Dimensionless Time Research Articles

Viscous Rankine vortices

A generalized version of the Rankine vortex is taken as initial state in an infinite fluid domain in two dimensions. The inner rigid-body motion of the Rankine vortex is surrounded by an outer irrotational vortex, where the inner flow and outer flow are allowed to have different amplitudes. We study the time evolution in a viscous fluid, where the kinematic viscosity scales the unit of dimensionless time. By an inverse Hankel transform, the Rankine vortex appears as an integrated continuous spectrum of axisymmetric Fourier–Bessel modes with radial wave numbers k. Each of these velocity modes is represented by a Bessel function J1(kr) where r is the radial distance from the vortex center. The amplitude of each individual mode will decay exponentially at a rate of νk2, where ν is the kinematic viscosity. The decaying continuous Fourier–Bessel spectrum is calculated analytically, while the evolution of the flow field is found by numerical evaluation of an inverse Hankel transform. We also consider the presence of a free surface in the gravity field, where pressure distribution in the vertical direction is hydrostatic. The far field remains irrotational during the viscous decay.

Time-Conformable fractal systems of natural convection of tall fin inside two circular cylinders suspended by NEPCM

The incompressible smoothed particle hydrodynamics (ISPH) scheme is advanced to handle the conformable fractal differential equations of natural convection for a tall fin inside a cavity barred by nano encapsulated phase change material (NEPCM). The bottom circular cylinder is occupied by a porous medium plus a nanofluid, while the upper circular cylinder is filled by a nanofluid only. The conformable fractal operators generalize the classic idea of differentiability and allow for the generation of new and universal rates of variation. So, the study's novelty is revealing the validity of these operators in creating a new environment to look for more extended natural convection systems. The pertinent parameters are dimensionless time parameter τ(0-0.325), Rayleigh number Ra(103-106), Darcy parameter Da(10-2-10-5), cold source length LCold0.5-2.5, Stefan parameter Ste0.2-0.8, conformable fractal parameter α(0.93-1), and fusion temperature θf(0.05-0.95). The main outcomes showed the responsibility of α in speeding up the phase change process and the transition procedure of the convection flow. The nanofluid speed is reduced in the porous layer of a cavity, especially at the lower Darcy parameter. Different thermal conditions are altering the phase change material and strength of isotherms within a cavity.

Study on cavern evolution and performance of three mixers in agitation of yield-pseudoplastic fluids

The hydrodynamic performance of three mixers (single shaft central mixer (SSC), single shaft off-centred mixer (SSO), dual shaft off-centred mixer (DSO), was investigated in the mixing of yield-pseudoplastic fluids (xanthan gum solutions) in the laminar regime. To explore and determine the efficiency of three mixers, both numerical and experimental approaches were adopted. The fluid rheology was described by the Herschel–Bulkley rheological model. Computational fluid dynamics was employed to simulate the apparent viscosity distribution, mixing time, and the flow pattern inside the stirred tank. The developed model was validated through experimentally measured torque. The influence mechanism of the rotational speed and fluid rheology on the cavern evolution was explored deeply. The performances of three mixers in this work were compared at the constant power input and fluid rheology with respect to the flow pattern, mixing time, and mixing efficiency. The results verify that the faster the rotating speed, the greater influence of the fluid rheology on the cavern evolution, and the more uniform apparent viscosity distribution. Moreover, the mixing time decreases continuously as the increasing power consumption per unit volume, and the dimensionless mixing time of DSO mixer was nearly 42.8% and 6.1% shorter than that of SSC and SCO mixer at the same Reynolds number, respectively. According to the mixing efficiency criteria, these data also revealed that DSO was more efficient than SSC and SSO.

Experimental investigation of scour of sand beds by submerged circular vertical turbulent jets

The present work investigated the development of sand bed scour by submerged circular impinging vertical turbulent jets over a wide regime of jet diameters, exit velocities and impinging distances. The scour hole profiles were recorded with the optical method in order to present dynamic scour hole characteristics and their variation with any time. The results revealed that the scour profiles in the equilibrium state are similar and the geometries of the sour hole in the jet central region are only determined primarily by jet momentum flux. A semi-empirical equation has been developed for the maximum dimensionless scour depth in equilibrium state based on the obtained experimental data and theoretical analysis. The evolution of scour hole is found to be logarithmic, and three phases of temporal evolution were further distinguished. Finally, models for the prediction of variation of scour depth with time have been developed and validated, which could be used to assess the scour effects generated by impinging turbulent jets. The overall temporal evolution of the scour depth can be predicted by the erosion parameter Ec and the dimensionless time to reach equilibrium τ∞, which is superior to existing models in predicting the scouring process.

The Solution of Integrable nonlinear evolution equation with time-dependent coefficient

In this paper, we consider the evolution equation 𝑢𝑡 = [𝑚 + 𝑘𝜓(𝑢)]𝑢, 𝑡 > 0 where 𝑡 represents dimensionless time and 𝜓(𝑢) is given function of 𝑢. We focus attention on the case when 𝜓(𝑢) = 𝑘(𝑢 − 𝑎)(𝑢 − 1), while 𝑚 and 𝑘 are constants.

Numerical study of anomalous heat conduction in absorber plate of a solar collector using time-fractional single-phase-lag model

The primary purpose of this work is to analyze the intermediate behaviors in the thermal response of an absorber plate of a flat-plate solar collector, considering the non-Fourier effects. The Caputo fractional derivative is applied and the time-fractional single-phase-lag (FSPL) model is presented to study the non-diffusive process in the heat conduction through the absorber plates. In addition, the effect of variations in different parameters such as Vernotte number, dimensionless time, and thermo-physical parameter are studied on the temperature response of absorber plates. It has been apparent that the thermo-physical parameter can significantly affect the thermal behaviors of absorber plates, and that for small quantities of this parameter, the temperature distribution follows the wave-like behaviors. To validate this model, the fractional model is presented for a thin metal film, and non-diffusive heat conduction has been investigated in detail, and the results of the fractional model are compared to those of the dual-phase-lag (DPL) model, which proves the precision of the fractional model proposed in this work. Also, the effect of variation in the time rate of the initial condition has been conducted on the thermal distribution of metal films. It has been discussed that the fractional model proposed can describe a wide range of behavior in thermal response, including diffusive-like and wave-like behaviors. In addition, it has been found that the non-Fourier effects are quite remarkable at earlier times, so it would be important to consider such effects when the time instances are smaller than the relaxation time.

The role of dual-phase-lag (DPL) heat conduction model on transient free convection flow in a vertical channel

This work investigates the role of dual-phase-lag (DPL) heat conduction model on transient free convection flow of an incompressible viscous fluid in a vertical channel. The semi-analytical solutions for temperature, velocity, and skin-friction in a dimensionless form are presented in Laplace domain using the Laplace transform technique, while the Laplace expression are inverted back to the time domain, using Riemann sum approximation (RSA). The effects of dimensionless time, Prandtl number, thermal relaxation time, and thermal retardation time on dimensionless temperature and velocity profiles are graphically demonstrated. The numerical values for variation of dimensionless temperature, velocity, and skin-friction for pertinent flow parameters are computed and presented in tabular form. It is found that the increase in dimensionless time leads to an increase in both temperature and velocity, while decrease in thermal relaxation time and retardation time account for the increase in temperature and velocity. Also, the temperature is higher when thermal relaxation time precedes the thermal retardation time for air (Pr=0.71). However, the temperature is highly recorded when thermal retardation time precedes the thermal relaxation time for water (Pr=7.0).

Using capillary pressure curves when searching for analog objects

In this work, the capillary pressure curves were approximated using fractions of various types for the conditions of individual oil deposits of the West Siberian oil and gas province. A mathematical model of capillary curves in the coordinate axes of dimensionless time from the normalized water saturation has been created. The obtained models make it possible to search for analog objects and effectively solve the problems of increasing the efficiency of developing low-profitable deposits with hard-to-recover reserves based on comparing the regression equations of generalized models with models of the required deposits.

Input Uncertainty and Implication for Modeling Generic and High-Fidelity Transient Convection Problems

Transient processes and uncertainty propagation impacting the transient temperature variation profile for a plate heated from the top and convection cooled at the bottom surface are investigated. The model dimensionless input parameters, such as the Biot number Bi and dimensionless initial conditions, are formulated describing physical properties of the plate and ambient medium with subsequent impact on the dimensionless temperature variation. As is shown, in the case of small Bi, dimensionless relaxation time of the temperature variation toward its steady state is proportional to and can be very large. For large Bi, the temperature variation usually passes through a peak before reaching its stationary profile. Stochastic nature of the dimensionless temperature variation is explored. As is found, the amplitude of its stochastic spread depends, in general, on the mean values of the dimensionless inputs at a fixed standard deviation. As is also shown, dimensionless time evolution of the uncertainty amplitude depends crucially on standard deviations of the dimensionless input parameters; it may increase or decrease with time, or stay small over time. Finally, uncertainty propagation in a high-fidelity model of a copper block, used in an experimental setup, is compared with the developed generic plate model.

Experimental study on the rebound characteristics of high temperature alumina droplets impacting on an inclined cold wall

The rebound characteristics of high-temperature alumina droplets impacting on the cold wall of a solid rocket motor are of great significance for the accurate prediction of initial slag deposition and calculation of two-phase flow inside motors. In this paper, the impact experiment of alumina droplets on an inclined cold wall is carried out by a high-temperature alumina droplet impaction experiment system. The study shows that as the impact angle increases from 10° to 45°, three types of morphologies of rebound droplets are observed, namely multiple sharp corners mode, single “tail” mode, and “heart” mode, respectively. Under 10° impact angle condition, the first sharp angle is dominated by the tangential momentum component and the condensation on the wall; as the impact angle increases to 30°, the tangential momentum component has an increased influence on the rebound morphology, and the form of “tail” is influenced by the tangential momentum component and wall condensation; when the impact angle increases to 45°, the left contact surface partial detachment is dominated by rolling inertia. The study also found that the droplet size will profoundly affect the morphology of the droplet when it rebounds, and the phenomenon of “sharp corners” and “tail” gradually disappears as the droplet diameter decreases. As the impact angle increases, the dimensionless contact time of the droplet decreases, and the relationship between the dimensionless contact time and the normal Weber number of the droplet is obtained.

Research on the effect of asymmetric bubbles on the load characteristics of projectiles during an underwater salvo

This paper analyzes the effect of bubbles on the load characteristic of projectiles launched underwater with transverse-flow under different dimensionless launch time intervals. The realizable k−ε turbulence model and energy equation, as well as the volume of fluid method and overlapping grid technique, were adopted. Additionally, validations of numerical approach and grids independence validation were carried out. Evolution of bubbles at tube outlet, time-domain characteristic and frequency domain characteristic of lateral force, vertical force-torque, and motion characteristics are studied. The results show that spilled gas from the tube outlet fuses and moves in a transverse-flow direction. The pressure pulsation, which is caused by the bubble elastic effect, leads to high-frequency pulsation laws of the load characteristic. In the initial stage of the movement, the motion laws of projectiles under different launch time intervals are similar. At ΔT≤1.2, the flow interference between two projectiles is large, which seriously affects the ballistic stability and safety.

A nickel-based metal-organic framework for efficient SF6/N2 separation with record SF6 uptake and SF6/N2 selectivity

Seeking top-performing adsorbents with salient structural stability and renewability to realize efficient adsorption and enrichment of sulfur hexafluoride (SF6) from the gaseous blend is of great importance. Here, an ultramicroporous nickel-based metal-organic framework (MOF), termed Ni(NDC)(TED)0.5 with multiple naphthalene rings-functionalized pore environment, was synthesized to efficiently separate SF6/N2 mixture. Equilibrium adsorption results show that Ni(NDC)(TED)0.5 possesses a record IAST SF6/N2 selectivity (750) and SF6 uptake (61.86 cm3 cm−3), higher than all adsorbents reported so far, and resolves the trade-off phenomenon between SF6 adsorption capacity and SF6/N2 selectivity. In particular, the selectivity is 2.3 times that of the current highest material (SBMOF-1). Furthermore, theoretical calculations reveal that the pore centers of material are the most energetically-favorable preferential adsorption sites. Meanwhile, the stronger affinity between SF6 and framework is attributed to the shorter interaction distance between F atom on SF6 and pore wall. Breakthrough tests confirm this MOF can completely separate SF6/N2 mixture. The breakthrough uptake (56.60 cm3 cm−3) and dimensionless time (τ: 281.8) of this material for SF6 are separately 1.6 and 2.5 times that of the currently reported benchmark (Cu-MOF-NH2). In combination of excellent structural stability and recyclability, this material may be an ideal material for the recovery of SF6 from SF6/N2 mixture.

Numerical study of low Reynolds number effect on MHD mixed convection using CNT-oil nanofluid with radiation

An enclosure with a moving lid is commonly used in heat and mass transmission. Also, many investigations have been done so far on a mixed convective flow in a cavity, but no research has been done to observe the low Reynolds number effect in the presence of MHD and radiation in a cavity with a semi-circular heater incorporated kerosine oil-based CNT nanofluid. In addition, oil-based nanofluid makes the working fluid more stable at a higher temperature. This study numerically investigates the time-dependent effect of low Reynolds number on Kerosene oil-based CNT nanofluid with magnetic field and radiation. The governing equations were employed with the finite element method based Galerkin residual technique. Brownian motion of nanoparticles was considered to determine the thermal conductivity and dynamic viscosity. Lower values of Reynolds number are taken, such as 50 to 200 with fixed values of radiation parameter, the particle concentration, the Hartmann number, and the Richardson number. The results were illustrated as heat transfer and fluid flow for three dimensionless time conditions. Results indicate that increasing the fluid velocity improves the Nusselt number and drag force. The vorticity rises to 54% while increasing the fluid velocity, however, the pressure gradient and average temperature become lower. It is also found that the average fluid velocity is 2.2 times higher in the Re = 50 than in the Re = 100. For the time dependency of this study, the thermo-hydrodynamics behavior changes with dimensionless time. Finally, this study would be a guide for designing thermal devices related to heat transfer, especially using the Kerosene oil-based CNT nanofluid under different conditions.

Dimensionless Impedance Method for General Design of Surge Tank in Simple Pipeline Systems

The design of surge protection devices is a practical issue for the management of pressurized pipeline systems. Depending on the flow status, dimension, material, and fluid properties of a particular pipeline, the generation of hydraulic transients and their interactions with surge protection devices have been explored considering different conditions for various pipeline systems. The resonance between the pipeline elements and surge energy absorption function of the hydraulic structure should be adaptively considered for each pipeline system. To comprehensively address surge generation and surge alleviating process, this study introduced dimensionless equations of fluid motion and continuity, and their solutions were developed in the dimensionless frequency domain. The impact of the surge tank, pressure accumulator, and its connector were also developed in terms of dimensionless operators. The impact of distinct flow conditions and pipeline properties was successfully addressed by an integrated parameter, dimensionless resistance, which also provided a unified condition for water hammer similarity in reservoir pipeline surge tank pipeline valve (RPSPV) systems. The development of dimensionless hydraulic impedance expressions along a pipeline system and its conversion into a response function provides a normalized pressure response in the dimensionless time domain. Excellent agreement was found between transient simulations using the developed method and those obtained using existing methods. The integration of a dimensionless approach into a metaheuristic engine provides a general platform for surge tank (ST) design in the comprehensive bounds of flow and pipeline conditions.

Influence of large seed particle on acoustic particle interaction dynamics: A numerical study

Acoustic agglomeration as a promising preconditioning process for fine particle removal has been proven to be inefficient for submicron particles. In order to enhance the performance of acoustic agglomeration, large seed particles have been introduced into the flue gas. To understand the influence of seed particles on acoustic agglomeration, a nondimensional model of particle interaction was developed by taking into account all important particle interaction mechanisms. The simulated particle trajectories were validated against experimental data. The interaction dynamics of a seed particle and its neighboring fine particles was examined, and the dimensionless first collision time under different conditions was obtained. The results suggest that the enhancement of acoustic agglomeration with seed particle is mainly due to the acoustic wake effect. The overall collision kernel for the acoustic agglomeration was referred from the collision time. The results reveal that the dimensionless collision kernel almost increases linearly with the Stokes number of the seed particle, whereas its dependence on the Schmidt number of the fine particle varies significantly. The collision kernel for acoustic agglomeration was further compared with traditional collision kernels based on differential sedimentation, Brownian diffusion, laminar shear and turbulent shear. The results demonstrate that acoustic field indeed remarkably enhances the collision rate.

Cascade coalescence of droplets in a sudden expansion microchannel

Cascade coalescence refers to the successive coalescence of droplets induced by the shape change of coalescing droplets. In this paper, the dynamics of cascade coalescence in a sudden expansion microchannel is studied experimentally, focusing on the evolutions of dimensionless widths of the first neck and the second neck with dimensionless time. They conform to the same power law relationship as in double coalescence, and the exponent keeps constant under the change of the viscosity of dispersed phase. However, the viscosity of dispersed phase can affect the appearance time of the second neck, thus to affect the droplet deformation. The formation of the first neck is caused by the capillary waves on the interface, while the growth of the first neck could aggravate the instability of the flow field inside the droplet, and then induce the formation of the second neck. The increase of the viscosity of dispersed phase can inhibit the instability of flow field, accordingly inhibit the occurrence of cascade coalescence.

Role of thermophoresis on unsteady/steady mixed convective flow in a vertical channel having convective boundary conditions

A numerical as well as analytical investigation is performed to study time dependent/steady state mixed convection flow in a vertical channel in presence of thermophoresis having convective boundary conditions. The main objective of this paper is to present exact solutions for steady state mathematical model under relevant boundary conditions and numerical solutions for time dependent situation under relevant initial and boundary conditions. The impact of various controlling parameters such as dimensionless time t, Schmidt number Sc, Biot numbers Bi_{1} and Bi_{2}, buoyancy ratio b and thermophoretic coefficient k have on the flow patterns is discussed. Graphical results show that the effect of increasing two or more of the parameters simultaneously with high mixed convection parameter changes the flow from bi-directional to unidirectional. Also, the occurrence of a flow reversal depends on buoyancy and dimensional time. Furthermore, there exists a convergence of Sherwood number values at the cold plate when thermophoretic values are high.Article HighlightsWhen buoyancy dominates the flow, a decrease of reverse flow at the cold plate is observed as thermophoresis approaches its peak.If Schmidt number increases simultaneously with time, a wider region across the channel where concentration of particles is zero is observed.When thermophoretic values are low, an increment in time reduces Sherwood numbers. Sherwood number values are observed to converge at the cold plate when thermophoretic values are high. These findings have implications in the developments of thermophoretic cells used in biochemical and medical researches because Sherwood numbers imply negative concentration fluxes at boundaries.

BPNN and CNN-based AI modeling of spreading and icing pattern of a water droplet impact on a supercooled surface

A water droplet impacting on a supercooled surface normally experiencing spreading and freezing is a complex process involving fluid flow, heat transfer, and phase change. We established two models to, respectively, predict the spreading dynamics of a water droplet impact on a supercooled surface and classify the icing patterns to predict the corresponding surface supercooling degree. Six important factors are used to characterize droplet spreading, including Reynolds number, Weber number, Ohnesorge number, surface supercooling degree, the maximum spreading factor, and the dimensionless maximum spreading time. A Back Propagation Neural Network model, including four inputs and two outputs, is established, containing a hidden layer with 15 neurons to perform the non-linear regression training on the spreading factors of 778 groups of an impact water droplet. The trained model is adopted to predict the spreading factors of 86 groups of a water droplet impact on the supercooled surface. The second model is developed to discern and classify the experimentally captured three different icing patterns. Different clustering methods are performed on 116 icing images, including gray-scale and red-green-blue (RGB) clustering. Then, two convolution neural network models of VGG-19 (Visual Geometry Group-19) and VGG-16 are established to classify, train, and test the icing images by gray-scale and RGB clustering methods. The K = 2 gray-scale clustering and the VGG-19 model exhibits the highest accuracy at 90.57%. The two models developed in this study can, respectively, predict the essential factors characterizing spreading dynamics of an impact droplet on a cold surface and predict surface supercooling degree based on an icing pattern.

A study on the flow interference characteristics of projectiles successively launched underwater

This paper analyzes the flow interference characteristics of projectiles successively launched underwater with 6 degrees of freedom for different dimensionless launch time intervals and different dimensionless transverse-flow speeds. The realizable k−ε turbulence model and energy equation, as well as the volume of fluid method and overlapping grid technique, are used. Additionally, a verification of the numerical method and a validation of the grid independence are presented. The pressure distribution on the inflow side and backside, the hydrodynamic parameters, the trajectory, and the pitch attitude are studied with the focus on the evolution of hairpin vortex packets in free wake flow. The results show that the hairpin vortex packet in the free wake flow is composed of a multistage hairpin vortex and a low-speed streak region with a stream scale that runs along the interior of the hairpin vortex packet. At higher transverse-flow speeds, the pressure coefficient and hydrodynamic coefficient of the second projectile increase as the launch time interval increases. Due to the effects of transverse flow, when the secondary projectile passes through the core region of the wake vortex, the pressure of uneven distribution characteristics greatly reduces and the trajectory stability increases. To maximize the efficiency and success rate of projectiles successively launched underwater, the second projectile should be launched at ΔT=2.0.

Unsteady periodic natural convection in a triangular enclosure heated sinusoidally from the bottom using CNT-water nanofluid

This research examines the natural convection phenomena in a triangular enclosure, assumed as a mechanical chamber. Water-based CNT-nanofluid was used as the fluid. The nature of the flow is unsteady, and a sinusoidal heat source is situated at the bottom of the triangle. The inclined two walls of the triangle are assumed as cold temperature. Based on the finite element method, dimensionless nonlinear governing equations were obtained employing the Galerkin weighted residual method. Brownian motion of nanoparticles was considered to determine the thermal conductivity and dynamic viscosity. Rayleigh number (Ra), oscillation period τp, and dimensionless time τ are assumed as primary controlling factors, and nanofluid concentration is considered as constant φ = 0.04. The result indicates that the heat transfer rate displays varied patterns varying the Rayleigh number, and it rises as the oscillation period increases. The fluid temperature and flow fields exhibit periodic behavior due to the sinusoidal heat source. The findings of this work can be utilized to build an effective cooling or heating system for the mechanical chamber, ensuring that temperature distributions are effective and consistent.