CSD spillage is defined as “any soil that is dislodged above the lowest cutter tip trajectory of a single swing, but is not sucked into the suction pipe”. In addition to higher energy consumption and material wear for delivering the targeted depth, spillage can lead to a variety of environmental issues. As of yet, no analytical model exists in literature that can estimate spillage rates for a given set of cutting parameters. This thesis presents the Sand-Rock Cutting Spillage Model (SRCSM), an engineering model that is particle size-agnostic and makes use of cutting parameters that are all available to the dredge operator.
Prediction accuracy of 5 percentage point is achieved with a two-disc potential flow model complemented with empirical closing relationships. A triad of forces governs flow in the cutter head for typical cutting conditions: a centrifugal, suction and gravitational force are considered. For the centrifugal pump effect, and centrifugal pump effect only, the flow inside the cutter is considered steady, non-gravitational, inviscid and non-axial. This allows for the derivation of a pressure-discharge affinity law from the Navier-Stokes. The axial pump effect is governed by the mixture velocity at the suction mouth. It is hypothesized that the pressure difference over the discs drives an inflow at the disc closest to the nose. Centrifugal advection and rapid redeposition spillage are considered the two most significant spillage types out of the six classified. Centrifugal advection can be determined by identifying the onset of radial outflow at the disc near the cutter ring. The magnitude of rapid redeposition flow and its concentration depend on mixing effects that are proportional to the ratio particle settling velocity and the mixture velocity squared. The model is calibrated with three coefficients. User input parameters are the cutter geometry, cut-type factor fd,type (-1 for under-cut), bank slope angle ξ, cutter inclination angle λ, bank height h, step size lstep, rotational velocity ω, settling velocity vts, swing velocity vs, mixture velocity vm and material densities.
Spillage=f(Dring,Dnose,Dpipe,b,fd,type,ξ,γ,h,lstep,ω,vts,vs,vm,ρq,ρb,ρw )
For calibration, an inverse flow number θ-1 is used that is proportional to the ratio of centrifugal flow over mixture flow. Spillage rates from SRCSM are in high agreement with reference data for sand (Miltenburg, 1983) and rock (Den Burger, 2003) in an under-cut swing. A sensitivity analysis suggests that most cutter head dynamics are adequately incorporated. The model is less reliable for (non-typical) inverse flow numbers of θ-1= 6 [-] and higher due to a mixture velocity that drops below zero. In addition, the model is calibrated for a relatively high cutter inclination angle of 45 [deg] and bank angle of 45 [deg]. Caution should be observed with the results. It is also suggested that mixing effects related to the swing velocity are incorporated more explicitly in the model. For typical sand cutting conditions, the highest spillage reduction (-4.6%) is achieved by a 1 [%] smaller step size. For rock, the highest spillage reduction (-0.63%) is achieved for a 1 [%] decrease in swing velocity. Spillage appears to follow the theorem of Ellington (1934): it don’t mean a thing if it ain’t got that swing.