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NASA NTRS1999

Potential Flow Interactions With Directional Solidification

The effect of convective melt motion on the growth of morphological instabilities in crystal growth has been the focus of many studies in the past decade. While most of the efforts have been directed towards investigating the linear stability aspects, relatively little attention has been devoted to experimental and numerical studies. In a pure morphological case, when there is no flow, morphological changes in the solid-liquid interface are governed by heat conduction and solute distribution. Under the influence of a convective motion, both heat and solute are redistributed, thereby affecting the intrinsic morphological phenomenon. The overall effect of the convective motion could be either stabilizing or destabilizing. Recent investigations have predicted stabilization by a flow parallel to the interface. In the case of non-parallel flows, e.g., stagnation point flow, Brattkus and Davis have found a new flow-induced morphological instability that occurs at long wavelengths and also consists of waves propagating against the flow. Other studies have addressed the nonlinear aspects (Konstantinos and Brown, Wollkind and Segel)). In contrast to the earlier studies, our present investigation focuses on the effects of the potential flow fields typically encountered in Hele-Shaw cells. Such a Hele-Shaw cell can simulate a gravity-free environment in the sense that buoyancy-driven convection is largely suppressed, and hence negligible. Our interest lies both in analyzing the linear stability of the solidification process in the presence of potential flow fields, as well as in performing high-accuracy nonlinear simulations. Linear stability analysis can be performed for the flow configuration mentioned above. It is observed that a parallel potential flow is stabilizing and gives rise to waves traveling downstream. We have built a highly accurate numerical scheme which is validated at small amplitudes by comparing with the analytically predicted results for the pure morphological case. We have been able to observe nonlinear effects at larger times. Preliminary results for the case when flow is imposed also provide good validation at small amplitudes.

Buddhavarapu, Sudhir S.↗
NASA NTRS1999

A New Compendium of Unsteady Aerodynamic Test Cases for CFD: Summary of AVT WG-003 Activities

With the continuous progress in hardware and numerical schemes, Computational Unsteady Aerodynamics (CUA), that is, the application of Computational Fluid Dynamics (CFD) to unsteady flowfields, is slowly finding its way as a useful and reliable tool (turbulence and transition modeling permitting) in the aircraft, helicopter, engine and missile design and development process. Before a specific code may be used with confidence it is essential to validate its capability to describe the physics of the flow correctly, or at least to the level of approximation required, for which purpose a comparison with accurate experimental data is needed. Unsteady wind tunnel testing is difficult and expensive; two factors which dramatically limit the number of organizations with the capability and/or resources to perform it. Thus, unsteady experimental data is scarce, often classified and scattered in diverse documents. Additionally, access to the reports does not necessarily assure access to the data itself. The collaborative effort described in this paper was conceived with the aim of collecting into a single easily accessible document as much quality data as possible. The idea is not new. In the early 80's NATO's AGARD (Advisory Group for Aerospace Research & Development) Structures and Material Panel (SMP) produced AGARD Report No. 702 "Compendium of Unsteady Aerodynamic Measurements", which has found and continues to find extensive use within the CUA Community. In 1995 AGARD's Fluid Dynamics Panel (FDP) decided to update and expand the former database with new geometries and physical phenomena, and launched Working Group WG-22 on "Validation Data for Computational Unsteady Aerodynamic Codes". Shortly afterwards AGARD was reorganized as the RTO (Research and Technology Organization) and the WG was renamed as AVT (Applied Vehicle Technolology) WG-003. Contributions were received from AEDC, BAe, DLR, DERA, Glasgow University, IAR, NAL, NASA, NLR, and ONERA. The final publication with the results of the exercise is expected in the second part of 1999. The aim of the present paper is to announce and present the new database to the Aeroelasticity community. It is also intended to identify, together with one of the groups of end users it targets, deficiencies in the compendium that should be addressed by means of new wind tunnel tests or by obtaining access to additionally existing data.

Ruiz-Calavera, Luis P.↗
NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗
NASA NTRS1998

Modeling Electric Field Influences on Plasmaspheric Refilling

We have a new model of ion transport that we have applied to the problem of plasmaspheric flux tube refilling after a geomagnetic disturbance. This model solves the Fokker-Planck kinetic equation by applying discrete difference numerical schemes to the various operators. Features of the model include a time-varying ionospheric source, self-consistent Coulomb collisions, field-aligned electric field, hot plasma interactions, and ion cyclotron wave heating. We see refilling rates similar to those of earlier observations and models, except when the electric field is included. In this case, the refilling rates can be quite different that previously predicted. Depending on the populations included and the values of relevant parameters, trap zone densities can increase or decrease. In particular, the inclusion of hot populations near the equatorial region (specifically warm pancake distributions and ring current ions) can dramatically alter the refilling rate. Results are compared with observations as well as previous hydrodynamic and kinetic particle model simulations.

Liemohn, M. W.↗
NASA NTRS2000

Aerodynamic Lift and Moment Calculations Using a Closed-Form Solution of the Possio Equation

In this paper, we present closed-form formulas for the lift and moment coefficients of a lifting surface in two dimensional, unsteady, compressible, subsonic flow utilizing a newly developed explicit analytical solution of the Possio equation. Numerical calculations are consistent with previous numerical tables based on series expansions or ad hoc numerical schemes. More importantly, these formulas lend themselves readily to flutter analysis, compared with the tedious table-look-up schemes currently in use.

Lin, Jensen↗
NASA NTRS2000

Radiative Transfer and Satellite Remote Sensing of Cirrus Clouds Using FIRE-2-IFO Data

Under the support of the NASA grant, we have developed a new geometric-optics model (GOM2) for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. From comparisons with the results computed by the finite difference time domain (FDTD) method, we show that the novel geometric-optics can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as approximately 6. We demonstrate that the present model converges to the conventional ray tracing method for large size parameters and produces single-scattering results close to those computed by the FDTD method for size parameters along the minimum dimension smaller than approximately 20. We demonstrate that neither the conventional geometric optics method nor the Lorenz-Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20. On the satellite remote sensing algorithm development and validation, we have developed a numerical scheme to identify multilayer cirrus cloud systems using AVHRR data. We have applied this scheme to the satellite data collected over the FIRE-2-IFO area during nine overpasses within seven observation dates. Determination of the threshold values used in the detection scheme are based on statistical analyses of these satellite data.

Source record↗
NASA NTRS2001

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels. From the governing equation level, we condition the Euler equations in two steps. The first step is to split the inviscid flux derivatives into a conservative and a non-conservative portion that satisfies a so called generalized energy estimate. This involves the symmetrization of the Euler equations via a transformation of variables that are functions of the physical entropy. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the second step is to reformulate the split Euler equations in perturbation form with the new unknowns as the small changes of the conservative variables with respect to their large stagnation values. From the numerical scheme level, a stable sixth-order central interior scheme with a third-order boundary schemes that satisfies the discrete analogue of the integration-by-parts procedure used in the continuous energy estimate (summation-by-parts property) is employed.

Mueller, B.↗
NASA NTRS2001

A Coupled Plasma and Sheath Model for High Density Reactors

We present a coupled plasma and collisionless; sheath model for the simulation of high density plasma processing reactors. Due to inefficiencies in numerical schemes and the resulting computational burden, a coupled multidimensional plasma and sheath simulation has not been possible model for gas mixtures and high density reactors of practical interest. In this work we demonstrate that with a fully implicit algorithm and a refined computational mesh, a self-consistent plasma and sheath simulation is feasible. We discuss the details of the model equations, the importance of ion inertia, and the resulting sheath profiles for argon and chlorine plasmas. We find that at low operating pressures (10-30 mTorr), the charge separation occurs only within a 0.5 mm layer near the surface in a 300 mm inductively coupled plasma etch reactor. A unified model eliminates the use of off-line or loosely coupled sheath models with simplifying assumptions which generally lead to uncertainties in ion flux and sheath electrical properties.

Deepak, Bose↗
NASA NTRS2001

Discontinuous Galerkin Methods for NonLinear Differential Systems

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

Barth, Timothy↗
NASA NTRS2001

Computational Hemodynamics Involving Artificial Devices

This paper reports the progress being made towards developing complete blood flow simulation capability in human, especially, in the presence of artificial devices such as valves and ventricular assist devices. Devices modeling poses unique challenges different from computing the blood flow in natural hearts and arteries. There are many elements needed such as flow solvers, geometry modeling including flexible walls, moving boundary procedures and physiological characterization of blood. As a first step, computational technology developed for aerospace applications was extended in the recent past to the analysis and development of mechanical devices. The blood flow in these devices is practically incompressible and Newtonian, and thus various incompressible Navier-Stokes solution procedures can be selected depending on the choice of formulations, variables and numerical schemes. Two primitive variable formulations used are discussed as well as the overset grid approach to handle complex moving geometry. This procedure has been applied to several artificial devices. Among these, recent progress made in developing DeBakey axial flow blood pump will be presented from computational point of view. Computational and clinical issues will be discussed in detail as well as additional work needed.

Kwak, Dochan↗
NASA NTRS1994

Navier-Stokes Flowfield Simulation of Boeing 747-200 as Platform for SOFIA

Steady and unsteady viscous, three-dimensional flowfields are calculated using a thin layer approximation of Navier-Stokes equations in conjunction with Chimera overset grids. The finite-difference numerical scheme uses structured grids and a pentadiagonal flow solver called "OVERFLOW". The configuration of Boeing 747-200 has been chosen as one of configurations to be used as a platform for the SOFIA (Stratospheric Observatory For Infrared Astronomy). Initially, the steady flowfield of the full aircraft is calculated for the clean configuration (without a cavity to house telescope). This solution is then used to start the unsteady flowfield of a configuration containing cavity housing the observation telescope and its peripheral units. Analysis of unsteady flowfield in the cavity and its influence on the tail empennage, as well as the noise due to turbulence and optical quality of the flow are the main focus of this study. For the configuration considered here, the telescope housing cavity is located slightly downstream of the portwing. The entire flow-field is carefully constructed using 45 overset grids and consists of nearly 4 million grid points. All the computations axe done at one freestream flow condition of M(sub infinity) = 0.85, alpha = 2.5deg, and a Reynolds of Re = 1.85x10deg

Srinivasan, G.R.↗
NASA NTRS2001

Extension of a System Level Tool for Component Level Analysis

This paper presents an extension of a numerical algorithm for network flow analysis code to perform multi-dimensional flow calculation. The one dimensional momentum equation in network flow analysis code has been extended to include momentum transport due to shear stress and transverse component of velocity. Both laminar and turbulent flows are considered. Turbulence is represented by Prandtl's mixing length hypothesis. Three classical examples (Poiseuille flow, Couette flow, and shear driven flow in a rectangular cavity) are presented as benchmark for the verification of the numerical scheme.

Majumdar, Alok↗
NASA NTRS1999

Numerical Simulations of Acoustically Driven, Burning Droplets

This computational study focuses on understanding and quantifying the effects of external acoustical perturbations on droplet combustion. A one-dimensional, axisymmetric representation of the essential diffusion and reaction processes occurring in the vicinity of the droplet stagnation point is used here in order to isolate the effects of the imposed acoustic disturbance. The simulation is performed using a third order accurate, essentially non-oscillatory (ENO) numerical scheme with a full methanol-air reaction mechanism. Consistent with recent microgravity and normal gravity combustion experiments, focus is placed on conditions where the droplet is situated at a velocity antinode in order for the droplet to experience the greatest effects of fluid mechanical straining of flame structures. The effects of imposed sound pressure level and frequency are explored here, and conditions leading to maximum burning rates are identified.

Kim, H.-C.↗
NASA NTRS1995

Simulations Of On Demand Vortex Generators

The development of a two-dimensional viscous incompressible flow generated by an off center thin oscillating bd on top of a cavity is studied computationally as a prototype of vortex generators. The lid is placed asymmetrically over the cavity so that the gap size is different on either side of the cavity. An adaptive numerical scheme, based on high resolution viscous vortex methods, is used to integrate the vorticity/velocity formulation of the Navier-Stokes equations with the no-slip boun.lary condition enforced on the lid and cavity walls. Depending on the a amplitude and frequency of the oscillation as well as the the gap size, vorticity is ejected in the fluid above the cavity either from the large and/or the small gap. The results of the computations complement ongoing experimental work.

Koumoutsakos, P.↗
NASA NTRS1997

Application of a Chimera Full Potential Algorithm for Solving Aerodynamic Problems

A numerical scheme utilizing a chimera zonal grid approach for solving the three dimensional full potential equation is described. Special emphasis is placed on describing the spatial differencing algorithm around the chimera interface. Results from two spatial discretization variations are presented; one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The presentation is highlighted with a number of transonic wing flow field computations.

Holst, Terry L.↗
NASA NTRS1997

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

Barth, Timothy↗
NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.

Barth, Timothy J.↗
NASA NTRS2001

Large Eddy Simulation of a Near Sonic Turbulent Jet and Its Radiated Noise

In this paper numerical simulations are used to calculate the turbulence dynamics simultaneously with the sound field for a high-speed near-sonic (Ma=0.9) compressible jet at two Reynolds numbers of 3,600 and 72,000. LES (Large Eddy Simulation) in conjunction with accurate numerical schemes is used to calculate the unsteady flow and sound in the near field of the jet. It is shown that the jet mean parameters, mean velocity fields and turbulence statistics are in good agreement with experimental data and results from other simulations. The sound in the near-field is calculated directly from the simulations. The calculations are shown to capture the peak in the dilatation and pressure spectra around a Strouhal number St=0.25-0.3, in agreement with typical jet-noise spectra measured in experiments. Dilatation contours in the near-field show the formation of acoustic waves with a dominant wavelength of 3.2-4 jet diameters, corresponding to the peak in the dilatation spectra. As expected, the non-compact noise sources are found to be most dominant in the region corresponding to the end of the potential core. The contribution of the LES model to the radiated noise appears to be weak and does not contaminate the sound field with spurious high-frequency noise. However, the frequency spectra of the sound show a rapid falloff away from the peak frequency. This is attributed to the quasi-laminar state of the shear-layers in the region prior to potential core closure, and a possible effect of insufficient azimuthal resolution at the observed location. Further analysis of the effect of the LES model, especially at high frequencies, is needed.

Constantinescu, G. S.↗