Characteristics of Apollo-type lunar orbits
Numerical integration of equations for time rate change of lunar satellite orbits for Apollo project
Born, G. H.↗
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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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Hydraulic characteristics of spatially varied flow in a trapezoidal channel.
Dynamic equation for spatially varied flow in trapezoidal channel derived from principle of momentum conservation
Mirza, S.↗
Principles and application of shock-tubes and shock tunnels
The principles, theoretical flow equations, calculation techniques, limitations and practical performance characteristics of basic and high performance shock tubes and shock tunnels are presented. Selected operating curves are included.
Ried, R. C.↗
Research study on stabilization and control modern sampled-data control theory
The methods of continuous and discrete describing function analysis were applied to predicting the existence of self-sustained oscillations in the single-axis model of the large space telescope system with nonlinear control moment gyroscope friction characteristics. It is shown that the stability equations may be solved by a numerical-iterative technique using the describing function analysis, instead of the usual graphical methods. The numerical method is found to be effective in leading to a convergent solution rapidly, with an appropriate guess of the initial condition.
Kuo, B. C.↗
Propagation of plane waves in flow through a variable area duct
Duct geometry is an important factor that influences the transmission of sound in a duct. Nonconstant area produces variations in steady flow quantities through the duct, which can cause reflections of acoustic disturbances and the creation of standing wave patterns, and which can attenuate and disperse propagating waves. To study the problem, a second-order-accurate numerical method has been developed. The method of characteristics is used to solve the acoustic equations with the assumption of quasi-one-dimensional flow in the duct. Numerical results are presented over a broad range of frequencies. Low-frequency results are compared with approximate solutions for compact nozzles and high-frequency calculations are compared with results from the short-wave theory. The numerical results are also compared with an analytical solution of the acoustic equations for exponential horn sections with zero mean flow to further establish the validity of the numerical method.
King, L. S.↗
An investigation of the vibration characteristics of shrouded-bladed-disk rotor stages
Coupled differential equations of motion are given for application to a rotating, pretwisted and heated beam under the effects of thermal stresses and gas bending loads. The circumferential modes of the multi-blade vibration of a bladed-disk rotor stage were studied. A finite element method was developed for the dynamic and static deformation analysis of the blade. The deformations of a bladed disk and a shrouded-bladed disk were studied by introducing a special bladed-disk element and a special shrouded-blade element. Some features of the vibration of part-span-shrouded, bladed-disk rotor stages are discussed. The static deformation, thermal stress and gas bending effects on the blade vibration were presented previously.
Chen, L.-T.↗
Energy loss by resonance line photons in an absorbing medium
The mean path length of photons undergoing repeated scatterings in media of large optical thickness is calculated from accurate numerical solutions of the transfer equation including the effect of frequency redistribution characteristic of combined Doppler and natural broadening. Energy loss by continuous absorption processes, such as ionization or dust absorption, is discussed, and asymptotic scaling laws for the energy loss, the mean path length, and the mean number of scatterings are inferred from the numerical data.
Hummer, D. G.↗
Charged particle concepts for fog dispersion
Charged particle techniques hold promise for dispersing warm fog in the terminal area of commercial airports. This report focuses on features of the charged particle technique which require further study. The basic physical principles of the technique and the major verification experiments carried out in the past are described. The fundamentals of the nozzle operation are given. The nozzle characteristics and the theory of particle charging in the nozzle are discussed, including information from extensive literature on electrostatic precipitation relative to environmental pollution control and a description of some preliminary reported analyses on the jet characteristics and interaction with neighboring jets. The equation governing the transfer of water substances and of electrical charge is given together with a brief description of several semi-empirical, mathematical expressions necessary for the governing equations. The necessary ingredients of a field experiment to verify the system once a prototype is built are described.
Frost, W.↗
Error propagation in the numerical solutions of the differential equations of orbital mechanics
The relationship between the eigenvalues of the linearized differential equations of orbital mechanics and the stability characteristics of numerical methods is presented. It is shown that the Cowell, Encke, and Encke formulation with an independent variable related to the eccentric anomaly all have a real positive eigenvalue when linearized about the initial conditions. The real positive eigenvalue causes an amplification of the error of the solution when used in conjunction with a numerical integration method. In contrast an element formulation has zero eigenvalues and is numerically stable.
Bond, V. R.↗
Algebraic grid generation
The numerical solution of partial differential equations about irregular geometries and with varying characteristic scales has created the need for coordinate systems and associated transformations which reflect both geometric and physical requirements. The process of finding coordinate transformations in discrete representations is called 'grid generation'. The present investigation is concerned with three algebraic grid generation methods. The methods include transfinite interpolation, the multisurface method, and the two-boundary technique. Interpolation formulas, in terms of homotopic mappings and constraints in terms of point positions and/or derivatives are the essential elements of the techniques. The methods are relatively simple to understand, they are explicit and do not require extensive computational effort, and they have a high degree of generality.
Smith, R. E.↗
Viscous relaxation of a compressible spherical shell
Analytical solutions for analyzing viscous relaxation of a compressible mantle to surface loading are developed. Two different models are considered: one in which the density step of the core-mantle boundary is held fixed and the other in which the mass of the earth remains invariant with respect to variations of equation of state parameters. For thermodynamic parameters characteristic of the mantle, relaxation times of the fundamental and first overtone modes change by no more than about 30 percent for degree less than four. For a given initial depression, the ratio between the velocity in the lower mantle and that at the surface is bigger for incompressible models than for compressible models. Eigenfunctions between the two models also differ in appearance throughout the mantle, with the incompressible ones being larger for the second model. These results would suggest that the resolution of mantle viscosity may be impaired by the smaller excitation in the lower mantle due to effects of mantle compressibility.
Li, Guoying↗
A controls engineering approach for analyzing airplane input-output characteristics
An engineering approach for analyzing airplane control and output characteristics is presented. State-space matrix equations describing the linear perturbation dynamics are transformed from physical coordinates into scaled coordinates. The scaling is accomplished by applying various transformations to the system to employ prior engineering knowledge of the airplane physics. Two different analysis techniques are then explained. Modal analysis techniques calculate the influence of each system input on each fundamental mode of motion and the distribution of each mode among the system outputs. The optimal steady state response technique computes the blending of steady state control inputs that optimize the steady state response of selected system outputs. Analysis of an example airplane model is presented to demonstrate the described engineering approach.
Arbuckle, P. Douglas↗
Further applications of a Figure-of-Merit in space missions
A redesigned figure-of-merit (FoM) approach is described with respect to its applications in projects that employ in situ resource utilization (ISRU) and advanced modular engines. The FoM considers long-term effects, reliability of hardware, and risks inherent to new technologies, as well as significant design parameters. A spreadsheet is utilized to describe the FoM by means of key mission characteristics and combinations of the characteristic inputs in terms of precise governing equations. Results of the FoMs for historical and Mars Sample Return (MSR) missions are given for the conventional mission as well as an ISRU mission for the MSR. A detailed description of the most effective Mars mission is presented, showing how different factors affect the FoM. The results demonstrate that the FoM gives quantitative results based on overall mission design, allowing intercomparisons of similar missions. The FoM can be used as a screening parameter by modifying aspects of the mission by means of the R-factor.
Preiss, Bruce↗
A new energy transfer model for turbulent free shear flow
A new model for the energy transfer mechanism in the large-scale turbulent kinetic energy equation is proposed. An estimate of the characteristic length scale of the energy containing large structures is obtained from the wavelength associated with the structures predicted by a weakly nonlinear analysis for turbulent free shear flows. With the inclusion of the proposed energy transfer model, the weakly nonlinear wave models for the turbulent large-scale structures are self-contained and are likely to be independent flow geometries. The model is tested against a plane mixing layer. Reasonably good agreement is achieved. Finally, it is shown by using the Liapunov function method, the balance between the production and the drainage of the kinetic energy of the turbulent large-scale structures is asymptotically stable as their amplitude saturates. The saturation of the wave amplitude provides an alternative indicator for flow self-similarity.
Liou, William W.-W.↗
Modeling of the coupled magnetospheric and neutral wind dynamos
This report summarizes the progress made in the first year of NASA Grant No. NAGW-3508 entitled 'Modeling of the Coupled Magnetospheric and Neutral Wind Dynamos.' The approach taken has been to impose magnetospheric boundary conditions with either pure voltage or current characteristics and solve the neutral wind dynamo equation under these conditions. The imposed boundary conditions determine whether the neutral wind dynamo will contribute to the high-latitude current system or the electric potential. The semi-annual technical report, dated December 15, 1993, provides further detail describing the scientific and numerical approach of the project. The numerical development has progressed and the dynamo solution for the case when the magnetosphere acts as a voltage source has been evaluated completely using spectral techniques. The simulation provides the field-aligned current distribution at high latitudes due to the neutral wind dynamo. A number of geophysical conditions can be simulated to evaluate the importance of the neutral wind dynamo contribution to the field-aligned current system. On average, field-aligned currents generated by the neutral wind dynamo contributed as much as 30 percent to the large-scale field-aligned current system driven by the magnetosphere. A term analysis of the high-latitude neutral wind dynamo equation describing the field aligned current distribution has also been developed to illustrate the important contributing factors involved in the process. The case describing the neutral dynamo response for a magnetosphere acting as a pure current generator requires the existing spectral code to be extended to a pseudo-spectral method and is currently under development.
Thayer, Jeffrey P.↗
On the nonlinear stability of viscous modes within the Rayleigh problem on an infinite flat plate
The stability has been investigated of the unsteady flow past an infinite flat plate when it is moved impulsively from rest, in its own plane. For small times the instantaneous stability of the flow depends on the linearized equations of motion which reduce in this problem to the Orr-Sommerfeld equation. It is known that the flow for certain values of Reynolds number, frequency and wave number is unstable to Tollmien-Schlichting waves, as in the case of the Blasius boundary layer flow past a flat plate. With increase in time, the unstable waves only undergo growth for a finite time interval, and this growth rate is itself a function of time. The influence of finite amplitude effects is studied by solving the full Navier-Stokes equations. It is found that the stability characteristics are markedly changed both by the consideration of the time evolution of the flow, and by the introduction of finite amplitude effects.
Webb, J. C.↗
Modeling of aircraft unsteady aerodynamic characteristics. Part 2: Parameters estimated from wind tunnel data
Aerodynamic equations with unsteady effects were formulated for an aircraft in one-degree-of-freedom, small-amplitude, harmonic motion. These equations were used as a model for aerodynamic parameter estimation from wind tunnel oscillatory data. The estimation algorithm was based on nonlinear least squares and was applied in three examples to the oscillatory data in pitch and roll of 70 deg triangular wing and an X-31 model, and in-sideslip oscillatory data of the High Incidence Research Model 2 (HIRM 2). All three examples indicated that a model using a simple indicial function can explain unsteady effects observed in measured data. The accuracy of the estimated parameters and model verification were strongly influenced by the number of data points with respect to the number of unknown parameters.
Klein, Vladislav↗
On the Stochastic Quantization Method: Characteristics and Applications to Singular Systems
Introducing the generalized Langevin equation, we extend the stochastic quantization method so as to deal with singular dynamical systems beyond the ordinary territory of quantum mechanics. We also show how the uncertainty relation is built up to the quantum mechanical limit with respect to fictitious time, irrespective of its initial value, within the framework of the usual stochastic quantization method.
Kanenaga, Masahiko↗