Flow Topology Optimization Research Articles

Turbulence effects in the topology optimization of compressible subsonic flow

AbstractTurbulence significantly influences fluid flow topology optimization, and this has already been verified under the incompressible flow regime. However, the same cannot be said about the compressible flow regime, in which the density field now affects and couples all of the fluid flow and turbulence equations and makes obtaining the adjoint model, which is necessary for topology optimization, extremely difficult. Up to now, the turbulence phenomenon has still not been considered in compressible flow topology optimization, which is what is being proposed and analyzed here. Rather than being based in the Reynolds‐Averaged Navier–Stokes (RANS) equations which are defined only for incompressible flow, the equations are now based on the Favre‐Averaged Navier–Stokes (FANS) equations, which are the counterpart of the RANS equations for compressible flow and feature different dependencies and terms. The compressible turbulence model being considered is the compressible version of the Spalart–Allmaras model, which differs from the usual Spalart–Allmaras model, since now there are some new spatially varying density and specific heat terms that depend on the primal variables and that act over some of the turbulence terms of the overall model. The adjoint equations are obtained by using an automatic differentiation scheme through a coupled software platform. The optimization algorithm is IPOPT, and some examples are presented to show the effect of turbulence in the compressible flow topology optimization.

Large-scale 3D multiphysics topology optimization of flow–heat–structural models including an islands constraint

This article demonstrates a large-scale 3D topology optimization problem formulation for components in need of internal cooling owing to surrounding hot gas flow. A conjugate heat transfer model is used and the goal of the optimization problem is to maximize the thermal performance subject to a coolant consumption limit. As a model problem, the interior design of a gas turbine guide-vane-like geometry is considered. High-quality finite element meshes are generated automatically by means of a voxelization method. A structural compliance constraint for thermo-mechanical loads, and a constraint for the suppression of free-floating structural parts, are included in the problem formulation. For the latter, an analytical expression for the constraint limit is derived. Several numerical examples indicate that the proposed problem formulation is able to generate interesting conceptual designs for interior-vane-cooling solutions.

A turbulent flow topology optimization method for diverging tee resistance reduction

The resistance of local components in piping and duct systems significantly affects the energy consumption of fans and pumps, accounting for 40–60 % of the total building energy consumption. In this paper, an improved topology optimization method for variable density turbulent flow is proposed to design a low-resistance diverging tee structure in piping and duct systems. The advantages of the improved optimization method over the traditional method are analyzed using finite element numerical simulation, and the applicability of the proposed method is verified in the Reynolds number range of 0.6 × 105–2.6 × 105. In order to ensure the resistance reduction effect of the topology diverging tee under multiple operating conditions, the local resistance coefficients under nine flow ratios were simulated and calculated using the finite volume method. The results show that the topology diverging tee can significantly reduce the resistance. Compared with the traditional tee, the maximum resistance reduction rates in the straight-through direction and branch direction reached 63 % and 59 %, respectively. In addition, the intensity of secondary flow in five downstream sections was analyzed based on the dimensionless parameter Se. Finally, the actual resistance reduction effect of the topology diverging tee was experimentally verified. The optimization method and analysis results proposed in this study can provide a reference for the optimal design of pipelines with low resistance in energy-saving operation of buildings and in engineering fields such as petroleum and chemical industries.

Flow Topology Optimization at High Reynolds Numbers Based on Modified Turbulence Models

Flow topology optimization (TopOpt) based on Darcy’s source term is widely used in the field of TopOpt. It has a high degree of freedom, making it suitable for conceptual aerodynamic design. Two problems of TopOpt are addressed in this paper to apply the TopOpt method to high-Reynolds-number turbulent flow that is often encountered in aerodynamic design. First, a strategy for setting Darcy’s source term is proposed based on the relationship between the magnitude of the source term and some characteristic variables of the flow (length scale, freestream velocity, and fluid viscosity). Second, we construct two modified turbulence models, a modified Launder–Sharma k − ϵ (LSKE) model and a modified shear stress transport (SST) model, that consider the influence of Darcy’s source term on turbulence and the wall-distance field. The TopOpt of a low-drag profile in turbulent flow is studied using the modified LSKE model. It is demonstrated by comparing velocity profiles that the model can reflect the influence of solids on turbulence at Reynolds numbers as high as one million. The TopOpt of a rotor-like geometry, which is of great importance in aerodynamic design, is conducted using the modified SST model. In all the cases considered, the drag, the total pressure loss, and the energy dissipation are significantly reduced by TopOpt, indicating the proposed model’s ability to handle the TopOpt of turbulent flow.

Topology optimization for flow machine rotor design considering resonance and low mass density flows

When designing structures that take part in rotating fluid flow machines, one important effect that may be taken into account is resonance, which is evaluated through the modal analysis. Under rotating conditions, the formulation and behavior of the structure changes, requiring a new formulation. Thus, this work formulates the fluid flow topology optimization for rotating resonance, while also considering a low mass density (compressible or incompressible) fluid flow. Therefore, three different effects are considered in the fluid flow-based design: from the modal analysis, from the solid structure, and from the low mass density fluid flow. The topology optimization problem is formulated for a simplified 2D model of a rotating fluid flow device, and a nodal design variable. The topology optimization is performed through an integer linear programming algorithm. Numerical examples are presented for the developed topology optimization formulation.

Optimal design of the diphasic flow pattern in water electrolyzers with CFD-independent multiphysics model

The diphasic flow in the flow channel in water electrolyzers is one of the most significant phenomena affecting the efficiency of power-to-hydrogen. The produced bubbles during electrolysis will cover the catalyst layer, isolating the contact between the electrolyte and the catalyst. The topology of the flow channel, determining the bubble distribution on the catalyst, should be well-designed to attenuate the insulated bubble effect. Aiming at maximizing the hydrogen production rate from flow topology optimization, a CFD-independent multiphysics model is proposed in this paper considering the bidirectional coupling between electrochemical reaction and diphasic flow. Unlike the traditional diphasic models whose resolving depends on CFD methods, the proposed model features a node association matrix recording the topology of the flow channel, so that the multiphysics fields can be obtained through a set of matrix equations. By comparing the results with the CFD model, the resolving of the proposed model accelerates over 50 times at maximum, while the multiphysics fields can be obtained with different flow topologies at an accuracy loss within 5% by increasing the differencing segments. Therefore, the model can be applied to the optimization of the flow topology due to outperforming mathematical properties. By weighing the bubble accumulation and pressure drop in the paralleled flow channel, the optimal topology can be acquired for minimized bubble effect with various structural parameters of the flow channel in pursuit of maximum power-to-hydrogen efficiency.

Turbulent flow topology optimization in nuclear reactor pressure vessel via NURBS-based particle hydrodynamics (NBPH) topology optimization framework

Turbulent flow topology optimization in nuclear reactor pressure vessel via NURBS-based particle hydrodynamics (NBPH) topology optimization framework

Hybrid geometry trimming algorithm based on Integer Linear Programming for fluid flow topology optimization

In this work, a hybrid geometry trimming algorithm based on Topology Optimization of Binary Structures (TOBS) is proposed to design fluid flow devices with reduced seepage. The problem of solid reintroduction during optimization is solved by combining the geometry trimmed functional with the extended porous domain functional in a multi-objective function. The method is evaluated in the topology optimization of fixed-geometry fluidic diodes, which is a class of problems known to present difficulties related to high fluid penetration in the porous regions. Also, a new convergence criterion for TOBS is proposed to eliminate the necessity of selecting a convergence tolerance and to avoid running the optimization for cycles of the same designs. Fluidic diodes are designed for several Reynolds numbers (Re) to prove the effectiveness of the proposed formulation. The forward problem is solved by the Finite Element Method (FEM), and the sensitivities are calculated via automatic differentiation. The optimization problem is solved by Integer Linear Programming.

Blood flow topology optimization considering a thrombosis model

Blood flow topology optimization considering a thrombosis model

Large-Scale Topology Optimization of Transient Incompressible Flow with Building-Cube Method

In recent years, topology optimization methods have been adopted not only for structural problems but also for fluid flow problems. Topology optimization for unsteady flows requires a fine mesh, which is computationally expensive. Therefore, we propose an transient incompressible flow topology optimization method based on the building cube method (BCM), which is suitable for massively parallel computing. BCM is a type of hierarchical Cartesian mesh method that has been reported to have very good scalability. The transient Navier-Stokes equations in the topology optimization procedure are solved by a finite volume discretization based on the BCM. The sensitivity of the objective function is obtained by continuous sensitivity analysis based on the adjoint variables method.

Reactive fluid flow topology optimization with the multi-relaxation time lattice Boltzmann method and a level-set function

This paper presents a topology optimization algorithm based on the lattice Boltzmann method coupled with a level-set method for increasing the efficiency of reactive fluid flows. The multi-relaxation time model is considered for the lattice Boltzmann collision operator, allowing higher Reynolds numbers flow simulations compared to the ordinary single-relaxation time model. The cost function gradient is obtained with the derivation of the adjoint-state formulation for the fully coupled problem. The proposed method is tested successfully on several numerical applications involving Reynolds numbers from 10 up to 1,000, as well as with different Damkohler and Peclet numbers. A limitation of the maximal pressure drop is also applied. The obtained results demonstrate that the proposed numerical method is robust and efficient for solving topology optimization problems of reactive fluid flows, in different operating conditions.

Effects of Grid Spacing on Topology Optimization of Flow around an Object

Effects of Grid Spacing on Topology Optimization of Flow around an Object

A Heuristic Method Using Hessian Matrix for Fast Flow Topology Optimization

We propose a heuristic optimization method for a density-based fluid topology optimization using a Hessian matrix. In flow topology optimization, many researches use a gradient-based method. Convergence rate of a gradient method is linear, which means slow convergence near the optimal solution. For faster convergence, we utilize a Hessian matrix toward the end of the optimization procedure. In the present paper, we formulate a fluid optimization problem using the lattice Boltzmann method and heuristically solve the optimization problem with using an approximated sensitivity. In the formulation of a Hessian matrix, we use a heuristic trick in order to formulate it as a diagonal matrix. By the heuristics, the computation cost is decreased drastically. The validity of the method is studied via numerical examples.

Applications of automatic differentiation in topology optimization

The goal of this article is to demonstrate the applicability and to discuss the advantages and disadvantages of automatic differentiation in topology optimization. The technique makes it possible to wholly or partially automate the evaluation of derivatives for optimization problems and is demonstrated on two separate, previously published types of problems in topology optimization. Two separate software packages for automatic differentiation, CoDiPack and Tapenade are considered, and their performance and usability trade-offs are discussed and compared to a hand coded adjoint gradient evaluation process. Finally, the resulting optimization framework is verified by applying it to a non-trivial unsteady flow topology optimization problem.

Fluid flow topology optimization in PolyTop: stability and computational implementation

We present a Matlab implementation of topology optimization for fluid flow problems in the educational computer code PolyTop (Talischi et al. 2012b). The underlying formulation is the well-established porosity approach of Borrvall and Petersson (2003), wherein a dissipative term is introduced to impede the flow in the solid (non-fluid) regions. Polygonal finite elements are used to obtain a stable low-order discretization of the governing Stokes equations for incompressible viscous flow. As a result, the same mesh represents the design field as well as the velocity and pressure fields that characterize its response. Owing to the modular structure of PolyTop, incorporating new physics, in this case modeling fluid flow, involves changes that are limited mainly to the analysis routine. We provide several numerical examples to illustrate the capabilities and use of the code. To illustrate the modularity of the present approach, we extend the implementation to accommodate alternative formulations and cost functions. These include topology optimization formulations where both viscosity and inverse permeability are functions of the design; and flow control where the velocity at a certain location in the domain is maximized in a prescribed direction.

Erratum to: A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method

Erratum to: A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method

Optimal partition layout of expansion chamber muffler with offset inlet/outlet

An optimal partition layout inside an expansion chamber muffler with an offset inlet/outlet is systematically designed by using topology optimization to achieve the desired characteristics in terms of acoustics and fluid mechanics. To that end, a partition volume minimization problem is formulated by applying acoustical and flow topology optimization methods. The partition volume is set as an objective function with constraints imposed on the target values of the transmission loss and pressure drop. The finite element method is employed for the acoustical and flow analyses. A design variable is assigned to each finite element such that it changes continuously between 0 and 1 to determine the state of the associated finite element. The design variables are updated during the optimization process and parameterized to converge to 0 or 1 at the end of the process. Finite elements with design variables of 1 build up rigid partitions which are optimally placed to achieve the target values of transmission loss and pressure drop. Different optimal partition layouts are obtained depending on the target frequency, the target values of transmission loss and pressure drop, and the initial values of the design variables. An experiment-based validation strongly supports the validity of the proposed muffler design method.

3507 流れ場のトポロジー最適化においてニュートン法を用いることによる収束性の向上とグレースケール問題の回避(OS3-9 設計と最適化IX)

We propose a fluid topology optimization method using a Newton-gradient-hybrid scheme. The method converges in small computation time. In addition, the boundary between fluid and solid region is clearly distinguished. In the method, the domain is updated concurrently with solving a flow field. The flow field is solved by the lattice Boltzmann method (LBM). Due to the formulation of LBM and the optimization algorithm, the Hessian matrix is a diagonal matrix. The Hessian matrix is not generally positive semidefinite since the flow topology optimization problem is a nonconvex problem. Hence, we employ a Newton method for positive definite part of the Hessian marix, and employ a gradient method for negative semidefinite part.

A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method

A topology optimization method for fluid flow using transient information is proposed. In many conventional methods, the design domain is updated using steady state information which is obtained af...

Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method

A discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice Boltzmann method (LBM) with multiple-relaxation-times (MRT) is developed. The lattice Boltzmann fluid solver is supplemented by a porosity model using a Darcy force. The continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels. The adjoint LBM equation, which is used to compute the gradient of the optimization objective with respect to the design variables, is derived in moment space and found to be as simple as the original LBM. The moment based spatial momentum derivatives used to express the discrete objective functional (cost function) have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field. This is particularly useful if dissipation is a design criterion as demonstrated in this paper. The method is validated by a detailed comparison with results obtained by Borrvall et al. for Stokes flow. While their approach is only valid for Stokes flow (i.e. very low Reynolds numbers) our approach in its present form can in principle be applied for flows of different Reynolds numbers just like the Navier–Stokes equation based approaches. This point is demonstrated with a bending pipe example for various Reynolds numbers.