Combinations Of Dimensionless Parameters Research Articles

The analytical solutions of squeezing flow and heat transfer in an horizontal filtering channel

Flow and heat transfer dynamics inside different industrial chambers play a vital role in understanding momentum and heat transfer during industrial operations. Analysis of such flow and heat transfer helps operators to know how the system works. To better understand the filtration process, the current study analytically investigated the internal flow and heat transfer through a porous horizontal filter channel under the influence of a uniform magnetic field while removing unwanted contaminations from the fluid inside the filter chamber. Thus, the novelty of the current study is to advance the filtration process by investigating how the top moving wall, which aims to minimise filter cake formation, affects permeates outflow (the current design). The partial differential equations (PDEs) model representing the internal flow and heat transfer during filtration is transformed into a system of ordinary differential equations (ODEs) using Lie point symmetry reduction without changing the dynamics under investigation. After that, the transformed equations are solved analytically using the perturbation approximation technique. The comparative analysis between the obtained semi-analytical and NDSolve numerical solutions was used to show the correlation of internal flow, temperature, and pressure profiles. The obtained solutions are used to find the best combination of dimensionless parameters that arise from flow and heat transfer dynamics that lead to optimum outflow. Graphical analysis of flow and heat transfer dynamics are used to indicate the combination of parameters that leads to maximum outflow based on scientific evidence. It is observed that, on average, the velocity increases significantly by 122.55% across all cases of Re ranging from 0 to 3.2 at the top permeable wall y=1. This significant increase is due to the motion of the moving wall and fluid injection happening at y=1. The results show that more chamber volume, small pores size, weak injection, weak magnetic force, and less Joule heating are crucial to increase internal temperature and permeate outflow velocity during filtration.

Investigation of oscillations in katabatic Prandtl slope flows

AbstractDynamically unstable katabatic Prandtl slope flows are studied via numerical simulations and spectral analysis. Results confirm the presence of aperiodic temporal and spatial oscillations in the flow fields due to the emergence and propagation of flow instabilities. Damped en masse oscillations are observed to dominate the initial oscillatory stage of laminar katabatic slope flows. Stationary longitudinal rolls, which are dominant at shallow slopes, are observed to meander with increasing stratification perturbation parameter and the average distance between the rolls exhibits a strong dependence on slope inclination for slope angles less than . At much steeper slopes, traveling slope waves emerge and they are transported at the mean jet velocity. Both types of instability rolls coexist for certain combinations of dimensionless parameters, forming intricate structures that break into smaller eddies as the flow becomes more dynamically unstable. In the dynamically unstable nonturbulent regime, en masse oscillations are insignificant, but their normalised frequency can be used to discern the type of flow instability.

The separatrix operational space of ASDEX Upgrade due to interchange-drift-Alfvén turbulence

The efficient operation of a tokamak is limited by several constraints, such as the transition to high confinement or the density limits occurring in both confinement regimes. These particular boundaries of operation are derived in terms of a combination of dimensionless parameters describing interchange-drift-Alfvén turbulence without any free adjustable parameter. The derived boundaries describe the operational space at the separatrix of the ASDEX Upgrade tokamak, which is presented in terms of an electron density and temperature existence diagram. The derived density limits are compared against Greenwald scaling. The power threshold and role of ion heat flux for the transition to high confinement are discussed.

Mixing viscoplastic fluids in stirred vessels over multiple scales: A combined experimental and CFD approach

Dye visualisation techniques and CFD are used to characterise the flow of viscoplastic Carbopol™ solutions in stirred vessel systems over multiple scales. Centrally-mounted, geometrically-similar Rushton turbine (RT) impellers are used to agitate various Carbopol 980 (C980) fluids. The dimensionless cavern diameters, Dc/D, are scaled against a combination of dimensionless parameters: Rem−0.3Rey0.6n−0.1ks−1, where Rem, Rey, n and ks are the modified power-law Reynolds number, yield stress Reynolds number, flow behaviour index and impeller geometry constant, respectively. Excellent collapse of the data is demonstrated for the fluids and range of flows investigated. Additional data are collected using a pitched-blade turbine (PBT) with cavern size similarity being shown between the RT and PBT datasets. These results are important in the context of scale-up/scale-down mixing processes in stirred vessels containing complex fluids and can be used to show that flow similarity can be achieved in these systems if the processes are scaled appropriately.

Preferential Deposition of Snow and Dust Over Hills: Governing Processes and Relevant Scales

AbstractPreferential deposition of snow and dust over complex terrain is responsible for a wide range of environmental processes and accounts for a significant source of uncertainty in the surface mass balances of cold and arid regions. Despite the growing body of literature on the subject, previous studies reported contradictory results on the location and magnitude of deposition maxima and minima. This study aims at unraveling the governing processes of preferential deposition in a neutrally stable atmosphere and to reconcile seemingly inconsistent results of previous works. For this purpose, a comprehensive modeling approach is developed, based on large eddy simulations of the turbulent airflow, Lagrangian stochastic model of particle trajectories, and immersed boundary method to represent the underlying topography. The model is tested against wind tunnel measurements of dust deposition around isolated and sequential hills. A scale analysis is then performed to investigate the dependence of snowfall deposition on the particle Froude and Stokes numbers, which fully account for the governing processes of inertia, flow advection, and gravity. Model results suggest that different deposition patterns emerge from different combinations of dimensionless parameters, with deposition maxima located either on the windward or the leeward slope of the hill. Additional simulations are performed, to test whether the often used assumption of inertialess particles yields accurate deposition patterns. Results indicate that this assumption can be justified when snowflakes present dendritic shape but may generate unrealistic results for rounded particles. We finally show that our scale analysis provides qualitatively similar results for hills with different aspect ratios.

Numerical Study on the Natural Convection of Air in a Cubic Cavity Subjected to a Yawing Motion

Natural convections subjected to multi-Degree of Freedom (DoF) motion are much more complex than those in static case, and those subjected to yawing motion are the simplest and ideal case for investigating their characteristics due to less interactive parameters. In this paper, the characteristic of natural convection under yawing motion was studied systematically to clarify the interaction between yawing motion and thermal-dynamic behavior. First of all, the mathematical model was established in a non-inertial coordinate system, and the dimensionless governing equations were derived. Subsequently, the governing equations were discretized in the framework of the finite volume method, and a computer code was developed and validated. After that, the natural convection under yawing motion was calculated with different combinations of dimensionless parameters, and the influence of rotation frequency and amplitude on heat and mass transfer was investigated. It was found that the yawing motion plays a notable role in flow and heat transfer, depending on the relative magnitudes of rotation-induced velocity and buoyancy-induced velocity: At a lower Rayleigh number of 104, the Nusselt number on hot boundary is enhanced by approximately 25% when the rotation period is changed from 12 s to 2 s; while the changing in rotation period from 12 s to 2 s did not induce obvious difference in hot-boundary Nusselt number for a higher Rayleigh number of 105. It is concluded that the vertical-axis harmonic rotation enhances heat transfer if the rotation-induced velocity dominates the flow. The clarification of natural convection characteristic in yawing motion provides convenience for analyzing that in other multi-DoF systems.

Numerical Investigation into the Two-Phase Convective Heat Transfer within the Hold of an Oil Tanker Subjected to a Rolling Motion

A crude oil tanker usually encounters a rolling motion during sea transportation, which leads to rotational movement and sometimes a sloshing of the liquid hold. This rolling-induced body motion seriously affects the thermal and hydraulic behavior of the liquid hold, which then affects the heating process and heat preservation of the tanker. Clarification of the involved thermal and hydraulic characteristics is the basic requirement for establishment of a scientific heating scheme and heat preservation method. A two-phase 3D model considering the free liquid surface and non-Newtonian behavior of the fluid was established for the thermal calculation of the liquid holds in oil tankers. The thermal and hydraulic characteristics of the liquid hold were investigated under different combinations of dimensionless parameters, and the combined effect of rolling and fluid non-Newtonian behavior was investigated. It was found that rolling intensifies the heat transfer based on the combination of the Richardson number (Ri) and the rotation-strength number (ω*), and non-Newtonian behavior of the fluid effectively affects the heat transfer in a rolling motion. This research is expected to provide a reference for design and optimization of the heating and heat preservation method for oil tanker operation.

Investigating the capability of two hybrid intelligence methods to predict bedform dimensions of alluvial channels

Abstract Dimensions of river bedforms have an effect on total roughness. The complexity of bedform development causes empirical methods to differentiate from each other in predicting bedform dimensions. In this paper, two novel hybrid intelligence models based on a combination of the group method of data handling (GMDH) with the harmony search (HS) algorithm and shuffled complex evolution (SCE) have been developed for predicting bedform dimensions. A data set of 446 field and laboratory measurements were used to evaluate the ability of the developed models. The results were compared to conventional GMDH models with two kinds of transfer functions and an empirical formula. Also, five different combinations of dimensionless parameters as input variables were examined for predicting bedform dimensions. Results reveal that GMDH-HS and GMDH-SCE have good performance in predicting bedform dimensions, and all artificial intelligence methods were dramatically different to the empirical formula of van Rijn showing that using these methods is a key to solving complexity in predicting bedform dimensions. Also, comparing different combinations of dimensionless parameters reveals that there is no significant difference between the accuracy of each combination in predicting bedform dimensions.

Non-Vortex Topological Solitons of the Gauge Model

A (2+1)-dimensional gauge model is investigated. The presence of additional local U(1) symmetry, not associated with a physical gauge field, leads to the existence in the given model of two-dimensional non-vortex topological solitons carrying unquantized magnetic flux. Topological solitons of the given type were found numerically for fixed values of the model parameters. Analytical calculations of some properties of non-vortex topological solitons were performed. Universal dependences of the energy and magnetic flux of a non-vortex topological soliton on a dimensionless combination of parameters of the gauge model were obtained numerically. A comparative analysis of the properties of a non-vortex topological soliton and an Abrikosov–Nielsen–Olesen classical vortex is provided.

Regulated CRISPR Modules Exploit a Dual Defense Strategy of Restriction and Abortive Infection in a Model of Prokaryote-Phage Coevolution.

CRISPRs offer adaptive immunity in prokaryotes by acquiring genomic fragments from infecting phage and subsequently exploiting them for phage restriction via an RNAi-like mechanism. Here, we develop and analyze a dynamical model of CRISPR-mediated prokaryote-phage coevolution that incorporates classical CRISPR kinetics along with the recently discovered infection-induced activation and autoimmunity side effects. Our analyses reveal two striking characteristics of the CRISPR defense strategy: that both restriction and abortive infections operate during coevolution with phages, driving phages to much lower densities than possible with restriction alone, and that CRISPR maintenance is determined by a key dimensionless combination of parameters, which upper bounds the activation level of CRISPRs in uninfected populations. We contrast these qualitative observations with experimental data on CRISPR kinetics, which offer insight into the spacer deletion mechanism and the observed low CRISPR prevalence in clinical isolates. More generally, we exploit numerical simulations to delineate four regimes of CRISPR dynamics in terms of its host, kinetic, and regulatory parameters.

Revised predictive equations for salt intrusion modelling in estuaries

Abstract. For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equations for the Van der Burgh coefficient $K$ and the dispersion at the seaward boundary D0. Here we have improved these equations by using an expanded database, including new previously un-surveyed estuaries. Furthermore, we derived a revised predictive equation for the dispersion at tidal average condition and with the boundary situated at the well identifiable inflection point where the estuary changes from wave-dominated to tide-dominated geometry. We used 89 salinity profiles in 30 estuaries (including seven recently studied estuaries in Malaysia), and empirically derived a range of equations using various combinations of dimensionless parameters. We split our data in two separated data sets: (1) with more reliable data for calibration, and (2) with less reliable data for validation. The dimensionless parameters that gave the best performance depended on the geometry, tidal strength, friction and the Richardson number. The limitation of the equations is that the friction is generally unknown. In order to overcome this problem, a coupling has been made with the analytical hydraulic model of Cai et al. (2012), which makes use of observed tidal damping and by which the friction can be determined.

Onset of Convection with Internal Heating in a Porous Medium Saturated by a Nanofluid

Linear stability analysis was applied to the onset of convection due to internal heating in a porous medium saturated by a nanofluid. A model in which the effects of thermophoresis and Brownian motion are taken into account is employed. We utilized more realistic boundary conditions than in the previous work on this subject; now the nanofluid particle fraction is allowed to adapt to the temperature profile induced by the internal heating, subject to the requirement that there is zero perturbation flux across a boundary. The results show that the presence of the nanofluid particles leads to increased instability of the system. We identified two combinations of dimensionless parameters that are the major controllers of convection instability in the layer.

Quadrupole moments of rotating neutron stars and strange stars

We present results for models of neutron stars and strange stars constructed using the Hartle-Thorne slow-rotation method with a wide range of equations of state, focusing on the values obtained for the angular momentum $J$ and the quadrupole moment $Q$, when the gravitational mass $M$ and the rotational frequency $\Omega$ are specified. Building on previous work, which showed surprising uniformity in the behaviour of the moment of inertia for neutron-star models constructed with widely-different equations of state, we find similar uniformity for the quadrupole moment. These two quantities, together with the mass, are fundamental for determining the vacuum space-time outside neutron stars. We study particularly the dimensionless combination of parameters $QM/J^2$ (using units for which $c=G=1$). This quantity goes to 1 in the case of a Kerr-metric black hole and deviations away from 1 then characterize the difference between neutron-star and black-hole space-times. It is found that $QM/J^2$ for both neutron stars and strange stars decreases with increasing mass, for a given equation of state, reaching a value of around 2 (or even less) for maximum-mass models, meaning that their external space-time is then rather well approximated by the Kerr metric. If $QM/J^2$ is plotter against compactness $R/2M$ (where $R$ is the radius), it is found that the relationship is nearly unique for neutron-star models, independent of the equation of state, while it is significantly different for strange stars. This gives a new way of possibly distinguishing between them.

Analysis and computation of gravity-induced migration in porous media

Motivated by the problem of gravity segregation in an inclined porous layer, we present a theoretical analysis of interface evolution between two immiscible fluids of unequal density and mobility, both in two and three dimensions. Applying perturbation theory to the appropriately scaled problem, we derive the governing equations for the pressure and interface height to leading order, obtained in the limit of a thin gravity tongue and a slightly dipping bed. According to the zeroth-order approximation, the pressure profile perpendicular to the bed is in equilibrium, a widely accepted assumption for this class of problems. We show that for the inclined bed two-dimensional problem, in the reference frame moving with the mean gravity-induced advection velocity, the interface motion is dictated by a degenerate parabolic equation, different from those previously published. In this case, the late-time behaviour of the gravity tongue can be derived analytically through a formal expansion of both the solution and its two moving boundaries. In three dimensions, using a moving coordinate along the dip direction, we obtain an elliptic–parabolic system of partial differential equations where the fluid pressure and interface height are the two dependent variables. Although analytical results are not available for this case, the evolution of the gravity tongue can be investigated by numerical computations in only two spatial dimensions. The solution features are identified for different combinations of dimensionless parameters, showing their respective influence on the shape and motion of the interface.

An Effective Continuum Model for the Gas Evolution in Internal Steam Drives

Summary We derive an effective continuum model to describe the nucleation and subsequent growth of a gas phase from a supersaturated liquid in a porous medium, driven by heat transfer. The evolution of the gas results from the reduction of the system pressure at a constant rate. The model addresses two stages before the onset of bulk gas flow, nucleation, and gas-phase growth. The problem arises in internal steam drive—for example, of the type recently discussed in blowdown experiments in carbonate rocks (Dehghani et al.,1 Dehghani and Kamath2). Important quantities, such as the fraction of pores that host activated sites, the deviation from thermodynamic equilibrium, the maximum supersaturation, and the critical gas saturation depend crucially on the nucleation characteristics of the medium. We use heterogeneous nucleation models in the form of pre-existing gas, trapped in hydrophobic cavities, to investigate the nucleation behavior. Using scaling analysis and a simpler analytical model, we show that the relevant quantities during nucleation can be expressed in terms of a simple combination of dimensionless parameters, which include rate effects. The subsequent evolution of the gas phase and the approach to the critical gas saturation are also described using numerical and analytical models. The theory predicts that the maximum supersaturation in the system is a weakly increasing function of the decline rate. This function depends sensitively on the probability density function of the nucleation cavity sizes. It also predicts that the final nucleation fraction, and thus the critical gas saturation, is a power law of the decline rate. The theory for both nucleation and phase growth is then compared with available experimental data.

Parametric Analysis of the Continuous Stirred Tank Reactor Model

A parametric analysis is carried out for the continuous stirred tank reactor model involving a single exothermic reaction. Local bifurcations of the steady state, including Andronov–Hopf bifurcations, are analyzed for a first-order reaction. The steady-state multiplicity and neutrality lines are described in explicit form for various combinations of dimensionless parameters. Typical parametric and phase portraits of the dynamic system are presented. Parametric analysis is also carried out for the nth-order reaction nA → B, the oxidation reaction A + O2 → B, and an arbitrary kinetic function.

Model for the gas evolution in a porous medium driven by solute diffusion

AbstractAn effective continuum model is derived to describe the nucleation and subsequent growth of a gas phase from a supersaturated, slightly compressible binary liquid in a porous medium, driven by solute diffusion. The evolution of the gas results from reducing the system pressure at a constant rate or withdrawing the liquid at a constant rate. The model addresses two stages before the onset of bulk gas flow, nucleation and gas‐phase growth. Negligible gradients due to gravity or viscous forces are assumed, so the critical gas saturation signaling the onset of bulk gas flow is only a function of the nucleation fraction. Important quantities characterizing the process, such as the pore number fraction hosting activated sites, deviation from thermodynamic equilibrium, maximum supersaturation, and critical gas saturation, depend crucially on the nucleation characteristics of the medium. Heterogeneous nucleation models using preexisting gas trapped in hydrophobic cavities or in terms of a rate‐dependent nucleation are used to investigate the nucleation behavior. Using a simpler analytical model the relevant quantities during nucleation can be expressed in terms of a simple combination of dimensionless parameters. The theory predicts that the maximum supersaturation is a weakly increasing function of rate, which in the region of typical experimental parameters can be approximated as a power law. It depends sensitively on the probability density function of nucleation cavity sizes. The final nucleation fraction (thus, the critical gas saturation) is predicted to be a power law of the decline rate. The theoretical exponents agree well with experimental data. The subsequent evolution of the gas phase and the approach to the critical gas saturation is also described.