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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 424827, 13 pages
Research Article

Analytical Solutions of the Balance Equation for the Scalar Variance in One-Dimensional Turbulent Flows under Stationary Conditions

1Environment and Sustainable Development Department (SFE), Ricerca sul Sistema Energetico (RSE) SpA, Via Rubattino 54, 20134 Milan, Italy
2Department of Civil and Environmental Engineering, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
3ENEA, Casaccia, Via Anguillarese 301, Santa Maria di Galeria, 00123 Rome, Italy

Received 10 November 2014; Accepted 26 December 2014

Academic Editor: Xiao-Jun Yang

Copyright © 2015 Andrea Amicarelli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study presents 1D analytical solutions for the ensemble variance of reactive scalars in one-dimensional turbulent flows, in case of stationary conditions, homogeneous mean scalar gradient and turbulence, Dirichlet boundary conditions, and first order kinetics reactions. Simplified solutions and sensitivity analysis are also discussed. These solutions represent both analytical tools for preliminary estimations of the concentration variance and upwind spatial reconstruction schemes for CFD (Computational Fluid Dynamics)—RANS (Reynolds-Averaged Navier-Stokes) codes, which estimate the turbulent fluctuations of reactive scalars.