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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle

A comprehensive set of motion equations for a multi-actuated flight vehicle is presented. The dynamics are derived from a vector approach that generalizes the classical linear perturbation equations for flexible launch vehicles into a coupled three-dimensional model. The effects of nozzle and aerosurface inertial coupling, sloshing propellant, and elasticity are incorporated without restrictions on the position, orientation, or number of model elements. The present formulation is well suited to matrix implementation for large-scale linear stability and sensitivity analysis and is also shown to be extensible to nonlinear time-domain simulation through the application of a special form of Lagrange s equations in quasi-coordinates. The model is validated through frequency-domain response comparison with a high-fidelity planar implementation.

Orr, Jeb S.↗
NASA NTRSDate not supplied

Adjoint-Based Minimization of X-59 Sonic Boom Noise Via Control Surfaces

A multidisciplinary design optimization methodology to directly minimize the ground-level noise generated by a supersonic aircraft's sonic boom is presented. A gradient-based optimizer is coupled with a Cartesian Euler flow solver and an atmospheric propagation tool to forge a unique design capability. Adjoint formulations for both the flow solver and propagation tool are also coupled to provide sensitivities in an efficient manner. The design method is demonstrated on the X-59 Low-Boom Flight Demonstrator by optimizing control surface deflections to improve ground-level noise while maintaining trimmed cruise flight. Two noise minimization examples and a noise maximization are presented. All optimized designs result in measurable improvement in the ground-level noise objective. Extensive surveys of the design space confirm that the optimization method is effective in finding a local optimum. Moreover, repeated application of the method with varying initial design points also demonstrates the robustness of the method.

ARMD↗
NASA NTRSDate not supplied

Sonic Boom Ground Noise Minimization Via the Adjoint Method

A multidisciplinary design optimization methodology to directly minimize the ground-level noise generated by the sonic boom of a high altitude supersonic body is presented. A Cartesian Euler flow solver is coupled with an atmospheric propagation tool to create a ground-noise analysis capability for supersonic bodies. Adjoint formulations for both the flow solver and propagation tool are also coupled to compute sensitivities of shape variations in the body in a highly efficient manner. A gradient-based optimizer is then introduced to forge a valuable design capability. Output-based mesh adaptation that is driven directly by ground-level noise is employed to increase accuracy and provide error estimation. The design method is demonstrated first on a simple axisymmetric body with few design variables to evaluate the efficacy of the optimization scheme. Guided by the results of this initial case, the problem is then repeated with somewhat different design variables to further demonstrate the capabilities of the design method. Finally, the method is applied to a real-world problem by optimizing control surface deflection settings of a low-boom aircraft to minimize ground noise while maintaining trimmed, level flight.

ARMD↗
NASA NTRS1978

Variation of solar cell sensitivity and solar radiation on tilted surfaces

An empirical study was performed (1) to evaluate the validity of various insolation models used to compute solar radiation incident on tilted surfaces from global data measured on horizontal surfaces and (2) to determine the variation of solar cell sensitivity to solar radiation over a wide range of atmospheric condition. Evaluation of the insolation data indicates that the isotropic sky model of Liu and Jordan underestimates the amount of solar radiation falling on tilted surfaces by as much as 10%. An anisotropic-clear-sky model proposed by Temps and Coulson was also evaluated and found to be deficient under cloudy conditions. A new model, formulated herein, reduced the deviations between measured and predicted insolation to less than 3%. Evaluation of solar cell sensitivity data indicates small change (2-3%) in sensitivity from winter to summer for tilted cells. The feasibility of using such global data as a means for calibrating terrestrial solar cells as done by Treble is discussed.

Klucher, T. M.↗
NASA NTRS1989

An investigation of using an RQP based method to calculate parameter sensitivity derivatives

Estimation of the sensitivity of problem functions with respect to problem variables forms the basis for many of our modern day algorithms for engineering optimization. The most common application of problem sensitivities has been in the calculation of objective function and constraint partial derivatives for determining search directions and optimality conditions. A second form of sensitivity analysis, parameter sensitivity, has also become an important topic in recent years. By parameter sensitivity, researchers refer to the estimation of changes in the modeling functions and current design point due to small changes in the fixed parameters of the formulation. Methods for calculating these derivatives have been proposed by several authors (Armacost and Fiacco 1974, Sobieski et al 1981, Schmit and Chang 1984, and Vanderplaats and Yoshida 1985). Two drawbacks to estimating parameter sensitivities by current methods have been: (1) the need for second order information about the Lagrangian at the current point, and (2) the estimates assume no change in the active set of constraints. The first of these two problems is addressed here and a new algorithm is proposed that does not require explicit calculation of second order information.

Beltracchi, Todd J.↗
NASA NTRS1995

Sensitivity analysis for the dynamic response of thermoviscoplastic shells of revolution

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric, fully-coupled, thermoviscoplastic response of shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of large-strain, transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be viscoplasticity with strain hardening and thermal hardening, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used for the shell equations with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. The energy-balance equation is solved using a Galerkin procedure, with the temperature as the fundamental unknown. Spatial discretization is performed in one dimension (meridional direction) for the momentum and constitutive equations of the shell, and in two dimensions (meridional and thickness directions) for the energy-balance equation. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) for the momentum equation; a predictor-corrector version of the trapezoidal rule is used for the energy-balance equation; and an explicit scheme consistent with the central difference method is used to integrate the constitutive equations. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading.

Kulkarni, Makarand↗
NASA NTRS1992

A model for the characterization of the spatial properties in vestibular neurons

Quantitative study of the static and dynamic response properties of some otolith-sensitive neurons has been difficult in the past partly because their responses to different linear acceleration vectors exhibited no "null" plane and a dependence of phase on stimulus orientation. The theoretical formulation of the response ellipse provides a quantitative way to estimate the spatio-temporal properties of such neurons. Its semi-major axis gives the direction of the polarization vector (i.e., direction of maximal sensitivity) and it estimates the neuronal response for stimulation along that direction. In addition, the semi-minor axis of the ellipse provides an estimate of the neuron's maximal sensitivity in the "null" plane. In this paper, extracellular recordings from otolith-sensitive vestibular nuclei neurons in decerebrate rats were used to demonstrate the practical application of the method. The experimentally observed gain and phase dependence on the orientation angle of the acceleration vector in a head-horizontal plane was described and satisfactorily fit by the response ellipse model. In addition, the model satisfactorily fits neuronal responses in three-dimensions and unequivocally demonstrates that the response ellipse formulation is the general approach to describe quantitatively the spatial properties of vestibular neurons.

Non-NASA Center↗
NASA NTRS1984

Rational approach for assumed stress finite elements

A new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co-ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4-node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.

Pian, T. H. H.↗
NASA NTRS1974

Sensitivity analysis of torsional vibration characteristics of helicopter rotor blades. Part 2: Aerodynamics and sensitivity analysis

A theoretical investigation of dynamic response characteristics of rotor blades was carried out with special emphasis on torsional degrees-of-freedom. Coupled equations of motion for flapwise bending and torsion were formulated at varying azimuth positions for rotor blades with noncollinear aerodynamic, elastic and mass axes. Both structural and aerodynamic mass, damping and stiffness coefficients were included. The variations of a sample blade at different flight conditions were investigated from these equations. The obtained numerical results were illustrated. The sensitivity of overall blade vibration characteristics to torsional oscillations was also investigated from the equations of motion for the sample blade. The illustrated results show the importance of torsional degrees-of-freedom in rotor blade analysis. Various possibilities of improving the overall response by tuning blade geometric, structural and aerodynamic characteristics are discussed.

Bratanow, T.↗
NASA NTRS1982

Linearized transfer between coplanar circular orbits using blow down propulsion system

A closed form solution is presented for the coplanar transfer between nearby circular orbits for spacecraft using their own blow down propulsion system. The decaying thrust is applied along the local horizontal and the linearized equation of motion in the orbital elements formulation are used to describe the transfer which consists of a thrust-coast-relight program. Sensitivity partials are also presented analytically in order to study the effect of maneuver execution errors and various other parameters affecting the blow down propulsion system characteristics on the transfer. This strategy is applied to study the transfer of the TOPEX spacecraft from the Shuttle parking orbit to its final operational orbit.

Kechichian, J. A.↗
NASA NTRS1987

Design sensitivity analysis for an aeroelastic optimization of a helicopter blade

The sensitivity of vibratory hub loads of a four-bladed hingeless rotor with respect to blade design parameters is investigated using a finite element formulation in space and time. Design parameters include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity from aerodynamic center, blade bending stiffnesses (flap, lag and torsion). Hub loads selected are 4/rev vertical hub shear and 3/rev hub moment in the rotating reference frame. The sensitivity derivatives of vertical hub loads with respect to blade design parameters are compared using two approaches, finite difference scheme and analytical approach using chain rule differentiation. The analytical derivative approach developed as an integral part of response solution (finite element in time) is a powerful method for an aeroelastic optimization of a helicopter rotor.

Lim, Joon↗
NASA NTRS1990

Near-wall modelling of compressible turbulent flows

Work was carried out to extend the near-wall models formulated for the incompressible Reynolds stress equations to compressible flows. The idea of splitting the compressible dissipation function into a solenoidal part that is not sensitive to changes of compressibility indicators and a compressible part that is directly affected by these changes is adopted. This means that all models involving the dissipation rate could be expressed in terms of the solenoidal dissipation rate and an equation governing its transport could be formulated to close the set of compressible Reynolds stress equations. The near-wall modelling of the dissipation rate equation is investigated and its behavior near a wall is studied in detail using k-epsilon closure. It is found that all existing modelled equations give the wrong behavior for the dissipation rate near a wall. Improvements are suggested and the resultant behavior is found to be in good agreement with near-wall data. Furthermore, the present modified k-epsilon closure is used too calculate a flat plate boundary layer and the results are compared with four existing k-epsilon closures. These comparisons show that all closures tested give essentially the same flow properties, except in a region very close to the wall. In this region, the present k-epsilon closure calculations are in better agreement with measurements and direct simulation data; in particular, the behavior of the dissipation rate.

So, Ronald M. C.↗
NASA NTRS1990

On the effects of grid ill-conditioning in three dimensional finite element vector potential magnetostatic field computations

The effects of finite element grid geometries and associated ill-conditioning were studied in single medium and multi-media (air-iron) three dimensional magnetostatic field computation problems. The sensitivities of these 3D field computations to finite element grid geometries were investigated. It was found that in single medium applications the unconstrained magnetic vector potential curl-curl formulation in conjunction with first order finite elements produce global results which are almost totally insensitive to grid geometries. However, it was found that in multi-media (air-iron) applications first order finite element results are sensitive to grid geometries and consequent elemental shape ill-conditioning. These sensitivities were almost totally eliminated by means of the use of second order finite elements in the field computation algorithms. Practical examples are given in this paper to demonstrate these aspects mentioned above.

Wang, R.↗
NASA NTRS1988

Computational aspects of sensitivity calculations in transient structural analysis

A key step in the application of formal automated design techniques to structures under transient loading is the calculation of sensitivities of response quantities to the design parameters. This paper considers structures with general forms of damping acted on by general transient loading and addresses issues of computational errors and computational efficiency. The equations of motion are reduced using the traditional basis of vibration modes and then integrated using a highly accurate, explicit integration technique. A critical point constraint formulation is used to place constraints on the magnitude of each response quantity as a function of time. Three different techniques for calculating sensitivities of the critical point constraints are presented. The first two are based on the straightforward application of the forward and central difference operators, respectively. The third is based on explicit differentiation of the equations of motion. Condition errors, finite difference truncation errors, and modal convergence errors for the three techniques are compared by applying them to a simple five-span-beam problem. Sensitivity results are presented for two different transient loading conditions and for both damped and undamped cases.

Greene, William H.↗
NASA NTRS1981

The effects of surface evaporation parameterizations on climate sensitivity to solar constant variations

The effects of two different evaporation parameterizations on the sensitivity of simulated climate to solar constant variations are investigated by using a zonally averaged climate model. One parameterization is a nonlinear formulation in which the evaporation is nonlinearly proportional to the sensible heat flux, with the Bowen ratio determined by the predicted vertical temperature and humidity gradients near the earth's surface (model A). The other is the formulation of Saltzman (1968) with the evaporation linearly proportional to the sensible heat flux (model B). The computed climates of models A and B are in good agreement except for the energy partition between sensible and latent heat at the earth's surface. The difference in evaporation parameterizations causes a difference in the response of temperature lapse rate to solar constant variations and a difference in the sensitivity of longwave radiation to surface temperature which leads to a smaller sensitivity of surface temperature to solar constant variations in model A than in model B. The results of model A are qualitatively in agreement with those of the general circulation model calculations of Wetherald and Manabe (1975).

Chou, S.-H.↗
NASA NTRS2004

The Robustness of Acoustic Analogies

Acoustic analogies for the prediction of flow noise are exact rearrangements of the flow equations N(right arrow q) = 0 into a nominal sound source S(right arrow q) and sound propagation operator L such that L(right arrow q) = S(right arrow q). In practice, the sound source is typically modeled and the propagation operator inverted to make predictions. Since the rearrangement is exact, any sufficiently accurate model of the source will yield the correct sound, so other factors must determine the merits of any particular formulation. Using data from a two-dimensional mixing layer direct numerical simulation (DNS), we evaluate the robustness of two analogy formulations to different errors intentionally introduced into the source. The motivation is that since S can not be perfectly modeled, analogies that are less sensitive to errors in S are preferable. Our assessment is made within the framework of Goldstein's generalized acoustic analogy, in which different choices of a base flow used in constructing L give different sources S and thus different analogies. A uniform base flow yields a Lighthill-like analogy, which we evaluate against a formulation in which the base flow is the actual mean flow of the DNS. The more complex mean flow formulation is found to be significantly more robust to errors in the energetic turbulent fluctuations, but its advantage is less pronounced when errors are made in the smaller scales.

Freund, J. B.↗
NASA NTRSDate not supplied

A Wall-Modeled LES Perspective for the High Lift Common Research Model Using LAVA

A new immersed boundary Wall-Modelled Large Eddy Simulation (WMLES) formulation is developed to study high-lift aerodynamics on the NASA High-Lift Common Research Model (HL-CRM). A sequence of Cartesian Octree grids with sizes ranging from 100 Million through 2.02 Billion grid points is utilized to systematically assess grid-sensitivity and convergence for the in-tunnel (QinetiQ) configuration of the model, and remarkable agreement between the immersed boundary and the curvilinear body-aligned WMLES formulations is reported on grids with comparable resolutions. In the free-air configuration of the model, consistent predictions between the Curvilinear Overset and the Cartesian Octree formulations are reported for angles of attack up to C(L,max) at a=19.57. However, some differences in the onset of stall are seen between the two methods for a>20°: while the curvilinear WMLES experiences wing-root separation with increasing angle of attack (Topology A), the Cartesian Octree formulation shows a different flow topology characterized by boundary layer weakness on the main element, emanating from the pylon-wing attachment (Topology B). In order to obtain further insight into the two-distinct topologies, carefully designed numerical experiments to isolate effects of the model standoff and the tunnel wall-boundary layers are conducted using the immersed boundary WMLES formulation. The increased incidence angle-of-attack on the inboard portion of the wing due to the standoff is shown to be sufficient for triggering a switch from Topology B to Topology A in Cartesian WMLES. The role of the floor boundary layer is further examined in detail by identification of additional corner-flow vorticity generated by the viscous juncture flow interactions between the floor boundary layer and the standoff leading to formation of a strong coherent and persistent vortex on the belly-side of the fuselage. The intensity of this vortex is shown to increase with the thickness of the floor boundary layer. A further increase in the incidence angle of attack near the leading-edge strake caused by the presence of this belly-side vortex is quantified for two-distinct floor boundary layers. Both of the floor boundary layers considered result in the onset of large scale wing-root separation at a=21.47in non-confined (free-air) configurations.

TTT↗
NASA NTRS1973

Reentry guidance for Space Shuttle

An explicit guidance scheme is outlined which provides the appropriate energy management in order for the shuttle orbiter to reach any location within the required footprint. Considering the orbiter as entering the earth's atmosphere, expressions for the downrange, crossrange, and the time of the termination of the entry phase as functions of the control variables are developed. Performing an order-of-magnitude analysis of the terms in these expressions, only dominant terms are retained. Analytical expressions for the elements of the sensitivity matrix which represents the partial derivatives of the desired range with respect to control variables are formulated. Using the Gauss-Jordan inversion technique, the required change in guidance commands as a function of the deviations in the downrange and crossrange are explicitly computed.

Causey, W.↗