Topology optimization of channel flow problems

This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low-to-moderate Reynolds numbers. This makes the flow problem nonlinear and hence a nontrivial extension of the work of Borrvall and Petersson (2003).Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity-driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc.     

Topology optimization of internal partitions in a flow-reversing chamber muffler for noise reduction

A topology-optimization-based design method for a flow-reversing chamber muffler is suggested to maximize the transmission loss value at a target frequency considering flow power dissipation. Rigid partitions for high noise reduction should be carefully placed inside the muffler to avoid extreme flow power dissipation due to a 180° change in flow direction from an inlet to an outlet. The optimal flow path for minimum flow power dissipation is well known to change depending on the Reynolds number, which is a function of the inlet flow velocity. To optimize the partition layout with an optimal flow path in an expansion chamber at a given Reynolds number, a flow-reversing chamber muffler design problem is formulated by topology optimization. The formulated topology optimization problem is implemented using the finite element method with a gradient-based optimization algorithm and is solved for various design conditions such as the target frequencies, rigid partition volumes, Reynolds numbers, non-design domain settings, and allowed amounts of flow power dissipation. The effectiveness of our suggested approach is verified by comparing the optimized partition layouts obtained by the suggested method and previous methods.     

Bi-objective topology optimization of asymmetrical fixed-geometry microvalve for non-Newtonian flow

Fixed-geometry microvalves such as Tesla microvalves rely on the inertial forces of the fluid to allow flow in the desired direction while inhibiting flow in undesired direction. In the traditional topology optimization design methods of fixed-geometry microvalves, single objective function is used to minimize the energy dissipation of forward flow. And several previous studies have widely used diodicity to indicate the performance of fixed-geometry microvalves, which is defined as the ratio of the pressure drop of reverse flow to that of the forward flow. However, higher diodicity does not reflect the degree of forward energy dissipation, leading to a significant pumping power is required to drive flow. Therefore, treating the forward flow pressure drop and its performance independently by a bi-objective formulation is preferable to design fixed-geometry microvalve. This paper proposes a bi-objective topology optimization design method and uses the regularization constraint to design asymmetrical fixed-geometry microvalve for non-Newtonian flow. Several numerical examples with different bifurcation angles, Darcy number and weight coefficients of the bi-objective functions are studied and the validity of the topology optimization method presented in this paper is demonstrated.

     

Topology optimization applied to the design of 2D swirl flow devices

The design of fluid devices, such as flow machines, mixers, separators, and valves, with the aim to improve performance is of high interest. One way to achieve it is by designing them through the topology optimization method. However, there is a specific large class of fluid flow problems called 2D swirl flow problems which presents an axisymmetric flow with (or without) flow rotation around the axisymmetric axis. Some devices which allow such simplification are hydrocyclones, some pumps and turbines, fluid separators, etc. Once solving a topology optimization problem for this class of problems using a 3D domain results in a quite high computational cost, the development and use of 2D swirl models is of high interest. Thus, the main objective of this work is to propose a topology optimization formulation for 2D swirl flow fluid problem to design these kinds of fluid devices. The objective is to minimize the relative energy dissipation considering the viscous and porous effects. The 2D swirl laminar fluid flow modelling is solved by using the finite element method. A traditional material model is adopted by considering nodal design variables. An interior point optimization (IPOPT) algorithm is applied to solve the optimization problem. Numerical examples are presented to illustrate the application of this model for various 2D swirl flow cases.     

Design optimization of laminar flow machine rotors based on the topological derivative concept

Flow machines are very important to industry, being widely used on various processes. Thus, performance improvements are relevant and can be achieved by using topology optimization methods. In particular, this work aims to develop a topological derivative formulation to design radial flow machine rotors by considering laminar flow. Based on the concept of traditional topology optimization approaches, in the adopted topological derivative formulation, solid or fluid material is distributed at each point of the domain. This is achieved by combining Navier–Stokes equations on a rotary referential with Darcy’s law equations. This strategy allows for working in a fixed computational domain, which leads to a topology design algorithm of remarkably simple computational implementation. In the optimization problem formulation, a multi-objective function is defined, aiming to minimize the energy dissipation, vorticity and power considering a volume constraint. The constrained optimization problem is rewritten in the form of an unconstrained optimization problem by using the Augmented Lagrangian formalism. The resulting multi-objective shape functional is then minimized with help of the topological derivative concept. In the context of this article, the topological derivative represents the exact sensitivity with respect to the nucleation of an inclusion within the design domain and the obtained analytical (closed) formula can be evaluated through a simple post processing of the solutions to the direct and adjoints problems. Both mentioned features allow for obtaining the optimized designs in few iterations by using a minimal number of user defined algorithm parameters. All equations and the derived continuous adjoint equations are solved through finite element method. As a result, two-dimensional designs of flow machine rotors are obtained by using this methodology. Their performance is analyzed by evaluating velocity and pressure distributions inside rotor.     

Design of cellular structures for optimum efficiency of heat dissipation

Metal cellular material is a new material attractive for its light weight and potential multifunctionality. In the present paper, we study cylindrical structures made of linear metal cellular material. The outer surface of the cylindrical structure is subjected to thermal boundary condition, and cooling fluid is forced through the cylinder to remove heat through the inner cell walls. Optimum design aims at maximization of heat dissipation efficiency under prescribed flow pressure. Two classes of design variables, relative density, and local aperture distribution of cellular material are to be determined by optimization under given total material volume constraints. Although similar to the structural topology optimization concept of material distribution, our formulation results in a structure with realistic cellular material of finite-sized aperture. Numerical results for different cross-sectional shapes and thermal boundary conditions are presented. Interestingly, our present formulation leads to optimum designs for cellular structures that mimic natural biomaterials. We discuss in general the guideline for cellular structure design to maximize heat dissipation efficiency based on insights from these optimization results.     

Topological derivatives applied to fluid flow channel design optimization problems

Topology optimization methods application for viscous flow problems is currently an active area of research. A general approach to deal with shape and topology optimization design is based on the topological derivative. This relatively new concept represents the first term of the asymptotic expansion of a given shape functional with respect to the small parameter which measures the size of singular domain perturbations, such as holes and inclusions. In previous topological derivative-based formulations for viscous fluid flow problems, the topology is obtained by nucleating and removing holes in the fluid domain which creates numerical difficulties to deal with the boundary conditions for these holes. Thus, we propose a topological derivative formulation for fluid flow channel design based on the concept of traditional topology optimization formulations in which solid or fluid material is distributed at each point of the domain to optimize the cost function subjected to some constraints. By using this idea, the problem of dealing with the hole boundary conditions during the optimization process is solved because the asymptotic expansion is performed with respect to the nucleation of inclusions – which mimic solid or fluid phases – instead of inserting or removing holes in the fluid domain, which allows for working in a fixed computational domain. To evaluate the formulation, an optimization problem which consists in minimizing the energy dissipation in fluid flow channels is implemented. Results from considering Stokes and Navier-Stokes are presented and compared, as well as two- (2D) and three-dimensional (3D) designs. The topologies can be obtained in a few iterations with well defined boundaries.     

Topology optimization of three-dimensional structures using optimum microstructures

In this paper, optimum three-dimensional microstructures derived in explicit analytical form by Gibianski and Cherkaev (1987) are used for topology optimization of linearly elastic three-dimensional continuum structures subjected to a single case of static loading. For prescribed loading and boundary conditions, and subject to a specified amount of structural material within a given three-dimensional design domain, the optimum structural topology is determined from the condition of maximum integral stiffness, which is equivalent to minimum elastic complicance or minimum total elastic energy at equilibrium.The use of optimum microstructures in the present work renders the local topology optimization problem convex, and the fact that local optima are avoided implies that we can develop and present a simple sensitivity based numerical method of mathematical programming for solution of the complete optimization problem.Several examples of optimum topology designs of three-dimensional structures are presented at the end of the paper. These examples include some illustrative full three-dimensional layout and topology optimization problems for plate-like structures. The solutions to these problems are compared to results obtained earlier in the literature by application of usual two-dimensional plate theories, and clearly illustrate the advantage of the full three-dimensional approach.     

Topology optimization of channel cooling structures considering thermomechanical behavior

Structural and Multidisciplinary Optimization - A topology optimization method is presented to design straight channel cooling structures for efficient heat transfer and load carrying capabilities....     

Shape design optimization of an expansion step in a channel with moving boundaries for a viscous flow

A shape design optimization problem for viscous flows has been investigated in the present study. An analytical shape design sensitivity expression has been derived for a general integral functional by using the adjoint variable method and the material derivative concept of optimization. A channel flow problem with a backward facing step and adversely moving boundary wall is taken as an example. The shape profile of the expansion step, represented by a fourth-degree polynomial, is optimized in order to minimize the total viscous dissipation in the flow field. Numerical discretizations of the primary (flow) and adjoint problems are achieved by using the Galerkin FEM method. A balancing upwinding technique is also used in the equations. Numerical results are provided in various graphical forms at relatively low Reynolds numbers. It is concluded that the proposed general method of solution for shape design optimization problems is applicable to physical systems described by nonlinear equations.     

Non-newtonian laminar flow machine rotor design by using topology optimization

Flow machines are widely used in industry through devices such as hydraulic turbines and pumps. Most part of these devices work with newtonian fluids, however, there are some specific devices dedicated to work with non-newtonian fluids, such as blood pumps. The main function of a blood pump is to have a suitable hydraulic performance while maintaining good haematological compatibility which consists of avoiding hemolysis (release of hemoglobin from red blood cells) and thrombosis (clotting). However, the challenge of improving the performance of these non-newtonian fluid machines requires the solution of an inverse-based design optimization problem, in which an oriented search must be conducted to obtain the optimized design. The rotor is a main component in the non-newtonian pump and the design of rotor topology can play an important role in the pump performance and its haematological conditions. Thus, performance improvement of these devices can be achieved by using topology optimization techniques. The optimization of pump hydraulic performance can be achieved by minimizing dissipative energy and power consumption and for the improvement of the haematological conditions, it is proposed to minimize the vorticity. Thus, in this work, topology optimization techniques are applied for designing the rotor pump such that the energy dissipation, vorticity, and power consumption are minimized considering non-Newtonian fluid. A two-dimensional finite element derived for a rotating frame is applied to model the rotor flow behavior. The modeling predicts the flow field between relative two blades of a rotor without considering the influence of the volute. A modified Cross model is adopted for the non-Newtonian fluid modeling. It is assumed that the fluid is flowing an idealized porous medium subjected to a friction force, which is proportional to the fluid velocity and the inverse local permeability. A porous flow model is considered with a continuous (gray) permeability design variable for each element that defines the local permeability of the medium and allows the transition between fluid and solid property. The design optimization problem is solved by using the method of moving asymptotes (MMA). Numerical examples are presented to illustrate this methodology aiming blood pump applications. A comparison among designs obtained by considering newtonian and non-newtonian fluid is included. Finally, it is verified that an improvement of the hemolysis index can be achieved by minimizing the vorticity in the rotor.     

基于无网格局部Petrov-Galekin法的板结构拓扑优化

为将无网格法的优势集成到结构拓扑优化中,基于无网格局部Petrov-Galerkin(Meshless Local Petrov-Galerkin,MLPG)法进行板结构的拓扑优化.基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP...     

Topology optimization of steady and unsteady incompressible Navier–Stokes flows driven by body forces

This paper presents the topology optimization method for the steady and unsteady incompressible Navier–Stokes flows driven by body forces, which typically include the constant force (e.g. the gravity) and the centrifugal and Coriolis forces. In the topology optimization problem, the artificial friction force with design variable interpolated porosity is added into the Navier–Stokes equations as the conventional method, and the physical body forces in the Navier–Stokes equations are penalized using the power-law approach. The topology optimization problem is analyzed by the continuous adjoint method, and solved by the finite element method in conjunction with the gradient based approach. In the numerical examples, the topology optimization of the fluidic channel, mass distribution of the flow and local velocity control are presented for the flows driven by body forces. The numerical results demonstrate that the presented method achieves the topology optimization of the flows driven by body forces robustly.     

基于格子波尔兹曼方法的机舱散热耦合分析

为指导前保险杠格栅及开口设计,研究冷却系统在特定工况下的散热性能和流场分布,建立具有详细的发动机舱几何信息的整车模型,利用格子波尔兹曼方法模拟整车在数字风洞中的热性能,得到机舱内流场和温度场以及散热器出水温度.分析结果与实验数据一致性很好,因此格子波尔兹曼方法很适合解决具有复杂几何结构的机舱散热问题.基于对标模型,针对前保险杠格栅的开口和格栅形式提出改进优化建议.经过多轮优化,散热器的散热能力提升6.94%.     

Application of entransy to optimization design of parallel thermal network of thermal control system in spacecraft

For distribution optimization of the flow rate of cold fluid and heat transfer area in the parallel thermal network of the thermal control system in spacecraft,a physical and mathematical model is set up,analyzed and discussed with the entransy theory.It is found that the optimization objective of this problem and the optimization direction of the extremum entransy dissipation principle are consistent in theory.For a two-branch thermal network system,the distributions of the flow rate of the cold fluid and ...     

Design of periodic elastoplastic energy dissipating microstructures

The design of periodic elastoplastic microstructures for maximum energy dissipation is carried out using topology optimization. While the topology optimization of elastic microstructures has been performed in numerous studies, microstructural design considering inelastic behavior is relatively untouched due to a number of reasons which are addressed in this study. An RVE-based multiscale model is employed for computational homogenization with periodic boundary constraints, satisfying the Hill-Mandel principle. The plastic anisotropy which may be prevalent in materials fabricated through additive manufacturing processes is considered by modeling the constitutive behavior at the microscale with Hoffman plasticity. Discretization is done using enhanced assumed strain elements to avoid locking from incompressible plastic flow under plane strain conditions and a Lagrange multiplier approach is used to enforce periodic boundary constraints in the discrete system. The design problem is formulated using a density-based parameterization in conjunction with a SIMP-like material interpolation scheme. Attention is devoted to issues such as dependence on initial design and enforcement of microstructural connectivity, and a number of optimized microstructural designs are obtained under different prescribed deformation modes.

     

基于热平衡和结构强度的发动机 分析平台开发及其应用

建立发动机缸体和缸盖的动力学、燃烧和流体有限元模型,进行发动机热平衡、冷却散热和结构强度研究。创建发动机正向设计和分析方法,革新产品开发流程,自主开发热平衡计算平台。建立发动机缸内和水套传热、流体、温度场、强度的计算模型库,设计水套优化方法和流场评价标准,正向计算发动机热平衡和水套散热。通过2个应用案例,证明该平台在发动机热平衡计算和结构分析与评估中的作用。该平台可为发动机热平衡、冷却散热和结构强度的正向设计提供基础。     

热—板传输系统的稳定性分析

本文研究由处于相邻区域的板方程和热方程构成的耦合系统的稳定性质, 其中耦合来自两个区域的交界 面上的传输边界条件. 在该传输系统中, 热方程起着控制器的作用, 且耗散通过交界面传输并影响板方程. 文献[1] 证明了在板方程上施加额外的控制器时, 该二维传输系统的能量呈指数衰减. 通过应用频域方法, 椭圆方程的正则 性理论等, 可以得到: 仅由热方程的耗散即可使得闭环系统指数稳定. 这一指数稳定的结论与相应的一维传输系统 的性质吻合. 最后, 文章还分析了不同传输边界条件下的板–热耦合系统的稳定性.     

Finite prism method based topology optimization of beam cross section for buckling load maximization

The use of the finite element method (FEM) for buckling topology optimization of a beam cross section requires large numerical cost due to the discretization in the length direction of the beam. This investigation employs the finite prism method (FPM) as a tool for linear buckling analysis, reducing degrees of freedom of three-dimensional nodes of FEM to those of two-dimensional nodes with the help of harmonic basis functions in the length direction. The optimization problem is defined as the maximization problem of the lowest eigenvalue, for which a bound variable is introduced and set as the design objective to treat mode switching phenomena of multiple eigenvalues. The use of the bound formulation also helps the proposed optimization to treat beams having local plate buckling modes as the fundamental modes as well as beams having global buckling modes. The axial stress is calculated according to the distribution of material modulus which is interpolated using the SIMP approach. Optimization problems finding cross-section layouts from rectangular, L-shaped and generally-shaped design domains are solved for various beam lengths to ascertain the effectiveness of the proposed method.     

压电风扇与散热器组合系统的散热性能及其改进

为提高散热器的散热性能,将压电风扇分别与直肋和针肋式散热器组合进行散热,利用FLUENT软件仿真其散热流场并计算其协同角,分析2种散热器的散热性能特点。考虑压电风扇的振动特性,将直肋式散热器的肋片改为扇形布置,并根据仿真结果进一步将该散热器扇形肋片的后端改为针肋,设计新型散热器。根据散热器温度和协同角分布对散热器的散热性能进行评价分析,结果表明：自然散热时,针肋散热器的散热性能最好,且协同角相对较小;当压电风扇工作时,新型散热器散热性能最好,可比原直肋散热器组合温度降低4 K,比原针肋散热器组合温度降低2 K。新型散热器仅通过改变散热器的肋片布置即可明显改善散热器的散热性能。