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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗
NASA NTRS2009

Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations

The practical benefits of the hyper-accuracy properties of the discontinuous Galerkin method are examined. In particular, we demonstrate that some flow attributes exhibit super-convergence even in the absence of any post-processing technique. Theoretical analysis suggest that flow features that are dominated by global propagation speeds and decay or growth rates should be super-convergent. Several discrete forms of the discontinuous Galerkin method are applied to the simulation of unsteady viscous flow over a two-dimensional cylinder. Convergence of the period of the naturally occurring oscillation is examined and shown to converge at 2p+1, where p is the polynomial degree of the discontinuous Galerkin basis. Comparisons are made between the different discretizations and with theoretical analysis.

Atkins, Harold L.↗
NASA NTRS2010

Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗
NASA NTRS2013

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Chang, Sin-Chung↗
NASA NTRS2013

Computations on Wings With Full-Span Oscillating Control Surfaces Using Navier-Stokes Equations

A dual-level parallel procedure is presented for computing large databases to support aerospace vehicle design. This procedure has been developed as a single Unix script within the Parallel Batch Submission environment utilizing MPIexec and runs MPI based analysis software. It has been developed to provide a process for aerospace designers to generate data for large numbers of cases with the highest possible fidelity and reasonable wall clock time. A single job submission environment has been created to avoid keeping track of multiple jobs and the associated system administration overhead. The process has been demonstrated for computing large databases for the design of typical aerospace configurations, a launch vehicle and a rotorcraft.

Equations↗
NASA NTRS1986

A relaxation technique for the parabolized Navier-Stokes (PNS) equations

A rapidly converging relaxation technique for the parabolized Navier-Stokes equations has been devised. The scheme is applicable in both supersonic and subsonic flows, but it is discussed here in the context of supersonic flows. The upstream propagating acoustic influence in the subsonic part of the flow is introduced semi-implicitly through the streamwise momentum equation applied on the body, and through a forward-differencing on the streamwise pressure gradient term in the interior. This procedure yields a new boundary condition on the energy in the total energy equation. The pressure-velocity system in the subsonic layer is coupled, but the positive time-like marching characteristic of the governing equations is still maintained. The relaxation technique is demontrated to work for a three-dimensional flow over a cone-flare in supersonic flight.

Kaul, Upender K.↗
NASA NTRS1985

Foundations for the numerical solution of the Euler equations

The Navier-Stokes equations represent an extremely good model of the physical phenomena encountered in most aeronautical problems. However, the computational resource needed to solve the Navier-Stokes equations are so large that even with today's supercomputers, it is necessary to make use of simpler models. A large number of external aerodynamic problems can be accurately described by a simpler model. This model consists of an outer inviscid flow plus a boundary-layer thickness correction for the vehicle shape. The outer inviscid model may be represented by the potential equation or by the Euler equation. The present paper provides the foundations for the numerical solution of the Euler equations. The governing equations are considered, taking into account conservation laws, the medium, the differential form of the conservation laws, generalized solutions, shock-fitting, and characteristics. Attention is also given to initial and boundary conditions, existence and uniqueness, and rotational phenomena.

Salas, M. D.↗
NASA NTRS1991

Time-accurate finite difference solutions to the incompressible Navier-Stokes/energy equations

Two new algorithms for solving coupled Navier-Stokes and energy equations are presented. The algorithms are compared with available Navier-Stokes solutions for the model problem of a driven-cavity-flow over a range of Reynolds numbers. It is noted that the algorithms represent two different implementations of the fractional step approach to the solution of the coupled Navier-Stokes and energy equations using the Boussinesq approximation.

Mirfakhraee, Ali↗
NASA NTRS1983

Application of the implicit MacCormack scheme to the PNS equations

The two-dimensional parabolized Navier-Stokes equations are solved using MacCormack's (1981) implicit finite-difference scheme. It is shown that this method for solving the parabolized Navier-Stokes equations does not require the inversion of block tridiagonal systems of algebraic equations and allows the original explicit scheme to be employed in those regions where implicit treatment is not needed. The finite-difference algorithm is discussed and the computational results for two laminar test cases are presented. Results obtained using this method for the case of a flat plate boundary layer are compared with those obtained using the conventional Beam-Warming scheme, as well as those obtained from a boundary layer code. The computed results for a more severe test of the method, the hypersonic flow past a 15 deg compression corner, are found to compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

Lawrence, S. L.↗
NASA NTRS1987

Down-to-earth supercomputing at NASA Ames

The requirements for computers for aerospace vehicle design problems, in particular fluid dynamics, are examined. The levels of approximation to Navier-Stokes equations are: (1) linearized inviscid form, (2) nonlinear inviscid equation, (3) Reynolds-averaged Navier-Stokes equation, (4) large eddy simulation with models for subgrid scale turbulence, and (5) full Navier-Stokes equations to calculate laminar/turbulent transition and turbulence dissipation. The Cray 2 with 256 megaword memory and 4.1 nsec clock and the Cray X-MP/48 with a 128 megaword memory and a 9.5 nsec clock of the Ames facility are described, and an example revealing their applicability is presented. The use of zonal methods to simulate aerodynamic flow fields numerically is discussed. Consideration is given to the development of a program for simulation of aerodynamic flow fields, the compilers, symbolic debuggers, the scheduling of multiple CPUs, and the analysis and storage of the data.

Stevens, Kenneth G., Jr.↗
NASA NTRS1994

Direct numerical simulation of sheared turbulent flow

The summer assignment to study sheared turbulent flow was divided into three phases which were: (1) literature survey, (2) computational familiarization, and (3) pilot computational studies. The governing equations of fluid dynamics or Navier-Stokes equations describe the velocity, pressure, and density as functions of position and time. In principle, when combined with conservation equations for mass, energy, and thermodynamic state of the fluid a determinate system could be obtained. In practice the Navier-Stokes equations have not been solved due to the nonlinear nature and complexity of these equations. Consequently, the importance of experiments in gaining insight for understanding the physics of the problem has been an ongoing process. Reasonable computer simulations of the problem have occured as the computational speed and storage of computers has evolved. The importance of the microstructure of the turbulence dictates the need for high resolution grids in extracting solutions which contain the physical mechanisms which are essential to a successful simulation. The recognized breakthrough occurred as a result of the pioneering work of Orzag and Patterson in which the Navier-Stokes equations were solved numerically utilizing a time saving toggling technique between physical and wave space, known as a spectral method. An equally analytically unsolvable problem, containing the same quasi-chaotic nature as turbulence, is known as the three body problem which was studied computationally as a first step this summer. This study was followed by computations of a two dimensional (2D) free shear layer.

Harris, Vascar G.↗
NASA NTRS1987

Computation of non-linear acoustics in two-dimensional blade-vortex interactions

The propagation characteristics of the interaction between a vortex and a helicopter airfoil are investigated by a variety of methods, and a comparison is made between solutions to the linearized transonic small disturbance equation, transonic small disturbance equation, Euler equations, and Navier-Stokes equations. Although the first two methods are able to accurately predict the propagation of acoustic waves, they are unable to accurately describe the initial formation of acoustic waves. The Euler and Navier-Stokes equations are shown to be well suited to the investigation of acoustic waves and give approximately the same results.

Baeder, J. D.↗
NASA NTRS1971

Boundary layer transition: A review of theory, experiment and related phenomena

The overall problem of boundary layer flow transition is reviewed. Evidence indicates a need for new, basic physical hypotheses in classical fluid mechanics math models based on the Navier-Stokes equations. The Navier-Stokes equations are challenged as inadequate for the investigation of fluid transition, since they are based on several assumptions which should be expected to alter significantly the stability characteristics of the resulting math model. Strong prima facie evidence is presented to this effect.

Kistler, E. L.↗
NASA NTRS1981

Basic lubrication equations

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Hamrock, B. J.↗