On the continuation of a potential gas flow across the sonic line
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A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (1) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (2) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (3) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over- or under-expansion jet.
There is a need for experimental measurements in complex turbulent flows that originate from very well-defined initial conditions. Testing of large-eddy simulations and other higher-order computation schemes requires inlet boundary condition data that are not normally measured. The use of fully developed upstream conditions offers a solution to this dilemma so that the upstream conditions can be adequately computed at any level of sophistication. The plane diffuser experiment by Obi et al. (1993) has received a lot of attention because it has fully-developed inlet conditions and it includes separation from a smooth wall, subsequent reattachment and redevelopment of the downstream boundary layer. The objective of this study is to provide careful qualification and detailed measurements in a recreation of the Obi experiment. The work will include extensive documentation of the flow two-dimensionality and detailed measurements required for testing of flow computations.
The objective of this study is to provide careful qualification and detailed measurements in a re-creation of the Obi experiment. The work will include extensive documentation of the flow two-dimensionality and detailed measurements required for testing of flow computations. Also important to this study is the close interaction of the experimental and computational groups to improve the utility of the data obtained and the accuracy of computation.
Charts are presented for the determination of certain flow properties in the flow properties in the flow field and on the surface of cones and wedges at Mach numbers from about 1 to 100 in a perfect gas wigh a ratio of specific heats of 5/3. In addition, a table of the isentropic subsonic flow parameters is included.
In this paper we introduce a high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by numerical experiments.
The compressible Navier-Stokes equations for two-dimensional and three-dimensional flow are solved for nonaxisymmetric nozzle configurations. Both internal flow alone and combined internal and external flow cases are considered. An implicit approximate factorization algorithm is employed to solve the governing equations which are cast in terms of a body-fitted coordinate system. Turbulence closure is accomplished with a composite algebraic model. Two-dimensional results for a wedge plug nozzle flow in the form of surface pressures compare favorably with experimental data. Three-dimensional calculations for two nonaxisymmetric nozzles are also presented and compared with data.
Leading edge bluntness and ramp deflection angle effects on laminar boundary layer separation in hypersonic flow
Chapman-Ferraro approximation for magnetic interior field line configuration in plasma flow around two dimensional dipole, allowing for tail formation and neutral sheet
The application of a spectral method to the computation of transonic potential flow about an arbitrary lifting airfoil is discussed. An iterative solution algorithm is described, which was found to be robust, fairly efficient, and fit well in a multigrid coontext. Details of the application to the transonic potential flow problem are given. Results from the spectral technique for both subcritical flow and supercritical flow with shocks are given and compared with results from state-of-the-art finite-difference airfoil codes.
The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.
Two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative induction of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa - epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa - epsilon model predictions are included.
Hot-wire measurements were made in the boundary layer, the separated region, and the near wake for flow past a NACA 4412 airfoil at maximum lift. The Reynolds number based on chord was 1,500,000. Special care was taken to achieve a two-dimensional mean flow. Data were obtained at several thousand locations in the flow field. These data include intermittency, two components of mean velocity, and mean values for three double, four triple, and five quadruple products of two velocity fluctuations. No information was obtained about the third (spanwise) velocity component. Smoothing and interpolating routines were used to determine intermittency, two components of mean velocity, and mean values of three double, four triple, and five quadruple products of two velocity fluctuations on a fine rectangular mesh aligned with the airfoil chord. The data are presented in contour plots, in three-dimensional plots, and in tabular form. The format used to store the experimental data in digital form is described and a computer program which illustrates how this data can be accessed is presented.
An overview of 'Aerodynamic systems design of axial flow compressors' is presented. Numerous chapters cover topics such as compressor design, potential and viscous flow in two dimensional cascades, compressor stall and blade vibration, and compressor flow theory. Theoretical aspects of flow are also covered. This work is based substantially on a three-volume Confidential Research Memorandum f h t issued by the National Advisory Committee for Aeronautics in 1956 and declassified in .1958 for release to the general public. The material, which was of a fundamental character, has been updated for the present edition in the light of subsequent developments in the field and has been carefully reexamined for current validity by members of the staff of the NASA Lewis Research Center, Cleveland, Ohio. It is now published for the first time in a single volume to meet continuing demand for the information and to make it readily available in convenient form to the engineering community both within and outside the National Aeronautics and Space Administration.
Separated flow in two dimensional and axisymmetric nozzles with various wall contours, determining flow structure and shock-boundary layer interaction
The transient and steady thermal convection in microgravity is described. The approach is applicable to many three dimensional flows in containers of various shapes with various thermal gradients imposed. The method employs known analytical solutions to two dimensional thermal flows in simpler geometries, and does not require recourse to numerical calculations by computer.