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Leonard, A.

Publications and source records attributed to Leonard, A..

36 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Vortex simulation of an inviscid shear layer

The accuracy of the vortex-blob method was tested by simulating a free-shear-layer instability, Kirchhoff's elliptical vortex, and a circular vortex. The main numerical parameters in the vortex-blob method are the density of the vortices, and the distribution of vorticity within each vortex core. The growth rate of a periodic unstable mode of the shear layer was calculated numerically and compared with the exact result. The error is only a few percent for about 10 rows of vortex blobs. The error is reduced by decreasing the spacing between vortices and, correspondingly, the core size. In the simulation of the motion of the elliptical vortex, the rotation of the boundary, without change of shape, and the circular particle paths of the vortical fluid were well simulated. For the circular vortex, optimum sets of parameters were obtained by comparing them with the exact velocity. The results are consistent with convergence theories of the vortex-blob method. In particular, second-order convergence is observed with a Gaussian core from velocity calculation.

Nakamura, Y.↗
NASA NTRS1982

A new numerical method for the simulation of three-dimensional flow in a pipe

A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction. Previously announced in STAR as N82-31644

Leonard, A.↗
NASA NTRS1981

Computation of separated flows by a vortex-tracing algorithm

Numerical solutions for two-dimensional, time-dependent, separated flows around bodies are obtained, using a new version of the vortex method. This method provides an efficient representation of flows involving large regions of separation. The modifications incorporated in the new version, which improve its accuracy, versatility, and computing speed, are described. The computer cost is only of the order of the 3/2 power on N, instead of N-squared, for each step with N vortices. Arbitrary shapes can be treated; a conformal mapping is not required. Special attention is paid to the viscous character of the solution and to the accurate computation of the pressure distribution at the body surface. The vortex solution for the outer flow is coupled to an inner solution for the attached part of the boundary layer. Numerical results are presented for several bluff bodies exhibiting dependence on Reynolds number, for stationary airfoils under steady or transient conditions and for oscillating airfoils, including dynamic stalls. These results are compared with other available results, analytical or experimental, and demonstrate the enhanced reliability and accuracy of the improved method.

Spalart, P. R.↗
NASA NTRS1981

Simulation of three-dimensional incompressible flows with a vortex-in-cell method

A new method for the numerical simulation of three-dimensional incompressible flows is described. The vortex-in-cell (VIC) method presented traces the motion of the vortex filaments in the velocity field which these filaments create. The velocity field is not calculated directly by the Biot-Savart law of interaction but by creating a mesh-record of the vorticity field, then integrating a Poisson's equation via the fast Fourier transform to generate a mesh-record of the velocity field. The computed scales of motion are assumed to be essentially inviscid. Viscous of subgrid-scale effects are incorporated into a filtering procedure in wave vector space. Results of tracing a periodic array of single vortex rings are compared with a Green's function calculation. The agreement is very good.

Couet, B.↗
NASA NTRS1981

Mixing layer simulation by an improved three-dimensional vortex-in-cell algorithm

An extension is presented of the three-dimensional vortex-in-cell (VIC) method that allows for the simulation of incompressible turbulent flows such as plane mixing layers and wakes with exact boundary conditions in the normal direction. The vorticity is assumed to be confined between two parallel planes and the turbulence is assumed to be homogeneous in the two directions parallel to the planes. As an application, an analysis is presented of the evolution of the plane mixing layer subjected to random two- and three-dimensional initial disturbances.

Couet, B.↗
NASA NTRS1980

Vortex methods for flow simulation

Recent progress in the development of vortex methods and their applications to the numerical simulation of incompressible fluid flows are reviewed. Emphasis is on recent results concerning the accuracy of these methods, improvements in computational efficiency, and the development of three-dimensional methods. Simulations of several example flows which display some of the strengths and weaknesses of vortex methods are presented.

Leonard, A.↗
NASA NTRS1980

Turbulent structures in wall-bounded shear flows observed via three-dimensional numerical simulators

Three recent simulations of tubulent shear flow bounded by a wall using the Illiac computer are reported. These are: (1) vibrating-ribbon experiments; (2) study of the evolution of a spot-like disturbance in a laminar boundary layer; and (3) investigation of turbulent channel flow. A number of persistent flow structures were observed, including streamwise and vertical vorticity distributions near the wall, low-speed and high-speed streaks, and local regions of intense vertical velocity. The role of these structures in, for example, the growth or maintenance of turbulence is discussed. The problem of representing the large range of turbulent scales in a computer simulation is also discussed.

Leonard, A.↗
NASA NTRS1980

Vortex methods for two- and three-dimensional flow simulations

The point vortex and vortex blob methods for two dimensional flows are presented. Several results are discussed concerning the numerical analysis of the latter scheme, e.g., the preservation of globally conserved quantities and the analysis of the spatial discretization error resulting from the convection of fixed blobs of vorticity. An application to the two dimensional mixing layer is briefly described. The contour dynamics method is also discussed. The simulation of three dimensional flows with vortex methods is discussed. A natural way to represent the vorticity is in the form of closed tubes of filaments of vorticity, although other schemes are examined. Applications to aircraft trailing vortices and to a turbulent spot in a laminar boundary layer are presented. Hybrid schemes that use an Eulerian mesh to solve the Poisson equation for the velocity field are discussed. The goal of these schemes is to avoid the high cost of the Biot-Savart integration if many vortex elements are used while enjoying most of the advantages of pure Lagrangian schemes.

Leonard, A.↗
NASA NTRS1979

Vortex simulation of three-dimensional, spotlike disturbances in a laminar boundary layer

The growth of a turbulent spot in a laminar boundary layer as the spot evolves from a localized disturbance in the layer, is simulated numerically using a three-dimensional vortex filament description of the vorticity field. The filaments are marked with a sequence of node points which are tracked in a Lagrangian reference frame. Velocity computation is done by Biot-Savart integration. Although some discrepancies with experiment appear to exist in the near wall region, the gross properties of the spot, including the velocities of the leading and trailing edges and the velocity perturbations away from the wall, are in good agreement with experiment.

Leonard, A.↗
NASA NTRS1979

Vortex simulation of three-dimensional, spotlike disturbances in a laminar boundary layer

The growth of a turbulent spot in a laminar boundary layer, as the spot evolves from a localized disturbance in the layer, is simulated numerically using a three-dimensional vortex filament description of the vorticity field. The filaments are marked with a sequence of mode points which are tracked in a Lagrangian reference frame. Velocity computation is done by Biot-Savart integration. Although some discrepancies with experiment appear to exist in the near wall region, the gross properties of the spot, including the velocities of the leading and trailing edges and the velocity perturbations away from the wall, are in good agreement with experiment.

Leonard, A.↗
NASA NTRS1979

Three-dimensional simulation of the free shear layer using the vortex-in-cell method

We present numerical simulations of the evolution of a mixing layer from an initial state of uniform vorticity with simple two- and three-dimensional small perturbations. A new method for tracing a large number of three-dimensional vortex filaments is used in the simulations. Vortex tracing by Biot-Savart interaction originally implied ideal (non-viscous) flow, but we use a 3-d mesh, Fourier transforms and filtering for vortex tracing, which implies 'modeling' of subgrid scale motion and hence some viscosity. Streamwise perturbations lead to the usual roll-up of vortex patterns with spanwise uniformity maintained. Remarkably, spanwise perturbations generate streamwise distortions of the vortex filaments and the combination of both perturbations leads to patterns with interesting features discernable in the movies and in the records of enstrophy and energy for the three components of the flow.

Couet, B.↗
NASA NTRS1979

Numerical simulation of turbulent flows with a three-dimensional vortex-in-cell method

A three-dimensional vortex-in-cell method has been developed for the evaluation of local flow fields due to a family of vortex filaments which employs the principles and architecture of a code developed for magnetic field evaluation in plasma simulations. The computational effort in the new method, as compared to 'vortex pushing' by direct Biot-Savarat interaction, increases directly, rather than quadratically, with the number of vortex elements. The method is well suited for studying large number of vortex filaments or rings and can be used for simulating continuous vorticity.

Buneman, O.↗
NASA NTRS1976

Simulation of three-dimensional separated flows with vortex filaments

A Lagrangian vorticity method for numerical simulation of three-dimensional separated flows with vortex filaments, about solid bodies, is discussed. The method is an extension of an earlier one for three-dimensional rotational flows away from solid boundaries e.g., jets, vortex rings, and aircraft trailing vortices after initial rollup. In this method an harmonic contribution to the velocity field is computed at each time step to ensure tangency of the velocity field at the boundary. The mechanics of the boundary layer are approximated with sufficient accuracy so that the separation lines are located correctly on the surface of the body.

Leonard, A.↗
NASA NTRS1975

Numerical simulation of interacting, three-dimensional vortex filaments

Unsteady three-dimensional fluid flows which are characterized by low viscosity and the presence of distinct regions of high vorticity embedded in an otherwise irrotational flow are considered, taking into account the case in which an intermingling of vortex filaments appears. Incompressible flows of the considered type are simulated with the aid of an approach in which the vorticity distribution is modeled in terms of continuous closed filaments. It is attempted to track these filaments in a Lagrangian reference frame.

Leonard, A.↗
NASA NTRS1974

Energy cascade in large-eddy simulations of turbulent fluid flows

The derivation of smoothed or filtered momentum and continuity equations for large-scale, energy-containing eddies is considered. Questions regarding the energy loss of large-scale turbulence are discussed along with aspects of turbulent diffusion of a passive scalar. It is found that the large-scale fluctuations satisfy filtered or averaged momentum and continuity equations. An averaging of the nonlinear advection term yields two terms.

Leonard, A.↗