Search NASA⌕ Search

SEARCH · Search NASA

Results for “Sample Calculations”

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 19 records

Description of a computer program to calculate reacting supersonic internal flow fields with shock waves using viscous characteristics: Program manual and sample calculations

A computer program for calculating internal supersonic flow fields with chemical reactions and shock waves typical of supersonic combustion chambers with either wall or mid-stream injectors is described. The usefulness and limitations of the program are indicated. The program manual and listing are presented along with a sample calculation.

Cavalleri, R. J.↗

Probabilistic Requirements (Partial) Verification Methods Best Practices Improvement. Variables Acceptance Sampling Calculators: Empirical Testing

The NASA Engineering and Safety Center was requested to improve on the Best Practices document produced for the NESC assessment, Verification of Probabilistic Requirements for the Constellation Program, by giving a recommended procedure for using acceptance sampling by variables techniques as an alternative to the potentially resource-intensive acceptance sampling by attributes method given in the document. In this paper, the results of empirical tests intended to assess the accuracy of acceptance sampling plan calculators implemented for six variable distributions are presented.

Johnson, Kenneth L.↗

Probabilistic Requirements (Partial) Verification Methods Best Practices Improvement. Variables Acceptance Sampling Calculators: Derivations and Verification of Plans

The NASA Engineering and Safety Center was requested to improve on the Best Practices document produced for the NESC assessment, Verification of Probabilistic Requirements for the Constellation Program, by giving a recommended procedure for using acceptance sampling by variables techniques. This recommended procedure would be used as an alternative to the potentially resource-intensive acceptance sampling by attributes method given in the document. This document contains the outcome of the assessment.

Johnson, Kenneth L.↗

Attenuation of sound in ducts with acoustic treatment: A generalized approximate equation

A generalized approximate equation for duct lining sound attenuation is presented. The specification of two parameters, the maximum possible attenuation and the optimum wall acoustic impedance is shown to completely determine the sound attenuation for any acoustic mode at any selected wall impedance. The equation is based on the nearly circular shape of the constant attenuation contours in the wall acoustic impedance plane. For impedances far from the optimum, the equation reduces to Morse's approximate expression. The equation can be used for initial acoustic liner design. Not least important is the illustrative nature of the solutions which provide an understanding of the duct propagation problem usually obscured in the exact calculations. Sample calculations using the approximate attenuation equation show that the peak and the bandwidth of the sound attenuation spectrum can be represented by quite simple functions of the ratio of actual wall acoustic resistance to optimum resistance.

Rice, E. J.↗

Attenuation of sound in ducts with acoustic treatment - A generalized approximate equation

A generalized approximate equation for duct lining sound attenuation is presented. The specification of two parameters, the maximum possible attenuation and the optimum wall acoustic impedance is shown to completely determine the sound attenuation for any acoustic mode at any selected wall impedance. The equation is based on the nearly circular shape of the constant attenuation contours in the wall acoustic impedance plane. For impedances far from the optimum, the equation reduces to Morse's approximate expression. The equation can be used for initial acoustic liner design. Not least important is the illustrative nature of the solutions which provide an understanding of the duct propagation problem usually obscured in the exact calculations. Sample calculations using the approximate attenuation equation show that the peak and the bandwidth of the sound attenuation spectrum can be represented by quite simple functions of the ratio of actual wall acoustic resistance to optimum resistance.

Rice, E. J.↗

Theory of the optimally coupled Q-switched laser

The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.

Degnan, John J.↗

Computational methodology for radiation heat transfer in the flowfield of an AOTV

A computational methodology is developed for the calculation of radiation heat transfer in a non-scattering medium where nonequilibrium conditions exist and give rise to complex spectra. The specific problem of radiation in an aeroassisted orbital transfer vehicle (AOTV) flowfield is addressed. Nonequilibrium radiation from the gases around a hypersonic vehicle is evaluated using the NASA-Ames NEQAIR program together with a three-dimensional geometrical flowfield model. Nonequilibrium compositions and temperatures are taken from NASA-Langley 3-D hypersonic flowfield calculations that include real-gas effects and finite-rate chemical kinetics. It is shown that the concept of a transmission path adjustment, together with precomputations of curves of growth based upon local properties at flowfield locations, facilitates radiation calculations. Sample calculations of directional and spectral distributions of gas radiation received upon a hypersonic vehicle are presented.

Fuehrer, P. L.↗

A Flight Investigation of Exhaust-heat De-icing

The National Advisory Committee for Aeronautics conducted exhaust-heat de-icing tests in flight to provide data needed in the application of this method. The capacity to extract heat from the exhaust gas for de-icing purposes, the quantity of heat required, and other factors were examined. The results indicate that a wing-heating system employing a spanwise exhaust tube within the leading edge of the wing removed 30 to 35 percent of the heat from exhaust gas entering the wing. Data are given from which the heat required for ice prevention can be calculated. Sample calculations have been made on the basis of existing engine power/wing area ratios to show that sufficient heating can be obtained for ice protection on modern transportation airplanes, provided that uniform distribution of the heat can be secured.

Jones, Alun R↗

A Flight Investigation of Exhaust-Heat De-Icing, Special Report

The National Advisory Committee for Aeronautics has conducted exhaust-heat de-icing tests inflight t o provide data needed in the application of this method of ice prevention. Thc capacity to extract heat from the exhaust gas for de-icing purposes, the quantity of heat required, and other factors were examined. The results indicate that a wing-heating system employing a spanwise exhaust tube within the leading edge of the wing will make available for de-icing purposes between 30 and 35 percent of the exhaust-gas heat. Data are given by which the heat required for ice prevention can be calculated. Sample calculations have been made, on a basis of existing engine power over wing area ratios, to show that sufficient heating can be obtained for ice protection on modern transport airplanes,

Rodert, Lewis A.↗

Rates of elementary reactions - Measurement and applications

Techniques used for characterizing elementary chemical reaction kinetics are explored. Flash- or laser-photolysis (FP) involves producing reactive species on the psec time scale and monitoring the changes spectroscopically. In the discharge flow (DF) method, reactive species are produced continuously in a flow of an inert gas containing the reactants. FP avoids surface and transport effects, while DF allows several reactions to be studied in different regions of one flow. Transport and surface boundary layer models are defined for DF calculations and sample calculations are carried out to illustrate the difficulties inherent in theoretically defining the rate constants for elementary reactions. Applications of the models thus far derived in atmospheric science and combustion studies are discussed.

Kaufman, F.↗

Measurement of the O18 to O16 isotope ratio for characterizing oxide surface layers on LDEF samples

Calculations indicate that measurement of the O-16 to O-18 isotope ratio in oxide layers formed on the surfaces of the Long Duration Exposure Facility (LDEF) samples would provide a powerful tool for distinguishing between layers formed at high altitudes and layers formed at low altitudes, as for example during the retrieval of a satellite. In principle, this ratio may be used to date the formation of the oxide layers.

Sagalyn, Paul L.↗

A numerical method for the exact calculation of airloads associated with impulsively started wings

A numerical method is developed to calculate three-dimensional potential flows due to the steady and impulsive motion of isolated wing and wing-wing interaction problems. The velocity potential is represented by a discrete set of constant-doublet quadrilaterals on wing and wake surfaces. The exact surface boundary condition is enforced, and the solution is obtained in a step-by-step fashion, configurations being impulsively started from rest. Free-wake geometries are generated for each time step with Rankine or Lamb viscous vortex segments used in wake-velocity calculations. Sample results include calculated performance to steady state for a thick wing and indicial lift of a wing-wing interaction problem.

Summa, J. M.↗

Diffracted and head waves associated with waves on nonseparable surfaces

A theory is presented for computing waves radiated from waves on a smooth surface. With the assumption that attention of the surface wave is due only to radiation and not to dissipation in the surface material, the radiation coefficient is derived in terms of the attenuation factor. The excitation coefficient is determined by the reciprocity condition. Formulas for the shape and the spreading of the radiated wave are derived, and some sample calculations are presented. An investigation of resonant phase matching for nonseparable surfaces is presented with a sample calculation. A discussion of how such calculations might be related to resonant frequencies of nonseparable thin shell structures is included. A description is given of nonseparable surfaces that can be modeled in the vector that facilitates use of the appropriate formulas of differential geometry.

Barger, Raymond L.↗

Charge-exchange plasma generated by an ion thruster

The charge exchange plasma generated by an ion thruster was investigated experimentally using both 5 cm and 15 cm thrusters. Results are shown for wide ranges of radial distance from the thruster and angle from the beam direction. Considerations of test environment, as well as distance from the thruster, indicate that a valid simulation of a thruster on a spacecraft was obtained. A calculation procedure and a sample calculation of charge exchange plasma density and saturation electron current density are included.

Kaufman, H. R.↗

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Glass, Christopher E.↗

Aerothermodynamics of Pyrolizing Surfaces in Hypersonic Rarefied Flows

Direct simulation Monte Carlo (DSMC) calculations of rarefied flows about entry bodies typically employ a fixed surface temperature or a radiative-equilibrium energy balance to compute that temperature. Such boundary conditions neglect any effects of heat capacitance and heat conduction in the spacecraft heat shield and, therefore, provide an upper bound for the surface temperature. Such calculations also neglect pyrolysis from the heat shield which can be significant for a high-energy incident flow at very low densities. Accurate prediction of both heating and aerodynamic forces requires including pyrolysis and surface heat transfer in the models for gas-surface interaction employed in DSMC methods. Although these physical models have long appeared in various continuum flow calculation codes, they have only recently appeared in DSMC codes which are required to simulate rarefied flows during entry at high altitudes. In the current implementation, routines from the widely distributed Charring Material Thermal Response and Ablation (CMA) program are coupled into a DSMC code to calculate the one-dimensional heat transfer into the carbon phenolic heat shield at each point on a vehicle surface. Temperature-dependent material properties, surface re-radiation, and in-depth pyrolysis were included in the calculation, but surface ablation was neglected. Sample calculations for entry of the Galileo probe into the atmosphere of Jupiter demonstrate that including pyrolysis in the model leads to significant differences in predicted aerodynamics. Granted, the drag coefficient does not depend strongly on the surface temperature which can itself be significantly below the radiative equilibrium value during entry. However, the surface mass flux due to pyrolysis of the material is significant once the probe drops to altitudes characterized by transition flow. This leads to a noticeable increase in drag and a decrease in heating compared to a body without pyrolysis.

Haas, Brian L.↗

Free-stream disturbances, continuous eigenfunctions, boundary-layer instability and transition

A rational foundation is provided for the application of the linear stability theory of parallel shear flows to transition prediction. An explicit method is given for carrying out the necessary calculations. The expansions are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbance in the inner boundary layer near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer, in that the amplitudes of the discrete Tollmein-Schlichting waves are an extremely small fraction of the amplitude of the disturbance.

Salwen, H.↗

Free-stream disturbance, continuous Eigenfunctions, boundary-layer instability and transition

A rational foundation is presented for the application of the linear shear flows to transition prediction, and an explicit method is given for carrying out the necessary calculations. The expansions used are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbances in the inner boundary layer, near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer in that the amplitudes of the discrete Tollmien-Schlicting waves are an extremely small fraction of the amplitude of the disturbance.

Grosch, C. E.↗