A Residual Thermodynamic Analysis of Inert Wear and Attrition, Part 1: Theory

Abstract

An open-system irreversible thermodynamic analysis on inert wear and attrition is presented. The aim is to derive a theory which may be implemented in computational fluid dynamics flow solvers. In order to conduct analysis on the differential scale, it is shown that traditional macroscopic-scale concepts, earlier well-established in the literature, cannot be immediately applied. Hence, new differential concepts are introduced. It is argued that the overall analysis can be split up into sub-processes, where different types of specific sub-processes of wear and attrition may be extracted, and directly connected with the corresponding breakage or deformation of either ductile-or brittle-type target materials. Applying the residual thermodynamics framework, the new concepts of wear work and attrition work (at adiabatic conditions) can be defined, which typically only represent a small -often negligible -fraction of the total work.Keywords: Differential; residual; wear work; attrition work. Introduction 1.1 Scope of Present PaperTraditional "simple" wear models [1] work excellently for developing new wear-resistant materials and analyzing specific engineering wear problems (of fixed geometry).The traditional approach aims at analyzing apparent net wear in terms of experimental operating parameters as model input. For instance, Finnie's single-particle ductile erosion model [2] and Archard's empirical model [3] applied for ductile abrasion, are generally considered to represent well-proven models. In most situations, one may connect an empirical-or general black-box model to experiments.Since the end of 1980's, Eulerian Computational Fluid Dynamics (CFD) analysis on wear is attempted. The merits of a CFD analysis is discussed by e.g. [4][5][6][7][8][9][10][11][12][13][14].The utilization or implementation of a traditional wear model in a CFD flow solver, is not straightforward. The problem at hand is that a CFD solver models a number of variables on the grid-cell scale, providing local forces, mass-flows, and momentum-and energy balances. If applying a traditional wear model, locally in a grid cell, and reversing the analysis, it can be shown that the traditional wear model input variables (which are different than the variables simulated by a CFD flow solver), combined with knowledge on the experimental conditions at which the traditional wear model was originally developed, would translate into a different set of Eulerian local forces, massflows, and momentum-and energy balances, as the set computed by the CFD flow solver. Hence, at the same grid cell position, a double set of the same Eulerian variables exists, which hence, creates serious problems of physical inconsistency. Several cases of erratic implementations of traditional wear models in CFD solvers can be found in the literature -and is discussed below.

A Residual Thermodynamic Analysis of Inert Wear and Attrition, Part 2: Applications

“…(30) in [1], gives for the case of ductile wear: term abrasion or erosion ductile wall CS, 1 proc no 21, , proc , …”

“…In the following, the boundary-condition model Eq. (1) in [1] is applied in all situations involving the ductile wear process. This boundary condition is a good approximation, as it in principle allows the modelling of any averaged forces acting on the so-called gross contacting area of the target surface, for any type of averaged flow.…”

“…In [5], also, much higher instantaneous erosion rates were modelled in the initial period of impact of a dense particle jet, supposedly in agreement with Finnie's observations.] Another possible means to analyze the wear work or attrition work is to consider various ways of estimating the parameters incorporated in the basic Eulerian residual-work expressions presented in [1]. For instance, for the ductile wear expression involving parameters particle concentration, particle-phase viscosity, slip-flow coefficient, and flow gradients, all components which are possible to individually estimate.…”

“…The prospects of developing a less empirical theory of inert wear and attrition is investigated in [1].…”

“…A couple of different differential representations of some basic modes of inert wear and attrition were proposed in [1]. (Several other types of wear, described in the literature, are not covered in the following.)…”