arXiv subjects

Maarten Blommaert

Publications and source records attributed to Maarten Blommaert.

8 recordsLinked to original sources

arXiv2026

Optimal Heat Storage Sizing for District Heating Networks to Maximize Electricity Revenue from Combined Heat and Power Units

Integrating heat storages in district heating networks (DHNs) supports managing dynamic characteristics such as heat-demand variations and changing energy prices, and the intermittency of renewable sources. A common application are DHNs with combined heat and power (CHP) units, where a storage allows shifting heat extraction to periods with favorable electricity prices. Although the benefits of heat storage in DHNs are well established, determining the optimal storage size remains challenging due to the diversity of DHNs in terms of heat sources, production and consumption patterns, network heat losses, and fuel costs. This paper presents a scalable, automated methodology for optimizing short-term heat storage in DHNs using mathematical optimization. The nonlinear, physics-based approach models the DHN, heat producers, and storages simultaneously to minimize total economic cost through optimal storage sizing, explicitly considering time-varying heat-production costs, heat demands, and heat losses. The methodology is demonstrated on a 3rd-generation CHP-DHN in Belgium with 30 consumers, exceeding the scale of previous physics-based storage-sizing studies. For this system, optimal storage integration reduces the 20-year cost by 730 k EUR (16.5%), from 4.41 M EUR to 3.68 M EUR. The reduction results from a 1.07 M EUR decrease in heat-production cost achieved by shifting heat extraction to periods of low electricity prices, while the storage investment amounts to 323 k EUR. A comparison to a commonly used simplified storage sizing method, which fails to identify the optimal storage size, demonstrates the advantage of the proposed holistic, physics-based optimization approach in ensuring feasible designs, accurate cost assessments, and optimal storage sizing.

math.OC↗

arXiv2025

Optimal Sizing and Material Choice for Additively Manufactured Compact Plate Heat Exchangers

Advances in additive manufacturing (AM) enable new opportunities to design compact heat exchangers (cHEXs) by leveraging flexible geometries to improve energy and material efficiency. However, it is well known that reducing size in counterflow cHEXs can degrade effectiveness due to axial heat conduction through the solid material, which depends strongly on material thermal conductivity and wall thickness. Understanding the interaction between fundamental heat transfer mechanisms and manufacturing constraints is essential for designing next generation compact thermal systems that fully exploit AM's shaping flexibility. This study investigates how material selection and AM thin wall limitations influence the maximum achievable power density in compact plate heat exchangers. An optimization framework evaluates six materials including plastic, austenitic steel, Al2O3, AlN, aluminum, and copper under fixed pressure drop and effectiveness, while accounting for AM specific thickness constraints and a minimum plate spacing to address fouling risks. Results show that copper consistently yields the lowest power density despite having the highest thermal conductivity, whereas plastic achieves the highest power density across most optimization scenarios. Without manufacturing or fouling constraints, plastic outperforms the baseline steel design by nearly three orders of magnitude. With uniform plate thickness or fouling constraints, the performance gap narrows, making plastic and austenitic steel comparable. When material specific thickness limits are applied, plastic again leads in compactness due to its superior thin wall manufacturability. These findings highlight that AM constraints strongly affect cHEX compactness and that lower conductivity materials can outperform metals such as copper in power dense heat exchanger designs.

cs.CE↗

arXiv2025

A Unit-Cell Shape Optimization Approach for Maximizing Heat Transfer in Periodic Fin Arrays at Constant Solid Temperature

Periodic fin structures are often employed to enhance heat transfer in compact cooling solutions and heat exchangers. Adjoint-based optimization methods are able to further increase the heat transfer by optimizing the fin geometry. However, obtaining optimal geometries remains challenging in general because of the high computational cost of full array simulations. In this paper, a unit cell optimization approach is presented that starts from recently developed macro-scale models for isothermal solid structures. The models exploit the periodicity of the problem to reduce the computational cost of evaluating the array heat transfer to that of a single periodic unit cell. By combining these models with a geometrically-constrained free-shape optimization approach, optimal fin geometries are obtained for the periodic fin array that maintain a minimal fin distance. Moreover, using an augmented Lagrangian approach, also the average pressure gradient and barycenter of the fin can be fixed. On a fictitious use-case, heat transfer increases up to 104 \% are obtained. When also flow rate is constrained in addition to maintain a high effectiveness, only up to 8 \% heat transfer increase is observed. Finally, the errors of the unit-cell optimization approach are investigated, indicating that with a good choice of cost functional formulation, errors of the approach as low as 1-2 \% can be obtained for the periodically developed part of the array. Finally, the entrance effect to the heat transfer is found to be non-negligible with a contribution of 10-15 \% for the considered fin array. This advocates for further research to extend the unit-cell models towards improved modeling of entrance effects.

cs.CE↗

arXiv2024

Decarbonization of Existing Heating Networks through Optimal Producer Retrofit and Low-Temperature Operation

District heating networks are considered a key factor for enabling emission-free heat supply, while many existing networks still heavily rely on fossil fuels. With district heating network pipes easily exceeding a lifetime of 30 years, there is a growing potential to retrofit the heat producers of existing networks to enable low-emission heat supply. Today, the heat producer retrofit for district heating networks usually focuses on simplified approaches, where the non-linear nature of the design problem is relaxed or not considered at all. Some approaches take non-linearities into account but use optimization routines that are either not scalable to large problems or are not reliable in obtaining an optimal solution, such as parameter optimization and sensitivity studies. This paper presents an automated design approach, to decarbonize existing heating networks through optimal producer retrofit and ultimately enabling 4th generation operation. The approach uses multi-objective, mathematical optimization to balance CO2 emissions and network costs, by assessing different CO2 prices, and is based on a detailed physical model. The optimizer is given the freedom to choose the producer types, their capacities, and for each period, their supplied heat and supply temperature. A non-linear heat transport model accurately accounts for heat and momentum losses throughout the network, and ensures the feasibility of the proposed design and operation. The multi-period formulation incorporates temporal changes in heat demand and environmental conditions throughout the year. By formulating a continuous problem and using adjoint-based optimization, the automated approach remains scalable towards large scale applications. The design approach was assessed on a medium-sized 3rd generation DHN case and was able to optimally retrofit the heat producers.

math.OC↗

arXiv2024

A Multi-Period Topology and Design Optimization Approach for District Heating Networks

The transition to 4th generation district heating creates a growing need for scalable, automated design tools that accurately capture the spatial and temporal details of heating network operation. This paper presents an automated design approach for the optimal design of district heating networks that combines scalable density-based topology optimization with a multi-period approach. In this way, temporal variations in demand, supply, and heat losses can be taken into account while optimizing the network design based on a nonlinear physics model. The transition of the automated design approach from worst-case to multi-period shows a design progression from separate branched networks to a single integrated meshed network topology connecting all producers. These integrated topologies emerge without imposing such structures a priori. They increase network connectivity, and allow for more flexible shifting of heat loads between different producers and heat consumers, resulting in more cost-effective use of heat. In a case study, this integrated design resulted in an increase in waste heat share of 42.8 % and a subsequent reduction in project cost of 17.9 %. We show how producer unavailability can be accounted for in the automated design at the cost of a 3.1 % increase in the cost of backup capacity. The resulting optimized network designs of this approach connect multiple low temperature heat sources in a single integrated network achieving high waste heat utilization and redundancy, highlighting the applicability of the approach to next-generation district heating networks.

cs.CE↗

arXiv2023

Non-linear Topology Optimization of District Heating Networks: A benchmark of Mixed-Integer and Adjoint Approaches

The widespread use of optimization methods in the design phase of District Heating Networks is currently limited by the availability of scalable optimization approaches that accurately represent the network. In this paper, we compare and benchmark two different approaches to non-linear topology optimization of District Heating Networks in terms of computational cost and optimality gap. The first approach solves a mixed-integer non-linear optimization problem that resolves the binary constraints of pipe routing choices using a combinatorial optimization approach. The second approach solves a relaxed optimization problem using an adjoint optimization approach, and enforces a discrete network topology through penalization. Our benchmark shows that the relaxed penalized problem has a polynomial computational cost scaling, while the combinatorial solution scales exponentially, making it intractable for practical-sized networks. We also evaluate the optimality gap between the two approaches on two different District Heating Network optimization cases. We find that the mixed-integer approach outperforms the adjoint approach on a single-producer case, but the relaxed penalized problem is superior on a multi-producer case. Based on this study, we discuss the importance of initialization strategies for solving the optimal topology and design problem of District Heating Networks as a non-linear optimization problem.

math.OC↗

arXiv2022

Economic Topology Optimization of District Heating Networks using a Pipe Penalization Approach

In the presented study, a pipe penalization approach for the economic topology optimization of District Heating Networks is proposed, drawing inspiration from density-based topology optimization. For District Heating Networks, the upfront investment is a crucial factor for the rollout of this technology. Today, the pipe routing is usually designed relying on a linearization of the underlying heat transport problem. This study proposes to solve the optimal pipe routing problem as a non-linear topology optimization problem, drawing inspiration from density-based topology optimization. The optimization problem is formulated around a non-linear heat transport model and minimizes a detailed net present value representation of the heating network cost. By relaxing the combinatorial problem of pipe placement, this approach remains scalable for large-scale applications. A discrete network topology and near-discrete pipe design is achieved by using an intermediate pipe penalization strategy. For a realistic test case, the proposed algorithm achieves a discrete network topology and near-discrete pipe design that outperforms simple post-processing steps.

cs.CE↗

arXiv2020

An adjoint optimization approach for the topological design of large-scale district heating networks based on nonlinear models

This article deals with the problem of finding the best topology, pipe diameter choices, and operation parameters for realistic district heating networks. Present design tools that employ non-linear flow and heat transport models for topological design are limited to small heating networks with up to 20 potential consumers. We introduce an alternative adjoint-based numerical optimization strategy to enable large-scale nonlinear thermal network optimization. In order to avoid a strong computational cost scaling with the network size, we aggregate consumer constraints with a constraint aggregation strategy. Moreover, to align this continuous optimization strategy with the discrete nature of topology optimization and pipe size choices, we present a numerical continuation strategy that gradually forces the design variables towards discrete design choices. As such, optimal network topology and pipe sizes are determined simultaneously. Finally, we demonstrate the scalability of the algorithm by designing a fictitious district heating network with 160 consumers. As a proof-of-concept, the network is optimized for minimal investment cost and pumping power, while keeping the heat supplied to the consumers within a thermal comfort range of 5 %. Starting from a uniform distribution of 15 cm wide piping throughout the network, the novel algorithm finds a network lay-out that reduces piping investment by 23 % and pump-related costs by a factor of 14 in less than an hour on a standard laptop. Moreover, the importance of embedding the non-linear transport model is clear from a temperature-induced variation in the consumer flow rates of 72 %.

cs.CE↗