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At least 127 records · Page 7

The numerical dynamic for highly nonlinear partial differential equations

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Lafon, A.↗

Thermal emission of nonspherical particles

The thermal emission of nonspherical particles is studied by applying the fluctuation dissipation theorem to calculate the Stokes' vector source terms in radiative transfer theory. Generally, all the four Stokes' parameters in the source term are nonzero and are proportional to the absorption coefficient in the backward direction. The measurements of active and passive remote sensing are related by showing that within the framework of radiative transfer theory, the emissivity of vertically and horizontally polarized waves can be expressed in terms of the bistatic scattering coefficients in the usual manner. In addition, the emissions of the third and fourth Stokes' parameters are also expressed in terms of bistatic scattering coefficients.

Tsang, L.↗

The electron distribution function upstream from the earth's bow shock

A general analytic theory for the distribution function of particles backstreaming from an arbitrary shock in a magnetized plasma is presented. Particle motions are shown to be restricted to two-dimensional planes. A general form for the source term describing upstreaming particles accelerated at the shock is presented along with explicit source terms for planar and parabolic shocks. The origin and form of the escape velocity cutoff for a shock in a magnetized plasma are discussed. The distribution function upstream of a finite planar shock and a parabolic shock in two dimensions is calculated, and an analytic approximation of the cutoff velocity at points in the upstream region is derived. The theory is then applied to the earth's bow shock, calculating distribution functions and the nature and spatial variation of the cutoff velocity. The theory for the particle distribution upstream of the bow shock is compared with the model of Filbert and Kellogg (1979).

Cairns, Iver H.↗

Grid generation for general 2-D regions using hyperbolic equations

A method for applying a hyperbolic grid generation scheme to the construction of meshes in general 2-D regions has been developed. This approach, which follows the theory developed by Steger and Chaussee (1980) and the algorithm outlined by Kinsey and Barth (1984), is based on improving local grid control. This is accomplished by adding an angle control source term to the equations and using a new algorithm for computing the volume source term. These modifications lead to superior methods for fixing the 'local' problems of hyperbolic grid generation, namely, propagation of initial discontinuities and formation of grid shocks (crossing grid lines). More importantly, a method for solving the global problem of constraining the grid with more than one boundary (internal grid generation) has been developed. These algorithms have been implemented in an interactive grid generation program and the results for several geometries are presented and discussed.

Cordova, Jeffrey Q.↗

The sound of moving bodies

The importance of the quadrupole source term in the Ffowcs, Williams, and Hawkings (FWH) equation was addressed. The quadrupole source contains fundamental components of the complete fluid mechanics problem, which are ignored only at the risk of error. The results made it clear that any application of the acoustic analogy should begin with all of the source terms in the FWH theory. The direct calculation of the acoustic field as part of the complete unsteady fluid mechanics problem using CFD is considered. It was shown that aeroelastic calculation can indeed be made with CFD codes. The results indicate that the acoustic field is the most susceptible component of the computation to numerical error. Therefore, the ability to measure the damping of acoustic waves is absolutely essential both to develop acoustic computations. Essential groundwork for a new approach to the problem of sound generation by moving bodies is presented. This new computational acoustic approach holds the promise of solving many problems hitherto pushed aside.

Brentner, Kenneth Steven↗

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

Bryson, Steve↗

Accelerating the computation of steady state solutions for non-equilibrium, chemically reacting flow fields

The objective of the study is to develop a technique for accelerating the computation of steady state solutions for nonequilibrium chemically reacting flow fields using the time marching method. To achieve this, a better initial condition is introduced for the time marching scheme to achieve a faster convergence to the steady state solution. This is done by replacing the source terms of the original system of equations, which are responsible for the sitffness, by approximate source terms. It is shown that the saving in computation time increases in direct proportion to the stiffness of the flow model, with a factor of 10 increase in convergence rate observed for the models tested in this study.

Krispin, Jacob↗

Application of a Momentum Source Model to the RAH-66 Comanche FANTAIL

A Momentum Source Model has been revised and implemented in the flow solver OVERFLOW-D. In this approach, the fan forces are evaluated from two-dimensional airfoil tables as a function of local Mach number and angle-of-attack and applied as source terms in the discretized Navier-Stokes equations. The model revisions include a new model for forces in the tip region and axial distribution of the source terms. The model revisions improve the results significantly. The Momentum Source Model agrees well with a discrete blade model for all computed collective pitch angles. The two models agree well with experimental data for thrust vs. torque. The Momentum Source Model is a good complement to Discrete Blade Models for ducted fan computations. The lower computational and labor costs make parametric studies, optimization studies and interactional aerodynamics studies feasible for cases beyond what is practical with a Discrete Blade Model today.

Nygaard, Tor A.↗

Guiding Principles for Geochemical/Thermodynamic Model Development and Validation in Nuclear Waste Disposal: A Close Examination of Recent Thermodynamic Models for H + —Nd 3+ —NO 3 - (—Oxalate) Systems

Development of a defensible source-term model (STM), usually a thermodynamical model for radionuclide solubility calculations, is critical to a performance assessment (PA) of a geologic repository for nuclear waste disposal. Such a model is generally subjected to rigorous regulatory scrutiny. In this article, we highlight key guiding principles for STM model development and validation in nuclear waste management. We illustrate these principles by closely examining three recently developed thermodynamic models with the Pitzer formulism for aqueous H + —Nd 3+ —NO 3 - (—oxalate) systems in a reverse alphabetical order of the authors: the XW model developed by Xiong and Wang, the OWC model developed by Oakes et al., and the GLC model developed by Guignot et al., among which the XW model deals with trace activity coefficients for Nd(III), while the OWC and GLC models are for concentrated Nd(NO 3 ) 3 electrolyte solutions. The principles highlighted include the following: (1) Principle 1. Validation against independent experimental data: A model should be validated against experimental data or field observations that have not been used in the original model parameterization. We tested the XW model against multiple independent experimental data sets including electromotive force (EMF), solubility, water vapor, and water activity measurements. The results show that the XW model is accurate and valid for its intended use for predicting trace activity coefficients and therefore Nd solubility in repository environments. (2) Principle 2. Testing for relevant and sensitive variables: Solution pH is such a variable for an STM and easily acquirable. All three models are checked for their ability to predict pH conditions in Nd(NO 3 ) 3 electrolyte solutions. The OWC model fails to provide a reasonable estimate for solution pH conditions, thus casting serious doubt on its validity for a source-term calculation. In contrast, both the XW and GLC models predict close-to-neutral pH values, in agreement with experimental measurements. (3) Principle 3. Honoring physical constraints: Upon close examination, it is found that the Nd(III)-NO 3 association schema in the OWC model suffers from two shortcomings. Firstly, its second stepwise stability constant for Nd(NO 3 ) 2+ (log K 2 ) is much higher than the first stepwise stability constant for NdNO 3 2+ (log K 1 ), thus violating the general rule of (log K 2 –log K 1 ) < 0, or $\frac{K1}{K2}$>1. Secondly, the OWC model predicts abnormally high activity coefficients for Nd(NO 3 ) 2 + (up to ~900) as the concentration increases. (4) Principle 4. Minimizing degrees of freedom for model fitting: The OWC model with nine fitted parameters is compared with the GLC model with five fitted parameters, as both models apply to the concentrated region for Nd(NO 3 ) 3 electrolyte solutions. The latter appears superior to the former because the latter can fit osmotic coefficient data equally well with fewer model parameters. The work presented here thus illustrates the salient points of geochemical model development, selection, and validation in nuclear waste management.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Numerical study of supersonic combustion using a finite rate chemistry model

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

Chitsomboon, T.↗

Numerical solutions of the complete Navier-Stokes equations

The objective of this study is to compare the use of assumed pdf (probability density function) approaches for modeling supersonic turbulent reacting flowfields with the more elaborate approach where the pdf evolution equation is solved. Assumed pdf approaches for averaging the chemical source terms require modest increases in CPU time typically of the order of 20 percent above treating the source terms as 'laminar.' However, it is difficult to assume a form for these pdf's a priori that correctly mimics the behavior of the actual pdf governing the flow. Solving the evolution equation for the pdf is a theoretically sound approach, but because of the large dimensionality of this function, its solution requires a Monte Carlo method which is computationally expensive and slow to coverage. Preliminary results show both pdf approaches to yield similar solutions for the mean flow variables.

Hassan, H. A.↗

Numerical Methods For Chemically Reacting Flows

Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.

Leveque, R. J.↗

Part 2 of a Computational Study of a Drop-Laden Mixing Layer

This second of three reports on a computational study of a mixing layer laden with evaporating liquid drops presents the evaluation of Large Eddy Simulation (LES) models. The LES models were evaluated on an existing database that had been generated using Direct Numerical Simulation (DNS). The DNS method and the database are described in the first report of this series, Part 1 of a Computational Study of a Drop-Laden Mixing Layer (NPO-30719), NASA Tech Briefs, Vol. 28, No.7 (July 2004), page 59. The LES equations, which are derived by applying a spatial filter to the DNS set, govern the evolution of the larger scales of the flow and can therefore be solved on a coarser grid. Consistent with the reduction in grid points, the DNS drops would be represented by fewer drops, called computational drops in the LES context. The LES equations contain terms that cannot be directly computed on the coarser grid and that must instead be modeled. Two types of models are necessary: (1) those for the filtered source terms representing the effects of drops on the filtered flow field and (2) those for the sub-grid scale (SGS) fluxes arising from filtering the convective terms in the DNS equations. All of the filtered-sourceterm models that were developed were found to overestimate the filtered source terms. For modeling the SGS fluxes, constant-coefficient Smagorinsky, gradient, and scale-similarity models were assessed and calibrated on the DNS database. The Smagorinsky model correlated poorly with the SGS fluxes, whereas the gradient and scale-similarity models were well correlated with the SGS quantities that they represented.

Okongo, Nora↗

Characterization of Gas Bremsstrahlung sources at the Electron-Ion Collider

This report estimates the potential impact of Gas Bremsstrahlung, generated as the electron beam traverses the straight sections of the storage ring and impinges onto selected locations of the Electron-Ion Collider. The source terms were calculated for routine operation scenarios at three different energies: 5, 10 and 18 GeV, using the FLUKA Monte Carlo particle transport and interaction code. The source term’s power distributions were validated and compared with the Gas Bremsstrahlung produced in the long straight sections of the National Synchrotron Light Source II storage ring.

43 PARTICLE ACCELERATORS↗

Treating convection in sequential solvers

The treatment of the convection terms in the sequential solver, a standard procedure found in virtually all pressure based algorithms, to compute the flow problems with sharp gradients and source terms is investigated. Both scalar model problems and one-dimensional gas dynamics equations have been used to study the various issues involved. Different approaches including the use of nonlinear filtering techniques and adoption of TVD type schemes have been investigated. Special treatments of the source terms such as pressure gradients and heat release have also been devised, yielding insight and improved accuracy of the numerical procedure adopted.

Shyy, Wei↗

Upwind Swirl Coupling In Navier-Stokes Calculations

Convergence in axisymmetric flows speeded. Improved treatment devised for swirl-coupling source terms in finite-difference Navier-Stokes calculations of axisymmetric flow. Essence of improvement to treat radial- and swirl-velocity source terms in implicit manner wherever possible. Results in faster convergence and in convergence in some cases in which explicit treatment does not yield convergence at all.

Williams, Morgan↗

High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves

In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows.

Wang, W.↗

Three-dimensional grids as solutions of elliptic systems

An elliptic grid generation scheme is described which produces a curvilinear, boundary-fitted grid for highly swept wings with sharp leading edges. The three-dimensional integration domain is segmented in successive crossflow sections wherein the physical coordinates are transformed to computational coordinates by solving an elliptic set of two quasi-linear differential equations. Grid points are clustered in the vicinity of the wing surface, especially in the neighborhood of the leading edges. The formulation of the source terms in the equations governing the transformation contains adjustable parameters which are determined from limiting forms of the elliptic equations along the boundaries. The source terms are assigned to each grid point by interpolation of these parameters into the interior domain. The formulation does not depend on the boundary shape or on the distribution of the grid points along the boundaries. For the first time, the discretized governing equations have been solved using a fast AF1 iteration scheme.

Hartwich, P.-M.↗