Evaluation of two RANS turbulence models in predicting developing mixed convection within a heated horizontal pipe W. GRASSI and D. TESTI* Department of Energetics, University of Pisa, via Diotisalvi, 2-56126 Pisa, Italy (Received 24 May 2007; in final form 11 September 2007) The developing weakly turbulent regime of mixed convection in a uniformly heated horizontal pipe was first studied experimentally, by means of heat transfer measurements in the following ranges of dimensionless numbers: 3.19 , Re £ 10 23 , 6.39, 1.80 , Gr h £ 10 28 , 4.20. The working fluid was FC-72e, with Pr ¼ 12.4. In order to gain a better insight into the thermo-fluid dynamics involved in the phenomenon and obtain the velocity and temperature fields at every point of the fluid domain, numerical simulations were performed by means of commercial software. Turbulence was modelled by using the Reynolds averaged Navier – Stokes equations (RANS) approach. Two closures of the governing equations were evaluated: realizable k – 1 (RKE) model and renormalization-group k – 1 (RNG) model. Both models were capable of reproducing the observed physical trends. However, deviations from the experimental data lower than 20% were obtained only in the entry-zone with the RKE model, while the RNG model gave fair predictions only in developed or quasi-developed flow. Keywords: k – 1 models; RANS equations; Heat transfer prediction; Turbulent mixed convection; Buoyancy; Developing flow International Journal of Computational Fluid Dynamics ISSN 1061-8562 print/ISSN 1029-0257 online q 2007 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/10618560701684470 Nomenclature Symbol Quantity SI Unit b duct thickness m c fluid specific heat J kg 21 K 21 C m parameter defined in equation (6) D duct inner diameter m f generic scalar quantity undergoing turbulent fluctuations n.a. kfl mean component of f n.a. f 0 fluctuating component of f n.a. g gravity acceleration vector ms 22 G buoy generation of k due to buoyancy Wm 23 h heat transfer coefficient Wm 22 K 21 I turbulent intensity L h heated length m Gr Grashof number based on the wall superheat Gr h Grashof number based on the wall heat flux Nu Nusselt number p pressure Pa Pr Prandtl number Pr t turbulent Prandtl number for energy q wall heat flux Wm 22 R Reynolds stress tensor Pa Re Reynolds number Ra Rayleigh number s distance from the beginning of the heated zone m t time s *Corresponding author. Tel.: þ 39-050-2217-109. Fax: þ 39-050-2217-150. Email: daniele.testi@ing.unipi.it International Journal of Computational Fluid Dynamics, Vol. 21, Nos. 7–8, August–September 2007, 267–276 Downloaded By: [Testi, Daniele] At: 15:38 5 December 2008