Experimental K-factor Research Articles

Using Experiments, 3D Scanning, and CFD to Analyze the Variance in Energy Losses Through Pipe Elbows

Pipe bends, or elbows, cause energy loss in pipelines due to the flow conditions they create. This energy loss has traditionally been approximated based on published minor loss coefficients, known as k-factors. However, the energy losses of elbows can vary based on geometric characteristics, which may not be accounted for in the published k-factors. The purpose of this research was to quantify the variance in energy loss resulting from elbows with geometric differences and to determine appropriate methods for approximating these variances using computational fluid dynamics (CFD). Eight polyvinyl chloride (PVC) elbows were physically tested in a hydraulic laboratory to determine the individual loss coefficients. The resulting data show that the minor loss coefficient k for two short-radius elbows of the same nominal size can vary by up to 51%. The same tests on two of the elbows were repeated using CFD, in which they were modeled two different ways: 1) using the ideal geometry and 2) using the actual geometry. The actual geometry was captured using 3D scanning. Each geometry was used in a series of simulations, and the results were compared to the experimental data. The CFD simulations were able to reproduce similar variances between the two elbows as displayed in the physical tests, although they were unable to reproduce the same k-factors. When compared to the experimental k-factor data, using the actual geometries captured by 3D scanning was not consistently more accurate than using idealized geometries.

Partitioning of organics between ionic liquids and supercritical CO2: Limiting K-factors in [bmim][N(CN)2]–scCO2 system and generalized correlation with cation- and anion-specific LSERs

Infinite dilution partition coefficients (K-factors) of a selection of organic solutes in biphasic 1-n-butyl-3-methylimidazolium dicyanamide ([bmim][dca])–supercritical carbon dioxide (scCO2) system were obtained from retention measurements by open tubular capillary column supercritical fluid chromatography (SFC) with [bmim][dca] serving as the stationary liquid and scCO2 as the carrier fluid. Therefore, the SFC-based route to solute K-factors in ionic liquid (IL)–scCO2 systems is feasible even with low viscosity ILs such as [bmim][dca].The experimental K-factors in [bmim][dca]–scCO2 system were used to test an earlier generalized correlation of solute K-factors in IL–scCO2 systems. Further, another version of the generalized correlation was introduced and tested. In the linear solvation energy (LSER) part of the former correlation the IL has been treated as a single species whereas, in the new version, the IL cation- and anion-specific LSER part has been employed. The introduction of the ion-specific LSERs resulted in some performance improvement of the correlation.

$k$ -factor Test Voltage Function for Oscillating Lightning Impulses in Nonhomogenous Air Gaps

The k-factor function, called the test voltage function, in present standards IEEE Standard 4-2013 and IEC 60060-1, was determined years ago for voltages not higher than 100 kV and with relative overshoots around 15%. This paper presents the results of k-factor tests carried out for greater voltages up to +1.32 MV (equivalent to air-gap distances d = 2.5 m) and many test conditions. These test conditions are relative overvoltages, β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">'</sup> up to 35%, different damping ratios: from δ = 0 (overshoot) to δ =35% (oscillating waveform), and different electrical configurations of a nonhomogenous electric field using air gap factors K = 1 (rod plane) up to K =1,45 (rod conductor). The results show that the present k-factor function stated in both standards does not represent insulation behavior for large air-gap distances when the gap factor K is around 1. Only when the gap factor K increases to 2, are the experimental k-factor values closer to the standard k-factor function. A general formula for the k-factor, depending on the oscillation frequency, gap distance, and the electric-field nonhomogeneity, k (f, d ,K) is derived from the performed tests, taking also into account the k-factor results of the recent bibliography.

Procedures to Determine k-Factor Function for Air Gaps

The new IEC 60060-1 standard establishes the k-factor function to determine the test voltage value of lightning impulses with superimposed oscillations, but no rule is given to determine experimental k-factor values. Testing methods, testing setups, and formulas to determine k-factor values are some crucial issues to obtain good results. This paper describes the two procedures used in the investigation funded by the European community and referenced in the Annex D of the last edition of IEC 60060-1 standard to determine experimental k-factor for air gaps, one for nonhomogenous fields and other for quasihomogenous fields. Both procedures were implemented using a setup with only 1 generator and a setup with 2 generators. Compatibility of new experimental k-factor values determined for air gaps up to 900 kV in quasihomogenous field with the factor function stated in IEC 60060-1 is shown by means of several examples, but additional examples show a significant discrepancy for air clearances of a sharp rod-plate configuration in the voltage range 250 to 800 kV.

EELS of Niobium and Stoichiometric Niobium-Oxide Phases—Part II: Quantification

A comprehensive electron energy-loss spectroscopy (EELS) study of niobium (Nb) and stable Nb-oxide phases (NbO, NbO2, Nb2O5) was carried out. Part II of this work is devoted to quantitative EELS by means of experimental k-factors derived from the intensity ratio of the O-K edge and the Nb-M4,5 or Nb-M2,3 edges for all three stable Nb-oxides. The precision and accuracy of the quantification are investigated with respect to the influence of intensity-measurement energy windows, background subtraction, and sample thickness. Integration-window widths allowing optimum accuracy are determined. Owing to background-subtraction errors, the Nb-M4,5 edges rather than Nb-M2,3 are preferred for quantification. Different approaches are applied to improve the precision with regard to thickness-related errors. Thus, a precision up to +/-1.5% is achieved by averaging spectra from all three reference oxides to determine a k-factor using Nb-M4,5. Using the experimental k-factor, the determination of atomic concentration ratios CNb/CO in the range of 0.4 (Nb2O5) to 1 (NbO) was found to be possible with an accuracy of 0.6% (relative deviation between measured and nominal composition), whereas ratios of calculated partial ionization cross sections lead to less accurate results.

Experimental method for determining Cliff–Lorimer factors in transmission electron microscopy (TEM) utilizing stepped wedge-shaped specimens prepared by focused ion beam (FIB) thinning

An experimental method to determine the Cliff–Lorimer factor has been developed utilizing an ultra-wide double-wedge (UWDW) FIB membrane geometry with terraced steps that increase in thickness in increments of approximately 30 nm. Pure elements are deposited as thin films onto a single-crystal Si substrate and energy dispersive X-ray spectroscopy (EDS) is performed on each of the terrace steps. The linear relationship that exists between X-ray counts and specimen thickness can be established and the Cliff–Lorimer factor ( k-factor) determined. This method for experimental k-factor determination can be used as an alternative to intimately mixed standards, when they are difficult to obtain. The following general relation was developed to determine the k-factor by this method: k β− α =( m α / m β )( ρ β / ρ α ) where m α and m β are the slopes of X-ray intensity vs. thickness plots for elements α and β, respectively; and ρ α and ρ β are the mass densities of elements α and β. A polycrystalline Ni thin film on a single crystal Si substrate was used to test this method. The theoretical k-factor calculated for Ni and Si was k Ni–Si=1.50. Two k-factors were determined for the UWDW membrane using the appropriate microscope and detector conditions: k Right Ni–Si=1.51 for the terrace steps to the right of the specimen membrane, and k Left Ni–Si=1.56 for the terrace steps on the left side. These results agree to within 0.44% and 2.67%, respectively, of the calculated theoretical value.

Reduction of sampling and analytical errors for electron microscopic analysis of atmospheric aerosols

Electron microscopy-energy dispersive spectroscopy (EM/EDS) can be used to determine the elemental composition of individual particles. However, the accuracy with which atmospheric particle compositions can be quantitatively determined is not well understood. In this work we explore sources of sampling and analytical bias and methods of reducing bias. Sulfuric acid [H 2SO 4] and ammonium sulfate [(NH 4) 2SO 4] particles were collected on beryllium, silicon, and carbon substrates with similar deposition densities. While [(NH 4) 2SO 4] particles were observed on all substrates, [H 2SO 4] and ammonia-treated [H 2SO 4] particles could not be found on beryllium substrates. Interactions between the substrate and sulfuric acid particles are implicated. When measured with EM/EDS, [H 2SO 4] particles exposed to ammonia overnight were found having lower beam damage rates (0.000 ± 0.002 fraction s −1) than those without any treatment (0.023 ± 0.006 fraction s −1) For laboratory-generated [C 10H 6(SO 3Na) 2] particles, the composition determined using the experimental k-factors evaluated from independent particle standards of similar composition and size shows an error less than 20% for all constituents, while greater than 78% errors were found when k-factors were calculated from the theory. This study suggests (1) that sulfate beam damage can be reduced by exposure of atmospheric particle samples to ammonia before analysis, (2) that beryllium is not a suitable substrate for atmospheric particle analysis, and (3) calibration ( k-factor determination) using particle standards of similar size and composition to particles present in the atmosphere shows promise as a way of improving the accuracy of quantitative EM analysis.

Partitioning of uranium and rare earth elements in synroc: effect of impurities, metal additive, and waste loading

AEM techniques employing digital filtering, least squares profile fitting, and experimental k-factor calibrations were used to investigate 16 Synroc samples containing simulated Purex (PW-4b-D) HLW at loadings of 10, 15, 19, and 23 wt%. A second group of Synroc samples with 10 wt% HLW also contained additional impurities of F, Na, MgO, P 2O 5, and Fe 2O 3. A third set of samples with 10 wt% HLW contained different metal additions of Al, Ni, and Ti, and a sample with no metal addition for comparison. In samples with low Na 2O content, it was confirmed that element partitioning is mainly controlled by the ionic radius criterion, with smaller Y, Gd, and U ions having a preference for zirconolite and the larger Ce and Nd ions favoring perovskite. Average relative partitioning coefficients ( D Z P = metal oxide in zirconolite ÷ wt% metal oxide in perovskite ) of 8 samples with 10 wt% HLW and -∼0.5 wt% Na 2O are 0.14 ± 0.01, 0.39 ± 0.03, 1.7 ± 0.2, 3.8 ± 1.0, and 2.2 ± 0.8 for Ce, Nd, Gd, Y, and U, respectively. Element partitioning is not strongly affected by additional impurities of F, MgO, P 2O 5, or Fe 2O 3; metal addition; or waste loading. Additions of up to ∼3.6 wt% Na 2O lead to an increase in the amount of perovskite at the expense of zirconolite as well as a systematic shift in the partitioning of REEs and U from zirconolite into perovskite.

Comparison of experimental and theoretical XEDS k-factors as a function of accelerating voltage

For nearly fifteen years k-factor measurements have been made by varying the composition of the standards at fixed accelerating voltage and measuring the change in the experimental k-factor with atomic number. From this data a “best model” of the ionization cross-section is frequently proposed for use in quantitative analysis, however it is valid only at that fixed voltage. Few if any studies seek to determine the systematic variation in the k-factor with accelerating voltage. In this paper experimental measurements of the variation in the k-factor as a function of accelerating voltage are reported. With the advent of medium voltage analytical microscopes routinely available to the microscopy community, it becomes essential to understand how the k-factor varies with accelerating voltage in order that errors in quantitative analysis can be avoided should experimental or theoretical k-factors from lower voltage instruments are applied to the medium voltage regime.Electropolished specimens of β-NiAl were studied in a Philips CM30T electron microscope, equipped with a Be-Window Si(Li) detector interfaced to an EDAX 9900 Energy Dispersive Analysis System.

Fracture-mechanics investigations of cracks in rotating disks

Stress-intensity factorsK were determined both analytically and by using a photoelastic method for the simple case of a rotating solid disk containing radial cracks. Good agreement is found not only between the calculated and the experimentalK factors, but also between the static and the dynamic toughness values determined in ASTM tension tests and spin-burst tests. This confirms the applicability of linear-elastic fracture mechanics and the validity of the brittle-fracture criterion. In addition, the use of the simple superposition procedure is justified as a basis for the analysis. The possibilities of and the limitations on applying these results to practical situations are considered.