An experimental and multi-objective optimization study of a forced draft cooling tower with different fills

Energy Conversion and Management 111 (2016) 417–430

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

An experimental and multi-objective optimization study of a forced draft cooling tower with different fills Kuljeet Singh, Ranjan Das ⇑ School of Mechanical, Materials and Energy Engineering, Indian Institute of Technology Ropar, Nangal Road, Punjab 140001, India

a r t i c l e

i n f o

Article history: Received 26 August 2015 Accepted 31 December 2015 Available online 12 January 2016 Keywords: Forced draft Fills Multi-objective optimization NSGA-II Decision making score

a b s t r a c t In the present study, a forced draft mechanical cooling tower has been experimentally investigated using trickle, film and splash fills. Various performance parameters such as range, tower characteristic ratio, effectiveness and water evaporation rate are first analyzed for each fill. Thereafter, based upon the experimental data, pertinent correlations have been developed for performance parameters by considering mass flow rates of water and air as design variables. Each of the performance parameters is considered to be an individual objective function and all objectives are then simultaneously optimized for maximizing the performance of the cooling tower using elitist Non-Dominated Sorting Genetic Algorithm (NSGAII). The multi-objective optimization algorithm gives a set of possible combinations of design variables, which is referred as the optimal Pareto-front, out of which a unique combination is selected based upon a decision making criterion. The proposed decision making procedure evaluates a Decision Making Score (DMS) based on assigned performance priorities for each point of the Pareto-front. Depending on DMS a unique combination of design variables is then selected for each type of fill that maximizes the tower’s performance. These optimal points and the corresponding objective function are finally compared and based upon the highest DMS value, the wire-mesh (trickle) fill is found to be the most efficient fill under the present experimental conditions. The methodology presented in this work has been made more generalized, so that it can be easily implemented in industrial forced draft cooling tower operating under a wide range of temperatures. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction A forced draft cooling tower is a commonly used device in power plants which extracts heat from water coming out of the condenser and rejects it to atmosphere by means of air flow. It is primarily used to supply cooled water in various oil refineries, chemical processes, thermal power plants and air conditioning systems [1]. The basic principle of cooling tower is based upon evaporative cooling that is facilitated through direct contact of air and water. The stream of air evaporates some water into itself to produce the cooling effect for major portion of the water stream. Based upon their construction, cooling towers are broadly classified into two categories involving natural and mechanical draft. Natural draft cooling towers use the temperature difference between the hot air inside the cooling tower and the ambient air that assists the air flow through the cooling tower. Subsequently, water is sprayed against ⇑ Corresponding author at: School of Mechanical, Materials and Energy Engineering, Indian Institute of Technology Ropar, Nangal Road, Rupnagar, Punjab 140001, India E-mail address: [email protected] (R. Das). http://dx.doi.org/10.1016/j.enconman.2015.12.080 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

the air stream by nozzles and the evaporative cooling is finally achieved. As compared to natural draft cooling tower, the mechanical draft cooling tower uses a blower to facilitate air flow through the tower. Depending upon the fan/blower location, mechanical draft cooling towers can be further categorized into forced and induced draft types. In a forced draft cooling tower, fan either at the inlet or at the bottom pushes the air within the tower, whereas, in an induced draft type, a fan is installed either at the tower exit or at the top that allows the air to be drawn through the tower. Furthermore, depending upon flow directions of air and water, cooling towers can be again classified into counter and cross flow types. In mechanical draft cooling towers, fills (packing) play an important role in the rate of heat transfer between water and air by maintaining the contact time [2]. Cooling tower fills are generally of three types such as splash, trickle and film fills. Splash fill increases the heat transfer area between water and air by splashing water into small droplets using successive layers of splash bars. Wooden splash and plastic splash are some examples of splash fills. As compared to splash fills, trickle fills are comparatively finer, which are made up of either plastic or metal grids (e.g. wire mesh fills) and used for spreading the water into droplets. However, a film fill

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Nomenclature a Cp DMS e F f h K M Me meV m n Np p P Q R T U

interfacial area (m2/m3) specific heat at constant pressure kJ/(kg K) decision making score effectiveness (%) Pareto-front objective function specific enthalpy (kJ/kg) mass transfer coefficient kg/(m2 s) number of objective functions tower characteristic ratio or Merkel number water evaporation rate (kg/s) mass flow rate (kg/s) number of efficient points population size pressure (N/m2) random population offspring population range (°C) temperature (K) uncertainty

forms a thin film of water over the fill surface surrounded by air and accordingly the water is cooled [3]. Corrugated, flat and honeycomb fills fall under this category. To study the performance of the cooling tower, Merkel [4] proposed a method, popularly known as Merkel method, that is one of the oldest methods which simplifies the solution by making certain assumptions [5]. It is reported that Merkel method is simple to apply which gives correct result for the outlet water temperature if an appropriate value of the evaporation coefficient is used [6]. Making some simplifications in the assumptions of Merkel method, Jaber and Webb [7] proposed e-NTU method for crossflow and counter flow cooling towers. Subsequently, another popular method was demonstrated by Poppe and Rogener [8], which is commonly referred to as Poppe method. The reason behind the popularity of Poppe method is attributed to the fact that it accurately predicts the water content at the air outlet [9] which makes it practically suitable where the experimental data is unavailable. Many studies on cooling tower performance with different types of fills were reported by various researchers under various operating conditions. For example, Bedekar et al. [2] experimentally studied the performance of a counter flow cooling tower using film type packing and trends of different performance parameters were reported. Goshayshi [10] experimentally estimated the mass transfer and pressure drop characteristics employing corrugated fills installed in different arrangements. Kloppers and Kroger [11] proposed a correlation of the loss coefficient occurring due to the presence of frictional and drag effects for splash, trickle and film fills. Similarly, several studies have been reported which reveal the application of diverse fills (packing) with different orientations [12–16]. The optimization of cooling towers is an emerging area of interest for many researchers in order to either maximize the performance or to minimize the cost of the system. Toward this direction, Söylemez [17] proposed an optimal heat and mass transfer area to minimize the involved cost. Further, Söylemez [18] also theoretically optimized the thermo-hydraulic performance of a counter flow cooling tower and proposed an optimal water to air ratio under different inlet water temperature and ambient pressure. Cortinovis [19] proposed a model of a single objective optimization problem to minimize the operating cost of a mechanical draft cooling tower. Ramakrishnan and Arumugam [20] presented

V W x

volume of exchange core (m3) weightage factor design variable

Greek symbols x specific humidity (kg/kg of dry air) Subscripts a air abs absolute fg fluid–gas mixture norm normalized value sa saturated air at bulk water temperature wb wet bulb v vapor w water I index for Pareto-front i inlet o outlet t index for iteration

a model to predict and optimize the cold water temperature using the Response Surface Method (RSM) and Artificial Neural Network (ANN). Additionally, several studies have been also reported which optimize various operating parameters in order to minimize the total annual cost of cooling towers using different algorithms such as Mixed-Integer Non Linear Programming (MINLP), Artificial Bee Colony (ABC) and many more [21–24]. Recently, for design and cost optimization purpose, a simple method has been presented to calculate optimum packing height based upon Merkel equation [25]. Al-Bassam and Alasseri presented a comparison of variable frequency drives with dual speed motors in cooling tower application. The study has been further extended to optimization of electricity and water consumption using variable frequency drive fans [26]. Wang et al. proposed and implemented an optimization strategy for a fan operation using Non Negative Garrote (NNG) variable selection procedure [27]. It is revealed from the literature that majority of the optimization studies are aimed at a single objective. For a cooling tower, there are many performance parameters such as range, tower characteristic ratio, effectiveness, evaporation rate and all of them are required to be simultaneously considered for completely optimizing its overall performance. Based on this idea, in the present study a problem is formulated for a forced draft cooling tower involving different fills in which multiple performance parameters are optimized simultaneously. Three different types of fills such as wooden splash, wire mesh and honeycomb have been considered in the present work, where each of them respectively belongs to splash, trickle and film type. At first, for each type of fill (wooden splash, wire mesh and honeycomb), relevant objective functions are formulated for different performance parameters (range, tower characteristic ratio/Merkel number, effectiveness and evaporation rate) using the experimental data. These objective functions (4 for each type of fill) consist of two control variables (unknowns) involving mass flow rates of water and air. Next, for each type of fill, objective functions have been simultaneously optimized (either maximized or minimized) using multi-objective genetic algorithm and different combinations of water and air flow rates are obtained. These possible combinations are referred to as a single Pareto front (set of optimized points) optimizing each of the objective functions. Finally, after generating the Pareto front for each fill, the decision making approach has been proposed to select the most optimum

K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430

point (Pareto optimal) out of the available combinations. In the following section, the experimental setup has been discussed. 2. Experimental setup Referring Fig. 1, in the experimental setup of mechanical forced draft cooling tower, a centrifugal blower (with 100 mm eye diameter and operated using 1 phase AC motor with 1440 rpm) is installed at the inlet of the cooling tower, which forces air into the tower. A combination of manometer and orifice plate is fitted at the air inlet to measure the inlet air flow rate into the tower. The air is then directed over the fills where it comes into the contact

419

of water. The water enters the cooling tower from the top, where it flows over the fills and collected in a tank at the tower outlet. In the water tank a heater of 2 kW has been installed, which is operated through a digital temperature controller. After setting a required water inlet temperature, this heating mechanism heats the water to a defined temperature (40.5 ± 0.5 °C in this case). The water from the tank is then re-circulated by means of a centrifugal pump (operated using 1 phase AC motor having 2780 rpm) to the top of the tower again. A rotameter (range: 0–11 l/min) is fitted between water pump and water inlet, which is used to measure the flow rate of water through the tower. The water flow rate can be adjusted by a gate valve installed prior to the rotameter. The cross section area and height of fills are 0.09 m2 and 1.2 m, respectively. Suitable arrangement is provided to replace the fills of the cooling tower. In this experimental study, K-type thermocouples are used to measure the temperature at different locations. A data acquisition system (DAQ) by National Instruments is used to record the data from different thermocouples. While performing the experiment 8 thermocouples are used to record the temperature (at water inlet and outlet, in tank, DBT at air inlet and outlet, WBT at air inlet and outlet and ambient air temperature). To measure WBT at desired locations, a wet cotton wick is wrapped around the bead of the thermocouple. Before each run of experiment, this wick is wetted using water to ensure accurate reading. When air is forced through the system, WBT is obtained at the inlet and the outlet. The calibration of thermocouples has been done as per the procedure suggested by National Instruments [28]. For the calibration purpose, two reference temperatures are maintained using ice bath [29] and boiling water. Moreover, an alcohol-based thermometer (range
10–110 °C) has been immersed in reference temperature baths to ensure the accuracy of calibration [30]. Similarly, the manufacturer-calibrated rotameter has been re-calibrated by passing water at particular flow rate through it for 5 min. The water passed through the rotameter has been collected in tank and weighed to calculate the flow rate using given time and density [31]. Furthermore, the manometer requires no calibration, because it is a standard instrument due to its inherent accuracy and simplicity of operation [32]. In the succeeding section, the performance parameters are discussed. 3. Performance parameters The performance of a cooling tower can be primarily defined by its range, the tower characteristic ratio (Merkel number), the effectiveness and the evaporation rate. In the present study following performance parameters are considered. 3.1. Cooling water range Cooling tower range is defined as the temperature difference between inlet water and outlet water:

R ¼ T wi
T wo

ð1Þ

Further the range can be dependent upon several factors like the mass flow rates of air and water, the wet bulb temperature (WBT) and the dry bulb temperature (DBT) of inlet air. 3.2. Tower characteristic ratio

Fig. 1. Forced draft cooling tower experimental setup (a) line diagram (b) actual installation and (c) different fills: wire-mesh, honeycomb and wooden splash fills.

In a cooling tower, the heat transfer takes place due to two phenomena involving the sensible heat transfer and the evaporative heat transfer. Evaporative heat transfer further involves the mass transfer of water vapor into the air. This cumulative effect of both the heat transfer processes is accounted by Merkel [4] in a single equation mentioned below,

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mw C pw dT ¼ KadVðhsa
ha Þ ¼ ma dha

ð2Þ

Further, the integrated form of Merkel number can be represented as below,

Me ¼

KaV ¼ mw

Z

T wi T wo

C pw dT hsa
ha

ð3Þ

In order to solve Eq. (3), the Chebyshev four point method can be used [33], which is described as follows,

KaV ¼ mw

Z

T wi

T wo

  T w
T wo C pw dT 1 1 1 1 ffi i þ þ þ ðC pw Þ 4 Dh1 Dh2 Dh3 Dh4 hsa
ha

ð4aÞ

where the difference between the water inlet temperature, T wi and the wet bulb temperature of the inlet air, T wbi is known as ideal range of the cooling tower. 3.4. Evaporation rate of water Since the main heat transfer phenomenon in the cooling tower is the evaporative cooling, so it is important to examine the mass of water that evaporates with the air. In some of the cases the make up water (to compensate the evaporative losses) is a key influencing factor in the operating cost of the cooling tower. The water evaporation rate can be calculated using below relation,

meV ¼ ma ðxo
xi Þ

where

Dh1 ¼ ðhsa1
ha1 Þ; hsa1 at T wo þ 0:1ðT wi
T wo Þ and ha1 ¼ hai þ 0:1ðhao
hai Þ

ð4bÞ

Dh2 ¼ ðhsa2
ha2 Þ; hsa2 at T wo þ 0:4ðT wi
T wo Þ and ha2 ¼ hai þ 0:4ðhao
hai Þ

ð4cÞ

Dh3 ¼ ðhsa3
ha3 Þ; hsa3 at T wo þ 0:6ðT wi
T wo Þ and ha3 ¼ hai þ 0:6ðhao
hai Þ

ð4dÞ

ð4eÞ

The enthalpy of the air–water vapor mixture is calculated using the following relation [34],

  ha ¼ C pa ðT a
273:15Þ þ x hfga þ C pv ðT a
273:15Þ

ð5aÞ

where C pa and C pv are specific heats of air and water respectively and these are calculated at T = (Ta + 273.15)/2 as illustrated below,

C pa ¼ 1:045356  103
3:161783  10
1 ðTÞ þ 7:083814  10
4 ðT 2 Þ
2:705209  10
7 ðT 3 Þ

ð5bÞ
10

C pv ¼ 1:3605  10 þ 2:31334  ðTÞ
2:46784  10
13

þ 5:91332  10

6

ðT Þ

where xi and xo are the specific humidity corresponding to air inlet and outlet, respectively. Incorporating these factors the specific humidity, x can be calculated as below [1,34],   2501:6
2:3263  ðT wb
273:15Þ x¼ 2501:6 þ 1:8577  ðT a
273:15Þ
4:184  ðT wb
273:15Þ " # ð0:62509  pv wb Þ

ðpabs
1:005  pv wb Þ   1:00416  ðT a
T wb Þ
ð2501:6 þ 1:8577  ðT a
273:15Þ
4:184  ðT wb
273:15Þ

ð7bÞ

Dh4 ¼ ðhsa4
ha4 Þ; hsa4 at T wo þ 0:9ðT wi
T wo Þ and ha4 ¼ hai þ 0:9ðhao
hai Þ

3

ð7aÞ

5

ðT Þ

As mentioned in Eq. (7b), alongwith several factors, the specific humidity x depends on the vapor pressure (pv), that further depends on WBT. Since the evaporation is mainly responsible for cooling within the tower, so, the difference of WBT at inlet and outlet always lies in a wide range. In this study the difference between inlet and outlet WBT varies from 10 to 16 °C. This difference may be wider depending upon the ambient conditions and the type of the cooling tower. In the above equation, the vapor pressure of saturated vapor can be calculated using following relation,

pv ¼ 10 z N=m2

ð7cÞ

where

ð5cÞ

Here, it must be stated that the consideration of the temperaturedependency of specific heats makes the study more generalized. Therefore, this generalized methodology can be easily implemented by the end user in industrial cooling towers having wider temperature ranges. The latent heat at reference state is calculated in the following manner,

hfga ¼ 3:4831814  106
5:8627703  103 ð273:15Þ þ 12:139568  273:152
1:40290431  10
2 ð273:153 Þ ð5dÞ

     273:15 273:15 þ 5:02808  log 10 z ¼ 10:79586  1
T wb T wb   T   wb
1
4
8:29692 273:15 þ 1:50474  10 . . . 1
10      273:15
1 þ 4:2873  10
4 4:76955  1
T wb þ 2:786118312

ð7dÞ

Moreover, above generalized relations can be easily implemented for wider range industrial cooling towers in order to use the proposed methodology. 4. Methodology and optimization algorithm

3.3. Effectiveness Effectiveness of the cooling tower is a measure that compares its performance with the ideal operating output under identical conditions. It is defined either as the ratio of range to ideal range or range to the difference of the range and approach,

Range Range
Approach Range ¼ T wi
T wo

e¼

Approach ¼ T wo
T wbi T w
T wo e¼ i T wi
T wbi

ð6aÞ ð6bÞ ð6cÞ ð6dÞ

The first stage of this study involves the collection of experimental data for each type of fill (splash, trickle and film) installed inside the forced draft cooling tower. Before proceeding for the experiment calibration of thermocouples, rotameter and manometer has been carried out. Considering the full factorial four levels for water mass flow rate and four levels for air flow rate have been selected for this experimental study for each fill. Initially, the water in the tank is heated up to 40.5 ± 0.5 °C by means of an electric heater and this temperature is maintained throughout the experiment by means of a digital temperature controller. After achieving this water temperature, the water circulation pump and centrifugal blower are powered. The hot water is then entered from top of the cooling tower and distributed across the fills, where it comes

K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430

in contact with the air that is blown from bottom of the cooling tower. As air moves up, it gets heated and humidified, further humid warm air is discharged to the ambient and the cooled water is discharged to the storage tank. The temperatures at all relevant locations (as discussed earlier) are recorded for 10 min in steady state using LabVIEWTM in conjunction with the DAQ system. The same experimental procedure is adopted for each fill (wire-mesh, honeycomb and wooden splash) alongwith identical surrounding (ambient temperature 32.6 ± 0.35 °C) and other input conditions. The mass flow rate of water, mw is measured by means of rotameter and four levels are maintained as 0.1083, 0.125, 0.1417 and 0.1583 kg/s for each fill, whereas, mass flow rate of air, ma is measured with orifice plate in conjunction with manometer and four levels of air flow rate are maintained as 0.0173, 0.0192, 0.0203 and 0.0211 kg/s for each fill. It is worth to note here that the selected levels of water and air flow rates correspond to maximum and minimum ranges of the experimental setup. The proposed simultaneous optimization and decision making procedure in this work can be also implemented in industrial scale cooling towers to maximize the performance. After collecting the required temperature data, various performance parameters (the range, the tower characteristic ratio/Merkel number, the effectiveness and the evaporation rate) are calculated as mentioned in Section 3.1. After calculating desired performance parameters at each combination of mass flow rate of water and air (as used in the experiment) for each fill, a surface is fitted for each performance parameter using 3rd degree polynomial to obtain the correlations (as mentioned below):

 f ¼ c0 þ c1 ðmw Þ þ c2 ðma Þ þ c3 m2w þ c4 ðmw ma Þ þ c5 m2a     þ c6 m3w þ c7 m2w ma þ c8 mw m2a þ c9 m3a

The elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) is a modified form of multi-objective genetic algorithm, which was proposed by Deb et al. [35,36]. In NSGA-II method first a random population, Pt¼0 having size Np (50 in the present work) is created and the whole population is classified into various non-dominance levels or sets based upon the values of each objective function. The non-dominated set is a combination of the solutions among the set of solutions, which are not dominated by any associate of set P. This population is sorted according to its non-dominance level. To find the non-dominance, certain techniques are available, where each solution is compared with remaining solutions in the population. Such algorithms are further used to sort the whole population in decreasing order of non-dominance [37]. Level 1 or fitness is assigned to the best non-dominated solutions, which are found from the whole population. Similarly, non-dominated solutions of remaining population (ignoring level 1 non-dominated set) are found, which are assigned to be non-dominated solutions of level 2. This procedure is repeated until the entire population is sorted. Then, the offspring population, Q t is created using selection, crossover and mutation operations based upon previously found non-dominated solutions. In this work, crossover and mutation probabilities have been considered as 0.80 and 0.01, respectively. The population sizes of both parent population, Pt and offspring population, Q t are equal to Np. Next, a new population, St is created by combining these two populations (P t and Q t ) as indicated below,

ð8Þ

In these correlations the mass flow rate of water, mw and mass flow rate of air, ma are kept as design or control variables. Next, out of four performance parameters, the target of the designer is to maximize the range, tower characteristic ratio and effectiveness, whereas, the water evaporation rate needs to be minimized. In the present study, for each fill, these four objectives such as the range, the tower characteristic ratio, the effectiveness and the water evaporation rate have been optimized considering mass flow rate of water and air as design variables. To solve this multiobjective optimization problem NSGA-II is used and set of Pareto optimal front is obtained. Pareto optimal front is set of efficient points which simultaneously optimize all desired objective functions. After getting the Pareto front a normalized selection approach is proposed to select a unique combination of mass flow rate of water and air (design variables). In more complex case, if the flow rate of water is dependent upon the process or continuously varying depending upon the requirement, then the proposed method of optimization and selection enables the user to get an optimum value of air flow rate, ma for given mw. Moreover, for certain systems where the performance parameters are highly nonlinear functions of control variables the proposed methodology can be successfully implemented. The NSGA-II algorithm is discussed in detail in the following sub-section. 4.1. Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) The multi-objective optimization problem is worth for many engineering problems. The multi-objective optimization problem can be represented as follows, max or min

f ðxk Þ ¼ ½f 1 ðx1 ; x2 . . . ; xk Þ; f 2 ðx1 ; x2 . . . ; xk Þ; . . . ; f M ðx1 ; x2 . . . ; xk Þ ð9Þ

where, k = 1, 2, . . . , k, is number of design or control variables and M = 1, 2, . . . , M is number of objective functions.

421

Fig. 2. Flow chart of NSGA-II.

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K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430

St ¼ P t [ Q t

ð10Þ

solutions (mass flow rate of water and air). Fig. 2 represents the step by step procedure of NSGA-II for multi-objective optimization.

So, the size of St becomes 2Np. Further, the non-dominated sorting of combined population, St is performed in order to obtain different non-dominated Pareto fronts: F I , where, I = 1, 2, . . . , I depending upon number of fronts. The non-dominated fronts are the same as set of solutions corresponding to different levels based upon nondominated sorting. After this non-dominated sorting, new population P tþ1 ¼ ; (a null matrix) is created. Starting with I = 1, the new population is updated employing different fronts, F I (starting from level 1) [37], i.e.,

Ptþ1 ¼ Ptþ1 [ F I

until : jP tþ1 j þ jF I j < N p

4.2. Decision making After obtaining Pareto optimal front, the decision making is done to select a unique optimal combination of mass flow rate of water, mw and mass flow rate of air, ma for each fill. To do the decision making, the normalized decision making score against each combination is calculated using following relation,

DMS ¼ W R Rnorm þ W Me Menorm þ W e enorm
W meV meV norm

ð11Þ

In the above equation, Rnorm , Menorm , enorm and meV norm are the normalized values of objective function against each Pareto-front combination, whereas, W R , W Me , W e and W meV are the corresponding weighting factors to each performance parameter. The normalized values in Eq. (12) can be calculated as mentioned below:

Moreover, while producing the new population of size Np, it may be possible that the last front F I cannot be fully accommodated in generation of Ptþ1 . So, in order to tackle this situation, the crowding sorting operation is performed, which includes the most widely spread ðNp
jPtþ1 jÞ solutions. In this crowding sorting operation, a crowded tournament selection operator is used, that compares two solutions and declares the winner based upon its nondominance rank and local crowding distance in the population if rank is same [36]. Further, after creating the population Ptþ1 from best Pareto fronts, the termination condition (tolerance of average change in Pareto front or maximum generations) is checked. If the termination condition (number of stalled generations exceeding 100) is not satisfied, the offspring population, Q tþ1 is again created by means of binary crowded tournament selection, crossover and mutation operations. This iterative procedure is repeated until the population reaches the true Pareto-optimal front or set of efficient

Rnorm ¼ P

ð13aÞ

Mej

j¼1 Mej =n

enorm ¼ P n

ej



ð13bÞ



ð13cÞ

j¼1 ej =n

meV norm ¼ P n

meV j



ð13dÞ

j¼1 meV j =n

ma = 0.019 (kg/s) ma = 0.020 (kg/s) ma = 0.021 (kg/s)

3.5 3.0 2.5

0.11

0.12

0.13

0.14

0.15

Range of cooling tower, R (°C)

Range of cooling tower, R (°C)



4.0

4.0

2.0 0.10

Rj

n j¼1 Rj =n

Menorm ¼ P n

4.5 ma = 0.017 (kg/s)

ma = 0.017 (kg/s) ma = 0.020 (kg/s) ma = 0.021 (kg/s)

3.0

2.5

2.0 0.10

0.16

ma = 0.019 (kg/s)

3.5

Mass flow rate of water, mw (kg/s)

0.11

0.12

0.13

0.14

0.15

0.16

Mass flow rate of water, mw (kg/s)

(a)

(b)

Range of cooling tower, R (°C)

4.5 ma = 0.017 (kg/s) ma = 0.019 (kg/s)

4.0

ma = 0.020 (kg/s) ma = 0.021 (kg/s)

3.5 3.0 2.5 2.0 0.10

0.11

0.12

ð12Þ

0.13

0.14

0.15

0.16

Mass flow rate of water, mw (kg/s)

(c)

Fig. 3. Comparison of range against the variation in mass flow rates of water and air for different fills (a) wire mesh (b) honeycomb and (c) wooden splash.

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K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430

where j = 1, 2, . . . , n and n is number of efficient points or combinations available in Pareto-front. Therefore, incorporating above equations the decision making score, DMS is calculated for each Pareto-front combination and highest value of DMS is nothing but the optimal point or optimal combination of air and water flow rates which most precisely satisfies all objective functions. Furthermore, depending upon the user priority one can assign weighting factor to any of the performance parameter that is subsequently more important. Then after obtaining optimal combination of ma and mw, the best fill out of three fills (wooden splash, wire-mesh and honeycomb) is selected or proposed. It may be noted here that in this work although the optimization has been carried out by taking multiple objective functions, but at the same time the proposed decision making criteria reduced the problem to single objective which is easy to handle. Next, the analysis uncertainty involved in experiment is presented.

suggests that if w is function of certain independent variables x1 ; x2 ; x3 ; . . . xk ,

w ¼ f ðx1 ; x2 ; x3 ; . . . xk Þ

Now, let’s consider that uncertainty involved in each independent variable is U 1 ; U 2 ; U 3 ; . . . U k , respectively. Therefore, taking this uncertainty corresponding to each independent variable, the uncertainty implicated in final result, w can be estimated as given below:

ðU w Þ2 ¼

@xl

) ðU l Þ2

ð15Þ

Above equation to estimate the propagation of uncertainty from variables to final result has been presented by Kline and McClintock [39] as second power equation, whereas Moffat referred the same as root sum square (RSS) method [40]. In other words, Moffat and Kline and McClintock have used the same method to evaluate the propagation of uncertainty [41]. Further, depending upon number of independent variables the uncertainty U w can be represented as:

"

In the experimental investigation, the uncertainty of each instrument may affect the final results obtained using experimental data. So, it is important that uncertainty of each instrument and its effect on the final result is taken into account. Moffat [38] gave a theory to estimate the uncertainty in each experimental collection parameter as well as uncertainty involved in the final evaluated parameter. The following method to calculate the uncertainty

@w U1 @x1

Uw ¼

2



@w þ U2 @x2

2



@w þ U3 @x3

2



@w þ ... þ Uk @xk

2 #12

ð16Þ Moreover, the above expression can be further modified to calculate the relative uncertainty in the final result, w, i.e.,

0.40

0.30 ma = 0.017 (kg/s) ma = 0.019 (kg/s) ma = 0.020 (kg/s) ma = 0.021 (kg/s)

0.38 0.36 0.34

Tower characteristic ratio, Me

Tower characteristic ratio, Me

(  2 k X @w l¼1

5. Uncertainty analysis

0.32 0.30 0.28 0.26 0.24 0.10

ð14Þ

0.11

0.12

0.13

0.14

0.15

0.16

ma = 0.017 (kg/s) ma = 0.019 (kg/s) ma = 0.020 (kg/s) ma = 0.021 (kg/s)

0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.10

Mass flow rate of water, mw (kg/s)

0.11

0.12

0.13

0.14

0.15

0.16

Mass flow rate of water, mw (kg/s)

(a)

(b)

Tower characteristic ratio, Me

0.44 ma = 0.017 (kg/s) ma = 0.019 (kg/s) ma = 0.020 (kg/s) ma = 0.021 (kg/s)

0.42 0.40 0.38 0.36 0.34 0.32 0.30 0.28 0.26 0.10

0.11

0.12

0.13

0.14

0.15

0.16

Mass flow rate of water, mw (kg/s)

(c)

Fig. 4. Comparison of the tower characteristic ratio (Merkel number) with the change in mass flow rates of water and air for different fills (a) wire mesh (b) honeycomb and (c) wooden splash.

424

Uw ¼ w

K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430

"

1 @w U1 w @x1

2

 þ

1 @w U2 w @x2

2

 þ

1 @w U3 w @x3

2

 þ ... þ

1 @w Uk w @xk

2 #12

6. Results and discussion As mentioned earlier that in the present study four levels of mass flow rate of water, mw and mass flow rate of air, ma are taken to establish various correlations and to analyze the performance of the forced draft cooling tower with three different types of fills such as wire-mesh, honeycomb and wooden splash. Fig. 3 reveals the variation of the range of the cooling tower, R for different fills against the variation in the mass flow rate of water, mw and the mass flow rate of air, ma. As expressed using dashed and dotted trend lines, the range decreases continuously with the increase in water flow rate, mw for all air flow rates, ma. This is due to the fact that as the water flow rate increases for a fixed mass flow rate of air, the heat input is increased making no change in available air. So, it consequently decreases the range due to the resistance offered to heat transfer. On the other hand, range, R is found to be increasing with the increase in mass flow rate of air, ma for almost all values water flow rates, mw. This phenomenon is also obvious because with an increase in the air flow rate, the amount of air available for each droplet increases, which directly improves both sensible and evaporative heat transfer mechanisms and further results in an increase of the range. So, from Fig. 3 it is clear that the range, R is inversely proportional to mw and directly proportional to ma for all three types of fills (wire-mesh, honeycomb and wooden splash). In Fig. 4 the variation of the tower characteristic ratio (Merkel number, Me) is presented with the change in the mass flow rates of water and air for all three fills. Referring the dashed and dotted trend lines, it can be seen that, the tower characteristic ratio, Me (KaV/mw) is

ð17Þ

The uncertainties in the basic measured physical parameters are represented below, which are further used to estimated different performance parameters (the range, the tower characteristic ratio, the effectiveness and the water evaporation rate).

U ma =ma ¼ 0:01 U mw =mw ¼ 0:01

ð18aÞ ð18bÞ

U T =T ¼ 0:0002

ð18cÞ

The uncertainty of temperature has been estimated using the pffiffiffiffi standard deviation of mean (SDOM), which is given by rT = N , where rT and N are standard deviation and number of temperature readings recorded in steady state respectively [42]. Each experiment run has been carried out for 10 min under the steady state and during this DAQ system acquired the temperature data in every 0.1 s (10 times in 1 s). Further, the various performance parameters are calculated implementing these basic measurements (mw ; ma and T) and the maximum relative uncertainty in these performance parameters can be calculated using Eqs. (15)– (18):

U R =R ¼ 0:004

ð19aÞ

U Me =Me ¼ 0:004

ð19bÞ

U e =e ¼ 0:004

ð19cÞ

U meV =meV ¼ 0:01

ð19dÞ

22

26

ma = 0.017 (kg/s)

ma = 0.017 (kg/s)

ma = 0.021 (kg/s)

22 20 18

Effectiveness, e (%)

Effectiveness, e (%)

ma = 0.020 (kg/s)

ma = 0.020 (kg/s) ma = 0.021 (kg/s)

18 16 14 12

16 14 0.10

ma = 0.019 (kg/s)

20

ma = 0.019 (kg/s)

24

0.11

0.12

0.13

0.14

0.15

10 0.10

0.16

0.11

0.12

0.13

0.14

0.15

0.16

Mass flow rate of water, mw (kg/s)

Mass flow rate of water, mw (kg/s)

(a)

(b)

26 ma = 0.017 (kg/s) ma = 0.019 (kg/s)

Effectiveness, e (%)

24

ma = 0.020 (kg/s) ma = 0.021 (kg/s)

22 20 18 16 14 0.10

0.11

0.12

0.13

0.14

0.15

0.16

Mass flow rate of water, mw (kg/s)

(c)

Fig. 5. Comparison of the effectiveness with the variation in mass flow rates of water and air for different fills (a) wire mesh (b) honeycomb and (c) wooden splash.

425

0.00060

ma = 0.017 (kg/s) ma = 0.019 (kg/s) ma = 0.020 (kg/s) ma = 0.021 (kg/s)

0.00063 0.00060 0.00057

Evaporation rate, m eV (kg/s)

Evaporation rate, m eV (kg/s)

K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430

0.00054 0.00051 0.00048 0.00045

ma = 0.017 (kg/s) ma = 0.019 (kg/s) ma = 0.020 (kg/s) ma = 0.021 (kg/s)

0.00057 0.00054 0.00051 0.00048 0.00045 0.00042

0.00042 0.10 0.11 0.12 0.13 0.14 0.15 0.16

0.10 0.11 0.12 0.13 0.14 0.15 0.16

Mass flow rate of water, mw (kg/s)

Mass flow rate of water, mw (kg/s)

Evaporation rate, m eV (kg/s)

(a)

(b) ma = 0.017 (kg/s) ma = 0.019 (kg/s) ma = 0.020 (kg/s) ma = 0.021 (kg/s)

0.00068 0.00064 0.00060 0.00056 0.00052 0.00048 0.10

0.11

0.12 0.13 0.14

0.15

0.16

Mass flow rate of water, mw (kg/s)

(c)

Fig. 6. Variation of the evaporation rate against mass flow rates of water and air for different fills (a) wire mesh (b) honeycomb and (c) wooden splash.

Table 1 Coefficients used to develop the correlation of different performance parameters for each packing (fill). Coefficient Wire mesh Range, R (°C) Tower characteristic ratio, Me Effectiveness, e (%) Evaporation rate, meV (kg/s) Honeycomb Range, R (°C) Tower characteristic ratio, Me Effectiveness, e (%) Evaporation rate, meV (kg/s) Wood splash Range, R (°C) Tower characteristic ratio, Me Effectiveness, e (%) Evaporation rate, meV (kg/s)

c0

c1

c2

c3

c4

c5

c6

c7

c8

c9


334.2
14.909

524.4 127.456

4.89  104 1355.236


3016
658.19


1.75  104
4193.44


2.44  106
4.762  104

5899 1604.845

4.86  104 573.188

6.541  104 9.986  104

4.16  107 4.672  105

363
0.04577

3046 0.09023


7.824  104 6.466


2931
0.8981


3.134  105 3.901

5.485  106
345.597


3940 2.679

3.348  105
11.596

5.622  106
25.16


1.125  108 5984.885


248.1 8.227

45.2
61.517

3.96  104
789.753

861.3 565.296


2.12  104
1833.829


2.005  106 4.676  104


4400
476.058

5.949  104 2479.867

1.205  105 2.996  104

3.481  107
8.571  105

933.6
0.0718

1124
0.1155


1.506  105 12.195

7750 0.9024


2.539  105
0.5406

8.772  106
638.65


2.738  104
2.271

2.337  105 1.156

4.957  106 6.86


1.635  108 1.115  104


173.2
15.229


408.1
88.815

3.032  104 3069.695

1570 537.562

1.549  104 1316.74


1.606  106
1.637  105

2664
868.908


1.207  105
8202.096

3.841  105 1.895  104

2.669  107 2.797  106


741
0.01029


1150
0.3674

1.279  105 1.858

8623 0.0361


3.516  104 3.756


6.459  106
107.443


6926 0.361


1.956  105
10.485

2.076  106
28.533

1.068  108 1915.674

decreasing with an increase in the mass flow rate of water, mw at all flow rates of air, ma. This decreasing trend of the tower characteristic ratio, Me is basically due to increased resistance offered

to heat transfer between water and air within the cooling tower. As discussed earlier, this resistance decreases the range, R of the cooling tower and from Eq. (4) it can be clearly understood that

426

K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430

Fig. 7. Proposed correlation surface fitting of different parameters using 3rd order polynomial for wire mesh fill, (a) range (b) tower characteristic ratio (c) effectiveness and (d) evaporation rate.

the tower characteristic ratio, Me is directly proportional to the range. So, any depletion of the range will also lower the value of the tower characteristic ratio, Me. It is also revealed from

Fig. 4 that the tower characteristic ratio, Me increases with increase in the mass flow rate of air, ma, which is due to increase in the interfacial area, a.

427

K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430 Table 2 R-square, RMSE and uncertainty values for different correlations of performance parameters. Packing type

Wire mesh

Honeycomb

R-square

RMSE

U

R-square

RMSE

U

R-square

RMSE

U

Range, R (°C) Tower characteristic ratio, Me Effectiveness, e (%) Evaporation rate, meV (kg/s)

0.9885 0.9905 0.9975 0.9814

0.0902 0.0071 0.2780 8.47  10
6

0.0089 0.0009 0.0535 4.833  10
6

0.9972 0.9888 0.9952 0.9884

0.0363 0.0062 0.2917 6.5  10
6

0.0089 0.0008 0.0520 4.36  10
6

0.9950 0.9969 0.9964 0.9658

0.0574 0.0038 0.2718 9.67  10
6

0.0089 0.0010 0.0549 4.82  10
6

The effect on effectiveness, e is studied with the variation of mass flow rate of air, ma and the mass flow rate of water, mw, and is presented in Fig. 5. As presented, the effectiveness, e appears to be decreasing with an increase in the mass flow rate of water, mw, while at the same time it is found to be increasing with the increase in the mass flow rate of air, ma. With reference to Eq. (6) it is evident that the effectiveness, e is directly proportional to the range, R, so, the trends are similar as that of range due to the same reasons as mentioned previously. These trends hold good for all three types of fills (wire-mesh, honeycomb and wooden splash). In Fig. 6 the behavior of the water evaporation rate, meV with the change in flow rates of water and air for different fills has been revealed. In this particular analysis it is found that the mass evaporation of water, meV increases with the increase in mass flow rate of water, mw, which has been indicated using trend lines. This is due to the fact that as the mass flow rate of water increases, the heat transfer coefficient at the water side also increases, due to which more evaporative heat transfer occurs, which further leads to more evaporation rate [43]. Moreover, if the trend of the water evaporation rate, meV is considered with respect to different mass flow rates of air, ma, it is found that meV increases with an increase in ma. This phenomenon is expected because as the mass flow rate of air increases, it results in more evaporation due to more interfacial area, a. Next, after collecting experimental data for all three fills (wiremesh, honeycomb and wooden splash), different correlations are developed for various performance parameters (range, tower characteristic ratio, effectiveness and water evaporation rate) by fitting 3rd order polynomial in the collected data. As illustrated in Eq. (8), in the correlations the mass flow rate of water, mw and mass flow rate of air, ma are considered to be design variables. The relevant coefficients involved in each correlation of the range, the tower characteristic ratio, the effectiveness and the water evaporation rate for different fills are mentioned in Table 1. The fitted surfaces for different performance parameters for the wire-mesh type of fill are presented in Fig. 7. Table 2 consists of R-square, Root Mean Square Error (RMSE) and absolute uncertainties values involved in each performance parameter correlation for three different fills. The R-square value which is also known as the coefficient of determination is a measure of closeness of regression surface that is fitted to the collected data. The correlation is said to be good, if the R-square value is closer to 1. As presented in Table 2, it is well justified that all the correlations for each fill have good R-square values which reflects the goodness of relation. Moreover, RMSE is a measure of differences between the predicted value from the correlation and the actual value, which is closely related with Rsquare value of the correlation. The RMSE values for each correlation are found to be in good range due to high values of R-square. In Table 2, the values of absolute uncertainties are also given for each correlation which provides a better understanding about the preciseness of the proposed correlations. Now, the correlations or the required objective functions are obtained for different performance parameters with mw and ma as design variables for each type of fill (packing). Therefore, next the multi-objective optimization algorithm is applied to simultaneously optimize the relevant

Wooden splash

objective functions for each fill (packing). With reference to procedure revealed in Section 4.1, NSGA-II has been implemented for this purpose considering four objective functions (for the range, the tower characteristic ratio, the effectiveness and the water evaporation rate) for each fill (packing). The initial population for NSGA-II is considered to be 50 with 0.8 crossover fraction alongwith uniform mutation rate of 0.01. The lower bounds for mw and ma have been taken as 0.108 kg/s and 0.0173 kg/s respectively, whereas, the upper bounds for these two design variables are kept as 0.158 kg/s and 0.0212 kg/s, respectively. The maximum number of generations is set to be 200 and stall generations are taken as 100. The termination condition is formulated in such a way that the change in Pareto-front (objective functions evaluated at Pareto front) should be lower than 10
4 in 100 consecutive iterations (stall iterations). The final optimal Pareto front for each fill is presented in Fig. 8, which is set of 50 points. This Pareto front gives set of possible efficient points satisfying each of the four objective functions simultaneously. In the Pareto-front each efficient point is the combination of mass flow rate of water, mw and mass flow rate of air, ma optimizing each of the objective functions for a particular fill (packing). As mentioned earlier in Section 4.2, after obtaining the optimal Pareto front, the design making is done to find a unique combination of mw and ma for each fill (packing). Fig. 9 gives a clear idea of the decision making based upon DMS value, where an optimal combination of the mass flow rate of water and air has been selected from the Pareto front. As shown, DMS is first calculated for all 50 combinations and then an optimum combination of mw and ma has been selected based upon the highest DMS. The same most optimal combinations of design variables (mw and ma) are provided in Table 3 corresponding to each fill (wire-mesh, honeycomb and wooden splash) by assigning equal weightage to each performance parameter. Further, in the same table the performance parameters such as the range, the tower characteristic ratio (Merkel number), the effectiveness and the water evaporation rate corresponding to the optimal point are presented for each fill (packing). It is quite evident from Table 3 that the wire-mesh (trickle) type is the most favorable in terms of various performance parameters as its decision making score, DMS is highest as compared to all other fills under the present set of environmental conditions and experimental data. The wire mesh fill is found to be the efficient fill that maximizes the performance of forced draft cooling tower, because it precisely splits the water into fine droplets that further increases the interfacial area, a between water and air. The increased interfacial area promotes the heat transfer between two working fluids (water and air) which ultimately lead to performance maximization. Because water is distributed into fine droplets, the trickle type packing offers less resistance to the incoming air from the bottom that enhances the heat and mass transfer. But, in the case of honeycomb type packing, greater resistance is offered to the air, because air has to pass through different cells. Therefore the air at the outlet is least humid in the case of honey-comb fill. Consequently, the value of DMS is lowest for the honeycomb fill (film type) because the interfacial area, a is less in this case as compared to other fills. As explained in Section 4.2, the decision making can be also made

K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430

0.39

Effectiveness, e (%)

tio, M acteristic ra Tower char

e

0.38

22.00

0.37

23.00

0.36

24.00

0.35

25.00

0.34

26.00

0.33 0.32

-4

4.95x10 ) -4 4.80x10 kg/s ( -4 4.65x10 m eV , -4 te 4.50x10 ra n -4 it o 4.35x10 a or ap Ev

3.8

3.9 Ra 4.0 ng e, R 4.1 ( oC 4.2 )

4.3

0.28

15.50

0.27

16.50

0.26

17.50

0.25

18.50

0.24

19.50

0.23

20.50

0.22 -4

2.8 Ra ng 3.0 e, R ( oC 3.2 )

3.4

5.1x10 ) s g/ -4 (k 4.8x10 eV m , -4 4.5x10 rate n io t -4 a 4.2x10 or ap Ev

2.1

Optimal point 1.70

1.7 1.65

1.6

1.60 0.109 0.110

1.5 1.4

22.00 23.00

0.38

24.00

0.37

25.00 -4

4.0

(c)

0.0195

0.021 /s) g (k 0.020 ma , r 0.019 ai of 0.018 ate r w 0.017 flo s as M

5.8x10 ) s -4 5.6x10 (kg/ -4 V e 5.4x10 ,m -4 te 5.2x10 ra n io -4 t a 5.0x10 or ap Ev

Fig. 8. Pareto fronts for different fills (a) wire mesh (b) honeycomb and (c) wooden splash.

by assigning weightage factor to each performance parameter depending upon the priority. In Table 4, the case of wire-mesh packing has been presented, where the weightage factor has been assigned to different performance parameters depending upon the user’s choice. As shown, the first row of the table indicates the case where a higher priority or weightage has been assigned to the range. Further, with reference to the selection criterion, an optimum combination of mw and ma has been selected from the Pareto front based upon the highest DMS. Moreover, in a complex case

Optimal point

2.35

2.35 g score, DMS Decision makin

ristic ratio, Me Tower characte

21.00

3.6 Ra ng 3.7 e, R 3.8 ( oC 3.9 )

0.0200 0.111

(b)

0.41

3.5

0.0210 0.0205

1.3

1.2 0.1100 Ma 0.1125 ss flow rat 0.1150 eo fw ate 0.1175 r, m w (k g/s )

Effectiveness, e (%)

0.36

0.0182

0.021 s) g/ 0.020 (k a 0.019 r, m ai of 0.018 e t ra w 0.017 flo s as M

0.42

0.39

0.0189

0.1086

2.2

Ma 0.1083 ss flow 0.1086 rat eo fw 0.1089 ate r, m w (k g/s )

(b)

0.40

0.0203 0.0196

0.1084 0.1085

2.3

g score, DMS Decision makin

ratio, Me

2.32

(a)

0.29

ristic Tower characte

2.40

2.4

Effectiveness, e (%)

0.21 2.6

Optimal point

2.48

2.5

(a) 0.30

2.56

2.6 g score, DMS Decision makin

428

2.30

2.30

2.25

2.25 2.20

0.1084 0.1085 0.1086

2.15 2.10

0.021 0.020 0.019

2.05 2.00

Ma 0.10825 ss flow 0.10850 rat e o 0.10875 fw ate r, m 0.10900 w (k g/s )

0.022 ) s 0.021 (kg/ 0.020 m a r, 0.019 f ai o 0.018 rate w lo 0.017 sf as M

(c) Fig. 9. Selection based upon decision making score (DMS) for various fills (a) wire mesh (b) honeycomb and (c) wooden splash.

where the mass flow rate of water is either fixed or continuously varies, the proposed methodology enables the user to find an optimum value of ma for a given mw. This fact has been demonstrated in Table 5 for wire-mesh fill, where for a given value of mw, the optimum value of ma has been presented in order to maximize the performance. Therefore, proposed generalized methodology can be successfully implemented for any complex industrial cooling tower with wide range of temperatures and flow rates.

429

K. Singh, R. Das / Energy Conversion and Management 111 (2016) 417–430 Table 3 Pareto optimal for different types of fills based upon equal weighting factor decision making. Packing type

mw (kg/s)

ma (kg/s)

Wire mesh Honeycomb Wooden splash

0.1083 0.1083 0.1083

0.0199 0.0206 0.0211

Range, R (°C)

Tower characteristic ratio, Me

Effectiveness, e (%)

Evaporation rate, meV (kg/s)

Rnorm

0.3854 0.2851 0.4140

25.9039 20.1124 24.4832

4.7481  10
4 4.7878  10
4 5.8191  10
4

1.1804 0.8949 1.1131

Real value 4.1515 3.1472 3.9147

Menorm

enorm

meV norm

Decision making score, DMS

1.1657 0.8621 1.2520

1.2110 0.9403 1.1446

0.9814 0.9896 1.2027

2.5757 1.7077 2.3070

Rnorm

Menorm

enorm

meV norm

Decision making score, DMS

0.1870 0.5829 0.1930 0.1943

0.1990 0.2018 0.6086 0.2018

0.1717 0.1636 0.1643 0.4907

0.8253 0.8179 0.8347 0.1022

enorm

meV norm

Decision making score, DMS

1.3215 1.1731 1.0619 0.9670 0.8986

0.9525 1.0373 1.0632 1.0582 1.0531

2.7931 2.4154 2.0879 1.8146 1.6045

Normalized value

Table 4 Design making assigning different weighting factors to various performance parameters for wire-mesh fill. Weighting factor

WR 0.5 0.1667 0.1667 0.1667

W Me

mw (kg/s) We

0.1667 0.5 0.1667 0.1667

0.1667 0.1667 0.5 0.1667

ma (kg/s)

W meV 0.1667 0.1667 0.1667 0.5

Range, R (°C)

Tower characteristic ratio, Me

Effectiveness, e (%)

Evaporation rate, meV (kg/s)

Real value 0.1083 0.1083 0.1083 0.1083

0.0211 0.0199 0.0203 0.0199

4.2976 4.1515 4.1656 4.1515

0.3709 0.3854 0.3829 0.3854

Normalized value 25.5378 25.9039 26.0350 25.9039


4

4.983  10 4.748  10
4 4.770  10
4 4.748  10
4

0.6110 0.1967 0.1974 0.1967

Table 5 Optimal ma predictions for different given values of mw for wire-mesh fill based upon equal weighting factor decision making. Given mw (kg/s)

Optimal ma (kg/s)

0.11 0.12 0.13 0.14 0.15

0.0203 0.0197 0.0197 0.0195 0.0195

Range, R (°C)

Tower characteristic ratio, Me

Effectiveness, e (%)

Evaporation rate, meV (kg/s)

Rnorm

0.3825 0.3703 0.3417 0.3091 0.2818

25.5423 22.6734 20.5250 18.6905 17.3675

4.892  10
4 5.327  10
4 5.460  10
4 5.434  10
4 5.408  10
4

1.2078 1.1021 1.0027 0.9230 0.8629

Real value 4.1037 3.7445 3.4068 3.1360 2.9316

Menorm

Normalized value 1.2162 1.1775 1.0865 0.9828 0.8962

7. Conclusion

Acknowledgement

In the present study, an experimental investigation has been carried out on the forced draft cooling tower and a model to optimize its performance is proposed using trickle, film and splash fills. The performance of the cooling tower using wire-mesh, honeycomb and wooden splash fills has been analyzed in detail. Four important performance parameters such as the range, the tower characteristic ratio (Merkel number), the effectiveness and the water evaporation rate are considered for optimization with flow rates of water and air being taken as the design variables. A multi-objective optimization problem is formulated to optimize four performance parameters simultaneously for each fill in which the elitist Non-Dominated Sorting Genetic algorithm (NSGA-II) has been used as solution algorithm. Using the NSGA-II algorithm, the optimal Pareto-front has been obtained for each fill that involves possible combinations of mass flow rates of water and air. Then, from the available Pareto-front, a decision making procedure has been proposed based on decision making score to select a unique and the most optimal combination of mass flow rates of water and air. The decision making criterion also enables the user to control the tower performance by assigning priorities to different parameters as per the requirement. The present study reveals the different optimal operating points for each of three types of fills and out of these; the wire mesh type of fill has been found to be the most favorable fill operating under the present conditions. At last it has been concluded that the proposed methodology is generalized and can be easily implemented to optimize the performance of any forced draft cooling tower with much larger temperature ranges.

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