Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach

Topology Optimization of Two Fluid Heat Exchangers

A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for each of the fluid flows. A single design variable is used to describe the physical fields. The solid interface and the fluid domains are generated using an erosion-dilation based identification technique, which guarantees well-separated fluids, as well as a minimum wall thickness between them. Under the assumption of laminar steady flow, the two fluids are modelled separately, but in the entire computational domain using the Brinkman penalization technique for ensuring negligible velocities outside of the respective fluid subdomains. The heat transfer is modelled using the convection-diffusion equation, where the convection is driven by both fluid flows. A stabilized finite element discretization is used to solve the governing equations. Results are presented for two different problems: a two-dimensional example illustrating and verifying the methodology; and a three-dimensional example inspired by shell-and-tube heat exchangers. The optimized designs for both cases show an improved heat transfer compared to the baseline designs. For the shell-and-tube case, the full freedom topology optimization approach is shown to yield performance improvements of up to 113% under the same pressure drop

A prediction-correction based iterative convolution-thresholding method for topology optimization of heat transfer problems

In this paper, we propose an iterative convolution-thresholding method (ICTM) based on prediction-correction for solving the topology optimization problem in steady-state heat transfer equations. The problem is formulated as a constrained minimization problem of the complementary energy, incorporating a perimeter/surface-area regularization term, while satisfying a steady-state heat transfer equation. The decision variables of the optimization problem represent the domains of different materials and are represented by indicator functions. The perimeter/surface-area term of the domain is approximated using Gaussian kernel convolution with indicator functions. In each iteration, the indicator function is updated using a prediction-correction approach. The prediction step is based on the variation of the objective functional by imposing the constraints, while the correction step ensures the monotonically decreasing behavior of the objective functional. Numerical results demonstrate the efficiency and robustness of our proposed method, particularly when compared to classical approaches based on the ICTM.Comment: 29 pages, 25 figure

Innovative configurations of thermochemical energy storage devices by topology optimization

One of the main challenges to increasing the share of renewable energy sources in future energy scenarios is the mismatch between energy supply and demand. Thermal energy storage technologies have been identified as one possible solution to this challenge. Among the different thermal energy storage technologies, thermochemical energy storage devices are envisioned to have a large impact due to large theoretical energy density, negligible heat losses and possible heat-upgradation. Such devices rely on reversible chemical reactions where the energy is first stored in the form of chemical compounds generated by means of an endothermic reaction and recovered later on by recombining the compounds to drive an exothermic reaction. However, several technical limitations still hamper the successful introduction of thermochemical energy storage technologies in the market. In particular, the effective configuring of these devices is a complex engineering challenge due to the intrinsic dynamic operation, the complex multi-physics problems involved and the vast range of system requirements. Furthermore, standard design approaches are often driven by the analysts’ insight and experience, constraining the assessed configurations to a limited number of conceived solutions and precluding the full exploitation of the potential storage material. To break these barriers, this dissertation explores the use of topology optimization as a systematic design tool for the effective configuration of thermochemical energy storage devices Topology optimization is a form-finding methodology able to identify optimal designs without the need for any guess regarding the initial layout. Compared to conventional design approaches, the key advantage of topology optimization is thus its matchless design freedom. Novel enhancement pathways are identified by the analysis of the emerging design trends, and design solutions that outperform the current state-of-the-art are obtained. Specifically, this dissertation studies the heat transfer enhancement of reactive beds through the insertion of extended surfaces made of highly conductive material. Design guidelines for practitioners are derived from the analysis of the generated designs for variable bed properties, desired discharge time and bed size. Thus, the mass transfer enhancement of reactive beds is achieved through the generation of non-intuitive flow channel geometries aiming to effectively distribute gas reactants to reactive sites. Finally, the two approaches are combined to generate reactive beds employing optimized flow channel and extended surface geometries, ultimately leading to the concurrent enhancement of heat and mass transfer

Topology Optimization of Heat Exchangers

Heat exchangers have long been used in a wide variety of industrial applications, such as for energy recovery from by-products, temperature regulation in chemical processes, refrigeration, or cooling of car engines. Typically, each application requires a different type of heat exchanger such as, tube, shell, with/without phase change, mixing/non mixing etc. heat exchangers. Due to their importance, there has been an ongoing interest in reducing the perational/constructional costs and increasing the efficiency. A lot of research has be done in optimizing certain features of heat exchangers (e.g. tube dimensions, fin thickness etc.), but so far none of them investigates the optimization of the whole topology of a heat exchanger. The aim of this thesis is to optimize the structure of a two flow heat exchanger, by means of topology optimization. More specifically we aim to maximize the efficiency of heat transfer, given some predefined pressure drop and dimension constraints. These constraints are necessitated by the need of achieving a reduced operating (pressure drop) and manufacturing dimensions) costs. A heat exchanger, being a multi-physics system, can be described by two physical phenomena: the flow of the fluid and the heat transfer. In this study we focus on heat exchanger governed by an isothermal and incompressible Stokes flow with low Reynolds number, while the heat transfer is assumed to be advective-conductive heat transfer, without internal heat generation, characterised by a relatively high Peclet number. We evaluate two novel models for topology optimization of heat exchangers; the Fluid Tracking Model and the Multi-Material Model. Throughout the experimental evaluation we saw that the Multi-Material Model performs best. The Fluid Tracking Model did not produce optimal results and was unable to enforce non-mixing designs. The Multi-Material Model optimized designs that maximized the heat transfer surface area between the fluids. Furthermore the designs illustrated a wall at the interfaces of the two fluids, keeping the two flows separated. Both 2D and 3D cases were studied. The 3D optimal results achieved a moderate improvement in performance over a simple design of a concentric tube heat exchanger.Structural Optimization and MechanicsPrecision and Microsystems EngineeringMechanical, Maritime and Materials Engineerin