Volume Conservation Research Articles

Drawability and size effects for micro-arrayed deep drawing of Ni-Co/GO nanocomposite foils

For the first time, three different male dies (a rigid male die, an aluminum male die, and a nanoceramic powder male die) are used for a micro-arrayed deep drawing process using graphene oxide (GO) reinforced Ni-Co nanocomposite. Micro-parts with different shapes can be formed using the different male dies, and models to predict crack positions are established. The nanocomposite size effect leads to an increased depth-diameter ratio for decreasing female die diameters, and the conservation of volume leads to higher depth-diameter ratios and thinning rates. The reinforcing GO phase not only is able to improve the micro formability of the composite, but also inhibits grain growth at high temperature.

Quantitative risk assessment of continuous liquid spill fires based on spread and burning behaviours

Spill fires usually occur during the storage and transportation of hazardous materials, posing a threat to the people and environment in their immediate proximity. In this paper, a classical Quantitative Risk Assessment (QRA) method is used to assess the risk of spill fires. In this method, the maximum spread area and the steady burning area are introduced as parameters to clearly assess the range of influence of the spill fire. In the calculations, a modified spread model that takes into consideration the burning rate variation is established to calculate the maximum spread area. Furthermore, the steady burning area is calculated based on volume conservation between the leakage rate and the fuel consumption rate due to burning. Combining these two parameters with leakage frequency, flame model, and vulnerability model, the dynamic individual risk can be calculated quantitatively. Subsequently, large-scale experiments of spill fires on water and a glass sheet were conducted to verify the accuracy and application of the model. The results show that the procedure we developed can be used to quantitatively calculate the risk associated with a continuous spill fire.

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

ON A MATHEMATICAL MODEL DESCRIBING OPTIMAL PROCESSING MECHANISM OF DISPERSED GRANULAR MATERIALS IN GRAVITATIONAL FLOW WITH HORIZONTAL OR INCLINED VIBRATING SIEVE CLASSIFYING SCREENS

The investigation of motion and gravitational processing of disperse granular materials is very important for solution of a wide spectrum of technological processes, including the chemical technology of treatment (with or without the decoration-compression procedure) of granular mineral fertilizers and their drying and sorting/separation by means of vibrating sieve classifying screens, in particular. In this work, we have used the apparatus of the theory of continuous media for the mathematical modelling of dynamics of disperse granular materials, and by this we assume that a property of these materials is the distribution of a solid granular component inside of them. The elaborated mathematical model is based on the volume conservation law for granular components, on the momentum conservation law, as well as on the equations for stress tensor in the granular mineral fertilizers and equations for description of the Coulomb granular mineral fertilizers.

Conservation of spatial volume and the response of inertia and gravity

Conservation of spatial volume and the response of inertia and gravity

Nearshore hydrodynamics, beachface cobble transport and morphodynamics on a Pacific atoll motu

Measurements of wave transformation, beachface cobble transport and shoreline morphology change were undertaken over a 14month period at Fatato Island, a cobble and sand ‘motu’ on the southeast rim of Funafuti Atoll, Tuvalu. Results document significant cobble transport and beach profile change on Fatato during a year in the absence of any significant high energy wave events. Changes in beachface volume were measured on 11 across-shore beach profiles, and show marked variations of +7.1 and −7.01m3 between profiles and between survey periods. Net volumetric beachface change over the 14month experiment was approximately zero, indicating a balance between erosion and deposition and net conservation of sediment volume on the ocean shoreline. Cobble movement was measured using Passive Integrated Transponder (PIT) tags inserted in 300 randomly selected clasts (mean b-axis=75mm) on the mid-beachface. Tagged particles were re-surveyed after 6 and 14months, achieving 76% recovery, and identify large excursions of clasts on the beachface and dominant southwest alongshore transport, with an average net movement of 68m after 14months. A simple agent based probabilistic model was developed to simulate cobble movement and explore the coupling between hydrodynamic and shoreline processes. Model simulations reveal: predominant south-westerly cobble transport is driven by mean wave conditions associated with easterly trade winds, and; long-period swell events that approach the reef from the south drive episodic north-easterly transport reversals and significant onshore transport that can strand particles on the upper beach. Results present the first observations of morphodynamic behaviour of an atoll motu and highlight the highly dynamic nature of motu shorelines under mean energy conditions. Such results challenge conventional perspectives that motu are storm adjusted landforms that require extreme events to stimulate geomorphic change and inform future projections of island change.

A reformulation of the conservative level set reinitialization equation for accurate and robust simulation of complex multiphase flows

This paper presents an accurate and robust reinitialization equation for the conservative level set that does not significantly deform stationary surfaces. The compression and diffusion term of the reinitialization equation are reformulated to use a distance level set directly mapped from the conservative level set. The normals are calculated using a distance level set reconstructed from the interface using a fast marching method, increasing robustness and allowing the use of high order, non-TVD transport schemes. Using this new reinitialization equation, we present results for canonical test cases, such as Zalesak's disk and spurious currents, which show significant improvement. A simulation of a liquid–gas jet with Re=5000 is also presented to demonstrate the volume conservation properties of the method in more complex flows.

Total Exchange Flow, Entrainment, and Diffusive Salt Flux in Estuaries

AbstractThe linkage among total exchange flow, entrainment, and diffusive salt flux in estuaries is derived analytically using salinity coordinates, revealing the simple but important relationship between total exchange flow and mixing. Mixing is defined and quantified in this paper as the dissipation of salinity variance. The method uses the conservation of volume and salt to quantify and distinguish the diahaline transport of volume (i.e., entrainment) and diahaline diffusive salt flux. A numerical model of the Hudson estuary is used as an example of the application of the method in a realistic estuary with a persistent but temporally variable exchange flow. A notable finding of this analysis is that the total exchange flow and diahaline salt flux are out of phase with respect to the spring–neap cycle. Total exchange flow reaches its maximum near minimum neap tide, but diahaline salt transport reaches its maximum during the maximum spring tide. This phase shift explains the strong temporal variation of stratification and estuarine salt content through the spring–neap cycle. In addition to quantifying temporal variation, the method reveals the spatial variation of total exchange flow, entrainment, and diffusive salt flux through the estuary. For instance, the analysis of the Hudson estuary indicates that diffusive salt flux is intensified in the wider cross sections. The method also provides a simple means of quantifying numerical mixing in ocean models because it provides an estimate of the total dissipation of salinity variance, which is the sum of mixing due to the turbulence closure and numerical mixing.

High salt intake reprioritizes osmolyte and energy metabolism for body fluid conservation.

Natriuretic regulation of extracellular fluid volume homeostasis includes suppression of the renin-angiotensin-aldosterone system, pressure natriuresis, and reduced renal nerve activity, actions that concomitantly increase urinary Na+ excretion and lead to increased urine volume. The resulting natriuresis-driven diuretic water loss is assumed to control the extracellular volume. Here, we have demonstrated that urine concentration, and therefore regulation of water conservation, is an important control system for urine formation and extracellular volume homeostasis in mice and humans across various levels of salt intake. We observed that the renal concentration mechanism couples natriuresis with correspondent renal water reabsorption, limits natriuretic osmotic diuresis, and results in concurrent extracellular volume conservation and concentration of salt excreted into urine. This water-conserving mechanism of dietary salt excretion relies on urea transporter-driven urea recycling by the kidneys and on urea production by liver and skeletal muscle. The energy-intense nature of hepatic and extrahepatic urea osmolyte production for renal water conservation requires reprioritization of energy and substrate metabolism in liver and skeletal muscle, resulting in hepatic ketogenesis and glucocorticoid-driven muscle catabolism, which are prevented by increasing food intake. This natriuretic-ureotelic, water-conserving principle relies on metabolism-driven extracellular volume control and is regulated by concerted liver, muscle, and renal actions.

An Image-Domain Contrast Material Extraction Method for Dual-Energy Computed Tomography.

Conventional material decomposition techniques for dual-energy computed tomography (CT) assume mass or volume conservation, where the CT number of each voxel is fully assigned to predefined materials. We present an image-domain contrast material extraction process (CMEP) method that preferentially extracts contrast-producing materials while leaving the remaining image intact. Image processing freeware (Fiji) is used to perform consecutive arithmetic operations on a dual-energy ratio map to generate masks, which are then applied to the original images to generate material-specific images. First, a low-energy image is divided by a high-energy image to generate a ratio map. The ratio map is then split into material-specific masks. Ratio intervals known to correspond to particular materials (eg, iodine, calcium) are assigned a multiplier of 1, whereas ratio values in between these intervals are assigned linear gradients from 0 to 1. The masks are then multiplied by an original CT image to produce material-specific images. The method was tested quantitatively at dual-source CT and rapid kVp-switching CT (RSCT) with phantoms using pure and mixed formulations of tungsten, calcium, and iodine. Errors were evaluated by comparing the known material concentrations with those derived from the CMEP material-specific images. Further qualitative evaluation was performed in vivo at RSCT with a rabbit model using identical CMEP parameters to the phantom. Orally administered tungsten, vascularly administered iodine, and skeletal calcium were used as the 3 contrast materials. All 5 material combinations-tungsten, iodine, and calcium, and mixtures of tungsten-calcium and iodine-calcium-showed distinct dual-energy ratios, largely independent of material concentration at both dual-source CT and RSCT. The CMEP was successful in both phantoms and in vivo. For pure contrast materials in the phantom, the maximum error between the known and CMEP-derived material concentrations was 0.9 mg/mL, 24.9 mg/mL, and 0.4 mg/mL for iodine, calcium, and tungsten respectively. Mixtures of iodine and calcium showed the highest discrepancies, which reflected the sensitivity of iodine to the image-type chosen for the extraction of the final material-specific image. The rabbit model was able to clearly show the 3 extracted material phases, vascular iodine, oral tungsten, and skeletal calcium. Some skeletal calcium was misassigned to the extracted iodine image; however, this did not impede the depiction of the vasculature. The CMEP is a straightforward, image-domain approach to extract material signal at dual-energy CT. It has particular value for separation of experimental high-Z contrast elements from conventional iodine contrast or calcium, even when the exact attenuation coefficient profiles of desired contrast materials may be unknown. The CMEP is readily implemented in the image-domain within freeware, and can be adapted for use with images from multiple vendors.

Wastewater reuse potential for irrigated agriculture

This study analyzed the effects of population and urban growth on water demand for irrigation and other water users, as well as municipal wastewater quantity changes, by developing a new mathematical model. The model was developed to consider the potential for reuse of treated wastewater for agricultural irrigation, by analyzing the increasing quantity of wastewater production in an urban area. It was applied to a case study in Logan, Utah, whereby results from the model showed a total water demand of 0.7 and 1.27 m3/s in 2020 and 2050, respectively, while the model predicted that the average wastewater influent for Logan City would be more than double from 2010 to 2050. Accordingly, a model-predicted increase of 16% in the annual production of wastewater was observed from 2010 to 2025. The amount of wastewater production in 2030 was estimated to be 14.2 million m3/year, which is enough to produce food from irrigated agriculture for 11% of the future population of Logan City. This emphasizes the potential importance of reusing wastewater for irrigated agriculture. Water conservation was also studied and it showed that a 5% conservation of water volume could cover the needs of an additional 4.2 thousand people in 2030.

Model diagnostic analysis of cross-shelf flow in the northern South China Sea

To explore cross-shelf flow in the northern South China Sea, model diagnostic calculation was conducted using a regional, three-dimensional, primitive equation model (POM) and the climatological temperature and salinity fields supplied by the Generalized Digital Environment Model (version 3.0). Using the model calculations, we systematically evaluated the characteristics of cross-shelf flow and estimated its volume, heat, and salt transports in different sections along the continental slope. The dynamic process of cross-shelf flow was further analyzed using the vorticity balance. Results revealed the spatial distribution of the cross-shelf flow in the northern South China Sea. Between the 200– 2000 m isobaths, the horizontal distribution of cross-shelf flow was uniform, and strong cross-shelf flow was present in areas of the continental slope with complex topography. We selected three sections (S1, S2, and S3 along the 200, 500, and 1000 m isobaths, respectively) to characterize the cross-shelf flow. Three local maximal cross-shelf velocities in the on-shelf direction were detected in sections S1 and S2, but this feature was not clear in section S3. Strong cross-shelf flow (>2 cm/s) was present at about 115°E and 118°E of section S1 in winter. The annual mean cross-shelf volume transports in sections S1, S2, and S3 were 9.4, 15.8, and - 2.1 Sv, respectively. The heat content transports were 0.78, 0.84, and - 0.22 PW, respectively, and the salt content transports were 342.5, 575.0, and - 76.0 Gg s - 1, respectively. The cross-shelf flow was towards the shelf in the 200–500 m isobaths region and in the opposite direction in the 500–2000 m isobaths region. Cross-shelf transport was stronger in winter and weaker in summer in sections S1 and S2, but no seasonal difference was found in section S3. These cross-shelf transports of sea water, heat, and salt along the continental shelf reflect the main characteristics of cross-shelf flow. According to the volume transport between the three sections, flow convergence arose between sections S1 and S2 and divergence occurred between sections S2 and S3. In terms of volume conservation, these spatial distributions of flow convergence and divergence resulted in the cross-shelf flow. The along-shelf flow was the primary component of slope current, whereas cross-shelf flow contributed only about 15%–20%. Although cross-shelf flow was not as strong as along-shelf flow, its influence must not be ignored due to its huge volume, heat, and salt transports. Analysis of momentum balance revealed that the slope current was mainly controlled by the geostrophic equilibrium, in which the pressure gradient and Coriolis force played a dominated role. The cross-shelf flow was mainly barotropic in most regions, but it exhibited a baroclinic feature in the region east of 118°E. The analysis of barotropic vorticity balance indicated that the cross-shelf flow was mainly controlled by the joint effect of baroclinicity and bottom relief term (JEBAR), advection of the geostrophic potential vorticity term (APV), and the advection and diffusion term. The JEBAR term mainly controlled the cross-shelf flow along the continental slope due to the positive potential vorticity produced by the interaction between the baroclinic sea water and topography. To the east of 118°E, the instrusive Kuroshio Current led to interaction between baroclinic sea water and the continental slope, which increased the JEBAR term and therefore strengthened the cross-shelf flow.

Mass Entrainment Rate of an Ideal Momentum Turbulent Round Jet

We propose a two-phase-fluid model for a full-cone turbulent round jet that describes its dynamics in a simple but comprehensive manner with only the apex angle of the cone being a disposable parameter. The basic assumptions are that (i) the jet is statistically stationary and that (ii) it can be approximated by a mixture of two fluids with their phases in dynamic equilibrium. To derive the model, we impose conservation of the initial volume and total momentum fluxes. Our model equations admit analytical solutions for the composite density and velocity of the two-phase fluid, both as functions of the distance from the nozzle, from which the dynamic pressure and the mass entrainment rate are calculated. Assuming a far-field approximation, we theoretically derive a constant entrainment rate coefficient solely in terms of the cone angle. Moreover, we carry out experiments for a single-phase turbulent air jet and show that the predictions of our model compare well with this and other experimental data of atomizing liquid jets.

Energy-saving with low dimensional network in Physarum plasmodium

An adaptation process in the transportation network of Physarum plasmodium was investigated by measuring oxygen consumption during network formation. Simultaneously, the fractal dimension as a measure of network structure was estimated. Oxygen consumption decreased during the development of the network, whereas the network structure changed from a thin mesh-type to a thick dendritic type. Our data suggested that the morphology of the plasmodial network governed energy consumption; a low dimensional network in the sense of the fractal dimension reduced energy consumption. These data were supported by experimental results excluding biological reasons, such as differences in starvation/nutrient-fullness states, and aspects of mitochondrial distribution. Model analysis using the Physarum algorithm with volume conservation constraints confirmed the above findings.

A kinetic study of the spontaneous penetration of a water drop into a hydrophobic pore

The spontaneous penetration of a water drop into hydrophobic single-pored samples of varying inside and outside diameters was studied. During penetration, the radius of the water drop, its contact angle, the contact radius, and the penetration length inside the pore were measured against time. Experimental results showed that a water drop on the sample with the smaller pore had a longer penetration time than a water drop on the sample with the bigger pore. A pored sample with a small outside radius (thin tube) leads to a fast penetration rate presenting a parabolic trend in penetration versus time. The maximum penetration rate was observed when the contact angle was 90°. This is mainly due to the minimum radius of the drop at this angle as the drop radius directly relates to the Laplace pressure, which is the driving force in penetration. Two factors were identified as affecting penetration. The first is the receding contact angle leading to the stick-slip-like motion of a water drop. The second is the outside radius of a pored sample, which affects the penetration rate and trend. These factors were also correlated to the penetration process through theoretical analysis considering the geometry of the capillary system, volume conservation and momentum conservation. The initial contact angle and radius of a drop were determined by the outside radius of a pored sample, which changed Laplace pressure with time, thus influencing the penetration trend and rate. This indicates that a thin tube promotes fast penetration, and the point of maximum penetration rate was shown to be later during the penetration. Understanding the effects of outside radius and receding contact angle in the kinetic aspect of drop penetration into a hydrophobic pore is fundamentally important. This research is beneficial to the design of porous materials and in controlling the wetting and penetration process.

Aerosol transport throughout inspiration and expiration in the pulmonary airways.

Little is known about transport throughout the respiration cycle in the conducting airways. It is challenging to appropriately describe the time-dependent number of particles entering back into the model during exhalation. Modeling the entire lung is not feasible; therefore, multidomain methods must be used. Here, we present a new framework that is designed to simulate particles throughout the respiration cycle, incorporating realistic airway geometry and respiration. This framework is applied for a healthy rat lung exposed to ∼1μm diameter particles, chosen to facilitate parameterization and validation. The flow field is calculated in the conducting airways (3D domain) by solving the incompressible Navier-Stokes equations with experimentally derived boundary conditions. Particles are tracked throughout inspiration by solving a modified Maxey-Riley equation. Next, we pass the time-dependent particle concentrations exiting the 3D model to the 1D volume conservation and advection-diffusion models (1D domain). Once the 1D models are solved, we prescribe the time-dependent number of particles entering back into the 3D airways to again solve for 3D transport. The coupled simulations highlight that about twice as many particles deposit during inhalation compared to exhalation for the entire lung. In contrast to inhalation, where most particles deposit at the bifurcation zones, particles deposit relatively uniformly on the gravitationally dependent side of the 3D airways during exhalation. Strong agreement to previously collected regional experimental data is shown, as the 1D models account for lobe-dependent morphology. This framework may be applied to investigate dosimetry in other species and pathological lungs.

A monolithic 3D-0D coupled closed-loop model of the heart and the vascular system: Experiment-based parameter estimation for patient-specific cardiac mechanics.

A model for patient-specific cardiac mechanics simulation is introduced, incorporating a 3-dimensional finite element model of the ventricular part of the heart, which is coupled to a reduced-order 0-dimensional closed-loop vascular system, heart valve, and atrial chamber model. The ventricles are modeled by a nonlinear orthotropic passive material law. The electrical activation is mimicked by a prescribed parameterized active stress acting along a generic muscle fiber orientation. Our activation function is constructed such that the start of ventricular contraction and relaxation as well as the active stress curve's slope are parameterized. The imaging-based patient-specific ventricular model is prestressed to low end-diastolic pressure to account for the imaged, stressed configuration. Visco-elastic Robin boundary conditions are applied to the heart base and the epicardium to account for the embedding surrounding. We treat the 3D solid-0D fluid interaction as a strongly coupled monolithic problem, which is consistently linearized with respect to 3D solid and 0D fluid model variables to allow for a Newton-type solution procedure. The resulting coupled linear system of equations is solved iteratively in every Newton step using 2×2 physics-based block preconditioning. Furthermore, we present novel efficient strategies for calibrating active contractile and vascular resistance parameters to experimental left ventricular pressure and stroke volume data gained in porcine experiments. Two exemplary states of cardiovascular condition are considered, namely, after application of vasodilatory beta blockers (BETA) and after injection of vasoconstrictive phenylephrine (PHEN). The parameter calibration to the specific individual and cardiovascular state at hand is performed using a 2-stage nonlinear multilevel method that uses a low-fidelity heart model to compute a parameter correction for the high-fidelity model optimization problem. We discuss 2 different low-fidelity model choices with respect to their ability to augment the parameter optimization. Because the periodic state conditions on the model (active stress, vascular pressures, and fluxes) are a priori unknown and also dependent on the parameters to be calibrated (and vice versa), we perform parameter calibration and periodic state condition estimation simultaneously. After a couple of heart beats, the calibration algorithm converges to a settled, periodic state because of conservation of blood volume within the closed-loop circulatory system. The proposed model and multilevel calibration method are cost-efficient and allow for an efficient determination of a patient-specific in silico heart model that reproduces physiological observations very well. Such an individual and state accurate model is an important predictive tool in intervention planning, assist device engineering and other medical applications.

Tailoring volume magnetostriction of giant magnetostrictive materials by engineering magnetic domain morphology

Volume conservation is usually considered for the classic magnetostrictive materials during technical magnetization process. The present work reports the forced volume magnetostriction prior to saturation magnetization in the rare-earth giant magnetostrictive materials by engineering the initial magnetic domain morphology. It is found that the volume magnetostriction can be manipulated with the changeable sign and magnitude from about −200 × 10−6 at the thermal-demagnetized state to 450 × 10−6 at the domain-aligned state. Such behavior arises from the different domain pathways. On the light of these observations, the exploration of materials design and applications based on the volume magnetostriction effect might be facilitated.

Exceptional endocranium and middle ear of Stanocephalosaurus (Temnospondyli: Capitosauria) from the Triassic of Algeria revealed by micro-CT scan, with new functional interpretations of the hearing system

Temnospondyls form a large clade of extinct non-amniotic tetrapods. Although their external cranial anatomy is relatively well known, their endocranium (i.e. internal structures of the skull) remains poorly known due to the lack of well-preserved material with conservation of the original anatomic volume. Internal structures are generally crushed under the skull roof due to the frequent flattening of skulls during fossilization. Yet this region is of great paleobiological interest with respect to the hearing, nervous, and vascular systems. In addition, endocranial characters have already been shown to be phylogenetically very informative in various vertebrate groups (e.g. mammals, dinosaurs). An exquisite skull belonging to Stanocephalosaurus amenasensis from the Lower-Middle Triassic of the Zarzaitine Series (Algeria) has been investigated by X-ray micro-CT (computed tomography) scan. The resulting 3-D reconstruction of this unique specimen reveals highly detailed anatomy of the endocranial region, which is described herein. In addition, both columellar cavity and stapes morphologies lead to a new functional hypothesis for the stapes as part of an underwater hearing system. This endocranium description increases our knowledge of temnospondyl paleobiology and endocranial structure variability. The hearing system postulated in S. amenasensis provides an evolutionary scenario which is also compared with that of extant anurans.

The application of interactive dynamic virtual surgical simulation visualization method

In this paper, an interactive dynamic simulation method is proposed to solve computational models of soft tissue undergoing large deformation, collision detection, and volume conservation in medical surgical simulation visualization. During the process of implementation of the interactive dynamic simulation method, the point-based method is used to simulate the elastic solids undergoing large deformations and the position-based method is used to simulate the objects collision, friction and volume conservation. Numerical results demonstrate that the proposed method improves the efficiency and stability of the response of heterogeneous soft tissue undergoing contact or even the multi-organs interactions, and it can be extended to interactive biopsy and cutting simulation.