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NASA NTRS2001

B-spline Method in Fluid Dynamics

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

Botella, Olivier↗

NASA NTRS1986

Application of the TranAir full-potential code to complete configurations

The TranAir computer code solves the full-potential equation for transonic flow by combining a rectangular box of flow-field grid points with networks of surface panels. Complex geometry is easily represented since surface conforming flow-field grids are not used. Application of TranAir to the F-16A is presented for free-stream Mach numbers of 0.6 and 0.90, at an angle of attack of four degrees.

Erickson, L. L.↗

NASA NTRS1993

A nonconforming multigrid method using conforming subspaces

For second-order elliptic boundary value problems, we develop a nonconforming multigrid method using the coarser-grid correction on the conforming finite element subspaces. The convergence proof with an arbitrary number of smoothing steps for nu-cycle is presented.

Lee, Chang Ock↗

NASA NTRS1987

Transonic analysis of the F-16A with under-wing fuel tanks - An application of the TranAir full-potential code

Initial results obtained using the TranAir transonic full-potential code are presented for a fully configured F-16A geometry, including two 370-gal under-wing fuel tanks, at freestream Mach numbers of 0.6 and 0.9 and angle of attack of 4 deg. The geometry is modeled using surface panels, and the flow field is defined by a rectangular array of flow-field grid points. The paneled geometry is embedded within this rectangular flow field. By avoiding the use of surface-conforming flow-field grids, the modeling generality afforded by surface panels can be utilized to analyze very complex configurations in the transonic flow regime.

Madson, Michael D.↗

NASA NTRS1993

Improved Blending-Function Algebraic Generation Of Grids

Method of algebraic generation of grids used in computing flows incorporates blending-function techniques to obtain high degree of orthogonality of each grid on its bounding surfaces and to blend grid smoothly, making it conform to all boundaries. Demonstrated in two dimensions, and applied in continuing development of software for real-time interactive generation of three-dimensional grids with color graphical displays. Software used routinely in generating grids for computing flows of practical interest.

Ching-Chung Luh, Raymond↗

NASA NTRS1986

Development of a numerical procedure to map a general 3-d body onto a near-circle

Conformal mapping is a classical technique utilized for solving problems in aerodynamics and hydrodynamics. Conformal mapping is utilized in the construction of grids around airfoils, engine inlets and other aircraft configurations. These shapes are transformed onto a near-circle image for which the equations of fluid motion are discretized on the mapped plane and solved numerically by utilizing the appropriate techniques. In comparison to other grid-generation techniques such as algerbraic or differential type, conformal mapping offers an analytical and accurate form even if the grid deformation is large. One of the most appealing features is that the grid can be constrained to remain orthogonal to the body after the transformation. Hence, the grid is suitable for analyzing the supersonic flow past a blunt object. The associated shock as a coordinate surface adjusts its position in the course of computation until convergence is reached. The present work applied conformal mapping to 3-D bodies with no axis of symmetry such as the Aerobraking Flight Experiment (AFE) vehicle, transforming the AFE shape onto a near-circle image. A numerical procedure and code are used to generate grids around the AFE body.

Hommel, M. J.↗

NASA NTRS1988

An improved version of NCOREL: A computer program for 3-D nonlinear supersonic potential flow computations

A computer code called NCOREL (for Nonconical Relaxation) has been developed to solve for supersonic full potential flows over complex geometries. The method first solves for the conical at the apex and then marches downstream in a spherical coordinate system. Implicit relaxation techniques are used to numerically solve the full potential equation at each subsequent crossflow plane. Many improvements have been made to the original code including more reliable numerics for computing wing-body flows with multiple embedded shocks, inlet flow through simulation, wake model and entropy corrections. Line relaxation or approximate factorization schemes are optionally available. Improved internal grid generation using analytic conformal mappings, supported by a simple geometric Harris wave drag input that was originally developed for panel methods and internal geometry package are some of the new features.

Siclari, Michael J.↗

NASA NTRS1990

Simulation and analysis of a delta planform with multiple jets in ground effect

The three-dimensional, thin-layer Navier-Stokes equations on a body-conforming, overset, multiple-grid topology are solved in the present numerical simulations of the flow around a 60-deg delta-planform wing equipped with two thrust-reverser jets in ground-effect conditions. Such experimentally flow-visualized features as jet-deformation and ground vertex-formation are captured by these simulations; the loss of wing-borne lift due to the 'suck-down' phenomenon, which arises as the delta planform flies at low speeds in close proximity to the ground, is also well simulated.

Chawla, K.↗

NASA NTRS1992

Streamwise Upwind, Moving-Grid Flow Algorithm

Extension to moving grids enables computation of transonic flows about moving bodies. Algorithm computes unsteady transonic flow on basis of nondimensionalized thin-layer Navier-Stokes equations in conservation-law form. Solves equations by use of computational grid based on curvilinear coordinates conforming to, and moving with, surface(s) of solid body or bodies in flow field. Simulates such complicated phenomena as transonic flow (including shock waves) about oscillating wing. Algorithm developed by extending prior streamwise upwind algorithm solving equations on fixed curvilinear grid described in "Streamwise Algorithm for Simulation of Flow" (ARC-12718).

Goorjian, Peter M.↗

NASA NTRS1987

A comparison of two conformal mapping techniques applied to an aerobrake body

Conformal mapping is a classical technique which has been utilized for solving problems in aerodynamics and hydrodynamics. Conformal mapping has been successfully applied in the construction of grids around airfoils, engine inlets and other aircraft configurations. Conformal mapping techniques were applied to an aerobrake body having an axis of symmetry. Two different approaches were utilized: (1) Karman-Trefftz transformation; and (2) Point Wise Schwarz Christoffel transformation. In both cases, the aerobrake body was mapped onto a near circle, and a grid was generated in the mapped plane. The mapped body and grid were then mapped back into physical space and the properties of the associated grids were examined. Advantages and disadvantages of both approaches are discussed.

Hommel, Mark J.↗

NASA NTRS2006

Thermal Cycle Reliability of PBGA/CCGA 717 I/Os

Status of thermal cycle test results for a nonfunctional daisy-chained peripheral ceramic column grid array (CCGA) and its plastic ball grid array (PBGA) version. both having 560 I/Os. were presented in last year's conference. Test results included environmental data for three different thermal cycle regimes (-55 C/125 C, -55 C/100 C, and -50 C /75 C). Update information on these - especially failure type for assemblies with high and low solder volumes-were presented. The thermal cycle test procedure followed those recommended IPC-9701 for tin-lead solder joint assemblies. Revision A of this specification covers guideline thermal cycle requirements for Pb-free solder joints. Some background information discussed during release of this specification with its current guideline recommendations were also presented. In a recent reliability investigation a fully populated CCGA with 717 I/Os was also considered for assembly reliability. evaluation. The functional package is a field-programmable gate array that has much higher processing power than its previous version. This new package is smaller in dimension, has no interposer, and has a thinner column wrapped with copper for reliability improvement. This paper will also present thermal cycle test results for this package assembly and its plastic version with 728 I/Os. both of which were exposed to three different cycle regimes. Two cycle profiles were those specified by IPC- 9701A for tin-lead, i.e. -55 to 100 C and -55 to 125 C and one was a cycle profile specified by Mil-Std-883, i.e.. -65 C/150 C which is generally used for ceramic hybrid packages. Per IPC-9701 A, test vehicles were built using daisy chain packages and were continuously monitored. The effects of many process and assembly variables-including corner staking commonly used for improving resistance to mechanical loading such as drop and vibration loads--were also considered as part of the test matrix. Optical photomicrographs were taken at various thermal cycle intervals to document damage progress and behavior. Representative samples of these along with cross-sectional photomicrographs at higher magnification taken by scanning electron microscopy (SEM) to determine crack propagation and failure analyses for packages are also presented.

staking↗

NASA NTRS1990

A three-dimensional application with the numerical grid generation code: EAGLE (utilizing an externally generated surface)

Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) is a multiblock grid generation and steady-state flow solver system. This system combines a boundary conforming surface generation, a composite block structure grid generation scheme, and a multiblock implicit Euler flow solver algorithm. The three codes are intended to be used sequentially from the definition of the configuration under study to the flow solution about the configuration. EAGLE was specifically designed to aid in the analysis of both freestream and interference flow field configurations. These configurations can be comprised of single or multiple bodies ranging from simple axisymmetric airframes to complex aircraft shapes with external weapons. Each body can be arbitrarily shaped with or without multiple lifting surfaces. Program EAGLE is written to compile and execute efficiently on any CRAY machine with or without Solid State Disk (SSD) devices. Also, the code uses namelist inputs which are supported by all CRAY machines using the FORTRAN Compiler CF177. The use of namelist inputs makes it easier for the user to understand the inputs and to operate Program EAGLE. Recently, the Code was modified to operate on other computers, especially the Sun Spare4 Workstation. Several two-dimensional grid configurations were completely and successfully developed using EAGLE. Currently, EAGLE is being used for three-dimension grid applications.

Houston, Johnny L.↗

NASA NTRS1980

An electrostatic analog for generating cascade grids

Accurate and efficient numerical simulation of flows through turbomachinery blade rows depends on the topology of the computational grids. These grids must reflect the periodic nature of turbomachinery blade row geometries and conform to the blade shapes. Three types of grids can be generated that meet these minimal requirements: through-flow grids, O-type grids, and C-type grids. A procedure which can be used to generate all three types of grids is presented. The resulting grids are orthogonal and can be stretched to capture the essential physics of the flow. A discussion is also presented detailing the extension of the generation procedure to three dimensional geometries.

Adamczyk, J. J.↗

NASA NTRS1976

Calculation of the three-dimension, supersonic, inviscid, steady flow past an arrow-winged airframe, part 1

A detailed description of the procedure used to compute three dimensional, supersonic, inviscid, steady flows past airframes is given. No limitations are imposed on the geometry of the airplane. Suitable computational grids are generated by automatic conformal mappings. The equations of motion, with pressure, entropy, and velocity direction as basic unknowns, are written and discretized in the computational space. Special rules to approximate derivatives are given. Boundary points are treated by a modified method of characteristics.

Moretti, G.↗

NASA NTRS1989

Three dimensional unstructured grids for the solution of the Euler equations

The advancing front technique is being used to develop a code to generate grids around complex 3-D configurations for use in computing the invisid flow solutions by the Euler equations. By the advancing front technique points are introduced concurrently with the connectivity information so that a separate library is not required. The generation of a 3-D grid is accomplished in several steps. First the boundaries of the domain to be gridded must be described by two-, three- or four-sided surface patches. Next, a background mesh is required to control the grid spacing and stretching throughout the domain. This coarse tetrahedral grid is not required to conform to any of the boundaries. Next, each of the patches is mapped to 2-D, triangulated by the advancing front technique and mapped back to 3-D. These triangles form the initial front for the generation of the final tetrahedral mesh.

Gumbert, Clyde↗

NASA NTRS1993

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Tsiveriotis, K.↗

NASA NTRS1988

Incompressible and anelastic flow simulations on numerically generated grids

In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

Sharman, R. D.↗

NASA NTRS1976

Conformal mappings for computations of steady, three-dimensional, supersonic flows

The evaluation of steady, supersonic, three-dimensional inviscid flows is considered, taking into account the construction of suitable grids on the basis of a simple conformal mapping. A description is presented of an analytical mapping technique. The technique is illustrated with the aid of examples of mappings, involving nontrivial geometries. Attention is given to a wing-fuselage cross section, a FORTRAN program for the basic mapping, the coupling of mappings, and the equations of motion.

Moretti, G.↗