NUMERICAL AND EXPERIMENTAL INVESTIGATION OF TUBE BUNDLE HEAT EXCHANGER ARRANGEMENT EFFECT ON HEAT TRANSFER PERFORMANCE IN TURBULENT FLOWS
Year 2023,
Volume: 43 Issue: 2, 175 - 190, 17.11.2023
Erman Aslan
,
İmdat Taymaz
,
Kemal Çakır
,
Elif Eker Kahveci
Abstract
This study examines the friction factor, convective heat transfer, and area goodness factor of both inline and staggered tube bundles. The Finite Volume Method (FVM) is used for numerical simulations. Experimental and numerical approaches are utilized. Both 18.0 mm and 21.6 mm longitudinal distances are investigated. It is recommended to use ratio coefficients to reduce computation time. The proportion coefficients are used to obtain predictions for the three-dimensional cases based on the two-dimensional results or to transfer the 2D results to 3D. In addition, three turbulence models were utilized and compared within an Unsteady Reynolds Averaged Navier-Stokes (URANS) formulation. Experimental results validated numerical predictions. The thermal boundary conditions consist of a constant inlet temperature and a uniform heat flux on the support plate. Reynolds number is changed from 989 to 6352, while the Prandtl number remains at 0.70. Nusselt number and friction factor values have been observed to increase with increasing Reynolds number in all geometric configurations. The staggered configurations result in greater Nusselt number and friction factor values compared to inline configurations. The Nusselt number and pressure drop experience negative and positive effects, respectively, as the distance between rows decreases. SST turbulence models typically predict reasonable outcomes for all geometric configurations.
References
- Abed, N., and Afgan, I. (2017). A CFD study of flow quantities and heat transfer by changing a vertical to diameter ratio and horizontal to diameter ratio in inline tube banks using URANS turbulence models. International Communications in Heat and Mass Transfer, 89,18-30.
- Aburoma, M.M. , Cho, S.M., and Sawyer, R.H. (1975). Thermal/hydraulic design considerations for Clinch River breeder reactor plant intermediate heat exchangers, ASME, 75-WA/HT-101.
- Ansys-Fluent (2009) Ansys-Fluent 12.0 User’s Guide. Ansys Inc.
- Aslan, E., Taymaz, I., Benim, A.C.(2015). Investigation of LBM curved boundary treatments for unsteady flows. European Journal of Mechanics B/Fluids,51,68-74
- Aslan, E. (2016).Numerical investigation of the heat transfer and pressure drop on the tube bundle support plates for inline and staggered arrangements. Progress in Computational Fluid Dynamics,56(1),38-47
- Barmasian, H.R., and Hassan, Y.A. (1997). Large eddy simulation of turbulent crossflow in the tube bundles. Nuclear Engineering and Design, 172,103-122.
- Beale, S.B., and Spalding, D.B. (1999). A numerical study of unsteady fluid flow in inline and staggered tube banks. Journal of Fluids and Structures,13,723-754.
- Benim, A.C., Cagan, M., and Gunes, D. (2004). Computational analysis of heat transfer in turbulent pipe flow. International Journal of Thermal Science, 43,725-732.
- Benim, A.C., Ozkan, K., Cagan, M., and Gunes, D. (2007). Computational investigation of turbulent jet impinging onto rotating disk. International Journal of Numerical Methods for Heat and Fluid Flow, 17, 284-301.
- Benim, A.C., Chattopadhyay, H., and Nahavandi, A. (2011). Computational analysis of turbulent forced convection in a channel with a triangular prism. International Journal of Thermal Science, 50,1973-1983.
- Benim, A.C., Brillert, D., and Cagan, M. (2004). Investigation into the computational analysis of direct-transfer pre-swirl systems for gas turbine cooling. ASME Turbo Expo,4,453-460.
- Benim,A.C., Geiger, M., Doehler, S., Schoenenberger ,M., and Roemer, H. (1995). Modelling the flow in the exhaust hood of steam turbines under consideration of turbine-exhaust hood interaction, in Proc. 1st European. Conf. Turbomachinery - Fluid Dynamic and Thermodynamic Aspects: Computational Methods,pp.343-357.
- Benim, A.C., Pasqualotto, E., and Suh, S.H. (2008). Modelling turbulent flow past a circular cylinder by RANS, URANS, LES and DES. Progress in Computational Fluid Dynamics, An International Journal,8,299-307.
- Bouris, D., Papadakis, G., and Bergeles, G. (2001). Numerical evaluation of alternate tube configurations for particle deposition rate reduction in heat exchanger tube bundles. International Journal of Heat and Fluid Flow, 22 ,525-536.
- Brandt, F. (1985).Wärmeübertragung im Dampferzeugen und Wärmetauschen, FDBR-Fachverband Dampfkessel-Behälten-und Rohrleitungsbau, Essen: Vulkan-Verlag.
- Chattopadhyay, H., and Benim, A.C. (2011). Turbulent heat transfer over a moving surface due to impinging slot jets. Journal of Heat Transfer ,133 ,104502-1.
- Dagsöz, A.K. Bestimmung des Wörmeübergangs an Rohrbündel Tragplatten für Flucthende und Versetze Rohraordnungen. ITU Makine Fakültesi Isı Tekniği ve Ekonomi Araştırma Kurumu Bülteni 1975; 13.
- Durbin, P.A., and Reif, B.A.P. (2011). Statical theory and modelling for turbulent flows, (2nd ed.).Chichester,Wiley.
- Grimisson,E.D. (1937). Correlation and utilization of new data on flow resistance and heat transfer for crossflow of gases over tube banks. Trans. ASME, 59,583-594.
- Hamid, M.O.A., Zhang, B., and Yang, L. (2014). Application of field synergy principle for optimization fluid flow and convective heat transfer in a tube bundle of a pre-heater. Energy,76, 241-253.
- Hilpert, R. (1933). Wärmeabgabe von geheizten Drähten und Rohren im Luftstrom. Fors. Ingenieurwesen,(4):215-224.
- Holman, J.P. (1994). Experimental methods for engineers (6th ed.).McGraw-Hill Int.
- Horvat, A., Leskovar, M., and Mayko, B. (2006). Comparison of heat transfer conditions in tube bundle cross-flow for different tube shaped. International Journal of Heat and Mass Transfer, 49 ,1027-1038.
- Ibrahim, T.A., and Goma, A. (2009). Thermal performance criteria of elliptic tube bundle in cross flow. International Journal of Thermal Science ,48 , 2148-2158.
- Khan, M.G., Fartaj, A., and Ting, D.S. (2004). An experimental characterization of cross-flow cooling of air via an in-line elliptical tube array. International Journal of Heat Fluid Flow ,25,636-648.
- Kukulka, D.J., and Smith, R (2014). Heat transfer evaluation of an enhanced heat transfer tube bundle.Energy ,75,97-103.
- Kuppan T. Heat exchanger design handbook. New York: Marcel Deker Inc, 2000.
- Kwak, K.M., Torii, K., and Nishino, K. (2003). Heat transfer and pressure loss penalty for the number of tube rows of staggered finned-tube bundles with a single transverse row of winglets. International Journal of Heat Mass Transactions, 46, 175-180.
- Launder, B.E., and Spalding, D.B. (1974). The numerical computation of turbulence flows. Computer Methods Applied Mechanical Engineering, 3,269-289.
- Launder, B.E., and Massey, T.H. (1978).The numerical prediction of viscous flow and heat transfer in tube banks.Journal of Heat Transfer, 100,565-571.
- Lavasani, A.M., Bayat, H., and Maarefdoost, T. (2014). Experimental study of convective heat transfer from in-line cam shapped tube bank in crossflow. Applied Thermal Engineering, 65 ,85-93.
- Li, X., Zhu, D., Yin, Y., Liu, S., and Mo, X. (2018). Experimental study on heat transfer and pressure drop of twisted oval tube bundle in cross flow. Experimental Thermal Fluid Science, 99,251-258.
- Liao, L., and Liu, Z.H. (2011). Enhanced Boiling Heat Transfer of the Compact Staggered Tube Bundles under Sub-Atmospheric Pressures. Heat Transfer Engineering ,28,444-450.
- Lin, C.N., Liu, Y.W., and Leu, J.S. (2008). Heat Transfer and Fluid Flow Analysis for Plate-Fin and Oval Tube Heat Exchangers With Vortex Generators. Heat Transfer Engineering ,29,588-596.
- Lotfi, B., Zeng, M., Sunden, B., and Wang, Q. (2014). 3D numerical investigation of flow and heat transfer characteristics in smooth wavy fin-and-elliptical tube heat exchangers using new type vortex generators. Energy ,73,233-257.
- Maithani, R., Kumar, A., Zadeh, P.G., Safaei ,M.Z., and Gholamalizadeh, E. (2020). Empirical correlations development for heat transfer and friction factor of a solar rectangular air passage with spherical-shaped turbulence promoters. Journal of Thermal Analysis and Calorimetry, 139,1195–1212.
- Maqableh, A.M., Khadrawi, A.F., Al-Nimr, M.A., Ammoruah, S.A., and Benim, A.C. (2011). Heat transfer characteristics of parallel and counter flow micro-channel heat exchangers with varying wall resistance. Progress in Computational Fluid Dynamics, 11,318-328.
- Matos, R.S., Laursen, T.A., Vargas, J.V.C., and Bejan, A. (2004). Three-dimensional optimization of staggered finned circular and elliptic tubes in forced convection. International Journal of Thermal Science,43,447-487.
- Mavriodu, S.G., and Bouris, D.G. (2012). Numerical evaluation of a heat exchanger with inline tubes of different size for reduced fouling rates. International Journal of Heat and Mass Transfer, 55 ,5185-5195.
- Menter, F.R. (1994). Two equation eddy viscosity turbulence models for engineering applications. AIAA Journal, 32, 1598-1695.
- Menter, F.R., Kuntz, M., and Langtry, R.B., (2003). Ten years of experience with the SST turbulence model. Heat and Mass Transfer, 4,625-632.
- Menter, F.R., Langtry, R.B., Likki, S.R., Suzen, T.B., Huang, P.G., and Volker, S. (2006). A Correlation-Bases Transition Model Using Local Variables-Part-1: Model Formulation. Journal of Turbomachinery, 128 ,413-422.
- Mizushima, J., and Suehiro, N. (2005). Instability and transition of flow past two tandem circular cylinders. Physics Fluids ,14,104-107.
- Oclon, P., Lopata, S., Novak, M., and Benim, A.C. (2015). Numerical study on the effect of inner tube fouling on the thermal performance of high-temperature fin-and-tube heat exchanger. Progress in Computational Fluid Dynamics ,15,290-306.
- Oengoeren, A., and Ziada, S. (1992).Unsteady fluid forces acting on a square tube bundle in air cross-flow. in Proc. 1992 International Symposium on Flow-Induced Vibration and Noise,55-74.
- Ozturk, N.A., Ozalp, C., Canpolat, C., and Sahin, B. (2016). PIV measurement of flow through normal triangular cylinder arrays in the passage of a model plate-tube heat exchangers. International Journal of Heat Fluid Flow ,61(B),531-544.
- Pourdel, H., Afrouzi, H.H., Akbari, O.A., Miansari, M., Toghraie, D., Marzban, A., and Koveiti, A. (2019). Numerical investigation of turbulent flow and heat transfer in flat tube. Journal of Thermal Analysis and Calorimetry, 135,3471-3483.
- Taymaz, I., Aslan, E., and Benim, A.C. (2015). Numerical investigation of incompressible fluid flow and heat transfer across a bluff body in a channel flow. Thermal Science,19,537-547.
- Wilcox, D.C. (1988). Turbulence Modelling for CFD. DCW Industries.
- Yahiaoui, T., Ladjede, O., Imine, O. and Adjlout, L. (2016). Experimental and CFD investigations of turbulent cross flow in staggered tube bundle equipped with grooved cylinders. J Braz Soc Mech Sci Eng,38,163–175.
- You, Y., Xiao, S., Pan, N., and Deng, Z. (2017). Full Model Simulation of Shell side Thermal Augmentation of Small Heat Exchanger with Two Tube Passes. Heat Transfer Engineering, 39,1024-1035.
- Zhao, H., Liu, Z., Zhang, C., Guan, N., and Zhao, H. (2016). Pressure drop and friction factor of a rectangular channel with staggered mini pin fins of different shapes. Experimental Thermal Fluid Science ,71,57-69.
- Zheng, Z., Yang, W., Cai, Y., Wang, Q., and Zeng, G. (2020). Dynamic simulation on ash deposition and heat transfer behavior on a staggered tube bundle under high-temperature conditions. Energy, 190,116390.
TÜRBÜLANSLI AKIŞLARDA ISI TRANSFER PERFORMANSI ÜZERİNDEKİ BORU DEMETLİ ISI DEĞİŞTİRİCİ SIRALAMA ETKİSİNİN SAYISAL VE DENEYSEL İNCELENMESİ
Year 2023,
Volume: 43 Issue: 2, 175 - 190, 17.11.2023
Erman Aslan
,
İmdat Taymaz
,
Kemal Çakır
,
Elif Eker Kahveci
Abstract
Düzgün ve kaydırılmış sıralı hatlara sahip boru demetlerinin sürtünme faktörü, taşınımla ısı geçişi ve alan uyum faktörü özellikleri deneysel ve sayısal olarak incelenmiştir.Sonlu Hacim Yöntemi (FVM) kullanılmıştır. 18.0 mm ve 21.6 mm olmak üzere iki farklı uzunlamasına mesafe incelenmiştir. Daha az hesaplama için oran katsayılarının kullanılması önerilir. Orantı katsayıları, iki boyutta elde edilen sonuçlara dayanarak üç boyutlu durumlar için tahminler elde etmek, başka bir deyişle 2B sonuçları 3B'ye aktarmak için uygulanır.Bir URANS (farklı Kararsız Reynolds Ortalama Navier-Stokes) formülasyonunda üç türbülans modeli kullanıldı ve birbirleriyle karşılaştırıldı. Sayısal tahminler deneysel sonuçlarla doğrulandı.Isıl sınır koşulu olarak, girişte sabit sıcaklık uygulanır ve destek plakasında üniform ısı akışı gerçekleşir. Reynolds sayısı 989'dan 6352'ye değiştirilmiş ve Prandtl sayısı 0.70'de tutulmuştur. Nusselt sayısı ve sürtünme faktörü değerleri tüm geometrik konfigürasyonlar için Reynolds sayısı ile artmıştır .Kaydırılmış sıralamalar, düzgün düzenlemeye kıyasla daha büyük Nusselt sayısı ve sürtünme faktörü değerlerine yol açmıştır. Nusselt sayısı ve basınç düşüşü, sıralar arasındaki boyuna mesafenin azalmasıyla sırasıyla negatif ve pozitif etkiye sahiptir.Genel olarak, SST türbülans modelleri, tüm geometrik konfigürasyonlar için makul sonuçlar vermiştir.
References
- Abed, N., and Afgan, I. (2017). A CFD study of flow quantities and heat transfer by changing a vertical to diameter ratio and horizontal to diameter ratio in inline tube banks using URANS turbulence models. International Communications in Heat and Mass Transfer, 89,18-30.
- Aburoma, M.M. , Cho, S.M., and Sawyer, R.H. (1975). Thermal/hydraulic design considerations for Clinch River breeder reactor plant intermediate heat exchangers, ASME, 75-WA/HT-101.
- Ansys-Fluent (2009) Ansys-Fluent 12.0 User’s Guide. Ansys Inc.
- Aslan, E., Taymaz, I., Benim, A.C.(2015). Investigation of LBM curved boundary treatments for unsteady flows. European Journal of Mechanics B/Fluids,51,68-74
- Aslan, E. (2016).Numerical investigation of the heat transfer and pressure drop on the tube bundle support plates for inline and staggered arrangements. Progress in Computational Fluid Dynamics,56(1),38-47
- Barmasian, H.R., and Hassan, Y.A. (1997). Large eddy simulation of turbulent crossflow in the tube bundles. Nuclear Engineering and Design, 172,103-122.
- Beale, S.B., and Spalding, D.B. (1999). A numerical study of unsteady fluid flow in inline and staggered tube banks. Journal of Fluids and Structures,13,723-754.
- Benim, A.C., Cagan, M., and Gunes, D. (2004). Computational analysis of heat transfer in turbulent pipe flow. International Journal of Thermal Science, 43,725-732.
- Benim, A.C., Ozkan, K., Cagan, M., and Gunes, D. (2007). Computational investigation of turbulent jet impinging onto rotating disk. International Journal of Numerical Methods for Heat and Fluid Flow, 17, 284-301.
- Benim, A.C., Chattopadhyay, H., and Nahavandi, A. (2011). Computational analysis of turbulent forced convection in a channel with a triangular prism. International Journal of Thermal Science, 50,1973-1983.
- Benim, A.C., Brillert, D., and Cagan, M. (2004). Investigation into the computational analysis of direct-transfer pre-swirl systems for gas turbine cooling. ASME Turbo Expo,4,453-460.
- Benim,A.C., Geiger, M., Doehler, S., Schoenenberger ,M., and Roemer, H. (1995). Modelling the flow in the exhaust hood of steam turbines under consideration of turbine-exhaust hood interaction, in Proc. 1st European. Conf. Turbomachinery - Fluid Dynamic and Thermodynamic Aspects: Computational Methods,pp.343-357.
- Benim, A.C., Pasqualotto, E., and Suh, S.H. (2008). Modelling turbulent flow past a circular cylinder by RANS, URANS, LES and DES. Progress in Computational Fluid Dynamics, An International Journal,8,299-307.
- Bouris, D., Papadakis, G., and Bergeles, G. (2001). Numerical evaluation of alternate tube configurations for particle deposition rate reduction in heat exchanger tube bundles. International Journal of Heat and Fluid Flow, 22 ,525-536.
- Brandt, F. (1985).Wärmeübertragung im Dampferzeugen und Wärmetauschen, FDBR-Fachverband Dampfkessel-Behälten-und Rohrleitungsbau, Essen: Vulkan-Verlag.
- Chattopadhyay, H., and Benim, A.C. (2011). Turbulent heat transfer over a moving surface due to impinging slot jets. Journal of Heat Transfer ,133 ,104502-1.
- Dagsöz, A.K. Bestimmung des Wörmeübergangs an Rohrbündel Tragplatten für Flucthende und Versetze Rohraordnungen. ITU Makine Fakültesi Isı Tekniği ve Ekonomi Araştırma Kurumu Bülteni 1975; 13.
- Durbin, P.A., and Reif, B.A.P. (2011). Statical theory and modelling for turbulent flows, (2nd ed.).Chichester,Wiley.
- Grimisson,E.D. (1937). Correlation and utilization of new data on flow resistance and heat transfer for crossflow of gases over tube banks. Trans. ASME, 59,583-594.
- Hamid, M.O.A., Zhang, B., and Yang, L. (2014). Application of field synergy principle for optimization fluid flow and convective heat transfer in a tube bundle of a pre-heater. Energy,76, 241-253.
- Hilpert, R. (1933). Wärmeabgabe von geheizten Drähten und Rohren im Luftstrom. Fors. Ingenieurwesen,(4):215-224.
- Holman, J.P. (1994). Experimental methods for engineers (6th ed.).McGraw-Hill Int.
- Horvat, A., Leskovar, M., and Mayko, B. (2006). Comparison of heat transfer conditions in tube bundle cross-flow for different tube shaped. International Journal of Heat and Mass Transfer, 49 ,1027-1038.
- Ibrahim, T.A., and Goma, A. (2009). Thermal performance criteria of elliptic tube bundle in cross flow. International Journal of Thermal Science ,48 , 2148-2158.
- Khan, M.G., Fartaj, A., and Ting, D.S. (2004). An experimental characterization of cross-flow cooling of air via an in-line elliptical tube array. International Journal of Heat Fluid Flow ,25,636-648.
- Kukulka, D.J., and Smith, R (2014). Heat transfer evaluation of an enhanced heat transfer tube bundle.Energy ,75,97-103.
- Kuppan T. Heat exchanger design handbook. New York: Marcel Deker Inc, 2000.
- Kwak, K.M., Torii, K., and Nishino, K. (2003). Heat transfer and pressure loss penalty for the number of tube rows of staggered finned-tube bundles with a single transverse row of winglets. International Journal of Heat Mass Transactions, 46, 175-180.
- Launder, B.E., and Spalding, D.B. (1974). The numerical computation of turbulence flows. Computer Methods Applied Mechanical Engineering, 3,269-289.
- Launder, B.E., and Massey, T.H. (1978).The numerical prediction of viscous flow and heat transfer in tube banks.Journal of Heat Transfer, 100,565-571.
- Lavasani, A.M., Bayat, H., and Maarefdoost, T. (2014). Experimental study of convective heat transfer from in-line cam shapped tube bank in crossflow. Applied Thermal Engineering, 65 ,85-93.
- Li, X., Zhu, D., Yin, Y., Liu, S., and Mo, X. (2018). Experimental study on heat transfer and pressure drop of twisted oval tube bundle in cross flow. Experimental Thermal Fluid Science, 99,251-258.
- Liao, L., and Liu, Z.H. (2011). Enhanced Boiling Heat Transfer of the Compact Staggered Tube Bundles under Sub-Atmospheric Pressures. Heat Transfer Engineering ,28,444-450.
- Lin, C.N., Liu, Y.W., and Leu, J.S. (2008). Heat Transfer and Fluid Flow Analysis for Plate-Fin and Oval Tube Heat Exchangers With Vortex Generators. Heat Transfer Engineering ,29,588-596.
- Lotfi, B., Zeng, M., Sunden, B., and Wang, Q. (2014). 3D numerical investigation of flow and heat transfer characteristics in smooth wavy fin-and-elliptical tube heat exchangers using new type vortex generators. Energy ,73,233-257.
- Maithani, R., Kumar, A., Zadeh, P.G., Safaei ,M.Z., and Gholamalizadeh, E. (2020). Empirical correlations development for heat transfer and friction factor of a solar rectangular air passage with spherical-shaped turbulence promoters. Journal of Thermal Analysis and Calorimetry, 139,1195–1212.
- Maqableh, A.M., Khadrawi, A.F., Al-Nimr, M.A., Ammoruah, S.A., and Benim, A.C. (2011). Heat transfer characteristics of parallel and counter flow micro-channel heat exchangers with varying wall resistance. Progress in Computational Fluid Dynamics, 11,318-328.
- Matos, R.S., Laursen, T.A., Vargas, J.V.C., and Bejan, A. (2004). Three-dimensional optimization of staggered finned circular and elliptic tubes in forced convection. International Journal of Thermal Science,43,447-487.
- Mavriodu, S.G., and Bouris, D.G. (2012). Numerical evaluation of a heat exchanger with inline tubes of different size for reduced fouling rates. International Journal of Heat and Mass Transfer, 55 ,5185-5195.
- Menter, F.R. (1994). Two equation eddy viscosity turbulence models for engineering applications. AIAA Journal, 32, 1598-1695.
- Menter, F.R., Kuntz, M., and Langtry, R.B., (2003). Ten years of experience with the SST turbulence model. Heat and Mass Transfer, 4,625-632.
- Menter, F.R., Langtry, R.B., Likki, S.R., Suzen, T.B., Huang, P.G., and Volker, S. (2006). A Correlation-Bases Transition Model Using Local Variables-Part-1: Model Formulation. Journal of Turbomachinery, 128 ,413-422.
- Mizushima, J., and Suehiro, N. (2005). Instability and transition of flow past two tandem circular cylinders. Physics Fluids ,14,104-107.
- Oclon, P., Lopata, S., Novak, M., and Benim, A.C. (2015). Numerical study on the effect of inner tube fouling on the thermal performance of high-temperature fin-and-tube heat exchanger. Progress in Computational Fluid Dynamics ,15,290-306.
- Oengoeren, A., and Ziada, S. (1992).Unsteady fluid forces acting on a square tube bundle in air cross-flow. in Proc. 1992 International Symposium on Flow-Induced Vibration and Noise,55-74.
- Ozturk, N.A., Ozalp, C., Canpolat, C., and Sahin, B. (2016). PIV measurement of flow through normal triangular cylinder arrays in the passage of a model plate-tube heat exchangers. International Journal of Heat Fluid Flow ,61(B),531-544.
- Pourdel, H., Afrouzi, H.H., Akbari, O.A., Miansari, M., Toghraie, D., Marzban, A., and Koveiti, A. (2019). Numerical investigation of turbulent flow and heat transfer in flat tube. Journal of Thermal Analysis and Calorimetry, 135,3471-3483.
- Taymaz, I., Aslan, E., and Benim, A.C. (2015). Numerical investigation of incompressible fluid flow and heat transfer across a bluff body in a channel flow. Thermal Science,19,537-547.
- Wilcox, D.C. (1988). Turbulence Modelling for CFD. DCW Industries.
- Yahiaoui, T., Ladjede, O., Imine, O. and Adjlout, L. (2016). Experimental and CFD investigations of turbulent cross flow in staggered tube bundle equipped with grooved cylinders. J Braz Soc Mech Sci Eng,38,163–175.
- You, Y., Xiao, S., Pan, N., and Deng, Z. (2017). Full Model Simulation of Shell side Thermal Augmentation of Small Heat Exchanger with Two Tube Passes. Heat Transfer Engineering, 39,1024-1035.
- Zhao, H., Liu, Z., Zhang, C., Guan, N., and Zhao, H. (2016). Pressure drop and friction factor of a rectangular channel with staggered mini pin fins of different shapes. Experimental Thermal Fluid Science ,71,57-69.
- Zheng, Z., Yang, W., Cai, Y., Wang, Q., and Zeng, G. (2020). Dynamic simulation on ash deposition and heat transfer behavior on a staggered tube bundle under high-temperature conditions. Energy, 190,116390.