## 1 Introduction
For example, it was found that the Gyroid structure provided approximately 40% higher effective thermal conductivity in turbulent flow compared to laminar flow [22]. Microfluidic technology is widely utilized in chip channel manufacturing due to its efficiency, safety, and precise control. The design of the internal flow field and particle distribution plays a crucial role in enhancing mass transfer rates and reaction efficiency. In this context, a multi-field coupled particle flow modeling and control method is proposed, investigating particle distribution under ultrasonic excitation and establishing a multi-field mixing observation platform for validation. The findings indicate that the proposed modeling strategy effectively elucidates the evolution mechanism of the multi-field coupled flow field, while ultrasonic energy enhances overall flow distribution and ensures uniformity in particle distribution [23]. In a study conducted on the design and performance of TPMS-based heat exchangers under turbulent flow regime, researchers obtained various results. The flow and heat transfer performance of heat exchangers based on four TPMS structures (F-KS, PMY, FRD, and Gyroid) were numerically investigated using the k-\(\omega\) Shear Stress Transport turbulence model. It was observed that heat transfer was significantly influenced by turbulence, with the \(Nu\) increasing along with the \(Re\). The Fischer-Koch S (F-KS) model exhibited the best overall heat transfer performance. Increasing the flow velocity and volume fraction led to higher heat transfer coefficients, while an increase in volume fraction was also found to result in higher pressure drops [24]. The effectiveness of ultrasonic excitation strategies in controlling particle distribution in microfluidic channels has been demonstrated in previous studies. In this study, particle flow dynamics were modeled using the LBM-LES-DEM framework, and the role of ultrasonic excitation in preventing particle accumulation was revealed [25]. Turbulent flow, characterized by its chaotic and irregular nature, plays a crucial role in various engineering applications, including heat exchangers and bone implants. Recent advancements in additive manufacturing have enabled the fabrication of complex geometries, such as TPMS structures, which exhibit unique properties in terms of heat transfer and fluid flow under turbulent conditions. Experimental investigations of these structures under turbulent flow have largely confirmed the predictions of numerical studies [26]. This comprehensive approach aims to accelerate the multi-objective optimization of TPMS structures, paving the way for their utilization in the development of bone implants [27]. The numerical investigation examined convective heat transfer characteristics of aluminan-water nanofluids flowing through horizontal rib-shaped microchannels. This simulation was conducted under laminar flow conditions with nanoparticle volume fractions ranging from 0.01 to 0.04. Results demonstrated that the internal ribs enhanced heat transfer by intensifying turbulence in the flow [28]. This study provides a comprehensive investigation into the heat transfer performance of TPMS structured heat exchangers by employing both experimental and numerical analyses. The analysis focuses on two types of TPMS materials, Al and Ag, and evaluates their performance with two heat transfer fluids: pure distilled water and a nanofluid containing 0.6 vol% nanoparticles. A range of flow rates and a constant heat flux of 30.8 kW/m\({}^{2}\) were applied to assess the impact of the TPMS structure on heat dissipation and boundary layer formation. By integrating experimental measurements with numerical simulations, this study offers an in-depth understanding of heat transfer mechanisms and identifies the key parameters influencing the performance of TPMS-based cooling systems. These findings address existing gaps in the literature and provide valuable insights for optimizing TPMS-structured heat exchangers for enhanced thermal management.