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NASA NTRS1983

Emissions of second-harmonic auroral kilometric radiation

The cyclotron maser theory of Wu and Lee (1979) is used in treating second-harmonic auroral kilometric radiation (AKR). Good agreement is obtained with the ISIS 1 observation reported by Benson (1982). It is found that when the ratio of the electron plasma frequency to the electron gyrofrequency is less than 0.3, the fundamental AKR prevails over the second-harmonic AKR. When the value of this ratio is greater than or approximately equal to 0.3, the fundamental AKR may become weaker than the second-harmonic AKR, and when it is greater than 0.3 the fundamental AKR may diminish. It is also found that the second harmonic AKR with frequencies below twice the electron gyro-frequency can propagate downward.

Wu, C. S.↗

NASA NTRS1985

A study of the applicability of nucleation theory to quasi-thermodynamic transitions of second and higher Ehrenfest-order

The applicability of classical nucleation theory to second (and higher) order thermodynamic transitions in the Ehrenfest sense has been investigated and expressions have been derived upon which the qualitative and quantitative success of the basic approach must ultimately depend. The expressions describe the effect of temperature undercooling, hydrostatic pressure, and tensile stress upon the critical parameters, the critical nucleus size, and critical free energy barrier, for nucleation in a thermodynamic transition of any general order. These expressions are then specialized for the case of first and second order transitions. The expressions for the case of undercooling are then used in conjunction with literature data to estimate values for the critical quantities in a system undergoing a pseudo-second order transition (the glass transition in polystyrene). Methods of estimating the interfacial energy gamma in systems undergoing a first and second order transition are also discussed.

Barker, R. E., Jr.↗

NASA NTRS1986

Smoothing and the second law

The technique of obtaining second order, oscillation free, total variation diminishing (TVD), scalar difference schemes by adding a limited diffusion flux (smoothing) to a second order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell by cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second order spatial accuracy was found to have an extremely restrictive time step limitation (Delta t less than Delta x squared). Switching to an implicit scheme removed the time step limitation.

Merriam, Marshal L.↗

NASA NTRS1986

Classification of solar flares and the relationship between the first and second phases

A large data base on solar flares obtained during the last solar maximum years makes it necessary to revise the views on the relationship between the impulsive phase and the second phase of flares. Contrary to the view most popular before the launch of the Solar Maximum Mission, it is now known that relativistic electrons and gamma-ray-producing protons and ions are accelerated during the impulsive phase. Because flares producing nuclear gamma-rays are different from ordinary flares, it is concluded that additional processes take place in gamma-ray-line flares. Recent studies have shown that flares with gradual hard X-ray time profiles not only produce nuclear gamma-rays during the impulsive phase but also develop full-fledged second-phase phenomena. It is proposed that filament eruption plays a key role in gamma-ray-line flares. When an erupting filament interacts with an overlaying flare loop, relativistic electrons and energetic protons are produced during the impulsive phase. When the erupting filament fully distends the overlying flare loop, full-fledged second-phase phenomena, such as shocks, interplanetary energetic particles, mass ejections and etc. are observed. When the overlying flare loop is compact and strong enough to suppress the activated filament, gamma-rays are emitted during the first phase but no second-phase phenomena occur.

Bai, T.↗

NASA NTRS1987

Smoothing and the second law

The technique of obtaining second-order oscillation-free total -variation-diminishing (TVD), scalar difference schemes by adding a limited diffusive flux ('smoothing') to a second-order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell-by-cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second-order spatial accuracy was found to have extremely restrictive time-step limitation. Switching to an implicit scheme removed the time-step limitation.

Merriam, Marshal L.↗

NASA NTRS1989

On the state estimation of structures with second order observers

The use of Linear Quadratic Regulator (LQR) control synthesis techniques implies the availability of full state feedback. For vibration control of structures, usually only a limited number of states are measured from which an observer model reconstructs the full state. It is shown that using second order observers is a viable technique for reconstructing the unmeasured states of structures under mildly restrictive conditions. Moreover, the computational advantages of the second order observer as compared to a first order observer indicate that significantly larger observer models may be utilized. Numerical examples are used to demonstrate the performance of second order observers. The implications of second order observers in the development of Controls-Structures Interaction (CSI) technology is discussed.

Belvin, W. Keith↗

NASA NTRS1989

On the state estimation of structures with second order observers

The use of the linear quadratic regulator control synthesis techniques implies the availability of full state feedback. For vibration control of structures, usually only a limited number of states are measured from which an observer model reconstructs the full state. This paper shows that using second-order observers is a viable technique for reconstructing the unmeasured states of structures under mildly restrictive conditions. Moreover, the computational advantages of the second-order observer, as compared to a first-order observer, indicate that significantly larger observer models may be utilized. Numerical examples are used to demonstrate the performance of second-order observers. The implications of second-order observers in the development of the control/structures interaction technology is discussed.

Belvin, W. Keith↗

NASA NTRS1989

Orthogonal canonical forms for second-order systems

The authors prove that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations, while this reduction is always possible for the modal damping commonly assumed for models of flexible structures. The type of canonical form obtainable by means of orthogonal transformations acting on a second-order system is heavily dependent on the type of damping considered. If the damping matrix is merely positive semi-definite symmetric, it is generally not possible to obtain a reduction to Hessenberg-triangular form, while this reduction is trivial for zero or Rayleigh damping. If damping is modal, however, as is commonly assumed in structural models, the reduction exists and is nontrivial. Furthermore, reduction to triangular second-order Schur form is always possible for such damping: this canonical form appears likely to have applications to second-order system theory.

Williams, Trevor↗

NASA NTRS1989

Part A: Nonprincipal-plane scattering from flat plates: Second-order and corner diffractions

Two models of a flat plate for nonprincipal-plane scattering are explored. The first is a revised version of the Physical Optics/Physical Theory of Diffraction (PO/PTD) model with second-order PTD equivalent currents included to account for second-order interactions among the plate edges. The second model uses a heurisitcally derived corner diffraction coefficient to account for the corner scattering mechanism. The patterns obtained using the newer models were compared to the data of previously reported models, the Moment Method (MM), and experimental results. Near normal incidence, all the models agreed; however, near grazing incidence a need for higher-order and corner diffraction mechanisms was noted. In many instances the second-order and corner-scattered fields which were formulated improved the results.

Balanis, Constantine A.↗

NASA NTRS1991

Second coefficient of viscosity in air

Acoustic attenuation measurements in air were analyzed in order to estimate the second coefficient of viscosity. Data over a temperature range of 11 C to 50 C and at relative humidities between 6 percent and 91 percent were used. This analysis showed that the second coefficient of viscosity varied between 1900 and 20,000 times larger than the dynamic or first coefficient of viscosity over the temperature and humidity range of the data. In addition, the data showed that the molecular relaxation effects, which are responsible for the magnitude of the second coefficient of viscosity, place severe limits on the use of time-independent, thermodynamic equations of state. Compressible flows containing large streamwise velocity gradients, like shock waves, which cause significant changes in particle properties to occur during time intervals shorter than hundredths of seconds, must be modeled using dynamic equations of state. The dynamic model approach is described briefly.

Ash, Robert L.↗

NASA NTRS1991

Design of optimal second-order state estimators

The present consideration of the design of online computation-saving second-order state estimators for second-order vector-matrix differential systems proposes a class of such estimators which is proven to possess guaranteed convergence. A class of optimal second-order estimators is then obtained, and the conditions required for optimality are identified. The estimator proposed offers high performance in conjunction with online computation reductions sufficiently great to allow the estimation of the large number of state variables associated with control of large, flexible space structures represented by high-dimensional second-order systems.

Joshi, Suresh M.↗

NASA NTRS1991

On the interaction between first- and second-mode waves in a supersonic boundary layer

Linear stability theory predicts two or more types of unstable disturbances in a sufficiently high-speed boundary layer. These include the first mode, which is similar to the Tollmien-Schlichting waves found in low-speed flows, and the second mode, which does not depend strongly on the viscosity. Generally, the most unstable first mode is three-dimensional while the most unstable second mode is two-dimensional. The interaction between these two spatially unstable modes are studied by direct solution of the three-dimensional Navier-Stokes equations. It is found that the two-dimensional second mode causes a significant increase in the nonlinearity and in the three-dimensionality of the flowfield. The results suggest that this interaction may accelerate transition for flows where the second mode has a significant growth rate.

Maestrello, L.↗

NASA NTRS1992

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Tsang, Leung↗

NASA NTRS1992

Second order closure modeling of turbulent buoyant wall plumes

Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.

Zhu, Gang↗

NASA NTRS1992

Study of the second-order relativistic light deflection of the Sun using long-baseline fibre-linked interferometers: Laser-Interferometric Solar Relativity (LISOR) test

A propasal to study the second order light deflection in the solar gravitational field is presented. It is proposed to use 1 to 2 W frequency stabilized lasers on two microspacecraft about 0.25 degree apart in the sky with apparent positions near the Sun, and observe the relative angle of two spacecraft using ground based fiber linked interferometers with 10 km baseline to determine the second order relativistic light deflection effects. The first two years of work would emphasize the establishment of a prototype stabilized laser system and fiber linked interferometer. The first year, a prototype fiber linked interferometer would be set up to study the phase noise produced by external perturbations to fiber links. The second year, a second interferometer would be set up. The cancellation of phase drift due to fiber links of both interferometers in the same environment would be investigated.

Ni, Wei-Tou↗

NASA NTRS1992

Mechanical forces and their second messengers in stimulating cell growth in vitro

Mechanical forces play an important role in modulating the growth of a number of different tissues including skeletal muscle, smooth muscle, cardiac muscle, bone, endothelium, epithelium, and lung. As interest increases in the molecular mechanisms by which mechanical forces are transduced into growth alterations, model systems are being developed to study these processes in tissue culture. This paper reviews the current methods available for mechanically stimulating tissue cultured cells. It then outlines some of the putative 'mechanogenic' second messengers involved in altering cell growth. Not surprisingly, many mechanogenic second messengers are the same as those involved in growth factor-induced cell growth. It is hypothesized that from an evolutionary standpoint, some second messenger systems may have initially evolved for unicellular organisms to respond to physical forces such as gravity and mechanical perturbation in their environment. As multicellular organisms came into existence, they appropriated these mechanogenic second messenger cascades for cellular regulation by growth factors.

Vandenburgh, Herman H.↗

NASA NTRS1993

Second law analysis of a conventional steam power plant

A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine/generator sets from thermal to electrical. Combustion and heat transfer inside the boiler accounts for 53.83 percent of the total exergy destruction. Converting thermal energy into electrical energy is responsible for 41.34 percent of the total exergy destruction. Heat transfer across the condenser accounts for 2.89 percent of the total exergy destruction. Fluid flow with friction is responsible for 0.50 percent of the total exergy destruction. The boiler feed pump turbine accounts for 0.25 percent of the total exergy destruction. Fluid flow mixing is responsible for 0.23 percent of the total exergy destruction. Other equipment including gland steam condenser, drain cooler, deaerator and heat exchangers are, in the aggregate, responsible for less than one percent of the total exergy destruction. An energy analysis is also given for comparison of exergy cascade to energy cascade. Efficiencies based on both the first law and second law of thermodynamics are calculated for a number of components and for the plant. The results show that high first law efficiency does not mean high second law efficiency. Therefore, the second law analysis has been proven to be a more powerful tool in pinpointing real losses. The procedure used to determine total exergy destruction and second law efficiency can be used in a conceptual design and parametric study to evaluate the performance of other steam power plants and other thermal systems.

Liu, Geng↗

NASA NTRS1993

Dynamic localization and second-order subgrid-scale models in large eddy simulations of channel flow

The objective here is to test the Dynamic Localization (DL) model in a wall-bounded channel flow for numerical stability and accuracy of results. Algebraic stress models suggest that the model for the residual subgrid-scale (SGS) Reynolds stress and scalar flux should generally have terms comprising most of the unique products of the resolved strain (S) and rotation (R) tensors with S and the resolved scalar gradient. The standard dynamic SGS model uses a simple (Smagorinsky) base model for the residual Reynolds stress, which is made proportional to S, and down-gradient base models for residual scalar fluxes; these correspond to the lowest, 'first-order' terms in algebraic stress models. Temporal scaling terms in these base models are formed from the magnitude of the resolved strain rate. While this is appropriate for simple shear flows, it may not be appropriate for more complicated flows (relevant to geophysical and astrophysical problems) that include any combination of shear, rotation, buoyancy, etc. On the other hand, the coefficient in the dynamic SGS model readily adjusts itself to different flow conditions and may adequately take account of these effects without the need for more complicated base models. Cabot (1993) has begun to test the dynamic SGS model in buoyant flows (Rayleigh-Benard and internally heated convection) with and without buoyancy terms explicitly included in the scaling terms of the base model; no great differences were found in large eddy simulation (LES) results for the different base model scalings. The second objective in this work is to test base models with additional, 'second-order' terms (e.g., S(sup 2) and RS for the residual Reynolds stress). These terms have been found to improve large-scale flow predictions by kappa-epsilon models in the presence of rotation and shear. Second-order base models will be tested here in the LES of channel flow with and without solid-body rotation and compared with results from the standard first-order base models to determine if there are significant differences or improvements in results that would warrant the added complexity of the second-order base models.

Cabot, William H.↗