## 1 Introduction  
The dynamic characteristics of the muzzle flow field are closely associated with the firing process of the gun. For example, the effect of muzzle jet flow on the barrel influences the recoil of the barrel. The shock wave field of the muzzle may cause damage to neighbouring equipment and personnel. Therefore, numerous scholars have conducted research on this topic [1; 2; 3]. With the the development of high-performance computing and accurate numerical approaches, studying complex wave system using computational fluid dynamics (CFD) has become an important means to analyze the dynamic characteristics of muzzle flow fields. Different scholars have used various projectile model shapes for studying muzzle flow field. [PERSON] et al. [4; 5] used a flat-nosed model to study the dynamic processes of the flow field such as shock-wave and jet-flow interactions, shock-shock interactions, shock-wave/contact-surface interactions, and shock wave reflections. [PERSON] et al. [6; 7] studied the integrative process of a flat-nosed projectile accelerated by high-pressure gas to shoot out at a supersonic speed based on ALE (Arbitrary Lagrangian Eulerian) equations and a second-order precision Roe method that adopted chimera grids and a dynamic mesh. [PERSON] et al. [8; 9] used a cone nose model and simulated the non-equilibrium Euler equations with dynamic overlapped grids. [PERSON] et al. [10] studied the effect of gun recoil motion on the muzzle flow field using a cone nose model and CFD simulations of the axisymmetric Euler equations. [PERSON] et al. [11; 12] analyzed the dynamic characteristics of the flow field around a projectile when it was a cone-nose model flying out of the barrel with and without the muzzle device, respectively. [PERSON] et al. [13] studied the dynamic development and spatial distribution characteristics of the muzzle jet-flow wave system using a least-squares explicit meshless method based on a linear basis function. In that work, the numerical simulation of the muzzle flow field was performed considering a large displacement moving boundary and non-equilibrium chemical reactions. [PERSON] et al. (2014, 2015) studied the muzzle-flow field characteristics of a 300-mm DAVIS gun at speeds of 1730 m/s and 794 m/s with a blunt-nose model. The simulation in that work utilized the realizable k-\(\varepsilon\) turbulence model and a dynamic mesh which coupled the interior ballistic and the after-effect period. [PERSON] et al. (2016) determined a minimum overpressure scheme for a blunt-nosed projectile by studying the effect of gunpowder gas leakage to the projectile front caused by a bulge or leak channel added at different positions of the rear of a muzzle-loaded cannon. [PERSON] (2017) studied the flight attitude and flow field visualization of a spherical projectile by using shadowgraph and direct photography and near-field pressure measurements. Using these approaches, the shock interaction around the projectile was captured. [PERSON] (2018) studied the instability and production mechanism of the bow shock wave (BSW) at the projectile front for a projectile moving in low specific-heat ratio gas at high speeds using both experiments and numerical simulations. [PERSON] (2019) investigated the sabot discard behaviour after projectile ejection from the muzzle at a Mach number 4.0 using the six-degrees-of-freedom (6 DOF) rigid-body motion equations and 3D compressible flow equations implemented on a dynamic, unstructured tetrahedral mesh. Presently, the common projectile models include flat-nosed models, blunt-nosed models, and nosed cone models. The existing relevant literature does not typically describe reasons regarding the choice of projectile shape. Additionally, no work has systematically analyzed the relationships and differences among them. The purpose of the present work is to study the effect of projectile nose shapes on the dynamic characteristics of the muzzle flow field under identical firing conditions.