Dimensionless Time Research Articles

Numerical simulation on thermal stratification performance in thermocline water storage tank with multi-stage middle perforated obstacles

• Three 3D geometric models of thermocline water storage tanks with different numbers of obstacles were established. • The effects of inlet velocities on the tank were analyzed. • The variations of obstacle numbers affect seriously the thermal stratification. Water storage tank is a critical part of the thermal storage system. This paper established three 3D geometric models of cylindrical thermocline water storage tanks with different numbers of middle perforated obstacles to enhance the thermal storage performance of the water storage tank. The numerical simulation method was used to investigate the influence of the number of middle perforated obstacles and inlet velocity on the thermal stratification degree of the tank. Results showed that the increase in the middle perforated obstacle number could optimize the thermal stratification of the thermocline water storage tank. In addition, when v i increases from 0.15 m/s to 0.30 m/s, and the charging dimensionless time t* changes from 0.2 to 1, the value of the thermal stratification number Str of the one obstacle tank decreases, while the changing trend of the tank with two is opposite, and the Str of the tank with three is always close to 1. The thermocline thickness of the tank with different numbers of obstacles is quite different. An increase of the number of obstacles can effectively suppress the increase of the thermocline thickness at high v i in the tank, which means a superior thermal performance was achieved for the tank.

Decoherence effects in quantum nondemolition measurement induced entanglement between Bose–Einstein condensates

We study the robustness of quantum nondemolition (QND) measurement induced entanglement between Bose–Einstein condensates (BECs). We consider an experimental scheme where two BECs are placed in the paths of a Mach–Zehnder interferometer, and a QND interaction creates entanglement between coherent light and the atoms. We analyze the two dominant channels of decoherence, atomic dephasing and photon loss on the entangled states produced by this scheme. We calculate the effect of dephasing on the variance and expectation values of the spin operators, entanglement and correlation criteria. Our analysis does not use the Holstein–Primakoff approximation, and is capable of modelling long light–atom interaction times, producing non-Gaussian states beyond the two-mode squeezed states. In the presence of dephasing, the entangled states are robust in the macroscopic limit as long as the dimensionless interaction time is less than , where N is the number of atoms in the BEC. For photon loss, the entangled states generated by long interaction times show a remarkable robustness that makes the scheme promising for various quantum information applications.

Migration of a viscoelastic drop in a ratchet microchannel

We numerically investigate the deformation and migration of a viscoelastic droplet in a ratchet microchannel, a phenomenon that occurs in many practical applications and involves rich physics due to the associated complex geometry and non-Newtonian nature of the fluid. The numerical method required to handle viscoelastic fluid is also extremely challenging, especially when the Weissenberg number, a dimensionless relaxation time related to the viscoelastic fluids, is high. In the present study, we incorporate a log-conformation stabilization method that overcomes this numerical problem and examine the shape transition dynamics of a viscoelastic droplet for a wide range of parameters, including the wavelength and type of the ratchet, Weissenberg number, and Reynolds number. The droplet dynamics in a ratchet microchannel is compared to that in a straight channel. The presence of the ratchet section causes a distinct stress distribution in the viscoelastic droplet, which significantly influences the residence period, the shape of the droplet in the microchannel, and shape recovery dynamics when flowing out of the channel. • Deformation and migration of a viscoelastic droplet in a ratchet microchannel is investigated. • A log-conformation stabilization method is incorporated. • The wavelength and type of the ratchet play an important role in the dynamics and residence period. • The roles of Reynolds, Capillary, and Weissenberg numbers have been investigated. • The study may help understand the migration of biological cells in complex geometries.

Nonlinear Outcome of Coagulation Instability in Protoplanetary Disks. I. First Numerical Study of Accelerated Dust Growth and Dust Concentration at Outer Radii

Our previous linear analysis presents a new instability driven by dust coagulation in protoplanetary disks. The coagulation instability has the potential to concentrate dust grains into rings and assist dust coagulation and planetesimal formation. In this series of papers, we perform numerical simulations and investigate the nonlinear outcome of coagulation instability. In this paper (Paper I), we first conduct local simulations to demonstrate the existence of coagulation instability. Linear growth observed in the simulations is in good agreement with the previous linear analysis. We next conduct radially global simulations to demonstrate that coagulation instability develops during the inside-out disk evolution owing to dust growth. To isolate the various effects on dust concentration and growth, we neglect the effects of back-reaction to a gas disk and dust fragmentation in Paper I. This simplified simulation shows that neither back-reaction nor fragmentation is a prerequisite for local dust concentration via the instability. In most runs with weak turbulence, dust concentration via coagulation instability overcomes dust depletion due to radial drift, leading to the formation of multiple dust rings. The nonlinear development of coagulation instability also accelerates dust growth, and the dimensionless stopping time τ s reaches unity even at outer radii (>10 au). Therefore, coagulation instability is one promising process to retain dust grains and to accelerate dust growth beyond the drift barrier.

Effect of unsteady relative thermal and concentration boundary layer thickness on mixed convection in a partially heated contaminated enclosure

Double diffusive flow under mixed convection has become a significant area of research. This study aims to evaluate the Lewis number effect in such a double-diffusive problem in a roof-based air-ventilated system. The Lewis number 0.01 ≤ Le ≤ 5 was chosen for the study, considering other parameters as constant to observe the impact of different heat and mass transfer properties varying the dimensionless time 0.1 ≤ τ ≤ 1. The Galerkin residual technique was chosen to generate the governing equations. The outcomes have been plotted in streamlines, isotherms, isoconcentration, heat and mass transfer, average fluid temperature and mass concentration. The major findings elucidate that heat and mass transfer rate augments when Lewis number goes higher and vice versa. Moreover, when the thermal diffusivity is higher than the mass diffusivity, the average fluid temperature and mass concentration become lower. Overall, this study will be a guide on double-diffusive system design, such as roof-based air ventilation systems.

Speed of fragments ejected by an expanding liquid tin sheet

We experimentally investigate the speed of fragments produced by ligament breakup in laser-induced deformation of tin microdroplets into axisymmetric sheets. A double-frame backlit camera is used to obtain the speed of the fragments and the time of their detachment. We show that by normalizing these speeds to the initial expansion speed of the sheet, all data collapse onto a single universal curve that is a function of the dimensionless time ${t}_{d}/{\ensuremath{\tau}}_{c}$ only, where ${\ensuremath{\tau}}_{c}$ is the capillary time. We further find that this universal curve is explicitly independent of the droplet's Weber number.

Ionic Seebeck coefficient and figure of merit in ionic thermoelectric materials

Ionic thermoelectric (i-TE) materials have attracted much attention due to their large ionic Seebeck coefficients, but the basic relations between the property parameters and operation performances are still open questions. We derive the ionic Seebeck coefficient, Std, and the dimensionless ionic figure of merit, ZtdT, from the view of field evolutions of temperature, voltage, and ionic concentration. Different from traditional knowledge, only ionic Eastman entropies determine Std, while ionic diffusion coefficients can only affect the speed of the voltage to reach the steady state. The figure of merit for electronic thermoelectric materials is inapplicable for i-TE materials as the voltage build-up is dominated by the temperature field evolution instead of the capacitor constant. By combining the net charge storage and dimensionless response time, the proposed ZtdT can embody the transient and average efficiencies in i-TE materials, which also opens new windows for the optimization of i-TE materials.

Heat transfer analysis of phase change material composited with metal foam-fin hybrid structure in inclination container by numerical simulation and artificial neural network

Improving the heat transfer performance of phase change material (PCM) plays a crucial role in designing efficient latent heat thermal energy storage (LHTES) systems. The purpose of this study is to address and elucidate the effects of the metal foam-fin hybrid structure and the inclination angle on the phase change process by using the numerical simulation method. An experimental system for the validation of the numerical models is established. The solid–liquid phase interfaces, streamlines, liquid fraction (f), the dimensionless time (Fo×Ste), and average Nusselt number (Nu¯) of PCM in the container enclosure at inclination angles of 0°, 30°, 60°, and 90° with six kinds of enhanced heat transfer structures, including fin, metal foam, and metal foam-fin hybrid structures, are compared. Besides, the liquid fraction and Nu¯ during the phase change process are predicted by the artificial neural network (ANN). Results demonstrate that the optimized heat transfer performance of the metal foam-fin hybrid structure could reduce the melting time. In addition, the increase in the number of fins can improve the heat transfer performance and reduce heat accumulation in the top area with the inclination angle increasing. Compared to pure PCM at the inclination angle of 90°, the values of Fo×Ste of metal foam-1 fin and metal foam-5 fins hybrid structures are reduced by 52.69% and 60.02%, respectively. However, the energy storage density per unit volume decreases as a function of the increasing inclination angles and the number of fins within a case. Furthermore, the excellent predictions of f and Nu¯ are obtained by ANN with MSE and R2 of 9.6480 × 10−5, 0.9990 and 0.0150, 0.9937, respectively.

Numerical study on heat and mass transfer characteristics in a confined enclosure with variable buoyancy ratio

This numerical study was conducted to investigate the ventilation and airflow in a confined enclosure undergoing rapid inclusion of heat and contaminants representing air quality changes in working environments. A flow of air is passing inside a square enclosure with a heat source and a pollutant source on the right and bottom wall, creating double-diffusion, as well as two ventilation ducts on the upper sides asserting mixed convection. The Galerkin weighted residual method is implemented, which is based on the finite element method. For fixed values of Lewis number, Le = 0.5, Richardson number, Ri = 1, Reynolds number, Re = 100, and Prandtl number, Pr = 1.01, simulations were done with Buoyancy Ratio, Br = −10, 1, 10 and 20 over dimensionless time, τ = 0.1, 0.5, and 1.0. The results have been shown with the streamline, isothermal lines, iso-concentration lines, average Nusselt and Sherwood number, average fluid temperature, average mass concentration, and the average temperature at the square cavity's exit port plots. The findings have been discussed to ensure understanding of the changes in parameters, and an enhancement in heat as well as mass transfer was seen with the rapid change in dimensionless time. This specific study could be a guide for designing air conditioning and ventilation systems.

Numerical investigation of transient thermal behaviour of fully wet and porous moving semi-spherical fin

A variety of engineering applications demand efficient and adaptable fin structures for the intensification of heat exchange. The semi-spherical fin structures are useful in the field of refrigeration, chemical processing systems, aerospace etc. In this regard, the present article numerically investigates the transient thermal behaviour of a fully wet semi-spherical fin. The study incorporates the Darcy model as the fin is made up of porous material. Further, the fin is exposed to convective-radiative heat exchange and is subject to uniform motion. The heat balance equation has been reduced to get a nonlinear partial differential equation (PDE) which is computed by employing the finite difference method (FDM). The dimensionless terms are grouped together and their influence on the temperature distribution in a semi-spherical fin is studied. Also, the instantaneous heat transfer rate and the transient fin efficiency have been modelled and their variations with relevant parameters have been graphically depicted. And these are found be strong functions of Peclet number, wet porous nature and dimensionless time. As a main outcome the semi-spherical fin efficiency is positively influenced by the Peclet number. Along with the fundamental point of interest the results presented benefit the fin designing purposes.

Double-diffusive convection of two rods in a novel cavity saturated by porous media and suspended by nano-encapsulated phase change materials

The double-diffusive convection of two rotating rods inside an infinite-shaped saturated porous cavity filled by a suspension of nano-encapsulated phase change material was investigated numerically using the (ISPH) method. The cavity includes two rotating rods, (NEPCM) particles, and porous media. The inner left and right rods are located inside the left and right sides of an infinite-shaped cavity. In the present work, two types of boundary conditions between the inner rods and outer boundary walls of the cavity are considered. The results were produced for the dimensionless fusion temperature (0.05 ≤ ≤ 0.95), the length of the inner rotating rods (0.2 ≤ LR ≤ 0.6), the buoyancy ratio number (−2 ≤ N ≤ 2), the solid volume fraction (0.01 ≤ ϕ ≤ 0.05), the dimensionless time (0 ≤ ≤ 0.3) and Darcy number (10−2 ≤ Da ≤ 10−5). But, the Lewis and Stefan numbers were considered fixed at (Le = 10) and (Ste = 0.2), respectively. The effects of several parameters on the melting-solidification zones, temperature, concentration, and velocity fields were also investigated. It was found that the location and the strength of the melting-solidification zone are influenced significantly by the variation of the boundary conditions. The average Nusselt and Sherwood numbers are influenced clearly by the variation of the boundary conditions for rods and cavity walls and by increasing the length of the inner rods.

An analytical model for diffusion of chemicals under a thermal gradient in finite clayey soil

An analytical solution to non-isothermal diffusion of chemicals in finite porous medium with different combinations of boundary and initial conditions is presented. The average degree of diffusion was proposed to assess the contaminant removal efficiency from polluted soil with different initial contaminant concentration distribution conditions considering chemical and thermal diffusion. The dimensionless time factor for the average degree of diffusion U = 90% can be decreased by a factor of 8.4 in the case with rectangular initial solute concentration distribution considering thermal diffusion. An application of the model to study the effects of initial solute concentration distribution and adsorption on the average degree of diffusion show that both the adsorption performance of clayey soil to the contaminant and the initial solute concentration distribution have a significant effect on the average degree of diffusion. In the cases with rectangular and inverse triangular initial solute concentration distributions, when U = 50%, the times increase by factors of 2.2 and 5.3, respectively, compared to the case with triangular initial solute concentration distribution. An application of the model to study the effects of temperature on the average degree of diffusion of contaminant in polluted soil show that the temperature difference has a significant effect to promote the contaminant transport in clayey soil by increasing both of the thermal diffusion and chemical diffusion effect. It may be an effective method to remove contaminant from polluted soil by thermal diffusion.

Periodic Unsteady Natural Convection on CNT Nano-powder Liquid in a Triangular Shaped Mechanical Chamber

Nanoparticle is highly used in enhancing thermal performance, especially in lid-driven cavity flow in powder-related applications. Many researchers considered different conditions, such as MHD, radiation, and mixed convection incorporating nano liquid in such flow. However, no study was carried out with CNT-water nano liquid in a triangular cavity, heated sinusoidally under natural convection to determine the Rayleigh number (Ra) and nano-powder liquid concentration effect on heat transfer. As a result, this study attempts to find the Rayleigh number and particle concentration effects in such transient cavity flow. The governing equations were employed with the Galerkin residual method. While calculating the thermal conductivity and dynamic viscosity of the nano liquid, Brownian motion was taken into consideration. The four solid volume fractions (0.01, 0.05, 0.1, 0.15) and the Ra (104 ≤ Ra ≤ 106) were chosen to evaluate the impact within dimensionless time (0.1 ≤ τ ≤ 1). The findings have been shown by plotting the streamlines, isotherms, heat transfer variation, and pressure gradient. It is found that when the Rayleigh number goes up, the velocity, vorticity, and pressure gradient magnitude become high. But, the fluid flow vortices decrease with dimensionless time. Due to the sinusoidal heat flux conditions, the variation of the result was found to be sinusoidal as well. When the nanoparticle concentration rises, the heat transfer rate and average fluid temperature also increase. Therefore, the highest heat transfer rate is found using the nano liquid with a15% concentration.

Unsteady Natural Convection in a Porous Square Cavity Saturated by Nanofluid Using Buongiorno Model: Variable Permeability Effect on Homogeneous Porous Medium

This paper investigated numerically a natural convection in a porous cavity saturated by nanofluide. The left and right wall of the cavity are maintained at the hot-cold temperature respectively, the other walls are adiabatic. The two-phase Buongiorno model has been adopted to take account Brownian and thermophoretic diffusion in order to demonstrate the spatial distribution of the local nanoparticles concentration. After following the temporal evolution of the different structures (0<τ<5), Numerical simulations are performed to explore the effect of density buoyancy (104<Ra<106), the permeability of the homogeneous porous medium (10-5<Da<10-2), on the hydrodynamic, thermal and mass behavior. An original motivation was also introduced in our work to examine the effect of linearly variable permeability along the opposite direction of the cavity by varying the initial Darcy number from (10-5<Da<10-2) and fixing the final Darcy number Daf =10-5. The dimensionless partial differential equations are solved using the finite element method. The effects of the governing parameters on heat transfer are analyzed. Results indicate that the stationary regime is formed after the unsteady regime at dimensionless time τ = 0.3. The movement of nanofluide is strongly influenced by thermal buoyancy forces and depends on the Darcy number, heat transfer is accentuated for the homogenous medium compared to this one with variable permeability. It is found that the convective flow in a homogeneous porous medium is considerably affected by the variation of permeability and consequently the heat transfer is reduced.

Thermal performance of low melting point metal-based heat sinks for high-power airborne equipment

Low melting point metals (LMPMs) have greater potential to address the cooling difficulties of high-power airborne equipment than conventional phase change materials (PCMs). However, the heating power in existing LMPM-based heat sinks is generally low. Here, a bismuth-based alloy, Bi44.7Pb22.6In19.1Sn8.3Cd5.3, is adopted. Experiments were conducted in a pin fin heat sink (PFHS) and an empty heat sink (EHS) under 50–1500 W. Experimental results on the effect of PCMs indicate that heat sinks filled with LMPMs outperform n-dodecane. The heating wall temperature is decreased, and the holding time is prolonged significantly. The EHS and PFHS remain below 50 °C from 847 and 1268 s to 2209 and 2302 s at 50 W, respectively. Experimental data illustrate that for LMPM-based heat sinks, the heating wall temperature and holding time are improved by applying pin fins. The EHS and PFHS remain below 50 °C for 143 and 183 s at 500 W, respectively. However, the difference between the holding time below 70 °C for EHS and PFHS is reduced to ±3%. Experimental results reveal that increasing the heating power results in rising heating wall temperature and falling holding time. The holding time of the LMPM-based PFHS decreases from 2302 s at 50 W to 61 s at 1500 W, and the heating power effect weakens from approximately 50% at 100–200 W to approximately 10% at 900–1500 W. Moreover, the Nusselt number (Nu) decreases with increasing dimensionless time, but the decrease is increasingly smaller. A higher Rayleigh number correlated with a larger heating power leads to a higher Nu due to the intensive effect of natural convection. New dimensionless correlations of Nu are developed, yielding mean absolute deviations of 3.5% and 2.7% for the LMPM-based PFHS and EHS, respectively.

Binary droplet interactions in shear water-in-oil emulsion: A molecular dynamics study

The shear field and binary droplet interaction regimes of water-in-oil emulsions between parallel gold plates were investigated by molecular dynamics (MD) methods. The developed MD model was subjected to dimensional analysis and the dimensionless numbers that guarantee the similarity between the model and the actual system were identified as the capillary number (Ca), Reynolds number (Re), Weber number (We), and dimensionless time (τ). The effects of different pressures were compared by applying different forces perpendicular to the shear direction to the parallel plates. The heptane formed adsorbed layers on the gold plates, exhibited a shear thinning characteristic, and formed a no-slip uniform shear field driven by the parallel plates. The interactions between gold atoms and a heptane molecule have been investigated in depth by quantum chemical methods and it has been found that the nature of the adsorption is a van der Waals interaction. Three main binary droplet interaction regimes are produced in the presence of shear fields: coalescence, a temporary bridge formation, and sliding. The effects of capillary forces and shear effects on liquid bridges were discussed. Droplet trajectories and deformations under different pressure were analyzed. Finally, the effect of initial offset (ΔYin/2R) and Ca on the droplet interaction regime was investigated through regime maps. It was found that the coalescence regime has upper critical points for ΔYin/2R and Ca; droplet slipping occurs mainly at higher ΔYin/2R; the temporary bridge formation regime appears mainly at higher Ca. This study provides a new idea for understanding binary droplet interactions in shear emulsions.

A Theory for Estuarine Delta Formation with Finite Beach Length under Sediment Supplied from the River

Analytical solutions for a one-line model for shoreline changes are employed to investigate the formation of two wave-dominated river delta coastlines, along with a small-scale laboratory experiment. Since the present analytical solution can be applied only to a river delta with infinite shorelines, a new analytical solution was developed to consider the effects of lateral boundaries to the evolution of delta coastlines. It was determined that two demarcations represented by the dimensionless times t* can be used to judge whether the lateral boundaries have affected the coastline evolution or not. After the successful application of a new analytical solution to the experimental data, the new analytical solution was applied to predict the formation and deformation of the shorelines of the Ombrone River and Funatsu River deltas. Results obtained from the analysis showed that the new analytical solution can be used to describe well the formation and deformation of finite river-delta shorelines. Based on the two demarcations as represented by the dimensionless time t*, the shorelines of the Ombrone River and Funatsu River deltas are classified as finite shorelines.

A comparison between artificial neural network algorithms and empirical equations applied to submerged weir scour evolution prediction

Estimating the time evolution of a local scour hole downstream of submerged weirs can help determine the maximum scour depth and length and is essential to designing submerged weir foundations. In the current study, artificial neural networks with a backpropagation learning algorithm were used to estimate the temporal variation of scour profiles downstream of submerged weirs under clear water conditions. Physical factors, such as the flow condition, weir size, and sediment characteristics, are general scour considerations. Two sets of data combinations, namely original and non-dimensional data, were utilized in developing the backpropagation network (BPN) model. Using the data combinations and a trial-and-error method, the appropriate number of hidden neurons in the model architecture was determined. The results indicated that using non-dimensional variables as inputs in estimating the time evolution of scour holes downstream of a submerged weir is more suitable for the BPN model. Comparisons of the prediction results of the BPN model and an empirical regression formula revealed that the BPN model was more accurate and more direct in predicting the temporal variation of the local scour hole profile. In addition, sensitivity analysis showed that the dimensionless time exerted the most significant impact on the time evolution of the non-dimensional scour hole profile.

Molecular dynamics investigation of the vaporization characteristics of n-alkane blended fuels under different ambient conditions

Molecular dynamics (MD) simulation is a powerful tool to reveal the microscopic characteristics of supercritical transitions. However, the accuracy of MD depends strongly on the potential model that describes the interaction forces between atoms. In this study, four commonly used potential models for long-chain n-alkanes in MD simulations are evaluated, and a hybrid model is introduced. The vaporization and phase-transition characteristics of n-alkane blended fuels with different mole fractions are then explored under a wide variety of ambient conditions by using the hybrid model. Compared to the commonly used potentials, the hybrid model shows higher accuracy for predicting the thermodynamic and transport properties. In subcritical environments, vaporization belongs to typical two-phase evaporation with a sharp gas–liquid interface. The preferential evaporation of the light-end component is obvious, and the evaporation rate of the heavy-end component is maximized after the light-end component is consumed. Under supercritical conditions, the interface dissolves rapidly, the evaporation rates for both the light- and heavy-end components increase simultaneously, and both components coexist throughout the evaporation process. Based on the maximum potential energy and evaporation rate, a new criterion for the supercritical transition is proposed. The dimensionless transition time, which reflects the proportion of the sub/supercritical stage within the lifetime, is nearly independent of the ambient temperature and fuel composition; instead, it mainly depends on the ambient pressure. Finally, an empirical formula is obtained by curve-fitting to describe the variation in the dimensionless transition time with ambient pressure.

Thermocline dynamics in a thermally stratified water tank under different operation modes

The mantled solar heat storage (MSHS) tank can separate water utilization and heat collection, and its structure is not only conducive to the formation of temperature stratification, but also easy to be combined with the building, which has a wide range of application value. However, when it is in the simultaneous charging/discharging mode (CD-Mode), the mixing in the inner tank is affected by the heat transfer of the mantle exchanger, and the mixing mechanism and the development law need to be further explored. In this paper, the mixing mechanism of negative buoyancy jet at the inlet and the variation trend of thermocline in the tank under different operating modes were explored numerically and experimentally. As well as its influence on the overall thermal performance of the tank, a simple and feasible way to optimize the diffuser is discussed as well. It is found that in the CD-Mode, the mixing inside the water tank becomes more severe in the early stage of water use, and the thermocline thickness shows a trend of thickening first and then thinning over time. However, the mixing state is relatively stable during the whole water use period, and the change rate of thermocline thickness is smaller. But it is more affected by the inlet negative buoyancy jet than that in the discharging mode (D-mode), especially when the Rei number is large. Under the two operation modes, when the dimensionless time t* = 0.4–0.8, it enters the stable water use process, and the thermocline is in the stable development stage. The thickness of thermocline changes less in the CD-mode, which makes it easier for users to obtain longer hot water service time, reflecting the advantages of mantled heat exchange water tank in maintaining thermal stratification. For the working conditions studied, after optimized the diffuser, the hot water output rate can be 109.9% higher than the straight tube with the same tube length, and the hot water service time can be prolonged by 90.2%, which has practical application value.