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NASA NTRS1974

Large-amplitude hydromagnetic waves

Several aspects of the theory of large-amplitude hydromagnetic waves and their behavior in the interplanetary medium are examined. The characteristic modes of the full (i.e., nonlinearized) MHD equations and their modification by collisionless and finite-frequency effects are considered. Special attention is paid to the transverse Alfven mode, which is undamped and characterized by strictly constant pressure, density, and B; this seems to be the predominant propagating fluctuation at 1 AU. It is shown that its propagation in the small-wavelength (WKB) approximation is essentially identical to that of the small-amplitude Alfven wave of linearized theory. It is also suggested that its presence at 1 AU may provide a natural explanation of the observed power anisotropy of the fluctuations. A second-order analysis is used to study fluctuations that are not characteristic modes. It is found that for a small range of propagation directions, and subject to third-order effects, a finite-amplitude wave can exist that is linearly polarized with delta B perpendicular to both B sub zero and k; such a wave can damp nonlinearly.

Barnes, A.↗

NASA NTRS2007

General Equations of Motion for a Damaged Asymmetric Aircraft

There is a renewed interest in dynamic characteristics of damaged aircraft both in order to assess survivability and to develop control laws to enhance survivability. This paper presents a set of flight dynamics equations of motion for a rigid body not necessarily referenced to the body's center of mass. Such equations can be used when the body loses a portion of its mass and it is desired to track the motion of the body s previous center of mass/reference frame now that the mass center has moved to a new position. Furthermore, results for equations presented in this paper and equations in standard aircraft simulations are compared for a scenario involving a generic transport aircraft configuration subject to wing damage.

Bacon, Barton J.↗

NASA NTRS1974

Low thrust space vehicle trajectory optimization using regularized variables

Optimizing the trajectory of a low thrust space vehicle usually means solving a nonlinear two point boundary value problem. In general, accuracy requirements necessitate extensive computation times. In celestial mechanics, regularizing transformations of the equations of motion are used to eliminate computational and analytical problems that occur during close approaches to gravitational force centers. It was shown in previous investigations that regularization in the formulation of the trajectory optimization problem may reduce the computation time. In this study, a set of regularized equations describing the optimal trajectory of a continuously thrusting space vehicle is derived. The computational characteristics of the set are investigated and compared to the classical Newtonian unregularized set of equations. The comparison is made for low thrust, minimum time, escape trajectories and numerical calculations of Keplerian orbits. The comparison indicates that in the cases investigated for bad initial guesses of the known boundary values a remarkable reduction in the computation time was achieved. Furthermore, the investigated set of regularized equations shows high numerical stability even for long duration flights and is less sensitive to errors in the guesses of the unknown boundary values.

Schwenzfeger, K. J.↗

NASA NTRS1979

Investigation of aerodynamic characteristics of subsonic wings

An analytical strake design procedure is investigated. A numerical solution to the governing strake design equation is used to generate a series of strakes which are tested in a water tunnel to study their vortex breakdown characteristics. The strakes are scaled for use on a half-scale model of the NASA-LaRC general research fuselage with a 44 degrees trapezoidal wing. An analytical solution to the governing design equation is obtained. The strake design procedure relates the potential-flow leading-edge suction and pressure distributions to vortex stability. Several suction distributions are studied and those which are more triangular and peak near the tip generate strakes that reach higher angles of attack before vortex breakdown occurs at the wing trailing edge. For the same suction distribution, a conical rather than three dimensional pressure specification results in a better strake shape as judged from its vortex breakdown characteristics.

Dejarnette, F. R.↗

DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗

NASA NTRS2001

A Comparison of Three-Dimensional Simulations of Traveling-Wave Tube Cold-Test Characteristics Using CST MICROWAVE STUDIO and MAFIA

Previously, it was shown that MAFIA (solutions of Maxwell's equations by the Finite Integration Algorithm), a three-dimensional simulation code, can be used to produce accurate cold-test characteristics including frequency-phase dispersion, interaction impedance, and attenuation for traveling-wave tube (TWT) slow-wave structures. In an effort to improve user-friendliness and simulation time, a model was developed to compute the cold-test parameters using the electromagnetic field simulation software package CST MICROWAVE STUDIO (MWS). Cold-test parameters were calculated for several slow-wave circuits including a ferruled coupled-cavity, a folded waveguide, and a novel finned-ladder circuit using both MWS and MAFIA. Comparisons indicate that MWS provides more accurate cold-test data with significantly reduced simulation times. Both MAFIA and MWS are based on the finite integration (FI) method; however, MWS has several advantages over MAFIA. First, it has a Windows based interface for PC operation, making it very user-friendly, whereas MAFIA is UNIX based. MWS uses a new Perfect Boundary Approximation (PBA), which increases the accuracy of the simulations by avoiding stair step approximations associated with MAFIA's representation of structures. Finally, MWS includes a Visual Basic for Applications (VBA) compatible macro language that enables the simulation process to be automated and allows for the optimization of user-defined goal functions, such as interaction impedance.

Chevalier, C. T.↗

NASA NTRS2011

Experimental Waterflow Determination of the Dynamic Hydraulic Transfer Function for the J-2X Oxidizer Turbopump: Results and Interpretation - Part Two

Experimental results describing the hydraulic dynamic pump transfer matrix (Yp) for a cavitating J-2X oxidizer turbopump inducer+impeller tested in subscale waterflow are presented. The transfer function is required for integrated vehicle pogo stability analysis as well as optimization of local inducer pumping stability. Dynamic transfer functions across widely varying pump hydrodynamic inlet conditions are extracted from measured data in conjunction with 1D-model based corrections. Derived Dynamic transfer functions are initially interpreted relative to traditional Pogo pump equations. Water-to-liquid oxygen scaling of measured cavitation characteristics are discussed. Comparison of key dynamic transfer matrix terms derived from waterflow testing are made with those implemented in preliminary Ares Upper Stage Pogo stability modeling. Alternate cavitating pump hydraulic dynamic equations are suggested which better reflect frequency dependencies of measured transfer matrices.

Zoladz, Tom↗

NASA NTRS2011

Study of Anti-Vortex Baffle Effect in Suppressing Swirling Flow in LOX Tank

Yang, H. Q.↗

NASA NTRS1973

Analysis of vibration characteristics of thin plates covered with a thin viscous layer

The equation of motion was used to examine the problem of vibrations of a thin elastic plate covered with a thin viscous layer. Mathematical formulation and the solution of the problem are given.

Damashyavichyus, A. K.↗

NASA NTRS1978

Analysis of preflutter and postflutter characteristics with motion-matched aerodynamic forces

The development of the equations of dynamic equilibrium for a lifting surface from Lagrange's equation is reviewed and restated for general exponential growing and decaying oscillatory motion. Aerodynamic forces for this motion are obtained from the three-dimensional supersonic kernel function that is newly generalized to complex reduced frequencies. Illustrative calculations were made for two flutter models at supersonic Mach numbers. Preflutter and postflutter motion isodecrement curves were obtained. This type of analysis can be used to predict preflutter behavior during flutter testing and to predict postflutter behavior for use in the design of flutter suppression systems.

Cunningham, H. J.↗

NASA NTRS1996

Vibration Characteristics of Partially Covered Double-Sandwich Cantilever Beam

The differential equations of motion together with the boundary conditions for a partially covered, double-sandwich cantilever beam are derived. Bending and extension, rotational and longitudinal inertia of damping layers, and shear deformation and rotational and longitudinal inertia of the constraining layers and the primary beam are included in the equations. The theory is applicable for long as well as short, soft, or stiff damping layer, double-sandwich beams. Also, the effects of different parameters on the system loss factor and resonance frequency are discussed. Differences are found to exist with the previous beam model (called the Euler beam model) when the damping layers are stiff, when the thickness of the damping layer is large compared to the primary-beam thickness, and in the case of higher modes of vibration.

Chen, Qinghua↗

NASA NTRS2010

Characteristics of Whipple Shield Performance in the Shatter Regime

Ballistic limit equations define the failure of metallic Whipple shields in three parts: low velocity, shatter, and hypervelocity. Failure limits in the shatter regime are based on a linear interpolation between the onset of projectile fragmentation, and impulsive rupture of the shield rear wall. A series of hypervelocity impact tests have been performed on aluminum alloy Whipple shields to investigate failure mechanisms and performance limits in the shatter regime. Test results demonstrated a more rapid increase in performance than predicted by the latest iteration of the JSC Whipple shield BLE following the onset of projectile fragmentation. This increase in performance was found to level out between 4.0-5.0 km/s, with a subsequent decrease in performance for velocities up to 6.0 km/s. For a detached spall failure criterion, the failure limit was found to continually decrease up to a velocity of 7.0 km/s, substantially varying from the BLE, while for perforation-based failure an increase in performance was observed. An existing phenomenological ballistic limit curve was found to provide a more accurate reproduction of shield behavior that the BLE, however a number of underlying assumptions such as the occurrence of complete projectile fragmentation and the effect on performance of incipient projectile melt were found to be inaccurate. A cratering relationship based on the largest residual fragment size has been derived for application at velocities between 3.0-4.0 km/s, and was shown to accurately reproduce the trends of the experimental data. Further investigation is required to allow a full analytical description of shatter regime performance for metallic Whipple shields.

Ryan, S.↗

NASA NTRS1989

A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Bless, Robert R.↗

NASA NTRS2002

Flutter Analysis of a Transonic Fan

This paper describes the calculation of flutter stability characteristics for a transonic forward swept fan configuration using a viscous aeroelastic analysis program. Unsteady Navier-Stokes equations are solved on a dynamically deforming, body fitted, grid to obtain the aeroelastic characteristics using the energy exchange method. The non-zero inter-blade phase angle is modeled using phase-lagged boundary conditions. Results obtained show good correlation with measurements. It is found that the location of shock and variation of shock strength strongly influenced stability. Also, outboard stations primarily contributed to stability characteristics. Results demonstrate that changes in blade shape impact the calculated aerodynamic damping, indicating importance of using accurate blade operating shape under centrifugal and steady aerodynamic loading for flutter prediction. It was found that the calculated aerodynamic damping was relatively insensitive to variation in natural frequency.

Srivastava, R.↗

NASA NTRS1978

Characterization of acoustic disturbances in linearly sheared flows

The equation describing the plane wave propagation, the stability, or the rectangular duct mode characteristics in a compressible inviscid linearly sheared parallel, but otherwise homogeneous flow, is shown to be reducible to Whittaker's equation. The resulting solutions, which are real, viewed as functions of two variables, depend on a parameter and an argument, the values of which have precise physical meanings depending on the problem. The exact solutions in terms of Whittaker functions are used to obtain a number of known results of plane wave propagation and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). The usefulness of the exact solutions is then discussed in connection with the problems of plane wave propagation and the stability of a finite thickness layer with a linear velocity profile.

Koutsoyannis, S. P.↗

DOE OSTI2021

Secondary battery management system

A method and system for managing a battery system. The method including receiving at least one measured characteristic of the battery over a pre-defined time horizon from the at least one sensor, receiving at least one estimated characteristic of the battery from a electrochemical-based battery model based on differential algebraic equations, determining a cost function of a Moving Horizon Estimation based on the at least one measured characteristic and the at least one estimated characteristic, updating the electrochemical-based battery model based on the cost function, estimating at least one state of the at least one battery cell by applying the electrochemical-based battery model, and regulating at least one of charging or discharging of the battery based on the estimation of the at least one state of the at least one battery cell.

MirTabatabaei, Anahita↗

NASA NTRS1984

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic, and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching step sizes with the implicit shock fitting procedure. A correlation is found between the marching step size, Reynolds number, and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗

NASA NTRS1985

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗