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.

物理建模实验以及数值建模计算对于真实流动现象的科学调查是必不可少的。至于物理模型实验，通常将缩小比例与一或两个无量纲数相结合。与客观流动现象相关的多个无量纲数的同时相似对于物理建模是理想的，但在实践中被认为难以实现。本文在这方面提出了一个突破，考虑了多个无量纲数的同时相似性。流体的物理特性与物理模型的比例比之间的简单关系已经变得清晰，因为 Froude、Reynolds、Weber、Eötvös 和 Morton 数的同时相似。为了进行物理模型实验来表示铁水中的流动现象，证明了各种熔融金属（例如液态锡）的物理特性可以满足这些严格的要求。此外，这种用于对流动现象进行精确物理建模的新概念（名为 SMDN：多无量纲数的相似性）也被证明适用于多种液体的组合。这使得能够进行精确、安全和简单的物理模型实验，精确模拟高温系统中的工业操作。这一用于精确物理建模流动现象的新概念（名为 SMDN：多无量纲数的相似性）被证明也适用于多种液体的组合。这使得能够进行精确、安全和简单的物理模型实验，精确模拟高温系统中的工业操作。这一用于精确物理建模流动现象的新概念（名为 SMDN：多无量纲数的相似性）被证明也适用于多种液体的组合。这使得能够进行精确、安全和简单的物理模型实验，精确模拟高温系统中的工业操作。