# A Separated-Flow Model for 2-D Viscous Flows around Bluff Bodies Using the Panel Method
###### Abstract  
Panel methods have been applied to many fields of fluid owing to their computational efficiency. However, their applications are limited in simulating highly turbulent flow with separations due to the inviscid flow assumptions, such as those associated with train aerodynamics. Some researchers employed the wake models to simulate large vortices in the wake of trains with predetermined separation locations according to experimental results. In this paper, a modified 2-D constant source/vortex panel method for modelling the separated flow around 2-D bluff bodies is presented. The proposed separated-flow model includes the prediction of separation locations based on the integral boundary-layer method and the shear layer, and large vortices in the wake of the bluff bodies are modelled by the wake model. The proposed method is validated by comparing the calculated pressure distribution on a 2-D circular cylinder with the experimental results. The method is then applied to simulate the flow around a 2-D generic train and calculate the pressure distribution on the train. Since trains run very close to the ground, the effect of the ground configuration on the pressure distribution of the 2-D train is also investigated in this paper using the proposed method. The main contribution of the work is to present a 2-D separated-flow model with wake modelling and separation prediction. The proposed model can be used in the rapid evaluation of bluff-body aerodynamics. p 2  
order to capture the features of the thin boundary layer and small-scale eddies, which has led to ever-increasing simulation sizes that are computationally expensive and time consuming [6; 7; 8; 9]. Additionally, these numerical approaches are dependent on the grid quality, especially in high Reynolds numbers [10]. Furthermore, it is particularly computationally expensive and time consuming for simulating certain train operating conditions, such as the modelling of trains in tunnels [11], where the aspect of most concern is the pressure variations induced by the passage of the train. Although in line with the rapid development of high-performance computers, the computational performance of these methods has been improved, it can still require days, or hours at least, to complete a thorough simulation necessary to understand the key flow characteristics [10]. This current situation conflicts with the increasing demand for accurate, cost-effective tools to predict the aerodynamic behaviour of trains as well as other vehicles and structures [11; 12]. Owing to their high efficiency, meshless approaches can be the solutions to the present problems [13; 14]. The 3-D CFD simulations based on Navier-Stokes equations can track the flow features inside the tunnel due to the train passage; this method is computationally expensive and demands high-order discretisation schemes to avoid numerical instabilities [15; 16]. Owing to the large ratio of the tunnel length to its cross-section diameter, the flow inside the tunnel can be approximated by 1-D equations along the axial axis and solved by the method of characteristics (MOC) [17; 18], which provides reasonable results at a lower computational cost in predicting the propagation of the pressure waves inside the tunnels. However, the flow induced by the train at the entry portal of the tunnel is complex and three dimensional, which is hard to simulate using the MOC method, as well as the effects of the geometrical parameters of the tunnel portal and the train on the pressure waves [15; 19]. The panel method is an option to model trains in tunnels in two-dimensional (2-D) and three-dimensional (3-D) ways while maintaining lower computational costs at the same time. The authors intend to develop the 2-D model and 3-D model for trains in tunnels, and the first stage of our work is to simulate the flow around the 2-D train. This paper presents a 2-D separated-flow model, including separation prediction and wake modelling, to evaluate the pressure distributions around bluff bodies in high Reynolds number flows.