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22.5 Particle Erosion and Accretion Theory

Particle erosion and accretion rates can be monitored at wall boundaries. The erosion rate is defined as

 R_{\rm erosion} = \sum^{N_{\rm particles}}_{p=1}\frac{\dot{m}_p C(d_p) f(\alpha) v^{b(v)}} {A_{\rm face}} (22.5-1)

where $C(d_p)$ is a function of particle diameter, $\alpha$ is the impact angle of the particle path with the wall face, $f(\alpha)$ is a function of impact angle, $v$ is the relative particle velocity, $b(v)$ is a function of relative particle velocity, and $A_{\rm face}$ is the area of the cell face at the wall. Default values are $C=1.8 \times 10^{-9}$, $f=1$, and $b=0$.

Since $C$, $f$, and $b$ are defined as boundary conditions at a wall, rather than properties of a material, the default values are not updated to reflect the material being used. You will need to specify appropriate values at all walls. Values of these functions for sand eroding both carbon steel and aluminum are given by Edwards et al. [ 96].

The erosion rate as calculated above is displayed in units of removed material/(area-time), i.e., mass flux, and can therefore be changed accordingly to the defined units in FLUENT. The functions $C$ and $f$ have to be specified in consistent units to build a dimensionless group with the relative particle velocity and its exponent. To compute an erosion rate in terms of length/time (mm/year, for example) you can either define a custom field function to divide the erosion rate by the density of the wall material or include this division in the units for $C$ and/or $f$. Note that the units given by FLUENT when displaying the erosion rate are no longer valid in the latter case.

A variety of erosion models [ 107, 235, 95, 263, 138, 314] containing model constants [ 138, 95] and angle functions can be easily implemented into FLUENT. The equations describing some of the erosion models can be modified to appear in the form of the general equation describing the erosion rate, Equation  22.5-1. For example, the Tulsa Angle Dependent Model [ 95] described by Equation  22.5-2

 ER = 1559B^{-0.59} F_s v^{1.73} f({\alpha}) (22.5-2)

can be rewritten in the form of Equation  22.5-1 with the following substitutions:

$v^{1.73}$ = $v^{b(v)}$
$1559B^{-0.59} F_s$ = $C(d_p)$

where $ER$ is the erosion rate, $B$ is the Brinell hardness, and $F_s$ is a particle shape coefficient.

User-defined functions can be used to describe erosion models of any form. For more complex models, such as those models with varying function angles, $f({\alpha})$, the default Erosion Model in the wall Boundary Conditions panel cannot be used. Hence, a user-defined function should be used instead. For information on how to apply user-defined functions for DPM erosion models, refer to the DEFINE_DPM_EROSION macro in the separate UDF Manual , or contact your support engineer for further assistance.

Note that the particle erosion and accretion rates can be displayed only when coupled calculations are enabled.

The accretion rate is defined as

 R_{\rm accretion} = \sum^{N_{\rm particles}}_{p=1} \frac{\dot{m}_p}{A_{\rm face}} (22.5-3)

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