Fluid Motion Research Articles

Discontinuous solutions for the Navier–Stokes equations with density-dependent viscosity

We prove the existence of a unique global-in-time weak solution of the Navier–Stokes equations that govern the motion of a compressible viscous fluid with density-dependent viscosity in two-dimensional space. The initial velocity belongs to the Sobolev space H^{1}(\mathbb{R}^{2}) , and the initial fluid density is \alpha -Hölder continuous on both sides of a \mathscr{C}^{1+\alpha} -regular interface with some geometrical assumption. We prove that this configuration persists over time: the initial interface is transported by the flow to an interface that maintains the same regularity as the initial one. Our result generalizes a previous known result of Hoff [Comm. Pure Appl. Math. 55 (2002), 1365–140] and Hoff and Santos [Arch. Ration. Mech. Anal. 188 (2008), 509–543] concerning the propagation of regularity for discontinuity surfaces by allowing a more general non-linear pressure law and density-dependent viscosity. Moreover, it supplements the work by Danchin, Fanelli, and Paicu [Anal. PDE 13 (2020), 275–316] with global-in-time well-posedness, even for density-dependent viscosity, and we achieve uniqueness in a large space.

Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid

The article considers the mathematical model describing the joint motion of a viscous compressible heat-conducting fluid and a thermoelastic plate with a fine two-level thermoelastic bristly microstructure attached to it. The bristly microstructure consists of a great amount of taller and shorter bristles, which are periodically located on the surface of the plate, and the model under consideration incorporates a small parameter, which is the ratio of the characteristic lengths of the microstructure and the entire plate. Using classical methods in the theory of partial differential equations, we prove that the initial-boundary value problem for the considered model is well-posed. After this, we fulfill the homogenization procedure, i.e., we pass to the limit as the small parameter tends to zero, and, as a result, we derive the effective macroscopic model in which the dynamics of the interaction of the ‘liquid–bristly structure’ is described by equations of two homogeneous thermoviscoelastic layers with memory effects. The homogenization procedure is rigorously justified by means of the Allaire–Briane three-scale convergence method. The developed effective macroscopic model can potentially find application in further mathematical modeling in biotechnology and bionics taking account of heat transfer.

Coherent turbulent flow structure under plunging breaker on movable grain bed simulated by 3D DEM-MPS method

ABSTRACT Breaking waves transport momentum, gas, and sediment vertically. Recent particle image velocimetry (PIV) measurements have elucidated the coherent vortex and turbulence structures under breaking waves. However, clarifying three-dimensional fluid motion under breaking waves with PIV remains challenging. Although particle methods have performed wave-breaking simulations, they have never been validated through velocity distributions for breaking waves above movable sediment beds. This study simulated the sediment transport process under plunging waves using a 3D Lagrangian fluid-particle mixture model. The investigation focuses on the first wave plunging for a fundamental investigation. Our simulation shows the instantaneous velocity distributions at different wave phases, which agree with the PIV measurement. A physically-based turbulence extraction method is introduced: a numerical filter based on the coherence between the water elevation and horizontal velocity. Visualized three-dimensional vortex and turbulence structures are consistent with previous studies. The transport equation of the kinetic turbulence energy investigates the turbulence budget near the bed surface and emphasizes the negative contribution of the fluid-particle interaction. Our findings show that a contribution of the pressure gradient to offshore sediment transport. The pressure gradient is difficult to correlate to the water surface gradient and is derived from the large vortex induced by the plunging wave.

Hydroelectric energy conversion of waste flows through hydroelectronic drag

Hydraulic energy is a key component of the global energy mix, yet there exists no practical way of harvesting it at small scales, from flows with low Reynolds number. This has triggered a search for alternative hydroelectric conversion methodologies, leading to unconventional proposals based on droplet triboelectricity, water evaporation, osmotic energy, or flow-induced ionic Coulomb drag. Yet, these approaches systematically rely on ions as intermediate charge carriers, limiting the achievable power density. Here, we predict that the kinetic energy of small-scale "waste" flows can be directly and efficiently converted into electricity thanks to the hydroelectronic drag effect, by which an ion-free liquid induces an electronic current in the solid wall along which it flows. This effect originates in the fluctuation-induced coupling between fluid motion and electron transport. We develop a nonequilibrium thermodynamic formalism to assess the efficiency of such hydroelectric energy conversion, dubbed hydronic energy. We find that hydronic energy conversion is analogous to thermoelectricity, with the efficiency being controlled by a dimensionless figure of merit. However, in contrast to its thermoelectric analogue, this figure of merit combines independently tunable parameters of the solid and the liquid, and can thus significantly exceed unity. Our findings suggest strategies for blue energy harvesting without electrochemistry, and for waste flow mitigation in membrane-based filtration processes.

Filaments in and between galaxy clusters at low and mid-frequency with the SKA

Understanding the magnetised Universe is a major challenge in modern astrophysics, and cosmic magnetism has been acknowledged as one of the key scientific drivers of the most ambitious radio instrument ever planned, the Square Kilometre Array. With this work, we aim to investigate the potential of the Square Kilometre Array and its precursors and pathfinders in the study of magnetic fields in galaxy clusters and filaments through diffuse synchrotron radio emission. Galaxy clusters and filaments of the cosmic web are indeed unique laboratories in which to investigate turbulent fluid motions and large-scale magnetic fields in action, and much of what is known about magnetic fields in galaxy clusters comes from sensitive radio observations. Based on cosmological magneto-hydrodynamic simulations, we predict radio properties (total intensity and polarisation) of a pair of galaxy clusters connected by a cosmic-web filament. We use our theoretical expectations to explore the potential of polarimetric observations to study large-scale structure magnetic fields in the frequency ranges 50-350\,MHz and 950-1760\,MHz. We also present predictions for galaxy cluster polarimetric observations with the Square Kilometre Array precursors and pathfinders, such as the LOw frequency ARay 2.0 and the MeerKAT+ telescope. Our findings point out that polarisation observations are particularly powerful for the study of large-scale magnetic fields, since they are not significantly affected by confusion noise. The unprecedented sensitivity and spatial resolution of the intermediate-frequency radio telescopes make them the favourite instruments for the study these sources through polarimetric data, potentially allowing us to understand if the energy density of relativistic electrons is in equipartition with the magnetic field or rather coupled with the thermal gas density. Our results show that low-frequency instruments also represent a precious tool to study diffuse synchrotron emission in total intensity and polarisation.

Computation of Deformable Interface Two‐Phase Flows: A Semi‐Lagrangian Finite Element Approach

ABSTRACTThis work aims at presenting a new computational approach to study two and three dimensional two‐phase flows and two dimensional coalescence phenomenon using direct numerical simulation. The flows are modeled by the incompressible Navier–Stokes equations, which are approximated by the finite element method. The Galerkin formulation is used to discretize the Navier–Stokes equations in the spatial domain and the semi‐Lagrangian method is used to discretize the material derivative. In order to satisfy the Ladyzhenskaya–Babuška–Brezzi condition, high‐order stable pair of elements are used, with pressure and velocity fields being calculated on different degrees of freedom in the unstructured mesh nodes. The interface is modeled by an unfitted adaptive moving mesh, where interface nodes are tracked in a Lagrangian fashion and moved with the velocity solution of the fluid motion equations. The surface tension is computed using the interface curvature and the gradient of a Heaviside function, and added in the momentum equations as a body force. In order to avoid undesired spurious modes at the interface due to high property ratios, a smooth transition between fluid properties is defined on the interface region. Several benchmark tests have been carried out to validate the proposed approach, and the obtained results have demonstrated agreement with analytical solutions and numerical results reported in the literature. A coalescence model is also proposed based on geometric criteria and results show interesting dynamics.

Magnetohydrodynamic Motions of Oldroyd-B Fluids in Infinite Circular Cylinder That Applies Longitudinal Shear Stresses to the Fluid or Rotates Around Its Axis

Two classes of magnetohydrodynamic (MHD) motions of the incompressible Oldroyd-B fluids through an infinite cylinder are analytically investigated. General expressions are firstly established for shear stress and velocity fields corresponding to the motion induced by longitudinal shear stress on the boundary. For validation, the expression of the shear stress is determined by two different methods. Using an important remark regarding the governing equations for shear stress and fluid velocity corresponding to the two different motions, this expression is then used to provide the dimensionless velocity field of the MHD motion of the same fluids generated by a cylinder that rotates around its symmetry axis. Obtained results can generate exact solutions for any motion of this kind of Oldroyd-B fluids. Consequently, both types of motions are completely solved. For illustration, some case studies are considered, and adequate velocity fields are provided. The steady-state components of these velocities are presented in different forms whose equivalence is graphically proved. The influence of the magnetic field on the fluid behavior is graphically investigated. It was found that the fluid flows slower, and a steady state is earlier reached in the presence of a magnetic field. The fluid behavior when shear stress is given on the boundary is also investigated.

A dissipative extension to ideal hydrodynamics

Abstract We present a formulation of special relativistic, dissipative hydrodynamics (SRDHD) derived from the well-established Müller-Israel-Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and timescale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation timescales, it is roughly an order of magnitude faster than standard methods near the ideal limit.

Heat and mass transfer analysis on peristaltic transport of PTT fluid with wall properties

The current study is intended to examine the effect of heat and mass transfer on the peristaltic propulsion of the Pan-Thien-Tanner fluid in a cylindrical tube with wall properties. The complexity of the system is reduced by long wavelength and low Reynolds number strategy. The physical behavior of the peristaltic motion of the PTT fluid is explained and elucidated graphically for several values of various parameters connected with this flow problem. It has been revealed that raising the Source/Sink parameter values and the Weissenberg number results in a higher velocity profile. The outcomes embrace the key to understanding the human organs' physiological fluid motion, such as the chime moment in the small intestine and esophagus.

The influence of a non-uniform heat source/sink and Joule heating on the convective motion of a micropolar fluid in a chemically radiative MHD medium across a stretched sheet

The objective of the present exploration is to examine impactions of radiation, a non-uniform intensity source, and a permeable medium on a temperamental MHD blended convective micropolar liquid over an extended sheet subject to Joule heating. To transform the formulated problem into ordinary differential equations, the applicable similarity transformation is implemented. By utilizing R-K-F 4th -5th order approach with shooting method with MATLAB, the numerical solution is obtained. For the relevant profiles, the dimensionless parameters are visually displayed and described. Skin friction, the Nusselt number, and the Sherwood number have all been calculated using the answer found for the velocity, temperature, and concentration. With the assistance of line graphs, the impact of different flow factors being introduced into the problem is addressed. This research is conducted on the implications of MHD, porous, thermal radiation, viscous dissipation, Joule heating, non-liner thermal radiation and chemical reaction. For large values of micropolar parameter, the temperature is reduced and velocity and angular momentum distributions are raised. With the thermal radiation parameter, the temperature distribution gets better and thermal boundary layer is improved while the large values of Eckert number and non-uniform heat source or sink parameters, thermal boundary layer is improved. The higher thermal conductivity is proportional to the thickness of the thermal boundary layer. The concentration profile degrades with higher Schmidt number and chemical reaction parameter values. The current examination pertains to the significant subject matter of cooling of systems, artificial heart identification, oil-pipelined frictions, flow-tracers.

Highlighting the effects of gravity in a compact thermoacoustic heat pump

We present a numerical study of gravity impact on thermoacoustic heat pumping effects in a compact cavity used as a refrigeration device. More precisely, we show how gravity acts on the temperature distribution, on the mean temperature heat flux along the stack area and on flow dynamics. Studies are performed in a two-dimensional geometrical configuration which is simplified with respect to common experimental devices but sufficiently detailed to take into account the main physical mechanisms. Fluid motion, heat and mass transfer as well as compression/expansion effects are estimated from the computation of the Navier-Stokes equations in the low-Mach number hypothesis coupled with the heat equation in solid parts. The low-Mach number hypothesis is here relevant because the characteristic scale of the acoustic wavelength is much smaller than the geometrical length scales of the cavity. The operating mode is characterized by a moderate drive ratio, a fluid oscillating motion of moderate amplitude and fixed low frequency, typical of such devices. It is shown that when gravity is included, buoyancy effects modify the temperature and velocity fields as well as heat pumping efficiency.

Modeling with generalized flux theory for computational investigation of thermal enhancement in fluid with tri‐, di‐, and mono‐nanoparticles

AbstractTo study the influence of several factors (tri‐nanoparticles and relaxation time related to momentum, thermal, and concentration) on non‐Fourier transport of heat and mass, mathematical models are developed. The cases of tri‐, di‐, and mono‐nanofluids are considered. Flow and transport scenarios are translated into mathematical equations for which conservation laws and correlations for thermophysical properties are used. Boundary layer simplifications are used to approximate these mathematical models. The nondimensional set of problems is numerically solved using the finite element method (FEM). The solutions that are convergent and mesh‐free are obtained. The outcomes are compared to existing benchmarks. There is excellent consistency between the current and published results. The viscoelastic behaviors related to momentum, thermal, and solutal relaxation times are examined. It is also investigated how tri‐nanoparticles improve heat transmission in flow. The wall shear stresses for the mono‐, di‐, and tri‐nanofluids are calculated against momentum relaxation time. It is observed that tri‐nanofluid exerts the highest stress on the surfaces over which it flows. Therefore, while using these fluids, the surface should be ensured to bear the stresses; otherwise, failure of the system may take place. Thus, industrial applications and additional capability of surface be ensured. This looks at influence the Deborah number on the fluid motion. Deborah number is straightforwardly connected with relaxation time and it is found that higher is Deborah number lower will be the speed of fluid. As a consequence, viscous region will be narrow down. Thus, viscous dominant region is controllable by the using fluid of higher relaxation time. A significant enhancement in the thermal performance of Maxwell fluid occurs via the dispersion of tri‐nanoparticles ().

Electron Dissipation and Electromagnetic Work

AbstractWith the increase in technical capabilities of computer simulation in recent years, it has become feasible to quantify the degradation of fluid scale plasma and electromagnetic energies in favor of increases of internal energies. While it is understood that electromagnetic energy can be exchanged with fluid scale velocities, it is the pressure strain interaction that exchanges energy between fluid motions and internal energy. Here using simulations of both turbulence and reconnection we show that for electrons, the pressure strain and electromagnetic work are closely related and are frequently comparable when appropriate time and spatial averaging is applied. Otherwise, the instantaneous spatial averaged pressure strain and electromagnetic work are nearly equal for slowly evolving systems, like the reconnection case, while they differ significantly in rapidly evolving systems, like the turbulence case. This clarifies the relationship between these two quantities, which are each frequently used as measures of dissipation.

Simulating 2D Fluid Motion with the Smooth Particle Hydrodynamic Approach

Abstract Virtual two-dimensional (2D) fluid simulation is useful for directly simulating fluids in various situations, including geological simulations for landslides and fluid simulations for teaching. This research aims to simulate the behaviour of three different types of fluids (water, coconut oil, and glycerine) in a 2D container and analyse how these three types of fluids behave under various conditions, including interactions with boundaries. The research used Python programming to simulate fluids and the Wondershare Filmora X application to combine images. The Smooth Particle Hydrodynamics method simulated fluid in a 2D container with 10,000 particles by deriving the force density field directly from the Navier-Stokes equations. The Navier-Stokes equations were utilized to find the acceleration and velocity of fluid particles by considering external forces, internal forces, and gravity through this method. Acceleration and velocity were validated due to wall collisions, collisions with boundaries, and collisions between particles, which caused changes in particle position and velocity. During visualization, the fluid velocity decreased over time due to attenuation caused by interactions between neighbour particles, particles with boundaries, and particles with walls. From the simulation, it was observed that the fluid flowed from a higher place to a lower place, with fluid particles taking the shape of the container and the surface of the fluid forming waves. On the other hand, simulations with boundaries indicated that smaller gap sizes and higher viscosities led to increased difficulty in fluid penetration into the gap within the container.

On bifurcation of non-isolated singular points arising in a problem of two-phase fluid motion in a pipe

The dynamics of gas suspension in a pipe is studied. It is described by a system of three autonomous differential equations, whose equilibrium (singular) points are not isolated, but form several continuous curves. One of these curves belongs to the transonic plane. The dynamics in a neighborhood of this plane is interesting from the physical viewpoint. In this work, the dynamics in a neighborhood of the curves of singular points is investigated. The main tools of this work are the center manifold theorem and the reduction principle. A peculiarity of the system is that the curves of singular points intersect each other. Moreover, at the intersection point a bifurcation occurs. Results of the work are the description of the dynamics in a neighborhood of singular points, the proof that a curve of singular points belongs to a center manifold and the description of the bifurcation, which occurs at the intersection point of the curves of singular points.

Unsupervised Learning Bioreactor Regimes

Efficient operation of bioreactors is pivotal for the success of biomanufacturing. Traditional Computational Fluid Dynamics (CFD) simulations, while detailed, often suffer from long computation times and complexity, making them impractical for real-time applications. This study introduces a novel multivariate unsupervised learning algorithm for clustering bioreactors into coherent regions based on CFD-generated and real-world data. The resulting clusters can be used to determine regimes inside a reactor, or can work as an initial step for compartment models. Our method employs a custom k-means clustering algorithm that not only ensures spatial continuity within clusters but also optimizes the number of compartments based on clustering scores. This optimization process focuses on defining compartments clearly while retaining maximum information from the continuous body, as demonstrated by a Pareto front analysis. The efficacy and adaptability of this approach were validated through two case studies: a 202 m³ Rushton impeller bioreactor and an 840 m³ airlift reactor. The results underscore the benefits of 3-D compartmentalization in capturing the complex dynamics of fluid motion and cellular activities. By establishing a robust method for scaling down experiments and enhancing bioreactor design, this study paves the way for more efficient industrial applications.

Opracowanie konstrukcji świdra wiertniczego do zwiercania skał o różnych właściwościach mechanicznych

This paper presents a description of a bit design with a combined cutter layout, aimed at increasing the efficiency of breaking rocks with different mechanical properties. The results from industrial testing of the manufactured bits are analyzed, revealing the need to improve their hydraulic flushing system. Computer modeling was conducted using the Flow Simulation CAD/CAM package of the Solid Works system, where various models of the design options for the bit, the borehole bottom, and a segment of the drill string were created. For each variant, numerical calculations of the fluid motion were carried out using the finite element method. Based on the simulation results, optimal angles of inclination for the jet nozzles relative to the bit axis and their distance from this axis were determined. Key factors influencing the stability of the bit cutters, which destroy the rock by cutting with axial vibrations, were identified, and analytical dependencies for their predictive stability were derived. The wear rate of the bit cutters was determined by instantaneous values of such physical parameters as: the degree of wear, rock cutting speed, temperature, axial loading force on the cutter, and the friction coefficient at the contact between the cutter and rock. Temperature is especially impactful, reaching levels exceeding 1000°C in the cutting zone; it is often regarded as the primary factor influencing bit cutter stability. To maximize the efficiency of rock-breaking in the process of drilling wells, it is necessary to set the following vibration parameters: frequency, amplitude, and vibration mode, which can be determined from the results of mathematical modeling.

Revealing the dynamics of stagnant rings of third-grade fluid film with heat transfer in the presence of surface tension

In many engineering applications, including coating and lubrication operations, analyzing the temperature behavior of thin film flows on a vertically upward-moving tube is crucial to improving predictive models. This paper examines a steady third-grade fluid film flow with a surface tension gradient on a vertical tube. The mechanisms responsible for the fluid motion are upward tube motion, gravity, and surface tension gradient. This analysis focuses on heat transfer and stagnant ring dynamics. The formulated highly nonlinear ordinary differential equations are solved using the Adomian decomposition method. The conditions for stagnant rings and uniform film thickness are attained and discussed. The inverse capillary number C, Stokes number St, Deborah number De, and Brinkman number Br emerged as flow control parameters. The temperature of the fluid film rises with an increase in the C, St, De, and Br, whereas it decreases with an increase in thermal diffusion rate. The radius of stagnant rings tends to shrink by the increase in C, St, and De. When the value of De is high, third-grade fluid behaves like solids; only free drainage happens with smaller radius stagnant rings and high temperatures. A comparison between Newtonian and third-grade fluids regarding surface tension, velocity, temperature, stationary rings, and fluid film thickness is also provided.

Influence of space conjugate temperature varying non-uniform heat sink/source on hydromagnetic slip water-EG (50:50) nanofluid

Significant cooling is an essential requirement in the field of aeronautical and bio-medical engineering, nuclear reactor system, solar collectors, and in development of electronic chips etc. Involving rotating conical geometries. In view of this, flow and heat transfer over conical geometries subject to different constraints of motion are highly needed. Implementation of magnetic field subject to flow pattern controls the fluid motion thereby imparting better cooling. Consideration of nanofluid instead of regular fluid yields prominent cooling of the associated surface. Such relevance has motivated the authors to work on magnetohydrodynamics and heat transfer investigation of water-EG (50:50) mixture based Al2O3 and Fe3O4 past heated and rotating down-pointing upright cone subject to impact of space and temperature varying non-uniform heat source or sink. Numerical solution of dimensionless governing equations is accomplished by implementing Runge-Kutta method. The findings indicate that swirl and axial velocities peter out with rise in magnetic parameter while both exhibit opposite impact in response to slip parameter. Temperature profiles upgrade due to amplification of space and temperature dependent parameters. Skin friction and heat transportation upsurge with growth of solid volume fraction of nanoparticle.

Free movement of a near-wall particle in fluid of comparable density

The fundamental problem of nonlinear interaction between a freely moving particle and surrounding fluid flow is investigated for a density ratio of order unity, with potential applications to biomedical, environmental, and aerodynamic configurations. The interaction takes place near a fixed wall, with the particle being relatively thin. A mathematical model is presented, showing the fluid pressure forces to be dominant over the mass-acceleration effects in the particle motion (in contrast with previous analyses). The added mass due to the fluid motion, thus, greatly exceeds the body mass. Numerical simulations and asymptotic analysis reveal a range of possible particle motions. The main properties emerging are: (a) the distinction between collisions with the wall and fly-away responses; (b) the time scales involved in such behaviors; (c) the pressures and velocities induced at collision; (d) the occurrence of flow reversal in certain cases; and (e) the results being independent of the particle mass and moment of inertia as well as independent of the density ratio provided that the ratio is of order unity (0–7, say) or only slightly larger (8–30, say).