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At least 1,009 records · Page 56
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NASA NTRS1992

Multi-point inverse design of an infinite cascade of airfoils

This paper describes a practical method for the design of an infinite cascade in incompressible flow. The method is based on conformal mapping, and as a result it allows for multi-point design. The cascade blade to be determined is divided into a desired number of segments. Over each segment, the velocity distribution is prescribed together with an inlet or outlet flow angle at which this velocity distribution is to be achieved. In this way multi-point design requirements can be met. It is necessary to satisfy several conditions that arise to guarantee compatibility with the inlet and outlet flow as well as closure of the cascade blade. Satisfaction of these conditions does not necessarily result in a cascade with all the desired characteristics. For example, the cascade blades may be bulbous or crossed. Through Newton iteration, however, the desired characteristics may be prescribed by allowing for the adjustment of the design parameters that define the mathematical problem through conformal mapping. Several examples will be illustrated to demonstrate the capability of the method. It will be shown that the method is limited to the design of cascades with solidities of up to one.

Selig, Michael S.↗
NASA NTRS1992

Inverse sequential detection of parameter changes in developing time series

Progressive values of two probabilities are obtained for parameter estimates derived from an existing set of values and from the same set enlarged by one or more new values, respectively. One probability is that of erroneously preferring the second of these estimates for the existing data ('type 1 error'), while the second probability is that of erroneously accepting their estimates for the enlarged test ('type 2 error'). A more stable combined 'no change' probability which always falls between 0.5 and 0 is derived from the (logarithmic) width of the uncertainty region of an equivalent 'inverted' sequential probability ratio test (SPRT, Wald 1945) in which the error probabilities are calculated rather than prescribed. A parameter change is indicated when the compound probability undergoes a progressive decrease. The test is explicitly formulated and exemplified for Gaussian samples.

Radok, Uwe↗
NASA NTRS1992

Inverse problems: Fuzzy representation of uncertainty generates a regularization

In many applied problems (geophysics, medicine, and astronomy) we cannot directly measure the values x(t) of the desired physical quantity x in different moments of time, so we measure some related quantity y(t), and then we try to reconstruct the desired values x(t). This problem is often ill-posed in the sense that two essentially different functions x(t) are consistent with the same measurement results. So, in order to get a reasonable reconstruction, we must have some additional prior information about the desired function x(t). Methods that use this information to choose x(t) from the set of all possible solutions are called regularization methods. In some cases, we know the statistical characteristics both of x(t) and of the measurement errors, so we can apply statistical filtering methods (well-developed since the invention of a Wiener filter). In some situations, we know the properties of the desired process, e.g., we know that the derivative of x(t) is limited by some number delta, etc. In this case, we can apply standard regularization techniques (e.g., Tikhonov's regularization). In many cases, however, we have only uncertain knowledge about the values of x(t), about the rate with which the values of x(t) can change, and about the measurement errors. In these cases, usually one of the existing regularization methods is applied. There exist several heuristics that choose such a method. The problem with these heuristics is that they often lead to choosing different methods, and these methods lead to different functions x(t). Therefore, the results x(t) of applying these heuristic methods are often unreliable. We show that if we use fuzzy logic to describe this uncertainty, then we automatically arrive at a unique regularization method, whose parameters are uniquely determined by the experts knowledge. Although we start with the fuzzy description, but the resulting regularization turns out to be quite crisp.

Kreinovich, V.↗
NASA NTRS1993

Effective equations and the inverse cascade theory for Kolmogorov flows

We study the two-dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Weinan, E.↗
NASA NTRS1993

Detection of the 2165 inverse centimeter (4.619 micron) XCN band in the spectrum of L1551 IRS 5

We report the detection of a broad absorption band at 2165/cm in the spectrum of L1551 IRS 5. New laboratory results over the 2200-2100/cm wavenumber interval, performed with realistic interstellar ice analogs, suggest that this feature is due to a CN-containing compound. We will refer to this compound as XCN. We also confirm the presence of frozen CO through absorption bands at 2140/cm and 2135/cm. The relative abundance of solid state CO to frozen H2O is about 0.13 while the abundance of XCN seems comparable to that of frozen CO.

Tegler, Stephen C.↗
NASA NTRS1992

An explicit canopy BRDF model and inversion

Based on a rigorous canopy radiative transfer equation, the multiple scattering radiance is approximated by the asymptotic theory, and the single scattering radiance calculation, which requires an numerical intergration due to considering the hotspot effect, is simplified. A new formulation is presented to obtain more exact angular dependence of the sky radiance distribution. The unscattered solar radiance and single scattering radiance are calculated exactly, and the multiple scattering is approximated by the delta two-stream atmospheric radiative transfer model. The numerical algorithms prove that the parametric canopy model is very accurate, especially when the viewing angles are smaller than 55 deg. The Powell algorithm is used to retrieve biospheric parameters from the ground measured multiangle observations.

Liang, Shunlin↗
NASA NTRS1993

The inference of mantle viscosity from an inversion of the Fennoscandian relaxation spectrum

The theory of Peltier (1976) for mantle viscosity is adopted, within the framework of nonlinear Bayesian Inference, to invert the Fennoscandian relaxation spectra derived by McConnell (1968). A set of rigorous constraints which all models for the viscosity variation beneath Fennoscandian must satisfy is derived. These constraints are used to test the plausibility of a wide class of viscosity models. It is shown that a model with a weak asthenosphere overlying an isoviscous 10 exp 21 Pa s deep mantle provides to good fit to the relaxation spectrum. This is also true of models with a thin sublithospheric low-viscosity zone overlying a two-layer deep mantle with a moderate jump in viscosity across 670 km depth, and models with a viscosity jump of between four and six across isoviscous upper and lower mantle regions.

Mitrovica, J. X.↗
NASA NTRS1993

Aerodynamic inverse design and analysis for a full engine

A numerical design methodology for multistage turbomachinery is being developed that minimizes the use of experimental data required in the design process. This approach is resulting in an efficient method of enlarging the design database for turbomachinery blading. This capability has been demonstrated for blade sections, and the goal is to extend it to fully three dimensional, multistage configurations.

Sanz, Jose M.↗