Comparing the Monte Carlo Method to the Discrete Ordinates Methods in Fluent for Calculating Radiation Heat Transfer in a Small Particle Receiver

Abstract

The Combustion and Solar Energy Laboratory (C&SEL) at San Diego State University is developing a Small Particle Heat Exchange Receiver (SPHER) to absorb and transfer heat from concentrated solar radiation to a working fluid for a gas turbine. The SPHER is to be used with a Concentrated Solar Power (CSP) system where a heliostat field highly concentrates solar radiation on the optical aperture of the SPHER. The solar radiation is volumetrically absorbed by a unique carbon nanoparticle gas mixture within the cavity of the SPHER. This research focuses on comparing a Computational Fluid Dynamics (CFD) model using the ANSYS FLUENT Discrete Ordinates (DO) Model and a program developed by the C&SEL which uses a Monte Carlo Ray Trace (MCRT) method to calculate the spatial and directional distribution of radiation for an idealized solar receiver geometry. Previous research at the C&SEL has shown successful implementation of the MCRT method to calculate the spatial and directional distribution of radiation for an idealized solar receiver geometry. The MCRT method is highly accurate and will serve as the benchmark solution for this research. However the MCRT code takes several days to run, is inflexible to geometry changes, and is cumbersome to implement as the MCRT code needs to be rewritten for each new receiver geometry being considered. These factors necessitate the need to find an alternate method that accurately calculates the spatial and directional distribution of radiation for a solar receiver and can be efficiently implemented for various receiver geometries being studied. The Discrete Ordinates method is a new method for solving the Radiative Transport Equations (RTE) using a FORTRAN program, developed by the C&SEL, and the ANSYS FLUENT Discrete Ordinates model for calculating the RTE. The FORTRAN program calculates the proper inlet radiation boundary conditions that ANSYS FLUENT uses for calculating the RTE. The methodology used for determining the correct CFD mesh, radiative boundary conditions, optimal number of DO theta and phi discretization, as well as the optical properties of the working fluid will be presented in this paper. The main focus of this research is to compare two different methods for solving the Radiative Transport Equations within the idealized SPHER. The solution data for several cases using the previous coupled MCRT method and the ANSYS FLUENT Discrete Ordinates method is presented for both a collimated and diffuse gray radiation approximation. The case studies focus on researching how the MCRT method and Discrete Ordinates method differ when comparing critical receiver parameters such as the mean outlet temperature, wall temperature profile, outlet tube temperature profile, and total receiver efficiency while keeping the total inlet radiation flux of 5 MW and inlet mass flow rate of 5 kg/s constant. This research also presents a study on the optimal Discrete Ordinates angular discretization, as well as a study to determine the solution’s dependence on the number of inlet boundary conditions imposed on the window.