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Having read previous literature about vortex pump, we noticed that mechanisms of circulating flow and its relationship with energy transition remain unclear yet. However, this mechanism, which should be clarified, significantly influences the pump’s efficiency. To comply with the aim of investigating it, the 150WX-200-20 type pump is selected as study object in our present work.

Numerical simulation is conducted to formulate interactions between flow rate and geometric parameters of circulating flow with certain types of blade while experiments on inner flow are served as a witness to provide experimental confirmation of numerical results. Based on these, we coupled some parameters with the pump’s external performance to study their internal connections.

It is concluded that separatrix between circulating flow and other turbulent forms is not that clear under low flow rate. With flow increases, hydraulic losses coming of it will be dominant within the front chamber. Besides, we analogized circulating flow to vortices so as to make a quantitative analysis on its progressive evolution with changing flow, and vortices speaking for circulating flow can be divided into two groups. One is called main circulating flow vortex (hereinafter referred to as MCFV), which occurs all the time while subsidiary circulating flow vortices (hereinafter referred to as SCFV) appear in certain conditions. This context discusses the primary phase of our work with intent to follow up further with circulating flow characterized by vortices (hereinafter referred to as CFV). We confirmed that MCFV Vortex 1 (Vor1) directly influences the efficiency while SCFVs only play helping. As the flow goes to the given working condition, fluids in this pump tend to be steady with the size of CFVs getting larger and their shape being regular. Meanwhile, for MCFV Vor2 and Vor4, their geometric parameters are the key factors for efficiency. When CFVs become steady, they absorb other vortices nearby, as they have higher viscosity with the efficiency reaching its maximum.

The research results explore a new way to measure the circulating flow and help work out the causation of this flow pattern, which may be used to improve the vortex pump’s efficiency.

The purpose of this paper is to consider the leader-following formation control problem for nonholonomic vehicles based on a novel biologically inspired neurodynamics approach.

The interactions among the networked multi-vehicle system is modeled by an undirected graph. First, a distributed estimation law is proposed for each follower vehicle to estimate the state including the position, orientation and linear velocity of the leader. Then, a distributed formation tracking control law is designed based on the estimated state of the leader, where a bio-inspired neural dynamic is introduced to solve the impractical velocity jumps problem. Explicit stability and convergence analyses are presented using Lyapunov tools.

The effectiveness and efficiency of the proposed control law are demonstrated by numerical simulations and physical vehicle experiments. Consequently, the proposed protocol can successfully achieve the desired formation under connected topologies while tracking the trajectory generated by the leader.

This paper proposes a neurodynamics-based leader–follower formation tracking algorithm for multiple nonholonomic vehicles.