Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “APPROXIMATIONS”

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 1,603 records · Page 89
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

A Deterministic Interfacial Cyclic Oxidation Spalling Model: Algebraic Approximation, Descriptive Parameters, and Normalized Universal Curve - Part 2

A cyclic oxidation interfacial spalling model has been developed in Part 1. The governing equations have been simplified here by substituting a new algebraic expression for the series (Good-Smialek approximation). This produced a direct relationship between cyclic oxidation weight change and model input parameters. It also allowed for the mathematical derivation of various descriptive parameters as a function of the inputs. It is shown that the maximum in weight change varies directly with the parabolic rate constant and cycle duration and inversely with the spall fraction, all to the 1/2 power. The number of cycles to reach maximum and zero weight change vary inversely with the spall fraction, and the ratio of these cycles is exactly 1:3 for most oxides. By suitably normalizing the weight change and cycle number, it is shown that all cyclic oxidation weight change model curves can be represented by one universal expression for a given oxide scale.

Smialek, James L.↗
NASA NTRS2003

Sub-problem Optimization With Regression and Neural Network Approximators

Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.

Guptill, James D.↗
NASA NTRS2003

Atomistic Modeling of Nanostructures via the BFS Quantum Approximate Method

Ideally, computational modeling techniques for nanoscopic physics would be able to perform free of limitations on the type and number of elements, while providing comparable accuracy when dealing with bulk or surface problems. Computational efficiency is also desirable, if not mandatory, for properly dealing with the complexity of typical nano-strucured systems. A quantum approximate technique, the BFS method for alloys, which attempts to meet these demands, is introduced for the calculation of the energetics of nanostructures. The versatility of the technique is demonstrated through analysis of diverse systems, including multi-phase precipitation in a five element Ni-Al-Ti-Cr-Cu alloy and the formation of mixed composition Co-Cu islands on a metallic Cu(III) substrate.

Bozzolo, Guillermo↗
NASA NTRS1961

Constant Density Approximations for the Flow Behind Axisymmetric Shock Waves

The incompressible rotational flow equations are used to obtain solutions for the flow behind axisymmetric shock waves with conic longitudinal sections. The nonlinear part of the term due to rotation is retained in the analysis. Numerical results for standoff distance and stagnation point velocity gradient are presented for the case in which the shock wave is a paraboloid, a sphere, or an oblate or prolate ellipsoid. A similarity parameter is proposed which correlates approximately the flow behind geometrically similar shock waves at different free-stream conditions.

Munson, Albert G.↗
NASA NTRS2004

Approximate Solution for Choked Flow in Gas Seal Pads

Previous analyses of high pressure seals have considered adiabatic flow with friction but neglected effects of seal rotation. Most of this work analyzed a one-dimensional flow field. This works well to calculate stiffness and leakage of full circular seals, either face seals or annular ring seals. However, it cannot provide accurate results for a rectangular seal pad with its strongly two-dimensional flow field and its reliance on hydrodynamic forces to maintain a full fluid film. On the other hand, solutions of Reynolds lubrication equation have been obtained for the two-dimensional flow in a seal pad. But these solutions do not account for choking which occurs at high seal pressure ratios, nor do they consider the pressure loss that occurs in the entrance region of the flow field. The aim of the present work is to build on the Reynolds equation solution by use of an approximate choked flow analysis. This will account for the pressure losses in the flow entrance region, ensure that fluid velocities remain subsonic, and enable fluid inertial effects within the pad film to be accounted for. Results show that, in general, fluid inertia acts to decrease pad film load capacity and leakage, and increase film stiffness.

Fleming, David P.↗
NASA NTRS2004

Evidence from massive siderite beds for a CO2-rich atmosphere before approximately 1.8 billion years ago

It is generally thought that, in order to compensate for lower solar flux and maintain liquid oceans on the early Earth, methane must have been an important greenhouse gas before approximately 2.2 billion years (Gyr) ago. This is based upon a simple thermodynamic calculation that relates the absence of siderite (FeCO3) in some pre-2.2-Gyr palaeosols to atmospheric CO2 concentrations that would have been too low to have provided the necessary greenhouse effect. Using multi-dimensional thermodynamic analyses and geological evidence, we show here that the absence of siderite in palaeosols does not constrain atmospheric CO2 concentrations. Siderite is absent in many palaeosols (both pre- and post-2.2-Gyr in age) because the O2 concentrations and pH conditions in well-aerated soils have favoured the formation of ferric (Fe3+)-rich minerals, such as goethite, rather than siderite. Siderite, however, has formed throughout geological history in subsurface environments, such as euxinic seas, where anaerobic organisms created H2-rich conditions. The abundance of large, massive siderite-rich beds in pre-1.8-Gyr sedimentary sequences and their carbon isotope ratios indicate that the atmospheric CO2 concentration was more than 100 times greater than today, causing the rain and ocean waters to be more acidic than today. We therefore conclude that CO2 alone (without a significant contribution from methane) could have provided the necessary greenhouse effect to maintain liquid oceans on the early Earth.

Greenhouse Effect↗
NASA NTRS1992

Radiation Transport Around Axisymmetric Blunt Body Vehicles Using a Modified Differential Approximation

A moment method for computing 3-D radiative transport is applied to axisymmetric flows in thermochemical nonequilibrium. Such flows are representative of proposed aerobrake missions. The method uses the P-1 approximation to reduce the governing system of integro-di erential equations to a coupled set of partial di erential equations. A numerical solution method for these equations given actual variations of the radiation properties in thermochemical nonequilibrium blunt body flows is developed. Initial results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

Hartung, Lin C.↗
NASA NTRS1995

Back pain during 6 degrees head-down tilt approximates that during actual microgravity

Astronauts often experience back pain during spaceflight. Retrospectively, Wing et al. (14) found that during spaceflight, 14 of 19 Shuttle crewmembers experienced back pain, which they described as dull (62%), localized to the lower back (50%), and with an intensity of 2 on a 5-point scale. Further, the spine lengthens 4-7 cm in microgravity. Our objective was to compare back pain and spinal lengthening (body height increase) during simulated microgravity (6 degrees head-down tilt, HDT) with the same parameters during actual microgravity. Eight male subjects completed a modified McGill pain questionnaire with intensity graded from zero (no pain) to five (intense and incapacitating pain) each day at 7:00 pm during 2 d pre-HDT control, 16 d HDT, and 1 d post-HDT recovery periods. Also, the subjects' heights were measured each day while supine (control and recovery) and during HDT. Back pain increased from zero (pre-tilt control period) to 2.3 +/- 0.4 at days 1 to 3 of HDT, and was categorized as dull and/or burning pain in subjects' lower backs. Only 2 subjects reported any pain after day 9 of HDT and during recovery. Heights increased 2.1 +/- 0.5 cm by day 3 of HDT and remained at that level until the end of the HDT period. Although spinal lengthening in space is greater than that during HDT, the HDT model approximates the level, type, distribution, and time course of back pain associated with actual microgravity. In the HDT model, pain subsides in intensity when spinal lengthening stops.(ABSTRACT TRUNCATED AT 250 WORDS).

Non-NASA Center↗
NASA NTRS1952

An Approximate Method of Calculating the Deformations of Wings Having Swept, M or W, A, and Swept-Tip Plan Forms

An approximate method of calculating the deformations of wings of uniform thickness having swept, M or W, Delta, and swept-tip plan forms is presented. The method employs an adjustment to the elementary beam theory to account for the effect of the triangular root portion of a swept wing on the deformation of the outboard section of the wing. To demonstrate the general applicability of the method, the modified elementary theory is applied to the more complex M or W, Delta, and swept-tip plan forms as well as to swept plan forms. For the purpose of calculating angles of attack, it is shown that the unmodified elementary beam theory applied to that part of the wing outboard of the root triangle produces satisfactory results. However, for calculating deflections it is necessary to include the effects of the root-triangle deformation.

Zender, George W.↗
NASA NTRS2001

Gamma-Weighted Discrete Ordinate Two-Stream Approximation for Computation of Domain Averaged Solar Irradiance

An algorithm is developed for the gamma-weighted discrete ordinate two-stream approximation that computes profiles of domain-averaged shortwave irradiances for horizontally inhomogeneous cloudy atmospheres. The algorithm assumes that frequency distributions of cloud optical depth at unresolved scales can be represented by a gamma distribution though it neglects net horizontal transport of radiation. This algorithm is an alternative to the one used in earlier studies that adopted the adding method. At present, only overcast cloudy layers are permitted.

Kato, S.↗
NASA NTRS2005

Transient Approximation of SAFE-100 Heat Pipe Operation

Engineers at Los Alamos National Laboratory (LANL) have designed several heat pipe cooled reactor concepts, ranging in power from 15 kWt to 800 kWt, for both surface power systems and nuclear electric propulsion systems. The Safe, Affordable Fission Engine (SAFE) is now being developed in a collaborative effort between LANL and NASA Marshall Space Flight Center (NASA/MSFC). NASA is responsible for fabrication and testing of non-nuclear, electrically heated modules in the Early Flight Fission Test Facility (EFF-TF) at MSFC. In-core heat pipes must be properly thawed as the reactor power starts. Computational models have been developed to assess the expected operation of a specific heat pipe design during start-up, steady state operation, and shutdown. While computationally intensive codes provide complete, detailed analyses of heat pipe thaw, a relatively simple. concise routine can also be applied to approximate the response of a heat pipe to changes in the evaporator heat transfer rate during start-up and power transients (e.g., modification of reactor power level) with reasonably accurate results. This paper describes a simplified model of heat pipe start-up that extends previous work and compares the results to experimental measurements for a SAFE-100 type heat pipe design.

Bragg-Sitton, Shannon M.↗
NASA NTRS2005

An Approximate Ablative Thermal Protection System Sizing Tool for Entry System Design

A computer tool to perform entry vehicle ablative thermal protection systems sizing has been developed. Two options for calculating the thermal response are incorporated into the tool. One, an industry-standard, high-fidelity ablation and thermal response program was integrated into the tool, making use of simulated trajectory data to calculate its boundary conditions at the ablating surface. Second, an approximate method that uses heat of ablation data to estimate heat shield recession during entry has been coupled to a one-dimensional finite-difference calculation that calculates the in-depth thermal response. The in-depth solution accounts for material decomposition, but does not account for pyrolysis gas energy absorption through the material. Engineering correlations are used to estimate stagnation point convective and radiative heating as a function of time. The sizing tool calculates recovery enthalpy, wall enthalpy, surface pressure, and heat transfer coefficient. Verification of this tool is performed by comparison to past thermal protection system sizings for the Mars Pathfinder and Stardust entry systems and calculations are performed for an Apollo capsule entering the atmosphere at lunar and Mars return speeds.

Dec, John A.↗
NASA NTRS1999

Charge integration successive approximation analog-to-digital converter for focal plane applications using a single amplifier

An analog-to-digital converter for on-chip focal-plane image sensor applications. The analog-to-digital converter utilizes a single charge integrating amplifier in a charge balancing architecture to implement successive approximation analog-to-digital conversion. This design requires minimal chip area and has high speed and low power dissipation for operation in the 2-10 bit range. The invention is particularly well suited to CMOS on-chip applications requiring many analog-to-digital converters, such as column-parallel focal-plane architectures.

Zhou, Zhimin↗
NASA NTRS2006

An Approximate Ablative Thermal Protection System Sizing Tool for Entry System Design

A computer tool to perform entry vehicle ablative thermal protection systems sizing has been developed. Two options for calculating the thermal response are incorporated into the tool. One, an industry-standard, high-fidelity ablation and thermal response program was integrated into the tool, making use of simulated trajectory data to calculate its boundary conditions at the ablating surface. Second, an approximate method that uses heat of ablation data to estimate heat shield recession during entry has been coupled to a one-dimensional finite-difference calculation that calculates the in-depth thermal response. The in-depth solution accounts for material decomposition, but does not account for pyrolysis gas energy absorption through the material. Engineering correlations are used to estimate stagnation point convective and radiative heating as a function of time. The sizing tool calculates recovery enthalpy, wall enthalpy, surface pressure, and heat transfer coefficient. Verification of this tool is performed by comparison to past thermal protection system sizings for the Mars Pathfinder and Stardust entry systems and calculations are performed for an Apollo capsule entering the atmosphere at lunar and Mars return speeds.

Dec, John A.↗
NASA NTRS1940

An Approximate Method of Calculation of Relative Humidity Required to Prevent Frosting on Inside of Aircraft Pressure Cabin Windows, Special Report

This report has been prepare in response to a request for information from an aircraft company. A typical example was selected for the presentation of an approximate method of calculation of the relative humidity required to prevent frosting on the inside of a plastic window in a pressure type cabin on a high speed airplane. The results of the study are reviewed.

Jones, Alun R.↗
NASA NTRS2009

Recent Results on "Approximations to Optimal Alarm Systems for Anomaly Detection"

An optimal alarm system and its approximations may use Kalman filtering for univariate linear dynamic systems driven by Gaussian noise to provide a layer of predictive capability. Predicted Kalman filter future process values and a fixed critical threshold can be used to construct a candidate level-crossing event over a predetermined prediction window. An optimal alarm system can be designed to elicit the fewest false alarms for a fixed detection probability in this particular scenario.

Martin, Rodney Alexander↗