Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “characteristic equations”

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 919 records · Page 51

T-Matrix Computations of Light Scattering by Nonspherical Particles: A Review

We review the current status of Waterman's T-matrix approach which is one of the most powerful and widely used tools for accurately computing light scattering by nonspherical particles, both single and composite, based on directly solving Maxwell's equations. Specifically, we discuss the analytical method for computing orientationally-averaged light-scattering characteristics for ensembles of nonspherical particles, the methods for overcoming the numerical instability in calculating the T matrix for single nonspherical particles with large size parameters and/or extreme geometries, and the superposition approach for computing light scattering by composite/aggregated particles. Our discussion is accompanies by multiple numerical examples demonstrating the capabilities of the T-matrix approach and showing effects of nonsphericity of simple convex particles (spheroids) on light scattering.

Mischenko, Michael I.↗

Experience in distributed parameter modeling of the Spacecraft Control Laboratory Experiment (SCOLE) structure

The Spacecraft Control Laboratory Experiment (SCOLE) configuration is used to compare exact and approximate solutions of the partial differential equations which define its structural dynamics. The need for a proof model for evaluating competing control laws demands that solutions be generated which not only exhibit accurate modal characteristics, but precise static deflections as well. Because precise pointing is required, the motion of the end bodies of the Shuttle-attached antenna must be known with great accuracy. Modal models are attractive because of their stable solutions but require hundreds of modes to obtain a static deflection accuracy of only one percent. Although proportional damping in bending agrees well with experimental results using the SCOLE experimental apparatus, modes which involve both torsion and bending differ significantly from proportional damping. A lumped mass model is used to generate exact static deflections, but only approximate modal characteristics. Asymptotic solutions to the distributed parameter system approximate very accurately the modal characteristics at high mode numbers. Ways are examined for refining the approximate solutions by applying a first-order variation and by employing singular perturbation techniques which are usually limited to ordinary differential equations. The most accurate solutions of the distributed parameter model of SCOLE are obtained by combining exact and asymptotic solutions.

Taylor, L. W.↗

MATLAB Stability and Control Toolbox Trim and Static Stability Module

MATLAB Stability and Control Toolbox (MASCOT) utilizes geometric, aerodynamic, and inertial inputs to calculate air vehicle stability in a variety of critical flight conditions. The code is based on fundamental, non-linear equations of motion and is able to translate results into a qualitative, graphical scale useful to the non-expert. MASCOT was created to provide the conceptual aircraft designer accurate predictions of air vehicle stability and control characteristics. The code takes as input mass property data in the form of an inertia tensor, aerodynamic loading data, and propulsion (i.e. thrust) loading data. Using fundamental nonlinear equations of motion, MASCOT then calculates vehicle trim and static stability data for the desired flight condition(s). Available flight conditions include six horizontal and six landing rotation conditions with varying options for engine out, crosswind, and sideslip, plus three take-off rotation conditions. Results are displayed through a unique graphical interface developed to provide the non-stability and control expert conceptual design engineer a qualitative scale indicating whether the vehicle has acceptable, marginal, or unacceptable static stability characteristics. If desired, the user can also examine the detailed, quantitative results.

Kenny, Sean P.↗

Determination of control-surface characteristics from NACA plain-flap and tab data

The data from previous NACA pressure-distribution investigations of plain flaps and tabs have been analyzed and are presented in this paper in a form readily applicable to the problems of control-surface design. The experimentally determined variation of aerodynamic parameters with flap chord and tab chord are given in chart form and comparisons are made with the theory. With the aid of these charts and the theoretical relationships for a thin airfoil, the aerodynamic characteristics for control surfaces of any plan form with plain flaps and tabs may be determined. A discussion of the basic equations of the thin-airfoil theory and the development of a number of additional equations that will be helpful in tail design are presented in the appendixes. The procedure for applying the data is described and a sample problem of tail design is included. The data presented and the method of application set forth in this report should provide a reasonably accurate and satisfactory means of computing the aerodynamic characteristics of control surfaces.

TAIL SURFACES, HORIZONTAL - CHAR↗

On the Solution of the Continuity Equation for Precipitating Electrons in Solar Flares

Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis & Zharkova claim to have found an "updated exact analytical solution" to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii & Shmeleva, and many others is invalid. We show that the solution of Dobranskis & Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the "new" analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result.We conclude that Dobranskis & Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii & Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.

Sun: flares↗

Atmospheric temperature profiles derived through the inversion of a system of first order differential equations

Generation of vertical temperatures profiles from remotely sensed atmospheric radiance data is described as an analogous communications system. The radiative transport characteristics of the atmosphere encodes the continuous temperature profile into an 'n' element vector where 'n' is the number of channels in the satellite instrument. The temperature profile is a message transmitted from station A to station B and the link is the satellite instrument. At station B the decoder reproduces a continuous function which is the best estimate of the message encoded at station A. It is shown that the decoder must operate in a tuned mode where the parameters used in the encoder precisely determine the decoder parameters, and that the characteristics of the total message block must be given by a set of decoder constraints

Gatlin, J. A.↗

Airborne imaging spectrometer-2 - Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere

The reduction of AIS data to spectral radiance utilizing the detector responsivity equations developed by a laboratory calibration of the instrument with a BaSO4-coated integrating sphere is described. Estimates of the signal-to-noise ratio for laboratory and flight conditions are obtained. In addition, the effective in-flight instrumental spectral sampling interval is estimated by using atmospheric CO2 absorption lines generated from LOWTRAN simulations.

Conel, James E.↗

Arc-driven rail gun research

The equations describing the performance of an inductively-driven rail gun are analyzed numerically. Friction between the projectile and rails is included through an empirical formulation. The equations are applied to the experiment of Rashleigh and Marshall to obtain an estimate of energy distribution in rail guns as a function of time. The effect of frictional heat dissipation on the bore of the gun is calculated. The mechanism of plasma and projectile acceleration in a dc rail gun is described from a microscopic point of view through the establishment of the Hall field. The plasma conductivity is shown to be a tensor indicating that there is a small component of current parallel to the direction of acceleration. The plasma characteristics are evaluated as a function of plasma mass through a simple fluid mechanical analysis of the plasma. By equating the energy dissipated in the plasma with the radiation heat loss, the properties of the plasma are determined.

Ray, P. K.↗

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Dlugach, Janna M.↗

Comet Gas and Dust Dynamics Modeling

This software models the gas and dust dynamics of comet coma (the head region of a comet) in order to support the Microwave Instrument for Rosetta Orbiter (MIRO) project. MIRO will study the evolution of the comet 67P/Churyumov-Gerasimenko's coma system. The instrument will measure surface temperature, gas-production rates and relative abundances, and velocity and excitation temperatures of each species along with their spatial temporal variability. This software will use these measurements to improve the understanding of coma dynamics. The modeling tool solves the equation of motion of a dust particle, the energy balance equation of the dust particle, the continuity equation for the dust and gas flow, and the dust and gas mixture energy equation. By solving these equations numerically, the software calculates the temperature and velocity of gas and dust as a function of time for a given initial gas and dust production rate, and a dust characteristic parameter that measures the ability of a dust particle to adjust its velocity to the local gas velocity. The software is written in a modular manner, thereby allowing the addition of more dynamics equations as needed. All of the numerical algorithms are added in-house and no third-party libraries are used.

Von Allmen, Paul A.↗

Hi-alpha forebody design. Part 2: Determination of body shapes for positive directional stability

Computational Fluid Dynamics (CFD) has been used to study aircraft forebody flowfields at low speed high angle-of-attack conditions with sideslip. The purpose is to define forebody geometries which provide good directional stability characteristics under these conditions. The flows of the F-5A forebody and Erickson forebody were recomputed with better and refined grids. The results were obtained using a modified version of cfl3d to solve either the Euler equations or the Reynolds equations employing a form of the Baldwin-Lomax turbulence model. Based on those results, we conclude that current CFD methods can be used to investigate the aerodynamic characteristics of forebodies to achieve desirable high angle-of-attack characteristics. An analytically defined generic forebody model is described, and a systematic study of forebody shapes was then conducted to determine which shapes promote a positive contribution to directional stability at high angle-of-attack. A novel way of presenting the results is used to illustrate how the positive contribution arises. Based on the results of this initial parametric study, some guidelines for aerodynamic design to promote positive directional stability are presented.

Ravi, R.↗

Design and application of squeeze film dampers for turbomachinery stabilization

The steady-state transient response of the squeeze film damper bearing was investigated. Both the steady-state and transient equations for the hydrodynamic bearing forces are derived; the steady-state equations were used to determine the damper equivalent stiffness and damping coefficients. These coefficients are used to find the damper configuration which will provide the optimum support characteristics based on a stability analysis of the rotor-bearing system. The effects of end seals and cavitated fluid film are included. The transient analysis of rotor-bearing systems was conducted by coupling the damping and rotor equations and integrating forward in time. The effects of unbalance, cavitation, and retainer springs are included. Methods of determining the stability of a rotor-bearing system under the influence of aerodynamic forces and internal shaft friction are discussed.

Gunter, E. J.↗

An extended numerical manifold method for unsaturated soil-water interaction analysis at micro-scale

To investigate unsaturated soil-water interaction at micro-scale, this work extends the numerical manifold method (NMM) by incorporating a soil-water coupling model considering specific capillary water distribution and capillary force calculation. The soil skeleton is constructed by a soil skeleton generation algorithm with random polygons. To more realistically capture the interaction between soil grains and capillary water, a capillary mechanics-based geometric algorithm is proposed to iteratively calculate the capillary water distribution. The capillary forces corresponding to the capillary water distribution are calculated based on the Young-Laplace equation. The proposed capillary water solving framework is first verified by reproducing the soil-water characteristic curve and the capillary water distribution of an ideal contact-disk model against analytical solutions. To further validate the ability of the capillary water solving framework to predict hydraulic behavior of the real soil, a laboratory test on the Toyoura sand is reproduced numerically. Then an ideal direct shear test is performed to further validate the two-way soil-water coupling procedure, in which a comparison between the numerical and analytical results regarding the shear strength and matric suction is presented. Finally, microscopic hydraulic and compression tests are conducted on two soil specimens with the same porosity and mean grain diameter but different uniformity coefficients. The results elucidate that the extended method is a potential tool to explore unsaturated soil behaviors at micro-scale.

58 GEOSCIENCES↗

Synthesis of shuttle vehicle damping using substructure test results

An empirical method is developed for predicting the modal damping of a combined parallel-stage shuttle model by means of damping measurements performed on the individual substructures. Correlations are first determined for each component in terms of damping energy as a function of peak kinetic energy and modal amplitude. The results are then used to predict component damping energies corresponding to the respective kinetic energies and amplitudes that occur for the new modes of the combined system. Modal characteristics for the system, other than damping, are obtained by a real eigenvalue solution of dynamic equations developed by Hurty's procedure of substructures. System equations, which include component modal damping, are also solved by a complex eigenvalue approach for comparison with results of the empirical method.

Kana, D. D.↗

Strongly coupled stress waves in heterogeneous plates.

Consideration of coupled stress waves generated by an impulsive load applied at one end of a semiinfinite plate. For the field equations governing the one-dimensional coupled waves a hyperbolic system of equations is obtained in which a strong coupling in the second derivatives exists. The method of characteristics described by Chou and Mortimer (1967) is extended to cover the case of strong coupling, and a study is made of the transient stress waves in a semiinfinite plate subjected to an initial step input. Coupled discontinuity fronts are found to propagate at different velocities. The normal plate stress and the bending moment at different time regimes are illustrated by graphs.

Wang, A. S. D.↗

Heat transfer and fluid flow

Heat transfer and flow characteristics of UF6 flowing in a gas core reactor were analyzed through solution of the energy equation. The thermal-physical properties of UF6 are given.

Source record↗

Stability of higher-order Bragg interactions in active periodic media

The stability of waves in unbounded, longitudinally periodic media is studied for index and gain coupling. Time-independent periodic media are found to support both stable and absolutely unstable waves. The wave characteristics depend upon average gain or loss, coupling type, and Bragg order. The extended coupled waves equations provide explicit values of threshold, frequency, and temporal growth rate for instabilities at all Bragg resonances through the dispersion relation. Applications to multiharmonic periodicities and complex couplings are briefly discussed with particular note taken of possible reductions of the stability thresholds and removal of threshold degeneracies. Comparisons are made to the longitudinally bounded case of distributed feedback lasers.

Jaggard, D. L.↗