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NASA NTRS1993

The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows

We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.

Lufkin, Eric A.↗

NASA NTRS1999

An Efficient Objective Analysis System for Parallel Computers

A new atmospheric objective analysis system designed for parallel computers will be described. The system can produce a global analysis (on a 1 X 1 lat-lon grid with 18 levels of heights and winds and 10 levels of moisture) using 120,000 observations in 17 minutes on 32 CPUs (SGI Origin 2000). No special parallel code is needed (e.g. MPI or multitasking) and the 32 CPUs do not have to be on the same platform. The system is totally portable and can run on several different architectures at once. In addition, the system can easily scale up to 100 or more CPUS. This will allow for much higher resolution and significant increases in input data. The system scales linearly as the number of observations and the number of grid points. The cost overhead in going from 1 to 32 CPUs is 18%. In addition, the analysis results are identical regardless of the number of processors used. This system has all the characteristics of optimal interpolation, combining detailed instrument and first guess error statistics to produce the best estimate of the atmospheric state. Static tests with a 2 X 2.5 resolution version of this system showed it's analysis increments are comparable to the latest NASA operational system including maintenance of mass-wind balance. Results from several months of cycling test in the Goddard EOS Data Assimilation System (GEOS DAS) show this new analysis retains the same level of agreement between the first guess and observations (O-F statistics) as the current operational system.

Stobie, J.↗

NASA NTRS2012

TRMM Version 7 Level 3 Gridded Monthly Accumulations of GPROF Precipitation Retrievals

In July 2011, improved versions of the retrieval algorithms were approved for TRMM. All data starting with June 2011 are produced only with the version 7 code. At the same time, version 7 reprocessing of all TRMM mission data was started. By the end of August 2011, the 14+ years of the reprocessed mission data became available online to users. This reprocessing provided the opportunity to redo and enhance upon an analysis of V7 impacts on L3 data accumulations that was presented at the 2010 EGU General Assembly. This paper will discuss the impact of algorithm changes made in th GPROF retrieval on the Level 2 swath products. Perhaps the most important change in that retrieval was to replacement of a model based a priori database with one created from Precipitation Radar (PR) and TMI brightness temperature (Tb) data. The radar pays a major role in the V7 GPROF (GPROF2010) in determining existence of rain. The level 2 retrieval algorithm also introduced a field providing the probability of rain. This combined use of the PR has some impact on the retrievals and created areas, particularly over ocean, where many areas of low-probability precipitation are retrieved whereas in version 6, these areas contained zero rain rates. This paper will discuss how these impacts get translated to the space/time averaged monthly products that use the GPROF retrievals. The level 3 products discussed are the gridded text product 3G68 and the standard 3A12 and 3B31 products. The paper provides an overview of the changes and explanation of how the level 3 products dealt with the change in the retrieval approach. Using the .25 deg x .25 degree grid, the paper will show that agreement between the swath product and the level 3 remains very high. It will also present comparisons of V6 and V7 GPROF retrievals as seen both at the swath level and the level 3 time/space gridded accumulations. It will show that the various L3 products based on GPROF level 2 retrievals are in close agreement. The paper concludes by outlining some of the challenges of the TRMM version 7 level 3 products.

Stocker, E. F.↗

NASA NTRS1982

Computation of the steady viscous flow over a tri-element 'augmentor wing' airfoil

The augmentor wing consists of a main airfoil with a slotted trailing edge for blowing, and two smaller aft airfoils which shroud the jet. This configuration has been modeled for numerical simulation by a novel discretization procedure which generates four separate grids: three surface-oriented airfoil grids and one outer free-stream grid. Grid lines and slopes are continuous across boundaries, so grid overlap at common boundaries provides boundary information without interpolation. A two-dimensional unsteady thin-layer Navier-Stokes code is used to calculate the flow for the no-blowing case at freestream Mach number = 0.7, Re = 12,600.000, and angles-of-incidence = 1.05 deg. Qualitative agreement with experimental data indicates the utility of this procedure in the analysis of multi-element configurations.

Lasinski, T. A.↗

NASA NTRS1987

Multitasking for flows about multiple body configurations using the chimera grid scheme

The multitasking of a finite-difference scheme using multiple overset meshes is described. In this chimera, or multiple overset mesh approach, a multiple body configuration is mapped using a major grid about the main component of the configuration, with minor overset meshes used to map each additional component. This type of code is well suited to multitasking. Both steady and unsteady two dimensional computations are run on parallel processors on a CRAY-X/MP 48, usually with one mesh per processor. Flow field results are compared with single processor results to demonstrate the feasibility of running multiple mesh codes on parallel processors and to show the increase in efficiency.

Dougherty, F. C.↗

NASA NTRS1988

Gamma-ray and hard X-ray imaging of solar flares

The scientific and technical aspects of high-resolution gamma-ray and X-ray imaging of solar flares are discussed. The scientific necessity for imaging observations of solar flares and the implications of future observations for the study of solar flare electrons and ions are considered. Performance parameters for a future hard X-ray and gamma-ray imager are summarized. Techniques for high-energy photon imaging including direct collimation imaging, coded apertures, and modulation collimators are surveyed. The technique of Fourier-transform imaging is examined. The options for detectors and grid fabrication are reviewed. Several planned future high-energy imagers are described.

Prince, T. A.↗

NASA NTRS1990

CFD validation for aerodynamic flows - Challenge for the '90's

The process of computational fluid dynamics (CFD) validation is described from two perspectives, numerical error validation and physical model validation. Errors associated with time and space discretization, grid refinement, numerical dissipation, and level of solution convergence, are all possible sources of numerical error. The second aspect of CFD code validation is associated with the governing equations and the physical models, e.g., chemistry and turbulence models. This type of validation requires comparisons with carefully conducted experiments and is the primary aspect of the validation process discussed in this paper. Examples of validation are shown for selected Reynolds-averaged Navier-Stokes codes for conditions from transonic through hypersonic. Since code applications are becoming more complex, it no longer suffices to use data from surface or integral quantities alone to provide the required validation. Flow field surveys and experimental boundary condition measurements are emerging as critical data that must be obtained for CFD code validation. Progress in the overall level of validation is shown to be improving. However, future challenges remain, some of which are enumerated.

Marvin, Joseph G.↗

NASA NTRS1990

An investigation of design optimization using a 2-D viscous flow code with multigrid

Computational fluid dynamics (CFD) codes have advanced to the point where they are effective analytical tools for solving flow fields around complex geometries. There is also a need for their use as a design tool to find optimum aerodynamic shapes. In the area of design, however, a difficulty arises due to the large amount of computer resources required by these codes. It is desired to streamline the design process so that a large number of design options and constraints can be investigated without overloading the system. There are several techniques which have been proposed to help streamline the design process. The feasibility of one of these techniques is investigated. The technique under consideration is the interaction of the geometry change with the flow calculation. The problem of finding the value of camber which maximizes the ratio of lift over drag for a particular airfoil is considered. In order to test out this technique, a particular optimization problem was tried. A NACA 0012 airfoil was considered at free stream Mach number of 0.5 with a zero angle of attack. Camber was added to the mean line of the airfoil. The goal was to find the value of camber for which the ratio of lift over drag is a maximum. The flow code used was FLOMGE which is a two dimensional viscous flow solver which uses multigrid to speed up convergence. A hyperbolic grid generation program was used to construct the grid for each value of camber.

Doria, Michael L.↗

NASA NTRS1991

Navier-Stokes calculation of transonic flow past the NTF 65 deg delta wing

Models of four delta wings were built and tested in the 8 x 8 ft Transonic Wind Tunnel at LaRC. The wings are identical in planform shape with a swept-back angle of 65 degrees, but bear different leading edge profiles. The models were tested under pressurized and cryogenic conditions to simulate true flight Reynolds numbers. Data on the aerodynamic forces and pressure distributions at various locations on the wings were taken at various flight Mach numbers and angles of attack. Effects of high Reynolds number and leading edge radius on the aerodynamic characteristics of the wings are being accessed. To thoroughly understand the turbulent, vortical flow around the wings, an effort to perform computational aerodynamic analysis is being made. The objective of the analysis is to supplement and validate the experimental data and explain the high Reynolds number and leading edge effects. GRIDGEN, a software developed by General Dynamics, is being used to generate the grid topology for the flow field around the wings. The flow solver to be used is CFL3D, a computation fluid dynamics code developed at LaRC. Based on the geometric description of the wings, a FORTRAN program called WINGSURF was written to generate the databases defining the surface geometry of the wings. To match the true geometry of the models in the wind tunnel for realistic comparison with experimental results, databases defining the sting support for the wing models were also created by two other FORTRAN programs, STINJOIN and STINREAR. Listing of the programs are attached and the geometry of a typical wing model with the sting support is shown. Other aspects of the investigation are discussed.

Wu, Chivey C.↗

NASA NTRS1993

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 1: Theory and validations

This report documents the user input and output data requirements for the FEMNAS finite element Navier-Stokes code for real-gas simulations of external aerodynamics flowfields. This code was developed for the configuration aerodynamics branch of NASA ARC, under SBIR Phase 2 contract NAS2-124568 by Computational Mechanics Corporation (COMCO). This report is in two volumes. Volume 1 contains the theory for the derived finite element algorithm and describes the test cases used to validate the computer program described in the Volume 2 user guide.

Baker, A. J.↗

NASA NTRS1992

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 2: FEMNAS user guide

Manhardt, Paul D.↗

NASA NTRS2004

Investigation of Navier-Stokes Code Verification and Design Optimization

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Vaidyanathan, Rajkumar↗

NASA NTRS2009

Consistency, Verification, and Validation of Turbulence Models for Reynolds-Averaged Navier-Stokes Applications

In current practice, it is often difficult to draw firm conclusions about turbulence model accuracy when performing multi-code CFD studies ostensibly using the same model because of inconsistencies in model formulation or implementation in different codes. This paper describes an effort to improve the consistency, verification, and validation of turbulence models within the aerospace community through a website database of verification and validation cases. Some of the variants of two widely-used turbulence models are described, and two independent computer codes (one structured and one unstructured) are used in conjunction with two specific versions of these models to demonstrate consistency with grid refinement for several representative problems. Naming conventions, implementation consistency, and thorough grid resolution studies are key factors necessary for success.

Rumsey, Christopher L.↗

NASA NTRS1992

An installed nacelle design code using a multiblock Euler solver. Volume 1: Theory document

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.

Chen, H. C.↗

NASA NTRS1993

Reliability enhancement of Navier-Stokes codes through convergence enhancement

Reduction of total computing time required by an iterative algorithm for solving Navier-Stokes equations is an important aspect of making the existing and future analysis codes more cost effective. Several attempts have been made to accelerate the convergence of an explicit Runge-Kutta time-stepping algorithm. These acceleration methods are based on local time stepping, implicit residual smoothing, enthalpy damping, and multigrid techniques. Also, an extrapolation procedure based on the power method and the Minimal Residual Method (MRM) were applied to the Jameson's multigrid algorithm. The MRM uses same values of optimal weights for the corrections to every equation in a system and has not been shown to accelerate the scheme without multigriding. Our Distributed Minimal Residual (DMR) method based on our General Nonlinear Minimal Residual (GNLMR) method allows each component of the solution vector in a system of equations to have its own convergence speed. The DMR method was found capable of reducing the computation time by 10-75 percent depending on the test case and grid used. Recently, we have developed and tested a new method termed Sensitivity Based DMR or SBMR method that is easier to implement in different codes and is even more robust and computationally efficient than our DMR method.

Choi, K.-Y.↗

NASA NTRS2008

Rotor Airloads Prediction Using Unstructured Meshes and Loose CFD/CSD Coupling

The FUN3D unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been modified to allow prediction of trimmed rotorcraft airloads. The trim of the rotorcraft and the aeroelastic deformation of the rotor blades are accounted for via loose coupling with the CAMRAD II rotorcraft computational structural dynamics code. The set of codes is used to analyze the HART-II Baseline, Minimum Noise and Minimum Vibration test conditions. The loose coupling approach is found to be stable and convergent for the cases considered. Comparison of the resulting airloads and structural deformations with experimentally measured data is presented. The effect of grid resolution and temporal accuracy is examined. Rotorcraft airloads prediction presents a very substantial challenge for Computational Fluid Dynamics (CFD). Not only must the unsteady nature of the flow be accurately modeled, but since most rotorcraft blades are not structurally stiff, an accurate simulation must account for the blade structural dynamics. In addition, trim of the rotorcraft to desired thrust and moment targets depends on both aerodynamic loads and structural deformation, and vice versa. Further, interaction of the fuselage with the rotor flow field can be important, so that relative motion between the blades and the fuselage must be accommodated. Thus a complete simulation requires coupled aerodynamics, structures and trim, with the ability to model geometrically complex configurations. NASA has recently initiated a Subsonic Rotary Wing (SRW) Project under the overall Fundamental Aeronautics Program. Within the context of SRW are efforts aimed at furthering the state of the art of high-fidelity rotorcraft flow simulations, using both structured and unstructured meshes. Structured-mesh solvers have an advantage in computation speed, but even though remarkably complex configurations may be accommodated using the overset grid approach, generation of complex structured-mesh systems can require months to set up. As a result, many rotorcraft simulations using structured-grid CFD neglect the fuselage. On the other hand, unstructured-mesh solvers are easily able to handle complex geometries, but suffer from slower execution speed. However, advances in both computer hardware and CFD algorithms have made previously state-of-the-art computations routine for unstructured-mesh solvers, so that rotorcraft simulations using unstructured grids are now viable. The aim of the present work is to develop a first principles rotorcraft simulation tool based on an unstructured CFD solver.

Biedron, Robert T.↗

NASA NTRS2004

Discharge Chamber Primary Electron Modeling Activities in Three-Dimensions

Designing discharge chambers for ion thrusters involves many geometric configuration decisions. Various decisions will impact discharge chamber performance with respect to propellant utilization efficiency, ion production costs, and grid lifetime. These hardware design decisions can benefit from the assistance of computational modeling. Computational modeling for discharge chambers has been limited to two-dimensional codes that leveraged symmetry for interpretation into three-dimensional analysis. This paper presents model development activities towards a three-dimensional discharge chamber simulation to aid discharge chamber design decisions. Specifically, of the many geometric configuration decisions toward attainment of a worthy discharge chamber, this paper focuses on addressing magnetic circuit considerations with a three-dimensional discharge chamber simulation as a tool. With this tool, candidate discharge chamber magnetic circuit designs can be analyzed computationally to gain insight into factors that may influence discharge chamber performance such as: primary electron loss width in magnetic cusps, cathode tip position with respect to the low magnetic field volume, definition of a low magnetic field region, and maintenance of a low magnetic field region across the grid span. Corroborating experimental data will be obtained from mockup hardware tests. Initially, simulated candidate magnetic circuit designs will resemble previous successful thruster designs. To provide opportunity to improve beyond previous performance benchmarks, off-design modifications will be simulated and experimentally tested.

Steuber, Thomas J.↗

NASA NTRS2008

An Idealized, Single Radial Swirler, Lean-Direct-Injection (LDI) Concept Meshing Script

To easily study combustor design parameters using computational fluid dynamics codes (CFD), a Gridgen Glyph-based macro (based on the Tcl scripting language) dubbed BladeMaker has been developed for the meshing of an idealized, single radial swirler, lean-direct-injection (LDI) combustor. BladeMaker is capable of taking in a number of parameters, such as blade width, blade tilt with respect to the perpendicular, swirler cup radius, and grid densities, and producing a three-dimensional meshed radial swirler with a can-annular (canned) combustor. This complex script produces a data format suitable for but not specific to the National Combustion Code (NCC), a state-of-the-art CFD code developed for reacting flow processes.

Iannetti, Anthony C.↗