Award Date

May 2018

Degree Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Committee Member

Yi-Tung Chen

Second Committee Member

Mohamed Trabia

Third Committee Member

Zhonghai Ding

Fourth Committee Member

Hui Zhao

Number of Pages



The oxidation of stainless steel is influenced by the presence of oxygen in the surrounding medium; the oxygen reacts with the alloy to form an oxide. In certain environments, such as nuclear reactor coolant systems, minimal oxidation of the stainless steel containment functions as a protective shield from corrosive coolants such as liquid lead-bismuth eutectic.

In the current study, this minimal oxidation is evaluated for a system in which corrosion-resistant stainless steel alloy EP-823 is subject to an environment of flowing oxygenated liquid lead-bismuth eutectic at a temperature of 743 K, whereby the thickness of the forming oxide layer is attributed to diffusion of oxygen within a plane comprised of the alloy. Fick’s second law of diffusion and the advection-diffusion equation in one spatial dimension are utilized as the mathematical model. The diffusion problem attributed to the oxidation of metal alloys introduces complications in the domain due to: the change in density as the oxide is formed, the discontinuity in diffusion coefficients between the oxide and metal phases, and the occurrence of two moving boundaries – one separating the oxide and metal phase and the other, the interior unexposed boundary. These complications are resolved by transformations of: the space coordinate of the interface boundary, the calculating space coordinate, and the space coordinate of interior moving boundary. Hereby, the domain of the mathematical model is fixed. The discontinuity of the diffusion coefficients at the phase boundary is resolved by a final transformation.

The implicit numerical scheme applied to the mathematical model is described. This method, termed the ‘enthalpy method’, is typically used for moving boundary phase change problems. The implemented Newton-Raphson iterative technique for this finite difference method and the solution by a tri-diagonal

matrix algorithm are also described.

Input parameters for the numerical simulation are derived both from physical assumptions and from controlled experiments of the oxidation of EP-823 alloy, which had been previously determined an optimal corrosion-resistant steel [1]. Such parameters include the concentration of oxygen at interface, which is

determined by considering the solubility of oxygen in EP-823 alloy. The effective oxidation of the alloy is studied by assessing the oxidation of the alloys component metals. The plausible oxidation reactions and resulting oxides are compiled based on partial pressure of oxygen in lead-bismuth eutectic, temperature, and free energy of formation of the relevant oxides. Hereby, input parameters such as mass fraction of the metal in its component oxide and density of the metal were obtained. The experimentally determined scale removal rate was also used as an input. The diffusivity of oxygen in the oxide and metal phases was estimated based on the physical assumptions of higher porosity in the oxide phase.

The numerical results, which are in the form of the oxygen concentration profiles as a function distance from the calculating space coordinate at varying time intervals, contain the the calculated corresponding oxide layer thicknesses. The results are fit to a parabolic growth rate law, whereby the the growth rate,

kp, of each relevant oxide is determined. The growth of copper (I) oxide, aluminum (III) oxide, niobium (II) oxide, and tungsten (IV) oxide demonstrate good adherence to the parabolic rate law. The numerical kp values are benchmarked with the experimental effective kp value for EP-823. It is determined that the

experimental kp value is closest to the numerically determined kp values of aluminum (III) oxide and niobium (II) oxide.

From the kp values, the steady state thickness of each oxide, δs, is derived by the Tedmon model for oxidation-ablation. These values are benchmarked with the semi-empirically determined steady state thickness from the mentioned controlled experiments, which is 35.8 µm, and which is found to be closest to the

numerically determined δs value for niobium (II) oxide, at 20.1 µm.

In order to ascertain the numerically determined kp and δs values, further work in assessing and optimizing stability and convergence criteria must be done.

The Pilling-Bedworth ratio for the alloying metal oxides is also calculated. The ratios suggest that aluminum (III) oxide and niobium (II) oxide, for which the respective ratios are 1.27 and 1.37, are the most stable relative to the oxides of the other alloying metals.

Furthermore, by considering selective oxidation of alloying metals, co-precipitation, oxidation states of the metals, crystal structure, and ionic radii, the likelihood of the participation of certain alloying elements in the effective oxide layer can be gauged.

Thus, it is determined that the one-dimensional planar oxidation model can be effective as a preliminary tool in assessing the oxidation of the alloy in terms of participation of its component metals. Hereby, the objectives of the study are met.


Corrosion; Diffusion; Metal Alloys; Numerical Modeling; Oxidation; Stainless Steel


Engineering Science and Materials | Materials Science and Engineering