## 1 Introduction  
As the running speed of high-speed trains increases, aerodynamics play a much greater role in the safety and amenity issues of high-speed trains [1, 2]. Consequently, it is crucial to improve the aerodynamic performance of high-speed trains [3]. As near-ground vehicles with a large slenderness ratio and intricate structures [3, 4], high-speed trains cover a variety of running environments and experience prominent unsteady characteristics in the ambient flow field [5, 6]. The geometric design, along with running environments, act as major roles to affect aerodynamic performance of a high-speed train. However, running environments, restricted by road conditions and construction cost, cannot be changed greatly to improve the high-speed train's performance, whereas the geometric design becomes a favorable approach to improvement. The structural design for a high-speed train includes shape designs of both noses [7; 8; 9], design of key components [10; 11], and smooth design of the whole train [3]. Generally speaking, the head and the tail are identical for the convenience of dispatch and operation, and their performance to a large degree determines the whole train's aerodynamic performance. [PERSON] et al. [12], [PERSON] et al. [13], and [PERSON] et al. [14] studied the influence of the streamlined nose on the micropressure wave through two-dimensional design. [PERSON] et al. [15] carried out multiobjective optimization on geometric shapes of a high-speed train based on self-adaptive surrogate models. [PERSON] [16] performed an optimization of the train's front for the crosswind stability and optimization of vortex generators (VGs) for the purpose of drag reduction. [PERSON] et al. [17] proposed a vehicle modeling function (VMF) parametric method to parameterize the high-speed train's head and tail, and analyzed the influence of key design variables of the streamlined shape on the train aerodynamic performance. [PERSON] et al. [18] starting from the previous work proposed a three-dimensional parametric method suitable for engineering design of the streamlined shape of high-speed trains, and further performed a multiobjective aerodynamic optimization with use of particle swarm optimization method. High-speed trains' streamlined noses are designed with complicated surfaces and characterized by geographical and cultural environments of the countries where they are employed. Present parametric methods are mainly based on a given existing shape, but have trouble in designing unique and original streamlined shapes [6; 19], even the authors' new three-dimensional method [18; 20; 21] failed this goal. Therefore, the research based on current parametric methods could most likely achieve, other than a universally optimum nose shape, an optimized design for some particular and existing shapes. The streamlined structure is the determinant for types of the head and tail. As a result, the study of its impacts upon the aerodynamic performance of high-speed trains is fundamental for obtaining the nose shapes of the train with the best aerodynamic performance. [PERSON] et al. [22] carried out experiments for high-speed trains' noses with four different lengths and four different variation rates of cross-sectional area in a wind tunnel to study their influence on the drag and lift of the train model. [PERSON] et al. [23] studied the influence of some key design variables, namely the length of the head, characteristic sectional profiles, cowcatcher, cab window, and cross section of the train body, on the drag and lift force of the train model. [PERSON] et al. [24] made use of LES to study the length of the train head's influence on ambient flow field. [PERSON] et al. [3] compared and analyzed the aerodynamic performance of CRH380A and CRH380B which have been in service in China for over nine years. These studies have mainly described the relationships between the geometric shapes and aerodynamic performance but not yet specifically pointed out how the streamlined structures of the noses affect the flow field around a train.