# Radiation Heat Transfer Analysis in Two-Phase Mixture Associated with Liquid Metal Reactor Accidents

## Date of Award

2020

## Degree Name

Ph.D. in Mechanical Engineering

## Department

Department of Mechanical and Aerospace Engineering and Renewable and Clean Energy

## Advisor/Chair

Advisor: Jamie Ervin

## Abstract

Analytical study associated with liquid-metal fast breeder reactor (LMFBR) has beeninvestigated by using scattering and non-scattering mathematical radiation models. In the nonscattering model, the radiative transfer equation (RTE) was solved together with the continuityequations of mixture components under local thermodynamic equilibrium. A MATLAB code wasused to solve these equations. This application employed a numerical integration to compute thetemperature distribution within the bubble and the transient wall heat flux. First, in Rayleigh nonscattering model the particle size was 0.01 ╡m [6], and according to Mie theory principle, theabsorption coefficient for small particle -size distribution was estimated (k = 10 m-1 was used)from reference [7] at complex refractive index of UO2 at ? = 600 ╡m and x = 0.0785. A MATLABcode was used to solve the radiative heat equation (RTE) in spherical coordinates. The mixture isin local thermodynamic equilibrium inside the bubble which has a black body surface boundary.The mixture in the bubble contains three components: the non-condensable gas Xenon, Uraniumdioxide vapor, and fog. To simulate fuel bubble's geometry as realistically as possible, accordingto experimental observation, the energy equation in a spherical coordinate system has beensolved with the radiative flux heat transfer equation (RTE) to obtain the effect of fuel bubble'sgeometry on the transient radiative heat flux and to predict the transient temperature ivdistribution in the participating medium during a hypothetical core disruptive accident (HCDA) forliquid metal fast breeding reactor (LMFBR) for FAST.The transient temperature distribution in fog region was used to predict the amount ofcondensable UO2 vapor. The conclusion that can be drawn from the present study, is that the FuelAerosol Simulant Test (FAST) facility at Oak Ridge National Laboratory has a larger margin of safetysince the bubble rising time is greater than the bubble collapse time. Second in the scatteringmodel, the spherical harmonics method was used to solve the radiative heat transfer equation(RTE) in spherical coordinates, and the particle size was 0.07 ╡m [6]. The scattering coefficient ofUO2 particles (? = 1.24 m-1), was calculated using Mie theory at the same number of stable nucleiN (2.9 E15 nuclei/m3) that resulted from the absorption coefficient k = 0.082 m-1[7]. The P1approximation method was used to solve the radiative transfer equation (RTE) in sphericalcoordinates of participating medium confined between two concentric spheres. The surfaces ofthe spheres are assumed to be gray, diffusely emitting and diffusely reflecting boundaries, andisothermal boundary conditions were assumed at these surfaces. Marsak's boundary conditionwas used to compute the net radiative heat flux, q(?), and the incident radiation, G(?), to analyzeand interpret CVD experiments data that were conducted in the FAST facility at ORNL [8] and FastFlux Test Facility reactor (FFTF) at ANL. From this study, it can be concluded that there is greatermargin of safety when the bubble rise time is a greater than the bubble collapse time since thebubble collapses (UO2 condenses) before it can reach the top of the vessel. In addition, the worktransfer by itself can't completely eliminate the super-heated vapor, as the bubble contains noncondensable species which hinder condensation. However, it is reasonable to assume that worktransfer could decrease the amount of UO2 vapor contained in the bubble as it reached thecovergas [63].

## Keywords

Mechanical Engineering, Applied Mathematics, Chemical Engineering

## Rights Statement

Copyright © 2020, author

## Recommended Citation

Mohamed, Hmza Ashour, "Radiation Heat Transfer Analysis in Two-Phase Mixture Associated with Liquid Metal Reactor Accidents" (2020). *Graduate Theses and Dissertations*. 6858.

https://ecommons.udayton.edu/graduate_theses/6858