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Multi-objective optimization of axially flat finned cam-shaped and elliptical tube banks based on entropy generation and thermal hydraulic performance

Yıl 2025, Cilt: 16 Sayı: 4, 1059 - 1066, 30.12.2025
https://doi.org/10.24012/dumf.1809125

Öz

The use of different tube geometries in tube bank heat exchangers has a significant impact on thermal hydraulic performance and entropy generation. This study determined the geometric dimensions and operating conditions of a tube bank with in-line arrangement of cam-shaped and elliptical tubes with axially fins using a numerical optimization method. In order to maintain equal heat transfer surface areas, equivalent diameters (D_e=12.7 mm) were assumed for the tube geometries (cam and elliptical). The longitudinal (N_L ) and transversal (N_T ) configurations consist of four tubes. Diagrams of the multi-objective optimization workflow were established for two different tube geometries. The objective functions selected here were the reduction of entropy generation S_gen and the increase in thermal hydraulic performance (THP). The geometric optimization variables were the transversal tube spacing (y_interval ), longitudinal tube spacing (x_interval ) and longitudinal fin length (L_fin ), which varied within the ranges D_e⁄4 and D_e, respectively. The average velocity at the channel inlet V_in was used as the optimization variable for the operating condition and varies within the range 1 m/s

Kaynakça

  • [1] R. Hilpert, “Waermeabgabe von geheizten rohren and graehten,” Forschung Auf Dem Gebeit Des Ingenieurwesens, 1933, 4, 1027-1038.
  • [2] E. D. Grimison, “Correlation and utilization of new data on flow resistance and heat transfer for cross flow of gases over tube banks,” Trans. ASME., 1937, 59, 583-594.
  • [3] O. P. Bergelin, G. A. Brown, H. L. Hull, F. W. Sullivan, “Heat transfer and fluid friction during viscous flow across banks of tubes-III: a study of tube spacing and tube size,” Trans. A. Sot. Mech. Engrs., 1950, 72, 881-888.
  • [4] O. P. Bergelin, G. A. Brown, S. C. Doberstein, “Heat transfer and fluid friction during flow across banks of tubes-ıv: a study of the transition zone between viscous and turbulent row,” Trans. A. Sot. Mech. Engrs.,1952, 74, 953-960.
  • [5] A. Žukauskas, “Heat transfer from tubes in crossflow,” Advances in Heat Transfer, 1972, 8, 93–160.
  • [6] A. Žukauskas, R. Ulinskas, “Efficiency parameters for heat transfer in tube banks,” Heat Transfer Engineering, 1985, 6, 19-25.
  • [7] A. M. F. El-Shaboury, S. J. Ormiston, “Analysis of laminar forced convection of air crossflow in ın-line tube banks with nonsquare arrangements,” Numerical Heat Transfer, 2005, 48, 99-126, https://doi.org/10.1080/10407780590945452
  • [8] W. A. Khan, J. R. Culham, M. M. Yovanovich, “Convection heat transfer from tube banks in crossflow: analytical approach,” International Journal of Heat and Mass Transfer, 2006, 49, 4831–4838, https://doi.org/10.1016/j.ijheatmasstransfer.2006.05.042
  • [9] E. S. Gaddis, “Pressure drop of tube bundles in cross flow,” VDI Heat Atlas, Berlin, 2010, 1076-1091.
  • [10] A. Yılmaz, T. Yılmaz, “Analytical and experimental investigation of entropy generation for an in-line cross-flow tube bank,” Journal of Cukurova University Faculty of Engineering-Architecture, 2016, 31, 223-230, https://doi.org/10.21605/cukurovaummfd.317805
  • [11] A. Horvart, M. Leskovar, B. Mavko, “Comparison of heat transfer condition in tube bundle cross-flow for different tube shapes,” International Journal of Heat and Mass Transfer, 2006, 49, 1027-1038, https://doi.org/10.1016/j.ijheatmasstransfer.2005.09.030
  • [12] H. Bayat, A. M. Lavasani, T. Maarefdoost, “Experimental study of thermal-hydraulic performance of cam-shaped tube bundle with staggered arrangement,” Energy Conversion and Management, 2014, 85, 470-476, https://doi.org/10.1016/j.enconman.2014.06.009
  • [13] C. K. Mangrulkar, A. S. Dhoble, A. R. Deshmukh, S. A. Mandavgane, “Numerical ınvestigation of heat transfer and friction factor characteristics from in-line cam shaped tube bank in crossflow,” Appl. Therm. Eng., 2017, 110, 521-538, https://doi.org/10.1016/j.applthermaleng.2016.08.174
  • [14] W. A. Khan, J. R. Culham, M. M. Yovanovich, “Fluid flow and heat transfer from elliptical cylinder: analytical approach,” 37th AIAA Thermophys. Conf., 2004, 19.
  • [15] S. A. E. Sayed Ahmed, O. M. Mesalhy, T. M. Khass, A. H. Hassan, “Parametric study of air cooling process via water cooled bundle of wing-shaped tubes,” Egyptian International Journal of Engineering Sciences and Technology, 2012, 15, 1172-1184, 10.21608/eijest.2012.96756
  • [16] R. S. Matos, J. V. C. Vargas, T. A. Laursen, F. E. M. Saboya, “Optimization study and heat transfer comparison of straggered circular and elliptic tubes in forced convection,” International Journal of Heat and Mass Transfer, 2001, 44, 3953–3961, https://doi.org/10.1016/S0017-9310(01)00006-0
  • [17] A. Yılmaz, M. T. Erdinç, T. Yılmaz, “Optimization of crossflow staggered tube banks for prescribed pressure loss and effectiveness,” JTHT Thermophysics Heat Transfer, 2017, 31, 878–888, https://doi.org/10.2514/1.T5033
  • [18] N. Gharbi, A. Kheiri, M. Ganaoui, R. Blanchard, “Numerical optimization of heat exchangers with circular and non-circular shapes,” Case Studies in Thermal Engineering, 2015, 6, 194–203, https://doi.org/10.1016/j.csite.2015.09.006
  • [19] A. Yılmaz, T. Yılmaz, “Optimum design of cross-flow ın-line tube banks at constant wall temperature,” Heat Transfer Engineering, 2016, 37, 523–534, https://doi.org/10.1080/01457632.2015.1060753
  • [20] Engineering Equation Solver, F-Chart Software, 2018.
  • [21] M. T. Erdinç, “Computational thermal-hydraulic analysis and geometric optimization of elliptic and circular wavy fin and tube heat exchangers,” International Communications in Heat and Mass Transfer, 2023 140, 106518, https://doi.org/10.1016/j.icheatmasstransfer.2022.106518
  • [22] modeFRONTIER, Esteco S.p.A., 2023.
  • [23] Ansys Fluent User’s Guide, 2021.

Entropi üretimi ve termal hidrolik performansa dayalı eksenel olarak düz kanatlı kam şekilli ve eliptik boru demetlerinin çok amaçlı optimizasyonu

Yıl 2025, Cilt: 16 Sayı: 4, 1059 - 1066, 30.12.2025
https://doi.org/10.24012/dumf.1809125

Öz

Boru demeti ısı değiştiricilerde farklı boru geometrilerinin kullanımı, ısıl hidrolik performans ve entropi üretimi üzerinde önemli bir etkiye sahiptir. Bu çalışmada, sayısal bir optimizasyon yöntemi kullanılarak; düzgün sıralı dizilime sahip eksenel düz kanatlı, kam şekilli ve eliptik borulu boru demetinin geometrik boyutları ve çalışma koşulları belirlenmiştir. Eşit ısı transfer yüzey alanları sağlamak amacıyla, boru geometrileri (kam ve eliptik) için eşdeğer çaplar (D_e=12,7 mm) kabul edilmiştir. Konfigürasyonlar, boyuna (N_L ) ve enine (N_T ) dört borudan oluşmaktadır. İki farklı boru geometrisi için çok amaçlı optimizasyon iş akış şemaları oluşturulmuştur. Burada seçilen amaç fonksiyonları, entropi üretiminin (S_gen ) azaltılması ve ısıl hidrolik performansın (THP) artırılmasıdır. Geometrik optimizasyon değişkenleri; sırasıyla D_e⁄4 ve D_e arasında değişen enine borular arası boşluk (y_interval ), boyuna borular arası boşluk (x_interval ) ve boyuna kanat uzunluğudur (L_fin ). Çalışma koşulu için optimizasyon değişkeni olarak kanal girişindeki ortalama hız (V_in ) kullanılmış ve (1 m⁄s≤V_in≤6 m⁄s) aralığında değiştirilmiştir. Sonuç olarak, incelenen optimizasyon problemleri için elde edilen Pareto tasarımlar değerlendirildiğinde; elde edilen en düşük entropi üretim değerleri kam şekilli boru demeti için daha düşükken (5.05%), elde edilen en yüksek ısıl-hidrolik performans değerleri eliptik boru demeti için daha yüksektir (1.66%).

Kaynakça

  • [1] R. Hilpert, “Waermeabgabe von geheizten rohren and graehten,” Forschung Auf Dem Gebeit Des Ingenieurwesens, 1933, 4, 1027-1038.
  • [2] E. D. Grimison, “Correlation and utilization of new data on flow resistance and heat transfer for cross flow of gases over tube banks,” Trans. ASME., 1937, 59, 583-594.
  • [3] O. P. Bergelin, G. A. Brown, H. L. Hull, F. W. Sullivan, “Heat transfer and fluid friction during viscous flow across banks of tubes-III: a study of tube spacing and tube size,” Trans. A. Sot. Mech. Engrs., 1950, 72, 881-888.
  • [4] O. P. Bergelin, G. A. Brown, S. C. Doberstein, “Heat transfer and fluid friction during flow across banks of tubes-ıv: a study of the transition zone between viscous and turbulent row,” Trans. A. Sot. Mech. Engrs.,1952, 74, 953-960.
  • [5] A. Žukauskas, “Heat transfer from tubes in crossflow,” Advances in Heat Transfer, 1972, 8, 93–160.
  • [6] A. Žukauskas, R. Ulinskas, “Efficiency parameters for heat transfer in tube banks,” Heat Transfer Engineering, 1985, 6, 19-25.
  • [7] A. M. F. El-Shaboury, S. J. Ormiston, “Analysis of laminar forced convection of air crossflow in ın-line tube banks with nonsquare arrangements,” Numerical Heat Transfer, 2005, 48, 99-126, https://doi.org/10.1080/10407780590945452
  • [8] W. A. Khan, J. R. Culham, M. M. Yovanovich, “Convection heat transfer from tube banks in crossflow: analytical approach,” International Journal of Heat and Mass Transfer, 2006, 49, 4831–4838, https://doi.org/10.1016/j.ijheatmasstransfer.2006.05.042
  • [9] E. S. Gaddis, “Pressure drop of tube bundles in cross flow,” VDI Heat Atlas, Berlin, 2010, 1076-1091.
  • [10] A. Yılmaz, T. Yılmaz, “Analytical and experimental investigation of entropy generation for an in-line cross-flow tube bank,” Journal of Cukurova University Faculty of Engineering-Architecture, 2016, 31, 223-230, https://doi.org/10.21605/cukurovaummfd.317805
  • [11] A. Horvart, M. Leskovar, B. Mavko, “Comparison of heat transfer condition in tube bundle cross-flow for different tube shapes,” International Journal of Heat and Mass Transfer, 2006, 49, 1027-1038, https://doi.org/10.1016/j.ijheatmasstransfer.2005.09.030
  • [12] H. Bayat, A. M. Lavasani, T. Maarefdoost, “Experimental study of thermal-hydraulic performance of cam-shaped tube bundle with staggered arrangement,” Energy Conversion and Management, 2014, 85, 470-476, https://doi.org/10.1016/j.enconman.2014.06.009
  • [13] C. K. Mangrulkar, A. S. Dhoble, A. R. Deshmukh, S. A. Mandavgane, “Numerical ınvestigation of heat transfer and friction factor characteristics from in-line cam shaped tube bank in crossflow,” Appl. Therm. Eng., 2017, 110, 521-538, https://doi.org/10.1016/j.applthermaleng.2016.08.174
  • [14] W. A. Khan, J. R. Culham, M. M. Yovanovich, “Fluid flow and heat transfer from elliptical cylinder: analytical approach,” 37th AIAA Thermophys. Conf., 2004, 19.
  • [15] S. A. E. Sayed Ahmed, O. M. Mesalhy, T. M. Khass, A. H. Hassan, “Parametric study of air cooling process via water cooled bundle of wing-shaped tubes,” Egyptian International Journal of Engineering Sciences and Technology, 2012, 15, 1172-1184, 10.21608/eijest.2012.96756
  • [16] R. S. Matos, J. V. C. Vargas, T. A. Laursen, F. E. M. Saboya, “Optimization study and heat transfer comparison of straggered circular and elliptic tubes in forced convection,” International Journal of Heat and Mass Transfer, 2001, 44, 3953–3961, https://doi.org/10.1016/S0017-9310(01)00006-0
  • [17] A. Yılmaz, M. T. Erdinç, T. Yılmaz, “Optimization of crossflow staggered tube banks for prescribed pressure loss and effectiveness,” JTHT Thermophysics Heat Transfer, 2017, 31, 878–888, https://doi.org/10.2514/1.T5033
  • [18] N. Gharbi, A. Kheiri, M. Ganaoui, R. Blanchard, “Numerical optimization of heat exchangers with circular and non-circular shapes,” Case Studies in Thermal Engineering, 2015, 6, 194–203, https://doi.org/10.1016/j.csite.2015.09.006
  • [19] A. Yılmaz, T. Yılmaz, “Optimum design of cross-flow ın-line tube banks at constant wall temperature,” Heat Transfer Engineering, 2016, 37, 523–534, https://doi.org/10.1080/01457632.2015.1060753
  • [20] Engineering Equation Solver, F-Chart Software, 2018.
  • [21] M. T. Erdinç, “Computational thermal-hydraulic analysis and geometric optimization of elliptic and circular wavy fin and tube heat exchangers,” International Communications in Heat and Mass Transfer, 2023 140, 106518, https://doi.org/10.1016/j.icheatmasstransfer.2022.106518
  • [22] modeFRONTIER, Esteco S.p.A., 2023.
  • [23] Ansys Fluent User’s Guide, 2021.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Makine Mühendisliğinde Optimizasyon Teknikleri, Makine Mühendisliğinde Sayısal Yöntemler
Bölüm Araştırma Makalesi
Yazarlar

Mehmet Özkarakoç 0009-0000-0312-6707

Muhammet Nasıf Kuru 0000-0002-5941-1221

Gönderilme Tarihi 23 Ekim 2025
Kabul Tarihi 16 Aralık 2025
Yayımlanma Tarihi 30 Aralık 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 16 Sayı: 4

Kaynak Göster

IEEE M. Özkarakoç ve M. N. Kuru, “Multi-objective optimization of axially flat finned cam-shaped and elliptical tube banks based on entropy generation and thermal hydraulic performance”, DÜMF MD, c. 16, sy. 4, ss. 1059–1066, 2025, doi: 10.24012/dumf.1809125.
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