CHARACTERISTIC ROOTS FOR DONNELL'S EQUATIONS WITH UNIFORM AXIAL PRESTRESS.
Characteristic roots for donnells equations with uniform axial prestress
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Effect of Blade-root Fit and Lubrication on Vibration Characteristics of Ball-root-type Axial-flow-compressor Blades
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Hanson, Morgan P↗
The promotive effect of latrunculin B on maize root gravitropism is concentration dependent
The cytoskeleton has been proposed to be a key player in the gravitropic response of higher plants. A major approach to determine the role of the cytoskeleton in gravitropism has been to use inhibitors to disrupt the cytoskeleton and then to observe the effect that such disruption has on organ bending. Several investigators have reported that actin or microtubule inhibitors do not prevent root gravitropism, leading to the conclusion that the cytoskeleton is not involved in this process. However, there are recent reports showing that disruption of the actin cytoskeleton with the actin inhibitor, latrunculin B, promotes the gravitropic response of both roots and shoots. In roots, curvature is sustained during prolonged periods of clinorotation despite short periods of gravistimulation. These results indicate that an early gravity-induced signal continues to persist despite withdrawal of the constant gravity stimulus. To investigate further the mechanisms underlying the promotive effect of actin disruption on root gravitropism, we treated maize roots with varying concentrations of latrunculin B in order to determine the lowest concentration of latrunculin B that has an effect on root bending. After a 10-minute gravistimulus, treated roots were axially rotated on a one rpm clinostat and curvature was measured after 15 hours. Our results show that 100 nM latrunculin B induced the strongest promotive effect on the curvature of maize roots grown on a clinostat. Moreover, continuously gravistimulated roots treated with 100 nM latrunculin B exhibited stronger curvature responses while decapped roots treated with this concentration of latrunculin B did not bend during continuous gravistimulation. The stronger promotive effect of low concentrations of latrunculin B on the curvature of both clinorotated and continuously gravistimulated roots suggests that disruption of the finer, more dynamic component of the actin cytoskeleton could be the cause of the enhanced tropic responses of roots to gravity. c2003 COSPAR. Published by Elsevier Ltd. All rights reserved.
Non-NASA Center↗
Root elongation against a constant force: experiment with a computerized feedback-controlled device
Axial force was applied to the root tip of corn (Zea mays L. cv. Merit) seedlings using a computerized, feedback-controlled mechanical device. The system's feedback capability allowed continuous control of a constant tip load, and the attached displacement transducer provided the time course of root elongation. Loads up to 7.5 g decreased the root elongation rate by 0.13 mm h-1 g-1, but loads 7.5 to 17.5 g decreased the growth rate by only 0.04 mm h-1 g-1. Loads higher than 18 g stopped root elongation completely. Measurement of the cross-sectional areas of the root tips indicated that the 18 g load had applied about 0.98 MPa of axial pressure to the root, thereby exceeding the root's ability to respond with increased turgor pressure. Recorded time-lapse images of loaded roots showed that radial thickening (swelling) occurred behind the root cap, whose cross-sectional area increased with tip load.
Non-NASA Center↗
The Arabidopsis SKU5 gene encodes an extracellular glycosyl phosphatidylinositol-anchored glycoprotein involved in directional root growth
To investigate how roots respond to directional cues, we characterized a T-DNA-tagged Arabidopsis mutant named sku5 in which the roots skewed and looped away from the normal downward direction of growth on inclined agar surfaces. sku5 roots and etiolated hypocotyls were slightly shorter than normal and exhibited a counterclockwise (left-handed) axial rotation bias. The surface-dependent skewing phenotype disappeared when the roots penetrated the agar surface, but the axial rotation defect persisted, revealing that these two directional growth processes are separable. The SKU5 gene belongs to a 19-member gene family designated SKS (SKU5 Similar) that is related structurally to the multiple-copper oxidases ascorbate oxidase and laccase. However, the SKS proteins lack several of the conserved copper binding motifs characteristic of copper oxidases, and no enzymatic function could be assigned to the SKU5 protein. Analysis of plants expressing SKU5 reporter constructs and protein gel blot analysis showed that SKU5 was expressed most strongly in expanding tissues. SKU5 was glycosylated and modified by glycosyl phosphatidylinositol and localized to both the plasma membrane and the cell wall. Our observations suggest that SKU5 affects two directional growth processes, possibly by participating in cell wall expansion.
NASA Discipline Plant Biology↗
Rotor with Flattened Exit Pressure Profile
A rotor blade comprises an airfoil extending radially from a root section to a tip section and axially from a leading edge to a trailing edge, the leading and trailing edges defining a curvature therebetween. The curvature determines a relative exit angle at a relative span height between the root section and the tip section, based on an incident flow velocity at the leading edge of the airfoil and a rotational velocity at the relative span height. In operation of the rotor blade, the relative exit angle determines a substantially flat exit pressure ratio profile for relative span heights from 75% to 95%, wherein the exit pressure ratio profile is constant within a tolerance of 10% of a maximum value of the exit pressure ratio profile.
Baltas, Constantine↗
Geared Turbofan Engine Having a Reduced Number of Fan Blades and Improved Acoustics
A rotor blade comprises an airfoil extending radially from a root section to a tip section and axially from a leading edge to a trailing edge, the leading and trailing edges defining a curvature therebetween. The curvature determines a relative exit angle at a relative span height between the root section and the tip section, based on an incident flow velocity at the leading edge of the airfoil and a rotational velocity at the relative span height. In operation of the rotor blade, the relative exit angle determines a substantially flat exit pressure ratio profile for relative span heights from 75% to 95%, wherein the exit pressure ratio profile is constant within a tolerance of 10% of a maximum value of the exit pressure ratio profile.
Baltas, Constantine↗
Measurements of the free stream fluctuations above a turbulent boundary layer
This paper investigates the velocity fluctuations in the free stream above an incompressible turbulent boundary layer developing at constant pressure. It is assumed that the fluctuations receive contributions from three statistically independent sources: (1) one-dimensional unsteadiness, (2) free stream turbulence, and (3) the potential motion induced by the turbulent boundary layer. Measurements were made in a wind tunnel with a root-mean-square level of the axial velocity fluctuations of about 0.2 percent. All three velocity components were measured using an X-wire probe. The unsteadiness was determined from the spanwise covariance of the axial velocity, measured using two single wire probes. The results show that it is possible to separate the contributions to the r.m.s. level of the velocity fluctuations, without resorting to the dubious technique of high-pass filtering. The separation could be extended to the spectral densities of the contributions, if measurements of sufficient accuracy were available. The Appendix provides a general guide for the measurement of small free stream fluctuation levels.
Wood, David H.↗
Measurements of the Free-Stream Fluctuations above a Turbulent Boundary Layer
In this paper an investigation of the velocity fluctuations in the free stream above an incompressible turbulent boundary layer developing at constant pressure is described. It is assumed that the fluctuations receive contributions from three statistically independent sources: (1) one-dimensional unsteadiness, (2) free-stream turbulence, and (3) the irrotational motion induced by the turbulent boundary layer. Measurements were made in a wind tunnel with a root-mean-square level of the axial velocity fluctuations of about 0.2%. All three velocity components were measured using an X-wire probe. The unsteadiness was determined from the spanwise covariance of the axial velocity fluctuations, measured using two single-wire probes. The results show that it is possible to separate the contributions to the rms level of the velocity fluctuations without resorting to the dubious technique of high-pass filtering. This separation could be extended to the spectral densities of the contributions if measurements of sufficient accuracy were available.
Wood, D. H.↗
On Geomagnetism and Paleomagnetism
A statistical description of Earth's broad scale, core-source magnetic field has been developed and tested. The description features an expected, or mean, spatial magnetic power spectrum that is neither "flat" nor "while" at any depth, but is akin to spectra advanced by Stevenson and McLeod. This multipole spectrum describes the magnetic energy range; it is not steep enough for Gubbins' magnetic dissipation range. Natural variations of core multipole powers about their mean values are to be expected over geologic time and are described via trial probability distribution functions that neither require nor prohibit magnetic isotropy. The description is thus applicable to core-source dipole and low degree non-dipole fields despite axial dipole anisotropy. The description is combined with main field models of modem satellite and surface geomagnetic measurements to make testable predictions of: (1) the radius of Earth's core, (2) mean paleomagnetic field intensity, and (3) the mean rates and durations of both dipole power excursions and durable axial dipole reversals. The predicted core radius is 0.7% above the 3480 km seismologic value. The predicted root mean square paleointensity (35.6 mu T) and mean Virtual Axial Dipole Moment (about 6.2 lx 1022 Am(exp 2)) are within the range of various mean paleointensity estimates. The predicted mean rate of dipole power excursions, as defined by an absolute dipole moment <20% of the 1980 value, is 9.04/Myr and 14% less than obtained by analysis of a 4 Myr paleointensity record. The predicted mean rate of durable axial dipole reversals (2.26/Myr) is 2.3% more than established by the polarity time-scale for the past 84 Myr. The predicted mean duration of axial dipole reversals (5533 yr) is indistinguishable from an observational value. The accuracy of these predictions demonstrates the power and utility of the description, which is thought to merit further development and testing. It is suggested that strong stable stratification of Earth's uppermost outer core leads to a geologically long interval of no dipole reversals and a very nearly axisymmetric field outside the core. Statistical descriptions of other planetary magnetic fields are outlined.
Voorhies, Coerte V.↗
Prediction of far flow field in trailing vortices.
A finite-difference machine code is brought to bear on the wake-vortex problem in the quasi-cylindrical boundary-layer approximation. A turbulent-energy model containing new features is developed. Parameters of the model are evaluated by comparison of calculated velocities and turbulent intensities with measurements in an axisymmetric wake. Comparisons are made with a previous calculation of the decay of an isolated vortex and with wind tunnel and flight measurements in trailing vortices. A self-similar solution develops at large axial distance that decays with the square root of distance. A slower decay occurs in the preceding transition region.
Baldwin, B. S.↗
Interpretation of dispersion relations for bounded systems.
Treatment of the problem of constructing normal modes for an arbitrarily bounded system from roots of the linear dispersion relation D(omega, k) = 0 for the corresponding infinite or periodically bounded system. For a system described by continuous macroscopic variables, and of general cylindrical form, each transverse eigenmode gives rise to a set of axial normal modes constructed from a pair of dominant roots of D = 0 satisfying the boundary conditions which are characterized by complex reflection coefficients for the dominant waves. The implications of the results for the interpretation of experiments on plasma waves and instabilities on finite cylinders are discussed, with particular reference to the effects of end-plate damping and axial current on Q-machines.
Rognlien, T. D.↗
A boundary-coupled generalization of the Newcomb stability criterion
In magnetohydrodynamic problems in which there are boundaries in the axial or azimuthal symmetry directions, the energy principle involves multiple nonorthogonal trial perturbations. The subsequent Euler-Lagrange coupling of these allowed excitations necessitates a generalization of the Newcomb necessary-and-sufficient stability criterion. This extension, in which the absence of a conjugate point (instead of a simple zero) provides stability, is described in this paper. An important aspect of the proof involves the treatment of certain asymmetries which arise in the presence of the anisotropy caused by the magnetic field. The general method described here has applications to finite-length axial laboratory pinches and to astrophysical plasmas with rooted magnetic fields.
Ray, A.↗
Benchmark cyclic plastic notch strain measurements
Plastic strains at the roots of notched specimens of Inconel 718 subjected to tension-compression cycling at 650 C are reported. These strains were measured with a laser-based technique over a gage length of 0.1 mm and are intended to serve as 'benchmark' data for further development of experimental, analytical, and computational approaches. The specimens were 250 mm by 2.5 mm in the test section with double notches of 4.9 mm radius subjected to axial loading sufficient to cause yielding at the notch root on the tensile portion of the first cycle. The tests were run for 1000 cycles at 10 cpm or until cracks initiated at the notch root. The experimental techniques are described, and then representative data for the various load spectra are presented. All the data for each cycle of every test are available on floppy disks from NASA.
Sharpe, W. N., Jr.↗
Initial values for the integration scheme to compute the eigenvalues for propagation in ducts
A scheme for the calculation of eigenvalues in the problem of acoustic propagation in a two-dimensional duct is described. The computation method involves changing the coupled transcendental nonlinear algebraic equations into an initial value problem involving a nonlinear ordinary differential equation. The simplest approach is to use as initial values the hardwall eigenvalues and to integrate away from these values as the admittance varies from zero to its actual value with a linear variation. The approach leads to a powerful root finding routine capable of computing the transverse and axial wave numbers for two-dimensional ducts for any frequency, lining, admittance and Mach number without requiring initial guesses or starting points.
Eversman, W.↗
Imperfection surveys on a 10-ft-diameter shell structure
The results of an extensive imperfection survey on a 10-ft-diameter integrally stiffened cylindrical shell are presented. The shape of the measured initial imperfections is clearly influenced by details of the shell construction. The modal components of the measured imperfection surface as a function of the circumferential and of the axial wave numbers are calculated. The discrete axial power spectral density functions and the corresponding root-mean-square values of the imperfections are also determined for given circumferential wave numbers. Using the Fourier coefficients of the measured initial imperfections, buckling loads are calculated by solving the nonlinear Donnell-type imperfect shell equations iteratively. The calculated lowest buckling load compares favorably with the values usually recommended for similar shell structures.
Arbocz, J.↗
CFD Study of the J2-X LOX Two-Bladed Inducer in the Presence of a Circumferential Groove
Results are presented of a computational fluid dynamics (CFD) study done in support of water flow experiments of the J-2X Oxidizer Turbopump (OTP) 2-bladed inducer with a circumferential groove that were conducted at Marshall Space Flight Center (MSFC). Sub-scale water flow testing results indicate that the circumferential groove greatly reduces synchronous cavitation and subsequent bearing loads at a minimal performance cost, but the energy reappears as high order cavitation (HOC) that spans a relatively large frequency range. Thus, HOC may have implications for the full-scale OTP inducer in terms of reduced structural margin at higher mode frequencies. Simulations using the LOCI-Stream CFD program were conducted in order to explore the root physical cause of the HOC. It was found that the axial recirculation pattern in the circumferential groove causes high-swirl fluid to interact with the nearly-axial incoming fluid just above the inducer blades. The high-shear interface between the fluids is Kelvin-Helmholtz unstable, resulting in trains of low pressure regions or 'pearls' forming near the upstream edge of the groove. When the pressure in these regions becomes low enough and they get cut by the blade leading edge, HOC is thought to occur. Although further work is required, the numerical models indicate that the root cause of HOC is hydrodynamic. That is, the pearls are always present, even when cavitation is not. Comparisons to ongoing water flow experiments will be discussed, as well as predictions for the full-scale OTP inducer.
Coker, Robert↗
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.↗