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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.

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49 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

The art of spacecraft design: A multidisciplinary challenge

Actual design turn-around time has become shorter due to the use of optimization techniques which have been introduced into the design process. It seems that what, how and when to use these optimization techniques may be the key factor for future aircraft engineering operations. Another important aspect of this technique is that complex physical phenomena can be modeled by a simple mathematical equation. The new powerful multilevel methodology reduces time-consuming analysis significantly while maintaining the coupling effects. This simultaneous analysis method stems from the implicit function theorem and system sensitivity derivatives of input variables. Use of the Taylor's series expansion and finite differencing technique for sensitivity derivatives in each discipline makes this approach unique for screening dominant variables from nondominant variables. In this study, the current Computational Fluid Dynamics (CFD) aerodynamic and sensitivity derivative/optimization techniques are applied for a simple cone-type forebody of a high-speed vehicle configuration to understand basic aerodynamic/structure interaction in a hypersonic flight condition.

Abdi, F.↗
NASA NTRS1972

Nth-order flat approximation of the signum function by a polynomial

In the interval studied, the signum function, sgn x, was demonstrated to be uniquely approximated by an odd polynomial f sub n (x) of order 2n-1, for which the approximation is nth order flat with respect to the points (1,1) and (-1,-1). A theorem was proved which states that for even integers n or = 2, the approximating polynomial has a pair of nonzero real roots + or - x sub n such that the x sub n form a monotonically decreasing sequence which converges to the root of 2 as n approaches infinity. For odd n i, f sub n (x) represents a strictly increasing monotonic function for all real x. As n tends to infinity, f sub n (x) converges to sgn x uniformly in two interval ranges.

Hosenthien, H. H.↗
NASA NTRS1972

A class of neutral functional differential equations.

Formulation and study of the initial value problem for neutral functional differential equations. The existence, uniqueness, and continuation of solutions to this problem are investigated, and an analysis is made of the dependence of the solutions on the initial conditions and parameters, resulting in the derivation of a continuous dependence theorem in which the fundamental mathematical principles underlying the continuous dependence problem for a very general system of nonlinear neutral functional differential equations are separated out.

Melvin, W. R.↗
NASA NTRS1979

Application of Model Reference Adaptive Control System to Instrument Pointing System /IPS/

A Model Reference Adaptive Controller (MRAC) is derived for a Shuttle payload called the Instrument Pointing System (IPS). The unique features of this MRAC design are that total state feedback is not required, that the internal structure of the model is independent of the internal structure of the IPS, and that the model input is of bounded variation and not required a priori. An application of Liapunov's stability theorems is used to synthesize a control signal which assures MRAC asymptotic stability. Exponential observers are used to obtain the necessary state information to implement the control synthesis. Results are presented which show how effectively the MRAC can maneuver the IPS.

Waites, H. B.↗
NASA NTRS1972

On implicit equations in nonlinear network analysis.

Derivation of conditions for existence of unique solutions to implicit equations of the form y = f(x, u) or x = h(x, u) which are frequently encountered in the analysis of nonlinear networks. The existence of such solutions is demonstrated by applying the principle of contraction mapping and by ascertaining the possibility of a functional inversion according to the Palais (1959) theorem.

Sathe, S. T.↗
NASA NTRS1978

On the rotation of elliptical galaxies

The tensor virial theorem is applied to models of early-type galaxies. First the theorem is applied to rotating elliptical galaxies whose constant-density surfaces are similar ellipsoids. A relationship is obtained between the observed rotations and the forms of generally triaxial galaxies. By applying the results of Robert (1962) to the evaluation of the components of the Chandrasekhar tensor which occurs in this relationship, it is found that the form of a galaxy that lacks global velocity anisotropy uniquely determines the ratio of its rotational and random kinetic energies independently of the radial density profile of that galaxy. A distribution of three-dimensional prolate spheroids is derived which accounts for the observed distribution of ellipticities reported by Sandage, Freeman, and Stokes (1970). This is then used to derive curves giving the expected frequency of occurrence of galaxies of given rotational velocities for each of a number of different apparent elongations on the sky. It is found that if elliptical galaxies are prolate, there should be little correlation between apparent ellipticity and rotation velocity.

Binney, J.↗
NASA NTRS1996

Lattice Truss Structural Response Using Energy Methods

A deterministic methodology is presented for developing closed-form deflection equations for two-dimensional and three-dimensional lattice structures. Four types of lattice structures are studied: beams, plates, shells and soft lattices. Castigliano's second theorem, which entails the total strain energy of a structure, is utilized to generate highly accurate results. Derived deflection equations provide new insight into the bending and shear behavior of the four types of lattices, in contrast to classic solutions of similar structures. Lattice derivations utilizing kinetic energy are also presented, and used to examine the free vibration response of simple lattice structures. Derivations utilizing finite element theory for unique lattice behavior are also presented and validated using the finite element analysis code EAL.

Kenner, Winfred Scottson↗
NASA NTRS1957

A Theoretical Investigation of the Drag of Generalized Aircraft Configurations in Supersonic Flow

It seems possible that, in supersonic flight, unconventional arrangements of wings and bodies may offer advantages in the form of drag reduction. It is the purpose of this report to consider the methods for determining the pressure drag for such unconventional configurations, and to consider a few of the possibilities for drag reduction in highly idealized aircraft. The idealized aircraft are defined by distributions of lift and volume in three-dimensional space, and Hayes' method of drag evaluation, which is well adapted to such problems, is the fundamental tool employed. Other methods of drag evaluation are considered also wherever they appear to offer amplifications. The basic singularities such as sources, dipoles, lifting elements and volume elements are discussed, and some of the useful inter-relations between these elements are presented. Hayes' method of drag evaluation is derived in detail starting with the general momentum theorem. In going from planar systems to spatial systems certain new problems arise. For example, interference between lift and thickness distributions generally appears, and such effects are used to explain the difference between the non-zero wave drag of Sears-Haack bodies and the zero wave drag of Ferrari's ring wing plus central body. Another new feature of the spatial systems is that optimum configurations generally are not unique, there being an infinite family of lift or thickness distributions producing the same minimum drag. However it is shown that all members of an optimum family produce the same flow field in a certain region external to the singularity distribution. Other results of the study indicate that certain spatial distributions may produce materially less wave drag and vortex drag than comparable planar systems. It is not at all certain that such advantages can be realized in practical aircraft designs, but further investigation seems to be warranted.

Graham, E. W.↗
NASA NTRS1995

Analytical and phenomenological studies of rotating turbulence

A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process and reduction of dimensionality in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach which is based on the Green's method leads to the Poincare velocity variables and the Poincare transformation when applied to rotating turbulence. The effects of the rotation are now reflected in the modifications to the convolution of a nonlinear term. The Poincare transformed equations are used to obtain a time-dependent analog of the Taylor-Proudman theorem valid in the asymptotic limit when the non-dimensional parameter mu is identical to Omega(t) approaches infinity (Omega is the rotation rate and t is the time). The 'split' of the energy transfer in both direct and inverse directions is established. Secondly, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincare transformed Euler/Navier-Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, an unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou. In order to characterize the relative strength of rotation, another non-dimensional number, a spectral Rossby number, which is defined as the ratio of rotation and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced.

Mahalov, Alex↗
NASA NTRS1982

Construction of solutions for some nonlinear two-point boundary value problems

Constructive existence and uniqueness results for boundary value problems associated with some simple special cases of the second order equation y'' = f(x,y,y') 0 or = x or = 1, are sought. The approach considered is to convert the differential equation and boundary conditions to an integral equation via Green's functions, and then to apply fixed point and contraction map principles to a sequence of successive approximations. The approach is tested on several applied problems. Difficulties in trying to prove general theorems are discussed.

Pennline, J. A.↗
NASA NTRS1992

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Iannelli, G. S.↗
NASA NTRS2000

On The Computational Capabilities of Physical Systems: Relationship With Conventional Computer Science - Part 2

In the first of this pair of papers, it was proven that there cannot be a physical computer to which one can properly pose any and all computational tasks concerning the physical universe. It was then further proven that no physical computer C can correctly carry out all computational tasks that can be posed to C. As a particular example, this result means that no physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs; one cannot build a physical computer that can be assured of correctly "processing information faster than the universe does". These results do not rely on systems that are infinite, and/or non-classical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine. This generality is a direct consequence of the fact that a novel definition of computation - "physical computation" - is needed to address the issues considered in these papers, which concern real physical computers. While this novel definition does not fit into the traditional Chomsky hierarchy, the mathematical structure and impossibility results associated with it have parallels in the mathematics of the Chomsky hierarchy. This second paper of the pair presents a preliminary exploration of some of this mathematical structure. Analogues of Chomskian results concerning universal Turing Machines and the Halting theorem are derived, as are results concerning the (im)possibility of certain kinds of error-correcting codes. In addition, an analogue of algorithmic information complexity, "prediction complexity", is elaborated. A task-independent bound is derived on how much the prediction complexity of a computational task can differ for two different reference universal physical computers used to solve that task, a bound similar to the "encoding" bound governing how much the algorithm information complexity of a Turing machine calculation can differ for two reference universal Turing machines. Finally, it is proven that either the Hamiltonian of our universe proscribes a certain type of computation, or prediction complexity is unique (unlike algorithmic information complexity), in that there is one and only version of it that can be applicable throughout our universe.

Wolpert, David H.↗
NASA NTRS2006

An Efficient Approach for the Reliability Analysis of Phased-Mission Systems with Dependent Failures

We consider the reliability analysis of phased-mission systems with common-cause failures in this paper. Phased-mission systems (PMS) are systems supporting missions characterized by multiple, consecutive, and nonoverlapping phases of operation. System components may be subject to different stresses as well as different reliability requirements throughout the course of the mission. As a result, component behavior and relationships may need to be modeled differently from phase to phase when performing a system-level reliability analysis. This consideration poses unique challenges to existing analysis methods. The challenges increase when common-cause failures (CCF) are incorporated in the model. CCF are multiple dependent component failures within a system that are a direct result of a shared root cause, such as sabotage, flood, earthquake, power outage, or human errors. It has been shown by many reliability studies that CCF tend to increase a system's joint failure probabilities and thus contribute significantly to the overall unreliability of systems subject to CCF.We propose a separable phase-modular approach to the reliability analysis of phased-mission systems with dependent common-cause failures as one way to meet the above challenges in an efficient and elegant manner. Our methodology is twofold: first, we separate the effects of CCF from the PMS analysis using the total probability theorem and the common-cause event space developed based on the elementary common-causes; next, we apply an efficient phase-modular approach to analyze the reliability of the PMS. The phase-modular approach employs both combinatorial binary decision diagram and Markov-chain solution methods as appropriate. We provide an example of a reliability analysis of a PMS with both static and dynamic phases as well as CCF as an illustration of our proposed approach. The example is based on information extracted from a Mars orbiter project. The reliability model for this orbiter considers the various phases of Launch, Cruise, Mars Orbit Insertion, and Orbit. Some of the CCF for the orbiter in this mission include environmental effects, such as micrometeoroids, human operator errors, and software errors.

reliability analysis↗