Abstract
We develop a mathematical model for the cumulative erosion of a micro-particle in a channel system. At 90∘ bends in the system, a particle may deviate from the flow, impact the wall, and erode material. We highlight the case of the eroded material adhering to the particle, growing in size, and thus demonstrate how the damage accumulates exponentially with time. We describe and quantify the statistical nature of the evolution of particle growth and erosion (mass and location). We perform this analysis according to a number of realistic particle concentration distributions: uniform, Gaussian, and bimodal. A bimodal distribution, corresponding to the tubular pinch effect in suspension flows, results in unequal peak zones of erosion due to the flow characteristics.
Highlights
Wear is a natural process for materials, arising as a result of interactions between surfaces
Mathematical models that describe the key mechanisms for pipe wear are essential
The aim of this paper is to develop a mathematical model that describes the dominant contributions to pipe wear, to quantify the process and provide predictions that can act as safeguarding measures to avoid the aforementioned catastrophes
Summary
Wear is a natural process for materials, arising as a result of interactions between surfaces. It is observed that in systems where the flow conditions such as direction change rapidly, erosion is more prevalent than in straight pieces of pipes This applies to pipe bends, turbine blades, and many other industrial processes ?. We model the flow of particles in a viscous fluid through a channel bend. The exponentially detrimental erosion effects of a slowly growing particle would be seen in coolant systems designed to be untouched for decades, such as in tokamaks Such results are prohibitively time consuming to obtain experimentally. Regardless of whether they operate on small or large scales, the systems discussed all comprise fluid flow in long-and-thin channels Particles enter into the flow from the channel walls via corrosion due to oxidation or erosion due to impact. We demonstrate the process with three distributions: a uniform particle distribution, a Gaussian distribution, and a bimodal distribution to represent the tubular pinch effect in a channel ?
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