## 1 Introduction  
To facilitate the achievement of China's dual carbon goals (DCGs), it is imperative to actively develop the clean utilization technology of coal resources, specifically through clean coal technology. Among various clean coal technologies, coal gasification stands out as one of the most notable approaches. In particular, large-scale high-efficiency entrained-flow coal gasification technology has emerged as the most promising coal gasification method [1], and high-pressure dense-phase pneumatic conveying is a crucial component of this gasification technology. High-pressure dense-phase pneumatic conveying is widely applied in energy, chemical, metallurgical, power generation, pharmaceutical, and food processing industries due to its advantages, such as low gas velocity, high solid-gas ratio, low energy consumption, reduced gas consumption, and minimal pipeline wear. In the solid processing industry, it is estimated that the market value of the conveying systems could increase to \(\varepsilon 30\) billion by 2025 [2]. Therefore, high-pressure dense-phase pneumatic conveying technology possessessignificant market competitiveness and development potential. However, due to its high pressure, high solids volume fraction, and complex flow characteristics [3; 4], as well as numerous influencing factors (such as carrier gas properties, material properties, operating parameters, conveying parameters, and pipeline shape), the conveying characteristics of high-pressure dense-phase pneumatic conveying are extremely complex. Currently, the understanding of the conveying mechanism and characteristics remains inadequate. Many issues have not been properly addressed for high-pressure dense-phase pneumatic conveying, thus hindering its comprehensive and rational utilization in engineering applications. Horizontal pipes are crucial and commonly used pipelines in high-pressure dense-phase pneumatic conveying, generally accounting for the highest proportion of the whole conveying pipeline. However, during the conveying process in horizontal pipe, various types of metastable flow patterns, such as dune flow and slug flow, are prone to occur. And these flow patterns directly affect the stability of the conveying process and may even result in pipe blockages and conveying interruptions. In a sense, the stable and reliable operation of high-pressure dense-phase pneumatic conveying in horizontal pipe is the basic prerequisite and fundamental guarantee for the stable production of large-scale, high-efficiency, entrained-flow coal gasification systems. Therefore, the study of high-pressure dense-phase pneumatic conveying in horizontal pipe is of great practical significance. There are two main research methods for high-pressure dense-phase pneumatic conveying: experimental research and simulation research. Current research mainly focuses on the experimental research field of high-pressure dense-phase pneumatic conveying. Numerous scholars have conducted a large number of experimental studies from various perspectives using existing measurement techniques and equipment, yielding several valuable results related to pipeline resistance characteristics, flow patterns, conveying characteristics and stability [5; 6; 7; 8; 9; 10]. As is known, pneumatic conveying is a highly comprehensive discipline that involves multiple fields, such as fluid mechanics, mechanical engineering, and particle science. In particular, high-pressure dense-phase pneumatic conveying exhibits intricate nonlinear and non-equilibrium dynamic characteristics. However, the existing experimental equipment and measurement techniques are severely limited, making many crucial parameters for high-pressure dense-phase pneumatic conveying challenging to measure. As a result, the current state of experimental research has reached a bottleneck stage [6]. With the rapid development of computational fluid dynamics theory and the fast improvement of computer performance, simulation methods have become powerful research tools widely applied in the field of pneumatic conveying.