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The use of a fitted-shock multidomain spectral method for solving the time-dependent Euler equations of gasdynamics is described. The multidomain method allows short spatial scale features near the shock to be resolved throughout the calculation. Examples presented are of a shock-plane wave, shock-hot spot and shock-vortex street interaction.
A numerically exact spectral method for solving the time-dependent Schroedinger equation in spherical coordinates is described. The angular dependence of the wave function is represented on a two-dimensional grid of evenly spaced points. The fast Fourier transform algorithm is used to transform between the angle space representation of the wave function and its conjugate representation in momentum space. The time propagation of the wave function is evaluated using an expansion of the time evolution operator as a series of Chebyshev polynomials. Calculations performed for a model system representing H2 scattering from a rectangular corrugated surface yield transition probabilities that are in excellent agreement with those obtained using the close-coupling wave packet (CCWP) method. However, the new method is found to require substantially more computation time than the CCWP method because of the large number of grid points needed to represent the angular dependence of the wave function and the variation in the number of terms required in the Chebyshev representation of the time evolution operator.
A finite difference code was implemented for the compressible Navier-Stokes equations on the Connection Machine, a massively parallel computer. The code is based on the ARC2D/ARC3D program and uses the implicit factored algorithm of Beam and Warming. The codes uses odd-even elimination to solve linear systems. Timings and computation rates are given for the code, and a comparison is made with a Cray XMP.
A parametric study is presented to investigate the effect of reduced frequency of the leading-edge flaps on the locally-conical, unsteady, supersonic flow around a delta wing. This study covers symmetric and antisymmetric forced oscillation of the leading-edge flaps. The effects of the freestream Mach number and angle of attack are also presented. The problem is solved using time-accurate integration of the unsteady, compressible, thin-layer Navier-Stokes equations and the unsteady, linearized, Navier-displacement equations. The delta wing is of aspect ratio of 1.5 and its leading-edge flaps are hinged at 65 percent of the local-half span length. The reduced frequency is varied between 2 pi and pi/2. Two supersonic flow conditions have been investigated; the first is for a freestream Mach number of 2.4 and an angle of attack of 19 deg and the second is for a freestream Mach number of 1.5 and an angle attack of 15 deg.
A detailed numerical study of two-dimensional flow past a circular cylinder at moderately low Reynolds numbers was conducted using three different numerical algorithms for solving the time-dependent compressible Navier-Stokes equations. It was found that if the algorithm and associated boundary conditions were consistent and stable, then the major features of the unsteady wake were well-predicted. However, it was also found that even stable and consistent boundary conditions could introduce additional periodic phenomena reminiscent of the type seen in previous wind-tunnel experiments. However, these additional frequencies were eliminated by formulating the boundary conditions in terms of the characteristic variables. An analysis based on a simplified model provides an explanation for this behavior.
The proposed kinetic model for condensation under homogeneous conditions, and the onset of unidirectional cluster growth in supersaturated gases, does not suffer from the conceptual flaws that characterize classical nucleation theory. When a full set of simultaneous rate equation is solved, a characteristic time emerges, for each cluster size, at which the production rate, and its rate of conversion to the next size (n + 1) are equal. Procedures for estimating the essential parameters are proposed; condensation fluxes J(kin) exp ss are evaluated. Since there are practical limits to the cluster size that can be incorporated in the set of simultaneous first-order differential equations, a code was developed for computing an approximate J(th) exp ss based on estimates of a 'constrained equilibrium' distribution, and identification of its minimum.
A finite element absorbing boundary condition (FE-ABC) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. In contrast to the node-based elements, edge elements can treat geometries with sharp edges, are divergence-less, and easily satisfy the field continuity condition across dielectric interfaces. They do, however, lead to a higher unknown count but this is balanced by the greater sparsity of the resulting finite element matrix. Thus, the computation time required to solve such a system iteratively with a given degree of accuracy is less than the traditional node-based approach. The purpose is to examine the derivation and performance of the ABC's when applied to 2-D and 3-D problems and to discuss the specifics of our FE-ABC implementation.
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.
The generation of long-wavelength, viscous-inviscid interactive Goertler vortices is studied in the linear regime by numerically solving the time-dependent governing equations. It is found that time-dependent surface deformations, which assume a fixed nonzero shape at large times, generate steady Goertler vortices that amplify in the downstream direction. Thus, the Goertler instability in this regime is shown to be convective in nature, contrary to the earlier findings of Ruban and Savenkov. The disturbance pattern created by steady and streamwise-elongated surface obstacles on a concave surface is examined in detail, and also contrasted with the flow pattern due to roughness elements with aspect ratio of order unity on flat surfaces. Finally, the applicability of the Briggs-Bers criterion to unstable physical systems of this type is questioned by providing a counterexample in the form of the inviscid limit of interactive Goertler vortices.
An efficient multiblock Euler design code was developed for designing a nacelle installed on geometrically complex airplane configurations. This approach employed a design driver based on a direct iterative surface curvature method developed at LaRC. A general multiblock Euler flow solver was used for computing flow around complex geometries. The flow solver used a finite-volume formulation with explicit time-stepping to solve the Euler Equations. It used a multiblock version of the multigrid method to accelerate the convergence of the calculations. The design driver successively updated the surface geometry to reduce the difference between the computed and target pressure distributions. In the flow solver, the change in surface geometry was simulated by applying surface transpiration boundary conditions to avoid repeated grid generation during design iterations. Smoothness of the designed surface was ensured by alternate application of streamwise and circumferential smoothings. The capability and efficiency of the code was demonstrated through the design of both an isolated nacelle and an installed nacelle at various flow conditions. Information on the execution of the computer program is provided in volume 2.
The evaporation and combustion of a single droplet under forced and natural convection was studied numerically from first principles using a numerical scheme that solves the time-dependent multiphase and multispecies Navier-Stokes equations and tracks the sharp gas-liquid interface cutting across an arbitrary Eulerian grid. The flow fields both inside and outside of the droplet are resolved in a unified fashion. Additional governing equations model the interphase mass, energy, and momentum exchange. Test cases involving iso-octane, n-hexane, and n-propanol droplets show reasonable comparison rate, and flame stand-off distance. The partially validated code is, thus, readied to be applied to more demanding droplet combustion situations where substantial drop deformation render classical models inadequate.
The results of a numerical investigation to predict the flow field including wakes and mixing in axial-flow compressor rotors are presented. The wake behavior in a moderately loaded compressor rotor is studied numerically using a 3D incompressible Navier-Stokes solver with a high Reynolds number form of a turbulence model. The equations are solved using a time dependent implicit technique. The agreement between the measured data and the predictions is good; including the blade boundary-layer profiles, wake mean-velocity profiles, and decay. The ability of the pseudocompressibility scheme to predict the entire flow field including the near and far wake profiles and its decay characteristics, effect of loading, and the viscous losses of a 3D rotor flow field are demonstrated. The mixing in the downstream regions away from the hub and annulus walls is dominated by wake diffusion. In regions away from the walls the radial mixing is predominantly caused by the transport of mass, momentum, and energy by the radial component of velocity in the wake.
A parallel trajectory optimization algorithm is being developed. One possible mission is to provide real-time, on-line guidance for the National Aerospace Plane. The algorithm solves a discrete-time problem via the augmented Lagrangian nonlinear programming algorithm. The algorithm exploits the dynamic programming structure of the problem to achieve parallelism in calculating cost functions, gradients, constraints, Jacobians, Hessian approximations, search directions, and merit functions. Special additions to the augmented Lagrangian algorithm achieve robust convergence, achieve (almost) superlinear local convergence, and deal with constraint curvature efficiency. The algorithm can handle control and state inequality constraints such as angle-of-attack and dynamic pressure constraints. Portions of the algorithm have been tested. The nonlinear programming core algorithm performs well on a variety of static test problems and on an orbit transfer problem. The parallel search direction algorithm can reduce wall clock time by a factor of 10 for this part of the computation task.
Transient solutions were obtained for cooling a semitransparent material by radiation and conduction. The layer is in a vacuum environment so the only means for heat dissipation is by radiation from within the medium leaving through the boundaries. Heat conduction serves only to partially equalize temperatures across the layer. As the optical thickness is increased, steep temperature gradients exist near the boundaries when conduction is relatively small. A solution procedure is required that will provide accurate temperature distributions adjacent to the boundaries, or radiative heat losses will be in error. The approach utilized numerical Gaussian integration to obtain the local radiative source term, and a finite difference procedure with variable space and time increments to solve the transient energy equation.
Consideration is given to control formulations for vibration suppression of an active structure in slewing motions, the use if distributed sensing in control of large flexible spacecraft, an improved shooting method for solving minimum-time maneuver problems, and nonlinear slew maneuver dynamics of large flexible spacecrafts. Attention is also given to initial experiments in trusterless locomotion control of a free-flying robot, dynamic analysis to evaluate viscoelastic passive damping augmentation for the Space Shuttle Remote Manipulator System, initial experiments in cooperative manipulation from a moving platform, and intelligent pipelined control architecture for remote robotic applications.
The structure and characteristics of gaseous confined laminar diffusion flames are investigated by numerically solving the time-dependent two-dimensional axisymmetric conservation equations. The numerical model accounts for the important chemical and physical processes involved, including axial diffusion, viscous effects, radial convection, and finite-rate chemistry. The numerical results clearly show that the flame has a finite thickness and leakage of fuel vapor into the flame zone is possible. The effect of heat release is found to induce some radial flow. Predicted flame shape and dimensions are compared to the classical Burke-Schumann flame. The numerically calculated flame is observed to be about 15 percent taller and 5 percent narrower than that of the Burke-Schumann solution under the same conditions.
A numerical solution to the 20-moment set of transport equations has been found in order to study subauroral ionospheric outflows during periods of enhanced perpendicular ion drifts. The numerical model solves the time-dependent O(+) density, momentum, and both the parallel and perpendicular energy and heat flow equations in the 200-6000 km altitude range. Assuming perpendicular drifts of 3 km/s relative to the neutral atmosphere, we have found that anisotropic heating of O(+) (a result of ion-neutral collisions) leads to a temperature anisotropy, with perpendicular temperatures exceeding 8000 K and parallel temperatures greater than 5000 K (near 200 km altitude). Above approximately 2000 km, transport processes dominate the effects of collisions and wavelike oscillations in O(+) velocity, temperature and heat flux were noted.
An efficient multiblock Euler design method was developed for designing a nacelle installed on geometrically complex airplane configurations. This approach employed a design module based on a direct iterative surface curvature method developed at NASA-Langley. A multiblock Euler flow solver was used for computing flow around complex geometries. The flow solver used a finite-volume formulation with explicit time-stepping to solve the Euler equations. It used a multiblock version of the multigrid method to accelerate the convergence of the calculations. The design module successively updated the surface geometry to reduce the difference between the computed and target pressure distributions. In the flow solver, the change in surface geometry was simulated by applying surface transpiration boundary conditions to avoid repeated grid generation during design iterations. Smoothness of the designed surface was ensured by alternate application of streamwise and circumferential smoothings.