The Numerical Simulation Of The Two-dimensional Boundary Layer Over Rough Surfaces

Some key parts such as impellers are widely used in the fields of aerospace, energy power, etc. In practical applications, it is found that the surface topographies of these parts have a certain influence on the aerodynamic performance of the flow under the condition of the large Reynolds number. However, the researches on this field are very limited. It is very necessary to study the influence of rough surface on the aerodynamic performance of parts. In this case, this paper investigates the influence of array roughness elements with circular cross sections on the gas flow.First, the numerical simulation method that boundary layer combined with inviscid potential flow is utilized to study the flow over the rough surface, and a developed two-dimensional boundary layer partial differential governing equations are used to describe the flow over the rough surface.Secondly, the governing equations are transformed from the physical plane to the computational plane by applying the modified Illingsworth transformation, and an implicit finite difference method is used to discrete the transformed partial differential equations. Through the Illingsworth coordinate transformation, the governing equations are converted into the form that can be easily solved. Meanwhile, the scale became larger in all directions in the computational plane. Along the stream direction, the growth trend of turbulent boundary layer thickness is mild compared with the physical plane. It may therefore be helpful to improve the calculation accuracy. In the process of numerical computation, first order partial derivatives of the velocity and temperature with respect to abscissa are approximated by using the two point back difference scheme. First order partial derivative and second order partial derivative of the main variable with respect to ordinate are approximated by utilizing the three point Lagrange interpolation derivative formulas. Then, the nonlinear algebraic equations are obtained. A steady numerical solution is given on this basis.Thirdly, algebraic method is used to generate the rectangular grids, and a computational procedure is completely developed to calculate the two-dimensional turbulent boundary layer flow over rough surface. According to the characteristics of two-dimensional turbulent boundary layer flow, the spacing of the grid node near the wall is smaller and the distance is gradually increasing that is away from the wall. It can not only ensure the calculating precision, but also save computation time. Finally, the two-dimensional boundary layer over rough surface is analyzed by using the calculation program. The results of simulation show that the rough surface has a significant impact on gas flow, and the change of aerodynamic performance can also be caused by the change of characteristics parameters of roughness element such as height, diameter, spacing.