Important Dimensionless Groups Research Articles

Determination of Parameters Affecting the Estimation of Iceberg Draft

Recent offshore oil and gas loading facilities developed in the Arctic area have led to a considerable awareness of the iceberg draft approximation, where deep keel icebergs may gouge the ocean floor, and these submarine infrastructures would be damaged in the shallower waters. Developing reliable solutions to estimate the iceberg draft requires a profound understanding of the problem’s dominant parameters. As such, the dimensionless groups of the parameters affecting the iceberg draft estimation were determined for the first time in the present study. Using the dimensionless groups recognized and the linear regression (LR) analysis, nine LR models (i.e., LR 1 to LR 9) were developed and then validated using a comprehensive dataset, which has been constructed in this study. A sensitivity analysis distinguished the premium LR models and important dimensionless groups. The best LR model, as a function of all dimensionless parameters, was able to estimate the iceberg draft with the highest level of precision and correlation along with the lowest degree of complexity. The ratio of iceberg length to iceberg height as the “iceberg length ratio” and the ratio of iceberg width to iceberg height as the “iceberg width ratio” was detected as the important dimensionless groups in the estimation of the iceberg draft. An uncertainty analysis demonstrated that the best LR model was biased towards underestimating the iceberg drafts. The premium LR model outperformed the previous empirical models. Ultimately, a set of LR-based relationships were derived for estimating the iceberg drafts for practical engineering applications, e.g., the early stages of the iceberg management projects.

Theory of a Glazed Transpired Solar Collector in Natural Convection Mode

Abstract The theory of a glazed transpired collector solar air heater in natural convection mode has been developed. This was aimed at generating a framework for the experimental study of the performance of the collector. The theory involved the definition of some of the collector’s main geometries, the formulation of the energy balance on the collector, and the driving forces within the collector. The dimensional analysis was then applied to the formulations to obtain relationships between important dimensionless groups. The theory of the glazed transpired collector in natural convection mode provides a basis for the development of the collector for application in the areas of space heating and crop drying. This type of collector provides a solution to the challenge of space heating and crop drying at locations where electricity is not available and photovoltaic power is not affordable. It could also contribute to energy savings since it requires no electricity to work.

Numerical investigation and dimensionless erosion laws of solid particle erosion in plugged tees

In the process of oil and gas production, particle erosion is an important cause of pipe fitting failure. It is generally believed that the plugged tees have the potential to mitigate erosion. A computational fluid dynamics (CFD)-based erosion prediction numerical model is employed to investigate the gas-solid flow and erosion behavior in the plugged tees. The trajectories of particles released from different positions on the inlet cross-section are tracked. The phenomenon of particle recirculation is found in the plugged pipe through particle trajectory analysis. Combined with particle impact characteristics, the erosion morphology at the end region is analyzed. Erosion mitigation performance of the plugged tees is evaluated by comparison with elbows. Additionally, four important dimensionless groups are derived through dimensional analysis. Self-similarity behavior between these groups is extracted to establish two new dimensionless numbers that are suitable for the erosion prediction of the end region and the corner region, respectively.

Developing a dimensionless number for solid particle erosion with gas-liquid-solid flow in standard elbows

A new dimensionless number for erosion prediction in standard elbows under gas-liquid-solid flow conditions is developed. For this purpose, a machine learning algorithm is trained and used to generate erosion data. Then, three important dimensionless groups are extracted employing dimensional analysis. Next, self-similarity is established among these groups and a new dimensionless number (PnrTP) is developed. It is revealed that erosion can be predicted through mixture Reynolds number for different flow regimes, when the deviation from the homogenous no-slip conditions is accounted for. Furthermore, validation is performed against different experimental data for a wide range of flow and particle conditions.

Overcoming diffusion limitations in electrochemical microreactors using acoustic streaming

We provide a theoretical background on laminar flow electrochemical reactors and rationally map typically encountered operating regimes in literature. At the highest (mass transfer limited) current densities attainable, the Fourier number (Fo) and the Sherwood number (Sh) are identified as important dimensionless groups for design considerations. The critical Fourier number places a severe constriction on the production capacity of a microreactor, as it determines the maximum throughput for a reactor of fixed length and inter-electrode distance. This critical Fourier number indicates that the absence of convective mixing and the reliance on diffusion of the electroactive species is the key problem to address for further intensifying electrochemical microreactors. Computer simulations are then used to illustrate the steady-state as well as transient behavior of generic case studies. These simulations also show that the transient response to a voltage step can be used to experimentally verify that the absence of mixing is a major bottleneck of laminar flow reactors. A versatile tubular electrochemical reactor was developed and applied to an acetonitrile solution containing ferrocene and benzylbromide, which is a simple model system for investigating self-supported synthesis (i.e., electrosynthesis without intentionally added supporting electrolyte). The reactor was then fitted with piezoelectric elements that excite a resonating standing wave in the flow direction, resulting in pairs of counter-rotating vortices in the fluid (acoustic streaming). The sonicated experiments prove that ultrasound assisted mixing reduces the critical Fourier number, enabling self-supported synthesis at elevated flow rates and throughput.

Data-driven dimensional analysis of heat transfer in irradiated particle-laden turbulent flow

The study of thermal radiation interacting with particle-laden turbulence is of great importance in a wide range of scientific and engineering applications. The fundamental and applied study of such systems is challenging as a result of the large number of thermo-fluid mechanisms governing the underlying physics. This complexity is significantly reduced by transforming the problem of interest into its scale-free form by means of dimensional analysis techniques. However, the theoretical framework of classical dimensional analysis presents the limitations of not providing a unique set of dimensionless groups, and no support for measuring the relative importance between them. In the interest of addressing these shortfalls for multiphysics turbulent flow applications, we present a semi-empirical dimensional analysis approach to efficiently extract important dimensionless groups from data obtained by means of computational (or laboratory) experiments. The methodology presented is then used to characterize important dimensionless groups in irradiated particle-laden turbulence. The study concludes that two dimensionless groups are responsible for most of the variation in the system’s thermal response, with the absorption of radiation by particles, the radiative energy deposition rate and the turbulent flow mixing the most important thermo-fluid mechanisms. The generality of the results obtained can be leveraged to effectively reduce the dimensionality of irradiated particle-laden turbulent flows in research studies and in the design and optimization of similar systems.

Are Tornado Vortex Generators fit for purpose?

In recent years a number of Tornado Vortex Generators (TVGs) have been constructed and tested, with a view to providing facilities that can be used to determine wind loads on a variety of structures in tornado conditions. The scaling of TVGs has however proved to be contentious and different authors have taken different approaches. In this paper we address this issue and firstly present a formal dimensional analysis of the flow within full scale tornadoes and TGVs, which identifies a number of important dimensionless groups. We then consider a range of full-scale tornado data and, as far as possible, derive values of these dimensionless groups for each tornado. This analysis is then used to define the ranges of the dimensionless parameter for three tornado types (all of the two cell form) that can be used as simulation targets, rather unimaginatively naming them small, medium and large tornadoes. We then consider the performance of four medium to large TVGs in achieving these simulations. The analysis shows that the larger TVGs can achieve a range of geometrical similarities for the small and medium simulation targets, but none are able to achieve kinematic similarity, in that the ratio of circumferential to radial velocities are significantly lower than at full scale. Dynamic similarity (based on the Reynolds number) is of course not possible for physical models, but the analysis shows that in almost all cases the Reynolds number and model scales fall well below what would be considered acceptable in atmospheric boundary layer wind tunnels. We thus regretfully conclude that current TVGs are not wholly fit for purpose at the moment and are in need of significant modification if they are to be used to give reliable loading data. Alternatively it may be that the wind engineering community should consider different types of simulation to obtain the required information.

Sensitivity and feedback of wind-farm induced gravity waves.

Flow blockage by large wind farms leads to an upward displacement of the boundary layer, which may excite atmospheric gravity waves in the free atmosphere aloft and on the interface between the boundary layer and the free atmosphere. In the current study, we assess the sensitivity of wind-farm gravity-wave excitation to important dimensionless groups and investigate the feedback of gravity-wave induced pressure fields on wind-farm energy extraction. The sensitivity analysis is performed using a fast boundary-layer model that is developed to this end. It is based on a three-layer representation of the atmosphere in an idealised barotropic environment, and is coupled with an analytical wake model to account for turbine wake interactions. We first validate the model in 2D-mode with data from previous large-eddy simulations of "infinitely" wide wind farms, and then use the model to investigate the sensitivity of wind-farm induced gravity waves to atmospheric state and wind-farm configuration. We find that the inversion layer induces flow physics similar to shallow-water flow and that the corresponding Froude number plays a crucial role. Gravity-wave excitation is maximal at a critical Froude number equal to one, but the feedback on energy extraction is highest when the Froude number is slightly below one due to a trade-off between amplitude and upstream impact of gravity waves. The effect of surface friction and internal gravity waves is to reduce the flow perturbation and the related power loss by dissipating or dispersing perturbation energy. With respect to the wind-farm configuration, we find that gravity-wave induced power loss increases with wind-farm size and turbine height. Moreover, we find that gravity-wave effects are small for very wide or very long wind farms and attain a maximum at a width-to-depth ratio of around 3/2.

Experimental study of wall nucleation characteristics in flow boiling under subatmospheric pressures in a vertical square channel

Experiments have been conducted in a vertical square channel to investigate wall nucleation characteristics in subcooled boiling flows under subatmospheric pressure. The objective of this work is to provide a unique dataset to evaluate the scalability of existing models of nucleation characteristics for flow boiling conditions below atmospheric pressure as the performance of these models has not been investigated under these conditions. The experimental data is presented as a parametric study of the effects of important dimensionless groups on nucleation characteristics, specifically boiling number, Jakob number, and density ratio. Bubble departure diameters and departure frequencies are measured and compared to existing models. Some existing models are shown to predict departure diameter well but mainly overpredict departure frequency at low pressure.

A Scaling Method for Correlating Ex Situ and In Situ Measurements in PEM Fuel Cells and Electrolyzer

Correlating ex-situ measurements of Pt coverage using the thin film-rotating disk electrode (TF-RDE) and in-situ performance of proton exchange membrane (PEM) type fuel cells and electrolyzer is established. The TF-RDE has a smaller geometric electrode area, and, typically, lower Pt loading is used compared to the in-situ single cell of PEMs. The model equation for Pt contamination by adsorption mechanisms followed by dimensionless analysis enables us to find three important dimensionless groups, which has been shown to control the contamination phenomena. The capacity ratio of Pt loading and inlet concentration of the contaminant, the measure of the rate of reaction, and the coverage ratio of the contaminant is used to translate ex-situ to in-situ by providing the scaling factor that is key to the correlation. These scales lead to the prediction of the coverage on the Pt sites using the ex-situ adsorption isotherm. Also, dimensionless numbers are tested in in-situ performance tests of PEM fuel cells for validation.

Modeling a new design for extracting energy from geopressured geothermal reservoirs

Reducing geothermal energy recovery costs and environmental concerns has led to interest in modeling new borehole heat exchanger designs. These heat exchangers are environment-friendly because they inject all the geofluid back into the reservoir after harvesting its energy, resulting in zero mass withdrawal from the system. This study develops reduced-order reservoir models for quickly estimating production temperature and thermal recovery from borehole heat exchangers using inspectional analysis and predictive modeling. An inspectional analysis suggests that there are nineteen dimensionless numbers necessary to fully scale this design. These dimensionless numbers were used in the statistical modeling. A Box–Behnken experimental design was used to create the simulation runs. A rigorous sensitivity analysis was performed on these designed series of runs to identify the most important dimensionless groups in predicting the dimensionless response for different segments of time. The selected dimensionless groups along with the dimensionless production temperature and thermal recovery factor (response), were used in the regression models. The models were reduced and assessed using training and testing runs. Applications of the developed models are also presented. The approach presented in this paper is general and provides a means to interpret and develop predictive models from simulator outputs in other research areas.

Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations

A linear oscillator simultaneously subjected to stochastic forcing and parametric excitation is considered. The time required for this system to evolve from a low initial energy level until a higher energy state for the first time is a random variable. Its expectation satisfies the Pontryagin equation of the problem, which is solved with the asymptotic expansion method developed by Khasminskii. This allowed deriving closed-form expressions for the expected first passage time. A comprehensive parameter analysis of these solutions is performed. Beside identifying the important dimensionless groups governing the problem, it also highlights three important regimes which are called incubation, multiplicative and additive because of their specific features. Those three regimes are discussed with the parameters of the problem.

Regularized string model for nanofibre formation in centrifugal spinning methods

We develop a general regularized thin-fibre (string) model to predict the properties of non-Newtonian fluid fibres generated by centrifugal spinning. In this process the fibre emerges from a nozzle of a spinneret that rotates rapidly around its axis of symmetry, in the presence of centrifugal, Coriolis, inertial, viscous/shear-thinning, surface tension and gravitational forces. We analyse the effects of five important dimensionless groups, namely, the Rossby number ($Rb$), the Reynolds number ($Re$), the Weber number ($We$), the Froude number ($Fr$) and a power-law index ($m$), on the steady state trajectory and thinning of fibre radius. In particular, we find that the gravitational force mainly affects the fibre vertical angle at small arc lengths as well as the fibre trajectory. We show that for small $Rb$, which is the regime of nanofibre formation in centrifugal spinning methods, rapid thinning of the fibre radius occurs over small arc lengths, which becomes more pronounced as $Re$ increases or $m$ decreases. At larger arc lengths, a relatively large $We$ results in a spiral trajectory regime, where the fibre eventually recovers a corresponding inviscid limit with a slow thinning of the fibre radius as a function of the arc length. Viscous forces do not prevent the fibre from approaching the inviscid limit, but very strong surface tension forces may do so as they could even result in a circular trajectory with an almost constant fibre radius. We divide the spiral and circular trajectories into zones of no thinning, intense thinning and slow or ceased thinning, and for each zone we provide simple expressions for the fibre radius as a function of the arc length.

Important Parameter Groups in Thermal Protection of Polymers.

The problem of thermal protection is explored for two idiosyncratic reactive systems, namely a sacrificial heat-sink material and an intumescent system where a dynamically evolving insulation layer is produced from an initially thin coating. Relatively simple mathematical models of both systems are proposed that encompass the important physical characteristics of each situation and these models are analysed using a mixture of numerical and analytical techniques. Important dimensionless parameter groups are identified and domains of parameter space where thermal performance is particularly good- or particularly bad- are identified.

Wall nucleation modeling in subcooled boiling flow

The bubble departure characteristics are studied in flow boiling considering the available experimental data in the literature. The current bubble departure diameter and departure frequency models are reviewed and compared with the collected database, revealing the current modeling shortcomings in forced convective flows. Based on an energy balance approach at the heated surface, the important dimensionless groups are identified and correlated for the bubble departure diameter and departure frequency. These dimensionless groups are the Jakob number, Boiling number, density ratio, and Prandtl number. The bubble departure diameter data also suggests some effect of the flow geometry in mini-channels. The newly proposed semi-empirical models for the bubble departure diameter and departure frequency are shown based on the available database to be accurate to within ±22% and ±35% respectively. This work also identifies important future experimental considerations for the bubble departure characteristics including data at elevated pressures, larger Prandtl numbers, and around the boundary between mini and conventional channels.

An Isothermal Model for Predicting Performance Loss in PEMFCs from Balance of Plant Leachates

A model is presented for the contamination of a proton exchange membrane fuel cell (PEMFC), including adsorption onto the Pt catalyst, absorption into the membrane, and ion exchange with ionomeric components. Model predictions for three sources of voltage loss account for the two-dimensional, time-dependent contamination along the channel and into the membrane. The model is developed by considering the well-known concepts of Langmuir adsorption, partition coefficients, plug flow reactors (PFRs), and dimensionless analysis. The phenomena are shown to be controlled by three important dimensionless groups: a Damköhler number for the contamination reaction rate, a capacity ratio, and a coverage ratio for each contamination mechanism. These groups show how to scale ex situ equilibrium data for in situ predictions. The model predictions are shown to be reasonable when compared to in situ experiment data once ex situ data are used to provide reaction and equilibrium parameters. The predictions enable estimation of tolerance limits for leachates according to each mechanism. For typical parameters, the predicted voltage loss in the electrode ionomer by an ion-exchange mechanism shows slower reaction rates but greater performance losses than other mechanisms.

Determination of optimum gas holdup conditions in a three-phase fluidized bed by genetic algorithm

Experiments have been carried out in a 0.1 m internal diameter, 1.88 m height vertical Plexiglas column with an antenna type modified air sparger in the gas–liquid distributor section. This arrangement provides uniform mixing of the fluids, ensures the gas entering the fluidizing section as fine bubbles and reduces the pressure drop encountered through a conventional distributor used for the purpose. The important dimensionless groups which have influence on the gas holdup have been developed by the use of Buckingham Pi theorem. The relation of gas holdup with these dimensionless groups has been expressed in the form of a power law equation developed with very high correlation coefficient. Residual analysis has been carried out to validate the regression model. The optimum operating conditions for maximum gas holdup in a co-current three-phase fluidized bed have been predicted using genetic algorithm.

Prediction of Capillary Fluid Interfaces During Gas or Water Coning in Vertical Wells

Summary Gas and water coning significantly reduce oil production while increasing production costs. Simulation and experimental methods, coupled with simple analytical solutions or correlations, are typically used to identify the oil rate that minimizes coning and maximizes recovery. Current analytical solutions, however, are overly simplified in that they assume negligible capillary pressure, which leads to segregated flow. This paper presents new benchmark analytical solutions that relax this assumption and also allow for simultaneous two-phase flow. The new coning solutions apply to vertical wells where in-situ fluids are in vertical equilibrium. The development identifies the important dimensionless groups that control the effect of coning on oil recovery and illustrates how simultaneous two-phase flow affects capillary fluid levels in the formation. Dimensionless two-phase production windows are constructed to identify critical rates, the largest oil rate at which water (or gas) will not be produced. From comparisons to simulation, we show that critical flow rate estimates are accurate for aspect ratios greater than approximately 10. For aspect ratios less than 10, the critical rate estimates are always conservative.

Preparation of Microparticles by Micromixers: Characterization of Oil/Water Process and Prediction of Particle Size

A descriptive model for microparticle preparation by micromixers was developed to allow prediction of nascent microsphere size and provide a better understanding of a microscale oil/water (O/W) emulsion process. Nascent blank microparticles were prepared by an O/W emulsion method using a micromixer. Seven dimensionless groups were derived from the relevant process parameters. A multiple linear regression model was established on an empirical basis to describe the relationship between the key process parameters and the resulting Sauter particle diameter. The investigated micromixer is particularly suitable for processing of low-viscosity systems. The particle size is mainly controlled by flow velocity. Reynolds number and the viscosity ratio were found to be the most important dimensionless groups regarding the preparation procedure. Particle size was predicted with an accuracy up to 100% applying the empirically derived equations. An O/W process using micromixers for microparticle preparation with a multitude of influencing parameters was successfully characterized by application of dimensional analysis. Dimensionless groups turned out to be suitable for prediction of microparticle size with high precision.

A parametric study of a blown powder laser cladding and alloying process using a two-dimensional conduction model

A two-dimensional model has been developed to predict the temperature field and melt pool shape during blown powder laser cladding. A finite volume method has been used to solve the two-dimensional energy equation for a body moving relative to a stationary laser heat source. A boundary fitted coordinate system has been employed as the built-up surface geometry is complex. Important dimensionless groups representing laser parameters power ( P) and scanning speed ( U) and the process parameters built-up height and average dilution are identified. The effect of laser parameters on process parameters is investigated. For cladding P/U should always be kept low (less than 1) to reduce the average dilution, and in order to achieve the desired clad height the power level P should be controlled.