Shear Stress Correlations Research Articles

Long ranged stress correlations in the hard sphere liquid.

The smooth emergence of shear elasticity is a hallmark of the liquid to glass transition. In a liquid, viscous stresses arise from local structural rearrangements. In the solid, Eshelby has shown that stresses around an inclusion decay as a power law r-D, where D is the dimension of the system. We study glass-forming hard sphere fluids by simulation and observe the emergence of the unscreened power-law Eshelby pattern in the stress correlations of the isotropic liquid state. By a detailed tensorial analysis, we show that the fluctuating force field, viz., the divergence of the stress field, relaxes to zero with time in all states, while the shear stress correlations develop spatial power-law structures inside regions that grow with longitudinal and transverse sound propagation. We observe the predicted exponents r-D and r-D-2. In Brownian systems, shear stresses relax diffusively within these regions, with the diffusion coefficient determined by the shear modulus and the friction coefficient.

Decoupling of rotation and translation at the colloidal glass transition.

In dense particle systems, the coupling of rotation and translation motion becomes intricate. Here, we report the results of confocal fluorescence microscopy where simultaneous recording of translational and rotational particle trajectories from a bidisperse colloidal dispersion is achieved by spiking the samples with rotational probe particles. The latter consist of colloidal particles containing two fluorescently labeled cores suited for tracking the particle's orientation. A comparison of the experimental data with event driven Brownian simulations gives insights into the system's structure and dynamics close to the glass transition and sheds new light onto the translation-rotation coupling. The data show that with increasing volume fractions, translational dynamics slows down drastically, whereas rotational dynamics changes very little. We find convincing agreement between simulation and experiments, even though the simulations neglect far-field hydrodynamic interactions. An additional analysis of the glass transition following mode coupling theory works well for the structural dynamics but indicates a decoupling of the diffusion of the smaller particle species. Shear stress correlations do not decorrelate in the simulated glass states and are not affected by rotational motion.

First-Principles Investigation of the Effects of UF4 and ThF4 Fuels on the Structural, Dynamic, and Thermodynamic Properties of LiF-NaF.

An in-depth understanding and characterization of molten salt properties are necessary for the optimized design, efficient operation, and safety assurance of molten salt reactors (MSRs). Investigating molten salt properties in experimental settings can be challenging and time-consuming due to the high temperatures of interest, the salt's corrosiveness, purity and composition control, and health and safety concerns. Therefore, it is beneficial to perform computational screening to assist in the ultimate experimental measurements. Herein, we used first-principles molecular dynamics simulations to calculate several thermophysical, structural, and dynamic properties of eutectic LiF-NaF with fuel additives UF4 and ThF4. We found that with the incorporation of uranium or thorium, a prepeak appears in the structure factor, indicative of a medium-range structural ordering. Furthermore, we explore the mechanism through which these structural changes enhance shear stress correlations, thereby increasing the salt's viscosity. This work highlights the importance of studying the atomic-scale structure of molten salts and how the addition of fuel elements can substantially affect it.

Viscoelastic relaxation and topological fluctuations in glass-forming liquids.

A method for characterizing the topological fluctuations in liquids is proposed. This approach exploits the concept of the weighted gyration tensor of a collection of particles and permits the definition of a local configurational unit (LCU). The first principal axis of the gyration tensor serves as the director of the LCU, which can be tracked and analyzed by molecular dynamics simulations. Analysis of moderately supercooled Kob-Andersen mixtures suggests that orientational relaxation of the LCU closely follows viscoelastic relaxation and exhibits a two-stage behavior. The slow relaxing component of the LCU corresponds to the structural, Maxwellian mechanical relaxation. Additionally, it is found that the mean curvature of the LCUs is approximately zero at the Maxwell relaxation time with the Gaussian curvature being negative. This observation implies that structural relaxation occurs when the configurationally stable and destabilized regions interpenetrate each other in a bicontinuous manner. Finally, the mean and Gaussian curvatures of the LCUs can serve as reduced variables for the shear stress correlation, providing a compelling proof of the close connection between viscoelastic relaxation and topological fluctuations in glass-forming liquids.

Numerical simulation of wall shear stress and boundary layer flow from jetting cavitation bubble on unheated and heated surfaces

The physics of wall shear stress and boundary layer flow from jetting cavitation bubbles on unheated and heated surfaces was investigated numerically using a homogeneous mixture model based on a fully compressible Navier–Stokes solver. A spatial–temporal shear stress map and velocity field on unheated surfaces under several standoffs were considered first. Complex boundary layer flow, including separation vortex caused by an adverse pressure gradient and the generation of a thermal boundary layer because of skin friction with the shear flow, was discussed in detail. The tendency of different maximum shear stress for each standoff section was discussed with liquid film thickness and jet velocity. Also, we suggested maximum shear stress correlation equation for minimum film thickness and wall impact pressure as dimensionless form. As an expansion of previous studies, we examined bubble collapse–induced wall shear stress on a heated surface under various surface temperatures. The peak shear stress decreased with the lower Prandtl number flow. In the collapse phase, surface cooling by downward microjet and heat transfer with ring vortex were also captured. Consequently, we suggested correlation equations for primary and secondary peak shear stresses as function of Prandtl number and confirmed that the boundary layer flow including heat transfer can be well simulated.

Long-range correlations in elastic moduli and local stresses at the unjamming transition.

We explore the behaviour of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic p2 dependence of the correlations as the pressure p approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.

Extremely persistent dense active fluids.

We study the dynamics of dense three-dimensional systems of active particles for large persistence times τp at constant average self-propulsion force f. These systems are fluid counterparts of previously investigated extremely persistent systems, which in the large persistence time limit relax only on the time scale of τp. We find that many dynamic properties of the systems we study, such as the mean-squared velocity, the self-intermediate scattering function, and the shear-stress correlation function, become τp-independent in the large persistence time limit. In addition, the large τp limits of many dynamic properties, such as the mean-square velocity and the relaxation times of the scattering function, and the shear-stress correlation function, depend on f as power laws with non-trivial exponents. We conjecture that these systems constitute a new class of extremely persistent active systems.

Patterns of turbulent flow structures over dune shaped bed features under the influence of downward seepage

The research presents an experimental investigation on change in streamwise flow velocity and turbulent characteristics over a fixed dune shaped bed feature, in the presence and absence of downward seepage. Streamwise velocity, Reynolds Shear Stress (RSS), turbulent intensities, and third order correlation profiles are presented along the flow depth at eleven locations over the dune. Amplification in the values of streamwise velocities, RSS, and turbulent intensities has been observed at the initial sections on the stoss side as well as at the sections on the lee side of the dune under the influence of downward seepage. At the initial and lee side sections of the dune, average values of the streamwise velocity, RSS, and streamwise turbulent intensity along the depth of flow increase by ∼0.2 %−31 %, ∼9 %−50 %, and ∼2 %−30 % respectively, for the 10 % seepage condition as compared to the no seepage condition. For the 15 % seepage condition, there has been found an increase in these value values by ∼3 %−67 %, ∼52 %−150 %, and ∼35 %−43 % respectively, at the considered sections over the dune. Further, it has also been observed that under the influence of downward seepage, bed shear stress increases at the initialand lee side sectionsof the dune. Through the third order correlation studies, occurrence of rushing flow due to seepage was confirmed at the lee side and initial sections of the dune. Further analysis at the wake zone revealed a reduction in the values of second and third-order moments demonstrating greater streamwise flow of Reynolds stress and diffusion of vertical Reynolds stress in streamwise direction as a result of increased velocity owing to downward seepage. Results indicate that the introduction of seepage leads to the creation of large angled dunes with wake zone stretched in the flow direction as well as the same wake zone was found squeezed in the vertical direction.

Pseudo hard-sphere viscosities from equilibrium Molecular Dynamics

Transport coefficients like shear, bulk and longitudinal viscosities are sensitive to the intermolecular interaction potential and finite size effects when are numerically determined. For the hard-sphere (HS) fluid, such transport properties are determined almost exclusively with computer simulations. However, their systematic determination and analysis throughout shear stress correlation functions and the Green-Kubo formalism can not be done due to discontinuous nature of the interaction potential. Here, we use the pseudo hard-sphere (PHS) potential to determine pressure correlation functions as a function of volume fraction in order to compute mentioned viscosities. Simulation results are compared to available event-driven molecular dynamics of the HS fluid and also used to propose empirical corrections for the Chapman–Enskog zero density limit of shear viscosity. Moreover, we show that PHS potential is a reliable representation of the HS fluid and can be used to compute transport coefficients. The molecular simulation results of the present work are valuable for further exploration of HS-type fluids or extend the approach to compute transport properties of hard-colloid suspensions.

Theoretical modeling of heat transfer in vertical upward and downward annular flow boiling

This work entails experimental measurement and theoretical modeling of heat transfer coefficient (HTC) for annular flow boiling in upward and downward flow configurations. The working fluid used was HFE-7000 and experimental measurements were carried out inside a 6 mm sapphire tube coated externally with indium-tin-oxide (ITO) for Joule heating. The range of vapor quality, mass flux, and heat flux investigated were 0.15 − 0.7, 75–400 kg/(m2s), and 0.5 − 3.0 W/cm2, respectively. Theoretical models for predicting HTC in upward and downward flows were developed using heat-flux-dependent wall shear stress correlations and roll-wave-velocity-based interfacial damping function. It was found that interfacial damping depends on the Reynolds number of the liquid film. The proposed models predicted over 96% of the measured HTC within ±20% in both upward and downward flows and reproduced the heat flux dependence of the HTC. The models also predicted over 96% of the measured liquid film thickness within ±30% in both upward and downward flows.

Molecular simulations and hydrodynamic theory of nonlocal shear-stress correlations in supercooled fluids.

A supercooled fluid close to the glass transition develops nonlocal shear-stress correlations that anticipate the emergence of elasticity. We performed molecular dynamics simulations of a binary Lennard-Jones mixture at different temperatures and investigated the spatiotemporal autocorrelation function of the shear stress for different wavevectors, q, from a locally measured and Fourier-transformed stress tensor. Anisotropic correlations are observed at non-zero wavevectors, exhibiting strongly damped oscillations with a characteristic frequency ω(q). A comparison with a recently developed hydrodynamic theory [Maier et al., Phys. Rev. Lett. 119, 265701 (2017)] shows a remarkably good quantitative agreement between particle-based simulations and theoretical predictions.

A Mechanistic Model for Wellbore Cleanout in Horizontal and Inclined Wells

Summary The accumulation of rock cuttings, proppant, and other solid debris in the wellbore caused by inadequate cleanout remarkably impedes field operations. The cuttings removal process becomes a more challenging task as the coiled-tubing techniques are used during drilling and fracturing operations. This article presents a new hole cleaning model, which calculates the critical transport velocity (CTV) in conventional and fibrous water-based fluids. The study is aimed to establish an accurate mechanistic model for optimizing wellbore cleanout in horizontal and inclined wells. The new CTV model is established to predict the initiation of bed particle movement during cleanout operations. The model is formulated considering the impact of fiber using a special drag coefficient (i.e., fiber drag coefficient), which represents the mechanical and hydrodynamic actions of suspended fiber particles and their network. The dominant forces acting on a single bed particle are considered to develop the model. Furthermore, to enhance the precision of the model, recently developed hydraulic correlations are used to compute the average bed shear stress, which is required to determine the CTV. In horizontal and highly deviated wells, the wellbore geometry is often eccentric, resulting in the formation of flow stagnant zones that are difficult to clean. The bed shear stress in these zones is sensitive to the bed thickness. The existing wellbore cleanout models do not account for the variation in bed shear stress. Thus, their accuracy is limited when stagnant zones are formed. The new model addresses this problem by incorporating hydraulic correlations to account for bed shear stress variation with bed height. The accuracy of the new model is validated with published measurements and compared with the precision of an existing model. The use of fiber drag and bed shear stress correlations has improved model accuracy and aided in capturing the contribution of fiber in improving wellbore cleanout. As a result, for fibrous and conventional water-based fluids, the predictions of the new model have demonstrated good agreement with experimental measurements and provided better predictions than the existing model. Model predictions show a noticeable reduction in fluid circulation rate caused by the addition of a small quantity of fiber (0.04% w/w) in the fluid. In addition, results show that the existing model overpredicts the cleaning performance of both conventional and fibrous water-based muds.

MECHANICAL PROPERTIES ESTIMATION FROM TENSILE TESTING OF AA6063-AISI304L BIMETAL JOINTS FRICTION WELDED WITH DIFFERENT JOINING METHODS

This paper discusses the various joining methods with faying surface modifications used to join AA6063 and AISI304L dissimilar alloys by Rotary Friction Welding (RFW) process at different welding conditions mainly with friction pressure (FP), upset pressure (UP) and friction time (FT). This paper also studies the tensile behavior of the welded joints. The fabricated dissimilar joints were tested using universal testing machine against tensile load, and the mechanical properties of all 30 nos. of weld joints like elongation (%), strength coefficient ([Formula: see text]), strain hardening exponent ([Formula: see text]), strain hardening rate (TS/YS ratio), shear strength, etc. were calculated from the tensile testing results and plotted here with a standard error bar. Hollomon’s equation is considered here to study the stress and strain hardening relation and Von Mises yield criterion is considered for shear and yield stress correlation. Total elongation is also calculated from the initial and final length obtained during the tensile test. Since fracture ductility of the joints depends on the stress, strain, ‘[Formula: see text]’ and ‘[Formula: see text]’ values, it is important to study these mechanical properties and how the tensile results can be used for their estimation is detailed in this paper. The faying surfaces influence the mechanical properties as well.

Predication of wall shear stress of vertical upward co-current adiabatic air-water annular flow in pipes

Annular flow has been widely applied to industrials such as oil extraction, refrigerators, nuclear reactors and so on. Wall shear stress is one of the most important parameters for studying two-phase annular flow. When calculating wall shear stress from interfacial shear stress, the relationship between the wall shear stress and the interfacial shear stress is complicated and needs some parameters such as film thickness which requires high-precision measurement technique to acquire accurately. Besides, some wall shear stress correlations developed for annular flow are applicable to flow conditions at atmospheric pressure only. Because of these reasons, four databases for vertical upward co-current adiabatic air-water two-phase annular flow have been collected with wide range of flow conditions and different pressure conditions. Using these data, a simplified model between wall shear stress and interfacial shear stress is proposed. The new model is derived from the force balance analysis of the liquid film and gas core. As void fraction of annular flow is close to 1, the relationship between wall shear stress and interfacial shear stress can be simplified to be linearly. Based on this model and existing interfacial shear stress correlations, the wall shear stress can be calculated directly from flow conditions and fluid properties that can be readily obtained from experiments. Also, a new wall shear stress correlation calculated from wave velocities has been suggested. It is developed from frictional pressure drop correlation. Correlations for two-phase multiplier and wave velocity as well as pure empirical correlations also have been compared with existing databases. From data comparison, the newly proposed correlations in this study agree well with experimental data and other correlations with good prediction accuracy have been pointed out.

Response of a turbulent boundary layer to rapid freestream acceleration

In a wide range of fluid machinery, a turbulent boundary layer can be exposed to rapid transients of the freestream conditions. A simplified model of the boundary layer response would provide valuable guidance in understanding these situations in multiple engineering applications. To this end, a turbulent boundary flow, subject to freestream acceleration, was explored through high-fidelity simulations and Reynolds-averaged Navier–Stokes calculations. Test cases were considered in which the flow over a flat plate accelerated from Mach 0.3 up to 0.6 over two time scales, 10 ms and 25 ms. Based on data from the calculations, the integral boundary layer momentum equation was simplified to propose a new reduced-order model capable of computing the evolution of the boundary layer under external flow transients. Given the initial boundary layer height, and the temporal evolution of the freestream pressure, velocity, and density, the model predicts the transient development of the boundary layer. With the transient boundary layer profile known, the temporal history of the skin friction and heat transfer can be predicted, taking advantage of standard shear stress correlations and the Reynolds analogy.

Discussion on the pressure drop calculation for oil‐water separated flow using a one dimensional two‐fluid model

The purpose of this work is to seek the key factors influencing the pressure drop calculation for oil‐water separated flow using a one dimensional two‐fluid model. Closure relations published for the two‐fluid model such as interface configuration, wall, and interfacial shear stress correlations are summarized. Interface configurations are established by numerically solving the Young‐Laplace equation, correlated with the Bond number, contact angle, and water holdup. Results show that the interface transforms from concave to convex with the enlargement of the contact angle and becomes flat as the Bond number increases. For the pressure drop calculation, a limited difference of predicted accuracy between the curve and flat interface is found. Discussions of both the wall and interfacial friction factor correlation on the pressure drop calculation are performed. In contrast to the effect of the interfacial friction factor, the correlation of the wall friction factor is found to have more contributions. We validate the prediction accuracy of different wall frictions factors using eight groups of published experiment results, and one correlation is recommended and being further extended.

Stress auto-correlation tensor in glass-forming isothermal fluids: From viscous to elastic response

We develop a generalized hydrodynamic theory, which can account for the build-up of long-ranged and long-lived shear stress correlations in supercooled liquids as the glass transition is approached. Our theory is based on the decomposition of tensorial stress relaxation into fast microscopic processes and slow dynamics due to conservation laws. In the fluid, anisotropic shear stress correlations arise from the tensorial nature of stress. By approximating the fast microscopic processes by a single relaxation time in the spirit of Maxwell, we find viscoelastic precursors of the Eshelby-type correlations familiar in an elastic medium. The spatial extent of shear stress fluctuations is characterized by a correlation length ξ which grows like the viscosity η or time scale τ ∼ η, whose divergence signals the glass transition. In the solid, the correlation length is infinite and stress correlations decay algebraically as r-d in d dimensions.

Nature of intrinsic uncertainties in equilibrium molecular dynamics estimation of shear viscosity for simple and complex fluids.

We study two types of intrinsic uncertainties, statistical errors and system size effects, in estimating shear viscosity via equilibrium molecular dynamics simulations, and compare them with the corresponding uncertainties in evaluating the self-diffusion coefficient. Uncertainty quantification formulas for the statistical errors in the shear-stress autocorrelation function and shear viscosity are obtained under the assumption that shear stress follows a Gaussian process. Analyses of simulation results for simple and complex fluids reveal that the Gaussianity is more pronounced in the shear-stress process (related to shear viscosity estimation) compared with the velocity process of an individual molecule (related to self-diffusion coefficient). At relatively high densities corresponding to a liquid state, we observe that the shear viscosity exhibits complex size-dependent behavior unless the system is larger than a certain length scale, and beyond which, reliable shear viscosity values are obtained without any noticeable scaling behavior with respect to the system size. We verify that this size-dependent behavior is configurational and relate the characteristic length scale to the shear-stress correlation length.

Emergence of Long-Ranged Stress Correlations at the Liquid to Glass Transition.

A theory for the nonlocal shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. The long-ranged stress correlations can be traced to the coupling of shear stress to transverse momentum, which is ignored in the classic Maxwell model. To rescue this widely used model, we suggest a generalization in terms of a single relaxation time τ for the fast degrees of freedom only. This generalized Maxwell model implies a divergent correlation length ξ∝τ as well as dynamic critical scaling and correctly accounts for the far-field stress correlations. It can be rephrased in terms of generalized hydrodynamic equations, which naturally couple stress and momentum and furthermore allow us to connect to fluidity and elastoplastic models.

Contribution to viscosity from the structural relaxation via the atomic scale Green-Kubo stress correlation function.

We studied the connection between the structural relaxation and viscosity for a binary model of repulsive particles in the supercooled liquid regime. The used approach is based on the decomposition of the macroscopic Green-Kubo stress correlation function into the correlation functions between the atomic level stresses. Previously we used the approach to study an iron-like single component system of particles. The role of vibrational motion has been addressed through the demonstration of the relationship between viscosity and the shear waves propagating over large distances. In our previous considerations, however, we did not discuss the role of the structural relaxation. Here we suggest that the contribution to viscosity from the structural relaxation can be taken into account through the consideration of the contribution from the atomic stress auto-correlation term only. This conclusion, however, does not mean that only the auto-correlation term represents the contribution to viscosity from the structural relaxation. Previously the role of the structural relaxation for viscosity has been addressed through the considerations of the transitions between inherent structures and within the mode-coupling theory by other authors. In the present work, we study the structural relaxation through the considerations of the parent liquid and the atomic level stress correlations in it. The comparison with the results obtained on the inherent structures also is made. Our current results suggest, as our previous observations, that in the supercooled liquid regime, the vibrational contribution to viscosity extends over the times that are much larger than the Einstein's vibrational period and much larger than the times that it takes for the shear waves to propagate over the model systems. Besides addressing the atomic level shear stress correlations, we also studied correlations between the atomic level pressure elements.