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.

The objective of this study is to obtain a better understanding of the fundamental mechanisms governing the unsteady flow past airfoil leading edges. The approach taken is to study the leading edge in isolation and to use the semi-infinite parabola as a model for the leading-edges of conventional airfoils. Numerical solution methods were developed and implemented for the two-dimensional, unsteady, incompressible Navier-Stokes and boundary-layer equations for arbitrary motion of the parabola. Navier-Stokes solutions of the impulsively-started flow past a stationary parabola and of the flow past a pitching parabola compare well with the corresponding computational results for the NACA0012 airfoil. Navier-Stokes solutions for the pitching leading edge were obtained for chord Reynolds numbers up to half-a-million. The sequence of events leading to the unsteady breakaway of the boundary layer, in both the impulsive and pitchup cases, was qualitatively similar for the range of Reynolds numbers considered;We show using Navier-Stokes simulations that small perturbations in the flow field can lead to the formation of eddies in the boundary layer before flow reversal occurs in the base flow. The cases considered here are impulsive changes in the angle of attack, smooth but rapid variations in the angle of attack and introduction of small-amplitude inviscid vortices in the freestream. This type of eddy creation prior to base-flow reversal is a feature of the high-frequency Rayleigh instability. A study of the Reynolds-number scaling of the wavelength of these instabilities yielded a value reasonably close to that predicted by theory. A linear stability analysis of the boundary layer over the parabola was carried out to map the neutral curve for the Rayleigh instability. Preliminary indications are that the disturbances that lead to the eddies in the Navier-Stokes simulations are being initiated within the linearly unstable region bounded by the neutral curve. The linear stability analysis showed that the Rayleigh instability occurs a little after boundary layer velocity profiles become inflectional but much before flow reversal sets in.

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.

Use of composite materials is growing rapidly because they offer weight reduction, durability and better fatigue life as compared to metals. Despite of their advantages, there are some problems associated with the use of composites, and impact resistance is one of the weak areas in composites. Low speed impact damage has been the focus of attention of researchers for quite some time but studies of high speed impact damage is still in its preliminary stages. In this study, effects of ballistic impact on thin and thick composite panels were investigated. Damage due to high speed impact in composites is a complex phenomenon and it is difficult to analytically model all the events taking place during the impact;An experimental approach was used to study the damage from high speed impact and the Finite Element analysis was performed to understand the damage sequence. Thin symmetric quasi-isotropic and cross-ply laminates consisting of up to 16 layers were studied using experimental vibration and Finite Element analysis. It was found that frequency response of damaged plates is dependent on the stacking sequence of the laminate. Results also show that the natural frequencies of the damaged plates decrease for few initial modes and increase for some of the higher modes. It was observed that cross-ply laminates exhibit very little effect on the natural frequencies due to damage;Thick symmetric quasi-isotropic and cross-ply laminates consisting of 56 plies were also studied. Results demonstrate that damage size is dependent more on the shape and size of the impactor, rather than the impact energy. Faster bullets cause less damage as compared to slower bullets. Damage was found to be dependent on stacking sequence of the laminate. Cross-ply laminates suffer more damage than the quasi-isotropic laminates. Damage is dependent on the thickness of the laminate and is more in thicker laminates. Damage is always more towards the exit side than the entry surface;A model of bullet penetration into a composite laminate is presented and the failure due to inter-laminar shear stresses was explained through this model. The model was verified using a quasi-static Finite Element analysis. It was demonstrated that outer-most ply of the laminate fails first and maximum inter-laminar shear stresses occur between two outer-most plies, causing delamination. It was also demonstrated that inter-laminar shear stresses increase progressively, as the number of effective plies in the laminate reduce due to failure and it is strongly dependent on the stacking sequence.

The details of an interacting boundary layer algorithm capable of calculating large scale laminar separation past airfoils at low speeds is given. Rationale behind various convergence acceleration methods is given. It is shown that linear based acceleration methods are limited to 50% savings in convergence rate. A nonlinear extrapolation method is proposed and tested on two simple model problems. Savings exceed the 50% limitation of the previous methods. Boundary layer results for laminar flow past symmetric airfoils at zero incidence are presented as a test of the methods. Leading edge marginal separation results at finite Reynolds numbers are presented. Richardson extrapolation of successive calculations is used to improve accuracy. Results for a zero thickness uncambered plate at angle of attack are presented.

A time accurate compressible interactive boundary layer procedure for airfoils using the quasi-simultaneous method of Veldman is developed. It couples the high frequency transonic small disturbance equation with the complete set of unsteady compressible boundary equations in Levy-Lees variable form, using a pseudo-time derivative of displacement thickness for enhanced stability. Included is a simple procedure for time accurately updating the viscous wake location. The basis of the interaction is an extension of the asymptotic matching condition of Davis for unsteady compressible interaction. This analysis identifies several possible unsteady transonic separation structures and highlights the importance of the pseudo-time derivative in stabilizing the interaction. The method is applied to oscillating airfoils experiencing light shock-induced stall. Comparisons are made with several standard turbulence models. Shock-induced oscillatory flow about the 18% circular arc airfoil is investigated with this method and found to be modeled quite accurately.

Various Minimum-Time Turning Maneuvers for two high angle-of-attack, six-degree-of-freedom, aircraft models have been investigated. The primary aircraft model is for a nonlinear 6-DOF F-16 fighter aircraft with high angle-of-attack maneuverability. The other model is for a linearized 6-DOF F-18 fighter which also can be flown in the high angle-of-attack range. Standard 6-DOF equations are employed except that the Quaternion attitude representation system is used instead of Euler Angles to avoid the pitch angle singularity of Euler Angles;These Optimal Control problems have been transformed into Nonlinear Programming problems via Parameter Optimization techniques. Different parameterization techniques were tested on the Van der Pol Problem and Soliman's Problem and their variations before applying them on the main turning problems. These techniques include Control Parameterization and State Parameterization (Inverse Dynamics Approach). Also, a novel Control-Integration Method is proposed to find the discontinuous control history of the possible Singular Arc Problems. Different ways to deal with various types of constraints are also discussed. In particular, when dealing with path constraints of the original optimal control problems, an Extreme-Bounds-on-Intervals method was created. However, it has not been actually developed and tested. The resulting sparse Hessian matrix from this method can speed up the calculations if a specially arranged NLP code is used;The Sequential Quadratic Programming method is primarily relied on to search for the optimum. Several different performance indices are utilized, including 3-D minimum-time-to-turn and 3-D minimum-time-to-half-loop. Several new solutions for these maneuvers are obtained. Moreover, since multiple local minima are present, several global optimization schemes have been studied. A Genetic Algorithm, Adaptive Simulated Annealing, and a Hybrid method which combines the merits of both genetic algorithms and sequential quadratic programming have been used to find the global optimum.