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At least 433 records · Page 24

Impact of turbulence modeling on numerical accuracy and efficiency of compressible flow simulations

Discussed is the numerical implementation of turbulence models used in viscous compressible flow simulations and their performance described with respect to numerical accuracy, efficiency and stability. The basic approach utilizes the Reynolds-averaged compressible Navier-Stokes equations in which the Reynolds stresses and heat fluxes are mathematically modeled by suitable turbulence models. The turbulence models investigated include zero-, one-, and two-equation eddy viscosity models. The flow fields investigated include theoretical and supersonic flows about two-dimensional and axisymmetric bodies. Discussions concerning the numerical implementation of models include differencing procedures and boundary conditions used to assume numerical stability and accuracy. Numerical performance is also evaluated by comparing computations with experimental results.

Coakley, Thomas J.↗

Response of linear dynamic systems with random coefficients

Numerous models of physical systems contain parameters whose values are not known exactly. The physical and mathematical complexities arising in the prediction of the statistical behavior of such systems are discussed. Although the discussions are far from providing a satisfactory solution to such problems, they perhaps, by utilization of simple examples, will create a greater awareness of the statistical effect of random parameters.

Dickerson, J.↗

Combustion of hydrogen injected into a supersonic airstream (the SHIP computer program)

The mathematical and physical basis of the SHIP computer program which embodies a finite-difference, implicit numerical procedure for the computation of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction is described. The physical hypotheses built into the program include: a two-equation turbulence model, and a chemical equilibrium model for the hydrogen-oxygen reaction. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. The computer time required for a given case is approximately 1 minute on a CDC 7600 machine. A discussion of the assumption of parabolic flow in the injection region is given which suggests that improvement in calculation in this region could be obtained by use of the partially parabolic procedure of Pratap and Spalding. It is concluded that the technique described herein provides the basis for an efficient and reliable means for predicting the effects of hydrogen injection into supersonic airstreams and of its subsequent combustion.

Markatos, N. C.↗

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

Lee, S. S.↗

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

Przekwas, A. J.↗

CSM research: Methods and application studies

Computational mechanics is that discipline of applied science and engineering devoted to the study of physical phenomena by means of computational methods based on mathematical modeling and simulation, utilizing digital computers. The discipline combines theoretical and applied mechanics, approximation theory, numerical analysis, and computer science. Computational mechanics has had a major impact on engineering analysis and design. When applied to structural mechanics, the discipline is referred to herein as computational structural mechanics. Complex structures being considered by NASA for the 1990's include composite primary aircraft structures and the space station. These structures will be much more difficult to analyze than today's structures and necessitate a major upgrade in computerized structural analysis technology. NASA has initiated a research activity in structural analysis called Computational Structural Mechanics (CSM). The broad objective of the CSM activity is to develop advanced structural analysis technology that will exploit modern and emerging computers, such as those with vector and/or parallel processing capabilities. Here, the current research directions for the Methods and Application Studies Team of the Langley CSM activity are described.

Knight, Norman F., Jr.↗

Postbuckling analysis of shear deformable composite flat panels taking into account geometrical imperfections

The effects of initial geometrical imperfections on the postbuckling response of flat laminated composite panels to uniaxial and biaxial compressive loading are investigated analytically. The derivation of the mathematical model on the basis of first-order transverse shear deformation theory is outlined, and numerical results for perfect and imperfect, single-layer and three-layer square plates with free-free, clamped-clamped, or free-clamped edges are presented in graphs and briefly characterized. The present approach is shown to be more accurate than analyses based on the classical Kirchhoff plate model.

Librescu, L.↗

Introduction to the internal fluid mechanics research session

Internal fluid mechanics research at LeRC is directed toward an improved understanding of the important flow physics affecting aerospace propulsion systems, and applying this improved understanding to formulate accurate predictive codes. To this end, research is conducted involving detailed experimentation and analysis. The following three papers summarize ongoing work and indicate future emphasis in three major research thrusts: inlets, ducts, and nozzles; turbomachinery; and chemical reacting flows. The underlying goal of the research in each of these areas is to bring internal computational fluid mechanic to a state of practical application for aerospace propulsion systems. Achievement of this goal requires that carefully planned and executed experiments be conducted in order to develop and validate useful codes. It is critical that numerical code development work and experimental work be closely coupled. The insights gained are represented by mathematical models that form the basis for code development. The resultant codes are then tested by comparing them with appropriate experiments in order to ensure their validity and determine their applicable range. The ultimate user community must be a part of this process to assure relevancy of the work and to hasten its practical application. Propulsion systems are characterized by highly complex and dynamic internal flows. Many complex, 3-D flow phenomena may be present, including unsteadiness, shocks, and chemical reactions. By focusing on specific portions of a propulsion system, it is often possible to identify the dominant phenomena that must be understood and modeled for obtaining accurate predictive capability. The three major research thrusts serve as a focus leading to greater understanding of the relevant physics and to an improvement in analytic tools. This in turn will hasten continued advancements in propulsion system performance and capability.

Miller, Brent A.↗

An optimal GPS data processing technique for precise positioning

A mathematical formula to optimally combine dual-frequency GPS pseudorange and carrier phase (integrated Doppler) data streams into a single data stream is derived in closed form. The data combination reduces the data volume and computing time in the filtering process for parameter estimation by a factor of 4 while preserving the full data strength for precise positioning. The resulting single data stream is that of carrier phase measurements with both data noise and bias uncertainty strictly defined. With this mathematical formula the single stream of optimally combined GPS measurements can be efficiently formed by simple numerical calculations. Carrier phase ambiguity resolution, when feasible, is strengthened due to the preserved full data strength with the optimally combined data and the resulting longer wavelength for the ambiguity to be resolved.

Wu, Sien-Chong↗

Prediction of Fatigue Crack Growth Using Regularized Numerical Models

Though it is known in the engineering community that successful analyses rest upon the proper balance of (1) theoretical analysis of mathematical models, (2) physical experimentation and (3) computational simulation, this balance is currently handled in sometimes unwieldy and inefficient manner. It is proposed to investigate and develop rigorous and computationally efficient method to effectively combine all available information, from both experimental measurements and mathematical models, in the emulation of physical systems. This will be specifically applied to fatigue crack growth in metallic structures of interest to NASA.

Meade, Andrew J.↗

Numerical Calculation of the Drag Force Acting on an Insoluble Particle Moving in Front of a Solidifying Interface

The distribution of insoluble particles in a metal casting depends primarily on the interaction of the particles with the solid/liquid interface (SLI) during the solidification process. Whether a particle will be engulfed or continuously pushed by SLI is essentially determined by the balance of forces acting on the particle. An important component of this force balance is the drag force generated by the particle motion in front of the SLI. Previously developed mathematical models for particle/SLI interaction made use of steady-state solutions of this force provided by the lubrication theory. However, our numerical model based on the SLI tracking approach shows that not only the steady-state approach is inappropriate to model the interaction process but also that even at steady-state the theoretical solution underestimates the drag force. A regression analysis of steady-state numerical solutions for cylindrical particles moving normal to a flat SLI gave a relationship of the form F(sub d) (exp num) = (square root of 3) pi eta V(sub p)((R(sub p) / d) (exp 10 gamma/3)) as compared to the theoretical solution F(sub d) (exp theor) = 3 X (square root of 2) pi eta V(sub p)((R(sub p) / d) (exp 3/2)) where F(sub d) is the drag force, eta is the dynamic viscosity of the fluid, V(sub p) is the particle velocity, R(sub p) is the particle radius, gamma is Euler's constant (gamma is approximately equal to 0.577), and d is the width of the gap between the particle and the SLI. Model validation as well as the influence of the interface shape on the value of F(sub d) will also be discussed.

Catalina, Adrian V.↗

SINDA - Systems Improved Numerical Differencing Analyzer

Capability to model fluid flow added. SINDA is software system developed to solve physical problems governed by diffusion-type equations mathematically modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations. Adapted to wide range of problems represented by Fourier, Possion, Laplace, or other differential equations. Written in FORTRAN and Assembler.

Damico, Steve J.↗

Coupling of Transport and Chemical Processes in Catalytic Combustion

Catalytic combustors have demonstrated the ability to operate efficiently over a much wider range of fuel air ratios than are imposed by the flammability limits of conventional combustors. Extensive commercial use however needs the following: (1) the design of a catalyst with low ignition temperature and high temperature stability, (2) reducing fatigue due to thermal stresses during transient operation, and (3) the development of mathematical models that can be used as design optimization tools to isolate promising operating ranges for the numerous operating parameters. The current program of research involves the development of a two dimensional transient catalytic combustion model and the development of a new catalyst with low temperature light-off and high temperature stablity characteristics.

Bracco, F. V.↗

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Thompson, J. F.↗

The mathematical modeling of rapid solidification processing

The detailed formulation of and the results obtained from a continuum mechanics-based mathematical model of the planar flow melt spinning (PFMS) rapid solidification system are presented and discussed. The numerical algorithm proposed is capable of computing the cooling and freezing rates as well as the fluid flow and capillary phenomena which take place inside the molten puddle formed in the PFMS process. The FORTRAN listings of some of the most useful computer programs and a collection of appendices describing the basic equations used for the modeling are included.

Gutierrez-Miravete, E.↗