Search NASA⌕ Search

SEARCH · Search NASA

Results for “scaling theory”

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 145 records · Page 8

Analogies Between Colloidal Sedimentation and Turbulent Convection at High Prandtl Numbers

A new set of coarse-grained equations of motion is proposed to describe concentration and velocity fluctuations in a dilute sedimenting suspension of non-Brownian particles. With these equations, colloidal sedimentation is found to be analogous to turbulent convection at high Prandtl numbers. Using Kraichnan's mixing-length theory, we obtain scaling relations for the diffusive dissipation length delta(sub theta), the velocity variance delta u, and the concentration variance delta phi. The obtained scaling laws over varying particle radius alpha and volume fraction phi(sub ) are in excellent agreement with the recent experiment by Segre, Herbolzheimer, and Chaikin. The analogy between colloidal sedimentation and turbulent convection gives a simple interpretation for the existence of a velocity cut-off length, which prevents hydrodynamic dispersion coefficients from being divergent. It also provides a coherent framework for the study of sedimentation dynamics in different colloidal systems.

Tong, P.↗

Theoretical Technology Research for the International Solar Terrestrial Physics (ISTP) Program

During the last four years the UCLA (University of California, Los Angeles) IGPP (Institute of Geophysics and Planetary Physics) Space Plasma Simulation Group has continued its theoretical effort to develop a Mission Oriented Theory (MOT) for the International Solar Terrestrial Physics (ISTP) program. This effort has been based on a combination of approaches: analytical theory, large-scale kinetic (LSK) calculations, global magnetohydrodynamic (MHD) simulations and self-consistent plasma kinetic (SCK) simulations. These models have been used to formulate a global interpretation of local measurements made by the ISTP spacecraft. The regions of applications of the MOT cover most of the magnetosphere: solar wind, low- and high- latitude magnetospheric boundary, near-Earth and distant magnetotail, and auroral region. Most recent investigations include: plasma processes in the electron foreshock, response of the magnetospheric cusp, particle entry in the magnetosphere, sources of observed distribution functions in the magnetotail, transport of oxygen ions, self-consistent evolution of the magnetotail, substorm studies, effects of explosive reconnection, and auroral acceleration simulations. A complete list of the activities completed under the grant follow.

Ashour-Abdalla, Maha↗

Acoustic Experiment to Measure the Bulk Viscosity of Near-Critical Xenon in Microgravity

We plan a rigorous test of the theory of dynamic scaling by accurately measuring the bulk viscosity of xenon in microgravity 50 times closer to the critical temperature T(sub c) than previous experiments. The bulk viscosity zeta (or "second viscosity" or "dilational viscosity") will be determined by measuring the attenuation length of sound alpha lambda and also measuring the frequency-dependence of the speed of sound. For these measurements, we developed a unique Helmholtz resonator and specialized electro-acoustic transducers. We describe the resonator, the transducers, their performance on Earth, and their expected performance in microgravity.

Gillis, K. A.↗

Telescoping Mechanics: A New Paradigm for Composite Behavior Simulation

This report reviews the application of telescoping mechanics to composites using recursive laminate theory. The elemental scale is the fiber-matrix slice, the behavior of which propagates to laminate. The results from using applications for typical, hybrid, and smart composites and composite-enhanced reinforced concrete structures illustrate the versatility and generality of telescoping scale mechanics. Comparisons with approximate, single-cell, and two- and three-dimensional finite-element methods demonstrate the accuracy and computational effectiveness of telescoping scale mechanics for predicting complex composite behavior.

Chamis, C. C.↗

High Performance Rotating Detonation Rocket Engine for Mars Interplanetary Transport

NASA has successfully evaluated the performances and survivability of two additively manufactured (AM) continuously rotating detonation cycle rocket engine (RDRE) thrust chambers. The AM hardware was subjected to long duration continuous detonative environments in excess of 100 seconds. Performance trends were directly compared to theory and similar scale constant pressure engines with identical propellants. The performance benefits of RDREs include higher combustion efficiency at a more compact design trade space, which allow advantages for future NASA missions. A major finding of this work is that the heat fluxes experienced are substantially higher than traditional liquid rocket engines at the same operating conditions. In addition, completion of combustion occurs rapidly in an annular geometry at ¼ that of the L* and L’ of an equivalent state-of-the-art thrust chamber. Finally, all hardware survived the extreme environments and achieved the major goal of the test project by demonstrating hot fire conditions with detonation modes up to 133 seconds in duration. Follow-on efforts funded by STMD Early Career Initiative (ECI) award are now focused on achieving higher performances than the previous designs and closing the remaining technology risks.

Thomas Teasley↗

Theory and comparison with tests of two full-scale proprotors

A nine degrees-of-freedom theoretical model was developed for investigations of the dynamics of a proprotor operating in high inflow axial flight on a cantilever wing. The theory is described, and the results of the analysis are presented for two proprotor configurations: a gimballed, stiff-inplane rotor, and a hingeless, soft-inplane rotor. The influence of various elements of the theory are discussed, including the modeling used for the blade and wing aerodynamics, and the influence of the rotor lag degree of freedom. The results from full-scale tests of the two proprotors are presented and compared with the theoretical results.

Johnson, W.↗

Theory and comparison with tests of two full-scale proprotors

A nine-degrees-of-freedom theoretical model has been developed for investigations of the dynamics of a prop rotor operating in high inflow axial flight on a cantilever wing. The theory is described, and the results of the analysis are presented for two prop rotor configurations: a gimbaled, stiff in-plane rotor, and a hingeless, soft in-plane rotor. The influence of various elements of the theory is discussed, including the modeling used for the blade and wing aerodynamics and the influence of the rotor lag degree of freedom. The results from full-scale tests of these two prop rotors are presented and compared with the theoretical results.

Johnson, W.↗

Mathematical theory of a relaxed design problem in structural optimization

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Kikuchi, Noboru↗

Proportional and scale change models to project failures of mechanical components with applications to space station

In this paper we develop the mathematical theory of proportional and scale change models to perform reliability analysis. The results obtained will be applied for the Reaction Control System (RCS) thruster valves on an orbiter. With the advent of extended EVA's associated with PROX OPS (ISSA & MIR), and docking, the loss of a thruster valve now takes on an expanded safety significance. Previous studies assume a homogeneous population of components with each component having the same failure rate. However, as various components experience different stresses and are exposed to different environments, their failure rates change with time. In this paper we model the reliability of a thruster valves by treating these valves as a censored repairable system. The model for each valve will take the form of a nonhomogeneous process with the intensity function that is either treated as a proportional hazard model, or a scale change random effects hazard model. Each component has an associated z, an independent realization of the random variable Z from a distribution G(z). This unobserved quantity z can be used to describe heterogeneity systematically. For various models methods for estimating the model parameters using censored data will be developed. Available field data (from previously flown flights) is from non-renewable systems. The estimated failure rate using such data will need to be modified for renewable systems such as thruster valve.

Taneja, Vidya S.↗

Large-scale motions of the tropics in observations and theory

Charney (1963) characterized the tropical atmosphere in terms of a superposition of large regions of nearly nondivergent circulations containing local subdomains, or 'fissures', of active convection and latent heating. Tropical wave evolution is then appropriately treated in terms of quasi-rotational waves, to the extent that the divergent contribution is small. An attempt is presently made to interpret recent tropical analyses in the aforementioned terms, suggesting extensions of the simplest quasi-rotational model capable of reconciling observations and theory. First GARP Global Experiment (FGGE) observations suggest that strongly divergent local tropical circulations are forced by latent heating and produce important direct modifications of the total wind field; after describing the extent to which the resulting field consists of divergent and rotational components in different analyses of the FGGE data, independent supporting documentation of the results in terms of heating estimates and rainfall observations are given.

Paegle, J.↗

Large-scale flows and solar luminosity variations

The influence of a variation of the large-scale flows present in the solar convection zone on solar luminosity is examined. The convection zone is modeled as a plane-parallel fluid layer through which heat is transported by small-scale convection as described by the mixing-length theory, and the large-scale flow is treated as a small perturbation superposed on the layer. The excess energy transported by the flow is calculated and is found to depend critically on the mixing length. The excess luminosity is found to be carried as small-scale convective heat flow rather than bulk enthalpy transport throughout all but the top few percent of the convection zone. The results are applied to the specific examples of supergranules and giant cells.

Arendt, S.↗

A comparison of linear acoustic theory with experimental noise data for a small-scale hovering rotor

Linear acoustic calculations based on full aerodynamic data as input are presented and compared with measured cases reported by Boxwell et al. (1978). The full aerodynamic data are obtained using three programs giving radial loading, chordwise loading, and chordwise position of transition. It is shown that in the theoretical results the most significant noise source mechanism is due to blade thickness. Thus the conclusions of Boxwell et al. as to the importance of nonlinearities around the blades are upheld. These conclusions concern the width, shape and the level of the acoustic pressure calculated from linear acoustic theory. Some of the approximations involved in the application of acoustic analogy using quadrupole sources are discussed. It is necessary that the near- and far-field problems of rotating blades be treated together as shown for the case of an oscillating sphere.

Farassat, F.↗

On the fragmentation of asteroids and planetary satellites

A general scaling model is defined which allows the extrapolation of small-scale collisional fragmentation experiment results, and existing collisional theories are considered within its framework. Scaling based exclusively upon the specific energy, Q, of the event (the ratio of projectile kinetic energy to the mass of the target body) is shown to hold when (1) the projectile and target material properties do not depend on size or time scales, and (2) the collision is governed by kinetic energy independently of impact velocity. Because neither of these conditions should hold, serious doubt is cast on the validity of Q's use as the sole scaling parameter.

Housen, Kevin R.↗

Linear tearing modes of a forced current-sheet equilibrium

Linear tearing modes are studied in a nearly singular forced current-sheet equilibrium, such as could result from global magnetic forces in the solar corona. Growth rates for the tearing modes, determined by solving the linearized reduced MHD (Strauss) equations numerically, were found to scale as (gamma)tau(d) = about S exp 4/5 k(y) exp 4/5, where S is the Lundquist number, k(y) is the wavenumber, and tau(d) is the classical resistive diffusion time. This scaling is in agreement with predictions from analytical theory. Because of the faster S scaling of these modes compared to the tearing modes of a diffuse current-sheet equilibrium, the modes have much higher growth rates (by a factor of about 10,000) for coronal values of S (about 10 to the 12th). For coronal parameters, the growth times of these new modes are estimated to be on the order of several hours to days, as compared to growth times of months to years for the tearing modes in a diffuse current-shear equilibrium. The growth times are comparable to reconnection times scales required in models of coronal heating by magnetic field dissipation.

Liewer, Paulett C.↗

Large-scale velocity fields

The present evaluation of recent observational results bearing on the nature and characteristics of solar rotation gives attention to the status of current understanding on such large-scale velocity-field-associated phenomena as solar supergranulation, mesogranulation, and giant-scale convection. Also noted are theoretical suggestions reconciling theory and observations of giant-scale solar convection. The photosphere's global meridional circulation is suggested by solar rotation models requiring pole-to-equator flows of a few m/sec, as well as by the observed migration of magnetic activity over the solar cycle. The solar rotation exhibits a latitude and cycle dependence which can be understood in terms of a time-dependent convective toroidal roll pattern.

Howard, Robert F.↗

A statistical analysis of mesoscale rainfall as a random cascade

The paper considers the random cascade theory for spatial rainfall. Particular attention was given to the following four areas: (1) the relationship of the random cascade theory of rainfall to the simple scaling and the hierarchical cluster-point-process theories, (2) the mathematical foundations for some of the formalisms commonly applied in the develpment of statistical cascade theory, (3) the empirical evidence for a random cascade theory of rainfall, and (4) the way of using data for making estimates of parameters and for making statistical inference within this theoretical framework. An analysis of space-time rainfall data is presented. Cascade simulations are carried out to provide a comparison with methods of analysis that are applied to the rainfall data.

Gupta, Vijay K.↗