Premium
Quantifying the uncertainty introduced by discretization and time‐averaging in two‐fluid model predictions
Author(s) -
Syamlal Madhava,
Celik Ismail B.,
Benyahia Sofiane
Publication year - 2017
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.15868
Subject(s) - discretization , richardson extrapolation , extrapolation , grid , mathematics , autocorrelation , uncertainty quantification , algorithm , computer science , mathematical optimization , statistics , mathematical analysis , geometry
The two‐fluid model (TFM) has become a tool for the design and troubleshooting of industrial fluidized bed reactors. To use TFM for scale up with confidence, the uncertainty in its predictions must be quantified. Here, we study two sources of uncertainty: discretization and time‐averaging. First, we show that successive grid refinement may not yield grid‐independent transient quantities, including cross‐section–averaged quantities. Successive grid refinement would yield grid‐independent time‐averaged quantities on sufficiently fine grids. Then a Richardson extrapolation can be used to estimate the discretization error, and the grid convergence index gives an estimate of the uncertainty. Richardson extrapolation may not work for industrial‐scale simulations that use coarse grids. We present an alternative method for coarse grids and assess its ability to estimate the discretization error. Second, we assess two methods (autocorrelation and binning) and find that the autocorrelation method is more reliable for estimating the uncertainty introduced by time‐averaging TFM data. © 2017 American Institute of Chemical Engineers AIChE J , 63: 5343–5360, 2017