Added mass of a spherical cap body Miroslav Simcik n , Miroslav Puncochar, Marek C. Ruzicka Department of Multiphase Reactors, Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojova 135, 16502 Prague, Czech Republic 1 HIGHLIGHTS  Dispersed flow modeling.  Added mass coefficient for a cap- body.  Collective added mass in a swarm of cap bodies. GRAPHICAL ABSTRACT article info Article history: Received 16 May 2014 Received in revised form 2 July 2014 Accepted 11 July 2014 Available online 18 July 2014 Keywords: Spherical cap Added mass Single particle Particle swarm Correlations abstract The added mass coefficient C was determined for a single spherical-cap body moving in a uniform unbounded fluid. An approximate simple physical model for C was suggested and was well compared with the analytical result of Kendoush, which likely is the only available theoretical result in the literature, up to date. The correct result for C was obtained via direct numerical flow simulation with CFD. Both the rigid and deformable (bubble, drop) cap body was considered. An approximate model was suggested for the collective added mass in a swarm of spherical cap bodies. A relation was found between the added mass of an unbounded cap body and a bounded spherical body. Practical explicit correlation formulas for C were obtained, suitable for engineering modelling of multiphase flow systems with bubbles, drops and solids. A relation between the added mass, Darwin drift, and fluid mixing was also noted. & 2014 Published by Elsevier Ltd. 1. Introduction The goal of this contribution is to obtain information about the added mass (AM) coefficient C of a spherical-cap body moving in a uniform unbounded fluid. The reason is that this problem has not been paid sufficient attention, on the academic side. On the practical side, cap shaped bodies are common in many engineering applications dealing with dispersed multiphase systems (bubbles, drops, solids). Besides the article of Kendoush (2003, 2004), we could not find other contributions on the added mass of a cap body. The present study follows our two previous contributions on investigation into various area of the AM problem (Simcik et al., 2008; Simcik and Ruzicka, 2013). It is known (e.g. Batchelor, 1967) that the inertia reaction of a fluid with respect to an accelerating submerged body can be expressed by the inertia mass tensor M. It relates the vector a of the body acceleration to the vector F of the inertia force exerted by the fluid on the body (inertial resistance or reaction): F ¼ M  a: ð1:1Þ The mass tensor can be expressed as M¼ ρV C, where ρ is the fluid density, V is the body volume, and C is the inertia coefficient tensor. In the case with sufficient symmetry, the tensor C becomes Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science http://dx.doi.org/10.1016/j.ces.2014.07.015 0009-2509/& 2014 Published by Elsevier Ltd. 1 www.icpf.cas.cz n Corresponding author. E-mail address: simcik@icpf.cas.cz (M. Simcik). Chemical Engineering Science 118 (2014) 1–8