SEARCH · Search NASA

Results for “STREAM FUNCTION”

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 145 records · Page 8

All sources NASA NTRS DOE OSTI

NASA NTRS1983

Study of asymptotic incompressible flow in curved ducts using a multi-grid technique

Asymptotic flows inside curved ducts of rectangular as well as polar cross sections have been analyzed using the Navier-Stokes equations in terms of the axial velocity and vorticity and the cross-flow stream function. Numerical solutions of the three second-order coupled elliptic partial differential equations governing this flow have been obtained using the multi-grid-SI scheme, to determine fine-grid results for configurations with strong secondary flow.

Ghia, K. N.↗

NASA NTRS1984

Navier-Stokes calculations for the vortex of a rotor in hover

An efficient finite-difference scheme for the solution of the incompressible Navier-Stokes equation is used to study the vortex wake of a rotor in hover. The solution Procedure uses a vorticity-stream function formulation and incorporates an asymptotic far-field boundary condition enabling the size of the computational domain to be reduced in comparison to other methods. The results from the present method are compared with experimental data obtained by smoke flow visualization and hot-wire measurements for several rotor blade configurations.

Liu, C. H.↗

NASA NTRS1984

A modified least squares formulation for a system of first order equations

Second order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least squares formulation to a first order system. The additional boundary conditions which are necessary to solve the higher order equations are determined and numerical results are presented for the Cauchy-Riemann equations.

Hafez, M. M.↗

NASA NTRS1983

A study of non-unique solutions of the two-dimensional boundary layer equations at laminar separation and reattachment points

Nonunique laminar boundary layer equation solutions in direct problem calculations are identified for the case of accelerating flow. As a separation or reattachment point is approached, the multiple solutions approach each other and become identical. The computer code used to generate these results was developed for the solution of compressible, laminar or turbulent boundary layer, and free wake problems, in either direct or inverse mode. Similarity solutions in either a primitive variable or a stream function form are possible, and the resulting equations are solved by means of a modified Keller's Box scheme in which the energy equation and turbulence modeling equations are solved simultaneously with the continuity and momentum equations. Examples illustrating the nature of the solutions at the separation and reattachment points are presented.

Drela, M.↗

NASA NTRS1983

Application of a viscous-inviscid interaction procedure to predict separated flows with heat transfer

A viscous-inviscid interaction procedure is described for predicting heat transfer in separated flows. The separating flow in a rearward-facing step/asymmetric channel expansion is considered. For viscous regions, the boundary-layer momentum and continuity equations are solved inversely in a coupled manner by a finite-difference numerical scheme. The streamwise convective term is altered to permit marching the solution through regions of reversed flow. The inviscid flow is computed by numerically solving the Laplace equation for stream-function in the region bounded by the displacement surfaces used in the inverse boundary-layer solution. The viscous and inviscid solutions are repeated iteratively until the edge velocities obtained from both solutions are in agreement. Predictions using this method compare favorably with experimental data and other predictions.

Hall, E. J.↗

NASA NTRS1984

Calculations of separation bubbles using boundary-layer-type equations. I. II

Two-dimensional models of separated flows are presented with stream-function boundary equations. A patching procedure is employed to solve for unknowns in viscous-inviscid interactions simultaneously in order to derive strong coupling. The technique features simplified Navier-Stokes equations and is useful for flows around flat plates and more complex geometries such as airfoils and cascades. Sample calculations are provided for separated flows in diffusers and in the neighborhood of trailing edges. Massive bubbles and unclosed bubbles are noted to present difficulties for the models.

Halim, A.↗

NASA NTRS1985

Numerical studies of interacting vortices

To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two dimensional vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis.

Liu, G. C.↗

NASA NTRS1985

Review - Computational methods for internal flows with emphasis on turbomachinery

Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler approaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed.

Mcnally, W. D.↗

NASA NTRS1985

An implicit time-marching method for studying unsteady flow with massive separation

A fully implicit time-marching method is developed such that all spatial derivatives are approximated using central differences, but no use is made of any artificial dissipation. The numerical method solves the discretized equations using Alternating Direction Implicit-Block Gaussian Elimination technique. The method is implemented in the unsteady analysis, which solves the incompressible Navier-Stokes equations in terms of vorticity and stream function in generalized orthogonal coordinates. A clustered conformal C-grid is employed, and every effort is made to resolve the various length scales in the flow problem. The metric discontinuity at the branch-cut is treated appropriately using analytic continuation. Introduction of the BGE reordering permits implicit treatment of the branch cut in the numerical method. The vorticity singularity at the cusped trailing edge is also appropriately treated. This accurate and efficient implicit method is used to study flow at Re = 1000, past a 12-percent thick symmetric Joukowski airfoil at high angle of attack 30 and 53 deg.

Osswald, G. A.↗

NASA NTRS1985

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The conservative form of the unsteady Navier-Stokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, alpha = 5 deg, (2) Re = 1000, alpha = 15 deg, (3) Re = 10,000, alpha = 5 deg. No artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (3).

Ghia, K. N.↗

NASA NTRS1985

Stellar fibril magnetic systems. II - Two-dimensional magnetohydrodynamic equations. III - Convective counterflow

The dynamics of magnetic fibrils in the convective zone of a star is investigated analytically, deriving mean-field equations for the two-dimensional transverse motion of an incompressible fluid containing numerous small widely spaced circular cylinders. The equations of Parker (1982) are extended to account for the inertial effects of local flow around the cylinders. The linear field equation for the stream function at the onset of convection is then rewritten, neglecting large-scale heat transport, and used to construct a model of convective counterflow. The Kelvin impulse and fluid momentum, convective motion initiated by a horizontal impulse, and the effects of a viscous boundary layer are considered in appendices.

Parker, E. N.↗

NASA NTRS1985

A modified least squares formulation for a system of first-order equations

Hafez, M. M.↗

NASA NTRS1986

Numerical studies of porous airfoils in transonic flow

A numerical tool is constructed to examine the effects of a porous surface on transonic airfoil performance and to help understand the flow structure of passive shockwave/boundary layer interactions. The porous region is located near the shock with a cavity underneath it. This study is composed of two parts. Solved in the first part, with an inviscid-flow approach, is the transonic full-potential equation associated with transpiration boundary conditions which are obtained from porosity modeling. The numerical results indicate that a porous airfoil has a wave drag lower than that of a solid airfoil. The observed lambda-shock structure in the wind-tunnel testing can be predicted. Furthermore, the lift could be increased with an appropriate porosity distribution. In the second part of this work, the modified version of either an interactive boundary layer (IBL) algorithm or a thin-layer Navier-Stokes (TLNS) algorithm is used to study the outer flow, while a stream-function formulation is used to model the inner flow in the shallow cavity. The coupling procedure at the porous surface is based on Darcy's law and the assumption of a constant total pressure in the cavity. In addition, a modified Baldwin-Lomax turbulence model is used to describe the transpired turbulent boundary layer in the TLNS approach, while the Cebeci turbulence model is used in the IBL approach. According to the present analysis, a porous surface can reduce the wave drag appreciably, but can also increase the viscous losses. As has been observed experimentally, the numerical results indicate that the total drag is reduced at higher Mach numbers and increased at lower Mach numbers when the angles of attack are small. Furthermore, the streamline pattern of passive shock/boundary layer interaction are revealed.

Chow, C. Y.↗

NASA NTRS1985

Numerical algorithms for transonic inviscid flow calculations

It is pointed out that the supercritical wing is one of the most important features of modern transonic aerodynamics. The design of its shock free airfoil section depends on potential flow calculations. The present paper is concerned with the development of inviscid flow simulation methods based on potential formulations, taking into account also the problem of nonuniqueness of the potential solution. Nonisentropic and nonisoenergetic models are considered, and an alternative approach using the stream function is discussed. Attention is given to transonic small disturbance calculations, calculations based on the full potential equation, iterative methods, wave drag calculations, and an alternative form of Euler equations.

Hafez, M. M.↗

NASA NTRS1985

The use of a simplified isentropic model for short-term aviation forecasting

A simple, multiple-layer, isentropic potential vorticity forecast model is described for predicting short-term atmospheric changes between 12-hourly radiosonde observations. The model and the model initialization technique are described, and a case study with both convection and strong horizontal wind shear is discussed. The wind and stream function field forecasts and the forecast areas of convective instability are constrasted with observational results to assess the model's strengths and weaknesses. Excellent agreement is obtained between model predictions and observations.

Homan, J. H.↗

NASA NTRS1985

Pattern formation by particles settling in viscous flows

Results are reported of several simulations of the motions of small objects in two-dimensional cellular flows performed to study the evolution of the distributions of particle flows over time in processes such as sedimentation. Stream functions are defined in the form of a Hamiltonian system for the particle motions, with inertial and particle acceleration being neglected. Conditions are found for which the particles will become trapped in an oscillatory motion or the particle orbits attain an oscillary motion. Various simulation images are provided to illustrate the usefulness of the technique for modeling fractal swarms.

Smith, L. A.↗

NASA NTRS1986

Assimilation of scatterometer winds into surface pressure fields using a variational method

A variational formulation was used to assimilate Seasat-A scatterometer (SASS) surface wind measurements near and during a severe storm in the North Atlantic into conventional National Meteorological Center sea level pressure fields. An estimate of the relative vorticity at every point on a grid was calculated using each of these two data sets. A solution to a modified geostrophic stream function is found subject to the constraints that (1) the relative vorticities calculated from the data agree as closely as possible with the relative vorticities from the variational solution, and that (2) the average kinetic energy is a minimum. Results are obtained which support the idea that averaged satellite data can be treated as synoptic data. Direct substitution rather than a time-weighted insertion made from SASS winds generally resulted in more accurate pressure analyses. In addition, this relatively simple model provides surface pressure fields which agree extremely well with surface truth and the results of other investigators who required additional sources of input data into more complex models. It will be possible to obtain improved wind field maps from future scatterometer pressure fields in mid-latitudes.

Harlan, J., Jr.↗

NASA NTRS1986

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The conservative form of the unsteady Navier-Stokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, alpha = 5 deg., (2) Re =1000, alpha = 15 deg., (3) Re = 10,000, alpha = 5 deg. No artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (3).

Ghia, K. N.↗