Design and safety basis sludge characterization from exposure-adjusted radioisotopic source terms for N reactor fuel stored at K-East and K-West basins

In order to improve sewage sludge characterization for both dewatering and agricultural spreading, we have studied their electrical and rheological properties. On the one hand, electrical measurements give a picture of the microstructure of the material (charges, particles mobility), whereas on the other hand, rheological experiments describe its macrostructure (consistency). The interactions of the matter are the link between them. Our results showed that sludge becomes more conductive when its dry content (for a defined composition) or the temperature increases, and also during aging. In parallel its apparent viscosity increases with the dry content but decreases with the temperature or during aging. In each case a clear correlation was found between electrical and rheological parameters. This relationship clearly depends on sludge composition, and also on parameters such as the temperature, the observation frequency, the velocity range in the case of relaxation experiments. Finally, those types of experiments can be correlated to improve the comprehension of sludge structure and consistency characterization.

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Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽

10.3390/math9151799 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1799

Author(s):

Irene Gómez-Bueno ◽

Manuel Jesús Castro Díaz ◽

Carlos Parés ◽

Giovanni Russo

Keyword(s):

High Order ◽

Collocation Methods ◽

Quadrature Formulas ◽

Balance Laws ◽

Source Terms ◽

Time Step ◽

Systems Of Balance Laws ◽

Reconstruction Operator ◽

Non Linear ◽

Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

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New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions

Boundary Value Problems ◽

10.1186/s13661-020-01467-5 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Mohammad M. Al-Gharabli ◽

Adel M. Al-Mahdi ◽

Salim A. Messaoudi

Keyword(s):

Wide Class ◽

Relaxation Function ◽

Nonlocal Boundary ◽

Nonlocal Boundary Conditions ◽

General Assumption ◽

General Decay ◽

Source Terms ◽

Relaxation Functions ◽

Viscoelastic Equations ◽

General Source

Abstract This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$ k i , namely, $$\begin{aligned} k_{i}^{\prime }(t)\le -\xi _{i}(t) \Psi _{i} \bigl(k_{i}(t)\bigr),\quad i=1,2. \end{aligned}$$ k i ′ ( t ) ≤ − ξ i ( t ) Ψ i ( k i ( t ) ) , i = 1 , 2 . We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when $k_{i}(s) = s^{p}$ k i ( s ) = s p and p covers the full admissible range $[1, 2)$ [ 1 , 2 ) .

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Sheath formation in an oblique magnetic field - some comments on length scales and source terms

Journal of Physics Conference Series ◽

10.1088/1742-6596/768/1/012005 ◽

2016 ◽

Vol 768 ◽

pp. 012005

Author(s):

T Gyergyek ◽

J Kovačič

Keyword(s):

Magnetic Field ◽

Source Terms ◽

Length Scales ◽

Sheath Formation ◽

Oblique Magnetic Field

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A modulus-based multigrid method for nonlinear complementarity problems with application to free boundary problems with nonlinear source terms

Applied Mathematics and Computation ◽

10.1016/j.amc.2021.126015 ◽

2021 ◽

Vol 399 ◽

pp. 126015

Author(s):

Li-Li Zhang

Keyword(s):

Free Boundary ◽

Multigrid Method ◽

Complementarity Problems ◽

Free Boundary Problems ◽

Nonlinear Complementarity Problems ◽

Source Terms ◽

Boundary Problems ◽

Nonlinear Source ◽

Nonlinear Complementarity

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The Use of Rheology for Sludge Characterization

Water Science & Technology ◽

10.2166/wst.1982.0120 ◽

1982 ◽

Vol 14 (6-7) ◽

pp. 475-489 ◽

Cited By ~ 35

Author(s):

H W Campbell ◽

P J Crescuolo

Keyword(s):

Particle Size ◽

Sewage Sludge ◽

Test Procedures ◽

Particle Size Reduction ◽

Rotational Viscometer ◽

Polymer Addition ◽

Rheological Measurements ◽

Acceleration Rate ◽

Sludge Characterization ◽

Potential Use

Rheological measurements were conducted on a variety of anaerobically digested sewage sludges to evaluate the potential use of rheology in describing the effects of chemical conditioning on the physical characteristics of sludges. The objectives of the study were to evaluate the influence of the method of chemical conditioning on rheological measurements; to determine the response of the viscometer system to changes in the instrument variables; and to evaluate interrelationships between rheology and other physical properties. All rheological measurements were made using a coaxial rotational viscometer. Evaluation of a variety of test procedures identified that both the method of adding chemical conditioners, and the acceleration rate of the rotational viscometer, could significantly alter the shape of the rheograms. A suggested methodology was identified and selected samples were analyzed in triplicate to test the reproducibility of the procedures. Existing mathematical models do not adequately describe the variety of flow behaviour patterns observed with sewage sludge. The concepts of yield stress and apparent viscosity also have limited value due to problems of definition and calculation. A parameter termed the “instantaneous viscosity”, defined as the derivative of the flow curve, is suggested as being more suitable for describing sludge behaviour. The relationships between chemical conditioning, particle size distribution and applied shear were explored. As polymer addition increased, the sludge particles became more susceptible to shear breakup. The extent of particle size reduction was a function of the rate of shear and the time during which the shear was maintained.

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