Dimensionless Parameter Groups Research Articles

Investigation of a new methodology for the prediction of drawing force in deep drawing process with respect to dimensionless analysis

In this research, geometric parameters were given in dimensionless form by the Buckingham pi dimensional analysis method, and a series of dimensionless groups were found for deep drawing of the round cup. To find the best group of dimensionless geometric parameters, three scales are evaluated by commercial FE software. After analyzing all effective geometric parameters, a fittest relational model of dimensionless parameters is found. St12 sheet metals were used for experimental validation, which were formed at room temperature. In addition, results and response parameters were compared in the simulation process, experimental tests, and proposed dimensionless models. By looking at the results, it very well may be inferred that geometric qualities of a large scale can be predicted with a small scale by utilizing the proposed dimensionless model. Comparison of the outcomes for dimensionless models and experimental tests shows that the proposed dimensionless models have fine precision in determining geometrical parameters and drawing force estimation. Moreover, generalizing proposed dimensionless model was applied to ensure the estimating precision of geometric values in larger scales by smaller scales.

Temporal Fluctuations and Poroelasticity Can Generate Chaotic Advection in Natural Groundwater Systems

AbstractAlthough steady, isotropic Darcy flows are inherently laminar and nonmixing in the absence of diffusion, it is well understood that transient forcing via engineered pumping schemes can induce rapid, chaotic mixing flows in groundwater. In this study we explore the propensity for such mixing to arise in natural groundwater systems subject to cyclical forcings, for example, tidal or seasonal influences. Using a conventional linear groundwater flow model subject to tidal forcing, we show that under certain conditions these flows generate Lagrangian transport and mixing phenomena (chaotic advection) near the tidal boundary. We show that aquifer heterogeneity, storativity, and forcing magnitude cause reversals in flow direction over the forcing cycle which, in turn, generate coherent Lagrangian structures and chaos. These features significantly augment fluid mixing and transport, leading to anomalous residence time distributions, flow segregation, and the potential for profoundly altered reaction kinetics. We define the dimensionless parameter groups which govern this phenomenon and explore these groups in connection with a set of well‐characterized tidal systems. The potential for Lagrangian chaos to be present near discharge boundaries must be recognized and assessed in field studies.

Polymorph Selection by Continuous Crystallization in the Presence of Wet Milling

The polymorph selection in a continuous crystallization process combined with wet milling is investigated. To this end, a dimensionless population balance equation model accounting for secondary nucleation, crystal growth, and breakage is formulated and solved numerically. We show that a surprisingly small number of dimensionless parameter groups (combinations of kinetic parameters and operating conditions) is decisive in controlling the polymorphic outcome. Specifically, we show how the operating region where the stable polymorph is obtained can be enlarged by tuning the milling intensity, feed concentration, and residence time. We further rationalize the dependence of the mean size of the particles obtained, the fraction of solute recovered, and the productivity of such a process on the dimensionless variables. We showcase this for the model system l-glutamic acid crystallized from water and show that our analysis is in agreement with previously reported experimental studies. Summarizing, the analysis a...

A novel potential flow model for granular flow in two-dimensional flat-bottomed packed bed with centric discharge

Potential flow (PF) model exhibits some advantages to simulate granular flow in industrial packed beds such as an iron-making blast furnace. To change the status of solving PF equations in the flowing zone, based on the difference analysis between PF and actual flow, the components of granular flow resistance were confirmed, and a novel potential flow (NPF) model for the flow of packed particles was established. The obvious difference from the PF model is that the NPF model can simultaneously predict the stagnant zone and the distribution of velocities in the flowing zone. The stagnant zone or the flowing zone calculated with NPF model under certain boundary conditions is only determined by a dimensionless parameter group R⁎. R⁎ has a clear physical meaning, so it’s easy to decide the effect on the distribution of stagnant zone and granular flow velocities. Furthermore, NPF model was validated by experimental data obtained with a two-dimensional flat-bottomed packed bed with centric discharge. Predicted results respectively by PF and NPF models were also compared.

Tensile properties of an auxetic structure with re-entrant and chiral features—a finite element study

A re-entrant chiral auxetic (RCA) structure is a new structure, which comprises three topologies: re-entrant, trichiral and anti-trichiral. The aim of this study is to numerically investigate the influences of geometrical parameters of a RCA unit cell on the in-plane tensile properties. Finite element (FE) models were developed using commercial software, ABAQUS 6.11–2, and verified by experimental results. Based on the verified FE models, a parametric study was performed to examine the effects of geometrical parameters on the stress–strain curve and Poisson’s ratio of a RCA structure. In order to reduce the variables studied, three dimensionless groups of geometrical parameters were proposed. Results showed that the RCA structure predominantly deformed by bending and stretching of walls as well as rotation of cylinders. The RCA structure displayed high stress, low strain and large negative Poisson’s ratio when it was loaded in the X direction. On the other hand, the RCA structure exhibited low stress, high strain and a transition from negative to positive Poisson’s ratio when it was loaded in the Y direction. The geometrical parameters of the RCA structure had significant effects on its stress–strain curves and Poisson’s ratios. The findings of this study provide an insight into the mechanical response of the RCA structure under uniaixal tensile loading.

Parametric Dimensional Analysis on the Structural Response of An Innovative Subsurface Tension Leg Platform in Ultra-Deep Water

The innovative Subsurface Tension Leg Platform (STLP), which is designed to be located below Mean Water Level (M.W.L) to minimize direct wave loading and mitigate the effect of strong surface currents, is considered as a competitive alternative system to support shallow-water rated well completion equipment and rigid risers for large ultra-deep water oil field development. A detailed description of the design philosophy of STLP has been published in the series of papers and patents. Nonetheless, design uncertainties arise as limited understanding of various parameters effects on the structural response of STLP, pertaining to the environmental loading, structural properties and hydrodynamic characteristics. This paper focuses on providing quantitative methodology on how each parameter affects the structural response of STLP, which will facilitate establishing the unique design criteria as regards to STLP. Firstly, the entire list of dimensionless groups of input and output parameters is proposed based on Vaschy- Buckingham theory. Then, numerical models are built and a series of numerical tests are carried out for validating the obtained dimensionless groups. On this basis, the calculation results of a great quantity of parametric studies on the structural response of STLP are presented and discussed in detail. Further, empirical formulae for predicting STLP response are derived through nonlinear regression analysis. Finally, conclusions and discussions are made. It has been demonstrated that the study provides a methodology for better control of key parameters and lays the foundation for optimal design of STLP. The obtained conclusions also have wide ranging applicability in reference to the engineering design and design analysis aspects of deepwater buoy supporting installations, such as Grouped SLOR or TLR system.

Prediction of Shot Start Pressure for Rifled Gun System

Determination of short start pressure (SSP) for gun system has always been of paramount interest for gun designers. In this paper, a generalised model has been developed for theoretical prediction of SSP for rifled gun system using dimensional analysis approach. For this, parameters affecting the SSP of the gun like rifling dimensions, driving band dimensions, material properties of driving band, projectile mass and diameter are taken into consideration. For a particular case of large caliber rifled gun system, the model is established using linear relations among dimensionless groups of parameters. The model has been validated by data available from the open literature.

Band structure analysis of a thin plate with periodic arrangements of slender beams

This work analyzes the wave propagation in structures composed of a periodic arrangement of vertical beams rigidly joined to a plate substrate. Three different configurations for the distribution of the beams have been analyzed: square, triangular, and hexagonal. A dimensional analysis of the problem indicates the presence of three dimensionless groups of parameters controlling the response of the system. The main features of the wave propagation have been found using numerical procedures based on the Finite Element Method, through the application of the Bloch's theorem for the corresponding primitive unit cells. Illustrative examples of the effect of the different dimensionless parameters on the dynamic behavior of the system are presented, providing information relevant for design.

Dynamic lateral response of suction caissons

Deeper water installations of offshore wind turbines may be supported by jacket structures. This study investigates the dynamic response of suction caissons for jackets by analysing 3D finite element models in the frequency domain. The numerical modelling was firstly validated by analytical solutions for pile foundations. Groups of crucial dimensionless parameters related to the soil profile and the foundation geometry are identified and their effects on the response of suction caissons are studied. Static stiffness coefficients are presented in a form of mathematical formulas obtained by fitting the numerical results, pertaining foundations with different slenderness ratios and embedded in different soil profiles.Sensitivity of the dynamic impedances of suction caissons on the skirt length was showed in this study. Moreover, the results for the suction caissons indicated that the overall dynamic response is profoundly affected by the relative thickness of the soil layer and by the variation of soil stiffness with depth.

Enhancement of city breathability with half open spaces in ideal urban street canyons

The design guidelines for assessing the wind environment at the pedestrian level have become increasingly important in urban planning over the past few decades. The purpose of this study is therefore to conduct computational fluid dynamics simulations to examine the flow behavior of the aeration around the buildings, with and without an arcade design in an ideal situation in urban street canyons. The results suggest the effectiveness of adopting an arcade design to sustain a stable wind environment and improve the flow aeration over areas with urban street canyons. Computations are also carried out to examine the ventilation performance of the pedestrian pathway layer by varying the parameters of building height, canyon width, and height and width of the arcade. The simulated results are then further processed by using a multivariable regression analysis on a group of dimensionless parameters as well as visualization with the scaling law on arcade structures to facilitate a design for arcade buildings that would enhance city breathability. This correlation which uses multiple dimensionless parameters will act as a reference for future arcade designs.

The flow patterning capability of localized natural convection.

Controlling flow patterns to align materials can have various applications in optics, electronics, and biosciences. In this study, we developed a natural-convection-based method to create desirable spatial flow patterns by controlling the locations of heat sources. Fluid motion in natural convection is induced by the spatial fluid density gradient that is caused by the established spatial temperature gradient. To analyze the patterning resolution capability of this method, we used a mathematical model combined with nondimensionalization to correlate the flow patterning resolution with experimental operating conditions. The nondimensionalized model suggests that the flow pattern and resolution is only influenced by two dimensionless parameters, and , where Gr is the Grashof number, representing the ratio of buoyancy to the viscous force acting on a fluid, and Pr is the Prandtl number, representing the ratio of momentum diffusivity to thermal diffusivity. We used the model to examine all of the flow behaviors in a wide range of the two dimensionless parameter group and proposed a flow pattern state diagram which suggests a suitable range of operating conditions for flow patterning. In addition, we developed a heating wire with an angular configuration, which enabled us to efficiently examine the pattern resolution capability numerically and experimentally. Consistent resolutions were obtained between the experimental results and model predictions, suggesting that the state diagram and the identified operating range can be used for further application.

Prediction of the Particle Size Distribution Parameters in a High Shear Granulation Process Using a Key Parameter Definition Combined Artificial Neural Network Model

Various methodologies have been proposed in the literatures to predict the particle size distribution (PSD) in agglomeration processes. However, there is no universal model that can completely satisfy industrial needs due to the complexity of the agglomeration process and the unclear mechanisms of particle growth. A systematic approach using an artificial neural network (ANN) model to predict PSD parameters of different agglomeration processes in high shear mixer was developed. In order to reduce input dimensions, several dimensional or dimensionless parameter groups are defined to represent the raw material properties, equipment geometries, and operation conditions as inputs. According to statistical analysis, an ANN model combined with the key parameter definitions can predict product mean particle size (MPS) within an average absolute relative error (AARE) of 7.18%, a standard deviation (σ) of 7.72%, and a correlation coefficient (R) of 0.9657 (while for distribution span prediction AARE is 5.76%, σ is...

Distribution of incompressible flow within interdigitated channels and porous electrodes

This paper develops a general model with which to evaluate flow uniformity and pressure drop within interdigitated-channel structures, especially in the context of redox flow batteries. The governing equations are cast in dimensionless variables, leading to a set of characteristic dimensionless parameter groups. The systems of governing equations are solved computationally, with the results presented graphically. Because the results are general, the underlying model itself is not needed to apply the quantitative design guidelines. However, the paper presents and discusses all the information required to recreate the model as needed.

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.

Analytical solution for ultimate embedment depth and potential holding capacity of plate anchors

This paper proposes an analytical approach to evaluate the ultimate embedment depth and holding capacity that plate anchors can potentially achieve. Based on a plasticity model for anchor–soil interaction and compatible chain solution, detailed derivations are presented that allow the main dimensionless groups of input parameters to be identified. For typical cases where the weight of the anchor is negligible relative to its holding capacity, explicit expressions are provided in non-dimensional form for ultimate embedment and anchor capacity. A thorough parametric sensitivity study highlights the major factors affecting these quantities. Two practical examples are considered that demonstrate the proposed analytical approach for different types of anchors, in one case revealing significant scope for improved design of plate anchors in order to optimise performance.

在人工岛屿和沿海进行淡水存储和恢复的含水层设计

Artificial recharge of water to an aquifer for later recovery and use, otherwise known as artificial storage and recovery (ASR; Pyne 1995), is nowadays widely applied for seasonal or emergency water storage. Therefore, one would expect a lot of thought to be devoted to what the optimal aquifer conditions for ASR would be, but this does not appear to be the case. In some situations local hydrogeology may impact the selection of ASR sites; however, according to Pyne (1995), this is the exception rather than the rule since ASR wells are usually located where they provide the greatest benefit to the water utility or agency. This location is often in the vicinity of the supply area to reduce the costs and time of transportation. At that specific site, one deals with the existing local hydrogeology through well design and construction (e.g., Maliva and Missimer 2010; Zuurbier et al. 2014) and operation (Ward et al. 2009; Bakker 2010). In line with Pyne’s field experience, Lowry and Anderson (2006) distinguished physical properties of the aquifer and operational factors that control the recovery efficiency of ASR. Properties like porosity, hydraulic conductivity, aquifer thickness and density of native water, as well as quality, are regarded as predefined site-specific conditions, while operational factors such as injected volume, location of injection and recovery wells, recharge and recovery rates and storage duration, can be changed at the wellhead by the operator to optimize the ASR system. The most relevant research determining optimal aquifer conditions for ASR focused on the influence of aquifer properties on the recovery efficiency of ASR wells. These studies are, firstly, comparisons between ASR sites, such as the studies executed by e.g., Merritt (1986), Dillon et al. (2006), Lowry and Anderson (2006) and Misut and Voss (2007). On the other hand, there are theoretical considerations regarding dimensionless parameter groups in analytical solutions, as described by e.g., Esmail and Kimbler (1967), Ward et al. (2007, 2008, 2009) and Bakker (2010). The general outcomes of these studies indicate that porosity, hydraulic conductivity, vertical anisotropy, dispersivity, density of native water versus that of the injected water, and the thickness of the aquifer all influence the recovery efficiency. This makes sense because these aquifer properties determine the degree of the underlying recovery efficiency processes of mixing and density stratification. The question of which aquifer conditions are preferable for ASR is usually not relevant in practice because the costs of the required earth displacement and construction works are so high that they generally outweigh the economic benefits of ASR systems. However, the situation is different in the case of coastal expansions and artificial islands that are currently being constructed worldwide. The most well-known examples are probably the Palms and the islands of the World Archipelago in Dubai (UAE) with a mainly touristic purpose. Artificial islands are also constructed for industrial development such as Maasvlakte II in the Port of Rotterdam, the Netherlands. Recently, there is a tendency in densely populated delta cities for urban expansion toward the ocean; examples are Eko Atlantic in the City of Lagos, Nigeria, and the planned land reclamations in Jakarta Bay, Indonesia. Aquifers are, in fact, created in these projects and their conditions can be optimized for specific ASR applications. Specific sediment types may be chosen and different dredging techniques can be applied to create the Boptimal^ aquifer conditions for recharge and recovery in terms of porosity, conductivity, anisotropy, and dispersivity to control mixing processes and density stratification. Received: 1 September 2014 /Accepted: 4 March 2015 Published online: 21 April 2015

Scaling Parameters for Dynamic Diffusion-Reaction over Porous Catalysts

The effect of diffusion resistance in porous solid catalysts on reaction rate during periodic cycling of CO concentration is shown for CO oxidation over Pt/Al2O3 by numerical simulation. At some cycling frequencies, the average reaction rate during cycling is higher than the steady-state rate at the mean CO concentration, as expected for this nonlinear, reactant-inhibited reaction. In order to identify major aspects of dynamic diffusion-reaction behavior, a simple kinetic mechanism that shows the main features of CO oxidation and other reactions with significant inhibition by reactants is investigated. A single dimensionless parameter group, the dynamic diffusion coefficient, is added when going from steady-state to unsteady-state diffusion-reaction equations. In the dynamic diffusion coefficient, the rate at which the gas-phase reactant diffuses is reduced by the surface adsorption capacity of the catalyst. The frequency at which the peak average rate occurs is controlled by the dynamic diffusion coefficient.

Sensitivity studies of SCR fatigue damage in the touchdown zone using an efficient simplified framework for stress range evaluation

Steel catenary risers (SCRs) are widely used in deep water. Several sources of nonlinearities make SCR fatigue design challenging. Limited understanding of the influence of the various input parameters on the structural response of SCRs leads to unnecessarily high conservatism in design. Also, time consuming numerical simulations are usually performed to assess SCR fatigue damage which is inefficient, especially for early design stages.A simplified framework for fatigue analysis of SCRs in the touchdown zone (TDZ) has been developed previously, using artificial neural networks. The approach may be used to efficiently estimate maximum static and dynamic stress ranges in the TDZ, from which the fatigue damage can be deduced. Comparison of the maximum static and dynamic stress changes for a given input motion allows quantification of the dynamic amplification factor (DAF). This paper explores the sensitivity of the maximum dynamic stress ranges and DAF to the key dimensionless groups of input parameters and also certain individual input parameters. The study illustrates the usefulness of the proposed framework in understanding SCR behaviour in the TDZ, providing guidance on optimisation of SCR design from a fatigue perspective. The paper also reflects on the potential benefits of using DAFs for SCR fatigue design.

Experimental Analysis of Sediment Deposition Due to the Effect of an Upstream Reservoir Backwater

The phenomenon of aggradation due to sediment accumulation upstream reservoirs had been studied in this research. For this purpose, groups of experiments were conducted in a laboratory with 25 m long, 0.80 m wide and 0.70 m deep channel. A block was built at the end of the channel to work as a dam to impound water. The channel was supplied with drainage pipes on both sides to release water out in a manner similar to what happens in reservoirs. The bed of the channel was filled with sand of 0.80 mm median sieve diameter and 0.72 geometric standard deviation. The slope was 0.0093 for all experiments. Two sizes of sand were used representing the sediment. The median diameter and geometric standard deviation of the first were 0.365 mm and 0.46 mm, respectively. The second sample had 0.65 mm median diameter and 0.67 standard deviation. A total of 70 experiments were conducted in two groups to examine effects of sediment transport rate, particle size of sediment and flow velocity on aggradation characteristics. The results showed that there was a strong linear direct relationship between aggradation elements (length and depth) with the rate of sediment transport. Groups of dimensionless parameters affecting the aggradation characteristics were used to develop empirical equations to predict the length, maximum depth of aggradation and predict transient bed profile. The results of empirical approach were compared with the measurement data and previous numerical method. The results indicated that the percentage error was 19% to 31% for length of aggradation and -21% to 26% for maximum depth of aggradation. The results also showed that the sediment materials were deposited closer to the body of the dam when the released water from the dam is higher than the inflow.

Coupled Chemical Shrinkage and Consolidation: Some Benchmark Solutions

Mixtures of cement and mine waste are used as backfill in underground mines to provide support, which enables increased mineral extraction. Unlike most cemented material, the properties of mine backfill are relied upon immediately after cement is added and the material deposited underground. It is not only just the properties of the final cemented product but also the behaviour of cemented backfill during the hydration process that is important. During the hydration process, the backfill experiences chemically induced volume changes. These volume changes can lead to the development of effective stresses, which control the loads generated on barricade walls and the subsequent stability of unsupported faces. Although the processes that interact during cement hydration appear complex, the governing equation can be derived in terms of a small number of dimensionless parameter groups. The equation is simply the diffusion equation with a time-dependent source/sink term for which an analytical solution can be obtained under certain simplifying geometries. Approximate solutions can be obtained using a technique of analysis in which the mode shape of the spatial pore pressure variation is assumed. Such solutions provide benchmarks for simplified problems against which results of finite element modelling (for example) can be compared in order to confirm that the controlling mechanisms have been correctly identified.