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The purpose of this paper is to study the mechanochemical effect and self-growth mechanism of double-network (DN) gel and to provide a quasiperiodic model for rubber elasticity.

The chemical reaction kinetics is used to identify the mechanochemical transition probability of host brittle network and to explore the mechanical behavior of endosymbiont ductile network. A quasiperiodic model is proposed to characterize the cooperative coupling of host–endosymbiont networks using the Penrose tiling of a 2 × 2 matrix. Moreover, a free-energy model is formulated to explore the constitutive stress–strain relationship for the DN gel based on the rubber elasticity theory and Gent model.

In this study, a quasiperiodic graph model has been developed to describe the cooperative interaction between brittle and ductile networks, which undergo the mechanochemical coupling and mechanical stretching behaviors, respectively. The quasiperiodic Penrose tiling determines the mechanochemistry and self-growth effect of DNs.

It is expected to formulate a quasiperiodic graph model of host–guest interaction between two networks to explore the working principle of mechanical and self-growing behavior in DN hydrogels, undergoing complex mechanochemical effect. The effectiveness of the proposed model is verified using both finite element analysis and experimental results of DN gels reported in literature.

For underwater hydraulic machinery, the unique structure significantly enhances the three-dimensional non-uniformity of turbulence within the flow domain and high Reynolds number turbulence introduces complex effects on the machinery. Therefore, studying the turbulent flow characteristics in underwater hydraulic machinery is crucial for system stability.

This paper conducts a numerical analysis on a specific type of underwater hydraulic machinery. A numerical calculation model is established under stable inflow conditions to analyze the flow trends and pressure changes at different flow speeds. Subsequently, structural modifications are made to the underwater hydraulic machinery, and the characteristics of the velocity field, pressure field and vorticity distribution under different model parameters are analyzed.

The results indicate that changes in internal structure have a certain impact on flow characteristics. When the structural changes are significant, the fluid flow becomes more complex and pressure fluctuations become more intense. The research findings provide a scientific basis and theoretical guidance for the structural design of underwater hydraulic machinery and have significant research implications for controlling fluid-induced noise.

Affected by the inherent structural characteristics of the flow channel structure, the flow direction of the high-speed water flow changes drastically in the flow channel, so it is of great significance to study its flow characteristics for the stability of the system.