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NASA NTRS1988

Weak solutions of the three-dimensional vorticity equation with vortex singularities

The extension of the concept of vortex singularities, developed by Saffman and Meiron (1986) for the case of two-dimensional point vortices in an incompressible vortical flow, to the three-dimensional case of vortex sticks (vortons) is investigated analytically. The derivation of the governing equations is explained, and it is demonstrated that the formulation obtained conserves total vorticity and is a weak solution of the vorticity equation, making it an appropriate means for representing three-dimensional vortical flows with limited numbers of vortex singularities.

Winckelmans, G.↗

NASA NTRS1988

Prediction of time-dependent fuselage pressures in the wake of a helicopter rotor

A method is described for the analysis of the unsteady, incompressible potential flow associated with a helicopter. The fuselage, rotor, and rotor wake are considered together in forward flight. This method is particularly useful in low advance ratio flight due to the contribution of the deformed wake to the airloads imposed on the fuselage. The rotor geometry is prescribed and the unsteady wake geometry is computed from the local flow perturbation velocities. The fuselage is modeled as a non-lifting body of source panels and the rotor and its wake are modeled as a full vortex lattice. The rotor geometry is arbitrary and several rotor blades can be represented. The unsteady airloads are computed in the presence of the deformed rotor wake by a time-stepping technique. The wake is started impulsively from rest, allowing a natural convection of the wake with time.

Berry, John D.↗

NASA NTRS1989

Unsteady stagnation-point heat transfer during passage of a concentrated vortex

The unsteady boundary layer due to a single rectilinear vortex filament approaching a 2-D stagnation point is investigated. Assuming the vortex remains far from the surface, incompressible potential flow theory is used to determine the time dependent inviscid flow field. The unsteady boundary layer equations are solved by an alternating-direction-implicit finite-difference method. Two mechanisms which cause fluctuations in heat transfer are the unsteady velocity field in the boundary layer and secondly, the unsteady total temperature at the edge of the boundary layer. The relative importance of these mechanisms is dependent upon the total temperature fluctuations relative to the imposed temperature difference. As a vortex approaches a stagnation point it may be forced to one side of the stagnation line or the other, depending on its initial position. Results are presented for both of these cases.

Rigby, David L.↗

NASA NTRS1989

Least-squares finite element method for fluid dynamics

An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

Jiang, Bo-Nan↗

NASA NTRS1988

Finite elements: Theory and application

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

Dwoyer, D. L.↗

NASA NTRS1988

Analysis of crack closure under plane strain conditions

The phenomenon of plasticity-induced crack closure is associated with the development of residual material on the flanks of an advancing fatigue crack. While it is easy to see that this residual material can come from the side faces of a specimen under plane stress conditions, it is difficult to discover the origin of this extra volume of material on the crack flanks when it is assumed that plane deformations occur and plastic flow is incompressible. The purpose of this paper is to determine whether plasticity-induced fatigue crack closure occurs in an elastic-perfectly plastic body under plane strain conditions.

Fleck, Norman A.↗

NASA NTRS1988

Spectral element methods - Algorithms and architectures

Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered; the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling.

Fischer, Paul↗

NASA NTRS1989

Absolute and convective instability of a cylinder wake

The stability behavior of a circular cross-section cylinder's wake at Reynolds number values of up to 45 is presently investigated by means of local linear stability theory. The steady-wake profiles computed are Navier-Stokes solutions of a uniform, incompressible viscous flow around a cylinder obtained by a spectral method. An absolutely unstable region is found to begin to form at a Reynolds number of about 20, and grows with incresing Reynolds number. The onset of global instability response must be characterized by a critical length of an absolutely unstable region; a critical Reynolds number criterion and preferred frequency are proposed based on linear stability analysis.

Yang, X.↗

NASA NTRS1989

LU-SGS implicit algorithm for three-dimensional incompressible Navier-Stokes equations with source term

A numerical method is developed for solving the incompressible Navier-Stokes equations using the concept of pseudocompressibility. A lower-upper symmetric-Gauss-Seidel implicit scheme is developed for three-dimensional incompressible viscous flow computations. The present algorithm offers additional advantages when solving the flow equations with source terms. Complete vectorizability of the algorithm on oblique planes of sweep in three-dimensions is accomplished in a new flow solver, INS3D-LU code. Spatial differencing is a second-order accurate semi-discrete finite-volume method augmented by a third-order accurate numerical dissipation model which is based on spectral-radii. Comparison of numerical solutions for a curved duct with experimental data shows good agreement. The method is applied to calculate the inducer flow of the Space Shuttle Main Engine turbopump.

Yoon, Seokkwan↗

NASA NTRS1989

An improved, robust, axial line singularity method for bodies of revolution

The failures encountered in attempts to increase the range of applicability of the axial line singularity method for representing incompressible, inviscid flow about an inclined and slender body-of-revolution are presently noted to be common to all efforts to solve Fredholm equations of the first kind. It is shown that a previously developed smoothing technique yields a robust method for numerical solution of the governing equations; this technique is easily retrofitted to existing codes, and allows the number of circularities to be increased until the most accurate line singularity solution is obtained.

Hemsch, Michael J.↗

NASA NTRS1989

On helicity fluctuations and the energy cascade in turbulence

Recent conjectures concerning the correlation between regions of high local helicity and low dissipation are examined from a rigorous theoretical standpoint based on the Navier-Stokes equations. It is proven that only the solenoidal part of the Lamb vector omega x u (which is directly tied to the nonlocal convection and stretching of vortex lines) contributes to the energy cascade in turbulence. Consequently, it is shown that regions of low dissipation can be associated with either low or high helicity, a result which disproves earlier speculations concerning this direct connection between helicity and the energy cascade. Some brief examples are given along with a discussion of the consistency of these results with the most recent computations of helicity fluctuations in incompressible turbulent flows.

Speziale, Charles G.↗

NASA NTRS1989

Least-squares finite element method for fluid dynamics

Jiang, Bo-Nan↗

NASA NTRS1990

Development of an integrated BEM for hot fluid-structure interaction

A boundary element approach is developed for problems of hot fluid-structure interaction. The structure is idealized as a thermoelastic solid, and a time-domain, boundary-only integral formulation is described. Meanwhile, several approaches are discussed for the hot fluid. Integrals equations are developed for both compressible and incompressible thermoviscous flow. Due to the presence of nonlinear convective terms in the governing differential equations, domain discretization is generally required. However, with the introduction of reference velocities, volume modeling often can be confined to regions near obstacles and walls. All formulations are implemented for two-dimensional problems in GPO-BEST, a general purpose boundary element computer program. An overview of this numerical implementation is provided, along with several illustrative examples. The present fluid formulations are appropriate in the low to medium Reynolds number ranges; however, some enhancements required for higher speed simulations are noted.

Dargush, G. F.↗

NASA NTRS1990

Cascade aerodynamic gust response including steady loading effects

To predict the unsteady convected gust aerodynamic response of a cascade comprised of arbitrary thick and cambered aerofoils in an incompressible, inviscid, flow field, a complete first-order model is formulated. The flow is analyzed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components, each described by a Laplace equation. The strong dependence of the unsteady aerodynamics on the steady effects of aerofoil and cascade geometry and incidence angle is manifested in the coupling of the unsteady and steady flow fields through the unsteady boundary conditions. Analytical solutions in individual grid elements of a body-fitted computational grid are then determined, with the complete solution obtained by assembly of these local solutions. The validity and capabilities of this model and solution technique are then demonstrated by analyzing the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.

Chiang, Hsiao-Wei D.↗

NASA NTRS1991

Analytical methods for the development of Reynolds-stress closures in turbulence

The derivation of Reynolds-stress models for viscous incompressible turbulent flow on the basis of the Navier-Stokes and continuity equations is explored in an analytical review. The formulation of the basic equations is outlined, and particular attention is given to zero-equation and one-equation models based on eddy viscosity, two-equation (k-l, k-epsilon, and k-omega) models, and second-order closure models. The superior performance of the second-order models is demonstrated by numerical results for (1) the return to isotropy from anisotropic homogeneous turbulence, (2) homogeneous turbulent shear flow in a rotating frame, (3) and fully developed inhomogeneous turbulent channel flow in a rotating frame. The inherent limitations of the Reynolds-stress approach and areas for further improvement are discussed.

Speziale, Charles G.↗

NASA NTRS1990

Further two-dimensional code development for Stirling space engine components

The development of multidimensional models of Stirling engine components is described. Two-dimensional parallel plate models of an engine regenerator and a cooler were used to study heat transfer under conditions of laminar, incompressible oscillating flow. Substantial differences in the nature of the temperature variations in time over the cycle were observed for the cooler as contrasted with the regenerator. When the two-dimensional cooler model was used to calculate a heat transfer coefficient, it yields a very different result from that calculated using steady-flow correlations. Simulation results for the regenerator and the cooler are presented.

Ibrahim, Mounir↗

NASA NTRS1992

Semi-empirical model for prediction of unsteady forces on an airfoil with application to flutter

A semi-empirical model is described for predicting unsteady aerodynamic forces on arbitrary airfoils under mildly stalled and unstalled conditions. Aerodynamic forces are modeled using second order ordinary differential equations for lift and moment with airfoil motion as the input. This model is simultaneously integrated with structural dynamics equations to determine flutter characteristics for a two degrees-of-freedom system. Results for a number of cases are presented to demonstrate the suitability of this model to predict flutter. Comparison is made to the flutter characteristics determined by a Navier-Stokes solver and also the classical incompressible potential flow theory.

Mahajan, Aparajit J.↗

NASA NTRS1991

Center for Modeling of Turbulence and Transition (CMOTT). Research briefs: 1990

Brief progress reports of the Center for Modeling of Turbulence and Transition (CMOTT) research staff from May 1990 to May 1991 are given. The objectives of the CMOTT are to develop, validate, and implement the models for turbulence and boundary layer transition in the practical engineering flows. The flows of interest are three dimensional, incompressible, and compressible flows with chemistry. The schemes being studied include the two-equation and algebraic Reynolds stress models, the full Reynolds stress (or second moment closure) models, the probability density function models, the Renormalization Group Theory (RNG) and Interaction Approximation (DIA), the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Povinelli, Louis A.↗