Characterization of the dissipation of elbow effects in bubbly two-phase flows Mohan S. Yadav a , Ted Worosz a , Seungjin Kim a,⇑ , Kirk Tien b , Stephen M. Bajorek b a The Pennsylvania State University, Department of Mechanical and Nuclear Engineering, 230 Reber Building, University Park, PA 16802, USA b The United States Nuclear Regulatory Commission, Washington, DC 20555, USA article info Article history: Received 8 April 2014 Received in revised form 22 July 2014 Accepted 28 July 2014 Available online 10 August 2014 Keywords: Dissipation Elbow-effects Void fraction Bubbly flows abstract This study develops a method to characterize the elbow-region for vertical-upward-to-horizontal air– water bubbly two-phase flows through a 90° elbow with a non-dimensional centerline radius of curva- ture, R C /D, of three. The dissipation of the elbow-effects in the horizontal region downstream of the elbow is characterized by the change in the local void fraction distribution. To quantify the dissipation charac- teristics, the elbow-strength, S, is defined as the inverse of the second moment of the local void fraction distribution. It is found that the elbow-strength decreases exponentially with increasing development length in the elbow-region. The slope of decrease of the elbow-strength in the elbow-region is deter- mined by the dissipation parameter, b. The dissipation parameter determines the development length required for the elbow-effects on the two-phase flow parameters to become negligible. It is found that the dissipation parameter is a linear function of the mixture Reynolds number for the flow conditions investigated in the present study. Ó 2014 Elsevier Ltd. All rights reserved. Introduction The study of two-phase flow in straight pipes with different ori- entations and through various flow restrictions is very important for both practical applications and scientific advancement of the subject. Most energy systems, for example nuclear reactors, con- tain coolant channels that are arranged in varying orientations and that are interconnected by various flow restrictions such as elbows, valves, and tees. Flow restrictions can induce significant changes in the two-phase flow interfacial structures and their transport phenomena (Salcudean et al., 1983; Wang et al., 2004; Kim et al., 2007; Talley et al., 2009). Since the mass, momentum, and energy transfer in two-phase flow systems is governed by the interfacial structures, it is important to perform experiments and to develop models that capture the effects of flow restrictions on the interfacial structures. Most of the detailed studies on the interfacial structures have focused on two-phase flows in separate vertical-upward (Ishii and Kim, 2004), vertical-downward (Ishii et al., 2004), or horizontal (Talley et al., 2012) straight pipe geom- etries. However, flow restrictions such as vertical-upward elbows are essential to connect the vertical and horizontal pipes in practi- cal two-phase flow systems. Therefore, it is important to characterize the elbow-effects on two-phase flow parameters and develop a method to determine the length of the elbow-region. The elbow-region describes the sec- tion of the two-phase flow system where the elbow-effects are dominant. In general, the elbow-effects dissipate as the flow devel- ops downstream of the elbow. A few studies in the literature have considered the dissipation of elbow-effects in single-phase flow conditions (Sudo et al., 1998; Mattingly and Yeh, 1991). Moreover, these studies characterize the elbow-effect in terms of the strength or intensity of the secondary flow generated by the elbow (Sudo et al., 1998), which can be utilized to predict the length of the elbow-region in single-phase flows. However, there is a complete lack of studies that address the dissipation characteristics of the elbow-effects in two-phase flow conditions and model development for the elbow-region. In view of this, the objectives of the current study are: (1) to characterize the effects of a 90° vertical-upward elbow on two-phase flow parameters, (2) to define and identify the elbow-region in two- phase flow conditions, and (3) to develop a correlation to predict the length of the elbow-region in two-phase flow conditions. The study is divided into three major sections. The first section describes the experimental studies on the geometric effects of a 90° vertical-upward elbow on two-phase flow parameters. The second section presents a modeling strategy for two-phase flow systems with elbows. Both the experimental study and modeling http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.07.012 0301-9322/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +1 814 867 1783. E-mail address: skim@psu.edu (S. Kim). International Journal of Multiphase Flow 66 (2014) 101–109 Contents lists available at ScienceDirect International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow