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NASA NTRS2014

Coupled CFD-Thermal Analysis of Erosion Patterns Resulting from Nozzle Wedgeouts on the SRTMV-N2

The objective of this analysis was to study the effects of the erosion patterns from the introduction of nozzle flaws machined into the nozzle of the SRTMV-N2 (Solid Rocket Test Motor V Nozzle 2). The SRTMV-N2 motor was a single segment static subscale solid rocket motor used to further develop the RSRMV (Redesigned Solid Rocket Motor V Segment). Two flaws or "wedgeouts" were placed in the nozzle inlet parallel to the ply angles of that section to study erosion effects. One wedgeout was placed in the nose cap region and the other placed in the inlet ring on the opposite side of the bondline, separated 180 degrees circumferentially. A coupled CFD (Computational Fluid Analysis)-thermal iterative analytical approach was utilized at the wedgeouts to analyze the erosion profile during the burn time. The iterative CFD thermal approach was applied at five second intervals throughout the motor burn. The coupled fluid thermal boundary conditions were derived from a steady state CFD solution at the beginning of the interval. The derived heat fluxes were then applied along the surface and a transient thermal solution was developed to characterize the material response over the specified interval. Eroded profiles of each of the nozzle's wedgeouts and the original contour were created at each of the specified intervals. The final iteration of the erosion profile showed that both wedgeouts were "washedout," indicating that the erosion profile of the wedgeout had rejoined the original eroded contour, leaving no trace of the wedgeouts post fire. This analytical assessment agreed with post-fire observations made of the SRTMV-N2 wedgeouts, which noted a smooth eroded contour.

Ables, Catherine↗

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 NTRS2010

Analysis of the GPS Observations of the Site Survey at Sheshan 25-m Radio Telescope in August 2008

The processing of the GPS observations of the site survey at Sheshan 25-m radio telescope in August 2008 is reported. Because each session in this survey is only about six hours, not allowing the subdaily high frequency variations in the station coordinates to be reasonably smoothed, and because there are serious cycle slips in the observations and a large volume of data would be rejected during the software automatic adjustment of slips, the ordinary solution settings of GAMIT needed to be adjusted by loosening the constraints in the a priori coordinates to 10 m, adopting the "quick" mode in the solution iteration, and combining Cview manual operation with GAMIT automatic fixing of cycle slips. The resulting coordinates of the local control polygon in ITRF2005 are then compared with conventional geodetic results. Due to large rotations and translations in the two sets of coordinates (geocentric versus quasi-topocentric), the seven transformation parameters cannot be solved for directly. With various trial solutions it is shown that with a partial pre-removal of the large parameters, high precision transformation parameters can be obtained with post-fit residuals at the millimeter level. This analysis is necessary to prepare the follow-on site and transformation survey of the VLBI and SLR telescopes at Sheshan

Liu, L.↗

DOE OSTI2026

A conservative discontinuous Galerkin algorithm for particle kinetics on smooth manifolds

A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using both canonical and non-canonical Hamiltonian formulations. Our schemes apply to both formulations, but the canonical formulation results in a particularly efficient scheme that also conserves particle density and energy exactly. The collisionless update is coupled to a Bhatnagar-Gross-Krook (BGK) collision operator that provides a simplified model for relaxation to local thermodynamic equilibrium. An iterative scheme is constructed to ensure collisional invariants (density, momentum and energy) are preserved numerically. Rotation of the manifold is incorporated by modifying the Hamiltonian while ensuring a canonical formulation. Several test problems, including a kinetic version of the classical Sod shock problem, Kelvin-Helmholtz instability on the surfaces of a sphere and a hyperboloid, with and without rotations, are presented. A prospectus for further development of this approach to simulation of kinetic theory in general relativity is presented.

Discontinuous Galerkin↗

NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗

DOE OSTI2026

Analytical desmearing of Bonse–Hart ultra-small-angle neutron scattering data via truncated Abel inversion

A non-iterative analytical framework based on the truncated Abel inversion is developed for desmearing Bonse–Hart ultra-small-angle neutron scattering (USANS) data. The method directly inverts the slit-averaged intensity without empirical extrapolation or iterative regularization, establishing a closed-form relationship between the measured and intrinsic scattering profiles. Numerical benchmarks on representative models, including a rigid-line form factor, a Lorentzian function and a fractal structural model, demonstrate quantitative recovery of the ground-truth intensity across the full Q range. Application to a deuterated polystyrene/poly(2-vinylpyridine) blend further confirms that the approach yields smooth continuous profiles consistent with companion small-angle neutron scattering data. The truncated Abel inversion thus provides a stable, model-independent and physically transparent route for accurate desmearing of Bonse–Hart USANS measurements.

Huang, Guan-Rong [National Tsing Hua University, T↗

NASA NTRS1985

Marching iterative methods for the parabolized and thin layer Navier-Stokes equations

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Israeli, M.↗

NASA NTRS1985

Marching iterative methods for the Parabolized and Thin Layer Navier-Stokes equations

Israeli, M.↗

NASA NTRS1991

The L sub 1 finite element method for pure convection problems

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

Jiang, Bo-Nan↗

NASA NTRS1991

The L sub 1 finite element method for pure convection problems

Jiang, Bo-Nan↗

NASA NTRS1981

Spectral multigrid methods for elliptic equations

An alternative approach which employs multigrid concepts in the iterative solution of spectral equations was examined. Spectral multigrid methods are described for self adjoint elliptic equations with either periodic or Dirichlet boundary conditions. For realistic fluid calculations the relevant boundary conditions are periodic in at least one (angular) coordinate and Dirichlet (or Neumann) in the remaining coordinates. Spectral methods are always effective for flows in strictly rectangular geometries since corners generally introduce singularities into the solution. If the boundary is smooth, then mapping techniques are used to transform the problem into one with a combination of periodic and Dirichlet boundary conditions. It is suggested that spectral multigrid methods in these geometries can be devised by combining the techniques.

Zang, T. A.↗

NASA NTRS1991

Inverse problems in diffraction

A two-dimensional problem of diffraction of a plane electromagnetic wave on a smooth 2 pi-periodic surface is considered. A numerical algorithm solving this problem is developed. An inverse problem of determination of the shape of 2 pi-periodic surface using the performance data of reverse scattering is considered. The inverse problem was solved by means of minimization of the residual functional with the help of the gradient descent method. The initial data were calculated with the help of the numerical method. On each step of the iterative method of minimization, the residual functional was calculated approximately with the help of the small slope method. The examples of the shape determination are considered.

Mikheev, Andrew G.↗

NASA NTRS1996

Atomic Oxygen Durability of Second Surface Silver Microsheet Glass Concentrators

Second surface silver microsheet glass concentrators are being developed for potential use in future solar dynamic space power systems. Traditional concentrators are aluminum honeycomb sandwich composites with either aluminum or graphite epoxy face sheets, where a reflective aluminum layer is deposited onto an organic leveling layer on the face sheet. To protect the underlying layers, a SiO2 layer is applied on top of the aluminum reflective layer. These concentrators may be vulnerable to atomic oxygen degradation due to possible atomic oxygen attack of the organic layers at defect sites in the protective and reflective coatings. A second surface microsheet glass concentrator would be inherently more atomic oxygen durable than these first surface concentrators. In addition, a second surface microsheet glass concentrator design provides a smooth optical surface and allows for silver to be used as a reflective layer, which would improve the reflectivity of the concentrator and the performance of the system. A potential threat to the performance of second surface microsheet glass concentrators is atomic oxygen attack of the underlying silver at seams and edges or at micrometeoroid and debris (MMD) impacts sites. Second surface silver microsheet glass concentrator samples were fabricated and tested for atomic oxygen durability. The samples were iteratively exposed to an atomic oxygen environment in a plasma asher. Samples were evaluated for potential degradation at fabrication seams, simulated MMD impact sites, and edges. Optical microscopy was used to evaluate atomic oxygen degradation. Reflectance was obtained for an impacted sample prior to and after atomic oxygen exposure. After an initial atomic oxygen exposure to an effective fluence of approx. 1 x 10(exp 21) atoms/cm(exp 2), oxidation of the silver at defect sites and edges was observed. Exposure to an additional approx. 1 x 10(exp 21) atoms/cm(exp 2) caused no observed increase in oxidation. Oxidation at an impact site caused negligible changes in reflectance. In all cases oxidation was found to be confined to the vicinity of the seams, impact sites, edges or defect sites. Asher to in-space atomic oxygen correlation issues will be addressed.

deGroh, Kim K.↗

NASA NTRS2011

A New Inversion Routine to Produce Vertical Electron-Density Profiles from Ionospheric Topside-Sounder Data

Two software applications have been produced specifically for the analysis of some million digital topside ionograms produced by a recent analog-to-digital conversion effort of selected analog telemetry tapes from the Alouette-2, ISIS-1 and ISIS-2 satellites. One, TOPIST (TOPside Ionogram Scalar with True-height algorithm) from the University of Massachusetts Lowell, is designed for the automatic identification of the topside-ionogram ionospheric-reflection traces and their inversion into vertical electron-density profiles Ne(h). TOPIST also has the capability of manual intervention. The other application, from the Goddard Space Flight Center based on the FORTRAN code of John E. Jackson from the 1960s, is designed as an IDL-based interactive program for the scaling of selected digital topside-sounder ionograms. The Jackson code has also been modified, with some effort, so as to run on modern computers. This modification was motivated by the need to scale selected ionograms from the millions of Alouette/ISIS topside-sounder ionograms that only exist on 35-mm film. During this modification, it became evident that it would be more efficient to design a new code, based on the capabilities of present-day computers, than to continue to modify the old code. Such a new code has been produced and here we will describe its capabilities and compare Ne(h) profiles produced from it with those produced by the Jackson code. The concept of the new code is to assume an initial Ne(h) and derive a final Ne(h) through an iteration process that makes the resulting apparent-height profile fir the scaled values within a certain error range. The new code can be used on the X-, O-, and Z-mode traces. It does not assume any predefined profile shape between two contiguous points, like the exponential rule used in Jackson s program. Instead, Monotone Piecewise Cubic Interpolation is applied in the global profile to keep the monotone nature of the profile, which also ensures better smoothness in the final profile than in Jackson s program. The new code uses the complete refractive index expression for a cold collisionless plasma and can accommodate the IGRF, T96, and other geomagnetic field models.

Wang, Yongli↗

NASA NTRS1986

Transformation of two and three-dimensional regions by elliptic systems

Grid smoothing and orthogonalization procedures were developed and implemented in the construction of two and three dimensional grids. The procedures are based on the variational methods of grid generation. The two-dimensional examples were computed using the MSU IRIS Graphics Workstation. It was demonstrated that the elliptic grid generation equations, with arbitrary forcing functions, can be solved, in their variational formulation, using a gradient method. Since gradient methods have a global convergence property, the divergence problems often encountered when using SOR iterative methods can be avoided. It is not to be concluded, however, that SOR methods should be abandoned, since gradient methods tend to converge very slowly. In fact, slow convergence was the major problem encountered in the three-dimensional grids. Further progress was made on the continuing effort to develop conservative interpolation formulas for overlapping grids.

Mastin, C. Wayne↗

NASA NTRS1973

A computer program for calculating the perfect gas inviscid flow field about blunt axisymmetric bodies at an angle of attack of 0 deg

A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.

Zoby, E. V.↗

NASA NTRS2008

Design of a Mach-3 Nozzle for TBCC Testing in the NASA LaRC 8-ft High Temperature Tunnel

A new nozzle is being constructed for the NASA Langley Research Center 8-Foot High Temperature Tunnel. The axisymmetric nozzle was designed with a Mach-3 exit flow for testing Turbine-Based Combined-Cycle engines at a Mach number in the vicinity of the transition from turbojet to ramjet operation. The nozzle contour was designed using the NASA Langley IMOCND computer program which solves the potential equation using the classical method of characteristics. To include viscous effects, the design procedure iterated the MOC contour generation with CFD Navier-Stokes calculations, adjusting MOC input parameters until target nozzle-exit conditions were achieved in the Navier-Stokes calculations. The design process was complicated by a requirement to use the final 29.5 inches of an existing 54.5-inch exit-diameter Mach-5 nozzle contour. This was accomplished by generating a Mach-3 contour that matched the radius of the Mach-5 contour at the match point and using a 3rd order polynomial to create a smooth transition between the two contours. During the final evaluation of the design it was realized that the throat diameter is more than half that of the upstream mixing chamber. This led to the concern that large vortical structures generated in the mixer would persist downstream, affecting nozzle-exit flow. This concern was addressed by analyzing the results of three-dimensional, viscous, numerical simulations of the entire flowfield, from the exit of the facility combustor to the nozzle exit. An analysis of the solution indicated that large scale structures do not pass through the throat and that both the total temperature and species (CO2) are well mixed in the mixer, providing uniform flow to the nozzle and subsequently the test cabin.

Gaffney, Richard L., Jr.↗

NASA NTRS1993

Laplace's equation and the Dirichlet-Neumann map in multiply connected domains

A variety of problems in material science and fluid dynamics require the solution of Laplace's equation in multiply connected domains. Integral equation methods are natural candidates for such problems, since they discretize the boundary alone, require no special effort for free boundaries, and achieve superalgebraic convergence rates on sufficiently smooth domains in two space dimensions, regardless of shape. Current integral equation methods for the Dirichlet problem, however, require the solution of M independent problems of dimension N, where M is the number of boundary components and N is the total number of points in the discretization. In this paper, we present a new boundary integral equation approach, valid for both interior and exterior problems, which requires the solution of a single linear system of dimension N + M. We solve this system by making use of an iterative method (GMRES) combined with the last multipole method for the rapid calculation of the necessary matrix vector products. For a two-dimensional system with 200 components and 100 points on each boundary, we gain a speedup of a factor of 100 from the new analytic formulation and a factor of 50 from the fast multipole method. The resulting scheme brings large scale calculations in extremely complex domains within practical reach.

Greenbaum, A.↗