Inertial Surface Research Articles

Unified closure relationship for slug liquid holdup

AbstractSlug flow is a common flow pattern in pipes operating with gas–liquid mixtures. The slug flow's periodic behaviour affects the performance of multiphase transportation systems, which is generally predicted using mechanistic models. Mechanistic models are based on one‐dimensional mass and momentum conservation equations and require additional relationships to define a complete system of equations. These additional equations are usually called closure relationships. The slug liquid holdup () is one of the required closure relationships. In this paper a unified closure model for is proposed considering the energy balance and the interaction between inertial, gravitational, viscous, and surface tension forces. The model parameters' behaviour is described as a function of a new dimensionless number. The experimental data analysis shows that this number can quantitatively define two flow categories: ‘low viscosity flow’ and ‘medium/high viscosity flow’. Slug liquid holdup changes its behaviour in these regions due to the predominance of inertial–surface tension forces or gravitational–viscous forces, respectively. The proposed closure performs better than the existing mechanistic and empirical models.

Wind-Driven Motions of the Ocean Surface Mixed Layer in the Western Arctic

Abstract Observations of sea ice and the upper ocean from three moorings in the Beaufort Sea quantify atmosphere–ice–ocean momentum transfer, with a particular focus on the inertial-frequency response. Seasonal variations in the strength of mixed layer (ML) inertial oscillations suggest that sea ice damps momentum transfer from the wind to the ocean, such that the oscillation strength is minimal under sea ice cover. In contrast, the net Ekman transport is unimpacted by the presence of sea ice. The mooring measurements are interpreted with a simplified one-dimensional ice–ocean coupled “slab” model. The model results provide insight into the drivers of the inertial seasonality: namely, that a combination of both sea ice internal stress and ocean ML depth contribute to the seasonal variability of inertial surface currents and inertial sea ice drift, while under-ice roughness does not. Furthermore, the importance of internal stress in damping inertial oscillations is different at each mooring, with a minimal influence at the southernmost mooring (within the seasonal ice zone) and more influence at the northernmost mooring. As the Arctic shifts to a more seasonal sea ice regime, changes in sea ice cover and sea ice internal strength may impact inertial-band ice–ocean coupling and allow for an increase in wind forcing to the ocean.

Musculoskeletal modelling and simulation of oil palm fresh fruit bunch harvesting

Oil palm harvesting is a labor-intensive activity and yet it was rarely investigated. Studies showed that complementing human motion analysis with musculoskeletal modelling and simulation can provide valuable information about the dynamics of the joints and muscles. Therefore, this study aims to be the first to create and evaluate an upper extremity musculoskeletal model of the oil palm harvesting motion and to assess the associated Musculoskeletal Disorder (MSD) risk. Tests were conducted at a Malaysia oil palm plantation. Six Inertial Measurement Units (IMU) and Surface Electromyography (sEMG) were used to collect kinematics of the back, shoulder and elbow joints and to measure the muscle activations of longissimus, multifidus, biceps and triceps. The simulated joint angles and muscle activations were validated against the commercial motion capture tool and sEMG, respectively. The muscle forces, joint moments and activations of rectus abdominis, iliocostalis, external oblique, internal oblique and latissimus dorsi were investigated. Findings showed that the longissimus, iliocostalis and rectus abdominis were the primary muscles relied on during harvesting. The harvesters were exposed to a higher risk of MSD while performing back flexion and back rotation. These findings provide insights into the dynamical behavior of the upper extremity muscles and joints that can potentially be used to derive ways to improve the ergonomics of oil palm harvesting, minimize the MSD risk and to design and develop assistive engineering and technological devices or tools for this activity.

Effect of Inertial Surface on Surface Gravity Wave Propagation by Thick Rectangular Barrier

Effect of Inertial Surface on Surface Gravity Wave Propagation by Thick Rectangular Barrier

Whipping Behavior of Rice Flour Dough

In this study, the bubbles in rice flour dough were investigated under a constant temperature. The bubble size distribution is important for the control of food texture. If bubble sizes depend mainly on the inertial force, viscous force, and surface tension, then the normalized mean bubble diameter should be a function of the Reynolds number and Weber number. We obtained experimental data using a hand mixer, and compared the properties of doughs prepared using six rice flours; each flour was prepared through a different milling process. We also added the size effect of the rice flour particles as the Bond number. Furthermore, we performed a dynamic wettability test to estimate the wettability of the rice flour surface. The results of this test were described well by the Washburn equation, and dccosθ was calculated as a wettability parameter (where, dc: effective diameter of a capillary in a powder bed, cosθ: the contact angle). The mean bubble diameter (dbm) generated by whipping was expected to be affected by the thickness (d) of the rod of the mixer, its movement speed, physical properties of the material, and gravitational acceleration. Therefore, dimensionless mean diameter (dbm/d) was expressed by a dimensionless equation. The empirical equation obtained was generally applicable to the variety of materials selected for this study.

Rheology and scaling behavior of cascading granular flows in rotating drums

Mixing, agglomerating, and milling of granular materials within a rotating drum is often performed in the cascading flow regime; however, the scaling behavior of these industrial applications remains poorly understood. It involves both centrifugal forces and an inertial surface flow with a curved profile. By means of discrete element simulations, we investigate the rheology of cascading flows in rotating drums as a function of drum size, rotation speed, and filling degree. We find that the surface profile, described by the ratio between the steepest descent slope and an average slope, is strongly correlated with flow variables such as active layer thickness, contact force variability, and wall slip. We show that the flow variables cannot be scaled by Froude number alone but are instead nicely scaled by a dimensionless parameter that combines the Froude number with other system parameters. This scaling works even for small drums and low filling degrees where finite-size effects prevail and the slippage of particles at the drum wall considerably affects the cascading flow at the free surface. The observed correlation between this parameter and contact force fluctuations suggests that it may also be a relevant upscaling parameter for milling and agglomeration in rotating drums.

Heat Exchange and Nonisothermal Crystallization in Formation of a Plane Viscoelastic Film

The processes of heat exchange and of nonisothermal crystallization in the formation of a plane viscoelastic polymer film are investigated. The polymer melt is forced through a plane-slitted extrusion head, subjected to uniaxial stretching and simultaneously to cooling in air, and subsequently gaining access onto a batch-off cooling roll. It is assumed that the film is wide enough, and the distance between the extruder head and the batch-off roll is minimum to such a degree that it is possible to neglect the change in the sheet width in the process of longitudinal stretching. A steady nonisothermal process is considered. It is also considered that the gravity and inertial forces and surface stretching can be neglected. From the rheological point of view, the polymer melt represents a viscoelastic fluid. The upper-convected Maxwell model is used with viscosity depending on temperature and crystallinity degree. The mathematical model is complemented by the equation of kinetics of nonisothermal crystallization. The problem has been solved numerically by the method of finite differences.

Waves in a Centrifuged Layer of a Rotating Viscous Fluid with an Inertial Surface

A model for describing wave motions of a flotatimg, viscous, non-compressible fluid partially filling the cavity of a rapidly rotating circular cylinder is proposed. The floating fluid is a fluid with an inertial surface formed by small mass particles floating on a free surface without interaction. The gyroscopic waves in a centrifuged flotating fluid layer on a solid wall of the rotor cavity are studied.

Stability of a directional Marangoni flow.

Marangoni flows result from surface-tension gradients, and these flows occur over finite distances on the surface, but the subsequent secondary flows can be observed on much larger lengthscales. These flows play major roles in various phenomena, from foam dynamics to microswimmer propulsion. We show here that if a Marangoni flow of soluble surfactants is confined laterally, the flow forms an inertial surface jet. A full picture of the flows on the surface is exhibited, and the velocity profile of the jet is predicted analytically, and is successfully compared with the experimental measurements. Moreover, this straight jet eventually destabilizes into meanders. A quantitative comparison between the theory and our experimental observations yields a very good agreement in terms of critical wavelengths. The characterization and understanding of the 2D flows generated by confined Marangoni spreading is a first step to understand the role of inertial effects in the Marangoni flows with and without confinement.

Formation of composite fuels by coating aluminum powder with a cobalt nanocatalyst: Enhanced heat release and catalytic performance

Aluminum (Al) and Cobalt (Co) materials are used as a metal fuel and a burning rate catalyst in solid propellants, respectively. However, micro-sized Al fuel has a poor heat release performance because of inertial surface oxide layers, and a nano-sized Co catalyst tends to agglomerate due to high surface energy and magnetism. In this work, we successfully synthesize a new composite fuel by coating Al fuel with a Co catalyst (Co/Al) via a novel replacement reaction and experimentally investigate its heat release and catalytic performance. Our measurements show that the heat release efficiency of Al powder is greatly enhanced by coating only 4.6 wt% of Co. The high oxidation temperature of the formed composite fuel is advanced by 112 °C, and the heat release is approximately 1.5 times that of the raw Al. The Co/Al composite fuel displays excellent catalytic activity and stability toward the thermal decomposition of ammonium perchlorate (AP), thereby decreasing the high decomposition temperature of AP by approximately 150 °C. To the best of our knowledge, the promoting efficiencies of the high-temperature oxidation of Al and the high-temperature decomposition of AP are higher than those reported in literature. The heat release and catalytic thermal decomposition mechanisms of Co/Al composite fuel are proposed on the basis of experimental phenomena and results. Results confirm that the formation of composite fuel by coating Al powder with a Co nanocatalyst is an effective method to enhance the heat release of Al and the catalytic performance towards AP. The as-obtained Co/Al composite fuel is expected to have wide application prospects in solid propellants.

An Efficient Integral Equation Approach to Study Wave Reflection by a Discontinuity in the Impedance-Type Surface Boundary Conditions

We investigate the interaction of obliquely incident waves by a discontinuity in the surface of water whose bottom is composed of non-dissipative porous medium. The discontinuity arises when two inertial surfaces with different surface densities float on the surface of the water, thereby giving rise to two different impedance-type surface boundary conditions. The two-dimensional problem is solved by employing Green’s second identity which leads to two coupled Fredholm integral equations in the potential function and the velocity across the vertical line below the point of discontinuity. Expressions for the reflection and the transmission coefficients are determined in terms of the solutions of the integral equations. The numerical results for the reflection coefficient are validated against the well known results for the normal incidence of the surface waves and rigid bottom available in the literature. The reflection coefficient is also analyzed for different values of the surface densities of the inertial surfaces, porous effect parameter and the angle of incidence of the surface waves. It is observed that the porous bottom causes resonance in the reflection coefficient for a particular wave frequency. Graphs for the surface profiles are also presented which reveal that the presence of inertial surface reduces the heights of the waves in a significant amount.

Descent image based landing area terrain reconstruction technology for lunar landing mission

In this paper, we present a descent image based extraterrestrial terrain reconstruction technology, which has been successfully applied in China's first soft landing Chang'E-3 mission on moon. When scouting on the moon surface, the lunar rover (Jade Rabbit rover) requires reliable terrain information for navigation and positioning tasks. The descent image sequence acts as a link between the orbital images and the surface images. The proposed approach collects multilevel descent images, as well as inertial information from an inertial measurement unit and surface stereo vision information, to generalise a consistent surface model. A data fusion strategy is proposed to track the camera trajectory, and refined plane sweep stereo matching and 3D alignment technologies are analysed in this article. The onboard result, as well as on-earth simulation experiments, has shown that the discussed techniques are reliable to reconstruct the terrain information for the lunar rover's localisation and navigation.

Effect of feed yarn parameters on air-jet textured yarn properties

In this study we report on the effect of feed yarn parameters viz., filament fineness, filament shape and total linear density on physical bulk, instability and strength of air-jet textured yarns. The yarns were textured under optimum process parameters. The inertial mass, surface area and directional bending effect of filaments affect the physical bulk, stability of loops and tensile strength of air-jet textured yarns. It is observed that an increase in linear density of filament results in a decrease in air-jet textured yarn physical bulk and loss in tenacity, while instability increases. Higher total yarn denier leads to higher physical bulk and instability and lower loss in tenacity. Trilobal polyester filament produces highest physical bulk and loss in tenacity; and lowest yarn instability, while rice shaped filament show lowest physical bulk. Circular filament show intermediate physical bulk and loss in tenacity and highest instability.

Space Group Approximation of a Molecular Crystal by Classifying Molecules for Their Electric Potentials and Roughness on Their Inertial Ellipsoid Surface

In order to predict the most probable space group where a molecule crystallizes, it is assumed that molecular shape and electric potential distribution on the molecular surface are the main factors or predictors. However, to compare and classify molecules by these two factors seems to be very difficult for in general such different objects. Thus, in order to compare molecules, they are reduced to their inertial ellipsoid in which surface 26 equally spaced points were chosen where a roughness factor and an electric potential due to all atomic charges of the whole molecule are calculated. By this procedure, different molecules encoded by these two predictor vectors can be compared and classified, showing that molecules that crystallize in the same space group have more similar predictor vectors. This result opens the possibility to predict the more probable spatial group associated with a molecule.

Effect of compressive stress on the dispersion relation of the flexural–gravity waves in a two-layer fluid with a uniform current

The explicitly analytical solution is derived for the dispersion relation of the flexural-gravity waves in a two-layer fluid with a uniform current. The upper fluid is covered by a thin plate with the presence of the elastic, compressive and inertial forces. The density of each of the two immiscible layers is constant. The fluids of finite depth are assumed to be inviscid and incompressible and the motion be irrotational. A linear system is established within the framework of potential theory. A new representation for the dispersion relation of flexural-gravity waves in a two-layer fluid is derived. The critical value for the compressive force is analytically determined. The dispersion relation for the capillary-gravity with an inertial surface in a two-layer fluid can be obtained in parallel. Some known dispersion relations can be recovered from the present solution.

Transient flexural- and capillary-gravity waves due to disturbances in two-layer density-stratified fluid

Generation of the transient flexural- and capillary-gravity waves by impulsive disturbances in a two-layer fluid is investigated analytically. The upper fluid is covered by a thin elastic plate or by an inertial surface with the capillary effect. The density of each of the two immiscible layers is constant. The fluids are assumed to be inviscid and incompressible and the motion be irrotational. A point force on the surface and simple mass sources in the upper and lower fluid layers are considered. A linear system is established within the framework of potential theory. The integral solutions for the surface and interfacial waves are obtained by means of the Laplace-Fourier transform. A new representation for the dispersion relation of flexural- and capillary-gravity waves in a two-layer fluid is derived. The asymptotic representations of the wave motions are derived for large time with a fixed distance-to-time ratio with the Stokes and Scorer methods of stationary phase. It is shown that there are two different modes, namely the surface and interfacial wave modes. The wave systems observed depend on the relation between the observer's moving speed and the intrinsic minimal and maximal group velocities.

Cauchy-poisson problem for a two-layer fluid with an inertial surface

This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.

A gradient elasticity theory for second-grade materials and higher order inertia

Second-grade elastic materials featured by a free energy depending on the strain and the strain gradient, and a kinetic energy depending on the velocity and the velocity gradient, are addressed. An inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics. The state variables include the body momentum and the surface momentum, related to the velocity in a nonstandard way, as well as the concomitant mass-accelerations and inertial forces, which do intervene into the motion equations and into the force boundary conditions. The boundary traction is the sum of two parts, i.e. the Cauchy traction and the Gurtin–Murdoch traction, whereas the traction boundary condition exhibits the typical format of the equilibrium equation of a material surface (as known from the principles of surface mechanics) whereby the Gurtin–Murdoch traction (incorporating the inertial surface force) plays the role of applied surfacial force density. The body’s boundary surface constitutes a thin boundary layer which is in global equilibrium under all the external forces applied on it, a feature that makes it possible to exploit the traction Cauchy theorem within second-grade materials. This means that a second-grade material is formed up by two sub-systems, that is, the bulk material operating as a classical Cauchy continuum, and the thin boundary layer operating as a Gurtin–Murdoch material surface. The classical linear and angular momentum theorems are suitably extended for higher order inertia, from which the local motion equations and the moment equilibrium equations (stress symmetry) can be derived. For an isotropic material featured by four constants, i.e. the Lamé constants and two length scale parameters (Aifantis model), the dynamic evolution problem is characterized by a Hamilton-type variational principle and a solution uniqueness theorem. Closed-form solutions of the wave dispersion analysis problem for beam models are presented and compared with known results from the literature. The paper indicates a correct thermodynamically consistent way to take into account higher order inertia effects within continuum mechanics.

Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling

Law-of-the-wall (LOTW) scaling implies that at sufficiently high Reynolds numbers the mean velocity gradient ∂U/∂z in the turbulent boundary layer should scale on u∗/z in the inertia-dominated surface layer, where u∗ is the friction velocity and z is the distance from the surface. In 1992, Mason and Thomson pointed out that large-eddy simulation (LES) of the atmospheric boundary layer (ABL) creates a systematic peak in ϕ(z)≡(∂U/∂z)/(u∗/z) in the surface layer. This “overshoot” is particularly evident when the first grid level is within the inertial surface layer and in hybrid LES/Reynolds-averaged Navier–Stokes methods such as “detached-eddy simulation,” where the overshoot is identified as a “logarithmic layer mismatch.” Negative consequences of the overshoot—spurious streamwise coherence, large-eddy structure, and vertical transport—are enhanced by buoyancy. Several studies have shown that adjustments to the modeling of the subfilter scale (SFS) stress tensor can alter the degree of the overshoot. A comparison among simulations indicates a lack of grid independence in the prediction of mean velocity that originates in surface layer deviations from LOTW. Here we analyze the broader framework of LES prediction of LOTW scaling—including, but extending beyond, “the overshoot.” Our theory includes a criterion that is necessary to remove the overshoot but is insufficient for LES to produce constant ϕ(z)≡1/κ through the surface layer, and fully satisfy the LOTW. For mean shear to scale on u∗/z in the surface layer, we show that two additional criteria must be satisfied. These criteria can be framed in terms of three nondimensional variables that define a parameter space in which systematic adjustments can be made to the simulation to achieve LOTW scaling. This occurs when the three parameters exceed critical values that we estimate from basic scaling arguments. The essential difficulty can be traced to a spurious numerical LES viscous length scale that interferes with the dimensional analysis underlying LOTW. When this spurious scale is suppressed sufficiently to retrieve LOTW scaling, the LES has been moved into the supercritical “high accuracy zone” (HAZ) of our parameter space. Using eddy viscosity closures for SFS stress, we show that to move the simulation into the HAZ, the model constant must be adjusted together with grid aspect ratio in coordinated fashion while guaranteeing that the surface layer is sufficiently well resolved in the vertical by the grid. We argue that, in principle, both the critical values that define the HAZ and the surface layer constant κ when LOTW scaling is achieved can depend on details of the SFS (and surface stress) models applied in the LES. We carried out over 110 simulations of the neutral rough-surface ABL to cover a wide portion of the parameter space using a low dissipation spectral code, the Smagorinsky SFS stress model and a standard model for fluctuating surface stress. The overshoot was found to systematically reduce and ϕ(z) was found to systematically approach a constant value in the surface layer as the three parameters exceeded critical values and the LES moved into the HAZ, consistent with the theory. However, whereas constant ϕ(z) was achieved over nearly the entire surface layer as the LES is moved into the HAZ, the model for surface shear stress continues to disrupt LOTW scaling at the first couple grid levels, and the predicted von Kármán constant κ is lower than traditional values. In a comprehensive discussion, we summarize the primary results of subsequent studies where we minimize the spurious influence of the surface stress model and show that the surface stress model and the SFS stress model constant influence the predicted value of the von Kármán constant for LES in the HAZ.

Flexural- and capillary-gravity waves due to fundamental singularities in an inviscid fluid of finite depth

Wave motion due to line, point and ring sources submerged in an inviscid fluid are analytically investigated. The initially quiescent fluid of finite depth, covered by a thin elastic plate or by an inertial surface with the capillary effect, is assumed to be incompressible and homogenous. The strengths of the sources are time-dependent. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The perturbed flow is decomposed into the regular and the singular components. An image system is introduced for the singular part to meet the boundary condition at the flat bottom. The solutions in integral form for the velocity potentials and the surface deflexions due to various singularities are obtained by means of a joint Laplace–Fourier transform. To analyze the dynamic characteristics of the flexural- and capillary-gravity waves due to unsteady disturbances, the asymptotic representations of the wave motion are explicitly derived for large time with a fixed distance-to-time ratio by virtue of the Stokes and Scorer methods of stationary phase. It is found that the generated waves consist of three wave systems, namely the steady-state gravity waves, the transient gravity waves and the transient flexural/capillary waves. The transient wave system observed depends on the moving speed of the observer in relation to the minimal and maximal group velocities. There exists a minimal depth of fluid for the possibility of the propagation of capillary-gravity waves on an inertial surface. Furthermore, the results for the pure gravity and capillary-gravity waves in a clean surface can also be recovered as the flexural and inertial parameters tend to zero.