Study Of Shock Wave/Boundary Layer Interaction And Boundary Layer Transition Using High-order Numerical Scheme

Shock wave/boundary layer interaction and laminar-turbulent boundary layer transition represent complex flow phenomena that are associated with many aspects of designing issues of hypersonic vehicles,such as aerodynamic lift and drag,thermal protection system and the inlet to scramjet combustors.Therefore,understanding of the physical mechanisms underlying the phenomena of shock wave/boundary layer interaction and laminar-turbulent transition is of great importance to improve the flow quality,efficiency and reliability of the hypersonic vehicles.In present theses,researches of the unsteady shock wave/boundary layer interaction at movement conditions and the supersonic/hypersonic boundary layer transition induced by surface roughness element are carried out using high-order weighted compact nonlinear scheme(WCNS).Firstly,the governing equation and numerical method used in this study are introduced.For problem of shock wave/boundary layer interaction,the governing equation is unsteady Reynolds averaged Navier-Stokes equation,and the SA one-equation turbulence model is used.For problem of boundary layer transition,the governing equation is unsteady three-dimensional Navier-Stokes equation.The discretization of spatial terms of the governing equation is based on the fifth-order weighted compact nonlinear scheme(WCNS),and a second-order temporal accuracy implicit dual-time-step method is adopted for time integration.For unsteady flow calculation,a comparing study of explicit and implicit time marching schemes is implemented.The properties of explicit Runge-Kutta scheme and implicit backward differencing formulas(BDF)are studied by Fourier analysis and some numerical tests,and their performances in accuracy,stability and efficiency are compared.In the published papers,the research on implicit BDF scheme is mainly concentrated on the second-order discretization,whereas the third-order and more higher order discretizations are rarely discussed.The results in present theses show that the third-order BDF scheme is unstable when it is applied in unsteady flow computation,with obvious spurious numerical oscillations occurred.Therefore,it is proposed to adopt the second-order discretization for the implicit backward differencing formulas.In addition,the explicit Runge-Kutta scheme is usually thought to be possessing the advantage of high-order accuracy compared with the implicit BDF schemes.However,the results show that the use of explicit time marching scheme can result in an excessive number of time steps due to the stability limit on the time step size,which leads to notably decreasing of efficiency in comparison to implicit schemes.The accuracy of the high-order numerical method used in current study is validated against some benchmark problems.Firstly,flat-plate boundary layer flows such as incompressible and compressible laminar boundary layer,laminar boundary layer with roughness element and laminar-turbulent boundary layer transition are simulated by calculating Navier-Stokes equations using the high-order WCNS scheme.The numerical results show good agreement with theoretical solutions,experiments and relative numerical results.Thus,the accuracy of the high-order numerical method is validated to the flat-plate boundary layer flows.Secondly,shock wave/boundary layer interaction problems such as supersonic turbulent flat-plate boundary layer and supersonic compression corner are simulated by calculating Reynolds averaged Navier-Stokes equations,and the results are also compared with relative theoretical,experimental and numerical results.Good agreements are achieved,which prove the accuracy of current high-order numerical method again.The phenomenon of unsteady shock wave/boundary layer interaction due to movement of vehicles is investigated.Unsteady shock wave/boundary layer interaction is generated by movement of 2-D compression corner and 3-D hypersonic lifting-body.The unsteady characteristics of separation zone,surface pressure distribution and dynamic stability during the process of pitching up,pitching down and periodically pitching/yaw are analyzed,and the impacts of angular velocity,amplitude and frequency are also considered.The results of 2-D compression corner show that: When the model pitches up,the size of separation region becomes smaller,and when the model pitches down,the size of separation region becomes larger.When the model oscillate periodically,the size of separation region also oscillates periodically and the frequency of the oscillation agrees with each other.The effect of unsteady hysteresis can slow down the increasing or decreasing of the size of separation region.When the amplitude of model increases,the change of separation region becomes wider,and when the frequency of model increases,there is no obvious change in the size of separation region,but the effect of unsteady hysteresis becomes stronger.The results of 3-D lifting-body show that: When the lifting-body pitch/yaw periodically,the external shock wave sweeps up and down or left and right and interacts with the wing on the body(if the angle of pitching/yaw is large enough),that cause strong variation of pressure and heating rate on the surface of the wing.The effect of this interaction on the integral aerodynamic force and the damping-in-yaw derivative of the whole lifting-body is 2% approximately.The supersonic/hypersonic boundary layer transition induced by surface roughness element is researched finally.Firstly,the laminar-turbulent transition of a M=3 flat-plate boundary layer induced by a cylindrical roughness element is investigated both numerically and experimentally,and the typical flow structures as well as the mechanism underlying the effects of roughness on transition are analyzed.The results show that,for small roughness height,the shear layer instability in the wake region appears to be the leading mechanism for transition to turbulence.For large roughness height,strong unsteadiness is developed from the upstream separation zone and transition is immediately accomplished,which indicates that the absolute instability in upstream separation zone dominates the transition.Secondly,the effects of shape and width of roughness element on boundary layer transition at supersonic and hypersonic conditions of M=3.37,4.20,5.26 and 6.63 are studied.The results show that,among four different roughness shapes of cylinder,cuboid,diamond and hemisphere,the cuboid and diamond roughness element can trip the boundary layer transition most effectively,while the hemisphere roughness element trips transition most inefficiently.The effect of the cuboid roughness element characterized by a very early transition point,while the diamond roughness element characterized by a very wide turbulent wake region.When the width of the roughness element becomes larger,the area of the roughness wake region becomes wider accordingly,but the position of transition appears to be suspended.