Non-dimensional Number Research Articles

A steady-state semi-analytical approximation of melt pool evolution in pulsed laser surface melting

Pulsed laser surface melting (pLSM) is a technique that offers an efficient and effective way to modify the geometry surfaces without any addition or removal of material. The resultant surface geometry plays a critical role in several applications. This paper presents a steady-state thin-film approximation of the melt pool created by pLSM and the resulting semi-analytical solution for the evolved surface geometry. These predictions of the semi-analytical solution are then compared with a validated numerical solution. The comparison demonstrates a good match with errors ranging from ~4% to ~25% across several pulse durations. Larger errors are observed at comparatively lower and higher pulse duration. Smaller errors are observed for intermediate pulse duration values because of the deviation of non-dimensional numbers from their assumed orders. Overall, the thin-film solution is a reasonable and useful approximation of the evolved surface geometry through the pLSM process, thus saving significant computational costs.

海洋乱流現象を特徴付ける種々のスケールと無次元数，並びに渦拡散係数の推定

海洋乱流現象を特徴付ける種々のスケールと無次元数，並びに渦拡散係数の推定

RETRACTED: A novel approach for EMHD Williamson nanofluid over nonlinear sheet with double stratification and Ohmic dissipation

The current article highlights the non-Newtonian Williamson nanofluid with electro-magnetohydrodynamic (EMHD) flow over a nonlinear expanding sheet. Thermal and solutal stratification effects are considered due to the higher temperature difference and the impact of variable viscosity along with Ohmic dissipation is also incorporated. Transformation is applied for the conversion of physical partial differential equations (PDEs) into non-dimensional higher order nonlinear ordinary differential equations (ODEs). A well-known analytical approach known as the homotopy analysis method (HAM) is effectively applied to solve the differential equations. Different non-dimensional emerging parameters such as Weissenberg and Hartman number, Brownian motion and stratification parameters, stretching index, viscosity parameter, and Lewis number are used to check their impacts on velocity, concentration, and temperature profiles. To acquire the optimal solution through HAM, [Formula: see text] -curves are drawn. In the tabulated form, the numerical values for the non-dimensional Nusselt number and skin friction are arranged.

Study on MHD Flow over a Stretching Surface with Convective Boundary Condition by Numerical Method

The thermal and mass diffusive MHD flow through a stretching sheet has been inspected in the presence of a chemically reactive solute under convective boundary conditions in the present paper. The non-linear PDEs of the system concerning the flow, temperature, and species are recasted into a set of non-linear ODEs using ST. The consequential system of the differential equations is numerically resolved by using an implicit FDS in combination with the QL technique. The velocity ratio factor plays an important role in reducing the thickness of the velocity boundary layer, whereas the presence of magnetic parameters decreases the thickness of the velocity boundary layer profile. The study reveals that the fluid moves away from the surface during injection, resulting in a fall of the velocity gradient, whereas the opposite effect is observed in suction. The thermal and concentration boundary layer thicknesses are influenced by non-dimensional numbers, namely Prandtl and Schmidt numbers. The reaction rate parameter acts as a decelerating agent, and it thins the solute boundary layer formed in the neighborhood of the sheet. An increase in the convective parameter leads to an increase in the plate surface temperature. The present results of the paper are compared with the existing one, and good agreement is found between them.

An experimental study of interfacial dynamics during stratified oil-water draining from storage tank

Oil-water stratification is an inevitable phenomenon in the petroleum industry. The present study describes stratified oil-water draining from a square tank through a 9 mm diameter drain pipe. The purpose of this study is to understand the flow physics of oil as well as air entrainment in drain pipe during drainage of water. In order to observe the influence of the viscosity of oil on the entrainment and flow structure, two different oil-water stratifications are selected. In these two cases, the viscosity ratios of oil to water are 1.64 and 55, respectively. While draining, the flow of single-phase liquid in the drainpipe is transformed to two-phase liquid-liquid flow and then three-phase flow. A pointed tip of oil is formed as the oil-water interface approaches the drainpipe inlet. Different flow patterns, namely bubbly flow, slug flow, churn flow, elongated slug flow, jet flow, and annular flow, are observed as air and oil enter the drain pipe. Reverse flow is observed in the case of a higher viscosity ratio. An empirical correlation based on non-dimensional numbers has been proposed for describing the condition of no air entrainment in the drain pipe. Optical probes are used successfully to detect the presence of several regimes of air-oil-water and oil-water in the drainpipe.

Theoretical model for diffusion-reaction based drug delivery from a multilayer spherical capsule

Controlled drug delivery from a multilayer spherical capsule is used for several therapeutic applications. Developing a theoretical understanding of mass transfer in the multilayer capsule is critical for understanding and optimizing targeted drug delivery. This paper presents an analytical solution for the mass transport problem in a general multilayer sphere involving diffusion as well as drug immobilization in various layers due to binding reactions. An eigenvalue-based solution for this multilayer diffusion-reaction problem is derived in terms of various non-dimensional quantities including Sherwood and Damköhler numbers. It is shown that unlike diffusion-reaction problems in heat transfer, the present problem does not admit imaginary eigenvalues. The effect of binding reactions represented by the Damköhler numbers and outer surface boundary condition represented by the Sherwood number on drug delivery profile is analyzed. It is shown that a low Sherwood number not only increases drug delivery time, but also reduces the total mass of drug delivered. The mass of drug delivered is also shown to reduce with increasing Damköhler number. The impact of shell thickness is analyzed. The effect of a thin outer coating is accounted for by lumping the mass transfer resistance in series with convective boundary resistance, and a non-dimensional number involving the thickness and diffusion coefficient of the coating is shown to govern its impact on drug delivery characteristics. The analytical model presented here improves the understanding of mass transfer in a multilayer spherical capsule in presence of binding reactions, and may help design appropriate experiments for down-selecting candidate materials and geometries for drug delivery applications of interest.

CFD Based Non-Dimensional Characterization of Energy Dissipation Due to Verticle Slosh

We present the CFD based non-dimensional characterization of violent slosh induced energy dissipation due a tank under vertical excitation. Experimentally validated CFD is used for this purpose as an ideally suited and versatile tool. It is thus first demonstrated that a weakly compressible VoF based CFD scheme is capable of computing violent slosh induced energy dissipation with high accuracy. The resulting CFD based energy analysis further informs that the main source of energy dissipation during violent slosh is due liquid impact. Next, a functional relationship characterising slosh induced energy dissipation is formulated in terms of fluid physics based non-dimensional numbers. These comprised contact angle and liquid–gas density ratio as well as Reynolds, Weber and Froude numbers. The Froude number is found the most significant in characterising verticle violent slosh induced energy dissipation (in the absence of significant phase change). The validated CFD is consequently employed to develop scaling laws (curve fits) which quantify energy dissipation as a function of the most important fluid physics non-dimensional numbers. These newly developed scaling laws show for the first time that slosh induced energy dissipation may be expressed as a quadratic function of Froude number and as a linear function of liquid–gas density ratio. Based on the aforementioned it is postulated that violent slosh induced energy dissipation may be expressed as a linear function of tank kinetic energy. The article is concluded by demonstrating the practical use of the novel CFD derived non-dimensional scaling laws to infer slosh induced energy dissipation for ideal experiments (with exact fluid physics similarity to the full scale Aircraft) from (non-ideal) slosh experiments.

Evaluation on Coupling of Wall Boiling and Population Balance Models for Vertical Gas-Liquid Subcooled Boiling Flow of First Loop of Nuclear Power Plant

An accurate prediction of the interphase behaviors of the vertical gas-liquid subcooled boiling flow is meaningful for the first loop of a nuclear power plant (NPP). Therefore, the interphase behaviors including the bubble size distribution in the first loop of the NPP are analyzed, evaluated, and validated using various wall boiling models coupled with the population balance model (PBM) kernels in this paper. Firstly, nondimensional numbers of the first loop of the NPP and DEBORA (Development of Borehole Seals for High-Level Radioactive Waste) experiment test cases are analyzed with approximation. Secondly, five active nucleation site density models Nn coupled with the PBM kernel combination, four kernel combinations (C1~C4) with the Nn models are calculated and analyzed. Lastly, various behaviors including the bubble size distribution Sauter mean diameter (SMD) dp, void fraction α, gas superficial velocity jg, and liquid superficial velocity jl are compared and validated with the experimental data of the DEBORA-1 (P = 2.62 MPa). The results indicate that the two Nn models are suitable for the calculations of thefirst loop of the nuclear power plant. For instance, for the bubble size distribution SMD dp, the specified Nn model with C1 (maximum relative error 9.63%) has relatively better behaviors for the first loop of the NPP. Especially, the combination C1 is applicable for the calculation of the bubble size distribution dp, void fraction α and liquid superficial velocity jl while C4 is suitable for the calculation of the gas superficial velocity jg. These results can provide guidance for the numerical computation of the subcooled boiling flow in the first loop of the NPP.

Terminal velocity and drag coefficient for spherical particles

Empirical correlations and experimental works relating the drag coefficient (CD) of spheres to the Reynolds number (Re) and Re to the Archimedes number (Ar) were reviewed with a focus on the correlations applicable to the entire Re range. In addition, experiments with various spherical particles and fluids for the entire range of Re were conducted using high-speed video and added to the literature data. One of the correlations from the literature for Re-Ar and a modified correlation for CD–Re were found to best fit the experimental results. The analysis also established new correlations for Re–Ha (a non-dimensional number for velocity not including particle size) and CD–Ar. The latter is easier to use than the common CD–Re curve.

A new scaling number reveals droplet dynamics on vibratory surfaces

HypothesisDroplet spreading on surfaces is a ubiquitous phenomenon in nature and is relevant with a wide range of applications. In practical scenarios, surfaces are usually associated with certain levels of vibration. Although vertical or horizontal modes of vibration have been used to promote droplet dewetting, bouncing from immiscible medium, directional transport, etc., a quantitative understanding of how external vibration mediates the droplet behaviors remains to be revealed. MethodsWe studied droplets impacting on stationary and vibratory surfaces, respectively. In analogy to the Weber number We=ρUi2D0/γ, we define the vibration Weber number We*=ρUv2D0/γ to quantitively analyze the vibration-induced dynamic pressure on droplet behaviors on vibratory surfaces, where ρ,γ,D0,UiandUv are liquid density, surface tension, initial droplet diameter, impact velocity of the droplet, and velocity amplitude of vibration, respectively. FindingsWe demonstrate that the effect of vibration on promoting droplet spreading can be captured by a new scaling number expressed as We*/[We1\\2sin(θ/2)], leading to (Dm − Dm0)/Dm0 ∝ We*/[We1\\2sin(θ/2)], where θ is the contact angle, and Dm0 and Dm are the maximum diameter of the droplet on stationary and vibratory surfaces, respectively. The scaling number illustrates the relative importance of vibration-induced dynamic pressure compared to inertial force and surface tension. Together with other well-established non-dimensional numbers, this scaling number provides a new dimension and framework for understanding and controlling droplet dynamics. Our findings can also find applications such as improving the power generation efficiency, intensifying the deposition of paint, and enhancing the heat transfer of droplets.

Development of two-phase flow regime map for thermally stimulated flows using deep learning and image segmentation technique

Accurate prediction of the flow patterns is important for understanding the behavior and operation of thermo-fluidic phenomena in two-phase systems. Considering the importance of thermally induced flows in capillaries and their use in various processes, the thermo-hydrodynamics of two-phase flows in pulsating heat pipes (PHPs) have been studied. In the present research, flow regimes were identified in capillaries where the mass flow rate is difficult to deal with. A deep learning technique has been carried out to classify the flow patterns and extract their attributes in a particular capillary using multi-spectral segmentation. The modified Weber, Froude, and Bond numbers are used by considering the absolute velocities, accelerations, and bubble lengths for classifying the flow regime. Flow regime maps were plotted based on the proposed non-dimensional numbers by analyzing experimentally measured data sets and visual observation for methanol as a working fluid at six different heat levels (18,38,44,50,60, and 70 W). Four different flow regimes have been identified and classified as a bubbly flow, a slug flow, an elongated plug flow (transitional flow), and an annular/semi-annular flow, and a new flow regime map for thermally induced two-phase flows in a PHP is presented. The flow regime map gives quantifiable criteria for the calculation of bubbly, slug, and annular flow patterns. The present study will be useful for researchers analyzing a large number of two-phase flow images and to design two-phase passive heat transfer devices based on the flow regime map.

Competing thermal and solutal advection decelerates droplet evaporation on heated surfaces

We report the complex evaporation kinetics of saline sessile droplets on surfaces with elevated temperatures. Our previous studies show that on non-heated substrates, saline sessile droplets evaporate faster compared to the water counterparts. In the present study, we discover that on heated surfaces, the saline droplets evaporate slower than the water counterpart, thereby posing a counter-intuitive phenomenon. The reduction in the evaporation rates is directly dependent on the salt concentration and the surface wettability. Natural convection around the droplet and thermal modulation of surface tension is found to be inadequate to explain the mechanisms. Flow visualizations using particle image velocimetry (PIV) reveal that the morphed advection within the saline droplets is a probable reason behind the arrested evaporation. Infrared thermography is employed to map the thermal state of the droplets. A thermo-solutal Marangoni based scaling analysis is put forward and the major governing non-dimensional numbers have been accounted for in the analysis. It is observed that the Marangoni flow and internal advection borne of thermal and solutal gradients are competitive, thereby leading to the overall decay of internal circulation velocity compared to the equivalent pure water case, which reduces the evaporation rates. The theoretically proposed advection velocities conform to the experimental results. This study sheds rich insight on a novel species transport behaviour in saline droplets.

Scale analysis of electrochemical and thermal behaviour of a cylindrical spiral-wound lithium-ion battery

Design and sizing of lithium-ion battery is a challenging task because of inherent multiphysical and multiscale nature of this battery type. Detailed mechanistic models have been developed to resolve the design effects on physico-chemical processes taking place inside the battery and in turn, on battery performance. However, such models are hold back by their mathematically complexity and associated computational cost. In this paper, we come up with efficient design guidelines for Li-ion battery while addressing these model complexities. In essence, we carry out scale analysis of electrochemical and thermal behaviour of a cylindrical spiral wound Li-ion battery. We secure non-dimensional numbers and scales for the leading-order phenomena of charge, energy and species transport as well as associated heat generation and electrochemical reactions. The scales, in particular, provide quick quantification of variables such as temperature increase, potential losses and state of charge during charge/discharge. We verify reliability of the derived scales by comparing their predictions with the results from numerical simulations of an electrochemical-thermal model of battery. Overall, good agreement between the predictions from scales and simulations is obtained. The non-dimensional numbers and scales – which characterize the cell both thermally and electrochemically – are also discussed from the viewpoint of battery design.

Predicting ship ramming performance in thick level ice via experiments

ABSTRACT Polar sailing ships employ continuous and ramming operations to break ice when sailing in the Arctic or Antarctic waters. Upon encountering ice above a certain thickness, including icebergs and ice ridges, ramming methods are employed. The ship sailing performance while ramming ice is difficult to predict under complex ice conditions. To provide an accurate prediction of the ship sailing performance during the ramming operation under thick level ice conditions, we constructed a model ship in an ice tank to simulate a polar scientific research ship ramming thick ice. The nondimensional numbers were analysed to determine the ramming capacity of the ship. The experimental results show that the navigation performance of a ship is related to the ramming speed, and the ship penetration distance and local load increase linearly with the ship speed. Improvements for future ship design are proposed based on the results obtained in this study.

Vortex Shedding Frequency Scaling of Coherent Structures Induced by a Plasma Actuator

The spatial–temporal evolution of coherent structures generated by an asymmetrical dielectric barrier discharge (DBD) plasma actuator is an intriguing unsteady process with profound implications for revealing the controlling mechanism of the plasma actuator and promoting the control effect of the DBD plasma actuator at high wind speed and high Reynolds number. In this study, the induced coherent structures of the plasma actuator are studied systematically with a particle image velocimetry for a range of force coefficients (). Results indicate that the vortices that shed periodically from the downstream edge of the exposed electrode are a result of the amplification of natural disturbances in the jet shear layer. During later evolution, the adjacent vortices pair up to form a new vortex, leading to a reduction of the dominant frequency in the velocity spectra. Further downstream, the coherent vortical structures decay considerably, correlating with the shear-layer transition process in the plasma wall jet. The vortex shedding frequency is observed to scale with the force coefficient according to , which is of importance to the selection of the dominant frequency by adjusting the actuation parameters of the plasma actuator based on the characteristic frequency of the controlled flowfield and improving the control effect of the plasma actuator. With increasing force coefficient, the propagation speed of the roll-up vortices increases linearly, whereas the streamwise vortex spacing decreases monotonically. It is of great significance that the nondimensional Strouhal number based on the vortex shedding frequency, vortex propagation speed, and streamwise vortex spacing is proposed and varies slightly between 0.045 and 0.065, for all the tested cases, which lays a foundation for promoting the numerical simulation model of the plasma actuator and revealing the controlling mechanism of the flow control using the plasma actuator.

Mathematical modeling of steady MHD Casson fluid flow with stretching porous walls in existence of radiation, chemical reaction, and thermal diffusion effect

This expression presents the steady (independent of time) MagnetoHydroDynamics (MHD) Casson fluid (non‐Newtonian shear‐thinning) flow with thermal radiative impression between two equivalent plates within stretched porous walls. The mass and heat transfer experimentation founded in the company of buoyancy force, viscous dissipative impact, and thermo diffusion impact on squeezing flow are explained along with thermal radiative impression also with heat source/sink outcomes. The governing PDEs (partial differential equations) modified into ODEs (ordinary differential equations) via appropriate similarity modification. The ODEs are extricated by Runge–Kutta's fourth‐order scheme and shooting performance. The outcomes of several parameters (nondimensional numbers) on velocity, temperature, and concentration are evaluated with the service of diagrams and tables. The result displays that the fluid velocity growths with increment of Grashof number. The effect of Reynolds number, Hartman number (magnetic number), non‐Newtonian Casson fluid parameter, and so forth are also interpreted for velocity profile, mass transfer, and heat transfer. In the last, the skin friction coefficient, Sherwood number (mass transfer coefficient), and Nusselt numbers (heat transfer coefficient) are also reputed. Also, validation of the current paper is given in Table 2.

Significance of Stephen blowing and Lorentz force on dynamics of Prandtl nanofluid via Keller box approach

This investigation, scrutinizes the effects of Stephen blowing on Prandtl nanofluids transportation caused by a stretch in the sheet. The fluid temperature, thermal conductivity due to dispersion of nanoparticles with enhanced is investigated. Cartesian coordinates are used for flow equations. The similarity variables for momentum, temperature and concentration profiles, are utilized to modify the perceptions of governing flow. Nonlinear ODEs are gained from the governing PDEs and cracked down numerically by shooting and Keller box approach. The graphical and numerical sections are viewing the results for the velocity temperature and concentration fields against the independent parameters and non-dimensional numbers. As the boosting the values of material parameters α and βmove opposite on velocity profilef′(η) but similar effects of NtandNb are observed on both temperature and concentration profiles. The skin friction −f″(0)is profitable unhappy at the increase values of the Hartman number with the fluctuations in the value of Stephen blowing.(S = − 1,0,1). The conflicting behavior of Prandtl and Eckert numbers are detected on temperature profile. Physical explanation of the graphical segment is support to understand the performance of fluids flow.

Nonlinear EHD stability of cylindrical walters B' fluids: effect of an axial time periodic electric field

The current article is concerned with a nonlinear stability analysis of cylindrical Walters B' fluids. The system is pervaded by an axial time periodic electric field. A cylindrical interface is supposed to be disconnected from two dielectric fluids. The fluids are fully saturated in porous media. The motivation to scrutinize this area is attributed to the great attention it receives in many practical situations in physics and engineering applications. The implementation of the appropriate nonlinear boundary conditions of the linearized equations of motion yields a nonlinear characteristic dispersion equation. This equation manages the surface deflection of the surface waves. The use of the non-dimensional analysis resulted in various well-known non-dimensional numbers. A new approach to the characteristic equation is inspected by employing the Homotopy perturbation method (HPM). This new methodology resulted in a Klein-Gordon equation. Utilizing a travelling-wave solution to the linear part of the characteristic equation, a new restriction of the stability analysis appears. The investigation reveals the non-resonance as well as the resonance cases, and the stability criteria are established in both arguments. A set of diagrams is plotted to display the influence of various non-dimensional physical numbers on the stability profile and shows interesting features.

Effects of electric field on flow boiling heat transfer characteristics in a microchannel heat sink with various orientations

This study investigates the effects of the electric field in an inclined microchannel heat sink with a hydraulic diameter of 2 mm. The saturated flow boiling performance of a dielectric liquid R141b is experimentally characterized. An electrode fabricated with enameled copper wires is placed above the medium and energized to generate an electric field between it and the heated surface with the applied voltage from 0 V to 200 V. The thermal performance, with/without electric field, under various orientations from 0° to 90°, is evaluated at an inlet mass flux of 51.58 kg/(m2·s) and initial temperature of 299.15 K. Results show that the onset of nucleation boiling is delayed by the electric field. Electric field brings more production and rotary/lateral motion of bubbles which contributes to advance the flow pattern transition. Under the electric field, elongated bubbles burst and some vortexes appear in the liquid film, which has been recorded by the high-speed video camera. Overall, the electric field can remarkably promote the flow boiling heat transfer coefficient (HTC) in lower vapor quality regions, and the maximum enhancement ratio is obtained as 1.48 under present conditions. However, the microchannel prematurely dries out due to the electric field. In this research, flow boiling HTCs are sensitive to orientation. With a constant applied voltage, the performance declines between 0°∼90° while a special transition happens between 45°∼60° Based on the Gungor-Winterton correlation, and revised with the exponential function as well as a non-dimensional number representing the electric field force, a new HTC asymptotic model is developed by first considering the effects of the electric field with an error of ±15% to the experimental data.

Determination of Forced Convective Heat Transfer Coefficients on an Array of Discs

Forced convection heat transfer due to airflow across an array of thin discs is encountered in various engineering applications. In this work, a three-dimensional steady Reynolds-Averaged Navier-Stokes computational fluid dynamics (CFD) simulation is performed to investigate the phenomenon at the surfaces of an array of discs. A computational grid comprising of a solid domain representing the array of discs and a fluid domain denoting the airflow is set up. A two-step solution procedure is employed whereby first the airflow across the discs is simulated till convergence and then the heat transfer is calculated. The temperature of the air before the array of discs, that of each surface of the discs, and the wall heat flux are monitored to calculate average convective heat transfer coefficients (CHTCs). The CFD model is validated using a wind tunnel experiment and it is shown that both are in close agreement with each other based on the surface temperatures and average CHTC predictions. The CHTCs are found to be significantly higher on the upwind face of the discs compared to the downwind side. Finally, based on the simulations, a correlation based on the non-dimensional average Nusselt number versus Reynolds and Prandtl numbers is derived.