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In Euler-Lagrange models for particulate systems, the information exchange of multiphase coupling terms, i.e. drag force, heat transfer, or mass transfer, is often smoothed from particles' location to nearby computational cells when the cell and particle sizes are comparable. The diffusion-based smoothing is among the most popular approach. However, when it comes to polydisperse systems, the state-of-the-art constant diffusivity approach does not consider variation in particle sizes, resulting in an even smoothing of exchanged information across all particles with different sizes. In this paper, a particle-size dependent smoothing scheme named “non-constant diffusivity approach” is proposed. This approach distributes the exchanged information based on the local Sauter diameter d32 such that the area of influence per particle varies by size. The one-dimensional analytical solution of the non-constant diffusivity approach is first derived and two control parameters L⁎ and S are identified, where L⁎ determines the characteristic length of the diffusivity and S determines the magnitude of the diffusivity. Together they control the characteristic length scale ℓ˜c of the smoothing operation. In the one-dimensional study, it is found that the proposed smoothing method is most suitable for the dilute particulate regime. The investigation is extended to a three-dimensional dilute particle flow based on the experiment of the CRIEPI (Central Research Institute of Electric Power Industry) pulverized coal burner. It is shown that using the non-constant diffusivity smoothing, the prediction of the O2 concentration is more accurate than when using the constant diffusivity smoothing approach, which assumes a universal smoothing length for all sizes of particles. The findings suggest that when it comes to polydisperse particulate systems, the area of influence per particle on the fluid depends on the particle size. The proposed non-constant diffusivity approach can describe that with the benefits of cheap computational cost, conservation of exchanged quantities, and easy-to-implement.

Enhancing the efficiency of industrial water electrolysis for hydrogen production is important for the energy transition. In electrolysis, hydrogen is produced at the cathode, which forms bubbles due to the diffusion of dissolved hydrogen in the surrounding supersaturated electrolyte. Hydrogen (and oxygen) bubbles play an important role in the achievable electrolysis efficiency. The growth of the bubbles is determined by diffusive and convective mass transfer. In turn, the presence and the growth of the hydrogen bubbles affect the electrolysis process at the cathode. In the present study, we simulate the growth of a single hydrogen bubble attached to a vertical cathode in a 30 wt% KOH solution in a cathodic compartment represented by a narrow channel. We solve the Navier–Stokes equations, mass transport equations and potential equation for a tertiary current distribution. A sharp interface immersed boundary method with an artificial compressibility method for the pressure is employed. To verify the numerical accuracy of the method, we performed a grid refinement study and checked the global momentum and hydrogen mass balances. We investigate the effects of flow rate and operation pressure upon bubble growth behaviour, species concentrations, potential and current density. We compare different cases in two ways: for the same time and for the same bubble radius. We observe that increasing the flow velocity leads to a small increase in efficiency. Increasing the operation pressure causes higher hydrogen density which slows down the bubble growth. For a given bubble radius, increasing the pressure leads to a small decrease in efficiency.

The objective of this work is to establish a lift model which can account for the variation in the bubble spreading mechanism with different column aspect ratios. To this end, a strategic approach has been developed and applied to explore the dependency of the lift variation with local flow variables. Numerical simulations are performed by using Computational Fluid Dynamics - Discrete Particle Method (CFD-DPM) coupled with Volume of Fluid (VOF) method in the open-source framework OpenFOAM. Both homogeneous and heterogeneous bubbly flows are considered with the results from reported experiments in literature. It has been found that the local gas fraction and the vorticity are strongly correlated with the lift coefficient. However, using one of these two variables alone cannot describe the lift variation within the bubble columns. Finally, a unified lift model is established that depends on both local gas fraction and vorticity. Euler–Lagrange simulations using this lift model are demonstrated to provide excellent agreement on the bubbly dynamics with experiments of homogeneous bubbly flows and bubble swarms.

Large Eddy Simulations (LES) combined with the Flamelet Generated Manifold (FGM) approach has become popular for modeling turbulent flame/combustion of pulverized coal or biomass. In this paper, we incorporate a coarse-graining discrete element method (CG-DEM) with the FGM-LES for cost-effective Euler–Lagrange (EL) simulations of turbulent coal combustion. This developed method significantly reduces the computational burden in both Eulerian phase (via FGM) and Lagrangian phase (via CG) compared to conventional reactive EL simulations. The study is based on the experiment of the CRIEPI (Central Research Institute of Electric Power Industry) burner, which has been extensively used for model validation in literature. It is shown that the developed model can effectively reduce the computing cost while maintaining a good accuracy in predicting the pulverized coal flow dynamics as well as combustion performance. For this particular case, an optimal coarse-graining factor, the size ratio of coarse-grained parcels to original particles, of 2 is determined. A larger coarse-graining factor will create local concentrated regions of fuel and consequently lead to different combustion behavior.