Global steady state simulation of complex technological systems - an unified approach

1980 ◽  
Vol 45 (12) ◽  
pp. 3436-3459
Author(s):  
Josef Vrba
Keyword(s):  
Steady State ◽  
Linear Equations ◽  
Computational Algorithms ◽  
Algebraic Equations ◽  
Global Approach ◽  
Technological Systems ◽  
Unified Approach ◽  
Decomposition Level ◽  
Steady State Simulation

In general, mathematical models of steady state simulation schemas of complex technological processes are formed by sets of algebraic equations. The formal description of global approach to the solution of such sets is presented. The utilization of preliminary solution of linear equations of the set for its reduction and for the expression of dependency of the so-called eliminated variables on the remaining ones, as arguments of the reduced set, (i.e. the first decomposition level) is considered. The determination of disjoint subsystems of the reduced set (i.e. the subsets of nonlinear equations which may be solved serially and independently of each other in a sequence) and the determination of the hierarchy of their solution, when there are several such subsystems, is meant as the second decomposition level. The possibility of including of special models with particular computational algorithms in the equation-like model of complex system and the way of solution of such a problem with the mentioned two-level decomposition is also discussed. The including of both types of decomposition and the solution of the reduced set of equations in common computational block is dealt with.

A Diagonally Dominant Solution for the Cylinder End Problem

1981 ◽  
Vol 48 (4) ◽  
pp. 876-880 ◽  
Author(s):  
T. D. Gerhardt ◽  
Shun Cheng
Keyword(s):  
Infinite System ◽  
Linear Equations ◽  
Infinite Cylinder ◽  
Algebraic Equations ◽  
Precise Calculation ◽  
Linear Algebraic Equations ◽  
Present Solution ◽  
Diagonally Dominant ◽  
Expansion Coefficients

An improved elasticity solution for the cylinder problem with axisymmetric torsionless end loading is presented. Consideration is given to the specification of arbitrary stresses on the end of a semi-infinite cylinder with a stress-free lateral surface. As is known from the literature, the solution to this problem is obtained in the form of a nonorthogonal eigenfunction expansion. Previous solutions have utilized functions biorthogonal to the eigenfunctions to generate an infinite system of linear algebraic equations for determination of the unknown expansion coefficients. However, this system of linear equations has matrices which are not diagonally dominant. Consequently, numerical instability of the calculated eigenfunction coefficients is observed when the number of equations kept before truncation is varied. This instability has an adverse effect on the convergence of the calculated end stresses. In the current paper, a new Galerkin formulation is presented which makes this system of equations diagonally dominant. This results in the precise calculation of the eigenfunction coefficients, regardless of how many equations are kept before truncation. By consideration of a numerical example, the present solution is shown to yield an accurate calculation of cylinder stresses and displacements.

Steady-State Simulation of an Automotive Air Conditioning System Running on CO2

2007 ◽  
Author(s):  
Pedro P. Morais Filho ◽  
Jose´ Alberto R. Parise ◽  
Rui P. Marques da Silva
Keyword(s):  
Steady State ◽  
Cycle Performance ◽  
Algebraic Equations ◽  
Climate Control ◽  
Ambient Temperatures ◽  
Automotive Air Conditioning ◽  
Linear Algebraic Equations ◽  
State Regime ◽  
Suction Line Heat Exchanger ◽  
Steady State Simulation

This work presents a semi-empirical simulation of an automotive climate control system equipped with a transcritical vapor compression cycle running on carbon dioxide. The cycle components (a compressor, a throttling valve, an evaporator, a gas cooler, a suction accumulator and a suction line heat exchanger) were modeled to study the operation of the system, in the steady-state regime, under high ambient temperatures. The model took into account the severe conditions of tropical climates since the temperature at the inlet of the gas cooler is one of the predominant factors in the transcritical cycle performance. To assess the performance of the cycle, the thermodynamic model, reduced to a set of non-linear algebraic equations, was solved by a modified Newton-Raphson method. Reasonable agreement was found when results predicted by the model were compared with experimental data available in the literature.

scholarly journals Topological algorithm for forming nodal stresses of complex networks energy systems

2019 ◽  
Vol 139 ◽  
pp. 01066
Author(s):  
D.S. Akhmetbaev ◽  
A.R. Dzhandigulov ◽  
A.D. Akhmetbaev
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Complex Networks ◽  
Linear Equations ◽  
Distribution Coefficients ◽  
Topological Approach ◽  
Advantages And Disadvantages ◽  
Software Implementations ◽  
Node Voltage

The paper presents a new topological algorithm for the formation of nodal stresses of complex networks of power systems. The first step of the described algorithm is the search and determination of the values of all possible and specific trees of the graph corresponding to a given network of the power system. The well-known advantage of the topological approach compared to matrix methods, which allows one to obtain the final solution of non-linear equations of the steady state, has led to the development of many methods and corresponding software implementations. The paper provides a comparative analysis of the advantages and disadvantages of these methods. The main computational complexity of these methods is the search for 2 trees for each tree, which are obtained from it by dividing into two parts by removing any branch. A completely new topological approach that does not require finding 2 trees was proposed by one of the authors. The process of this method consists of the following steps: finding all possible graph trees, selecting specific graph trees, calculating the network node voltage. The work offers a unique algorithm for the implementation of these stages, which are implemented and tested at the software level. The result of the execution of the software package is the calculation of the steady state of a complex electric network using the distribution coefficients of the driving currents.

Determination of the steady-state kinetics in a spin-1 Ising model using path probability method

2020 ◽  
Vol 34 (30) ◽  
pp. 2050338 ◽  
Author(s):  
Songül Özüm ◽  
Rıza Erdem
Keyword(s):  
Steady State ◽  
Ising Model ◽  
Linear Equations ◽  
Kinetic Equations ◽  
Phenomenological Approach ◽  
Rate Equations ◽  
Probability Method ◽  
Steady State Kinetics ◽  
Path Probability Method

As a continuation of our previously published work, we propose a theoretical framework for the determination of steady-state kinetics in a spin-1 Ising model by the path probability method. The framework is based on the principles of non-equilibrium statistical physics and is quite different from the phenomenological approach. We construct a set of linear kinetic equations for the order parameters using the non-linear dynamic (or rate) equations in the presence of external magnetic field. From the steady-state solutions of the linear equations, an expression for the complex (or dynamic) magnetic susceptibility [Formula: see text] is derived. The temperature dependence of the magnetic dispersion relation [Formula: see text] and magnetic absorption factor [Formula: see text] has been studied in the ferromagnetic (FM) and paramagnetic (PM) phases as well as near the critical regime.

STEADY-STATE DETERMINATION OF FUEL-BOND NITROGEN IN DIESEL AND INDUSTRIAL GAS OIL

Clean Air ◽  
2007 ◽  
Vol 8 (4) ◽  
pp. 359-371
Author(s):  
A. Medeiros ◽  
R. Edenhofer ◽  
K. Lucka ◽  
H. Kohne
Keyword(s):  
Steady State ◽  
Gas Oil ◽  
State Determination

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

Calcium Budgets for Catchments as Interpreted by Strontium Isotopes

1989 ◽  
Vol 20 (2) ◽  
pp. 85-96 ◽  
Author(s):  
Gunnar Jacks ◽  
Göran Åberg ◽  
P. Joseph Hamilton
Keyword(s):  
Steady State ◽  
Forest Ecosystem ◽  
Coniferous Forest ◽  
Strontium Isotopes ◽  
Runoff Water ◽  
Weathering Rate ◽  
Weathering Rates ◽  
Exchangeable Calcium

Strontium isotopes in precipitation, soil and runoff water can be used to establish a ratio of wet plus dry deposited Sr to Sr released by weathering. This ratio is especially enhanced in areas with old acid Proterozoic rocks (0.6-2.5 Ga) and Archean rocks (>2.5 Ga). Since Sr and Ca behave in an analogous way in the coniferous forest ecosystem the results for Sr can be used for the determination of Ca. If the deposition of calcium can be calculated reasonably accurately the weathering rate can also be estimated. Five catchments have been investigated using this approach. Three of them seem to be close to a steady state, wherein the losses and gains of calcium to the system are equal. In the two southern-most catchments there seems to be an ongoing loss of exchangeable calcium. The loss by runoff occurs with sulphate being the dominant anion. Weathering rates of 1.5 to 4.8 kg Ca/ha year have been estimated.

A Graphical Method for Storage Coefficient Determination from Quasi-Steady State Flow Data

1996 ◽  
Vol 27 (4) ◽  
pp. 247-254 ◽  
Author(s):  
Zekâi Şen
Keyword(s):  
Steady State ◽  
Graphical Method ◽  
Pumping Test ◽  
Quasi Steady State ◽  
Flow Data ◽  
Steady State Flow ◽  
Storage Coefficient ◽  
State Flow ◽  
Aquifer Test

A simple, approximate but practical graphical method is proposed for estimating the storage coefficient independently from the transmissivity value, provided that quasi-steady state flow data are available from a pumping test. In the past, quasi-steady state flow distance-drawdown data have been used for the determination of transmissivity only. The method is applicable to confined and leaky aquifers. The application of the method has been performed for various aquifer test data available in the groundwater literature. The results are within the practical limits of approximation compared with the unsteady state flow solutions.

Operational Determination of the Activated Sludge Process Using Neural Networks

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2461-2464 ◽  
Author(s):  
R. D. Tyagi ◽  
Y. G. Du
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Steady State ◽  
Activated Sludge ◽  
Feedforward Neural Network ◽  
Training Data ◽  
Activated Sludge Process

A steady-statemathematical model of an activated sludgeprocess with a secondary settler was developed. With a limited number of training data samples obtained from the simulation at steady state, a feedforward neural network was established which exhibits an excellent capability for the operational prediction and determination.

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