## 1 Introduction  
Oil shale is an unconventional oil and gas resource, as coal, oil, and natural gas provide non-renewable fossil energy [1, 2]. Such resources worldwide are abundant, equivalent to more than 400 billion tons of synthetic shale oil, three times the world's crude reserves [3, 4]. The borehole hydraulic mining method has unique advantages for underground oil shale exploitation [5]. As shown in Figure 1, when borehole hydraulic mining technology is used to mine underground oil shale, first, drilling rigs must be used to drill holes that are 100-1000 mm in diameter and pass through oil shale layers. Second, the high-pressure water gun is inserted into the borehole, and the underground oil shale bed is broken into several small pieces by the high-pressure water jet from the nozzle connected to the end of the ejector. Then, it is stripped from the parent rock to form a solid-liquid two-phase flowable slurry at the bottom of the borehole. Finally, pneumatic or hydraulic lifting devices are used to extract slurry to the surface [6]. Borehole hydraulic mining technology has the advantages of low cost, short cycle, reliable use, easy operation, low labor intensity, and little environmental pollution [7]. High-pressure water jet broken rock is crucial to ensure the smooth implementation of oil shale borehole hydraulic mining [8; 9]. The entire underground oil shale deposit has to be broken into small pieces of rock and stripped off. A series of follow-up work can be carried out [10; 11]. The hydraulic performance of the nozzle determines the efficiency and quality of high-pressure water jet technology [12; 13]. Thus, it is necessary to study the hydraulic performance of the nozzle. Due to the mechanical properties of oil shale, it is most easily broken when the water jet is parallel to the bedding direction of the oil shale [14; 15]. The primary flow resistance of the straight cone nozzle appears in the outlet section. When drilling hydraulic mining oil shale, a high-pressure water jet often uses a straight cone nozzle because the straight cone nozzle can improve the jet quality [16; 17]. The structural parameters of the straight-cone nozzle are the key factors affecting the spray performance of the nozzle [18; 19]. The transition from the convergence section to the outlet section must be optimized. It is necessary to reduce the outlet section length as much as possible while satisfying the beam-gathering ability. All the optimization work involves increasing rock breaking effect, saving hydraulic energy, and improving energy conversion efficiency [20; 21]. [PERSON] et al. [22] chose a circular annular groove as a bionic unit and arranged the circular annular groove evenly on the inner cavity surface of a straight cone nozzle. The original smooth flow channel inside the nozzle became a bionic non-smooth surface structure, effectively improving the flow channel's hydraulic characteristics inside the nozzle. However, how the size of the circular annular groove affects the hydraulic characteristics of the internal flow channel of the nozzle has not been studied. In summary, based on the existing pressure drop formula of the variable cross-section of a circular tube, this study deduced the theoretical formula for the pressure drop calculation of a bionic circular tube (BCT). Using a genetic algorithm, combined with the pressure drop calculation formula of a BCT, the minimum pressure drop was taken as the optimization goal. The circular annular groove structure parameters of the inlet and outlet sections of the bionic straight cone nozzle (BSCN) were optimized. The optimal structural parameters of the BSCN were obtained by using genetic algorithm optimization analysis and CFD numerical simulation results. The drag reduction characteristics of BSCN were further analyzed. The research results can provide scientific and valuable references for borehole hydraulic mining of high-pressure water jets in oil shale drilling. At the same time,  
Figure 1: Borehole hydraulic mining schematic diagram.