# Comparison of Degassing Efficiency on a Foundry Degassing Unit Using Different Rotor Types
## 1 Introduction
Nevertheless, satisfactory modelling results can also be obtained when incomplete dynamic similarity is achieved, which is the case when not all similarity criteria are complied with. In such a case, the results may be semi-quantitative to qualitative. The deviation rate from the exact model is different in each specific case. Adherence to the modified Froude number in the form of Equation (1) is essential to achieve sufficiently accurate results for a multiphase flow, which is the case of aluminium refining using an inert gas [12; 13]:  
\[Fr_{N}=\frac{\rho_{g}\cdot v^{2}}{\rho_{l}\cdot g\cdot L} \tag{1}\]  
where \(\rho_{g}\)--gas density (kg\(\cdot\)m\({}^{-3}\)), \(\rho_{l}\)--liquid density (kg\(\cdot\)m\({}^{-3}\)), \(g\)--acceleration due to gravity (m\(\cdot\)s\({}^{-2}\)), \(L\)--liquid height in the model (m), \(v\)--gas injection velocity (m\(\cdot\)s\({}^{-1}\)). Provided that the above-described conditions are met, the obtained data can be used to set real equipment in a production plant [9; 10]. The second option consists of numerical modelling. Numerical modelling of the aluminium melt refining process with argon using a submersible rotation device is complex. The refining process is composed of multiple processes (a multiphase turbulent flow, transfer of mass and energy, etc.) which are described by their governing differential equations. An effective alternative of mathematical modelling using special software can be used to simulate and predict the aluminium melt refining process. Numerical modelling of flows and other phenomena such as heat and mass transfer, the course of chemical reactions, etc., is generally called computational fluid dynamics (CFD) [14]. Many authors have focused on aluminium melt refining thanks to the prevailing popularity of aluminium as a construction material [15; 16; 17; 18; 19; 20; 21; 22]. This technology includes various modifications whose history has been described by [24]. Currently, refining by inert gas using a submersible rotation device, called a foundry degassing unit (FDU), is used to refine the aluminium melt and reduce the content of hydrogen and other impurities [9; 25; 26]. The submersible device is composed of a hollow shaft and a rotor that blows the refining gas into the melt. Refining efficiency can be affected by many parameters, including the shape and position of the refining rotor, the rotational speed, the refining gas flow, etc. In this regard, physical modelling provides more possibilities for studying the processes and laws occurring in the volume of a vessel when aluminium is replaced with a model liquid. The scientific basis of aluminium melt refining technology using a rotational device has been established in previous studies [27; 28]. As determined by the authors of those studies, refining efficiency is largely dependent on the size of the bubbles of the gas being blown in. This size affects the size of the phase interface and thus also the transfer of mass [13; 29]. Moreover, smaller bubbles are slower in reaching the surface of the liquid, and thus their residence time in the liquid becomes longer. It has been determined that the required bubble parameters are best achieved using rotational degassing. Using a nozzle or a porous block, columns of large bubbles are obtained, and these bubbles rise to the surface above the blowing point. The rotor converts energy from the propelling device to kinetic energy and transfers this energy to the melt [30]. When rotational degassing is used, the rotor creates fine bubbles of inert gas and mixes these bubbles with the melt. These fine bubbles are homogeneously distributed in the ladle volume without disturbing the surface of the melt, thereby maximizing the phase interface between the gas and the melt. The way in which gas bubbles disintegrate in a mixing vessel with a rotor was investigated in studies [31; 32; 33].