Isotropic Flow Research Articles

Anomalous Scaling, Intermittency and Turbulence in Nematic Liquid Crystals

Turbulent electro-convective fluctuations induced in nematic liquid crystal (NLC) by an external oscillating electric field application are studied. Electrohydrodinamic instabilities, including chaotic dynamics and irregular pattern formation, are induced by electrical forces coupled to the flow, the conductivity and the bulk forces acting on the volume charges. In particular we investigate the scaling behavior of the probability density function (PDFs) of intensity fluctuations in a NLC driven through different regimes far from the cell plates, by using the confocal fluorescence microscopy technique. Both spectral properties and scaling behavior of light intensity fluctuations PDFs are analysed at different voltages. In weak turbulent regime, for intermediate voltages, PDFs are Gaussian at large scales, while show enhanced wings at smaller scales, showing the typical intermittency of the isotropic fluid flows. At higher voltages complex dynamical scattering regimes take place. A quantitative estimation of intermittency is obtained by PDFs modeling through the Castaing distribution, and structure functions are calculated in the framework of Extended Self-Similarity. Generation of small-scale fluctuations through a fragmentation process of large-scale structures are supported by the results. Moreover, the lingering anisotropic properties of the fluctuations are highlighted by the outcomes.

A new framework for simulating forced homogeneous buoyant turbulent flows

This work proposes a new simulation methodology to study variable density turbulent buoyant flows. The mathematical framework, referred to as homogeneous buoyant turbulence, relies on a triply periodic domain and incorporates numerical forcing methods commonly used in simulation studies of homogeneous, isotropic flows. In order to separate the effects due to buoyancy from those due to large-scale gradients, the linear scalar forcing technique is used to maintain the scalar variance at a constant value. Two sources of kinetic energy production are considered in the momentum equation, namely shear via an isotropic forcing term and buoyancy via the gravity term. The simulation framework is designed such that the four dimensionless parameters of importance in buoyant mixing, namely the Reynolds, Richardson, Atwood, and Schmidt numbers, can be independently varied and controlled. The framework is used to interrogate fully non-buoyant, fully buoyant, and partially buoyant turbulent flows. The results show that the statistics of the scalar fields (mixture fraction and density) are not influenced by the energy production mechanism (shear vs. buoyancy). On the other hand, the velocity field exhibits anisotropy, namely a larger variance in the direction of gravity which is associated with a statistical dependence of the velocity component on the local fluid density.

Absorption of waves by large-scale winds in stratified turbulence.

The atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and homogeneous flows. We study numerically the role of these waves and their interaction with the large-scale flow, consisting of vertically sheared horizontal winds. We calculate their space- and time-resolved energy spectrum (a four-dimensional spectrum) and show that most of the energy is concentrated along a dispersion relation that is Doppler shifted by the horizontal winds. We also observe that when uniform winds are let to develop in each horizontal layer of the flow, waves whose phase velocity is equal to the horizontal wind speed have negligible energy. This indicates a nonlocal transfer of their energy to the mean flow. Both phenomena, the Doppler shift and the absorption of waves traveling with the wind speed, are not accounted for in current theories of stratified wave turbulence.

Plastic deformation and ductility of magnesium AZ31B-H24 alloy sheet from 22 to 450 °C

Mg alloy AZ31B-H24 sheet was investigated through microstructural characterization and mechanical testing. Tension tests were conducted across a broad range of strain rates for temperatures from 22 up to 450°C, as were gas-pressure bulge tests for several forming pressures at 350°C. Tensile data were used to calculate flow stresses, tensile elongations, activation energies for creep and the Lankford coefficient, or R-value. The AZ31B material exhibits strong plastic anisotropy (R=7) at room temperature because of its basal crystallographic texture. Plastic anisotropy decreases with increasing temperature but demonstrates no sensitivity to strain rate until recrystallization occurs. Upon recrystallization, the R-value becomes sensitive to strain rate and continues decreasing with increasing temperature until it reaches a minimum (R=1–3) near approximately 300°C. Plastic anisotropy at these high temperatures is greatest at the fastest strain rate. This sensitivity to strain rate is attributed to a competition between dislocation-climb creep, which produces anisotropic flow and dominates at fast strain rates, and grain-boundary-sliding creep, which produces isotropic flow and dominates at slow strain rates. The mechanistic understanding developed for plastic flow in AZ31B was implemented in a material constitutive model for deformation at 350°C. A new aspect of this model is the inclusion of dislocation pipe diffusion as a potential accommodation mechanism for dislocation-climb creep. This model was validated against independent gas-pressure bulge test data through the predictions of a finite-element-method simulation, and the model provided quite accurate predictions of the experimental data.

Energy analysis and improved regularity estimates for multiscale deconvolution models of incompressible flows

This paper presents new analytical results and the first numerical results for a recently proposed multiscale deconvolution model (MDM) recently proposed. The model involves a large‐eddy simulation closure that uses a novel deconvolution approach based on the introduction of two distinct filtering length scales. We establish connections between the MDM and two other models, and, on the basis of one of these connections, we establish an improved regularity estimate for MDM solutions. We also prove that the MDM preserves Taylor‐eddy solutions of the Navier–Stokes equations and therefore does not distort this particular vortex structure. Simulations of the MDM are performed to examine the accuracy of the MDM and the effect of the filtering length scales on energy spectra for three‐dimensional homogeneous and isotropic flows. Numerical evidence for all tests clearly indicates that the MDM gives very accurate coarse‐mesh solutions and that this multiscale approach to deconvolution is effective. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling groundwater flow by lattice Boltzmann method in curvilinear coordinates

In order to promote the use of the lattice Boltzmann method (LBM) for the simulation of isotropic groundwater flow in a confined aquifer with arbitrary geometry, Poisson's equation was transformed into a curvilinear coordinate system. With the metric function between the physical and the computational domain established, Poisson's equation written in Cartesian coordinates was transformed in curvilinear coordinates. Following, the appropriate equilibrium function for the D2Q9 square lattice has been defined. The resulting curvilinear formulation of the LBM for groundwater flow is capable of modeling flow in domains of complex geometry with the opportunity of local refining/coarsening of the computational mesh corresponding to the complexity of the flow pattern and the required accuracy. Since the proposed form of the LBM uses the transformed equation of flow implemented in the equilibrium function, finding a solution does not require supplementary procedures along the curvilinear boundaries, nor in the zones requiring mesh density adjustments. Thus, the basic concept of the LBM is completely maintained. The improvement of the proposed LBM over the previously published classical methods is completely verified by three examples with analytical solutions. The results demonstrate the advantages of the proposed curvilinear LBM in modeling groundwater flow in complex flow domains.

Petrophysical Characterization of Bioturbated Sandstone Reservoir Facies In the Upper Jurassic Ula Formation, Norwegian North Sea, Europe

Abstract A petrophysical study of bioturbated shoreface sandstone rocks was completed by mapping local variations in air permeability measured in core samples acquired from the Upper Jurassic Ula Formation of the Norwegian Central Graben. Analysis of the shoreface fabrics resulting from bioturbation was studied using arithmetic, harmonic, and geometric numerical modeling and analytical techniques. The arithmetic mean best illustrates samples dominated by high volumes of horizontal or subvertical burrows (50–80%). The distal Skolithos to proximal Cruziana ichnofacies is an example of a rock fabric that can be characterized using the arithmetic mean. The harmonic mean best exemplifies samples dominated by low volumes of vertically oriented burrows (10–50%). The archetypal Skolithos ichnofacies is an example of a rock fabric that can be characterized using the harmonic mean. At extreme volumes of bioturbation (90–100%), isotropic flow units begin developing irrespective of burrow orientation. Numerical models of Ophiomorpha in two different sedimentary bedding features (laminated sandstone and massive sandstone) show that single-phase fluid flow is influenced by parameters such as burrow permeability, burrow connectivity, and bioturbation volume. Spot-permeametry measurements show that the Ophiomorpha burrows have higher permeability values than the host matrix. In the laminated-sandstone models, horizontal shale laminae and low bioturbation intensities promote lamination-parallel fluid flow. At higher volumes of bioturbation, fluid flow becomes increasingly isotropic due to greater amounts of burrow interpenetrations across mud laminae. In the massive-sandstone model, no flow barriers exist. As such, low volumes of bioturbation result in only minor influences on fluid flow. At higher volumes of bioturbation, greater burrow interconnectivity occurs and results in an enhancement of vertical and horizontal burrow permeabilities. Based on the results outlined above, this paper emphasizes the impact bioturbation plays in helping improve reservoir quality in the Ula Formation. Perhaps more importantly, the effectiveness of the numerical models presented to characterize fluid flow in different bioturbated fabrics (e.g., archetypal Skolithos ichnofacies) highlights the fact that the fluid-flow results outlined in this paper can also be applied more broadly to different shoreface successions using ichnofacies knowledge alone.

DNS of Differential Thermal and Mass Diffusions in Free Turbulent Shear Flows

The diffusion of scalars in turbulent flows is the combined effect of the molecular diffusion and the turbulent diffusion, and the latter usually dominates. We investigated the diffusion of scalars with different diffusivities through two canonical free turbulent shear flows, i.e., the mixing layer and the homogeneous isotropic flow, by means of direct numerical simulation (DNS). In the mixing layer, the molecular diffusion has a big impact on the diffusion of scalars in the laminar region where the scalar gradient is high. In the turbulent region, the molecular diffusion has a negligible effect on the diffusion. In the homogeneous isotropic flow, the higher molecular diffusivity strengths the dispersion of scalars of relatively smaller values. However, the molecular diffusion exhibits a counter effect on the scalar diffusion for the relatively larger value. This work is intended to figure out the feasibility of the assumption that the thermal and mass diffusions of a contaminated content are equal, in other words, unit Lewis number assumption, which is often adopted.

Experimental analysis of intermittency in electrohydrodynamic instability.

The properties of turbulent electroconvective fluctuations generated in a nematic liquid crystal under the action of an external oscillating electric field are investigated. In particular, the spectral properties and the scaling behaviour of probability density functions (PDFs) of light intensity fluctuations are considered at different voltages. At intermediate voltage, in the weak turbulent regime, PDFs are Gaussian at large scales and show increasingly enhanced wings at smaller scales, recalling the typical signature of intermittency in isotropic fluid flows. When the voltage is increased, dynamical scattering regimes appear, characterized by increasing complexity. In order to get a quantitative estimate of intermittency, PDFs are modeled through the Castaing distribution, and structure functions are estimated in the framework of Extended Self-Similarity. Results support the generation of small-scale fluctuations through a fragmentation process of large-scale structures. The persistent anisotropic properties of the fluctuations are highlighted by the results.

Study of in situ calibration performance of co-located multi-sensor hot-film and sonic anemometers using a ‘virtual probe’ algorithm

The performance of an in situ calibration technique, implementing neural network (NN) algorithms for co-located multi-wire hot-film and sonic anemometers, is studied. The NN-based calibration technique, proposed by Kit et al (2010 J. Atmos. Ocean. Technol. 27 23–41), allows performing direct measurement of fine scales in turbulent air flow, and offers a robust tool for measurements of micro-scale properties in atmospheric flows. Accuracy of the suggested calibration technique is examined in view of isotropic and anisotropic flow fields of various turbulence intensity (TI). Anisotropic velocity datasets of various TIs were generated using a ‘virtual probe’ simulating hot-film anemometer response to the sensed flow, while a kinematic model of homogeneous isotropic turbulent flow was implemented to generate isotropic flow datasets. NN calibration performance is examined by quantitative comparison between the original and reconstructed velocity components, using a specially constructed norm and by visual comparison of original and reconstructed time series. The examined NN calibration technique performance is shown to be of reasonable accuracy for all TI velocity fields examined, while a notable drop in accuracy is detected with the increase in TI. The reconstruction of isotropic velocity fields, using the NN algorithm for calibration, is apparently of slightly lower accuracy than in the case of anisotropic flows. The results are discussed in view of possible implementation of the suggested technique in direct field measurements of atmospheric turbulence fine scales.

Pair and multi-particle dispersion in numerical simulations of convective boundary layer turbulence

Tracer dispersion within a highly convective planetary boundary layer is studied by means of a large-eddy simulation (LES) model for the continuous phases describing the temperature and velocity fields, and with the Lagrangian tracking of particle trajectories. Particle velocities are decomposed into their resolved and unresolved (or sub-grid) components. The former are evaluated by interpolation from the LES velocity field, the latter are given by a Lagrangian kinematic model that correctly describes the turbulent dispersion of clouds of particles. It is shown that, thanks to the Lagrangian sub-grid model, a clear inertial range is detectable in the time domain. In this range, particle separation grows according to Richardson's law, and nicely compares with previous experimental and numerical measurements. The collective motion of four particles, initially located at the vertices of regular tetrahedra, is also studied. The evolution of tetrad shape and orientation is contrasted with those obtained in homogeneous and isotropic flows. Results show that an agreement is achieved at small time lags. At larger times, the boundary layer reveals its anisotropic structure and the tetrad shape statistics deviate from results obtained in ideal flows.

The Study of Groundwater Modeling of Plain Area in Shiyang River Basin - I Groundwater System Conceptual Model Construction

In order to construct the groundwater numerical simulation model, the study area was determined on the basis of the geological and hydrogeological conditions. Taking Feflow as operating platform, combining GIS with Surfer software, a study area of the structure of three-dimensional aquifer model was established, realizing the 3D visualization of a large area of the complex geological content. Combined with the hydrogeological conditions, three-dimensional geological structure of the model further generalization. The result showed that the aquifer of the vertical was generalized into the unconfined aquifer; based on the characteristics of lithology, structure, parameters and distribution of recharge and discharge in groundwater system, the study area groundwater system was characterized by isotropic saturated-unsaturated numerical flow model, and the equilibrium composition of the elements was analysed in study area, the partition of the aquifer hydrogeological parameters was divided, lay the foundation for groundwater numerical model simulation.

Influence of anisotropy on velocity and age distribution at Scharffenbergbotnen blue ice area

Abstract. We use a full-Stokes thermo-mechanically coupled ice-flow model to study the dynamics of the glacier inside Scharffenbergbotnen valley, Dronning Maud Land, Antarctica. The domain encompasses a high accumulation rate region and, downstream, a sublimation-dominated bare ice ablation area. The ablation ice area is notable for having old ice at its surface since the vertical velocity is upwards, and horizontal velocities are almost stagnant there. We compare the model simulation with field observations of velocities and the age distribution of the surface ice. No satisfactory match using an isotropic flow law could be found because of too high vertical velocities and much too high horizontal ones in simulations despite varying enhancement factor, geothermal heat flux and surface temperatures over large ranges. However, the existence of a pronounced ice fabric may explain the observed present-day surface velocity and mass balance distribution in the inner Scharffenbergbotnen blue ice area. Near absence of data on the temporal evolution of Scharffenbergbotnen since the Late Glacial Maximum necessitates exploration of the impact of anisotropy using prescribed ice fabrics: isotropic, single maximum, and linear variation with depth, in both two-dimensional and three-dimensional flow models. The realistic velocity field simulated with a noncollinear orthotropic flow law, however, produced surface ages in significant disagreement with the few reliable age measurements and suggests that the age field is not in a steady state and that the present distribution is a result of a flow reorganization at about 15 000 yr BP. In order to fully understand the surface age distribution, a transient simulation starting from the Late Glacial Maximum including the correct initial conditions for geometry, age, fabric and temperature distribution would be needed. This is the first time that the importance of anisotropy has been demonstrated in the ice dynamics of a blue ice area and demonstrates the need to understand ice flow in order to better interpret archives of ancient ice for paleoclimate research.

Multiscale three-point velocity increment correlation in turbulent flows

The three-point velocity increment correlation function is proposed to represent the multiscale correlations in turbulent flows. The inertial-inertial correlation and the inertial-dissipative correlation are discussed due to their endogenetic properties in turbulence and their roles in large-eddy simulation. The zero-correlation points are then emphasized as equilibrium points between them. The credibility of this theoretical result is numerically verified in both isotropic and anisotropic flows. Results imply the universality of this zero-correlation scaling in different turbulent flows. This work is expected to be a dependable theoretical base for creating multiscale subgrid models in large-eddy simulation. (C) 2014 Elsevier B.V. All rights reserved.

FINITE VOLUME METHOD OF MODELLING TRANSIENT GROUNDWATER FLOW

In the field of computational fluid dynamics, the f inite volume method is dominant over other numerical techniques like the finite difference and finite element methods because the underlying physical quantities are conserved at the discrete level. In the presen t study, the finite volume method is used to solve an isotropic transient groundwater flow model to obtain hydrauli c heads and flow through an aquifer. The objective is to discuss the theory of finite volume method and its applications in groundwater flow modelling. To achieve this, an orthogonal grid with quadrilateral contro l volumes has been used to simulate the model using mixed boundary conditions from Bwaise III, a Kampala Surburb. Results show that flow occurs from regions of high hydraulic head to regions of low hydraulic head un til a steady head value is achieved.

Sheath flow forming by using twisted micro-channel

We developed a twisted micro-channel in order to form a sheath flow in an integrated micro-fluidic chip. The new device has a central straight channel and two parts of 2-dimensional merging channel. It is twisted by 90 degree in between the first part and the second part. We applied the unique material property of polydimetylsiloxane (PDMS), that is elasticity; “easily bent and twisted”. The micro-channel configuration (width, length etc.) were designed to form an isotropic focusing flow. Distribution of particle's velocity in the section of the micro-channel down the junction points showed sheath flow forming.

Gamma ray bursts: flashing of polar jets

The observations by Fermi and Swift detected intense polar jets for the very massive objects from AGNs to GRBs irrespective of their natures. The jets contain enough Poynting energy as radiation with 90% or above gamma efficiency challenging the Fire ball and Synchrotron self Compton mechanism. Having the successful application of gravity induced electromagnetic radiation for the enigmatic isotropic energy flow ~10 �� ����� from GRBs, the questions regarding origin of jets are described precisely in terms of dynamical parameters for rotating objects using non homologous collapse model. Over theoretical consideration it is also shown neither deceleration at the collapse nor the rotation itself can produce jets.

Reproducibility of cerebrospinal venous blood flow and vessel anatomy with the use of phase contrast-vastly undersampled isotropic projection reconstruction and contrast-enhanced MRA.

The chronic cerebrospinal venous insufficiency hypothesis raises interest in cerebrospinal venous blood flow imaging, which is more complex and less established than in arteries. For accurate assessment of venous flow in chronic cerebrospinal venous insufficiency diagnosis and research, we must account for physiologic changes in flow patterns. This study examines day-to-day flow variability in cerebrospinal veins by use of 4D MR flow and contrast-enhanced MRA under typical, uncontrolled conditions in healthy individuals. Ten healthy volunteers were scanned in a test-retest fashion by use of a 4D flow MR imaging technique and contrast-enhanced MRA. Flow parameters obtained from phase contrast-vastly undersampled isotropic projection reconstruction and contrast-enhanced MRA scoring measurements in the head, neck, and chest veins were analyzed for internal consistency and interscan reproducibility. Internal consistency was satisfied at the torcular herophili, with an input-output difference of 2.2%. Percentages of variations in flow were 20.3%, internal jugular vein; 20.4%, azygos vein; 6.8%, transverse sinus; and 5.1%, common carotid artery. Retrograde flow was found in the lower internal jugular vein (4.8%) and azygos vein (7.2%). Contrast-enhanced MRA interscan κ values for the internal jugular vein (left: 0.474, right: 0.366) and azygos vein (-0.053) showed poor interscan agreement. Phase contrast-vastly undersampled isotropic projection reconstruction blood flow measurements are reliable and highly reproducible in intracranial veins and in the common carotid artery but not in veins of the neck (internal jugular vein) and chest (azygos vein) because of normal physiologic variation. Retrograde flow normally may be observed in the lower internal jugular vein and azygos vein. Low interrater agreement in contrast-enhanced MRA scans was observed. These findings have important implications for imaging diagnosis and experimental research of chronic cerebrospinal venous insufficiency.

Simulation Study of Thermotropic LCPs and Prediction of Normal Stress Difference at High Shear Rate

Abstract The shear viscosity and normal stress difference of two filled and two unfilled thermotropic liquid crystal polymer (TLCPs) were studied. The rigid and rod like molecules of TLCPs orientate differently at different shear rates. Under low shear rate, the molecules tend to align in the direction of the flow but also tumble and wagging on their own axis. The abnormal orientation of the molecules also depends upon temperature, fillers contents, aspect ratio and elastic nature of LCP molecules. These behaviors lead to unusual rheological properties of LCPs, such as negative first normal stress difference for filled LCPs at low shear rates. But with the increase of shear rate, the molecules are oriented in the direction of flow, which lead to isotropic flow at high shear rates. The complicated rheological properties and characteristic anisotropic properties of LCPs are modelled by recently developed Leonov's viscoselastic constitutive equations. Simulation has been carried out using Mathematica software and the characteristic anisotropic properties of LCPs have been identified. The experimentally measured viscosities at high shear rate have been compared with model predictions. Moreover, the normal stress differences using at high shear rates have been estimated using Leonov's model, which is experimentally not accessible.

Analytic solutions of the interstitial fluid flow models

In this paper, we present the analytic solutions of several continuum porous media models that describe the interstitial fluid flow in the interosseous membrane. We first compare the results of the Brinkman, Stokes and Darcy systems in describing the isotropic interstitial fluid flows. Our calculations show that the Stokes equations can well approximate the Brinkman equations when the Darcy number Da ≥ 0.2, while the Darcy model is an appropriate approximation to the Brinkman model in the interosseous membrane when Da ≤ 2×10−4. Yet, in most cases, the anisotropy dominates the interstitial fluid. Therefore, we build an anisotropic Darcy model and show that an isotropic model can be used as a suitable approximation when the ratio between the transverse and longitudinal permeabilities is no larger than 20. Lastly, we take the blood flow in capillaries into consideration as well and introduce the coupled Stokes-Darcy system to describe the cases comprising both the capillary and the interstitial domain. Our results reveal that the profile of the interface exchange flow is not exactly in the linear form as was widely adopted in the numerical simulation, instead, the flux near the artery and the vein is more significant, which in turn results in the increase of the maximum horizontal velocity in the interstitial space while the outflow rate remains the same.