An effective method for calculating the elements of thermal power plants, which are reduced to solving systems of partial differential equations

Alexander Kler,Danil Apanovich,Alexey Maximov,V.A Stennikov,N.I Voropai,F.-J Lin,S.P Filippov,C Rehtanz,M Negnevitsky,J.-Y Yoon,N.A Yusifbeyli,P Changwei,S.V Alekseenko,B Sereter

doi:10.1051/e3sconf/202020903029

Abstract

Calculations of dynamic processes in the elements of thermal power plants (TPP) (heat exchangers, combustion chambers, turbomachines, etc.) are necessary to justify permissible and optimal operating modes, the choice of design characteristics elements, assessing their reliability, etc. Such tasks are reduced to solving partial differential equations. At present time for such calculations are mainly used finite-difference method and finite element method. These methods are cumbersome and complex. The article proposes a method, the main idea of which is to reduce the solution of equations to solving linear programming problems (LP) is demonstrated by the example heat exchanger of periodic action. The mathematical description includes the following energy balance equations for gas and ceramics, respectively, on the plane, where - indicates the length of the heat exchanger, and - the operating time. Also provides a more complex model, taking into account the spread of heat inside the balls of the ceramic backfill.

Highlights

IntroductionCalculations of stationary and non-stationary modes of operation of a number of elements of thermal power plants (heat exchangers of various types, furnaces, combustion chambers, turbine grids, etc.) are reduced to solving systems of partial differential equations (PDE)
Calculations of stationary and non-stationary modes of operation of a number of elements of thermal power plants are reduced to solving systems of partial differential equations (PDE)
When using finite difference methods (FDM), a grid is constructed on the computational domain and for each of its nodes, based on the initial differential equations, a subsystem of algebraic equations is formed [1,2,3,4]

Summary

Introduction

Calculations of stationary and non-stationary modes of operation of a number of elements of thermal power plants (heat exchangers of various types, furnaces, combustion chambers, turbine grids, etc.) are reduced to solving systems of partial differential equations (PDE). It should be noted that with a coordinated selection of the number of finite elements, the number of nodes in the elements and the number of basis functions, it is possible to achieve that the residuals at the nodes of elements, subject to the specified conditions, will be equal to zero These conditions generate a system of algebraic equations, the solution of which gives linear combinations of basis functions that allow one to determine the desired variables at any point in the computational domain, which is an undoubted advantage of the FEM. Taking into account the indicated FDM, FVM and FEM defects, a more effective method for solving the system of PDE is proposed It is based on the search for such values of the coefficients of linear expansions of the basis functions, which represent the dependences of the functions sought from the system of PDE on the spatial coordinates and time, at which the residual maximum in absolute value reaches the minimum value, determined among all residuals at the given control points of the computational domain. If the initial system of PDE is linear, the proposed method, which can be called the method of control points, is reduced to solving a linear programming problem[11,12]

Mathematical problem statement

Heat exchanger mathematical model

Calculation results

Conclusions