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At least 199 records · Page 11

Steady incompressible potential flow around lifting bodies immersed in a fluid

The refinement was investigated of a method for evaluating the pressure distribution on a body surface of arbitrary shape in incompressible flow. The solution was obtained in terms of the velocity potential, through numerical approximations which require the use of a high speed digital computer. The box method and the modal method are described in detail, and were applied to a very thin, rectangular wing in incompressible, steady flow. The box method is found to be more practical as it is applicable to more general geometries (the modal method requires a new set of functions for each geometry), and requires less computer time (fifty percent of that required by the modal method for the same problem).

Chiuchiolo, E. A.↗

Calculation of incompressible fluid flow through cambered blades

Conformal mapping technique yields linear, approximate solutions for calculating flow of an incompressible fluid through staggered array of cambered blades for the cases of flow with partial cavitation and supercavitation. Lift and drag coefficients, cavitation number, cavity shape, and exit flow conditions can be determined.

Hsu, C. C.↗

Triangular spectral elements for incompressible fluid flow

We discuss the use of triangular elements in the spectral element method for direct simulation of incompressible flow. Triangles provide much greater geometric flexibility than quadrilateral elements and are better conditioned and more accurate when small angles arise. We employ a family of tensor product algorithms for triangles, allowing triangular elements to be handled with comparable arithmetic complexity to quadrilateral elements. The triangular discretizations are applied and validated on the Poisson equation. These discretizations are then applied to the incompressible Navier-Stokes equations and a laminar channel flow solution is given. These new triangular spectral elements can be combined with standard quadrilateral elements, yielding a general and flexible high order method for complex geometries in two dimensions.

Mavriplis, C.↗

Triangular spectral elements for incompressible fluid flow

We discuss the use of triangular elements in the spectral element method for direct simulation of incompressible flow. Triangles provide much greater geometric flexibility and are better conditioned and more accurate than quadrilateral elements when small angles arise. We employ a family of tensor product algorithms for triangles, allowing triangular elements to be handled with comparable arithmetic complexity to quadrilateral elements. The triangular discretizations are applied to the Poisson equation and are validated. The triangular discretizations are then applied to the incompressible Navier-Stokes equations, and a laminar channel flow solution is given. The new triangular spectral elements can be combined with standard quadrilateral elements, yielding a general and flexible high order method for complex geometries in two dimensions.

Mavriplis, Catherine↗

Numerical investigation of the onset of separation of an incompressible viscous flow from objects in ducts

Simulation has been used to investigate the phenomenon of separation of a steady flow of an incompressible viscous fluid from a symmetric object in a duct. Two essentially two-dimensional problems were studied: (1) an elliptical cylinder located between two parallel plates, and (2) a sphere placed on the axis of a cylindrical pipe. The steady-state vorticity transport equation and the second order differential equation relating vorticity and the stream function were iterated using the method of overrelaxation to obtain a solution for each set of initial conditions. The relationship between the Reynolds number corresponding to the onset of separation and the size of the object relative to the duct was found to be linear over a wide range.

Winchester, L. W., Jr.↗

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Loulou, Patrick↗

Efficient simulation of incompressible viscous flow over multi-element airfoils

The incompressible, viscous, turbulent flow over single and multi-element airfoils is numerically simulated in an efficient manner by solving the incompressible Navier-Stokes equations. The solution algorithm employs the method of pseudo compressibility and utilizes an upwind differencing scheme for the convective fluxes, and an implicit line-relaxation scheme. The motivation for this work includes interest in studying high-lift take-off and landing configurations of various aircraft. In particular, accurate computation of lift and drag at various angles of attack up to stall is desired. Two different turbulence models are tested in computing the flow over an NACA 4412 airfoil; an accurate prediction of stall is obtained. The approach used for multi-element airfoils involves the use of multiple zones of structured grids fitted to each element. Two different approaches are compared; a patched system of grids, and an overlaid Chimera system of grids. Computational results are presented for two-element, three-element, and four-element airfoil configurations. Excellent agreement with experimental surface pressure coefficients is seen. The code converges in less than 200 iterations, requiring on the order of one minute of CPU time on a CRAY YMP per element in the airfoil configuration.

Rogers, Stuart E.↗

Efficient simulation of incompressible viscous flow over multi-element airfoils

The incompressible, viscous, turbulent flow over single and multi-element airfoils is numerically simulated in an efficient manner by solving the incompressible Navier-Stokes equations. The computer code uses the method of pseudo-compressibility with an upwind-differencing scheme for the convective fluxes and an implicit line-relaxation solution algorithm. The motivation for this work includes interest in studying the high-lift take-off and landing configurations of various aircraft. In particular, accurate computation of lift and drag at various angles of attack, up to stall, is desired. Two different turbulence models are tested in computing the flow over an NACA 4412 airfoil; an accurate prediction of stall is obtained. The approach used for multi-element airfoils involves the use of multiple zones of structured grids fitted to each element. Two different approaches are compared: a patched system of grids, and an overlaid Chimera system of grids. Computational results are presented for two-element, three-element, and four-element airfoil configurations. Excellent agreement with experimental surface pressure coefficients is seen. The code converges in less than 200 iterations, requiring on the order of one minute of CPU time (on a CRAY YMP) per element in the airfoil configuration.

Rogers, Stuart E.↗

Numerical simulation of the incompressible internal flow through a tilting disk valve

A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady and unsteady flow calculations are performed by solving the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain into several simple subdomains is used. An algebraic turbulence model for internal flows is incorporated to reach the physiological values of Reynolds number. Good agreement is obtained between the numerical results and experimental measurements. It is found that the tilting disk valve causes large regions of separated flow, and regions of high shear.

Chang, I-Dee↗

Incompressible, Viscous Flow About An Ogive/Cylinder

Theoretical predictions and observations of incompressible viscous flow about body of revolution at angle of attack compared in report. Body consists of solid circular cylinder at downstream end and tapered in ogive of revolution to point on axis at upstream end. Study was test of modern numerical methods for solution of equations of fluid dynamics, conducted as step toward future work on more difficult problems.

Zilliac, Gregory G.↗

Effects of Adverse Pressure Gradient on the Incompressible Reattaching Flow Over a Rearward-Facing Step

The turbulent, incompressible reattaching flow over a rearward-facing step has been studied by many researchers over the years. One of the principal quantities determined in these experiments has been the distance from the step to the point (or region) where the separated shear layer reattaches to the surface (x(r)). The values for x(r)/h, where h is the step height, have covered a wider range than can reasonably be attributed to experimental technique or inaccuracy. Often the reason for a largely different value of x(r)/h can be attributed to an incompletely developed turbulent layer, or a transitional or laminar boundary layer. However, for the majority of experiments where the boundary layer is believed to be fully developed and turbulent, x(r)/h still varies several step heights; generally, 5 1/2 approximately < x(r)/h approximately < 7 1/2. This observed variation has usually been attributed to such variables as l/h (step length to height, h/delta (step height to initial boundary-layer thickness), R(e)(theta)), or the experimental technique for determining reattachment location. However, there are so many different combinations of variables in the previous experiments that it was not possible to sort out the effects of particular conditions on the location of reattachment. In the present experiment velocity profiles have been measured in and around the region of separated flow. Results show a large influence of adverse pressure gradient on the reattaching flow over a rearward-facing step that has not been reported previously. Further, the many previous experiments for fully developed, turbulent flow in parallel-walled channels have shown a range of reattachment location that has not been explained by differences in initial flow conditions. Although these initial flow conditions might contribute to the observed variation of reattachment location, it appears that the pressure gradient effect can explain most of that variation.

Kuehn, Donald M.↗

Numerical studies of incompressible viscous flow in a driven cavity

A series of project papers is presented in computational fluid dynamics. The work was performed during the 1973-74 academic year at Old Dominion University. Each paper briefly examines a numerical method(s) that can be applied to the Navier-Stokes equations governing incompressible flow in a driven cavity. Solutions obtained with a cubic spline procedure are also included.

Source record↗

Efficient simulation of incompressible viscous flow over single and multi-element airfoils

Incompressible viscous turbulent flows over single- and multiple-element airfoils are numerically simulated in an efficient manner by solving the incompressible Navier-Stokes equations. The solution algorithm uses the method of pseudocompressibility with an upwind-differencing scheme for the convective fluxes and an implicit line-relaxation scheme to study high-lift take-off and landing configurations and to compute lift and drag at various angles of attack up to stall. Two different turbulence models are tested in computing the flow over an NACA 4412 airfoil. The approach used for multiple-element airfoils involves the use of multiple zones of structured grids fitted to each element. Two different approaches are compared: a patched system of grids and an overlaid Chimera system of grids. Computational results are presented for two-element, three-element, and four-element airfoil configurations. Excellent agreement with experimental surface-pressure coefficients is seen. The code converges in less than 200 iterations, requiring on the order of one minute of CPU time on a CRAY YMP per element in the airfoil configuration.

Rogers, Stuart E.↗

Mathematical aspects of finite element methods for incompressible viscous flows

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Gunzburger, M. D.↗

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗