SEARCH · Engineering Papers

Results for “numerical solution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 559 records · Page 31

All sources NASA NTRS DOE OSTI

NASA NTRSDate not supplied

CFD and Experimental Data Comparisons for Conventional and AFC-Enabled CRM High-Lift Configurations

Numerical simulations have been performed for a simplified high-lift (SHL) version of the Common Research Model (CRM) configuration, where the Fowler flaps of a representative conventional high-lift (CRM-HL) configuration are replaced by a set of simple hinged flaps. These hinged flaps are equipped with integrated modular active flow control (AFC) cartridges on the suction surface of the flap shoulder, and the resulting geometry is known as the CRM-SHL-AFC configuration. The main objective is to make use of AFC devices on the CRM-SHL-Configuration to produce the aerodynamic performance (lift) comparable to that of the CRM-HL configuration over a large angle of attack range encompassing maximum lift conditions. For comparison purposes, computations are also per-formed for the CRM-HL configuration. In the current paper, PowerFLOWR©, a CFD code based on the Lattice Boltzmann method (LBM), is used to simulate the entire flow field associated with the CRM-SHL-AFC configuration equipped with a combination of two different types of AFC actuators. The transonic version of the PowerFLOWR© code that has been validated for high-speed flows is used to simulate the flow field generated by the high-momentum actuators required to mitigate reversed flow regions on the suction surfaces of the main wing and the flap. This study is focused on the AFC systems and actuator arrangements that had emerged based on the parametric studies conducted previously at the nominal landing condition. Comparisons of the numerical solutions for lift and surface pressures are presented here with the experimental data, demonstrating the usefulness of CFD for predicting the flow field and lift characteristics of AFC-enabled high-lift configurations over a broad angle of attack range. The numerical solutions predict the expected trends in aerodynamic forces with angle of attack variation.

Veer N Vatsa↗

NASA NTRS1981

Magnetohydrodynamic interaction of high-speed streams

Numerical solutions of a magnetohydrodynamic model are carried out to describe the nonlinear interaction of corotating high-speed streams near the solar equatorial plane. Two problems are studied. The first problem is to simulate the evolution of an idealized high-speed stream. Numerical solutions are obtained to represent the variations of flow velocity, magnetic field, plasma density, temperature, and conduction heat flux in the interaction region. They demonstrate that the dynamical interaction and heat conduction process are responsible for the thermal structure of a high-speed stream. The second problem deals with the formation of corotating shock waves near the leading edge of a broad stream resulting from the merging of characteristic curves. Corotating shocks do not necessarily occur in pairs; a reverse shock can be formed without a forward shock nearby.

Whang, Y. C.↗

NASA NTRS1994

Gasdynamic models of the solar wind/interstellar medium interaction

The interaction between the solar wind and the interstellar medium is modeled self-consistently using numerical solutions of the time-dependent gasdynamic equations in spherical and cylindrical coordinates. For the results presented here it is assumed that the solar system moves through the surrounding medium with a supersonic velocity. After an initial (nonequilibrium) state has been specified, the numerical solution follows the evolution in time until the interaction relaxes to a dynamic equilibrium. As would be expected, the solutions show the formation of a bow shock upstream of the traveling solar system to deflect the interstellar plasma around the cavity created by the solar wind. A terminiation shock also forms to slow and compress the solar wind plasma. For the simulation in spherical coordinates, the downstream portion of the termination shock reaches equilibrium more than three times further from the Sun than the equilibrium distance to the termination shock on the upstream side.

Steinolfson, R. S.↗

DOE OSTI2026

Assessment of the hydromechanical higher-order MPM for the simulation of geotechnical problems

The Material Point Method (MPM) has been increasingly used to simulate large strain deformations. Linear interpolation functions are commonly used to perform the spatial integration. It is well-known that the discontinuities in the interpolation function derivatives induce shock-like artifacts known as ‘cell-crossing’ error. These errors compound with volumetric locking errors when used with hydromechanical formulations for porous media, where different velocity fields are used for each phase. The capabilities of higher-order MPM frameworks have not been explored for real-scale geotechnical problems. As such, this paper aims to assess, validate, and further discuss a higher-order B-spline MPM (BS-MPM) framework. First, the BS-MPM framework is verified against the large-strain oedometer consolidation problem. Second, the framework is validated against a real-scale slope failure experiment triggered by pore water pressure recharge. Landslide features that are captured using the higher-order framework are specifically highlighted, and results (e.g., pore water pressure and deformation) are validated with field measurements. A generally convergent numerical solution is observed when using cubic interpolation functions. Third, a footing penetration problem is simulated using the multi-patch BS-MPM. Trends are examined with respect to penetration velocity and variation in hydraulic conductivity. The BS-MPM framework ultimately presents a stabilized numerical solution that captures plausible hydromechanical interaction trends important in geotechnical engineering applications.

36 MATERIALS SCIENCE↗

NASA NTRS1972

The k-space formulation of the n-dimensional scattering problem

The n-dimensional scattering problem is solved by means of a k-space formulation of the field equations, thereby replacing the conventional integral equation formulation by a set of two algebraic equations in two unknowns in two spaces (the constitutive equation being an algebraic equation in x-space). These equations are solved by an iterative method with the aid of the fast Fourier transform (FFT) algorithm connecting the two spaces, requiring very simple initial approximations. Since algebraic and FFT equations are used, the number of arithmetic multiple-add operations and storage allocations required for a numerical solution are reduced from the order of N sq (for solving the matrix equations resulting from the conventional integral equations) to the order of N(log base 2 of N) and N, respectively (where N is the number of data points required for the specification of the problem). The advantage gained in speed and storage is thus of the order of N/log base 2 of N and N, respectively. This method is thus considerably more efficient than the conventional matrix method, and permits exact numerical solutions for much larger problems. Arguments are presented toward the view that the field equations are more fundamental in k-space. The details and some numerical results of the application of this method to the three-dimensional electromagnetic scattering problems are presented as an example.

Bojarski, N. N.↗

NASA NTRS1981

Wave transience in a compressible atmosphere. I - Transient internal wave, mean-flow interaction. II - Transient equatorial waves in the quasi-biennial oscillation

Analytical and numerical solutions are obtained in an approximate quasi-linear model, to describe the way in which vertically propagating waves give rise to mean flow accelerations in an atmosphere due to the effects of wave transience. These effects in turn result from compressibility and vertical group velocity feedback, and culminate in the spontaneous formation and descent of regions of strong mean wind shear. The numerical solutions display mean flow accelerations due to Kelvin waves in the equatorial stratosphere, with wave absorption altering the transience mechanism in such significant respects as causing the upper atmospheric mean flow acceleration to be very sensitive to the precise magnitude and distribution of the damping mechanisms. The numerical simulations of transient equatorial waves in the quasi-biennial oscillation are also considered.

Dunkerton, T. J.↗

NASA NTRS1996

Implicity restarted Arnoldi/Lanczos methods for large scale eigenvalue calculations

Eigenvalues and eigenfunctions of linear operators are important to many areas of applied mathematics. The ability to approximate these quantities numerically is becoming increasingly important in a wide variety of applications. This increasing demand has fueled interest in the development of new methods and software for the numerical solution of large-scale algebraic eigenvalue problems. In turn, the existence of these new methods and software, along with the dramatically increased computational capabilities now available, has enabled the solution of problems that would not even have been posed five or ten years ago. Until very recently, software for large-scale nonsymmetric problems was virtually non-existent. Fortunately, the situation is improving rapidly. The purpose of this article is to provide an overview of the numerical solution of large-scale algebraic eigenvalue problems. The focus will be on a class of methods called Krylov subspace projection methods. The well-known Lanczos method is the premier member of this class. The Arnoldi method generalizes the Lanczos method to the nonsymmetric case. A recently developed variant of the Arnoldi/Lanczos scheme called the Implicitly Restarted Arnoldi Method is presented here in some depth. This method is highlighted because of its suitability as a basis for software development.

Sorensen, Danny C.↗

NASA NTRS1992

CSM solutions of rotating blade dynamics using integrating matrices

The dynamic behavior of flexible rotating beams continues to receive considerable research attention as it constitutes a fundamental problem in applied mechanics. Further, beams comprise parts of many rotating structures of engineering significance. A topic of particular interest at the present time involves the development of techniques for obtaining the behavior in both space and time of a rotor acted upon by a simple airload loading. Most current work on problems of this type use solution techniques based on normal modes. It is certainly true that normal modes cannot be disregarded, as knowledge of natural blade frequencies is always important. However, the present work has considered a computational structural mechanics (CSM) approach to rotor blade dynamics problems in which the physical properties of the rotor blade provide input for a direct numerical solution of the relevant boundary-and-initial-value problem. Analysis of the dynamics of a given rotor system may require solution of the governing equations over a long time interval corresponding to many revolutions of the loaded flexible blade. For this reason, most of the common techniques in computational mechanics, which treat the space-time behavior concurrently, cannot be applied to the rotor dynamics problem without a large expenditure of computational resources. By contrast, the integrating matrix technique of computational mechanics has the ability to consistently incorporate boundary conditions and 'remove' dependence on a space variable. For problems involving both space and time, this feature of the integrating matrix approach thus can generate a 'splitting' which forms the basis of an efficient CSM method for numerical solution of rotor dynamics problems.

Lakin, William D.↗

NASA NTRS1992

Computation of three-dimensional effects on two dimensional wings

A 2-D numerical investigation was performed to determine the effect of a Gurney flap on a NACA 4412 airfoil. A Gurney flap is a flat plate on the order of 1 to 3 percent of the airfoil chord length, oriented perpendicular to the airfoil chord line and located at the trailing edge of the airfoil. An incompressible Navier Stokes code, INS2D, was used to calculate the flow field about the airfoil. The fully turbulent results were obtained using the Baldwin-Barth one-equation turbulence model. Gurney flap sizes of 0.5, 1, 1.25, 1.5, 2, and 3 percent of the airfoil chord were studied. Computational results were compared with experimental results where possible. The numerical solutions show that the Gurney flap increases airfoil lift coefficient with only a slight increase in drag coefficient. Use of a 1.5 percent chord Gurney flap increases the maximum lift coefficient by approximately 0.3 and decreases the angle of attack for a given lift coefficient by more than 3 degrees. The numerical solutions exhibit detailed flow structures at the trailing edge and provide a possible explanation for the increased aerodynamic performance.

Cummings, Russell M.↗

NASA NTRS1992

Computational evaluation of an airfoil with a Gurney flap

A 2D numerical investigation was performed to determine the effect of a Gurney flap on a NACA 4412 airfoil. A Gurney flap is a flat plate on the order of 1 to 3 percent of the airfoil chord length, oriented perpendicular to the airfoil chord line and located at the trailing edge of the airfoil. An incompressible Navier Stokes code, INS2D, was used to calculate the flow field about the airfoil. The fully turbulent results were obtained using the Baldwin-Barth one-equation turbulence model. Gurney flap sizes of 0.5 , 1, 1.25, 1.5, 2, and 3 percent of the airfoil chord were studied. Computational results were compared with experimental results where possible. The numerical solutions show that the Gurney flap increases airfoil lift coefficient with only a slight increase in drag coefficient. Use of a 1.5 percent chord Gurney flap increases the maximum lift coefficient by approximately 0.3 and decreases the angle of attack for a given lift coefficient by more than 3 deg. The numerical solutions exhibit detailed flow structures at the trialing edge and provide a possible explanation for the increased aerodynamic performance.

Jang, Cory S.↗

NASA NTRS1972

Chemical nonequilibrium effects on the flow in the windward plane of symmetry of a blunted delta orbiter

The extent, and some of the consequences, of nonequilibrium effects in the inviscid orbiter flow field are examined. Calculations have been made for the reacting flow along selected streamlines in the windward plane of symmetry of a blunted delta shape representative of a shuttle orbiter. An approximate model of the pressure field in the windward plane of symmetry of a blunted delta wing was constructed from wind tunnel measurements of the body surface pressure distribution and approximate calculations of the shock shape and streamline locations. Numerical solutions for the flow along streamlines were obtained for this pressure distribution, and solutions were obtained for both equilibrium and finite-reaction rate, nonequilibrium chemical reactions. Since the streamtube solutions are much easier to compute than fully three-dimensional, reacting flows, results were obtained for a wide range of conditions. The validity of this approach is based on the assumptions that the pressure field is insensitive to nonequilibrium effects and that the flow along streamlines is quasi-one dimensional. Numerical solutions have been used to verify this approach for other blunted slender shapes such as spherically blunted cones.

Lordi, J. A.↗

NASA NTRS1974

Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies

A method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected region containing any number of arbitrarily shaped bodies is presented. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system. Numerical solutions for the lifting and nonlifting potential flow about Joukowski and Karman-Trefftz airfoils using this coordinate system generation show excellent comparison with the analytic solutions. The application to fields with multiple bodies is illustrated by a potential flow solution for multiple airfoils.

Thompson, J. F.↗

NASA NTRS1983

Calculation of afterbody flows with a composite velocity formulation

A recently developed technique for numerical solution of the Navier-Stokes equations for subsonic, laminar flows is investigated. It is extended here to allow for the computation of transonic and turbulent flows. The basic approach involves a multiplicative composite of the appropriate velocity representations for the inviscid and viscous flow regions. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli equation for the pressure, while the continuity equation reduces to the familiar potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary layers. The velocity components are computed with a coupled strongly implicity procedure. For transonic flows the artificial compressibility method is used to treat supersonic regions. Calculations are made for both laminar and turbulent flows over axisymmetric afterbody configurations. Present results compare favorably with other numerical solutions and/or experimental data.

Swanson, R. C.↗

NASA NTRS1974

Numerical and experimental studies of the natural convection within a horizontal cylinder

Numerical solutions are obtained for the quasi-compressible Navier-Stokes equations governing the time-dependent natural convection within a horizontal cylinder. The early flow development and wall heat transfer are obtained after a uniformly cold wall is imposed as a boundary condition on the cylinder. Results are also obtained for a time-varying cold wall as a boundary condition with windward explicit differencing used for the numerical solutions. The viscous truncation error associated with this scheme is controlled so that first-order accuracy is maintained in time and space. Experiments within a small-scale instrumented horizontal cylinder revealed the time development of the temperature distribution across the boundary layer as well as the decay of wall heat transfer with time. Agreement between temperature distributions obtained experimentally and numerically was generally good. The time decay of the dimensionless ratio of the Nusselt number to the one-fourth power of the Grashof number is found both numerically and experimentally, and good agreement is obtained between these two results over most of the cylinder wall.

Stewart, R. B.↗

NASA NTRS1983

Non-Newtonian Fluid Model Incorporated into Elastohydrodynamic Lubrication of Rectangular Contacts

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed, load, materials, and sliding velocity and limiting-shear-strength proportionality constant on dimensionless minimum film thickness was investigated. Fourteen cases were used in obtaining the minimum-film-thickness equation for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.

Jacobson, B. O.↗

NASA NTRS1984

Non-Newtonian fluid model incorporated into elastohydrodynamic lubrication of rectangular contacts

Jacobson, B. O.↗

NASA NTRS1977

Kinetic theory analysis of rarefied gas flow through finite length slots

A kinetic-theory analysis is made of the flow of a rarefied monatomic gas through a two-dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete-ordinate methods. The former method portrays the transition-regime characteristics well but has limitations in the free-molecule regime. The latter method gives accurate results in the free-molecule and slip regimes and bolsters confidence in the accuracy of the transition-regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytical solution of the moment equations for length-to-width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.

Raghuraman, P.↗

NASA NTRS2001

Modeling and Analysis of Wrinkled Membranes: An Overview

Thin-film membranes are basic elements of a variety of space inflatable/deployable structures. Wrinkling degrades the performance and reliability of these membrane structures, and hence has been a topic of continued interest. Wrinkling analysis of membranes for general geometry and arbitrary boundary conditions is quite challenging. The objective of this presentation is two-fold. Firstly, the existing models of wrinkled membranes and related numerical solution methods are reviewed. The important issues to be discussed are the capability of a membrane model to characterize taut, wrinkled and slack states of membranes in a consistent and physically reasonable manner; the ability of a wrinkling analysis method to predict the formation and growth of wrinkled regions, and to determine out-of-plane deformation and wrinkled waves; the convergence of a numerical solution method for wrinkling analysis; and the compatibility of a wrinkling analysis with general-purpose finite element codes. According to this review, several opening issues in modeling and analysis of wrinkled membranes that are to be addressed in future research are summarized, The second objective of this presentation is to discuss a newly developed membrane model of two viable parameters (2-VP model) and associated parametric finite element method (PFEM) for wrinkling analysis are introduced. The innovations and advantages of the proposed membrane model and PFEM-based wrinkling analysis are: (1) Via a unified stress-strain relation; the 2-VP model treat the taut, wrinkled, and slack states of membranes consistently; (2) The PFEM-based wrinkling analysis has guaranteed convergence; (3) The 2-VP model along with PFEM is capable of predicting membrane out-of-plane deformations; and (4) The PFEM can be integrated into any existing finite element code. Preliminary numerical examples are also included in this presentation to demonstrate the 2-VP model and PFEM-based wrinkling analysis approach.

Yang, B.↗