On the effect of cluster resolution in riser flows on momentum and reaction kinetic interaction Schalk Cloete, Shahriar Amini ⁎, Stein Tore Johansen Flow Technology group, Department of Process Technology, SINTEF Materials and Chemistry, Trondheim, Norway abstract article info Article history: Received 6 April 2010 Received in revised form 3 August 2010 Accepted 8 February 2011 Available online 15 February 2011 Keywords: Kinetic theory of granular flows Riser Fluidized bed Fine grid simulations of reactive gas–solid flows in a riser were carried out using an Eulerian multi-fluid kinetic theory of granular flow (KTGF) approach. A translationally periodic section of the riser was used to replicate experimental data collected in the fully developed region of a tall riser. The spatial and temporal resolution was varied in designed experiments to find an appropriate compromise between overall numerical accuracy and computational time. Results revealed that, when first order implicit timestepping is used, no timestep independence could be reached with timestep sizes that are practically feasible. Timestep independence could only be achieved by using second order implicit timestepping. Grid independence was studied in terms of cell width and cell aspect ratio. Solution independence could be reached at a cell width in the range of 10 particle diameters, but no complete grid aspect ratio independence could be achieved. Results suggested that grids with an aspect ratio smaller than one might be necessary to attain grid independent solutions. When sufficiently fine grids are used, however, the effect of a change in aspect ratio is sufficiently small to attain accurate solutions with an aspect ratio of two or lower. Certain important conversion measures were identified for scaling between simulation results collected in a 3D cylindrical domain and those predicted by a 2D planar simulation. System behavior predicted using these scaling rules agreed well with experimental results. © 2011 Elsevier B.V. All rights reserved. 1. Introduction The kinetic theory of granular flow (KTGF) is currently a well established method for simulating the hydrodynamic behavior of gas-particle systems. It has been validated for use in bubbling beds [1], but uncertainties still exist in the simulation of risers. The main area of concern in riser simulations is the formation of meso-scale particle clusters within the domain [2]. These clusters occur on very small time and length scales and require very fine spatial and temporal resolution to be accurately resolved. The fine grid and small time steps required can make even the simulation of a lab scale 2D riser prohibitively expensive. In order to make the KTGF applicable to coarser grids, research is under way to develop filtered drag laws [3–6] or even to represent the clusters as a separate phase [7]. These techniques are still in the development phase, however, and have not been thoroughly vali- dated. Furthermore, if chemical reactions are included, the reaction kinetics model will have to be filtered as well. Research into such filtered reaction models is yet to commence. The question then arises whether the modeling error will be smallest when filtered models are used to simulate large scale reactors or when results from small scale, finely resolved simulations are subsequently scaled up. Scale-up of riser processes seems to be accurate when certain dimensionless quantities, most markedly the ratio of particle diameter to riser diameter, are kept constant [8]. Also, since computational models are not subject to physical limitations, complete control over all the applicable dimensionless numbers is possible by altering different material and system properties. With the constant increase of computational capacities, this approach might become feasible in the near future. With the scale-up methodology in mind, this study is undertaken to determine the maximum spatial and temporal resolution required to adequately simulate reacting flows within a riser. Finely resolved studies might also make a significant contribution to the future development of filtered drag and reaction models. Results from this study will indicate the maximum reactor size that can reasonably be simulated with present computational capacities and quantify the importance of cluster resolution. 2. List of symbols 2.1. Main symbol definitions Greek symbols α Volume fraction Δt Time step size (s) Powder Technology 210 (2011) 6–17 ⁎ Corresponding author at: SINTEF Materials and Chemistry, Richard Birkelands Vei 3, 7034 Trondheim, Norway. Tel.: + 47 46639721. E-mail address: shahriar.amini@sintef.no (S. Amini). 0032-5910/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2011.02.003 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec