Prediction of thermal stratification in an engine-like geometry using a zero-dimensional stochastic reactor model
Artikel i vetenskaplig tidskrift, 2020

The prediction of local heat transfer and thermal stratification in the zero-dimensional stochastic reactor model is compared to direct numerical simulation published by Schmitt et al. in 2015. Direct numerical simulation solves the Navier–Stokes equations without incorporating model assumptions for turbulence and wall heat transfer. Therefore, it can be considered as numerical experiment and is suitable to validate approximations in low-dimensional models. The stochastic reactor model incorporates a modified version of the Euclidean Minimum Spanning Tree mixing model proposed by Subramaniam et al. in 1998. To capture the thermal stratification of the direct numerical simulation, the total enthalpy (H) is used as the only mixing limiting scalar within the newly proposed H-Euclidean-Minimum-Spanning-Tree. Furthermore, a stochastic heat transfer model is incorporated to mimic turbulence effects on local heat transfer distribution to the walls. By adjusting the Cϕ mixing time and Ch stochastic heat transfer parameter, the stochastic reactor model predicts accurately the thermal stratification of the direct numerical simulation. Comparing the Woschni, Hohenberg and Heinle heat transfer model shows that the modified Heinle model matches accurately the direct numerical simulation results. Thereby, the Heinle model accounts for the influence of turbulent kinetic energy on the characteristic velocity in the heat transfer coefficient calculation. This highlights the importance of incorporating turbulence effects in low-dimensional heat transfer models. Overall, the zero-dimensional stochastic reactor model with the H-Euclidean-Minimum-Spanning-Tree mixing model, the stochastic heat transfer model and the modified Heinle correlation have proven successfully the prediction of mean quantities like temperature and heat transfer and thermal stratification of the direct numerical simulation.

combustion engine

thermal stratification

Heat transfer

stochastic reactor model


T. Franken

Brandenburgische Technische Universität

C. Klauer


Martin Kienberg


Andrea Matrisciano

Chalmers, Mekanik och maritima vetenskaper, Förbränning och framdrivningssystem

F. Mauss

Brandenburgische Technische Universität

International Journal of Engine Research

1468-0874 (ISSN) 2041-3149 (eISSN)

Vol. 21 9 1750-1763


Teknisk mekanik


Strömningsmekanik och akustik



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