Turbulent Fluid Motion Research Articles

Modeling the Effect of Surfactant on Droplet Breakup in a Turbulent Flow

In many industrial applications oil drops suspended in water are broken down by turbulent fluid motion, assisted by the addition of surfactants. In this paper, we develop a model for the interactio...

Calculation of the turbulent boundary layer of a flat plate

The calculation of the turbulent boundary layer is performed when a steady flow of a viscous fluid flows around a flat plate. The calculation is based on a system of equations of turbulent fluid motion, obtained by generalizing Newton’s formula for the tangential stress in a fluid by giving it a power-law form followed by writing the corresponding rheological relationship in tensor form and substituting it into the equation of motion of a continuous medium in stresses. The use of this system for the problem of longitudinal flow around a flat plate after estimates of the boundary layer form made it possible to write a system of equations describing a two-dimensional fluid flow in the boundary layer of a flat plate. This system is reduced to one ordinary third-order equation, similarly to how Blasius performed it for a laminar boundary layer. When solving this equation, the method of direct reduction of the boundary value problem to the Cauchy problem was used. The results of this solution made it possible to determine expressions for the thickness of the boundary layer, displacement and loss of momentum. These values are compared with the available experimental data.

Three dimensional flows beneath a thin layer of 2D turbulence induced by Faraday waves

Faraday waves occur on a fluid being subject to vertical shaking. Although it is well known that form and shape of the wave pattern depend on driving amplitude and frequency, only recent studies discovered the existence of a horizontal velocity field at the surface, called Faraday flow. This flow exhibits attributes of two-dimensional turbulence and is replicated in this study. Despite the increasing attention towards the inverse energy flux in the Faraday flow and other not strictly two-dimensional (2D) systems, little is known about the velocity fields developing beneath the fluid surface. In this study, planar velocity fields are measured by means of particle image velocimetry with high spatio-temporal resolution on the water surface and at different depths below it. A sudden drop in velocity and turbulent kinetic energy is observed at half a Faraday wavelength below the surface revealing that the surface flow is the main source of turbulent fluid motion. The flow structures below the surface comprise much larger spatial scales than those on the surface leading to very long-tailed temporal and spatial velocity (auto-) correlation functions. The three-dimensionality of the flow is estimated by the compressibility, which increases strongly with depth while the divergence changes its appearance from intermittent and single events to a large scale pattern resembling 2D cut-planes of convection rolls. Our findings demonstrate that the overall fluid flow beneath the surface is highly three-dimensional and that an inverse cascade and aspects of a confined 2D turbulence can coexist with a three-dimensional flow.Graphic abstract

On the Eigen‐Mode Excitation of Linear Oscillators and the Earth's Polar Motion

AbstractBy transforming a 1D second‐order linear oscillator into a 2D first‐order polar motion differential equation, it can be shown that the finite smoothness (i.e., the presence of jump in finite order derivatives) of the applied Newtonian forcing constitutes the sufficient and necessary condition for instantaneous excitation of free eigen‐mode. This condition can be met by forcing functions originated from turbulent and multiphase fluid motions. Sub‐macroscopic transition time associated with astatic elastic deformation limits the physical smoothness of the applied forcing for the Earth's polar motion. Eigen‐modes can also be excited by an infinitely smooth forcing that has a finite domain of non‐zero values. The eigen‐period serves as a macroscopic timescale to characterize the inertia of a linear oscillator. If a zero mean irregular forcing of finite smoothness exhibits a high degree of randomness and the timescale is much shorter than the eigen‐period, then for negligible damping the eigen‐waveform will increase in proportion to the squareroot of time, while the waveform distortion is statistically a constant. As a result, the pattern of distinctive eigen‐oscillation will dominate the forced solution for longer enough duration.

On the Operation of an Electroacoustic Transducer Based on Electrokinetic Phenomena under Turbulent Fluid Motion

The paper considers equations describing the motion of a fluid in a porous medium under the action of an electric field in conditions of the formed turbulent mode of motion. Equations are given that describe the acoustic oscillations that occur in a fluid, the source of which can be not only an alternating, but also a constant electric field. The pulsating broadband acoustic oscillations arising under the action of a constant electric field can be spurious during the operation of electroacoustic transducers, which should be taken into account in their design. The results of field experiments on the model of an electroacoustic transducer confirm the theoretical results presented in the study. The stated theoretical and experimental results make it possible to solve the priority scientific–technical problem of designing and creating new types of acoustic emitters.

Investigation of macrosegregation for different dendritic arm spacing, casting temperature, and thermal boundary conditions in a direct-chill casting

The study of macrosegregation for different dendritic arm spacing, casting temperature, and cooling conditions in a Direct-Chill (DC) casting was investigated in the present study. The velocity variance-elliptic relaxation ( $$ \overline{{v^{2} }} - f $$ ) turbulence model was used to account for the turbulence effect in the bulk liquid and slurry region. The thermosolutal effect was implemented in the bulk liquid and slurry flow. The Scheil’s solute redistribution model was used to account for solute partitioning at the solidification interfaces. The pressure-based segregated time-dependent solver was used in the solution method to solve the flow equations. The model validation indicates loawer transition thickness due to: (1) efficient damping of the flow in the slurry zone by the turbulence viscous forces, (2) effective handling of the kinematic wall blocking effects in the vicinity of the slurry zone, and (3) strong mixing of the turbulent fluid motion that tends to decrease the distance between the solidus and liquidus isotherm. In all the cases investigated, it was evident that the thermal boundary condition at the secondary cooling zone, casting inlet temperature and secondary Dendritic Arm Spacing (DAS) affect the segregation ratio both at the centerline and the billet surface.

Flory-like statistics of fracture in the fiber bundle model as obtained via Kolmogorov dispersion for turbulence: A conjecture.

It has long been conjectured that (rapid) fracture propagation dynamics in materials and turbulent motion of fluids are two manifestations of the same physical process. The universality class of turbulence (Kolmogorov dispersion, in particular) is conjectured to be identifiable with the Flory statistics for linear polymers (self-avoiding walks on lattices). These help us to relate fracture statistics to those of linear polymers (Flory statistics). The statistics of fracture in the fiber bundle model (FBM) are now well studied and many exact results are now available for the equal-load-sharing (ELS) scheme. Yet, the correlation length exponent in this model was missing and we show here how the correspondence between fracture statistics and the Flory mapping of Kolmogorov statistics for turbulence helps us to make a conjecture about the value of the correlation length exponent for fracture in the ELS limit of FBM and, also, about the upper critical dimension. In addition, the fracture avalanche size exponent values at lower dimensions (as estimated from such mapping to Flory statistics) also compare well with the observations.

Influence of the shape of the pressureless trapezoidal channel and roughness on the pressure loss of the machine channels of the pumping stations

In this work, we consider the general equation of fluid motion in pressureless channels and the functional dependences of the coefficient of hydraulic friction on the Reynolds number, relative roughness, and the shape of the live section of the channel, as well as the resistance formulas for the simplest channels with respect to the cross-sectional shape (round and infinitely wide rectangular), and then for channels with a more complex cross-sectional shape. To take into account the effect (on the pressure loss) of the channel cross-sectional shape and the presence of a flow with a free surface in it, additional correction factors are introduced (using the hydraulic radius concept). In conclusion, it is concluded that the values of the mentioned correction factors can and should be refined only as a result of the relevant experiments. The work also examined the patterns of hydraulic resistance in engine channels of the correct form of a live section with uniform turbulent fluid motion. Formulas of hydraulic resistance in the machine channels of a simple and complex outline of a live section are given.

Two-phase flow measurement of sub-millimeter sized particles falling in water with grid-generated turbulence

Sediment transport is one key process in sedimentation problems. The dynamics of sediments in rivers will lead to an ecological change of the catchment. Among all complicated processes in sediment transport, the settling dynamics of solid particles in the water contribute to the water quality and geomorphology of a river channel directly. This paper aims at an investigation of the interaction between particle movement and water flow, with application to hydro-environment situations such as transport of fine sand sediment in natural streams. The Stokes number in this type of application is much smaller than unity at which enhancement of particle settling velocity by strong ambient turbulence has been observed in many numerical and laboratory studies. The present laboratory study is conducted to study the settling of sub-millimeter sized heavy particles in water with a relatively weak grid-generated turbulence. The two-phase flow is measured with the whole-field imaging techniques of particle image velocimetry (PIV) and particle tracking velocimetry (PTV). A two-camera PIV/PTV technique is used to obtain the instantaneous settling velocities of the solid particles and the turbulent water velocity field. Phase separation is based on an effective optical distinction of the two light scattering signals with fluorescent tagging on the solid particles. With this technique, it is found that in most cases of grid-generated turbulence the settling velocity of the heavy particles is slightly lower than the still water value. The falling heavy particles are also found to cause additional turbulence in the water with low ambient turbulence intensities. At one particular case of grid turbulence, the particles are found to fall with a depth-averaged settling velocity evidently higher than the still water value. The instantaneous turbulent fluid motions and particle trajectories tend to support the fast tracking effect to be related to the higher particle falling velocities.

Numerical simulation of conjugated heat exchange in the turbulent motion of fluid in an oil well

The mathematical model of conjugate heat exchange is proposed for the turbulent movement of reservoir oil in a vertical well section. The motion of the medium is described using a two-dimensional axisymmetric stationary formulation and boundary layer equations. The movement of the turbulent flow of reservoir oil due to reservoir energy is presented. The liquid medium is a mixture of reservoir oil with dissolved gas and formation water. The results of the numerical modeling are presented in the form of dependences of the changing flow rate, temperature, and mass fraction of paraffin deposits that occur along the full vertical extent of the well. The results obtained describe the thermobaric state of the well under the condition of conjugate heat exchange between the fluid flow and the production pipe.

Topology optimization method with finite elements based on the k-[formula omitted] turbulence model

A new finite element (FE) based topology optimization (TO) for turbulent flow was developed using the k−ε turbulent model, which is one of the Reynolds–Averaged Navier–Stokes (RANS) equations. Despite many innovative works on the subject of fluidic TO, it remains important to consider the impact of turbulent flow in TO. To consider the effect of complex turbulent fluid motion, this study considered the k−ε turbulent finite element model. To conduct a successful TO, the modification of the k−ε turbulent model to account for the topology evolutions during an optimization process is important. Correspondingly, to account for these effects, we proposed the addition of penalization terms to the original k−ε turbulent model. To validate the present approach and the effect of turbulent flow on optimized layouts, various two-dimensional designs were optimized by minimizing the turbulent kinetic or the turbulent dissipation energies. Numerical optimization results showed that it is possible to conduct the topology optimization for turbulent flow.

Dilution-Induced Physico-Chemical Changes of Metal Oxide Nanoparticles Due to Homeopathic Preparation Steps of Trituration and Succussion.

Although the presence of starting materials in extreme dilutions of homeopathic medicines has been established, the physico-chemical changes of these materials induced by the manufacturing steps-that is, solid-solid mixing involving grinding (trituration) and slurry mixing involving impact (succussion), followed by dilution-are still unknown. We subjected cupric oxide and zinc oxide nanoparticles (NPs) to the homeopathic processes of trituration and succussion, followed by dilution up to 6 cH. Particle image velocimetry was employed to analyze the fluid motion during succussion and its effect on the NPs. The resulting microstructural and chemical changes at different dilution steps were determined by X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy and transmission electron microscopy. The succussion triggered multi-sized bubble generation and turbulent fluid motion up to a duration of 400 ms, with maximum average velocity of 0.23 m/s. Due to 1% transfer of kinetic energy from a moving eddy with this velocity, upon collision, the rate of temperature change in a particle of size 1 µm and 1 nm was predicted to rise by approximately 102 K/s and 106 K/s respectively. During trituration, the oxide NPs reduced to metals and did not aggregate by remaining within lactose, but they converted to oxidized finer NPs after impact. Silicate chains leached from the vial cross-linked after third dilution, forming large macro-particles and encapsulating the NPs that were retained and carried at higher dilution steps. The results showed that the NPs sustained significant rate of temperature change due to energy transfer from moving eddies during succussion. Different physico-chemical changes, such as size reduction, successive reduction and oxidation of NPs, and morphological changes, were achieved through trituration and succussion. The retention of NPs within cross-linked poly-siloxane chains reveals the importance of both the borosilicate glass vial and the ethanol solution during preparation of homeopathic medicines.

Numerical Simulation of the Implosion Process in a Cylindrical Tank

The results of a numerical study of the implosion of a spherical gas cavity in a cylindrical tank filled with liquid are presented. Under the influence of a pressure drop, the fluid starts to move, and the gas cavity begins to collapse. Mathematical modeling of the nonstationary, nonisothermal, turbulent motion of a compressible fluid is based on the fluid volume method. The focus is on the generation of pressure waves in a fluid during an implosion process. The study involved changes in the initial pressure in the gas cavity. It is shown how the initial pressure in the gas cavity affects the peak pressure recorded at the control point and the time it takes to reach it. An approximation formula is obtained for calculation of the peak pressure of a spherical compression wave.

Multi-phase flow modeling of submarine landslides: Transformation from hyperconcentrated flows into turbidity currents

Sedimentary density flows are major agents of sediment transport on oceans. Occurring after submarine landslides, the sedimentary density flows experience a series of dilution processes. Such flows, then, transform from the hyperconcentrated flows into the concentrated ones, and finally turn into the turbidity currents. This study applies a sophisticated multi-phase flow model to simulate sedimentary density flows caused by submarine granular landslides over a simplified topography with an emphasis on their dilution mechanisms. This model takes account of the particle-particle interactions, the particle-fluid interactions, and the turbulent motions of fluid and particles in the momentum transports. The two effects on turbulence modulation are considered: one is due to the stratification and the other is caused by the correlation between the fluid and sediment turbulent motions. The numerical results suggest that the dilution mechanisms are highly related to Kelvin–Helmholtz vortices. In addition to erosion of the hyperconcentrated region by vortices, this study finds that strong stir in the concentrated region by the vortices is another important dilution mechanism. Compared with the outer regions of the vortices (with zero vorticity), the vortex cores (with non-zero vorticity) have less efficient dilution processes due to rigid-body rotations there. The vortex cores can trap the small particles for a while. The involved flow regimes are also presented. The numerical results reveal that the turbidity currents can be either turbulent or laminar when the Bagnold limit of concentration is adopted to define the boundary of turbidity currents.

A Novel Approach for Synthesis of Nickel-Rich Layered Oxide Cathode Materials with Tailored Morphology and Their Electrochemical Performance

The improvement in energy density of lithium ion batteries (LIBs) is primarily focused on the increase of the specific capacity of active materials and the cell voltage.[1] Transition metal (TM) oxide-based cathodes materials reach a high specific capacity through the optimization of the chemical composition with a higher Ni content and can be cycled up to 4.6 V.[2] However, the electrochemical performance of Ni-rich cathode materials depends strongly on their physical properties such as particle size, specific surface area or surface characteristics. The poor rate capability and capacity retention as well as the high first cycle irreversible capacity loss (ICL) and the low volumetric energy density of electrodes have to be improved by specific design of the particle shape. A spherical morphology with a narrow size distribution is the preferred particle shape and can only be synthesized during the co-precipitation of TM-hydroxides or -carbonates by a continuously stirred tank reactor (CSTR). Additionally, the CSTR-process allows a further improvement of the cathode materials during the synthesis of core-shell and full concentration-gradient particles.[2] In this work, the design and the operating principle of a novel Couette-Taylor-Flow-Reactor (CTFR) is evaluated regarding the synthesis of spherical shaped Ni-rich TM-precursors. The CTFR offers a continuous process and is constructed by two co‐axial arranged cylinders with a small gap and a low working volume. The rotational motion of the inner cylinder induces a turbulent Taylor‐vortex flow. Above the suitable Taylor number (Ta), a periodic and stable turbulent fluid motion is formed, which increases the fluid shear and the local concentration of educts and promotes the agglomeration of precipitates to uniform spherical particles with narrow particle size distribution.[3] Based on the co-precipitation of Ni-rich TM-precursors by a continuous CTFR, the influence of the reaction conditions on the properties of TM-precursor is investigated. The rotational speed, residence time, temperature and pH-value were varied in a broad range. The growth behavior of the particles, regarding the morphology, particle size distribution, tap density and chemical composition of TM-precursors as well as for lithiated cathode materials are investigated. The electrochemical properties of the corresponding cathode materials with their unique particle morphology in dependence of the co-precipitation conditions are comprehensively evaluated for finding the optimal synthesis conditions. [1] J. Betz, G. Bieker, P. Meister, T. Placke, M. Winter, R. Schmuch, Adv. Energy Mater. 2018, 1803170/1-18.[2] H. Li, P. Zhou, F. Liu, H. Li F. Cheng, J. Chen, Chem. Sci, DOI: 10.1039/c8sc03385d.[3] J.-M. Kim, S.-M. Chang, J.-H. Chang, W.-S- Kim, Colloids and Surfaces A: Physicochem. Eng. Aspects (2011) 384, 31-39.

Unimodal solutions of the generalized Constantin–Lax–Majda equation with viscosity

Steady-states of the generalized Constantin–Lax–Majda equation with the viscosity and an external force are computed numerically by the spectral method. This equation is regarded as a model for two-dimensional turbulent motion of incompressible viscous fluid. We demonstrate numerically that the equation admits unimodal solutions—solutions with one and only one peak and bottom, if the Reynolds number is sufficiently large. We also report some interesting properties of the spectra of unimodal solutions.

Integrated simulation of turbulent convection, radiation and conduction during a selenization process for large-scale CIGS thin films

A numerical methodology for simulations of multi-mode heat transfer during a selenization process for CIGS (Copper Indium Gallium Selenide) solar cell films has been developed. Turbulent fluid dynamics and convective heat transfer are simulated using a finite-volume large-eddy simulation (LES) technique while thermal conduction and radiation are predicted using finite-element methods. The computational methodology is validated for three heat transfer modes. Using the technique, a numerical study of heat transfer during the selenization process for deposition of a CIGS layer is performed to analyze the thermo-fluid phenomena occurring during the process. The present method is found to well predict temperature distribution on substrates as a function of both space and time. It is also analyzed that how turbulent fluid motions alter temperature distributions on the substrate during the selenization process.

Description and detection of burst events in turbulent flows

A mathematical and computational framework is developed for the detection and identification of coherent structures in turbulent wall-bounded shear flows. In a first step, this data-based technique will use an embedding methodology to formulate the fluid motion as a phase-space trajectory, from which state-transition probabilities can be computed. Within this formalism, a second step then applies repeated clustering and graph-community techniques to determine a hierarchy of coherent structures ranked by their persistencies. This latter information will be used to detect highly transitory states that act as precursors to violent and intermittent events in turbulent fluid motion (e.g., bursts). Used as an analysis tool, this technique allows the objective identification of intermittent (but important) events in turbulent fluid motion; however, it also lays the foundation for advanced control strategies for their manipulation. The techniques are applied to low-dimensional model equations for turbulent transport, such as the self-sustaining process (SSP), for varying levels of complexity.

Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma

Magnetic fields are ubiquitous in the Universe. The energy density of these fields is typically comparable to the energy density of the fluid motions of the plasma in which they are embedded, making magnetic fields essential players in the dynamics of the luminous matter. The standard theoretical model for the origin of these strong magnetic fields is through the amplification of tiny seed fields via turbulent dynamo to the level consistent with current observations. However, experimental demonstration of the turbulent dynamo mechanism has remained elusive, since it requires plasma conditions that are extremely hard to re-create in terrestrial laboratories. Here we demonstrate, using laser-produced colliding plasma flows, that turbulence is indeed capable of rapidly amplifying seed fields to near equipartition with the turbulent fluid motions. These results support the notion that turbulent dynamo is a viable mechanism responsible for the observed present-day magnetization.

A new variational multiscale formulation for stratified incompressible turbulent flows

For geophysical and environmental flows in the high-Reynolds-number regime, stable density stratification strongly affects the turbulent fluid motions. While turbulent flows, due to the presence of a cascade of spatial and temporal scales, present several challenges to accurate numerical approximation, density stratification in these flows exacerbates the situation further by suppressing vertical velocity fluctuations thereby enhancing the anisotropy of the turbulence. In this paper, based on the framework of residual-based variational multiscale (RBVMS) methods, we design a new numerical formulation for incompressible stratified flows that introduces coupling between the velocity fine scales and densityequation residual, and gives improved numerical performance as evidenced by the results of two challenging turbulent-flow simulations.