Classical Fluid Research Articles

Implementation of a New Smart-Lubricant Model Using Generalized Newtonian Approach in Soft Elastohydrodynamic Lubrication

Abstract This is an inceptive attempt to replace the classical Bingham fluid model with a continuous double Newtonian power-law-based constitutive equation for smart lubricants like magneto-rheological, electro-rheological, and ferro-fluids. The implementation of Bingham model in hydrodynamic (HD) and elastohydrodynamic (EHD) lubrication analyses is highly challenging and inconvenient due to its inherent discontinuity. Therefore, the present work demonstrates the use of an already existing rheological model with an appropriate set of parameters to describe the flow behavior of smart lubricants in a soft-EHD lubrication algorithm based on the generalized Newtonian approach. The formation of both floating and adherent cores validates the proposed model. An extensive parametric study is also performed to explore the effects of operating speed, load, and slide-to-roll ratio on the soft-EHL characteristics. The results are very promising, showing that it's possible to customize smart lubricants to match specific operating conditions. This is achieved by adjusting the yield stress value accordingly, allowing for the desired variation in lubrication characteristics.

A hybrid lattice Boltzmann/immersed boundary method/finite-difference model for thermal fluid-solid interactions

Particulate flows are frequently observed in both industrial and natural environments, and their simulation becomes particularly challenging when heat transfer is involved. This study introduces a hybrid numerical approach, combining the lattice Boltzmann Method (LBM), Immersed Boundary Method (IBM), and Finite Difference (FD) energy solver to alleviate the limitations observed in double distributed lattice Boltzmann methods and classical Computational Fluid Dynamics (CFD). The model incorporates an enhanced Hermite polynomial-based central moments collision operator. This enhancement boosts stability and overcomes the Galilean-invariant issues observed in classical LBM. For heat transfer, a Finite-Difference technique is employed for resolving the energy equation, discretizing the advection term through a Weighted Essentially Non-Oscillatory (WENO) approach. The Boussinesq approximation handles buoyancy forces, while the direct-forcing IBM manages fluid-particle interaction. Validation across various test cases confirms the model's accuracy, showcasing its ability to account for variations in thermal properties like specific heat capacity Cp over a wide range. The model is further utilized to investigate a reactor containing 300 catalyst particles. In summary, this hybrid methodology is found to be a promising tool for comprehensively studying and designing particle-laden systems with thermal effects.

Vortex merging in strongly coupled dusty plasmas using a visco-elastic fluid model

This work is a numerical study of the two-dimensional merging phenomena between two Lamb–Oseen co-rotating vortices in a viscoelastic fluid. We use a generalized hydrodynamics fluid model to study vortex merging in a strongly coupled dusty plasma medium, which exhibits characteristics similar to a viscoelastic fluid. Several aspects influencing the merging phenomena are considered: the aspect ratio (core size/separation distance), the relative circulation strengths of each vortex, and the coupling strength of the medium. Unlike classical hydrodynamic fluids, we find that for viscoelastic fluids, shear waves facilitate the merging events even for widely separated vortices. The merging process is accelerated in media with higher coupling strengths and the resultant vortex shape decays more quickly as well. It is also found that varying either the vortex scale or the vortex circulation strength can result in a similar merging process, where a smaller (larger) vortex acts like a vortex with weaker (stronger) circulation. Finally, we show that a Poynting-like conservation theorem is satisfied for the examined merging processes.

‘Quantum plumbing’ at the nanoscale

Nanofluidics could be used to purify water, generate energy and build nanoscale machines. But when water flows through a carbon nanotube, classical fluid mechanics breaks down, leading to puzzling experimental findings that researchers have attributed to an effect called “quantum friction”, as Philip Ball explains.

Three Carleman routes to the quantum simulation of classical fluids

We discuss the Carleman approach to the quantum simulation of classical fluids, as applied to (i) lattice Boltzmann, (ii) Navier–Stokes, and (iii) Grad formulations of fluid dynamics. Carleman lattice Boltzmann shows excellent convergence properties, but it is plagued by nonlocality which results in an exponential depth of the corresponding circuit with the number of Carleman variables. The Carleman Navier–Stokes offers a dramatic reduction of the number Carleman variables, which might lead to a viable depth, provided locality can be preserved and convergence can be achieved with a moderate number of iterates also at sizeable Reynolds numbers. Finally, it is argued that Carleman Grad might combine the best of Carleman lattice Boltzmann and Carleman Navier–Stokes.

Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

This paper investigates the structural changes in the turbulent motion of an incompressible fluid in the hydrodynamic entrance region of plane-parallel pressure motion. Movement in pressure hydromechanical systems usually occurs in a turbulent regime. Studying the patterns of changes in hydrodynamic parameters under conditions of stationary turbulent pressure motion in the inlet region is a very urgent task. The study was carried out on the basis of boundary layer equations. Taking into account the dependence of changes in the kinematic viscosity coefficient that occur between layers of fluid, a boundary value problem was formed. Analytical solutions have been obtained that make it possible to obtain patterns of changes in velocity and pressure in any effective flow section. Based on the general conclusions of the study, solutions were found for two cases: a) the velocity of the fluid entering the cylindrical pipe is constant; b) the velocity of the incoming fluid has a parabolic distribution. For these cases, using computer analysis of the data obtained, general graphs of velocity changes were constructed in various sections along the hydrodynamic entrance region. These graphs, which display the change in velocity along the entire length of the inlet, make it possible to obtain the velocity of fluid movement at any point along the inlet length and estimate the length of the transition zone. The results obtained are among the least studied issues of classical fluid mechanics and are of important theoretical interest. The results obtained are applicable for the correct construction of the hydrodynamic entrance region of machinery. A calculation formula has been obtained to determine the length of the hydrodynamic inlet region

Alternative routes to electron hydrodynamics

Viscous flow of interacting electrons in two dimensional materials features a bunch of exotic effects. A model resembling the Navier-Stokes equation for classical fluids accounts for them in the so called hydrodynamic regime. We perform a detailed analysis of the physical conditions to achieve electron hydrodynamic transport and find alternative routes: the application of a magnetic field or a high-frequency electric field in the absence of very frequent inelastic collisions. As a major conclusion, we show that the conventional requirement of frequent electron-electron collisions is too restrictive and, as a consequence, materials and phenomena to be described using hydrodynamics are widened. In view of our results, we discuss recent experimental evidence on viscous flow and point out alternative avenues to reduce electric dissipation in optimized devices.

Numerical analysis of velocity slip and magnetic Soret effect on dissipative Maxwell liquid motion about a stretching wall with heat source/sink

The main aim of present numerical analysis is to explore the effects of viscous dissipation and velocity slip on the two-dimensional steady-state viscous incompressible flow of Maxwell fluid over a stretching sheet under the infleunce of magnetic field. Novel collective effects of heat source/sink and Soret impacts have been included in the governing equations to explore the salient features of heat and mass transport mechanism. Further, the velocity slip is introduced into the boundary conditions to depict the momentum transport behavior in the flow region. A typical Maxwell fluid model is deployed to separate the non-Newtonian flow behavior from that of classical Newtonian fluids. However, the visco-elastic Maxwell fluid finds its abundant applications in various fields of engineering and medicine such as plastic sheet drawing, metallurgy, polymer sheet extrusion, chemical engineering, electronic cooling, injection molding and nuclear cooling and many others. Inspired by these applications, authors have made an attempt to disclose the magneto-thermo salient features of slip flow of Maxwell fluid over stretching wall under Soret effect. The current physical situation results the highly nonlinear coupled two-dimensional steady-state partial differential equations and which are not amenable to any of the direct techniques. Due to this, the suitable similarity transformations are deployed to reduce the dimensional complexity of the constructed partial differential equations. A robust Matlab-based bvp4c scheme is utilized as a basic tool to produce the similarity solutions of the governing equations. The computer generated numerical data is presented in view of flow, temperature and concentration profiles including physical quantities of interest like skin-friction coefficient, heat and mass transport rates for the various values of physical parameters range such as, 0 ≤ M ≤ 1 , 0 ≤ β ≤ 1 , − 0.3 ≤ λ ≤ 0.6 , − 0.2 ≤ Q ≤ 0.2 , 0 ≤ Ec ≤ 2.2 , 1.2 ≤ Pr ≤ 2.2 , 0 ≤ Sr ≤ 0.5 and 1.2 ≤ Sc ≤ 2.2 . Accordingly, it is noticed that, enhancing magnetic parameter decreases the Maxwell fluid flow and amplifies the temperature and concentration fields. Enlarging Maxwell fluid parameter decreases the velocity field and increases the temperature and concentration profiles. Amplified slip parameter diminished the Maxwell flow inside the flow regime. Increasing heat source/sink parameter amplifies the temperature field. Further, magnifying Soret number amplifies the concentration field. Magnitude of skin-friction coeffiecient enlarged with amplified magnetic and Maxwell fluid parameters. Heat and mass transport rates decayed with enhancement in heat source/sink and Soret parameters. Finally, it is described that, the present similarity solutions showing good agreement with the previously reported solutions in the literature and this fact confirms the accurateness of the used numerical method and the generated similarity solutions.

Fluctuation-response relation as a probe of long-range correlations in nonequilibrium quantum and classical fluids.

The absence of a simple fluctuation-dissipation theorem is a major obstacle for studying systems that are not in thermodynamic equilibrium. We show that for a fluid in a nonequilibrium steady state characterized by a constant temperature gradient the commutator correlation functions are still related to response functions; however, the relation is to the bilinear response of products of two observables, rather than to a single linear response function as is the case in equilibrium. This modified fluctuation-response relation holds for both quantum and classical systems. It is both motivated and informed by the long-range correlations that exist in such a steady state and allows for probing them via response experiments. This is of particular interest in quantum fluids, where the direct observation of fluctuations by light scattering would be difficult. In classical fluids it is known that the coupling of the temperature gradient to the diffusive shear velocity leads to correlations of various observables, in particular temperature fluctuations, that do not decay as a function of distance, but rather extend over the entire system. We investigate the nature of these correlations in a fermionic quantum fluid and show that the crucial coupling between the temperature gradient and velocity fluctuations is the same as in the classical case. Accordingly, the nature of the long-ranged correlations in the hydrodynamic regime also is the same. However, as one enters the collisionless regime in the low-temperature limit the nature of the velocity fluctuations changes: they become ballistic rather than diffusive. As a result, correlations of the temperature and other observables are still singular in the long-wavelength limit, but the singularity is weaker than in the hydrodynamic regime.

Freezing density scaling of transport coefficients in the Weeks-Chandler-Andersen fluid.

It is shown that the transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of the Weeks-Chandler-Andersen (WCA) fluid along isotherms exhibit a freezing density scaling (FDS). The functional form of this FDS is essentially the same or closely related to those in the Lennard-Jones fluid, hard-sphere fluid, and some liquefied noble gases. This proves that this FDS represents a quasi-universal corresponding state principle for simple classical fluids with steep interactions. Some related aspects, such as a Stokes-Einstein relation without a hydrodynamic diameter and gas-to-liquid dynamical crossover, are briefly discussed. Simple fitting formulas for the transport coefficients of the dense WCA fluid are suggested.

Thermo-mechanical coupled peridynamics simulation of concrete failure under fire scenarios

A coupled thermo-mechanical bond-based peridynamical (PD) method is developed to simulate thermal cracking processes in concrete. Based on the bond-based PD heat conduction and motion equations, the PD differential operator (PDDO) is used to express the classical computational fluid dynamics basic equations in a non-local integral form, establishing a PD model for the thermo-mechanical coupling problems. In this model, concrete is considered a heterogeneous material composed of aggregates and mortar, with material parameters assumed to be temperature-dependent. The multi-rate explicit time integration scheme is proposed to overcome the multi-scale time problem in coupled thermo-mechanical systems. The model is applied to simulate the transient heat transfer problem of a homogeneous plate. The results show good agreement with the analytical solution, providing evidence for the correctness and accuracy of the proposed coupled numerical method. The damage behavior of the borehole heated concrete plate is analyzed, followed by the simulation of the damage to the concrete plate under a fire scenario. The numerical results accurately predict the temperature distribution within the heterogeneous concrete and the resulting material damage. This study provides new theoretical basis for the fire resistance design and high-temperature performance improvement of concrete materials and structures.

Entropy generation analysis of a micropolar fluid in a corrugated channel with convective and slip conditions

This study focuses on examining the entropy generation in a corrugated channel, considering convective boundary conditions and slip flow, with a micropolar fluid. The governing equations for the micropolar fluid flow, including linear and angular momentum equations, as well as the energy equation, are solved using the perturbation technique. The effects of corrugations, slipping flow, and convective boundary conditions on the entropy generation and the flow behavior are analyzed. The results show that the entropy generation enhanced with the corrugation amplitude, while it reduced for the slip flow. Moreover, entropy generation is affected by the convective boundary conditions, and it is an increasing function with the convective heat transfer coefficient. Additionally, the study demonstrates that micropolar fluid exhibits distinct flow characteristics in comparison to classical Newtonian fluids. These findings have practical implications for the design and optimization of microfluidic devices, as well as for gaining insights into the behavior of micropolar fluids in various engineering applications.

Phenomenology of transition to quantum turbulence in flows of superfluid helium

Transition from laminar to turbulent states of classical viscous fluids is complex and incompletely understood. Transition to quantum turbulence (QT), by which we mean the turbulent motion of quantum fluids such as helium II, whose physical properties depend on quantum physics in some crucial respects, is naturally more complex. This increased complexity arises from superfluidity, quantization of circulation, and, at finite temperatures below the critical, the two-fluid behavior. Transition to QT could involve, as an initial step, the transition of the classical component, or the intrinsic or extrinsic nucleation of quantized vortices in the superfluid component, or a simultaneous occurrence of both scenarios—and the subsequent interconnected evolution. In spite of the multiplicity of scenarios, aspects of transition to QT can be understood at a phenomenological level on the basis of some general principles, and compared meaningfully with transition in classical flows.

Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street’ is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately 0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Hydrodynamics of quantum vortices on a closed surface

We develop a neutral vortex fluid theory on closed surfaces with zero genus. The theory describes collective dynamics of many well-separated quantum vortices in a superfluid confined on a closed surface. Comparing to the case on a plane, the covariant vortex fluid equation on a curved surface contains an additional term proportional to Gaussian curvature multiplying the circulation quantum. This term describes the coupling between topological defects and curvature in the macroscopic level. For a sphere, the simplest nontrivial stationary vortex flow is obtained analytically and this flow is analogous to the celebrated zonal Rossby-Haurwitz wave in classical fluids on a nonrotating sphere. For this flow the difference between the coarse-grained vortex velocity field and the fluid velocity field generated by vortices is solely driven by curvature and vanishes in the corresponding vortex flow on a plane when the radius of the sphere goes to infinity. Published by the American Physical Society 2024

Dynamic evolutions of Bohm sheaths and pre-sheaths

The time evolutions of the Bohm sheath and the related pre-sheath are analyzed as an initial value problem. The standard classical fluid model of a collisionless plasma is used with cold ions and Boltzmann distributed electrons. Numerical solutions of the basic equations show that a stationary plasma sheath itself is established within a few ion plasma periods. It is demonstrated analytically that for infinitely extended homogeneous plasmas in one spatial dimension, the only possible pre-sheath solution is dynamic, giving a steady expansion: no stationary solution exists for this one-dimensional case. The potential and density drops along the dynamic pre-sheath differ notably from the values found for stationary models suggested in the literature. Collisions give only formal changes to the collisionless results, and their substance remains the same in one spatial dimension. Cylindrical and spherical geometries, on the other hand, allow for physically acceptable, fully nonlinear, stationary solutions with analytical results given. These are supported by numerical solutions.

Modeling and analysis of Alpine skiing downhill based on the DPAS model considering four-way inhomogeneous environmental winds with digital twins at downhill course of the Beijing Olympic Winter Games

In Alpine skiing, the influence of the environment wind on the athlete is crucial. To accurately analyze the coupling effect of environment wind speed, wind direction, and the athlete’s skiing process, this paper establishes the kinematic equations of the athlete based on Newtonian classical mechanics and computational fluid dynamics (CFD) and proposes a discretization method for the course. Simulation results were obtained by using CFD to obtain digital twins for the course and its surroundings. The simulation results were also used as input to the wind parameters to analyze the athletes’ sliding performance. The Downhill Process in Alpine Skiing (DPAS) model was constructed to validate the actual downhill course in the Beijing Olympic Winter Games. An analytical framework for downhill skiing with way inhomogeneous winds was demonstrated to be a good simulation and validation of our analytical framework, proving its good simulatability and reliability. The downhill process is also subdivided into four phases: start-up acceleration phase, core acceleration phase, intermittent acceleration phase, and endurance sprint phase, based on the velocity-time curve derived from the actual course simulation. Tactical skiing strategies for skiers to improve their performance are proposed for the different stages of the process. We believe that the DPAS model can also be applied to other parts of Alpine skiing such as slalom, giant slalom, and super-G, and that the results can be used to suggest tactical strategies to improve performance.

Investigation of Magneto Hydrodynamics Properties of Reiner–Philippoff Nanofluid with Gyrotactic Microorganism in a Porous Medium

Investigation of Magneto Hydrodynamics Properties of Reiner–Philippoff Nanofluid with Gyrotactic Microorganism in a Porous Medium Nanofluids have many potential applications in engineering, medicine, and biotechnology due to their enhanced thermal, electrical, and optical properties. However, the flow and heat transfer characteristics of nanofluids are influenced by various factors, such as the type and size of nanoparticles, the base fluid, the magnetic field, the radiation, the chemical reaction, and the presence of microorganisms. Therefore, it is important to study the effects of these factors on the nanofluid flow and heat transfer using mathematical models and numerical methods. One of the mathematical models that can describe the nanofluid flow is the Reiner-Philippoff model, which is a classical non-Newtonian fluid model that accounts for the shear-thinning behaviour of some fluids. The Reiner-Philippoff model has been used to study the nanofluid flow over a stretching sheet, which is a simplified model of many industrial processes involving stretching or shrinking surfaces. However, most of the previous studies have neglected the effects of the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection on the nanofluid flow over a stretching sheet. The objective of this paper is to fill this gap by conducting a numerical investigation of the effects of the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection on a Reiner-Philippoff nanofluid of MHD flow through a stretching sheet. This also considers the effects of thermophoresis and Brownian motion, which are two mechanisms that govern the transport of nanoparticles in nanofluids. The article utilized a similarity transformation to reduce the governing partial differential equations into ordinary differential equations, which are then solved by using the MATLAB computational tool bvp4c technique. The paper also employs a hybrid numerical solution method using Runge-Kutta fourth order with a shooting technique and an optimization technique using the Bayesian regularization method for Runge-Kutta to improve the accuracy of the prediction outcomes. The main finding of this paper is that the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection have significant effects on the velocity, temperature, concentration, and motile microorganism profiles of the nanofluid flow over a stretching sheet. The paper also discusses how these effects can be controlled by varying the relevant parameters. This provides graphical results for the profiles of velocity, temperature, concentration, and motile microorganisms for different values of these parameters. The study also compares its results with some existing results in the literature and finds good agreement.

Liquid metal droplet dynamics

AbstractThe unique properties to combine the dual merits of both liquids and metals together make the gallium‐based liquid metal (LM) droplets a class of unconventional substitute which possess great potential for a group of newly emerging areas, such as stretchable electronics, soft devices, micro sensors and actuators. In addition, LM droplets are undoubtedly an intriguing target worth of pursuing in fundamental hydrodynamic investigations due to their extremely high surface tension nature compared to classical nonmetallic fluids. Since the discovery of the diverse transformation phenomena and self‐fueled droplet mollusks of LM that can move automatically in solution via single electricity or even without any external energy supply, tremendous attentions were attracted to this special fluidic object of LM droplets. Over the past decade, there has been a proliferation of explorations on LM droplet dynamics, while the involved contents are heterogeneous due to the interfacial physical/chemical activity of the LM and the diversity of the kinetic behaviors. To better understand and manipulate the droplet behavior and to promote further development of the LMs, this review is dedicated to summarize the latest progress and presents an overview on basic findings related to LM macro‐droplet dynamics. Firstly, the extended definition of LM droplets and the corresponding fabrication methods are given. Then, typical works on LM droplet dynamics are systematically interpreted based on their different behavior categories. Finally, the perspectives, main obstacles and challenges restricting the development of LM droplet dynamics are pointed out.

Quantum algorithm for lattice Boltzmann (QALB) simulation of incompressible fluids with a nonlinear collision term

We present a full quantum algorithm for the lattice Boltzmann method for simulating fluid flows, the only such algorithm to implement both the streaming and collision substeps as unitary operators using an efficient number of qubits. We use Hamiltonian simulation as the main route underlying the algorithm, and show that it uses qubits that scale logarithmically in the flow Reynolds number but gates that scale only polynomially. We motivate the discussion by a brief overview of existing attempts at simulating classical fluids on quantum computers and present a pedagogical discussion on assigning quantum operators to classical variables in both the streaming and the collision substeps, after highlighting the incompatibility of the latter with the implementations of the streaming step that exists in the literature. We use the Bhatnagar–Gross–Krook ansatz for the collision term, representing the relaxation toward an equilibrium distribution. For nonlinear collisions, we use Kowalski's framework that links the nonlinear dynamics of a system to the evolution of bosonic modes, assigning a Carleman linearization order to the truncation in the Fock space of the bosons. We present the qubit and gate complexities, in terms of the chosen accuracy and the Reynolds number. In the Appendix, we work out the details of implementing the operators of the truncated bosonic Fock space in terms of single-qubit gates as well as the error scaling for a general polynomial driving function.