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NASA NTRS1975

Shock-wave-induced turbulent boundary-layer separation at hypersonic speeds

An experiment is described that tests and guides computations of the interaction of a shock wave with a turbulent boundary layer. Numerical solutions of the time-averaged Navier-Stokes equations for the entire flow field employing algebraic eddy viscosity and turbulent Prandtl number models for shear stress and heat flux are presented and used to illustrate the dependence of the computations on the particulars of the turbulence models. To guide modifications in the models, the mean flow profiles and surface measurements of pressure, shear, and heat flux are analyzed critically. The results show that the models of eddy viscosity require substantial modifications in the interaction region. Improved solutions employing the experimentally modified models are presented.

Horstman, C. C.↗

NASA NTRS1978

Numerical solution of two-dimensional turbulent blunt body flows with an impinging shock

An implicit finite-difference method has been developed to compute two-dimensional, turbulent, blunt body flows with an impinging shock wave. The full time-averaged Navier-Stokes equations are solved with algebraic eddy viscosity and turbulent Prandtl number models employed for shear stress and heat flux. The irregular-shaped bow shock is treated as a discontinuity across which the Rankine-Hugoniot equations are applied. A Type III turbulent shock interference flow field has been computed and the numerical results compare favorably with existing experimental data. In addition, comparisons are made between the present implicit code and a previous explicit code.

Tannehill, J. C.↗

NASA NTRS1981

Numerical analysis of the scramjet-inlet flow field by using two-dimensional Navier-Stokes equations

A computer code was developed to solve the full two dimensional Navier-Stokes equations in a supersonic combustion ramjet (scramjet) inlet. In order to be able to consider a general inlet geometry with embedded bodies, a numerical coordinate transformation is used which generates a set of boundary-fitted curvilinear coordinates. The explicit finite difference algorithm of MacCormack is used to solve the governing equations. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow. The code can analyze both inviscid and viscous flows with no strut, one strut, or multiple struts in the flow field. The application of the two dimensional analysis in the preliminary parametric design studies of a scramjet inlet is discussed. Detailed results are presented for one model problem and for several actual scramjet-inlet configurations.

Kumar, A.↗

NASA NTRS1980

A tensor approach to modeling of nonhomogeneous nonlinear systems

Model following control methodology plays a key role in numerous application areas. Cases in point include flight control systems and gas turbine engine control systems. Typical uses of such a design strategy involve the determination of nonlinear models which generate requested control and response trajectories for various commands. Linear multivariable techniques provide trim about these motions; and protection logic is added to secure the hardware from excursions beyond the specification range. This paper reports upon experience in developing a general class of such nonlinear models based upon the idea of the algebraic tensor product.

Yurkovich, S.↗

NASA NTRS1982

Control pole placement relationships

Using a simplified Large Space Structure (LSS) model, a technique was developed which gives algebraic relationships for the unconstrained poles. The relationships, which were obtained by this technique, are functions of the structural characteristics and the control gains. Extremely interesting relationships evolve for the case when the structural damping is zero. If the damping is zero, the constrained poles are uncoupled from the structural mode shapes. These relationships, which are derived for structural damping and without structural damping, provide new insight into the migration of the unconstrained poles for the CFPPS.

Ainsworth, O. R.↗

NASA NTRS1983

Some aspects of mathematical and chemical modeling of complex chemical processes

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

Nemes, I.↗

NASA NTRS1986

Analysis of Scramjet Inlets

NASCRIN analyzes two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. Solves two-dimensional Euler or Navier-Strokes equations in conservative form by unsplit, explicit, two-step finitedifference method. More recent explicit/implicit, two-step scheme also incorporated for viscous flow analysis. Algebraic, two-layer eddy-viscosity model used for turbulent flow calculations.

Kumar, A.↗

NASA NTRS1984

User's guide for NASCRIN: A vectorized code for calculating two-dimensional supersonic internal flow fields

A computer program NASCRIN has been developed for analyzing two-dimensional flow fields in high-speed inlets. It solves the two-dimensional Euler or Navier-Stokes equations in conservation form by an explicit, two-step finite-difference method. An explicit-implicit method can also be used at the user's discretion for viscous flow calculations. For turbulent flow, an algebraic, two-layer eddy-viscosity model is used. The code is operational on the CDC CYBER 203 computer system and is highly vectorized to take full advantage of the vector-processing capability of the system. It is highly user oriented and is structured in such a way that for most supersonic flow problems, the user has to make only a few changes. Although the code is primarily written for supersonic internal flow, it can be used with suitable changes in the boundary conditions for a variety of other problems.

Kumar, A.↗

NASA NTRS1987

Analysis of Scramjet Inlets

NASCRIN program analyzes two-dimensional flow fields in supersoniccombustion ramjet (scramjet) inlets. Solves two-dimensional Euler or Navier-Stokes equations in conservative form by unsplit, explicit, two-step finite-difference method. More recent explicit/implicit, two-step scheme incorporated by analysis of viscous flow. Algebraic, two-layer eddy-viscosity model used for turbulent-flow calculations. Vectorized version, written for CDC CYBER 205, whereas scalar version, can be run on CRAY or other scalar computers.

Kumar, A.↗

NASA NTRS1989

Numerical simulation of flow through a two-strut scramjet inlet

A three-dimensional, Reynolds-averaged Navier-Stokes code has been used to numerically analyze flow through a two-strut, supersonic combustion ramjet (scramjet) inlet configuration. It solves the governing equations in full conservation form using either a fully explicit or explicit-implicit method. An algebraic, two-layer eddy-viscosity model is used for turbulent flow calculations. The analysis allows inclusion of end effects that are caused by the aft placement of the cowl on the underside of the inlet. A special grid has been developed to accommodate the struts embedded in the inlet flowfield. Detailed numerical results are presented here for the two-strut configuration, and a comparison is made with the available experimental results.

Kumar, Ajay↗

NASA NTRS1992

A turbulence model for iced airfoils and its validation

A turbulence model based on the extension of the algebraic eddy viscosity formulation of Cebeci and Smith developed for two dimensional flows over smooth and rough surfaces is described for iced airfoils and validated for computed ice shapes obtained for a range of total temperatures varying from 28 to -15 F. The validation is made with an interactive boundary layer method which uses a panel method to compute the inviscid flow and an inverse finite difference boundary layer method to compute the viscous flow. The interaction between inviscid and viscous flows is established by the use of the Hilbert integral. The calculated drag coefficients compare well with recent experimental data taken at the NASA-Lewis Icing Research Tunnel (IRT) and show that, in general, the drag increase due to ice accretion can be predicted well and efficiently.

Shin, Jaiwon↗

NASA NTRS1992

A turbulence model for iced airfoils and its validation

A turbulence model based on the extension of the algebraic eddy viscosity formulation of Cebeci and Smith developed for two-dimensional flows over smooth and rough surfaces is described for iced airfoils and validated for computed ice shapes obtained for a range of total temperatures varying from 28 to -15 F. The validation is made with an interactive boundary layer method which uses a panel method to compute the inviscid flow and an inverse finite difference boundary layer method to compute the viscous flow. The interaction between inviscid and viscous flows is established by the use of the Hilbert integral. The calculated drag coefficients compare well with recent experimental data taken at the NASA-Lewis Icing Research Tunnel (IRT) and show that, in general, the drag increase due to ice accretion can be predicted well and efficiently.

Shin, Jaiwon↗

NASA NTRS1992

Lunar materials processing system integration

The theme of this paper is that governmental resources will not permit the simultaneous development of all viable lunar materials processing (LMP) candidates. Choices will inevitably be made, based on the results of system integration trade studies comparing candidates to each other for high-leverage applications. It is in the best long-term interest of the LMP community to lead the selection process itself, quickly and practically. The paper is in five parts. The first part explains what systems integration means and why the specialized field of LMP needs this activity now. The second part defines the integration context for LMP -- by outlining potential lunar base functions, their interrelationships and constraints. The third part establishes perspective for prioritizing the development of LMP methods, by estimating realistic scope, scale, and timing of lunar operations. The fourth part describes the use of one type of analytical tool for gaining understanding of system interactions: the input/output model. A simple example solved with linear algebra is used to illustrate. The fifth and closing part identifies specific steps needed to refine the current ability to study lunar base system integration. Research specialists have a crucial role to play now in providing the data upon which this refinement process must be based.

Sherwood, Brent↗

NASA NTRS1992

A Regression Method for Comparing Launch Zone Ranges Derived From Different Sources

In modern fighter aircraft air-to-air missile launch acceptable ranges (LARs) are provided to the pilot for his launch decision. These LARs are calculated in the avionic software, using very simple algebraic equations and algorithms, that attempt to model complex missile behavior. Frequently these algorithms are revised to reflect inaccuracies discovered, when comparisons are made with missile six degree-of-freedom (6-DOF) simulations. The process of modifying this software has become expensive. In the past, these simple LAR generators were modified based only on subjective judgmental approach, with little regard to the missile range design limits. With reduced budgets a more rational methodology should be taken to assess whether or not simple fighter LAR generators need to be modified. Any LAR generator can produce large amounts of range (minimum and maximum) data over the board engagement limits of modem fighter and air-to-air missiles. This infinite population lends itself to some statistical methodology to access simple LAR accuracy and the need for software modification. The methodology should produce statistical parameters for use in the decision making process of modifying a simple fighter LAR generator. This paper presents a regression method, based on a missile range design limit philosophy. Acceptance criteria from the regression method are given that provide simple statistical parameters to aid in this decision making process.

Flight Testing↗

NASA NTRS1993

Flight control application of new stability robustness bounds for linear uncertain systems

This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.

Yedavalli, Rama K.↗

NASA NTRS1995

Second International Workshop on Harmonic Oscillators

The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.

Han, Daesoo↗

NASA NTRS1991

An Object-oriented Query Processor that Produces Monotonically Improving Approximate Answers

The paper describes an object-oriented query processor that makes approximate answers available if there is not enough time to produce an exact answer or if part of the database is unavailable. The accuracy of the approximate result produces improves monotonically with the amount of data retrieved to produce the result. The query processing algorithm is based on an approximate relational data model and works within a standard relational algebra framework. The query processor maintains an object-oriented view on an underlying level and can be implemented on a relational database system with little change to the relational architecture. We show how a monotone query processing strategy can be implemented, making effective use of semantic information presented by the object-oriented view.

Vrbsky, S. V.↗

NASA NTRS1991

A second-order modeling study of confined swirling flow

A numerical study of a confined strong swirling flow is presented. Computations are performed using a differential second-moment closure. The effect of inlet dissipation rate on calculated mean and turbulence fields is investigated. Two pressure-strain models with various model constants are examined to demonstrate their influences on the predicted results. Finally, comparison of the differential second-moment calculation is made with algebraic second-moment results to determine a better suited model for complex swirling flows.

Nikjooy, M.↗