Dimensionless Parameter Groups Research Articles

Semi-analytical solution for thermo-poro-elastic stresses in a wellbore cement plug and implications for cement properties that minimize risk of failure

In high temperature and high pressure environments, inducing pore pressure changes in low permeability cement can be problematic. Despite the typical design goal of achieving very low permeability in cement plugs for better isolation, this work reveals through a new semi-analytical TPE stress solution that lower permeability is not always ideal. In fact, such materials are unable to rapidly drain excess pore pressure compared to the rate at which it builds due to thermal changes may lead to the generation of internal tensile stress and increased risk of damage. This work identifies the parameter groups linked to the “permeability penalty” by utilizing dimensional and pairwise bivariate analysis through Monte Carlo sampling. It proposes two dimensionless parameter groups that divide into three distinct regions based on the likelihood of producing tensile effective stresses in a plug. This work provides a new wellbore cement design concept focuses on achieving the lowest permeability without risking failure from pore pressure buildup, rather than simply achieving the lowest possible permeability. Furthermore, this work for the first time highlights the important role of cement's specific heat in mitigating pore pressure buildup, paving a new path for enhancing this property in future cement design.

Selection Mechanism in Non-Newtonian Saffman–Taylor Fingers

We present an analytical approach to the problem of predicting the finger width of a simple fluid driving a non-Newtonian (power-law) fluid. Our analysis is based on the Wentzel–Kramers–Brillouin approximation, by representing the deviation from the Newtonian viscosity as a singular perturbation in a parameter, leading to a solvability condition at the finger tip, which selects a unique finger width from the family of solutions. We find that the relation between the dimensionless finger width, , and the dimensionless group of parameters containing the viscosity and surface tension, , has the form for the shear thinning case and for the shear thickening case, in the limit of small . This theoretical estimate is compared with the existing experimental, finger width data as well as the one computed with the linearized model, and a good agreement is found near the power-law exponent, .

Modeling hypoxia-related inflammation scenarios

Cells respond to hypoxia via the activation of three isoforms of Hypoxia Inducible Factors (HIFs), that are characterized by different activation times. HIF overexpression has many effects on cell behavior, such as change in metabolism, promotion of angiogenic processes and elicitation of a pro-inflammatory response. These effects are driving forces of malignant progression in cancer cells. In this work we study in detail hypoxia-induced dynamics of HIF1α and HIF2α, which are the most studied isoforms, comparing available experimental data on their evolution in tumor cells with the results obtained integrating the deduced mathematical model. Then, we examine the possible scenarios that characterize the link between hypoxia and inflammation via the activation of NFkB (Nuclear Factor k-light-chain-enhancer of activated B cells) when the dimensionless groups of parameters of the mathematical model change. In this way we are able to discuss why and when hypoxic conditions lead to acute or chronic inflammatory states.

Flow invariants in a channel obstructed by a line of inclined rods

An experiment is conducted in a rectangular channel obstructed by a transverse line of four inclined cylindrical rods. The pressure on the surface of a central rod and the pressure drop through the channel are measured varying the inclination angle of the rods. Three assemblies of rods with different diameters are tested. The measurements were analyzed applying momentum conservation principles and semi-empirical considerations. Several invariant dimensionless groups of parameters relating the pressure at key locations of the system with characteristic dimensions of the rods are produced. It was found that the independence principle holds for most of the Euler numbers characterizing the pressure at different locations, that is, the group is independent of the inclination angle provided that the inlet velocity projection normal to the rods is used to non-dimensionalize the pressure. The resulting semi-empirical correlations can be useful for designing similar hydraulic units.

Constitutive framework for rheologically complex interfaces with an application to elastoviscoplasticity

A framework is presented for the formulation of a class of continuum constitutive models for sharp interfaces with non-linear viscoelastic behaviour due to a considerable isotropic interfacial microstructure. For the formulation of a thermodynamically consistent elastoviscoplastic interface constitutive model we adapt an approach successful in describing the behaviour of bulk polymer glasses. The model has a clear separation between dilatation and shear, and is used to predict phenomena related to the plasticity of interfaces observed in the experimental literature, which is relevant for many applications. Stress–strain predictions in standard interfacial rheological flows, i.e. shear and dilatation, are investigated numerically. A predominantly elastic response is obtained at small deformations, with a transition to primarily plastic flow at high stress levels. In interfacial shear flow, strain softening and eventually a plastic plateau occur upon further deformation beyond the yield point. The yield stress and strain and (the relative strength of) the stress overshoot in interfacial shear flow are shown to be controlled by two dimensionless groups of parameters in the model. In interfacial dilatation, the model predicts elastoviscoplastic behaviour with a stress maximum and a decreasing stress without a plateau at even larger deformations. These phenomena are studied for various choices for the parameters in the model. • Framework for non-linear viscoelastic interface models is developed. • Thermodynamic consistency is intrinsically respected in the framework. • Existing viscoelastic interface models are reviewed. • New elastoviscoplastic interface model is proposed. • Qualitative agreement with experiments in both shear and dilatation is found.

Three‐dimensional slope stability predictions using artificial neural networks

AbstractTo enable assess slope stability problems efficiently, various machine learning algorithms have been proposed recently. However, these developments are restricted to two‐dimensional slope stability analyses (plane strain assumption), although the two‐dimensional results can be very conservative. In this study, artificial neural networks are adopted and trained to predict three‐dimensional slope stability and a program, SlopeLab has been developed with a graphical user interface. To reduce the number of variables, groups of dimensionless parameters to express stability of slopes in classic stability charts are adopted to construct the neural network architecture. The model has been trained with a dataset from slope stability charts for fully cohesive and cohesive‐frictional soils. Furthermore, the impact of concave plan curvature on slope stability that is usually found by excavation in practice is investigated by introducing a dimensionless parameter, relative curvature radius. Slope stability analyses have been conducted with numerical calculations and the artificial neural networks are trained with dimensionless data. The performance of the trained artificial neural networks has been evaluated with the correlation coefficient (R) and root mean square error (RMSE). High accuracy has been found in all the trained models in which R > 0.999 and RMSE < 0.15. Most importantly, the proposed program can help engineers to estimate 3D effects of a slope quickly from the ratio of the factors of safety, FS3D/FS2D. When FS3D/FS2D is large (such as larger than 1.2), a 3D numerical modelling on slope stability analyses that can consider complex 3D geometry and boundary condition is advised.

Artificial neural network model for predicting minimum fluidization velocity and maximum pressure drop of gas fluidized bed with different particle size distributions

The minimum fluidization velocity (Umf) and maximum pressure drop (ΔPmax) of a gas-solid fluidized bed are important hydrodynamic characteristics. The accurate information of these characteristics is required for obtaining the optimum design and operating conditions. In this study, a multi-layer perceptron (MLP) based on an artificial neural network was developed to accurately predict these hydrodynamic characteristics dealing with the influence of the particle size distribution (PSD). The MLP model parameters were adjusted by the backpropagation learning algorithm using wide ranges of experimental data from conducted experiments and collected literature. The five influential dimensionless groups of parameters were used for simultaneous estimation of the Umf and ΔPmax. Statistical accuracy analysis confirmed that a two-layer feedforward with thirteen hidden neurons was the best architecture for the MLP model in terms of absolute average relative deviation (AARD), mean square error (MSE) and regression coefficient (R2). The accuracy of Umf and ΔPmax was 10.36% and 8.35% with AARD, 1.7 × 10−4 and 0.0188 with MSE, and 0.9935 and 0.9152 by R2, respectively. Besides, the predictive performance of the developed model was compared with other literature models. The comparison shows the performance of the developed MLP model was acceptable.

Nonlinear and non-local analytical solution for Darcy–Forchheimer flow through a deformable porous inclusion within a semi-infinite elastic medium

Permeability is a nonlinear and non-local function of the intimate coupling between pore fluid flow and solid deformation in porous media. A class of related problems involves the effect of fluid injection or withdrawal on the transport properties of geomaterials. This paper presents an analytical solution for the nonlinear and non-local problem of fluid flow through a disk-shaped porous elastic inclusion below the free surface of an elastic half-space. The solution accounts for the following nonlinear mechanisms: (i) variations in the permeability coefficient due to the flow-induced deformation of the inclusion; (ii) the inertial losses of the pore fluid flow. The former and latter mechanisms are formulated using the Green's function for a dilatation centre in an elastic half-space and the Darcy–Forchheimer equation for fluid flow through porous media, respectively. An analytical perturbation solution to the considered problem is developed and validated against the numerical finite element solution to the same problem. The described nonlinear mechanisms are represented by two dimensionless parameter groups. The extreme values of these dimensionless groups govern the solution asymptotic behaviours mimicking the special-case solutions in which either mechanism is forced to vanish. The applied aspects of the solution are demonstrated through the wellbore performance index parameter that quantifies the subsurface rock ability to deliver the pore fluid toward or away from a wellbore in a porous reservoir. Unlike the linear models, the presented nonlinear solution captures the observed dependence of the performance index on the wellbore flow rate.

Anisotropic behaviors of helically corrugated cylindrical shells: Homogenized in-plane stiffness

Thin-walled corrugated structures have been widely used in engineering applications for centuries, because corrugation enables engineers to tailor directional dependent properties despite the structures being made of isotropic materials. However, the vast majority of research has paid attention to corrugated plates and relatively scarce studies are on corrugated shells. This paper, therefore, aims to investigate elastic behaviors of thin cylindrical shells that possess sinusoidal corrugating patterns in the helical direction. Elastic responses of undulated shells under three types of deformation, namely, axial elongation, axial torsion, and radial expansion are thoroughly investigated by using the finite-element method (FEM) via ABAQUS™. The effective stiffness of the corrugated cylinders is determined by a homogenization technique in a representative unit cell element. A variety of FEM models are created according to four groups of dimensionless parameters, i.e. radius-to-thickness ratio, radius-to-corrugating depth ratio, helical angle and the number of waveform (thread) in a cylinder cross section. The results show that the degree of anisotropy induced by the corrugated shells is different from that of a fiber-reinforced composite material, significantly sensitive to their configurations, and can be extraordinarily higher than the perfect round shell made of the same parent material. Unorthodox coupling quantities of torsional-axial, torsional-radial, and axial-radial coupling deformations are encountered at some specific geometries. Anisotropy design space in the form of spherical maps is given as a guideline to effectively design or select a proper helically corrugated cylindrical shell with the desired stiffness properties.

Development a new methodology for measuring deep drawing forces based on dimensionless evaluation

In this research work, dimensionless models based on geometric parameters have been developed for the deep drawing process of rectangular cups to reduce the manufacturing costs on a large scale of application in a noticeable way. In the following, geometric parameters were given in dimensionless form by the Π-Buckingham dimensional analysis method and a series of dimensionless groups were found for both circular and rectangular initial blank. To find the best group of dimensionless geometric parameters, different cup scales 1:1, 2:1, 4:1 and 5:1 are evaluated numerically by ABAQUS Finite Element (FE) software, validated by experimental work. After all effective geometric parameters have been analyzed, the best fitting relational model of dimensionless parameters is found for rectangular and circular blank separately. Various thicknesses of St12 sheet metals were used for experimental validation, which were formed at room temperature. Also, results and response parameters were compared in the simulation process, experimental tests and dimensionless models. By looking at the outcomes, it is demonstrated that the geometric qualities of a large scale can be predicted by a small scale, utilizing the proposed dimensionless model. A comparison of the outcomes for dimensionless models and experimental tests shows that proposed dimensionless models have a high degree of precision in determining geometrical parameters and the prediction of drawing force. Furthermore, the dimensionless analysis was generalized to ensure high precision estimation of geometric values for large geometric scales.

Oxygen transfer characteristics of bubbly jet in regular waves

The dissolved oxygen level is an important index of the water environment, and in this paper, the oxygen transfer of the bubbly jet in regular waves is investigated numerically and experimentally. The Reynolds-averaged Navier-Stokes equations, the re-normalisation group k-e equations, and the volume of fluid (VOF) technique are used along with a 2-D CFD model to simulate the wave and bubble motions as well as the turbulence, and a dissolved oxygen transport equation is used to model the oxygen transfer behavior both through the bubbly interface and the wave surface. A series of experiments are conducted to validate the mathematical model, with good agreement. In addition, a group of dimensionless parameters are defined from the wave parameter and the aeration parameter, and their relationships with the total oxygen transfer coefficient are explored. Furthermore, the dimensional analysis and the least squares methods are used to derive simple prediction formulas for the total oxygen transfer coefficient, and they are validated with the related experimental data.

Liquid-Liquid Flow Pattern Prediction Using Relevant Dimensionless Parameter Groups

Accurate predictions of flow patterns in liquid-liquid flow are critical to the successful design and operation of industrial and geo-energy systems where two liquids are jointly transported. Unfortunately, there is no unified flow pattern map, because all published maps are based on limited ranges of dimensional parameters. Dimensional analysis was performed on oil-water horizontal flows, to obtain some relevant dimensionless parameter groups (DPG) for constructing flow pattern maps (FPM). The following combinations of DPG were used: (i) the ratio of mixture Reynolds number to Eötvös number versus water fraction, (ii) the ratio of Weber number to Eötvös number versus water fraction, (iii) the mixture Froude number versus water fraction, (iv) the water Froude number versus oil Froude number, (v) the ratio of gravity force to viscous force versus water fraction. From twelve published experimental studies, 2696 data points were gathered and analysed covering a variety of flow patterns including stratified, stratified mixed, dispersed oil in water, dispersed water in oil, annular and slug flows. Based on the performed analysis, it was found that flow patterns could occupy more than one isolated region on the DPG-based flow pattern map. None of the combinations of DPG can mark out all the considered flow patterns, however, some combinations of DPG are particularly suitable for marking out the regions associated with some flow patterns.

Effects of height-asymmetric street canyon configurations on outdoor air temperature and air quality

This paper investigates the effects of height-asymmetric street canyon configurations on air temperature and air quality at the pedestrian level using the ANSYS Fluent® software. The study concerns the situation with a subtropical city where there is a predominant wind direction (as is the case in, e.g., Hong Kong) and where the direction of that wind is perpendicular to the street canyon, since this is the worst-case from air pollution and overheating point of view. In particular, this North-South oriented street has been studied with the realistic solar irradiance at two different sun directions, corresponding to morning (08:00) and afternoon (16:00) hours, respectively. Two step-up and two step-down North-South oriented street canyons are considered under two different incoming wind speeds (high and low). The corresponding ratios of upwind and downwind building heights are = 1/3, 2/3 and 3/1, 3/2, respectively.The results demonstrated that for the step-up canyon, a higher upwind building was found to produce a hotter air temperature only at a low wind speed and polluted more severely at both high and low wind speeds, compared with its lower upwind building counterpart. In contrast, for the step-down canyon, a higher downwind building was found to produce cooler air temperatures at both high and low wind speeds and accumulated more pollutants only at a low wind speed, compared with its lower downwind building counterpart. On the other hand, at the high wind speed, both air quality and thermal environment were better in the step-up canyon than in the step-down canyon. However, at the low wind speed, the air quality was higher in the step-down canyon than the step-up canyon, while the step-up canyon still provided better thermal environment than the step-down canyon. Moreover, a Richardson number (Ri) for the asymmetric street canyons is defined for the evaluation of the buoyancy force versus the inertial force. When |Ri| > 20, the flow field was mainly dominated by natural convection, and an increase of |Ri| resulted in an increase in the air temperature and a decrease in the pollutant concentration. In contrast, when |Ri| < 20, the flow field was dominated by forced convection, and the variation of |Ri| had an insignificant influence on air quality and air temperature. The simulated pollutant concentration and thermal environment results were further processed to obtain optimization guidelines for a north-south asymmetric canyon in the city centers of Hong Kong via the application of multivariate regression analysis with a group of dimensionless parameters. These guidelines will facilitate the renewal of north-south asymmetric street canyons while enhancing air quality and lowering air temperature by serving as a reference for architects.

General correlation for frost thermal conductivity on parallel surface channels

Growth of frost layer on cold fins of tube-fin heat exchangers leads to an increase in the pressure drop and a decrease in the frost thermal conductivity and thereby the heat transfer rate. There is a lack of a general model in the literature for estimating the frost thermal conductivity on parallel plate channels, including almost all parameters affecting this factor. In this study, for the first time, the general explicit semi-empirical correlations consist of dimensionless parameters are developed, which apply to parallel surface channels. The dimensionless input parameters include the wall temperature, air temperature, air velocity, frost porosity, relative humidity, specific heat of moist air, latent heat of sublimation, and operating time. The comparative results indicate that the best correlation predicts data points with an coefficient of determination, average absolute relative error, and relative root mean square error equal 0.9921, 2.755%, and 3.713%, respectively. Other available published correlations present higher deviations using the same dataset. Furthermore, to provide a good insight into this study, a sensitivity analysis is carried out employing the validated model. It is shown that the effective thermal conductivity of the frost layer is not only a function of frost density but also depends on a group of dimensionless parameters. It is observed that the thermal conductivity of the frost layer increases with the increase in the Reynolds number, Fourier number, air humidity, and it decreases with the increase in the dimensionless temperature, modified Jakob number, and porosity.

Evaluation of drawing force by a new dimensionless method in deep drawing process

In this research, geometric parameters were given in dimensionless form by the Π- Buckingham dimensional analysis method in the dimensionless group for deep drawing of a round cup. To find the best group of dimensionless parameters and the fittest dimensionless relational model, three scales of the cup are evaluated numerically by a commercial finite element software and stepwise regression modeling. After analyzing all effective geometric parameters, a fittest relational model among dimensionless parameters is found. In addition, the results of the new dimensionless model were compared with the simulation process and experimental tests. From the results, it is inferred that the geometric qualities of a large scale can be predicted with a small scale by the proposed dimensionless model. Comparing the results of the dimensionless model with experimental tests shows that the proposed dimensionless model has fine precision in the determination of geometrical parameters and drawing force estimation. Moreover, to evaluate the accuracy of the proposed dimensionless model, the predicted value of the model has been compared by the experimental results. It is shown that the dimensionless ratios of geometrical parameters can significantly affect the estimation of the drawing force by the proposed dimensionless model, but based on similarity law, because of the constant value of these dimensionless parameters in different scales, they could not be used for dimensionless analysis separately. It is also inferred that because of the effect of contact area on the coefficient of friction, which is changed by scale changing, the only dimensionless parameter that can significantly change the drawing force is the coefficient of friction. Finally, it is shown that the dimensionless geometrical parameter and the coefficient friction should be combined for dimensionless analysis.

Effects of frontal area density on outdoor thermal comfort and air quality

This paper systematically investigates the effects of the frontal area density of various three-dimensional (3D) array building models on the thermal comfort and air quality at the pedestrian level above four sidewalks (north, south, east and west). The buoyancy force for natural-convection flows and the realistic solar irradiance at local solar times (LSTs) from 0700 to 1700 are considered with five different frontal area densities (λF = 0.0825–1.25). By a combination of the Rayman model and the ANSYS Fluent® software, the CO concentration and physiologically equivalent temperature (PET) are solved numerically. The simulated CO concentration and PET results are considered as outdoor parameters of the air quality and thermal comfort. A critical λF is obtained for urban development by applying multivariable regression analysis to a group of dimensionless parameters. This analysis will facilitate the choice of building density and simultaneously enhance the air quality and thermal comfort. The results reveal that with an increase in λF, the PET decreases above most of sidewalks during the daytime, while only is a steady reduction of air quality observed above west and east sidewalks of spanwise streets. According to the multivariable regression analysis for Hong Kong, the building density should have a λF value between 0.82 and 0.84 to basically realize a PET <38 °C and CO concentration <30000 μg/m3 simultaneously in the daytime in June.

Dimensionless Groups of Parameters Governing the Ice-Seabed Interaction Process

AbstractPrediction of subgouge soil deformation during an ice gouging event is a challenging design factor in Arctic subsea pipelines. An accurate assessment of ice keel–seabed interaction requires expensive model testing and large deformation finite element analysis. Proposing reliable analytical/empirical solutions needs a deep understanding of the key parameters governing the problem. In this study, dimensional analysis of subgouge soil deformations was conducted and eight dimensionless groups of parameters were identified to facilitate proposing potential new solutions. A comprehensive dataset was established for horizontal and vertical subgouge deformations in both sand and clay seabed. Using the identified dimensionless groups, linear regression (LR) models were developed to estimate the horizontal and vertical deformation. Moreover, a sensitivity analysis (SA), as well as an uncertainty analysis (UA), was carried out to identify the superior LR models and the most influential parameter group. A high range of correlation coefficient (R), Nash-Sutcliffe efficiency coefficient (NSC), and variance accounted for (VAF) along with a low range of errors was achieved for the best LR model. The results of the superior LR models were also compared with the existing empirical equations. The study showed that the shear strength parameters of the seabed soil and the ratio of gouge depth to gouge width are the governing dimensionless parameters to model the horizontal and vertical subgouge soil deformations.

Dimensionless model based on dual phase approach for predicting thermal performance of thermocline energy storage system: Towards a new approach for thermocline thermal optimization

The focus of this study is the development of a dimensionless model that allows a better understanding of the thermocline storage system behavior. The proposed model is based on a dual phase approach. We had identified four remarkable dimensionless groups of parameters which control the thermocline system performances. The influence of each dimensionless group of parameters has been analyzed separately to understand its influence on the overall thermocline storage system performance. During this investigation, three concepts are deeply analyzed: the thermocline zone thickness, dimensionless discharge time and discharge efficiency. Using this model, we have demonstrated that, for each combination HTF/TESM, a universal optimum can be highlighted, which makes it possible to find, according to a given specification, the optimal configuration of the storage tank. Based on the obtained results, we had proposed a new reduced model based on dual-phase approach for rapid calculation of optimal sizing of a thermocline storage tank. The proposed method requires no discretization method and provides accuracy similar to those of the dual phase model but with a drastically reduced computation effort.

Parametric Dimensional Analysis on a C-H2 Smelting Reduction Furnace with Double-Row Side Nozzles

Higher requirements for steel smelting technology have been put forward based on the increasing awareness of energy conservation and environmental protection. In the field of iron making, carbon reduction processes are often used. In this study, molten iron was smelted by designing a C-H2 smelting reduction method. Although previous researchers have studied this through a large number of physical and numerical simulations, they have not yet refined general laws from the perspective of dimensional analysis. In this paper, a double-row side blow hydraulics simulation was carried out in the C-H2 smelting reduction furnace, and an entire list of dimensionless groups of input and output parameters was proposed based on its hydraulics simulation data. The expressions between the dimensionless group of mixing time and dimensionless groups such as Capillary number (Ca) and Lagrange group (La1) were obtained by multiple linear regression based on the experimental research results and data analysis. By verifying the calculated and experimental values of the dimensionless group of mixing time, it can be seen that both have a good positive correlation. This study provides a better methodology for controlling key parameters and lays the foundation for the optimal design of the process parameters for the C-H2 smelting reduction furnace.

Thermal Conductance of Interleaving Fins

Interleaving fins can significantly increase the heat transfer by increasing the effective area per unit base area. The fins are separated uniformly by a gap, which is filled with a flow medium to control the heat flux. The heat flux between the plates depends strongly on the thermal conductivity of the fin material and the medium between them as well as the dimensions. In earlier studies empirical a fitting method is used to determine the total effectiveness of the fins. However, it required complete characterization of the fins for each new set of operating conditions. In this paper, a simplified analytical model, but still preserving the main physical traits of the problem is developed. This model reveals the dimensionless parameter group containing both material properties and the fin geometry that govern the heat transfer. Rigorously testing of the model using a numerical finite element model shows an accuracy within 2% over a large parameter space, varying both dimensions and material properties. Lastly, this model is put to test with previously measured experimental data and a good agreement is obtained.