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Limitation of one-dimensional models of sedimentation and thickening


The earliest one-dimension dynamic clarifier model is established on the basis of mass conservation law for an ideal clarifier composed of a finite number of layers, and is used to simulate both underloading and overloading conditions. The estimation results indicate the original model can provide a sound predication in an underloading situation, but fails in identifying the sludge blanket level and underflow solids concentration in an overloading situation. Two improved models: the gravity flux constraint model and the dispersion model have been used to simulate both underloading and overloading conditions in order to test their reliability. Even though both of them can show the rise of sludge blanket height under the condition of overloading, their simulation results do not converge. Another obvious flaw of these two models is their sensitivity to the number of model layers, which means the simulation outcome is a function of the number of layers. This inappropriate phenomenon has been demonstrated by testing these two models in 10-layer, 30-layer and 50-layer situations,and the variation tendencies of their simulation outcomes are opposite. Method of characteristic (MOC) is a kind of numerical methods used to solve nonlinear hyperbolic partial differential equation. Given the fact that the original model is a nonlinear first-order hyperbolic partial differential equation, MOC is applicable to solve it. However, a brief analysis illustrates the mass conservation equation can only provide a positive characteristic line, and the negative line remains unknown. A possible method to figure out the negative one is set another equation based on the momentum or energy conservation.

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