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NASA NTRS2007

Symmetry, Statistics and Structure in MHD Turbulence

Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.

Shebalin, John V.↗

NASA NTRS2010

The Origins of Magnetic Structure in the Corona and Wind

One of the most important and most puzzling features of the coronal magnetic field is that it appears to have smooth magnetic structure with little evidence for non-potentiality except at two special locations: photospheric polarity inversions lines. (non-potentiality observed as a filament channel) and coronal hole boundaries, (observed as the slow solar wind). This characteristic feature of the closed-field corona is highly unexpected given that its magnetic field is continuously tangled by photospheric motions. Although reconnection can eliminate some of the injected structure, it cannot destroy the helicity, which should build up to produce observable complexity. I propose that an inverse cascade process transports the injected helicity from the interior of closed flux regions to their boundaries inversion lines and coronal holes, creating both filament channels and the slow wind. We describe how the helicity is injected and transported and calculate the relevant rates. I argue that one process, helicity transport, can explain both the observed lack and presence of structure in the coronal magnetic field. This work has been supported by the NASA HTP, SR&T, and LWS programs.

Antiochos, Spiro K.↗

NASA NTRS2012

Tire

A tire includes a plurality of helical springs. Each helical spring includes a first end portion, a second end portion, and an arching middle portion. Each helical spring is interlaced with at least one other helical spring thereby forming a laced toroidal structure extending about an entire circumference of the tire.

Benzing, II, James Alfred↗

NASA NTRS2016

Advanced Face Gear Surface Durability Evaluations

The surface durability life of helical face gears and isotropic super-finished (ISF) face gears was investigated. Experimental fatigue tests were performed at the NASA Glenn Research Center. Endurance tests were performed on 10 sets of helical face gears in mesh with tapered involute helical pinions, and 10 sets of ISF-enhanced straight face gears in mesh with tapered involute spur pinions. The results were compared to previous tests on straight face gears. The life of the ISF configuration was slightly less than that of previous tests on straight face gears. The life of the ISF configuration was slightly greater than that of the helical configuration.

fatigue↗

NASA NTRS2022

STITCH: A Subgrid-Scale Model for Energy Buildup in the Solar Corona

The solar corona routinely exhibits explosive activity, in particular coronal mass ejections and their accompanying eruptive ares, that have global-scale consequences. These events and their smaller counterparts, coronal jets, originate in narrow, sinuous lament channels. The key processes that form and evolve the channels operate on still smaller spatial scales and much longer time scales, culminating in a vast separation of characteristic lengths and times that govern these explosive phenomena. In this article, we describe implementation and tests of an efficient subgrid-scale model for generating eruptive structures in magnetohydrodynamics (MHD) coronal simulations. STITCH {STatistical InjecTion of Condensed Helicity { is a physics-based, reduced representation of helicity condensation: a process wherein small-scale vortical surface convection forms ubiquitous current sheets, and pervasive reconnection across the sheets mediates an inverse cascade of magnetic helicity and free energy, thereby forming the lament channels. We have developed a formalism, STITCH, that abstracts these complex processes into a single term in Ohm's law and the induction equation that directly injects tangential magnetic flux into the low corona. We show that our approach is in very good agreement with a full helicity-condensation calculation that treats all of the dynamics explicitly, while enabling substantial reductions in temporal duration and spatial resolution. In addition, we illustrate the flexibility of STITCH at forming localized lament channels and at energizing complex surface flux distributions that have sinuous boundaries. STITCH is simple to implement and computationally ecient, making it a powerful technique for physics-based modeling of solar eruptive events.

J T Dahlin↗

NASA NTRSDate not supplied

Vertical Lunar Regolith Conveying as a Flight Experiment in Simulated Lunar-Gravity

Regolith conveying will be an essential task for supplying regolith feedstock to In-Situ Resource Utilization (ISRU) reactor systems for regolith processing on the Moon and Mars. The Vertical Lunar Regolith Conveyor (VLRC) is a technology being developed at NASA Kennedy Space Center (KSC) as a regolith transport task for the GCD ISRU FLEET project led by NASA Glenn Research Center (GRC). Single test loop versions of the VLRC are being developed at NASA KSC as a technology demonstration for a flight experiment. The NASA Flight Opportunities program selected the VLRC for a technology demonstration opportunity on a future Blue Origin New Shepard suborbital launch vehicle to study regolith transport physics in a relevant environment in a vacuum chamber under simulated lunar gravity conditions in order to advance its technology readiness level (TRL) for future space applications. The VLRC system includes four primary subsystems to achieve the objectives of the lunar gravity (Lunar-G) flight experiment. (1) An eccentric vibratory conveyor stack to convey regolith particles consisting of three single-loop helical surface conveyors with each actuated by two vibratory motors that vibrate in unison. One of the three single-loops contains a 0.8°-3.1° inclined helical path and the other two contain a 1.6°-6.2° incline. (2) A stick-slip conveyor stack to convey regolith particles consisting of three single-loop helical surface conveyors with each actuated by the same motor to move in unison in a stick-slip motion. One of the three single-loops contains a 0.8°-3.1° inclined helical path and the other two contain a 1.6°-6.2° incline. (3) A regolith containment system to contain the regolith in each single-loop track during launch before the start of the experiment using containment caps that will be lifted in unison at the start of Lunar-G. (4) COTS cameras will record the motion of regolith and tracer particles. Post-flight analysis of the videos will be used to determine convey speeds and flow rates. The VLRC experiment will use the well-known technique of Particle Image Velocimetry (PIV) image analysis to determine the velocity of tracer particles entrained in the regolith flow. This velocity will be used to calculate the mass flow rate of the regolith being conveyed.

ISRU↗

NASA NTRS1974

Self-energized plasma compressor

The self-energized plasma compressor is described which compresses plasma discharged from a coaxial plasma generator. The device includes a helically shaped coil which is coaxially aligned with the center axis of the coaxial plasma generator. The plasma generator creates a current through the helical coil which, in turn, generates a time varying magnetic field that creates a force which acts radially upon the plasma. The coaxial plasma generator and helical coil move the plasma under high pressure and temperature to the narrow end of the coil. Positioned adjacent to the narrow end of the coil are beads which are engaged by the plasma to be accelerated to hypervelocities for simulating meteoroids.

Shriver, E. L.↗

NASA NTRS1978

Three-dimensional magnetohydrodynamic turbulence in cylindrical geometry

A theory is developed in which a perfectly conducting cylindrical wall is used to describe incompressible MHD turbulence. Dynamic equations of incompressible MHD and its associated fields are expanded in a system of vector eigenfunctions of the curl. The total energy, magnetic helicity, and cross helicity have simple quadratic expressions in the expansion coefficients. The invariants are temporally constant for a truncation at a large, but finite, number of coefficients. The invariants are used to construct canonical distributions. It is noted that for all initial conditions, including quiescent ones, the mean-square velocity fields have finite values. The stability problem is transformed into a search for values of the integral variants which minimize the mean-square velocity fields. This leads to an extremal helicity principle.

Montgomery, D.↗

NASA NTRS1978

The exact numerical calculation of propeller noise

This paper presents a method for computing the acoustic pressure signature of a propeller due to blade thickness and steady surface pressure loading including the effect of forward motion. The tip helical speed is restricted to subsonic. The formulation is based on the Ffowcs Williams-Hawkings exact result concerning the sound generation by moving bodies. The blade surface is described in a helical coordinate system by the blade angles, positions of the leading and trailing edges along the local pitch helix, and the camber and thickness distributions along the chord. The retarded distance of the moving acoustic source on an element of surface area of the propeller blade is obtained numerically by Newton's method. The surface integration over the propeller blades is carried out in the helical coordinate system using a double Gauss-Legendre formula. Good agreement was found between analytic and experimental results, both in the time and frequency domains. Some samples showing the effects of propeller geometry and tip Mach number on the acoustic signature are included.

Woan, C. J.↗

NASA NTRS1984

Stability of fluid flow in a cylindrical annulus

Helical flow in an annulus between two coaxial cylinders is investigated with regard to its stability against the formation of helical vortices of the type known as Taylor's annular vortices. Assuming the annulus to be small and the velocities to vary linearly with radius, it is shown that the problem can be reduced to the classical case of flow between two rotating cylinders. An appropriate stability criterion for helical flows is derived from Rayleigh's stability criterion applicable to such flows.

Ludwieg, H.↗

NASA NTRS1987

Cruise noise of the 2/9th scale model of the Large-scale Advanced Propfan (LAP) propeller, SR-7A

Noise data on the Large-scale Advanced Propfan (LAP) propeller model SR-7A were taken in the NASA Lewis Research Center 8 x 6 foot Wind Tunnel. The maximum blade passing tone noise first rises with increasing helical tip Mach number to a peak level, then remains the same or decreases from its peak level when going to higher helical tip Mach numbers. This trend was observed for operation at both constant advance ratio and approximately equal thrust. This noise reduction or, leveling out at high helical tip Mach numbers, points to the use of higher propeller tip speeds as a possible method to limit airplane cabin noise while maintaining high flight speed and efficiency. Projections of the tunnel model data are made to the full scale LAP propeller mounted on the test bed aircraft and compared with predictions. The prediction method is found to be somewhat conservative in that it slightly overpredicts the projected model data at the peak.

Dittmar, James H.↗

NASA NTRS1988

Numerical Simulation of Subsonic and Transonic Propeller Flow

The numerical simulation of 3-D transonic flow about a system of propeller blades is investigated. In particular, it is shown that the use of helical coordinates significantly simplifies the form of the governing equation when the propeller system is assumed to be surrounded by an irrotational flow field of an inviscid fluid. The unsteady small disturbance equation, valid for lightly loaded blades and expressed in helical coordinates, is derived from the general blade-fixed potential equation, given for an arbitrary coordinate system. The use of a coordinate system which inherently adapts to the mean flow results in a disturbance equation requiring relatively few terms to accurately model the physics of the flow. Furthermore, the helical coordinate system presented here is novel in that it is periodic in the circumferential direction while, simultaneously, maintaining orthogonal properties at the mean blade locations. The periodic characteristic allows a complete cascade of blades to be treated, and the orthogonality property affords straightforward treatment of blade boundary conditions. An ADI numerical scheme is used to compute the solution of the steady flow as an asymptotic limit of an unsteady flow. As an example of the method, solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an 8-bladed cascade. Both high and low advance ratio cases are computed and include a lifting as well as nonlifting cases. The nonlifting solutions obtained are compared to solutions from a Euler code.

Snyder, Aaron↗

NASA NTRS1987

Cruise noise of the 2/9 scale model of the Large-scale Advanced Propfan (LAP) propeller, SR-7A

Dittmar, James H.↗

NASA NTRS1989

In-flight measurement of propeller noise on the fuselage of an airplane

In-flight measurements of propeller noise on the fuselage of an OV-10A aircraft were obtained using a horizontal and a vertical microphone array. A wide range of flight conditions were tested including changes in angle of attack, sideslip angle, power coefficient, helical tip Mach number and advance ratio, and propeller direction of rotation. Results show a dependence of the level and directivity of the tones on the angle of attack and on the sideslip angle with the propeller direction of rotation, which is similar to results obtained in wind tunnel tests with advanced propeller designs. The level of the tones at each microphone increases with increasing angle of attack for inboard-down propeller rotation and decreases for inboard-up rotation. The level also increases with increasing slideslip angle for both propeller directions of rotation. Increasing the power coefficient results in a slight increase in the level of the tones. A strong shock wave is generated by the propeller blades even at relatively low helical tip Mach numbers resulting in high harmonic levels. As the helical tip Mach number and the advance ratio are increased, the level of the higher harmonics increases much faster than the level of the blade passage frequency.

Pla, Frederic G.↗

NASA NTRS1989

Multiwave Interactions in Turbulent Jets

Nonlinear wave-wave interactions in turbulent jets were investigated based on the integrated energy of each scale of motion in a cross section of the jet. The analysis indicates that two frequency components in the axisymmetric mode can interact with other background frequencies in the axisymmetric mode, thereby amplifying an enormous number of other frequencies. Two frequency components in a single helical mode cannot, by themselves, amplify other frequency components. But combinations of frequency components of helical and axisymmetric modes can amplify other frequencies in other helical modes. The present computations produce several features consistent with experimental observations such as: (1) dependency of the interactions on the initial phase differences, (2) enhancement of the momentum thickness under multifrequency forcing, and (3) the increase in background turbulence under forcing. In a multifrequency-excited jet, mixing enhancement was found to be a result of the turbulence enhancement rather than simply the amplification of forced wave components. The excitation waves pump energy from the mean flow to the turbulence, thus enhancing the latter. The high frequency waves enhance the turbulence close to the jet exit, but, the low frequency waves are most effective further downstream.

Mankbadi, Reda R.↗

NASA NTRS1990

Modern developments in shear flow control with swirl

Passive and active control of swirling turbulent jets is experimentally investigated. Initial swirl distribution is shown to dominate the free jet evolution in the passive mode. Vortex breakdown, a manifestation of high intensity swirl, was achieved at below critical swirl number (S = 0.48) by reducing the vortex core diameter. The response of a swirling turbulent jet to single frequency, plane wave acoustic excitation was shown to depend strongly on the swirl number, excitation Strouhal number, amplitude of the excitation wave, and core turbulence in a low speed cold jet. A 10 percent reduction of the mean centerline velocity at x/D = 9.0 (and a corresponding increase in the shear layer momentum thickness) was achieved by large amplitude internal plane wave acoustic excitation. Helical instability waves of negative azimuthal wave numbers exhibit larger amplification rates than the plane waves in swirling free jets, according to hydrodynamic stability theory. Consequently, an active swirling shear layer control is proposed to include the generation of helical instability waves of arbitrary helicity and the promotion of modal interaction, through multifrequency forcing.

Farokhi, Saeed↗

NASA NTRS1990

Statistical properties of ideal three-dimensional magnetohydrodynamics

Classical Gibbs ensemble methods are used to study the spectral structure of three-dimensional ideal MHD in periodic geometry. In this paper the equilibrium ensemble incorporates constraints of total energy, magnetic helicity, and cross helicity. Several new results are proven for ensemble averages, including the constraint that magnetic energy equal or exceed kinetic energy, and that cross helicity represents a constant fraction of magnetic energy across the spectral domain, for arbitrary size systems. Two zero-temperature limits are considered in detail, emphasizing the role of complete and partial condensaiton of spectral quantities to the longest wavelength states. The ensemble predictions are compared to direct numerical solution using a low-order truncation Galerkin spectral code. Implications for spectral transfer of nonequilibrium, dissipative turbulent MHD systems are discussed.

Stribling, T.↗

NASA NTRS1990

Galerkin approximations for dissipative magnetohydrodynamics

A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. The lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Benard convection, but in the region of believed applicability, its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al.

Chen, Hudong↗