Pipe bends are inevitable in industrial piping systems, turbomachinery, heat exchangers, etc. Computational fluid dynamics (CFD), which is commonly employed to understand the flow behavior in such systems has very accurate estimation but is computationally cost intensive. Thus, in this paper, an efficient computational approach for such computationally expensive problems is presented. Using genetic programming (GP), metamodels are built using a small number of samples points from the CFD data. These GP metamodels are then shown to be able to replace the actual CFD models with considerable accuracy. The applicability and suitability of the GP metamodels are validated using a variety of statistical metrics on the training as well as independent test data. It is shown that the use of metamodels leads to significant savings in computational cost.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Berger SA, Talbot L, Yao LS (1983) Flow in curved pipes. Annu Rev Fluid Mech 15(1):461–512
Smith FT (1976) Fluid flow into a curved pipe. Proc R Soc Lond A 351(1664):71–87
Rutten F, Schroder W, Meinke M (2005) Large-eddy simulation of low frequency oscillations of the Dean vortices in turbulent pipe bend flows. Phys Fluids 17(3):035107
Bradshaw P (1973) Effects of streamline curvature on turbulent flow, no. AGARD-AG-169. Advisory Group for Aerospace Research and Development, Paris
Goldstein S (1938) Modern developments in fluid mechanics, vol 2. Dover, New York, pp 601–607
Weske JR (1948) Experimental investigation of velocity distributions of downstream of single duct bends, NACA TN-1471, USA
Pruvost J, Legrand J, Legentilhomme P (2004) Numerical investigation of bend and torus flows, part I: effect of swirl motion on flow structure in U-bend. Chem Eng Sci 59(16):3345–3357
Hellstrom F, Fuchs L (2007) Numerical computations of steady and unsteady flow in bended pipes. In: 37th AIAA fluid dynamics conference and exhibit
Babovic V, Canizares R, Jensen HR, Klinting A (2001) Neural networks as routine for error updating of numerical models. J Hydraul Eng 127(3):181–193
Govindaraju RS, Rao AR (2013) Artificial neural networks in hydrology, vol 36. Springer, New York
Malekmohamadi I, Ghiassi R, Yazdanpanah MJ (2008) Wave hindcasting by coupling numerical model and artificial neural networks. Ocean Eng 35(3–4):417–425
Dey S, Mukhopadhyay T, Khodaparast HH, Kerfriden P, Adhikari S (2015) Rotational and ply-level uncertainty in response of composite shallow conical shells. Compos Struct 131:594–605
Dey S, Mukhopadhyay T, Khodaparast HH, Adhikari S (2015) Stochastic natural frequency of composite conical shells. Acta Mech 226:2537–2553
Dey S, Naskar S, Mukhopadhyay T, Gohs U, Spickenheuer A, Bittrich L, Sriramula S, Adhikari S, Heinrich G (2016) Uncertain natural frequency analysis of composite plates including effect of noise—a polynomial neural network approach. Compos Struct 143:130–142
Dey S, Mukhopadhyay T, Khodaparast HH, Adhikari S (2016) A response surface modelling approach for resonance driven reliability based optimization of composite shells. Period Polytech Civil Eng 60:103–111
Kalita K, Nasre P, Dey P, Haldar S (2018) Metamodel based multi-objective design optimization of laminated composite plates. Struct Eng Mech 67:301–310
Ghadai RK, Kalita K, Mondal SC, Swain BP (2018) PECVD process parameter optimization: towards increased hardness of diamond-like carbon thin films. Mater Manuf Process 32:1–9
Chakraborty S, Chattopadhyay PP, Ghosh SK, Datta S (2017) Incorporation of prior knowledge in neural network model for continuous cooling of steel using genetic algorithm. Appl Soft Comput 58:297–306
Dey S, Dey P, Datta S (2017) Design of novel age-hardenable aluminium alloy using evolutionary computation. J Alloy Compd 704:373–381
Khatir Z, Thompson H, Kapur N, Toropov V, Paton J (2013) Multi-objective computational fluid dynamics (CFD) design optimisation in commercial bread-baking. Appl Therm Eng 60(1):480–486
Mehl M, Chen J-Y, Pitz WJ, Sarathy SM, Westbrook CK (2011) An approach for formulating surrogates for gasoline with application toward a reduced surrogate mechanism for CFD engine modeling. Energy Fuels 25(11):5215–5223
Mukhopadhyay T, Chakraborty S, Dey S, Adhikari S, Chowdhury R (2017) A critical assessment of Kriging model variants for high-fidelity uncertainty quantification in dynamics of composite shells. Arch Comput Methods Eng 24(3):495–518
Karsh PK, Mukhopadhyay T, Dey S (2018) Stochastic dynamic analysis of twisted functionally graded plates. Compos B Eng 147:259–278
Dey S, Mukhopadhyay T, Adhikari S (2017) Metamodel based high-fidelity stochastic analysis of composite laminates: a concise review with critical comparative assessment. Compos Struct 171:227–250
Keshtegar B, Mert C, Kisi O (2018) Comparison of four heuristic regression techniques in solar radiation modeling: kriging method vs RSM, MARS and M5 model tree. Renew Sustain Energy Rev 81:330–341
Can B, Heavey C (2012) A comparison of genetic programming and artificial neural networks in metamodeling of discrete-event simulation models. Comput Oper Res 39(2):424–436
Xu C, Rangaiah GP, Zhao XS (2015) Application of artificial neural network and genetic programming in modeling and optimization of ultraviolet water disinfection reactors. Chem Eng Commun 202(11):1415–1424
Ghadai R, Kalita K, Mondal SC, Swain BP (2019) Genetically optimized diamond-like carbon thin film coatings. Mater Manuf Process 1:1–12. https://doi.org/10.1080/10426914.2019.1594273
Tripathi MK, Ganguly S, Dey P, Chattopadhyay PP (2016) Evolution of glass forming ability indicator by genetic programming. Comput Mater Sci 118(56–65):56–65
Dutta P, Nandi N (2015) Effect of Reynolds number and curvature ratio on single phase turbulent flow in pipe bends. Mech Mech Eng 19(1):5–16
Dutta P, Saha SK, Nandi N, Pal N (2016) Numerical study on flow separation in 90 pipe bend under high Reynolds number by k–ε modelling. Eng Sci Technol 19(2):904–910
Dutta P, Nandi N (2018) Numerical study on turbulent separation reattachment flow in pipe bends with different small curvature ratio. J Inst Eng (India) Ser C 1:1–10
Tu J, Yeoh GH, Liu C (2018) Computational fluid dynamics: a practical approach. Butterworth-Heinemann, Oxford
Koza JR (1994) Genetic programming II. MIT Press, Cambridge
Koza JR (1999) Genetic programming III. Morgan Kaufmann, San Francisco
Barricelli NA et al (1954) Esempi numerici di processi di evoluzione. Methodos 6(21–22):45–68
Roache PJ (1994) Perspective: a method for uniform reporting of grid refinement studies. J Fluids Eng 116(3):405–413
Ono A, Kimura N, Kamide H, Tobita A (2011) Influence of elbow curvature on flow structure at elbow outlet under high Reynolds number condition. Nucl Eng Des 241(11):4409–4419
Zhao D, Xue D (2010) A comparative study of metamodeling methods considering sample quality merits. Struct Multidisc Optim 42:923–938
Mukhopadhyay T, Dey TK, Chowdhury R, Chakrabarti A (2015) tructural damage identification using response surface-based multi-objective optimization: a comparative study. Arab J Sci Eng 40(4):1027–1044
Mukhopadhyay T (2018) A multivariate adaptive regression splines based damage identification methodology for web core composite bridges including the effect of noise. J Sandwich Struct Mater 20(7):885–903
Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box. J Global Optim 13:455–492
Sudo K, Sumida M, Hibara H (1998) Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend. Exp Fluids 25(1):42–49
Kim J, Yadav M, Kim S (2014) Characteristics of secondary flow induced by 90-degree elbow in turbulent pipe flow. Eng Appl Comput Fluid Mech 8(2):229–239
This study was not funded by any grant.
Conflict of interest
The authors declare that they have no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Ganesh, N., Dutta, P., Ramachandran, M. et al. Robust metamodels for accurate quantitative estimation of turbulent flow in pipe bends. Engineering with Computers 36, 1041–1058 (2020). https://doi.org/10.1007/s00366-019-00748-7
- Genetic programming (GP)
- Pipe bend
- Turbulent flow