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NASA NTRS1999

Probabilistic Structural Analysis Methods (PSAM) for Select Space Propulsion System Components

Probabilistic Structural Analysis Methods (PSAM) are described for the probabilistic structural analysis of engine components for current and future space propulsion systems. Components for these systems are subjected to stochastic thermomechanical launch loads. Uncertainties or randomness also occurs in material properties, structural geometry, and boundary conditions. Material property stochasticity, such as in modulus of elasticity or yield strength, exists in every structure and is a consequence of variations in material composition and manufacturing processes. Procedures are outlined for computing the probabilistic structural response or reliability of the structural components. The response variables include static or dynamic deflections, strains, and stresses at one or several locations, natural frequencies, fatigue or creep life, etc. Sample cases illustrates how the PSAM methods and codes simulate input uncertainties and compute probabilistic response or reliability using a finite element model with probabilistic methods.

Source record↗

NASA NTRS2001

Displacement Models for THUNDER Actuators having General Loads and Boundary Conditions

This paper summarizes techniques for quantifying the displacements generated in THUNDER actuators in response to applied voltages for a variety of boundary conditions and exogenous loads. The PDE (partial differential equations) models for the actuators are constructed in two steps. In the first, previously developed theory quantifying thermal and electrostatic strains is employed to model the actuator shapes which result from the manufacturing process and subsequent repoling. Newtonian principles are then employed to develop PDE models which quantify displacements in the actuator due to voltage inputs to the piezoceramic patch. For this analysis, drive levels are assumed to be moderate so that linear piezoelectric relations can be employed. Finite element methods for discretizing the models are developed and the performance of the discretized models are illustrated through comparison with experimental data.

Wieman, Robert↗

NASA NTRS1975

A general algorithm using finite element method for aerodynamic configurations at low speeds

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Balasubramanian, R.↗

NASA NTRS2014

Mean Flow Augmented Acoustics in Rocket Systems

Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) − (lambda/c)(exp 2)(psi) − M(dot)[M(dot)(del)(del(psi))] − 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)−2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The present study employs the COMSOL Multphysics framework to solve the coupled eigenvalue problem using the finite element approach. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluated the gas flow inside of a solid rocket motor using St. Robert's law modeling solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are used by the coefficient form of the mathematics module to determine the eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. Pertinent results from these analyses are the complex valued eigenvalue and eigenvectors. Comparisons are made to the French results to evaluate the modeling approach. A comparison of the French results with that of the present analysis is displayed in figures 1 and 2, respectively. The graphic shows the first tangential eigenvector's real (a) and imaginary (b) values.

Fischbach, Sean R.↗

NASA NTRS1989

Explicit modeling of composite plates and beams in the dynamics of multibody systems

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed.

Amirouche, F. M. L.↗

NASA NTRSDate not supplied

Design Exploration of a Transonic Cruise Slotted Airfoil

A knowledge-based aerodynamic design method, CDISC, has been leveraged for the computational design exploration of the cruise slotted airfoil as a drag-saving technology for single aisle, transonic transport aircraft. Aerodynamic predictions were generated using the NASA USM3D Reynolds-averaged Navier-Stokes flow solver, and laminar flow assessments were conducted using the NASA BLSTA3D boundary layer profile solver paired with the LASTRAC stability analysis and transition prediction software. The CDISC design method was used to parametrically vary several slotted-airfoil design variables to understand their impact on aerodynamic performance. In addition to establishing best practices for slotted airfoil design, it was observed that the historically noted skin-friction penalty for cruise slotted airfoils was attributed to the low-Reynolds-number boundary layer of the flap. At cruise, this skin-friction penalty negated any potential decrease in pressure drag enabled by the cruise slotted airfoil architecture. This observation led to the development of an Aft-Laminar Multi-element Airfoil concept that uses airfoil shaping to promote natural laminar flow on the flap. At cruise conditions, the concept is predicted to offer a 2.7% reduction in sectional drag relative to a fully turbulent supercritical airfoil. Off-design analyses showed that laminar flow could be maintained with near-cruise variations in angle of attack and Mach number, resulting in sustained aerodynamic efficiency improvements and a delay in the drag rise Mach number. A low-speed, high-lift analysis at takeoff conditions predicted a maximum lift coefficient of 2.4 could be achieved by use of a variable-camber leading edge on the main element and simple deflection of the flap. These computationally-predicted benefits have motivated future research toward an aft-laminar cruise slotted wing design as an incremental step toward the application of natural laminar flow technology on transonic commercial transports.

Brett R Hiller↗

NASA NTRS2021

Comparison of chemical lateral boundary conditions for air quality predictions over the contiguous United States during pollutant intrusion events

The National Air Quality Forecast Capability (NAQFC) operated in U.S.’s National Oceanic and Atmospheric Administration (NOAA) provides the operational forecast guidance for ozone and fine particulate matters with aerodynamic diameters less than 2.5μm (PM2.5) over the contiguous 48 U.S. states (CONUS) using the Community Multi-scale Air Quality (CMAQ) model. The existing NAQFC uses climatological chemical lateral boundary conditions ( CLBCs), which cannot capture pollutant intrusion events originating outside of the model domain. In this study, we developed a model framework to use dynamic CLBCs from the Goddard Earth Observing System Model, version 5 (GEOS) to drive NAQFC. A mapping of the GEOS chemical species to the CMAQ’s Carbon Bond 5 (CB05)-Aero6 species was developed. The utilization of the GEOS dynamic CLBCs in NAQFC showed the best overall performance in simulating the surface observations during the Saharan dust intrusion and Canadian wildfire events in summer 2015.The simulated PM2.5 was improved from 0.18 to 0.37 and the mean bias was reduced from -6.74 μg/m3 to -2.96 μg/m3 over CONUS. Although the effect of CLBCs on the PM2.5 correlation was mainly near the inflow boundary, its impact on the background concentrations reached further inside the domain. The CLBCs could affect background ozone concentrations through the inflows of ozone itself and its precursors, such as CO. It was further found that the aerosol optical thickness (AOT) from satellite retrievals correlated well with the column CO and elemental carbon from GEOS. The satellite-derived AOT CLBCs generally improved the model performance for the wildfire intrusion events during a summer 2018 case study, and demonstrated how satellite observations of atmospheric composition could be used as an alternative method to capture the air quality effects of intrusions when the global model CLBCs, such as GEOS CLBCs, are not available.

Community Multi-scale Air Quality (CMAQ) model↗

NASA NTRSDate not supplied

On The Incorporation of Both Function-Driven Requirements and Topology Optimization in The Development of Lunar Launch & Landing Pads

In the design of additively manufactured structures, there can be a constant battle between focusing on function-driven design and topology optimization in an attempt to improve a products ability to meet all requirements. Function-driven optimization is defined as the process of identifying the best design parameters that satisfy project functionality requirements. Function-driven optimization is typically implemented by a designer(s) who, instead of computational limitations, has human bias for the input or inputs determined. On the other hand, topology optimization is defined as a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions, and constraints with the goal of maximizing the performance of the system. In topology optimization, the work is defined by the limited mathematical inputs and computationally available goals/restraints. If not evaluated simultaneously, these two approaches can result in fundamentally different design concepts meant to address the same requirements. NASA’s Artemis program includes the development of a base camp near the lunar South Pole. After site selection is made, one of the first infrastructure elements needed will be a launch and landing pad (LLP). The construction of such a pad will prevent damage to nearby structures from plume-surface interaction (PSI) while also providing a stable platform for the lander. These benefits reduce the required distance between the established landing zones and other settlement infrastructure. In this paper, the authors evaluate the requirements associated with lunar LLP development, application of both functional and topological optimization techniques, methodologies to combine the two techniques, and potential impacts on final design of such a pad.

In-situ↗

NASA NTRS1982

Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil

Two efforts to numerically simulate the flow about the Augmentor-Wing airfoil in the cruise configuration using the GRAPE elliptic partial differential equation grid generator algorithm are discussed. The Augmentor-Wing consists of a main airfoil with a slotted trailing edge for blowing and two smaller airfoils shrouding the blowing jet. The airfoil and the algorithm are described, and the application of GRAPE to an unsteady viscous flow simulation and a transonic full-potential approach is considered. The procedure involves dividing a complicated flow region into an arbitrary number of zones and ensuring continuity of grid lines, their slopes, and their point distributions across the zonal boundaries. The method for distributing the body-surface grid points is discussed.

Sorenson, R. L.↗

NASA NTRS1988

Transfinite element methodology for nonlinear/linear transient thermal modelling/analysis - Progress and recent advances

The 'transfinite element method' (TFEM) proposed by Tamma and Railkar (1987 and 1988) for the analysis of linear and nonlinear heat-transfer problems is described and demonstrated. The TFEM combines classical Galerkin and transform approaches with state-of-the-art FEMs to obtain a flexible hybrid modeling scheme. The fundamental principles of the TFEM and the derivation of the governing equations are reviewed, and numerical results for sample problems are presented in extensive graphs and briefly characterized. Problems analyzed include a square plate with a hole, a rectangular plate with natural and essential boundary conditions and varying thermal conductivity, the Space Shuttle thermal protection system, a bimaterial plate subjected to step temperature variations, and solidification in a semiinfinite liquid slab.

Tamma, Kumar K.↗

NASA NTRS1989

Nonlinear mesomechanics of composites with periodic microstructure

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

Walker, Kevin P.↗

NASA NTRS1992

Crack-mouth displacements for semielliptical surface cracks subjected to remote tension and bending loads

The exact analytical solution for an embedded elliptical crack in an infinite body subjected to arbitrary loading was used in conjunction with the finite element alternating method to obtain crack-mouth-opening displacements (CMOD) for surface cracks in finite plates subjected to remote tension. Identical surface-crack configurations were also analyzed with the finite element method using 20-noded element for plates subjected to both remote tension and bending. The CMODs from these two methods generally agreed within a few percent of each other. Comparisons made with experimental results obtained from surface cracks in welded aluminum alloy specimens subjected to tension also showed good agreement. Empirical equations were developed for CMOD for a wide range of surface-crack shapes and sizes subjected to tension and bending loads. These equations were obtained by modifying the Green-Sneddon exact solution for an elliptical crack in an infinite body to account for finite boundary effects. These equations should be useful in monitoring surface-crack growth in tests and in developing complete crack-face-displacement equations for use in three-dimensional weight-function methods.

Raju, Ivatury S.↗

NASA NTRS1994

The buckling response of symmetrically laminated composite plates having a trapezoidal planform area

The focus of this work is the buckling response of symmetrically laminated composite plates having a planform area in the shape of an isosceles trapezoid. The loading is assumed to be inplane and applied perpendicular to the parallel ends of the plate. The tapered edges of the plate are assumed to have simply supported boundary conditions, while the parallel ends are assumed to have either simply supported or clamped boundary conditions. A semi-analytic closed-form solution based on energy principles and the Trefftz stability criterion is derived and solutions are obtained using the Rayleigh-Ritz method. Intrinsic in this solution is a simplified prebuckling analysis which approximates the inplane force resultant distributions by the forms Nx=P/W(x) and Ny=Nxy=0, where P is the applied load and W(x) is the plate width which, for the trapezoidal planform, varies linearly with the lengthwise coordinate x. The out-of-plane displacement is approximated by a double trigonometric series. This analysis is posed in terms of four nondimensional parameters representing orthotropic and anisotropic material properties, and two nondimensional parameters representing geometric properties. For comparison purposes, a number of specific plate geometry, ply orientation, and stacking sequence combinations are investigated using the general purpose finite element code ABAQUS. Comparison of buckling coefficients calculated using the semi-analytical model and the finite element model show agreement within 5 percent, in general, and within 15 percent for the worst cases. In order to verify both the finite element and semi-analytical analyses, buckling loads are measured for graphite/epoxy plates having a wide range of plate geometries and stacking sequences. Test fixtures, instrumentation system, and experimental technique are described. Experimental results for the buckling load, the buckled mode shape, and the prebuckling plate stiffness are presented and show good agreement with the analytical results regarding the buckling load and the prebuckling plate stiffness. However, the experimental results show that for some cases the analysis underpredicts the number of halfwaves in the buckled mode shape. In the context of the definitions of taper ratio and aspect ratio used in this study, it is concluded that the buckling load always increases as taper ratio increases for a given aspect ratio for plates having simply supported boundary conditions on the parallel ends. There are combinations of plate geometry and ply stackling sequences, however, that reverse this trend for plates having clamped boundary conditions on the parallel ends such that an increase in the taper ratio causes a decrease in the buckling load. The clamped boundary conditions on the parallel ends of the plate are shown to increase the buckling load compared to simply supported boundary conditions. Also, anisotropy (the D16 and D26 terms) is shown to decrease the buckling load and skew the buckled mode shape for both the simply supported and clamped boundary conditions.

Radloff, H. D., II↗

NASA NTRS1991

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.

Mavriplis, Dimitri J.↗

NASA NTRS1991

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

Mavriplis, D. J.↗

NASA NTRS1990

The effect of coatings and liners on heat transfer in a dry shaft-bush tribosystem

The temperatures due to frictional heating within a solid lubricated or coated journal bearing were analyzed by using a finite element method. A solid model of the shaft-bush tribocontact was generated with an eight-node, three-dimensional, first-order isoparametric heat-transfer element and the Patran solid modeler software. The Patmar (Patran-Marc) translator was used to help develop the Marc-based finite element program for the system; this software was used on the Cray X-MP supercomputer to perform a finite element analysis of the contact. The analysis was performed for various liner materials, for thin, hard, wear-resistant coated bearings, and for different geometries and thermal cooling boundary conditions. The analyses indicated that thermal conductivity of the liner or coating material is the most vital thermal parameter that controls the interface temperature. In addition to design variations, the proximity of the cooling source to the heat-flux-generating interface is critically important to the temperature control in the system.

Ghosh, Mihir K.↗

NASA NTRS2001

Investigation of Conjugate Heat Transfer in Turbine Blades and Vanes

We report on work carried out to develop a 3-D coupled Finite Volume/BEM-based temperature forward/flux back (TFFB) coupling algorithm to solve the conjugate heat transfer (CHT) which arises naturally in analysis of systems exposed to a convective environment. Here, heat conduction within a structure is coupled to heat transfer to the external fluid which is convecting heat into or out of the solid structure. There are two basic approaches to solving coupled fluid structural systems. The first is a direct coupling where the solution of the different fields is solved simultaneously in one large set of equations. The second approach is a loose coupling strategy where each set of field equations is solved to provide boundary conditions for the other. The equations are solved in turn until an iterated convergence criterion is met at the fluid-solid interface. The loose coupling strategy is particularly attractive when coupling auxiliary field equations to computational fluid dynamics codes. We adopt the latter method in which the BEM is used to solve heat conduction inside a structure which is exposed to a convective field which in turn is resolved by solving the NASA Glenn compressible Navier-Stokes finite volume code Glenn-HT. The BEM code features constant and bi-linear discontinuous elements and an ILU-preconditioned GMRES iterative solver for the resulting non-symmetric algebraic set arising in the conduction solution. Interface of flux and temperature is enforced at the solid/fluid interface, and a radial-basis function scheme is used to interpolated information between the CFD and BEM surface grids. Additionally, relaxation is implemented in passing the fluxes from the conduction solution to the fluid solution. Results from a simple test example are reported.

Kassab, A. J.↗

NASA NTRS1991

Time-domain finite elements in optimal control with application to launch-vehicle guidance

A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

Bless, Robert R.↗