research article dynamic time-delay characteristics and

Research ArticleDynamic Time-Delay Characteristics and StructuralOptimization Design of Marine Gas Turbine Intercooler

Ning-bo Zhao1 Xue-you Wen12 and Shu-ying Li1

1 College of Power and Energy Engineering Harbin Engineering University Harbin 150001 China2Harbin Marine Boiler and Turbine Research Institute Harbin 150078 China

Correspondence should be addressed to Ning-bo Zhao zhaoningbo314126com

Received 14 June 2014 Revised 29 July 2014 Accepted 31 July 2014 Published 28 August 2014

Academic Editor Gongnan Xie

Copyright copy 2014 Ning-bo Zhao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Aiming at the rapid mobility of marine gas turbine and the dynamic time-delay problem of intercooler for intercooled cycle marinegas turbine the dynamic simulation model of intercooler was set up based on effectiveness-number of transfer units (120576-NTU)and lumped parameter method in this paper The model comprehensively considers related physical properties dependent ontemperature Dynamic response characteristics of gas outlet temperature and pressure and coolant outlet temperature of intercoolerwith different materials and coolants in the change of operation condition of marine gas turbine were analyzed in detail Besidesthis paper explored the use of simulated annealing algorithm for structural optimization of intercooler The results showed thatboth material and coolant were the significant factors that affected the heat transfer and dynamic performance of intercooler Theheat transfer and dynamic performance of the intercooler obtained by using simulated annealing algorithm were better than thoseof preliminary design

1 Introduction

In recent years high-power (more than 25MW) marinegas turbine has aroused the attention of every country[1] Intercooled (IC) cycle or intercooled regenerated (ICR)cycle technology is a feasible method to develop high-power marine gas turbine which may represent a majordevelopment tendency for a new generation of marine mainpropulsion plants [2] The successful application of WR-21 marine gas turbine further verified the feasibility andeffectiveness of intercooled regenerated cycle technology toincrease engine power for marine gas turbine [3]

As an important part of intercooled or intercooled regen-erated cycle marine gas turbine intercooler will directlyinfluence the performance of engine The existence of inter-cooler can aggravate the time-delay characteristics of fluidflow and heat transfer which make it difficult to match thethermodynamic parameters and develop appropriate controlstrategies for gas turbine system and then may influence themaneuverability performance of ship

In the past half century many scholars have carried outextensive research from different aspects and made someachievements of both theory and practice about intercooledor intercooled regenerated cycle gas turbine The researchactivitiesmainly focused on intercooled or intercooled regen-erated cycle gas turbine performance analysis [4ndash10] numeri-cal simulation on flow and heat transfer of intercooler [11ndash13]and thermodynamic design and optimization of intercooledsystem [14ndash16] Li et al [4ndash6] studied the dynamic behav-iors and flow parameters optimization of intercooled cyclemarine gas turbine based on simulationmethodThrough thesimulation study of fuel supply rate they obtained the bestfuel supply rate curve of intercooled cycle marine gas turbineBased on the finite time thermodynamic theory the powerand efficiency of an open or closed cycle intercooled gasturbine power plant were analyzed and optimized by adjust-ing the low pressure compressor inlet relative pressure dropthe mass flow rate and the distribution of pressure lossesalong the flow path by Wang et al [7ndash10] According to theactual operation condition of intercooled system for a certain

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 701843 14 pageshttpdxdoiorg1011552014701843

2 Mathematical Problems in Engineering

intercooled cyclemarine gas turbine Dong et al [11ndash13]madea preliminary thermodynamic analysis and design by usingeffectiveness-number of transfer units (120576-NTU) method andanalyzed the influence of intercooler structural parametersand coolant parameters on the steady-state performance ofintercooler On the base of structure features of plain finrectangular channels they also investigated the coupled char-acteristics of fluid flow and heat transfer by using numericalsimulation approach Through numerical computing Li etal [14] and Dong et al [12] obtained the pressure distri-bution temperature distribution and velocity distributionof intercooler entire flow path which provided beneficialreference to design and apply intercooler Xiao [15] discussedthe effects of intercooler structure parameters on its flow andheat transfer performance based on effectiveness-numberof transfer units (120576-NTU) method Then they analyzed thedynamic performance and thermal inertia of intercoolerunder varying operation conditions Their research resultsshowed that intercooler had the obvious thermal inertiacharacteristics which could directly affect the accuracy andreliability of the control system Besides Zhang [16] estab-lished the dynamic simulation model by using the lumpedparameter method and analyzed the dynamic response ofgas outlet temperature of intercooler under varying operationconditionsTheir conclusions were consistent with the resultsthat have been reported in literature [15] They also foundthat heat exchanger weight had a significant influence on thedynamic performance of intercooler

From the literatures described above very few studieshave been performed on the thorough discussion of relevantfactors that could affect the dynamic time-delay character-istics of intercooler There were also very few studies whichdiscussed the structural optimization design of intercoolerusing artificial intelligent algorithm Besides the dynamicsimulation analyses in the existing literatures only consideredthe change of gas inlet temperature of intercooler whichbelonged to the single variable perturbation analysis How-ever all the gas inlet temperature pressure andmass flow rateof intercooler will change in practical applicationsThereforeit is meaningful to study the dynamic behaviors of intercoolerwith multivariable perturbation

The objectives of this study are to investigate the flowand heat transfer coupling dynamic time-delay problem andstructural optimization design of intercooler for intercooledcycle marine gas turbine In this study the dynamic simula-tion model of intercooler is modeled based on effectiveness-number of transfer units (120576-NTU) and lumped parame-ter method In order to improve the modeling accuracytemperature dependent thermophysical properties are takeninto account due to large temperature differences in theintercooler Then three different types of substrate materials(copper alumina and copper-nickel alloy) and two differentcoolants (water and ethylene glycol) are considered to investi-gate the effect of substrate materials and coolants on dynamicperformance of intercooler in detail Finally a simulatedannealing (SA) algorithm based optimization technique forintercooler will be developed which minimizes the totalweight of intercooler under given space and performancerestrictions

Low pressurecompressor

High pressure High pressurecompressor

Combustionchamber

On-engineintercooler

Off-engineintercooler

Air inlet

turbine

turbine

turbineLow pressure

Power

Exhaust

Figure 1 Principle diagram of intercooled cycle marine gas turbine

2 Intercooler Problem Descriptionand Thermodynamic Model

21 Problem Description of Intercooled System As the keycomponent intercooled system is located between the lowpressure compressor and high pressure compressor Theintercooler system lowers the high pressure compressor inlettemperature which can reduce the power consumption ofhigh pressure compressor and increase the power output ofthe whole marine gas turbine system

The principle diagram of intercooled cycle marine gasturbine is shown in Figure 1 Intercooler system is com-posed of two parts namely on-engine intercooler (plate-fin heat exchanger) and off-engine intercooler (plate heatexchanger)Theon-engine intercooler is designed to decreasethe temperature of the pressurized gas coming out of the lowpressure compressor Then the coolant passes through off-engine intercooler which transfers heat from the coolant tothe seawater in order to reduce the temperature of coolantCompared with off-engine intercooler on-engine intercooleris more important for marine gas turbine because it has adirect influence on the gas turbine performance

According to the requirements of intercooled cycle threeperformance parameters should be considered for on-engineintercooler (1) Reasonable pressure drop of the fluid (espe-cially for gas) including the pressure drop of inlet channelscore part and outlet channels When the pressure drop ofgas is too high it will give an additional burden on thehigh pressure compressor to keep a constant pressure ratiowhichmeansmore fuel consumption (2) Reasonable thermalefficiency of intercooler which can effectively lower outlettemperature of gas under given space (3) Reasonable weightof intercooler There may have a greater thermal inertiawhen the weight is heavier Therefore how to realize theoptimization design of high efficiency compact intercooler isone of the important problems for intercooled system

Due to the complexity in the structure of the intercoolerthe detailed information of the fluid flow and heat transferin intercooler can scarcely be described Different substratematerials and coolants have different heat transfer perfor-mance which can influence the flow and heat transfer perfor-mance of intercooler So the effects of different materials and

Mathematical Problems in Engineering 3

L1L2

L3

Gas(fluid a)

Coolant

(fluid b)

Figure 2 Schematic representation of reverse flow plate-fin inter-cooler

120575p

H Sf tf

120575s

Figure 3 Detailed view of straight fin

coolants on dynamic performance of intercooler are worthstudying in detail

22 Thermal Modeling of Intercooler Figures 2 and 3 depicta schematic view of a reverse flow plate-fin intercoolerwith straight fins and the basic geometric structure of finsrespectively The following assumptions will be used for theanalysis

(1) The number of fin layers for the gas side (119873119886) is

assumed to be one more than the coolant side (119873119887)

That is119873119886= 119873119887+ 1

(2) Intercooler works in a steady-state condition(3) The thickness of all the fins is assumed uniform and

the thermal resistance can be negligible because thethickness is too small

(4) All the parts are made of same material(5) The influences of fouling and corrosion are neglected

In this study since the output temperature of the fluidsis unspecified the 120576-NTU method is used to assess the flowand heat transfer performance of intercooler in the modelingprocessThe effectiveness of reverse flow plate-fin intercooleris proposed as

120576 =

1 minus exp [minusNTU (1 minus Cr)]1 minus Cr exp [minusNTU (1 minus Cr)]

(1)

where Cr = 119862min119862max is heat capacity ratio NTU is thenumber of transfer units Considering the thermal resistanceof the walls NTU can be determined by

1

NTU=

119862min119880119860

1

119880119860

=

1

120578ef119886ℎ119886119860119886+

120575119901

120582119901119860119901

+

1

120578ef119887ℎ119887119860119887

(2)

Generally the flow state of fluids can affect the convectiveheat transfer coefficient For the fluids in the fully developedturbulent flow and transition region the heat transfer coeffi-cient is calculated in terms of Gnielinski [18] which is givenas

ℎ =

Nu120582119863

(3)

Nusselt number and hydraulic diameter can be calculatedas follows

Nu =(1198912) (Reminus1000)Pr

1 + 127(1198912)05

(Pr23 minus 1)

119863 =

2 (119867 minus 119905119891) (119878119891minus 119905119891)

119867 + 119878119891minus 2119905119891

(4)

Reynolds number and Prandtl number are defined asbelow

Re =120588119906119863

120583

Pr =119862119901120583

120582

(5)

And the Fanning factor 119891 is given as

119891 =

1

(158 ln Reminus328)2 (6)

For the fluids in the fully developed laminar flow the heattransfer coefficient is calculated in terms of Colburn factor[19 20] which is given as

ℎ =

119895119866119862119901

Pr23 (7)

Mass flow velocity can be obtained as follows

119866 =

119882

119860ff (8)

The Fanning factor 119891 and Colburn factor 119895 are given as

119891 = exp [0106566(ln Re)2 minus 212158 (ln Re) + 582505]

119895 = exp [0103109(ln Re)2 minus 191091 (ln Re) + 3211] (9)


In this study the effective circulation area for the two sidesis formulated as

119860ff119886 =119873119886(1198712 minus 2120575

119904) (119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886)

119878119891119886

119860ff119887 =119873119887(1198712 minus 2120575

119904) (119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887)

119878119891119887

(10)

The heat transfer areas of intercooler for the two sides arecalculated by

119860119886= 21198731198861198711 (1198712 minus 2120575

119904) [1 +

(119867119886minus 2119905119891119886)

119878119891119886

]

119860119887= 21198731198871198711 (1198712 minus 2120575

119904) [1 +

(119867119887minus 2119905119891119887)

119878119891119887

]

(11)

Heat transfer efficiencies of heat transfer surface for thetwo sides are obtained by

120578ef119886 =(119878119891119886minus 119905119891119886) + 120578119891119886(119867119886minus 119905119891119886)

119878119891119886+ 119867119886minus 2119905119891119886

120578ef119887 =(119878119891119887minus 119905119891119887) + 120578119891119887(119867119887minus 119905119891119887)

119878119891119887+ 119867119887minus 2119905119891119887

(12)

Heat transfer efficiencies of fin for the two sides areformulated as

120578119891119886=

tan (05119898119886119867119886)

05119898119886119867119886

120578119891119887=

tan (05119898119887119867119887)

05119898119887119867119887

(13)

Fin factors for the two sides are defined as follows

119898119886= radic

2ℎ119886

120582119891119886119905119891119886

119898119887= radic

2ℎ119887

120582119891119887119905119891119887

(14)

Therefore the effective heat transfer area for the two sidescan be calculated by

119860ef119886 = 21198731198861198711 (1198712 minus 2120575119904) [(119878119891119886minus 119905119891119886) + 120578119891119886(119867119886minus 119905119891119886)

119878119891119886

]


119878119891119887

]

(15)

Heat transfer rate is obtained as follows

119876 = 120576119862min (119879in119886 minus 119879in119887) (16)

To simplify the computation this study only considers thepressure drop of inlet channels core part and outlet channelsThe total pressure drops for every side are defined as below

Δ119875 = Δ1198751minus Δ1198752+ Δ1198753 (17)

whereΔ1198751is the pressure drop caused by the change of cross-

sectional area from the deflector outlet to fin inlet Δ1198752is the

pressure drop caused by the change of cross-sectional areafrom fin inlet to deflector outlet Δ119875

3consists of two pressure

drops namely frictional pressure drops and pressure dropscaused by change of channel areaThey can be determined asfollows

Δ1198751=

1198662

2120588in(1 minus 120572

2

+ 119870in)

Δ1198752=

1198662

2120588out(1 minus 120572

2

minus 119870out)

Δ1198753=

1198662

2120588in[2(

120588in120588out

minus 1) + (

41198911198711

119863

)

120588in120588

]

(18)

where 119870in and 119870out are empirical coefficient and can beobtained from literature [21] 120588 is the average density of fluidswhich is calculated by

120588 =

120588in + 120588out2

(19)

Therefore the pressure drop loss rate of fluids for the twosides is obtained by

120574119886=

Δ119875119886

119875in119886

120574119887=

Δ119875119887

119875in119887

(20)

23 Dynamic Simulation Modeling of Intercooler Thedynamic time-delay of intercooler is one important factorthat influences the maneuverability of marine gas turbineConsidering the operation characteristics of intercooler inpractical application lumped parameter model is used toconstruct the dynamic simulation model of intercooler Thefollowing assumptions will be used for the analysis

(1) The inside flow of fin channel is simplified as the onedimension and the velocity of fluids is uniform in thesame section

(2) The temperature of metal wall varies along with thedirection of fluids flow and the radial temperaturedifference of metal wall is neglected

(3) The heat capacity of gas is neglected compared withthat of metal wall

Considering the above assumptions the mass conserva-tion equations for the two sides can be given as

119882in119886 = 119882out119886

119882in119887 = 119882out119887(21)


And the energy conservation equations for the two sidesare formulated as

119881119886

119889

119889119905

(120588119898119886119862119901119898119886

119879119898119886)

= 119882in119886119862119901in119886119879in119886 minus119882out119886119862119901out119886119879out119886

minus ℎ119886119860ef119886 (119879119898119886 minus 119879119908)

119881119887

119889

119889119905

(120588119898119887119862119901119898119887

119879119898119887)


+ ℎ119887119860ef119887 (119879119908 minus 119879119898119887)

(22)

where 119879119898119886

and 119879119898119887

are the average temperature for the twosides and are calculated by

119879119898119886=

119879in119886 + 119879out119886

2

119879119898119887=

119879in119887 + 119879out119887

2

(23)

The channel volumes for the two sides are obtained by

119881119886=

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

119881119887=

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

(24)

The temperature of metal wall is obtained as follows

119872119908119862119901119908

119889

119889119905

119879119908= ℎ119886119860ef119886 [119879119898119886 minus 119879119908] minus ℎ119887119860ef119887 [119879119908 minus 119879119898119887]

(25)

In order to further raise the precision of simulation themodel considers related physical properties dependent ontemperature

3 Dynamic Performance Analysis andDiscussions for Intercooler

Based on effectiveness-number of transfer units (120576-NTU) andlumped parameter method mentioned earlier the dynamicsimulation model of intercooler is established by computersimulation software MATLABSIMULINK which can beseen in Figure 4

31 Model Validation In order to verify the correctness andvalidity of the simulation model established in this paper acase study taken from the work of Wen is considered [17]The straight fin is used on the gas and coolant side Thepreliminary structure of the intercooler is shown in Table 1Table 2 lists the inlet parameters of gas under different gasturbine operation conditions Water is chosen as the coolantand its inlet temperature and mass flow are assumed to be

Table 1 Preliminary structure of the intercooler [17]

Parameters ValuesNumber of gas side fin layers119873

11988636

Fin pitch of gas side 119878119891119886

(m) 14 times 10minus3

Plate pitch of gas side119867119886(m) 62 times 10minus3

Fin thickness of gas side 119905119891119886


Number of coolant side fin layers119873119887

35Fin pitch of coolant side 119878

119891119887(m) 14 times 10minus3

Plate pitch of coolant side119867119887(m) 3 times 10minus3

Fin thickness of coolant side 119905119891119887


Side plate thickness 120575sp (m) 16 times 10minus3

Plate thickness 120575119901(m) 5 times 10minus4

Seal thickness 120575119904(m) 6 times 10minus3

Intercooler length 1198711 (m) 035Intercooler width 1198712 (m) 04266

Table 2 The inlet parameters of gas under different gas turbineoperation conditions [17]

Operationconditions

Inlet pressure(Pa)

Inlet temperature(∘C)

Inlet massflow (kgs)

100 302963 15525 729385 288460 14945 685270 277647 14355 641058 258919 13545 573647 240192 12735 506335 221464 11925 438917 170000 10725 3290

Table 3 Thermophysical parameters of different materials

Material typeThermal

conductivity(WmsdotK)

Specific heatcapacity(JkgsdotK)

Density(kgm3)

Copper-nickel alloy 385 380 8890Copper 401 386 8960Aluminum 237 897 2700

constant under different gas turbine operation conditionswhich are 20∘C and 200 kgs respectively The intercooleris made of copper-nickel alloy Some useful thermophysicalparameters of copper-nickel alloy are mentioned in Table 3

Figures 5 6 and 7 show the comparisons of the simulationresults in this paper with the thermodynamic calculationand numerical simulation results that have been reported inliterature [17] From Figures 5ndash7 it is obvious that the outlettemperature and pressure drop loss rate of gas and outlettemperature of coolant obtained by using the simulationmodel (variable properties) are basically consistent withthe thermodynamic calculation results reported in literature[17] The maximum deviation of pressure drop loss rateof gas is about 08 between simulation model (variableproperties) and thermodynamic calculationmethod In otherwords the simulation model (variable properties) can be


2

1

3

5

4

1

3

2

On

Sys

Tcool in

Tcool out

Tcool in

Gcool in

Gcool in

Pair in

Pair inPair out

Pair out

Pair in

Tair in

Tair in

Tair in

Tair outGair in

Gair in

Gair in

Tair out

Tair out

Tcool out

Tcool out

Tcool in

Gcool in

Figure 4 Dynamic simulation model of intercooler

considered correct and feasible The simulation results alsoshow that both the outlet temperatures of gas and coolantcan decrease when the operation conditions of gas turbineare reduced In addition the analysis and comparisons ofthe results demonstrate that the pressure drop loss rate ofgas obtained by using the numerical simulation method islower than that calculated by using other two methods atsome operation conditions The reason is that only the flowresistance loss of gas side is considered during the numericalsimulation processes Comparing the results obtained by twosimulation models in this paper with those of literature [17]we also can conclude that the simulation model (variableproperties) is more accurate and appropriate Moreoverthe convergence speed can be significantly improved whenconsidering the influence of temperature on thermal physicalproperty parameters Therefore the simulation model (vari-able properties) is used to analyze and discuss the dynamicperformance of intercooler in the following section

32 Material Effects on Dynamic Performance Material isone of the important factors which affect the structural

strength and heat transfer performance of intercooler Inthe following analysis we will focus on investigating theeffects of different material on dynamic performance ofintercooler The geometric dimensions of the intercooler andthe thermophysical properties of materials (copper-nickelalloy copper and aluminum) studied here are listed inTables 1 and 3 Water is chosen as the coolant and its inlettemperature and mass flow are assumed to be constant underdifferent gas turbine operation conditions which are 20∘Cand 200 kgs respectively For the gas turbine the operationcondition linearly changes from 35 to 70 in 5 secondsand the related inlet operation parameters of gas are given inTable 2

The dynamic response curve of the outlet temperatureand pressure of gas and the outlet temperature of coolantwith different materials in the change of operation conditionof gas turbine are shown in Figures 8 9 and 10 It may beclearly observed in Figures 8ndash10 that the outlet temperaturesof gas and coolant change obviously in the previous stagesand their gradients become smaller over time for allmaterialsThe thermal inertia characteristic of intercooler is so obviousthat it is necessary to consider the effect of intercooler on


20 40 60 80 10020

25

30

35

40

45

50

Operation condition ()

Numberical simulation results [17]Thermodynamic calculation results [17]Simulation results in this paper (variable properties)Simulation results in this paper (constant properties)

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)

Figure 5 Comparisons of simulation outlet temperature of gas withthe results reported in literature [17]

20 40 60 80 100

40

36

32

28

24

20

Pres

sure

dro

p lo

ss ra

te o

f gas

()



Figure 6 Comparisons of simulation pressure drop loss rate of gaswith the results reported in literature [17]

the thermodynamic performance of gas turbine In additiona careful inspection of Figures 8ndash10 reveals that intercoolermade of copper or aluminum has the better heat transferperformance than that made of copper-nickel alloy Andthe intercooler made of copper has the best heat transferperformance since it has the highest thermal conductivityHowever the dynamic response time of intercooler made ofaluminum is the shortest as compared with the intercoolermade of the other types of materials This is due to the factthat aluminum has the lowest density The larger the value

20 40 60 80 10022

24

26

28

30

32

34



Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)

Figure 7 Comparisons of simulation outlet temperature of coolantwith the results reported in literature [17]

Time (s)

AluminumCopper

Copper-nickel alloy

40

36

32

28

240 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)

Figure 8 Dynamic response curve of the outlet temperature of gaswith different materials

of density is the longer the dynamic response time of theintercooler will be From Table 3 it can be seen that the threematerials ordered by decreasing density are (1) copper (2)copper-nickel alloy and (3) aluminum These suggest thatthe weight of intercooler is the important factor on affectingthe thermal inertia of intercooler which is consistent withthe result of the other literatures [16] Additionally the outletpressure of gas is less affected by materials and there isno obvious flow time delay characteristic because gas has ahigher velocity

To sumupmaterial is a significant factorwhich affects theheat transfer and dynamic performance of intercooler From


210

220

230

240

250

260

270

280

Time (s)0 10 20 30 40 50 60 70 80

Pou

ta(k

Pa)

Out

let p

ress

ure o

f gas

AluminumCopper

Copper-nickel alloy

Figure 9 Dynamic response curve of the outlet pressure of gas withdifferent materials

24

25

26

27

28

29

30

AluminumCopper

Copper-nickel alloy

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)

Figure 10 Dynamic response curve of the outlet temperature ofcoolant with different materials

the point of view of heat transfer performance and dynamictime-delay characteristics aluminum has a slightly betterperformance than the other materials However consideringthe application environment copper-nickel alloy is oftenused as the material of intercooler because it has goodanticorrosion and excellent strength

33 Coolant Effects on Dynamic Performance Although thecopper-nickel alloy has good anticorrosion and excellentstrength its heat transfer performance is relatively poorand dynamic delay response time is longer than the othermaterials Therefore it is very important to improve the heattransfer and dynamic performance of intercooler from otheraspects

Coolant seems to be another crucial factor in determiningthe heat transfer and dynamic performance of intercoolerAs the most common and cheap coolant water freezes ata low temperature which can lead to intercooler failure Inorder to solve this problem ethylene glycol mixed with waterin different volume percentages is typically used to lowerthe aqueous freezing point of the heat transfer medium inthe practical industrial applications [22] Ethylene glycol andwater (EGwater) can withstand low temperatures down tominus60∘C [23] However it can cause an erosive action on theintercooler which causes fouling and affects the heat transferperformance of intercooler Besides this fluidmixture is toxicso that it is a potential danger for staff

In the following analysis we are interested in investigatingthe effects of different coolants on dynamic performanceof intercooler Water and EGwater (50 50 by mass) arechosen as the coolant and the inlet temperature and massflow of two coolants are assumed to be constant underdifferent gas turbine operation conditions which are 20∘Cand 200 kgs respectively The properties of two coolantsat different temperature are available in ASHRAE [24] Theintercooler ismade of copper-nickel alloy For the gas turbinethe operation condition linearly changes from 35 to 70 in5 seconds and the related inlet operation parameters of gasare given in Table 2

Figures 11 12 and 13 show the dynamic response curveof the outlet temperature and pressure of gas and the outlettemperature of coolant with different coolants in the changeof operation condition of gas turbine From Figures 11ndash13it is easy to see that the intercooler has better heat transferperformance and smaller thermal inertia when water isused as coolant The outlet temperature and dynamic delayresponse time of gas obtained by using water as coolantcan reduce about 3∘C and 15 seconds respectively comparedwith those obtained by using EGwater as coolant The mainreason may come from the fact that water has higher heatcapacity and thermal conductivity and lower viscosity thanEGwater In other words the coolants with higher thermalconductivity and heat capacity but lower viscosity showbetterheat transfer performance and thermal inertia Meanwhilethe results also show that the dynamic delay response timeof gas is shorter than that of every coolant This is due tothe fact that coolants have higher heat capacity and thermalconductivity Additionally the outlet pressure of gas is lessaffected by coolants and there is no obvious flow time delaycharacteristic

These findings suggest that all the applied conditions ofcoolants corrosion resistant properties of materials and theflow heat transfer performance requirements of intercoolershould be considered when selecting the coolants for inter-cooler

4 Optimal Design of Intercooler Based onSimulated Annealing Algorithm

The design of intercooler involves a large number of geo-metric and operating variables that need to meet the flowand heat transfer performance requirement under some


28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)

Figure 11 Dynamic response curve of the outlet temperature of gaswith different coolants

210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)

Figure 12Dynamic response curve of the outlet pressure of gaswithdifferent materials

constraints [15] The conventional optimization methodsbecome very cumbersome and laborious to solve the opti-mization problem In recent times some nontraditionalprobabilistic search algorithms namely genetic algorithm(GA) [25ndash27] particle swarm optimization (PSO) algorithm[28] and harmony search (HS) algorithm [20] have beenapplied to the optimization of various heat exchangersWang et al [25] presented the GA for the optimizationof microturbine recuperators from technical and economicstandpoints and discussed the solution strategies under twodifferent fitness functions Their results showed that GA

24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)


has good global search capability to realize the compactdesign of recuperators However GA is not very effective forthe local search space problem Compared with GA PSOalgorithm has the ability of memory But PSO algorithmhas a shortcoming of converging prematurely after gettingtrapped into some local optima and considers it to be theglobal optima Besides the acceleration constants and inertiaweight should be given reasonably since they are employedto control the exploration abilities of the swarm and affectthe convergence behavior When PSO algorithm is appliedto a multidimensional complex problem scenario it becomesnearly impossible to get out from that local optima and reachout for the global optima due to some constraints Moreoverthe evolutionary algorithms such as GA PSO algorithm andHS algorithm cannot deal with the constraints directly andmany constraint handling methods should be employed tohelp the optimization process [20]

As previously mentioned it is a constraints optimizationproblem for the structure optimization design of intercoolerThe penalty function method is often used to transferconstrained condition into unconstrained condition [20 26]which may affect the optimization results As a stochasticoptimization technique simulated annealing algorithm wasfirst put forward by Metropolis in 1953 and it was employedto seek an optimal combination byKirkpatrick et al until 1983[29] This algorithm simulates the thermodynamic processof slow cooling of molten metals to achieve the minimumfunction value in an optimization problem so it has beenwidely used in solving sophisticated optimization problems[30] Compared with GA and PSO algorithm SA algorithmcan hinder the premature convergence to the local optimaand diverge the particles using its strong ability of localsearch


Start

Initialize parameters

Randomly select initial

Randomly select new

Calculate the function

Accept the new solution and update

the best solution

Finish iteration

Finish terminationconditions

Drop temperature slowly

Yes No

Accept the new Yes

No

Yes

No

Yes

No

Output the best solution

solution X = Xo

solution X998400

value Δf = f(X998400) minus f(X)

Δf le 0

X = X998400 Xlowast = X998400

solution X = X998400

Exp(minusΔfT) gt R(0 1)

T0 and Tf

Figure 14 Flowchart of simulated annealing algorithm applied forthe optimization of intercooler

41 Simulated Annealing Algorithm For the following opti-mization problem the basic optimization process based onsimulated annealing algorithm is shown in Figure 14

min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)

where119891(119883) is the objective function 119892119894(119883) and ℎ

119895(119883) are the

constraint equations and equilibrium equations respectivelyFromFigure 14 we can see that simulated annealing algo-

rithm mainly includes two circle processes inner and outercircle processes The purpose of the outer circle processes isto decrease annealing temperature In every iteration of innercircle processes the new solution is obtained and evaluatedby the Metropolis criterion to determine whether the newsolution will be accepted or not The following shows thedetails of the basic optimization processes

Step 1 Set initial temperature 119879 = 1198790(1198790gt 0) cooling rate

V and final temperature 119879119891

Step 2 Randomly select initial solution 119883 and the approxi-mation of the optimal solution119883lowast from all possible solutions119883 = 119883

lowast

= 1198830

Step 3 Randomly select disturbance to obtain the newsolution1198831015840 from the sets of all possible neighbors of119883

Step 4 Calculate the function value 119891(119883) and 119891(1198831015840) byobjective function respectively Δ119891 = 119891(1198831015840) minus 119891(119883)

Step 5 If Δ119891 le 0 then the new solution is accepted andthe approximation of the optimal solution is updated 119883 =

1198831015840 119883lowast = 1198831015840

Step 6 If Δ119891 gt 0 randomly select 119877 from uniformdistribution on the interval (0 1) If 119875(Δ119891) = exp(minusΔ119891119879) gt119877(0 1) then the new solution is accepted but it is a worsesolution 119883 = 119883

1015840 Or else the current solution remainsunchanged

Step 7 Repeat the above Steps 3ndash6 until loop iteration stepsmeet the requirements

Step 8 Check termination criterion and output the optimalsolution

Simulated annealing algorithm uses the cooling processand the Metropolis algorithm to control the search processso this algorithm can leap from the local minimum duringthe search and handle any type of variable easily includingnoncontinuous functions and nondifferential functions [29]

42 Objective Function Optimization Variables and Con-straints The results reported in literature [16] showed thatthe weight of intercooler is an important factor to affect itsthermal inertiaWith the increase of theweight of intercoolerthe thermal inertia increases rapidly Therefore the totalweight of intercooler is selected as the optimal objectivefunction in this study

min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)

When putting all the relevant values the above equationcan be simplified and expressed as

min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)

Considering the basic assumptions mentioned abovethe plate pitches for the two sides fin pitch fin thicknessintercooler length intercooler width and numbers of finlayers for gas side are taken as the optimization variables in


Table 4 Variation ranges of design parameters and performanceconstraints of intercooler

Parameters Minimum MaximumNumber of gas side fin layers119873

11988630 40


(m) 15 times 10minus3 3 times 10minus3

Plate pitch of gas side119867119886(m) 4 times 10minus3 7 times 10minus3



Plate pitch of coolant side119867119887(m) 2 times 10minus3 45 times 10minus3

Intercooler length 1198711 (m) 031 038Intercooler width 1198712 (m) 0400 0500Effectiveness 120576 () 85Pressure drop loss rate of gas side 120574

119886() 5

this study All the above optimization variables are consideredas structural constraints which are expressed as

st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)

In order to achieve the design requirements the heattransfer efficiency required of intercooler and the pressuredrop loss rate of gas are considered as the performanceconstraints which can be given as follows

st 1198928 (119883) 997904rArr 120576 ge 120576min1198929(119883) 997904rArr 120574

119886le 120574119886max

(30)

43 Optimal Design Results of Intercooler This sectionexplores the use of simulated annealing (SA) algorithmfor structure optimization of intercooler and discusses theeffects of structure optimization on dynamic performance ofintercooler The intercooler is made of copper-nickel alloyWater is chosen as the coolant and the inlet temperature andmass flow of two coolants are assumed to be constant underdifferent gas turbine operation conditions which are 20∘Cand 200 kgs respectively Gas turbine operates in a 100condition

In this study the seven design variables such as the platepitches for the two sides fin pitch fin thickness intercoolerlength intercooler width and numbers of fin layers for gasside are selected as the optimization variables All variablesare continuous except the number of gas side layersThe otherstructural parameters of intercooler such as plate thicknessseal thickness and side plate thickness are considered to beconstant as listed in Table 1 and are not to be optimizedThe variation ranges of the design variables and performanceconstraints of intercooler have been mentioned in Table 4

Figure 15 shows the effectiveness convergence diagramas objective function A significant decrease in the objec-tive function has been observed in the beginning of theevaluation process after 100 iterations After approximate6000 iterations the changes in the objective function become

0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400

Number of iterations

Wei

ght o

f int

erco

oler

(kg)

Figure 15 Evolution process for minimum weight based on simu-lated annealing algorithm

Table 5 The structure comparisons of preliminary design andsimulated annealing algorithm

Parameters Preliminarydesign

Optimaldesign

Number of gas side fin layers119873119886 36 37







Intercooler length 1198711 (m) 0350 03222Intercooler width 1198712 (m) 04266 04045

Table 6 The performance comparisons of preliminary design andsimulated annealing algorithm


Optimaldesign

Effectiveness 120576 () 8497 8704Pressure drop loss rate of gas side 120574

119886() 317 362

Weight119872119908(kg) 139145 113987

relatively low Finally the minimum weight of intercooleris found after 7000 iterations with the value of 113987 kgTables 5 and 6 show the preliminary design of intercoolerand optimum structure which are obtained from simulatedannealing algorithm The increment of 207 has beenobserved in efficiency of intercooler by optimization methodin comparisonwith preliminary design Besides theweight ofintercooler has decreased from 139145 kg to 113987 kg whilethe pressure drop loss rate of gas side has increased from317 to 362

The dynamic response curve of the outlet temperatureand pressure of gas and outlet temperature of coolantwith different intercoolers (preliminary design and optimumstructure) in the linear change of operation condition of gas


26

28

30

32

34

36

38

Preliminary designOptimal design

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)

Figure 16 Dynamic response curve of the outlet temperature of gaswith different intercoolers

210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)

Figure 17Dynamic response curve of the outlet pressure of gaswithdifferent intercoolers

turbine from 35 to 70 in 5 seconds are shown in Figures16 17 and 18 From Figures 16ndash18 it is clear that the inter-cooler optimized by simulated annealing algorithmhas betterheat transfer performance and smaller thermal inertia Theoutlet temperature of gas obtained by simulated annealingalgorithm can reduce about 3∘C compared with that obtainedby preliminary design The dynamic delay response timesof gas and coolant sides of preliminary intercooler are 115seconds and 20 seconds longer than those obtained by thesimulated annealing algorithm These findings suggest thatoptimal design based on artificial intelligence algorithm isavailable and necessary to realize the high compact design of

24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)

Figure 18 Dynamic response curve of the outlet temperature ofcoolant with different intercoolers

intercooler which can further affect the overall performanceof intercooled cycle marine gas turbine

5 Conclusions

This study studied the dynamic time-delay characteristics ofmarine gas turbine intercooler and showed the successfulusage of the simulated annealing (SA) algorithm in theoptimal design of intercooler On the basis of the workpresented in this study the following conclusions could bemade A generalized simulation model was developed tocarry out the dynamic performance analysis of intercoolerbased on the effectiveness-number of transfer units andlumped parametermethodThe analytical results of an exam-ple showed that the simulation model (variable properties)established in this study was correct and feasible The effectsof substrate materials and coolants on the dynamic time-delay characteristics of intercooler were analyzed in detailThe results showed that both material and coolant were thesignificant factors that affected the heat transfer and dynamicperformance of intercooler For all materials and coolantsgas side had a slightly smaller thermal inertia than liquidside When other conditions were constant better thermalperformance and smaller thermal inertia were noted forthe materials with higher thermal conductivity and lowerdensity than that for the material with lower thermal con-ductivity and higher density Besides the coolant with higherthermal conductivity and specific heat but lower viscositywas beneficial to improve the heat transfer performanceand thermal conductivity of intercooler However the outletpressure of gas was less affected by materials and coolantsand there was no obvious flow time-delay characteristicThe present study demonstrated successful application ofsimulated annealing technique for the structure optimizationof intercooler considering minimum weight as objective


functions The improvement of heat transfer and dynamicperformance was observed for intercooler obtained by usingsimulated annealing algorithm compared with preliminarilydesign showing the improvement potential of the artificialintelligent technique for intercooler optimization

Notation

119860 Heat transfer surface area (m2)119860ef Effective heat transfer area (m2)119860ff Free flow area (m2)119862 Heat capacity rate (WK)Cr 119862min119862max119862119901 Specific heat (JkgsdotK)

119863 Hydraulic diameter (m)119891 Fanning friction factor119891(119883) Objective function119892(119883) Constraint function119866 Mass flow velocity (kgm2sdots)ℎ Convective heat transfer coefficient (Wm2sdotK)ℎ(119883) Balance function119867 Plate pitch (m)119895 Colburn factor119870 Drag coefficient of channel1198711 Heat exchanger length (m)1198712 Heat exchanger width (m)1198713 Heat exchanger height (m)119872 Weight (kg)119898 Fin parameters factor119873 Number of fin layersNTU Number of transfer unitsNu Nusselt number119875 Pressure (Pa)Pr Prandtl number119876 Heat duty (W)Re Reynolds number119878119891 Fin pitch (m)

119879 Temperature (∘C)119905119891 Fin thickness (m)

119880 Overall heat transfer coefficient (Wm2sdotK)119906 Flow velocity (ms)119881 Volume (m3)V Cooling rate (∘Cs)119882 Mass flow rate (kgs)

Greek Letters

120578ef Effective heat transfer surface efficiency120578119891 Heat transfer efficiency of fin

120575 Thickness (m)120582 Thermal conductivity (WmsdotK)120583 Viscosity (Nm2sdots)120588 Density (kgm3)120576 Effectiveness120572 The ratio of channel free flow area and cross-sectional

area120574 Pressure drop loss rate

Subscripts

119886 Gas119887 Coolant119901 Plate119904 Sealsp Side plate119908 Wallin Inletout Outletmax Maximummin Minimum

Conflict of Interests

The authors declared that there is no conflict of interestsregarding the publication of this paper

References

[1] X Y Wen and D M Xiao ldquoFeasibility study of an intercooled-cycle marine gas turbinerdquo Journal of Engineering for GasTurbines and Power vol 130 no 2 Article ID 022201 2008

[2] X Y Wen and D M Xiao ldquoA new concept concerning thedevelopment of high-power marine gas turbinesrdquo Ship Scienceand Technology vol 29 no 4 pp 17ndash21 2007 (Chinese)

[3] S B Shepard T L Bowen and J M Chiprich ldquoDesignand development of the WR-21 intercooled recuperated (ICR)marine gas turbinerdquo Journal of Engineering for Gas Turbines andPower vol 117 no 3 pp 557ndash562 1995

[4] S Y Li Z T Wang J Q Wang and P P Luo ldquoSimulation studyon fuel supply rate curve of marine inter-cooled gas turbinerdquoShip Engineering vol 32 no 5 pp 15ndash18 2010 (Chinese)

[5] Y L Ying Y P Cao and S Y Li ldquoResearch on fuel supplyrate of marine intercooled-cycle engine based on simulationexperimentrdquo International Journal of Computer Applications inTechnology vol 47 no 4 pp 212ndash221 2013

[6] Y L Ying Y P Cao S Y Li and Z T Wang ldquoStudy onflowparameters optimisation formarine gas turbine intercoolersystem based on simulation experimentrdquo International Journalof Computer Applications in Technology vol 47 no 1 pp 56ndash672013

[7] W H Wang L G Chen and F R Sun ldquoPower optimization ofa real closed intercooled regenerated gas turbine cyclerdquo ChineseJournal ofMechanical Engineering vol 41 no 4 pp 55ndash58 2005

[8] W H Wang L G Chen F R Sun and C Wu ldquoPerformanceoptimisation of open cycle intercooled gas turbine powerplant with pressure drop irreversibilitiesrdquo Journal of the EnergyInstitute vol 81 no 1 pp 31ndash37 2008

[9] W H Wang L G Chen and F R Sun ldquoThermodynamicoptimization of a triple-shaft open intercooled recuperated gasturbine cycle Part 1 description and modelingrdquo InternationalJournal of Low-Carbon Technologies 2013

[10] W H Wang L G Chen and F R Sun ldquoThermodynamicoptimization of a triple-shaft open intercooled recuperatedgas turbine cycle Part 2 power and efficiency optimizationrdquoInternational Journal of Low-Carbon Technologies 2013

[11] C ZWen andW Dong ldquoNumerical simulation of heat transferand fluid flow on marine gas turbine intercoolerrdquo Journal ofAerospace Power vol 25 no 3 pp 654ndash658 2010


[12] W Dong C Mao J J Zhu and Y Chen ldquoNumerical andexperimental analysis of inlet non-uniformity influence onintercooler performancerdquo in Proceeding of the ASME TurboExpo 2012 Turbine Technical Conference and Exposition (GT12) pp 349ndash357 Copenhagen Denmark June 2012

[13] P Gao and W Dong ldquoOptimal analysis of flow parameters formarine gas turbine intercoolerrdquo Aeroengine vol 37 no 4 pp29ndash32 2011 (Chinese)

[14] Z Li H B Zhang X Y Wen and D M Xiao ldquoNumericalsimulation of an intercooler for a complex-cycle Marine gasturbinerdquo Journal of Engineering for Thermal Energy and Powervol 23 no 2 pp 148ndash152 2008 (Chinese)

[15] X XiaoThe optimization design modeling and control of the gasturbine intercooler [MS thesis] Shanghai Jiao Tong University2013 (Chinese)

[16] S K Zhang Simulation research on performance of marineintercooled cycle gas turbine [MS thesis] China Ship Researchand Development Academy 2012 (Chinese)

[17] C Z Wen Design and study on intercooling heat exchanger ofmarine gas turbine [MS thesis] Shanghai Jiao Tong University2009 (Chinese)

[18] V Gnielinski ldquoNew equations for heat and mass transfer inturbulent pipe and channel flow (Neue Gleichungen fur denWarmemdashund den Stoffubergang in turbulent durchstromtenRohren und Kanalen)rdquo Forschung im Ingenieurwesen vol 41no 1 pp 8ndash16 1975

[19] H Peng and X Ling ldquoOptimal design approach for the plate-finheat exchangers using neural networks cooperated with geneticalgorithmsrdquo Applied Thermal Engineering vol 28 no 5-6 pp642ndash650 2008

[20] M Yousefi R Enayatifar A N Darus and A H AbdullahldquoOptimization of plate-fin heat exchangers by an improvedharmony search algorithmrdquo Applied Thermal Engineering vol50 no 1 pp 877ndash885 2013

[21] S HWang Plate-FinHeat Exchanger Chemical Industry PressBeijing China 1984 (Chinese)

[22] F C McQuiston J D Parker and J D Spitler HeatingVentilating and Air Conditioning JohnWiley amp Sons NewYorkNY USA 2000

[23] P K Namburu D K Das K M Tanguturi and R SVajjha ldquoNumerical study of turbulent flow and heat transfercharacteristics of nanofluids considering variable propertiesrdquoInternational Journal ofThermal Sciences vol 48 no 2 pp 290ndash302 2009

[24] ASHRAE Handbook Fundamentals American Society of Heat-ing Refrigerating and Air-Conditioning Engineers AtlantaGa USA 2005

[25] Q W Wang H X Liang G N Xie M Zeng L Q Luo and ZP Feng ldquoGenetic algorithm optimization for primary surfacesrecuperator of microturbinerdquo Journal of Engineering for GasTurbines and Power vol 129 no 2 pp 436ndash442 2007

[26] G N Xie B Sunden and Q W Wang ldquoOptimization ofcompact heat exchangers by a genetic algorithmrdquo AppliedThermal Engineering vol 28 no 8-9 pp 895ndash906 2008

[27] L Gosselin M Tye-Gingras and F Mathieu-Potvin ldquoReviewof utilization of genetic algorithms in heat transfer problemsrdquoInternational Journal of Heat and Mass Transfer vol 52 no 9-10 pp 2169ndash2188 2009

[28] R V Rao and V K Patel ldquoThermodynamic optimization ofcross flow plate-fin heat exchanger using a particle swarm opti-mization algorithmrdquo International Journal of Thermal Sciencesvol 49 no 9 pp 1712ndash1721 2010

[29] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[30] J M Reneaume and N Niclout ldquoPlate fin heat exchangerdesign using simulated annealingrdquo Computer Aided ChemicalEngineering vol 9 pp 481ndash486 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


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Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


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Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


intercooled cyclemarine gas turbine Dong et al [11ndash13]madea preliminary thermodynamic analysis and design by usingeffectiveness-number of transfer units (120576-NTU) method andanalyzed the influence of intercooler structural parametersand coolant parameters on the steady-state performance ofintercooler On the base of structure features of plain finrectangular channels they also investigated the coupled char-acteristics of fluid flow and heat transfer by using numericalsimulation approach Through numerical computing Li etal [14] and Dong et al [12] obtained the pressure distri-bution temperature distribution and velocity distributionof intercooler entire flow path which provided beneficialreference to design and apply intercooler Xiao [15] discussedthe effects of intercooler structure parameters on its flow andheat transfer performance based on effectiveness-numberof transfer units (120576-NTU) method Then they analyzed thedynamic performance and thermal inertia of intercoolerunder varying operation conditions Their research resultsshowed that intercooler had the obvious thermal inertiacharacteristics which could directly affect the accuracy andreliability of the control system Besides Zhang [16] estab-lished the dynamic simulation model by using the lumpedparameter method and analyzed the dynamic response ofgas outlet temperature of intercooler under varying operationconditionsTheir conclusions were consistent with the resultsthat have been reported in literature [15] They also foundthat heat exchanger weight had a significant influence on thedynamic performance of intercooler

From the literatures described above very few studieshave been performed on the thorough discussion of relevantfactors that could affect the dynamic time-delay character-istics of intercooler There were also very few studies whichdiscussed the structural optimization design of intercoolerusing artificial intelligent algorithm Besides the dynamicsimulation analyses in the existing literatures only consideredthe change of gas inlet temperature of intercooler whichbelonged to the single variable perturbation analysis How-ever all the gas inlet temperature pressure andmass flow rateof intercooler will change in practical applicationsThereforeit is meaningful to study the dynamic behaviors of intercoolerwith multivariable perturbation

The objectives of this study are to investigate the flowand heat transfer coupling dynamic time-delay problem andstructural optimization design of intercooler for intercooledcycle marine gas turbine In this study the dynamic simula-tion model of intercooler is modeled based on effectiveness-number of transfer units (120576-NTU) and lumped parame-ter method In order to improve the modeling accuracytemperature dependent thermophysical properties are takeninto account due to large temperature differences in theintercooler Then three different types of substrate materials(copper alumina and copper-nickel alloy) and two differentcoolants (water and ethylene glycol) are considered to investi-gate the effect of substrate materials and coolants on dynamicperformance of intercooler in detail Finally a simulatedannealing (SA) algorithm based optimization technique forintercooler will be developed which minimizes the totalweight of intercooler under given space and performancerestrictions

Low pressurecompressor

High pressure High pressurecompressor

Combustionchamber

On-engineintercooler

Off-engineintercooler

Air inlet

turbine

turbine

turbineLow pressure

Power

Exhaust

Figure 1 Principle diagram of intercooled cycle marine gas turbine

2 Intercooler Problem Descriptionand Thermodynamic Model

21 Problem Description of Intercooled System As the keycomponent intercooled system is located between the lowpressure compressor and high pressure compressor Theintercooler system lowers the high pressure compressor inlettemperature which can reduce the power consumption ofhigh pressure compressor and increase the power output ofthe whole marine gas turbine system

The principle diagram of intercooled cycle marine gasturbine is shown in Figure 1 Intercooler system is com-posed of two parts namely on-engine intercooler (plate-fin heat exchanger) and off-engine intercooler (plate heatexchanger)Theon-engine intercooler is designed to decreasethe temperature of the pressurized gas coming out of the lowpressure compressor Then the coolant passes through off-engine intercooler which transfers heat from the coolant tothe seawater in order to reduce the temperature of coolantCompared with off-engine intercooler on-engine intercooleris more important for marine gas turbine because it has adirect influence on the gas turbine performance

According to the requirements of intercooled cycle threeperformance parameters should be considered for on-engineintercooler (1) Reasonable pressure drop of the fluid (espe-cially for gas) including the pressure drop of inlet channelscore part and outlet channels When the pressure drop ofgas is too high it will give an additional burden on thehigh pressure compressor to keep a constant pressure ratiowhichmeansmore fuel consumption (2) Reasonable thermalefficiency of intercooler which can effectively lower outlettemperature of gas under given space (3) Reasonable weightof intercooler There may have a greater thermal inertiawhen the weight is heavier Therefore how to realize theoptimization design of high efficiency compact intercooler isone of the important problems for intercooled system

Due to the complexity in the structure of the intercoolerthe detailed information of the fluid flow and heat transferin intercooler can scarcely be described Different substratematerials and coolants have different heat transfer perfor-mance which can influence the flow and heat transfer perfor-mance of intercooler So the effects of different materials and


L1L2

L3

Gas(fluid a)

Coolant

(fluid b)


120575p

H Sf tf

120575s






That is119873119886= 119873119887+ 1





120576 =


(1)


1

NTU=

119862min119880119860

1

119880119860

=

1

120578ef119886ℎ119886119860119886+

120575119901

120582119901119860119901

+

1

120578ef119887ℎ119887119860119887

(2)


ℎ =

Nu120582119863

(3)


Nu =(1198912) (Reminus1000)Pr

1 + 127(1198912)05

(Pr23 minus 1)

119863 =

2 (119867 minus 119905119891) (119878119891minus 119905119891)

119867 + 119878119891minus 2119905119891

(4)


Re =120588119906119863

120583

Pr =119862119901120583

120582

(5)


119891 =

1

(158 ln Reminus328)2 (6)


ℎ =

119895119866119862119901

Pr23 (7)


119866 =

119882

119860ff (8)






119860ff119886 =119873119886(1198712 minus 2120575

119904) (119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886)

119878119891119886

119860ff119887 =119873119887(1198712 minus 2120575

119904) (119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887)

119878119891119887

(10)


119860119886= 21198731198861198711 (1198712 minus 2120575

119904) [1 +

(119867119886minus 2119905119891119886)

119878119891119886

]

119860119887= 21198731198871198711 (1198712 minus 2120575

119904) [1 +

(119867119887minus 2119905119891119887)

119878119891119887

]

(11)


120578ef119886 =(119878119891119886minus 119905119891119886) + 120578119891119886(119867119886minus 119905119891119886)

119878119891119886+ 119867119886minus 2119905119891119886

120578ef119887 =(119878119891119887minus 119905119891119887) + 120578119891119887(119867119887minus 119905119891119887)

119878119891119887+ 119867119887minus 2119905119891119887

(12)


120578119891119886=

tan (05119898119886119867119886)

05119898119886119867119886

120578119891119887=

tan (05119898119887119867119887)

05119898119887119867119887

(13)


119898119886= radic

2ℎ119886

120582119891119886119905119891119886

119898119887= radic

2ℎ119887

120582119891119887119905119891119887

(14)



119878119891119886

]


119878119891119887

]

(15)


119876 = 120576119862min (119879in119886 minus 119879in119887) (16)


Δ119875 = Δ1198751minus Δ1198752+ Δ1198753 (17)






Δ1198751=

1198662

2120588in(1 minus 120572

2

+ 119870in)

Δ1198752=

1198662

2120588out(1 minus 120572

2

minus 119870out)

Δ1198753=

1198662

2120588in[2(

120588in120588out

minus 1) + (

41198911198711

119863

)

120588in120588

]

(18)


120588 =

120588in + 120588out2

(19)


120574119886=

Δ119875119886

119875in119886

120574119887=

Δ119875119887

119875in119887

(20)






119882in119886 = 119882out119886

119882in119887 = 119882out119887(21)



119881119886

119889

119889119905

(120588119898119886119862119901119898119886

119879119898119886)


minus ℎ119886119860ef119886 (119879119898119886 minus 119879119908)

119881119887

119889

119889119905

(120588119898119887119862119901119898119887

119879119898119887)


+ ℎ119887119860ef119887 (119879119908 minus 119879119898119887)

(22)

where 119879119898119886

and 119879119898119887


119879119898119886=

119879in119886 + 119879out119886

2

119879119898119887=

119879in119887 + 119879out119887

2

(23)


119881119886=

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

119881119887=

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

(24)


119872119908119862119901119908

119889

119889119905


(25)







11988636








119891119887(m) 14 times 10minus3









Operationconditions

Inlet pressure(Pa)



100 302963 15525 729385 288460 14945 685270 277647 14355 641058 258919 13545 573647 240192 12735 506335 221464 11925 438917 170000 10725 3290





Density(kgm3)





2

1

3

5

4

1

3

2

On

Sys

Tcool in

Tcool out

Tcool in

Gcool in

Gcool in

Pair in

Pair inPair out

Pair out

Pair in

Tair in

Tair in

Tair in

Tair outGair in

Gair in

Gair in

Tair out

Tair out

Tcool out

Tcool out

Tcool in

Gcool in







20 40 60 80 10020

25

30

35

40

45

50



Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


20 40 60 80 100

40

36

32

28

24

20

Pres

sure

dro

p lo

ss ra

te o

f gas

()





20 40 60 80 10022

24

26

28

30

32

34



Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)


Time (s)

AluminumCopper

Copper-nickel alloy

40

36

32

28

240 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)





210

220

230

240

250

260

270

280

Time (s)0 10 20 30 40 50 60 70 80

Pou

ta(k

Pa)

Out

let p

ress

ure o

f gas

AluminumCopper

Copper-nickel alloy


24

25

26

27

28

29

30

AluminumCopper

Copper-nickel alloy

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)











28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)



24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)





Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










L1L2

L3

Gas(fluid a)

Coolant

(fluid b)


120575p

H Sf tf

120575s






That is119873119886= 119873119887+ 1





120576 =


(1)


1

NTU=

119862min119880119860

1

119880119860

=

1

120578ef119886ℎ119886119860119886+

120575119901

120582119901119860119901

+

1

120578ef119887ℎ119887119860119887

(2)


ℎ =

Nu120582119863

(3)


Nu =(1198912) (Reminus1000)Pr

1 + 127(1198912)05

(Pr23 minus 1)

119863 =

2 (119867 minus 119905119891) (119878119891minus 119905119891)

119867 + 119878119891minus 2119905119891

(4)


Re =120588119906119863

120583

Pr =119862119901120583

120582

(5)


119891 =

1

(158 ln Reminus328)2 (6)


ℎ =

119895119866119862119901

Pr23 (7)


119866 =

119882

119860ff (8)






119860ff119886 =119873119886(1198712 minus 2120575

119904) (119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886)

119878119891119886

119860ff119887 =119873119887(1198712 minus 2120575

119904) (119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887)

119878119891119887

(10)


119860119886= 21198731198861198711 (1198712 minus 2120575

119904) [1 +

(119867119886minus 2119905119891119886)

119878119891119886

]

119860119887= 21198731198871198711 (1198712 minus 2120575

119904) [1 +

(119867119887minus 2119905119891119887)

119878119891119887

]

(11)


120578ef119886 =(119878119891119886minus 119905119891119886) + 120578119891119886(119867119886minus 119905119891119886)

119878119891119886+ 119867119886minus 2119905119891119886

120578ef119887 =(119878119891119887minus 119905119891119887) + 120578119891119887(119867119887minus 119905119891119887)

119878119891119887+ 119867119887minus 2119905119891119887

(12)


120578119891119886=

tan (05119898119886119867119886)

05119898119886119867119886

120578119891119887=

tan (05119898119887119867119887)

05119898119887119867119887

(13)


119898119886= radic

2ℎ119886

120582119891119886119905119891119886

119898119887= radic

2ℎ119887

120582119891119887119905119891119887

(14)



119878119891119886

]


119878119891119887

]

(15)


119876 = 120576119862min (119879in119886 minus 119879in119887) (16)


Δ119875 = Δ1198751minus Δ1198752+ Δ1198753 (17)






Δ1198751=

1198662

2120588in(1 minus 120572

2

+ 119870in)

Δ1198752=

1198662

2120588out(1 minus 120572

2

minus 119870out)

Δ1198753=

1198662

2120588in[2(

120588in120588out

minus 1) + (

41198911198711

119863

)

120588in120588

]

(18)


120588 =

120588in + 120588out2

(19)


120574119886=

Δ119875119886

119875in119886

120574119887=

Δ119875119887

119875in119887

(20)






119882in119886 = 119882out119886

119882in119887 = 119882out119887(21)



119881119886

119889

119889119905

(120588119898119886119862119901119898119886

119879119898119886)


minus ℎ119886119860ef119886 (119879119898119886 minus 119879119908)

119881119887

119889

119889119905

(120588119898119887119862119901119898119887

119879119898119887)


+ ℎ119887119860ef119887 (119879119908 minus 119879119898119887)

(22)

where 119879119898119886

and 119879119898119887


119879119898119886=

119879in119886 + 119879out119886

2

119879119898119887=

119879in119887 + 119879out119887

2

(23)


119881119886=

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

119881119887=

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

(24)


119872119908119862119901119908

119889

119889119905


(25)







11988636








119891119887(m) 14 times 10minus3









Operationconditions

Inlet pressure(Pa)



100 302963 15525 729385 288460 14945 685270 277647 14355 641058 258919 13545 573647 240192 12735 506335 221464 11925 438917 170000 10725 3290





Density(kgm3)





2

1

3

5

4

1

3

2

On

Sys

Tcool in

Tcool out

Tcool in

Gcool in

Gcool in

Pair in

Pair inPair out

Pair out

Pair in

Tair in

Tair in

Tair in

Tair outGair in

Gair in

Gair in

Tair out

Tair out

Tcool out

Tcool out

Tcool in

Gcool in







20 40 60 80 10020

25

30

35

40

45

50



Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


20 40 60 80 100

40

36

32

28

24

20

Pres

sure

dro

p lo

ss ra

te o

f gas

()





20 40 60 80 10022

24

26

28

30

32

34



Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)


Time (s)

AluminumCopper

Copper-nickel alloy

40

36

32

28

240 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)





210

220

230

240

250

260

270

280

Time (s)0 10 20 30 40 50 60 70 80

Pou

ta(k

Pa)

Out

let p

ress

ure o

f gas

AluminumCopper

Copper-nickel alloy


24

25

26

27

28

29

30

AluminumCopper

Copper-nickel alloy

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)











28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)



24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)





Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119860ff119886 =119873119886(1198712 minus 2120575

119904) (119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886)

119878119891119886

119860ff119887 =119873119887(1198712 minus 2120575

119904) (119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887)

119878119891119887

(10)


119860119886= 21198731198861198711 (1198712 minus 2120575

119904) [1 +

(119867119886minus 2119905119891119886)

119878119891119886

]

119860119887= 21198731198871198711 (1198712 minus 2120575

119904) [1 +

(119867119887minus 2119905119891119887)

119878119891119887

]

(11)


120578ef119886 =(119878119891119886minus 119905119891119886) + 120578119891119886(119867119886minus 119905119891119886)

119878119891119886+ 119867119886minus 2119905119891119886

120578ef119887 =(119878119891119887minus 119905119891119887) + 120578119891119887(119867119887minus 119905119891119887)

119878119891119887+ 119867119887minus 2119905119891119887

(12)


120578119891119886=

tan (05119898119886119867119886)

05119898119886119867119886

120578119891119887=

tan (05119898119887119867119887)

05119898119887119867119887

(13)


119898119886= radic

2ℎ119886

120582119891119886119905119891119886

119898119887= radic

2ℎ119887

120582119891119887119905119891119887

(14)



119878119891119886

]


119878119891119887

]

(15)


119876 = 120576119862min (119879in119886 minus 119879in119887) (16)


Δ119875 = Δ1198751minus Δ1198752+ Δ1198753 (17)






Δ1198751=

1198662

2120588in(1 minus 120572

2

+ 119870in)

Δ1198752=

1198662

2120588out(1 minus 120572

2

minus 119870out)

Δ1198753=

1198662

2120588in[2(

120588in120588out

minus 1) + (

41198911198711

119863

)

120588in120588

]

(18)


120588 =

120588in + 120588out2

(19)


120574119886=

Δ119875119886

119875in119886

120574119887=

Δ119875119887

119875in119887

(20)






119882in119886 = 119882out119886

119882in119887 = 119882out119887(21)



119881119886

119889

119889119905

(120588119898119886119862119901119898119886

119879119898119886)


minus ℎ119886119860ef119886 (119879119898119886 minus 119879119908)

119881119887

119889

119889119905

(120588119898119887119862119901119898119887

119879119898119887)


+ ℎ119887119860ef119887 (119879119908 minus 119879119898119887)

(22)

where 119879119898119886

and 119879119898119887


119879119898119886=

119879in119886 + 119879out119886

2

119879119898119887=

119879in119887 + 119879out119887

2

(23)


119881119886=

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

119881119887=

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

(24)


119872119908119862119901119908

119889

119889119905


(25)







11988636








119891119887(m) 14 times 10minus3









Operationconditions

Inlet pressure(Pa)



100 302963 15525 729385 288460 14945 685270 277647 14355 641058 258919 13545 573647 240192 12735 506335 221464 11925 438917 170000 10725 3290





Density(kgm3)





2

1

3

5

4

1

3

2

On

Sys

Tcool in

Tcool out

Tcool in

Gcool in

Gcool in

Pair in

Pair inPair out

Pair out

Pair in

Tair in

Tair in

Tair in

Tair outGair in

Gair in

Gair in

Tair out

Tair out

Tcool out

Tcool out

Tcool in

Gcool in







20 40 60 80 10020

25

30

35

40

45

50



Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


20 40 60 80 100

40

36

32

28

24

20

Pres

sure

dro

p lo

ss ra

te o

f gas

()





20 40 60 80 10022

24

26

28

30

32

34



Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)


Time (s)

AluminumCopper

Copper-nickel alloy

40

36

32

28

240 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)





210

220

230

240

250

260

270

280

Time (s)0 10 20 30 40 50 60 70 80

Pou

ta(k

Pa)

Out

let p

ress

ure o

f gas

AluminumCopper

Copper-nickel alloy


24

25

26

27

28

29

30

AluminumCopper

Copper-nickel alloy

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)











28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)



24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)





Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119881119886

119889

119889119905

(120588119898119886119862119901119898119886

119879119898119886)


minus ℎ119886119860ef119886 (119879119898119886 minus 119879119908)

119881119887

119889

119889119905

(120588119898119887119862119901119898119887

119879119898119887)


+ ℎ119887119860ef119887 (119879119908 minus 119879119898119887)

(22)

where 119879119898119886

and 119879119898119887


119879119898119886=

119879in119886 + 119879out119886

2

119879119898119887=

119879in119887 + 119879out119887

2

(23)


119881119886=

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

119881119887=

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

(24)


119872119908119862119901119908

119889

119889119905


(25)







11988636








119891119887(m) 14 times 10minus3









Operationconditions

Inlet pressure(Pa)



100 302963 15525 729385 288460 14945 685270 277647 14355 641058 258919 13545 573647 240192 12735 506335 221464 11925 438917 170000 10725 3290





Density(kgm3)





2

1

3

5

4

1

3

2

On

Sys

Tcool in

Tcool out

Tcool in

Gcool in

Gcool in

Pair in

Pair inPair out

Pair out

Pair in

Tair in

Tair in

Tair in

Tair outGair in

Gair in

Gair in

Tair out

Tair out

Tcool out

Tcool out

Tcool in

Gcool in







20 40 60 80 10020

25

30

35

40

45

50



Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


20 40 60 80 100

40

36

32

28

24

20

Pres

sure

dro

p lo

ss ra

te o

f gas

()





20 40 60 80 10022

24

26

28

30

32

34



Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)


Time (s)

AluminumCopper

Copper-nickel alloy

40

36

32

28

240 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)





210

220

230

240

250

260

270

280

Time (s)0 10 20 30 40 50 60 70 80

Pou

ta(k

Pa)

Out

let p

ress

ure o

f gas

AluminumCopper

Copper-nickel alloy


24

25

26

27

28

29

30

AluminumCopper

Copper-nickel alloy

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)











28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)



24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)





Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










2

1

3

5

4

1

3

2

On

Sys

Tcool in

Tcool out

Tcool in

Gcool in

Gcool in

Pair in

Pair inPair out

Pair out

Pair in

Tair in

Tair in

Tair in

Tair outGair in

Gair in

Gair in

Tair out

Tair out

Tcool out

Tcool out

Tcool in

Gcool in







20 40 60 80 10020

25

30

35

40

45

50



Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


20 40 60 80 100

40

36

32

28

24

20

Pres

sure

dro

p lo

ss ra

te o

f gas

()





20 40 60 80 10022

24

26

28

30

32

34



Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)


Time (s)

AluminumCopper

Copper-nickel alloy

40

36

32

28

240 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)





210

220

230

240

250

260

270

280

Time (s)0 10 20 30 40 50 60 70 80

Pou

ta(k

Pa)

Out

let p

ress

ure o

f gas

AluminumCopper

Copper-nickel alloy


24

25

26

27

28

29

30

AluminumCopper

Copper-nickel alloy

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)











28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)



24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)





Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










20 40 60 80 10020

25

30

35

40

45

50



Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


20 40 60 80 100

40

36

32

28

24

20

Pres

sure

dro

p lo

ss ra

te o

f gas

()





20 40 60 80 10022

24

26

28

30

32

34



Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)


Time (s)

AluminumCopper

Copper-nickel alloy

40

36

32

28

240 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)





210

220

230

240

250

260

270

280

Time (s)0 10 20 30 40 50 60 70 80

Pou

ta(k

Pa)

Out

let p

ress

ure o

f gas

AluminumCopper

Copper-nickel alloy


24

25

26

27

28

29

30

AluminumCopper

Copper-nickel alloy

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)











28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)



24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)





Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










210

220

230

240

250

260

270

280

Time (s)0 10 20 30 40 50 60 70 80

Pou

ta(k

Pa)

Out

let p

ress

ure o

f gas

AluminumCopper

Copper-nickel alloy


24

25

26

27

28

29

30

AluminumCopper

Copper-nickel alloy

Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb

(∘C)











28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)



24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)





Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










28

30

32

34

36

38

40

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f gas

Tou

ta

(∘C)


210

220

230

240

250

260

270

280

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let p

ress

ure o

f gas

Pou

ta

(kPa

)



24

26

28

30

32

WaterEGwater

Time (s)0 15 30 45 60 75 90 105

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)





Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Start



Randomly select new



the best solution

Finish iteration



Yes No

Accept the new Yes

No

Yes

No

Yes

No


solution X = Xo

solution X998400


Δf le 0

X = X998400 Xlowast = X998400



T0 and Tf



min 119891 (119883) 119883 = [1199091 1199092 119909

119899]

st 119892119894 (119883) le 0 119894 = 1 2 119898

ℎ119895(119883) = 0 119895 = 1 2 119897

(26)


119895(119883) are the






lowast

= 1198830




1198831015840 119883lowast = 1198831015840







min119872119908= 120588119908(119881 minus 119881

119886minus 119881119887) (27)


min119872119908= 120588119908[11987111198712 (119873

119886119867119886+ 119873119887(119867119887+ 2120575119901) + 2120575sp)

minus

(119867119886minus 119905119891119886) (119878119891119886minus 119905119891119886) 1198711119873

119886(1198712 minus 2120575

119904)

119878119891119886

minus

(119867119887minus 119905119891119887) (119878119891119887minus 119905119891119887) 1198711119873

119887(1198712 minus 2120575

119904)

119878119891119887

]

(28)





11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












11988630 40








119886() 5


st

1198921(119883) 997904rArr 119867

119886min le 119867119886 le 119867119886max1198922(119883) 997904rArr 119867

119887min le 119867119887 le 119867119887max1198923(119883) 997904rArr 119878

119891119886min le 119878119891119886 le 119878119891119886max

1198924(119883) 997904rArr 119905

119891119886min le 119905119891119886 le 119905119891119886max

1198925(119883) 997904rArr 1198711min le 1198711 le 1198711max

1198926(119883) 997904rArr 1198712min le 1198712 le 1198712max

1198927(119883) 997904rArr 119873

119886min le 119873119886 le 119873119886max

(29)



119886le 120574119886max

(30)




0 2000 4000 6000 8000 100001100

1150

1200

1250

1300

1350

1400


Wei

ght o

f int

erco

oler

(kg)




Optimaldesign











Optimaldesign


119886() 317 362

Weight119872119908(kg) 139145 113987




26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










26

28

30

32

34

36

38


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f gas

Tou

ta(∘

C)


210

220

230

240

250

260

270

280


Time (s)0 10 20 30 40 50 60 70 80

Out

let p

ress

ure o

f gas

Pou

ta(k

Pa)



24

25

26

27

28

29

30


Time (s)0 10 20 30 40 50 60 70 80

Out

let t

empe

ratu

re o

f coo

lant

Tou

tb(∘

C)



5 Conclusions




Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Notation





Greek Letters




Subscripts




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article dynamic time-delay characteristics and

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