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At least 667 records · Page 37

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NASA NTRS1988

Implications of truncating semi-infinite physical domains on the accuracy of the solutions to the N-S equations

Numerical techniques for solving the Navier-Stokes equations of laminar incompressible flow over a forward-facing step on a semiinfinite flat plate are evaluated analytically and by means of sample computations. A primitive-variable method with pseudocompressibility and full mapping of the semiinfinite domain is compared with a vorticity/stream-function method with a truncated domain, applying a flux-corrected explicit finite-difference procedure to solve the discretized transport equations. The results are presented in graphs and compared with published experimental data. The solutions obtained with the truncated-domain methods are shown to be inaccurate, even in cases when they are smooth.

Dekruif, Jeffery S.↗

NASA NTRS1988

Model structure of a cosmic-ray mediated stellar or solar wind

An idealized hydrodynamic model is presented for the mediation of a free-streaming stellar wind by galactic cosmic rays or energetic particles accelerated at the stellar wind termination shock. The spherically-symmetric stellar wind is taken to be cold; the only body force is the cosmic ray pressure gradient. The cosmic rays are treated as a massless fluid with an effective mean diffusion coefficient k proportional to radial distance r. The structure of the governing equations is investigated both analytically and numerically. Solutions for a range of values of k are presented which describe the deceleration of the stellar wind and a transition to nearly incompressible flow and constant cosmic ray pressure at large r. In the limit of small k the transition steepens to a strong stellar wind termination shock. For large k the stellar wind is decelerated gradually with no shock transition. It is argued that the solutions provide a simple model for the mediation of the solar wind by interstellar ions as both pickup ions and the cosmic ray anomalous component which together dominate the pressure of the solar wind at large r.

Lee, M. A.↗

NASA NTRS1988

Solution of the Neumann pressure problem in general orthogonal coordinates using the multigrid technique

The multigrid (MG) technique has been advanced for use with Neumann boundary-value problems in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of incompressible flow using the velocity-pressure formulation of the Navier-Stokes equations. The finite-difference representation of the problem and the formulation of the restriction and coarse-grid correction operators are examined in detail. Maintaining consistency between these and the integral constraint associated with the Neumann problem is found to be critical for the success of the MG technique. The influence of the smoothing operator is examined by employing Gauss-Seidel, alternating-direction implicit, and strongly implicit techniques. The MG procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 14, depending on the type of smoothing operator employed and the values of the problem parameters.

Ghia, U.↗

NASA NTRS1989

Analysis Of Straight And Wavy Annular Seals

Rotordynamic coefficients derived. Report presents analysis of incompressible flow in annular turbopump seal with straight or radially/axially wavy (azimuthally symmetrical) surface facing shaft. Purpose of analysis to quantify effects of waviness on rotordynamic coefficients of seal. Whirl-frequency ratio of wavy rough seal considerably less than straight rough seal.

Scharrer, Joseph K.↗

NASA NTRS1989

Two-dimensional numerical simulation of a Stirling engine heat exchanger

The first phase of an effort to develop multidimensional models of Stirling engine components is described; the ultimate goal is to model an entire engine working space. More specifically, parallel plate and tubular heat exchanger models with emphasis on the central part of the channel (i.e., ignoring hydrodynamic and thermal end effects) are described. The model assumes: laminar, incompressible flow with constant thermophysical properties. In addition, a constant axial temperature gradient is imposed. The governing equations, describing the model, were solved using Crank-Nicloson finite-difference scheme. Model predictions were compared with analytical solutions for oscillating/reversing flow and heat transfer in order to check numerical accuracy. Excellent agreement was obtained for the model predictions with analytical solutions available for both flow in circular tubes and between parallel plates. Also the heat transfer computational results are in good agreement with the heat transfer analytical results for parallel plates.

Ibrahim, Mounir B.↗

NASA NTRS1989

Discussion of the potential and limitations of direct and large-eddy simulations

The full text of the discussion paper presented at the Whither Turbulence Workshop on the potential and limitations of direct and large-eddy simulations is provided. Particular emphasis is placed on discussing the role of numerics and mathematical theory in direct simulations of both compressible and incompressible flows. A variety of unresolved issues with large-eddy simulations such as their implementation in high-order finite difference codes, problems with defiltering, and modifications to accommodate integrations to solid boundaries are elaborated on. These as well as other points are discussed in detail along with the authors' views concerning the prospects for future research.

Hussaini, M. Y.↗

NASA NTRS1988

Aerodynamic applications of an efficient incompressible Navier-Stokes solver

A robust and accurate upwind scheme based on flux-difference splitting for three-dimensional, incompressible flows in general coordinates is described. Viscous effects are included through a thin-layer approximation to the Navier-Stokes equations. Turbulent flows are simulated with extensions to the Baldwin-Lomax (1978) turbulence model. The effects of accuracy and gridding on the computed flow field results are assessed. The results obtained from the code for vortical flows over a delta wing, a double delta wing, and a tangent-ogive forebody compare well with experimental data.

Hartwich, Peter M.↗

NASA NTRS1987

A new method for the aerodynamic analysis of lifting surfaces

The use of the original Ffowcs Williams and Hawkings equation to improve the solution to simple problems of two-dimensional and incompressible flow is studied. It is shown that a linear formulation, with the quadrupole term neglected, leads to better correlation with the results of potential theory. A solution to steady and two-dimensional problems is developed and applied to families of elliptic cylinders and symmetric airfoils.

Brandao, Mauricio Pazini↗

NASA NTRS1989

Computational fluid dynamics - A personal view

This paper provides a personal view of computational fluid dynamics. The main theme is divided into two categories - one dealing with algorithms and engineering applications and the other with scientific investigations. The former category may be termed computational aerodynamics, with the objective of providing reliable aerodynamic or engineering predictions. The latter category is essentially basic research, where the algorithmic tools are used to unravel and elucidate fluid-dynamic phenomena hard to obtain in a laboratory. A critique of the numerical solution techniques for both compressible and incompressible flows is included. The discussion on scientific investigations deals in particular with transition and turbulence.

Hussaini, M. Y.↗

NASA NTRS1987

Effect of roughness on the stability of boundary layers

An analysis is conducted on the effect of imperfections consisting of humps and dips on the stability of incompressible flows over flat plates. The mean flow is calculated using interacting boundary layers. Linear quasiparallel spatial stability is used to calculate the growth rates and mode shapes of two-dimensional disturbances. Then, the amplification factor is computed. A search for the most dangerous frequency is conducted based on an amplification factor of 9 in the shortest distance. Correlations are made with the transition experiment of Walker and Greening using the e sup 9 method.

Nayfeh, Ali H.↗

NASA NTRS1989

Time-dependent viscous incompressible Navier-Stokes equations - The finite difference Galerkin formulation and streamfunction algorithms

Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.

Goodrich, John W.↗

NASA NTRS1990

Unsteady incompressible aerodynamics and forced response of detuned blade rows

A mathematical model is developed and utilized to demonstrate the enhanced forced response behavior associated with aerodynamic, structural, and combined aerodynamic-structural detuning of a loaded rotor operating in an incompressible flow field. The unsteady aerodynamic gust response and oscillating cascade aerodynamics are determined by developing both a complete first-order unsteady aerodynamic analysis and a locally analytical solution in individual grid elements of a body fitted computational grid. The aerodynamic detuning is accomplished by means of alternate circumferential airfoil spacing, with alternate blade structural detuning also considered. The beneficial forced response effects of these detuning techniques are then demonstrated by applying this model to various detuned rotor configurations.

Chiang, Hsiao-Wei D.↗

NASA NTRS1989

Two-dimensional numerical simulation of a Stirling engine heat exchanger

The first phase of an effort to develop multidimensional models of Stirling engine components is described. The ultimate goal is to model an entire engine working space. Parallel plate and tubular heat exchanger models are described, with emphasis on the central part of the channel (i.e., ignoring hydrodynamic and thermal end effects). The model assumes laminar, incompressible flow with constant thermophysical properties. In addition, a constant axial temperature gradient is imposed. The governing equations describing the model have been solved using the Crack-Nicloson finite-difference scheme. Model predictions are compared with analytical solutions for oscillating/reversing flow and heat transfer in order to check numerical accuracy. Excellent agreement is obtained for flow both in circular tubes and between parallel plates. The computational heat transfer results are in good agreement with the analytical heat transfer results for parallel plates.

Ibrahim, Mounir↗

NASA NTRS1990

The stability of a three-dimensional laminar boundary layer on a swept flat plate

The linear stability of the laminar boundary layer on a swept flat plate with an imposed favorable pressure gradient was studied utilizing a linear stability model which accounts for streamline curvature for three-dimensional incompressible flows. Calculations were performed for an effective leading-edge sweep angle of 42.5 degrees and freestream velocity of 19 m/s. Computed disturbance amplification rates for the spectrum of amplified frequencies and wavelengths for stationary crossflow vortices were compared with experimental results.

Collier, F. S., Jr.↗

NASA NTRS1990

A numerical study of longitudinal vortex interaction with a boundary layer

A numerical study of vortex generator aerodynamics has been carried out with a reduced set of Navier-Stokes equations. These are used to model the physical process of longitudinal vortex interaction with a turbulent boundary layer on a flat plate in incompressible flow. Comparison with experimental data is used to validate the approach, and detailed predictions are made. Results show an increase in skin friction and a decrease in integral layer thicknesses where the flow is toward the wall, and the reverse where the flow is away from the wall. The major controlling parameters of vortex strength, spacing and height are each found to have optimum values for which the efficiency of boundary-layer thinning is maximized. Vortex core spreading and secondary vorticity produced in the layer are observed and studied, as well as circulation decay and other features of the flow.

Russell, D. A.↗

NASA NTRS1990

The structure and dynamics of bubble-type vortex breakdown

A unique discrete form of the Navier-Stokes equations for unsteady, three-dimensional, incompressible flow has been used to study vortex breakdown numerically. A Burgers-type vortex was introduced along the central axis of the computational domain, and allowed to evolve in space and time. By varying the strength of the vortex and the free stream axial velocity distribution, using a previously developed Rossby number criterion as a guide, the location and size of the vortex breakdown region was controlled. While the boundaries of the vortex breakdown bubble appear to be nominally symmetric, the internal flow field is not. Consequently, the mechanisms for mixing and entrainment required to sustain the bubble region are different from those suggested by earlier axisymmetric models. Results presented in this study, for a Reynolds number of 200, are in good qualitative agreement with higher Reynolds number experimental observations, and a variety of plots have been presented to help illuminate the fluid physics.

Spall, R. E.↗

NASA NTRS1991

Development of the wake behind a circular cylinder impulsively started into rotatory and rectilinear motion: Intermediate rotation rates

The temporal development of two-dimensional viscous incompressible flow generated by a circular cylinder started impulsively into steady rotatory and rectilinear motion is studied by integration of a velocity/vorticity formulation of the governing equations, using an explicit finite-difference/pseudo-spectral technique and an implementation of the Biot-Savart law. Results are presented for a Reynolds number of 200 (based on the cylinder diameter 2a and the magnitude U of the rectilinear velocity) for several values of the angular/rectilinear speed ratio alpha = (omega x a)/U (where omega is the angular speed) up to 3.25. Several aspects of the kinematics and dynamics of the flow not considered earlier are discussed. For higher values of alpha, the results indicate that for Re = 200, vortex shedding does indeed occur for alpha = 3.25. The shedding process is; however, very different from that which gives rise to the usual Karman vortex street for alpha = 0. In particular, consecutive vortices shed by the body can be shed from the same side and be of the same sense, in contrast to the nonrotating case, in which mirror-image vortices of opposite sense are shed alternately on opposite sides of the body. The implications of the results are discussed in relation to the possibility of suppressing vortex shedding by open or closed-loop control of the rotation rate.

Chen, Yen-Ming↗

NASA NTRS1991

A multi-point inverse airfoil design method based on conformal mapping

An exact method of multipoint inverse airfoil design for incompressible flow is presented. Multipoint design is handled by dividing the airfoil into a number of desired segments. For each segment the velocity distribution is prescribed together with an angle of attack at which the prescribed velocity distribution is to be achieved. In this manner, multipoint design objectives can be taken into account in the initial specification of the velocity distribution. In order for the multipoint inverse airfoil design problem to be well posed, three integral constraints and several conditions arise which must be satisfied. Further restrictions are imposed if the airfoil is to have a specified pitching moment, thickness ratio, or other constraints. The system of equations is solved partly as a linear system and partly through multidimensional Newton iteration. Since the velocity distribution is prescribed about the circle in the angular coordinate, specification of the velocity in terms of arc length is handled through the multidimensional Newton iteration as well. The current formulation sets the stage for a more general multipoint inverse airfoil design method in which it will be possible to specify the velocity distribution, some boundary-layer development, or the surface geometry along a segment.

Selig, Michael S.↗