Stirred Mill (Power, Heath): Difference between revisions
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== Model theory == | == Model theory == | ||
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Heath et al. (2017) proposed the following relationship for the power draw, <math>P</math> (kW), of a HIGmill with castellated rotors:{{Heath et al. (2017)}} | Heath et al. (2017) proposed the following relationship for the power draw, <math>P</math> (kW), of a HIGmill with castellated rotors:{{Heath et al. (2017)}} | ||
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The Reynolds number, <math>\mathrm{Re}</math>, requires the settling velocity, <math>U_{\rm s}</math>, which itself requires the Reynolds number. Therefore an iterating numerical solution is necessary to resolve the slip velocity. | The Reynolds number, <math>\mathrm{Re}</math>, requires the settling velocity, <math>U_{\rm s}</math>, which itself requires the Reynolds number. Therefore an iterating numerical solution is necessary to resolve the slip velocity. | ||
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=== Additional notes === | === Additional notes === | ||
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The Heath et al. (2017) publication appears to contain a printing error, where the value of coefficient <math>k_4</math> is inadvertently referred to as <math>k_2</math>.{{Heath et al. (2017)}} | The Heath et al. (2017) publication appears to contain a printing error, where the value of coefficient <math>k_4</math> is inadvertently referred to as <math>k_2</math>.{{Heath et al. (2017)}} | ||
Furthermore, the coefficient <math>k_1</math> appears twice, in both the equations for <math>P</math> and <math>p_{\rm s,c}</math>.{{Heath et al. (2017)}} The <math>p_{\rm s,c}</math> term itself also appears in <math>P</math> and is adjusted by <math>k_4</math>, making the <math>k_1</math> repetition unusual, and somewhat redundant. It is probable that the presence of <math>k_1</math> in the equation for <math>p_{\rm s,c}</math> is also a printing error and should be omitted. This is supported by application of the power model to industrial HIGmill specifications, which produces an appropriate result only with the equations as presented above. | Furthermore, the coefficient <math>k_1</math> appears twice, in both the equations for <math>P</math> and <math>p_{\rm s,c}</math>.{{Heath et al. (2017)}} The <math>p_{\rm s,c}</math> term itself also appears in <math>P</math> and is adjusted by <math>k_4</math>, making the <math>k_1</math> repetition unusual, and somewhat redundant. It is probable that the presence of <math>k_1</math> in the equation for <math>p_{\rm s,c}</math> is also a printing error and should be omitted. This is supported by application of the power model to industrial HIGmill specifications, which produces an appropriate result only with the equations as presented above. | ||
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== Excel == | == Excel == | ||
Latest revision as of 07:11, 1 May 2025
Description
This article describes the Heath et al. (2017) method for estimating the power draw of a castellated rotor High Intensity Grinding stirred mill (HIGmill).[1]
Model theory
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Additional notes
Excel
The Heath HIG stirred mill power model may be invoked from the Excel formula bar with the following function call:
=mdMillPower_Heath(Parameters as Range)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
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:
|
where:
|
 Figure 1. Example showing the selection of the Parameters (blue frame), and Results (light blue frame) arrays in Excel. |
SysCAD
The Heath power model is an optional calculation for stirred mill units. If selected, the input and display parameters below are shown.
| Tag (Long/Short) | Input / Display | Description/Calculated Variables/Options |
|---|---|---|
| Heath | ||
| HelpLink | 
|
Opens a link to this page using the system default web browser. Note: Internet access is required. |
| MillDiameter | Input/Display | Inside diameter of the mill. |
| RotorTipDiameter | Input/Display | Diameter of the rotor at the tip. |
| RotorShaftDiameter | Input | Diameter of the rotor shaft. |
| MediaBedHeight | Input/Display | Height of the media (bead) bed. |
| NumSubmergedDiscs | Input | Number of submerged discs. |
| MediaDiameter | Input/Display | Diameter of the media (beads). |
| MediaVolFrac | Input | Volume fraction of media solids in the charge/bed. |
| MediaDensity | Input | Density of media. |
| SlurryDensity | Display | Density of slurry in the feed (or load for Dynamic). |
| SlurryViscosity | Input | Dynamic viscosity of slurry. |
| Feed.SLVolFlow / Feed.SLQv | Display | Volumetric flow rate of slurry into the mill. |
| RotorSpeed | Input/Display | Rotational speed of the rotor. |
| Iterations | Display | Number of internal iterations required to solve settling velocity equations. |
| RotorTipVelocity | Display | Velocity of the rotor at the tip. |
| ReynoldsNumber / Re | Display | Reynolds number. |
| SettlingVelocity / Us | Display | Stokes settling velocity. |
| SlipVelocity / Uslip | Display | Fluid slip velocity. |
| RiseVelocity / Urise | Display | Fluid rise velocity. |
| GravityPressure / psg | Display | Pressure due to gravitational force. |
| CentrifugalPressure / psc | Display | Pressure due to centrifugal force. |
| GrossPower | Display | Gross power drawn by the mill. |
References
- ↑ Heath, A., Keikkala, V., Paz, A. and Lehto, H., 2017. A power model for fine grinding HIGmills with castellated rotors. Minerals Engineering, 103, pp.25-32.