Evaluation of service pressure regulation strategy on the performance of a rural water network based on pulse demand; using the method of characteristics

Reducing the occurrence of pipe bursts, reducing leakage, and reducing energy consumption are the three main goals in implementing pressure control programs in water distribution networks. Service Pressure Regulation Strategy is an evolved approach that encompasses all goals of pressure management. This paper has investigated this approach in a rural network with hydraulic complexities as a case study so that some parts of the network have excess pressure and other low pressure. A computer code based on the Method of Characteristics (MOC) has been developed for network hydraulic analysis. The generated code analyzes unsteady flow, pressure-driven demand analysis, and dynamic adjustment of pressure control valves based on the target node. Also, the experimental results of a laboratory network have been applied to validate and calibrate the numerical simulation. In addition, by measuring the flow rate and pressure of the network and the results of the MNF method, three consumption patterns were used to generate pulsed nodal demands. Studies show that creating Pressure-Management Areas by hydraulic analysis by MOC will determine the best control strategies. The mean pressure has decreased 54% by applying this strategy. Furthermore, the average fluctuations of pressure have reduced from 9.7 meters to 3.5 meters.

Accretion and ablation in deformable solids with an Eulerian description: examples using the method of characteristics

Accretion and ablation, i.e., the addition and removal of mass at the surface, are important in a wide range of physical processes, including solidification, growth of biological tissues, environmental processes, and additive manufacturing. The description of accretion requires the addition of new continuum particles to the body, and is therefore challenging for standard continuum formulations for solids that require a reference configuration. Recent work has proposed an Eulerian approach to this problem, enabling side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduced the elastic deformation as an additional kinematic descriptor of the added material, and its evolution has been shown to be governed by a transport equation. In this work, the method of characteristics is applied to solve concrete simplified problems motivated by biomechanics and manufacturing. Specifically, (1) for a problem with both ablation and accretion in a fixed domain and (2) for a problem with a time-varying domain, the closed-form solution is obtained in the Eulerian framework using the method of characteristics without explicit construction of the reference configuration.

Stress-deformed state of the shell with a small initial deflection under the action of the end load

Purpose of work. Construction of method for calculating the stress-strain state of cylindrical shell with small initial deflection, to which an end load is applied, using the method of characteristics. Comparison of the calculation results of the obtained model with the works of other authors in this area. Research methods. For the calculation, the equations of motion of the Timoshenko type shell were used, taking into account both the shear deformation and inertia of rotation, and some nonlinear terms, to which the method of characteristics was applied. To obtain the equations of shell motion, the Hamilton-Ostrogradsky variational principle was used. Results method is proposed for calculating the stress-strain state of a cylindrical shell with a small initial deflection using characteristics. Comparative analysis of the calculation results with research in this area by other authors, which showed the effectiveness of the proposed method. Scientific novelty. The equations of the classical theory of shells, based on the Kirchhoff-Love hypotheses, which do not take into account the shear deformation and inertia of rotation, as well as linear equations of the Timoshenko type, have become widespread. In this work, a model of the stress-strain state of an axisymmetric shell with small initial deflections is constructed, taking into account both shear deformation and rotational inertia, and some nonlinear terms. Practical value. The proposed method can be used to calculate the stress-strain state of structures in which thin shells are present as elements, taking into account small initial deflection. This method makes it possible to study the influence of the characteristics of the initial deflection on the stress-strain state of the entire structure.

Solutions of problems for the wave equation with conditions on the characteristics

In this paper we obtain a classical solution of the one-dimensional wave equation with conditions on the characteristics for different areas this problem is considered in. The analytical solution is constructed by the method of characteristics. In addition, the uniqueness of the obtained solution is proved. The necessity and sufficiency of the matching conditions for given functions of the problem are proved. When these conditions are satisfied and the given functions are smooth enough, the classical solution of the considered problem exists.

MATHEMATICAL MODELING OF THERMOGASDYNAMIC PROCESSES IN PISTON ENGINES

A method for calculating the non-stationary gas flow in the exhaust pipeline of a piston engine by the method of solitary waves of finite amplitude is presented. The comparison of experimental data and calculation results by the method of characteristics and obtained when considering the process of propagation of solitary waves through the exhaust pipeline of a piston engine equipped with a pulsed turbocharging system is shown.