Validation of simplified P_N models for radiative transfer in combustion systems

Abstract

SUMMARYThis paper illustrates the use of simplified P N approximations as a tools of achieving verification of codes and simulations of radiative transfer in combustion systems. The main advantage of considering these models is the fact that the integro-differential equation for radiative transfer can be replaced by a set of differential equations which are independent of angle variable, compatible to the partial differential equations of flow and combustion, and easy to solve using standard numerical discretizations. Validation of these models is then performed by comparing predictions to measurements for a three-dimensional diffusion flame. The good agreement between measurements and predictions indicates that the simplified P N models can be used to incorporate radiation transfer in combustion systems at very low computational cost without relying on discrete ordinates or Monte Carlo methods.

Finite element P1solution of unsteady thermal flow past a circular cylinder with radiation

“…The simplified P N approximations have also been studied in [9,13,15] for glass manufacturing, in [16] for crystal growth, in [17][18][19] for gas turbines, and in [20] for low Mach number flows. Recently, validation of the simplified P N approximations with experimental measurements has been carried out in [21] for a three-dimensional diffusion flame. In the current work, we extend the SP 1 approximations to the radiation-convection flow past a cylinder.…”

Solving an optimal control problem of complex heat transfer using machine learning methods

“…The relevance of the search for the new algorithms to solve the complex heat transfer systems is determined by practical applications in the production of glass [1] and in the combustion chambers [2]. The system consists of the differential heat transfer equation and integrodifferential equation of radiative transfer.…”

Asymptotic derivation and numerical investigation of time-dependent simplified equations

“…Originally intended for applications in nuclear engineering, the SP N equations are, indeed, implemented and used for neutron transport problems nowadays [2,6,18,9]. After first theoretical foundations for the SP N method were provided, a wide range of additional applications has been developed mainly in the past decade, e.g., radiative cooling of glass [30,11], radiative transfer in tissue [22], fluorescence tomography [23], design of combustion chambers for gas turbines [35,36], crystal growth of semitransparent materials [1], and photon and electron radiotherapy [24].…”