P l 810 V Tcrd

where t is the bed shear stress and Tcrd is the critical shear stress for deposition. The bed shear stress corresponding to the high speed operation of the flume was taken as the critical shear stress for deposition for the current application of the model. It is possible to measure the critical shear stress for deposition precisely by successively lowering the shear stress until the deposition of the sediment begins.

8.5.1.4 Erosion Flux, Fe

The erosion flux Fe is taken as zero. This is in accordance with the recent finding of Winterwerp,23 who argued that the equation of Krone can be interpreted as a combined erosion-deposition formula for erosion-limited conditions. Considering the erosion flux, while using the Krone's equation for deposition is equivalent to considering the erosion flux twice.

8.5.1.5 Collision Efficiency Parameter, fi

As indicated earlier, the collision efficiency parameter accounts for the different coagulation mechanisms that are present in the freshwater flocculation process. Here, the parameter is treated as a calibration factor and was determined as part of the calibration process. If this parameter is determined through calibration as it has been done here, then the model can also be used for saltwater flocculation.

8.5.1.6 Collision Frequency Functions Kb, Ksh, K\, Kys

The collision frequency functions given by Equations (8.4) to (8.7) were determined for flows in the rotating flume using the dissipation rate of kinetic energy of turbulence e given by the PHOENICS' model simulations.

8.5.1.7 Model for the Growth-Limiting Effect of Turbulence

The growth-limiting effect of turbulence was modeled using the scheme proposed by Tambo and Watanabe.24 According to their scheme, a collision-agglomeration function was used as a multiplier for the collision-frequency function to produce an effective collision frequency that produced an optimum floc size distribution for the given turbulence level. The collision-agglomeration function recommended by Tambo and Watanabe24 is as follows:

where R is the number of primary particles contained in a floc under consideration and S is the number of primary particles contained in the maximum floc for the given turbulence level. The parameters a0 and n assumed values of 1 and 6, respectively, as recommended by Tambo and Watanabe.24 This approach is an indirect way in which the breakup of particles during collision is handled.

0 0

Post a comment