(62d) A Quadrature-Based Uncertainty Quantification Approach in a Multiphase Gas-Particle Flow Simulation in a Riser
In simulations of industrial systems, it is important to have an estimate of the distributions of errors due to uncertainty in the model parameters and input data. This can be accomplished by developing uncertainty quantification tools that can be combined with available CFD codes. Here a non-intrusive, quadrature-based, uncertainty quantification (QBUQ) method is presented. The approach relies on Gaussian quadrature formulae to generate the set of samples of the distribution of the uncertain parameters of the model. A numerical simulation is performed for each sample, and the moments of the system response are directly computed from the simulation results by means of quadrature formulae. These moments are then used to determine the reconstructed distribution function of the values of the system response by means of the extended quadrature method of moments .
The QBUQ procedure is demonstrated by considering a riser of a circulating fluidized bed as an example application. The mean particle size, the superficial gas velocity, and the solids circulating rate are assumed to be the uncertain input parameters. The system is simulated with a standard two-fluid model with kinetic theory closures for the particulate phase  implemented into MFIX. Simulation results are compared with the experimental data of the challenge problem released by National Energy Technology Laboratory (NETL) in 2010 . The effect of uncertainty on the pressure drop inside the fluidized bed and on the phase velocities are examined. Mean values and 95% confidence intervals of pressure drop and particle velocities are compared with experiment results. The reconstructed probability distribution function of the system response is provided for the two quantities studied.
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 D. Gidaspow, Multiphase flow and fluidization, Academic Press, 1994.
 NETL/PSRI challenge problem 3 2010, https://mfix.netl.doe.gov/challenge/index_2010.php.
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