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At least 325 records · Page 18

On the rates of convergence of the finite element method

The rate of convergence of the finite element method is a function of the strategy by which the number of degrees-of-freedom are increased. Alternative strategies are examined in the light of recent theoretical results and computational experience.

Babuska, I.↗

Acoustic propagation in partially choked converging-diverging ducts

A computer model based on the wave-envelope technique is used to study acoustic propagation in converging-diverging hard walled and lined circular ducts carrying near sonic mean flows. The influences of the liner admittance, boundary layer thickness, spinning mode number, and mean Mach number are considered. The numerical results indicate that the diverging portion of the duct can have a strong reflective effect for partially choked flows.

Kelly, J. J.↗

Investigation of installation effects of single-engine convergent-divergent nozzles

An investigation was conducted in the Langley 16-Foot Transonic Tunnel to determine installation effects on single-engine convergent-divergent nozzles applicable to reduced-power supersonic cruise aircraft. Tests were conducted at Mach numbers from 0.50 to 1.20, at angles of attack from -3 degrees to 9 degrees, and at nozzle pressure ratios from 1.0 (jet off) to 8.0. The effects of empennage arrangement, nozzle length, a cusp fairing, and afterbody closure on total aft-end drag coefficient and component drag coefficients were investigated. Basic lift- and drag-coefficient data and external static-pressure distributions on the nozzle and afterbody are presented and discussed.

Burley, J. R., II↗

Convergence acceleration of viscous flow computations

A multiple-grid convergence acceleration technique introduced for application to the solution of the Euler equations by means of Lax-Wendroff algorithms is extended to treat compressible viscous flow. Computational results are presented for the solution of the thin-layer version of the Navier-Stokes equations using the explicit MacCormack algorithm, accelerated by a convective coarse-grid scheme. Extensions and generalizations are mentioned.

Johnson, G. M.↗

A static investigation of yaw vectoring concepts on two-dimensional convergent-divergent nozzles

The flow-turning capability and nozzle internal performance of yaw-vectoring nozzle geometries were tested in the NASA Langley 16-ft Transonic wind tunnel. The concept was investigated as a means of enhancing fighter jet performance. Five two-dimensional convergent-divergent nozzles were equipped for yaw-vectoring and examined. The configurations included a translating left sidewall, left and right sidewall flaps downstream of the nozzle throat, left sidewall flaps or port located upstream of the nozzle throat, and a powered rudder. Trials were also run with 20 deg of pitch thrust vectoring added. The feasibility of providing yaw-thrust vectoring was demonstrated, with the largest yaw vector angles being obtained with sidewall flaps downstream of the nozzle primary throat. It was concluded that yaw vector designs that scoop or capture internal nozzle flow provide the largest yaw-vector capability, but decrease the thrust the most.

Berrier, B. L.↗

Investigation of installation effects on twin-engine convergent-divergent nozzles

An investigation was conducted in the Langley 16-Foot Transonic Tunnel to determine installation effects on convergent-divergent nozzles applicable to twin-engine reduced-power supersonic cruise aircraft. Tests were conducted at Mach numbers from 0.50 to 1.20, angles of attack from -5 deg to 9 deg, and at nozzle pressure ratios from jet off (1.0) to 8.0. The effects of empennage arrangement, nozzle length, and afterbody closure on total and component drag coefficients were investigated.

Bare, E. A.↗

Stability and Convergence of Underintegrated Finite Element Approximations

The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.

Oden, J. T.↗

Determination of rainfall and condensational heating in the South Pacific convergence zone during FGGE SOP-1

The role of cloud related diabatic processes in maintaining the structure of the South Pacific Convergence Zone is discussed. The method chosen to evaluate the condensational heating is a diagnostic cumulus mass flux technique which uses GOES digital IR data to characterize the cloud population. This method requires as input an estimate of time/area mean rainfall rate over the area in question. Since direct observation of rainfall in the South Pacific is not feasible, a technique using GOES IR data is being developed to estimate rainfall amounts for a 2.5 degree grid at 12h intervals.

Robertson, F. R.↗

A two-dimensional analysis of laser heat addition in converging nozzles

The two-dimensional equations of motion describing the interaction between a laser beam and a flowing gas are considered. An implicit numerical scheme is used to solve these equations for unchoked flow through a converging-diverging nozzle. Separate grids are used for the fluid dynamics and the radiation equations. The effects of beam focusing and cross-beam intensity profiles are included. The calculations are based upon real gas properties for all quantities except the gas absorptivity, which is taken as a constant. The solutions contain the expected hot central core region with cool gas near the walls. This results in steep temperature gradients in both the streamwise and cross-stream directions. The absorption zone acts as a blockage in the nozzle causing a nonuniform velocity profile at the inlet and an overall decrease in mass flow. The absorption region also forces the streamlines to move away from the axis of symmetry, although this effect is not strong.

Molvik, G. A.↗

Accelerated convergence for incompressible flow calculations

Two improved algorithms which solve the steady-state Navier-Stokes equations, PISO and SIMPLER, are studied. Computations were carried out on progressively finer grids for the driven cavity and flow over a backward-facing step. The effects of relaxation factor, number of grid nodes and number of sweeps through the pressure equations are studied to evaluate the performance of the PISO and SIMPLER schemes. Results show that these improved schemes accelerate the convergence rate of the solution generally by a factor of two as compared to the SIMPLE method.

Neely, G. M.↗

Theory versus experiment for the rotordynamic coefficients of annular gas seals. Part 2: Constant clearance and convergent-tapered geometry

The leakage and rotordynamic coefficients of constant-clearance and convergent-tapered annular gas seals were measured in an experimental test facility. The results are presented along with the theoretically predicted values. Of particular interest is the prediction that optimally tapered seals have significantly larger direct siffness than straight seals. The experimental results verify this prediction. Generally the theory does quite well, but fails to predict the large increase in direct stiffness when the fluid is pre-rotated.

Nelson, C. C.↗

A convergent series expansion for hyperbolic systems of conservation laws

The discontinuities piecewise analytic initial value problem for a wide class of conservation laws is considered which includes the full three-dimensional Euler equations. The initial interaction at an arbitrary curved surface is resolved in time by a convergent series. Among other features the solution exhibits shock, contact, and expansion waves as well as sound waves propagating on characteristic surfaces. The expansion waves correspond to he one-dimensional rarefactions but have a more complicated structure. The sound waves are generated in place of zero strength shocks, and they are caused by mismatches in derivatives.

Harabetian, E.↗

On the convergence of difference approximations to scalar conservation laws

A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Osher, S.↗

Accelerated convergence for incompressible flow calculations

Two improved algorithms which solve the steady-state Navier-Stokes equations, PISO and SIMPLER, are studied. Computations were carried out on progressively finer grids for the driven cavity and flow over a backward-facing step. The effects of relaxation factor, number of grid nodes and number of sweeps through the pressure equations are studied to evaluate the performance of the PISO and SIMPLER schemes. Results show that these improved schemes accelerate the convergence rate of the solution generally by a factor of two as compared to the SIMPLE method.

Neely, G. M.↗

On convergence of computation of chemically reacting flows

The computational problems associated with high-temperature flows undergoing finite-rate ionization reactions is investigated. The conservation equations governing chemical species and vibrational and electron energies are solved simultaneously with those for overall mass, momentum, and energy for a one-dimensional subsonic flow, through a constant-area duct, originating behind a normal shock wave, using an implicit time-marching technique. Boundary conditions are imposed in the form of characteristic wave variables accounting for the effects of chemical reactions on the speed of sound. Converging solutions are obtained for cases in which chemical reactions are weak, but difficulty is encountered in other cases. The cause of the difficulty is investigated and shown to be the sharp pressure disturbances produced by such reactions.

Park, C.↗

Cyclone development in the South Pacific convergence zone during FGGE, 10-17 January 1979

An analysis is presented of the life cycles of three different South Pacific cyclones. Emphasis is given to two of the cyclones which propagate south-eastward along the western edge of the South Pacific convergence zone (SPCZ) and reach middle latitudes before decaying. The analysis is based on imagery from the GOES-West Satellite and on data from the European Center for Medium Range Weather Forecasts (EMWF). A comparison between estimates of the mean sea level pressure in the vicinity of the cyclones taken at observation stations and from ECMWF predictions shows good agreement when the cyclone disturbances are above grid-scale. The propagation characteristics of the cyclones are discussed in detail.

Vincent, D. G.↗