Numerical simulation and analysis of five-stage lifting pump by improved turbulence model and catastrophe theory

Abstract

How to theoretically describe the process of turbulence formation emains an unsolved problem. A new method is presented in this paper for quantitatively researching the turbulence phase transition based on a dimensionless method and catastrophe theory. Then, the formula of energy spectrum density Ek, with the wave number and time-scale index strictly derived from the folding catastrophe model, can quantitatively explain the energy in the turbulent system, inherited from large eddies and transferred to small eddies until viscous dissipation occurs, theoretically and physically. As an example, solid–liquid two-phase flow in a five-stage lifting pump for a 6000 m deep-sea mining system is analyzed based on a structured mesh by numerical simulation, in which this turbulence model is validated. This method provides equations that can give a quantitative analysis with a physical explanation for turbulence formation, which not only provides a new insight into the turbulence, but also can be applied to other complex phase transitions.

Keywords

• turbulence
• catastrophe theory
• lifting pump
• deep-sea mining
• complex phase transitions