Dimensional analysis of partial discharge initiated by a metallic particle adhering to the spacer surface in a gas-insulated system

Partial discharges (PDs) constitute important phenomena in a Gas-Insulated System (GIS) that warrant recognition (and, subsequently, mitigation) as they are obvious symptoms of system degradation. This paper proposes the application of dimensional analysis, based on Buckingham pi theorem, for characterizing PDs provoked by the presence of metallic particles adhering to the spacer surface in a GIS employing SF6 (Sulphur hexafluoride). The ultimate goal of the analysis is to formulate the relationships that express three PD indicator quantities, namely current, charge, and energy, in terms of six independent quantities that collectively influence these indicators. These six quantities (henceforth referred to as the influencing, determining or affecting variables) include the level of applied voltage, the SF6 pressure, the length and position of the particle on the spacer, the duration of voltage application, and the gap between electrodes. To compute the pertinent dimensionless products, we implement three computational methods based on matrix operations. These three methods produce exactly the same dimensionless products, which are subsequently used for constructing the models depicting the relationships between each of the three PD dependent quantities and the common six determining variables. The models derived provide partial quantitative information and facilitate qualitative reasoning about the considered phenomenon.

SIMULATION OF DESIGN VARIABLES EFFECT ON PERFORMANCE OF A COMMON BEANS (Phaseolus vulgaris L) PORTABLE THRESHER

In Kenya, threshing of common beans is mainly by traditional method using sticks and animal tramping, which are slow, inefficient and tedious. Consequently, there is a need to develop portable threshers locally available in the market for small and medium-scale farmers. The objective of this study was to simulate design variables effect on the performance of a common beans portable thresher. Sizing of design variables and parameters was key in development of bean thresher. This could be achieved by costly experiments or use of prediction mathematical model equation. The later method was used by developing mathematical models from combination of Buckingham pi theorem and reference to other similar work in literature. The predicting equation for power requirement, grain losses, grain damages, efficiency and throughput capacity were developed and validated using experimental thresher from the same study. The results showed that there was a positive correlation with R2 of 0.9. Based on actual data and 10% absolute residual error interval, the prediction performance of the developed models were above 77%. The results noted that increase in cylinder peripheral speed of the pegs resulted into increase in power requirement, bean grains damages, threshing efficiency and throughput capacity. Also increase in effective cylinder diameter caused increase in threshing efficiency and grain damages.

Mathematical Model for Scaling up Bioprocesses Using Experiment Design Combined with Buckingham Pi Theorem

Scaling up bioprocesses from the experimental to the pilot or industrial scale involves heuristics and scale relationships that are far from the specific phenomena and are usually not connected to the experimental data. In complex systems, the scaling-up methodology must connect the experimental data with the tools of engineering design. In this work, a two-stage gold bioleaching process was used as a case study to develop a mathematical model of bioprocess scaling that combines the design of experiments with dimensional analysis using the Buckingham Pi theorem to formulate a predictive model that allows scaling up bioprocesses. It was found that the C/N, C/K, and T/C ratios are dimensionless factors that can explain the behavior of a system. Using the Pearson Product–Moment bivariate analysis, it was found that the dimensionless factors C/N and C/K were correlated with the leaching potential of the fermented broth at 1060 cm−1. With these results, a non-linear logarithmic model based on dimensionless parameters was proposed to explain the behavior of the system with a correlation coefficient of R2 = 0.9889, showing that the optimal conditions to produce fermented broth comprised a C/N ratio close to 50 and a C/K ratio close to 800, which allows predicting the scaling of the bioprocess.

Numerical simulation and experimental study on hematite production by oxidation of mill scale

Mill scale is a waste product from steel hot rolling processes and containing a high amount of FeO and Fe3O4. It is crucial to recycle and reuse this waste for the recovery into a metallic iron or its single oxide derivative. One of the end products of mill scale oxidation is hematite which has multitude of uses in various application. In this present study, mill scale is converted to hematite by roasting a mixture of mill scale at a specific set of conditions at 900°C for a varied time under ambient air environment by addition of pelletized limestone as a heat storage media. In this work, the Dimensionless Degree of Oxidation Prediction Model (DDOPM) has been constructed to gain hematite purity approach in the resulting powder by using Matlab. The Buckingham Pi Theorem is used to find dimensionless parameters considering the effect of different parameters including the geometric factor of tubular horizontal furnace used, characteristic of mill scale, ambient air factor, and thermal characteristics of limestone. The degree of oxidation from experimental result was obtained from XRF analysis and compared to the result of DDOPM to show the correlation between the experimental and numerical.

Hydrology without dimensions

By rigorously accounting for dimensional homogeneity in physical laws, the Pi theorem and the related self-similarity hypotheses allow us to achieve a dimensionless reformulation of scientific hypotheses in a lower dimensional context. This paper presents applications of these concepts to the partitioning of water and soil on terrestrial landscapes, for which the process complexity and lack of first principle formulation make dimensional analysis an excellent tool to formulate theories that are amenable to empirical testing and analytical developments. The resulting scaling laws help reveal the dominant environmental controls for these partitionings. In particular, we discuss how the dryness index and the storage index affect the long term rainfall partitioning, the key nonlinear control of the dryness index in global datasets of weathering rates, and the existence of new macroscopic relations among average variables in landscape evolution statistics. The scaling laws for the partitioning of sediments, the elevation profile, and the spectral scaling of self-similar topographies also unveil tantalizing analogies with turbulent fluctuations.

Slug Frequency Prediction Model for Fluid Flow in Flowline Bends

The prediction of slug frequency for two-phase slug flow during multiphase transportation of oil reservoir productions is crucial in the design of slug controllers for petroleum processing installations. Mechanistic based slug prediction models have not had much successful application due to the difficulty in modelling the non-linear interface motion during slug development. The mechanism of slugging in offshore flowline-riser is complicated and requires rigorous experimental sampling and testing. This process can be time-consuming and costly. In this study, a new correlation is developed for the prediction of severe slugging frequency. The new model is developed based on the results of scaled experimental design. Dimensional analysis approach using the Buckingham pi-theorem is used in developing the two-phase correlation. The model development involves non-dimensional empirical correlations in terms of relevant dimensionless groups, which are obtained based on the design of the experiment. A broad range of experimental data from 10 varied choke opening size was used. The new correlation predicts 92.3% of the measurements within ±8% absolute error and the mean absolute deviation of the correlation is about 6.13%. The newly developed correlation can be applied for flow rates between 0.1 kg/s and 0.6 kg/s and choke openings between 10-98%.

Dimensional analysis of structural response in complex biological structures

The solution to many engineering problems is obtained through the combination of analytical, computational and experimental methods. In many cases, cost or size constraints limit testing of full-scale articles. Similitude allows observations made in the laboratory to be used to extrapolate the behavior to full-scale system by establishing relationships between the results obtained in a scaled experiment and those anticipated for the full-scale prototype. This paper describes the application of the Buckingham Pi theorem to develop a set of non-dimensional parameters that are appropriate for describing the problem of a distributed load applied to the rostrum of the paddlefish. This problem is of interest because previous research has demonstrated that the rostrum is a very efficient structural system. The ultimate goal is to estimate the response of a complex, bio-inspired structure based on the rostrum to blast load. The derived similitude laws are verified through a series of numerical experiments having a maximum error of 3.39%.

Implications of Buckingham's Pi Theorem to the Study of Similitude in Discrete Structures: Introduction of the RFN, μN and the SN Dimensionless Numbers and the Concept of Structural Speed

Motivated by the need to evaluate the seismic response of large capacity gravity energy storage systems (potential energy batteries) such as the proposed frictional Multiblock Tower Structures (MTS) recently discussed by Andrade et al. [1], we apply Buckingham's Pi Theorem [2] to identify the most general forms of dimensionless numbers and dynamic similitude laws appropriate for scaling discontinuous multiblock structural systems involving general restoring forces resisting inertial loading. We begin by introducing the dimensionless “mu-number” (μN) appropriate for both gravitational and frictional restoring forces and then generalize by introducing the “arbitrary restoring force number” (RFN). RFN is subsequently employed to study similitude in various types of discontinuous or discrete systems featuring frictional, gravitational, cohesive, elastic and mixed restoring forces acting at the block interfaces. In the process, we explore the additional consequences of inter and intra-block elasticity on scaling. We also formulate a model describing the mechanism of structural signal transmission for the case of rigid MTS featuring inter-block restoring forces composed of elastic springs and interfacial friction, introducing the concept of “structural speed”. Finally, we validate our results by demonstrating that dynamic time-histories of field quantities and structural speeds between MTS models at various scales are governed by our proposed similitude laws, thus demonstrating the consistency of our approach.