Quasi-1D model for exhaust gas and pipe with convective and temperature dependent emissivity based radiative heat losses. (1st August 2020) - Abishek, S.; Balachandar, R.; Barron, R.
Highlights: Quasi-1D model for predicting automotive exhaust gas and pipe temperatures is developed. Convective and temperature dependent emissivity based radiative heat losses are accounted. The quasi-1D model is validated using 3D CFD and in conjunction with the literature. Influence of emissivity and its temperature coefficient are quantified. Friction factor for external axial turbulent flow over a pipe is correlated using CFD. Abstract: Knowledge of accurate exhaust gas and pipe temperatures are critical for efficient design of automotive underbody components and exhaust systems. Prediction of these temperatures requires precise evaluation of the flow, and radiative and convective heat transfer rates inside and around the pipe. In this work, a quasi one-dimensional (quasi-1D) thermal framework is developed by modeling the energy balance for the exhaust gas and the pipe wall, accounting for both forced convection and radiation heat transfer, and effects of temperature dependent emissivity. The dimensionless governing equations for the quasi-1D model are solved iteratively at steady state using finite difference. The flow inside the pipe is assumed to be hydrodynamically fully developed and thermally developing, while that outside is assumed to be simultaneously developing. The predicted Nusselt numbers as well as gas and pipe temperatures under both laminar and turbulent internal or external flows are validated using conjugate computational fluid dynamics (CFD) simulations carried out using OpenFOAM and in conjunction with experimental or theoretical data available in literature. The convective heat transfer coefficients on the inner or outer pipe walls required to close the quasi-1D formulation are evaluated from skin-friction correlations developed from separate CFD simulations carried out in this work and by applying the Chilton-Colburn analogy, or from literature. It is found that surface radiation on the outer wall plays a critical role in the overall heat transfer characteristics of the exhaust pipe and can result in the reduction of dimensionless pipe temperatures by over 40% for a variation in emissivity from 0 to 1. It is also found that the influence of temperature dependence of emissivity can be important in cases where surface radiation is the dominating mode of heat loss from the pipe. A reduction in the dimensionless pipe temperature of up to 12% was found for an increase in the temperature coefficient of emissivity from 0 to 1, for the representative cases studied.