Simple Analytical Model Research Articles

Analysis of phase data from ground vibration measurements above a leaking plastic water pipe

One way to locate a buried plastic water pipe is to measure the surface vibration due to a leak in the region above the pipe, and to process the data to infer the pipe location. This paper investigates the physical mechanisms that propagate leak noise through the pipe and the surrounding soil to the ground surface. An analysis is carried out of the relative phase between vertical ground vibration measurements at points in a grid above the pipe. The study involves experimental measurements from a site in the UK with a more realistic leak mechanism compared to recent research, a simplified analytical model to gain insight into the underlying physics, and a numerical model to validate some of the assumptions made in the derivation of the analytical model. Three waves are principally involved in propagating leak noise to the ground surface from the pipe, namely the predominantly fluid-borne wave in the pipe, and the shear and compressional waves in the soil radiating from the pipe. Their influence on the ground surface vibration is investigated through measured and simulated phase contours over a rectangular grid of surface velocity measurements. It is shown how shear and compressional waves combine to affect the shape of the lines of constant phase on the ground. The results demonstrate the potential of the proposed analytical and numerical models to investigate wave radiation from buried water pipes, and possible pipe location strategies using phase data from surface vibration measurements.

High-resolution modeling of overflush and its implications for fracture productivity

Hydraulic fracturing operations typically aim to create a highly conductive fracture that will intensify well production or injectivity. At the end of pumping, a fluid without proppant, called flush, is injected to clean the wellbore and tubing of the remaining slurry. Overflush is the situation when flush volume exceeds the volume between the wellhead and perforations so that flush fluid enters the propped fracture and washes out the near-wellbore region of propped fracture. In this work, we examine overflush impact on fracture closure near perforations in detail by considering several overflush scenarios and running simulations using a suite of high-resolution models of fracturing itself, fracture closing on proppant, and productivity. We show that at certain conditions, overflush has no impact on well productivity or may even enhance it. Additionally, we develop a simplified analytical model of well production for an axisymmetric overflushed region and compare the model results to precise numerical simulations. We consider several overflush scenarios, both beneficial and unfavorable. It was found that the dominant role in the formation of overflushed region geometry is that of Saffman–Taylor instability, the manifestation of which leads to the formation of long channels that with high possibility do not cause fracture closure with pressure decrease during production and can remain open even at large pressure drawdown. The work has both research and practical interest and demonstrates an integral approach to numerical overflush modeling. In addition, it gives basis for the revision of the existing “harmful overflush” paradigm.

Permeability in barrier membranes: Comparison between experiments, direct calculations, and analytical models

AbstractThis paper compares direct calculations, experimental data and analytical models in materials with controlled barrier microstructure. Confocal Raman was used to follow mass transport of a penetrant, hexadecanol (HDOL), through the barrier structure. produced by carving holes in specific positions and orientations in a polydimethylsiloxane (PDMS) matrix. Finite element method (FEM) was used to predict maps of HDOL concentration around the obstacles, which were directly compared to Raman data. Effective diffusion coefficients were obtained in homogeneized microstructures of slender obstacles in diluted and semi‐concentrated obstacles regimes. Results were compared with predictions of simple analytical models: Nielsen, Lape, those derived from the ideas of Bharadwaj (Greco; Greco and Maffezzolli), and those developed from FEM simulations (Minelli et al. and Dondero et al.). For the first time, predictions of these widely used analytical models could be tested against well‐controlled barrier membranes. The influence of obstacle orientation, size polydispersity and eventual aggregation, all features occurring in real polymeric nanocomposites are analyzed. Some limitations about the use of simple analytical models to interpret permeability data in real nanocomposites are discussed.

Stiffness Characteristics and Analytical Model of a Flange Joint with a Spigot

Flange joints with spigots are widely used in aero-engines. The spigot will restrict the shear slipping between flanges, which, in turn, affects the stiffness characteristics of the joint. The current model and research on flange joints without spigots may not be suitable for the dynamic characteristics of aero-engines. Moreover, the complexity of contact pairs limits the application of the flange joint finite element (FE) model in aero-engine dynamics analysis. Therefore, a simplified analytical model of a flange joint with a spigot is proposed in this paper. First, the stiffness characteristic of the flange joint with a spigot is studied using the FE method. Second, a corresponding experiment is executed to verify the result of the FE analysis. Furthermore, based on the former FE and experimental analysis, one section of a flange joint is simulated by the Jenkins friction model and a spring. Then, a simplified analytical model of the entire flange joint is built according to the different statuses of each section. Finally, a simulation analysis of the stiffness characteristic is performed. The result shows that the simplified analytical model can be utilized to describe the bending stiffness characteristic of the flange joint with a spigot.

Simulative Quantification of the Supersonic Discharge Process of Cold Gas Airbag Inflators

Abstract A simulative method for quantifying the discharge process of cold gas airbag inflators is presented. The pressure, mass flow and the influences of the flow field are relevant to a robust and predictive airbag deployment. Simulations in this regard are compared and validated with experimental data. It turns out that simulated mean pressures inside the inflator deviate by 5–10% from measured data. A complex and highly turbulent flow field with supersonic and subsonic flow emerges. An influential longitudinal vortex forms in the cold gas inflator, leading to a highly dynamic discharge process. This vortex would not be found with the current state-of-the-art methods, such as the simple tank test or analytical models. It is shown that a simple turbulence model such as the k−ω shear stress transport predicts the flow field with sufficient accuracy in comparison with the large eddy simulation. Real gas effects must be taken into account inside the high-pressure reservoir, leading to a faster discharge compared to the ideal gas, due to faster moving expansion waves in the reservoir. Real gas effects outside the high-pressure reservoir seem to be negligible. A simplified simulation model was developed that uses only part of the whole cold gas inflator model and serves as a good practical approach for airbag deployment simulations, with less computational effort. Thus, the method presented here can provide high-quality inflow data for airbag deployment simulations.

Mechanical Characterization of AA8006 Aluminum Alloy through Cold Free Forming Test

In this work, for the first time thin, sheets of AA8006 aluminum alloy, that are commonly used for food packaging, were mechanically characterized through an unconventional free-forming technique that was performed at room temperature. This technique constitutes an economically effective solution to determine the constitutive equation of a metal sheet subjected to two-axes stresses. This state of stress reproduces the behavior of the material during the forming process better than the more traditional tensile test, which involves uniaxial stress. Specifically, the material constants were determined by using a simplified analytical model applied to the results of the experimental tests of the free forming process carried out at room temperature and constant pressure. Therefore, the obtained material constant values were used to simulate the same free-forming tests using FEM. In conclusion, the numerical results were in agreement with the experimental ones, thus confirming the goodness of the developed numerical model.

Experimental Assessment of Correlative Approaches for the Prediction of Leakage Flow through Labyrinth Seals

Simple analytical models can be employed to estimate the leakage mass flow rate from labyrinth seals, resulting in a quick procedure, well suited for the early design process. Different formulas were proposed by many authors during the past decades and most of them employ a carry-over factor and a flow coefficient to predict the mass flow rate across the clearance area. The present work aims to compare the analytical prediction with the results of an experimental campaign. The experimental results were retrieved from a dedicated test rig for both a straight-through and a stepped labyrinth seal. Hence, for each seal, the effect of the clearance size, the Reynolds number and the pressure ratio has been investigated. Starting from the experimental required inputs, six different correlations are considered, with both direct and indirect methods. The results are shown as a function of pressure ratio and clearance gap. Despite some differences in the comparison, and most of the used correlation underestimate the measured mass flow rate, some general trends and guidelines can be highlighted.

Degradation of trichloroethylene vapors by micrometric zero-valent Fe[sbnd]Cu and Fe[sbnd]Ni bimetals under partially saturated conditions

The degradation of trichloroethylene (TCE) vapors by zero-valent Iron-Copper (Fe–Cu) and Iron-Nickel (Fe–Ni) bimetals with 1%, 5% and 20% weight content (%wt) of Cu or Ni was tested in anaerobic batch vapor systems carried out at ambient room temperature (20 ± 2 °C) under partially saturated conditions. The concentrations of TCE and byproducts were determined at discrete reaction time intervals (4 h-7 days) by analyzing the headspace vapors. In all the experiments, up to 99.9% degradation of TCE in the gas phase was achieved after 2–4 days with zero-order TCE degradation kinetic constants in the range of 134–332 g mair−3d−1. Fe–Ni showed a higher reactivity towards TCE vapors compared to Fe–Cu, with up to 99.9% TCE dechlorination after 2 days of reaction, i.e., significantly higher than zero-valent iron alone that in previous studies was found to achieve comparable TCE degradation after minimum 2 weeks of reaction. The only detectable byproducts of the reactions were C3–C6 hydrocarbons. Neither vinyl chloride or dichloroethylene peaks were detected in the tested conditions above their method quantification limits that were in the order of 0.01 g mair−3. In view of using the tested bimetals in horizontal permeable reactive barriers (HPRBs) placed in the unsaturated zone to treat chlorinated solvent vapors emitted from contaminated groundwater, the experimental results obtained were integrated into a simple analytical model to simulate the reactive transport of vapors through the barrier. It was found that an HPRB of 20 cm could be potentially effective to ensure TCE vapors reduction.

Noise and Vibration of Permanent Magnet Synchronous Electric Motors: A Simplified Analytical Model

Design of electric motors, especially for automotive applications where early design choices have significant impacts on the final results, in terms of both cost and performances, is a matter of primary importance, with direct consequences on the entire vehicle. Common practice lacks of simple, yet reliable, analytical method to evaluate vibration and noise emission of permanent magnet synchronous motors (PMSMs), and this is the gap that the work here proposed aims to fill. In particular, electric vehicles noise requirements have added a design opportunity to manufacturers, that, depending on the type of costumers they are selling their products to, need to comply with different preferences. Accurately estimate noise emissions of such complex machines is a difficult matter, that can be fully exploited only at the end of the design process. The paper aims to provide a simple, yet accurate enough, tool to estimate the noise emission of electrical motors at the early stage of the design, giving engineers and researchers a tool to drive their choices. An equivalent curved beam model is employed for modelling the structural vibration of the stator when subjected to electromagnetic forces. The sound pressure amplitudes are analytically derived based on the acoustic solution for infinitely long cylindrical radiators. Part of the innovation lays on the fact that the contributions of both radial and tangential forces are taken into account, and a discussion on the effect and influence of the latter on the stator acoustic emission is presented. The sound pressure radiated from the outer surface of the stator is calculated, and a unique indicator of sound emission, named Sound Pressure Level (SPL), is determined. The proposed method is validated against data of two PMSMs from literature, showing good agreement with experiments, proving the method is a reliable tool for electric motor designers to be used especially during the early stage of design.

Topology Development and Performance Analysis of a Dual-Stator Permanent Magnet Arc Motor

In this paper, a dual-stator permanent magnet (PM) arc motor (DS-PMAM) with improved torque density is investigated for some specific direct-drive applications. The proposed DS-PMAM can be considered as the combination of the PM arc motor and the stator-PM motor. Benefiting from two different stator structure, two sets of armature windings are employed to improve the inner space utilization ratio and torque densities. The motor structure and working principle of the DS-PMAM are firstly introduced. The simplified analytical model is derived to provide a solid theoretical guidance for optimization design parameters selection. Then, the design considerations including the slot/rotor pole combination, the armature winding design, and the key structural parameters analysis are carried out to obtain the optimal motor performances of the DS-PMAM. After that, the electromagnetic characteristics of the DS-PMAM are evaluated together with the comparison with the inner-rotor PMAM, the outer-rotor PMAM, the surface-mounted PM PMAM, and the DS flux reversal PMAM. Finally, a prototype is manufactured and fully tested. Relevant experimental results verify the correctness of the FE analysis and the feasibility of this proposed design.

A Simplified Analytical Elastoplastic Embedment Depth Model of Proppant Based on the Drucker–Prager Yield Criterion

A Simplified Analytical Elastoplastic Embedment Depth Model of Proppant Based on the Drucker–Prager Yield Criterion

Unraveling Twisty Linear Polarization Morphologies in Black Hole Images

We investigate general relativistic magnetohydrodynamic simulations to determine the physical origin of the twisty patterns of linear polarization seen in spatially resolved black hole images and explain their morphological dependence on black hole spin. By characterizing the observed emission with a simple analytic ring model, we find that the twisty morphology is determined by the magnetic field structure in the emitting region. Moreover, the dependence of this twisty pattern on spin can be attributed to changes in the magnetic field geometry that occur due to the frame dragging. By studying an analytic ring model, we find that the roles of Doppler boosting and lensing are subdominant. Faraday rotation may cause a systematic shift in the linear polarization pattern, but we find that its impact is subdominant for models with strong magnetic fields and modest ion-to-electron temperature ratios. Models with weaker magnetic fields are much more strongly affected by Faraday rotation and have more complicated emission geometries than can be captured by a ring model. However, these models are currently disfavoured by the recent EHT observations of M87*. Our results suggest that linear polarization maps can provide a probe of the underlying magnetic field structure around a black hole, which may then be usable to indirectly infer black hole spins. The generality of these results should be tested with alternative codes, initial conditions, and plasma physics prescriptions.

Aerodynamic modelling of a tilt-wing transition corridor

With the recent rapid evolution of the UAM class concepts in past years, the re-emerged interest in VTOL concepts and their aerodynamics arises. The tilt-wing is one of the possible solutions for such a vehicle. Recent decades of tilt-wing aerodynamic research point to the importance of the understanding transition regime from cruise to hover. Especially the wing stall phenomena which affect descent capabilities and control during the landing phase. Understanding such a regime is crucial for optimal wing design. This paper presents several approaches to the modelling of aerodynamic forces during the critical phase of transition. Computations are aimed particularly to the edge of the flight envelope. The low to high fidelity methods are employed and compared with the results of low-speed wind tunnel testing. The results from high fidelity methods match well with experimental results but the proposed simple analytical model fails in prediction of the transition corridor in the most critical regimes.

Benefits of sourcing alternative inputs of manufacturers for suppliers

A downstream manufacturer can procure high‐quality inputs from its upstream raw material supplier to produce finished products with high quality. The manufacturer may also have the option to source alternative cheaper low‐quality inputs to partially replace the inputs from its supplier to produce finished products of lower quality. That is, the manufacturer can use a mixture of the supplier's inputs and alternative ones in product design such that product quality depends on the proportion of each input used in products. We endogenize this product quality decision in a simple analytical model to study the impact of this option on the supplier's profits. Intuitively, the option of sourcing alternative inputs could hurt the supplier in two ways: It sells fewer inputs, and it needs to set a lower wholesale price due to competitive pressure. However, our study reveals an opposite finding: The supplier can benefit not only by selling more inputs but also by setting a higher wholesale price when the manufacturer has the option of sourcing alternative low‐quality inputs. This interesting finding is due to the wholesale price push‐up effect: The upstream supplier may deliberately raise the wholesale price when sourcing alternative inputs is an option for the downstream manufacturer. This increased wholesale price encourages the manufacturer to use a higher proportion of alternative cheaper inputs in its product design; as a result, the manufacturer's marginal cost is reduced, which leads to a decrease in its retail price. Therefore, consumer demand for the manufacturer's products becomes higher, which in turn results in higher manufacturer demand for the supplier's inputs. Moreover, we show that despite this higher wholesale price, the manufacturer can earn higher profits by optimally charging a lower retail price. Furthermore, we find that the wholesale price of the supplier's inputs can exceed the manufacturer's retail price, thereby leading to a negative profit margin for the manufacturer from using the supplier's inputs. Finally, we demonstrate the robustness of our findings under several model extensions.

Correction to “A Simple Analytical Model for THz Band Path Loss”

In the above article <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , an analytical model for THz band transmittance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> ) is devised as the joint function of distance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> ), altitude ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula> ), and frequency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> ). In <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , the last paragraph of Section II should be corrected as follows, also replacing <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1, eq. (6)]</xref> with <xref ref-type="disp-formula" rid="deqn1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(1)</xref> .

Learning Environment and Learning Facilities: Numeracy Literacy for Class V Elementary School Students during the Pandemic

The numeracy literacy of Indonesian students could be higher. Complete learning facilities can support the achievement of student learning outcomes. This study aims to analyze the effect of the learning environment and learning facilities on students' numeracy literacy. This type of research is quantitative with ex-post facto research methods with a survey design. The overall population consists of 24 state primary schools with a total of 523 students. The sampling technique uses cluster sampling. Methods of data collection through questionnaires/questionnaires, questions and document study. The instrument used in this research is a questionnaire. Data analysis in this study uses a simple regression analysis model and multiple regression. The results showed that the learning environment negatively and significantly affected the numeracy literacy of fifth-grade elementary school students. The state of the learning environment around students is quite good, but the response in the form of numeracy literacy learning results is low. Second, the learning environment and facilities influence students' numeracy literacy. Third, the learning environment and facilities negatively and significantly affect numeracy literacy.

Experimental and theoretical comparison of ion properties from nanosecond laser-produced plasmas of metal targets

The ion emission properties of laser-produced plasmas as a function of laser intensities between 4–50 GW cm−2 and varying angles with respect to the target normal were investigated. The plasmas were produced by focusing 1064 nm, 6 ns pulses from an Nd:YAG laser on various metal targets. The targets used for this study include Ti, Mo, and Gd (Z=22,42,64). It is noted that all ion profiles are composed of multiple peaks—a prompt emission peak trailed by three ion peaks (ultrafast, fast, and thermal). Experimentally, it is shown that each of these ion peaks follows a unique trend as a function of laser intensity, angle, and distance away from the target. Theoretically, it is shown that simple analytical models can be used to explain the properties of the ions. The variations in the ion velocity and density as a function of laser intensity are found to be in good agreement with theoretical models of sheath acceleration, isothermal self-similar expansion, and ablative plasma flow for various ion peaks.

Effects of post-fracture repeated impacts and short-term temperature gradients on monolithic glass elements bonded by safety films

Weathering and operational conditions, as known, have significant impact on typical constituent materials which are used for many construction applications. Among others, structural glass solutions can suffer for these effects in terms of major modification of material properties of interlayers, bonds, connections, gaskets and polymeric components in general. In this paper, the attention is given to the effects of repeated low-amplitude impacts and short-term temperature gradients for the characterization of load-bearing capacity in monolithic glass elements retrofitted by safety films. Especially for existing glass systems which are made of monolithic glass with limited strength and resistance capacity against ordinary and accidental mechanical loads, safety films are commercially available for retrofit interventions. They are primarily expected to keep together glass fragments in case of breakage, and thus minimize possible injuries. Besides, after first fracture, the so obtained glass-film composite elements have uncertain residual mechanical capacity against ordinary loads, given that it mostly depends on thin films composed of Polyethylene terephthalate (PET)-layers and pressure sensitive adhesives (PSAs). To this aim, a set of experiments (for a total of 950 configurations) is carried out in laboratory conditions (30 °C) on small-scale samples of fractured annealed monolithic glass elements bonded by commercial safety films, under repeated low-amplitude impacts / vibrations (S1-TR series), or additionally subjected to preliminary short-term thermal gradients (S2-TC1 series cooled at +5 °C and S3-TC2 series at −20 °C). Localized impacts are quantified in acceleration peaks in the range of 2 ÷ 14 m/s2 and rotations at supports in the order of 15 ÷ 20°. The interpretation of dynamic experimental results is carried out in terms of post-fracture vibration frequency (based on classical operational modal analysis techniques) and used, with the support of simplified analytical models or Finite Element (FE) numerical simulations, to characterize the response of cracked glass-film samples. Most importantly, the vibration frequency decrease is used to quantify their residual load-bearing capacity under unfavourable conditions, and to quantify the post-critical benefit of thin bonding safety films under unfavourable conditions.

A simple analytical model for bamboo-reinforced slopes using modified Bishop method

Introduction: Embankments are constructed in many places for transportation purposes such as railways and roads. The stability of slopes in embankments has always been a concern, especially in cohesionless soils. There are many methods to increase the safety factor of cohesionless soil slopes using geogrids, geocells, concrete piles, and so on. The conventional material used to stabilize slopes has a huge impact on the environment. Nowadays, researchers are using natural fibers such as bamboo and coir fiber for stabilization purposes.Methods: In this paper, bamboo piles are used to stabilize slopes. The bamboo piles are inserted vertically on the slope face to increase the shear strength and stability against slope failure. A limit equilibrium method has been developed to estimate the stability of a slope improved by friction piles after modifying the Bishop method of slices. The stability of the slope is analyzed for both the reinforced conditions and the unreinforced conditions using the developed analytical formula.Results and Discussion: The analytical equations were developed by considering three modes of slope failure: shear failure of the bamboo piles along the failure surface, movement of the upper part of the soil, leaving the bamboo pile embedded in the base soil, and pulling out of the bamboo along with the upper part of the soil mass. Further validation of the results is carried out with the limit equilibrium method-based software SLOPE/W using a modified Bishop method. The factor of safety increased after reinforcing the slope with bamboo piles for all three modes.

Lateral deformation behaviour of structural internal replacement pipe repair systems

Structural internal replacement pipe (SIRP) systems are emerging composite technologies for the repair of circumferentially cracked host pipes or pipes with joints subject to lateral deformation caused by the surface loads from vehicular traffic. However, laboratory experiments to investigate the suitability of different SIRP systems in repairing full-scale pipes are a very costly and time-consuming process. This paper investigated numerically the behaviour of SIRP repair systems under lateral deformation using the three-dimensional finite element analysis (FEA). The FEA model was validated from the results of the full-scale experimental test. The effect of the crack width of the host pipe, thickness, and material properties of the SIRP, on the bending behaviour of the pipe repair system, was evaluated. The results of the analyses show that the effect of the thickness and elastic modulus of the SIRP on the lateral deformation behaviour is dependent on the width of the circumferential crack in the host pipe. A simplified analytical model based on Fibre model analysis (FMA) and incorporating an average stress factor for host pipes with a narrow crack width was developed to reliably describe the lateral deformation behaviour of the SIRP systems.