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Fortran computer program for calculating velocities and streamlines for two-dimensional incompressible flow in axial blade rows
Perturbation solutions for laminar incompressible flow in semiporous and fully porous channels are compared. The perturbation parameter measures the amount of suction or blowing at the porous wall. The velocity profile and the wall friction parameter are more affected by suction or blowing for the semiporous channel than for the fully porous channel. For blowing through the wall, the pressure decreases in channel direction for both channels; with sufficiently high suction rates, the analysis showed that the pressure rises in flow direction for the fully porous channel.
A new formulation (including the choice of variables, their non-dimensionalization, and the form of the artificial viscosity) is proposed for the numerical solution of the full Navier-Stokes equations for compressible and incompressible flows with heat transfer. With the present approach, the same code can be used for constant as well as variable density flows. The changes of the density due to pressure and temperature variations are identified and it is shown that the low Mach number approximation is a special case. At zero Mach number, the density changes due to the temperature variation are accounted for, mainly through a body force term in the momentum equation. It is also shown that the Boussinesq approximation of the buoyancy effects in an incompressible flow is a special case. To demonstrate the new capability, three examples are tested. Flows in driven cavities with adiabatic and isothermal walls are simulated with the same code as well as incompressible and supersonic flows over a wall with and without a groove. Finally, viscous flow simulations of an oblique shock reflection from a flat plate are shown to be in good agreement with the solutions available in literature.
This viewgraph presentation gives an overview of viscous incompressible flow computations for three-dimensional steady and unsteady flows. Details are given on the use of computational fluid dynamics (CFD) as an engineering tool, solution methods for incompressible Navier-Stokes equations, numerical and physical characteristics of the primitive variable approach, and the role of CFD in the past and in current engineering and research applications.
The incompressible laminar flow around single and double rows of an infinite number of posts between two flat plates has been calculated numerically. A C-grid with periodic boundary conditions has been used. The angle of attack, measured from the line normal to the row of posts, was varied between zero and less than 90 deg. The pressure loading was computed for all of the posts in each of these cases. Most of these calculations have been carried out on the Numerical Aerodynamic Simulation Cray 2 at NASA Ames Research Center.
Aerodynamic characteristics of thin, highly cambered airfoils in incompressible flow
A finite difference scheme for three-dimensional steady laminar incompressible flows is presented. The Navier-Stokes equations are expressed conservatively in terms of velocity and pressure increments (delta form). First order upwind differences are used for first order partial derivatives of velocity increments resulting in a diagonally dominant matrix system. Central differences are applied to all other terms for second order accuracy. The SIMPLE pressure correction algorithm is used to satisfy the continuity equation. Numerical results are presented for cubic cavity flow problems for Reynolds numbers up to 2000 and are in good agreement with other numerical results.
A finite difference scheme for three-dimensional steady laminar incompressible flows is presented. The Navier-Stokes equations are expressed conservatively in terms of velocity and pressure increments (delta form). First order upwind differences are used for first order partial derivatives of velocity increments resulting in a diagonally dominant matrix system. Central differences are applied to all other terms for second order accuracy. The SIMPLE pressure correction algorithm is used to satisfy the continuity equation. Numerical results are presented for cubic cavity flow problems for Reynolds numbers up to 2000 and are in good agreement with other numerical results.
The calculation of the incompressible and irrotational flow in the vicinity of tips and corners of thin, lifting wings is considered. It is shown that the important characteristics of the flow are governed by an eigenvalue problem, which is nonlinear at the trailing edge because of the shed wake (assumed to be in the wing plane). A new solution method was devised because either the existing methods were not valid for the trailing edge case or they would have required excessive amounts of computer time. The new method, which is fundamentally different than the previous ones, was used to calculate solutions for a number of cases, including some for which correct answers had not previously been obtained. Two of these solutions were used to determine the validity of drag and leading-edge-suction distributions near the tips of a delta wing and a swept wing as calculated by using both the vortex lattice method and a kernel function method. The calculations for the swept wing resolved the question of whether or not the induced drag should be zero at the wing tip.
Method for numerical solution of Navier-Stokes equations of viscous, incompressible flow developed based on use of fractional-step procedure. Accurate to second order in both space and time. Attempt made to minimize Poisson-equation difficulties by choosing pressures at centers and volume fluxes across faces of computational cells as dependent variables instead of familiar Cartesian components of velocity. Choice ensures satisfaction of discrete equation of conservation of mass to within round-off errors in any coordinate system and has favorable effects on convergence properties.
A variety of numerical simulations of transition and turbulence in incompressible flow are presented to compare the commonly used rotation form with the skew-symmetric (and other) forms of the nonlinear terms. The results indicate that the rotation form is much less accurate than the other forms for spectral algorithms which include aliasing errors. For de-aliased methods the difference is minimal.
Vortex flow modeling is used to calculate the steady inviscid incompressible flow past one, two and three delta wing configurations. The wings are modeled with vortex lattices and the leading and trailing-edge sheets are modeled by segmented straight vortex filaments. Aerodynamic characteristics are obtained for a range of geometry and angle of attack.
The problem of steady incompressible flow for lifting surfaces is considered. An integral equation is solved relating the values of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface and the wake are divided into small quadrilateral surface elements. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each lifting surface element and equal to their values at the centroids of the lifting surface elements. This yields a set of linear algebraic equations. An iteration procedure is used to obtain the wake geometry: the velocities at the corner points of the wake elements are calculated and the wake streamlines are aligned to be parallel to the velocity vector. The procedure is repeated until convergence is attained.
The use of incompressible approximations in deriving solutions to the Lighthill wave equation was investigated for problems where an analytical solution could be found. A particular model problem involves the determination of the sound field of a spherical oscillating bubble in an ideal fluid. It is found that use of incompressible boundary conditions leads to good approximations in the important region of high acoustic wave number.
Report discusses methods for numerical simulation of Navier-Stokes equations of viscous, incompressible flow, with emphasis on pseudocompressibility method. Advanced computational techniques reviewed contribute to improved designs by rapidly providing detailed information about conditions at all points in flow fields of proposed designs.
The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.
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.
This paper presents viewgraphs of time-accurate simulations of unsteady incompressible flow with moving boundaries.