Capturing aerosol droplet nucleation and condensation bursts using PISO and TVD schemes

A mathematical model for single-species aerosol production and transport is formulated, and solved using an adapted PISO algorithm. The model is applied to a laminar flow diffusion chamber, using a finite volume method on a collocated grid. In tran- sient simulations, a sharp scalar front (e.g., vapor mass fraction), is shown to introduce unphysical oscillation in the solution, when applying a second order linear interpolation in the convective terms. At increased grid resolution, these oscillations are strongly at- tenuated. When applying a TVD scheme (here the MUSCL scheme), a time-accurate monotonicity-preserving solution is obtained. The numerical dissipation introduced by the MUSCL scheme implies increased spatial resolution to restore high accuracy levels. We develop a one-dimensional grid refinement algorithm, which relates the grid density in one direction to the magnitude of the scalar gradient. In combination with the MUSCL scheme, this gives accurate results, with a significant reduction in computational effort, in comparison with a uniform fine grid

Improved PISO algorithms for modeling density varying flow in conjugate fluid–porous domains

Two modified segregated PISO algorithms are proposed, which are constructed to avoid the development of spurious oscillations in the computed flow near sharp interfaces of conjugate fluid–porous domains. The new collocated finite volume algorithms modify the Rhie–Chow interpolation to maintain a correct pressure–velocity coupling when large discontinuous momentum sources associated with jumps in the local permeability and porosity are present. The Re-Distributed Resistivity (RDR) algorithm is based on spreading flow resistivity over the grid cells neighboring a discontinuity in material properties of the porous medium. The Face Consistent Pressure (FCP) approach derives an auxiliary pressure value at the fluid–porous interface using momentum balance around the interface. Such derived pressure correction is designed to avoid spurious oscillations as would otherwise arise with a strictly central discretization. The proposed algorithms are successfully compared against published data for the velocity and pressure for two reference cases of viscous flow. The robustness of the proposed algorithms is additionally demonstrated for strongly reduced viscosity, i.e., higher Reynolds number flows and low Darcy numbers, i.e., low permeability of the porous regions in the domain, for which solutions without unphysical oscillations are computed. Both RDR and FCP are found to accurately represent porous media flow near discontinuities in material properties on structured grids

Eulerian modeling of inertial and diffusional aerosol deposition in bent pipes

This paper presents a sectional Eulerian aerosol model for size-dependent droplet deposition at walls of the domain, driven by both diffusion and inertia. The model is based on the internally mixed assumption and employs the formulation for compressible aerosols. It is validated in a bent pipe geometry against models and experimental and numerical data from literature. Good agreement is found in both the diffusion and inertial deposition regimes. To improve the overprediction of inertial deposition by a boundary treatment that adopts zero-gradient droplet wall velocity, we use a corrected wall velocity, based on an analytical solution of the droplet motion near the wall. In the bent pipe setting the corrected wall velocity is found to reduce the overprediction of deposition and is less sensitive to grid refinement. We also show that refining the computational mesh near the pipe wall improves the predicted deposition efficiency, significantly. Finally, we present a parameter study varying the Reynolds number and the bend curvature. The deposition efficiency curve is recorded for droplet diameters ranging from the nanometer scale to beyond the micrometer scale, which is a unique contribution of this paper. The complete size range is simulated in only one simulation, due to the sectional approach. In the diffusion-dominated regime an increase in Reynolds number leads to a gradual enhancement of deposition. In the inertial regime, where droplet drift dominates deposition, a much stronger dependence on the Reynolds number is found. The dependence of the deposition on the bend curvature is less pronounced. The results shown in this paper establish the role of Eulerian simulation in predicting deposition of aerosol droplets and are useful for understanding size-dependent aerosol deposition in other more complex confined geometries

Characteristics-based sectional modeling of aerosol nucleation, condensation and transport

Aerosols can be generated by physical processes such as nucleation, conden- sation and coalescence. To predict spatially varying statistical properties of such aerosols, e.g., the size distribution of the droplets, these processes must be captured accurately. We model nucleation using classical nucleation theory, whereas the con- densational growth is captured with a molecular diffusivity model. The droplet size distribution is discretized using a sectional approach, in which droplets are charac- terized in terms of a number of fixed droplet size bins. Often, in such a formula- tion, the numerical time step restrictions arising from condensation and nucleation are more pronounced than those of the corresponding fluid flow, thereby signifi- cantly limiting the global time step size. We propose a moment-conserving method in which this limitation is avoided, by utilizing the analytical solutions of the spa- tially homogeneous nucleation-condensation subproblem. The method is validated against experimental and numerical data of a laminar flow diffusion chamber, and shows an excellent agreement while being restricted only by a flow-related time step criterion

Dataset for CFD4NRS-9 conference paper "Simulation of noble metal particle growth and removal in the molten salt fast reactor"

<p>Dataset used for the results presented in the CFD4NRS-9 conference paper "Simulation of noble metal particle growth and removal in the molten salt fast reactor". Also the code used to generate results is included (it is also publicly available at https://github.com/edofrederix/flotationFoam), and contains a README with instructions. The plots can be generated with their respective Python files.</p&gt

Poly-dispersed modeling of bubbly flow using the log-normal size distribution

The bubble size distribution plays an important role in interfacial mass, momentum and energy transfer between bubbles and their carrier liquid in bubbly flow. Accurate modeling of the size distribution is therefore key. A Log-Normal presumed Number Density Function (LNpNDF) approach is proposed, which is embedded into the two-fluid model. Two additional moment transport equations are formulated which are shown to be consistent with the two-fluid model. From the moments, the size distribution can be fully reconstructed using the assumption that its underlying shape is log-normal. This methodology offers closure for the modeling of processes such as bubble coalescence, break-up and bubble poly-celerity. Special attention is paid to the concept of poly-celerity, which is shown to play an important role in the evolution of finite-width size distributions. A new average diameter, which is based on the fifth and third moment of the size distribution, is proposed, and it is shown that this diameter is a more suitable quadrature node for the modeling of bubble–liquid Stokes-like drag. The paper lays the mathematical foundation for a pragmatic, computationally efficient and effective poly-dipsersed method for the modeling of dispersed two-phase flow

Reynolds-averaged modeling of turbulence damping near a large-scale interface in two-phase flow

The two-fluid Euler-Euler model can be used for the description of co-existing stratified and dispersed multiphase flow within one flow domain. For realistic engineering applications, turbulence is often modeled in the Reynolds-averaged Navier-Stokes (RANS) framework where closure of the Reynolds stresses is mostly achieved using the turbulent viscosity formulation. It is a well-known problem that at large-scale interfaces between two phases such turbulence modeling breaks down as turbulent viscosity in the vicinity of an interface is over-predicted. To address this issue, we adopt the Egorov approach (Egorov et al., 2014) which locally damps turbulence near the interface. This model is based upon the idea that at a large-scale interface the lighter phase may see the heavier phase much like a solid wall, suggesting a wall-like treatment of turbulent dissipation at the interface. The implementation of the model inside a two-phase formulation of the k–ω model is discussed, and shown to give good predictions of interfacial turbulence in co-current stratified two-phase flow. The Egorov approach is extended to the k–ε model, which may be relevant for a large array of engineering applications in which the k–ε model is more effective than the k-ω model. It is shown that the non-dimensional Egorov approach coefficient is grid dependent. We introduce a new formulation of the interfacial damping term in the two-fluid Euler-Euler model which gives more consistent results for different computational grids in comparison to the original formulation of the Egorov approach. This feature, as well as its straightforward implementation in both the k–ω and k–ε models, make the new model useful to a large array of multiphase engineering problems in which interfacial turbulence damping is relevant