## Numerical Study of the Effect of Changing Tube Pitches on Heat and Flow Characteristics from Tube Bundles in Cross Flow

**Author(s): **Petinrin M. O.^{1*}, Towoju O. A.^{2}, Ajiboye S. A.^{1}, Zebulun O. E.^{1}

**Affiliation(s):**

^{1 }University of Ibadan, Oduduwa Rd., Ibadan, Nigeria;

^{2 }Adeleke University, P.M.B. 250, Ede-Osogbo Rd., Ede, Osun State, Nigeria

** ^{*}Corresponding Author’s Address: **layopet01@yahoo.com

**Issue:** Volume 6; Issue 2 (2019)

**Dates:**Paper received: September 26, 2018

The final version of the paper received: April 4, 2019

Paper accepted online: April 9, 2019

**Citation:**Petinrin, M. O., Towoju, O. A., Ajiboye, S. A., Zebulun, O. E. (2019). Numerical study of the effect of changing tube pitches on heat and flow characteristics from tube bundles in cross flow.

*Journal of Engineering Sciences,*Vol. 6(2), pp. E1-E10, doi: 10.21272/jes.2019.6(2).e1.

**DOI:** 10.21272/jes.2019.6(2).e1

**Research Area: ** MECHANICAL ENGINEERING: Computational Mechanics

**Abstract.** Tube bundles are found in various heat transfer equipment for thermal energy transfer between fluids. However, the inter-spatial arrangement of the tubes of any tube bundle is a determining factor for its thermal and hydraulic performance. In this paper, the effect of varying the transverse and longitudinal pitches downstream staggered circular tube bundle on the heat transfer and flow characteristic was numerically analyzed. Seven variations of tube arrangements were studied by changing the tube pitches within a Reynolds number range of 7 381 to 22 214. The analyses were carried out using the k-ε equation model imposed with the realizability constraint and were solved with finite volume CFD code, COMSOL Multiphysics. The results obtained were found to be in good agreement with existing correlations. The tube bundles with decreasing pitches demonstrated better heat transfer performance while those with increasing pitches exhibited a lower friction factor. Thus, the best thermal-hydraulic performance was obtained from increasing pitch arrangements.

**Keywords:** cross flow, varying pitch, tube bundle, heat transfer, thermal-hydraulic performance.

**References:**

- Li, X., Wu, X., He, S. (2014). Numerical investigation of the turbulent cross flow and heat transfer in a wall bounded tube bundle.
*Int. J. Therm. Sci.*, Vol. 75, pp. 127–139. doi:10.1016/j.ijthermalsci.2013.08.001. - Chakrabarty, S. G., Wankhede, U. S. (2012). Flow and heat transfer behaviour across circular cylinder and tube banks with and without splitter plate, Vol. 2.
- Khan, W. A., Culham, J. R., Yovanovich, M. M. (2006). Convection heat transfer from tube banks in crossflow: Analytical approach.
*Int. J. Heat Mass Transf.*, Vol. 49, pp. 4831–4838. doi:10.1016/j.ijheatmasstransfer.2006.05.042. - Jeong, J. H., Nam, K. W., Min, J. K., Kim, K. S., Ha, M. Y. (2011). The effects of the evaluation method on the average heat transfer coefficient for a mini-channel tube bundle.
*Int. J. Heat Mass Transf.*, Vol. 54, pp. 5481–5490. doi:10.1016/j.ijheatmasstransfer.2011.07.043. - Mandhani, V., Chhabra, R., Eswaran, V. (2002). Forced convection heat transfer in tube banks in cross flow.
*Chem. Eng. Sci.*, Vol. 57, pp. 379–391. doi:10.1016/S0009-2509(01)00390-6. - Li, X., and Wu, X. (2013). Thermal mixing of the cross flow over tube bundles.
*Int. J. Heat Mass Transf.*, Vol. 67, pp. 352–361. doi:10.1016/j.ijheatmasstransfer.2013.08.031. - Mehrabian, M. (2007). Heat transfer and pressure drop characteristics of cross flow of air over a circular tube in isolation and/or in a tube bank.
*Arab. J. Sci. Eng.,*Vol. 32, pp. 365–376. - Buyruk, E. (1999). Heat transfer and flow structures around circular cylinders in cross-flow.
*Tr. J. Eng. Environ. Sci.*, Vol. 23, pp. 299–315. - Bergman, T. L., Lavine, A. S., Incropera, F. P., Dewitt, D. P. (2011).
*Fundamentals of Heat and Mass Transfer*. John Wiley and Sons, New Jersey. - Mangrulkar, C. K., Dhoble, A. S., Deshmukh, A. R., Mandavgane, S. A. (2017). Numerical investigation of heat transfer and friction factor characteristics from in-line cam shaped tube bank in crossflow.
*Therm. Eng.*, Vol. 110, pp. 521–538. doi:10.1016/j.applthermaleng.2016.08.174. - Tahseen, T. A., Rahman, M. M., Ishak, M. (2014). An experimental study of air flow and heat transfer over.
*J. Automot. Mech. Eng.*, Vol. 9, pp. 1487–1500. - Mohanty, R. L., Swain, A., Das, M. K. (2018). Thermal performance of mixed tube bundle composed of circular and elliptical tubes.
*Sci. Eng. Prog*. doi:10.1016/j.tsep.2018.02.009. - Barcellos, S. V., Bartz, C. R., Endres, C. L., Moller, L. A. M. (2003). Velocity and pressure fluctuations on inclined tube banks submitted to turbulent flow.
*Brazilian Soc. Mech. Sci. Eng.*, Vol. 25. - Toolthaisong, S., Kasayapanand, N. (2013). Effect of attack angles on air side thermal and pressure drop of the cross flow heat exchangers with staggered tube arrangement.
*Energy Procedia*, Vol. 34, pp. 417–429. doi:10.1016/j.egypro.2013.06.770. - Lee, D., Ahn, J., Shin, S. (2013). Uneven longitudinal pitch effect on tube bank heat transfer in cross fl ow.
*Therm. Eng.*, Vol. 51, pp. 937–947. doi:10.1016/j.applthermaleng.2012.10.031. - Hofmann, R., Frasz, F., Ponweiser, K. (2007). Heat transfer and pressure drop performance comparison of finned-tube bundles in forced convection.
*WSEAS Trans. Heat Mass Transf.*, Vol. 2. - Hofmann, R., Frasz, F., Ponweiser, K. (2008). Experimental analysis of enhanced heat transfer and pressure-drop of serrated finned-tube bundles with different fin geometries.
*5th WSEAS Int. Conf. Heat Mass Transf.*, pp. 54–62. - Hofmann, R., Frasz, F., Ponweiser, K. (2008). Performance evaluation of solid and serrated finned-tube bundles with different fin geometries in forced convection.
*5th Eur. Therm. Conf.*, Netherlands. - Gaddis, E. S. (2010). Pressure drop of tube bundles in cross flow.
*VDI Heat Atlas, Springer-Verlag, Berlin Heidelberg*, pp. 1099–1114. - Horvat, A., Leskovar, M., Mavko, B. (2006). Comparison of heat transfer conditions in tube bundle cross-flow for different tube shapes.
*J. Heat Mass Transf.*, Vol. 49, pp. 1027–1038. doi:10.1016/j.ijheatmasstransfer.2005.09.030. - Nouri-Borujerdi, A., Lavasani, A. M. (2007). Experimental study of forced convection heat transfer from a cam shaped tube in cross flows.
*J. Heat Mass Transf.*, Vol. 50, pp. 2605–2611. doi:10.1016/j.ijheatmasstransfer.2006.11.028. - Lavasani, A. M., Bayat, H., Maarefdoost, T. (2014). Experimental study of convective heat transfer from in-line cam shaped tube bank in crossflow.
*Therm. Eng.*, Vol. 65, pp. 85–93. doi:10.1016/j.applthermaleng.2013.12.078. - Du, X. P., Zeng, M., Dong, Z. Y., Wang, Q. W. (2014). Experimental study of the effect of air inlet angle on the air-side performance for cross-flow finned oval-tube heat exchangers.
*Therm. Fluid Sci.*, Vol. 52, pp. 146–155. doi:10.1016/j.expthermflusci.2013.09.005. - Bassi, F., Crivellini, A., Rebay, S., Savini, M. (2005). Discontinuous Galerkin solution of the Reynolds-averaged Navier–Stokes and k-ω turbulence model equations.
*Fluids*, Vol. 34, pp. 507–540. doi:10.1016/j.compfluid.2003.08.004. - Kuzmin, D., Mierka, O., Turek, S. (2007). On the implementation of the k-ε turbulence model in incompressible flow solvers based on a finite element discretization.
*J. Comput. Sci. Math.*, Vol. 1, pp. 193–206. - Park, C. H., Park, S. O. (2005). On the limiters of two-equation turbulence models.
*J. Comut. Fluid Dyn.*, Vol. 19, pp. 79–86. doi:10.1080/10618560412331286292. - Sveningsson, A., Davidson, L. (2003). Assessment of realizability constraints and boundary conditions in v2-f turbulence models.
*Heat Mass Transf.*, Vol. 4, pp. 585–592. - Young, M. E., Ooi, A. (2004). Turbulence models and boundary conditions for bluff body flow.
*15th Australas. Fluid Mech. Conf.*, Sydney. - Ferziger, J. H., Peric, M. (2002).
*Computational Methods for Fluids Dynamics*. Springer-Verlag, Berlin. - Tannehill, J. C., Anderson, D. A., Pletcher, R. H. (1997).
*Computational Fluid Mechanics and Heat Transfer*. Taylor and Francis, Washington. - Wilcox, D. C. (2006).
*Turbulence Modeling for CFD*. DCW Industries, California. - Gaddis, E. S. (2010). Pressure drop in the outer shell of heat exchangers.
*VDI Heat Atlas, Springer-Verlag, Berlin Heidelberg*, pp. 1115–1128. - Holman, J. P. (2010).
*Heat Transfer*. McGraw-Hill, New York. - Zukauskas, A., Ulinskas, R. (1985). Efficiency parameters for heat transfer in tube banks.
*Heat Transf. Eng.*, Vol. 6, pp. 19–25. - Aiba, S., Tsuchida, H., Ota, T. (1982). Heat transfer around tubes in staggered tube banks.
*JSME*, Vol. 25, pp. 927–933.