Shape Optimization of Microchannels Using Surrogate Modelling

2018 ◽  
Author(s):  
Muhammad Ansab Ali ◽  
Tariq S. Khan ◽  
Saqib Salam ◽  
Ebrahim Al Hajri
Keyword(s):  
Shape Optimization ◽  
Heat Sink ◽  
Pareto Front ◽  
Sampling Method ◽  
Design Space ◽  
Latin Hypercube Sampling ◽  
Optimum Shape ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Computational Resources

To minimize the computational and optimization time, a numerical simulation of 3D microchannel heat sink was performed using surrogate model to achieve the optimum shape. Latin hypercube sampling method was used to explore the design space and to construct the model. The accuracy of the model was evaluated using statistical methods like coefficient of multiple determinations and root mean square error. Thermal resistance and pressure drop being conflicting objective functions were selected to optimize the geometric parameters of the microchannel. Multi objective shape optimization of design was conducted using genetic algorithm and the optimum design solutions are presented in the Pareto front. The application of the surrogate methods has predicted the performance of the heat sink with the sufficient accuracy employing significantly lower computational resources.

Enhanced Multi-Objective Optimization of a Microchannel Heat Sink Using Multiple Surrogates Modeling

2009 ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Heat Sink ◽  
Design Space ◽  
Surrogate Models ◽  
Pareto Optimal ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Design Variables

A liquid flow microchannel heat sink has been studied and optimized with the help of three-dimensional numerical analysis and multiple surrogate methods. Two objective functions, thermal resistance and pumping power have been selected to assess the performance of the microchannel heat sink. The design variables related to the microchannel top and bottom widths, depth and fin width, which contribute to objective functions, have been identified and design space has been explored through some preliminary calculations. Design of experiments was performed and a three-level full factorial design was selected to exploit the design space. The numerical solutions obtained at these design points were utilized to construct surrogate models namely Response Surface Approximations and Kriging. A hybrid multi-objective evolutionary algorithm coupled with surrogate models and a gradient-based search algorithm is applied to find global Pareto-optimal solutions. Since, the surrogate models are highly problem-dependent, the accuracy of the two surrogate models has been discussed in view of their predictions at on- and off-Pareto-optimal front. The trade-off analysis was performed in view of the two competing objectives. The Pareto-optimal sensitivity (change in value along the Pareto-optimal front) of the design variables has been found out to economically compromise with the design variables contributing relatively less to the objective functions. The application of the multiple surrogate methods not only improves quality of multi-objective optimization but also gives the feedback of the fidelity of the model near the optimum region.

scholarly journals An Analytical Study in Multi-physics and Multi-criteria Shape Optimization

2021 ◽  
Author(s):  
Hanno Gottschalk ◽  
Marco Reese
Keyword(s):  
Shape Optimization ◽  
Physical System ◽  
Pareto Front ◽  
Optimization Problem ◽  
Analytical Study ◽  
Static Pressure ◽  
Hausdorff Metric ◽  
Objective Functions ◽  
Hölder Continuous ◽  
Turbine Vane

AbstractA simple multi-physical system for the potential flow of a fluid through a shroud, in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi-criteria shape optimization problem, where the shape of the component is allowed to vary under a certain set of second-order Hölder continuous differentiable transformations of a baseline shape with boundary of the same continuity class. As objective functions, we consider a simple loss model for the fluid dynamical efficiency and the probability of failure of the component due to repeated application of loads that stem from the fluid’s static pressure. For this multi-physical system, it is shown that, under certain conditions, the Pareto front is maximal in the sense that the Pareto front of the feasible set coincides with the Pareto front of its closure. We also show that the set of all optimal forms with respect to scalarization techniques deforms continuously (in the Hausdorff metric) with respect to preference parameters.

Thermal Optimization of a Microchannel Heat Sink With Trapezoidal Cross Section

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Shape Optimization ◽  
Thermal Resistance ◽  
Objective Function ◽  
Response Surface ◽  
Heat Sink ◽  
Fractional Factorial ◽  
Surface Model ◽  
Microchannel Heat Sink ◽  
Reference Shape ◽  
Design Variables

A microchannel heat sink shape optimization has been performed using response surface approximation. Three design variables related to microchannel width, depth, and fin width are selected for optimization, and thermal resistance has been taken as objective function. Design points are chosen through a three-level fractional factorial design of sampling methods. Navier–Stokes and energy equations for steady, incompressible, and laminar flow and conjugate heat transfer are solved at these design points using a finite volume solver. Solutions are carefully validated with the analytical and experimental results and the values of objective function are calculated at the specified design points. Using the numerically evaluated objective-function values, a polynomial response surface model is constructed and the optimum point is searched by sequential quadratic programming. The process of shape optimization greatly improves the thermal performance of the microchannel heat sink by decreasing thermal resistance of about 12% of the reference shape. Sensitivity of objective function to design variables has been studied to utilize the substrate material efficiently.

Multiobjective Optimization of a Microchannel Heat Sink Using Evolutionary Algorithm

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Performance Optimization ◽  
Heat Sink ◽  
Algorithm Design ◽  
Pareto Optimal ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Design Variables ◽  
Polynomial Response Surface

A multiobjective performance optimization of microchannel heat sink is carried out numerically applying surrogate analysis and evolutionary algorithm. Design variables related to microchannel width, depth, and fin width are selected, and two objective functions, thermal resistance and pumping power, are employed. With the help of finite volume solver, Navier–Stokes analyses are performed at the design sites obtained from full factorial design of sampling methods. Using the numerically evaluated objective function values, polynomial response surface is constructed for each objective functions, and multiobjective optimization is performed to obtain global Pareto optimal solutions. Analysis of optimum solutions is simplified by carrying out trade-off with design variables and objective functions. Objective functions exhibit changing sensitivity to design variables along the Pareto optimal front.

An Optimum Design Method for a Thermal-Fluid Device Incorporating Multiobjective Topology Optimization With an Adaptive Weighting Scheme

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Yuki Sato ◽  
Kentaro Yaji ◽  
Kazuhiro Izui ◽  
Takayuki Yamada ◽  
Shinji Nishiwaki
Keyword(s):  
Topology Optimization ◽  
Heat Exchange ◽  
Pressure Drop ◽  
Optimum Design ◽  
Heat Sink ◽  
Pareto Front ◽  
Design Method ◽  
Optimization Method ◽  
Microchannel Heat Sink ◽  
Topology Optimization Method

This paper proposes an optimum design method for a two-dimensional microchannel heat sink under a laminar flow assumption that simultaneously provides maximal heat exchange and minimal pressure drop, based on a topology optimization method incorporating Pareto front exploration. First, the formulation of governing equations for the coupled thermal-fluid problem and a level set-based topology optimization method are briefly discussed. Next, an optimum design problem for a microchannel heat sink is formulated as a bi-objective optimization problem. An algorithm for Pareto front exploration is then constructed, based on a scheme that adaptively determines weighting coefficients by solving a linear programming problem. Finally, in the numerical example, the proposed method yields a Pareto front approximation and enables the analysis of the trade-off relationship between heat exchange and pressure drop, confirming the utility of the proposed method.

Optimization of an Additively Manufactured U-Bend Channel Using A Surrogate-Based Bayesian Method

2021 ◽  
Author(s):  
Shinjan Ghosh ◽  
Sudeepta Mondal ◽  
Ryan Wardell ◽  
Erik Fernandez ◽  
Jayanta S. Kapat ◽  
...  
Keyword(s):  
Pressure Drop ◽  
Turbulent Flow ◽  
Design Space ◽  
Cfd Simulation ◽  
Turbine Blades ◽  
Latin Hypercube Sampling ◽  
Pressure Profile ◽  
Optimum Shape ◽  
Data Set ◽  
Bend Channel

Abstract CFD-based design optimization of turbulent flow scenarios is usually computationally expensive due to requirement of high-fidelity simulations. Previous studies prove that one way to reduce computational resource usage is to employ Machine Learning/Surrogate Modeling approaches for intelligent sampling of data points in the design space and is also an active area of research, but lacks enough experimental validation. Such a method has been used to optimize the shape of a U-bend channel for the minimization of pressure drop. U-bends are an integral part of serpentine cooling channels inside gas turbine blades but also contribute to total pressure drop by more than 20%. Reducing this pressure loss can help in more efficient cooling at low pumping power. A ‘U-bend’ or 180-degree bend shape has been used from literature, and a 16-dimensional design space has been created using parametrized spline curves, which creates a variety of shapes inside a given bounding box. A Latin Hypercube Sampling (LHS) was carried out for populating the initial design space with output data from the CFD simulation. After training a surrogate model on this data set, Bayesian updates were used to search for an optimum using an exploration vs exploitation approach. The resulting optimum shape showed that pressure drop was lowered by almost 30%, when compared to the baseline. The aim of this study is to experimentally validate this method using 3D printed models of the baseline and optimum channels respectively. Pressure taps placed across stream-wise locations on these channels helped to create a pressure profile for turbulent flow at a Reynolds number of 17000, for comparison to CFD results.

Multi-Functional Optimization of Sandwich Panel with Bio-Inspired Lightweight Structure Cores

2013 ◽  
Vol 461 ◽  
pp. 73-80
Author(s):  
Zhen Yu Lu ◽  
Ce Guo ◽  
Chun Sheng Zhu ◽  
Zhen Dong Dai
Keyword(s):  
Objective Function ◽  
Sampling Method ◽  
Sandwich Panel ◽  
Heat Dissipation ◽  
Latin Hypercube Sampling ◽  
Objective Functions ◽  
Functional Optimization ◽  
Effective Medium Model ◽  
Surface Method ◽  
Lightweight Structure

The overall heat dissipation coefficients of the sandwich panels with bio-inspired lightweight composite cores were analyzed by using the effective medium model, Then the effective heat dissipation objective function of the panel was constructed. The author took advantage of the Latin hypercube sampling method to sample the experimental data and then to calculate it. On this basis, the static and dynamic mechanical objective functions of the panel were obtained by using the response surface method. Finally, the overall objective function was constructed and solved to achieve the target of multi-functional optimization.

scholarly journals Optimization of a Wavy Microchannel Heat Sink with Grooves

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 373
Author(s):  
Min-Cheol Park ◽  
Sang-Bum Ma ◽  
Kwang-Yong Kim
Keyword(s):  
Thermal Resistance ◽  
Friction Factor ◽  
Heat Sink ◽  
Latin Hypercube Sampling ◽  
Groove Depth ◽  
Working Fluid ◽  
Microchannel Heat Sink ◽  
Factorial Method ◽  
Design Variables ◽  
Full Factorial

In this study, a wavy microchannel heat sink with grooves using water as the working fluid is proposed for application to cooling microprocessors. The geometry of the heat sink was optimized to improve heat transfer and pressure loss simultaneously. To achieve optimization goals, the average friction factor and thermal resistance were used as the objective functions. Three dimensionless parameters were selected as design variables: the distance between staggered grooves, groove width, and groove depth. A modified Latin hypercube sampling (LHS) method that combines the advantages of conventional LHS and a three-level full factorial method is also proposed. Response surface approximation was used to construct surrogate models, and Pareto-optimal solutions were obtained with a multi-objective genetic algorithm. The modified LHS was proven to have better performance than the conventional LHS and full factorial methods in the present optimization problem. A representative optimal design showed that both the thermal resistance and friction factor improved by 1.55% and 3.00%, compared to a reference design, respectively.

Multi-criteria shape optimization of open-spandrel concrete arch bridges: Pareto front development and decision-making

2019 ◽  
Vol 16 (5) ◽  
pp. 670-680
Author(s):  
Majid Pouraminian ◽  
Somayyeh Pourbakhshian
Keyword(s):  
Decision Making ◽  
Particle Swarm Optimization ◽  
Shape Optimization ◽  
Decision Maker ◽  
Pareto Front ◽  
Optimization Problem ◽  
Objective Functions ◽  
Swarm Optimization ◽  
Content Type ◽  
Arch Bridges

Purpose This paper aims to study the shape of the concrete arched bridge by particle swarm optimization algorithm. Design/methodology/approach Finite element model of open-spandrel concrete arch bridges was constructed using a number of parameters. Design variables of optimization problem include height of skewback abutment, height of arch crown, position of crown with respect to global axes and left and right radius of up and down arches. After parametric modeling of bridge geometry and application of multi-objective particle swarm optimization, the shape optimization of bridge arch was determined. The concrete volume used in bridge substructure construction and maximum principal tensile stress of concrete arch body was adopted as two objective functions in this study. The optimization problem aims to minimize the two objective functions. Geometric and stress constraints are also included in the problem. Findings Based on the results presented in the paper, the Pareto front is generated which helps the decision-maker or designer to pick the compromise solution from among 20 optimum designs according to their subjective preferences or engineering judgment, respectively. Moreover, to help the decision-maker, the two multiple objective decision-making methods were used for selection of the best solution from among nondominated solutions. Originality/value This research aims to solve an interesting optimization problem in structural engineering. Optimization of arch bridges structure was done for reducing construction costs and increasing safety for the first time.

Two-Dimensional Optimization of a Stent for an Aneurysm

2010 ◽  
Vol 4 (2) ◽  
Author(s):  
K. Srinivas ◽  
S. Townsend ◽  
C. J. Lee ◽  
T. Nakayama ◽  
M. Ohta ◽  
...  
Keyword(s):  
Design Space ◽  
Cerebral Aneurysms ◽  
Latin Hypercube Sampling ◽  
Proximal Region ◽  
Flow Diversion ◽  
Two Dimensional ◽  
Objective Functions ◽  
Nondominated Solutions ◽  
Dimensional Version ◽  
Dimensional Optimization

This work attempts to optimize stents that are implanted at the neck of coronary or cerebral aneurysms to effect a flow diversion. A two-dimensional version of the stent, which is a series of struts and gaps placed at the neck, is considered as the first step. Optimization is carried out based on the principles of exploration of design space using reductions in velocity and vorticity in the aneurysm dome as the objective functions. Latin hypercube sampling first develops 30–60 samples of a strut-gap arrangement. Flow past an aneurysm with each of these samples is computed using the commercial software FLUENT and the objective functions evaluated. This is followed by a Kriging procedure that identifies the nondominated solutions to the system, which are the optimized candidates. Three different cases of stents with rectangular or circular struts are considered. It is found that placing struts in the proximal region of the neck gives the best flow diversion.

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