Probabilistic entrainment of particles from a rectangular cavity in turbulent open channel flows
Date of Issue2017
School of Civil and Environmental Engineering
Nanyang Technological University, Singapore
Entrainment of river-bed material from scour protection works such as grade control structures, has shown to have devastating consequences on the safety of hydraulic structures, as witnessed repeatedly in Taiwan’s Toucian river during typhoon-induced floods. The entrainment of stones from between the gaps of the enormous concrete blocks used in these control structures has been the predominant factor behind their failure, with Lai et al. (2010) attributing gap scour to have been responsible for a massive 35.5% of the associated damages. Although researchers in the past have studied sediment entrainment extensively, their studies have exclusively dealt with entrainment on flat sediment beds only, rather than from these cavities. The flow field in cavities such as gaps between these armor blocks can be highly turbulent and 3-dimensional, clearly in vivid contrast to the primarily unidirectional flow on flat beds. This spatial as well as temporal randomness in the turbulent cavity flow is likely to make the particle entrainment process highly probabilistic in nature, when compared to flat bed unidirectional flow fields which have low spatial variations near the sediment bed. Accordingly, experiments are conducted to investigate this entrainment phenomenon from a rectangular cavity using a frequentist probabilistic approach; and the role of different experimental parameters is examined to develop a comprehensive understanding of this stochastic entrainment process. The parameters used here are – particle characteristics, cavity depth, free-stream flow velocity, cavity length (or cavity aspect ratio). Results from the experiments reveal that particle entrainment occurs over a wide range of particle properties and cavity depth, with varying degree of success, rather than 100% entrainment and no-entrainment being strictly demarcated by a critical or threshold value as was proposed by Sumer et al. (2001). The cavity flow field is seen to undergo significant transitions with increase in cavity depth, from 1-dimensional to 3-dimensional, with the latter comprising secondary flows, flow reversals, eddies, etc. The particle entrainment too is affected by this changing flow field, with entrainment probability following a reverse S-shaped curve and entrainment durations following a lognormal distribution. The probabilistic aspect of this entrainment process is best highlighted when, despite keeping all test parameters constant, particles are still observed to entrain sometimes in 10 seconds, sometimes in 1 – 2 minutes, and at other times no entrainment occurs even for as long as 10 minutes duration. The particle Shields parameter values (obtained from shear velocity in the free-stream region) are compared to the critical values in Shields (1936) and Sumer et al. (2001). The comparison reveals that particle entrainment from a cavity which is several times deeper than the particle diameter, can be attained even at Shields’ parameter values significantly lower than the critical values proposed in these two studies. This aspect of the entrainment process becomes more apparent when the cavity flow fields are examined, which shows higher vertical velocity and higher turbulent kinetic energy (TKE) near the cavity downstream edge compared to that in the free-stream region. This is in spite of the lower streamwise velocity at the cavity edge. Visualization of the instantaneous vectors surrounding an entraining particle further reveals how intricately the entrainment is influenced by the randomness in the flow which is changing from one instant to another. Finally, the effect of the cavity geometry on particle entrainment is studied in its entirety by keeping the cavity aspect ratio constant, but varying the cavity length and depth separately. It is observed that the cavity depth plays a more crucial role in determining the particle entrainment probability than the cavity length. Additionally, the cavity flow field is decomposed using the Proper Orthogonal Decomposition (POD) method to study the influence of cavity depth on the large-scale (LS) eddies. Although it would appear that particle entrainment from a shallower cavity is easier, the POD results show that the LS eddies at lower cavity depths have correspondingly lower TKE content due to the lower flow depth present at the cavity. These lower energy LS eddies in shallow depths sometimes negate the ease of entrainment from shallow cavities and lead to a reduced entrainment probability, especially for particles with relatively lower Shields parameter.