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NASA NTRS1994

Split mandrel versus split sleeve coldworking: Dual methods for extending the fatigue life of metal structures

It is common practice to use split sleeve coldworking of fastener holes as a means of extending the fatigue life of metal structures. In search of lower manufacturing costs, the aerospace industry is examining the split mandrel (sleeveless) coldworking process as an alternative method of coldworking fastener holes in metal structures. The split mandrel process (SpM) significantly extends the fatigue life of metal structures through the introduction of a residual compressive stress in a manner that is very similar to the split sleeve system (SpSl). Since the split mandrel process is significantly less expensive than the split sleeve process and more adaptable to robotic automation, it will have a notable influence upon other new manufacture of metal structures which require coldworking a significant number of holes, provided the aerospace community recognizes that the resulting residual stress distributions and fatigue life improvement are the same for both processes. Considerable testing has validated the correctness of that conclusion. The findings presented in this paper represent the results of an extensive research and development program, comprising data collected from over 400 specimens fabricated from 2024-T3 and 7075-T651 aluminum alloys in varied configurations, which quantify the benefits (fatigue enhancement and cost savings) of automating a sleeveless coldworking system.

Rodman, Geoffrey A.↗

NASA NTRS1979

Relative motions of fragments of the split comets. III - A test of splitting and comets with suspected multiple nuclei

A quantitative test of splitting for comets with suspected multiple nuclei has been formulated using a model which assumes the motions of cometary fragments to be due primarily to outgassing. The model expresses the relative motion of the cometary fragments in terms of the time of splitting and the differential force, which are determined by measurements of the position angle and the separation distance between fragments. The test is applied to 18 comets suspected of having multiple nuclei, of which the comets Sawerthal 1888 I, Campbell 1914 IV, Whipple-Fedtke-Tevzadze 1943 I, Honda 1955 V, Wild 1968 III and Tago-Sato-Kosaka 1969 IX were found to be clear cases of split comets and Davidson 1889 IV and Periodic Giacobini 1896 V were judged to be likely candidates. At least three of the secondary nuclei confirmed can be classified as short-lived companions, while only two appear to be persistent.

Sekanina, Z.↗

NASA NTRS1999

Entropy Splitting and Numerical Dissipation

A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework.

Yee, H. C.↗

NASA NTRS2019

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Ols- son & Oliger (1994), Gerritsen & Olsson (1996), and Yee et al. (2000) is revisited. The entropy splitting is a form of skew-symmetric splitting of the nonlinear Euler flux derivatives. Central differencing applied to the entropy splitting form of the Euler flux derivatives together with SBP difference operators will, hereafter, be referred to as entropy split schemes. This study is prompted by the recent growing interest in numerical methods for which a discrete entropy conservation law holds, a discrete global entropy conservation can be proved and/or the numerical method possesses a stable entropy in the framework of SBP difference operators and L2-energy norm estimate. The objective of this paper is to recast the entropy split scheme as the re- cent definition of an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for non- linear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grub- ber splitting.

Sjogreen, Bjorn↗

NASA NTRS1985

Longitudinal splitting in unidirectional composites, analysis and experiments

An experimental study is conducted to determine the fracture behavior of center notched, unidirectional graphite/epoxy laminates when subjected to tensile loading. The actual behavior is compared to the behavior predicted by a mathematical model based on classical shear-lag assumptions. The model allows for damage to occur in the form of longitudinal matrix yielding and splitting with the matrix assumed to fail in pure shear. Results indicate that the model is capable of predicting split initiation stress levels accurately, but does not describe the subsequent split growth adequately. The model predicts rapid split growth following split initiation due to shear failure, while the actual behavior involves a slow split growth region prior to the rapid growth region. It is suggested that transverse matrix normal stresses are responsible for split initiation and the early, slow split growth. The model predicts the actual initiation stress levels reliably, and also appears to be able to predict the point at which the shear failure mode begins to dominate. The shear failure mode does eventually dominate, but at a slower rate than predicted. The nonuniform structure of the graphite/epoxy laminates is thought to be responsible for decreasing the split growth rate due to shear failure.

Goree, J. G.↗

NASA NTRS1987

Experimental evaluation of longitudinal splitting in unidirectional composites

An experimental study was conducted to determine the fracture behavior of centernotched, unidirectional graphite/epoxy laminates when subjected to tensile loading. The actual behavior is compared to the behavior predicted by a mathematical model based on classical shear-lag assumptions. Experimental results show the fracture behavior to consist of two modes of longitudinal matrix splitting. After split initiation, a region of slow, stable split growth occurs. This is followed by a distinct transition into a rapid split growth region. However, the shear-lag model predicts a single region of rapid longitudinal split growth behavior with unbounded splitting occurring after approximately a ten percent increase in the applied stress over the split initiation stress. It is therefore concluded that the classical shear-lag model does not accurately predict the complete longitudinal split growth behavior in a brittle matrix composite. This shortcoming in the model and some results obtained from related elasticity solutions are discussed and it is suggested that the slow, stable split growth region is likely dominated by transverse matrix normal stresses which are not accounted for in the classical shear-lag model.

Wolla, Jeffrey M.↗

NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗

NASA NTRS1988

Initial high-degree p-mode frequency splittings from the 1988 Mt. Wilson 60-foot Tower Solar Oscillation Program

The initial frequency splitting results of solar p-mode oscillations obtained from the 1988 helioseismology program at the Mt. Wilson Observatory are presented. The frequency splittings correspond to the rotational splittings of sectoral harmonics which range in degree between 10 and 598. They were obtained from a cross-correlation analysis of the prograde and retrograde portions of a two-dimensional (t - v) power spectrum. This power spectrum was computed from an eight-hour sequence of full-disk Dopplergrams obtained on July 2, 1988, at the 60-foot tower telescope with a Na magneto-optical filter and a 1024x1024 pixel CCD camera. These frequency splittings have an inherently larger scatter than did the splittings obtained from earlier 16-day power spectra. These splittings are consistent with an internal solar rotational velocity which is independent of radius along the equatorial plane. The normalized frequency splittings averaged 449 + or - 3 nHz, a value which is very close to the observed equatorial rotation rate of the photospheric gas of 451.7 nHz.

Rhodes, Edward J., Jr.↗

NASA NTRS1992

Magnetic photon splitting and gamma ray burst spectra

The splitting of photons into two photons becomes both possible and significant in magnetic fields in excess of 10(exp 12) Gauss. Below the threshold energy, 2m sub e c(exp 2) for single photon pair production, splitting can be an astronomically observable phenomenon evident in gamma ray burst spectra. In such circumstances, it was found that magnetic photon splitting reprocesses the gamma ray burst continuum by degrading the photon energy, with a net effect that is quite similar to pair cascade reprocessing of the spectrum. Results are presented for the spectral modifications due to splitting, taking into account the different probabilities for splitting for different polarization modes. Unpolarized and polarized pair cascade photon spectra form the input spectra for the model, which calculates the resulting splitting reprocessed spectra numerically by solving the photon kinetic equations for each polarization mode. This inclusion of photon polarizations is found to not alter previous predictions that splitting produce a significant flattening of the hard X ray continuum and a bump at MeV energies below a pair production turnover. The spectrum near the bump is always strongly polarized.

Baring, Matthew G.↗

NASA NTRS2002

Torque Splitting by a Concentric Face Gear Transmission

Tests of a 167 Kilowatt (224 Horsepower) split torque face gearbox were performed by the Boeing Company in Mesa, Arizona, while working under a Defense Advanced Research Projects Agency (DARPA) Technology Reinvestment Program (TRP). This paper provides a summary of these cooperative tests, which were jointly funded by Boeing and DARPA. Design, manufacture and testing of the scaled-power TRP proof-of-concept (POC) split torque gearbox followed preliminary evaluations of the concept performed early in the program. The split torque tests were run using 200 N-m (1767 in-lbs) torque input to each side of the transmission. During tests, two input pinions were slow rolled while in mesh with the two face gears. Two idler gears were also used in the configuration to recombine torque near the output. Resistance was applied at the output face gear to create the required loading conditions in the gear teeth. A system of weights, pulleys and cables were used in the test rig to provide both the input and output loading. Strain gages applied in the tooth root fillets provided strain indication used to determine torque splitting conditions at the input pinions. The final two pinion-two idler tests indicated 52% to 48% average torque split capabilities for the two pinions. During the same tests, a 57% to 43% average distribution of the torque being recombined to the upper face gear from the lower face gear was measured between the two idlers. The POC split torque tests demonstrated that face gears can be applied effectively in split torque rotorcraft transmissions, yielding good potential for significant weight, cost and reliability improvements over existing equipment using spiral bevel gearing.

Filler, Robert R.↗

NASA NTRS2004

Measurements With a Split-Fiber Probe in Complex Unsteady Flows

A split-fiber probe was used to acquire unsteady data in a research compressor. A calibration method was devised for a split-fiber probe, and a new algorithm was developed to decompose split-fiber probe signals into velocity magnitude and direction. The algorithm is based on the minimum value of a merit function that is built over the entire range of flow velocities for which the probe was calibrated. The split-fiber probe performance and signal decomposition was first verified in a free-jet facility by comparing the data from three thermo-anemometric probes, namely a single-wire, a single-fiber, and the split-fiber probe. All three probes performed extremely well as far as the velocity magnitude was concerned. However, there are differences in the peak values of measured velocity unsteadiness in the jet shear layer. The single-wire probe indicates the highest unsteadiness level, followed closely by the split-fiber probe. The single-fiber probe indicates a noticeably lower level of velocity unsteadiness. Experiments in the NASA Low Speed Axial Compressor facility revealed similar results. The mean velocities agreed well, and differences in the velocity unsteadiness are similar to the case of a free jet. A reason for these discrepancies is in the different frequency response characteristics of probes used. It follows that the single-fiber probe has the slowest frequency response. In summary, the split-fiber probe worked reliably during the entire program. The acquired data averaged in time followed closely data acquired by conventional pneumatic probes.

Lepicovsky, Jan↗

NASA NTRS1994

Responses of soybean to ammonium and nitrate supplied in combination to the whole root system or separately in a split-root system

To address the questions of whether allocation of carbohydrates to roots is influenced by ionic form of nitrogen absorbed and whether allocation of carbohydrates to roots in turn influences proportionality between NH4+ and NO3- uptake from mixed sources, NH4+ and NO3- were supplied separately to halves of a split-root hydroponic system and were supplied in combination to a whole-root system. Dry matter accumulation in the split-root system was 18% less in the NH4(+)-fed axis than in the NO3(-)-fed axis. This, however, does not indicate that partitioning of carbohydrate between the two axes was different. Most of the reduction in dry matter accumulation in the NH4(+)-fed axis can be accounted for by the retransport of CH2O equivalents from the root back to the shoot with amino acids produced by NH4+ assimilation. Uptake of NH4+ or NO3- by the respective halves of the split-root system was proportional to the estimated allocation of carbohydrate to that half. When NH4+ and NO3- were supplied to separate halves of the split-root system, the cumulative NH4+ to NO3- uptake ratio was 0.81. When supplied in combination to the whole-root system, the cumulative NH4+ to NO3- uptake ratio was 1.67. Thus, while the shoot may affect total nitrogen uptake through the export of carbohydrates to roots, the shoot (common for halves of the split-root system) apparently does not exert a direct effect on proportionality of NH4+ and NO3- uptake by roots. For whole roots supplied with both NH4+ and NO3-, the restriction in uptake of NO3- may involve a stimulation of NO3- efflux rather than an inhibition of NO3- influx. While only the net uptake of NH4+ and NO3- was measured by ion chromatography, monitoring at approximately hourly intervals during the first 3 days of treatment revealed irregularly occurring intervals of both depletion (net influx) and enrichment (net efflux) in solutions. In the case of NH4+, numbers of net efflux events were similar (21 to 24 out of 65 sequential sampling intervals) whether NH4+ was supplied with NO3- to whole-root systems or separately to an axis of the split-root system. In the case of NO3-, however, the number of net efflux events increased from 8 when NO3- was supplied to a separate axis of the split-root system to between 19 and 24 when NO3- was supplied with NH4+ to whole-root systems.

Non-NASA Center↗

NASA NTRS2019

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Olsson & Oliger, Gerritsen & Olsson, and Yee et al. (15, 7, 37) is revisited. The objective of this paper is to prove for the first time that the entropy split scheme is an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for nonlinear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. The proof is to replace the spatial derivatives by summation-by-parts (SBP) difference operators in the entropy split form of the equations using the physical entropy of the Euler equations. The numerical boundary closure follows directly from the SBP operator. No additional numerical boundary procedure is required. In contrast, Tadmor-type entropy conserving schemes (31) using mathematical entropies and more recently in (35], do not naturally come with a numerical boundary closure and a generalized SBP operator has to be developed (18). Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grubber splitting.

Sjogreen, Bjorn↗

NASA NTRS1941

Wind-Tunnel Investigation of Perforated Split Flaps for Use as Dive Brakes on a Tapered NACA 23012 Airfoil

Aerodynamic characteristics of a tapered NACA 23012 airfoil with single and double perforated split flaps have been determined in the NACA 7- by 10-foot wind tunnel. Dynamic pressure surveys were made behind the airfoil at the approximate location of the tail in order to determine the extent and location of the wake for several of the flap arrangements. In addition, computations have been made of an application of perforated double split flaps for use as fighter brakes. The results indicated that single or double perforated split flaps may be used to obtain satisfactory dive control without undue buffeting effects and that single or double perforated split flaps may also be used as fighter brakes. The perforated split flaps had approximately the same effects on the aerodynamic and wake characteristics of the tapered airfoil as on a comparable rectangular airfoil.

WING FLAPS, SPLIT - PERFORATED↗

NASA NTRS1982

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics for real and perfect gases

A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.

Lombard, C. K.↗

NASA NTRS1991

A new flux splitting scheme

A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.

Liou, Meng-Sing↗

NASA NTRS1993

An upwind, kinetic flux-vector splitting method for flows in chemical and thermal non-equilibrium

We have developed new upwind kinetic difference schemes for flows with non-equilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Splitting the velocity distribution at the Boltzmann level is seen to result in a flux-split Euler scheme and is called Kinetic Flux Vector Splitting (KFVS). Extensions to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing nonequilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van Leer and Roe for a quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, and viscous flow over a cone at zero angle-of-attack. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.

Eppard, W. M.↗

NASA NTRS1993

A new flux splitting scheme

Liou, Meng-Sing↗