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Results for “Analytic linearization”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

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.↗
NASA NTRS2008

On the Development of Parameterized Linear Analytical Longitudinal Airship Models

In order to explore Titan, a moon of Saturn, airships must be able to traverse the atmosphere autonomously. To achieve this, an accurate model and accurate control of the vehicle must be developed so that it is understood how the airship will react to specific sets of control inputs. This paper explains how longitudinal aircraft stability derivatives can be used with airship parameters to create a linear model of the airship solely by combining geometric and aerodynamic airship data. This method does not require system identification of the vehicle. All of the required data can be derived from computational fluid dynamics and wind tunnel testing. This alternate method of developing dynamic airship models will reduce time and cost. Results are compared to other stable airship dynamic models to validate the methods. Future work will address a lateral airship model using the same methods.

aerobot↗
NASA NTRS1984

The dynamic fission instability and the origin of the Moon

A theory for the formation of the Moon which involves the dynamic fission of a rapidly rotating protoplanet, which might then result in the formation of the Earth and the Moon is discussed. The fission hypothesis was originally based on analytic, linearized models of the growth of asymmetry in homogenous bodies. The fully nonlinear evolution of the dynamic instability in inviscid, compressible bodies was calculated by numerical techniques. It was found that the dynamic instability degenerates into the ejection of a ring of matter with a substantial fraction of the mass, leaving behind a central body with most of the mass. The linearized analytical approach and the numerical approach were used to show that dynamic fission probably does not occur in rocky protoplanets. The numerical calculations are performed with a fully three dimensional hydrodynamical code, which allows the nonlinear, time evolution of the instability to be followed. Sequences of uniformly rotating equilibria were constructed and are used as the initial models for the fission calculations. An initially imposed asymmetry consisting of a 10% binary perturbation in the density was found to disappear on the rotational period time scale. No dynamic instability occurred. This result are verified by including the velocity dissipation terms in the linearized analysis of the stability of a Maclaurin spheroid: the dynamic instability disappears when the simulated viscous dissipation terms are included. It is concluded that any rocky body, even with considerable partial melt or a molten core, should be stable to dynamic fission; any rotational instability that occurs can only result in equatorial mass loss.

Boss, A. P.↗
NASA NTRS1986

Confinement of thermocapillary floating zone flow by uniform rotation

Smith and Greenspan (1984) examined theoretically the idea of using a uniform rotation of the floating zone system to confine the thermocapillary flow in crystal growth experiments to the melt sidewall, leaving the interior of the melt passive. Here, that model is extended to a full zone with a more realistic temperature distribution imposed on the sidewall, and both linear and nonlinear thermocapillary flows are theoretically studied. Linearized, analytical solutions are found using singular perturbation theory and the various sidewall boundary layers described by Greenspan (1969) for rotating fluids. The analytical and linearized numerical results are compared, and the linear and nonlinear flows are discussed. The results demonstrate that the thermocapillary flow is strong and that rotation cannot confine the flow. Temperature advection by strongly nonlinear flow is significant even for the small Prandtl number of silicon.

Fowlis, W. W.↗
NASA NTRS1985

Perturbations of the Richardson number field by gravity waves

An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

Wurtele, M. G.↗
NASA NTRS1992

Response of a stably stratified atmosphere to low-level heating - An application to the heat island problem

Two-dimensional airflow characteristics past a heat island are investigated using both a linear analytic model and a nonlinear numerical model in the context of the response of a stably stratified atmosphere to specified low-level heating in a constant shear flow. Results from the steady-state, linear, analytic solutions exhibit typical flow response fields that gravity waves produce in response to the local heat source in the presence of environmental flow. The magnitude of the perturbation vertical velocity is shown to be much larger in the shear-flow case than in the uniform-flow case. Two distinct flow features are observed for larger heating amplitude (hence, larger nonlinearity factor): the gravity-wave-type response field on the upstream side of the heat island and the strong updraft circulation cell located on the downstream side. As the heating amplitude increases, the updraft circulation cell strengthens and shifts farther downwind. The strong updraft cell is believed to be partly responsible for precipitation enhancement observed on the downstream side of the heat island. It is found that the continuing downwind propagation of the updraft circulation cell is related to basic-state wind speed.

Baik, Jong-Jin↗
NASA NTRSDate not supplied

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗
NASA NTRS1989

Simple analytic potentials for linear ion traps

A simple analytical model was developed for the electric and ponderomotive (trapping) potentials in linear ion traps. This model was used to calculate the required voltage drive to a mercury trap, and the result compares well with experiments. The model gives a detailed picture of the geometric shape of the trapping potenital and allows an accurate calculation of the well depth. The simplicity of the model allowed an investigation of related, more exotic trap designs which may have advantages in light-collection efficiency.

Janik, G. R.↗
NASA NTRS1990

Simple analytic potentials for linear ion traps

A simple analytical model was developed for the electric and ponderomotive (trapping) potentials in linear ion traps. This model was used to calculate the required voltage drive to a mercury trap, and the result compares well with experiments. The model gives a detailed picture of the geometric shape of the trapping potential and allows an accurate calculation of the well depth. The simplicity of the model allowed an investigation of related, more exotic trap designs which may have advantages in light-collection efficiency.

Janik, G. R.↗
NASA NTRS2024

A Systematic Methodology for Modeling and Attitude Control of Multi-body Space Telescopes

This paper derives a symbolic multi-body rigid nonlinear model for a space telescope using Stoneking’s implementation of Kane’s method. This symbolic nonlinear model is linearized using Matlab symbolic functions diff and inv because the analytic linearization is intractable for manual derivation. The linearized system model is then used to design the controllers using both linear quadratic regulator (LQR) and robust pole assignment methods. The closed-loop systems for the two designs are simulated using both the rigid model as well as a second model containing flexible modes. The performances of the two designs are compared based on the simulation testing results. Our conclusion is that the robust pole assignment design offers better performance than that of the LQR system in terms of actuator usage and pointing accuracy. However, the LQR approach remains an effective first design step that can inform the selection of real eigenvalues for robust pole assignment. The proposed method may be used for the modeling and controller designs for various multi-body systems.

Modeling↗
NASA NTRS1991

Approximations for inclusion of rotor lag dynamics in helicopter flight dynamics models

Approximate forms are suggested for augmenting linear rotor/body response models to include rotor lag dynamics. Use of an analytically linearized rotor/body model has shown that the primary effect comes from the additional angular rate contributions of the lag inertial response. Addition of lag dynamics may be made assuming these dynamics are represented by an isolated rotor with no shaft motion. Implications of such an approximation are indicated through comparison with flight test data and sensitivity of stability levels with body rate feedback.

Mckillip, Robert, Jr.↗
NASA NTRS1986

Toward comparing experiment and theory for corroborative research on hingeless rotor stability in forward flight (an experimental and analytical investigation of isolated rotor-flap-lag stability in forward flight)

For flap-lag stability of isolated rotors, experimental and analytical investigations are conducted in hover and forward flight on the adequacy of a linear quasisteady aerodynamics theory with dynamic inflow. Forward flight effects on lag regressing mode are emphasized. Accordingly, a soft inplane hingeless rotor with three blades is tested at advance ratios as high as 0.55 and at shaft angles as high as 20 degrees. The 1.62 m model rotor is untrimmed with an essentially unrestricted tilt of the tip path plane. In combination with lag natural frequencies, collective pitch settings and flap-lag coupling parameters, the data base comprises nearly 1200 test points (damping and frequency) in forward flight and 200 test points in hover. By computerized symbolic manipulation, a linear analytical model is developed in substall to predict stability margins with mode identificaton. To help explain the correlation between theory and data it also predicts substall and stall regions of the rotor disk from equilibrium values. The correlation shows both the strengthts and weaknesses of the theory in substall.

Gaonkar, G.↗
NASA NTRS2008

Production of Magnetic Turbulence by Cosmic Rays Drifting Upstream of Supernova Remnant Shocks

I will present results of our recent two- and three-dimensional Particle-In-Cell simulations of magnetic-turbulence production by cosmic-ray ions drifting upstream of supernova remnant shocks. These studies' aim is twofold: test recent predictions of strong amplification in short wavelength, non-resonant wave modes, and study the subsequent evolution of the magnetic turbulence, including its backreaction on cosmic-ray trajectories. We confirm that the drifting cosmic rays give rise to a turbulent magnetic field, but show that an oblique filamentary mode grows more rapidly than the non-resonant parallel modes found in analytical theory. The field perturbations grow more slowly than estimated using a quasi-linear analytical approach for the parallel plane-wave mode, and saturate in amplitude at deltaB/B approximately equal to 1. The backreaction of the magnetic turbulence on the particles leads to an alignment of the bulk-flow velocities of the cosmic rays and the background medium. This is an essential characteristic of cosmic ray-modified shocks: the upstream flow speed is continuously changed by the cosmic rays. The reduction of relative drift between cosmic rays and background medium accounts for the saturation of the instability at only moderate magnetic-field amplitudes. It is possible that the prolonged magnetic field growth observed in recent MHD simulations results from a cosmic-ray current assumed to be constant and thus immune to the backreaction from the turbulent field. We speculate that the parallel plane-wave mode found in analytical treatments very quickly leads co filamentation, which we observe in our PIC modeling and is also apparent in the MHD simulations.

Stroman, Thomas↗
NASA NTRS2015

Description, Usage, and Validation of the MVL-15 Modified Vortex Lattice Analysis Capability

MVL-15 is the most recent version of the Modified Vortex-Lattice (MVL) code developed within the Aerodynamics Systems Analysis Branch (ASAB) at NASA LaRC. The term "modified" refers to the primary modification of the core vortex-lattice methodology: inclusion of viscous aerodynamics tables that are linked to the linear solution via iterative processes. The inclusion of the viscous aerodynamics inherently converts the MVL-15 from a purely analytic linearized method to a semi-empirical blend which retains the rapid execution speed of the linearized method while empirically characterizing the section aerodynamics at all spanwise lattice points. The modification provides a means to assess non-linear effects on lift that occur at angles of attack near stall, and provides a means to determine the drag associated with the application of design strategies for lift augmentation such as the use of flaps or blowing. The MVL-15 code is applicable to the analyses of aircraft aerodynamics during cruise, but it is most advantageously applied to the analysis of aircraft operating in various high-lift configurations. The MVL methodology has been previously conceived and implemented; the initial concept version was delivered to the ASAB in 2001 (van Dam, C.), subsequently revised (Gelhausen, P. and Ozoroski, T. 2002 / AVID Inc., Gelhausen, P., and Roberts, M. 2004), and then overhauled (Ozoroski, T., Hahn, A. 2008). The latest version, MVL-15 has been refined to provide analysis transparency and enhanced to meet the analysis requirements of the Environmentally Responsible Aviation (ERA) Project. Each revision has been implemented with reasonable success. Separate applications of the methodology are in use, including a similar in-house capability, developed by Olson, E. that is tailored for structural and acoustics analyses. A central premise of the methodology is that viscous aerodynamic data can be associated with analytic inviscid aerodynamic results at each spanwise wing section, thereby providing a pathway to map viscous data to the inviscid results. However, a number of factors can sidetrack the analysis consistency during various stages of this process. For example, it should be expected that the final airplane lift curve and drag polar results depend strongly on the geometry and aerodynamics of the airfoil section; however, flap deflections and flap chord extensions change the local reference geometry of the input airfoil, the airplane wing, the tabulated non-dimensional viscous aerodynamics, and the spanwise links between the linear and the viscous aerodynamics. These changes also affect the bound circulation and therefore, calculation and integration of the induced angle of attack and induced drag. MVL-15 is configured to ensure these types of challenges are properly addressed. This report is a comprehensive manual describing the theory, use, and validation of the MVL-15 analysis tool. Section 3 summarizes theoretical, procedural, and characteristic features of MVL-15, and includes a list of the files required to setup, execute, and summarize an analysis. Section 4, Section 5, Section 6, and Section 7 combine to comprise the User's Guide portions of this report. The MVL-15 input and output files are described in Section 4 and Section 5, respectively; the descriptions are supplemented with example files and information about the file formats, parameter definitions, and typical parameter values. Section 6 describes the Wing Geometry Setup Utility and the 2d-Variants Utility files that simplify and assist setting up a consistent set of MVL-15 geometry and aerodynamics input parameters and input files. Section 7 describes the use of the 3d-Results Presentation Utility file that can be used to automatically create summary tables and charts from the MVL-15 output files. Section 8 documents the Validation Results of an extensive and varied validation test matrix, including results of an airplane analysis representative of the ERA Program. A start-to-finish example of the airplane analysis procedure is described in Section 7.

Ozoroski, Thomas A.↗
NASA NTRS1979

Attenuation of sound in a low Mach number nozzle flow

The energy conversion mechanisms which govern the emission of low frequency sound from an axisymmetric jet pipe of arbitrary nozzle contraction ratio in the case of low Mach number nozzle flow are discussed. The energy of the incident sound which flows through the nozzle is used to maintain two distinct characteristic disturbances in the exterior fluid. First, there is the emitted radiation which has the directivity equivalent to that of a monopole-dipole combination. Second, essentially incompressible vortex waves are induced on the jet by vortex shedding from the lip of the nozzle and may involve the excitation of instability modes. Two linearized analytical models are examined to determine the partition of the emitted energy between the radiation field and the vortex waves. One of these is an exact linear theory in which the jet boundary is treated as a vortex sheet. The second model assumes that the width of the mean shear layer of the jet cannot be neglected. The results are discussed with reference to recent nozzle attenuation measurements.

Howe, M. S.↗
NASA NTRS1987

Design sensitivity analysis of nonlinear structural response

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.

Cardoso, J. B.↗