Applying uncertainty quantification to multiphase flow computational fluid dynamics

Stochastic Discrete Equation Method (sDEM) for two-phase flows

“…where the velocities are set equal to the relative speed of sound of the kth phasē (34) and the reference total energy is…”

“…Some reference test-cases are performed to demonstrate the convergence properties and the efficiency of the overall scheme: the linear advection problem for both smooth and discontinuous initial conditions, the inviscid Burgers equation and the 1D Euler system of equations to model an uncertain shock tube problem obtained by the well-known Sod shock problem [33]. Actually, in the literature, the most part of stochastic studies in two-phase flows deal with non-intrusive approaches [34][35][36][37][38][39][40]. This is maybe due to the complexity in adapting intrusive methods to the rich system of equations governing two-phase flows, that can include conservative and non-conservative terms.…”

Experimental data for code validation: Horizontal air jets in a semicircular fluidized bed of Geldart Group D particles

“…42 Through UQ, a model is used not only to predict the best-estimate solution by using mean values of measured properties, but also to quantify the uncertainty in the model predictions, that is, model form uncertainty, by propagating measured input uncertainties through the model and into the solution itself. [46][47][48][49][50][51] In this work, we aim to provide experimental data for CFD-DEM model validation including UQ, extending the existing database 52 to a more complex system: a semicircular fluidized bed with pairs of opposing horizontal air jets. By considering UQ throughout the validation process it is also possible to extrapolate model form uncertainty from a validation phase-space (that is, the region of conditions for which experimental data exists) to a case of true model prediction in which no experimental data exists.…”

“…43 Used extensively in other fields, 44,45 a verification and validation (V&V) framework including UQ has only recently emerged within the gas-solid multiphase CFD community. [46][47][48][49][50][51] In this work, we aim to provide experimental data for CFD-DEM model validation including UQ, extending the existing database 52 to a more complex system: a semicircular fluidized bed with pairs of opposing horizontal air jets. This system is widely used in engineering processes to aid fluidization 53,54 and solid mixing, 55 to introduce gas reactants 56 or to perform particle attrition.…”

Quantifying the uncertainty introduced by discretization and time‐averaging in two‐fluid model predictions

“…Conversely, uncertainty quantification can be used to identify the critical parameters or submodels that introduce the most uncertainty in predictive simulations. Gel and coworkers used the Sobol' sensitivity indices method to show, for example, that the particle–particle restitution coefficient contributed the most to the variability observed in the predicted mean bed height. Gel and others used a Bayesian method to quantify the uncertainty in a fluidized bed gasifier model.…”