View source for Stirred Mill (Power, Heath)

== Description ==

This article describes the '''Heath''' (Heath et al. 2017) method for estimating the power draw of a High Intensity Grinding (HIG) stirred mill.{{Heath et al. (2017)}}

== Model theory ==

{{Under construction|section}}

== Excel ==

The Heath HIG stirred mill power model may be invoked from the Excel formula bar with the following function call:

<syntaxhighlight lang="vb">=mdMillPower_Heath(Parameters as Range)</syntaxhighlight>

{{Excel (Text, Help, No Arguments)}}

The ''Parameters'' array and model results are defined below in matrix notation, along with an example image showing the selection of the same arrays in the Excel interface:

{| 
|- style="vertical-align:top;"
|
:<math>Parameters=
\begin{bmatrix}
d_{\rm ID}\text{ (m)}\\
d_{\rm r}\text{ (m)}\\
d_{\rm s}\text{ (m)}\\
h_{\rm b}\text{ (m)}\\
n_{\rm d}\\
d_{\rm b}\text{ (m)}\\
\rho_{\rm m}\text{ (v/v)}\\
\rho_{\rm b}\text{ (t/m}^3\text{)}\\
\rho_{\rm s}\text{ (t/m}^3\text{)}\\
\mu\text{ (N.s/m}^2\text{)}\\
Q\text{ (m}^3\text{/s)}\\
N_{\rm r}\text{ (rpm)}\\
\end{bmatrix},\;\;\;\;\;\;

\mathit{mdMillPower\_Heath} =
\begin{bmatrix}
P\text{ (kW)}\\
\text{Iterations}\\
v_{\rm r}\text{ (m/s)}\\
\text{Re}\\
U_{\rm s}\text{ (m/s)}\\
U_{\rm slip}\text{ (m/s)}\\
U_{\rm rise}\text{ (m/s)}\\
\rho_{\rm s,g}\text{ (t/m}^3\text{)}\\
\rho_{\rm s,c}\text{ (t/m}^3\text{)}\\
\end{bmatrix}\;\;\;\;\;\;\;\;\;\;\;\;
</math>

where:
* <math>d_{\rm ID}</math> is the internal diameter of the mill (m)
* <math>d_{\rm r}</math> is the rotor tip diameter (m)
* <math>d_{\rm s}</math> is the rotor shaft diameter (m)
* <math>h_{\rm b}</math> is the height of the bead bed (m)
* <math>n_{\rm d}</math> is the number of submerged discs
* <math>d_{\rm b}</math> is the bead diameter (m)
* <math>\phi_{\rm m}</math> is the fraction of mill volume occupied by beads (v/v)
* <math>\rho_{\rm b}</math> is the density of the grinding beads (t/m<sup>3</sup>)
* <math>\rho_{\rm s}</math> is the density of slurry (t/m<sup>3</sup>)
* <math>\mu</math> is the slurry viscosity (N.s/m<sup>2</sup>)
* <math>Q</math> is the volumetric flow rate of slurry feed to the mill (m<sup>3</sup>/s)
* <math>N_{\rm r}</math> is the rotational speed of the rotor (rpm)
* <math>P</math> is mill power (kW)
* <math>\text{Iterations}</math> is the number of internal iterations
* <math>v_{\rm r}</math> is the rotor tip velocity (m/s)
* <math>\text{Re}</math> is the Reynolds Number
* <math>U_{\rm s}</math> is the Stokes settling rate (m/s)
* <math>U_{\rm slip}</math> is  is the slip velocity (m/s)
* <math>U_{\rm rise}</math> is the rise velocity (m/s)
* <math>\rho_{\rm s,g}</math> is the solids pressure due to gravity (N/m<sup>2</sup>)
* <math>\rho_{\rm s,c}</math> is the solids pressure due to centrifugal force (N/m<sup>2</sup>)


| [[File:StirredMillPowerHeath1.png|left|frame|Figure 1. Example showing the selection of the '''Parameters''' (blue frame), and '''Results''' (light blue frame) arrays in Excel.]]
|}

== SysCAD ==

{{Under construction|section}}

== References ==

[[Category:Excel]]
[[Category:SysCAD]]