Transitional non-Newtonian flow in half-round channels

Abstract

The prediction of non-Newtonian transitional flow in open channels is even more complex than for pipe flow. Not much work has been done in the field. The application is in mine waste and sludge disposal where it is important to distinguish between laminar, transitional and turbulent flows. Transitional flow is often characterised by its unstable nature. Thus, it is important to predict the transition region so it can be avoided. The non-Newtonian fluids namely kaolin and bentonite suspensions and CMC solutions at different concentrations were tested in two different flumes of 10 m long by 300 mm wide and 10 m long by 150 mm wide half round tilting flume which could be tilted up to 5 degrees. The rheology of the fluids was tested in an in-line tube viscometer with 3 tubes of diameters 13 mm, 28 mm and 80 mm. Flow depth and flow rate measurements were taken in the flumes at various flow rates spanning laminar and turbulent conditions and at different slopes from 1 to 5 degrees. The relationship between Froude and Reynolds numbers were used for these predictions. The same approach was followed in this work and new models were developed for half round channels using an appropriate Reynolds number and Froude number. Haldenwang (2003) and Haldenwang et al (2010) proposed models for predicting the onset of transition and full turbulence in rectangular channels. This method was extended to half round channels. Fitton (2008) established a model for predicting the point of laminar-turbulent transition. After comparing the critical velocity values for both models, it was found that they were both less accurate. Fitton (2008) approach used the relationship between the friction factor and the Reynolds number whereas Haldenwang et al (2010) method used the relationship between the Froude number and the Reynolds number. Since the Froude number shows the onset of transition better than the friction factor (Haldenwang, 2003). Haldenwang’s (2003) approach was selected to establish new critical Reynolds numbers for the onset and end of transitional flow for half round channels. The transition model proposed by Fitton (2008) for half-round channels was tested and the new developed model performed better than the one published. When using Haldenwang’s approach, the channel shape effect and the onset of turbulent flow were also observed. Key words: Open channel flow, non-Newtonian, rheology, laminar, transition, turbulence.