Air Classifier (Altun): Difference between revisions

Revision as of 04:43, 19 May 2023

This article describes the Altun and Benzer (2014) model for air classification.^[1]

This section is currently under construction. Please check back later for updates and revisions.

The Altun air classifier model may be invoked from the Excel formula bar with the following function call:

=mdUnit_AirClassifier_Altun(Parameters as Range, Size as Range, Feed as Range, OreSG Range)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.

The required inputs are defined below in matrix notation with elements corresponding to cells in Excel row ( $i$ ) x column ( $j$ ) format:

Parameters={\begin{bmatrix}D{\text{ (m)}}\\{\mathit {AF}}{\text{ (m}}^{3}{\text{/h)}}\\{\mathit {RS}}{\text{ (m/s)}}\\k_{\alpha }\\n_{\alpha }\\k_{d_{50}}\\n_{d_{50}}\\k_{C}\\n_{C}\\k_{\beta }\\n_{\beta }\\c_{\beta }\\(Q_{\rm {M,F}})_{\rm {L}}{\text{ (t/h)}}\\\end{bmatrix}},\;\;\;\;\;\;Size={\begin{bmatrix}d_{1}{\text{ (mm)}}\\\vdots \\d_{p}{\text{ (mm)}}\\\end{bmatrix}},\;\;\;\;\;\;Feed={\begin{bmatrix}(Q_{\rm {M,F}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,F}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,F}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,F}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}},\;\;\;\;\;\;OreSG={\begin{bmatrix}(\rho _{\rm {S}})_{1}{\text{ (t/m}}^{\text{3}}{\text{)}}&\dots &(\rho _{\rm {S}})_{m}{\text{ (t/m}}^{\text{3}}{\text{)}}\\\end{bmatrix}}

where:

$D$ is the classifier chamber diameter (m)
${\mathit {AF}}$ is the air flow rate (m³/h)
${\mathit {RS}}$ is rotor speed (m/s)
$k$ is an equation coefficient
$n$ is an equation exponent
$c$ is an equation constant
$(Q_{\rm {M,F}})_{\rm {L}}$ is the mass flow rate of liquids in the feed (t/h)'
$p$ is the number of size intervals
$m$ is the number of ore types
$d_{i}$ is the size of the square mesh interval that mass is retained on (mm)
$d_{i+1}<d_{i}<d_{i-1}$ , i.e. descending size order from top size ( $d_{1}$ ) to sub mesh ( $d_{p}=0$ mm)
$\rho _{\rm {S}}$ is the density of solids (t/m³)

The results are displayed in Excel as an array corresponding to the matrix notation below:

{\mathit {mdUnit\_AirClassifier\_Altun}}={\begin{bmatrix}{\begin{bmatrix}{\mathit {DL}}{\text{ (kg/m}}^{3}{\text{)}}\\F{\text{ (t/h)}}\\\alpha \\d_{\rm {50c}}{\text{ (mm)}}\\C{\text{ (frac)}}\\\beta \\\beta ^{*}\\(Q_{\rm {M,OF}})_{\rm {L}}{\text{ (t/h)}}\\(Q_{\rm {M,UF}})_{\rm {L}}{\text{ (t/h)}}\\\end{bmatrix}}{\begin{array}{cccccc}{\begin{bmatrix}{\bar {d}}_{1}{\text{ (mm)}}\\\vdots \\{\bar {d}}_{n}{\text{ (mm)}}\end{bmatrix}}&{\begin{bmatrix}(Q_{\rm {M,UF}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,UF}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,UF}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,UF}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}}&{\begin{bmatrix}(Q_{\rm {M,OF}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,OF}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,OF}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,OF}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}}&{\begin{bmatrix}(P_{\rm {OF}})_{1}{\text{ (frac)}}\\\vdots \\(P_{\rm {OF}})_{n}{\text{ (frac)}}\end{bmatrix}}\\\\\\\\\\\\\\\end{array}}\end{bmatrix}}

where:

${\mathit {DL}}$ is the dust loading (kg/m³)
$F$ is the flow rate of -36+3 µm size particles in the feed (t/h)
$\alpha$ is the sharpness parameter of the Whiten-Beta efficiency curve
$d_{\rm {50c}}$ is the cut size parameter of the Whiten-Beta efficiency curve (mm)
$C$ is the bypass parameter of the Whiten-Beta efficiency curve (frac)
$\beta$ is a fish-hook parameter of the Whiten-Beta efficiency curve
$\beta ^{*}$ is a fish-hook parameter of the Whiten-Beta efficiency curve
$(Q_{\rm {M,OF}})_{\rm {L}}$ is the mass flow rate of liquids to the overflow stream (t/h)
$(Q_{\rm {M,UF}})_{\rm {L}}$ is the mass flow rate of liquids to the underflow stream (t/h)
$P_{\rm {OF}}$ is the partition fraction to overflow (frac)