Identifying Important Parameters for Modeling Turbulent Prandtl Number Through Statistical Apparoach
Introduction
Heat transfer rate is predicted less accurately with Reynolds-averaged Navier-Stokes (RANS) than velocity field. It is found in different studies (Crimaldi et al., 2006 and Kang et al. 2009, CTR Ann. Res. Brief) that turbulent Prandtl number may vary largely over space in complex flows. However, turbulent Prandtl number is assumed to be a constant (~1) in RANS. Therefore, spatial variation of turbulent Prandtl number may be related to heat transfer error of RANS with respect to Direct Numerical Simulation (DNS).
Spatial Variation of Turblent Prandtl Number in a Wedged Channel
Temperature & Velocity Profiles of the Flow
Temperature Profile
Velocity Profile
01
CFD Simulations On the Wedged Channel to Collect Turbulent Statstics
In order to model turbulent Prandtl number, important parameters from turbulent statistics of the wedged channel are selected first. As selection processes, correlations of the parameters with turbulent Prandtl number, Minimum Spanning Tree (MST) and Least Absolute Shrinkage and Selection Operator (LASSO) are used.
02
Correlations of the Parameters
MST method visually provides relationships between the parameters, where closer distance indicates more spatially related and a parameter with more connections with others denote its importance in the pool.
03
Minimum Spanning Tree
MST method visually provides relationships between the parameters, where closer distance indicates more spatially related and a parameter with more connections with others denote its importance in the pool.
04
Least Absolute Shrinkage and Selection Operator
LASSO, on the other hand, composes a linear combination of the parameters where its errors are reduced and only important variables are included in the combination.
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Modelled Prt
Modelling of Turbulent Prandtl Number (Prt)
Parameters selected from these approaches were gathered to devise a model of turbulent Prandtl number and it showed a similar spatial variation as that of DNS. This research showed a possibility that using a modeled tubulent Prandtl number may reduce the heat transfer error of RANS with respect to DNS.
DNS Prt