Numerical Experiments in Unsteady Flows Through the Use of Full Navier- Stokes Equations
Numerical Experiments in Unsteady Flows Through the Use of Full Navier- Stokes Equations

Author:

Publisher:

Published: 1991

Total Pages: 149

ISBN-13:

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The numerical simulations of impulsively started flow, non- impulsively started flow, sinusoidally oscillating flow, and, finally, co- existing flow (with mean and oscillatory components) past a circular cylinder have been investigated in great detail through the use of several compact schemes with the Navier-Stokes vorticity/stream function formulation for various Reynolds numbers, frequency parameters, and ambient flow/oscillating flow combinations using VAX-3520 and NASA's Supercomputers. Extensive sensitivity analysis has been performed to delineate the effects of time step, outer boundary, nodal points on the cylinder, and the use of higher order polynomials in the calculation of the gradient of wall vorticity. The results have been compared with those obtained experimentally. In many cases the predicted wake region, vorticity and pressure distributions, and the time-variation of the force coefficients have shown excellent agreement with those obtained experimentally.

Numerical Experiments with the Two- and Three-dimensional Unsteady Navier-Stokes Equation
Numerical Experiments with the Two- and Three-dimensional Unsteady Navier-Stokes Equation

Author: Gustave John Hokenson

Publisher:

Published: 1973

Total Pages: 0

ISBN-13:

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The two- and three-dimensional unsteady Navier-Stokes equations are solved numerically for the flow field about an impulsively started flat plate. In attempting to obtain an exact time dependent solution, several significant results were observed. First, with regard to the formulation of the differential equations themselves, it appears that Poisson's equation for the pressure field is a fundamental equation in as much as it allows us to solve for pressure moat exactly at any given time. Secondly, the difference equations must be carefully and consistently formulated. In this research, a non-uniform lateral grid, a unique interpretation of the continuity equation, and leap frog integration in time proved to be valuable techniques in obtaining an exact solution. (Author).

Numerical Experiments with the Two- and Three-Dimensional Unsteady Navier-Stokes Equations
Numerical Experiments with the Two- and Three-Dimensional Unsteady Navier-Stokes Equations

Author: Gustave Hokenson

Publisher:

Published: 1973

Total Pages: 80

ISBN-13:

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The two- and three-dimensional unsteady Navier-Stokes equations are solved numerically for the flow field about an impulsively started flat plate. In attempting to obtain an exact time dependent solution, several significant results were observed. First, with regard to the formulation of the differential equations themselves, it appears that Poisson's equation for the pressure field is a fundamental equation in as much as it allows us to solve for pressure moat exactly at any given time. Secondly, the difference equations must be carefully and consistently formulated. In this research, a non-uniform lateral grid, a unique interpretation of the continuity equation, and leap frog integration in time proved to be valuable techniques in obtaining an exact solution. (Author).

Navier-Stokes Simulations of Unsteady Transonic Flow Phenomena
Navier-Stokes Simulations of Unsteady Transonic Flow Phenomena

Author: National Aeronautics and Space Administration (NASA)

Publisher: Createspace Independent Publishing Platform

Published: 2018-07-18

Total Pages: 148

ISBN-13: 9781723230561

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Numerical simulations of two classes of unsteady flows are obtained via the Navier-Stokes equations: a blast-wave/target interaction problem class and a transonic cavity flow problem class. The method developed for the viscous blast-wave/target interaction problem assumes a laminar, perfect gas implemented in a structured finite-volume framework. The approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the blast-waves with stationary targets. The inviscid flux is evaluated using either of two upwind techniques, while the full viscous terms are computed by central differencing. Comparisons of unsteady numerical, analytical, and experimental results are made in two- and three-dimensions for Couette flows, a starting shock-tunnel, and a shock-tube blockage study. The results show accurate wave speed resolution and nonoscillatory discontinuity capturing of the predominantly inviscid flows. Viscous effects were increasingly significant at large post-interaction times. While the blast-wave/target interaction problem benefits from high-resolution methods applied to the Euler terms, the transonic cavity flow problem requires the use of an efficient scheme implemented in a geometrically flexible overset mesh environment. Hence, the Reynolds averaged Navier-Stokes equations implemented in a diagonal form are applied to the cavity flow class of problems. Comparisons between numerical and experimental results are made in two-dimensions for free shear layers and both rectangular and quieted cavities, and in three-dimensions for Stratospheric Observatory For Infrared Astronomy (SOFIA) geometries. The acoustic behavior of the rectangular and three-dimensional cavity flows compare well with experiment in terms of frequency, magnitude, and quieting trends. However, there is a more rapid decrease in computed acoustic energy with frequency than observed experimentally owing to numerical dissipatio...

Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows
Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows

Author: Michel Deville

Publisher: Vieweg+Teubner Verlag

Published: 2013-03-09

Total Pages: 234

ISBN-13: 3663002217

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The GAMM-Commi ttee for Numerical Methods in Fluid Mechanics (GAMM-Fachausschuss für Numerische Methoden in der Strömungsmechanik) has sponsored the organization of a GAMM Workshop dedicated to the numerical simulation of three dimensional incompressible unsteady viscous laminar flows to test Navier-Stokes solvers. The Workshop was held in Paris from June 12th to June 14th, 1991 at the Ecole Nationale Superieure des Arts et Metiers. Two test problems were set up. The first one is the flow in a driven-lid parallelepipedic cavity at Re = 3200 . The second problem is a flow around a prolate spheroid at incidence. These problems are challenging as fully transient solutions are expected to show up. The difficulties for meaningful calculations come from both space and temporal discretizations which have to be sufficiently accurate to resol ve detailed structures like Taylor-Görtler-like vortices and the appropriate time development. Several research teams from academia and industry tackled the tests using different formulations (veloci ty-pressure, vortici ty velocity), different numerical methods (finite differences, finite volumes, finite elements), various solution algorithms (splitting, coupled ...), various solvers (direct, iterative, semi-iterative) with preconditioners or other numerical speed-up procedures. The results show some scatter and achieve different levels of efficiency. The Workshop was attended by about 25 scientists and drove much interaction between the participants. The contributions in these proceedings are presented in alphabetical order according to the first author, first for the cavi ty problem and then for the prolate spheroid problem. No definite conclusions about benchmark solutions can be drawn.

Numerical Solutions for Steady and Unsteady Oscillatory Flow about an Axi-symmetric Inlet
Numerical Solutions for Steady and Unsteady Oscillatory Flow about an Axi-symmetric Inlet

Author: Richard W. Newsome

Publisher:

Published: 1983

Total Pages: 188

ISBN-13:

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The unsteady, compressible, Reynolds-averaged Navier-Stokes equations were solved for the flow field about an external compression axi-symmetric inlet with a length to diameter ratio, L/D = 15.88, at Mach 2.0 and a Reynolds number based on diameter, ReD = 2.36 times 10 to the 6th power, operating in the near-critical and subcritical flow regimes. The near-critical solution reached a stable steady state while the subcritical solutions attained an unstable bounded oscillatory state, characterized by large amplitude pressure oscillations and traveling shock waves. This phenomenon is a result of a shear layer instability combined with a closed-loop feedback of reflected disturbances and the naturally occurring self-sustained oscillations are commonly known as buzz. Numerical results are given in terms of Mach contours, velocity field plots, pressure-time traces at selected stations, as well as mass flux and other mass-averaged quantities along the duct length. Comparison with experiment is also given. (Author).