arXiv subjects

Martine Baelmans

Publications and source records attributed to Martine Baelmans.

At least 19 recordsLinked to original sources

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 one-dimensional numerical model for system performance prediction of loop heat pipes and its validation

Developing high power density electronics requires effective and highly reliable cooling techniques with low thermal resistance and high heat removal capacity. Loop heat pipes (LHPs) are one kind of two-phase heat transfer device which can meet all these requirements. A physics-based one-dimensional numerical model has been elaborated to further develop this promising electronics cooling solution. In addition, an experimental setup using water as coolant, and which includes an LHP built with transparent materials, is used to validate the numerical model. This validation is obtained by comparing the numerical results with the temperature measurements, the two-phase flow section length in the condenser line, and an energy balance evaluation. The numerical model is then used to predict the system performance of the LHP under investigation. The results indicate that this LHP can only work in fixed conductance mode for the given operating conditions. Further, the influence of the charging mass is assessed. For low charging masses, both the natural convection cooled condenser and the compensation chamber casing can be fully utilized to dissipate the input heat, which can exceed {29.9 W} when the coolant saturation temperature is at {100 \celsius}. The operational limits for LHPs are investigated. For the current LHP under given operating conditions, the heat dissipation limit restricts the maximum input heat power, which in turn induces the activation of the heat leakage limit and the liquid-filling limit. It is shown that the condenser with higher heat dissipation capacity and lower thermal resistance will therefore enlarge the operational envelope.

physics.flu-dyn↗

arXiv2025

The effect of neon seeding on plasma edge transport in EAST

The effect of neon seeding on different transport mechanisms in EAST is investigated by analyzing SOLPSITER simulations. By evaluating the agreement between experimental observations and the performed simulations, four simulations are selected for a detailed analysis. In this analysis, it is shown that the presence of neon reduces the influence of drifts on the simulated profiles. In the simulation results, double peaked profiles/profiles with two valleys are observed at the divertor targets which can be explained by the parallel drift velocities These drifts move particles from the outboard towards the inboard side and, in that way, also increase the ionization sources at the inboard side. It is shown that Ne+ leaks towards the core making it difficult to perform experiments which contain as much neon as in the SOLPS-ITER simulations. In fact, the level of neon in the experiments is limited by the HL backtransition which takes place if higher order states of neon ionize in the core and cause in that way too much core radiation. Furthermore, the analysis of the radiated power profiles suggests that the presence of other radiators besides neon is important to bring the experiments into detachment. The ionization of deuterium is the most important neutral reaction present in the simulations. The amount of ionized deuterium is decreased when large amounts of neon are present and the anomalous transport is modified. Therefore, it is concluded that for the analyzed simulations, neon increases the radiated power fraction, decreases the deuterium ionization, increases the neutral friction, but does not manage to cause significant influence of deuterium recombination. As a consequence, volumetric recombination only plays a minor role in the studied simulations.

physics.plasm-ph↗

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↗

arXiv2025

Predicting the statistical error of analog particle tracing Monte Carlo

Large particle systems are often described by high-dimensional (linear) kinetic equations that are simulated using Monte Carlo methods for which the asymptotic convergence rate is independent of the dimensionality. Even though the asymptotic convergence rate is known, predicting the actual value of the statistical error remains a challenging problem. In this paper, we show how the statistical error of an analog particle tracing Monte Carlo method can be calculated (expensive) and predicted a priori (cheap) when estimating quantities of interest (QoI) on a histogram. We consider two types of QoI estimators: point estimators for which each particle provides one independent contribution to the QoI estimates, and analog estimators for which each particle provides multiple correlated contributions to the QoI estimates. The developed statistical error predictors can be applied to other QoI estimators and nonanalog simulation routines as well. The error analysis is based on interpreting the number of particle visits to a histogram bin as the result of a (correlated) binomial experiment. The resulting expressions can be used to optimize (non)analog particle tracing Monte Carlo methods and hybrid simulation methods involving a Monte Carlo component, as well as to select an optimal particle tracing Monte Carlo method from several available options. Additionally, the cheap statistical error predictors can be used to determine a priori the number of particles N that is needed to reach a desired accuracy. We illustrate the theory using a linear kinetic equation describing neutral particles in the plasma edge of a fusion device and show numerical results. The code used to perform the numerical experiments is openly available.

physics.comp-ph↗

arXiv2024

Developed and quasi-developed macro-scale heat transfer in micro- and mini-channels with arrays of offset strip fins subject to a uniform heat flux

In the present work, we examine to what degree the heat transfer can be described as developed on a macro-scale level in typical micro- and mini-channels with offset strip fin arrays subject to a uniform heat flux, considering flow entrance and side-wall effects. Full-scale numerical heat transfer simulations are conducted to determine the extent of the developed macro-scale heat transfer region within the arrays. We find that the onset point of developed heat transfer increases linearly with the Péclet number and channel width. However, the thermal development lengths remain limited relative to the overall channel length. Therefore, the local macro-scale heat transfer coefficient can be modeled by developed Nusselt number correlations with discrepancies below 25% in both the developed and developing heat transfer regions. We observe that quasi-developed heat transfer prevails over nearly the entire entrance region of the channel and significantly contributes to the main heat transfer characteristics, particularly the eigenvalues and amplitudes of the dominant temperature modes. Additionally, we analyze the impact of channel side walls on the temperature field's periodicity and the macro-scale temperature profile, which we characterize through an effective heat transfer coefficient. Our comprehensive numerical data covers various fin height-to-length ratios up to 1, fin pitch-to-length ratios up to 0.5, and channel aspect ratios ranging from 1/5 to 1/17, encompassing Reynolds numbers from 28 to 1224. Two sets of Prandtl number and thermal conductivity ratio are investigated, corresponding to the combinations of copper/air, and copper/water.

physics.flu-dyn↗

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

Numerical implications of including drifts in SOLPS-ITER simulations of EAST

The inclusion of drifts in plasma edge codes like SOLPS-ITER is required to match simulation data with experimental profiles. However, this remains numerically challenging. In this paper, the effect of some numerical factors on the final plasma solution is investigated. This study is performed on three EAST simulations in upper single null configuration: an attached purely deuterium case, an attached case with limited Ne-seeding and a detached Ne-seeded case. The effects of the anomalous conductivity and anomalous thermo-electric coefficient on the plasma potential are investigated. Next, the effect of the employed grids is shown. In order to investigate these effects, accurate drift simulations are needed. Therefore, the employed time step and used numerical parameters are discussed for the three studied simulations. For all presented simulations, it is verified that the restriction of the grid to the first flux surface tangent to the main chamber wall has only a small effect on the divertor solution. This means that the main power dissipation takes place inside the simulated domain and only a small fraction of the power is leaving the B2.5 grid trough the grid boundary closest to the first wall. Finally the effect of drifts on the asymmetry between the inner and outer target for EAST simulations is demonstrated.

physics.plasm-ph↗

arXiv2023

Developed and quasi-developed macro-scale flow in micro- and mini-channels with arrays of offset strip fins

We investigate to what degree the steady laminar flow in typical micro- and mini-channels with offset strip fin arrays can be described as developed on a macro-scale level, in the presence of channel entrance and side-wall effects. Hereto, the extent of the developed and quasi-developed flow regions in such channels is determined through large-scale numerical flow simulations. It is observed that the onset point of developed flow increases linearly with the Reynolds number and channel width, but remains small relative to the total channel length. Further, we find that the local macro-scale pressure gradient and closure force for the (double) volume-averaged Navier-Stokes equations are adequately modeled by a developed friction factor correlation, as typical discrepancies are below 15% in both the developed and developing flow region. We show that these findings can be attributed to the eigenvalues and mode amplitudes which characterize the quasi-developed flow in the entrance region of the channel. Finally, we discuss the influence of the channel side walls on the flow periodicity, the mass flow rate, as well as the macro-scale velocity profile, which we capture by a displacement factor and slip length coefficient. Our findings are supported by extensive numerical data for fin height-to-length ratios up to 1, fin pitch-to-length ratios up to 0.5, and channel aspect ratios between 1/5 and 1/17, covering Reynolds numbers from 28 to 1224.

physics.flu-dyn↗

arXiv2023

Hilbert expansion based fluid models for kinetic equations describing neutral particles in the plasma edge of a fusion device

Neutral particles in the plasma edge of fusion devices based on magnetic confinement are described by a transient kinetic equation incorporating ionization, recombination, and charge-exchange collisions. In charge-exchange dominated regimes, the neutral particle velocity distribution approaches the drifting Maxwellian defined by the mean velocity and temperature of the plasma. This enables model order reduction from the kinetic equation to approximate fluid models. We derive transient fluid models consistent with the kinetic equation by exploring a splitting based approach. We split the kinetic equation in sources and sinks on the one hand, and transport combined with charge-exchange on the other hand. Combining transport with charge-exchange collisions allows for deriving Hilbert expansion based fluid models. The retrieved fluid models depend on the assumed importance (scaling) of the different terms in the split equation describing transport and charge-exchange. We explore two scalings: the hydrodynamic scaling and the diffusive scaling. The performance of the fluid models with respect to a discrete velocity model and a Monte Carlo reference solver is assessed in numerical experiments. The code used to perform the numerical experiments is openly available.

physics.plasm-ph↗

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

Nusselt number for steady periodically developed heat transfer in micro- and mini-channels with arrays of offset strip fins subject to a uniform heat flux

In this work, the Nusselt number is examined for periodically developed heat transfer in micro- and mini-channels with arrays of offset strip fins, subject to a constant heat flux. The Nusselt number is defined on the basis of a heat transfer coefficient which represents the spatially constant macro-scale temperature difference between the fluid and solid during conjugate heat transfer. Its values are determined numerically on a single unit cell of the array for Reynolds numbers between 1 and 600. Two combinations of the Prandtl number and the thermal conductivity ratio are selected, corresponding to air and water. It is shown that the Nusselt number correlations from the literature mainly apply to air in the transitional flow regime in larger conventional channels if the wall temperature remains uniform. As a result, they do not correctly capture the observed trends for the Nusselt number in micro- and mini-channels subject to a constant heat flux. Therefore, new Nusselt number correlations, obtained through a least-squares fitting of 2282 numerical simulations, are presented for air and water. The suitability of these correlations is assessed via the Bayesian approach for parameter estimation and model validation. The correlations respect the observed asymptotic trends and limits of the Nusselt number for all the geometrical parameters of the offset strip fins. In addition, they predict a linear dependence of the Nusselt number on the Reynolds number, in good agreement with the data from this work. Nevertheless, a detailed analysis reveals a more complex scaling of the Nusselt number with the Reynolds number, closely related to the underlying flow regimes, particularly the weak and strong inertia regimes. Finally, through 62 additional simulations, the influence of the material properties on the Nusselt number is illustrated and compared to the available literature.

physics.flu-dyn↗

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↗

arXiv2021

Friction factor for steady periodically developed flow in micro-and mini-channels with arrays of offset strip fins

In this work, the friction factor for steady periodically developed flow through micro-and mini-channels with periodic arrays of offset strip fins is analyzed. The friction factor is studied numerically on a unit cell of the array for Reynolds numbers ranging from 1 to 600, and fin height-to-length ratios below 1. It is shown that the friction factor correlations from the literature, which primarily focus on larger conventional offset strip fin geometries in the transitional flow regime, do not predict the correct trends for laminar flow in micro-and mini-channels. Therefore, a new friction factor correlation for micro-and mini-channels with offset strip fin arrays is constructed from an extensive set of numerical simulations through a least-squares fitting procedure. The suitability of this new correlation is further supported by means of the Bayesian approach for parameter estimation and model validation. The correlation predicts an inversely linear relationship between the friction factor and the Reynolds number, in accordance with our observation that a strong inertia regime prevails over nearly the entire range of investigated Reynolds numbers. Yet, through a more detailed analysis, also the presence of a weak inertia regime and a transitional regime is identified, and the transitions from the strong inertia regime are quantified by means of two critical Reynolds numbers. Finally, the new correlation also incorporates the asymptotic trends that are observed for each geometrical parameter of the offset strip fin array, and whose origins are discussed from a physical perspective.

physics.flu-dyn↗

arXiv2021

Turbulent kinetic energy in 2D isothermal interchange-dominated scrape-off layer ExB drift turbulence: Governing equation and relation to particle transport

This paper studies the turbulent kinetic energy ($k_\perp$) in 2D isothermal electrostatic interchange-dominated ExB drift turbulence in the scrape-off layer and its relation to particle transport. An evolution equation for the former is analytically derived from the underlying turbulence equations. Evaluating this equation shows that the dominant source for the turbulent kinetic energy is due to interchange drive, while the parallel current loss to the sheath constitutes the main sink. Perpendicular transport of the turbulent kinetic energy seems to play a minor role in the balance equation. Reynolds stress energy transfer also seems to be negligible, presumably because no significant shear flow develops under the given assumptions of isothermal sheath-limited conditions in the open field line region. The interchange source of the turbulence is analytically related to the average turbulent ExB energy flux, while a regression analysis of TOKAM2D data suggests a model that is linear in the turbulent kinetic energy for the sheath loss. A similar regression analysis yields a diffusive model for the average radial particle flux, in which the anomalous diffusion coefficient scales with the square root of the turbulent kinetic energy. Combining these three components, a closed set of equations for the mean-field particle transport is obtained, in which the source of the turbulence depends on mean flow gradients and $k_\perp$ through the particle flux, while the turbulence is saturated by parallel losses to the sheath. Implementation of this new model in a 1D mean-field code shows good agreement with the original TOKAM2D data over a range of model parameters.

physics.plasm-ph↗

arXiv2020

A comparison of source term estimators in coupled finite-volume/Monte-Carlo methods with applications to plasma edge simulations in nuclear fusion

In many applications, such as plasma edge simulation of a nuclear fusion reactor, a coupled PDE/kinetic description is required, which is usually solved with a coupled finite-volume/Monte-Carlo method. Different procedures have been proposed to estimate the source terms in the finite volume part that appear from the Monte Carlo part of the simulation. In this paper, we present a systematic comparison of the variance and computational cost of a coherent set of such estimation procedures. We compare the different estimation procedures for mass in a simplified forward-backward scattering model problem, where an analytical comparison is possible, and for mass and momentum in a model problem with realistic scattering. Our results reveal a non-trivial dependence of the optimal choice of estimator on the model parameters and show that different estimation procedures prevail for different quantities of interest.

math.NA↗

arXiv2020

Kinetic-diffusion asymptotic-preserving Monte Carlo algorithm for Boltzmann-BGK in the diffusive scaling

We develop a novel Monte Carlo strategy for the simulation of the Boltzmann-BGK model with both low-collisional and high-collisional regimes present. The presented solution to maintain accuracy in low-collisional regimes and remove exploding simulation costs in high-collisional regimes uses hybridized particles that exhibit both kinetic behaviour and diffusive behaviour depending on the local collisionality. In this work, we develop such a method that maintains the correct mean, variance, and correlation of the positional increments over multiple time steps of fixed step size for all values of the collisionality, under the condition of spatial homogeneity during the time step. In the low-collisional regime, the method reverts to the standard velocity-jump process. In the high-collisional regime, the method collapses to a standard random walk process. We analyze the error of the presented scheme in the low-collisional regime for which we obtain the order of convergence in the time step size. We furthermore provide an analysis in the high-collisional regime that demonstrates the asymptotic-preserving property.

math.NA↗

arXiv2020

Multilevel Asymptotic-Preserving Monte Carlo for Particle Simulations

We develop a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport equation with a Bhatnagar-Gross-Krook (BGK) collision operator. This equation occurs, for instance, in mathematical models of the neutral particles in the plasma edge of nuclear fusion reactors. In this context, the Kinetic-Diffusion Monte Carlo method is known to maintain accuracy both in the low-collisional and the high-collisional limit, without an exploding simulation cost in the latter. We show that, by situating this method within a Multilevel Monte Carlo (MLMC) framework, using a hierarchy of larger time step sizes, the simulation cost is reduced even further. The different levels in our ML-KDMC method are connected via a new and improved recipe for correlating particle trajectories with different time step sizes. Furthermore, a new and more general level selection strategy is presented. We illustrate the efficiency of our ML-KDMC method by applying it to a one-dimensional test case with nonhomogeneous and anisotropic plasma background. Our method yields significant speedups compared to the single-level KDMC scheme, both in the low and high collisional regime. In the high-collisional case, our ML-KDMC outperforms the single-level KDMC method by several orders of magnitude.

math.NA↗