A new simple equation for the prediction of filter expansion during backwashing Elif Soyer and Omer Akgiray ABSTRACT Elif Soyer (corresponding author) Department of Environmental Engineering, Istanbul Technical University, Maslak-Istanbul, Turkey Tel.: +90 212 285 6785 Fax: +90 212 285 3781 E-mail: esoyer@ins.itu.edu.tr Omer Akgiray Department of Environmental Engineering, Marmara University, Goztepe-Istanbul, Turkey Fluidization experiments have been carried out with glass spheres, plastic spheres and several sieved fractions of silica sand, garnet sand, perlite and crushed glass. The effect of particle shape on expansion behavior is investigated. Sphericity as determined using the Ergun equation and fixed-bed head loss data is employed to quantify the shape effect. It is found that the influence of particle shape depends on the Reynolds number based on backwash velocity. A new equation that accounts for particle shape is proposed. For the materials studied, the proposed equation gives excellent agreement with both the spherical and the non-spherical particle data. Key words | backwash, filter media, fluidization, particle shape, sphericity, water treatment INTRODUCTION AND THEORY Liquid – solid fluidization has a number of applications in engineering (Epstein 2003b). The expansion of granular filter media during backwashing is of particular interest (Droste 1997; AWWA 1999; Akkoyunlu 2003). It is impor- tant to have an understanding of fluidization principles and an ability to predict bed expansion as a function of liquid velocity to design such systems properly. More often than not, the media involved are not spherical and it is necessary to have an expansion model that can be applied to beds of non-spherical particles. Numerous equations have been proposed to predict the expansion of liquid fluidized beds of spheres. Reviews and listings of such equations can be found in Garside & Al-Dibouni (1977), Couderc (1985), Hartman et al. (1989), Di Felice (1995) and Epstein (2003a). An evaluation of these equations has recently been presented by Akgiray & Soyer (2006). Very few general equations exist, however, for non- spherical media (Cleasby & Fan 1981; Dharmarajah & Cleasby 1986; Akgiray & Saatc ¸ i, 2001; Akkoyunlu 2003; Akgiray et al. 2004). Furthermore, the accuracies of the expansion models for non-spherical media have not been evaluated in a satisfactory manner to date. Akgiray & Soyer (2006) noted that, while most expan- sion models are strictly restricted to spheres, a correlation method explained by Richardson & Meikle (1961) may be generalized to handle non-spherical media. In this approach, a dimensionless friction factor f is plotted against a modified Reynolds number Re 1 . The friction factor is defined as follows: f ¼ R r V 1  2 ð1Þ where R ¼ force per unit area of grains, r ¼ density of the fluid, 1 ¼ porosity of the bed and V ¼ fluid velocity based on the empty cross section of the bed. The porosity 1 for the fluidized bed is calculated by the relation L(1 2 1) ¼ L 0 (1 2 1 0 ), where L ¼ depth of the fluidized bed, L 0 ¼ depth of the fixed bed and 1 0 ¼ fixed-bed porosity. Equation (1) holds for both fixed and fluidized beds. For a fluidized bed under steady state conditions, the upward frictional force on the particles is balanced by the effective gravitational force. The net gravitational force is the weight of the particles less the upward force attributable doi: 10.2166/aqua.2009.090 336 Q IWA Publishing 2009 Journal of Water Supply: Research and Technology—AQUA | 58.5 | 2009