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At least 109 records · Page 6

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NASA NTRS1976

Adaptation of a general circulation model to ocean dynamics

A primitive-variable general circulation model of the ocean was formulated in which fast external gravity waves are suppressed with rigid-lid surface constraint pressires which also provide a means for simulating the effects of large-scale free-surface topography. The surface pressure method is simpler to apply than the conventional stream function models, and the resulting model can be applied to both global ocean and limited region situations. Strengths and weaknesses of the model are also presented.

Turner, R. E.↗

NASA NTRS1976

Turbulent atmospheric flow over a backward-facing step

The phenomenon of atmospheric shear layer separation over a man-made structure such as a building (modeled as a backward-facing step) has been analyzed theoretically by (1) solving the two-dimensional equations of motion in the two variables, stream function and vorticity, and by (2) employing an approximate integral technique. Boundary conditions for the undisturbed flow are that of the turbulent atmospheric shear flow over a rough terrain. In the first approach a two-equation model of turbulence was used. In the second approach an approximate technique was utilized in an attempt to describe the details of the flow in the recirculation zone behind the step. The results predict velocity profiles in sufficient detail that the presence of the corner eddy in the region of negative surface pressure gradient is evident. The magnitude of the reversed flow velocity in the recirculation eddy has been found to agree with that found from experiments. Also, a surface eddy viscosity distribution has been an outgrowth of the method which realistically follows the magnitude of the surface pressure gradient distribution as found experimentally.

Kaul, U. K.↗

NASA NTRS1977

Numerical solutions of Navier-Stokes equations for the structure of a trailing vortex

The structure and decay of a trailing vortex were analyzed during the numerical solutions of the full Navier-Stokes equations. Unsteady forms of the governing equations were recast in terms of circulation, vorticity, and stream function as dependent variables, and a second upwind finite difference scheme was used to integrate them with prescribed initial and boundary conditions. The boundary conditions at the outer edge and at the outflow section of the trailing vortex were considered. Different models of the flow were postulated, and solutions were obtained describing the development of the flow as integration proceeds in time. A parametric study was undertaken with a view to understanding the various phenomena that may possibly occur in the trailing vortex. Using the Hoffman and Joubert law of circulation at the inflow section, the results of this investigation were compared with experimental data for a Convair 990 wind model and a rectangular wing. With an exponentially decaying law of circulation at the inflow section and an adverse pressure gradient at the outer edge of the trailing vortex, solutions depict vortex bursting through the sudden expansion of the core and/or through the stagnation and consequent reversal of the flow on the axis. It was found that this bursting takes place at lower values of the swirl ratio as the Reynolds number increases.

Jain, A. C.↗

NASA NTRS1977

Liquid jet impingement normal to a disk in zero gravity

The free surface shapes of circular liquid jets impinging normal to sharp-edged disks in zero gravity are determined. Zero gravity drop tower experiments yielded three distinct flow patterns that were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted that indicated regions where viscous forces were not significant in the computation of free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane, where the stream function and velocity potential became the coordinates. The resulting nonlinear equations were solved by standard finite difference methods, and comparisons were made with the experimental data for the inertia dominated regime.

Labus, T. L.↗

NASA NTRS1977

Numerical solutions for viscous and potential flow about arbitrary two-dimensional bodies using body-fitted coordinate systems

A procedure for numerical solution of the time-dependent, incompressible Navier-Stokes equations for the flow about arbitrarily shaped two-dimensional bodies is given. This solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having a coordinate line coincident with the body contour regardless of its shape. The implicit solution utilizes the vorticity-stream function formulation with a false-position iterative adjustment of the surface vorticity in satisfaction of the no-slip boundary condition. Excellent agreement with the Blasius boundary layer solution is obtained for a semi-infinite flat plate. Results are presented for Reynolds numbers up to 2000 for several airfoils and a cambered rock.

Thames, F. C.↗

NASA NTRS1977

Neutrally stable atmospheric flow over a two-dimensional rectangular block

The phenomena of atmospheric flow over a two dimensional surface obstruction such as a building modeled as a rectangular block are analyzed by an approach using the Navier-Stokes equations with a two equation model of turbulence. The partial differential equations for the vorticity, stream function, turbulence kinetic energy, and turbulence length scale are solved by a finite difference technique. The predicted results are in agreement with the limited experimental data available. Current computed results show that the separation bubble originates from the upper front corner of the block and extends approximately 11.5 block heights behind the block. The decay of the mean velocity along the wake center line coincides almost perfectly with the experimental data. The vertical profiles of the mean velocity defect are also in reasonable agreement with wind tunnel results. Velocity profiles in the mixing region are shown to agree with the error function profile typically found in the shear layer. Details of the behavior of the turbulence kinetic energy and the turbulence length scale are also discussed.

Shieh, C. F.↗

NASA NTRS1978

Dynamic stall of an oscillating airfoil

Unsteady separated boundary layers and wakes were studied by investigating flow past an oscillating airfoil which in part models the retreating blade stall on the helicopters. The Navier-Stokes equations in terms of the vorticity and stream function for laminar flow were solved to determine the flow field around a modified NACA 0012 airfoil. After a fully developed flow was determined at zero incidence, the airfoil was oscillated in pitch through an angle of attack range from 0 deg to 20 deg. The computed streamlines during this pitch-up motion are in qualitative agreement with the trajectories of air bubbles observed in water tunnel experiments conducted with a NACA 0012 airfoil under the same conditions. During the pitch-down motion of the airfoil, the computed flow patterns cannot be compared with the experiments because the trajectories of air bubbles intersect.

Mehta, U. B.↗

NASA NTRS1978

Laser-velocimeter surveys of merging vortices in a wind tunnel: Complete data and analysis

The merger of two corotating vortices was studied with a laser velocimeter designed to measure the two cross-stream components of velocity. Measurements were made at several downstream distances in the vortex wake shed by two semispan wings mounted on the wind-tunnel walls. The velocity data provided wall-defined contours of crossflow velocity, stream function, and vorticity for a variety of test conditions. Downstream of the merger point, the vorticity was found to be independent of the downstream distance for radii smaller than r/b = 0.05. For larger radii, the vorticity depended on the distance from the wing. Upstream of the merger, a multicell vorticity pattern was found.

Corsiglia, V. R.↗

NASA NTRS1978

Laser-velocimeter surveys of merging vortices in a wind tunnel

The merger of two vortices was studied with a laser velocimeter designed to measure the two cross-stream components of velocity. Measurements were made at several downstream distances in the vortex wake shed by two semispan wings mounted on the wind tunnel walls. The velocity data provided well difined contours of cross-flow velocity, stream function and vorticity. Downstream of the merger point the vorticity was shown to be independent of the downstream distance for small radii, and at larger radii was dependent on the distance from the wing rather than from the merger point. Upstream of the merger point a multicell vorticity pattern was shown.

Corsiglia, V. R.↗

NASA NTRS1978

Steady flow of a non-Newtonian fluid through a contraction

A steady-state analysis is conducted to examine the basic flow structure of a non-Newtonian fluid in a domain including an inflow region, a contraction region, and an outflow region. A Cartesian grid system is used throughout the entire flow domain, including the contraction region, thus creating an irregular grid cell structure adjacent to the curved boundary. At node points adjacent to the curved boundary symmetry conditions are derived for the different flow variables in order to solve the governing difference equations. Attention is given to the motion and non-Newtonian constitutive equations, the boundary conditions, the numerical modeling of the non-Newtonian equations, the stream function contour lines for the non-Newtonian fluid, the vorticity contour lines for the non-Newtonian fluid, the velocity profile across the contraction, and the shear stress contour lines for the non-Newtonian fluid.

Gatski, T. B.↗

NASA NTRS1978

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Kurtz, L. A.↗

NASA NTRS1978

Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions

A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.

Rubin, S. G.↗

NASA NTRS1980

A rapid implicit-explicit solution to the two-dimensional time dependent incompressible Navier-Stokes equations

A second-order time-accurate and spatially factored algorithm was used in a finite difference scheme for the numerical solution of the time-dependent, incompressible, two dimensional Navier-Stokes equations in conservation-law form using vorticity and stream function variables. The systems of equations are solved at each time step by an iterative technique. Numerical results were obtained for a circular cylinder at a Reynolds number of 15, and an NACA 0012 airfoil at zero angle of attack at Reynolds numbers of 10 to the third and 10 to the fourth powers. The results are in agreement with another numerical technique, and the computing time required to obtain the steady state solution at the Reynolds number of 10 to the 4th power was 49.7 sec on CDC 7600 computer using a 65 x 84 computational grind.

Davis, J. E.↗

NASA NTRS1979

A two dimensional model of viscous slot flow

The effects of viscosity on flows through slots are investigated. Using Briley's formulation of the Alternating Direction Implicit method together with the Thompson transformation, numerical solution of viscous incompressible flow through a slot is simulated, for Reynolds number 1000 and openness ratio one tenth. The problem is formulated in terms of stream function and vorticity. A wall iteration of Israeli type is employed to iteratively induce the no slip condition on velocity.

Cooke, C. H.↗

NASA NTRS1981

Numerical solutions of atmospheric flow over semielliptical simulated hills

Atmospheric motion over obstacles on plane surfaces to compute simulated wind fields over terrain features was studied. Semielliptical, two dimensional geometry and numerical simulation of flow over rectangular geometries is also discussed. The partial differential equations for the vorticity, stream function, turbulence kinetic energy, and turbulence length scale were solved by a finite difference technique. The mechanism of flow separation induced by a semiellipse is the same as flow over a gradually sloping surface for which the flow separation is caused by the interaction between the viscous force, the pressure force, and the turbulence level. For flow over bluff bodies, a downstream recirculation bubble is created which increases the aspect ratio and/or the turbulence level results in flow reattachment close behind the obstacle.

Shieh, C. F.↗

NASA NTRS1981

Weighted-mean scheme for solving incompressible viscous flow

The problem of how a boundary layer responds to the motion of a convexed vortex on a porous wall was investigated. The wall velocity is approximately given by Darcy's law. The vorticity-stream function approach was adopted for solving Navier-Stokes equations of two dimensional incompressible viscous flows. The weighted-mean scheme was used for constructing finite difference approximations of spatial derivatives. Several test problems were solved and numerical results demonstrate clearly the accuracy, stability, and efficiency of the scheme. The weighted mean scheme then can be applied to the vortical flow problem.

Huynh, Q. Q.↗

NASA NTRS1980

Navier-Stokes calculations with a coupled strongly implicit method. II Spline deferred-corrector solutions

The coupled strongly implicit (CSIP) method described previously is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equations. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered (equal to or less than 1000). In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.

Rubin, S. G.↗

NASA NTRS1981

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Chen, C.-J.↗