Some analytic solutions to the linearized Boltzmann equation with the ellipsoidal model
Linearized Boltzmann equation analytic solutions for rarefied gas dynamic problems, using ellipsoid model
Giddens, D. P.↗
SEARCH · Engineering Papers
Results for “Linear Models”
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.
An analytically linearized helicopter model with improved modeling accuracy
An analytically linearized model for helicopter flight response including rotor blade dynamics and dynamic inflow, that was recently developed, was studied with the objective of increasing the understanding, the ease of use, and the accuracy of the model. The mathematical model is described along with a description of the UH-60A Black Hawk helicopter and flight test used to validate the model. To aid in utilization of the model for sensitivity analysis, a new, faster, and more efficient implementation of the model was developed. It is shown that several errors in the mathematical modeling of the system caused a reduction in accuracy. These errors in rotor force resolution, trim force and moment calculation, and rotor inertia terms were corrected along with improvements to the programming style and documentation. Use of a trim input file to drive the model is examined. Trim file errors in blade twist, control input phase angle, coning and lag angles, main and tail rotor pitch, and uniform induced velocity, were corrected. Finally, through direct comparison of the original and corrected model responses to flight test data, the effect of the corrections on overall model output is shown.
Jensen, Patrick T.↗
Generation of linear dynamic models from a digital nonlinear simulation
The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.
Daniele, C. J.↗
The linear star model and dynamical instability.
Pulsation properties of star models with linear density distribution, considering radial, adiabatic contraction and dynamical stability
DENSITY DISTRIBUTION↗
A linear stochastic model of the human operator
A linear stochastic model of the human operator is developed and applied to the problem of piloted control of an aircraft. The pilot and aircraft are modeled as linear time-invariant systems containing both process and measurement noise. The loop closure by the pilot is determined by formulating the problem as an optimal stochastic control problem. The solution to the optimal control problem yields not only the pilot's optimal control output which he uses to control the vehicle, but also the optimal combination of his observations of the vehicle states upon which the pilot bases his control. A method is presented so that, using experimental pilot vehicle data, the cost functional which is minimized in the optimal control problem will be numerically equal to the pilot rating that the pilot would associate with the given vehicle and task.
Durrett, J. C.↗
Linear and non-linear dynamic models of a geared rotor-bearing system
A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.
Kahraman, Ahmet↗
Black-box models for linear integrated circuits
Black box modeling of linear integrated circuits for computer analysis in frequency domain
Murray-Lasso, M. A.↗
Improved analytic longitudinal response analysis for axisymmetric launch vehicles. Volume I - Linear analytic model
Improved analytic longitudinal response analysis for axisymmetric launch vehicles - linear model
AXISYMMETRIC BODY↗
Transition Analysis for the CRM-NLF Wind Tunnel Configuration using Transport Equation Models and Linear Stability Correlations
Transition models based on auxiliary transport equations augmenting the Reynolds-averaged Navier-Stokes (RANS) framework rely upon transition correlations that were derived from a limited number of low-speed experiments. Furthermore, these models often account for only a subset of the relevant transition mechanisms and/or cannot accurately predict the sensitivity of those mechanisms to the changes in significant flow parameters. A preceding investigation had targeted the assessment of the transport-equation-based transition models in NASA's OVERFLOW 2.3b solver, namely, the amplification factor transport (AFT-2017b) equation model coupled with the Spalart-Allmaras RANS model and the Langtry-Menter transition models (LM2009 without crossflow effects and LM2015 including the modeling of crossflow transition) implemented with Menter’s shear-stress transport equation (SST2003) RANS model. Comparisons with recent measurements at transonic freestream conditions on the Common Research Model with Natural Laminar Flow (CRM-NLF) reinforced our earlier finding that all three of the above models significantly underpredict the reported extent of the laminar flow region over the entire span of the wing, regardless of the dominant instability mechanism(s) underlying the onset of the transition process. The underprediction of the laminar flow extent was attributed to the failure of the above models in accounting for the stabilizing effect of compressibility on the amplification of Tollmien-Schlichting instabilities. Based on previous linear stability studies related to compressibility effects, the present work proposes modifications to the two classes of transition models that reduce to the original form of each model at low subsonic speeds and do not require any nonlocal flow information or additional transport equation(s). The modifications are shown to significantly improve the predicted laminar extent of the flow and compare well against the data from the CRM-NLF experiment. Additionally, a previous assessment of transition prediction based on the dual, nonparallel N -factor method in conjunction with linear parabolized stability equations (PSE) is extended to additional angles of attack to provide the first comprehensive assessment of transition models based on nonparallel disturbance amplification over the CRM-NLF. In general, the transition criterion based on the dual, nonparallel N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at R eMAC = 15 million for all angles of attack investigated herein and provides additional validation of the improved predictions from the compressibility-corrected transition models.
CFD modeling↗
Transition Analysis for the CRM-NLF Wind Tunnel Configuration using Transport Equation Models and Linear Stability Correlations
Transition models based on auxiliary transport equations augmenting the Reynolds-averaged Navier-Stokes (RANS) framework rely upon transition correlations that were derived from a limited number of low-speed experiments. Furthermore, these models often account for only a subset of the relevant transition mechanisms and/or cannot accurately predict the sensitivity of those mechanisms to the changes in significant flow parameters. A preceding investigation had targeted the assessment of the transport-equation-based transition models in NASA's OVERFLOW 2.3b solver, namely, the amplification factor transport (AFT-2017b) equation model coupled with the Spalart-Allmaras RANS model and the Langtry-Menter transition models (LM2009 without crossflow effects and LM2015 including the modeling of crossflow transition) implemented with Menter’s shear-stress transport equation (SST2003) RANS model. Comparisons with recent measurements at transonic freestream conditions on the Common Research Model with Natural Laminar Flow (CRM-NLF) reinforced our earlier finding that all three of the above models significantly underpredict the reported extent of the laminar flow region over the entire span of the wing, regardless of the dominant instability mechanism(s) underlying the onset of the transition process. The underprediction of the laminar flow extent was attributed to the failure of the above models in accounting for the stabilizing effect of compressibility on the amplification of Tollmien-Schlichting instabilities. Based on previous linear stability studies related to compressibility effects, the present work proposes modifications to the two classes of transition models that reduce to the original form of each model at low subsonic speeds and do not require any nonlocal flow information or additional transport equation(s). The modifications are shown to significantly improve the predicted laminar extent of the flow and compare well against the data from the CRM-NLF experiment. Additionally, a previous assessment of transition prediction based on the dual, nonparallel N -factor method in conjunction with linear parabolized stability equations (PSE) is extended to additional angles of attack to provide the first comprehensive assessment of transition models based on nonparallel disturbance amplification over the CRM-NLF. In general, the transition criterion based on the dual, nonparallel N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at R eMAC = 15 million for all angles of attack investigated herein and provides additional validation of the improved predictions from the compressibility-corrected transition models.
CFD modeling↗
Modeling of linear time-varying systems by linear time-invariant systems of lower order.
A method for modeling linear time-varying differential systems by linear time-invariant systems of lower order is proposed, extending the results obtained by Bierman (1972) by resolving such qualities as the model stability, various possible models of differing dimensions, and the uniqueness or nonuniqueness of the model coefficient matrix. In addition to the advantages cited by Heffes and Sarachik (1969) and Bierman, often by modeling a subsystem of a larger system it is possible to analyze the overall system behavior more easily, with resulting savings in computation time.
Nosrati, H.↗
Linear simulation of the stationary eddies in a GCM. II - The 'Mountain' model
Linear stationary wave theory is used to account for zonal asymmetries of the winter-averaged tropospheric circulation obtained in a GCM. The eddy zonal velocity field in the upper troposphere indicates that the orographic and thermal plus transient contributions are nearly equal in amplitude, while the eddy meridional velocity field (which is dominated by shorter zonal scales) shows the orographic contribution to be dominant. The two contributions are found to be roughly in phase over the east Asian coast, and they contribute roughly equal amounts to the low level Siberian high. Results indicate that the 300 mb extratropical response to tropical forcing reaches 50 gpm over Alaska, and that the responses to sensible heating and lower tropospheric transients are strongly anticorrelated.
Nigam, Sumant↗
B-737 Linear Autoland Simulink Model
The Linear Autoland Simulink model was created to be a modular test environment for testing of control system components in commercial aircraft. The input variables, physical laws, and referenced frames used are summarized. The state space theory underlying the model is surveyed and the location of the control actuators described. The equations used to realize the Dryden gust model to simulate winds and gusts are derived. A description of the pseudo-random number generation method used in the wind gust model is included. The longitudinal autopilot, lateral autopilot, automatic throttle autopilot, engine model and automatic trim devices are considered as subsystems. The experience in converting the Airlabs FORTRAN aircraft control system simulation to a graphical simulation tool (Matlab/Simulink) is described.
Belcastro, Celeste↗
Modeling of linear isentropic flow systems
A modeling approach for linear isentropic flow systems based on the quasi-one-dimensional Euler equations of non-viscous, compressible flow are presented. Such systems are representative of certain high speed propulsion systems. Accurate models useful in control system studies are developed. A supersonic inlet is considered, and the resulting set of partial differential equations with boundary conditions is solved for a linear transfer matrix using Laplace transforms.
Sarantopoulos, Athan D.↗
Modeling of linear isentropic flow systems
A modeling approach for linear isentropic flow systems based on the quasi-one-dimensional Euler equations of non-viscous, compressible flow are presented. Such systems are representative of certain high speed propulsion systems. Accurate models useful in control system studies are developed. A supersonic inlet is considered, and the resulting set of partial differential equations with boundary conditions is solved for a linear transfer matrix using Laplace transforms.
Sarantopoulos, Athan D.↗
A componential model of human interaction with graphs: 1. Linear regression modeling
Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.
Gillan, Douglas J.↗
Numerical derivation of linear perturbation model from nonlinear real-time vehicle simulations - A means of validation and increased credibility
A numerical technique has been developed which generates linear perturbation models from nonlinear real-time aircraft vehicle simulations at Langley Research Center. The technique is very general and can be applied to simulations of any system described by nonlinear differential equations. Linear models about various trim conditions have been obtained from simulations of the Boeing 737, Northrop F5-E, Cessna 180, Sikorsky CH-54, and NASA/Army Rotor Systems Research Aircraft (RSRA). One use of the derived linear models is as a validation and verification tool for the nonlinear simulation.
Dieudonne, J. E.↗
Wavefront Sensing for WFIRST with a Linear Optical Model
In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.
Jurling, Alden S.↗