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 55 records · Page 3

All sources NASA NTRS DOE OSTI

NASA NTRS2022

Future Climate Change Under SSP Emission Scenarios with GISS-E2.1

This paper presents the response to anthropogenic forcing in the GISS-E2.1 climate models for the 21st century Shared Socioeconomic Pathways emission scenarios within the Coupled Model Intercomparison Project Phase 6 (CMIP6). The experiments were performed using an updated and improved version of the NASA Goddard Institute for Space Studies (GISS) coupled general circulation model that includes two different versions for atmospheric composition: A non-interactive version (NINT) with prescribed composition and a tuned aerosol indirect effect and the One-Moment Aerosol model (OMA) version with fully interactive aerosols which includes a parameterized first indirect aerosol effect on clouds. The effective climate sensitivities are 3.0°C and 2.9°C for the NINT and OMA models, respectively. Each atmospheric version is coupled to two different ocean general circulation models: The GISS ocean model (E2.1-G) and HYCOM (E2.1-H). We describe the global mean responses for all future scenarios and spatial patterns of change for surface air temperature and precipitation for four of the marker scenarios: SSP1-2.6, SSP2-4.5, SSP4-6.0, and SSP5-8.5. By 2100, global mean warming ranges from 1.5°C to 5.2°C relative to 1,850–1,880 mean temperature. Two high-mitigation scenarios SSP1-1.9 and SSP1-2.6 limit the surface warming to below 2°C by the end of the 21st century, except for the NINT E2.1-H model that simulates 2.2°C of surface warming. For the high emission scenario SSP5-8.5, the range is 4.6–5.2°C at 2100. Due to about 15% larger effective climate sensitivity and stronger transient climate response in both NINT and OMA CMIP6 models compared to CMIP5 versions, there is a stronger warming by 2100 in the SSP emission scenarios than in the comparable Representative Concentration Pathway (RCP) scenarios in CMIP5. Changes in sea ice area are highly correlated to global mean surface air temperature anomalies and show steep declines in both hemispheres, with the largest sea ice area decreases occurring during September in the Northern Hemisphere in both E2.1-G (−1.21 × 106 km2/°C) and E2.1-H models (−0.94 × 106 km2/°C). Both coupled models project decreases in the Atlantic overturning stream function by 2100. The largest decrease of 56%–65% in the 21st century overturning stream function is produced in the warmest scenario SSP5-8.5 in the E2.1-G model, comparable to the reduction in the corresponding CMIP5 GISS-E2 RCP8.5 simulation. Both low-end scenarios SSP1-1.9 and SSP1-2.6 also simulate substantial reductions of the overturning (9%–37%) with slow recovery of about 10% by the end of the 21st century (relative to the maximum decrease at the middle of the 21st century).

climate models↗

NASA NTRS1973

FORTRAN program for calculating velocities and streamlines on the hub-shroud mid-channel flow surface of an axial- or mixed-flow turbomachine. 1: User's manual

A FORTRAN 4 computer program has been developed that obtains a subsonic or shock-free transonic flow solution on the hub-shroud mid-channel flow surface of a turbomachine. The blade row may be fixed or rotating, and may be twisted and leaned. Flow may be axial or mixed, up to 45 deg from axial. Upstream and downstream flow variables may vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the flow surface; and approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference stream-function solution. Transonic solutions are obtained by a velocity-gradient method, using information from a finite-difference stream-function solution at a reduced mass flow.

Katsanis, T.↗

NASA NTRS1974

FORTRAN program for calculating velocities and streamlines on the hub-shroud mid-channel flow surface of an axial-or mixed-flow turbomachine. 2: Programmer's manual

A FORTRAN-IV computer program, MERIDL, has been developed that obtains a subsonic or shock-free transonic flow solution on the hub-shroud mid-channel flow surface of a turbomachine. The blade row may be fixed or rotating and may be twisted and leaned. Flow may be axial or mixed, up to 45 deg from axial. Upstream and downstream flow variables can vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the flow surface and approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference stream-function solution. Transonic solutions are obtained by a velocity-gradient method, using information from a finite-difference stream-function solution at a reduced mass flow.

Katsanis, T.↗

NASA NTRS1977

Revised FORTRAN program for calculating velocities and streamlines on the hub-shroud midchannel stream surface of an axial-, radial-, or mixed-flow turbomachine or annular duct. 1: User's manual

A FORTRAN 4 computer program was developed that obtains a detailed subsonic or shock-free transonic flow solution on the hub-shroud midchannel stream surface of a turbomachine. The blade row may be fixed or rotating, and the blades may be twisted and leaned. Flow may be axial, mixed, or radial. Upstream and downstream flow variables may vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the stream surface as well as approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference, stream-function solution. Transonic solutions are obtained by a velocity-gradient method that uses information from a finite-difference, stream-function solution at a reduced mass flow.

Katsanis, T.↗

NASA NTRS1989

A finite difference treatment of Stokes-type flows: Preliminary report

The equations Laplacian operator omega = 0, (1.1a) and omega = Laplacian operator Chi, (1.1b) describe, in suitable units, 2-D Stokes flow of an incompressible fluid occupying a domain D in which omega is the vorticity and Chi is the stream function. The flow is uniquely determined by specifying the velocity on the boundary B of D, a condition which leads to specifying the stream function Chi and its normal derivative Chi sub n on B. A mathematically similar problem arises in describing the equilibrium of a flat plate in structural mechanics where a related 1-D problem by finite difference or finite element methods is to introduce effective methods for imposing the boundary conditions through which (1.1a) is coupled to (1.1b). These models thus provide a simple starting point for examining the general treatment of boundary conditions for more general time dependent Navier-Stokes incompressible flows. For the purpose of discussion it is assumed that D is a square domain. A standard finite difference method to solve (1.1) is to introduce a uniform grid and then use standard five point finite difference operators to express each equation in (1.1). At any point on the boundary B a value of Chi is specified by the boundary conditions but a value of omega at the same boundary mesh point will also be required to complete the computation. Methods are discussed which overcome the difficulty in solving these problems.

Rose, M. E.↗

NASA NTRS1983

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Abolhassani, J. S.↗

NASA NTRS1991

Ground-based PIV and numerical flow visualization results from the surface tension driven convection experiment

The Surface Tension Driven Convection Experiment (STDCE) is a Space Transportation System flight experiment to study both transient and steady thermocapillary fluid flows aboard the United States Microgravity Laboratory-1 (USML-1) Spacelab mission planned for June, 1992. One of the components of data collected during the experiment is a video record of the flow field. This qualitative data is then quantified using an all electric, two dimensional Particle Image Velocimetry (PIV) technique called Particle Displacement Tracking (PDT), which uses a simple space domain particle tracking algorithm. Results using the ground based STDCE hardware, with a radiant flux heating mode, and the PDT system are compared to numerical solutions obtained by solving the axisymmetric Navier Stokes equations with a deformable free surface. The PDT technique is successful in producing a velocity vector field and corresponding stream function from the raw video data which satisfactorily represents the physical flow. A numerical program is used to compute the velocity field and corresponding stream function under identical conditions. Both the PDT system and numerical results were compared to a streak photograph, used as a benchmark, with good correlation.

Pline, Alexander D.↗

NASA NTRS1991

Ground-based PIV and numerical flow visualization results from the Surface Tension Driven Convection Experiment

Pline, Alexander D.↗

NASA NTRS1983

A direct method for the solution of unsteady two-dimensional incompressible Navier-Stokes equations

The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream function in generalized curvilinear orthogonal coordinates to facilitiate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the transport equation using the alternating-direction implicit method, whereas the stream-function equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a back-step in a doubly infinite channel, using clustered conformal coordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behavior of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honor the multiple length scales of the separated-flow model problem. The asymptotic behavior of the finite-differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order accurate wiggle-free solutions, i.e., with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem.

Ghia, K. N.↗

NASA NTRS1982

Finite analytic numerical solution of axisymmetric Navier-Stokes and energy equations

Convective heat transfer for steady state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature and heat transfer coefficients for flow with Reynolds number of 5.0, 100.0, 1000.0, and 2000.0, and Prandtl number of 0.1, 1.0, and 10.0 with uniform grid sizes are reported for axisymmetric pipe with sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic solution is stable, converges rapidly, and simulates the convection of fluid flow accurately since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values thereby minimizing the false numerical diffusion.

Chen, C.-J.↗

NASA NTRS1979

A simplified model for the viscous crossflow in a slotted test section

A simplified physical model was constructed which simulates the viscous crossflow in a fluid layer near the slots at a fixed streamwise location in a slotted wind tunnel. For low to moderate Reynolds numbers, numerical solutions of the two dimensional, incompressible Navier-Stokes equations in stream function and vorticity, which govern the model flow, were obtained. Fairly general slot geometry was incorporated by means of the Thompson-Thames-Mastin transformation. An approximate factorization scheme with cyclic acceleration parameters was employed to solve a finite difference analog of the stream function equation. The vorticity equation was numerically solved with a modified version of the classical alternating direction implicit scheme. Although no quantitative assessment of solution accuracy can be made, numerical results for variations in incremental wall pressure around the slat are at least qualitatively similar to some experimental results.

Cooke, C. H.↗

NASA NTRS1981

A simplified model for the viscous crossflow in a slotted test section

A simplified physical model is constructed which simulates the viscous crossflow in a fluid layer near the slots at a fixed streamwise location in a slotted wind tunnel. For low to moderate Reynolds numbers, numerical solutions of the two-dimensional, incompressible Navier-Stokes equations in stream function and vorticity, which govern the model flow, are obtained. Fairly general slot geometry is incorporated by means of the Thompson-Thames-Mastin transformation. An approximate factorization scheme with cyclic acceleration parameters is employed to solve a finite difference analog of the stream function equation. The vorticity equation is numerically solved with a modified version of the classical alternating direction implicit (ADI) scheme. Although no quantitative assessment of solution accuracy can be made, numerical results for variations in incremental wall pressure around the slot are at least qualitatively similar to some experimental results of Berndt and Sorenson.

Cooke, C. H.↗

NASA NTRS1983

Embedded cavity drag in steady and unsteady flows

The numerical solution of the laminar boundary-layer flow over an embedded cavity is studied. The purpose is to examine the relevant drag characteristics of laminar cavity flow. The solution field is obtained in terms of velocity and vorticity variables, with the stream function and pressure derivable from the directly computed variables. An analysis and comparison is made among four square cavities, ranging in size from 0.25 to 1.00 boundary-layer thicknesses deep. The dominant flow features are examined in the vicinity of the cavity by means of the stream function and iso-vorticity contours. The dominant physics in the overall drag characteristics of the flow is examined by an analysis of the pressure and wall shear stress distributions in the cavity, and upstream and downstream of the cavity. Pressure forces and frictional forces in, and in the vicinity of, the cavity are determined. Stress relaxation distances, both upstream and downstream of the cavity, are calculated and analyzed. The flow dynamics of the boundary-layer flow over an embedded cavity is summarized. Finally, the relevance of the results to the control of flow separation in such flows is discussed.

Gatski, T. B.↗

NASA NTRS1984

Embedded cavity drag in steady and unsteady flows

The numerical solution of the laminar boundary-layer flow over an embedded cavity is studied. The purpose of the study is to examine the relevant drag characteristics of laminar cavity flow. The solution field is obtained in terms of velocity and vorticity variables, with the stream function and pressure derivable from the directly computed variables. An analysis and comparison is made among four square cavities, ranging in size from 0.25 to 1.00 boundary-layer thicknesses deep. The dominant flow features are examined in the vicinity of the cavity by means of the stream function and iso-vorticity contours. The dominant physics in the overall drag characteristics of the flow is examined by an analysis of the pressure and wall shear stress distributions in the cavity, and upstream and downstream of the cavity. Pressure forces and frictional forces in, and in the vicinity of, the cavity are determined. Stress relaxation distances, both upstream and downstream of the cavity, are calculated and analyzed. The flow dynamics of the boundary-layer flow over an embedded cavity is summarized. Finally, the relevance of the present results to the control of flow separation in such flows is discussed.

Gatski, T. B.↗

NASA NTRS1983

Modeling of steady, rotational, transonic winds from rotating stars and galaxies

The theory of steady transonic winds from condensed bodies is extended to general, two-dimensional, axisymmetric systems. A stream function is used to reduce the gasdynamics equations to a single, second-order differential equation plus an algebraic equation for the density. The approach extends Parker's (1958) quasi-one-dimensional theory, which uses Bernoulli's theorem, to a complete two-dimensional calculation which includes vorticity and rotation. The conceptual basis of the stream function approach is described in detail, and a numerical method for solving the resulting equations is presented. The applications illustrate solutions for stellar (spherical source surface) and galactic (oblate spheroidal source surface) models. Among other things, it is found that for rapidly rotating stellar models the Coriolis force dominates the centrifugal terms and the streamlines bend toward the rotation axis as a consequence of the axisymmetry. For both the rotating and nonrotating galaxy models, the streamlines bend toward the equator.

Kopriva, D. A.↗

NASA NTRS1991

The turbomachine blading design using S2-S1 approach

The boundary conditions corresponding to the design problem when the blades being simulated by the bound vorticity distribution are presented. The 3D flow is analyzed by the two steps S2 - S1 approach. In the first step, the number of blades is supposed to be infinite, the vortex distribution is transformed into an axisymmetric one, so that the flow field can be analyzed in a meridional plane. The thickness distribution of the blade producing the flow channel striction is taken into account by the modification of metric tensor in the continuity equation. Using the meridional stream function to define the flow field, the mass conservation is satisfied automatically. The governing equation is deduced from the relation between the azimuthal component of the vorticity and the meridional velocity. The value of the azimuthal component of the vorticity is provided by the hub to shroud equilibrium condition. This step leads to the determination of the axisymmetric stream sheets as well as the approximate camber surface of the blade. In the second step, the finite number of blades is taken into account, the inverse problem corresponding to the blade to blade flow confined in each stream sheet is analyzed. The momentum equation implies that the free vortex of the absolute velocity must be tangential to the stream sheet. The governing equation for the blade to blade flow stream function is deduced from this condition. At the beginning, the upper and the lower surfaces of the blades are created from the camber surface obtained from the first step with the assigned thickness distribution. The bound vorticity distribution and the penetrating flux conservation applied on the presumed blade surface constitute the boundary conditions of the inverse problem. The detection of this flux leads to the rectification of the geometry of the blades.

Luu, T. S.↗

NASA NTRS1986

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force. I - Discontinuities in the torsion

Consideration is given to the static force-free equilibrium of a magnetic field in which all of the lines of force connect without knotting between parallel planes. The field is formed by continuous deformation from an initial uniform field, and is conventiently described in terms of the scalar function psi, which is the stream function for the incompressible wrapping and interweaving of the lines of force. Local compression and expansion of the lines of force is described in terms of the scalar function Phi. Equilibrium in the field requires satisfaction of two independent equations which cannot be accomplished without the full freedom of both psi and Phi. It is shown that discontinuities in the torsional characteristics of the lines occur when psi is predetermined by an arbitrary pattern. Discontinuities in the winding pattern of the lines can lead to discontinuities in the associated current sheets.

Parker, E. N.↗

NASA NTRS1988

On a modified streamline curvature method for the Euler equations

A modification of the streamline curvature method leads to a quasilinear second-order partial differential equation for the streamline coordinate function. The existence of a stream function is not required. The method is applied to subsonic and supersonic nozzle flow, and to axially symmetric flow with swirl. For many situations, the associated numerical method is both fast and accurate.

Cordova, Jeffrey Q.↗