Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Normal form methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Theory of strong turbulence by renormalization

The hydrodynamical equations of turbulent motions are inhomogeneous and nonlinear in their inertia and force terms and will generate a hierarchy. A kinetic method was developed to transform the hydrodynamic equations into a master equation governing the velocity distribution, as a function of the time, the position and the velocity as an independent variable. The master equation presents the advantage of being homogeneous and having fewer nonlinear terms and is therefore simpler for the investigation of closure. After the closure by means of a cascade scaling procedure, the kinetic equation is derived and possesses a memory which represents the nonMarkovian character of turbulence. The kinetic equation is transformed back to the hydrodynamical form to yield an energy balance in the cascade form. Normal and anomalous transports are analyzed. The theory is described for incompressible, compressible and plasma turbulence. Applications of the method to problems relating to sound generation and the propagation of light in a nonfrozen turbulence are considered.

Tchen, C. M.↗
NASA NTRS1983

The Riemann disks. II - Stability

The Riemann disks are the two-dimensional analogs of the Riemann S-type ellipsoids. They form a simple yet rich family of galactic bar models. A method is developed to find their normal modes to arbitrary order, and the stability analysis is carried out for all modes with order not greater than 5.

Weinberg, M. D.↗
NASA NTRS1956

A reevaluaion of data on atmospheric turbulence and airplane gust loads for application in spectral calculations

The available information on the spectrum of atmospheric turbulence is first briefly reviewed. On the basis of these results, methods are developed for the conversion of available gust statistics normally given in terms of counts of gusts or acceleration peaks into a form appropriate for use in spectral calculations. The fundamental quantity for this purpose appears to be the probability distribution of the root-mean-square gust velocity. Estimates of this distribution are derived from data for a number of load histories of transport operations; also, estimates of the variation of this distribution with altitude and weather condition are derived from available data and the method of applying these results to the calculation of airplane gust-response histories in operations is also outlined. (author)

Press, Harry↗
NASA NTRS1991

An approximate viscous shock layer approach to calculating hypersonic flows about blunt-nosed bodies

An approximate axisymmetric method has been developed which can reliably calculate fully viscous hypersonic flows over blunt-nosed bodies. By substituting Maslen's second order pressure expression for the normal momentum equation, a simplified form of the viscous shock layer (VSL) equations is obtained. This approach can solve both the subsonic and supersonic regions of the shock layer without a starting solution for the shock shape. Since the method is fully viscous, the problems associated with coupling a boundary-layer solution with an inviscid-layer solution are avoided. This procedure is significantly faster than the parabolized Navier-Stokes (PNS) or VSL solvers and would be useful in a preliminary design environment. Problems associated with a previously developed approximate VSL technique are addressed. Surface heat transfer and pressure predictions are comparable to both VSL results and experimental data. The present technique generates its own shock shape as part of its solution, and therefore could be used to provide more accurate initial shock shapes for higher-order procedures which require starting solutions.

Cheatwood, F. MCN.↗
NASA NTRS1976

Fully unsteady subsonic and supersonic potential aerodynamics of complex aircraft configurations for flutter applications

The paper presents a general theory of steady, oscillatory or fully unsteady, subsonic and supersonic aerodynamics for aircraft of arbitrary shape. The finite element method is used to obtain the time functional relationship between aerodynamic potential and its normal derivative (normal wash) in a form suitable for computational analysis. The matrix of the aerodynamic influence coefficients, as necessary for flutter calculations, is obtained as a result. The theory is implemented in a computer program, and some typical results obtained with this program are presented.

Tseng, K.↗
NASA NTRS1992

The recovery of asteroids after two observations

It is shown that a generalization of the use of 'Vaisala orbits', briefly mentioned at the Asteroids 2 Conference, can be very conveniently accomplished by means of an inversion of the 'GEM' form of the Gauss method. The procedure can also be applied to Apollo objects and to indeterminate cases of normal three-observation orbit computation, and there is also a simple extension to situations involving four or more observations.

Marsden, Brian G.↗
NASA NTRS1992

Kinetic structure of slow shocks - Effects of the electromagnetic ion/ion cyclotron instability

The structure of slow magnetosonic shocks in the low beta regime is analyzed with attention given to ion heating and the effects of waves upstream of the electromagnetic ion/ion cyclotron (EMIIC) instability. Shock formation is assessed by means of three methods - a relaxation method and two based on dynamic flow interactions - to determine the effects of initialization and boundary conditions on the formation. Good solutions are found with the piston method and the similar flow-flow method in which the plasma is injected from two boundaries to form two slow shocks. Plasma parameters and shock normal angle are found to be the key variables dictating the structure of the magnetosonic shocks. Four unique classes of resultant shock structures are described in which classical, steady, or nonsteady behavior is found. The analysis also yields insight into the relationship between EMIIC instability and ion dissipation.

Omidi, N.↗
NASA NTRS1991

An approximate viscous shock layer technique for calculating chemically reacting hypersonic flows about blunt-nosed bodies

An approximate axisymmetric method was developed which can reliably calculate fully viscous hypersonic flows over blunt nosed bodies. By substituting Maslen's second order pressure expression for the normal momentum equation, a simplified form of the viscous shock layer (VSL) equations is obtained. This approach can solve both the subsonic and supersonic regions of the shock layer without a starting solution for the shock shape. The approach is applicable to perfect gas, equilibrium, and nonequilibrium flowfields. Since the method is fully viscous, the problems associated with a boundary layer solution with an inviscid layer solution are avoided. This procedure is significantly faster than the parabolized Navier-Stokes (PNS) or VSL solvers and would be useful in a preliminary design environment. Problems associated with a previously developed approximate VSL technique are addressed before extending the method to nonequilibrium calculations. Perfect gas (laminar and turbulent), equilibrium, and nonequilibrium solutions were generated for airflows over several analytic body shapes. Surface heat transfer, skin friction, and pressure predictions are comparable to VSL results. In addition, computed heating rates are in good agreement with experimental data. The present technique generates its own shock shape as part of its solution, and therefore could be used to provide more accurate initial shock shapes for higher order procedures which require starting solutions.

Cheatwood, F. Mcneil↗
NASA NTRS1973

A computer program for calculating the perfect gas inviscid flow field about blunt axisymmetric bodies at an angle of attack of 0 deg

A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.

Zoby, E. V.↗
NASA NTRS1979

Axisymmetric internal flows with shocks

Internal flow problems with supersonic entrance conditions and subsonic exit conditions are studied. The suitability of applying the transonic-small disturbance theory to internal flows is examined and found to be very limited. The full inviscid equations in nonconservative form are solved by relaxation. Jump conditions which conserve mass and normal momentum are applied explicitly at shock waves. This method is suitable for solving flows which include supersonic-subsonic shock waves nearly normal to the streamlines.

Rizk, M. H.↗
NASA NTRS1982

Diamond Sheet: A new diamond tool material

Diamond sheet is termed a diamond tool material because it is not a cutting tool, but rather a new material from which a variety of different tools may be fabricated. In appearance and properties, it resembles a sheet of copper alloy with diamond abrasive dispersed throughout it. It is capable of being cut, formed, and joined by conventional methods, and subsequently used for cutting as a metal bonded diamond tool. Diamond sheet is normally made with industrial diamond as the abrasive material. The metal matrix in diamond sheet is a medium hard copper alloy which has performed well in most applications. This alloy has the capability of being made harder or softer if specific cutting conditions require it. Other alloys have also been used including a precipitation hardened aluminum alloy with very free cutting characteristics. The material is suitable for use in a variety of cutting, surfacing, and ring type tools, as well as in such mundane items as files and sandpaper. It can also be used as a bearing surface (diamond to diamond) and in wear resistant surfaces.

Mackey, C. R.↗
NASA NTRS2011

Synthesis of Elongated Microcapsules

One of the factors that influence the effectiveness of self-healing in functional materials is the amount of liquid healing agents that can be delivered to the damaged area. The use of hollow tubes or fibers and the more sophisticated micro-vascular networks has been proposed as a way to increase the amount of healing agents that can be released when damage is inflicted. Although these systems might be effective in some specific applications, they are not practical for coatings applications. One possible practical way to increase the healing efficiency is to use microcapsules with high-aspect-ratios, or elongated microcapsules. It is understood that elongated microcapsules will be more efficient because they can release more healing agent than a spherical microcapsule when a crack is initiated in the coating. Although the potential advantage of using elongated microcapsules for self healing applications is clear, it is very difficult to make elongated microcapsules from an emulsion system because spherical microcapsules are normally formed due to the interfacial tension between the dispersed phase and the continuous phase. This paper describes the two methods that have been developed by the authors to synthesize elongated microcapsules. The first method involves the use of an emulsion with intermediate stability and the second involves the application of mechanical shear conditions to the emulsion.

Li, Wenyan↗
NASA NTRS1972

Correlation for temperature profiles in the plane of symmetry downstream of a jet injected normal to a crossflow

A correlation method is presented for approximating the temperature distribution in the plane of symmetry downstream of a jet injected normal to a uniform crossflow. Correlations are developed for the scaling parameters required to define the temperature profile at any desired location from the dimensionless universal form which has been experimentally observed. Profiles calculated using the correlation methods are compared with experimental profiles for several momentum and density ratios at various downstream distances.

Holdeman, J. D.↗
NASA NTRS1972

Composite overwrapped metallic tanks

Work is reported for fabricating and testing the fiberglass overwrapped titanium pressure vessel for cryogenic service. Difficulties encountered in the tank liner fabrication phase involved explosive forming, vacuum annealing, chemical milling and electron beam welding. While each of these processes and the nondestructive test methods employed are normally considered to be individually reliable, the combination of poor material together with fabrication and development reversals prevented the full achievement of the desired end results. Eight tanks plus a prototype and tool proofing article were produced. Six of the vessels failed during the hydrostatic sizing operation. One of the remaining tanks was hydrostatically pressurized to burst and the other was pressurized repeatedly at 75 F from 100 psi to the operating pressure until failure occurred. As a result, it is not possible to draw firm conclusions as to the true value of the design concept due to the problems encountered in the program.

Caudill, C. L.↗
NASA NTRS1986

Solving Large Systems of Normal Equations

SOLVE II program combines any number of sets of normal equations and obtains solution vector and related statistics. Normal equations of square, nonnegative definite matrix form. Program utilizes only upper symmetric portion of matrix. Program uses partitioned Cholesky decomposition method for matrix inversion to accommodate large parameter systems.

Putney, B.↗
NASA NTRS1989

A performance comparison of integration algorithms in simulating flexible structures

Asymptotic formulas for the characteristic root errors as well as transfer function gain and phase errors are presented for a number of traditional and new integration methods. Normalized stability regions in the lambda h plane are compared for the various methods. In particular, it is shown that a modified form of Euler integration with root matching is an especially efficient method for simulating lightly-damped structural modes. The method has been used successfully for structural bending modes in the real-time simulation of missiles. Performance of this algorithm is compared with other special algorithms, including the state-transition method. A predictor-corrector version of the modified Euler algorithm permits it to be extended to the simulation of nonlinear models of the type likely to be obtained when using the discretized structure approach. Performance of the different integration methods is also compared for integration step sizes larger than those for which the asymptotic formulas are valid. It is concluded that many traditional integration methods, such as RD-4, are not competitive in the simulation of lightly damped structures.

Howe, R. M.↗
NASA NTRS1981

Closed form evaluation of symmetric two-sided complex integrals

Evaluation of two-sided complex integrals is often required when analyzing linear systems to determine signal variances resulting from stochastic inputs and system noise bandwidths. Algebraic solutions of integrals in a closed matrix equation form, using coefficients of the numerator and denominator polynomials, are presented. The closed forms provide the possibility of obtaining some insight into parameter sensitivity in addition to greatly reducing the computational complexity required by the normal method of evaluation by residues.

Winkelstein, R.↗
NASA NTRS2016

Internship Abstract and Final Reflection

The primary objective for this internship is the evaluation of an embedded natural language processor (NLP) as a way to introduce voice control into future space suits. An embedded natural language processor would provide an astronaut hands-free control for making adjustments to the environment of the space suit and checking status of consumables procedures and navigation. Additionally, the use of an embedded NLP could potentially reduce crew fatigue, increase the crewmember's situational awareness during extravehicular activity (EVA) and improve the ability to focus on mission critical details. The use of an embedded NLP may be valuable for other human spaceflight applications desiring hands-free control as well. An embedded NLP is unique because it is a small device that performs language tasks, including speech recognition, which normally require powerful processors. The dedicated device could perform speech recognition locally with a smaller form-factor and lower power consumption than traditional methods.

Sandor, Edward↗