Dimensional Analysis Technique Research Articles

Long-Range Electrostatic Adhesive Contact Between an Elastic Half-Space and a Rigid Indenter With Power-Law Profile

Abstract In this study, the electrostatic adhesive contact between a smooth indenter with a power-law geometry and an elastic half-space is studied using both a theoretical and numerical approach. Both the indenter and substrate are coated with an electrically insulating layer. The Maxwell stress and hard-wall constraint are applied to describe the interaction between the indenter and elastic counter face. By assuming electrostatic adhesion as a long-range interaction, we derived a theoretical relation between external load and contact radius. We show that the theoretical and numerical results are plausible when the Tabor parameter is small. However, when the Tabor parameter is large, the numerical results get closer to the Johnson–Kendall–Roberts (JKR) limit. The generalized Tabor parameter, which depends on the applied voltage and indenter shape, has been derived by following the technique of dimensional analysis.

Manufacturing and performance evaluation of Al/SiC/coconut & bagasse ash composite using novel integrated dimensional analysis (DA) and adaptive neuro fuzzy inference system (ANFIS) techniques

Manufacturing and performance evaluation of Al/SiC/coconut & bagasse ash composite using novel integrated dimensional analysis (DA) and adaptive neuro fuzzy inference system (ANFIS) techniques

Dimensional and experimental analysis for predicting the material removal rate in AJM

ABSTRACT One of the upcoming methods for machining brittle and heat-sensitive materials is abrasive jet machining (AJM) where the process of erosion aids in material removal. This is accomplished by the impact of abrasives transported using a stream of gas having high velocity onto the workpiece. The erosion mechanism is a complicated process, which involves cutting, fracturing and micro structural transformation, thereby causing the evaluation of response parameter like rate of material removed (MRR) an arduous task. In this paper, an effort has been made to develop a semi-empirical model for predicting MRR in hole machining of soda-lime glass by utilising dimensional analysis (DA) technique. In this model, the compressive stress developed during the impact of loading and velocity of the particle are considered as a function of work material, selected abrasive material properties and process parameters. The validation of the evolved model was carried out with experiments that involve process parameters such as operating pressure, stand of distance (SOD) and abrasive particle size. From the analysis, it’s found that the predicted MRR model created by the dimensional analysis method gave an average error of 11.8%. thereby giving a reasonably compatible value with experimental results.

A type system for formal verification of cyber-physical systems C/C++ software

The subject: This study focuses on improving the quality of Cyber-Physical System (CPS) software by eliminating incorrect usage of units of measurement and orientation in C/C++ programs. Incorrect usage often leads to critical errors that conventional systems cannot effectively prevent. Manual examination of code using dimensional and orientation analysis can detect these errors in physical equations, but these methods become impractical when dealing with complex physical computations. Objectives: As suggested by Siano, the proposed approach uses physical quantities and prefixes defined by the International System of Units and orientation operations on physical objects. The elaborated system incorporates dimensional and orientation analysis and metaprogramming techniques. The methods used are dimensional & orientational analysis and metaprogramming. The following results were obtained: ensuring consistency of the units, incorporating orientation operations into the programming model for accurately handling physical object rotations and alignments, and using Siano’s work to precisely manipulate object orientation, thereby reducing the likelihood of orientation-related errors. Checking physical dimensions and orientations during the compilation stage identifies potential software defects before code execution, thereby reducing debugging time and lowering the cost of addressing issues later in development. The elaborated system represents a crucial step towards safer and more dependable Cyber-Physical System applications. This approach allows us to identify approximately 90% of incorrect usage of program variables; additionally, it detects over 50% of erroneous operations during compilation and execution of large-scale programs in real-world conditions. Conclusions. Scientific novelty: it proposed and developed a specialized C++-type library for formal compile-time software verification of Cyber-Physical Systems software. The proposed C++-type library leverages dimensional and orientational analysis to enhance software quality, reliability, and real-time formal verification. Although the proposed method for formal verification is not tailor-made for cyber-physical objects and systems, given its primary focus on software-level concerns, it does exhibit adaptability for verifying general-purpose software that incorporates various physical parameters. This versatility extends to diverse domains such as educational, gaming, and simulation software.

Forecasting empirical formula for suspended sediment load prediction at upstream of Al-Kufa barrage, Kufa City, Iraq

Abstract The objective of this study was to predict the suspended sediment load at upstream of the Al Kufa barrage. Ten cross-sections in the upstream region have been identified to collect field measurements. As part of the inquiry, the fluid and hydraulic parameters were measured in the field and sediment samples were collected in sections to develop an empirical formula. These variables included the gravitational constant (g), hydraulic radius (R h), mean velocity (V), median particle size (d 50), river top breadth (B), kinematic viscosity (v), and (ρ) water density. The formula was created using both statistical analysis and dimensional analysis techniques. The results showed that the newly developed formula agreed well between the calculated and observed suspended sediment discharges based on the determination coefficient R 2 of 0.979. There was a very high acceptance between the average sediment discharge from the new formula, equal to 7.365 kg/s, and the average sediment discharge from field measurements (7.142 kg/s).

Indirect solution modeling of melting behavior of SiO2 based on the image processing technology

AbstractThe utilization of tempered blast‐furnace slag through the direct fiber forming process to produce high‐value thermal insulation materials offers a dual benefit: it efficiently utilizes the latent heat in the unused slag and significantly increases the value of blast‐furnace slag utilization. However, measuring the melting properties of iron slag at high temperatures is challenging. In this study, the melting behavior of SiO2 in a high‐temperature molten pool was investigated. We employ dynamic visual data (video stream) captured via a non‐contact charge coupled device video recording system to extract SiO2 contours through image processing. The change in image centroid characteristics is used to establish a convolution function relationship, and MATLAB's traversal search algorithm determines the centroid position of SiO2. Given that SiO2 is proportionate to crucible pixels, the area of the SiO2 is calculated through pixel statistics within these contours. A new indirect method is then proposed to process image information to obtain SiO2 volume and mass at different time points. An exponential fitting yields the melting rate function of SiO2. Finally, this indirect method has been compared with shape from shading, quantitative characterization, and dimensional analysis techniques. Besides, the strengths and limitations of each method have been discussed. Our findings reveal that the indirect solution method presented here boasts straightforward calculation steps and imposes minimal image format requirements, which provides theoretical and technical support for the direct fiber forming process of blast‐furnace slag.

Application of a Semi-Empirical Approach to Map Maximum Urban Heat Island Intensity in Singapore

Differences in land surface characteristics across a city produce great spatial and temporal variability in air temperature. This fact is particularly pronounced between urban and surrounding rural areas giving rise to the canopy-layer urban heat island (CL-UHI) phenomenon. In the present study, we apply the dimensional analysis technique to develop a simple semi-empirical equation to map daily maximum CL-UHI (UHImax) intensities during nighttime over the city of Singapore for specific weather conditions. By adopting the methodology proposed by Theeuwes et al., but selecting meteorological and morphological parameters that affect UHImax intensity most for Singapore, evaluation of the developed equation shows good agreement with observations (RMSE = 1.13 K and IOA = 0.76). Model performance depends strongly on wind conditions and is best during weak winds when ‘ideal’ conditions for UHI development are approached (RMSE = 0.65 K and IOA = 0.85). Results using the simple equation developed to map UHImax intensities in Singapore under dry weather conditions are comparable to those obtained from more sophisticated numerical models, which demand significant computational resources, and the complex parameterizations involved require expertise to carry out the simulations. The resulting maps of the present study can be used to investigate less favorable thermal conditions and assess population vulnerability to a certain temperature excess, as well as provide insights for urban planning strategies of mitigation measures according to the land cover and morphology of a location.

Dimensionality reduction of non-buoyant microconfined high-pressure transcritical fluid turbulence

This work utilizes a novel data-driven methodology to reduce the dimensionality of non-buoyant microconfined high-pressure transcritical fluid turbulence. Classical dimensional analysis techniques are limited by the non-uniqueness of scale-free groups and the lack of a general strategy for quantifying their importance. Instead, the data-driven approach utilized is based on augmenting Buckingham’s π theorem with ideas from active subspaces to overcome these limitations. Through this methodology, a principal dimensionless group has been identified that efficiently describes the behavior of the system in terms of normalized bulk turbulent kinetic energy. Additionally, a simplified version of the new dimensionless group is proposed, which presents the structure of a Reynolds number augmented with dynamic viscosity, thermal conductivity, or equivalently Prandtl number and isobaric heat capacity, and specific gas constant to account for thermophysical effects. Finally, the results obtained in this study, which is based on a realistic regime inspired by nitrogen at high-pressure microfluidic conditions, can be generalized to other fluids using the principle of corresponding states.

Actuation Behavior of Hydraulically Amplified Self-Healing Electrostatic (HASEL) Actuator via Dimensional Analysis

Electroactive polymer (EAP) actuators are an example of a novel soft material device that can be used for several applications including artificial muscles and lenses. The field of EAPs can be broken down into a few fields; however, the field that will be discussed in this study is that of Soft Electrohydraulic (SEH or EH) actuators. The device that will specifically be studied is the Hydraulically Amplified Self-Healing Electrostatic (HASEL) actuator. The design of the HASEL actuator is simple. There are two compliant films that house a dielectric liquid, and with the application of a voltage potential, there is an output displacement and force. However, the actuation mechanism is more complex, thus there is a need to understand theoretically and experimentally how the actuator works. This study analytically describes the electrode closure and the experimental testing of the actuators. Then, dimensional analysis techniques are used to determine what factors are contributing to the function of the actuator. For this study, eight dimensionless Π groups were found based on the derived analytical equation. These Π groups were determined based on the input voltage, density, viscosity, and elastic modulus of the materials; these were chosen because of their major contribution to the experimental data. The Π groups that are of particular importance are related to the characteristic length, which is directly related to the displacement of the fluid, the fluid velocity, the fluid pressure, and the dielectric constant. From this study, relationships between the output force, the electrostatic contributions, and other parameters were determined. All in all, this type of analysis can provide guidance on the development of high-performance HASEL actuators.

A Case for Micromachines in Laboratory-Based DFIG Wind Turbine Systems for Fault Studies

For laboratory-based systems, the selection of components is critical to ensure proper representation of the actual system. In past investigations, researchers made use of small-scale off-the-shelf wound rotor induction machines (WRIMs) to perform laboratory-based studies. However, there are no reports validating their applicability in comparison to using the actual machines. In this regard, this paper investigates the correlation between the dimensional parameters and the electrical asymmetry indicators for a large-scale wind generator and laboratory-based generators. For the latter, a comparison is made between using a standard small-scale off-the-shelf WRIM and a micromachine. It is shown that the harmonic frequencies in a healthy machine and those due to inherent asymmetries appear at the same positions on the stator current spectrum for the three machines. However, there is a difference in the amplitudes of these components, given their dependence on the winding factors for a specific machine. The dimensional analysis techniques used to scale down the large-scale generator into a micromachine ensure that these parameters are related. However, this is not the case for the standard small-scale WRIM. Further work demonstrates the correlation of the fault-related harmonics between the micromachine and the large-scale machine for a rotor inter-turn fault condition. Micromachines are designed to ensure that the time constants are proportional representations of the larger machine, thus providing an accurate reflection of what is expected under transient operating conditions of wind turbines. This would assist in the development of condition monitoring strategies that are suited for the actual systems in the industry.

Районирование при обосновании вероятности необходимости осушения земель и методы снижения загрязненности дренажного стока

Purpose: to develop mechanisms for territory zoning according to demand for land drainage and the volume of substances leaching with drainage runoff and to identify the methods for reducing the pollution of drainage runoff. All calculations are made using the example of macrozonal zoning of drainage when growing strategically important crops: spring wheat and potatoes – using the example of the European part of Russia. Materials and methods. The justification for drainage was carried out using the bioclimatic method of V. V. Shabanov. A dimensional analysis technique and laboratory experiments on leaching soil monoliths for determining the main factors influencing the leaching of substances from soil were used. Results. A justification of reclamation measures (drainage) for regions and districts of the Russian Federation was carried out using the example of grains and potatoes. The main water protection measures reducing the polluting impact on water intakes from drainage runoff include: the creation of biological engineering structures; passive measures – precise reclamation aimed at managing the conditions for the drainage runoff formation, taking into account soil heterogeneity based on the zoning of drainage and the volume of nutrient leaching from drained lands. Conclusions. The European part of Russia has been zoned based on demand for drainage. A low degree of demand for land drainage when growing spring wheat was noted on approximately 40 % of the area and high degree was noted on 50 %. When growing potatoes, these areas account for 20 and 50 % of the area, respectively. The influence of factors on the drainage runoff formation and the volume of substance leaching was revealed. Water protection measures are proposed: construction of biological engineering structures and carrying out precise reclamation as a way to control the water regime of soils.

Implementing High Dimensional Reduction Analysis on Histocytometric Data.

In a previous protocol article, we demonstrated construction of a histocytometry pipeline that is capable of both segmenting highly aggregated cell populations and retaining the original intensity data range of the input microscopy images. In the protocol presented here, using the output from the aforementioned article, we demonstrate how to phenotype the data using the high dimensional reduction analysis technique optimized t-distributed stochastic neighbor embedding (opt-t-SNE) and compare it to traditional manual gating. Additionally, we present a protocol illustrating the advantage of the inclusion of cell junction/membrane markers for accurately segmenting highly aggregated cell populations in ilastik. © 2022 Wiley Periodicals LLC. Basic Protocol 1: Phenotyping lymph node populations using manual gating Basic Protocol 2: Phenotyping lymph node populations using t-SNE dimensional reduction Support Protocol: ilastik segmentation using a pan marker.

Performance Evaluation of Waste Stabilization Pond for Treatment of Wastewater from a Tertiary Institution Campus Located in Jos North Local Government Area, Plateau State, Nigeria

Appropriate treatment of wastewater before disposal into the environment or reuse is very important in the quest to protect the environment and safeguard public health. This paper investigated the performance evaluation of a waste stabilization pond (WSP) for treatment of wastewater from a tertiary institution campus located in Jos North Local Government Area of Plateau State in North Central Nigeria. The waste stabilization pond of the tertiary institution campus was designed for a wastewater flow rate of 12,945 m3/day. In order to evaluate the performance of the WSP, a model was developed following the Froude’s number dimensional analysis technique. The model was evaulated based on a wastewater flow of 0.4 m3/day. The final effluent from the maturation pond had 80 mg/L BOD, 195 mg/L COD, 75 CFU/100ml Total Coliforms, 610 mg/L Total solids, 19 mg/L Total Nitrogen, 210 mg/L Chloride, 28 mg/L Phosphate, 1.3 mg/L Ammonia and 7.0 pH. The WSP was able to achieve an overall efficiency of 77.78% reducing all quality parameters to recommended limited with exception of total nitrogen and phosphate. The implementation of this design will go along way to aid the treatment of wastewater from the campus of the university.

A new Sliding Mode Control tuning approach for second-order inverse-response plus variable dead time processes

This work addresses a new set of tuning rules for Sliding Mode Control (SMC) applied to second-order inverse-response plus variable dead time processes. Descriptions of the dynamics of inverse response systems and sliding-mode controllers are first provided. Then, we present the design process for the set of SMC tuning rules, using dimensional analysis, experimental design, optimization, and model reduction techniques for set-point tracking. The obtained expressions are simple, which eases the application of the proposed step-by-step systematic methodology. The performance and robustness of the proposed SMC tuning method are compared to other well-known controllers, and then applied to a Van de Vusse isothermal reactor, which is a complex nonlinear second-order inverse-response system that exhibits variable dead time. The performance achieved with the new SMC tuning method is good for set-point tracking, while exhibiting a good behavior for disturbance rejection, and can be applied considering a wide-range of parameters of the process’ transfer function.

Neural-network based approach for modeling wall-impact breakage of agglomerates in particle-laden flows applied in Euler–Lagrange LES

The present study proposes a novel modeling approach for predicting the wall-impact breakage of agglomerates in wall-bounded particle-laden turbulent flows based on artificial neutral networks (ANN). The suggested model is especially useful for efficient Euler-Lagrange simulation methods relying on the hard-sphere approach and the equivalent-sphere model for the agglomerate structure, allowing LES predictions of high mass loadings. Based on the impact conditions, i.e., the impact velocity, the impact angle, the number of included primary particles and the diameter of the primary particles, the outcomes of the breakage events are forecasted using two pre-trained artificial neural networks. The first network is concerned with the prediction of the possibility of breakage and the resulting fragment size distribution, whereas the second network predicts the post-breakage velocities of the fragments. The supervised training of the employed networks relies on a database obtained by extensive DEM simulations of agglomerate wall-impacts covering wide ranges of impact conditions, which were partially reported in Khalifa and Breuer (2020, 2021) for developing a breakage model based on a dimensional analysis and regression techniques. In the present contribution, the database mainly comprising the normal or oblique impact case is extended by adding results for the practically relevant shear impact case of wall-bounded particle-laden flows at extremely small impact angles, i.e., 3° and practically flat (0.2°). In addition, the breakage behavior of agglomerates containing very small numbers of particles are investigated under different impact angles and primary particle sizes. The ANN model is employed in Euler-Lagrange LES predictions of duct flows taking three Reynolds numbers and agglomerates of two powders distinguished by the size of the primary particles into account. The results obtained are compared with those based on a previous regression model (Khalifa and Breuer, 2021). In general, a good agreement between the results is found. However, the new ANN model is more widely applicable since the shear impact case is taken into account, which leads to subtle differences enhancing the reliability of the predictions.

Topological Analysis of Syntactic Structures

We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality, of hierarchical clustering structures, and of non-trivial loops. We show there are relations that hold across language families and additional relations that are family-specific. We then analyze the trees describing the merging structure of persistent connected components for languages in different language families and we show that they partly correlate to historical phylogenetic trees but with significant differences. We also show the existence of interesting non-trivial persistent first homology groups in various language families. We give examples where explicit generators for the persistent first homology can be identified, some of which appear to correspond to homoplasy phenomena, while others may have an explanation in terms of historical linguistics, corresponding to known cases of syntactic borrowing across different language subfamilies.

Statistical shape analysis of the tricuspid valve in hypoplastic left heart sydrome.

Hypoplastic left heart syndrome (HLHS) is a congenital heart disease characterized by incomplete development of the left heart. Children with HLHS undergo a series of operations which result in the tricuspid valve (TV) becoming the only functional atrioventricular valve. Some of those patients develop tricuspid regurgitation which is associated with heart failure and death and necessitates further surgical intervention. Repair of the regurgitant TV, and understanding the connections between structure and function of this valve remains extremely challenging. Adult cardiac populations have used 3D echocardiography (3DE) combined with computational modeling to better understand cardiac conditions affecting the TV. However, these structure-function analyses rely on simplistic point-based techniques that do not capture the leaflet surface in detail, nor do they allow robust comparison of shapes across groups. We propose using statistical shape modeling and analysis of the TV using Spherical Harmonic Representation Point Distribution Models (SPHARM-PDM) in order to generate a reproducible representation, which in turn enables high dimensional low sample size statistical analysis techniques such as principal component analysis and distance weighted discrimination. Our initial results suggest that visualization of the differences in regurgitant vs. non-regurgitant valves can precisely locate populational structural differences as well as how an individual regurgitant valve differs from the mean shape of functional valves. We believe that these results will support the creation of modern image-based modeling tools, and ultimately increase the understanding of the relationship between valve structure and function needed to inform and improve surgical planning in HLHS.

Discharge equation of semi-circular side weirs: An experimental study

Side weirs are diverting structures and usually used for diverting and controlling the water flow into the side open channel. The present study deals with an experimental study regarding the hydraulic performance of side weirs with semi-circular vertical sections along the main channel. As flow depth of the main channel increases the top flow width of the semi-circular side weir (SCSW) increases which is an advantage when high discharge enters the main channel and should be immediately diverted for safety reasons. In this study, the flow discharge of semi-circular sharp-crested side weirs and their affecting parameters are investigated. To investigate the hydraulic behavior and geometric characteristics of the SCSWs, a comprehensive laboratory study including 155 tests (for three weir diameters 0.25, 0.30 and 0.40 m) was conducted in a physical model under subcritical flow conditions. Flow discharge of the SCSW was investigated in relation to height, diameter and flow head of side weir, also approach Froude number (Froude number at upstream end of the side weir) and main channel width. Three different discharge models were developed based on; purely dimensional analysis technique, classical weir equation with linear water surface and classical weir equation with horizontal water surface profile (conventional weir theory along with dimensional analysis technique). The presented mathematical discharge models enable estimation of discharge along the SCSW with acceptable accuracy (best model has an average error of 1.87% with a maximum error of 6.31%) compared with the measured data under subcritical flow conditions. Additionally, a relationship was proposed for computing the limiting flow depth at the downstream end of the SCSW. Experimental results confirm that the proposed relationship well explains the behavior of flow over the SCSW regarding the downstream flow conditions.

STUDY THE SLOPE STABILITY OF EARTHEN DAM USING DIMENSIONAL ANALYSIS TECHNIQUES

Slope stability is calculated using several methods. All these methods produce estimated results based on inaccurate assumptions, and their results were particularly acceptable. Furthermore, these methods rely on supposing and segmenting the surface of failure as well as performing complex calculations. This paper introduces the “Dimensional Analysis Technique” as a new approach for dealing with earthen slopes. Four dimensionless groups (Formula presented) were driven to calculate the slope stability of a homogeneous filtered at the downstream earth dam. Geo-Slope and Geo-Seep software are used to compute Factor of Safety by Spencer’s method. The derived formula shows that estimated upstream water levels match the calculated results and reasonably fit with coefficient of determination (R2) greater than to .97. Results suggest that the Dimensional Analysis Technique is a safe and new direct method to track the stability of the natural earth slope. (Less)

Nonlinear numerical simulation of physical shaking table test, using three different soil constitutive models

Dynamic response records of pile performance during earthquakes are limited mainly due to the challenges of recording the seismic soil–pile response. This limitation has led to an inadequacy in providing a standardized basis for the calibration and validation of the available analytical and numerical methods developed for seismic soil–pile superstructure interaction problems. To bridge this gap, a series of numerical simulations of scaled, shaking table tests of model piles in soft clay has been developed in the current study. This paper aims to accurately identify all aspects and critical parameters in the numerical simulation and propose the most suitable soil constitutive model. Three soil constitutive models are selected as advanced models for soft soil, namely, the modified Mohr–Coulomb, Drucker–Prager/cap plasticity, and Cam–clay models. Similar to the physical test case study, this numerical analysis uses dimensional analysis techniques to identify scale modelling criteria and develop a scaled soil and pile-supported structure model correctly. The 3D nonlinear numerical models are developed using the Abaqus software.