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NASA NTRS1996

Numerical Modeling of Spray Combustion with an Unstructured-Grid Method

The present unstructured-grid method follows strictly the basic finite volume forms of the conservation laws of the governing equations for the entire flow domain. High-order spatially accurate formulation has been employed for the numerical solutions of the Navier-Stokes equations. A two-equation k-epsilon turbulence model is also incorporated in the unstructured-grid solver. The convergence of the resulted linear algebraic equation is accelerated with preconditioned Conjugate Gradient method. A statistical spray combustion model has been incorporated into the present unstructured-grid solver. In this model, spray is represented by discrete particles, rather than by continuous distributions. A finite number of computational particles are used to predict a sample of total population of particles. Particle trajectories are integrated using their momentum and motion equations and particles exchange mass, momentum and energy with the gas within the computational cell in which they are located. The interaction calculations are performed simultaneously and eliminate global iteration for the two-phase momentum exchange. A transient spray flame in a high pressure combustion chamber is predicted and then the solution of liquid-fuel combusting flow with a rotating cup atomizer is presented and compared with the experimental data. The major conclusion of this investigation is that the unstructured-grid method can be employed to study very complicated flow fields of turbulent spray combustion. Grid adaptation can be easily achieved in any flow domain such as droplet evaporation and combustion zone. Future applications of the present model can be found in the full three-dimensional study of flow fields of gas turbine and liquid propulsion engine combustion chambers with multi-injectors.

Shang, H. M.↗

NASA NTRS1977

Mathematical modelling of a human external respiratory system

A closed system of algebraic and common differential equations solved by computer is investigated. It includes equations which describe the activity pattern of the respiratory center, the phrenic nerve, the thrust produced by the diaphragm as a function of the lung volume and discharge frequency of the phrenic nerve, as well as certain relations of the lung stretch receptors and chemoreceptors on various lung and blood characteristics, equations for lung biomechanics, pulmonary blood flow, alveolar gas exchange and capillary blood composition equations to determine various air and blood flow and gas exchange parameters, and various gas mixing and arterial and venous blood composition equations, to determine other blood, air and gas mixing characteristics. Data are presented by means of graphs and tables, and some advantages of this model over others are demonstrated by test results.

Source record↗

NASA NTRS1997

State-Space System Realization with Input- and Output-Data Correlation

This paper introduces a general version of the information matrix consisting of the autocorrelation and cross-correlation matrices of the shifted input and output data. Based on the concept of data correlation, a new system realization algorithm is developed to create a model directly from input and output data. The algorithm starts by computing a special type of correlation matrix derived from the information matrix. The special correlation matrix provides information on the system-observability matrix and the state-vector correlation. A system model is then developed from the observability matrix in conjunction with other algebraic manipulations. This approach leads to several different algorithms for computing system matrices for use in representing the system model. The relationship of the new algorithms with other realization algorithms in the time and frequency domains is established with matrix factorization of the information matrix. Several examples are given to illustrate the validity and usefulness of these new algorithms.

Juang, Jer-Nan↗

NASA NTRS1980

A Navier-Stokes fast solver for turbulence modeling applications

A computer code for the evaluation and/or optimization of the predicative potential of second order turbulent closure models in simple two dimensional flow configurations is discussed. A procedure for the numerical solution of the steady constant property Navier-Stokes equations are described together with algebraic, one dimensional and two dimensional equations of turbulence closure models. Four turbulence models are compared with several sets of experimental data. The effects of initial conditions and boundary conditions are also described. The effects of purely numerical parameters, such as mesh size, boundary locations, and convergence criteria are presented.

Murphy, J. D.↗

NASA NTRS1965

Phase 1, simulation of selected discrete networks. Volume one - The logic model Final report

Methodology and Boolean equations for constructing discrete network system model

DISCRETE FUNCTION↗

NASA NTRS1972

On the algebraic structure of bilinear systems.

It is shown that a particular bilinear model is both quite general and easy to work with. A basic structure theory is developed with the aid of previous results. Some preliminary ideas are discussed together with the system interconnection, the canonical form, questions of controllability, aspects of observability, and equivalent realizations. It is pointed out that in actually determining equivalent realizations for systems and in the classification of systems, the results available in the study of Lie algebras are of fundamental importance.

Brockett, R. W.↗

NASA NTRS1982

Comparison Between Experiment and Prediction for a Transonic Turbulent Separated Flow

Solutions of the time-dependent, mass-averaged Navier-Stokes equations are compared In detail with experimental results obtained on an axisymmetric "bump" model at a transonic Mach number that produced an extensive separated now region. In addition, an inverse boundary method is evaluated for this type of flow. The Cebeci-Smith algebraic and the Wilcox-Rubesin two-equation turbulence models used in the Navier-Stokes calculations both predict the maximum boundary-layer displacement thickness generated by the interaction reasonably well, with the details of the now best described with the two-equation formulation. However, both models predict a shock location substantially farther aft on the bump than observed experimentally. This error in shock location was slightly less with the two-equation model (0.12 chord compared with 0.16 chord). In the vicinity of the shock, the calculations predict a more rapid increase in turbulent shear stress than observed in the experimental results; this more rapid increase is believed to be the cause or the poor predictions in shock position.

Johnson, D. A.↗

NASA NTRSDate not supplied

Advances in Modeling Solar System Internet Structures and their Data Flows

With an ever-increasing presence in space, there is also an increasing burden on existing communications infrastructure. We are heading towards an inflection point where the traditional approach of scheduled, single-path communications for space will no longer be viable. One answer is Delay Tolerant Networking (DTN), which takes the once disparate system of point-to-point links and unifies them in a networked architecture, thereby making communications more scalable. However, much work remains for discovering and harnessing the underlying theory of DTN. For example, in the terrestrial setting the interplay between routing domains is well-understood, however this is not the case in DTNs. In this paper, we build up the fundamental foundations of DTN, with an emphasis on modeling time varying networks and data flows across them, with examples of cross-domain routing in a DTN. A lofty goal of DTN is to enable the so-called Solar System Internet (SSI), which implies a standardized and robust suite of protocols. These protocols include routing across disconnected networks using store, carry, and forward mechanisms, which is necessary due to the disconnections, delays, and mobility intrinsic to space networks. Due to these factors, each of which generalize traditional networking, there is a deep and rich theory of DTNs. Here we build off of past successes to broaden this theory while striving to keep actionable results a goal for future implementations and operations. The approach includes modeling the unicast, broadcast, and multicast communications using the language of hypergraphs, which capture the geometric properties of such networked communications algebraically. Also inherent to these networks is their time-varying nature, particularly given mobility, and hence we also cultivate modeling techniques that respect this time dependence. This leads us to develop models using tools from category theory and algebraic geometry, which provide a language well-suited to describing synchronization and optimization over such networks. We also introduce and study a novel generalization of curvature applicable to time-evolving networks, which provides quantitative controls on diffusion processes on the network. Because an interplanetary network would feature links with propagation delays the preclude discovery (feedback) mechanisms, they will always feature a scheduled component. However, it is beneficial to support discovery where possible. While DTNs do not yet have strong definitions for their analogues of autonomous systems or network areas, we show how to join dynamic and schedule-based routing domains, using the language of sheaves, which marks progress towards such definitions. We conclude with a discussion of the progress made, as well as suggestions for future work.

Delay Tolerant Networking↗

NASA NTRS1991

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Stoll, Frederick↗

NASA NTRS1993

Spatial operator algebra for flexible multibody dynamics

This paper presents an approach to modeling the dynamics of flexible multibody systems such as flexible spacecraft and limber space robotic systems. A large number of degrees of freedom and complex dynamic interactions are typical in these systems. This paper uses spatial operators to develop efficient recursive algorithms for the dynamics of these systems. This approach very efficiently manages complexity by means of a hierarchy of mathematical operations.

Jain, A.↗

NASA NTRS1996

A Computational Fluid Dynamic and Heat Transfer Model for Gaseous Core and Gas Cooled Space Power and Propulsion Reactors

A computational model based on the axisymmetric, thin-layer Navier-Stokes equations is developed to predict the convective, radiation and conductive heat transfer in high temperature space nuclear reactors. An implicit-explicit, finite volume, MacCormack method in conjunction with the Gauss-Seidel line iteration procedure is utilized to solve the thermal and fluid governing equations. Simulation of coolant and propellant flows in these reactors involves the subsonic and supersonic flows of hydrogen, helium and uranium tetrafluoride under variable boundary conditions. An enthalpy-rebalancing scheme is developed and implemented to enhance and accelerate the rate of convergence when a wall heat flux boundary condition is used. The model also incorporated the Baldwin and Lomax two-layer algebraic turbulence scheme for the calculation of the turbulent kinetic energy and eddy diffusivity of energy. The Rosseland diffusion approximation is used to simulate the radiative energy transfer in the optically thick environment of gas core reactors. The computational model is benchmarked with experimental data on flow separation angle and drag force acting on a suspended sphere in a cylindrical tube. The heat transfer is validated by comparing the computed results with the standard heat transfer correlations predictions. The model is used to simulate flow and heat transfer under a variety of design conditions. The effect of internal heat generation on the heat transfer in the gas core reactors is examined for a variety of power densities, 100 W/cc, 500 W/cc and 1000 W/cc. The maximum temperature, corresponding with the heat generation rates, are 2150 K, 2750 K and 3550 K, respectively. This analysis shows that the maximum temperature is strongly dependent on the value of heat generation rate. It also indicates that a heat generation rate higher than 1000 W/cc is necessary to maintain the gas temperature at about 3500 K, which is typical design temperature required to achieve high efficiency in the gas core reactors. The model is also used to predict the convective and radiation heat fluxes for the gas core reactors. The maximum value of heat flux occurs at the exit of the reactor core. Radiation heat flux increases with higher wall temperature. This behavior is due to the fact that the radiative heat flux is strongly dependent on wall temperature. This study also found that at temperature close to 3500 K the radiative heat flux is comparable with the convective heat flux in a uranium fluoride failed gas core reactor.

Anghaie, S.↗

NASA NTRS1966

Theory of thermal similitude with applications to spacecraft - A survey.

Mathematical theory of dimensional analysis and similitude, application to spacecraft thermal design and experimental results

MATRIX ALGEBRA↗

NASA NTRS1973

Development of guidelines for the definition of the relavant information content in data classes

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

Schmitt, E.↗

NASA NTRS1975

An experimental and numerical investigation of shock-wave induced turbulent boundary-layer separation at hypersonic speeds

An experiment designed to test and guide computations of the interaction of an impinging shock wave with a turbulent boundary layer is described. Detailed mean flow-field and surface data are presented for two shock strengths which resulted in attached and separated flows, respectively. Numerical computations, employing the complete time-averaged Navier-Stokes equations along with algebraic eddy-viscosity and turbulent Prandtl number models to describe shear stress and heat flux, are used to illustrate the dependence of the computations on the particulars of the turbulence models. Models appropriate for zero-pressure-gradient flows predicted the overall features of the flow fields, but were deficient in predicting many of the details of the interaction regions. Improvements to the turbulence model parameters were sought through a combination of detailed data analysis and computer simulations which tested the sensitivity of the solutions to model parameter changes. Computer simulations using these improvements are presented and discussed.

Marvin, J. G.↗

NASA NTRS1979

Comparative study of solar optics for paraboloidal concentrators

Different analytical methods for computing the flux distribution on the focal plane of a paraboloidal solar concentrator are reviewed. An analytical solution in algebraic form is also derived for an idealized model. The effects resulting from using different assumptions in the definition of optical parameters used in these methodologies are compared and discussed in detail. These parameters include solar irradiance distribution (limb darkening and circumsolar), reflector surface specular spreading, surface slope error, and concentrator pointing inaccuracy. The type of computational method selected for use depends on the maturity of the design and the data available at the time the analysis is made.

Wen, L.↗

NASA NTRS1982

Input/output models for general aviation piston-prop aircraft fuel economy

A fuel efficient cruise performance model for general aviation piston engine airplane was tested. The following equations were made: (1) for the standard atmosphere; (2) airframe-propeller-atmosphere cruise performance; and (3) naturally aspirated engine cruise performance. Adjustments are made to the compact cruise performance model as follows: corrected quantities, corrected performance plots, algebraic equations, maximize R with or without constraints, and appears suitable for airborne microprocessor implementation. The following hardwares are recommended: ignition timing regulator, fuel-air mass ration controller, microprocessor, sensors and displays.

Sweet, L. M.↗

NASA NTRS1990

Frequency analysis via the method of moment functionals

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Pearson, A. E.↗

NASA NTRS1991

Frequency analysis via the method of moment functionals

Pearson, A. E.↗