* Corresponding author. Tel.: 001 508 831 5350; fax: 001 508 831 5853; e-mail: agdixon@wpi.edu. Presently at Procter and Gamble, European Supply Co., Mechelen, Belgium. Chemical Engineering Science 54 (1999) 2433}2439 Computational #uid dynamics simulations of #uid #ow and heat transfer at the wall}particle contact points in a "xed-bed reactor S.A. Logtenberg, M. Nijemeisland, A.G. Dixon* Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, USA Abstract An accurate description of the #uid #ow and heat transfer within a "xed-bed reactor is desirable. The prevailing models of #uid #ow invoke either a constant velocity (plug-#ow) pro"le, or make use of a single axial velocity component with radial variation across the tube diameter. However, di$culties in predicting reactor performance and the wide disagreement between e!ective heat transfer coe$cients suggest that these are oversimpli"ed pictures of the real-#ow situation. Computational #uid dynamics is a means that could improve our understanding of "xed-bed #uid #ow and heat transfer, by solving the 3D Navier}Stokes equations. Simulations are presented for an improved geometry, compared to previous studies, of 10 solid spheres in a tube with a tube-to-particle ratio of 2.43, that includes both particle to particle and also wall to particle contacts. Simulations are also reported with heat generation from the spheres. The simulation results show strong #ow components towards the wall and away from the wall, thereby transporting heat. The #ow around the contact points themselves shows stagnant regions, due to the high shear of the solid surfaces. A high velocity gradient in the radial direction is observed between two layers of spheres, which clearly shows how the heat transfer is increased within the bed. Regions of back-#ow are also observed, in qualitative agreement with literature experimental studies.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Fixed bed; Computational #uid dynamics; Heat transfer; Fluid #ow; Velocity pro"les; Packed-bed reactor 1. Introduction The problem of understanding and predicting the heat transfer and #uid #ow in a "xed-bed reactor is one of long-standing. In particular, narrow tubes of low tube- to-particle diameter ratio (N), in the range of 3}8, present di$culties, due to the presence of wall e!ects across the entire bed radius. However, such tubes are usually used for reactions with strong heat e!ects, to facilitate removal of reaction heat. A recent new approach to this problem is the use of computational #uid dynamics (CFD) to model #uid #ow and heat transfer near the wall, and thus to contribute to improving our understanding of these phenomena. 1.1. Fixed-bed heat transfer Nowadays, "xed-bed reactors are one of the most commonly-used reactor types in industry. However, even though this reactor has been investigated by many re- searchers over the last 40 years, no consensus over the heat transfer behavior is found amongst researchers (Li and Finlayson, 1977; Tsotsas and Schlu K nder, 1990; Vortmeyer and Haidegger, 1991). The reason for this lies in the complexity of the problem and the limitations of experimental studies. Over the past decades a lot of attention has been given to modeling heat transfer behav- ior in "xed-bed reactors. Most models that are available in the literature are based on lumping heat transfer mech- anisms into easier to use models. Today, reactor engin- eers still prefer to describe the heat transfer behavior by means of a two-dimensional pseudo-homogeneous model (Vortmeyer and Haidegger, 1991), normally referred to as the standard model, which neglects temper- ature di!erences between the #uid and solid phases. The 0009-2509/99/$ } see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 4 4 5 - X