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The thin-layer Navier-Stokes equations are coupled with a zonal scheme (or domain-decomposition method) to develop the Transonic Navier-Stokes (TNS) wing-alone code. TNS has a total of four zones and is extended to a total of 16 zones for the wing-fuselage version of the code. Results are computed on the Cray X-MP-48 and compared with experimental data.
A ray-shooting approach is presented for calculating the interior radar cross section (RCS) from a partially open cavity. In the problem considered, a dense grid of rays is launched into the cavity through the opening. The rays bounce from the cavity walls based on the laws of geometrical optics and eventually exit the cavity via the aperture. The ray-bouncing method is based on tracking a large number of rays launched into the cavity through the opening and determining the geometrical optics field associated with each ray by taking into consideration (1) the geometrical divergence factor, (2) polarization, and (3) material loading of the cavity walls. A physical optics scheme is then applied to compute the backscattered field from the exit rays. This method is so simple in concept that there is virtually no restriction on the shape or material loading of the cavity. Numerical results obtained by this method are compared with those for the modal analysis for a circular cylinder terminated by a PEC plate. RCS results for an S-bend circular cylinder generated on the Cray X-MP supercomputer show significant RCS reduction. Some of the limitations and possible extensions of this technique are discussed.
A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.
The implementation and performance of a finite-difference algorithm for the compressible Navier-Stokes equations in two or three dimensions on the Connection Machine are described. This machine is a single-instruction multiple-data machine with up to 65536 physical processors. The implicit portion of the algorithm is of particular interest. Running times and megadrop rates are given for two- and three-dimensional problems. Included are comparisons with the standard codes on a Cray X-MP/48.
A CFD technique is described in which the finite-rate chemistry in thermal and chemical nonequilibrium air is fully and implicitly coupled with the fluid motion. Developed for use in the suborbital hypersonic flight speed range, the method accounts for nonequilibrium vibrational and electronic excitation and dissociation, but not ionization. The steady-state solution to the resulting system of equations is obtained by using a lower-upper factorization and symmetric Gauss-Seidel sweeping technique through Newton iteration. Inversion of the left-hand-side matrices is replaced by scalar multiplications through the use of the diagonal dominance algorithm. The code, named CENS2H (Compressible-Euler-Navier-Stokes Two-Dimensional Hypersonic), is fully vectorized and requires about 8.8 x 10 to the -5th sec per node point per iteration using a Cray X-MP computer. Converged solutions are obtained after about 2400 iterations. Sample calculations are made for a circular cylinder and a 10 percent airfoil at 5 deg angle of attack. The calculated cylinder flow field agrees with that obtained experimentally. The code predicts a 10 percent change in lift, drag, and pitching moment for the airfoil due to the thermochemical phenomena.
An efficient particle simulation technique, developed for use on vector architecture based supercomputers for studying hypersonic rarefied gas flows is employed to simulate the complex wake generated by Mach six flow over a 10 deg half-angle wedge for freestream Reynolds numbers of 1780 and 3560. Data obtained are compared against higher Reynolds number experimental results. Simulations utilized as many as 10 to the 5th computational cells and 10 to the 7th simulated particles having power-law interaction potentials. A code performance of 1.8-2.4 microsec of Cray-2 CPU time to process a single particle per timestep is achieved. Diffuse adiabatic and isothermal wedge surface models are used in this investigation. Although the wedge geometry is two-dimensional, the simulation incorporates a width-wise direction, resulting in a three-dimensional computation.
A modified artificial compressibility formulation is derived from a preconditioned low Mach number compressible formulation, and these two methods are compared on a two-dimensional laminar leading edge flow using a LBI/ADI solution algorithm. The two methods are essentially equivalent with appropriate preconditioning parameters and have the same convergence rates and efficiency, giving 4 orders of residual reduction in about 75 iterations with a vectorized CRAY-XMP run time of 20 seconds for 3000 grid points.
The fully three-dimensional, time-dependent compressible Navier-Stokes equations in cylindrical coordinates are presently used, in conjunction with the multistage Runge-Kutta numerical integration scheme for solution of the governing flow equations, to simulate complex flowfields within turbomechanical components whose pertinent effects encompass those of viscosity, compressibility, blade rotation, and tip clearance. Computed results are presented for selected cascades, emphasizing the code's capabilities in the accurate prediction of such features as airfoil loadings, exit flow angles, shocks, and secondary flows. Computations for several test cases have been performed on a Cray-YMP, using nearly 90,000 grid points.
The incompressible Navier-Stokes equations are numerically solved for steady flow around an ogive-cylinder (fineness ration 4.5) at angle of attack. The three-dimensional vortical flow is investigated with emphasis on the tip and the near wake region. The implicit, finite-difference computation is performed on the CRAY X-MP computer using the method of pseudo-compressibility. Comparisons of computational results with results of a companion towing tank experiment are presented for two symmetric leeside flow cases of moderate angles of attack. The topology of the flow is discussed and conclusions are drawn concerning the growth and stability of the primary vortices.
Data analysis and numerical modeling efforts that are related to the 1986 Satellite Precipitation and Cloud Experiment (SPACE) are discussed. Progress during this period includes the following: further testing and development of the RAMS numerical modeling system on the Alabama CRAY X-MP/24; a continuation of the observational analysis of the 13 July 1986 mesoscale convective system (MCS); and an initial investigation of a small MCS that formed over the COHMEX region on 15 July 1986. Details for each of these individual tasks are given.
The Rai ROTOR1 code for two-dimensional, unsteady viscous flow analysis was applied to a supersonic throughflow fan stage design. The axial Mach number for this fan design increases from 2.0 at the inlet to 2.9 at the outlet. The Rai code uses overlapped O- and H-grids that are appropriately packed. The Rai code was run on a Cray XMP computer; then data postprocessing and graphics were performed to obtain detailed insight into the stage flow. The large rotor wakes uniformly traversed the rotor-stator interface and dispersed as they passed through the stator passage. Only weak blade shock losses were computerd, which supports the design goals. High viscous effects caused large blade wakes and a low fan efficiency. Rai code flow predictions were essentially steady for the rotor, and they compared well with Chima rotor viscous code predictions based on a C-grid of similar density.
The objective is to present the activities at TRW in developing the capability to simulate the behavior of large flexible multibody space structures. The features of the simulation tools are: (1) to accommodate all rigid/flexible body degrees-of-freedom which incorporate the control system models and external forces, (2) to provide the flexibility to incorporate engineering-defined models and to retain parameters of significance to the engineer, (3) to reduce the computation cost by one order of magnitude (two orders of magnitude compared to a CRAY 1S), and (4) to keep it versatile so that radical variations in anticipated space structures can be accommodated. The current computer tools to simulate multibody systems appear not only to be very costly and time consuming, but also do not produce the desired fidelity of the mathematical models. In summary, a multibody simulation tool will be developed in the near future which will allow solution of the dynamics and controls of the deployment of the LDR backup structure, or the problem associated with the robotic assembly of the structure. The tools will allow the engineer to define the modeling technique and solve problems in less time and at reduced cost.
A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi) = (M)(phi)(omega), where (K) and (M) are of order N, and (omega) is order of q. The concurrent solution of the eigenproblem is based on the multifrontal/modified subspace method and is achieved in a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm was successfully implemented on a tightly coupled multiple-instruction multiple-data parallel processing machine, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macrotasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. A parallel finite element dynamic analysis program, p-feda, is documented and the performance of its subroutines in parallel environment is analyzed.
With the present availability of parallel processors of vastly different architectures, there is a need for a common language interface to multiple types of machines. The parallel C compiler, currently under development, is intended to be such a language. This language is based on the belief that an algorithm designed around fine-grained parallelism can be mapped relatively easily to different parallel architectures, since a large percentage of the parallelism has been identified. The compiler generates a FORTH-like machine-independent intermediate code. A machine-dependent translator will reside on each machine to generate the appropriate executable code, taking advantage of the particular architectures. The goal of this project is to allow a user to run the same program on such machines as the Massively Parallel Processor, the CRAY, the Connection Machine, and the CYBER 205 as well as serial machines such as VAXes, Macintoshes and Sun workstations.
A parallel algorithm for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi)=(M)(phi)(omega), where (K) and (M) are of order N, and (omega) is of order q is presented. The parallel algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm has been successfully implemented on a tightly coupled multiple-instruction-multiple-data (MIMD) parallel processing computer, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor, or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macro-tasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18 and 3.61 are achieved on two, four, six and eight processors, respectively.
The Bunch-Kaufman algorithm is the method of choice for factoring symmetric indefinite matrices in many applications. However, the Bunch-Kaufman algorithm does not take advantage of high-performance architectures such as the Cray Y-MP. Three new algorithms, based on Bunch-Kaufman factorization, that take advantage of such architectures are described. Results from an implementation of the third algorithm are presented.
The background response of a gas ionizing proportional x ray detector is estimated by solving the one dimensional photon transport equation for two regions using Monte Carlo techniques. The solution was effected using the SSL VAX 780 and the CRAY XMP computers at Marshall Space Flight Center. The isotropic photon energy spectrum encompassing the range from 1 to 1000 KeV incident onto the first region, the shield, is taken so as to represent the measured spectrum at an altitude of 3 mb over Palastine, Texas. The differential energy spectrum deposited in the gas region, xenon, over the range of 0 to 100 KeV is written to an output file. In addition, the photon flux emerging from the shield region, tin, over the range of 1 to 1000 KeV is also tabulated and written to a separate file. Published tabular cross sections for photoelectric, elastic and inelastic Compton scattering as well as the total absorption coefficient are used. Histories of each incident photon as well as secondary photons from Compton and photoelectric interactions are followed until the photon either is absorbed or exits from the regions under consideration. The effect of shielding thickness upon the energy spectrum deposited in the xenon region for this background spectrum incident upon the tin shield was studied.
The Integrated Structural Modeling (ISM) program is being developed for the Air Force Weapons Laboratory and will be available for Air Force work. Its goal is to provide a design, analysis, and simulation tool intended primarily for directed energy weapons (DEW), kinetic energy weapons (KEW), and surveillance applications. The code is designed to run on DEC (VMS and UNIX), IRIS, Alliant, and Cray hosts. Several technical disciplines are included in ISM, namely structures, controls, optics, thermal, and dynamics. Four topics from the broad ISM goal are discussed. The first is project configuration management and includes two major areas: the software and database arrangement and the system model control. The second is interdisciplinary data transfer and refers to exchange of data between various disciplines such as structures and thermal. Third is a discussion of the integration of component models into one system model, i.e., multiple discipline model synthesis. Last is a presentation of work on a distributed processing computing environment.