Search NASA⌕ Search

SEARCH · Search NASA

Results for “Curve fitting”

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 199 records · Page 11

Development of a computer code for calculating the steady super/hypersonic inviscid flow around real configurations. Volume 1: Computational technique

A numerical procedure has been developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second order accurate finite difference scheme is used to integrate the three dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.

Marconi, F.↗

Development of a computer code for calculating the steady super/hypersonic inviscid flow around real configurations. Volume 2: Code description

A numerical procedure was developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.

Marconi, F.↗

Development of a solid propellant viscoelastic dynamic model

The results of a one year study to develop a dynamic response model for the Space Shuttle Solid Rocket Motor (SRM) propellant are presented. An extensive literature survey was conducted, from which it was concluded that the only significant variables affecting the dynamic response of the SRM propellant are temperature and frequency. Based on this study, and experimental data on propellants related to the SRM propellant, a dynamic constitutive model was developed in the form of a simple power law with temperature incorporated in the form of a modified power law. A computer program was generated which performs a least-squares curve-fit of laboratory data to determine the model parameters and it calculates dynamic moduli at any desired temperature and frequency. Additional studies investigated dynamic scaling laws and the extent of coupling between the SRM propellant and motor cases. It was found, in agreement with other investigations, that the propellant provides all of the mass and damping characteristics whereas the case provides all of the stiffness.

Hufferd, W. L.↗

Correlations for determining thermodynamic properties of hydrogen-helium gas mixtures at temperatures from 7,000 to 35,000 K

Simple relations for determining the enthalpy and temperature of hydrogen-helium gas mixtures were developed for hydrogen volumetric compositions from 1.0 to 0.7. These relations are expressed as a function of pressure and density and are valid for a range of temperatures from 7,000 to 35,000 K and pressures from 0.10 to 3.14 MPa. The proportionality constant and exponents in the correlation equations were determined for each gas composition by applying a linear least squares curve fit to a large number of thermodynamic calculations obtained from a detailed computer code. Although these simple relations yielded thermodynamic properties suitable for many engineering applications, their accuracy was improved significantly by evaluating the proportionality constants at postshock conditions and correlating these values as a function of the gas composition and the product of freestream velocity and shock angle. The resulting equations for the proportionality constants in terms of velocity and gas composition and the corresponding simple realtions for enthalpy and temperature were incorporated into a flow field computational scheme. Comparison was good between the thermodynamic properties determined from these relations and those obtained by using a detailed computer code to determine the properties. Thus, an appreciable savings in computer time was realized with no significant loss in accuracy.

Zoby, E. V.↗

RTLS entry load relief parameter optimization

The results are presented of a study of a candidate load relief control law for use during the pullup phase of Return-to-Launch-Site (RTLS) abort entries. The control law parameters and cycle time which optimized performance of the normal load factor limiting phase (load relief phase) of an RTLS entry are examined. A set of control law gains, a smoothing parameter, and a normal force coefficient curve fit are established which resulted in good load relief performance considering the possible aerodynamic coefficient uncertainties defined. Also, the examination of various guidance cycle times revealed improved load relief performance with decreasing cycle time. A .5 second cycle provided smooth and adequate load relief in the presence of all the aerodynamic uncertainties examined.

Crull, T. J.↗

Results of the asteroid-meteoroid particle experiment on Pioneer 11

The Asteroid-Meteoroid Detector, an electro-optical instrument that detects and measures particles in space by sensing the sunlight reflected from them, is part of the payload of both the Pioneer 10 and 11 spacecraft. The Pioneer 11 instrument is essentially identical to that on Pioneer 10, with some minor modifications. Reduction of the Pioneer 11 data was complicated by the failure of one of the four sensor channels at about 1.1 AU from the sun. Detailed analysis yielded 51 events between 1.0 and 3.5 AU, which were used to determine the particle concentration distribution in that region of space. Weighted curve-fitting of the results shows agreement with the concentrations derived from Pioneer 10 to within about a factor of two. As with the Pioneer 10 results, the exponent of the size dependency varies from about -1.7 for 100-micron radius particles to about -3.2 for 10-cm bodies. The instrument, its operation, and the method of data analysis are reviewed.

Soberman, R. K.↗

Some new results on the statistics of radio wave scintillation. I - Empirical evidence for Gaussian statistics

This paper presents an analysis of ionospheric scintillation data which shows that the underlying statistical structure of the signal can be accurately modeled by the additive complex Gaussian perturbation predicted by the Born approximation in conjunction with an application of the central limit theorem. By making use of this fact, it is possible to estimate the in-phase, phase quadrature, and cophased scattered power by curve fitting to measured intensity histograms. By using this procedure, it is found that typically more than 80% of the scattered power is in phase quadrature with the undeviated signal component. Thus, the signal is modeled by a Gaussian, but highly non-Rician process. From simultaneous UHF and VHF data, only a weak dependence of this statistical structure on changes in the Fresnel radius is deduced. The signal variance is found to have a nonquadratic wavelength dependence. It is hypothesized that this latter effect is a subtle manifestation of locally homogeneous irregularity structures, a mathematical model proposed by Kolmogorov (1941) in his early studies of incompressible fluid turbulence.

Rino, C. L.↗

Numerical determination of the transmissibility characteristics of a squeeze film damped forced vibration system

Numerical solutions of the governing equations of motion of a liquid squeeze film damped forced vibration system were carried out to examine the feasibility of using a liquid squeeze film to cushion and protect large structures, such as buildings, located in areas of high seismic activity. The mathematical model used was that for a single degree of freedom squeeze film damped spring mass system. The input disturbance was simulated by curve fitting actual seismic data with an eleventh order Lagranging polynomial technique. Only the normal component of the seismic input was considered. The nonlinear, nonhomogeneous governing differential equation of motion was solved numerically to determine the transmissibility over a wide range of physical parameters using a fourth-order Runge-Kutta technique. It is determined that a liquid squeeze film used as a damping agent in a spring-mass system can significantly reduce the response amplitude for a seismic input disturbance.

Sutton, M. A.↗

Outdoor performance results for NBS Round Robin collector no. 1

The efficiency of a PPG flat-plate solar collector was evaluated utilizing an outdoor solar collector test facility at the NASA-Lewis Research Center, as part of the National Bureau of Standards 'round robin' collector test program. The correlation equation for collector thermal efficiency Eta curve fit of the data was: Eta = 0.666 - 1.003(Btu/hr-sq ft-F) Theta, where the parameter Theta is the difference between the average fluid temperature and the ambient temperature, all divided by the total flux impinging on the collector.

Miller, D. R.↗

A Remotely Operated Multiple Array Acoustic Range (ROMAAR) and its application for the measurement of airplane flyover noise footprints

The ROMAAR now in operation at NASA will allow direct measurement and display of aircraft noise in several measurement units during takeoff, landing, and flyby operations. This information, in addition to its application in terms of ground noise footprints, will also permit determination of the statistical variation of footprints or contours due to the atmosphere or aircraft operational parameters, and a measure of the impact of various noise reduction techniques and hardware on ground noise footprints. The methods, techniques, and equipment developed for the ROMAAR concept are applicable to CTOL, STOL, General Aviation, and VTOL aircraft. ROMAAR represents a unique combination of state of the art digital and analog noise recording methods, computer-controlled digital communications methods, radar-tracking facilities, quick-look weather capabilities, and a large data handling facility complemented by a large capacity curve fitting and plotting routine. The ROMAAR is set apart from the standard airport noise monitoring system by having the unique features mentioned above plus the fact that at present as many as 38 separate (but simultaneous) noise measurements can be made for each aircraft overflight.

Hilton, D. A.↗

Transient excitation and data processing techniques employing the fast fourier transform for aeroelastic testing

The development of testing techniques useful in airplane ground resonance testing, wind tunnel aeroelastic model testing, and airplane flight flutter testing is presented. Included is the consideration of impulsive excitation, steady-state sinusoidal excitation, and random and pseudorandom excitation. Reasons for the selection of fast sine sweeps for transient excitation are given. The use of the fast fourier transform dynamic analyzer (HP-5451B) is presented, together with a curve fitting data process in the Laplace domain to experimentally evaluate values of generalized mass, model frequencies, dampings, and mode shapes. The effects of poor signal to noise ratios due to turbulence creating data variance are discussed. Data manipulation techniques used to overcome variance problems are also included. The experience is described that was gained by using these techniques since the early stages of the SST program. Data measured during 747 flight flutter tests, and SST, YC-14, and 727 empennage flutter model tests are included.

Jennings, W. P.↗

Indirect synthesis of multidegree-of-freedom transient systems

The indirect synthesis method is developed and shown to be capable of leading a near-optimal design of multidegree-of-freedom and multidesign-element transient nonlinear dynamical systems. The basis of the approach is to select the open design parameters such that the response of the portion of the system being designed approximates the limiting performances solution. The limiting performance problem can be formulated as one of linear programming by replacing all portions of the system subject to transient disturbances by control forces and supposing that the remaining portions are linear as are the overall kinematic constraints. One then selects the design parameters that respond most closely to the limiting performance solution, which can be achieved by unconstrained curve-fitting techniques.

Chen, Y. H.↗

A new approach to the pulsed thermocouple for high gas temperature measurements

Pulsed thermocouple systems can be used to measure gas temperatures above the melting point of the thermocouple by various techniques of short term or intermittent exposure of the thermocouple operating at lower temperatures. This paper describes an approach which uses a thermocouple cooled by a small jet of inert gas. When a measurement is to be made, the cooling jet is turned off and the thermocouple allowed to heat up to near its melting point, at which time the cooling is reapplied. The final temperature which the thermocouple should have attained is then calculated by extrapolating an exponential curve fit to the data. Temperature measurements can be recorded and displayed in near real time by using modern high-speed computing systems to perform these calculations. Examples of the technique applied to high temperature jet engine combustor development are presented.

Glawe, G. E.↗

Emittance and absorptance of NASA ceramic thermal barrier coating system

Spectral emittance measurements were made on a two-layer ceramic thermal barrier coating system consisting of a metal substrate, a NiCrAly bond coating and a yttria-stabilized zirconia ceramic coating. Spectral emittance data were obtained for the coating system at temperatures of 300 to 1590 K, ceramic thickness of zero to 0.076 centimeter, and wavelengths of 0.4 to 14.6 micrometers. The data were transformed into total hemispherical emittance values and correlated with respect to ceramic coating thickness and temperature using multiple regression curve fitting techniques. The results show that the ceramic thermal barrier coating system is highly reflective and significantly reduces radiation heat loads on cooled gas turbine engine components. Calculation of the radiant heat transfer within the nonisothermal, translucent ceramic coating material shows that the gas-side ceramic coating surface temperature can be used in heat transfer analysis of radiation heat loads on the coating system.

Liebert, C. H.↗

Silicon solar cells from transition metal doped Czochralski and web crystals

The influence of metallic impurities on solar cell characteristics has been examined to establish the cost sensitive purity versus performance trade-offs. Solar cells were fabricated on 2 to 4 ohm-cm p-type substrates obtained by Czochralski and dendritic web growth processes. Controlled amounts of metallic impurities were introduced into the melt during growth and included Fe, Cr, Mn, Ni, Cu, Ti, V, Zr, Mg, Zn, and Al. Impurity concentrations in the crystals were determined using emission and mass spectrographic techniques and in some cases by neutron activation analysis. The solar cells were characterized by means of a computer program to curve-fit measured voltage-current data. The principal effect of the added impurities is a degradation of lifetime and diffusion length.

Davis, J. R.↗

An optimal Space Shuttle ascent trajectory for the first orbital flight test

An optimal solution of the ascent trajectory of the Space Shuttle for the first orbital flight test is presented; the optimization is a minimum propellant, four-control problem in yaw angle, roll angle, pitch angle and vacuum thrust of each Space Shuttle main engine. Piecewise linear segments with juncture points treated as parameters are employed to model the controls. Equations of motion for a three-dimensional flight with pitch plane moment balance about an oblate are integrated numerically with a fourth-order Runge-Kutta method; two- and one-dimensional cubic spline function curve fits of aerodynamic coefficients are used during the first and second stages, respectively. The constraint minimization problem is solved with the Davidon-Fletcher-Powell function method.

Johnson, I. L., Jr.↗

AAA gunnermodel based on observer theory

The Luenberger observer theory is used to develop a predictive model of a gunner's tracking response in antiaircraft artillery systems. This model is composed of an observer, a feedback controller and a remnant element. An important feature of the model is that the structure is simple, hence a computer simulation requires only a short execution time. A parameter identification program based on the least squares curve fitting method and the Gauss Newton gradient algorithm is developed to determine the parameter values of the gunner model. Thus, a systematic procedure exists for identifying model parameters for a given antiaircraft tracking task. Model predictions of tracking errors are compared with human tracking data obtained from manned simulation experiments. Model predictions are in excellent agreement with the empirical data for several flyby and maneuvering target trajectories.

Kou, R. S.↗

An improved supersonic, three-dimensional, external, inviscid flow field code

A numerical procedure was developed to compute the inviscid super/hypersonic flow fields about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects for equilibrium air are included using curve fits of Mollier charts. This report deals only with modifications to these procedures in four specific areas: inlet mass ingestion, subsonic axial Mach number, improved conformal mappings, and vehicles flying at yaw. In each area both the modifications to the computational procedures and computer code are discussed.

Marconi, F.↗