A new nonequilibrium turbulence closure model has been developed for computing wall bounded two-dimensional turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present model has been evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the new nonequilibrium turbulence model accurately captures the history effects of convection and diffusion on turbulence.

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute two- and three-dimensional (3-D) chemically reacting, turbulent flows with hydrogen-air chemistry. The code is a modification of the 3-D upwind PNS (UPS) airflow code. The code solves the PNS equations using a finite-volume, upwind, TVD (Total Variation Diminishing) method based on Roe's approximate Riemann solver that has been modified to account for nonequilibrium effects. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. Two turbulence models have been incorporated into the code including an algebraic model, that has the ability to account for internal flows with multiple walls, and a two-equation ([kappa]-[epsilon]) turbulence model. For the two-equation turbulence model option, the code solves the turbulence transport equations in an uncoupled manner from the fluids equations. With these enhancements, the UPS code is now capable of computing the chemically reacting flow in scramjet (supersonic combustion ramjet) engines. Various component test cases have been used to validate the code. The computed results are in good agreement with the available numerical and analytical solutions and experimental data. Finally, the full capabilities of the new code have been demonstrated with a 3-D tip-to-tail numerical calculation of the integrated aerodynamic and propulsive flowfields of a generic hypersonic space plane. Two test cases, one with power-off and one with power-on, were considered to study the flow structure around such a configuration. Both tip-to-tail cases were successfully computed in this study.

A finite-volume code has been written to solve the complete, Reynolds-averaged Navier-Stokes equations around unconventional airfoils. The numerical algorithm is based on a flux-difference splitting form of a total variation diminishing (TVD) scheme. Various modifications to the scheme have been incorporated to provide a spatially second-order-accurate scheme in physical space. The scheme is conservative at steady state but employs nonconservative differencing during the integration to steady state to allow incorporation of implicit boundary conditions in the farfield. A zero-equation eddy viscosity model has been employed to represent the effects of turbulence. The code is validated by comparisons with flat plate and NACA 0012 data. Excellent results were obtained for both attached flow and shock induced separation cases. Numerical results are also presented for transonic flow over an unconventional airfoil and show good agreement.

The goal of this research is to produce a robust, parabolized Navier-Stokes (PNS) code that will significantly reduce the computer time required to calculate flows about complex vehicles with embedded subsonic/separated regions. The major drawback of "current day" PNS codes is that they cannot be used to compute separated regions which occur near canopies, wing-body junctures, etc. As a result, Navier-Stokes (NS) codes are often used to compute the entire flowfield despite the fact that a PNS code requires at least one order of magnitude less computer time and storage;An innovative approach has been developed to permit a PNS code to compute embedded regions that cause upstream influence. In this approach, the embedded region is automatically detected and the streamwise extent is determined prior to the computation or while the computation is in progress. The PNS equations are then solved with an iterative (IPNS) algorithm in this region to duplicate the results that would he obtained with a NS code. Once the embedded region is computed, the algorithm returns to the standard space-marching PNS mode until the next embedded region is encountered. This method has been incorporated into NASA's upwind PNS (UPS) code and validated by applying it to several 2-D test cases. These test cases include flows over compression ramps, shock-boundary-layer interactions, flows over expansion corners, and flow over a general geometry with multiple embedded regions. The results computed using this approach are in excellent agreement with NS computations and experimental data;In addition, new correlation functions have been developed that accurately predict the streamwise extent of the embedded regions for all of the geometries considered. This is the first time that any correlation (theoretical or empirical) has been shown to accurately predict where the single-sweep PNS method is inaccurate for a wide range of flow conditions. These correlation functions in conjunction with the IPNS algorithm permit completely automatic computation of steady, laminar supersonic flowfields with embedded subsonic/separated regions using a space-marching code as the primary flow solver.