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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Large-eddy simulation of a backward facing step flow using a least-squares spectral element method

We report preliminary results obtained from the large eddy simulation of a backward facing step at a Reynolds number of 5100. The numerical platform is based on a high order Legendre spectral element spatial discretization and a least squares time integration scheme. A non-reflective outflow boundary condition is in place to minimize the effect of downstream influence. Smagorinsky model with Van Driest near wall damping is used for sub-grid scale modeling. Comparisons of mean velocity profiles and wall pressure show good agreement with benchmark data. More studies are needed to evaluate the sensitivity of this method on numerical parameters before it is applied to complex engineering problems.

Chan, Daniel C.↗
NASA NTRS1973

Finite Element Method for Thermal Analysis

A two- and three-dimensional, finite-element thermal-analysis program which handles conduction with internal heat generation, convection, radiation, specified flux, and specified temperature boundary conditions is presented. Elements used in the program are the triangle and tetrahedron for two- and three-dimensional analysis, respectively. The theory used in the program is developed, and several sample problems demonstrating the capability and reliability of the program are presented. A guide to using the program, description of the input cards, and program listing are included.

Heuser, J.↗
NASA NTRS1976

Hybrid finite element methods

The purpose of this paper is to show how Lagrange multipliers can be used with finite elements to achieve a number of desirable properties in the underlying approximation. For elliptic boundary value problems, variational principles can be developed in which all boundary conditions are natural. In fluid flow problems, one can endow the approximations with physically essential conservation laws.

Fix, G. M.↗
NASA NTRS1976

On a 3-D singularity element for computation of combined mode stress intensities

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Atluri, S. N.↗
NASA NTRS1977

Optimal solar sail planetocentric trajectories

The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.

Sackett, L. L.↗
NASA NTRS1980

Wind-tunnel measurements and comparison with flight of the boundary layer and heat transfer on a hollow cylinder at Mach 3

The wind tunnel tests were conducted both with and without boundary layer trips at Mach 3 and nominal free stream Reynolds numbers per meter ranging from 3.3 x 10 the 6th power. Instrumentation consisted of pressure orifices, thermocouples, a boundary layer pitot pressure rake, and a floating element skin friction balance. Measurements from both wind tunnel and flight were compared with existing engineering prediction methods.

Stallings, R. L., Jr.↗
NASA NTRS1991

The application of time-dependent wavepacket methods to reactive scattering

Several methods for performing numerically exact reactive scattering calculations using time-dependent wavepackets are reviewed. The basic idea is to take the multiarrangement reactive problem and reformulate it as one or more inelastic ones. In the simplest method, total reaction probabilities are extracted by calculating the flux of the wavepacket as it leaves the interaction region in the direction of the reactive arrangement. To make this practical, complex potentials that absorb the wavepacket before it reaches the numerical grid boundary are used. Methods that generate observables ranging from total, energy-averaged reaction probabilities up to energy- and state-resolved S-matrix elements are used. Techniques for efficiently performing the necessary inelastic wavepacket propagation are also reviewed.

Neuhauser, Daniel↗
NASA NTRS1996

Investigation of the Interaction of External Disturbances with Roughened Flat Plate Boundary Layer

The interaction of an external disturbance with a laminar boundary layer over a flat plate with distributed roughness is investigated using combined experimental and numerical methods. The experiment is modeled with an unsteady boundary layer code using second order backward differencing. The simulation includes the second order scattering from roughness elements at and near the first streamwise station of predicted boundary layer instability. A comparison of experimental measurements of the boundary layer perturbation due to the wake from a vibrating ribbon with the computed first order forced boundary layer perturbation showed excellent agreement. Second order roughness induced eigenfunctions from boundary layer theory are examined and compared with other forms of excitation

Davis, Sanford S.↗
NASA NTRS1983

A finite element approach for predicting nozzle admittances

A finite element method is used to predict the admittances of axisymmetric nozzles. It is assumed that the flow in the nozzle is isentropic and the disturbances are small so that linear analyses apply. An approximate, two dimensional compressible model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear wave equation. The differential form of the acoustic equation is transformed to an integral equation by using Galerkin's method, and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. The boundary conditions are described for both straight and curved sonic lines. A two dimensional FEM with linear elements is used to solve the acoustic equation. A one dimensional FEM is also used to solve the reduced equation of Crocco, and the solution verifies the sufficiency of the boundary residual formulation. Comparison between computed admittances and experimental data is shown to be quite good.

Sigman, R. K.↗
NASA NTRS1975

Duct acoustics and acoustic finite element method

A comprehensive solution method - Acoustic Finite Element Method - has been proposed. In order to generate confidence in the method proposed, the problem of influence of shear flow in a two-dimensional channel on sound propagation from an arbitrary source distribution has been theoretically formulated. From the preliminary investigation of application of acoustic finite element method, it seems that it can provide solutions to problems concerning the transmission of sound in variable area ducts, or in ducts in which the boundary layer depends on the streamwise variable, or in ducts with discontinuities in lining impedance and with end termination impedances, both the inlet and exhaust jet flows being taken into account.

Kapur, A.↗
NASA NTRS1980

Grid generation using coarse, smooth finite elements

Grid quality solutions of a wide variety of equations can be generated to fit reasonable functional boundary conditions in two dimensions using very coarse rectangular finite elements. Some wavy operators (with no natural variational expression) were tried in order to demonstrate the method's versatility.

Dickson, L. J.↗
NASA NTRS1986

On 3-D inelastic analysis methods for hot section components (base program)

A 3-D Inelastic Analysis Method program is described. This program consists of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain)and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (Marc-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this report.

Wilson, R. B.↗
NASA NTRS2016

Development of a Perfectly Matched Layer Technique for a Discontinuous-Galerkin Spectral-Element Method

The perfectly matched layer (PML) technique is developed in the context of a high- order spectral-element Discontinuous-Galerkin (DG) method. The technique is applied to a range of test cases and is shown to be superior compared to other approaches, such as those based on using characteristic boundary conditions and sponge layers, for treating the inflow and outflow boundaries of computational domains. In general, the PML technique improves the quality of the numerical results for simulations of practical flow configurations, but it also exhibits some instabilities for large perturbations. A preliminary analysis that attempts to understand the source of these instabilities is discussed.

Spectral-Element↗
NASA NTRS1996

The Prediction of Ducted Fan Engine Noise Via a Boundary Integral Equation Method

A computationally efficient Boundary Integral Equation Method (BIEM) for the prediction of ducted fan engine noise is presented. The key features of the BIEM are its versatility and the ability to compute rapidly any portion of the sound field without the need to compute the entire field. Governing equations for the BIEM are based on the assumptions that all acoustic processes are linear, generate spinning modes, and occur in a uniform flow field. An exterior boundary value problem (BVP) is defined that describes the scattering of incident sound by an engine duct with arbitrary profile. Boundary conditions on the duct walls are derived that allow for passive noise control treatment. The BVP is recast as a system of hypersingular boundary integral equations for the unknown duct surface quantities. BIEM solution methodology is demonstrated for the scattering of incident sound by a thin cylindrical duct with hard walls. Numerical studies are conducted for various engine parameters and continuous portions of the total pressure field are computed. Radiation and duct propagation results obtained are in agreement with the classical results of spinning mode theory for infinite ducts.

Boundary integral equation↗
NASA NTRSDate not supplied

DeepONet-Assisted Optimization of Surface Topography for Transition Delay in a Mach 4.5 Boundary Layer

We use deep learning, an ensemble variational technique (EnVar), and direct numerical simulations(DNS) to design an optimal topography for a two-dimensional roughness element that delays the on-set of laminar-turbulent transition in a Mach 4.5 flat-plate boundary layer. Deep operator networks (DeepONets), which have the known ability to learn complex nonlinear operators within dynamical systems, are used for machine learning. For the baseline configuration of a smooth flat plate, the second-mode waves at the DNS inflow cause a quick nonlinear breakdown of the high-speed boundary layer within the computational domain. Results reported in the present study validate the ability of DeepONets to model the transition delay via a given topography of the roughness element. The computing cost to optimize the rough-ness element for minimal skin-friction drag is substantially lowered by the DeepONets-based reduced-order model. In comparison to the baseline method of EnVar optimization based on DNS alone, the DeepONets-based EnVar optimizer is able to delay transition past the outflow boundary of the computational domain while utilizing almost 5–6 times fewer DNS.

Machine Learning↗
NASA NTRS2010

Numerical Computations of Hypersonic Boundary-Layer over Surface Irregularities

Surface irregularities such as protuberances inside a hypersonic boundary layer may lead to premature transition on the vehicle surface. Early transition in turn causes large localized surface heating that could damage the thermal protection system. Experimental measurements as well as numerical computations aimed at building a knowledge base for transition Reynolds numbers with respect to different protuberance sizes and locations have been actively pursued in recent years. This paper computationally investigates the unsteady wake development behind large isolated cylindrical roughness elements and the scaled wind-tunnel model of the trip used in a recent flight measurement during the reentry of space shuttle Discovery. An unstructured mesh, compressible flow solver based on the space-time conservation element, solution element (CESE) method is used to perform time-accurate Navier-Stokes calculations for the flow past a roughness element under several wind-tunnel conditions. For a cylindrical roughness element with a height to the boundary-layer thickness ratio from 0.8 to 2.5, the wake flow is characterized by a mushroom-shaped centerline streak and horse-shoe vortices. While time-accurate solutions converged to a steady-state for a ratio of 0.8, strong flow unsteadiness is present for a ratio of 1.3 and 2.5. Instability waves marked by distinct disturbance frequencies were found in the latter two cases. Both the centerline streak and the horse-shoe vortices become unstable downstream. The oscillatory vortices eventually reach an early breakdown stage for the largest roughness element. Spectral analyses in conjunction with the computed root mean square variations suggest that the source of the unsteadiness and instability waves in the wake region may be traced back to possible absolute instability in the front-side separation region.

Chang, Chau-Lyan↗
NASA NTRS1999

High-Resolution Genuinely Multidimensional Solution of Conservation Laws by the Space-Time Conservation Element and Solution Element Method

In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.

Himansu, Ananda↗
NASA NTRS1985

On the penetration of a hot diapir through a strongly temperature-dependent viscosity medium

The ascent of a hot spherical body through a fluid with a strongly temperature-dependent viscosity has been studied using an axisymmetric finite element method. Numerical solutions range over Peclet numbers of 0.1 - 1000 from constant viscosity up to viscosity variations of 100,000. Both rigid and stress-free boundary conditions were applied at the surface of the sphere. The dependence of drag on viscosity variation was shown to have no dependence on the stress boundary condition except for a Stokes flow scaling factor. A Nusselt number parameterization based on the stress-free constant viscosity functional dependence on the Peclet number scaled by a parameter depending on the viscosity structure fits both stress-free and rigid boundary condition data above viscosity variations of 100. The temperature scale height was determined as a function of sphere radius. For the simple physical model studied in this paper pre-heating is required to reduce the ambient viscosity of the country rock to less than 10 to the 22nd sq cm/s in order for a 10 km diapir to penetrate a distance of several radii.

Daly, S. F.↗