Geometrical Correction Factor Research Articles

Calibration system correction factor for measuring the reference air kerma rate (RAKR) applied to high dose rate 192Ir sources (HDR)

The aim of this study was to use computer simulation to analyze the impact of the aluminum fixing support on the Reference Air Kerma (RAK), a physical quantity obtained in a calibration system that was experimentally developed in the Laboratory of Radiological Sciences of the University of the State of Rio de Janeiro (LCR-UERJ). Correction factors due to scattered radiation and the geometry of the 192Ir sources were also sought to be determined. The computational simulation was validated by comparing some parameters of the experimental results with the computational results. These parameters were: verification of the inverse square law of distance, determination of (RAKR), analysis of the source spectrum with and without encapsulation, and the sensitivity curve of the Sourcecheck 4PI ionization chamber response, as a function of the distance from the source along the axial axis, using the microSelectron-v2 (mSv2) and GammaMedplus (GMp) sources. Kerma was determined by activity in the Reference air, with calculated values of 1.725 × 10−3 U. Bq−1 and 1.710 × 10−3 U. Bq−1 for the ionization chamber NE 2571 and TN 30001, respectively. The expanded uncertainty for these values was 0.932% and 0.919%, respectively, for a coverage factor (k = 2). The correction factor due to the influence of the aluminum fixing support for measurements at 1 cm and 10 cm from the source was 0.978 and 0.969, respectively. The geometric correction factor of the sources was ksg = 1.005 with an expanded uncertainty of 0.7% for a coverage factor (k = 2). This value has a difference of approximately 0.2% compared to the experimental values.

Multiscale Modeling of Flow in Rod Bundles: From Direct Numerical Simulation and Subchannel to Coarse-Mesh CFD

Fast and accurate evaluation of flow and heat transfer phenomena in rod bundles is a problem of long-standing interest in nuclear engineering. Computational fluid dynamics (CFD) can provide accurate but relatively time-intensive estimates, such that simulations of very long transients with high spatial detail are infeasible. On the other hand, subchannel codes require relatively low computational time and can provide pin-level estimates, but have substantial empiricism in evaluating aspects such as crossflows and turbulent mixing coefficients. A multiscale method (SC+) for bridging this accuracy/speed gap, based on the Subchannel CFD (SubChCFD) method of Liu et al. [Nucl. Eng. Design, Vol. 355, paper 110318 (2019)], is demonstrated and developed here with a focus on a 5 × 5 square rod bundle geometry. The method has been newly implemented into the commercial code STAR-CCM+ and benchmarked against Liu et al.’s data. The 5 × 5 geometry was chosen in part due to the availability of direct numerical simulation (DNS) data at a relevant Reynolds number of a similar configuration for comparison. The SC+ results are variously compared against results from DNS, large eddy simulation, wall-resolved Reynolds-averaged Navier-Stokes, and coarse-mesh CFD methods. As an expansion to the original SubChCFD approach, a simple Hi2Lo approach is demonstrated using the DNS data as a correction to the original friction factor correlations employed. This is verified to improve the predictions. Additional test cases with geometric perturbations are pursued, illustrating the flexibility of SC+. The potential of this method for modeling the narrow gap vortex instability, which would represent an advancement over standard subchannel approaches, is also assessed. The method is expanded to include transverse flow losses, which was found to improve the results for modeling the gap instability. Initial extensions of SC+ for hexagonal rod bundles are also presented; some inaccuracies for the coarsest meshes prompted a detailed investigation of the mesh convergence behavior of the method. Geometric correction factors were devised that provided substantial improvement on these very coarse meshes, improving the prospects of SC+ for wider usage. Future work plans are to expand the methodology to wire-wrapped rod bundles and to implement the method into Pronghorn, with a unified pipeline via the Cardinal wrapper between the codes NekRS, Pronghorn, and BISON, to solve fuel performance problems of direct interest to industry.

ZAFG Method for Quantitative Characterization of Spherical Particles: Deriving a Universal Equation for Geometrical Correction.

This study introduces a universal equation to calculate the geometrical correction factor (G) as the fourth factor in the conventional ZAF method for quantifying spherical particles (specifically, NIST-K411 glass microspheres mounted on bulk carbon substrate). Note that the fluorescence correction factor (F) is not considered in this study. Our findings demonstrate that the G factor, as a function of the particle diameter (D) and the range of emitted X-rays in a bulk sample (Xe), provides the best model. Xe depends on the chemical composition and accelerating voltage. We observed excellent agreement between the G factor predicted by our model and experimental data obtained from NIST-K411 standard particles. Our results show that when Xe is greater than D, the G factor decays exponentially, independent of the incident electron energy, X-ray lines, and chemical composition of the particles. We also found that when DXe > 1, the particle behaves as a bulk sample, and G = 1. Notably, our data indicate that the G factor depends only on DXe, not on the chemical composition or beam energy.

Uniform space-charge-limited current for a two-dimensional planar emitter with nonzero monoenergetic initial velocity

While characterizing space-charge-limited current (SCLC) is important for numerous applications, no analytical solutions for SCLC with monoenergetic initial velocity exist for two-dimensional (2D) geometries. Here, we derive approximate closed-form solutions for uniform SCLC with monoenergetic emission of electrons in a 2D planar diode, where emission is restricted to a long patch of width W for electrodes separated by a distance D. We also derive a semiempirical approach for estimating the SCLC for these cases by treating the geometric and velocity correction factors as multiplicative corrections to the SCLC for a one-dimensional vacuum diode given by the Child–Langmuir (CL) law. We show that the SCLC for a finite patch with nonzero velocity can exceed the CL law by three orders of magnitude. The theoretically calculated SCLCs for various emission widths and initial velocities in the 2D diode agree well with particle-in-cell simulations using the over-injection method in XOOPIC; they agree with the semiempirical relationship for lower initial velocities. In the limit of high initial velocity, the geometry and velocity corrections to the CL law cannot be decoupled, invalidating the assumption of the semiempirical approach and causing it to diverge from the theoretical solution and XOOPIC simulations. These results provide valuable estimates for determining the onset of virtual cathode formation for photocathodes and thermionic cathodes, which operate in the over-injection regime to avoid beam quality degradation.

Modified Residual Property Model For Fracture Mechanics

In this paper, the application requirement of the Residual Property Model based on the decrescent exponential function is reduced to only one mechanical test data. For this, by using Creager and Paris's elastic stress field equation in front of the blunt elliptical hole, the theoretical radius was chosen for the tip curvative and the maximum stress in the load direction at the tip is ensured to be equal the fracture toughness. Thus, the workload of the model is reduced by making the u exponent in the e-u function dependent on the geometric correction factor and the crack length. It was applied to the laminated composite specimens with three-point bending and the specimens including circular hole, and critical fracture stress values close to actual values were achieved.

Simulation of heat conduction and thermal cracking of brittle materials using the particle-based discontinuous deformation analysis

This paper proposes a particle heat conduction and expansion model (PHCE) in the context of particle-based discontinuous deformation analysis (PDDA) to simulate the heat conduction and thermal cracking of brittle materials. The thermal-mechanical coupling model consists of three parts. In the first part, a virtual rectangular heat conduction channel is assumed between each active contact pairs. The temperature distribution is solved based on the heat conduction equation and the network of the channels. In the second part, the particle radii are updated according to the thermal expansion. In the third part, the mechanical analysis is carried out with the new particle radii. To correctly reproduce the macroscopic thermal conductivity, a geometrical correction factor is introduced, which is found related to the porosity and coordination number. The proposed coupling model, abbreviated as PHCE-PDDA, is verified by three examples, the steady-state heat conduction, transient heat conduction and the thermal mechanical coupling test. Furthermore, two thermal cracking problems are also modeled. The initiation and propagation of the thermal cracks can be well captured. The final crack patterns agree well with those observed from experiments, indicating that the proposed method is effective for the modelling of heat conduction and thermal cracking in brittle materials.

Using the Stress Concentration Factor in Determining the Fracture Toughness

This paper offers the use of stress concentration factor in determining the critical fracture stress and fracture toughness of polymeric composite materials at various crack length ratios. The stress intensity factor has been turned into a function of the stress concentration factor derived from the maximum stress occurring at the notch tip and the tip stress generated by the force applied to the sample. This conversion allowed the use of a fixed theoretical radius (1.2732 mm) instead of the actual radius of the notch or crack. On the edge cracked three-point bending and tensile samples, the specified method detects the three point bending fracture stresses with a maximum error rate of 1.2%. This study also establishes a relationship between the clamped end and the pin-loaded tensile specimens and states that the underlying mechanism of the stress intensity factor of the clamped end tensile specimen is based on the normalization of the stress intensity factor of the pin-loaded conditions with the geometric correction factor.

A universal model of electrochemical safety limits in vivo for electrophysiological stimulation.

Electrophysiological stimulation has been widely adopted for clinical diagnostic and therapeutic treatments for modulation of neuronal activity. Safety is a primary concern in an interventional design leveraging the effects of electrical charge injection into tissue in the proximity of target neurons. While modalities of tissue damage during stimulation have been extensively investigated for specific electrode geometries and stimulation paradigms, a comprehensive model that can predict the electrochemical safety limits in vivo doesn’t yet exist. Here we develop a model that accounts for the electrode geometry, inter-electrode separation, material, and stimulation paradigm in predicting safe current injection limits. We performed a parametric investigation of the stimulation limits in both benchtop and in vivo setups for flexible microelectrode arrays with low impedance, high geometric surface area platinum nanorods and PEDOT:PSS, and higher impedance, planar platinum contacts. We benchmark our findings against standard clinical electrocorticography and depth electrodes. Using four, three and two contact electrochemical impedance measurements and comprehensive circuit models derived from these measurements, we developed a more accurate, clinically relevant and predictive model for the electrochemical interface potential. For each electrode configuration, we experimentally determined the geometric correction factors that dictate geometry-enforced current spreading effects. We also determined the electrolysis window from cyclic-voltammetry measurements which allowed us to calculate stimulation current safety limits from voltage transient measurements. From parametric benchtop electrochemical measurements and analyses for different electrode types, we created a predictive equation for the cathodal excitation measured at the electrode interface as a function of the electrode dimensions, geometric factor, material and stimulation paradigm. We validated the accuracy of our equation in vivo and compared the experimentally determined safety limits to clinically used stimulation protocols. Our new model overcomes the design limitations of Shannon’s equation and applies to macro- and micro-electrodes at different density or separation of contacts, captures the breakdown of charge-density based approaches at long stimulation pulse widths, and invokes appropriate power exponents to current, pulse width, and material/electrode-dependent impedance.

Измерение акустических характеристик компактных бетонных строительных конструкций с помощью импакт-эхометода

The impact-echo method is a resonant technique, which is based on using a short duration mechanical impact to generate stress waves and a transducer to monitor the surface displacement due to the arrival of direct and reflected stress waves. The impact-echo method controls concrete building structures, which the measured thickness H is at least six times smaller than other dimensions, and does not control compact samples, which the thickness H is comparable to other dimensions. The problem of compact objects control is that on the spectrum of a compact sample it is impossible to clearly determine the resonance frequency f0 ~ 1/Н against the background of numerous closely spaced frequency peaks. Another reason is that due to the strong influence of the geometric factor in compact samples, a geometric correction factor β is require to calculated for each new compact object. The article proposes a solution of these problems by using the multiplicative impact-echo method and various variants of the correlation impact-echo method.

Four-point probe geometric correction factor for isotropic cylindrical samples with non-equal probe distances

Resistivity of ceramics is usually measured by the DC-four-point-probe setup, which requires a geometric correction factor (GCF). We calculated a GCF for the general case of unequally spaced, in-line probes on isotropic, cylindrical specimens of variable size, radius and thickness. An analytical expression was obtained for the potential difference between the voltage probes by solving Laplace's equation. We show how the relative error of GCF varies with the number of Bessel functions and the number of extrema in them. GCF’s sensitivity vis-à-vis probe distances, sample radius r0 and thickness d was studied to provide an error estimate dependent on measurement errors in those parameters. Contour plots of r0-d provide GCF values without additional calculations, if the instrument’s specifications are the same. Our GCF reproduced the final results from a commercial instrument very well. The deviation between the two results was 1.5% in our temperature range of 25°–300 °C.

General scaling laws of space charge effects in field emission

The characteristics of field electron and ion emission change when the space charge formed by the emitted charge is sufficient to suppress the extracting electric field. This phenomenon is well described for planar emitting diodes by the one dimensional (1D) theory. Here we generalize for any 3D geometry by deriving the scaling laws describing the field suppression in the weak space charge regime. We propose a novel corrected equivalent planar diode model, which describes the space charge effects for any geometry in terms of the 1D theory, utilizing a correction factor that adjusts the diode’s scaling characteristics. We then develop a computational method, based on the particle-in-cell (PIC) technique, which solves numerically the space charge problem. We validate our theory by comparing it to both our numerical calculations and existing experimental data, either of which can be used to obtain the geometrical correction factor of the corrected equivalent planar diode model.

Radiação global e difusa diária na região de transição Cerrado-Amazônia brasileira

This study aimed to analyze the seasonal variations in atmospheric transmissivity and solar radiation (global and diffuse) on the horizontal surface in Sinop, Mato Grosso (MT) (11.865°S, 55.485°W, and altitude of 371 m) from 06/02/2011 to 12/31/2014. The values of diffuse radiation were measured using the Melo-Escobedo-Oliveira (MEO) shadow ring, with application of astronomical, geometric, and anisotropic correction factors. The analysis of atmospheric transmissivity was based on the classification of sky cover as cloudy, partly cloudy, partially clear, or clear. The diffuse radiation showed similar behavior to the radiation at the top of the atmosphere, reaching a maximum between October and April (rainy season), while the global radiation displayed higher levels during the dry season (May to September). The average daily global radiation ranged from 22.75±0.61 MJ m−2 d−1 in August to 16.44±1.45 MJ m−2 d−1 in January. In Sinop, cloudy and partly cloudy skies occurred on 45.6% of days and atmospheric transmissivity of global radiation was greater than 55% on 54.6% of days. The variations in diffuse radiation in the region were influenced by cloudiness and the concentration of biomass burning aerosol particles. The diffuse radiation can represent 8.02%–99.12% of the global radiation and 5.33%–29.01% of solar energy incident at the top of the atmosphere.

Hall‐effect sensors based on AlGaN/GaN heterojunctions on Si substrates for a wide temperature range

The authors report experimental investigations on Hall sensors based on AlGaN/GaN heterojunctions grown on silicon 111 (Si 111) substrates. Realisation of two-dimensional electron gas-based Hall sensors on Si substrates can have the advantages of low cost and integrability with complementary metal-oxide semiconductor circuits. Design and fabrication of such Hall sensors and their characterisation over a wide temperature range of 75 to 500 K are reported. The authors experimentally investigate the temperature dependence of the transresistances, sheet resistance and current-related sensitivity (or gain) of such Hall sensors. The current-related sensitivity is shown to be reasonably constant over the complete temperature range and certain inevitable variations in current-related sensitivity can easily be compensated. The temperature dependence of the transresistance can be used for such compensation. The variation of the geometrical correction factor of the Hall sensor with the applied magnetic field strength and the operating temperature is also studied. The authors also demonstrate the possibility of realising Hall sensors with a high geometrical correction factor ( ≈0.97), which is practically insensitive to variations in temperature ( ≃2% from 75 to 500 K) and applied magnetic field, for applications such as in electromechanical devices.

On the cause and correction of the anomalously high contact angles measured on soils and granular materials

Anomalously high water contact angles are often measured for soils or other granular materials when using a goniometer which is designed for use with flat surfaces. For many years such high contact angles have been rationalised in terms of Cassie and Baxter, and/or Wenzel models for contact angles on non‐planar surfaces, but it is becoming increasingly apparent that the theories behind these models are fundamentally flawed. Here, we present an alternative interpretation of these anomalously high contact angles which takes into consideration how a water drop sits on the particulate surface, and propose a geometric correction factor to address this anomaly. Experimental data from studies with precisely arranged needles and spheres, and model and natural soils, were used to explore this approach and examine the validity of the method. Application of the correction factor to measurements of water drops on 1 mm diameter steel spheres hydrophobised with paraffin wax gave a reduction of the measured contact angle of 140.4(±0.6)° to a corrected contact angle of 108.2(±1.0)°, which is within 3.5° of the flat‐plane contact angle for water on the wax of 111.7(±0.6)°. For paraffin wax coated soils, measured contact angles are shown to be 15–25° higher than comparable flat-plane contact angle. This correction factor may be useful in interpreting goniometer contact angle measurements of irregular surfaces since it is the flat-plane, rather than measured, contact angle which gives a measure of the polarity/hydrophobicity of the surface.

Построение дисперсионной зависимости корректирующего коэффициента при контроле компактных изделий квадратного сечения импакт-эхометодом

This paper presents results of calculation of the geometric correction factor β of the compact square-sectioned samples. It is shown by simulation that in compact samples thickness resonance type changes from longitudinal wave to Lamb wave. Furthermore, the geometric correction factor varies over a wide range and nonlinear in compact samples. The dispersion curve of the geometric correction factor β for compact square-sectioned samples is built.

The nature of specimen-size-effect on fatigue crack growth and net-section fracture mechanics approach to extract the size-independent behavior

A specimen-size-effect is found in the experimental fatigue crack growth behavior of single-edge-cracked fracture specimens, where the specimen length-to-width ratio was varied by about a factor of four. This effect appears from certain geometric correction factors (GCFS) used for the calcuation of the stress intensity range in fracture mechanics. It is shown that the net-section-based fracture mechanics approach provides a unique correlation of the fatigue crack growth data, for all specimen sizes, when the change in the net-section strain energy is used as the crack driving force parameter. The fatigue crack growth data could be correlated extremely well, when an effective specimen length, including the elastic strain energy of the specimen portion within the grips, is included in the driving force calculations. This effective length is determined by shear-lag analysis. It is also demonstrated that a true size-independent fatigue crack growth behavior can be obtained through the net-section based approach, using the concept of the change in net-section strain energy.

A Study of the Geometrical Correction Factor and the Membrane Thickness on the Sensitivity of the Transversal Piezoresistive Pressure Sensor

The sensitivity of four-terminal devices like Hall and piezoresistive sensors is very dependent on its geometric parameters. This dependence is modeled by the Geometrical Correction Factor (G). The majority of these studies take very time-consumption analytical calculations for the analysis of G. In order to simplify this analysis, we present numerical analyses using FEM (Finite Element Method) for the most common geometrical forms of four-terminal devices. This result is general for any fourterminal-shaped sensors and can be used to optimize the sensor aspect ratio leading the maximization of G. In addition, FEM was also used to evaluate the membrane´s thickness influence over the sensor sensitivity by analyzing the in-plane mechanical stress behavior on the sensor active area. Experimental result of a new topology of pressure sensor is also presented, which maximizes G in comparison with conventional four-terminal devices and also improves its sensitivity. A special designed anisotropic wet etching system was used to post-process the sensor membrane. This anisotropic wet etching system allows the fabrication of well-defined membranes with thickness of 20 μm ± 3 μm and roughness as low as 90 nm rms.

Research on Electrical Characteristics of Mixed Media Based on Computer Simulation Technology

Computer technology is mainly used to study the electrical characteristics of mixed media through calculation and analysis of its equivalent dielectric constant. Since the geometric distribution, content, and structural shape characteristics of different phases in the mixed media will affect the equivalent dielectric constant to varying degrees, we need to analyze the relevant factors. However, when analyzing the relationship between the geometric distribution characteristics of each phase and the equivalent permittivity in a mixed medium, the traditional hybrid formula analysis method cannot meet the actual needs of complex equivalent equivalent permittivity research. Therefore, we must adopt computer simulation technology and use relevant simulation software to realize the conversion between geometric distribution and correction factor. In addition, we can also modify the mixing formula through the porosity function to accurately understand the electrical properties of the mixed medium.

Correlation between eye lens doses and over apron doses in interventional procedures.

Measurements of eye lens dose using over apron dosimeters with a geometric correction factor is an international accepted practice. However, further knowledge regarding geometric correction factors in different contexts is required. The authors studied the correlation between eye lens dose and over apron dosimetry for different medical specialties in eleven hospitals, using a standardized protocol, two independent over apron dosimeters (worn at chest and at neck levels) and a dedicated calibration procedure. The results show good correlation between subjects working on the same medical specialty for 5 specialties: Interventional Radiology, Vascular Surgery, Vascular Radiology, Hemodynamics and Neuroradiology. The geometric correction factors resulting from this study could be used to estimate eye lens dose using over apron dosimeters, which are more comfortable than eye lens dosimeters, as reported by the study subjects, as long as the increased uncertainty of the over apron dosimetry compared to the dedicated eye lens dosimetry is acceptable.

Spectral Analysis of Forbush Decreases Using a New Yield Function

The Forbush decreases of the cosmic ray intensity observed on 24 December 2014 and on 8 September 2017 were chosen for cosmic ray spectral analysis. At first an analytical study of the solar and geomagnetic parameters of these events was carried out due to the fact that both are typical cosmic ray events. Hourly cosmic ray data of the neutron monitor stations obtained from the high-resolution neutron monitor database were used for calculating the cosmic ray density and anisotropy variations. Following the method of the coupling coefficients, the galactic cosmic ray spectral index was calculated using the technique of Wawrzynczak and Alania (Adv. Space Res. 45, 622, 2010). A newly presented yield function by Mishev, Usoskin, and Kovaltsov (J. Geophys. Res. 118, 2783, 2013) including a geometrical correction factor, already used in the spectral analysis of the cosmic ray ground level enhancements, was applied for the first time to the case of Forbush decreases. A comparison of these results during the events is performed by using two other coupling functions: the function presented in the work of Clem and Dorman (Space Sci. Rev. 93, 335, 2000) and the one in the work of Belov and Struminsky (Proc. 25th Int. Cosmic Ray Conf. 1, 201, 1997). The latter includes an extension for neutron monitor stations with rigidity $1~\mbox{GV} < R < 2.78~\mbox{GV}$ . The obtained spectral index and the calculated cosmic ray intensity in the heliosphere during the two Forbush decreases after the coupling by these three functions are presented and discussed.