The Characteristics Tracing Method And Its Applications

It is eager to solve the inverse design problem of the supersonic and hypersonic inner flow field.It relates with the complex physics mechanism,such as shock waves,boundary layer,and the interaction between shock waves and boundary layer.The problem is governed by the hyperbolic partial differential equations of three variables on the mathematics,which is also tough to be solved.Combing the mathematic concept of the residual correction with the physical nature of the supersonic flow field,the characteristics tracing method(CTM)is proposed to design 3-D supersonic viscous flow field.This inverse design method can decrease the flow loss,avoid the interference of the complex shock waves,and improve the aerodynamic performance.The CFD solver is adopted as a flow analytical tool in the characteristics tracing method.The residual correction methodology and its numerical algorithm are studied,and the viscous effects are considered so that the supersonic viscous flow field can be designed straight with the CTM.The CTM is applied to design 2-D supersonic nozzles(the outlet Ma is 3.0)and curve ducts(the Ma on the centerline is always 2.0).With the prescribed Ma distribution on the centerline,the inviscid contour and the viscous one are designed respectively.The flow field in the diamond zones of the resulting nozzles is of high equality,and the supersonic viscous flow turns without shock waves in the resulting curve ducts.According to the viscous shape,a nozzle is machined for the schlieren experiment.The experimental results agree with that in the numerical simulations.The CTM is extended to design 3-D supersonic flow field.According to the geometrical properties of the flow field,the reference plane is proposed,on which characteristics are traced,to reduce the tracing of the Mach cone.Rectangular supersonic ducts,square to circular transition ducts,and circular to square transition ducts are designed for both inviscid and viscous flow.Uniform flow is obtained in the diamond zone.The inverse design of 3-D supersonic viscous flow field with specified parameters distribution is realized by the CTM.The numerical properties of the CTM are studied by analyzing the issues in the design.The influences on the design precision produced by the grid size,still/growing grid,tracing step,and the tracing scheme are investigated.The results reveal that a proper number of still grids are sufficient to satisfy the design precision,and the tracing step should be set by forecasting the special design case.Additionally,it is the best to select the characteristic origin from the interior of the current step.A criterion of the CTM is established to guide the preferences.