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NASA NTRS1994

Aerodynamic shape optimization of a HSCT type configuration with improved surface definition

Two distinct parametrization procedures of generating free-form surfaces to represent aerospace vehicles are presented. The first procedure is the representation using spline functions such as nonuniform rational b-splines (NURBS) and the second is a novel (geometrical) parametrization using solutions to a suitably chosen partial differential equation. The main idea is to develop a surface which is more versatile and can be used in an optimization process. Unstructured volume grid is generated by an advancing front algorithm and solutions obtained using an Euler solver. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an automatic differentiator precompiler software tool. Aerodynamic shape optimization of a complete aircraft with twenty four design variables is performed. High speed civil transport aircraft (HSCT) configurations are targeted to demonstrate the process.

Thomas, Almuttil M.↗

NASA NTRS2012

A New and General Formulation of the Parametric HFGMC Micromechanical Method for Three-Dimensional Multi-Phase Composites

The recent two-dimensional (2-D) parametric formulation of the high fidelity generalized method of cells (HFGMC) reported by the authors is generalized for the micromechanical analysis of three-dimensional (3-D) multiphase composites with periodic microstructure. Arbitrary hexahedral subcell geometry is developed to discretize a triply periodic repeating unit-cell (RUC). Linear parametric-geometric mapping is employed to transform the arbitrary hexahedral subcell shapes from the physical space to an auxiliary orthogonal shape, where a complete quadratic displacement expansion is performed. Previously in the 2-D case, additional three equations are needed in the form of average moments of equilibrium as a result of the inclusion of the bilinear terms. However, the present 3-D parametric HFGMC formulation eliminates the need for such additional equations. This is achieved by expressing the coefficients of the full quadratic polynomial expansion of the subcell in terms of the side or face average-displacement vectors. The 2-D parametric and orthogonal HFGMC are special cases of the present 3-D formulation. The continuity of displacements and tractions, as well as the equilibrium equations, are imposed in the average (integral) sense as in the original HFGMC formulation. Each of the six sides (faces) of a subcell has an independent average displacement micro-variable vector which forms an energy-conjugate pair with the transformed average-traction vector. This allows generating symmetric stiffness matrices along with internal resisting vectors for the subcells which enhances the computational efficiency. The established new parametric 3-D HFGMC equations are formulated and solution implementations are addressed. Several applications for triply periodic 3-D composites are presented to demonstrate the general capability and varsity of the present parametric HFGMC method for refined micromechanical analysis by generating the spatial distributions of local stress fields. These applications include triply periodic composites with inclusions in the form of a cavity, spherical inclusion, ellipsoidal inclusion, discontinuous aligned short fiber. A 3-D repeating unit-cell for foam material composite is simulated.

Haj-Ali, Rami↗

NASA NTRS1997

Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition.

Thomas, A. M.↗

NASA NTRS1985

An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures.

Derose, T. D.↗

NASA NTRS1993

An experimental parametric study of geometric, Reynolds number, and ratio of specific heats effects in three-dimensional sidewall compression scramjet inlets at Mach 6

The effects of the decrease in the ratio of specific heats have been investigated in generic 3D sidewall compression scramjet inlets with leading-edge sweep angles of 30 and 70 degrees. The effects of a decrease in ratio of specific heats were seen by comparing data from two facilities in two test gases: in the Langley Mach 6 CF4 Tunnel in tetrafluoromethane and in the Langley 15-Inch Mach 6 Air Tunnel in perfect gas air. In addition to the simulated real gas effects, the parametric effects of cowl position, contraction ratio, leading-edge sweep, and Reynolds number were investigated in the 15-Inch Mach 6 Air Tunnel. The models were instrumented with a total of 45 static pressure orifices distributed on the sidewalls and baseplate. Surface streamline patterns were examined via oil flow, and schlieren videos were made of the external flow field. The results of these tests have significant implications to ground based testing of inlets in facilities which do not operate at flight enthalpies.

Holland, Scott D.↗

NASA NTRS1993

An Experimental Parametric Study of Geometric, Reynolds Number, and Ratio of Specific Heats Effects in Three-Dimensional Sidewall Compression Scramjet Inlets at Mach 6

Since mission profiles for airbreathing hypersonic vehicles such as the National Aero-Space Plane include single-stage-to-orbit requirements, real gas effects may become important with respect to engine performance. The effects of the decrease in the ratio of specific heats have been investigated in generic three-dimensional sidewall compression scramjet inlets with leading-edge sweep angles of 30 and 70 degrees. The effects of a decrease in ratio of specific heats were seen by comparing data from two facilities in two test gases: in the Langley Mach 6 CF4 Tunnel in tetrafluoromethane (where gamma=1.22) and in the Langley 15-Inch Mach 6 Air Tunnel in perfect gas air (where gamma=1.4). In addition to the simulated real gas effects, the parametric effects of cowl position, contraction ratio, leading-edge sweep, and Reynolds number were investigated in the 15-Inch Mach 6 Air Tunnel. The models were instrumented with a total of 45 static pressure orifices distributed on the sidewalls and baseplate. Surface streamline patterns were examined via oil flow, and schlieren videos were made of the external flow field. The results of these tests have significant implications to ground based testing of inlets in facilities which do not operate at flight enthalpies.

Holland, Scott D.↗

NASA NTRS1996

Geometric Model for a Parametric Study of the Blended-Wing-Body Airplane

A parametric model is presented for the blended-wing-body airplane, one concept being proposed for the next generation of large subsonic transports. The model is defined in terms of a small set of parameters which facilitates analysis and optimization during the conceptual design process. The model is generated from a preliminary CAD geometry. From this geometry, airfoil cross sections are cut at selected locations and fitted with analytic curves. The airfoils are then used as boundaries for surfaces defined as the solution of partial differential equations. Both the airfoil curves and the surfaces are generated with free parameters selected to give a good representation of the original geometry. The original surface is compared with the parametric model, and solutions of the Euler equations for compressible flow are computed for both geometries. The parametric model is a good approximation of the CAD model and the computed solutions are qualitatively similar. An optimal NURBS approximation is constructed and can be used by a CAD model for further refinement or modification of the original geometry.

Mastin, C. Wayne↗

NASA NTRS2004

Dynamics of Aerosol Particles in Stationary, Isotropic Turbulence

A detailed study of the dynamics of sub-Kolmogorov-size aerosol particles in stationary isotropic turbulence has been performed. The study combined direct numerical simulations (DNS; directed by Prof. Collins) and high-resolution experimental measurements (directed by Prof. Meng) under conditions of nearly perfect geometric and parametric overlap. The goal was to measure the accumulation of particles in low-vorticity regions of the flow that arises from the effect commonly referred to as preferential concentration. The grant technically was initiated on June 13, 2000; however, funding was not available until July 11, 2000. The grant was originally awarded to Penn State University (numerical simulations) and SUNY-Buffalo (experiments); however, Prof. Collins effort was moved to Cornell University on January 2002 when he joined that university. He completed the study there. A list of the specific tasks that were completed under this study is presented.

Collins, Lance R.↗

NASA NTRS1984

An urnful of blinding functions

There is a fundamental connection between the mathematical theory of discrete probability distributions and the parametric curves and surfaces of computer-aided geometric design. It is no accident that the blending functions of Bezier curves and surfaces have an obvious probabilistic interpretation, nor is it a coincidence that the normalized uniform B-spline basis functions also model a simple stochastic process. The link between probability and geometry, and how to exploit simple probabilistic arguments to derive many of the classical geometric properties of the parametric curves and surfaces currently in vogue in computer-aided geometric design is discussed. This probabilistic approach is also used to introduce many new types of curves and surfaces, and it is demonstrated how probability theory can be used to simplify, unify, and generalize many well-known results.

Goldman, R. N.↗

NASA NTRS2004

Parametric Study on the Response of Compression-Loaded Composite Shells With Geometric and Material Imperfections

The results of a parametric study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thinwalled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The imperfections considered include initial geometric shell-wall midsurface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these imperfections on the nonlinear responses and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable response characteristics.

Hilburger, Mark W.↗

NASA NTRS1979

A critical examination of stresses in an elastic single lap joint

The results of an approximate nonlinear finite-element analysis of a single lap joint are presented and compared with the results of a linear finite-element analysis, and the geometric nonlinear effects caused by the load-path eccentricity on the adhesive stress distributions are determined. The results from finite-element, Goland-Reissner, and photoelastic analyses show that for a single lap joint the effect of the geometric nonlinear behavior of the joint has a sizable effect on the stresses in the adhesive. The Goland-Reissner analysis is sufficiently accurate in the prediction of stresses along the midsurface of the adhesive bond to be used for qualitative evaluation of the influence of geometric or material parametric variations. Detailed stress distributions in both the adherend and adhesive obtained from the finite-element analysis are presented to provide a basis for comparison with other solution techniques.

Cooper, P. A.↗

NASA NTRS1986

Riblets for aircraft skin-friction reduction

Energy conservation and aerodynamic efficiency are the driving forces behind research into methods to reduce turbulent skin friction drag on aircraft fuselages. Fuselage skin friction reductions as small as 10 percent provide the potential for a 250 million dollar per year fuel savings for the commercial airline fleet. One passive drag reduction concept which is relatively simple to implement and retrofit is that of longitudinally grooved surfaces aligned with the stream velocity. These grooves (riblets) have heights and spacings on the order of the turbulent wall streak and burst dimensions. The riblet performance (8 percent net drag reduction thus far), sensitivity to operational/application considerations such as yaw and Reynolds number variation, an alternative fabrication technique, results of extensive parametric experiments for geometrical optimization, and flight test applications are summarized.

Walsh, Michael J.↗

NASA NTRS1992

Engine structures modeling software system: Computer code. User's manual

ESMOSS is a specialized software system for the construction of geometric descriptive and discrete analytical models of engine parts, components and substructures which can be transferred to finite element analysis programs such as NASTRAN. The software architecture of ESMOSS is designed in modular form with a central executive module through which the user controls and directs the development of the analytical model. Modules consist of a geometric shape generator, a library of discretization procedures, interfacing modules to join both geometric and discrete models, a deck generator to produce input for NASTRAN and a 'recipe' processor which generates geometric models from parametric definitions. ESMOSS can be executed both in interactive and batch modes. Interactive mode is considered to be the default mode and that mode will be assumed in the discussion in this document unless stated otherwise.

Source record↗

NASA NTRS1999

Nonlinear Local Bending Response and Bulging Factors for Longitudinal Cracks in Pressurized Cylindrical Shells

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or "bulging factors" that account for increased stresses due to curvature for longitudinal cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in graphs of the bulging factor as a function of the applied load and as a function of geometric parameters that include the shell radius, the shell thickness and the crack length. The computed bulging factors are compared with solutions based on linear shallow shell theory, and with semi-empirical solutions that approximately account for the nonlinear deformation in the vicinity of the crack. The effect of biaxial loads on the computed bulging factors is also discussed.

Rose, Cheryl A.↗

NASA NTRS2000

Nonlinear Local Bending Response and Bulging Factors for Longitudinal and Circumferential Cracks in Pressurized Cylindrical Shells

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased stresses due to curvature for longitudinal and circumferential cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in the form of contour plots of the bulging factor as a function of two nondimensional parameters: the shell curvature parameter, lambda, which is a function of the shell geometry, Poisson's ratio, and the crack length; and a loading parameter, eta, which is a function of the shell geometry, material properties, and the applied internal pressure. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant. Simple empirical expressions for the bulging factor are then derived from the numerical results and shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks. The numerical results are also compared with analytical solutions based on linear shallow shell theory for thin shells, and with some other semi-empirical solutions from the literature, and limitations on the use of these other expressions are suggested.

Young, Richard D.↗

NASA NTRS1997

Locating Geometric Primitives by Pruning the Parameter Space

This paper examines the extraction of geometric primitives from two- and three-dimensional image data. The geometric primitives are represented by parametric manifolds in the image space, such as circles, planes, and cylinders.

geometric primitives image data parameter space im↗

NASA NTRS2023

Multiphysics Modeling of Electrode Dissolution under Hydrodynamic Conditions in Low Conductivity Water

Efficient plug-flow electrochemical reactors are characterized by their ability to effectively convert species with significant ionic strength and/or with the assistance of a well-behaved electrolyte. Because of the classic electroconductivity requirement, electrochemical reactors are not particularly attractive options for applications with low-conductivity conditions, especially for low-pressure feeds. However, these reactors can still find application in dedicated processes such as ultra-clean water conditioning and biological-coupled separation systems. Consequently, a multi-physics model was developed using COMSOL Multiphysics to characterize different reactor-design conditions based on the Tertiary Current Distribution which accounts for the effects of expected variations in electrolyte composition and ionic strength on the electrochemical process, as well as solution resistance and electrode kinetics. The modelling framework presented here employs single-phase laminar fluid flow, the Nernst-Planck equation, the water-based electroneutrality condition, and concentration-dependent overpotentials. This investigation particularly explores the electrolysis process of “anodic dissolution,” in which elemental species dissociate from the solid matrix of the electrode and enter the liquid phase of the electrolyte as soluble ions. The reactor configuration of interest has a rectangular parallel-electrode design and is operated galvanostatically. A series of parametric studies are carried out to inspect the response of the system when hydrodynamic, kinetic, and geometric conditions are changed. The parametric sweep resulted in variable effluent concentrations and system voltage, which reveal underlaying optimization patterns for electrode dissolution in low conductivity water.

Multiphysics↗

NASA NTRS2000

Nonlinear Bulging Factors for Longitudinal and Circumferential Cracks in Cylindrical Shells Subjected to Combined Loads

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased crack-tip stresses due to curvature for longitudinal and circumferential cracks in unstiffened cylindrical shells subjected to combined loads are presented. Nondimensional parameters varied in the study include the shell curvature parameter, l , which is a function of the shell radius, the shell wall thickness, and the crack length; a pressure loading parameter, h , which is a function of the shell geometry, material properties and the applied internal pressure; and a biaxial loading parameter, c , which is the ratio of the farfield axial stress to the farfield circumferential stress. The major results are presented in the form of contour plots of the bulging factor as a function of these three nondimensional parameters. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant, and show the effect of the biaxial loads on the value of the bulging factor. Simple empirical expressions for the bulging factor are then derived from the numerical results and are shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks.

Young, Richard D.↗