Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts Entry length convective heat transfer in a monolith: The effect of upstream turbulence Ivan Cornejo a,b , Gonzalo Cornejo b , Petr Nikrityuk a , Robert E. Hayes a,* a Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada b Departamento de Ingenieria Quimica y Ambiental, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile ARTICLE INFO Keywords: Monolith Channels Turbulence Nusselt CFD Catalytic converter ABSTRACT In a typical practical monolith reactor implementation, turbulent flow in a large pipe or inlet header enters small monolith channels. After some distance the flow becomes fully developed laminar flow. It has been shown that the distance over which the turbulence transitions to laminar flow is significant. This paper reports results of investigation into the value of the Nusselt number in the entry region of a circular tube under conditions of decaying turbulence. Large Eddy Simulations (LES) are used to model the flow. LES simulations show that the Nusselt number is significantly larger in the entry region compared to the classical case of developing laminar flow. The entry length Nu number depends not only on the inverse Graetz number, but also independently on the Reynolds number, turbulence length scale and upstream turbulence intensity. A general correlation is developed that relates the Nu number in the entry region to the inverse Graetz number, Reynolds number, inlet turbulence intensity and turbulence length scale. 1. Introduction Monolith reactors are extensively used in the automotive industry as catalytic converters. A typical converter consists of a metallic carcass containing the monolith, an inlet diffuser, and an outlet cone, as shown in Fig. 1. To add catalyst metals, such as platinum, palladium or rho- dium, a coating process is performed which results in a thin layer of washcoat fixed to the inner walls of the channels of the monolith, where the chemical reactions occur. In automotive applications the converter is fed with the exhaust from the engine, which is fully turbulent in the exhaust pipe with a Reynolds number (Re) of the order of 10 4 . Due to the size of the monolith channels, the Re decreases by orders of magnitude inside them, down to sub-critical values. Based on that, the flow in the channels is often assumed to be fully laminar along the entire substrate. In reality, at the diffuser-monolith interface the turbulence in the dif- fuser collides with the walls of the monolith and it is forced into the channels, producing an acceleration due to the reduction of the open frontal area [1,2]. Vortices larger than the cross-section of the channels break into smaller ones and enter the substrate. Despite the low Re, the turbulence does not disappear spontaneously; it decreases at a rate dominated by the Re, in some cases over a distance that covers a sig- nificant portion of the channel. The magnitude of the effect of such turbulence on the key variables of the converter, such as the pressure drop, and heat and mass transfer inside the substrate, is still a matter of discussion among the community. The performance of the reactor, and the fuel efficiency of the engine, ultimately relies on the design of the substrate and the catalyst, making an accurate description of the phe- nomena inside of the channels important. The motivation of this paper is to build an understanding of the effect of the turbulence entering the monolith and to quantify the magnitude of its impact on the effective heat and mass transfer coefficients between the fluid and the channel walls. In typical catalytic converters, the monolith is made from ceramic and contains thousands of parallel channels. Since the hydraulic dia- meter of the channels is of the order of one millimetre, it is very difficult to measure local profiles of velocity or temperature inside the substrate without affecting them. Even when it is possible to make measure- ments, it is done at the expense of the accuracy of the result [3]. Re- action rate constants have an exponential dependence on the tem- perature, which is often higher close to the entrance of the channels during normal operation. It is precisely there where the turbulence plays a role as well, reinforcing the motivation of this study. The main focus is the evaluation of the convective heat transfer coefficient along the channels, and to make a comparison of the Nusselt (Nu) with and without turbulence entering the channels. Turbulence is characterised by the presence of a series of vortices of several sizes that improve significantly the transport of momentum, heat and mass. Since https://doi.org/10.1016/j.ijthermalsci.2018.12.044 Received 16 August 2018; Received in revised form 28 November 2018; Accepted 28 December 2018 * Corresponding author. E-mail address: hayes@ualberta.ca (R.E. Hayes). International Journal of Thermal Sciences 138 (2019) 235–246 1290-0729/ © 2018 Published by Elsevier Masson SAS. T