scholarly journals Entropy production minimization in a multicomponent diabatic distillation column

2020 ◽  
Vol 24 (3 Part B) ◽  
pp. 2256-2266
Author(s):  
Momcilo Spasojevic ◽  
Milovan Jankovic ◽  
Damir Djakovic
Keyword(s):  
Entropy Production ◽  
Thermodynamic Characteristics ◽  
Optimization Procedure ◽  
Goal Function ◽  
Optimization Method ◽  
Control Variables ◽  
Partial Linearization ◽  
Numerical Minimization ◽  
Complex Optimization ◽  
Diabatic Distillation

This work presents a procedure for direct numerical minimization of entropy production in a diabatic tray column with heat exchanged on the trays as control variables, as opposed to previously used procedures with temperature on the trays as control variables. The procedure, which had previously been demonstrated on a binary mixture, was in this work applied to a multicomponent mixture, with minor modifications. The procedure comprised the complex optimization method and the Ishii-Otto method for solving the equations of a column model based on the iterative Newton-Raphson technique with partial linearization of the equations. The desired separation of the components was realized by the addition of a penalty function to the goal function, i.e. entropy production in the column. The required thermodynamic characteristics were calculated by the Soave equation of state. As an illustration, an industrial debutanizer with five components was used whose data, obtained by simulation, were compared with the optimization results of a diabatic column with the same desired separation and number of trays. After the diabatic column optimization procedure, the value of 91.91 J/Ks was obtained as the best result for entropy production. According to the best solution, entropy production in the diabatic column was 23.2% lower than in the adiabatic column. The heat to be removed from the column increased by 24.7%, while the heat to be added to the column increased by 28.8%.

scholarly journals A new approach to entropy production minimization in diabatic distillation column with trays

2010 ◽  
Vol 14 (2) ◽  
pp. 317-328 ◽  
Author(s):  
Momcilo Spasojevic ◽  
Milovan Jankovic ◽  
Damir Djakovic
Keyword(s):  
Entropy Production ◽  
Distillation Column ◽  
Direct Methods ◽  
Iterative Solution ◽  
Theoretical Models ◽  
Optimization Method ◽  
Control Variables ◽  
Heat Quantity ◽  
Diabatic Distillation ◽  
Model Linearization

Previous approach to direct numerical minimization of entropy production in diabatic distillation column in order to determine heat quantity to be exchanged at trays was based on temperatures on trays as control variables and it was applied only to simple binary columns. Also, previously developed theoretical models for determining optimal exchanged heat profile were determined only at such columns and while they were approximated they produced worse results than numerical minimum of entropy production. In this paper, as control variables for minimization, exchanged heat on the trays is used. It enables application to complex multicomponent diabatic columns. Ishii-Otto global method, based on model linearization and iterative solution by Newton-Raphson technique, is applied for solving column mathematical model. Needed thermodynamical properties for ideal systems are calculated using Lewis-Randall ideal solution model, and for non-ideal slightly polar systems they are calculated using Soave equation of state. Five direct methods are used for numerical optimization. Applied approach is successfully demonstrated at frequently used example of distillation of benzene and toluol mixture by using for these purposes specially written program. Simplex method appeared to be the most convenient optimization method for the considered problem.

Dimensioning a recovery boiler furnace using mathematical optimization

TAPPI Journal ◽  
2015 ◽  
Vol 14 (2) ◽  
pp. 119-129 ◽  
Author(s):  
VILJAMI MAAKALA ◽  
PASI MIIKKULAINEN
Keyword(s):  
Radial Basis Function Network ◽  
High Capacity ◽  
Mathematical Optimization ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Performance Criteria ◽  
Boiler Furnace ◽  
Starting Point ◽  
Recovery Boiler ◽  
Base Design

Capacities of the largest new recovery boilers are steadily rising, and there is every reason to expect this trend to continue. However, the furnace designs for these large boilers have not been optimized and, in general, are based on semiheuristic rules and experience with smaller boilers. We present a multiobjective optimization code suitable for diverse optimization tasks and use it to dimension a high-capacity recovery boiler furnace. The objective was to find the furnace dimensions (width, depth, and height) that optimize eight performance criteria while satisfying additional inequality constraints. The optimization procedure was carried out in a fully automatic manner by means of the code, which is based on a genetic algorithm optimization method and a radial basis function network surrogate model. The code was coupled with a recovery boiler furnace computational fluid dynamics model that was used to obtain performance information on the individual furnace designs considered. The optimization code found numerous furnace geometries that deliver better performance than the base design, which was taken as a starting point. We propose one of these as a better design for the high-capacity recovery boiler. In particular, the proposed design reduces the number of liquor particles landing on the walls by 37%, the average carbon monoxide (CO) content at nose level by 81%, and the regions of high CO content at nose level by 78% from the values obtained with the base design. We show that optimizing the furnace design can significantly improve recovery boiler performance.

Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

2005 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Structural Topology ◽  
Energy Concept ◽  
Conceptual Design Phase ◽  
Complementary Strain ◽  
Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

Structural Optimization of Composite Panel with Lamination Parameters and Equivalent Stiffness Laminate Method

2014 ◽  
Vol 496-500 ◽  
pp. 429-435
Author(s):  
Xiao Ping Zhong ◽  
Peng Jin
Keyword(s):  
Genetic Algorithm ◽  
Structural Optimization ◽  
Composite Structure ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Composite Panel ◽  
Analysis Tool ◽  
Equivalent Stiffness ◽  
Lamination Parameters ◽  
Design Variables

Firstly, a two-level optimization procedure for composite structure is investigated with lamination parameters as design variables and MSC.Nastran as analysis tool. The details using lamination parameters as MSC.Nastran input parameters are presented. Secondly, with a proper equivalent stiffness laminate built to substitute for the lamination parameters, a two-level optimization method based on the equivalent stiffness laminate is proposed. Compared with the lamination parameters-based method, the layer thicknesses of the equivalent stiffness laminate are adopted as continuous design variables at the first level. The corresponding lamination parameters are calculated from the optimal layer thicknesses. At the second level, genetic algorithm (GA) is applied to identify an optimal laminate configuration to target the lamination parameters obtained. The numerical example shows that the proposed method without considering constraints of lamination parameters can obtain better optimal results.

Performance analysis of wave rotor based on response surface optimization method

2021 ◽  
pp. 1-18
Author(s):  
Peiqi Liu ◽  
Mingyu Feng ◽  
Xinyu Liu ◽  
Haitao Wang ◽  
Dapeng Hu
Keyword(s):  
Entropy Production ◽  
Response Surface ◽  
Relative Velocity ◽  
Pressure Ratio ◽  
Pressure Fluctuations ◽  
Optimization Method ◽  
Wave Rotor ◽  
Compression Waves ◽  
Isentropic Expansion ◽  
Response Surface Optimization

Abstract An optimized wave rotor refrigerator (WRR) that can convert part of the expansion work into shaft work to improve the refrigeration performance is obtained by optimization method. Bézier curve is used to establish a two-dimensional simplified model, and response surface method and NLPQL optimization algorithm are used to search for the optimal wave rotor structure. The results show that the optimized wave rotor shape is rear back bending. Compared with original rotor, the isentropic expansion efficiency of the optimized rotor is higher under different pressure ratios and relative velocity, and changes more gently under different pressure ratios. Moreover, the expansion power of the optimized rotor is mainly converted into shaft powder, while the pressure energy and thermal energy increase at the hot end is relatively small. The pressure fluctuations on the inlet and outlet sides of the optimized rotor are smoother, and the compression waves that are constantly reflected during the low-temperature exhaust stage have a smaller intensity, which helps to improve the performance of WRR. The optimized rotor can significantly reduce the entropy production in the refrigeration process, especially the entropy production by velocity gradients. When the pressure ratio is 2.0 and relative velocity is 23 m/s, the isentropic expansion efficiency increases from 56.8% of the original rotor to 62.08% of the optimized rotor.

scholarly journals Path Planning for Mobile Objects in Four-Dimension Based on Particle Swarm Optimization Method with Penalty Function

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yong Ma ◽  
M. Zamirian ◽  
Yadong Yang ◽  
Yanmin Xu ◽  
Jing Zhang
Keyword(s):  
Particle Swarm Optimization ◽  
Penalty Function ◽  
Particle Swarm ◽  
Goal Function ◽  
Optimization Method ◽  
Mobile Object ◽  
Time Varying ◽  
Swarm Optimization ◽  
Calculus Of Variation ◽  
Mobile Objects

We present one algorithm based on particle swarm optimization (PSO) with penalty function to determine the conflict-free path for mobile objects in four-dimension (three spatial and one-time dimensions) with obstacles. The shortest path of the mobile object is set as goal function, which is constrained by conflict-free criterion, path smoothness, and velocity and acceleration requirements. This problem is formulated as a calculus of variation problem (CVP). With parametrization method, the CVP is converted to a time-varying nonlinear programming problem (TNLPP). Constraints of TNLPP are transformed to general TNLPP without any constraints through penalty functions. Then, by using a little calculations and applying the algorithm PSO, the solution of the CVP is consequently obtained. Approach efficiency is confirmed by numerical examples.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

The Nature Of Strategic-Decision-Making Models

2011 ◽  
pp. 241-271
Author(s):  
Tamio Shimizu ◽  
Marley Monteiro de Carvalho ◽  
Fernando Jose Barbin
Keyword(s):  
Decision Making ◽  
Goal Function ◽  
Optimization Method ◽  
Strategic Decision ◽  
Optimal Decision ◽  
Problem Solution ◽  
Goal Functions ◽  
Optimal Decision Making ◽  
The Individual ◽  
Optimum Solution

In the multiple goal function problems, there is no optimum solution fully satisfying all goals at the same time. The individual goal’s functions are, in general, conflicting and it is not possible to have an optimization method to solve the problem. There is usually a consensus solution satisfying minimal criteria of optimum values for each individual goal function. This consensus is based on the Pareto’s principle presented in chapter nine. The optimal decision making in problems with multiple goals will be analyzed at the end of this chapter (Goicoechea et al., 1982; Keeney & Raiffa, 1976; Dyson, 1990; Saaty, 1980, 1994; Bonabeau, 2003; Charan, 2001; Choo, 1998; Day et al., 1997). In considering restrictions across several scenarios, the problem solution becomes more difficult due to the high number of possible combinations of goal functions and scenarios to be considered.

scholarly journals Modified grey wolf method for optimization of PM motors

2019 ◽  
Vol 28 ◽  
pp. 01020
Author(s):  
Łukasz Knypiński
Keyword(s):  
Mathematical Model ◽  
Permanent Magnet ◽  
Permanent Magnet Synchronous Motor ◽  
Computer Software ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Grey Wolf ◽  
Electromagnetic Devices ◽  
The Mathematical Model ◽  
Grey Wolf Algorithm

The paper presents an algorithm and computer software for the optimization of electromagnetic devices. The mathematical model of the optimization method was presented. The modification of the classical grey wolf algorithm was developed. The modification consists in decreasing the coefficient responsible for the possibility of migration individuals in the permissible area of solved task. The optimization procedure was elaborated in the Borland Delphi environment. The optimization of the rotor of the line-start permanent magnet synchronous motor has been carried out. It has been pointed out that the grey wolf algorithm is effective method for optimization of electromagnetic devices.

scholarly journals Optimizing the 3D Distributed Climate inside Greenhouses Using Multi-Objective Optimization Algorithms and Computer Fluid Dynamics

Energies ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2873 ◽  
Author(s):  
Kangji Li ◽  
Wenping Xue ◽  
Hanping Mao ◽  
Xu Chen ◽  
Hui Jiang ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Field Experiments ◽  
Climate Model ◽  
Pareto Frontier ◽  
Environmental Parameters ◽  
Optimization Method ◽  
Crop Growth ◽  
Control Variables ◽  
Greenhouse Production ◽  
Multi Objective

As one of the major production facilities in agriculture, a greenhouse has many spatial distributed factors influencing crop growth and energy consumption, such as temperature field, air flow pattern, CO 2 concentration distribution, etc. By introducing a hybrid computational fluid dynamics–evolutionary algorithm (CFD-EA) method, this paper constructs a micro-climate model of greenhouse with main environmental parameters optimized. Considering environmental factors’ spatial influences together with energy usage simultaneously, the optimal solutions of control variables for crop growth are calculated. A commercial greenhouse located in east China is chosen for the method validation. Field experiments using temperature/velocity sensor matrix are carried out for CFD accuracy investigation. On this basis, the proposed optimization method is employed to search for the optimal control variables and parameters corresponding to the environmental Pareto frontier. By the proposed multi-objective scheme, we believe the method can provide set point basis for the design and regulation of large/medium-sized greenhouse production with high spatial resolution.

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