Dimensionless Time Research Articles

Reconstruction of digital filter parameters when changing the data arrival period

We consider the problem of forming an algorithm for the operation of a digital filter that provides processing, according to a certain law, of discrete samples x[k] of some continuous signal x(t) at the moments of quantization tк=k ∙T0, where T0 -[second]- is the discreteness period in time, and k=0,1,2,.. is the integer variable defining dimensionless discrete time. This work poses and solves the problem of forming the digital filter parameters restructuring, which ensures that the filtering properties remain unchanged when the frequency of information is changed, in particular, the constancy of the frequency and pseudo-frequency characteristics of the filter. An algorithm for restructuring the numerical parameters of the filter based on information about the time intervals of information arrival has been developed. At the stage of filter development, a special conversion matrix is formed for the specified parameters, and at the stage of filter operation in real time, an operational recalculation of the digital filter parameters is performed. For the test example, the calculation results are given, showing good tuning accuracy and stable filter characteristics with a significant change in the quantization frequency.

Water flooding of sandstone oil reservoirs: Underlying mechanisms in imbibition vs. drainage displacement

In this work the effect of wettability in waterfloods of viscous oil is investigated in a combination of experiments in sandpacks and microfluidic chips. Thirty-nine sand-pack flooding experiments were conducted to investigate the effect of core wettability, oil viscosity, and injection velocity on oil recovery to water flooding. An in-line densitometer, installed downstream of the core, was used to record the instantaneous fluid production and help understanding the mechanism of oil displacement in porous media. Additional microfluidic experiments were conducted to understand the mechanism of viscous oil displacement in imbibition vs. drainage.The effect of injection velocity on oil recovery is a strong function of core wettability and oil viscosity. In water-wet systems, below a critical viscosity (∼60 mPa s), increasing injection velocity enhances oil displacement. In more viscous oil systems, injection velocity reduction improves imbibition. This is confirmed through visualization in microfluidic tests. Post breakthrough bypassed oil is produced in the form of low viscosity oil in water emulsion. In oil-wet waterflooding, oil imbibition into the preformed water channels pinches off (snaps-off) some continuous fingers, diverting water to un-swept regions. This temporary channel closure can explain the cyclic pressure build-ups observed oil-wet core flooding experiments. casein oil-wet systems, oil is produced as a series of viscous oil slugs rather than an emulsion.A new dynamic dimensionless time is presented to quantify imbibition time to which imbibition data are well correlated. This number along with the previously presented “viscous drainage number” can quantify different mechanisms responsible for oil displacement in systems of different viscosity ratio, injection velocity, and core wettability. The proposed dimensionless numbers can be used to determine expected viscous oil recovery efficiency in different wettability systems.

A modified Lattice Boltzmann method for predicting the effective thermal conductivity of open-cell foam materials

The heat transfer in porous media have attracted wide attention in various scientific studies. The microstructure model of open-cell foam is reconstructed using the random generation method satisfying the microstructure stochastic properties. A modified Lattice Boltzmann method (LBM) is proposed to resolve the heat transport equations for predicting effective thermal conductivity (ETC). The proposed LBM simulation introduces the additional coefficient to moderate the difference in dimensionless relaxation time between solid and gas phase. The modified LBM simulation reliability is validated by comparing with numerical models and available experimental results. Simulations are conducted to evaluate the effects of a larger range of porosity, ambient pressure, temperature and intrusion mediums on heat transfer. The results indicate that the 400 K is considered as a turning point in the ETC dependence on temperature. At low porosity, the ETC fluctuates more sharply compared to high porosity. The impact of ambient pressure on the ETC is divided into three levels: P < 10 kPa, the ETC is almost insensitive to pressure fluctuation; 10 kPa < P < 100 kPa, the ETC slightly increases with the pressure increase; P > 100 kPa, the ETC significantly increases. The proposed LBM simulation combined with the random generation method is an efficient tool to predict the heat transfer for open-cell foam.

Deformation and acceleration of water droplet in continuous airflow

The present work investigates the deformation and acceleration of water droplets in continuous airflow. The numerical approach is based on the level set method for capturing the liquid–gas interface and the projection method for solving the three-dimensional incompressible Navier–Stokes equations. The effects of the incoming airflow velocity (10–100 m/s), initial droplet diameter (20–100 μm), and supercooling on water droplet deformation are investigated. The results indicate that the droplet enters the breakup regime at a critical Weber number of 10, which agrees with the published literature. A dimensionless deformation factor L is defined to describe the droplet deformation. The results confirm that the extreme values of L increase with increasing Weber number during droplet movement. Two models are proposed to predict the minimum deformation factor and the corresponding dimensionless time. The effect of supercooling on water droplet deformation is analyzed, and it is found that the deformation factor of supercooled droplets is lower than that of room-temperature droplets, while supercooled water droplets exhibit greater acceleration. Furthermore, based on the numerical results, a model governed by the Weber number and the Ohnesorge number is proposed for predicting droplet acceleration.

A non-field analytical method for gas dissolution under forced compression

This paper presents an extension of the non-field analytical method—known as the method of Kulish—to model gas dissolution into a liquid due to forced compression. Solutions are obtained for the time evolution of pressure (and, hence, mass concentration) at the gas–liquid interface. These solutions are in the form of series with respect to fractional differ-integral operators. The asymptotic solutions for the two limiting cases of compression—slow and fast compression—have been established as well. Then several particular examples of the law of gas volume variation are considered. Among them, the law of a linear volume variation is the most interesting for practical purposes, in which case numerical values of the dimensionless pressure as a function of dimensionless time are provided.

Mathematical modeling of unsteady flow with uniform/non-uniform temperature and magnetic intensity in a half-moon shaped domain

The mathematical modeling of two-dimensional unsteady free convective flow and thermal transport inside a half-moon shaped domain charged in the presence of uniform/non-uniform temperature and magnetic effects with Brownian motion of the nanoparticles has been conducted. Thirty-two types of nanofluids in a combination of various nanoparticles and base fluids having different sizes, shapes, and solid concentrations of nanoparticles are chosen to examine the better performance of heat transfer. The circular boundary is cooled while the diameter boundary is heated with uniform/non-uniform temperature. An external uniform/non-uniform/periodic magnetic field is imposed along diameter. The powerful partial differential equations solver, finite element method of Galerkin type, has been engaged in numerical simulation. The numerical solution's heat transfer mechanism reaches a steady state from the unsteady situation within a very short dimensionless time of about 0.65. The thermal transport rate enhances for increasing buoyancy force whereas decreases with higher magnetic intensity. The uniform thermal condition along the diameter of half-moon gives a higher thermal transport rate compared to non-uniform heating conditions. The non-uniform magnetic field provides greater values of the mean Nusselt number than the uniform field. In addition, the outcomes also predict that a better rate of temperature transport for kerosene-based nanofluid than water-based, ethylene glycol-based, and engine oil-based nanofluid. The heat transfer rate is observed at about 67.86 and 23.78% using Co-Kerosene and Co-water nanofluids, respectively, with an additional 1% nanoparticles volume fraction. The blade shape nanoparticles provide a better heat transfer rate than spherical, cylindrical, brick, and platelet shapes. Small size nanoparticles confirm a higher value of average Nusselt number than big size. Mean Nusselt number increases 22.1 and 5.4% using 1% concentrated Cu-water and Cu-engine oil nanofluid, respectively than base fluid.

Numerical Simulations of a Freely Falling Rigid Sphere in Bounded and Unbounded Water Domains

Abstract Numerical studies were conducted on the hydrodynamics of a freely falling rigid sphere in bounded and unbounded water domains to investigate the drag coefficient, normalized velocity, pressure coefficient, and skin friction coefficient as a function of dimensionless time. The bounded domain was simulated by bringing the cylindrical water container’s wall closer to the impacting rigid sphere and linking it to the blockage ratio (BR), defined as the ratio of the projection area of a freely falling sphere to that of the cross-sectional area of the cylindrical water container. Six cases of bounded domains (BR = 1%, 25%, 45%, 55%, 65%, and 75%) were studied. However, the unbounded domain was considered with a BR of 0.01%. In addition, the k–ω shear stress transport (SST) turbulence model was used, and the computed results of the bounded domain were compared with those of other studies on unbounded domains. In the case of the bounded domain, which has a higher value of BR, a substantial reduction in normalized velocity and an increase in the drag coefficient were found. Moreover, the bounded domain yielded a significant increase in the pressure coefficient when the sphere was half-submerged; however, an insignificant effect was found on the skin friction coefficient. In the case of the unbounded domain, a significant reduction in the normalized velocity occurred with a decrease in the Reynold number (Re), whereas the drag coefficient increases with a decrease in Reynolds number.

Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

AbstractInjection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction. For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.

Radiation effect on unsteady MHD mixed convection of kerosene oil-based CNT nanofluid using finite element analysis

This work conducts a numerical analysis of thermal radiation with a semicircular heater on the middle part of the bottom wall and a sliding lid on the top in a square enclosure. Magnetohydrodynamic (MHD) unsteady mixed convection for kerosene oil-based CNT nanofluid is studied. The finite element-based Galerkin residual technique is used to obtain nonlinear dimensionless governing equations. The thermal conductivity and dynamic viscosity models incorporate nanoparticle Brownian motion. Simulations were conducted for Reynolds number = 100, Hartmann number = 10, Richardson number = 1, and particle concentration = 0.05. The effects of fluid velocity magnitude, pressure gradient, temperature gradient magnitude, average temperature, bulk temperature, drag force of the sliding lid, and Nusselt number of the semicircular heater were investigated for different radiation parameters and dimensionless time. Results showed that increasing radiation intensity and dimensionless time improves fluid velocity, pressure gradient, and temperature gradient but decreases the heat transfer rate of the semicircular heater. Furthermore, the drag force of the moving lid is likewise found to be substantially dependent on the radiation parameter as well as dimensionless time. It is worth noted that after a while, the considered parameter exhibits consistent behavior.

Thermophysical properties of Kerosene oil-based CNT nanofluid on unsteady mixed convection with MHD and radiative heat flux

Oil-based nanofluids are used to strengthen the stability of nanofluids as well as their thermophysical properties when they are exposed to high temperatures. The time-dependent thermophysical characteristics of multiwalet carbon nanotubes for kerosine oil-based nanofluid are numerically explored in this study. Considering a constant magnetic field, the radiative domain is examined in a lid-driven squared shape cavity with a semicircular heater on the middle part of the bottom wall. The Galerkin residual technique based on finite elements is used to obtain nonlinear dimensionless governing equations. Thermal conductivity along with dynamic viscosity models integrate Brownian motion of nanoparticles. The Reynolds number, the Hartmann number, the Radiation Parameter and the Richardson number are assumed to be constant to account for the fluctuation in solid volume fraction (ϕ = 0% to 10%). The results demonstrated that particle concentration improves the nanofluid’s thermophysical properties from 1 to 9 times than the 0% concentration and the heat transfer rate from 1 to 3 times. In addition, dimensionless time enhances all except the heat transfer rate and drag force of the sliding lid. It is worth noting that the considered parameter exhibits consistent behavior after a while.

Enhanced production of Bacopa saponins by repeated batch strategy in bioreactor.

Cultivation of cell suspension culture of Bacopa monnieri targeting the production of bacosides was explored in a 5-l stirred tank reactor using statistically optimized conditions. The bioreactor cultivation conditions were modified and this led to profuse biomass growth (2.81 ± 0.20g/l) and total bacosides (1.26 ± 0.23mg/g in cells and 0.60 ± 0.11mg/l in fermenter broth) production in 9days. The values of static volumetric mass transfer coefficient (kLa), dimensionless mixing time (Nm) were measured in the bioreactor. The culture grew efficiently and produced enhanced amount of bacoside A (5.59 ± 0.41mg/g total bacosides in cells and 3.12 ± 0.13mg/l in the fermenter broth) using one cycle of repeated batch strategy adopted in the bioreactor for 15days. The intracellular concentration of bacoside A3 (1.18 ± 0.11mg/g), bacopaside II (2.09 ± 0.35mg/g), bacopaside X (0.79 ± 0.17mg/g) and bacopasaponin C (2.24 ± 0.23mg/g) were significantly higher in repeated batch as compared to batch bioreactor cultivation. The yield of total bacosides in the fermenter broth was 5-times higher in repeated batch as compared to batch cultivation. This strategy can be helpful for the enhanced production of other valuable triterpenoid saponins.

Pore-scale simulation of adaptive pumping remediation in heterogeneous porous media

Spilled petroleum hydrocarbons pose a long-term threat to surrounding soil and groundwater, so the design of related remediation methods exhibits a growing global concern. Numerous innovative methods have been developed based on Pump-and-Treat (P&amp;T) technology, which is the most commonly used decontamination method. Understanding the pore scale remediation mechanism of adaptive pumping is essential to the development of a decontamination scheme. In this study, the phase-field method was used to capture the evolution of the two-phase interface in a pore scale heterogeneous model during the period of adaptive pumping, and the influences of displacement patterns and wettability on remediation efficiency were investigated systematically. The results demonstrate that the model has the shortest dimensionless breakthrough time under mix-wet conditions, while it has the longest dimensionless breakthrough time under water-wet conditions. Compared with positive pumping, the growth of the ultimate remediation efficiency of adaptive pumping reaches the maximum (11.39%) under mix-wet conditions with Ca = −4.7, M = −2. The remediation mechanism of the adaptive pumping includes increasing the swept area near the boundary, extending the maintenance time of the driving pressure difference, and expanding the interfacial area between the injected fluid and the contaminant. These mechanisms indicate that a higher remediation efficiency can be obtained when adaptive pumping is applied combined with some innovative decontamination approaches, such as chemically enhanced flushing technology and in situ thermal treatment technology.

Mixed convection heat transfer in a lid-driven enclosure with a double-pipe heat exchanger

The numerical investigation of mixed convection in a heat exchanger with double-pipe, where the upper lid is given a constant velocity, is presented in this paper. The governing equations, as well as the boundary conditions, define the physical problem. The boundary conditions and governing equations are translated into non-dimensional form and solved by means of a finite-element methodology based on the Galerkin weighted residual. The investigation is conducted for three different governing parameters; namely, Prandtl number (Pr), Richardson number (Ri) and Reynolds number (Re). The outcomes are presented in terms of streamlines, isotherms and average heat transfer rate. Computations are done for a range of Ri (0.01 ≤ Ri ≤ 10), Re (50 ≤ Re ≤ 500), and Pr (1 ≤ Pr ≤ 10) for different dimensionless time (τ = 0.1, 0.5, 1). It is found that the influence of Ri on streamlines, isothermal lines, and heat transfer rate is significant and the maximum heat transfer is gained when values of Ri and Re are higher and Pr is lower. It is also found that the flow strength increases substantially with time and multiple vortices emerge as the convection rate increases.

Small-scale fluctuation and scaling law of mixing in three-dimensional rotating turbulent Rayleigh-Taylor instability.

The effect of rotation on small-scale characteristics and scaling law in the mixing zone of the three-dimensional turbulent Rayleigh-Taylor instability (RTI) is investigated by the lattice Boltzmann method at small Atwood number. The mixing zone width h(t), the root mean square of small scale fluctuation, the spectra, and the structure functions are obtained to analyze the rotating effect. We mainly focus on the process of the development of plumes and discuss the physical mechanism in the mixing zone in rotating and nonrotating systems. The variation of kinetic energy spectra E_{u} and temperature energy spectra E_{θ} with the dimensionless rotation Ωτ demonstrate the suppression effect of rotation. Two scaling laws between the mixing layer width h(t) and dimensionless time t/τ are obtained at various Coriolis forces(sqrt[h(t)]≃t^{0.9} and sqrt[h(t)]≃t^{0.35}). The rotation increasingly suppresses the growth of the mixing layer width h(t). The velocity and temperature fluctuations are also suppressed by the rotation effect. The relation between the Nusselt number (Nu) and the Rayleigh number (Ra) indicates that the heat transfer is suppressed by the rotation effect in the rotating RT system. The width of the inertial subrange increasingly narrows with increasing Ωτ.

On the Diffusion-controlled Transport and Accumulation of Lithium in an Electrode of a Lithium-based Galvanic Cell

The presented formulation in this paper provides the information in the form of lithium concentration profiles and lithium accumulation in the solid-state active material particles of a porous bed cathode of a lithium based galvanic cell as a function of dimensionless time during the cell discharge period under the condition of lithium diffusion in the cathode active material being a predominant process affecting the cell voltage versus time performance. The computed data is deemed to be useful in the predetermination of required cell discharge time corresponding to a desired state-of-charge of a lithium-based galvanic cell under the above-mentioned condition.

Long-time solutions of scalar hyperbolic reaction equations incorporating relaxation and the Arrhenius combustion nonlinearity

Abstract We consider an initial-value problem based on a class of scalar nonlinear hyperbolic reaction–diffusion equations of the general form $$\begin{align*} &amp; u_{\tau\tau}+u_{\tau}=u_{{xx}}+\varepsilon (F(u)+F(u)_{\tau} ), \end{align*}$$in which ${x}$ and $\tau $ represent dimensionless distance and time, respectively, and $\varepsilon&amp;gt;0$ is a parameter related to the relaxation time. Furthermore, the reaction function, $F(u)$, is given by the Arrhenius combustion nonlinearity, $$\begin{align*} &amp; F(u)=e^{-{E}/{u}}(1-u), \end{align*}$$in which $E&amp;gt;0$ is a parameter related to the activation energy. The initial data are given by a simple step function with $u({x},0)=1$ for ${x} \le 0$ and $u({x},0)=0$ for ${x}&amp;gt; 0$. The above initial-value problem models, under certain simplifying assumptions, combustion waves in premixed gaseous fuels; here, the variable $u$ represents the non-dimensional temperature. It is established that the large-time structure of the solution to the initial-value problem involves the evolution of a propagating wave front, which is of reaction–diffusion or reaction–relaxation type depending on the values of the problem parameters $E$ and $\varepsilon $.

Measuring binary black hole orbital-plane spin orientations

Binary black hole spins are among the key observables for gravitational wave astronomy. Among the spin parameters, their orientations within the orbital plane, ${\ensuremath{\phi}}_{1}$, ${\ensuremath{\phi}}_{2}$ and $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}={\ensuremath{\phi}}_{1}\ensuremath{-}{\ensuremath{\phi}}_{2}$, are critical for understanding the prevalence of the spin-orbit resonances and merger recoils in binary black holes. Unfortunately, these angles are particularly hard to measure using current detectors, LIGO and Virgo. Because the spin directions are not constant for precessing binaries, the traditional approach is to measure the spin components at some reference stage in the waveform evolution, typically the point at which the frequency of the detected signal reaches 20 Hz. However, we find that this is a poor choice for the orbital-plane spin angle measurements. Instead, we propose measuring the spins at a fixed dimensionless time or frequency near the merger. This leads to significantly improved measurements for ${\ensuremath{\phi}}_{1}$ and ${\ensuremath{\phi}}_{2}$ for several gravitational wave events. Furthermore, using numerical relativity injections, we demonstrate that $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}$ will also be better measured near the merger for louder signals expected in the future. Finally, we show that numerical relativity surrogate models are key for reliably measuring the orbital-plane spin orientations, even at moderate signal-to-noise ratios like $\ensuremath{\sim}30--45$.

Design of an electrochemical flow reactor prototype to the electro-oxidation of amoxicillin in aqueous media using modified electrodes with transition metal oxides

This research study integrated the development of modified large-size catalytic electrodes while employing painting and electrophoresis for Ti anodes and a proposed cylindrical reactor design using computational fluid dynamics (CFD) and experimental characterization tests. These development studies explored flow-by and parallel flow reactor configurations to remediate aqueous Amoxicillin (AMX). Simulation studies suggested that the velocity magnitude field and resident time distribution (RTD) curves were improved when the parallel flow configuration was employed. These findings followed based on the width and tail of the calculated RTD when both configurations were considered. The improved behaviors were associated with the avoiding of canalization or low-velocity stagnation zones in the reactor. Additionally, in the parallel flow configuration, the RTD curve maximum was reached near the dimensionless time, θ = 1, when general laminar flow rates (Re of 85 and 113) were used. Through both calculated potential and current distributions, in the parrel flow system, the potential field has a uniform distribution in the flow direction, with minimal edge formation. Since flow and electrical simulation suggested that the parallel flow configuration is better able to perform an electrochemical process, it was chosen and a processor was constructed. The constructed prototype achieved a maximum degradation efficiency of 92.3% (COD), and abatement of acute toxicity, in the reactor equipped with an electrophoretic modified anode, employing a current density of 7.5 A m−2.

Time reversal of waves in hydraulics: experimental and theoretical proof with applications

Time reversal of waves is an intriguing wave property that underpins a breadth of applications in physics and engineering. Waves contain information about their sources and the media through which they propagate. Thus, time reversal of measured wave signals has the potential of localizing and characterizing wave sources and of inferring the properties of the medium. Herein, we experimentally demonstrate the time reversibility of acoustic waves propagating in water-filled viscoelastic high-density polyethylene (HDPE) pipes. Evidently, the two mechanisms that restrict time reversal are the stability of wave paths to perturbations and damping. Perturbations, however, are found to grow slowly in time (∼t 1/2) and are not critical for the time reversal of waves. To evaluate the effect of damping, we perform an order of magnitude analysis on the non-reversible terms of the coupled waveguide momentum equations and derive a dimensionless time reversal parameter TR showing that damping develops linearly with time (i.e. TR ∼ t). Subsequently, we apply the TR parameter to our experiments and relevant experimental proofs from the literature to find that the time reversal of waves only holds for TR ∼ 1 or less; hence providing a criterion to estimate the range over which time reversal-based wave techniques and methodologies are valid. Finally, we discuss the various existing applications of time reversal in hydro-environmental research and engineering and anticipate that the presented work will stimulate further development.

Nucleation in sessile saline microdroplets: induction time measurement via deliquescence-recrystallization cycling.

Induction time, a measure of how long one will wait for nucleation to occur, is an important parameter in quantifying nucleation kinetics and its underlying mechanisms. Due to the stochastic nature of nucleation, efficient methods for measuring large numbers of independent induction times are needed to ensure statistical reproducibility. In this work, we present a novel approach for measuring and analyzing induction times in sessile arrays of microdroplets via deliquescence/recrystallization cycling. With the help of a recently developed image analysis protocol, we show that the interfering diffusion-mediated interactions between microdroplets can be eliminated by controlling the relative humidity, thereby ensuring independent nucleation events. Moreover, possible influence of heterogeneities, impurities, and memory effect appear negligible as suggested by our 2-cycle experiment. Further statistical analysis (k-sample Anderson-Darling test) reveals that upon identifying possible outliers, the dimensionless induction times obtained from different datasets (microdroplet lines) obey the same distribution and thus can be pooled together to form a much larger dataset. The pooled dataset showed an excellent fit with the Weibull function, giving a mean supersaturation at nucleation of 1.61 and 1.85 for the 60 pL and 4 pL microdroplets respectively. This confirms the effect of confinement where smaller systems require higher supersaturations to nucleate. Both the experimental method and the data-treatment procedure presented herein offer promising routes in the study of fundamental aspects of nucleation kinetics, particularly confinement effects, and are adaptable to other salts, pharmaceuticals, or biological crystals of interest.