Search NASA⌕ Search

SEARCH · Search NASA

Results for “Two dimensional flow”

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.

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

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

On the far-field stream function condition for two-dimensional incompressible flows

The present demonstration of the usefulness of the integral series expansion of the stream function as a far-field computational boundary condition shows the method to require only a 10-percent/time-step increase in computational effort over alternative boundary conditions, in the case of implementation of unsteady problems using a direct elliptic solver. So long as the vorticity was encompassed within the computational domain, the method proved sufficiently accurate to yield virtually identical results for two widely different domains. While the integral-series condition yielded the best results for periodic flow, the Neumann condition gave comparable accuracy with less computation time for the steady-flow case despite its inability to treat periodic flow with vortex shedding.

Sa, Jong-Youb↗
NASA NTRS1997

Computation of Sound Generated by Flow Over a Circular Cylinder: An Acoustic Analogy Approach

The sound generated by viscous flow past a circular cylinder is predicted via the Lighthill acoustic analogy approach. The two dimensional flow field is predicted using two unsteady Reynolds-averaged Navier-Stokes solvers. Flow field computations are made for laminar flow at three Reynolds numbers (Re = 1000, Re = 10,000, and Re = 90,000) and two different turbulent models at Re = 90,000. The unsteady surface pressures are utilized by an acoustics code that implements Farassat's formulation 1A to predict the acoustic field. The acoustic code is a 3-D code - 2-D results are found by using a long cylinder length. The 2-D predictions overpredict the acoustic amplitude; however, if correlation lengths in the range of 3 to 10 cylinder diameters are used, the predicted acoustic amplitude agrees well with experiment.

Brentner, Kenneth S.↗
NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1978

Solution of axisymmetric and two-dimensional inviscid flow over blunt bodies by the method of lines

Comparisons with experimental data and the results of other computational methods demonstrated that very accurate solutions can be obtained by using relatively few lines with the method of lines approach. This method is semidiscrete and has relatively low core storage requirements as compared with fully discrete methods since very little data were stored across the shock layer. This feature is very attractive for three dimensional problems because it enables computer storage requirements to be reduced by approximately an order of magnitude. In the present study it was found that nine lines was a practical upper limit for two dimensional and axisymmetric problems. This condition limits application of the method to smooth body geometries where relatively few lines would be adequate to describe changes in the flow variables around the body. Extension of the method to three dimensions was conceptually straightforward; however, three dimensional applications would also be limited to smooth body geometries although not necessarily to total of nine lines.

Hamilton, H. H., II↗
NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux difference splitting method was extended to treat 2-D viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-state Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗
NASA NTRS1994

Comments regarding two upwind methods for solving two-dimensional external flows using unstructured grids

Steady flow over the leading portion of a multicomponent airfoil section is studied using computational fluid dynamics (CFD) employing an unstructured grid. To simplify the problem, only the inviscid terms are retained from the Reynolds-averaged Navier-Stokes equations - leaving the Euler equations. The algorithm is derived using the finite-volume approach, incorporating explicit time-marching of the unsteady Euler equations to a time-asymptotic, steady-state solution. The inviscid fluxes are obtained through either of two approximate Riemann solvers: Roe's flux difference splitting or van Leer's flux vector splitting. Results are presented which contrast the solutions given by the two flux functions as a function of Mach number and grid resolution. Additional information is presented concerning code verification techniques, flow recirculation regions, convergence histories, and computational resources.

Kleb, W. L.↗
NASA NTRS1978

Flying-hot-wire study of two-dimensional mean flow past an NACA 4412 airfoil at maximum lift

Hot-wire measurements have been made in the boundary layer, the separated region, and the near wake for flow past an NACA 4412 airfoil at maximum lift. The Reynolds number based on chord was about 1,500,000. The main instrumentation was a hot-wire probe mounted on the end of a rotating arm. A digital computer was used to control synchronized sampling of hot-wire data at closely spaced points along the probe arc. Ensembles of data were obtained at several thousand locations in the flow field. The data include intermittency, two components of mean velocity, and twelve mean values for double, triple, and quadruple products of two velocity fluctuations. The data are available on punched cards in raw form and also after use of smoothing and interpolation routines to obtain values on a fine rectangular grid aligned with the airfoil chord. The data are displayed in the paper as contour plots.

Coles, D.↗
NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1987

Analysis of Scramjet Inlets

NASCRIN program analyzes two-dimensional flow fields in supersoniccombustion ramjet (scramjet) inlets. Solves two-dimensional Euler or Navier-Stokes equations in conservative form by unsplit, explicit, two-step finite-difference method. More recent explicit/implicit, two-step scheme incorporated by analysis of viscous flow. Algebraic, two-layer eddy-viscosity model used for turbulent-flow calculations. Vectorized version, written for CDC CYBER 205, whereas scalar version, can be run on CRAY or other scalar computers.

Kumar, A.↗
NASA NTRS1994

A three dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes

A three-dimensional unstructured mesh Reynolds averaged Navier-Stokes solver is described. Turbulence is simulated using a single field-equation model. Computational overheads are minimized through the use of a single edge-based data-structure, and efficient multigrid solution technique, and the use of multi-tasking on shared memory multi-processors. The accuracy and efficiency of the code are evaluated by computing two-dimensional flows in three dimensions and comparing with results from a previously validated two-dimensional code which employs the same solution algorithm. The feasibility of computing three-dimensional flows on grids of several million points in less than two hours of wall clock time is demonstrated.

Mavriplis, D. J.↗
NASA NTRS1973

Unsteady turbulent boundary layers in two-dimensional, incompressible flow.

The paper presents the results of some calculations aimed at studying the characteristics of turbulent boundary layers in unsteady flow. The calculations were performed using the method of Singleton and Nash, which is based on the turbulent kinetic energy equation. Emphasis is placed on the approach to zero wall stress, and the results show the extent to which onset of this condition can be delayed by the effects of time dependence. The delay is not associated merely with alleviation of the pressure gradients, and quasi-steady methods cannot readily be used to calculate this type of flow.

Nash, J. F.↗
NASA NTRS1973

Experimental and theoretical investigations in two-dimensional transonic flow.

Experimental and theoretical results are presented from a study of the flow over a family of transonically scaled circular-arc bodies mounted in a solid-wall wind tunnel. Data are presented for Reynolds numbers between 30,000 and 3,600,000, based on chord. The high Reynolds number results are compared with computations based on inviscid theory, and are used to investigate transonic similarity and the behavior of the flow near choking. The results at low Reynolds number are used to demonstrate the effect of viscosity on the overall flowfield, and comparisons are made with existing laminar viscous/inviscid interaction theory.

Collins, D. J.↗
NASA NTRS1981

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Chen, C.-J.↗
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 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.↗
NASA NTRS1986

Vortical dissipation in two-dimensional shear flows

An exact expression is derived for the viscous dissipation function of a real homogeneous and isotropic fluid, which has terms associated with the square of vorticity, wave radiation, and dilatation. The implications of the principle of maximal dissipation rate, are explored by means of this equation for a parallel channel flow and a cylindrical vortex flow. The consequences of a condition of maximum dissipation rate on the growth of disturbances in an unsteady, laminar shear layer are apparently consistent with predictions and observations of maximum growth rate of vortical disturbances. Finally, estimates of the magnitudes of several dissipative components of an unsteady vortex flow are obtained from measurements of a periodic wall jet.

Horne, W. Clifton↗