Flow Solution Research Articles

Non-equilibrium turbulent boundary layers in high reynolds number flow at incompressible conditions: effects of streamline curvature and three dimensionality

The physics and computational prediction of turbulent boundary layer flow over axisymmetric and three-dimensional bodies are examined. Three cases were considered for which extensive experimental results and companion Reynolds-averaged Navier Stokes (RANS) solutions were obtained and/or available in the open literature. These cases all have Reynolds numbers based upon the freestream velocity and body geometric scale on the order of 10 5 to 10 6 , which is large for laboratory scales but small compared to the maximum scales observed for full-scale vehicles. Despite significant differences in approach flow fields and geometries for these three cases, some common themes emerged in the findings. All cases involved complications due to pressure gradients combined with streamwise curvature, and all exhibited regions of turbulence reduction due to accelerated flow. These complications led to discrepancies in computed results even in attached flow regions where it is often assumed that RANS models provide reliable predictions. The authors recommend further work on modelling approaches that can capture rapid distortion effects on turbulence transport that can be incorporated into industry-useful frameworks. Two cases involving laterally symmetric, three-dimensional wall-mounted hills with aft-body separation revealed that asymmetric mean flow fields are likely to result. This finding has been observed in experiments conducted in multiple facilities and in computations using multiple solvers and turbulence models. It is concluded that non-unique and asymmetric global flow solutions are fundamental to flow cases with lateral geometric symmetry involving turbulent boundary layer separation. Further work is also needed to accurately predict low-frequency unsteadiness due to geometries that produce non-unique mean flow fields. For such flows, it remains to be definitively determined whether experimentally observed modes of the mean flow are equivalent, or nearly equivalent, to asymmetric mean flow solutions obtained using RANS approaches.

On the uniqueness of the solution and finite-dimensional attractors for the 3D Flow with dynamic slip boundary condition

On the uniqueness of the solution and finite-dimensional attractors for the 3D Flow with dynamic slip boundary condition

Optimal Power Flow Solution Integrated with TCSC to Improved Voltage Profile and Losses Reduction in Power System Using Effective Intelligent Technique

Optimal Power Flow Solution Integrated with TCSC to Improved Voltage Profile and Losses Reduction in Power System Using Effective Intelligent Technique

Saturation Mobility of 100 cm2 V-1 s-1 in ZnO Thin-Film Transistors through Quantum Confinement by a Nanoscale In2O3 Interlayer Using Spray Pyrolysis.

In this study, we present a comprehensive study on the fabrication and characterization of heterojunction In2O3/ZnO thin-film transistors (TFTs) aimed at exploiting the quantum confinement effect to enhance device performance. By systematically optimizing the thickness of the crystalline In2O3 (c-In2O3) layer to create a narrow quantum well, we observed a significant increase in saturation mobility (μSAT) from 12.76 to 97.37 cm2 V-1 s-1. This enhancement, attributed to quantum confinement, was achieved through the deposition of a 3 nm c-In2O3 semiconductor via spray pyrolysis. Various In2O3 layer thicknesses (2-5 nm) were obtained by adjusting precursor solution concentration, flow rate, and number of spray cycles. Post annealing treatments were employed to reduce the defects at the interface and within the oxide film, enhancing device stability and performance. Transmission electron microscopy (TEM) confirmed the uniformity of the c-In2O3 film thickness, while variations in thickness significantly influenced TFT performance, particularly the turn-on voltage (VGS) due to changes in the carrier concentration. Ultraviolet photoelectron spectroscopy (UPS) and X-ray photoelectron spectroscopy (XPS) supported the formation of a potential well with a two-dimensional electron gas (2DEG). The study of single and multiple superlattice structures of consecutive c-In2O3 and c-ZnO layers provided insights into the effects of multiple quantum wells on the TFT performance. This research presents an advanced approach to TFT optimization, highlighting high reliability, and environmental and bias stabilities. These lead to enhanced mobility and performance uniformity through the precise control of c-In2O3 layer thickness for the quantum confinement effect.

A critical state μ(I)-rheology model for cohesive granular flows

The dynamic behaviour of granular media can be observed widely in nature and in many industrial processes. Yet, the modelling of such media remains challenging as they may act with solid-like and fluid-like properties depending on the rate of the flow and can display a varying apparent friction, cohesion and compressibility. Over the last two decades, the $\mu (I)$ -rheology has become well established for modelling granular liquids in a fluid mechanics framework where the apparent friction $\mu$ depends on the inertial number $I$ . In the geo-mechanics community, modelling the deformation of granular solids typically relies on concepts from critical state soil mechanics. Along the lines of recent attempts to combine critical state and the $\mu (I)$ -rheology, we develop a continuum model based on modified cam-clay in an elastoplastic framework which recovers the $\mu (I)$ -rheology under flow. This model permits a treatment of plastic compressibility in systems with or without cohesion, where the cohesion is assumed to be the result of persistent inter-granular attractive forces. Implemented in a two- and three-dimensional material point method, it allows for the trivial treatment of the free surface. The proposed model approximately reproduces analytical solutions of steady-state cohesionless flow and is further compared with previous cohesive and cohesionless experiments. In particular, satisfactory agreements with several experiments of granular collapse are demonstrated, albeit with shear bands which can affect the smoothness of the surface. Finally, the model is able to qualitatively reproduce the multiple steady-state solutions of granular flow recently observed in experiments of flow over obstacles.

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution.Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(nlogn) instead of the typical O(n3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

Generic Level Sets in Mean Curvature Flow are BV Solutions

We show that a generic level set of the viscosity solution to mean curvature flow is a distributional solution in the framework of sets of finite perimeter by Luckhaus and Sturzenhecker, which in addition saturates the optimal energy dissipation rate. This extends the fundamental work of Evans and Spruck (J Geom Anal 5(1):79–116, 1995), which draws a similar connection between the viscosity solution and Brakke flows.

Solute Transport in a Multi-Channel Karst System with Immobile Zones: An Example of Downtown Salado Spring Complex, Salado, Texas

To investigate the influence of flow rate increment on the solute transport parameter of immobile zones in a karst system, a dye tracer test was conducted in the Downtown Salado Spring Complex (DSSC) comprising three springs: Big Boiling, Anderson, and Doc Benedict springs. The Multiflow two-region nonequilibrium model (2RNE) was used to simulate the breakthrough curve (BTC) of the springs, and changes in the solute transport parameters in response to flow rate increment were observed. The simulation result showed that the 2RNE model was capable of reproducing the BTC of all the DSSC springs, with an R-squared value greater than 0.9 in all flow rate increment scenarios. The research demonstrates that a positive correlation will exist between the flow rate and solute transport parameter of the immobile zones if the tracer transport to the spring is truly influenced by immobile zones. In contrast, a negative correlation will exist between the flow rate and mass transfer coefficient if the immobile zone has less influence. Overall, the research provides insights into contaminant movement in karst by documenting how tracers are retained in the immobile fluid zone.

General synthetic iterative scheme for non-equilibrium dense gas flows

The recently-developed general synthetic iterative scheme (GSIS), which is tailored for non-equilibrium dilute gas, has been extended to find the steady-state solutions of the non-equilibrium dense gas flows based on the Shakhov-Enskog model, resolving the problems of slow convergence and requirement of ultra-fine grids in near-continuum flows that exist in the conventional iterative scheme. The key ingredient of GSIS is the tight coupling of the mesoscopic kinetic equation and the macroscopic synthetic equations that are exactly derived from the kinetic equation. On the one hand, high-order terms computed from the velocity distribution function provide the higher-order constitutive relations describing the non-equilibrium effects for the macroscopic synthetic equations. On the other hand, the macroscopic quantities obtained from the macroscopic synthetic equations are used to guide the evolution of the velocity distribution function in the kinetic equation. The efficiency and accuracy of GSIS are demonstrated in several test cases, including the shock wave passing through a cylinder and the pressure-driven dense gas flows passing through parallel plates and porous media. The effects of denseness are analyzed in a wide range of gas rarefaction.

Optimal operation of three-phase unbalanced active distribution system based on semidefinite relaxation and convex-concave procedure

The three-phase distribution optimal power flow (D-OPF) problem has attracted much attention in recent years due to practical requirements for managing distributed energy resources and multi-energy customers in unbalanced active distribution systems. To deal with the strong nonconvexity of the three-phase OPF problem, this paper develops the semidefinite programming (SDP) formulation of three-phase OPF problems considering the mutual coupling in multi-phase networks. Instead of directly dropping the rank-one constraints, a sequential convex optimization algorithm based on the convex-concave procedure (CCP) is proposed for recovering a feasible and optimal solution of three-phase power flow. The proposed iterative algorithm not only has high computational efficiency but also guarantees the optimality when the semidefinite relaxation or second-order cone relaxation method is inexact. Case studies on various IEEE testing distribution systems verify that the proposed algorithm recovers the feasible and optimal power flow solution. It also exhibits a relatively low number of iterations and short solving time in large-scale IEEE testing systems.

The method of fundamental solutions for multi-particle Stokes flows: Application to a ring-like array of spheres

A method is presented for calculating Stokes flow around multiple particles of arbitrary shape. It uses the Method of Fundamental Solutions (MFS) applied to single particles, combined with an iterative scheme to resolve the many particle-particle hydrodynamic interactions; an approach that is reminiscent of the Method of Reflections. The attractive features of the proposed method are inherited from the MFS — simplicity and accuracy — while providing orders of magnitude computational speed-up for large particle systems. The method is verified through a series of test cases, including those involving strong lubrication forces and non-spherical particles. Unlike applications of the Method of Reflections reported in the literature, the iterative scheme we propose (a block Gauss-Seidel approach to solving a particle-particle interaction matrix) converges for all the cases we consider, for both resistance and mobility problems. The scheme is applied to the study of Stokes flow around ring-like arrays of spheres. We show that the relationship between globally applied velocity or force to the response of individual spheres can be described by just 5 coefficients (or 9 in total) for any given configuration. The results indicate that for 7–10 spheres in sedimentation, there exists a certain spacing that produces steady-state translation of the ring, independent of its orientation. For large numbers of spheres, slender-body theory can be applied to the problem, providing remarkably close agreement to the numerical results over a wide range of parameters.

An analytical solution for non-Darcian flow induced by variable-rate pumping in a radially heterogeneous confined aquifer

An analytical solution for non-Darcian flow induced by variable-rate pumping in a radially heterogeneous confined aquifer

Steady solutions of quasi-geostrophic flows in basins, gulfs and channels on a β-plane

Steady solutions of quasi-geostrophic flows in basins, gulfs and channels on a <i>β</i>-plane

Effect of the flow-force relationships used in two parameter modelling of freezing and vitrification protocols for bovine embryos

Cells may become damaged by strong volume changes and related intracellular changes during slow freezing or vitrification. These osmotic events can be modelled mathematically, using descriptions of transmembrane flow of solute and water. We compared different variants of an often used 2-parameter (2P) formalism in fitting of an empirical shrink-swell curve of a bovine embryo in 5 vol% glycerol, and in simulations of CPA loading and removal in a vitrification protocol. In its original form, the 2P model uses a flow-force relationship for the flux of CPA that is not analogous to that for water (asymmetrical), but in the other variants used, the flow-force relationships for water and CPA are analogous to each other (symmetrical). The effect of used model on estimated values for Lp and Ps in 5 vol% glycerol was small. Also the effect on shrinking and swelling in vitrification media was small, but the original 2P model predicted stronger swelling of embryos during one-step CPA removal. One variant that we compared simply assumes Raoult's law, i.e. M = m, even in very concentrated solutions We conclude that this simple model is easy and appropriate for simulating osmotic events of embryos. But if a method for correcting for the deviation from Raoult's law is used, a symmetrical model seems more appropriate than the original (asymmetrical) 2P model.

Integrable flows on null curves in the Anti-de Sitter 3-space

Abstract We formulate integrable flows related to the Korteweg–De Vries (KdV) hierarchy on null curves in the anti-de Sitter 3-space ( AdS ). Exploiting the specific properties of the geometry of AdS , we analyze their interrelationships with Pinkall flows in centro-affine geometry. We show that closed stationary solutions of the lower order flow can be explicitly found in terms of periodic solutions of a Lamé equation. In addition, we study the evolution of non-stationary curves arising from a 3-parameter family of periodic solutions of the KdV equation.

Two-species model for nonlinear flow of wormlike micelle solutions. Part II: Experiment

Applications often expose wormlike micelle solutions to a very wide range of shear and temperature conditions. The two-species model presented in Part I [Salipante et al., J. Rheol. 68 (2024)] describes the nonlinear rheology over a wide range of shear rates. Here, we compare the model predictions to measurements using a combination of microcapillary and rotational rheology to measure the viscosity of surfactant solutions across seven decades of shear rate and five decades of viscosity. The effect of temperature is studied between 20 and 60 °C for different surfactant concentrations. Model parameters are determined from both small-amplitude shear measurements and fitting to the nonlinear data. Under shear stress, the model predicts due to hindered combination kinetics that the average micelle length decreases from several micrometers to a few hundred nanometers. At sufficiently high stress, the micelle shear rheology exhibits a transition from entangled wormlike behavior to a dilute rod rheology in agreement with the model. Transient stress-growth measurements exhibit a large overshoot, which is rather well predicted by the model with hindered combination rate. Microcapillary flow birefringence also is adequately predicted by the model, confirming the accuracy of its predicted micelle lengths and exhibiting a marked change in stress-optic response at the transition between entangled polymers and dilute rods. The relaxation of retardance after flow cessation follows model predictions that include micelle-micelle interactions, which are sensitive to the rotational diffusivity and length. These methods can be applied broadly to explore relationships between composition and performance.

Two-species model for nonlinear flow of wormlike micelle solutions. Part I: Model

We develop a rheological model to approximate the nonlinear rheology of wormlike micelles using two constitutive models to represent a structural transition at high shear rates. The model is intended to describe the behavior of semidilute wormlike micellar solutions over a wide range of shear rates whose parameters can be determined mainly from small-amplitude equilibrium measurements. Length evolution equations are incorporated into reactive Rolie-Poly entangled-polymer rheology and dilute reactive-rod rheology, with a kinetic exchange between the two models. Although the micelle length is remarkably reduced during flow, surprisingly, we propose that they are not shortened by stress-enhanced breakage, which remains thermally driven. Instead, we hypothesize that stretching energy introduces a linear potential that decreases the rate of recombination and reduces the mean micelle length. This stress-hindered recombination approach accurately describes transient stress-growth upon start-up shear flow, and it predicts a transition of shear viscosity and alignment response observed at high shear rates. The proposed mechanism applies only when self-recombination occurs frequently. The effect of varying the relative rate of self-recombination on the rheology of wormlike micelles at high shear rates is yet to be explored.

Stokes' second problem exact solution for hybrid nanofluid flow along an exponentially accelerating vertical surface

Stokes' second problem exact solution for hybrid nanofluid flow along an exponentially accelerating vertical surface

Self-similar solution for laminar bubbly flow evolving from a vertical plate

The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a mixture model formulation for the two-phase flow, considering variable density (beyond Boussinesq), viscosity and hydrodynamic bubble dispersion. Introducing a new change of coordinates, inspired by the Lees–Dorodnitsyn transformation, we obtain a new self-similar solution for the laminar boundary layer equations. The results predict a wall gas fraction and gas plume thickness that increase with height to the power of 1/5 before asymptotically reaching unity and scaling with height to the power 2/5, respectively. The vertical velocity scales with height to the power of 3/5. Our analysis shows that self-similarity is only possible if gas conservation is entirely formulated in terms of the gas specific volume instead of the gas fraction.

Magneto-Stokes flow in a shallow free-surface annulus

In this study, we analyse ‘magneto-Stokes’ flow, a fundamental magnetohydrodynamic (MHD) flow that shares the cylindrical-annular geometry of the Taylor–Couette cell but uses applied electromagnetic forces to circulate a free-surface layer of electrolyte at low Reynolds numbers. The first complete, analytical solution for time-dependent magneto-Stokes flow is presented and validated with coupled laboratory and numerical experiments. Three regimes are distinguished (shallow-layer, transitional and deep-layer flow regimes), and their influence on the efficiency of microscale mixing is clarified. The solution in the shallow-layer limit belongs to a newly identified class of MHD potential flows, and thus induces mixing without the aid of axial vorticity. We show that these shallow-layer magneto-Stokes flows can still augment mixing in distinct Taylor dispersion and advection-dominated mixing regimes. The existence of enhanced mixing across all three distinguished flow regimes is predicted by asymptotic scaling laws and supported by three-dimensional numerical simulations. Mixing enhancement is initiated with the least electromagnetic forcing in channels with order-unity depth-to-gap-width ratios. If the strength of the electromagnetic forcing is not a constraint, then shallow-layer flows can still yield the shortest mixing times in the advection-dominated limit. Our robust description of momentum evolution and mixing of passive tracers makes the annular magneto-Stokes system fit for use as an MHD reference flow.