SEARCH · Engineering Papers

Results for “Navier”

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 433 records · Page 24

All sources NASA NTRS DOE OSTI

NASA NTRS1985

Navier-Stokes computations for exotic airfoils

An efficient hyperbolic grid generator with improvements for handling sharp corners and concave surfaces is combined with an efficient and accurate Navier-Stokes flow solver. This combination is applied to some rather complex two-dimensional airfoil configurations. Steady separated flow about an iced leading edge of an airfoil is presented. Unsteady viscous separated flows past an airfoil at two angles of attack with a spoiler deployed at 60 degrees are presented and compared with experiment. The spoiler computations are performed with two different topological maps of the physical domain to the computational domain. Innovative graphical techniques for both the static and unsteady display of the flow fields are presented and discussed.

Barth, T. J.↗

NASA NTRS1985

Analysis of turbulent underexpanded jets. I - Parabolized Navier-Stokes model, SCIPVIS

A new computational model (SCIPVIS) is described which predicts the multiple-cell wave/shock structure in underexpanded or overexpanded turbulent jets. SCIPVIS solves the parabolized Navier-Stokes jet-mixing equations utilizing a shock-capturing approach in supersonic regions of the jet and a pressure-split approach in subsonic regions. Turbulence processes are represented by the solution of compressibility-corrected two-equation turbulence models. SCIPVIS presently analyzes jets exhausting into a quiescent or supersonic external stream for which a single-pass spatial-marching solution can be obtained. The features of SCIPVIS are reviewed, and calculations are described exhibiting the influence of turbulence modelling, jet temperature, and flight velocity on the jet shock structure.

Dash, S. M.↗

NASA NTRS1985

Numerical simulation of flow through scramjet inlets using a three-dimensional Navier-Stokes code

A three-dimensional Reynolds-averaged Navier-Stokes code has been used to numerically analyze flow through a two-strut, supersonic combustion ramjet (scramjet) inlet configuration. It solves the governing equations in full conservation form using either the fully explicit or explicit-implicit method due to MacCormack. An algebraic two-layer eddy viscosity model is used for turbulent flow calculations. The analysis allows inclusion of end effects which are caused by the aft placement of the cowl on the underside of the inlet. A special grid has been developed to accommodate the struts embedded in the inlet flow field. Detailed numerical results are presented here for the two-strut configuration, and a comparison is made with the available experimental results.

Kumar, A.↗

NASA NTRS1985

On the accuracy of the pseudocompressibility method in solving the incompressible Navier-Stokes equations

The method of pseudocompressibility is being tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite-difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibility for solving the pressure field, coupled with an implicit, approximate-factorization scheme. This coupling is known as the pseudocompressibility method. The pseudocompressibility method introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. However, these waves limit the time-accuracy of the computations. The effects of these waves are analyzed and criteria are set for choosing the pseudocompressibility parameters that govern the pressure wave speed. Test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.

Rogers, S. E.↗

NASA NTRS1985

A fourth-order scheme for the unsteady compressible Navier-Stokes equations

A computational scheme is described which is second-order accurate in time and fourth-order accurate in space (2-4). This method is applied to study the stability of compressible boundary layers. The laminar compressible Navier-Stokes equations are solved with a time harmonic inflow superimposed on the steady state solution. This results in spatially unstable modes. It is shown that the second-order methods are inefficient for calculating the growth rates and phases of the unstable modes. In contrast the fourth-order method yields accurate results on relatively coarse meshes.

Bayliss, A.↗

NASA NTRS1985

Upwind relaxation algorithms for the Navier Stokes equations

The development of upwind relaxation algorithms for obtaining efficient steady-state solutions to the compressible Navier-Stokes equations is described. The method is second-order accurate spatially and naturally disipative, using third-order flux splitting of the pressure and convective terms and second-order central differencing for shear and heat flux terms. A line Gauss-Seidel relaxation approach, shown to be unconditionally stable for model convection and diffusion equations, is used. The algorithm is demonstrated for several flows using the thin-layer form of the equations, including the problem of shock-induced separation over a flat plate.

Thomas, J. L.↗

NASA NTRS1985

Navier-Stokes simulations of rotor-stator interaction using patched and overlaid grids

An accurate numerical analysis of the flows associated with rotor-stator configurations in turbomachinery can be very helpful in optimizing the performance of turbomachinery. In this study the unsteady, thin-layer, Navier-Stokes equations are solved using a system of patched and overlaid grids for a rotor-stator configuration of an axial turbine. The equations necessary for an accurate transfer of information between the several grids are briefly described within the framework of an iterative, implicit algorithm. Results in the form of Mach number contours, time-averaged pressures, unsteady pressures, amplitudes, and phase are presented. The numerical results are also compared with experimental data and the agreement is found to be good.

Rai, M. M.↗

NASA NTRS1985

Three dimensional CSCM method for the compressible Navier-Stokes equations with application to a multi-nozzle exhaust flowfield

The effective design of three-dimensional flow systems such as a clustered multinozzle shrouded exhaust system requires detailed analysis of the internal flowfield. It is pointed out that new numerical techniques on the most modern vector computers are making these analyses practicable. In this paper, the upwind differenced implicit conservative supracharacteristics method (CSCM) for three-dimensional viscous flow is presented. The new method is an implicit 'method of planes' symmetric Gauss-Seidel relaxation scheme. The data is conveniently stored on successive planes along the streamwise coordinate, and the system of equations is solved twice in each successive plane of the streamwise coordinate. The developed new three-dimensional compressible Navier-Stokes algorithm combines the best features of the storage and computationally efficient space marching procedures with the generality of time dependent techniques to solve flows with elliptic and streamwise separated flows.

Bardina, 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 NTRS1985

Numerical solutions of Navier-Stokes equations for a Butler wing

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Abolhassani, J. S.↗

NASA NTRS1985

Computational aspects of zonal algorithms for solving the compressible Navier-Stokes equations in three dimensions

Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The flow field immediately adjacent to the wing surface is resolved with fine grid zones and solved using a Navier-Stokes algorithm. Flow field regions removed from the wing are resolved with less finely clustered grid zones and are solved with an Euler algorithm. Computational issues associated with this zonal approach, including data base management aspects, are discussed. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects. Additional cases with significant shock induced separation on the upper wing surface are also presented.

Holst, T. L.↗

NASA NTRS1985

A fourth-order scheme for the unsteady compressible Navier-Stokes equations

Bayliss, A.↗

NASA NTRS1985

Marching iterative methods for the parabolized and thin layer Navier-Stokes equations

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Israeli, M.↗

NASA NTRS1986

Steady supersonic Navier-Stokes solutions of a 75 deg delta wing

Steady solutions about a slender sharp edged delta wing in a supersonic freestream for moderate and high angles of attack are obtained numerically by time integration of the unsteady compressible three dimensional laminar Navier-Stokes equations. The main features of the flow, including primary and secondary separation, and vortex position and strength, are adequately simulated in the numerical solutions. Improved resolution of the computational grid in the leading edge region from a previous solution had considerable effect on the accuracy of the solutions. Good agreement between numerical solutions and experimental data was obtained for two cases. A local timestepping procedure is used to speed convergence by approximately a factor of two.

Buter, T. A.↗

NASA NTRS1986

Efficient solution methods for the Navier-Stokes equations

Implicit finite difference schemes for solving two-dimensional and three-dimensional Euler and thin layer Navier-Stokes equations are addressed. The methods are demonstrated in fully vectorized codes for a Cray type architecture. The Beam and Warming implicit approximate factorization algorithm in generalized coordinates is used. The methods are either time accurate or accelerated non-time accurate steady state schemes. Acceleration and efficiency modifications such as matrix reduction, diagonalization, and flux split schemes are presented. Two dimensional inviscid and viscous calculations (e.g., airfoils with a deflected spoiler, circulation control airfoils, and unsteady buffeting) and of three dimensional viscous elliptical bodies, exhausting boattails, and generic oblique wing computations are discussed.

Pulliam, T. H.↗

NASA NTRS1986

Navier-Stokes computations for exotic airfoils

A hyperbolic grid generator with improvements for handling sharp corners and concave surfaces combined with a Navier-Stokes flow solver is applied to complex two dimensional airfoil configurations. Steady separated flow about an iced leading edge of an airfoil is presented. Unsteady viscous separated flows past an airfoil at two angles of attack with a spoiler deployed at 60 deg are compared with experiment. The spoiler computations are performed with two different topological maps of the physical domain to the computational domain. Graphical techniques for the static and unsteady display of the flow fields are discussed.

Barth, T. J.↗

NASA NTRS1986

Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and application

The Rai (1984,85) patch-boundary scheme for the Euler equations is described. The integration methods used to update the interior grid points are are discussed. Stability of patch-boundary schemes and the use of these schemes in Navier-Stokes calculations are mentioned. Results for inviscid, supersonic flow over a cylinder, blast wave diffraction by ramp, and the motion of a vortex in a freestream are presented. These test cases demonstrate the quality of solutions possible with the scheme.

Rai, M. M.↗

NASA NTRS1985

A spectral collocation method for the Navier-Stokes equations

A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.

Malik, M. R.↗