Use Of Dimensionless Parameters Research Articles

A Critical Evaluation of Using Physics-Informed Neural Networks for Simulating Voltammetry: Strengths, Weaknesses and Best Practices

The recent explosion of applications of physics-informed neural networks (PINNs) as a discretization-free tool to solve partial differential equations (PDEs) shows great potential for applications in electroanalytical simulations. However, a simple, naive PINN approach may fail to make analytical level predictions in even only moderately complicated systems. Here, we explore eight test cases, spanning 1D to 3D simulations, including both cyclic voltammetry and chronoamperometry, and a wide selection of electrode geometries from macroelectrode, (hemi-)spherical electrode, microband electrode, cube electrode and microdisc electrode to serve the dual-purposes of expanding PINNs to more challenging electrode geometries and to recommend best practices in the context of electroanalytical simulation. These best practices, include the use of dimensionless parameters, non-zero conditioning times, mathematical transformation of PDEs, sequence-to-sequence training, adaptive weights algorithms, optimal batch sizing, domain decomposition, learning rate scheduling and transformation of coordinates. These suggested best practices are the intended key contribution of this paper, as to position future PINN users with a well-informed starting position for generic electroanalytical PINN simulations, to avoid known difficulties and to skip the trial-and-error phase with hyperparameter tuning. We believe that these recommendations can serve as primers for PINN simulations for sophisticated Multiphysics problems, and make PINN simulations more accessible.

Simulation of an ammonia-water absorption cycle using exchanger effectiveness

• NH 3 /H 2 O absorption chiller modeling based on exchanger effectiveness. • Tuning of the numerical model on experimental results. • Comparison of simplified and effectiveness-based modeling. • Characterization of performance for changing operating conditions. • Parametric study changing the size of components. This paper presents the numerical simulation of an efficient ammonia-water single-stage absorption chiller integrating a new combined desorber, able to produce and purify the refrigerant vapor. An experimental campaign was conducted on the pilot plant by varying the main operating parameters, namely the temperatures of external sources and the mass flow rate of the working fluid. Direct experimental measures were analyzed and indirect calculation of other physical quantities was used for tuning of the numerical models. First, a simplified model of the cycle was developed, based on fixed effectiveness and pinch temperatures. Absolute values and tendencies outside nominal working conditions were not sufficiently accurate to predict the performance of the cycle even at the small scale, so more accurate modeling was undertaken. Accordingly, components were characterized by effectiveness, modeled using three operating parameters: the Jakob number ( Ja ), the number of transfer units ( NTU ) and the energetic ratio ( R en ). The small average errors for calculated effectiveness confirm that these parameters are well suited for the application studied. Global cycle model results showed errors compared to experimental results below 6% for the COP and 15% for the cooling power output. The tuned model was used to perform a parametric analysis on the dimension of the components, highlighting the performance improvements/reductions obtainable by increasing/decreasing their size. The use of dimensionless parameters makes this approach well suited for analysis at larger scales of industrial interest, the development of more complex or combined cycles as well as to perform techno-economic or exergo-economic analysis.

Horizontal capacity of base isolation rubber devices under large vertical design stress, valued through full-scale tests

An experimental campaign to investigate the effect of vertical stress on horizontal capacity of rubber bearings is argued in this paper. Results from a test program on full-scale HDRBs are discussed. They concern three different bearings (ϕ = 500–600 – 700 mm), having variable shape factors [S1 = 19,44–22,72] [ S2 2,8 ÷ 3,4]. The experimental data refer mainly to static shear tests, at varying levels of shear strain (up to γ = 250%) combined to increasing compressive stress (from 6 MPa to 20 MPa). Re-creating load conditions similar to the one occurring in situ, the experimental tests want to assess the impact of growing vertical stress on device horizontal deformability. The elaborations of data underline a progressive decrease of horizontal stiffness when even higher pressure acts. This is confirmed by visible softening effects that occur when horizontal displacement exceeds a certain percentage of device diameter, variable with the value of the applied compressive stress. This response is undoubtedly related to variations in axial load carrying capacity of bearings under large deformations: for this reason, evaluations on the critical load have been included in the discussion. Analytical formulations have been compared to experimental results to support the argumentations. The elaborations have been accompanied by the use of dimensionless parameters, in particular the ratio γ/S2, available also for design aims: this type of representation helps to evaluate deformation limits for rubber devices.

Ultimate bearing capacity of two interfering strip footings on sand overlying clay

Foundations may be constructed at close spacings. Prior investigations have presented insights into the interference effect of two nearby shallow foundations on homogenous soils. However, soils are often deposited in layers, such as a sand layer overlying clay. Hence, the interference effect of two adjacent foundations on their ultimate bearing capacity for sand overlying clay has been a relevant topic, which is complex because it is tied to a coupling effect of the geometric configurations and the soil properties. In this paper, the ultimate bearing capacity of two interfering strip footings on sand overlying clay is determined using an upper-bound limit state plasticity method known as discontinuity layout optimization (DLO). The solution is illustrated as design charts constructed through the use of dimensionless parameters. Parametric studies are performed to explore the influence of geometric and strength parameters on the bearing capacity and the failure mechanism. A simplified model is developed based on the data obtained from DLO. Validations are carried out to demonstrate the accuracy of the developed model using various statistical criteria, including coefficient of determination (R2), arithmetic mean and coefficient of variation.

Hydrodynamic Model of Transport System

A hydrodynamic model of production systems with a flow method of organizing production is considered. The basic macro-parameters of the state of the production flow line and the relationship between them are determined. The choice of a lot of moment approximation for modelling the production line is justified. It is shown that the conveyor-type flow line is a complex dynamic system with distributed parameters. The boundary value problem is formulated for the longitudinal vibrations of the conveyor belt when the material moves along the transportation route. It is assumed that there is no sliding of material along the conveyor belt, and the deformation that occurs in the conveyor belt is proportional to the applied force (Hooke's elastic deformation model). The significant effect of the uneven distribution of the material along the transportation route on the propagation velocity of dynamic stresses in the conveyor belt is shown. When constructing the boundary and initial conditions, the recommendations of DIN 22101: 2002-08 were used. The mechanism of the occurrence of longitudinal vibrations of the conveyor belt when the material moves along the transportation route is investigated. The main parameters of the model that cause dynamic stresses are determined. It is shown that dynamic stresses are formed as a result of a superposition of stresses in the direct and reflected waves. Analytical expressions are written that make it possible to calculate the magnitude of dynamic stresses in a conveyor belt and determine the conditions for the occurrence of destruction of the conveyor belt. The characteristic phases of the initial movement of the material along the technological route are considered. The process of the emergence of dynamic stresses with the constant and variable acceleration of the conveyor belt is investigated. The dynamics of stress distribution along the transportation route is presented. It is shown that the value of dynamic stresses can exceed the maximum permissible value, which leads to the destruction of the conveyor belt or structural elements. The transition period is estimated, which is required to ensure a trouble-free mode of transport operation during acceleration or braking of the conveyor belt. The use of dimensionless parameters allows us to formulate criteria for the similarity of conveyor systems.

Ultimate bearing capacity of strip footings on sand overlying clay under inclined loading

In this paper, the bearing capacity and the failure mechanism of obliquely loaded footings on sand overlying clay are determined by using discontinuity layout optimization (DLO) procedure. The solution is illustrated as a set of design charts with the use of dimensionless parameters. Parametric studies are performed to show that soil properties, geometric parameters, and load inclinations are all related to the bearing capacity and failure pattern. A simplified model is developed based on artificial data generated through DLO. Validations are carried out to demonstrate the accuracy of the developed model.

Impact energy absorption of bio-inspired tubular sections with structural hierarchy

Structural hierarchy in nature can be mimicked in order to develop novel composites and structures with desirable properties. In this study, hierarchy is introduced at multiple length scales into tubular sections that can be utilised as energy absorbing systems in various industries. The proposed hierarchical tubular section is inspired by the micro- to nano-architecture of biological materials, such as tendon and muscle, which can be mimicked by packing smaller tubes into a tube of a higher hierarchical level. The process can be repeated for creating tubular sections of higher orders of structural hierarchy, regardless of size or choice of materials. Numerical experiment has revealed that the impact energy absorption capability can be improved significantly when hierarchy is introduced and greater enhancement is achieved for higher-order hierarchical sections. A parametric study has been undertaken, and with the use of dimensionless parameters, the robustness and the generality of the phenomenon are demonstrated.

Flow reversal of laminar mixed convection for supercritical CO2 flowing vertically upward in the entry region of asymmetrically heated annular channel

Numerical investigation has been performed in order to determine the onset of flow reversal occurrence for buoyancy assisted flow of supercritical CO2 through vertical annular channel of finite length with heated inner wall. The outer wall was considered adiabatic. Only steady state and laminar mixed convection cases were considered in order to study the involved heat transfer phenomena in a fundamental level. Results gave a clear insight of the flow reversal mechanism and highlighted buoyancy as the driving force of the aforementioned phenomenon. Furthermore, according to the results, two different flow reversal maps were constructed with the use of dimensionless parameters. Results clarifies that the dominance of free convection is vital for the onset of the flow reversal. More specifically, free convection must be higher from both conductive and forced convective heat transfer. In addition, mass flux suppresses the mentioned phenomenon, while heat flux aids the presence of flow reversal.

Energy balance in high-quality cutting of steel by fiber and CO2 lasers

The energy balance of laser cutting of low-carbon and stainless steel sheets with the minimum roughness of the cut surface is experimentally studied. Experimental data obtained in wide ranges of cutting parameters are generalized with the use of dimensionless parameters (Peclet number and absorbed laser energy). It is discovered for the first time that the minimum roughness is ensured at a certain value of energy per unit volume of the melt (approximately 26 J/mm3), regardless of the gas type (oxygen or nitrogen) and laser type (fiber laser with a wavelength of 1.07 μm or CO2 laser with a wavelength of 10.6 μm).

Determination Discharge Capacity of Triangular Labyrinth Side Weir Using Multi-Layer Neural Network (ANN-MLP)

statistic indexes have been used to assess the accuracy of the results. The results of the examinations indicate that using MLP model along with simultaneous use of dimensionless parameters for the purposes of estimating discharge coefficient: the ratio of water behind the weir to the channel width (h/b), ratio of weir crest length to weir height (L/W), relative Froude number (F=V/√(2Side weirs are used in open channels to control flood and the flow passing through it. Discharge capacity is one of the crucial hydraulic parameters of side weirs. The aim of this study is to determine the effect of the intended dimensionless parameters on predicting the discharge coefficient of triangular labyrinth side weir. MAPE, RMSE, and Rgy)) and vertex angle (ϴ), offered the best results (MAPE= 0.67, R2= 0.99, RMSE = 0.009) in comparison with other models.

The Hyperbolic Sine Cardinal and the Catenary

SummaryThe hyperbolic function sinh(x)/x receives scant attention in the literature. We show that it admits a clear geometric interpretation as the ratio between length and chord of a symmetric catenary segment. The inverse, together with the use of dimensionless parameters, furnishes a compact, explicit construction of a general catenary segment of given length hanging from supports of different heights.

Metrics of separation performance in chromatography: Part 2. Separation performance of a heating ramp in temperature-programmed gas chromatography

Metrics of separation performance described in Part 1 of this series were applied here to theoretical evaluation of performance of a heating ramp in temperature-programmed GC. As in Part 1, the dependence of the separation (Δs) of two arbitrarily spaced peaks (the number of σ-slots between them) on operational parameters of GC analysis was treated here as the main building block for construction of other performance metrics. Simple expressions describing Δs of two peaks eluting during isobaric linear heating ramp and dependence of Δs on the heating rate, on column efficiency and on the peak spacing were derived. The use of dimensionless heating rate and other dimensionless operational parameters made these expressions universally suitable for different column dimensions, heating rates, carrier gas types, flow rates, etc. The use of dimensionless parameters also made it possible to express Δs as a simple function of the earlier introduced chromatographically meaningful characteristic parameters of thermodynamics of solute–column interactions. The expressions for Δs developed here, together with the ones described in Part 1 were used for theoretical prediction of total separation capacity (sc), total peak capacity (nc), and total number of resolved peaks in temperature-programmed analysis controlled by a balanced temperature program consisting of a linear heating ramp preceded by specially designed balanced temperature plateau. A numerical example of these parameters for a particular column, heating rate, carrier gas, and its flow rate is also provided. It has been shown that nc obtainable in temperature-programmed analysis is 2–3 times larger than that obtainable in equally long isothermal analysis using the same column and gas. Comparison of this improvement with potentially more than an order of magnitude larger peak capacity of GC×GC has been discussed. Also described are the speed of analysis (the number of σ-slots per unit of time), and other characteristics of the separation performance of a heating ramp. In many respects, metric Δs is similar to the widely known metric of resolution (Rs). Advantages of Δs over Rs as a metric of the separation performance, as well as the advantages of other metrics utilized here over their widely known counterparts are discussed.

An Introduction to Dimensionless Parameters in the Study of Viscous Fluid Flows

It has been suggested that there is a need to deepen the understanding of fluid dynamics in the introductory physics course and to offer interesting experiments to do so.1 To address this need we have developed a laboratory experiment and the supporting analysis to demonstrate the role of viscosity and the interestingly mysterious use of dimensionless parameters in fluid dynamics.2 Since viscosity indicates the frictional dependence between the layers of a flowing fluid, a thoughtful student may ask why or when viscosity can be neglected. The laboratory experiment presented here uses common fluids to provide a concrete answer to this question and an easily understandable example of the role of dimensionless parameters in fluid dynamics.

Modeling of the dynamic adsorption of an anionic dye through ion-exchange membrane adsorber

The present study examines the dynamic adsorption through ion-exchange membrane adsorbers. The model used in the study includes convection, axial dispersion with simultaneous adsorption and desorption of the solute in the membrane. Adsorption and desorption processes give the Langmuir isotherm for the equilibrium. The mathematical model makes use of dimensionless parameters in terms of characteristic times for the different mechanisms that take place during the process (convection, dispersion, adsorption and desorption characteristic times). The model has five independent dimensionless parameters. Three of these parameters are related to the equilibrium isotherm and the other two are related to the dynamic process. Equilibrium and dynamic experiments were carried out in order to fit their respective parameters. In order to examine the suitability of the model to describe real processes, the adsorption of an anionic dye (Orange-G) through the ion-exchange membrane adsorber was investigated as a function of dye and KCl concentration, obtaining strong correlation between fitted and experimental breakthrough curves. The results show the relative importance of axial dispersion, adsorption and desorption as a function of operational variables.

An overview of models for viscothermal wave propagation, including fluid structure interaction

In acoustics, the standard wave propagation models neglect the effects of viscosity and thermal conductivity. When waves propagate in narrow tubes or thin layers these simplifications might not be accurate. This paper presents an overview of models that take the effects of inertia, viscosity, thermal conductivity and compressibility into account. Based on the use of dimensionless parameters, three classes of models are outlined. The most important dimensionless parameter is the shear wave number, an unsteady Reynolds number that indicates the ratio between inertial and viscous effects. These viscothermal wave propagation models can be coupled to structural models to capture the fluid structure interaction. Analytical solutions can be found for these coupled analysis cases only for simple geometries and boundary conditions. For more complex geometries, numerical models were developed. Examples of applications of these models are also presented.

Inter-machine comparison of intrinsic toroidal rotation in tokamaks

Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with MA ∝ βN, although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with βN = 2.6, an intrinsic rotation Alfven Mach number of MA ≃ 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input.

Viscothermal wave propagation, including acousto-elastic interaction

Standard wave equation models neglect the effects of viscosity and thermal conductivity on acoustic wave propagation. For wave propagation in narrow tubes or thin layers, like in MEMS devices, this might not be accurate. This presentation outlines models that take the effects of inertia, viscosity, thermal conductivity and compressibility into account. Three classes of models are described and characterized based on the use of dimensionless parameters. The most important parameter is the shear wave number, an unsteady Reynolds number that indicates the ratio between inertial and viscous effects. It is shown that for most applications the low reduced frequency model is sufficient and the most efficient. The wave propagation models are coupled to the structural models to capture the acousto-elastic interaction. For simple geometries, analytical solutions can be found for these coupled analysis cases. For more complex geometries, a finite element model was developed, based on the low reduced frequency model, in which viscothermal acoustic finite elements are coupled to structural elements. Examples of applications are presented.

Flow Modeling in Pressurized Systems Revisited

Assuming 1D flow in pressurized systems, transient analyses can be performed using a number of well-established models. In the short-term timescale, practical problems are solved using either elastic or rigid models, whereas in the long-term scale a quasi-static model is more convenient. These models can be obtained by simplifying the general equations for flow of an elastic fluid. A brief overview of these models is presented, with the major emphasis being on the use of dimensionless parameters to define the range of their applicability for simple hydraulic systems. Guidelines for applicability are presented in the form of graphs and equations. The effects of resistance, inertia, and elasticity may vary in relative importance under different circumstances. The present analysis provides a unified approach to represent each of these effects using a different parameter.

On the use of dimensionless parameters in acid-base theory: VI. The buffer capacities of equimolar binary mixtures of monovalent weak protolytes as compared to that of bivalent protolytes.

The general equation for the relative molar buffer capacity, earlier shown to be valid for bivalent acids, bases, and ampholytes, is shown to hold also for equimolar, binary mixtures of monovalent protolytes if only the parameter s = square root of K1'/4K2' is exchanged for t = s + 1/4s. The same applies to the equations for the mean valence of the two classes of protolytes. As a consequence thereof, the titration and buffer capacity curves of a bivalent protolyte are identical with those of a monovalent protolyte with a pK' value equal to the with those of a monovalent protolyte with a pK' value equal to square root of K1'K2' of the bivalent one (the isoprotic point of an ampholyte). For a hypothetical bivalent acid, base, or ampholyte with s = 1, delta pK' = log 4, this implies that the intrinsic rather than the hybrid dissociation constants are responsible for the titration and buffer capacity curves.

On the use of dimensionless parameters in acid-base theory. VII. The pH of solutions of salts of a strong acid and a weak base or vice versa.

The equation for the hydrogen ion activity in solutions of salts of a strong acid and a weak base, or vice versa, is of the third degree. Nevertheless, explicit equations for pH of such solutions can be formulated as linear functions of the logarithm of the salt concentration. The equations are valid within the major parts of pH and concentration intervals of experimental interest. The ranges of validity are given in terms of mathematically defined pH intervals. Close relations with pH of free base or free acid solutions of the same concentration as the salt are demonstrated. For instance, the pH difference between solutions of the salt and the free base or acid having unit activities is +/- 7 pH units.