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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 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Application of the finite element method to rotary-wing aeroelasticity

Recent research in rotary-wing aeroelasticity has indicated that all fundamental problems in this area are inherently nonlinear. The non-linearities in this problem are due to the inclusion of finite slopes, due to moderate deflections, in the structural, inertia and aerodynamic operators associated with this aeroelastic problem. In this paper the equations of motion, which are both time and space dependent, for the aeroelastic problem are first formulated in P.D.E. form. Next the equations are linearized about a suitable equilibrium position. The spatial dependence in these equations is discretized using a local Galerkin method of weighted residuals resulting in a finite element formulation of the aeroelastic problem. As an illustration the method is applied to the coupled flap-lag problem of a helicopter rotor blade in hover. Comparison of the solutions with previously published solutions establishes the convergence properties of the method. It is concluded that this formulation is a practical tool for solving rotary-wing aeroelastic stability or response problems.

Friedmann, P.↗
NASA NTRS1979

Examination of the flap-lag stability of rigid articulated rotor blades

A critical examination of flap-lag stability of a centrally hinged, spring-restrained rigid blade in both hover and forward flight is presented. Several differences in the equations of motion for blade flap-lag stability in the existing literature are identified. A rigorous and systematic development of these equations for a rigid articulated blade in forward flight shows the existence of some linear aerodynamic coupling terms associated with blade steady-state flapping and lagging in the perturbation equations. The differences identified are shown to be associated with whether or not the lag hinge flaps with the blade. The implications of these differences on stability are examined, and it is shown that the pitch-lag coupling terms associated with a hinge arrangement in which the lag hinge flaps with the blade have a marked influence on flap-lag stability, depending on the system parameters.

Kaza, K. R. V.↗
NASA NTRS1982

Coupled flap-lag-torsional dynamics of hingeless rotor blades in forward flight

The aeroelastic stability and response problem of the coupled flap-lag-torsional dynamics of an isolated hingeless rotor blade in forward flight is considered. Linear, quasi-steady aerodynamics below stall is included. The spatial dependence of the partial differential nonliner equations of motion is discretized using a multimodal Galerkin method. The nonlinear time dependent equilibrium position (steady state response) about which the equations are linearized is obtained by solving a sequence of linear periodic response problems (quasilinearization). Results illustrating blade behavior in forward flight for both soft-in-plane and stiff-in-plane designs are presented. Quasilinearization provides a clear indication of the cases when nonlinear terms due to moderate deflections are important. The results indicate that nonlinearities affect system stability much more than system response. This implies that for obtaining blade vibrations and loads, approximate analytical models based on linearized formulations could be employed, whereas for determining blade stability a more accurate nonlinear analysis would be required.

Friedmann, P. P.↗
NASA NTRS1984

A solution of Mx(double dot) + Cx(dot) + Kx = 0 applicable to the design of active dampers

A solution is presented for the equations of motion for the damped linear oscillator, Mx(double dot) + Cx(dot) + Kx = 0. The algorithm solves a transformed set of equations in terms of the modal variables of the undamped system and, at the same time, solves the adjoint equation of the transformed problem. The adjoint solution is normalized to give the inverse of the solution matrix of the transformed problem. The normalized inverse is useful in design for direct computation of sensitivity derivatives of damping ratios with respect to damping rates. The algorithm is programmed to reduce storage requirements by a factor of three-fourths compared to standard complex eigenvalue subroutines. A numerical example is included.

Thurston, G. A.↗
NASA NTRS1984

Crashworthiness of light aircraft fuselage structures: A numerical and experimental investigation

The dynamic behavior of aircraft fuselage structures subject to various impact conditions was investigated. An analytical model was developed based on a self-consistent finite element (CFE) formulation utilizing shell, curved beam, and stringer type elements. Equations of motion were formulated and linearized (i.e., for small displacements), although material nonlinearity was retained to treat local plastic deformation. The equations were solved using the implicit Newmark-Beta method with a frontal solver routine. Stiffened aluminum fuselage models were also tested in free flight using the UTIAS pendulum crash test facility. Data were obtained on dynamic strains, g-loads, and transient deformations (using high speed photography in the latter case) during the impact process. Correlations between tests and predicted results are presented, together with computer graphics, based on the CFE model. These results include level and oblique angle impacts as well as the free-flight crash test. Comparisons with a hybrid, lumped mass finite element computer model demonstrate that the CFE formulation provides the test overall agreement with impact test data for comparable computing costs.

Nanyaro, A. P.↗
NASA NTRS1986

Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

Chen, J.↗
NASA NTRS1987

Steady flow past sudden expansions at large Reynolds number. II - Navier-Stokes solutions for the cascade expansion

The equations of motion in the steady laminar flow past a sudden expansion at large Reynolds number, R, reduce to the boundary layer equations as R tends to the freestream valve, when the longitudinal length scale of the separated eddy increases linearly and indefinitely with R. A global Newton method is presently used to obtain finite difference solutions to the steady Navier-Stokes equations up to R of 1000 for a uniform inflow past a cascade of sudden expansions. For large expansion ratio values, the eddy length increases linearly with R; for smaller values, however, where boundary layer equation solutions could not be found, the steady solutions to the Navier-Stokes equations approach the limit of an inviscid eddy in length with increasing R.

Milos, Frank S.↗
NASA NTRS1989

The role of shock induced trailing-edge separation in limit cycle oscillations

The potential role of shock induced trailing edge separation (SITES) in limit cycle oscillations (LCO) was established. It was shown that the flip-flop characteristics of transition to and from SITES as well as its hysteresis could couple with wing modes with torsional motion and low damping. This connection led to the formulation of a very simple nonlinear math model using the linear equations of motion with a nonlinear step forcing function with hysteresis. A finite difference solution with time was developed and calculations were made for the F-111 TACT were used to determine the step forcing function due to SITES transition. Since no data were available for the hysteresis, a parameter study was conducted allowing the hysteresis effect to vary. Very small hysteresis effects, which were within expected bounds, were required to obtain reasonable response levels that essentially agreed with flight test results. Also in agreement with wind tunnel tests, LCO calculations for the 1/6 scale F-111 model showed that the model should have not experienced LCO.

Cunningham, Atlee M., Jr.↗
NASA NTRS1989

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Weatherill, Warren H.↗
NASA NTRS1989

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Buttrill, Carey S.↗
NASA NTRS1990

Three-dimensional instability of rotating flows with oscillating axial strain

The equations of motion for perturbed uniformly rotating flows with uniform axial-time periodic strain, are derived from the Navier-Stokes equations in the low Mach number limit. The perturbation equations admit exponentially growing three-dimensional solutions for which the amplification factors per period are computed for a range of compression and swirl ratios. It is found that for a given compression ratio, the flow is stable for swirl ratios, but at high swirl ratios the flow is unstable with the amplification factor dependent on wave angle but independent of wavelength. For an unstable swirl ratio, higher compression ratios yield larger amplification factors.

Mansour, Nagi N.↗
NASA NTRS1992

Adaptive attitude control and momentum management for large-angle spacecraft maneuvers

The fully coupled equations of motion are systematically linearized around an equilibrium point of a gravity gradient stabilized spacecraft, controlled by momentum exchange devices. These equations are then used for attitude control system design of an early Space Station Freedom flight configuration, demonstrating the errors caused by the improper approximation of the spacecraft dynamics. A full state feedback controller, incorporating gain-scheduled adaptation of the attitude gains, is developed for use during spacecraft on-orbit assembly or operations characterized by significant mass properties variations. The feasibility of the gain adaptation is demonstrated via a Space Station Freedom assembly sequence case study. The attitude controller stability robustness and transient performance during gain adaptation appear satisfactory.

Parlos, Alexander G.↗
NASA NTRS1993

Computational Control Workstation: Users' perspectives

A Workstation has been designed and constructed for rapidly simulating motions of rigid and elastic multibody systems. We examine the Workstation from the point of view of analysts who use the machine in an industrial setting. Two aspects of the device distinguish it from other simulation programs. First, one uses a series of windows and menus on a computer terminal, together with a keyboard and mouse, to provide a mathematical and geometrical description of the system under consideration. The second hallmark is a facility for animating simulation results. An assessment of the amount of effort required to numerically describe a system to the Workstation is made by comparing the process to that used with other multibody software. The apparatus for displaying results as a motion picture is critiqued as well. In an effort to establish confidence in the algorithms that derive, encode, and solve equations of motion, simulation results from the Workstation are compared to answers obtained with other multibody programs. Our study includes measurements of computational speed.

Roithmayr, Carlos M.↗
NASA NTRS1987

A study of some approximations in the modeling of a coupled rotor/fuselage aeromechanical system

Equations of motion for a three-bladed hingeless rotor coupled to a gimbal-supported fuselage are developed. A brief derivation of the equations is presented, including the assumptions made, the ordering scheme, and a discussion of both the source of the aerodynamic axial load term and the reason for differences due to hinge sequence. The solution of the equations is discussed, including linearization, the use of multiblade coordinates to eliminate periodic coefficients, and specialization to a root-sprung model. The treatment of the blade root offset by using an ordering scheme to neglect higher-order terms is found to affect results in pitch and roll. A small aerodynamic loading term in the blade axial direction has a significant effect at large collective pitch settings, as does the choice of a flap-lag or a lag-flap transformation sequence for blade motion. The results for a hingeless rotor also differ significantly from those for the root-sprung model when the nonrotating natural frequencies are matched.

Blelloch, P. A.↗
DOE OSTI2021

A High Resolution Simulation of a Single Shock-Accelerated Particle

We report particle drag models, which capture macroviscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a two-dimensional axisymmetric Navier–Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted using the hydrocode FLAG. FLAGs capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated—a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAGs Navier–Stokes and heat diffusion solutions and to provide a rationale for recent experimental particle drag measurements.

42 ENGINEERING↗
DOE OSTI2020

A Numerical Simulation of a Single Shock-Accelerated Particle

Particle drag models, which capture macro viscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a 2D axisymmetric Navier-Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted in the hydrocode FLAG. FLAG’s capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated – a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAG’s Navier-Stokes and heat diffusion solutions, and to provide a rationale for recent experimental particle drag measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗