Applications Of Stream Function Method In Boundary Layer Flow Problems

The computational fluid dynamics(CFD)method predicts the flow field in the boundary layer region of turbine blade by solving the governing equation of the outflow.The governing equation of the flow field is the Navier Stokes equation,and its solving process is very resource consuming.Although the calculation methods and computer technology have a great development,but for the preliminary design of engineering,efficient and accurate estimation method is still the goal of engineering.In this paper,the boundary layer method based on the stream function method is used to solve the complex boundary layer flow problems by solving the governing equation of the two-dimensional boundary layer region in the fraction stream function coordinate system,which greatly improves the efficiency of the solving process.At the same time,based on the boundary layer method,the interaction between the jet and the main stream in film cooling is analyzed,and a numerical method for film cooling is established by using the conservation of momentum and energy.Specifically,the research work of this paper is as follows:(1)The boundary layer method is used to simulate the incompressible laminar plate flow and the incompressible turbulent plate flow.Taking the results of laminar flow theory as the comparison object,the thickness of velocity boundary layer,thickness of displacement boundary layer,thickness of momentum boundary layer,friction coefficient,Stanton number and Nusselt number are calculated.It is found that the boundary layer method can simulate the incompressible flow well.(2)The boundary layer method is used to simulate the compressible turbulent plate flow.Taking the results of the boundary layer calculation program TEXSTAN as the comparison object,the momentum Reynolds number,stagnation enthalpy Reynolds number,friction coefficient,Stanton number,Nusselt number,convective heat transfer coefficient and heat flow density are calculated.It is found that the boundary layer method can simulate the compressible flow well.(3)The film cooling method based on the boundary layer method is used to simulate the single film hole and the multi film hole plate flow.Taking the results of the commercial software COMSOL as the comparison object,the cooling efficiency of the downstream of the film hole is calculated.It is found that the film cooling method proposed in this paper can simulate the film cooling well.(4)The cooling efficiency of the downstream of the film hole is compared when the film hole diameter is 0.0005 m,0.001 m and 0.002 m,the incident angle is 30°,45° and 60°,the incident velocity is 2.5m/s,5m/s and10m/s,the incident temperature is 500 K,530K and 560 K.It is found that when the film hole diameter is 0.002 m,the incident angle is 60°,the incident velocity is 10m/s and the incident temperature is 500 K,the jet has the largest attachment distance on the solid surface and the best cooling effect.