Simple Flow Model Research Articles

Mathematical Modeling of Destabilizing Gas Condensate Droplets in Water Emulsions Using the Population Balance Method

AbstractThe emulsion of hydrocarbon components in water is usually found in the wastewater of refineries. In this work, a mathematical modeling of the destabilization process of gas condensate droplets in water emulsions was constructed using the population balance equation, and the coalescence coefficient (agglomeration kernel) of different demulsifiers (KENON 20, KENON 4, KENON 2, CTAB, SDS, Span 80, Span 60, Polyamide, Polyacrylamide and an EO/PO block copolymer of dodecan-1-ol) was obtained. For modeling, it needs droplets size distribution before adding a demulsifier at time = 0 and after adding a demulsifier at time = 1 h and 2 h. For this purpose, the numerical method of Crank-Nicolson by MATLAB software was applied. Additionally, the growth of gas condensate droplets was modeled by the population balance, and the agglomeration kernel for each demulsifier with the help of two models (simple flow and sum of the volumes) was determined. Moreover, the dependency of the agglomeration kernel to time was obtained. The results showed that the accuracy of the sum of the volumes model was better than the simple flow model to describe destabilization of the emulsion with demulsifiers. Furthermore, the agglomeration kernel of demulsifiers increases with increasing the demulsification time.

Microvascular flow dictates the compromise between spatial resolution and acquisition time in Ultrasound Localization Microscopy

Medical ultrasound is a widely used diagnostic imaging technique for tissues and blood vessels. However, its spatial resolution is limited to a sub-millimeter scale. Ultrasound Localization Microscopy was recently introduced to overcome this limit and relies on subwavelength localization and tracking of microbubbles injected in the blood circulation. Yet, as microbubbles follow blood flow, long acquisition time are required to detect them in the smallest vessels, leading to long reconstruction of the microvasculature. The objective of this work is to understand how blood flow limits acquisition time. We studied the reconstruction of a coronal slice of a rat’s brain during a continuous microbubble injection close to clinical concentrations. After acquiring 192000 frames over 4 minutes, we find that the biggest vessels can be reconstructed in seconds but that it would take tens of minutes to map the entire capillary network. Moreover, the appropriate characterization of flow profiles based on microbubble velocity within vessels is bound by even more stringent temporal limitations. As we use simple blood flow models to characterize its impact on reconstruction time, we foresee that these results and methods can be adapted to determine adequate microbubble injections and acquisition times in clinical and preclinical practice.

Development of the Stage Flow Relations for a Tropical Watershed

The effluent discharge from wastewater treatment plants can permeate through the ground and become a major source of contaminant to ecosystems and water bodies. These toxic contaminants can transport and find a way to the ocean via underground streams harming the aquatic life and promoting algal blooms. This paper presents meteorological and hydrological data collection and analysis to better understand the characteristics of the effluent discharge from the wastewater treatment plant and receiving water in Toguan watershed on the Island of Guam so as to support future regulatory discussions regarding modification of permit conditions and/or water quality standards to achieve compliance. Hydrological data such as rainfall, turbidity and stream level were collected over a period of two years. Crossflow measurements for two stations, one downstream, the other upstream of the effluent discharge point were collected bi-weekly, except at times of very low flow or dangerously high storm runoff in the stream. To better understand the behavior of the Toguan River sub-watersheds, aerial photos were taken from a single-engine Cessna aircraft. By analyzing the collected hydrological data, the relationships among the stream level, volume discharge and rainfall, were developed. The manually collected crossflow data allowed for the calculation of a rating curve for the Toguan River. This effort was somewhat hampered by prolonged drought conditions during roughly half of the period of data collection that severely limited the amount of crossflow measurements taken at high stage heights. The continuous measurement of stream level and rainfall allowed for a more comprehensive analysis of the relationship between the stage height and rainfall. Finally, a complimentary stream stage height short-term prediction scheme was developed using a routing model, and refinements to the stream flow discharge curve using a simple model for open channel flow is also presented. A further benefit of the study was the establishment of a baseline for the hydrologic conditions of the Toguan watershed which can be used to assess changes related to any future improvements to the wastewater treatment plant operations or other significant developments within this watershed.

Photoevaporation of Molecular Clouds in Regions of Massive Star Formation as Revealed through H2 and Brγ Emission

Abstract We examine new and pre-existing wide-field, continuum-corrected, narrowband images in H2 1-0 S(1) and Brγ of three regions of massive star formation: IC 1396, Cygnus OB2, and Carina. These regions contain a variety of globules, pillars, and sheets, so we can quantify how the spatial profiles of emission lines behave in photodissociation regions (PDRs) that differ in their radiation fields and geometries. We have measured 450 spatial profiles of H2 and Brγ along interfaces between H ii regions and PDRs. Brγ traces photoevaporative flows from the PDRs, and this emission declines more rapidly with distance as the radius of curvature of the interface decreases, in agreement with models. As noted previously, H2 emission peaks deeper into the cloud relative to Brγ, where the molecular gas absorbs far-UV radiation from nearby O stars. Although PDRs in IC 1396, Cygnus OB2, and Carina experience orders of magnitude different levels of ionizing flux and have markedly differing geometries, all of the PDRs have spatial offsets between Brγ and H2 on the order of 1017cm. There is a weak negative correlation between the offset size and the intensity of ionizing radiation and a positive correlation with the radius of curvature of the cloud. We can reproduce both the size of the offsets and the dependencies of the offsets on these other variables with simple photoevaporative flow models. Both Brγ and H2 1-0 S(1) will undoubtedly be targeted in future James Webb Space Telescope observations of PDRs, so this work can serve as a guide to interpreting these images.

Construction and validation of a statistical model for the nonlinear Kelvin-Helmholtz instability under compressible, multimode conditions

A new model for the evolution of compressible, multimode Kelvin-Helmholtz (KH) instability is presented. The model is built upon compressible single vortex evolution and two-vortex interaction, resulting in a statistical description of the compressible KH mixing zone evolution. These two building blocks, which, due to complicated compressibility effects and the presence of shock waves, cannot be derived using simple flow models, are validated by novel supersonic high-energy-density physics experiments. The model was validated against numerical simulations, experimental results, and previous phenomenological models, confirming the compressible KH scaling law in the self-similar regime in good agreement with simulations and a compilation of experimental data. Moreover, the model extends and confirms the logical validity of previous work, done in the incompressible regime. Therefore, it sheds new light on the evolution of compressible shear layers up to the self-similar regime.

Evaluation of the Temperature Regime of the Rods of the Inductor of an MHD Stirrer for Possible Use in an Industrial Aluminum Furnace

In the production of aluminum alloys, the melt must be stirred in the bath of a furnace. For this purpose, it is convenient to use MHD stirrers. However, MHD stirrers that are used in production in practice are mainly linear traveling-field inductors, which cannot be sufficiently effective because of their design features. Their size is much smaller than the linear dimensions of the bath, and the poles of their magnetic circuits are outside the bath walls and the insulation layer; therefore, the traveling magnetic field that influences the molten metal is significantly reduced. For this reason, the electrical power consumed by these MHD stirrers is high (hundreds of kilovolt–amperes). A device in the form of a system of rods (buses) connected in parallel to a three-phase power network and placed in close proximity to the molten metal immediately under the bottom of the bath may be an alternative to these stirrers. The main problem associated with this device is the cooling of rods via the removal of the Joule heat that is released during the passage of an electric current in the rods and the heat received from the molten metal in the bath in the furnace. The simplest way to withdraw the released heat is the convective movement of air in the tubular rods (it is not necessary to use special additional equipment). When conducting multivariant engineering calculations in designing such devices, it is necessary to determine the values of a cooling convective air flow in the hollow rods of the inductor of an MHD stirrer. In the present paper, we propose a numerical calculation of the temperature field in the aluminum furnace and a simple model for the convective air flow that passes through the rods of the inductor of an MHD stirrer. Based on this model and using the results of the physical experiments performed in this study, a simple semiempirical engineering formula for the approximate computation of the convective air-motion velocity in the hollow rods of an MHD stirrer is derived.

Transport of Polymer Particles in Oil–Water Flow in Porous Media: Enhancing Oil Recovery

We study a heuristic, core-scale model for the transport of polymer particles in a two phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when polymers are injected after the initial waterflood. The recovery mechanism is believed to be microscopic diversion of the flow, where injected particles can accumulate in narrow pore throats and clog it, in a process known as a log-jamming effect. The blockage of the narrow pore channels lead to a microscopic diversion of the water flow, causing a redistribution of the local pressure, which again can lead to the mobilization of trapped oil, enhancing its recovery. Our objective herein is to develop a core-scale model that is consistent with the observed production profiles. We show that previously obtained experimental results can be qualitatively explained by a simple two-phase flow model with an additional transport equation for the polymer particles. A key aspect of the formulation is that the microscopic heterogeneity of the rock and a dynamic altering of the permeability must be taken into account in the rate equations.

Impact excitation of a seismic pulse and vibrational normal modes on asteroid Bennu and associated slumping of regolith

We consider an impact on an asteroid that is energetic enough to cause resurfacing by seismic reverberation and just below the catastrophic disruption threshold, assuming that seismic waves are not rapidly attenuated. In asteroids with diameter less than 1 km we identify a regime where rare energetic impactors can excite seismic waves with frequencies near those of the asteroid’s slowest normal modes. In this regime, the distribution of seismic reverberation is not evenly distributed across the body surface. With mass-spring model elastic simulations, we model impact excitation of seismic waves with a force pulse exerted on the surface and using three different asteroid shape models. The simulations exhibit antipodal focusing and normal mode excitation. If the impulse excited vibrational energy is long lasting, vibrations are highest at impact point, its antipode and at high surface elevations such as an equatorial ridge. A near equatorial impact launches a seismic impulse on a non-spherical body that can be focused on two additional points on an the equatorial ridge. We explore simple flow models for the morphology of vibration induced surface slumping. We find that the initial seismic pulse is unlikely to cause large shape changes. Long lasting seismic reverberation on Bennu caused by a near equatorial impact could have raised the height of its equatorial ridge by a few meters and raised two peaks on it, one near impact site and the other near its antipode.

Development of a dynamic external CFD and BES coupling framework for application of urban neighbourhoods energy modelling

Current building energy models are weak at representing the interactions between neighbourhoods of buildings in cities. The effect of a neighbourhood on the local microclimate is complex, varying from one building to another, meaning that neighbourhood effects on the airflow around a particular building. A failure to account for this may lead to the miss-calculation of heat transfer and energy demand. Current building energy simulation (BES) tools apply convective heat transfer coefficient (CHTC) correlations, which were developed by using a simplified model of wind flow that neglects neighbourhood effects. Computational Fluid Dynamics (CFD) techniques are able to model these neighbourhood effects and can be used to improve CHTC correlations.This work aims to develop a framework that couples CFD and BES tools to enhance the modelling of outdoor convective heat transfer in different urban neighbourhoods. A dynamic external coupling method was used to combine the benefits from both domains. Firstly, a microclimate CFD model was validated before the coupling stage using wind tunnel data. Secondly, the framework was tested using a benchmark model of a building block. Fully converged values of the surface temperature and CHTC were achieved at each time-step by the BES and CFD domains. The results highlight the importance of neighbourhood effect while the prediction of the hourly averaged external convection using coupling method can amend the simulation by up to 64% comparing to the standalone conventional BES models with DOE-2 CHTC approach.

Periodic orbit analysis for the deterministic path-preference traffic flow cellular automaton

The path-preference traffic flow cellular automaton is suggested to model the dynamics of transcription. The main difference from the simple traffic flow model is that it contains another preferential paths at some sites. In this paper, we propose an exact analysis for the simplest version of this model. We find that the density of particles is dominant to the dynamics of this cellular automaton and observed that there are not only expected phase shift but also several gaps as the density increases. By considering the behavior of periodic orbits, we also determine the point where such gaps in the flow appear and the exact value of the flow.

How rheological properties affect fine-line screen printing of pastes: a combined rheological and high-speed video imaging study

Fine-line screen printing is still a great challenge due to the lack of overall understanding between the rheological properties and screen printing process. Here, we prepared ZnO pastes including ethyl cellulose or Thixatrol Max as an additive introducing different physical mechanisms of structure and flow control. Yield stress, viscosity, and its recovery after high shear were obtained using rotational rheometry. Filament breakup was determined in uniaxial elongational tests. Pastes were printed using a commercial screen designed for Si-solar cell front-side metallization, and the process was monitored with high temporal and spatial resolution using a transparent glass substrate and a high-speed imaging setup. Length of the pre-injection zone ahead of the squeegee scales inversely with yield stress and length of the cling zone behind the squeegee is proportional to filament rupture strain, irrespective of used additive. Paste spreading observable at the busbar and fine-line intersection takes place within 100 ms, irrespective of sample composition, demonstrating that fine-line electrode width is determined within the pre-injection zone where the paste is under pressure. A simple flow model is proposed relating electrode width to the reciprocal product of yield stress and high shear viscosity consistent with experimental data including both types of pastes.

An extended quasi two-phase mass flow model

Employing a physics-based full dimensional two-phase mass flow model (Pudasaini, 2012), we construct an extended quasi two-phase bulk mixture model for a debris flow as a mixture of non-Newtonian viscous fluid and solid particles down a channel. The newly derived model is a set of highly non-linear, coupled mass and momentum balance equations together with virtual mass force induced extended pressure Poisson equation. The model includes mechanically very important first order, and novel effects of drag, virtual mass force and mobility of the fluid at the interface with solid particles in the mixture flow. These aspects were not included in the previous simple bulk mixture models. We demonstrate that these new mechanical aspects of drag, virtual mass and mobility play dominant role in the mass flow dynamics; as seen in the extended inertial coefficients, mixture viscosities, mixture and phase velocities and pressure. This shows that we must retain these effects to obtain physically more accurate results for wider application potential. There are additional contributions to the mixture viscosity due to mobility and diffusion of mass fluxes. Diffusion process seem to be much more complex for the bulk mixture flow than for the two-phase flow. The new extended model leads to the exclusive emergence of diffusion and anti-diffusion fluxes and the associated diffusion- and anti-diffusion viscosities, and mass flux enhancement. The system could be diffusion only or, simultaneously could also include important anti-diffusion process. Comparison between the diffusion and anti-diffusion viscosities reveals fundamentally different mechanical processes in mixture mass flows. Typically, anti-diffusion process is pronounced for higher solid fraction. Furthermore, the main mechanics governed by the extended mixture viscosity, and dynamical variables (mixture pressure and velocities) are all controlled by the drag, virtual mass and mobility. The drag intensity in bulk mixture flow appears to be much more sensitive and non-linear than in the two-phase flow. The new model that retains several important physics of two-phase mass flow is expected to simulate mixture velocities and pressure much faster than the two-phase flow model, but physically more accurate than the previous simple mixture flow models. The two-phase dynamics can be reconstructed with the velocity and pressure drifts. Model solutions are extensively presented and discussed for extended inertial coefficients, drag intensities, mass flux enhancement, incipient and depositional processes, mixture viscosity, and diffusion and anti-diffusion processes. This shows the realistic application potential of the new extended model.

Reaction-infiltration instability in a compacting porous medium

Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonovet al. (J. Geophys. Res., vol. 100 (B10), 1995, pp. 20433–20450) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for the critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelengths and growth rates of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of, first, how advection or diffusion over the reactive time scale sets the horizontal length scale of channels and, second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record.

On Improving Computational Efficiency of Simplified Fluid Flow Models

Single-core computational efficiency of several iterative methods for numerical solution of nonsymmetric linear systems originating from simplified fluid flow models is evaluated together with different preconditioning techniques in terms of solution behaviour and the overall rate of convergence. A previously developed simplified 3D CFD model, which involves the solution of linear systems of orders usually from units to tens of thousands, is used to generate test cases. The respective Java software application employs the Parallel Colt linear algebra library. This is to ensure that the corresponding sparse matrix computations needed in different solution and preconditioning methods are carried out in as efficient a manner as possible to minimize the influence of the computer implementation itself. Measures (warm-up phase etc.) are taken to eliminate the effects of JVM specific behaviour such as JIT compilation.

(Invited) Water Transport Along Si/Si Direct Wafer Bonding Interfaces

Direct bonding interfaces exhibit, before annealing, a narrow density gap due to the contact interactions of facing surface asperities and their incomplete compression. This gap makes a narrow channel (width<1nm) along which water is able to move. This is evidenced clearly from the defect distribution in Si/Si hydrophilic bonding showing clearly a rim of defects whose extent is related to the kinetics of water penetration [1]. A simple model of capillary flow has been used in a first attempt to describe the kinetics of water penetration [2] under such very high confinement but this model fails to reproduce some of the experimental observations as e.g. the increase of wetting front width with penetration length, or the water distribution in case of reversed flow. We shall describe these experimental results, recording kinetics of water flow under varying amplitude and direction of chemical potential gradients (e.g. relative humidity) and different temperatures. These experiments allow a direct test of the dependence of flow kinetics with various parameters such as viscosity and surface energies. Finally we shall establish from basic principles the equation of propagation, which is shown to be a porous medium equation type [3]: ∂ρ/∂t= D/2ρ0 ∂2ρ 2 /∂x2 where ρ is the interface areal density of water and D a constant “diffusion” coefficient depending on the wetting characteristics of the surface , the geometry of the gap and the water viscosity. Solutions of this equation will be given with boundary conditions corresponding to the wafer bonding interface situation. They exhibit features intermediate between sharp water front propagation (as described by Lucas-Washburn type of models) and diffusion equation, in agreement with experiments. REFERENCES [1] M. Tedjini et al. Appl. Phys. Lett. 109, 111603 (2016) [2] F. Rieutord,et al ECS Trans. 2016 volume 75( 9) , 163-167 [3] J. L. Vazquez, The Porous Medium Equation: Mathematical Theory, Clarendon Press Oxford (2007)

Entropy and heat transfer analysis using Cattaneo-Christov heat flux model for a boundary layer flow of Casson nanofluid

Abstract A numerical investigation of Casson nanofluid flow, heat transfer and entropy generation over a horizontal porous stretching surface is carried out in the present research. The simplified flow model includes the effect of Lorentz forces, Cattaneo-Christov heat flux, thermal radiation and non-uniform stretching of porous surface. Similarity technique is employed to reduce the governing nonlinear partial differential equations to a set of nonlinear ordinary differential equations. The resulting set is then solved using finite difference numerical scheme to approximate the solutions for the velocity, temperature and the entropy profiles. Furthermore, the skin friction factor and the heat exchange rate at the boundary have been computed and explored graphically. The numerical computations are carried for Cu - H 2 O and TiO 2 - H 2 O nanofluids. The significant findings of the study are the negative impact of Lorentz forces on the nanofluid motion within the boundary layer and the increase in temperature due to increase in non-Newtonian parameter, thermal radiation parameter and the sheet convection parameter. Moreover Cu - H 2 O nanofluid is detected as superior thermal conductor than TiO 2 - H 2 O nanofluid.

Uncertainty analysis: influence of hydraulic fracturing on overlying aquifers in the presence of leaky abandoned wells

Model uncertainty analysis can quantify uncertainty both prior to calibration and postcalibration if the calibration dataset appropriately informs parameter estimates and model predictions. In certain cases calibration data (observations or measurements) may not be immediately apparent, but calibration datasets can be developed from related data for model interrogation and quantification and minimization of uncertainty. This study applies a series of techniques to investigate uncertainty in a simple numerical model of upward flow (leakage) through an abandoned oil and gas well converted into a water well in hydraulically fractured shale. Model calibration was achieved by developing a limited calibration dataset from well-specific measurements at a horizontal well in the Eagle Ford Shale play. Uncertainty in the calibrated model was interrogated using sensitivity, linear, and nonlinear analyses available in the PEST suite. Sensitivity analysis suggests that flowback after hydraulic fracturing could be crucial in reducing leakage. Linear analyses indicate horizontal-well production rates and long-term reservoir pressures are valuable measurements to collect when evaluating potential leakage. Nonlinear analyses identify the range in predictive uncertainty of potential leakage. The results underscore the need to evaluate and include additional types of well data in public records, such as flowback and produced water volumes. Overall, the results of this study illustrate the utility of uncertainty analyses with a limited calibration dataset applied to a simple model.

Rapid Core Formation in Terrestrial Planets by Percolative Flow: In-Situ Imaging of Metallic Melt Migration Under High Pressure/Temperature Conditions

Core formation has left a lasting geochemical signature on the Earth. In order to constrain the composition of the Earth we must fully understand the processes by which newly formed Earth, and the bodies which accreted to it, differentiated. Percolation of iron-rich melt through solid silicate has been invoked as a mechanism for differentiation and core formation in terrestrial bodies in the early solar system. However, to date the contribution of percolation to core formation cannot be assessed due to the absence of data on Fe-rich melt migration velocities. Here we use a novel experimental design to investigate textural changes in an analogue system, Au melt in polycrystalline h-BN, under the high pressure/temperature (PT) of core formation at 3 GPa, relevant to core formation in the early solar system. Using a combination of high resolution, in-situ X-ray tomography and fast 2-D radiographic imaging, we obtain the first direct data on melt migration velocities at high PT. Melt migration is highly variable and episodic, driven by variations in differential pressure during melt migration and matrix compaction. Smaller scale melt processes, representing migration of melt along pre-existing melt networks, give comparatively fast velocities of 0.6-60 µms-1. Ex-situ experiments are used to compare melt networks in analogue systems to Fe-rich melt in silicates. Two competing processes for melt migration are percolation of melt along grain boundaries, and hydraulic fracturing induced by melt injection. Typically, both processes are noted in experimental and natural systems, although the relative importance of each mechanism is variable. Using a simple model for melt flow through a porous media, migration velocities determined here account for full differentiation of Earth-sized bodies within 101 to 103 Myr, for submicron diameter melt bands, or within a few Myr or micron-sized melt bands. This is consistent with rapid timescales inferred from geochemistry for core formation in planetesimals, implying that percolation may have had an important contribution to core differentiation in the Earth.

Modeling of the Two-Dimensional Flow Caused by Sea Conditions and Wind Stresses on the Example of Dead Vistula

Abstract The article presents the results of two-dimensional modeling of flows caused by the sea conditions and wind stresses on the example of Dead Vistula. Based on the available bathymetric data, a numerical model of the river section was created, which was supplemented with data on the position of the water table depending on hydrometeorological conditions. To describe the flow field in steady conditions, a simplified model of two-dimensional flow in the form of the bi-harmonic Helmholtz equation for the current function has been adopted, taking into account additional impacts caused by wind stresses on the water surface. Then the current function was converted into the velocity vector components. This equation, supplemented with appropriate boundary conditions, has been solved numerically using the finite difference method. On the basis of the available literature, 4 variants of hydrometeorological conditions were adopted, depending on the direction and strength of wind and sea conditions. The obtained results were compared with the results of published measurements taken on the studied section of the river. These calculations were the basis for the implementation of a two-dimensional model of the spread of pollutants in the studied section of the Dead Vistula.

Erosion estimation of guide vane end clearance in hydraulic turbines with sediment water flow

The end surface of guide vane or head cover is one of the most serious parts of sediment erosion for high-head hydraulic turbines. In order to investigate the relationship between erosion depth of wall surface and the characteristic parameter of erosion, an estimative method including a simplified flow model and a modificatory erosion calculative function is proposed in this paper. The flow between the end surfaces of guide vane and head cover is simplified as a clearance flow around a circular cylinder with a backward facing step. Erosion characteristic parameter of [Formula: see text] is calculated with the mixture model for multiphase flow and the renormalization group (RNG) k–[Formula: see text] turbulence model under the actual working conditions, based on which, erosion depths of guide vane and head cover end surfaces are estimated with a modification of erosion coefficient K. The estimation results agree well with the actual situation. It is shown that the estimative method is reasonable for erosion prediction of guide vane and can provide a significant reference to determine the optimal maintenance cycle for hydraulic turbine in the future.