Analysis of hysteresis and phase shifting phenomena in unsteady three-dimensional wakes

The aerodynamic characteristics of automobiles are greatly influenced by the unsteady change in the direction of relative airflow. The aim of this paper is to analyse how such a change influences vehicle wake flow patterns. An analysis was conducted on a simplified model capable of reproducing the typical structures encountered under the aerodynamic conditions of an automobile. The results were processed by mapping the steady and unsteady total pressure losses around the model. The findings should enable automobile development engineers inter alia to identify and analyse the physical phenomena that occur when a vehicle is subjected to a sudden gust of side wind.List of symbols B rod - l length of rod B (m) - angle of rod B (degrees) - D disk - P connection point between disk D and rod B - M_o drive motor of disk D - O centre of rotation of disk D - e radius of disk D (m) - angle of disk (degrees) - t moment of time t (s) - _o angle (degrees) at instant of time t=0 - d diameter of model (m) - C centre of rotation of model - x_c abscissa of centre of rotation C of model (m) - M connection point between model and rod B - pi value=3.14159 - incidence of model (degrees) - _M maximum value of incidence (degrees) - _m minimum value of incidence (degrees) - angular amplitude (degrees) - _c critical angle of incidence (degrees) for steady evolutions - critical angle of incidence (degrees) for the unsteady evolutions - ̄ mean angle of incidence (degrees) - angle (degrees) of the model such that =+ - pulse (rad s^–1) - T period (s) - f frequency (Hz) - R radius of model in meter (m) - velocity vector of incident airflow - V_o intensity of velocity vector (m s^–1) - P_io total pressure associated with upstream airflow velocity (Pa) - P_i local total pressure (Pa or J m^–3) - density (kg m^–3) - C_x drag coefficient - total pressure coefficient - (m, n) dimensions of grid: lines m, columns n - x X coordinate of sampling plane (m) - y_j Y coordinate of point of index j for j[1,n] - z_k Z coordinate of point of index k for k[1,m] - P_i(x,y_j,z_k,(t)) continuous data of unsteady total pressure (Pa) - discrete data of unsteady total pressure (Pa) - N number of tomographic images, from 1 upwards over an oscillation period T - maximum value of total pressure coefficients for steady evolutions - maximum value of total pressure coefficients for unsteady evolutions and increasing incidences - maximum value of total pressure coefficients for unsteady evolutions and decreasing incidences - differential between and - differential between and - phase shifting (degrees)