John Steinhoff

Application of Vorticity Confinement to Prediction of the Flow over Complex Bodies

The vorticity cone nement technique, which represents a very effective, unie ed way of treating complex, highReynolds-number separated e ows with thin convecting vortices, as well as thin attached boundary layers, over complex solid bodies. Conventional Eulerian computational methods are discussed and then contrasted with vorticity cone nement, which is also Eulerian. The basic assumptions in vorticity cone nement, are reviewed, and then the method itself is briee y outlined. Following the description, representative results are presented: First, two-dimensional results for convecting vortices and Cauchy ‐Riemann e ow over a cylinder are presented. These describe, respectively, the salient features of the method for convecting vortices and for e ow over solid surfaces, embedded in a uniform Cartesian grid. Then, three-dimensional results for e ow over complex cone gurations, including a complete rotorcraft, are presented.

Numerical method for vorticity confinement in compressible flow

It is well known that modern computational fluid dynamics codes based on Eulerian descriptions do not adequately handle flows involving the convection of thin vortical layers. These layers often remain very thin and persist long distances without significant dissipation. Over the past decade, Steinhoff has introduced a class of methods, generally known as vorticity confinement, which have been used successfully to predict complex flows, particularly involving helicopter rotors. These methods have involved an incompressible finite difference formulation. We extend vorticity confinement to compressible flows by noting that the confinement term added to the momentum equation in Steinhoffs formulation may be interpreted as a body force. We can then extend the approach to compressible flows by adding the contribution of this body force to the integral conservation laws. The development of a finite volume compressible vorticity confinement scheme then follows directly. We have implemented the scheme with a matrix artificial dissipation and a new matrix confinement term. Results are presented for supersonic shear layers, vortices moving in a uniform stream, and vortex separation on the leeward surface of a flat plate delta wing at supersonic speed

Numerical vorticity confinement for vortex-solid body interaction problems

A new numerical method based on adding a term to the Euler/Navier-Stokes equations has demonstrated that it can effectively treat vortex-dominated flows using low-order numerical schemes and coarse grids. With the technique, numerical diffusion introduced by convection schemes can be eliminated when solving the modified flow governing equations. The modification of the velocity field, which conserves the total vorticity, essentially convects the vorticity toward its local extreme to offset the numerical diffusion. This method preserves the vortex structure even when vortices travel through a coarse grid region. The method is implemented separately with two distinctive basic solvers: a Navier-Stokes flow solver based on a vorticity-velocity formulation and an Euler solver based on a velocity-pressure formulation. Problems presented in this paper include airfoil dynamic stall, vortex-airfoil interaction, and vortex-fuselage interactions.

Accelerated finite-volume calculation of transonic potential flows

A fully-conservative finite-volume algorithm is applied to the calculation of transonic potential flows past isolated airfoils and through two-dimensional channels. The difference equations are solved by a multi-grid technique which uses an alternating-direction-implicit method as a smoothing algorithm. The finite-volume formulation provides a very powerful framework within which to treat flows past complicated geometries, while the multi-grid/alternating-direction scheme provides rapid convergence of the solution to very small residuals. Results of calculations using the algorithm are presented for the isolated airfoil and transonic channel test cases provided by the Symposium organizers.

Capture of contact discontinuities and shock waves using a discontinuity confinement procedure

The issues of the capturing and the nondiffusive resolution of contact discontinuities and shocks were investigated using a multidimensional discontinuity confinement technique. This new scheme was developed using an antidiffusion convection and residual correction distribution which are closely related to the vortex confinement method of Steinhoff. The discontinuity confinement procedure is developed using a cell-vertex fluctuation-splitting framework. This formulation provides a simple and multidimensional procedure that can be used with any monotone basic solver. A comparison of the resolution of the confinement scheme with a higher-order dimensionally split upwind scheme and several solutions on adaptive unstructured grids demonstrate that the new method has the ability to much more sharply resolve complex regions with contact discontinuities. Moreover, the quality of the solution does not deteriorate over many time iterations or long spatial distances. Solutions for several 2D steady problems are presented to demonstrate the high resolution property of the new scheme. (Author)

A multimicroprocessor approach to numerical analysis: An application to gaming problems

A parallel processing system is described that consists of a minicomputer host and a set of bipolar microcomputer modules. It is argued that such a system in which the microcomputers operate with little mutual interaction should be effective for an important class of problems in numerical analysis. In particular, estimates are given for the operation of the system on a problem in gaming theory. In this problem, the extensive I/O and software capabilities of the minicomputer provide ease of use for a large part of the problem. The relatively simple part of the problem, which requires almost all of the computational time, is executed in parallel on the microcomputers. It is argued that the system, with 10 to 20 modules, would offer one to two orders of magnitude more speed at several orders of magnitude less cost than current large general-purpose machines. The potential for the development of new algorithms that exploit fully the characteristics of the new devices is discussed.

Large Reynolds Number Turbulence Modeling with Vorticity Confinement

compute flow fields with thin vortical regions. These thin vortical elements, appearing as vortex sheets and filaments, are an integral feature of turbulent flow. An extension to the traditional Vorticity Confinement method is investigated as an ecient LES-type of turbulence model. Of primary interest is the Taylor-Green vortex in which the flow transitions from laminar to turbulent. Generally transitional flows are dicult to compute using LES methods as the sub-grid scale (SGS) models often initiate instabilities at incorrect times: This makes this flow a good test of the models. Also presented is the decay of a randomly stirred turbulent flow. Vorticity Confinement results are compared against analytical and computational results of both DNS and LES types.

Numerical vorticity capturing for vortex-solid body interaction problems

A new numerical method based on adding a term to the Euler/Navier-Stokes equations has been demonstrated it can effectively treat vortex-dominated flows using low-order numerical schemes and coarse grids. The numerical diffusion introduced by convection schemes can be eliminated by modifying the velocity field as a result of solving the modified flow governing equations. The modification of the velocity field, which conserves the total vorticity, essentially convects the vorticity toward its local extreme to offset the numerical diffusion. This method preserves the vortex structure even when vortices travel on coarse grid region. The method is implemented with two distinctive codes: a Navier-Stokes flow solver based on vorticity-velocity formulation and an Euler code based on velocity-pressure formulation. Problems presented in this paper include airfoil dynamic stall, vortex airfoil interaction, and vortex-fuselage interactions.

A New Numerical Approach for Rotorcraft Aerodynamics Using Vorticity Confinement

The Vorticity Confinement method is used in conjuction with uniform Cartesian grids for computing flows of blunt bodies. These bodies are defined on the uniform grid by a smooth function where the function is designated zero on the body surfaces. A unique computation procedure is applied to all the grid points with the confinement performed outside the body based on the vorticity whereas inside the body based on the function. For flows around streamline-like bodies, such as a wing, the computation is performed on body-fitted grids where these grids can be encompassed by the uniform grid. Flow informations are transferred between the body-fitted grids and the uniform grid, where one or more blunt bodies are embedded, through an overset grid technique. However, there is no hole-cutting needed since the solid bodies are explicitly defined, by the smooth function. A N AC AGO 12 wing download under a rotor is computed by the combined approach with a generic nacelle at the wing tip.

An Optimization Technique for Computing Chromatic Corrections in Heavy Ion Focussing Systems

An optimization algorithm is described for computing field strengths for a set of corrective sextupole magnets in a heavy ion focussing system. Initial results are presented which show that, in some cases, the beam transmission through a 1 mm pellet canbe increased from an uncorrected value of about 60% to over 90%. The method should be useful for systems where, due to constraints or the presence of a number of abberations, no straight-forward theory exists for directly computing the field strengths.