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NASA NTRSDate not supplied

Control Effector Unsaturation Modification to the Cascading Generalized Inverse Control Allocation Algorithm

Control allocation has sufficiently progressed such that it is used in front-line fighter aircraft such as the F-18Superhornet and the F-35 Joint Strike Fighter. Published literature shows the F-35 utilizes Nonlinear Dynamic Inversion in conjunction with an Effector Blender that incorporates the Cascading Generalized Inverse control allocation algorithm. While the Cascading Generalized Inverse algorithm is one of the premier generalized inverse methods, it does suffer from three deficiencies. In particular, it suffers from an inability to achieve some desired outcomes, it intermittently provides non-optimal solutions and generally fails to preserve moment direction near maximal achievable moments. An effector unsaturation method based on a Scalar Difference Quadratic was first introduced and implemented on the iterative Prediction Method control allocation algorithm which was shown to consistently achieve optimal (weighted) control allocation solutions throughout the entire Attainable Moment Set while preserving desired moment direction. In this paper, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the baseline algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Numerical case studies demonstrate that the Modified Cascading Generalized Inverse algorithm resolves the aforementioned deficiencies.

Michael J Acheson↗

NASA NTRSDate not supplied

Modified Cascading Generalized Inverse Control Allocation

The current aviation revolution towards electric propulsion aircraft (e.g., electric vertical takeoff-and-landing) brings unique control challenges. These vehicles are typically over-actuated (more effectors than desired control outcomes), may require control strategies for the three phases of flight (hover, transition and cruise), and currently have limited electric power availability. These vehicle challenges bring the need for optimal control allocation to the forefront of research. A leading control allocation algorithm, used in current flight vehicles, is the Cascading Generalized Inverse (CGI). Unfortunately, the Cascading Generalized Inverse algorithm is unable to achieve some desired outcomes, it intermittently provides non-optimal allocations, and it may fail to preserve moment direction near maximal achievable outcomes. In this research, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Rigorous theory is shown that the Modified Cascading Generalized Inverse performs better at obtaining optimal allocations for all attainable outcomes. Numerical case studies for over-actuated vehicles demonstrate resolution to the aforementioned deficiencies.

Control Allocation↗

NASA NTRSDate not supplied

Modified Cascading Generalized Inverse Control Allocation

Control Allocation↗

NASA NTRS2001

Computationally efficient control allocation

A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.

Durham, Wayne↗

NASA NTRS1996

Analysis of Subgrid Eddy Diffusivity in Turbulence Using Direct Numerical Simulation Databases

Direct numerical simulation data in isotropic turbulence at Taylor-scale Reynolds number 90 are used to compute subgrid transfer and spectral eddy diffusivities for passive scalars at Schmidt numbers 1 and 1/8. The results are consistent with spectral transfer processes dominated by a local forward cascade in wavenumber space which is a consequence of moderately nonlocal interactions in the scalar fields. Data decompositions show that resolvable-subgrid interactions make (in general) substantially stronger contributions than fully-subgrid interactions to the eddy diffusivity, which has a non-negligible inverse cascade, or backscatter, component. The eddy diffusivity has a strong cusp at wavenumbers close to the cutoff value separating resolvable and subgrid ranges. At low wavenumbers the eddy diffusivity is generally small, but there the details depend on Schmidt number. The behavior of the subgrid turbulent Schmidt number (the ratio of effective eddy viscosity to eddy diffusivity) is observed to depend strongly on Schmidt number. In interpreting the results at a given spectral cutoff it is important to note that the spectrum of less diffusive scalars (of higher Schmidt number) has more high-wavenumber content.

Yeung, P. K.↗

NASA NTRS1999

Horizontal Wavenumber Spectra of Winds, Temperature and Trace Gases During the Pacific Exploratory Missions: Gravity Waves, Quasi-Two-Dimensional Turbulence, and Vortical Modes - 2

We examine the horizontal wavenumber spectra of horizontal velocity and potential temperature collected by aircraft above the Pacific Ocean to determine whether gravity waves, quasi-two-dimensional (Q-2-D) turbulence, or vortical modes dominate atmospheric fluctuations at scale sizes of 1-100 km and altitudes of 2-12 km. We conclude from the study of Doppler-shifting effects that Q-2-D turbulence and/or vortical modes are more prevalent than gravity waves over the ocean, except in the equatorial zone. The results are consistent with recent numerical simulations of Q-2-D turbulence, which show that the characteristic inverse cascade of energy is greatly facilitated by the presence of background rotation. Furthermore, a Stokes-parameter analysis reveals the general paucity of coherent wavelike motions, although specific cases of gravity-wave propagation are observed. Finally, a case study of a long flight segment displays a k(sup -3) horizontal velocity variance spectrum at scales longer than about 100 km. A Stokes-parameter analysis indicates that these large-scale fluctuations were likely due to vortical modes rather than inertio-gravity waves.

Cho, John Y. N.↗

NASA NTRS1944

The conformal transformation of an airfoil into a straight line and its application to the inverse problem of airfoil theory

A method of conformal transformation is developed that maps an airfoil into a straight line, the line being chosen as the extended chord line of the airfoil. The mapping is accomplished by operating directly with the airfoil ordinates. The absence of any preliminary transformation is found to shorten the work substantially over that of previous methods. Use is made of the superposition of solutions to obtain a rigorous counterpart of the approximate methods of thin-airfoils theory. The method is applied to the solution of the direct and inverse problems for arbitrary airfoils and pressure distributions. Numerical examples are given. Applications to more general types of regions, in particular to biplanes and to cascades of airfoils, are indicated. (author)

Mutterperl, William↗

NASA NTRS1982

Two-and-a-half-dimensional magnetohydrodynamic turbulence

The homogeneous turbulence for which fluctuating magnetic fields and velocity fields are independent of one spatial coordinate but still possess all three components are studied to form a generalized two-and-half dimensional geometry. The integral of the z-vector potential and the magnetic helicity are shown to be ideal invariants, and the basic dynamical variables and the equations of uniform-density incompressible magnetohydrodynamics are defined. The possibility of simultaneous inverse cascades is considered, and Kolmogoroff dimensional analysis is employed to infer omnidirectional inverse cascade spectra. Implications of a selective decay hypothesis, where a tendency exists in the initial value problem for the ideal invariants directly cascaded to higher wavenumbers to be selectively dissipated, and the possibility of a dynamo action in the considered geometry, are examined.

Montgomery, D.↗

NASA NTRS1987

Automated design of controlled diffusion blades

A numerical automation procedure has been developed to be used in conjunction with an inverse hodograph method for the design of controlled diffusion blades. With this procedure a cascade of airfoils with a prescribed solidity, inlet Mach number, inlet air flow angle, and air flow turning can be produced automatically. The trailing edge thickness of the airfoil, an important quantity in inverse methods, is also prescribed. The automation procedure consists of a multidimensional Newton iteration in which the objective design conditions are achieved by acting on the hodograph input parameters of the underlying inverse code. The method, although more general in scope, is applied in this paper to the design of axial flow compressor blade sections, and a wide range of examples is presented.

Sanz, Jose M.↗

NASA NTRS1988

Automated design of controlled-diffusion blades

Sanz, J. M.↗

NASA NTRS1989

Automated design of controlled diffusion blades

A numerical automation procedure was developed to be used in conjunction with an inverse hodograph method for the design of controlled diffusion blades. With this procedure a cascade of airfoils with a prescribed solidity, inlet Mach No., inlet air flow angle and air flow turning can be produced automatically. The trailing edge thickness of the airfoil, an important quantity in inverse methods, is also prescribed. The automation procedure consists of a multi-dimensional Newton iteration in which the objective design conditions are achieved by acting on the hodograph input parameters of the underlying inverse code. The method, although more general in scope, is applied to the design of axial flow turbomachinery blade sections, both compressors and turbines. A collaborative effort with U.S. Engine Companies to identify designs of interest to the industry will be described.

Sanz, Jose M.↗

NASA NTRS1983

Turbulence analysis of the Jovian upstream 'wave' phenomenon

As Voyager 2 approached Jupiter's bow shock, large-amplitude fluctuations were seen in both the magnetic field and plasma fluid velocity. These fluctuations generally coincided with the occurrence of long-lived energetic particle events similar to the upstream waves often observed near the earth's bow shock. In this paper an analysis of the magnetic field and plasma observations using spectral methods is presented. The characteristic spectral features related to the upstream waves are generally seen near 1 mHz. The measured correlation lengths of these fluctuations suggest that they are coherent over only a few wavelengths. The analysis is consistent with the hypothesis that these fluctuations are driven by streaming ions, possibly protons. No evidence for the existence of whistler waves is found. It is argued that some of the observed spectral features suggest that dynamical turbulent processes are occurring in the uptream wave region, including a possible observation of an inverse cascade of magnetic helicity to large spatial scales.

Smith, C. W.↗

NASA NTRS2007

Wide-Temperature-Range Integrated Operational Amplifier

A document discusses a silicon-on-insulator (SOI) complementary metal oxide/semiconductor (CMOS) integrated- circuit operational amplifier to be replicated and incorporated into sensor and actuator systems of Mars-explorer robots. This amplifier is designed to function at a supply potential less than or equal to 5.5 V, at any temperature from -180 to +120 C. The design is implemented on a commercial radiation-hard SOI CMOS process rated for a supply potential of less than or equal to 3.6 V and temperatures from -55 to +110 C. The design incorporates several innovations to achieve this, the main ones being the following: NMOS transistor channel lengths below 1 m are generally not used because research showed that this change could reduce the adverse effect of hot carrier injection on the lifetimes of transistors at low temperatures. To enable the amplifier to withstand the 5.5-V supply potential, a circuit topology including cascade devices, clamping devices, and dynamic voltage biasing was adopted so that no individual transistor would be exposed to more than 3.6 V. To minimize undesired variations in performance over the temperature range, the transistors in the amplifier are biased by circuitry that maintains a constant inversion coefficient over the temperature range.

Mojarradi, Mohammad↗

NASA NTRS1994

Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. Volume 1: Theory development and parametric studies

Typical analytical models for interaction between rotor and stator in a turbofan analyze the effect of wakes from the rotor impinging on the stator, producing unsteady loading, and thereby generating noise. Reflection/transmission characteristics of the rotor are sometimes added in a separate calculation. In those models, there is a one-to-one relationship between wake harmonics and noise harmonics; that is, the BPF (blade passing frequency) wake harmonic causes only the BPF noise harmonic, etc. This report presents a more complete model in which flow tangency boundary conditions are satisfied on two cascades in relative motion for several harmonics simultaneously. By an extension of S.N. Smith's code for two dimensional flat plate cascades, the noise generation/frequency scattering/blade row reflection problem is solved in a single matrix inversion. It is found that the BPF harmonic excitation of the stator scatters considerable energy in the higher BPF harmonics due to relative motion between the blade rows. Furthermore, when swirl between the rotor and stator is modeled, a 'mode trapping' effect occurs which explains observations on fans operating at rotational speeds below BFP cuton: the BPF mode amplifies between blade rows by multiple reflections but cannot escape to the inlet and exit ducts. However, energy scattered into higher harmonics does propagate and dominates the spectrum at two and three times BPF. This report presents the complete derivation of the theory, comparison with a previous (more limited) coupled rotor/stator interaction theory due to Kaji and Okazaki, exploration of the mode trapping phenomenon, and parametric studies showing the effects of vane/blade ratio and rotor/stator interaction. For generality, the analysis applies to stages where the rotor is either upstream or downstream of the stator and to counter rotation stages. The theory has been coded in a FORTRAN program called CUP2D, documented in Volume 2 of this report. It is concluded that the new features of this analysis - unsteady coupling, frequency scattering, and flow turning between rotor and stator - have a profound effect on noise generation caused by rotor/stator interaction. Treating rotors and stators as isolated cascades is not adequate for noise analysis and prediction.

Hanson, Donald B.↗

DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1979

Possible inverse cascade behavior for drift-wave turbulence

The turbulent spectral properties of the dynamical equation of Hasegawa and Mima (1978) governing the evolution of the electrostatic potential in drift-wave turbulence is investigated for two formulations of the problem: (1) as a nondissipative initial value problem, with the potential represented by a truncated Fourier series with large number of terms, and (2) as a dissipative problem with a small viscous dissipation at very short spatial scales, and a long wavelength forcing term at longer wavelengths. It is found that Hasegawa and Mima's prediction for the nondissipative, truncated initial value modal problem is accurate, but substantial differences exist for the forced dissipative case between computer results and analytical predictions based on a wave kinetic equation of Kadomtsev. Much better agreement is found with a simple dual-cascade model based on Kraichnan's generalization of Kolmogorov's cascade arguments.

Fyfe, D.↗

NASA NTRS1995

Pair cascades in extragalactic jets. 1: Gamma rays

A model of the approximately 0.1-10 GeV gamma-ray jets observed by the EGRET instrument on the Compton Gamma Ray Observatory (CGRO) is developed. It is shown that the soft X-ray background in an active galactic nuclei (AGN) contributes an opacity to pair production and that a gamma-ray photosphere or 'gamma-sphere' can be defined whose radius increases with gamma-ray energy E(sub gamma). It is proposed that the observed gamma-ray emission is due to inverse Compton scattering of the ambient soft X-rays by relativistic pairs accelerated in situ by shock fronts in a relativistic jet. For a wide range of assumed physical conditions, the emission at a given E(sub gamma) originates from near the associated gamma-spheres; emission from below the gamma-sphere initiates a cascade down to the energy where the gamma-rays can escape freely. In this model, the slope of the emergent gamma-ray spectrum is determined by the scattered, soft X-ray spectrum and the variation of the particle acceleration rate with jet radius. In general it is expected that the variation in the gamma-ray flux will be either slower or later at higher energy. It is also shown that the efficiency of conversion of energy from injected high-energy pairs to 0.1-10 GeV gamma-rays is typically high so that the models are radiatively efficient. It is argued that the observed gamma-ray jets are likely to be particle-dominated, though magnetically confined. The gamma-ray spectrum should continue down to an energy approximately 5 MeV emitted from an annihilation radius within which the pair content of the jet is limited by annihilation. This is probably the site of the beamed hard X-ray emission. It is speculated that the relativistic jets associated with radio-loud AGNs are powered electromagnetically by a spinning black hole and that they are collimated by an encircling MHD wind leaving the accretion disk at a slower speed. Powerful FR2 radio sources are formed when the hole spins rapidly and the relativistic core accelerates the MHD sheath; low-power FR1 sources ensue when the opposite occurs. Finally, it is suggested that the key factor which determines whether or not a given active nucleus can form a jet and a radio to gamma-ray nonthermal continuum is the central density of mass-losing stars which, when large, precludes the formation of a super-Alfvenic, collimating wind.

Blandford, R. D.↗

DOE OSTI2025

General kinetic ion-induced electron emission model for metallic walls applied to biased Z-pinch electrodes

A kinetic ion-induced electron emission (IIEE) model for general applications is developed to obtain the emitted electron energy spectrum for a distribution of ion impacts on a metallic surface. We assume an ionization cascade mechanism and use empirical models for the ion and electron stopping powers. The emission spectrum and the secondary electron yield (SEY) are validated for a variety of materials. The IIEE model is used to study the effect of IIEE on the plasma-material interactions of Z-pinch electrodes. Un-magnetized Boltzmann-Poisson simulations are performed for a Z-pinch plasma doubly bounded by two biased copper electrodes with and without IIEE at bias potentials from 0 to 9 kV. At the anode, the SEY decreases from 0 to 1 kV, but then increases at higher bias potentials. At the cathode, the SEY is much larger due to higher energy ion bombardment and grows with bias potential. As the bias potential increases, the emitted cathode electrons are accelerated to higher energies into the domain, collisionally heating the plasma. Above 1 kV, the heating is strong enough to increase the plasma potential. Despite SEY greater than 1, only a classical sheath forms as opposed to a space-charge limited or inverse sheath due to the emitted electron flux not reaching the space charge current saturation limits. Furthermore, the current in the emissionless cases saturates to a value lower than experiment. With IIEE, the current does not saturate and continues to increase with the 4 kV case, matching most closely with the experiment.

Carbon based materials↗