scholarly journals An Iterative Method for Shape Optimal Design of Stokes–Brinkman Equations with Heat Transfer Model

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Wenjing Yan ◽  
Feifei Jing ◽  
Jiangyong Hou ◽  
Zhiming Gao ◽  
Nannan Zheng
Keyword(s):  
Optimal Design ◽  
Minimax Problem ◽  
Transfer Model ◽  
Dissipation Energy ◽  
Brinkman Equations ◽  
Design Variables ◽  
Continuous Adjoint Method ◽  
Eulerian Derivative ◽  
The Cost ◽  
Continuous Adjoint

This work is concerned with the shape optimal design of an obstacle immersed in the Stokes–Brinkman fluid, which is also coupled with a thermal model in the bounded domain. The shape optimal problem is formulated and analyzed based on the framework of the continuous adjoint method, with the advantage that the computing cost of the gradients and sensitivities is independent of the number of design variables. Then, the velocity method is utilized to describe the domain deformation, and the Eulerian derivative for the cost functional is established by applying the differentiability of a minimax problem based on the function space parametrization technique. Moreover, an iterative algorithm is proposed to optimize the boundary of the obstacle in order to reduce the total dissipation energy. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of our method.

A continuous adjoint-based aeroacoustic shape optimization for multi-mode duct acoustics

2017 ◽  
Vol 232 (21) ◽  
pp. 3897-3914 ◽  
Author(s):  
Sheng Qiu
Keyword(s):  
Optimization Method ◽  
Adjoint Equations ◽  
Duct Acoustics ◽  
Design Variables ◽  
Adjoint Variables ◽  
Duct Geometry ◽  
The Cost ◽  
Continuous Adjoint ◽  
Multi Mode ◽  
Inlet Duct

A multi-mode adjoint-based optimization method is proposed for the noise reduction optimization in multi-mode duct acoustics problems. The objective is to minimize the amplitude of sound from an inlet duct on the wall and integral line while maintaining the aerodynamic performance. The complete detailed derivation of the adjoint equations and their corresponding adjoint boundary conditions are presented firstly based on the multi-mode linear Euler equations. With the solved adjoint variables, the final expression of the cost function gradient with respect to the design variables is formulated. The sensitivity derivative computed by the continuous adjoint method is validated by comparing with that obtained using finite difference method. Up to 50 design variables are involved in the adjoint optimization to ensurely provide an adequate design space. And a quasi-Newton Broyden–Fletcher–Goldfarb–Shanno algorithm is utilized to determine an improved intake duct geometry based on the objective function gradient provided by the adjoint solution. Finally, two multi-mode optimization of a typical inlet duct confirms the flexibility of the multi-mode adjoint-based framework and the efficiency of the multi-mode adjoint-based technique.

scholarly journals Analytical Models for Optimal Design of a Trapezoidal Composite Channel Cross-Section

2021 ◽  
Vol 31 (1) ◽  
pp. 118-138
Author(s):  
Somayyeh Pourbakhshian ◽  
Majid Pouraminian
Keyword(s):  
Optimal Design ◽  
Cost Function ◽  
Objective Function ◽  
Cross Section ◽  
Analytical Models ◽  
Channel Cross Section ◽  
Roughness Coefficient ◽  
Composite Channel ◽  
Design Variables ◽  
The Cost

Abstract In this paper, several analytical models are presented for the optimal design of a trapezoidal composite channel cross-section. The objective function is the cost function per unit length of the channel, which includes the excavation and lining costs. To define the system, design variables including channel depth, channel width, side slopes, freeboard, and roughness coefficients were used. The constraints include Manning’s equation, flow velocity, Froude number, and water surface width. The Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm was used to solve the optimization problem. The results are presented in three parts; in the first part, the optimal values of the design variables and the objective function are presented in different discharges. In the second part, the relationship between cost and design variables in different discharges is presented in the form of conceptual and analytical models and mathematical functions. Finally, in the third part, the changes in the design variables and cost function are presented as a graph based on the discharge variations. Results indicate that the cost increases with increasing water depth, left side slope, equivalent roughness coefficient, and freeboard.

Turbine Blade Aerodynamic Optimization on Unstructured Grids Using a Continuous Adjoint Method

2012 ◽  
Author(s):  
M. Zeinalpour ◽  
K. Mazaheri ◽  
A. Irannejad
Keyword(s):  
Turbine Blade ◽  
Adjoint Method ◽  
Suction Side ◽  
Adjoint Equations ◽  
Inverse Design ◽  
Aerodynamic Optimization ◽  
Design Variables ◽  
Continuous Adjoint Method ◽  
Flow Variables ◽  
Continuous Adjoint

A gradient based optimization using the continuous adjoint method for inverse design of a turbine blade cascade is presented. The advantage of the adjoint method is that the objective function gradients can be evaluated by solving the adjoint equations with coefficients depending on the flow variables. This method is particularly suitable for aerodynamic design optimization for which the number of design variables is large. Bezier polynomials are used to parameterize suction side of the turbine blade. The numerical convective fluxes of both flow and adjoint equations are computed by using a Roe-type approximate Riemann solver. An approximate linearization is applied to simplify the calculation of the numerical flux of adjoint variables on the faces of computational cell. The problem examined is that of the inverse design of NASA C3X blade that reproduces a given pressure distributions over its surfaces. Adjoint results show a good agreement with those obtained by finite-difference method.

Optimal Design Variables to Minimize the Cost of Materials the Stator of Asynchronous Machine

2016 ◽  
Vol 27 (2) ◽  
pp. 157-168 ◽  
Author(s):  
Juliana Almansa Malagoli ◽  
José Roberto Camacho ◽  
Mauricio Valencia Ferreira da Luz
Keyword(s):  
Optimal Design ◽  
Asynchronous Machine ◽  
Design Variables ◽  
Cost Of Materials ◽  
The Cost

Structural Analysis and Optimal Design of Lightweight Skate for Loading and Unloading

2013 ◽  
Vol 785-786 ◽  
pp. 1258-1261
Author(s):  
In Pyo Cha ◽  
Hee Jae Shin ◽  
Neung Gu Lee ◽  
Lee Ku Kwac ◽  
Hong Gun Kim
Keyword(s):  
Topology Optimization ◽  
Structural Analysis ◽  
Optimal Design ◽  
Optimization Techniques ◽  
Normal Operation ◽  
Stress And Strain ◽  
Initial Model ◽  
Design Variables ◽  
Model Set ◽  
Main Frame

Topology optimization and shape optimization of structural optimization techniques are applied to transport skate the lightweight. Skate properties by varying the design variables and minimize the maximum stress and strain in the normal operation, while reducing the volume of the objective function of optimal design and Skate the static strength of the constraints that should not degrade compared to the performance of the initial model. The skates were used in this study consists of the main frame, sub frame, roll, pin main frame only structural analysis and optimal design was performed using the finite element method. Simplified initial model set design area and it compared to SM45C, AA7075, CFRP, GFRP was using the topology optimization. Strength does not degrade compared to the initial model, decreased volume while minimizing the stress and strain results, the optimum design was achieved efficient lightweight.

scholarly journals Modeling, Simulation and Uncertain Optimization of the Gun Engraving System

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 398
Author(s):  
Tong Xin ◽  
Guolai Yang ◽  
Fengjie Xu ◽  
Quanzhao Sun ◽  
Alexandi Minak
Keyword(s):  
Performance Evaluation ◽  
Optimal Design ◽  
Resistance Force ◽  
Gas Temperature ◽  
Evaluation Indexes ◽  
Uncertain Optimization ◽  
Design Variables ◽  
Set Up ◽  
Rotating Band ◽  
Percent Decrease

The system designed to accomplish the engraving process of a rotating band projectile is called the gun engraving system. To obtain higher performance, the optimal design of the size parameters of the gun engraving system was carried out. First, a fluid–solid coupling computational model of the gun engraving system was built and validated by the gun launch experiment. Subsequently, three mathematic variable values, like performance evaluation indexes, were obtained. Second, a sensitivity analysis was performed, and four high-influence size parameters were selected as design variables. Finally, an optimization model based on the affine arithmetic was set up and solved, and then the optimized intervals of performance evaluation indexes were obtained. After the optimal design, the percent decrease of the maximum engraving resistance force ranged from 6.34% to 18.24%; the percent decrease of the maximum propellant gas temperature ranged from 1.91% to 7.45%; the percent increase of minimum pressure wave of the propellant gas ranged from 0.12% to 0.36%.

Application and Research of Digital Technology in Optimal Design of CNC Floor Boring and Milling Machine

2012 ◽  
Vol 429 ◽  
pp. 111-115
Author(s):  
Zhen Long Leng ◽  
Jin Feng Yang ◽  
Qun Ping Liu ◽  
Xun Deng
Keyword(s):  
Numerical Simulation ◽  
Optimal Design ◽  
Digital Technology ◽  
Three Dimensional ◽  
Milling Machine ◽  
Machine Model ◽  
Digital Modeling ◽  
Key Technologies ◽  
The Cost ◽  
Interference Checking

This paper focuses on application of the three-dimensional digital modeling, numerical analysis and optimization, digital control and other key technologies which provide technical support for the design and development in CNC floor boring and milling machine manufactruing. The three-dimensional digital modeling, digital assembly, interference checking help to eliminate some hidden trouble before processing and assembly. Numerical simulation reduces the cost and shortens the cycle of designand manufactruing in the optimal design of the machine. This technique has been successfully applied to a CNC Floor Boring and Milling Machine Model, which has been running for three years and achieved satisfactary economic result.

scholarly journals Power-to-Syngas: A Parareal Optimal Control Approach

2021 ◽  
Vol 9 ◽  
Author(s):  
Andrea Maggi ◽  
Dominik Garmatter ◽  
Sebastian Sager ◽  
Martin Stoll ◽  
Kai Sundmacher
Keyword(s):  
Optimal Control ◽  
Water Gas Shift ◽  
Control Approach ◽  
Renewable Power ◽  
Reverse Water Gas Shift ◽  
Time Modeling ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint ◽  
Water Gas ◽  
First Time

A chemical plant layout for the production of syngas from renewable power, H2O and biogas, is presented to ensure a steady productivity of syngas with a constant H2-to-CO ratio under time-dependent electricity provision. An electrolyzer supplies H2 to the reverse water-gas shift reactor. The system compensates for a drop in electricity supply by gradually operating a tri-reforming reactor, fed with pure O2 directly from the electrolyzer or from an intermediate generic buffering device. After the introduction of modeling assumptions and governing equations, suitable reactor parameters are identified. Finally, two optimal control problems are investigated, where computationally expensive model evaluations are lifted viaparareal and necessary objective derivatives are calculated via the continuous adjoint method. For the first time, modeling, simulation, and optimal control are applied to a combination of the reverse water-gas shift and tri-reforming reactor, exploring a promising pathway in the conversion of renewable power into chemicals.

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