Explicit formulation for suspended concentration distribution with near-bed particle deficiency

• We propose an explicit model for particle concentration distribution.
• Almedeij's asymptotic matching method is employed.
• Model predicts near bed particle deficiency (type II profile) well.
• Model produces best fit accuracy results in dilute and dense flow conditions.
• This study focuses on a new application of Almedeij's matching method.

An explicit expression for concentration distribution in suspension in a turbulent flow with near-bed particle deficiency (i.e. where the maximum concentration appears at some distance above the bed, referred to as ‘type II profile’ in the present work) is proposed. Initially, an asymptotic solution is expressed in each of the region after dividing the entire flow depth into two regions: inner suspension region and outer suspension region. The final model is obtained by deploying Almedeij's asymptotic matching method. Efficiency of the model is tested for dilute and dense flow through pipes and open-channels. The model is compared with available experimental data as well as with other suitable models existing in the literature. Good agreement between the observed value and computed result, and minimum error indicate that the present model is more accurate in predicting particle concentration distribution for type II profile under different flow conditions. The important finding of this study is that particle lift depends on particle size, particle density, particle fluctuating intensity and volumetric concentration. Results show that type II profile may occur for both sand and gravel particles. In addition, it is shown that in dense turbulent flow the location of maximum concentration point depends on average volumetric concentration.

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