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State-of-the-Art of Research on Optimization of Shell and Tube Heat Exchangers by Methods of Evolutionary Computation

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Abstract

This paper presents a comprehensive state-of-the-art review of optimization by evolutionary computation methods of shell and tubes heat exchangers (STHE) of single segmental baffles. It is seen that the heat transfer coefficient to the shell side is calculated by the Kern method or by the Bell Delaware method, and that the pressure drop to the shell side is calculated by the Kern method or by the Bell Delaware method or by the Peters and Timmershaus method. It is verified the use of evolutionary computation algorithms in single-objective and multiobjective optimization of STHE, and that most related work used the total cost function of STHE. And among the contributions presented, there were implementations and applications of different evolutionary computation algorithms, or study of the STHE optimization problem by different objective functions, such as ecological, entransy dissipation, field synergy, and cost of the life cycle. Also, it was possible to verify some gaps in the work related to STHE optimization, among them, can be cited the need for greater application of decision-making methods that relate technical, economic and managerial aspects applied to the solution of the STHE. And it is suggested for future work the development of the STHE model subject to delimited uncertainties; and the formalization of a standard STHE optimization problem, so that it can serve as a reference for comparing the different optimization algorithms, and applying metrics to evaluate the advantages that are obtained when using a new algorithm for the same problem.

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Abbreviations

ABC:

Artificial bee colony

ACO:

Ant colony optimization

ARGA:

Adaptive range genetic algorithm

BA:

Bat algorithm

BBO:

Biogeography-based algorithm

BSA:

Backtracking search algorithm

BF:

Brute force

CC:

Capital cost

CEGA:

Controlled elitist genetic algorithm

CI:

Cohort intelligence

CSA:

Cuckoo search algorithm

CSO:

Civilized swarm optimization

DE:

Differential evolution

DEACO:

Differential evolution and ant colony optimization

EA:

Evolutionary algorithms

EDNFF:

Entransy dissipation number to fluid friction

EDNHC:

Entransy dissipation number to heat conduction

EI:

Economic index

E-JA:

Elitist-Jaya algorithm

ENI:

Environmental index

FA:

Firefly algorithm

FOA:

Falcon optimization algorithm

GA:

Genetic algorithm

GSA:

Gravitational search algorithm

HSA:

Harmony search algorithm

ICA:

Imperialist competitive algorithm

ITHS:

Intelligent tuned harmony search

I-ITHS:

Improved intelligent tuned harmony search

JA:

Jaya algorithm

LCC:

Life cycle cost

MCS:

Monte Carlo simulation

MOO:

Multiobjective optimization

MOPSO:

Multi-objective particle swarm optimization

MTLBO:

Modified teaching–learning-based optimization algorithm

NSGA II:

Non-dominated sorting genetic algorithm II

NR:

Not reported

OC:

Operating cost

PP:

Predador prey

PROMETHEE:

Preference ranking organization method for enrichment evaluations

PSO:

Particle swarm optimization

QPSO:

Quantum particle swarm optimization

QPSOZ:

Quantum particle swarm optimization combined with Zaslavskii chaotic map sequences

SA:

Simulated annealing

SCA:

Sine–cosine algorithm

SCAOCE:

Sum of annual operating cost and exergetic cost

SI:

Sustainability index

SOI:

Social index

SOO:

Single-objective optimization

SSFSN:

Shell side field synergy number

STHE:

Shell and tube heat exchanger

TC:

Total cost

TDE:

Tsallis differential evolution

TEDN:

Total entransy dissipation number

TEMA:

Tubular Exchanger Manufacturers Association

TOPSIS:

Technique for order performance by similarity to the ideal solution

A :

Area, or cross flow area (m\(^2\))

a :

Tube layout

AA :

First term of the Bhatti and Shah correlation

BB :

Second term of the Bhatti and Shah correlation, this factor multiplies the Reynolds number of the flow inside the tubes

bc :

Baffle cut (%)

cc :

Dittus-Bolter correlation constant

CL :

Tube layout constant

CTP :

Tube count constant

d :

Diameter (m)

D :

Diameter (m)

esp :

Wall thickness of the tubes (m)

f :

Friction factor in the flow in the shell

FF :

Correction factor for logarithmic mean temperature difference

FQPT :

Pressure drop factor in the tubes

G :

Fluid mass velocity based on the minimum free area (kg/m\(^2\) s)

h :

Heat transfer coefficient (W/m\(^2\) K)

k :

Thermal conductivity of fluid (W/m K)

L :

Spacing or length (m)

\(\dot{m}\) :

Mass flow rate (kg/s)

N :

Number of sealing strips or number of tubes or number of baffles

np :

Number of passes

Nu:

Nusselt number

P :

Pitch (m) or pumping power (W)

Pr:

Prandtl number

Q :

Heat transfer rate (W)

Re:

Reynolds number

v :

Flow velocity (m/s)

\(\delta\) :

Clearance (m)

\(\Delta P\) :

Pressure drop (Pa)

\(\varepsilon\) :

Effectiveness

\(\theta\) :

Angle between two radii intersected at the inside shell wall with the baffle cut (radians)

\(\phi\) :

Viscosity correction factor.

\(\rho\) :

Density (kg/m\(^3\))

\(\sigma\) :

Ratio of minimum free flow area to frontal area

b :

Baffles

e :

Equivalent

i :

Inside the tube

o :

Outside the tube

p :

Pattern

s :

Shell side

t :

Tubes side

otl :

Tube bundle

ss :

Sealing strips

s, t :

Shell side and tubes side

\(c_1\) :

Empirical coefficient

\(f_{alocat}\) :

Fluid allocation

\(f_{ss}\) :

Friction factor

\(E_{E}'\) :

Ecological (W)

\(k_c\) :

Contraction loss coefficient at tube entrance

\(k_e\) :

Expansion loss coefficient at tube outlet

\(I_s\) :

Area increment

\(j_{hs}\) :

Thermal factor

\(m_1\) :

Empirical coefficient

\(r_d\) :

Fouling factor \((\hbox {m}^{2}\,^{\circ }\hbox {C}/\hbox {W})\)

\(R_{fall}\) :

Allowed fouling resistance \((\hbox {m}^2\,^{\circ }\hbox {C}/\hbox {W})\)

\(sh_{types}\) :

Shell head types

\(T_{c,o}\) :

Cold side fluid output temperature \((^{\circ }\hbox {C})\)

\(t_{mat}\) :

Tube material

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Acknowledgements

”This study was financed in part by the Coordenação de Aperfeiçãoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001”.

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Authors and Affiliations

  1. Department of Mechanical Engineering, PUC-MG, Belo Horizonte, Brasil

    Wagner Henrique Saldanha & Felipe Raul Ponce Arrieta

  2. IBMEC - Belo Horizonte, 300 Rio Grande do Norte Street, Funcionários, Belo Horizonte, MG, 30.130-130, Brasil

    Felipe Raul Ponce Arrieta

  3. Department of Electrical Engineering, PUC-MG, Belo Horizonte, Brasil

    Gustavo Luís Soares

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  1. Wagner Henrique Saldanha
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  3. Gustavo Luís Soares
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Appendix: Variables related to STHE optimization problems

Appendix: Variables related to STHE optimization problems

The variables used in the related works are presented in Tables 9 and 10, they are: tube layout pattern (\(a_p\)), number of passes (np), length of the tubes (\(L_t\)), wall thickness of the tubes (esp), outer diameter of the tubes (\(d_o\)), inner diameter of tubes (\(d_i\)), baffle spacing (\(L_b\)), baffle cut (bc), tube-to-baffle diametrical clearance (\(\delta _{tb}\)), shell-to-baffle diametrical clearance (\(\delta _{sb}\)), inner diameter of the shell (\(D_s\)), outer diameter of the tube bundle (\(D_{otl}\)), tube pitch (\(P_t\)), number of tubes (\(N_{t}\)), number of baffles (\(N_b\)), number of sealing strips (\(N_{ss}\)), cold side fluid output temperature (\(T_{c,o}\)), angle between two radii intersected at the inside shell wall with the baffle cut (\(\theta _{b}\)), allowed fouling resistance (\(R_{fall}\)), tube material (\(t_{mat}\)), shell head types (\(sh_{types}\)), fluid allocation (\(f_{alocat}\)).

Table 9 Variables related to the main optimization problems of STHE—part 1
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Table 10 Variables related to the main optimization problems of STHE—part 2
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Saldanha, W.H., Arrieta, F.R.P. & Soares, G.L. State-of-the-Art of Research on Optimization of Shell and Tube Heat Exchangers by Methods of Evolutionary Computation. Arch Computat Methods Eng 28, 2761–2783 (2021). https://doi.org/10.1007/s11831-020-09476-4

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