The application of the methodology is demonstrated on real measured data from a plant and a natural draft CT. The area with irregularities in the analyzed CT was identified from the air velocity and temperature profiles measured by the CTP method. The investigated region in the CT was replaced by a ‘‘healthier’’ region of the same size. The result of the improved state was lower outlet water temperature from the CT which was predicted by the CT model. Consequently, the increase in power, estimated by the empirical model of the plant, was expected. The repaired region, comprehending approximately 16% of the CT’s total area, yielded 0.765 MW average increase in the power output based on 1 week’s analysis.
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The extensive analysis that comprehended the discretized CT plane area as well as 1-week power plant’s operation required a huge amount of computational effort. Hence, a new aspect of solving the Poppe equations was examined and a faster numerical solution is proposed. The investigation showed that solving Poppe equations does not require iteration procedure as the unknown variables are practically independent of the initial guess. As a result the solution is faster for approximately factor 2 with practically no effect on the computational accuracy. References [1] Berman LD. Evaporative cooling of circulating water. London: Pergamon; 1961. [2] Heat exchanger design handbook. NY: Hemisphere Publishing Corporation; 1983. [3] Qureshi BA, Zubair SM. Second-law-based performance evaluation of cooling towers and evaporative heat exchangers. Int J Therm Sci 2007;46(2): 188–98. [4] Thirapong M, Wanchai A, Somchai W. Effects of inlet relative humidity and inlet temperature on the performance of counterflow wet cooling tower based on exergy analysis. Energy Convers Manage 2008;49(10):2795–800. [5] Kröger DG. Air-cooled heat exchangers and cooling towers: thermal-flow performance, evaluation and design. New York: Begell House, Inc.; 1998. [6] Gan G, Riffat SB, Shao L, Doherty P. Application of CFD to closed-wet cooling towers. Appl Therm Eng 2001;21(1). [7] Kloppers JC, Kröger DG. The Lewis factor and its influence on the performance prediction of wet-cooling towers. Int J Therm Sci 2005;44(9). [8] Kranc SC. Optimal spray patterns for counterflow cooling towers with structured packing. Appl Math Model 2007;31(4):676–86. [9] Liqing S. Application of the no-padding and atomizing cooling tower to industrial circulating cooling water. Metall Power 2002 [Chinese language]. [10] Mortensen KP, Conley SN. Film fill fouling in counterflow cooling towers. Mechanism and design. CTI J 1994;15(2). [11] Qureshi BA, Zubair SM. A complete model of wet cooling towers with fouling in fills. Appl Therm Eng 2006;26:1982–9. [12] Khan JUR, Zubair SM. A study of fouling and its effects on the performance of counter flow wet cooling towers. Proc Inst Mech Eng, Part E: J Process Mech Eng 2004;218(1):43–52. [13] Gañán J et al. Influence of the cooling circulation water on the efficiency of a thermonuclear plant. Appl Therm Eng 2005;25:485–94. [14] Barigozzi G, Perdichizzi A, Ravelli S. Wet and dry cooling systems optimization applied to a modern waste-to-energy cogeneration heat and power plant. Appl Energy 2011;88:1366–76. [15] Novak M, Širok B, Blagojevic B, Hocevar M, Rotar M. CTP method – diagnostic method for control of cooling tower operation. VGB Power Tech 2003;83(1–2). [16] Širok B, Rotar M, Hocˇevar M, Dular M, Smrekar J, Bajcar T. Improvement of the thermodynamic properties in a natural-draft cooling tower. J Mech Eng 2007;53(5):270–84. [17] Smrekar J, Kuštrin I, Oman J. Methodology for evaluation of cooling tower performance – part 1: Description of the methodology. Energy Convers Manage 2011;52(11):3257–64. [18] Bošnjakovic´ F. Technical thermodynamics. Dresden: Theodor Steinkopf; 1965. [19] VDI – Heat Atlas. Calculation guideline for the heat transfer, calculation of draft cooling equipment (Mj). Springer; 2002. [20] Hampe E. Cooling towers. Berlin: VEB Verlag fur Bauweses; 1975. [21] Smrekar J. Influence of operating conditions in cooling tower on power plant efficiency. Master thesis, University of Ljubljana; 2004. [22] Stoer J, Bulirsch R. Introduction to numerical analysis. NY: Springer-Verlag; 1980.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Methodology for evaluation of cooling tower performance – Part 2: Application of the methodology and computational aspects of Poppe equations J. Smrekar a,⇑, A. Senegacˇnik b, C. Führer c a
Department of Mechanical and Structural Engineering and Materials Science, University of Stavanger, 4036 Stavanger, Norway Department of Power Engineering, University of Ljubljana, Aškercˇeva 6, SI-1000 Ljubljana, Slovenia c Department of Numerical Analysis, Lund University, P.O. Box 118, SE 22100 Lund, Sweden b
a r t i c l e
i n f o
Article history: Received 26 April 2010 Received in revised form 4 May 2011 Accepted 11 May 2011 Available online 22 July 2011 Keywords: Cooling tower Power plant Poppe model Cooling tower performance Methodology Real data
a b s t r a c t A methodology for evaluation of natural draft cooling tower (CT) performance and its application is presented. The study establishes the connection between CT performance and power output. It can estimate a change in a CT’s efficiency as well as an increase in power output as a function of cooling water temperature and load to the plant. The methodology consists of three subparts, i.e. Cooling Tower Profiler (CTP) method, CT model and a model of the power plant that are described in the first part of the paper. The second part focuses on application of the methodology in a way that minimizes error of the CT model. One week of data from the power plant were acquired for the analysis. In the CT a small area with irregularities was examined, and increased efficiency and power output are estimated by the methodology. Furthermore, another aspect of solving Poppe equations is examined resulting in reduced computational effort by approximately a half without losing any computational accuracy. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Growing consumption of fossil fuels presents a rising concern related to global warming issues. Scientists and politicians have been trying to mitigate greenhouse gases in many different ways. One of the biggest pollutants is power plants using fossil fuels for production of electricity and/or heat, for which demands are still growing. Increasing efficiency of such energy systems is one of the solutions that can considerably reduce environmental pollution. In order to continuously mitigate greenhouse gases, constant improvements of energy systems and their monitoring are necessary. As power plants are complex systems, an optimization of local parts as well as their tuning on a system level must be considered. In this paper the focus is given to a power plant with a natural draft cooling tower (CT). CTs remain widely used in power producing industry and air conditioning systems for cooling circulating water [1,2]. In conventional power plants approximately a half of the energy delivered by fuel is rejected from a cooling system. Even though this energy is low with exergy, improvements in heat rejection may significantly contribute to fuel savings as the energy flows through cooling system are huge. In this respect an explanation of the CT performance from an exergy point of view and its ⇑ Corresponding author. Tel.: +47 51832164; fax: +47 51831050. E-mail address: [email protected] (J. Smrekar). 0196-8904/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2011.05.004
trends for optimization can be found in [3,4]. This leads to a desire to better understand the operation of the CT and to optimize its design parameters [5]. Gan et al. [6] applied CFD code to predict the performance of a closed CT by using a two-phase flow of air and water droplets on the outside tube. The predicted thermal performance is compared with experimental measurements. Kloppers and Kröger [7] found out that exactly the same definition of Lewis factor must be applied in fill performance analysis and subsequent CT performance analysis. Kranc [8] looked into design of spray patterns for counterflow CTs and concluded that for a particular nozzle manifold and packing arrangement, a performance limitation exists due to the inherently non-uniform pattern of water flow. CTs have been in operation for more than five decades and proper attention in terms of monitoring and maintenance has not been given to them. Overhauls of turbines and boilers are conducted on regular bases while degradation of CTs is usually not considered. Broken packing, plugged nozzles, growing algae, broken eliminators, etc. [9] are some of the common problems in CT operation which deteriorate the CT and thence system efficiency. In 1990s Mortensen and Conley [10] put an effort to understand and reproduce the primary fouling mechanism in a controlled and accelerated laboratory regimen on a number of fill configurations to optimize geometry. Qureshi and Zubair [11] worked on modeling strategy of fouling in CT fills and incorporated it in the CT model to study performance evaluation problems. Khan and Zubair [12] validated similar model on experimental data.
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Nomenclature
e g a, b CT CTP F Pgen Q T T 0w2 m N w
computational accuracy efficiency/% coefficients cooling tower Cooling Tower Profiler function power on generator/MW heat flow/MW temperature/°C or K numerical solution of the outlet water temperature from the CT/°C mass flow rate/(kg/s) number of intervals humidity ratio/(kgwater vapor/kgdry air)
Performance of a cooling system has an important impact reflecting in corresponding back pressure in condensator and hence plant’s power output. Not many studies have been reported where the impact of the CT on power output is investigated. Barigozzi et al. [14] studied wet and dry cooling systems optimization at a CHP plant. Parametric analysis showed the significance of the cooling systems’ operation on the power output and the generated data were further used for optimization of the processes. Gañán et al. [13] presented a study showing the relation between the power output and the water temperature to condenser based on different cooling sources. However, all mentioned studies involve power plant with a CT analysis as a standalone component. Anomalies in CT are usually reflected on a local basis and are thus hard to identify. As the plane area of a natural draft CT is huge, the local irregularities can significantly affect the CT performance. The Cooling Tower Profiler (CTP) measuring technique [15] can be used for identification of such irregularities. The CTP is based on a mobile unit measuring the air temperature and velocity profiles across the plane area of CTs and it is a part of the methodology presented in this paper. The measured data on a local basis can thus be used to improve the thermodynamic performance of a CT [16]. However, the studies deal mainly with the identification of irregularities and thermodynamic improvements of CT operation whereas the impact of the local irregularities on existing CT performance and furthermore on the plant’s power output have not been investigated so far. In general, usual obstacle is that extensive measurements with suitable measuring technique and compatible method for CT analysis on a local basis are required. Nevertheless, the CTP measuring technique established a good base to evaluate the magnitude of local irregularities and their effect on power output as presented in this paper. The measured profiles are used in a CT model that presents the second part of the methodology. Its base is the Poppe model that does not require information about the constructional characteristics of a CT. These are practically impossible to measure in practice on a degraded CT. The Poppe model in conjunction with measured profiles can estimate an influence of irregularities on outlet cooling water temperature. The latter parameter is the input parameter to the empirical model of the power plant developed as the third part of the methodology. Hence, an estimation of power increase as a function of cooling water temperature and plant’s load is possible. The three subparts of the presented methodology are described in more detail in the first part of this paper [17]. In the second part of the paper, focus is given to application of the methodology covering several aspects:
x, y
length/m
Subscripts 1 inlet 2 outlet a air atm atmosphere CT cooling tower gen generator i denotation of the local scale PP power plant p initial guess w water wb wet bulb
Demonstration of the proposed methodology which has established the bridge between CT performance and plant’s power output. By application of the methodology, the impact of local irregularities in the CT on the power output and system’s efficiency can be studied. Minimization of systematic error of the methodology. It is practically impossible to measure the changes in constructional characteristics across the plane area of a real natural draft CT. Hence, the modeling on the local basis of the CT has to be done as a ‘‘black-box’’ modeling. A calculation procedure is proposed where the methodology is applied in a way that subtracts systematic errors of the models. Examination of numerical integration of Poppe equations. The modeling presented in this work is of large scale demanding a large amount of computational effort. In this respect faster calculation with practically no loss in computational accuracy is reported. The application of the methodology was done on 1 week of measured data from a power plant and a natural draft CT. The significance of efficient CT operation and its impact on power output are depicted. 2. Motivation and base for the analysis Focus is given to application of the proposed methodology the intention of which is to yield minimal error in predicted parameters. As a natural draft CT is a huge construction its evaluation is a challenging task. There are many practical issues related to measurements from the feasibility as well as the measuring point of view. CTs are huge constructions with relatively harsh environment in it. These make it practically impossible to measure changes in the CT’s characteristics, especially in its concealed parts (e.g. packing, nozzles). Measuring inlet air conditions to the packing is also not practical. Moreover, today there is no commercially available measuring instrument of air humidity that would enable reliable measurements in the CT where the air is normally supersaturated. Hence, these constraints necessitate a different approach accompanied by assumptions. For the presented methodology, these constraints and assumptions are discussed in the first part of the paper [17]. In the second part of the paper the motivation was to apply the methodology in a way that alleviates those assumptions and reduces the error of the applied models. An example of an application of the methodology is presented on real measured data from a natural draft CT and 345 MWe power plant. The analysis focuses on a part of the CT with irregularities. The base is air velocity and temperature profiles, presented in Fig. 1, which were measured above the drift eliminators. The effect
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Fig. 1. Air velocity and temperature profiles measured above the drift eliminators in the CT.
of reparation of the irregularities on power output was studied for a 1-week period covering the broad range of the plant’s operational as well as ambient conditions. 3. Application of the methodology for evaluation of CT performance The irregularities, which can be clearly identified in both air temperature and velocity profiles (Fig. 1), were the object of analysis in this study. Fig. 2 shows the selection of the area with irregularities (full square) and the condition in the CT after reparation. The Poppe model does not consider CT characteristics; instead it is based on empirical formulation of Lewis factor [18] and (measured) conditions. Hence, the symmetrical area of the same size with respect to the x-axis was used (dashed square) to represent the state after reparation. As such conditions do not reflect the state that would be achieved by new constructional elements, the analysis can be considered on the ‘‘safe-side’’. If the characteristics of new CT elements are available, the data representing operation with the new elements can be simulated and applied instead. On the basis of the measured profiles, it is possible to predict what kinds of irregularities are taking place. From Fig. 1 high air temperatures and low air velocities can be detected in the analyzed region. The measurements indicate that pressure losses, which led
to decreased velocity, could emerge due to damaged packing and/ or eliminators. High air temperatures still signify that the heat and mass transfer is high which, on the other hand, indicates that the water distribution system is working properly. By visual inspection of the investigated region, it was confirmed that the packings are the cause of irregularities in the analyzed CT. 3.1. Calculation procedure One of the most important parts of the methodology is the way of applying it. The goal is to minimize the systematic error of the CT model as it is not known for the particular CT. The solution is in calculating the differences which subtract the model’s systematic error. This is feasible by application of the CT model and the profiles in a way that yields the measured outlet water temperature presenting the original performance of the CT. Then, by applying the modified profiles (representing the conditions after reparation) and the CT model on the local basis, a new outlet water temperature is predicted reflecting the reparation. Fig. 3 shows a flow chart of the calculation procedure. It is outlined as follows: 1. Determination of CT efficiency on the basis of the measured inlet and outlet CT water temperatures and the ambient wet bulb temperature.
Fig. 2. Detection of the irregularities in the CT operation and the state after reparation.
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In Step 3, the Poppe model with measured integral CT parameters is used to calculate the average state of the air in the CT which changes with the operational condition of the plant as well as with ambient conditions. Then, in Step 4, the air velocity and temperature profiles are adapted to the new state in the CT according to the two criteria. Since the average state is calculated with the Poppe model, its application on a local scale yields the same measured outlet water temperature from the CT as was used in Step 3. Later on in Step 6, the Poppe model is applied on the local basis for calculation of the modified state in the CT. Operating with the differences subtracts the systematic error of the Poppe model and similarly of the empirical model of the plant in Step 7 (for more on the systematic error of the empirical model of the plant refer to Section 3.1.2 in the first part of the paper [17]).
3.2. Results of the CT analysis
Hence, the Poppe model is adapted to the integral measured inlet and outlet water temperatures to and from the CT respectively. This means that backward calculation on the local scale results in the same value as the measured outlet water temperature from CT. At the same time, the energy balance equation Qw = Qa is preserved according to the control volume of the CT (Fig. 6 in the first part of the paper [17]). 1. Providing conditions presenting the repaired CT. In this study, the area of the same size (symmetrical with respect to the xaxis) was used as denoted by the dashed line in Fig. 2. It did not represent the modifications that would be achieved by installing new packing, but nevertheless it sufficed for approximation of potential improvements. By known characteristics of new CT elements, the simulated data can be applied instead. 2. The modified profiles, representing a new state in the CT, are used as the boundary conditions to the Poppe model. The estimation of new conditions, i.e. calculation of the local outlet water temperatures from packing and the air humidities above eliminators across the CT, are determined. On the basis of these, the new outlet water temperature from the CT is calculated. 3. In the final step, the empirical model of the plant is employed and the increase in power output is estimated on the basis of the measured outlet water temperature and the estimated one.
50
40
/%
1. Using the Poppe method for the CT analysis, the average air temperature and humidity in the CT are calculated. 2. Discretization and superposition of the air temperature and mass flow rate profiles in order to match an operational condition of the CT. The superposition fulfills the two criteria: (i) the sum of the local air mass flow rates equals the total air mass flow rate, determined in Step 2; (ii) the average value of the local air temperatures equals the average value of the air temperature in the CT, determined in Step 3.
4
30
CT
ð1Þ
Δη
i
/%
h
gCT ¼ 1 exp 0:8696ðmw =ma Þ1:061
CT
2. Estimation of the total air mass flow rate through the CT on the basis of the measured total water mass flow rate, CT efficiency and CT characteristic. In this study, the CT characteristic used was determined according to Hampe’s model [20] and for the analyzed CT is [21]:
Analysis comprehended 1 week’s data from the plant which were also used for the validation of the empirical model of the plant (Section 3.1.2, first part of the paper [17]). As mentioned, the data were previously examined and the measurements deviating from the normal operation were eliminated from the database. For the analysis of the CT performance, a 30 min interval was used and 331 operational points throughout 1 week were examined. For each operational point the analysis related to the region with irregularities in the CT was conducted according to the flow chart in Fig. 3. Fig. 4 shows the CT efficiency on the left axis and its increase due to the reparation of irregularities on the right axis. The average CT efficiency in the 1-week analysis was 41% and its average increase 2.95%. The increase in CT efficiency resulted in a power increase as shown in the following figure. Fig. 5 shows the power output on the left axis and the power increase on the right axis. The average power output in the analyzed period was 295.590 MW and the average power increase due to reparation of the region with irregularities was 0.765 MW which correspond to 0.26%. The average power increase is relatively low, but it should be considered that the modified region comprehended only 16% of the total plane area of the CT. For the period of 1 week the difference of the average local air mass flow rates and temperatures of the two symmetrical regions are 0.29 kg/s and 1.1 °C respectively. Looking at the air mass flow rate, which defines the efficiency of the CT (Eq. (1)), the 0.29 kg/s difference represents 26% decrease with respect to the reference (symmetrical) region. Therefore, the irregularities can be considered of the low-scale magnitude.
η
Fig. 3. Flow chart for the evaluation of CT performance.
3
2 0
1
2
3
4
5
6
7
time / days Fig. 4. CT efficiency and its increase due to reparation of irregularities.
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300
250
1,1
200
0,9 0,7 0,5
0
1
2
3
4
5
6
7
ΔPgen / MW
Pgen / MW
340
0,3
wp2 ¼ watm þ 0:01mw =ma
time / days Fig. 5. Operation of the power plant and the power increase due to reparation of irregularities.
ηPP / %
40,4 40 39,6 39,2 0.14 38,8
0.1
ΔηPP / %
0.12
0.08
0
1
2
3
4
sive computational effort. In this respect the Poppe equations were examined in order to find a faster computational solution whilst, if possible, keeping the accuracy unchanged. The original Poppe equations [15], of which computational procedure has not been evaluated, were solved by the shooting method [22] and unknown variables were computed iteratively as presented schematically in Fig. 7. Left flow chart in Fig. 7 shows that if the difference between the initial guess of the humidity ratio and the computed humidity at the outlet of the CT is not within a given accuracy threshold e, then the calculated humidity ratio is used as an initial guess in the next iteration. This procedure usually converges in up to three iterations with accuracy of 104 and by using the following equation for the initial guess [19]:
5
6
7
0.06
time / days Fig. 6. Power plant efficiency and its increase due to reparation of irregularities.
Fig. 6 shows power plant efficiency and its increase due to the reparation of irregularities. The average thermal power plant efficiency was 40.08% and its increase due to reparation of irregularities in the CT was 0.11%. The increase in efficiency is expectedly low corresponding to the relatively small examined area and low-scale irregularities in the CT. The above figures show high correlation among them which is dictated by the plant’s operation. By comparing Figs. 4 and 5, it can be noticed that the CT efficiency is strongly influenced by the plant’s operation. The operational condition is determined by the thermal load to the plant and hence a higher load results in higher efficiencies of both the plant and CT. Considering the plant, this is due to operation closer to the nominal one while looking at the CT, a higher rejected heat rate from the condenser consequently results in a higher draft through the natural draft CT. An analogical explanation applies for the increments in power and both efficiencies. Hence, the plant’s operation closer to the nominal yields a higher increase in the power and efficiency of the plant as the result of CT reparation. 4. Computational aspects of Poppe equations The methodology for evaluation of CT performance is based on measurements on the local basis of a CT. In this study the plane area of the CT was discretized and 3177 nodes were used for calculation in each operational condition. Throughout 1 week of data 331 different conditions were analyzed, resulting in a comprehen-
ð2Þ
A closer look at the computation procedure reveals that iterations are not needed as the result is rather insensitive on the initial guess as long as the guess is within reasonable boundaries. A sufficiently good guess can already be achieved by Eq. (2). Moreover, the estimate is required to be computed only once for each operational condition as each node in the discretized plane area of the CT is calculated sequentially and a solution from the adjacent node can be used as initial guesses in the next node. The computation of Poppe equations without iteration means that only one good shot of initial guess suffices and the loop, which is denoted by a dashed line in the left flow chart of Fig. 7, is not needed. Hence, the proposed solution looks as depicted in the right flow chart of Fig. 7. When the integration is finished, the calculated humidity at the outlet is used in energy and mass balance equation, denoted by F, which yields the outlet water temperature. As there is no iteration applied, this simplifies the computational procedure and makes the numerical code much faster. Fig. 8 shows the humidity ratio above eliminators and corresponding outlet water temperature from packing as functions of the initial guess at different numbers of intervals and for the case where air gets supersaturated. In the left plot an initial guess, applying Eq. (2), is denoted with the red asterisk. The dashed line represents the equations that are being solved:
w2 ¼ Fðwp2 Þ
ð3Þ
where F represents Poppe equations and w2 the solution. From the left plot in Fig. 8, it can be seen that the calculated humidity ratio is practically independent of its initial guess and that the number of intervals does not significantly influence the accuracy of calculation. From approximately 10 intervals on, the difference in the solution is marginal. The independent solution indicates that the iterative procedure is not required for the case where air gets supersaturated and hence only one relatively good shot of initial guess is needed. This can be confirmed by the corresponding right plot showing practically constant outlet water temperature (second unknown variable) from the packing as a function of the initial guess. Looking at the biggest difference of calculated humidity ratio in the left plot, i.e. 1.38 105 kg/kg, the corresponding outlet water temperature difference is 104 °C. In the case of unsaturated air above the eliminators, a similar conclusion to the supersaturated state can be drawn, as can be seen from Fig. 9. The relationship between calculated humidity ration and its initial guess is also practically independent and therefore the iterations are not needed. The difference in the calculated humidity ratio with changing initial guess from 5.0 103 to 3.5 102 kg/kg is 1.1 105 kg/ kg. A small change of less than 0.01 °C by applying 15 intervals can be noticed for the outlet water temperature in the right plot. In the case of unsaturated air the number of intervals plays a higher role than in the case where air gets supersaturated. From the
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Fig. 7. Scheme of the conventional and proposed computational approach.
17.74
0.035
w2=F(wp2) 0.03
17.736 17.734
/ °C
17.732
w2
0.02
17.73
T
w2 / (kg/kg)
0.025
5 intervals 10 intervals 15 intervals 20 intervals 25 intervals
17.738
5 intervals 10 intervals 15 intervals 20 intervals 25 intervals Eq. (2)
17.728 0.015 17.726 17.724 0.01 17.722 0.005 0.01
0.02
0.03
initial guess wp2 / (kg/kg)
17.72
0.01
0.02
0.03
initial guess wp2 / (kg/kg)
Fig. 8. Humidity ratio above packing and outlet water temperature from packing (unknown variables) as functions of initial guess for the supersaturated air.
right plot it can also be seen that from approximately 10 intervals on, the solution becomes practically independent of the initial guess and also reaches a good accuracy. The example corresponds to air with a relative humidity of 0.83 above the packing. It was confirmed that approaching the saturated state, the already small non-linearity diminishes further. 4.1. Examination and comparison of the computational approaches on the analyzed data The two examples in the previous section are presented for two different boundary conditions with respect to saturation of air above eliminators. To validate the non-iterative code, it has to be tested in a broad range examining different boundary conditions. In this regard the 1-week data proved to be suitable for the task.
The plant’s operational conditions varied in the wide operational range as can be seen in Fig. 5. Consequently these variations resulted in even more intensified differences with respect to waterto-air mass flow rates and air temperatures above the eliminators on the local basis of the CT (Fig. 1). The ambient conditions in the analyzed week also varied quite extensively, i.e. ambient temperature varied from 3 to 12.5 °C and relative humidity from 36% to 100%. In the analysis the iterative code presented the reference case as an arbitrary accuracy can be achieved. For this task the accuracy was set to 104. On the other hand, the accuracy for the non-iterative code does not need to be specified since there is no loop. In the following, the two codes are compared looking at the discretized area in the CT. The case with the highest average difference in the outlet water temperature from the 1-week analysis is re-
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0.035
2
p2
5 intervals 10 intervals 15 intervals 20 intervals 25 intervals Eq. (2)
0.03
17.9
17.85
Tw2 / °C
0.025
w2 / (kg/kg)
17.95
w =F(w )
0.02
5 intervals 10 intervals 15 intervals 20 intervals 25 intervals
17.8
17.75
0.015 17.7 0.01
0.005
17.65
0.01
0.02
0.03
initial guess wp2 / (kg/kg)
17.6
0.01
0.02
0.03
initial guess wp2 / (kg/kg)
Fig. 9. Humidity ratio above packing and outlet water temperature from packing (unknown variables) as functions of initial guess for the unsaturated air.
Fig. 10. Difference in outlet water temperatures computed with the two codes.
ported. Fig. 10 shows the difference between the outlet water temperatures computed with the two codes.
From a numerical point of view, the profile change in the figure indicates that the initial guess has an influence on the solution accuracy. On the other hand, the difference varying from 0.023 to 0.014 °C is negligible from an engineering point of view. When applying Eq. (2) for estimation of the initial guess, average absolute difference was 0.0064 °C and maximum difference 0.0231 °C. When applying the solution from the adjacent node for the initial guess, the average value dropped to 0.0017 °C. When conducting extensive analysis as the one in this study, the calculation time is of high importance. When applying the iterative integration the average number of iterations for 1 week of analysis was 2.1 when setting 15 intervals and accuracy of 104. This also means that the calculation time was 2.1 times longer in comparison with the simplified code without a significant decrease in accuracy. Using the solution from the adjacent node for the initial guess reduced the average number of iterations by approximately 15% to 1.8 iterations. Optimal operation of natural draft CTs requires that cooling air gets saturated in order to use the whole potential of evaporative cooling. Usually the saturation point is met. In the case of analyzed data the air above the eliminators was calculated to be supersaturated in all cases. However, since there is a possibility that the air does not meet saturation point and can thus be unsaturated above
Fig. 11. Relative humidity above eliminators and difference between the iterative and non-iterative code in computed outlet water temperature from the packing.
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eliminators, the non-iterative code was also examined under such conditions. For demonstrational purposes an operational condition was simulated where the air does not meet saturation point. This usually happens at the circumference of a CT where the air flow is the highest and at its driest state. The result is presented in Fig. 11 showing the relative humidity above eliminators and the difference between the codes in computed outlet water temperature from the packing. The left plot shows, as expected, that the unsaturated air appears at the circumference of the CT. Relative humidity is the lowest, i.e. 0.76, at left side of the CT as can be noticed from Fig. 11. The corresponding right plot shows the biggest difference between the two codes exactly in that region with the highest air flow. However, it was still negligible with the average absolute difference being 0.0077 °C and a maximum difference of 0.0248 °C (the case with application of Eq. (2)). In comparison with the case where air gets supersaturated (Fig. 10), the conclusion can be rather similar and the performance of the non-iterative code is also acceptable. The non-iterative approach was tested in a wide range with respect to boundary conditions showing that the accuracy was preserved with significant reduction in computational time. Thus, the simplified approach appears to be an improved solution in comparison with the original one. It should be also pointed out that to make a CT analysis consistent, only one approach should be used. 5. Conclusions In the second part of the paper the application of the developed methodology is demonstrated. Modeling on the local basis of a CT was done as a ‘‘black-box’’ modeling, since changes in characteristics of a CT’s components are hard to assess. In this respect the Poppe model for CT analysis, which does not require information about CT characteristics, was applied. A calculation procedure is proposed that minimizes the error of the methodology. The application of the methodology is demonstrated on real measured data from a plant and a natural draft CT. The area with irregularities in the analyzed CT was identified from the air velocity and temperature profiles measured by the CTP method. The investigated region in the CT was replaced by a ‘‘healthier’’ region of the same size. The result of the improved state was lower outlet water temperature from the CT which was predicted by the CT model. Consequently, the increase in power, estimated by the empirical model of the plant, was expected. The repaired region, comprehending approximately 16% of the CT’s total area, yielded 0.765 MW average increase in the power output based on 1 week’s analysis.
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The extensive analysis that comprehended the discretized CT plane area as well as 1-week power plant’s operation required a huge amount of computational effort. Hence, a new aspect of solving the Poppe equations was examined and a faster numerical solution is proposed. The investigation showed that solving Poppe equations does not require iteration procedure as the unknown variables are practically independent of the initial guess. As a result the solution is faster for approximately factor 2 with practically no effect on the computational accuracy. References [1] Berman LD. Evaporative cooling of circulating water. London: Pergamon; 1961. [2] Heat exchanger design handbook. NY: Hemisphere Publishing Corporation; 1983. [3] Qureshi BA, Zubair SM. Second-law-based performance evaluation of cooling towers and evaporative heat exchangers. Int J Therm Sci 2007;46(2): 188–98. [4] Thirapong M, Wanchai A, Somchai W. Effects of inlet relative humidity and inlet temperature on the performance of counterflow wet cooling tower based on exergy analysis. Energy Convers Manage 2008;49(10):2795–800. [5] Kröger DG. Air-cooled heat exchangers and cooling towers: thermal-flow performance, evaluation and design. New York: Begell House, Inc.; 1998. [6] Gan G, Riffat SB, Shao L, Doherty P. Application of CFD to closed-wet cooling towers. Appl Therm Eng 2001;21(1). [7] Kloppers JC, Kröger DG. The Lewis factor and its influence on the performance prediction of wet-cooling towers. Int J Therm Sci 2005;44(9). [8] Kranc SC. Optimal spray patterns for counterflow cooling towers with structured packing. Appl Math Model 2007;31(4):676–86. [9] Liqing S. Application of the no-padding and atomizing cooling tower to industrial circulating cooling water. Metall Power 2002 [Chinese language]. [10] Mortensen KP, Conley SN. Film fill fouling in counterflow cooling towers. Mechanism and design. CTI J 1994;15(2). [11] Qureshi BA, Zubair SM. A complete model of wet cooling towers with fouling in fills. Appl Therm Eng 2006;26:1982–9. [12] Khan JUR, Zubair SM. A study of fouling and its effects on the performance of counter flow wet cooling towers. Proc Inst Mech Eng, Part E: J Process Mech Eng 2004;218(1):43–52. [13] Gañán J et al. Influence of the cooling circulation water on the efficiency of a thermonuclear plant. Appl Therm Eng 2005;25:485–94. [14] Barigozzi G, Perdichizzi A, Ravelli S. Wet and dry cooling systems optimization applied to a modern waste-to-energy cogeneration heat and power plant. Appl Energy 2011;88:1366–76. [15] Novak M, Širok B, Blagojevic B, Hocevar M, Rotar M. CTP method – diagnostic method for control of cooling tower operation. VGB Power Tech 2003;83(1–2). [16] Širok B, Rotar M, Hocˇevar M, Dular M, Smrekar J, Bajcar T. Improvement of the thermodynamic properties in a natural-draft cooling tower. J Mech Eng 2007;53(5):270–84. [17] Smrekar J, Kuštrin I, Oman J. Methodology for evaluation of cooling tower performance – part 1: Description of the methodology. Energy Convers Manage 2011;52(11):3257–64. [18] Bošnjakovic´ F. Technical thermodynamics. Dresden: Theodor Steinkopf; 1965. [19] VDI – Heat Atlas. Calculation guideline for the heat transfer, calculation of draft cooling equipment (Mj). Springer; 2002. [20] Hampe E. Cooling towers. Berlin: VEB Verlag fur Bauweses; 1975. [21] Smrekar J. Influence of operating conditions in cooling tower on power plant efficiency. Master thesis, University of Ljubljana; 2004. [22] Stoer J, Bulirsch R. Introduction to numerical analysis. NY: Springer-Verlag; 1980.