Applied Thermal Engineering 30 (2010) 2378e 2378e2385
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m/ m/ l o c a t e / a p t h e r m e n g
Optimization of �re tube heat recovery steam generators for cogeneration plants through genetic algorithm Ali Behbahani-nia , Mahmood Bagheri, Rasool Bahrampoury *
Department of Mechanical Engineering, K.N. Toosi university of technology, Mollasadra St., Tehran, Iran
a r t i c l e
i n f o
Article history: Received 23 September 2009 Accepted 5 June 2010 Available online 16 June 2010 Keywords: Firetube HRSG Cogeneration Optimization Genetic Algorithm Thermoeconomic Multi-objective
a b s t r a c t
In the present paper, a small cogeneration system including a gas microturbine and a �re tube heat recovery steam generator (HRSG) is considered. The HRSG system is optimized considering two different objective functions. Sum of the exergy losses resulting from the gases leaving the stack and the exergy destructi destruction on due to the internal internal irrevers irreversibil ibility ity is considere considered d as the �rst objective function while the second objective function is considered to be the sum of annualized values of the capital cost and the cost of the energy loss. The cost of energy loss includes the cost of the loss by hot gases leaving the stack and the cost of the reduction in the power production in the microturbine as the result of the pressure drop in the HRSG. Finally multi-objective optimization method via genetic algorithm is employed to � nd the optimum values of the design parameters. A decision making process based on � nding the closest point to the ideal point is used. Results of different optimum points on the Pareto front are compared and discussed. The results show that the thermodynamic optimization doesn t lead to major improvement of the total cost of the HRSG although the thermoeconomic and multi-objective methods improve the total cost of the system due decrease decrease in the cost of energy energy loss due to decrease decrease in the pinch point. point. 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Due to the daily progress in the gas turbine technology cogeneration systems having gas turbines as their prime movers have became prevalent. In these systems in addition to supplying the electricity demand, heating and/or cooling load of the building can be supplied supplied using absorpti absorption on chillers chillers and heat recovery recovery steam gener generato ators. rs. This This result resultss in lower lower fuel fuel consum consumpt ption ion and lower lower emission [1] [1].. Fig. Fig. 1 illustr illustrate atess the schema schematic tic view view of a small small cogeneration system with a gas turbine prime mover. Heat recovery steam generators are one of the most important componen components ts of a cogenerat cogeneration ion system which have a signi�cant impact on its ef �ciency. Heat recovery steam generators are classi�ed into two groups of water tube and �re tube. In water tube boilers boilers water water �ows ows insi inside de pipe pipess and and gas gas �ows ows inside inside the shell shell while while in � re tube ones gas � ows inside pipes and two phase water boils inside the shell. Generally, when the mass � ow rate of the output gas is lower than 7 kg/s, it is not economical to use water tube HRSGs [2] [2].. For For gas gas micr microt otur urbi bine ness havi having ng a powe powerr outp output ut of 30e 30e800 kW, the use of � � re tube HRSGs is inevitable. Commercial buildings, light duty industrial facilities including food processing,
*
Corresponding Corresponding author. author. Tel.: þ 98 9123548379; fax: þ 98 2188677273. E-mail address: alibehbahanin
[email protected] [email protected] (A. Behbahani-nia).
1359-4311/$ e 1359-4311/$ e see front matter 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.06.007 doi:10.1016/j.applthermaleng.2010.06.007
’
chemical industries etc. which have rather simultaneous heat and electrical electrical demands are among the most appropriate appropriate choices for microturbine-based CHP systems and thus, �re tube HRSGs. The condit condition ionss in which which exhau exhaust st hot gases have have a high high press pressur ure e is another case where �re tube HRSGs are preferred to water tube ones. Furthermore, when the exhaust gases are dirty and the gas �ow is dry and includes includes entrainments entrainments of particles particles,, it is recomrecommend mended ed to use use a �re tube tube HRSG HRSG.. Manyof Manyof the the exha exhaus ustt gas gas stre stream amss in the petroche petrochemical mical applicatio applications ns are examples examples of this situation situation [3] [3].. In all the above-menti above-mentioned oned applicatio applications, ns, using �re tube tube HRSGs HRSGs result resultss in reduction of the costs. Different methods have been used in order to optimize heat recovery steam generators. In references [4,5] [4,5] second second law analysis of heat recovery generators is presented. In reference [6] reference [6] optimum optimum values of some of the operating parameters are found by minimizing exergy loss. Results of aforementioned papers may not be used in practice because they may lead to a design with unreasonable capital cost. The method which compromises both of the ef �ciency and capital the cost is thermoeconomic. The objective functions functions base on thermoeco thermoeconomic nomic method method depends depends on applicatio application n of the HRSG and local costs of energy and construction of a new system. In references [7,8] [7,8],, a thermoeconomic objective function was proposed in order to optimize heat recovery steam generators for the combined cycle power plants. The method was used to optim optimize ize the pinch pinch point point for multi multi press pressur ure e water water tube tube heat heat
A. Behbahani-nia et al. / Applied Thermal Engineering 30 (2010) 2378e 2385
Nomenclature A C e, C f C p D _ E f F ff h H h f HRSG I _ k K K , K m L, L e _ m n f N H Nu N w P P.P S S T, S L T
heat transfer surface area (m2) cost of electricity ($/kW h), cost of fuel ($/m3) speci�c heat (kj/kg K) tube diameter (m) exergy rate (kW) friction factor objective function fouling factor (m2 K/W) heat transfer coef �cient (W/m2 K), enthalpy (kJ/kg) number of working hours of the HRSG in a year �n height (m) heat recovery steam generator irreversibility (kW) ratio of speci�c heats, C p/C v unit volume capital costs ($/m3) gas thermal conductivity, tube metal conductivity (W/ m K) length (m), equivalent length (m) mass � ow rate (kg/s) �n density (�ns/m) number of tube rows deep nusselt number number of rows wide pressure (kpa) pinch point entropy (kj/kg K) transverse and longitudinal pitch of tubes (m) temperature (K)
recovery steam generators. As pointed out by the authors the pinch point obtained in this work were surprisingly lower than what was suggested by the designers, in addition, the geometrical parameters were not optimized in this paper. References [9] and [10] have proposed a two steps algorithm, the �rst step of which is minimizing the pressure drop in a constant heat transfer load. The second step is geometric minimization of HRSG s compactness factor, while thermal parameters are held constant based on the former optimization. Although the algorithm which was presented in this paper demonstrates a great deal of progress compared to the previous works but the heat transfer rate and therefore, pinch temperature difference are known in advance while this parameter is usually considered as a decision variable in the HRSG design. In other words, a comprehensive algorithm should include a way to optimize the pinch temperature difference since this parameter signi�cantly affects the HRSG performance and cost. In reference [11] a thermodynamic method was suggested in order to optimize heat exchanger layout in a HRSG. ’
U V V L m
DP DT m DW e h r
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overall heat transfer coef �cient (W/m2 K) volume (m3) gas velocity in evaporator pipes (m/s) viscosity (pa s) pressure drop (kpa) log-mean temperature difference (K) reduction of power (kW) exergetic ef �ciency ef �ciency density (kg/m3)
Subscripts convective, compressor C destruction D Eco economizer Eva evaporator fuel F �n f gas g inner, inside tube, inlet i loss L non-luminous N outer, outside tube, outlet o atm atmosphere (Restricted dead state) product P steam s Sh superheater turbine t water w Kth component K
In all of the reviewed works, water tube heat recovery boilers are optimized. The objective functions are used in these works are base on this assumption that they are used in combined cycle power plants. This work concerns on optimization of � re tube heat recovery steam generator in order to use in cogeneration systems. The suggested algorithm in this work is based on multi-objective optimization method. The �rst objective function in this work is sum of the exergy loss and the exergy destruction inside the HRSG and the second objective function is a thermoeconomic objective function introduced in this work for cogeneration systems. 2. Problem statement
Schematic of a cogeneration system which is based on a microturbine is shown in Fig. 1. The heat output from the microturbine is recovered in a � re tube HRSG. The Pressure and the temperature of the generated steam are constant due to the process requirements. A deaerator, removes the air from the input water of the inlet feed water of the HRSG. The objective is to � nd optimum values of the pinch point and some other design variables of the HRSG. Fig. 2 shows schematic of a �re tube HRSG used in the aforementioned CHP plants. In the � re tube HRSGs only the evaporator has a � re tube structure and the superheater and the economizer have water tube structures. In order to reduce costs, economizers with �nned surfaces are often used. The path of the water stream is illustrated in the � gure by dashed lines. 3. Design of the HRSG
Fig. 1. A cogeneration system with a gas turbine prime mover.
Two stages of calculations are needed to design an HRSG. The �rst stage is performance calculations or thermodynamic design. In
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Fig. 2. Fire tube HRSG with an economizer, an evaporator and a superheater.
this stage the general con�guration of the HRSG and positions of different surfaces are determined. The second stage is the thermal design. In this stage, the surface area of thermal surfaces is determined. 3.1. Thermodynamic design
Before the thermodynamic design, one needs to select values of the pinch point and the approach point. Pinch and approach points are the most important performance parameters of an HRSG. The pinch point is temperature difference between the gas � owing out from the evaporator and the saturated steam inside the evaporator (Fig. 3). Reducing the pinch point leads to a lower stack loss. However, cost of the HRSG and the pressure drop is increased. Approach point is the temperature difference between the outlet water from the economizer and the saturated water in the evaporator. In single pressure HRSGs, decreasing the approach point improves the performance of the HRSG. However, steam formation in the economizer imposes limits on the approach point [2]. The values of these parameters are determined using the manufacturers experience. The pinch point is optimized in this work. Knowing these two parameters, steam mass �ow rate is obtained using the �rst law of thermodynamics for a control volume containing both the superheater and the evaporator. ’
_ m T g 1 T g 3 g C pg
_ ¼ m w ðhs2 hw2 Þ
(1)
Using heat balances for each of the components, gas temperature at the inlet and exit of each component of the HRSG can be obtained. 3.2. Thermal design
In the thermal design, once the overall heat transfer coef �cient is determined, the surface area of each component of the HRSG (economizer, superheater and evaporator) can be obtained. A brief review of the thermal design of a �re tube HRSG is presented in Appendix A. The radiative heat transfer coef �cient is determined using the method presented in reference [12]. 4. Exergy analysis of the HRSG
Exergy is the maximum obtainable work which can be taken from the inlet energy. Using an exergy analysis, those components of the system which have the highest thermodynamic inef �ciencies are recognized. The exergy intake to an HRSG includes chemical and physical exergies of the inlet gas � ow. The chemical exergy of the inlet gas � ow will not be recovered and will be discharged to the atmosphere through the stack. Exergy is not conserved and can be destroyed within a system due to irreversibility. It can also be lost when there is a material �ow or energy transfer to the surroundings [13]. The exergy loss equals to the exergy rate of the hot gas leaving the economizer and is calculated as follows: _ _ E g h g 4 hatm T atm S g 4 S atm L ¼ m
(2)
The most important factors of exergy destruction in all components of the HRSG (economizer, evaporator, and superheater) are the irreversibility resulting from the heat transfer and friction. Exergy destruction rate at the Kth component of the system is: _ _ _ E D;K ¼ E F ;K E P ;K
Fig. 3. Temperature pro�le of the HRSG.
(3)
_ _ Where E P ;K and E F ;K are exergy rates of the product and the fuel of the Kth component, respectively, which are evaluated considering the desired outcome of using that component and the resources
A. Behbahani-nia et al. / Applied Thermal Engineering 30 (2010) 2378e 2385
spent for that outcome. In [13] and [14], fuel and product exergies are determined for each component, using the following equations: _ _ E g h g ;in;K h g ;out;K T atm S g ;in;K S g ;out;K F ;K ¼ m
(4)
_ _ E w hw;out;K hw;in;K T atm S w;out;K S w;in;K P ;K ¼ m
(5)
One of the main parameters in evaluating performance and optimization of thermal systems is the exergetic ef �ciency. It is de�ned as the ratio of product to fuel for each component: eK
¼
_ E P ;K
(6)
_
E F ;K
5. Economical analysis
Total annual cost of an HRSG is de�ned in this work as sum of the cost of heat transfer surface area and the cost of energy loss as follows:
(7)
C tot ¼ C cc þ C loss
Construction cost of thermal surfaces in an HRSG depends mainly on its weight. The total cost of construction of an HRSG includes other costs such as shell, the casing and the pipe work. The annualized capital cost for construction of an HRSG is as follows
(8)
C cc ¼ CRF PEC
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Table 2 Variation intervals of decision variables.
Item
Value
C e C f H CRF K eco K eva K sh
0.078 $/Kw hr 0.168 $/m3 5840 h/year 0.2385 39 195 $/m3 42 425 $/m3 115 146 $/m3 0.915
hBoiler
_ m g C pg T g ;out;eco T atm H C sl ¼ C f hBoiler LHV
(11)
where LHV is the lower heating value of natural gas, H is the number of working hours of the HRSG in a year and h Boiler is ef �ciency of a typical conventional boiler. In the third part of the cost of reduced power production in the turbine due to pressure drop is accounted for. This pressure loss is neglected in some of previous works [7,8]. In references [9,10], the pressure loss is minimized but the effect of it on the gas turbinewas neglected. In references [2,3], this reduced power production is considered equivalent to a power of a fan required to overcome the friction. The optimum value of gas-side velocity in HRSGs such as the other kind of heat exchangers may be found by trade-off between the weight or cost of heat transfer surface area and the fan power work required to overcome the pressure loss. The methods which don t consider the pressure loss may not be used to � nd an optimum value for the gas-side velocity. In this work, reduction of power generated in the gas turbine is modeled simply by assuming that the mass �ow of the gas and ef �ciency of the turbine don t change. This assumption is base on this fact that the pressureloss in HRSGs is very small with respect to the pressure in the outlet of combustion chamber of the gas turbine. The power loss in the turbine is calculated as follows: ’
where CRF is the capital recovery factor. PEC is cost of heat transfer surface area and other costs such as casing and equipments. It is assumed that PEC to be a function of heat transfer surface area and may be calculated as follows
(9)
PEC ¼ ðK eco V eco þ K eva V eva þ K sh V sh Þ
in which K is cost of unit volume of the heat transfer surface area. In the estimation of the K eva, all costs related to the shell, insulation and machining which are functions of its size and con�guration of thermal surfaces are taken into account. There is two main source of energy loss in an HRSG. The stack loss and reduction of power generation in gas turbine due to pressure loss in the HRSG.
C loss ¼ C sl þ C pl
(10)
’
DW
_ ¼ m g C pg ht T 3
k1=k
P atm P 3
k1=k
!
P atm þ DP P 3
where T 3 and P 3 are respectively the temperature and pressure of exhaust gas of the combustion chamber which enters the turbine [16]. Finally, costs of this power loss are obtained via (13), where C e is the cost of electricity in Iran.
The discharge of hot gases through the stack results in loss of energy. The cost of the equal fuel equivalent to wasted energy by these losses is given by: Table 1 Coef �cients required for calculation of costs.
Variables
P.P ( K) Pressure drop (kpa) Evaporator V L (m/s) di (m) Economizer L (m) S T/ do S L/do h f (m) n f ( �ns/m) Superheater L (m) S T/ do S L /do
Lower limit 0.001 e
Upper limit 40 5
15 0.015
50 0.040
1 1.5 1.5 0.005 75
3.5 4.15 4.15 0.020 275
1 1.5 1.5
2.5 4.15 4.15
(12)
Fig. 4. The general structure of problem solving by genetic algorithm.
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Table 3 Continuous output of the gas turbine in ISO condition.
Item
Value
Output power Pressure ratio Mass � ow rate Exhaust temperature Fuel Compressor ef �ciency Turbine ef �ciency
600 Kw 8.6 5 kg/s 570 C Gaseous 0.8 0.8
C pl ¼
DW H
C e
(13) Fig. 5. Pareto optimal frontier.
Constants used in economic analysis are given in Table 1. 6. Optimization
The considered set of optimization parameters and their associated constraints, considering practical restraints, are presented in Table 2. In addition, the temperature of the dew point of the stack output gas is limited to 110 C. 6.1. Objective function
De�ning an appropriate objective function is a vital step in optimization of any system. Considering a single thermodynamic objective function, which can be minimizing the irreversibility within the system, might leads to uneconomical design. Since the economical considerations have a great importance in design of engineering systems, the designer must consider the total cost of the project alongside achieving the maximum thermodynamics ef �ciency. Therefore, one of the common objective functions which simultaneously contain both capital cost and energy or exergy cost, is thermoeconomic objective function. In this work, a multiobjective optimization method is used to consider both of the above objective functions. 6.1.1. Thermodynamic objective function A suitable objective in thermodynamic optimization is minimizing the sum of irreversibility within the HRSG. In the HRSG, irreversibility is sum of the total exergy loss and exergy destruction in each single component of the system. By minimizing this objective function the ef �ciency will be maximized.
I _ ¼
X
_ _ E D;K þ E L
(14)
K
6.1.2. Thermoeconomic objective function In the thermoeconomic approach, sum of the levelized values of energy or exergy and capital costs are selected as the objective function. The objective function used in this work is sum of the capital cost and energy costs introduced in equation (7). Table 4 Operational conditions of the HRSG.
Item
Value
HRSG Pressure Output steam temperature Blow down Supply water temperature Supply water pressure Dew point temperature Deaerator pressure
550 kpa 196 C 5% 21 C 100 kpa 110 C 100 kpa
6.1.3. Multi-objective optimization Weighted values of the thermodynamic objective function and the thermoeconomic objective function is considered as the objective function as follows
F ¼
a
I _
I _ref
þ ð1 aÞ
C tot C tot; ref
(15)
Considering a ¼ 0 and a ¼ 1 leads to optimization of the thermoeconomic and thermodynamic objective functions respectively. The result is a set of optimum solutions, called Pareto solutions, each of which is a trade-off between considered objective functions. The designer can choose any set of optimal solutions, by selecting desired value of a between 0 and 1. 6.2. Optimization method
Genetic algorithm is utilized as the optimization method in the present work. Genetic algorithm, thanks to its evolutional nature, canwork with any type of objective function, constraints and in any sort of space. In this algorithm, the solution space is exhaustively searched and there is less possibility to be trapped in a local optimum. In genetic algorithms, any possible answer is represented by a series of genes, called a chromosome. A selected population of chromosomes is called a society and a society in a speci�c segment of time is called a generation. After de�ning the objective function, an initial society is generated. This initial population is evaluated and each chromosome is given a ranking. If the solution requirements are not met, the step of going to a new generation including selection, mating and mutation with the aim of improving the Table 5 Results of optimization.
Variables
Base case
P.P (K) 19 Pressure 1.66 drop (kpa) Evaporator V L (m/s) 29 di (m) 0.029 Economizer L (m) 1.77 S T/ do 2 S L/do 2.3 h f (m) 0.0132 n f (�ns/m) 98 Superheater L (m) 1.6 S T/ do 1.7 S L/do 2
Thermodynamic Multi-Objective opt. opt.
Thermoeconomic opt.
5.63 1.24
6.59 2.28
6.26 3.22
15 0.04
29.36 0.022
36.48 0.020
3. 5 1.81 2.62 0.0168 275
3.5 1.84 2.69 0.0105 275
3.35 1.9 2.83 0.0203 216
2.5 2.64 4.15
2.37 2.19 4.15
2.24 2.14 3.43
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Fig. 6. Exergetic ef �ciency of components of the HRSG, before and after optimization. Fig. 7. Comparison of annual costs of the HRSG before and after the optimization.
answers is taken. The general structure of problem solving by genetic algorithm is shown in Fig. 4 [15]. 7. Results
In this work, a cogeneration system is considered base on a 600 kW microturbine made by NIIGATA POWER. Speci �cation of the gas turbine is given in Table 3. Some operational parameters of the system to be designed are given in Table 4. Fig. 5 presents the generated Pareto front base on dimensional values. The ideal point shown in the �gure is de�ned a point in which both objectives have their optimum values independent to the other objective. As shown in Fig. 5 this point is not located on the Pareto curve. In fact minimizing sum of exergy loss and destruction increases the capital cost which leads to increase in the thermoeconomic objective function. Therefore this ideal point may not exist and there is not any weighting function correspond to this ideal point.The multi-objectivepoint is selected as the closest point to the ideal point. The three speci�c points which represent thermodynamic, thermoeconomic and the multi-objective function optimum points are also shown. The results of optimum designs based on three objective functions are presented in Table 5 and are compared to an existing HRSG. The optimum value of the gas-side velocity may be found by trade-off between capital cost and the pressure drop. The thermodynamic objective function in which the capital cost is not taken into account, may not be used to �nd an optimum value for the gasside velocity and as can be seen the optimum value base on this objective function is on the boarder of the interval. Fig. 6 compares exergetic ef �ciencies of components of the HRSG for four different designs. The lowest amount of improvement happened in the evaporator, meaning that the major part of the exergy destruction in the evaporator is inevitable. Table 6 compares different components of the exergy analysis for four designs. The results show increase of the production in all three optimum points with respect to the base case. This improvement is Table 6 Comparison of the values of exergy destructions for components and exergy loss between the base case and various optimization approaches.
Item
Base case
Thermodynamic opt.
Multiobjective opt.
Thermoeconomic opt.
E Deco (kW) E Deva (kW) E Dsh (kW) E L (kW) E P (kW)
22.94 619 24.49 286.05 597.37
19.37 593.49 20.62 237.8 678.7
18.72 595.1 21.87 239.3 675
18.49 605.8 22.09 239.5 664.12
due to decrease in the pinch point in all the three designs with respect to the existing design as presented in the Table 5. In references [2,3], pinch point temperatures for evaporators with bare tubes are suggested to be 70 C. This is due to the need to achieve an economical thermal area with a reasonable pressure drop. As can be seen in Fig. 7, most of the costs in the thermoeconomic function are related to the thermal losses. By decreasing the pinch point temperature to 6.26 C correspond to thermoeconomic optimum point at the expense of increasing the capital costs and reduction of power production of the turbine, more heat is recovered and annual costs of the heat loss have signi�cantly reduced. At the same time, by optimizing other thermal variables of the HRSG, the lowest thermal surface area is obtained for this pinch point. Fig. 7 compares different components of the economic analysis of the HRSG for four designs. As can be seen, the thermodynamic optimization doesn t lead to major improvement of the total cost of the HRSG as compared to the base case. The results show using multi-objective optimization improves the cost of the work loss in the HRSG as compared to the thermoeconomic optimization. This improvement is obtained by decreasing the gas-side velocity (Table 5) via increasing the capital cost. Table 5 shows that the optimum designs are obtained mostly by improvements in design variables of the evaporator. This is due to the fact that thermal variables in the economizer and the superheater have considerably lower effects on the � nal cost. ’
8. Conclusion
In this paper, a �re tube HSRG is successfully optimized. Two different objective functions were suggested. The �rst one is sum of the exergy destruction and exergy loss and the second objective function is sum of the capital cost and energy loss in term of money. Finally, a multi-objective optimization is carried out in order to �nd optimum values of the design variables. Three optimum points based on three objective functions were compared and discussed. The results show that the design base on the thermodynamic objective function is not capable to �nd optimum values for the gas-side velocity. This design doesn t improve the total cost of the HRSG with respect to the existing design due to increase in the capital cost. The thermoeconomic and multi-objective functions are capable to � nd optimum values for all of decision variables. The results of economic analysis shows that during the life time of an HRSG, fuel expenses constitute the major part of its costs. This show that the pinch point suggested in existing references is higher than the optimum value. It was also found that costs involving pressure drop in an HRSG also have a considerable amount. The ’
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results of multi-objective optimization decrease the pressure loss via increasing capital cost of the HRSG as compared to thermoeconomic optimization. In all three designs, the major optimization is due to change in design variables of the evaporator. In this type of optimization, variables moved towards reducing the operational costs of the HRSG, by reducing the heat loss. The optimal value of the pinch point based on multi-objective optimization was obtained as 6.26 C. It is evident that while fuel costs increase, manufacturers should move towards a higher heat recovery in � re tube HRSGs. Appendix A
The second step in designing an HRSG is designing its thermal surfaces. In this step, the surface area of the evaporator, economizer and superheater surfaces are determined. In this section, the thermal design of a � re tube HRSG is brie �y explained. A.1. Economizer
G ¼
_ m g ½S T Ao LN w
Ao ¼ do þ 2n f bh f
_ _ m w ðh2 h1 Þ ¼ m g Cp g T g 3 T g 4 ¼ UADT m
(A-1)
A.1.3.2. Non-luminous heat transfer coef �cient. The in�uence of nonluminous heat transfer is negligible at low temperatures. Determining this coef �cient requires the use of very accurate charts which are given in [12]. A.1.4. Gas-side pressure drop The pressure drop of the gas moving through economizer tubes is: DP g
¼
ð f þ aÞG2 N H 500r g
AT 1 þ þ h f ho Aw
do do ln di 2K m
AT þ ff o Ai
þ ff i
(A-2)
where AT , AW , and A i are the total area, average area and the tubes wall area and h f is the � n ef �ciency.
’
A.1.2. Convective heat transfer coef �cient inside tube The convective heat transfer coef �cient inside tubes is calculated via DittuseBoelter relationship [17].
hC ¼ 110:9u0:8
f ¼ C 2 C 4 C 6
F 1 ¼
C P
0:4
m
do þ 2h f do
F 1 d1i :8
(A-3)
K 0:6
(A-4)
A.2.2. Pressure drop of the gas-side The pressure drop of the gas �ow inside evaporator tubes is calculated via:
¼
8:098 104 f ðLe Þu2 rdi
0:316
A.3. Superheater
(A-5)
A.1.3.1. Convective heat transfer coef �cient outside tube. ESCOA equation is used here to determine the convective heat transfer coef �cient outside tube in � nned surfaces.
hC ¼ C 1 C 3 C 5
0:5
0:25
! T g T f
GC p
K mC p
0:67
(A-6)
(A-11)
friction factor for turbulent � ow is:
A.1.3. Heat transfer coef �cient outside tube (gas-side) The heat transfer coef �cient outside tube has two terms of convection and radiation.
do þ 2h f do
(A-10)
A.2.1. Heat transfer coef �cients inside and outside tube The heat transfer coef �cient inside tube of the tube (gas-side) contains two parts of convective heat transfer coef �cient and radiative heat transfer coef �cient. The heat transfer coef �cient inside tube is calculated using (A-3), whereas the thermophysical properties of the gas should be in the equation. Proper values of the water side heat transfer coef �cient are given in [2].
f ¼
A.2. Evaporator
Where u is the mass � ow rate of water in each tube and d i is the tube inner diameter.
ho ¼ hN þ hC
Coef �cients C 1 to C 6 are given in [2].
DP g
(A-9)
In �re tube evaporators, the hot gas �ows in the tubes. heat transfer coef �cients inside and outside tube are required to calculate the overall heat transfer coef �cient.
A.1.1. Overall heat transfer coef �cient
A T hi Ai
(A-8)
Where b is the �n thickness, h f is the �n height, n f is the �n density, G is the mass velocity of gas, and A o is the obstruction area [3].
’
The friction factor for in-line arrangement is:
Economizers are used to preheat the inlet water of the HRSG s evaporator and usually contain �nned surfaces. After the thermal balance and obtaining heat transfer coef �cients and calculating the Log-mean temperature difference, the area of the evaporator can be calculated [3].
1 ¼ U o
(A-7)
Re0:25
(A-12)
Thermal design of the superheater is similar to the evaporator, except that the convective heat transfer coef �cient is calculated as follows: A.3.1. Convective heat transfer coef �cient outside tube There are a variety of methods for obtaining convective heat transfer coef �cient outside tubes of the superheater. One of the suitable methods for obtaining Nusselt number is using Grimson equation:
Nu ¼ BReN ¼
hC d o K
(A-13)
A. Behbahani-nia et al. / Applied Thermal Engineering 30 (2010) 2378e 2385
Coef �cients N and B are given in [3] for bare tubes and for in-line and staggered arrangements. A.3.2. Pressure drop of the gas �ow in the superheater
DP g
¼
fG2 N H 495:69r g
(A-14)
The friction factor ( f g ) is obtained using the following relationship for a in-line arrangement and 2000 < Re < 40000:
"
f g ¼ Re0:15 0:044 þ
0:08ðS T =do Þ ðS L = do 1Þð0:43þ1:13do =S L Þ
#
(A-15)
References [1] Bernaed F. Kolanowski, Small-scale Cogeneration Handbook. Marcell Dekker Inc, New York, 2003. [2] V. Ganapathy, Industrial Boilers and Heat Recovery Steam Generators. Design, Applications and Calculations, Marcel Dekker, Inc, 2003. [3] V. Ganapathy, Waste Heat Boiler Deskbook. Fairmont press, India, 1991. [4] C.J. Butcher, B.V. Reddy, Second law analysis of a waste heat recovery based power generation system. International Journal of Heat and Mass Transfer 50 (2007) 2355e2363.
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[5] B.V. Reddy, G. Ramkiran, K. Ashok Kumar, P.K. Nag, Second law analysis of a waste heat recovery steam generator. International Journal of Heat and Mass Transfer 45 (2002) 1807e1814. [6] C. Casarosa, A. Franco, Thermodynamic optimization of the operative parameters for the heat recovery in combined power plants. International Journal of Thermodynamics. ISSN: 1301-9724 4 (No.1) (March-2001). ISSN: 1301-9724 43e52. [7] C. Casarosa, F. Donatini, A. Franco, Thermoeconomic optimization of heat recovery steam generators operating parameters for combined plants. Energy 29 (2004) 389e414. [8] Alessandro Franco, Alessandro Russo, Combined cycle plant ef �ciency increase based on the optimization of the heat recovery steam generator operating parameters. International Journal of Thermal Sciences 41 (2002) 843e859. [9] Alessandro Franco, Nicola Giannini, A general method for the optimum design of heat recovery steam generators. Energy 31 (2006) 3342 e3361. [10] Alessandro Franco, Nicola Giannini, Optimum thermal design of modular compact heat exchangers structure for heat recovery steam generators. Applied Thermal Engineering 25 (2005) 1293e1313. [11] M. Mohagheghi, J. Shayegan, Thermodynamic optimization of design variable and heat exchangers layout in HRSGs for CCGT using genetic algorithm. App;ied Thermal Engineering 29 (2009) 290e299. [12] Steven C. stultz, John B. Kitto, Steam, Its Generation and Use, fortieth edition. The Babcock & Wilcox Company, 1992. [13] Adrian Bejan, Gearge Tsatsaronis, Michael Moran, Thermal Design and Optimization. John Wiley&Sons, Canada, 1996. [14] T.J. Kotas, The Exergy Method of Thermal Plant Analysis, fourth ed. Krieger Publishing Company, 1995. [15] Melanie Mitchell, An Introduction to Genetic Algorithms. a bradford book of mit press, 1999, � fth printing. [16] Anthony Giampaolo, Gas Turbine Handbook: Principles and Practices, third ed. Published by The Fairmont Press, Inc, 2006. [17] V. Ganapathy, Applied Heat Transfer. Pennwell Books, Tulsa, 1982.
