Topology optimization of fluid flows requires the computation of the cost function gradient. Based on the partial differential equations that govern the physics, the only efficient manner to do so is using the adjoint-state method. This article highlights the property that the cost gradient is naturally not well calculated when the cost function incorporates macroscopic data at the boundary, in a LBM framework. This is due to the advection nature of Boltzmann equations which are in terms of distribution functions at the mesoscopic scale, while the cost function incorporates variables at the macroscopic scale. Two methodologies are proposed to improve the accuracy of the gradient calculation: shifting the domain of integration of the cost function and a lumping strategy. This lumping strategy has proved to constitute a substantial improvement.

Data Centers (DCs) are proliferating throughout the world, and their energy consumption is increasing. Therefore, optimizing the energy efficiency of the server environment becomes crucial. For this purpose, the usual key metric is the Power Unit Efficiency (PUE). However, this measurement only occurs when a Data Center (DC) becomes operational. The current study builds a methodological tool to estimate PUE metrics before the DC is built, by bringing together concepts from Information Technology (IT) and energy laws. Firstly, a consumption study is carried out on a small university DC with a power of 140 kW. An energy behavior pattern is drawn based on 5 minutes time-step data collected over a recent period of 7 years, from 2016 to 2023, making this dataset relevant for a benchmark of historical DC server energy consumption. Secondly, a dynamic model is built to integrate the variable energy behavior and the weather-dependent system environment. In this way, the short time PUE tau reflects interesting non-constant values, exhibiting maximum and minimum performances of the DC. The results of the dynamic model are compared to the actual measurements and show a deviation of 5% between measurements and predictions. Temporal variations of PUE are strongly correlated with temperature variations during a day. In contrast, server environments exhibit an almost constant consumption, except for High Performance Computing (HPC) during the working days, for which the energy demand is higher than during nights. This approach is also used to make long-term predictions evaluating the impact of global warming on DC efficiency as an example. In this study, a prediction was made for the years 2035 and 2065 and could be easily implemented by manufacturers as a reliable method to estimate PUE during the pre-construction and projection phases of DC in a context of rapid climate change.

This paper evaluates the impact of dataset characteristics on the accuracy of temperature prediction models for coupled GPUs in Data Center (DC). Using synthetic data generated via ODEs, we compare eight data generation methods and demonstrate the data content influence prediction accuracy.

Droplet behavior influenced by wettability distribution is a pertinent field of research with applications in lab-on-a-chip and heat transfer devices among others. Some have proposed patterned surfaces with controlled variation of wettability to orient the direction of the droplet motion or to increase its velocity. These patterns are arrived upon with experience and knowledge of this phenomenon. In this research paper, the authors used a mathematical approach to the physical problem by using a gradient based optimizer for maximizing droplet velocity. Given some initial conditions, the optimizer marches toward the optimum wettability distribution profile. The droplet motion is modeled in two dimensions (i.e., on the xy-plane), on a plate having a wettability distribution in one dimension (i.e., along the x axis). The single component pseudopotential model allows for the quantification of the wettability distribution as a distribution of a pseudodensity of the solid nodes of the flat plate. Starting with several monotonous analytical profiles, a quadratic convex profile allows us to reach the maximum mean velocity for the threshold droplet displacement. Different sets of initial profiles, length of the plate (L), and diameter of the droplet (D) are tested. For smaller L/D ratio, the optimal wettability distributions exhibit non-trivial features: profiles can be non-monotonous, and wettability gradient could be locally null. With the increase in the L/D ratio, these specificities tend to be less prominent and optimal profiles converge to the quadratic convex one. The main innovation and significance of the paper is that mathematical optimization algorithms have been used conjointly with a multiphase lattice Boltzmann model solver to address for the first time the droplet race defined as: “what is the best wettability profile in order for a droplet to reach a desired location as quickly as possible?”

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.

The thermal design of an industrial shell-and-tube condenser requires the use of heat transfer coefficients, usually obtained from tables or correlations. Willing to develop a numerical model for design purposes, the present authors noticed the surprising diversity of correlations for the shellside heat transfer coefficient in the case of pure vapour condensation outside of horizontal smooth tubes. In order to shed light on this specific topic, a bibliographic study was therefore initiated. This comprehensive review is meant to provide the designers with means to understand how each correlation was obtained, from the assumptions to the resolution method. Thus two main phenomena are well accounted for in this paper: vapour shear stress and condensate inundation. Indeed, the review lists the most important contributions to this field and details their interconnections. Consequently, the present authors conclude this paper with their recommendations.

In this work, we report the existence of a stoichiometric regime where the performances of operating polymer electrolyte membrane (PEM) fuel cells are entirely governed by the mass transport in the cathode channels. An analytical model of the fuel cell stoichiometric regime is derived and evidenced experimentally: from the cell spectral signature at low frequency based on electrochemical impedance spectroscopy, and from the current density distribution measured using a segmented current collector. The existence of such regime provides a simple way to characterize, model and predict PEM fuel cell performances.

The present paper deals with Heat Exchanger sizing methods and offers a comparison between two of them: 1D global method and CFD porous media method. Following Prithiviraj et al. work [1], new developments are based on recent knowledge acquired on porous media, using a coupling strategy of a three-dimensional commercial code with an in-house code library. The distributed hydraulic resistance concept and the numerical model are briefly described and confronted with pressure drop measurements from an experimental E-type STHE setup (shell-and-tube heat exchanger) from the literature. The present paper will put into perspective capabilities and limits of each method with needs for heat exchanger rating. Flow rate repartition is calculated with CFD-porous media using Tinker’s current approach. This new analysis provides a complete comparison with 1D global method. It also reveals the major impact of leakage flow rate between baffle and tubes. The numerical estimation of pressure losses, consistent with experimental measurements of Halle et al. [2], implies that our future work will include thermal performance characterization and geometrical optimization.

Polymer Electrolyte Membrane (PEM) fuel cells are considered as promising clean sources for automotive applications. A key challenge to reduce the cost of this technology is to increase the power density by operating PEM fuel cells at high current densities. One strategy is to improve the 3D structure of the gas diffusion layer (GDL) located between the channel and the catalyst layer (CL). At the cathode side, this GDL is used to evacuate the liquid water toward the channel while providing access to the oxygen to the CL [1]. Although innovative GDL structures have been proposed, a better understanding of the liquid water would help to design better GDL. In particular, few works have investigated the liquid water transport after several hours of steady state fuel cell operating conditions although changes in liquid water preferential pathway have been observed [2]. Such changes are not predicted in theory, and a physical explanation of these mechanisms is still required. In this presentation, we investigate ex situ the change of liquid water preferential pathways through PEM fuel cell GDLs. Liquid water breakthough from the GDL to the fuel cell channels is mimicked using a microfluidic PDMS device with embedded GDLs. Liquid water is injected through the GDL to the microchannel, and changes in liquid water pathways are observed after several hours of operations. These changes in liquid water pathway are attributed to the dynamic of droplet eruption in fuel cell microchannel. To validate this assumption, a small capillary network with is built. It is shown that after the liquid water breakthrough, the pressure variation due to the growth of the water droplets in the microchannel enables the liquid water to invade smaller capillaries which at the end can change the preferential path. The experimental observations reported in this work show that the invasion percolation theory can be used to predict the preferential pathway at the onset of the liquid water breakthrough, but pressure-induced dynamic transport [3] due the water droplet eruption in the channel has also to be taken into account to predict the preferential pathway after long time of fuel cell operation. References [1] T. Yoshida, K. Kojima, Toyota MIRAI Fuel Cell Vehicle and Progress Toward a Future Hydrogen Society, Interface Mag. 24 (2015) 45–49. [2] Z. Lu, M.M. Daino, C. Rath, S.G. Kandlikar, Water management studies in PEM fuel cells, part III: Dynamic breakthrough and intermittent drainage characteristics from GDLs with and without MPLs, Int. J. Hydrogen Energy. 35 (2010) 4222–4233. [3] S. Chevalier, C. Josset, B. Auvity, Fluid dynamic breakthrough in two connected capillaries: From stationary to oscillating state, Phys. Fluids. 29 (2017) 102102.

In this work, the change of liquid water preferential pathways through PEM fuel cell Gas Diffusion Layers (GDL) with ex situ devices is investigated. A capillary network constituted of two connected micro channels is first developed. It is shown that once the larger channel has been invaded, the pressure variation due to the growth of the water droplets at the channel tip enables the liquid water to invade the smaller capillary channel. At the end, the liquid preferential path is modified. This result is then generalized considering a real GDL. Liquid water is injected through the GDL to a micro channel, and changes in liquid water pathways are observed after several hours of operations. The reported experimental observations show that pressure-induced dynamic transport due the water droplet eruption in the channel has to be taken into account to predict the preferential pathway after long time of fuel cell operation.

Polymer Electrolyte Membrane (PEM) fuel cells are considered as promising clean sources for automotive applications. A key challenge to reduce the cost of this technology is to increase the power density by operating PEM fuel cells at high current densities. Part of the research are focused in developing and designing new materials for this technology such as advanced catalyst layers (CL), new gas diffusion layers (GDL) structure, or innovative cell assembly conditions (clamping pressure, channel design…)[1]. To assess the performance of new materials, in situ characterisation techniques are required. Electrochemical impedance spectroscopy (EIS) is one of the most used technique to characterise the material impact onto the fuel cell mass/charge transfer, ohmic resistance and mass transport. However, due to the large number of parameters which has to be identified, inaccuracy in the identification process may arise leading to incorrect fuel cell material properties characterisation [2]. In authors’ recent work [3], it was shown that current density distributions can be used as a useful information to characterise fuel cell material properties. Thus, in this communication we will present a segmented cell designed and built to measure current density distribution along the channel while allowing optical access inside the channel to visualise the presence of liquid water. A range of fuel cell GDLs is characterised in situ in this cell for a range of operating conditions. The effective diffusivity of the GDLs is directly obtained from the current density distribution without any knowledge of the other fuel cell parameter (membrane ohmic resistance or CL kinetics). The values of effective diffusivity obtained using our methodology are compared to the ones obtained through EIS measurements, and their respective accuracy will be discussed. In addition, examples on the use of this characterisation cell to assess the performance of channel designs and fuel cell assembly conditions will be given. The results presented in this communication will introduce a novel fuel cell characterisation methodology which can strongly improve the development of more efficient fuel cell systems. References [1] T. Yoshida, K. Kojima, Toyota MIRAI Fuel Cell Vehicle and Progress Toward a Future Hydrogen Society, Interface Mag. 24 (2015) 45–49. [2] S. Chevalier, D. Trichet, B. Auvity, J.C. Olivier, C. Josset, M. Machmoum, Multiphysics DC and AC models of a PEMFC for the detection of degraded cell parameters, Int. J. Hydrogen Energy. 38 (2013) 11609–11618. [3] S. Chevalier, C. Josset, B. Auvity, Analytical solutions and dimensional analysis of pseudo 2D current density distribution model in PEM fuel cells, Renew. Energy. 125 (2018) 738–746.

This paper presents an adjoint Lattice Boltzmann Method (LBM) coupled with the Level-Set Method (LSM) for topology optimization of thermal fluid flows. The adjoint-state formulation implies discrete velocity directions in order to take into account the LBM boundary conditions. These boundary conditions are introduced at the beginning of the adjoint-state method as the LBM residuals, so that the adjoint-state boundary conditions can appear directly during the adjoint-state equation formulation. The proposed method is tested with 3 numerical examples concerning thermal fluid flows, but with different objectives: minimization of the mean temperature in the domain, maximization of the heat evacuated by the fluid, and maximization of the heat exchange with heated solid parts. This latter example, treated in several articles, is used to validate our method. In these optimization problems, a limitation of the maximal pressure drop and of the porosity (number of fluid elements) is also applied. The obtained results demonstrate that the method is robust and effective for solving topology optimization of thermal fluid flows.

In this work, an analytical solution for the low frequency polymer electrolyte membrane (PEM) fuel cell impedance is derived. A relationship between the low frequency phase shift induced by the oscillations of gas concentration in the channels is found, and it is shown that the phase is a function of the oxygen stoichiometry, λ, and the oxygen residence time, τc, in the channels. Experimental measurements of PEM fuel cell impedances are performed, and the analytical model is found to be in great agreement for λ≤3 and τc>0.2 s for a large set of experimental conditions and channel geometries. Finally, we report reduced models for the maximum phase shift induced by the gas oscillations in the channels and for the characteristic frequency at which this phenomenon is the most pronounced. This work gives new insights regarding the mechanisms that govern the low frequency fuel cell impedance at λ≤3, and thus paves the way for improved fuel cell mass transport characterisations.

In this paper, a new dimensionless pseudo 2D steady state current density distribution model along the channel of a polymer electrolyte membrane (PEM) fuel cell is presented. This model includes four fundamental phenomena observed in PEM fuel cell cathode such as the air concentration depletion along the channel, the mass transport through the gas diffusion layer (GDL), the charge transport through the membrane and the electrochemical transfer in the catalyst layer (CL). A dimensional analysis is performed, and three dimensionless parameters are found to govern the current density distribution along the channel: a Peclet number at the channel/GDL interface, a Damkhöler number at the GDL/CL interface, and a Wagner number at the CL/PEM interface. Four regimes of operation are defined based on the values of these dimensionless numbers, and for each of them new analytical solutions are developed. A good agreement with the experimental measurements of current density distribution reported in literature is found, concluding that the macroscopic PEM fuel cell physic is well described by our model. The specific operating regime described with relatively simple equations of current density distributions paves the way for a better control of fuel cell operation and performance, and in situ characterisation of fuel cell material properties.

This paper presents the optimization of the driving strategy of a high efficiency fuel cell based power train. This power train is developed to equip a light duty urban-concept vehicle that runs energetic races. The objective is to go the furthest with the lowest quantity of fuel. A comprehensive dynamical model is presented, including the mechanical requirement, the thermal behavior of the fuel cell stack and the various losses and consumptions of the power train devices. This model is next integrated into a global optimization algorithm, to determine the best race strategy to be adopted. These results are validated on experimental measurements, obtained during a real race at the Shell Eco-Marathon, in 2015.

The determination of optimal designs is an important objective in many engineering applications, including in convective heat transfer aera. This communication aims to present a topology optimization method for thermal flow problems. The cost function gradient is computed via an adjoint-state method. As the problem is solved with the Lattice Boltzmann Method, the adjoint-state equations are computed using a similar strategy than for LBM and are called Adjoint Lattice Boltzmann Equations (ALBE). This method is validated with a 2d thermal flow topology optimization problem with the objective of the mean temperature minimization subject to a pressure drop constraint.

In this paper, we investigate the pore structure and the impacts of Haines jumps on the change in preferential pathways (called the dynamic breakthrough) during fluid percolation through thin porous media. Two capillaries connected in parallel are used to represent a thin porous medium, and Haines jumps are observed through the formation of droplets. Using a droplet growth model and experimental visualisations, the change in preferential pathways is shown to be strongly influenced by the pore lengths, pore radii ratios, and droplet detachment volumes. This work provides a better understanding of the redevelopment of continuous fluid paths observed through thin porous media in electrochemical systems.

In this work, air velocities in the channels of an operating polymer electrolyte membrane fuel cell are measured using electrochemical impedance spectroscopy (EIS). From the equations of the oxygen transport in fuel cell channels, we derive an analytical expression of the channel impedance at low frequencies which is a function of the operating conditions, the channel geometry and air velocity only. Air velocities are computed using a nonlinear curve fitting of the analytical channel impedance to the single cell impedance measured at current densities ranging from 0.16 to 0.5 A/cm(2) under various air stoichiometries. Our results show less than 13% of relative error between the theoretical air velocities given by the mass flow controller and those measured from the fuel cell impedance for current densities lower than 0.42 A/cm(2). A direct application of this work is the real-time diagnostic of fuel cell channel clogging in stack configuration. (C) 2016 The Electrochemical Society. All rights reserved.

The motivation for the present work was to demonstrate clearly the effects of surface wettability on the two-phase flow in channels for PEMFC applications. Actually, these wettability effects are still controversial in the literature. The experimental investigation was conducted in isothermal conditions with ex situ dedicated experimental apparatus. Two channel materials with two different wettabilities were tested.In both hydrophobic and hydrophilic configurations, starting from a dry channel, the first emitted droplets left a residual liquid film in the channel corners and/or on the channel walls. These liquid films that spread all along the channel made the two-phase flow unstable. Finally, no distinction could be made between the two-phase flow regimes in hydrophilic and hydrophobic configurations. Our conclusions explain why the effects of surface wettability on fuel cells have been so unclear in the literature. For flow rates representative of a fuel cell application, it was impossible to draw flow pattern maps because of a lack of reproducibility. Based on the present results, the strict limit between slugs and droplets or droplets and film does not seem justified. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.