A Space-Marching Algorithm With Application To Scramjet Components Optimization Design

As a candidate powerplant for the hypersonic flight vehicles, scramjet has been studied extensively all over the world, but there are still many technical problems remaining unsolved, such as efficient flowfield simulation tools and aerodynamic integrated design tools, etc. The traditional CFD methods, i.e. time iterative algorithms based on Full Navier-Stokes (FNS) Equations, have achieved great development and been widely used in scramjet integrated design. But it is so time-consuming that it is very difficult to integrate them into the aerodynamic optimization design process of scramjet and its components.A new single-sweep Parabolized Navier-Stokes algorithm (SSPNS), a highly accurate, highly efficient supersonic/hypersonic flowfield simulation method, is developed. And it is successfully used in the aerodynamic optimization design process of scramjet inlets and single expansion ramp nozzles (SERNs).Firstly, a time iterative FNS algorithm is presented. It is a finite volume method (FVM) based on implicit lower-upper symmetric Gauss-Seidel (LU-SGS) time integration, and several typical upwind schemes, including van Leer scheme, Roe scheme, AUSM-family schemes, LDFSS schemes, and 2-order NND schemes, etc. Five typical flows, including 1D Sod tube, colliding flow, laminar/turbulent flat plate boundary flow, shock-boundary interaction on a flat plate and hypersonic inlet flow, are investigated using this method. Results show that the hybrid upwind schemes, such as AUSM-family schemes and LDFSS schemes, have higher viscous resolution and discontinuities resolution. They are applicable to supersonic/hypersonic flowfield simulations.Secondly, theoretical analysis is focused on the mathematic properties about the Parabolized Navier-Stokes (PNS) Equations, especially on the treatment of streamwise pressure gradient. Then the original implicit time iterative LU-SGS method is successfully extended to integrate the PNS Equations in the streamwise space direction. And the space-marching algorithm SSPNS is formulated. Five typical flows, including supersonic flat plate flow, 15°ramp hypersonic flow, cone flows with different angles of attack, hypersonic corner flow, and shock-boundary interaction flow on a flat plate, are computed with the SSPNS codes. Numerical results of the first 3 examples agreed well with those obtained from NASA's UPS PNS codes and experimental results by Tracy or Holden et al. The five-shock structure of the corner flow is also computed well. But the separation zone of the shock-boundary interaction flow is not captured satisfactorily. Several scramjet component flowfields, including 4 hypersonic inlet flows and 2 SERN flows, are also obtained with the SSPNS codes. Results of inlets, such as flow structures, wall pressure distributions, and friction coefficients, show good agreement with numerical results of UPS, SCRAMIN NS codes, and experimental results by NASA. SSPNS results of the 2D and 3D SERN flows also agree well with NASA's experimental results. By comparison with the FNS flow solvers, the SSPNS codes show at least 1~2 order of magnitude speed faster and 1 order of magnitude of storage saving in the 3D side-compression hypersonic inlet flowfield simulation. All these numerical results prove that SSPNS is a highly efficient, highly accurate algorithm for steady supersonic/ hypersonic flows, especially for 3D cases.Thirdly, theoretical comparison analysis is carried out between traditional gradient based optimization methods and global random optimization methods, such as Genetic Algorithms (GAs), etc. It is concluded that GAs are typical random heuristic methods, and more suitable for nonlinear discontinuous optimization problems than traditional methods.Fourthly, a novel 2D inlet which can self-start at relay Mach number (Ma = 3.5) is designed. Then single- or multi-objective optimization designs of this 2D inlet are carried out on cruise operation point (Ma=7.0) by Sequential Quadratic Programming (SQP), Multi-Island GA (MIGA), and multi-objective GAs, including NCGA and NSGA-II. The inlet flowfields are calculated with SSPNS in these optimization design processes. Single objective optimization results show pressure recovery maximum model is better than effective kinetic energy coefficient maximum model. Multi-objective optimization results reveal the tradeoffs of pressure recovery, static pressure rise, and drag coefficients. Based on multi-objective design process, a two-point design and a design point choosing process are investigated. Results show if design point is set at cruise point, the off-design mass capture coefficients is relatively low; whereas if the design Mach number is 6.5, the 2D inlet will get good overall operation performances along the constant dynamic pressure trajectory.Lastly, the same optimization design methods are applied to design several 2D SERNs. The single objective optimization design result shows that the objective, thrust coefficient is improved, but the lift coefficient is too small. In the 2- and 3-objective optimization design, tradeoffs of thrust coefficient, lift coefficient and pitching moment coefficient, are obtained.