Physical Modelling for the Precise Representation of Flow Phenomena Based on Simultaneous Similitude of Multiple Dimensionless Numbers

Physical modelling experiments, together with numerical modelling calculations, are essential for scientific investigations of real flow phenomena. As for the physical model experiments, it has been common to combine reduced scale ratios with one or two dimensionless number(s) similitude(s). Simultaneous similitude of multiple dimensionless numbers concerned with the objective flow phenomena is ideal for physical modelling but was considered difficult to realize in practice. This paper presents a breakthrough in this matter, with a consideration of the simultaneous similitude of multiple dimensionless numbers. A simple relationship between the physical properties of fluids and the scale ratio of a physical model has become clear, for the simultaneous similitude of the Froude, Reynolds, Weber, Eötvös and Morton numbers. For conducting physical model experiments to represent flow phenomena in molten iron, it is demonstrated that the physical properties of various molten metals, such as liquid tin, can meet these stringent requirements. Furthermore, this new concept for the precise physical modelling of flow phenomena (named SMDN: Similitude of Multiple Dimensionless Numbers) is shown to be also feasible for combinations of many types of liquids. This enables precise, safe, and easy physical model experiments to be conducted, that exactly mimic industrial operations in higher-temperature systems.