Basis Of Dimensional Analysis Research Articles

High-speed projectile perforation of nickel-based Inconel 718 superalloy plates: Experiments and modeling

Understanding ballistic behavior of structural materials is important for their applications in aeronautical and astronautical industries. We investigate perforation of 2-mm thick Inconel 718 superalloy plates by spherical stainless steel 304 projectiles with high-speed photography at impact velocities ranging from 548 ms−1 to 1360 ms−1. Postmortem target samples are characterized with optical metallography, scanning electron microscopy and electron backscatter diffraction as regards bullet hole morphology and deformation. Grain refinement and shear banding are the main microstructural deformation modes near the bullet holes. Shear dominated deformation and tension–shear dominated deformation of target material occur sequentially in bullet hole along the impact direction. The morphologies of bullet holes and postmortem projectiles are obtained from the experiments and simulations. The effect of projectile deformation on ballistic behavior of the target is investigated. On the basis of dimensional analysis, a quadratic relation is derived between the energy absorption ratio of target and the dimensionless postmortem projectile diameter, along with a phenomenological model that can well predict projectile residual velocities.

On the parameterization of phytoplankton primary production in water ecosystem models

Parametrization of the formation of organic matter in ecological models is traditionally carried out by using the dependence of the Michaelis – Menten – Monod type [Monod, 1942], which describes the growth rate of algal biomass depending on the factor limiting their development. One of the biggest drawbacks of these dependences is the presence of empirical parameters in them, which in a complex way depend on environmental factors and are an individual characteristic of various types of algae. These parameters in the models actually become fitting coefficients that provide the best fit between observational data and modeling results, which does not allow for effective diagnostics and forecasting of the state of aquatic ecosystems. In this work, on the basis of dimensional analysis, a parametrization was obtained that describes the photosynthesis of algae depending on the parameters relatively easily measured in natural conditions - total solar radiation, phytoplankton biomass, and water transparency. Parametrization has been verified according to observations on more than 30 different types of lakes located in different regions of the world. The calculated data are in satisfactory agreement with the data of field observations, both qualitatively and quantitatively. Discrepancies in field and calculated data may be due to the fact that the species composition of algae in lakes of different trophic status is not taken into account, which can lead to errors in assessing the efficiency of using solar radiation. Discrepancies may also be related to the total solar radiation, rather than photosynthetic active radiation, which varies in different geographic and atmospheric conditions. The proposed parametrization can be used in the development of mathematical models of lake ecosystems, as well as to determine the trophic status of poorly studied water bodies.

Dynamic scaling laws of spatial grid structures under inner explosion considering material and geometric distortions

It is a key issue to assure that the experimental results of scaled-down models of long-span spatial grid structure under inner blasting loads can truly reflect the characteristics of their prototype structure. The existing method to deal with the dynamic scaling laws of structures is not suitable for long-span spatial grid structures subjected to inner explosion. This paper derives and modifies the dynamic scaling laws among scaled-down models and full-size structure under inner explosion on the basis of dimensional analysis, taking long-span cylindrical grid shell structure as research case and considering the strain-rate effect, yield stress and dimension distortions. In this article, the improved scaling laws were verified and proved by comparing the simulation results with the test results of long-span cylindrical grid shell structure and its scaled-down models. The research results revealed that the maximum errors of the peak values of displacement responses and strain responses between the scaled-down model and the prototype were unacceptable without considering material and geometric distortions. Moreover, the empirical formulae to calculate the mass of explosive based on specific impulse were proposed and the corrected method to predict the inner explosion responses of full-size structure according to the results of scaled-down model tests was presented.

Evaluation of Thermodynamic and Optical Properties of Sixteen Ionic Liquids at Different Temperatures

Introduction: Based on the dimensional analysis, ρ -u- thermodynamic and ρ -uoptical properties correlations have been applied to sixteen ionic liquids at different temperatures. The objective of the present work is to employ these relations to ionic liquids. The experimental values of ρ and u have been reported in the literature at different temperatures. We have computed thermal expansivity (α), isothermal compressibility (βT), heat capacities ratio (γ), internal pressure (Pint), pseudo-Grüneisen parameter (Г), the energy of vaporization (ΔEV), enthalpy of vaporization (ΔHV), cohesive energy density (ced), solubility parameter (δ), refractive index (n), molar refraction (RM) and polarisability (αp) for these liquids. Method: Correlations between density-sound velocity and several thermodynamic properties have been derived on the basis of dimensional analysis On the basis of dimensional analysis, a number of useful and important thermodynamic relations were deduced in terms of density (ρ) and speed of sound (u). Result: Results were found to be quite satisfactory. Keeping in view = uncertainty in the experimental values of ρ and u, as well as some approximations used, the agreement between experimental and theoretical values was found to be quite satisfactory. Discussion: Density (ρ) and ultrasonic speed (u) data of sixteen RTILs at different temperatures have been taken from the literature. Calculated values of α, βT, Pint, γ, CP-CV, and, Г were obtained from empirical relations. The experimental values of α were given for making a comparison. Conclusion: Based on the dimensional analysis, our recently developed correlations between ρ-u- thermodynamic and ρ-u- optical properties have been found to be quite successful when applied to sixteen ionic liquids for the first time. α, βT, γ, Pint, γEVap, ΔHVap, ced, δ as well as RM and αp were calculated at various temperatures.

Design Characteristics of Venturi Aeration System

The crucial phenomenon of air and water mixing together is called aeration. The venturi aeration is mainly responsible to transfer air directly through the atmosphere into the flowing water attribute to its simplicity and reliability. A water tank of 1000 litres capacity having dimensions 100 × 100 × 100 cm3 was used to conduct the experiments for aeration for the purpose of studying the characteristics of venturi aeration system design. Venturi having three significant sections i.e. inlet, constricted and outlet section, used as a differential pressure producer basis on Bernoulli’s theorem where the middle section of the venturi often called as constricted section is responsible for the energy conversion, which transfers oxygen by aspirating air into the constricted section and producing interfacial area between the air and water. On the basis of dimensional analysis, non-dimensional numbers associated with geometric, dynamic and process parameters were analysed. The non-dimensional geometric parameters like throat length (tl), hole distance from beginning of throat (hd), throat hole diameter (th) were optimized and additionally conducted at constant flow rate (vw=0.396 m/s). To assess the performance of designed venturi, the selection of different tl as 20, 40, 60, 80 and 100 mm, with varying number of holes inserted, depends on the tl and keeping th constant at 2 mm. The SAE values were initiated more with increasing tl. The maximum SAE values was obtained with maximum number of holes open as 6.200 × 10-3 kg O2/kWh for 100 mm tl. A constant flow rate was maintained to construct the equations for the prediction of venturi aeration system’s characteristics via simulations. For the purpose of simulations different geometric conditions of the venturi design system were considered. The simulation equations developed for tl based on the Re and Fr are subjected to 12.655 × 10-5 > Re > 2.531 × 10-5 and 1.251 < Fr < 6.256, respectively. It was also concluded that from the non-dimensional study, the simulation equation developed for NDSAE based on the tl be valid and subjected to 3.890× 103< NDSAE <0.215× 103.

The charmed string: self-supporting loops through air drag

The string shooter experiment uses counter-rotating pulleys to propel a closed string forward. Its steady state exhibits a transition from a gravity-dominated regime at low velocity towards a high-velocity regime where the string takes the form of a self-supporting loop. Here we show that this loop of light string is not suspended in the air due to inertia, but through the hydrodynamic drag exerted by the surrounding fluid, namely air. We investigate this drag experimentally and theoretically for a smooth long cylinder moving along its axis. We then derive the equations describing the shape of the string loop in the limit of vanishing string radius. The solutions present a critical point, analogous to a hydraulic jump, separating a supercritical zone where the wave velocity is smaller than the rope velocity, from a subcritical zone where waves propagate faster than the rope velocity. This property could be leveraged to create a white hole analogue similar to what has been demonstrated using surface waves on a flowing fluid. Loop solutions that are regular at the critical point are derived, discussed and compared to the experiment. In the general case, however, the critical point turns out to be the locus of a sharp turn of the string, which is modelled theoretically as a discontinuity. The hydrodynamic regularisation of this geometrical singularity, which involves non-local and added mass effects, is discussed on the basis of dimensional analysis.

Investigation of the Propagation Characteristics of Underwater Shock Waves in Underwater Drilling Blasting

During the first‐stage project of the main channel of Ningbo‐Zhoushan Port’s Shipu Harbor, underwater shock waves were monitored. By analyzing a typical measured pressure time history curve, the characteristics of underwater shock waves in an engineering context were obtained. We obtained a traditional exponential attenuation formula for underwater shock waves based on the measured data, simplified the model of underwater drilling blasting based on engineering practice, deduced a revised formula for underwater shock wave peak overpressure on the basis of dimensional analysis, established a linear fitting model, and obtained the undetermined coefficients of the revised formula using a linear regression analysis. In addition, the accuracies of the two formulas used to predict underwater shock wave peak overpressure and the significance order of influence and influence mechanism of factors included in the revised formula on the underwater shock wave peak overpressure were discussed.

Increasing the quality of excavators’ planetary reduction gearboxes on the basis of dimensional analysis and geometrical characteristics of tooth wheels

The article describes the problem of extending operational electrically driven excavators’ reducing gear boxes which break down nearly every six months. The main reason of the function loss is the breakdown of the bearing assembly of one of the pinions. The authors performed kinematic, dynamic and geometric calculation of gearing to detect the breakdown reasons. The main reason is that alignment condition is not provided in the differential part and in the power return gear. All toothed gear wheels must be manufactured with the positive bias of the generating rack profile, but in fact all pinions and idle gears are manufactured with negative bias. This lead to an intolerable radial clearance in the gearing and skew of the floating master gears.

On the dynamic generalization of the anisotropic Eshelby ellipsoidal inclusion and the dynamically expanding inhomogeneities with transformation strain

The self-similarly dynamically (subsonically) expanding anisotropic ellipsoidal Eshelby inclusion is shown to exhibit the constant stress “Eshelby property” in the interior domain of the expanding inclusion on the basis of dimensional analysis, analytic properties and the proof for the static inclusion alone. As an example of this property and the application of the dynamic Eshelby tensor (constant in the interior domain), it is shown that the Eshelby equivalent inclusion method always allows for the determination of the equivalent transformation strain for a self-similarly dynamically expanding inhomogeneous spherical inclusion when the Poisson's ratio is in the real range (positive definiteness of the strain energy). Thus, the solution of dynamically self-similarly expanding inhomogeneities (chemical phase change) with transformation strain can be obtained, as well as the driving force per unit area of the expanding inhomogeneity.

Experimental and numerical investigation of fluid flow hydrodynamics in porous media: Characterization of pre-Darcy, Darcy and non-Darcy flow regimes

In the present study, incompressible single phase fluid percolation through different types (homogeneous and mixed isotropic) of porous media was investigated experimentally. The functional relation of pressure gradient with velocity was presented on the basis of dimensional analysis in terms of friction factor and Reynolds number based on different characteristic length (i.e. particle diameter and permeability of porous media). The experimental pressure drop data were analyzed by rigorous non-linear regression analysis. The different flow regimes exist in porous media flow were characterized and demarked according to the analysis of solid-fluid interaction, and the generation of the pressure and the viscous drags in terms of different types of Reynolds numbers ReDRePReK¯. Three significant flow regimes (pre-Darcy, Darcy and non-Darcy Forchheimer flow regime) with two transition regimes (transition to Darcy and weak inertia flow regime) were observed. In addition, numerical modeling and simulations were also performed to understand the relevant micro-flow phenomena localized in the pore domain and simulation results were compared with experimental data.

Numerical Simulation and Formulation of Wave Run-Up on Dam Face due to Ground Oscillations Using Major Earthquake Acceleration Records

AbstractA previously developed computational model is used for wave run-up analysis in a generic two-dimensional reservoir subjected to major earthquake acceleration records. The model is based on numerical solution of the Navier-Stokes equations and pressure equation considering compressibility effects. An existing model has been revised by the volume of fluid (VOF) method with piecewise linear interface calculation (PLIC) to be able to compute violent wave motion in the reservoir and to predict the maximum wave run-up on the dam crest attributable to ground oscillations during an earthquake. The numerical method and the computer code are validated by comparing the free-surface waves with the data available in the literature. The surface wave run-up on a vertical dam is simulated for different reservoir depths using major earthquake acceleration records. Simulations show that the maximum wave height on a dam body depends on the maximum positive ground velocity. On the basis of dimensional analysis, simul...

Numerical study on upheaval buckling of pipe-in-pipe systems with full contact imperfections

Upheaval buckling may occur in high-temperature and high-pressure subsea pipe-in-pipe (PIP) systems. Finite element method and dimensional analysis method are used to investigate the upheaval buckling response and critical buckling force of PIP systems with full-contact imperfections. Results show that imperfections, along with clearance (the gap between the centralizer and outer pipe) and stiffness ratio of the inner and outer pipe, influence buckling response and buckling force. Two empirical formulas that correspond to two typical imperfection profiles are proposed to calculate the critical upheaval buckling force of PIP systems on the basis of dimensional analysis and numerical results. The proposed empirical formulas show good accuracy.

Critical Assessment of Visco-elastic Damping Models Used in DEM Simulations

The contact between particles is an important task in simulating the behaviour of particle assemblies. Conventionally, the dissipative contribution to the normal contact force is described by viscoelastic damping, where the concept of the constant coefficient of restitution (COR) is extensively explored in Discrete Element Method (DEM) simulations. From the previous studies it is known that different models provide different time-histories during the contact even for the equal values of the COR.In the present investigation, a comparative study of various nonlinear damping models for spherical particles is given on the basis of dimensional analysis. The research aims to demonstrate how the differences observed in a single particle collision contribute to the collective behaviour of particles in multi-particle systems and thereby affect the sensitivity of DEM results for various damping models. The selected samples of 3D granular flows have been solved numerically to illustrate the contribution of the damping models to the dynamic behaviour during the impact. The current report presents the results obtained in studying the behaviour of particles during the filling of a hopper, the discharge and the motion of the particles on the bottom-plane of a rectangular box. Moreover, the most popular nonlinear damping models reported by Lee and Herrmann, Brilliantov, Tsuji and modified Tsuji models have been examined. The results of the present study allow us to define basic tendencies observed, when various models are applied.

Modeling the batch power of mill

This paper presents a new method of modeling the batch power of mill on the basis of dimensional analysis and criterion equations. The grinding batch is represented by the grinding bodies, material and medium that is used to provide the flow of raw material through the mill, and most commonly water or air. The rate of energy consumption in the mill is regulated by the charge density and it presents the charge density. The feed power is dependent on the type of media milling body and prior to the treatment of mineral raw materials. Approximate power mill defined engine power is the power of batch mill highest charge density. In the work is varied density in batch laboratory mills and defined a model of batch power mill which we used in the adaptation of the mill plants in new industrial plant. The present model of the feed mill power is checked on industrial exploitation of quartz raw materials in Lukic polje near Milici. The process of mechano-chemical treatment defines as venture milling with longer residence time of material in the mill and small batch densities, all with the aim to reduce the force with which the batch effect on grain mineral resources. Radicality of fragmentation varies with the density of charge so that the densities obtained with smaller sized features special milling products with a narrower range of narrow size class and thus increased the specific surface area and reactivity.

Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

AbstractThis paper focuses on the characterization and the stochastic modelling of the fluid acceleration in turbulent channel flow. In the first part, the acceleration is studied by direct numerical simulation (DNS) at three Reynolds numbers (${\mathit{Re}}_{\ast } = {u}_{\ast } h/ \nu = 180$, 590 and 1000). It is observed that whatever the wall distance is, the norm of acceleration is log-normally distributed and that the variance of the norm is very close to its mean value. It is also observed that from the wall to the centreline of the channel, the orientation of acceleration relaxes statistically towards isotropy. On the basis of dimensional analysis, a universal scaling law for the acceleration norm is proposed. In the second part, in the framework of the norm/orientation decomposition, a stochastic model of the acceleration is introduced. The stochastic model for the norm is based on fragmentation process which evolves across the channel with the wall distance. Simultaneously the orientation is simulated by a random walk on the surface of a unit sphere. The process is generated in such a way that the mean components of the orientation vector are equal to zero, whereas with increasing wall distance, all directions become equally probable. In the third part, the models are assessed in the framework of large-eddy simulation with stochastic subgrid acceleration model (LES–SSAM), introduced recently by Sabel’nikov, Chtab-Desportes & Gorokhovski (Euro. Phys. J. B, vol. 80, 2011, p. 177–187), and designed to account for the intermittency at subgrid scales. Computations by LES–SSAM and its assessment using DNS data show that the prediction of important statistics to characterize the flow, such as the mean velocity, the energy spectra at small scales, the viscous and turbulent stresses, the distribution of the acceleration can be considerably improved in comparison with standard LES. In the last part of this paper, the advantage of LES–SSAM in accounting for the subgrid flow structure is demonstrated in simulation of particle-laden turbulent channel flows. Compared to standard LES, it is shown that for different Stokes numbers, the particle dynamics and the turbophoresis effect can be predicted significantly better when LES–SSAM is applied.

Determination of minimum pressure drop at different plate spacings and air velocity in a wave‐plate mist eliminator

ABSTRACTIn this article, the flow pressure drop across a wave‐plate mist eliminator has been studied experimentally by changing both the air velocity and the plate spacing. The measured values for pressure losses have been compared with the results of the available formulas. Despite the literature, this study shows that by decreasing the plate spacing, the pressure loss will not remain constant. Results show that decreasing the plate spacing from 11.5 to 9.5 mm leads to a decrease in pressure loss. However, further decrease in spacing will result in an increased pressure loss. On the basis of dimensional analysis, a dimensionless variable is defined for spacing, and it is shown that the value of 0.24 for this variable gives the minimum pressure coefficient for all cases studied by current experimental setup. Copyright © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.

Theory of heat transfer during condensation in microchannels

A theoretical model for condensation in microchannels takes account of the effects of gravity and streamwise shear stress on the condensate surface as well as the transverse pressure gradient due to surface tension in the presence of change in condensate surface curvature. Numerical solutions of the relevant conservation equations have been obtained for various channel shapes, dimensions, vapor-to-surface temperature differences and vapor mass fluxes. The theory is reviewed and updated. The effect of channel inclination is included and new results are presented. When using boundary conditions of uniform vapor and surface temperature it is found that, over a certain length of channel, the local mean (around the channel perimeter) heat-transfer coefficient is essentially independent of gravity and vapor shear stress. For the surface tension dominated regime, an equation for the Nusselt number as a function of a single dimensionless group, analogous to that occurring in the simple Nusselt theory except that the gravity term is replaced by a surface tension term, has been derived both on the basis of dimensional analysis and by approximate theory. The equation represents all of the data satisfactorily. This is a step towards the goal of representing the solutions, including those conditions where shear stress and gravity play important roles, by relatively simple dimensionless algebraic equations, valid for any fluid and channel geometry, for convenient use in design and optimization.

Acceleration of DEM algorithm for quasistatic processes

AbstractThe discrete element method (particle dynamics) is an invaluable tool for studying the complex behavior of granular matter. Its main shortcoming is its computational intensity, arising from the vast difference between the integration time scale and the observation time scale (similar to molecular dynamics). This problem is particularly acute for macroscopically quasistatic deformation processes. We first provide the proper definition of macroscopically quasistatic processes, on the basis of dimensional analysis, which reveals that the quasistatic nature of a process is size‐dependent. This result sets bounds for application of commonly used method for computational acceleration, based on superficially increased mass of particles. Next, the dimensional analysis of the governing equations motivates the separation of time scales for the numerical integration of rotations and translations. We take advantage of the existence of fast and slow variables (rotations and translations) to develop a two‐timescales algorithm based on the concept of inertial manifolds suggested by Gear and Kevrekidis. The algorithm is tested on a 2D problem with axial strain imposed by rigid plates and pressure on lateral boundaries. The benchmarking against the accurate short‐time step results confirms the accuracy of the new algorithm for the optimal arrangement of short‐ and long‐time steps. The algorithm provides moderate computational acceleration. Copyright © 2010 John Wiley & Sons, Ltd.

Bed expansion and fluctuation in cylindrical gas solid fluidized beds with stirred promoters

A profound and fundamental understanding of bed dynamics such as bed expansion ratio and bed fluctuation ratio of irregular particles of binary mixtures has been made in a cylindrical fluidized column for gas solid systems, resulting in a predictive model for fluidized beds. In the present work attempt has been made to study the effect of various system parameters (viz. rotational speed of the promoter, initial static bed height, superficial velocity of the fluidizing medium, particle size and density) on the bed dynamics through experimentation. The correlations for the bed dynamics have been developed on the basis of dimensional analysis. It was observed that the calculated values of bed dynamics agree well with the experimental values in most of the cases.

The use of physical modeling in the optimisation of a primary separation vessel feedwell

AbstractA physical modeling program was undertaken to assess and eliminate a significant vessel wear problem observed in a primary separation vessel used in the recovery of bitumen from oil sands. A 1:20 scale model was fabricated, and process rates and materials were selected on the basis of dimensional analysis. Experiments showed that the existing feedwell produced poor circumferential distribution and formed a localised jet that entered the vessel over a narrow sector. Tests were then conducted with several different modifications to the feedwell to improve the flow distribution. The final design produced uniform circumferential distribution and a modest improvement in model separation efficiency. This design has been in commercial service for several years and has eliminated the local wear problems.