Mathematical expression of pressure gradient in the flow of spherical capsules less dense than water Ismail Teke, Deniz Ulusarslan * Department of Mechanical Engineering, Yildiz Technical University, 34349 Istanbul, Turkey Received 17 August 2005; received in revised form 27 November 2006 Abstract This study yielded a mathematical expression to calculate the pressure gradient (DP/L) m of the flow of a spherical capsule train. An experimental investigation was carried out to determine pressure drops of two-phase mixture flow of spherical ice capsules and water inside the pipelines of cooling systems. Instead of ice capsules, spherical capsules made of polypropylene material whose density (870 kg/m 3 ) is similar to that of ice were used in the experiments. Flow behavior of the spherical capsules, 0.08 m outer diameter, was observed in the measuring section inside plexiglass pipes, 0.1 m inner diameter (ID) and 6 m in length; pressure drops were measured on the 4 m section. The investigation was carried out in the 1.2 · 10 4 < Re < 1.5 · 10 5 range and under transport concentration (C tr ) by 5–30%. Dimensionless numbers of the physical event were found out by conducting a dimensional analysis, so that mixture density was expressed in terms of specific grav- ity and in situ concentration. After arriving at certain conclusions based on the relevant experimental findings and obser- vations, empirical and mathematical models which can be used for calculation of the pressure gradient were developed. Comparison of the mathematical model with the experimental findings revealed that pressure drop values deviated by 2.7% on average for 2.5 · 10 4 < Re < 1.5 · 10 5 . Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Two-phase flow; Spherical capsule train; Pipeline; Pressure drop; Mathematical model; Cooling systems 1. Introduction Utilization of spherical ice capsules in cooling systems is still relatively new method. Since the latent heat of ice is very high, the same mass discharge provides more cooling, or the cooling process is ensured to be more economical on the grounds that less mass discharge and pipes smaller in diameter are required. Utilization of spherical ice capsules which occupy 80–90% of pipe’s diameter will be an innovation in cooling technology and bring various advantages. 0301-9322/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2006.11.002 * Corresponding author. Tel.: +90 212 2597070; fax: +90 212 2616659. E-mail address: ulusars@yildiz.edu.tr (D. Ulusarslan). International Journal of Multiphase Flow 33 (2007) 658–674 www.elsevier.com/locate/ijmulflow