Dimensionless Surface Research Articles

Advanced Method for Determining Land Plot’s Physical Surface

This study examines the issue of the accuracy of physical surface calculations for land plots with complex configurations and reliefs. The goal of the study was to develop a methodology for determining the surface area of land plots with complex configurations and reliefs. The presented model was based on the finite element method. The developed method allows one to evaluate a relief’s complexity by using a dimensionless mean physical surface complexity factor; a Fortran program was developed for the methodology. Experiments that proved the effectiveness of the methodology and a comparative analysis of those areas that were calculated by the presented method and TIN model were carried out. The research findings proved the practicability of the methodology for calculating the physical surfaces of land plots with complex configurations. The presented methodology can be used for flood modeling, landscape and vertical planning, etc.

Spectral parametrization of random particle-packings

We present a novel method of particle-monolayer parametrization, based on least-squares fitting to the power spectral density of the monolayer image. An important advantage of this technique is avoiding the identification of individual particles. Using two images of random particle assemblies, found in the literature, we demonstrate the implementation of the method. Specifically, we determine the dimensionless particle radius and surface coverage, with their standard errors. For homogeneous monolayers of monodisperse particles, the errors are on the order of 1%. The errors increase with particle polydispersity and monolayer heterogeneity. We also show that the method is not sensitive to distortion in apparent particle size, frequently occurring in optical microscopy and AFM measurements.

Effect of Strain Rate on the Structure Properties of Silica Aerogel

Silica aerogel is a versatile material used in adsorption, filtration, and thermal insulation. However, its mechanical strength is a notable weakness, making it prone to damage. This study utilized molecular dynamics simulations to investigate the mechanical properties of aerogels. We compared the simulation results with the data from the experiments. The dimensionless specific surface areas of both are nearly identical at densities below 0.7 g/cm³. We explored the impact of strain rate on aerogel properties. The compression rate had minimal effects on stress and density during uniaxial compression. The specific surface area exhibited an initial increase followed by a decrease with a rising compression rate, peaking at 2 1/ns. Furthermore, we determined the solid thermal conductivity of the aerogel, which was 0.0764 W/(m·K) without strain. The solid thermal conductivity showed little variation with compression rate but was highly sensitive to density. The stretching rate during uniaxial stretching influenced the heat transfer coefficient, density, specific surface area, and stress. However, in the low-strain region (strain < 0.3), the tensile rate had a negligible impact on these performance metrics. This investigation offers a theoretical analysis of the mechanical properties of aerogels, establishing a foundational understanding of their efficient application.

Gravitational collapse of relativistic compact objects in higher dimension

In this work, we present an iterative method for gravitational collapse in higher dimensions. A framework is developed in a post-quasi-static regime with non-comoving coordinates. The internal five-dimensional system is smoothly matched with the corresponding outer Vaidya space-time over the boundary surface (BS). This correspondence provides a set of dimensionless surface equations in higher dimensions. The physical quantities such as Doppler shift, luminosity, and redshift at the BS of gravitating systems can be described through these surface equations. This procedure offers valuable insights that facilitate comprehension of the behavior of compact objects.

A Modified Model of Micro-Scale Gas Seepage in Rock Porous Media

It is of significance to study the micro-scale gas seepage mechanism in rock porous media due to shale gas exploitation and prevention of tunnel gas explosion. However, current microscale seepage models have problems, such as poor accuracy or small computational domain. In this work, a representative volume element scale microscopic seepage model with high precision and large computational domain is established using the lattice Boltzamnn method. In the representative volume element scale model, micro-scale effect is considered by the Beskok-Karniadakis correction relationship. Then the accuracy of the representative volume element scale model is improved by proposing an equivalent resistance correction coefficient. The correction coefficient value is obtained by comparing the calculated result for the flow rate at a representative volume element scale and more precise pore scale. For example, when the porosity is 0.9 and the dimensionless specific surface area is 30, the corrected model can reduce the average deviation from 34.38 to 0.14%. Finally, to expand the applicability of the proposed model, a correlation for the correction coefficient is introduced as a function of the Knudsen number, porosity of porous media, and dimensionless specific surface area. The mean absolute percentage deviation of the correction coefficient correlation is 9.25%.

Dynamics of a cavitation bubble confined in a thin liquid layer at null Kelvin impulse

In this work, we experimentally and numerically investigate cavitation bubble dynamics in a thin liquid layer surrounded by gas. We focus on configurations featuring strongly confined bubbles at dimensionless bubble-free surface stand-off distances D* below unity. Additionally, we impose the condition of null Kelvin impulse, subjecting a bubble to the oppositely equal influence of two opposing free surfaces, resulting in the formation of two convergent water jets. We observe a diverse spectrum of jetting phenomena, including broad jets, mushroom-capped jets, and cylindrical jets. These jets become progressively thinner and faster with lower D* values, reaching radii as small as 3% of the maximal bubble radius and speeds up to 150 m/s. Numerical results reveal a linear relationship between the jet impact velocity and the local curvature at the bubble region proximal to the free surface. This suggests that the magnitude of bubble deformation during its growth phase is the primary factor influencing the observed fivefold increase in the jet impact velocity in the parameter space considered. Our findings show that bubble collapse intensity is progressively dampened with increased confinement of its environment. As D* decreases beyond a critical value, the liquid layer separating the bubble and ambient air thins, leading to the onset of interfacial shape instabilities, its breakdown, and bubble atomization. Furthermore, we compare bubbles at zero Kelvin impulse to corresponding anisotropic scenarios with a single free surface, revealing that the dynamics of axial jets until the time of impact is primarily influenced by the proximal free surface. The impact of convergent axial jets at null Kelvin impulse results in local pressure transients up to 100 MPa and triggers the formation of a fast and thin annular outflow in the form of a liquid sheet, affected by the Rayleigh–Plateau and flapping shape instability.

Numerical Investigation of Single and Double Steps in Planing Hulls

Incorporating steps into a hull reduces the wetted surface, promoting improved hydrodynamic lift and reduced resistance at high speeds, provided that the step is designed appropriately. Traditional hydrodynamics studies rely on scaled model testing in towing tanks, but numerical tools offer a more efficient alternative. This study focused on investigating the hydrodynamic performance of stepped hulls by modifying the parent hull of the Naples Systematic Series (C1). The Computational Fluid Dynamics (CFD) code SIEMENS PLM STAR CCM+ version 2302 was used for simulations, including four different beam Froude numbers (FrB = 1.13, 2.22, 2.56, and 2.96) and a total of 15 hull configurations with single and double steps. By employing a three-dimensional computational analysis of multiphase flow using Dynamic Fluid–Body Interaction (DFBI) and overset mesh, various performance parameters such as resistance coefficient, dimensionless wetted surface, sinkage, and dynamic trim were analyzed. The accuracy of the CFD results was confirmed through comparison with experimental data and grid uncertainty assessment. The study demonstrated that placing a single step near the transom decreased trim and increased resistance and wetted surface. Conversely, positioning a step in the forward section reduced the trim angle at lower step heights but increased trim at higher step heights in single-stepped hulls. The application of these findings contributes to the design optimization of stepped hulls for enhanced performance in high-speed maritime applications.

Multi-physical analysis of ablation for C/C composites based on peridynamics

C/C composite material is one of the most widely used thermal protection materials for hypersonic vehicles. As coupled with fluid dynamics, chemical reaction, heat transfer and ablation recession, its numerical simulation is challenging and complicated. In this study, a multi-physical analysis approach for the stripping process during ablation based on peridynamics is proposed. Aerodynamic parameters and heat flux distribution are determined by empirical formulas. The energy balance on the ablative wall has been taken into account for the thermal boundary conditions and the temperature field is obtained by using bond-based peridynamics. Then, the temperature-dependent dimensionless mass flux and surface recession rate are evaluated by solving the equations involving mass conservation of surface elements and chemical equilibrium of reactions. Meanwhile, considering the breaking of bonds and the deletion of material points in this model, the phenomenon of ablation and stripping process of material on the surface can be simulated. A C/C one-dimensional model is built to verify the effectiveness of the methodology, and the peridynamic results agree with the experimental observation from literatures well. Finally, after combining fluid dynamics, chemical reaction, heat transfer and ablation recession, the exterior shape and temperature field at a nose tip of a hypersonic vehicle are predicted.

Inclusion of unsteady heat conduction in regular bodies subject to uniform surface heat flux in a heat transfer course

The present study is concerned with the analysis of unsteady heat conduction in regular bodies (large plane wall, long cylinder, and sphere) with constant initial temperature, prescribed surface heat flux and thermal properties of the solid that are invariant with temperature. Surprisingly, this important topic is absent in textbooks on heat transfer. The exact evaluation of the dimensionless surface temperatures varying with the dimensionless time in the regular bodies over the entire dimensionless time domain [Formula: see text] is carried out with a symbolic algebra code. Thereafter, regression analysis is applied to the data gathered for the dimensionless surface temperatures varying with the dimensionless time of the regular bodies inside the dimensionless “small time” time sub-domains [Formula: see text]. The dimensionless threshold time [Formula: see text] is a decisive parameter that establishes the borderline between the “small time” sub-domain [Formula: see text] and the “large time” sub-domain [Formula: see text] comprising the entire dimensionless time domain [Formula: see text]. Based on regression analysis, compact asymptotes are constructed for the dimensionless surface temperatures varying with the dimensionless time inside the dimensionless “small time” sub-domain [Formula: see text]. At the end, agreements with the dimensionless exact, analytical surface temperature distributions (the baseline solutions) valid for the dimensionless time sub-domain [Formula: see text]. are considered of excellent quality.

Nonlinear electrophoretic velocity of a spherical colloidal particle

Electrophoresis is the motion of a charged colloidal particle in an electrolyte under an applied electric field. The electrophoretic velocity of a spherical particle depends on the dimensionless electric field strength $\beta =a^*e^*E_\infty ^*/k_B^*T^*$ , defined as the ratio of the product of the applied electric field magnitude $E_\infty ^*$ and particle radius $a^*$ , to the thermal voltage $k_B^*T^*/e^*$ , where $k_B^*$ is Boltzmann's constant, $T^*$ is the absolute temperature, and $e^*$ is the charge on a proton. In this paper, we develop a spectral element algorithm to compute the electrophoretic velocity of a spherical, rigid, dielectric particle, of fixed dimensionless surface charge density $\sigma$ over a wide range of $\beta$ . Here, $\sigma =(e^*a^*/\epsilon ^*k_B^*T^*)\sigma ^*$ , where $\sigma ^*$ is the dimensional surface charge density, and $\epsilon ^*$ is the permittivity of the electrolyte. For moderately charged particles ( $\sigma ={O}(1)$ ), the electrophoretic velocity is linear in $\beta$ when $\beta \ll 1$ , and its dependence on the ratio of the Debye length ( $1/\kappa ^*$ ) to particle radius (denoted by $\delta =1/(\kappa ^*a^*)$ ) agrees with Henry's formula. As $\beta$ increases, the nonlinear contribution to the electrophoretic velocity becomes prominent, and the onset of this behaviour is $\delta$ -dependent. For $\beta \gg 1$ , the electrophoretic velocity again becomes linear in field strength, approaching the Hückel limit of electrophoresis in a dielectric medium, for all $\delta$ . For highly charged particles ( $\sigma \gg 1$ ) in the thin-Debye-layer limit ( $\delta \ll 1$ ), our computations are in good agreement with recent experimental and asymptotic results.

Thermal performance of elliptical pins on a semicircular concave surface in the staggered array jet impingement cooling

In a jet impingement cooling, decreasing heat transfer on the last jet's region due to the strong crossflow significantly increases thermal stress on the material. Thus, the main objectives of this study are to achieve relatively more uniform heat transfer distribution and enhance heat transfer on the surface compared to conventional jet impingement cooling (CJIC) configuration by mounting elliptical pins on the impingement regions. From this point of view, we have investigated the thermal performance of elliptical pins mounted on the impingement region of a staggered array jet impingement cooling (SJIC) on the semicircular concave surface. Numerical analyses were performed under various Reynolds numbers (Re = 5000, 15000, and 25000), jet nozzle-to-target surface spacing (0.5 ≤ G/d ≤ 8.0), and dimensionless orifice plate-target surface gaps (H/d = 4.0 and 8.0). Average Nusselt (Nu) numbers, local Nu contours, flow properties, and Thermal Performance Factor (TPF) on pinned and smooth target surfaces were studied in detail. Results showed that the local and area-averaged Nu numbers increased with reducing G/d and roughening of the surface with elliptical pins compared to conventional SJIC. Maximum heat transfer enhancement was obtained as 55.68% at H/d = 8.0 with extended jets (G/d = 0.5) and elliptical pin roughening surface design. Besides, the highest TPF on the pinned surface is achieved as 1.10 by G/d = 2.0 and H/d = 8.0 at Re = 25000. Furthermore, mounting elliptical pins on the surface provided more uniform heat transfer distribution on the surface compared to flat surface by means of significantly enhancing heat transfer on the last jet region.

Hydrodynamic and aeration characteristics of an aerator of a surging water tank with a vertical baffle under a horizontal sinusoidal motion

To address the hypoxia problem in seawater, this paper proposes an aerator for a surging water tank with a vertical baffle and experimentally and numerically investigates its hydrodynamic and aeration characteristics under a horizontal sinusoidal motion. The intrinsic relationships of the dimensionless maximum wave surface run-up, maximum air pressure, and airflow rate are examined with the ratios of tank surging amplitude to still water depth, tank surging frequency to natural frequency, water exchange height to still water depth, and air hole area to plan area of the sub-tank, respectively. In particular, the dimensionless maximum wave surface run-up reaches its peak when the tank surging frequency fe approaches the natural frequency f1 of the individual sub-tank sloshing mode, and the maximum dimensionless airflow rate appears when the tank surging frequency fe approaches the natural frequency fs of the U-tube sloshing mode. The ratio of the tank surging amplitude to the still water depth and fe/fs play minor roles in the dimensionless maximum air pressure. Furthermore, two methods are used to deduce the prediction formulas for the dimensionless airflow rate. The symbolic regression method performs better than the multivariate non-linear regression method.

Heat transfer performance assessment for precise accelerated control cooling of the hot heavy clad plate

In this study, the heat transfer characteristics are estimated to determine the internal temperature distribution of the hot heavy clad plate from the measured surface temperature prior to the accelerated control cooling process. The temperature prediction accuracy is verified by the advanced inverse heat transfer method (A-IHTM). It is found that the plate temperature distribution can be considered with the quasi-equilibrium state within the temperature deviation rate of 0.1 °C/s. The results have been also verified through a comparison with an analytical method over time, using dimensionless surface temperature. The comparison yielded a standard deviation of 0.027 and root mean squared error (RMSE) of 0.0574 in dimensionless temperature, indicating that the numerical method is a viable option for accurately predicting the temperature distribution in the hot heavy clad plate during the accelerated control cooling process. The internal temperature distribution of the heavy plate changes non-linearly. This phenomenon is defined as the “heat capacity effect” considering the enthalpy change. With the heat transfer characteristics, the cooling process of heavy clad plate could be controlled within finish cooling temperature deviation of 14.7 °C, cooling rate deviation of 0.7 °C/s. Also, the cooling control accuracy for the finish cooling temperature can be improved by 12.6 % with the satisfied mechanical property of heavy clad plate for corrosion resistance.

Thermocapillary convection in superimposed layers of self-rewetting fluids: Analytical and lattice Boltzmann computational study

Self-rewetting fluids (SRFs), such as aqueous solutions of long-chain alcohols, exhibit anomalous quadratic dependence of surface tension on temperature having a minimum and with a positive gradient. When compared to the normal fluids (NFs) that have negative gradient of surface tension on temperature, the SRFs can be associated with significantly modified interfacial dynamics, which have recently been exploited to enhance flow and thermal transport in various applications. In this work, first, we develop a new analytical solution of thermocapillary convection in superimposed two SRF layers confined within a microchannel that is sinusoidally heated on one side and maintained at a uniform temperature on the other side. Then, a robust central moment lattice Boltzmann method using a phase-field model involving the Allen-Cahn equation for interface tracking, two-fluid motion, and the energy transport for numerical simulations of SRFs is constructed. The analytical and computational techniques are generally shown to be in good quantitative agreement with one another. Moreover, the effect of the various characteristic parameters on the magnitude and the distribution thermocapillary-driven motion is studied. The thermocapillary flow patterns in SRFs are shown to be strikingly different when compared to the NFs: For otherwise the same conditions, the SRFs result in eight periodic counterrotating thermocapillary convection rolls, while the NFs exhibit only four such vortices. Moreover, the direction of the circulating fluid motion in such vortical structures for the SRFs is found to be towards the hotter zones on the interfaces, which is opposite to that in NFs. These features are found to be sustained even as the interfaces deforms in simulations. By tuning the sensitivity coefficients of the surface tension on temperature, it is shown that not only the magnitude of the thermocapillary velocity can be significantly manipulated, but also the overall flow patterns as well. It is also demonstrated that the thermocapillary convection can be enhanced if the SRF layer adjacent to the nonuniformly heated wall is made relatively thinner or has higher thermal conductivity ratio or has smaller viscosity when compared to that of the other fluid layer. The peak Marangoni velocity is found to be increased by a factor of 2 by doubling the dimensionless quadratic surface tension sensitivity coefficient and by about an order of magnitude as the fluid thickness ratio is changed from 1/3 to 3.

Development of bubble dynamic parameter models in subcooled flow boiling of saline solution

Concentrated saline solutions are inevitably used as coolants in the industry heat exchangers. From the aspect of simulation prediction, the closure models for RPI model, including the models of bubble departure diameter (Dw), departure frequency (f) and active nucleation site density (Nw), are of great importance for the overall success of heat transfer calculation. However, the applicability of the existing closure models for the nucleate flow boiling of saline solutions is yet to be answered. In this paper, the experiments of subcooled flow boiling of the NaCl solutions with concentration range of 0%–6% were conducted. The experimental data of the three bubble parameters, Dw, f and Nw, were obtained under different operating conditions, making up for the shortage of the bubble parameter data of saline solution in literature. The impacts of key influencing parameters for each of the three bubble parameters were discussed. For model development, the prediction performance of several existing representative Dw, f and Nw models on saline solution were studied. The results indicate that the available models for Dw, f and Nw show rather large deviations for saline solutions. Therefore, new models for Dw, f and Nw were developed according to the correlation method and the influencing parameter analyses. The parameters and dimensionless groups, which can be used to characterize the variations of Nw, Dw and f, were determined. The dimensionless parameters including Boiling number (Bo), density ratio (ρ⁎), dimensionless surface tension, Prandtl number and a suggested dimensionless temperature (ΛT), can be used to characterize the variation of Dw. And the dimensionless groups of Bo, ρ⁎, ΛT, and the non-dimensional bubble departure diameter, can be used to correlating with the non-dimensional departure frequency. As for Nw, the wall superheat and solution concentration are the most critical factors for model correlating. The new correlations for predicting the Dw, f and Nw during subcooled flow boiling in both the pure water and saline solutions were built and validated.

Effects of wide-range copper surface wettability on spray cooling heat transfer

This study conducted a spray cooling experiment to investigate the effects of varying surface wettability on the heat transfer performance of modified copper surfaces in both single- and two-phase regimes. The contact angles of the test surfaces ranged from 0° to 150°. The spray cooling experiment was performed using deionized water. The results indicated that surface wettability influenced heat transfer performance during spray cooling. In the nonboiling regime, the surface with higher hydrophilicity exhibited higher heat transfer performance owing to the larger wetting area available for heat transfer. The surface temperature of the superhydrophobic surface reached saturation at a relatively low heat flux; therefore, nucleation occurred rapidly, and the increase in the heat transfer coefficient intensified as the heat flux increased. Consequently, the heat transfer performance of the hydrophobic surface exceeded that of the plain surface in the two-phase regime. Evaporation fraction values were derived for the various test surfaces. Finally, a dimensionless surface wettability number, defined as the ratio of the droplet contact diameter to the droplet height, was used to establish heat transfer prediction models considering surface wettability in the single-phase and two-phase regimes. The heat transfer performance in the single-phase and two-phase regimes could be predicted within error bands of 18 % and 33.3 %, respectively.

Phosphate removal by Ca(OH)2-treated natural minerals: Experimental and modeling studies

Adsorption of phosphate phosphorus (PO4-P) from wastewater onto eco-friendly geosorbents has gained great attention aiming at recovering an essential nutrient for crop production. Notably, the literature on PO4-P aqueous-phase adsorption kinetics is limited to the application of either empirical reaction-based models lacking a physical significance or over-simplified diffusion-based models frequently used outside their applicability area. In this study, equilibrium and kinetic experiments are presented under a wide range of phosphate concentrations (50–500 mg P/L) using sustainable and low-cost modified adsorbents. The kinetics of PO4-P adsorption from aqueous solutions onto Ca(OH)2-treated zeolite (CaT-Z) and bentonite (CaT-B) was analyzed by a dimensionless two-phase homogeneous surface diffusion model (TP-HSDM) assuming constant diffusivity coupled with the double selectivity isotherm equation (DSM). The TP-HSDM fit to the data at four initial P concentrations (50, 100, 200 and 300 mg/L) resulted in an average relative error of 14.6% and 17.4% from the experimental data for CaT-Z and CaT-B, respectively. The average surface diffusion coefficient (Ds) ranged from 2.5 × 10-10 to 8.7 × 10-10 cm2/s for CaT-Z and from 1.6 × 10-10 to 4.78 × 10-9 cm2/s for CaT-B. The external mass transfer coefficient (kf) ranged from 2.72 × 10-4 to 8.38 × 10-4 cm/s for CaT-Z and from 5.63 × 10-4 to 2.24 × 10-3 cm/s for CaT-B. The dimensionless Biot (Bi) number exhibited values in the order of magnitude of 105 indicating that the intraparticle diffusion is the controlling mass transfer mechanism for both materials.

An approximate analytical solution for the movement of the phase change front in latent thermal energy storage heat exchangers

Latent thermal energy storage (LTES) heat exchangers are being applied in a wide range of energy systems. However, there is no analytical method to determine the outlet temperature of LTES heat exchangers from its operational conditions. This hinders experimental data reduction and sizing of these components for specific energy systems. The present paper develops an analytical model for the overall phase fraction and outlet heat transfer fluid temperature for planar LTES heat exchangers. The method is developed with solutions of the Stefan problem. The analytical results are validated based on a numerical model using the same assumptions as the analytical model. The analytical solution can be reduced to a limited set of parameters which are a dimensionless time and heat exchanger surface area. This limited set of parameters can form the basis for experimental data reduction of LTES heat exchangers.

Magnetohydrodynamic Natural Convection of Water in an L-Shaped Container Filled With an Aluminum Metal Foam

Abstract The current research employed computational simulation to assess magnetohydrodynamic (MHD) natural convection in an L-shaped container with a metal foam, which has a variety of engineering applications. The originality of this study is the use of numerical simulation combined with multi-objective optimization in terms of cooling rate enhancement and entropy generation reduction to investigate the optimal natural convection regimes. The influence of varied aspect ratios (AR), tilted angles of the container (θ), Hartmann number (Ha), and porosities (Φ) on the cooling rate with regard to the average Nusselt number (Nuave), Nusselt number enhancement (NNE), dimensionless surface temperature ([Ts]) and entropy generation (S) were evaluated. According to the findings of this study, little effect was found to be exerted by the MHD and θ on the Nuave, Ts, and S except for a porosity of 0.9. Furthermore, the Nuave and NNE enhance while the Ts and S reduce as the aspect ratio AR increases. In this case, the maximum increase in NNE was 8.78 times, with the greatest reductions in Ts and S as AR = 0.8, Φ = 0.1, θ = 0 deg, and Ha = 0 compared to the least favorable design. Thus, this optimum investigation of the CFD yields a novel approach and valuable recommendations for the optimum design of cooling in an L-shaped container.

Heat transfer analysis from moving convection-radiative triangular porous fin exposed to heat generation

The aim of this work is to analyze the enhancement in the heat transfer and investigate the efficiency of moving, porous and triangular fins. The influence of the various dimensionless parameters, like porosity, radiation-conduction, Peclet number, thermo-geometric parameters, convection-conduction, and surface temperature are analyzed on the efficiency of moving, porous and triangular fins. The model is investigated numerically as well as analytically by using DTM. The result is compared to check the accuracy of the semi-analytical solution, where good agreement is obtained. The effects of the considered parameters on the temperature distribution and efficiency of the considered fins are studied to investigate better efficiency, which plays a significant role in mechanical engineering.