Journal articles: 'Turbulent fluid flows'

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Tuckerman, Laurette S., Matthew Chantry, and Dwight Barkley. "Patterns in Wall-Bounded Shear Flows." Annual Review of Fluid Mechanics 52, no. 1 (January 5, 2020): 343–67. http://dx.doi.org/10.1146/annurev-fluid-010719-060221.

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Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

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Sofiadis, G., and I. Sarris. "Reynolds number effect of the turbulent micropolar channel flow." Physics of Fluids 34, no. 7 (July 2022): 075126. http://dx.doi.org/10.1063/5.0098453.

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The turbulent regime of non-Newtonian flows presents a particular interest as flow behavior is directly affected by the internal microstructure type of the fluid. Differences in the dispersed phase of a particle laden flow can either lead to drag reduction and turbulence attenuation or to drag and turbulence enhancement in polymer flows and dense suspensions, respectively. A general concept of non-Newtonian fluid flow may be considered in a continuous manner through the micropolar theory, recognizing the limitations that bound this theory. In recent articles [Sofiadis and Sarris, “Microrotation viscosity effect on turbulent micropolar fluid channel flow,” Phys. Fluids 33, 095126 (2021); Sofiadis and Sarris, “Turbulence intensity modulation by micropolar fluids,” Fluids 6, 195 (2021)], the micropolar viscosity effect of the turbulent channel flow under constant Reynolds number and its turbulent modulation were investigated. The present study focuses on the investigation of the turbulent micropolar regime as the Reynolds number increases in a channel flow. Findings support that the micropolar stress, which was found to assist turbulence enhancement in the present model, attenuates as Re increases. Effects on the friction behavior of the flow, as Reynolds number increases, become more important for cases of higher micropolar viscosity, where a reverse drag behavior is observed as compared to lower micropolar viscosity ones. Finally, turbulence intensification for these cases declines close to the wall in contrast to lower micropolar viscosity flows, which manage to sustain high turbulence and increase drag in the near-wall region along with Re.

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Vassilicos, J. Christos. "Dissipation in Turbulent Flows." Annual Review of Fluid Mechanics 47, no. 1 (January 3, 2015): 95–114. http://dx.doi.org/10.1146/annurev-fluid-010814-014637.

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Nazarov, F. Kh. "Comparing Turbulence Models for Swirling Flows." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 2 (95) (April 2021): 25–36. http://dx.doi.org/10.18698/1812-3368-2021-2-25-36.

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The paper considers a turbulent fluid flow in a rotating pipe, known as the Taylor --- Couette --- Poiseuille flow. Linear RANS models are not suitable for simulating this type of problems, since the turbulence in these flows is strongly anisotropic, which means that solving these problems requires models accounting for turbulence anisotropy. Modified linear models featuring corrections for flow rotations, such as the SARC model, make it possible to obtain satisfactory solutions. A new approach to turbulence problems has appeared recently. It allowed a novel two-fluid turbulence model to be created. What makes this model different is that it can describe strongly anisotropic turbulent flows; moreover, it is easy to implement numerically while not being computationally expensive. We compared the results of solving the Taylor --- Couette --- Poiseuille flow problem using the novel two-fluid model and the SARC model. The numerical investigation results obtained from the novel two-fluid model show a better agreement with the experimental data than the results provided by the SARC model

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Eidelman, A., T. Elperin, N. Kleeorin, A. Markovich, and I. Rogachevskii. "Experimental detection of turbulent thermaldiffusion of aerosols in non-isothermal flows." Nonlinear Processes in Geophysics 13, no. 1 (April 24, 2006): 109–17. http://dx.doi.org/10.5194/npg-13-109-2006.

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Abstract. We studied experimentally a new phenomenon of turbulent thermal diffusion of particles which can cause formation of the large-scale aerosol layers in the vicinity of the atmospheric temperature inversions. This phenomenon was detected experimentally in oscillating grids turbulence in air flow. Three measurement techniques were used to study turbulent thermal diffusion in strongly inhomogeneous temperature fields, namely Particle Image Velocimetry to determine the turbulent velocity field, an image processing technique to determine the spatial distribution of aerosols, and an array of thermocouples for the temperature field. Experiments are presented for both, stably and unstably stratified fluid flows, by using both directions of the imposed mean vertical temperature gradient. We demonstrated that even in strongly inhomogeneous temperature fields particles in turbulent fluid flow accumulate at the regions with minimum of mean temperature of surrounding fluids due to the phenomenon of turbulent thermal diffusion.

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Chaouat, Bruno. "Simulations of Channel Flows With Effects of Spanwise Rotation or Wall Injection Using a Reynolds Stress Model." Journal of Fluids Engineering 123, no. 1 (November 16, 2000): 2–10. http://dx.doi.org/10.1115/1.1343109.

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Simulations of channel flows with effects of spanwise rotation and wall injection are performed using a Reynolds stress model. In this work, the turbulent model is extended for compressible flows and modified for rotation and permeable walls with fluid injection. Comparisons with direct numerical simulations or experimental data are discussed in detail for each simulation. For rotating channel flows, the second-order turbulence model yields an asymmetric mean velocity profile as well as turbulent stresses quite close to DNS data. Effects of spanwise rotation near the cyclonic and anticyclonic walls are well observed. For the channel flow with fluid injection through a porous wall, different flow developments from laminar to turbulent regime are reproduced. The Reynolds stress model predicts the mean velocity profiles, the transition process and the turbulent stresses in good agreement with the experimental data. Effects of turbulence in the injected fluid are also investigated.

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Wood, Brian D., Xiaoliang He, and Sourabh V. Apte. "Modeling Turbulent Flows in Porous Media." Annual Review of Fluid Mechanics 52, no. 1 (January 5, 2020): 171–203. http://dx.doi.org/10.1146/annurev-fluid-010719-060317.

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Turbulent flows in porous media occur in a wide variety of applications, from catalysis in packed beds to heat exchange in nuclear reactor vessels. In this review, we summarize the current state of the literature on methods to model such flows. We focus on a range of Reynolds numbers, covering the inertial regime through the asymptotic turbulent regime. The review emphasizes both numerical modeling and the development of averaged (spatially filtered) balances over representative volumes of media. For modeling the pore scale, we examine the recent literature on Reynolds-averaged Navier–Stokes (RANS) models, large-eddy simulation (LES) models, and direct numerical simulations (DNS). We focus on the role of DNS and discuss how spatially averaged models might be closed using data computed from DNS simulations. A Darcy–Forchheimer-type law is derived, and a prior computation of the permeability and Forchheimer coefficient is presented and compared with existing data.

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Graham, Michael D., and Daniel Floryan. "Exact Coherent States and the Nonlinear Dynamics of Wall-Bounded Turbulent Flows." Annual Review of Fluid Mechanics 53, no. 1 (January 5, 2021): 227–53. http://dx.doi.org/10.1146/annurev-fluid-051820-020223.

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Wall-bounded turbulence exhibits patterns that persist in time and space: coherent structures. These are important for transport processes and form a conceptual framework for important theoretical approaches. Key observed structures include quasi-streamwise and hairpin vortices, as well as the localized spots and puffs of turbulence observed during transition. This review describes recent research on so-called exact coherent states (ECS) in wall-bounded parallel flows at Reynolds numbers Re [Formula: see text] 104; these are nonturbulent, nonlinear solutions to the Navier–Stokes equations that in many cases resemble coherent structures in turbulence. That is, idealized versions of many of these structures exist as distinct, self-sustaining entities. ECS are saddle points in state space and form, at least in part, the state space skeleton of the turbulent dynamics. While most work on ECS focuses on Newtonian flow, some advances have been made on the role of ECS in turbulent drag reduction in polymer solutions. Emerging directions include applications to control and connections to large-scale structures and the attached eddy model.

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Bradshaw, Peter. "Heat transfer in turbulent fluid flows." International Journal of Heat and Fluid Flow 8, no. 4 (December 1987): 338. http://dx.doi.org/10.1016/0142-727x(87)90076-2.

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Mathai, Varghese, Detlef Lohse, and Chao Sun. "Bubbly and Buoyant Particle–Laden Turbulent Flows." Annual Review of Condensed Matter Physics 11, no. 1 (March 10, 2020): 529–59. http://dx.doi.org/10.1146/annurev-conmatphys-031119-050637.

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Fluid turbulence is commonly associated with stronger drag, greater heat transfer, and more efficient mixing than in laminar flows. In many natural and industrial settings, turbulent liquid flows contain suspensions of dispersed bubbles and light particles. Recently, much attention has been devoted to understanding the behavior and underlying physics of such flows by use of both experiments and high-resolution direct numerical simulations. This review summarizes our present understanding of various phenomenological aspects of bubbly and buoyant particle–laden turbulent flows. We begin by discussing different dynamical regimes, including those of crossing trajectories and wake-induced oscillations of rising particles, and regimes in which bubbles and particles preferentially accumulate near walls or within vortical structures. We then address how certain paradigmatic turbulent flows, such as homogeneous isotropic turbulence, channel flow, Taylor–Couette turbulence, and thermally driven turbulence, are modified by the presence of these dispersed bubbles and buoyant particles. We end with a list of summary points and future research questions.

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Ferreira, V. G., A. C. Brandi, F. A. Kurokawa, P. Seleghim Jr., A. Castelo, and J. A. Cuminato. "Incompressible Turbulent Flow Simulation Using theκ-ɛModel and Upwind Schemes." Mathematical Problems in Engineering 2007 (2007): 1–26. http://dx.doi.org/10.1155/2007/12741.

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In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynoldsκ-ɛmodel and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005)) is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of theFreeflowsimulation system (Castello et al. (2000)). A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

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Zhou, Y., and J. C. Vassilicos. "Related self-similar statistics of the turbulent/non-turbulent interface and the turbulence dissipation." Journal of Fluid Mechanics 821 (May 25, 2017): 440–57. http://dx.doi.org/10.1017/jfm.2017.262.

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The scalings of the local entrainment velocity$v_{n}$of the turbulent/non-turbulent interface and of the turbulence dissipation rate are closely related to each other in an axisymmetric and self-similar turbulent wake. The turbulence dissipation scaling implied by the Kolmogorov equilibrium cascade phenomenology is consistent with a Kolmogorov scaling of$v_{n}$whereas the non-equilibrium dissipation scaling reported for various turbulent flows in Vassilicos (Annu. Rev. Fluid Mech., vol. 47, 2015, pp. 95–114), Dairayet al.(J. Fluid Mech., vol. 781, 2015, pp. 166–195), Goto & Vassilicos (Phys. Lett. A, vol. 379 (16), 2015, pp. 1144–1148) and Obligadoet al.(Phys. Rev. Fluids, vol. 1 (4), 2016, 044409) is consistent with a different scaling of $v_{n}$. We present results from a direct numerical simulation of a spatially developing axisymmetric and self-similar turbulent wake which supports this conclusion and the assumptions that it is based on.

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Wang, T., T. W. Simon, and J. Buddhavarapu. "Heat Transfer and Fluid Mechanics Measurements in Transitional Boundary Layer Flows." Journal of Engineering for Gas Turbines and Power 107, no. 4 (October 1, 1985): 1007–15. http://dx.doi.org/10.1115/1.3239804.

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Experimental results are presented to document hydrodynamic and thermal development of flat-plate boundary layers undergoing natural transition. Local heat transfer coefficients, skin friction coefficients, and profiles of velocity, temperature, and Reynolds normal and shear stresses are presented. A case with no transition and transitional cases with 0.68 percent and 2.0 percent free-stream disturbance intensities were investigated. The locations of transition are consistent with earlier data. A late-laminar state with significant levels of turbulence is documented. In late-transitional and early-turbulent flows, turbulent Prandtl number and conduction layer thickness values exceed, and the Reynolds analogy factor is less than, values previously measured in fully turbulent flows.

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Tsukahara, Takahiro, and Yasuo Kawaguchi. "Proposal of Damping Function for Low-Reynolds-Numberk-εModel Applicable in Prediction of Turbulent Viscoelastic-Fluid Flow." Journal of Applied Mathematics 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/197628.

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A low-Reynolds-numberk-εmodel applicable for viscoelastic fluid was proposed to predict the frictional-drag reduction and the turbulence modification in a wall-bounded turbulent flow. In this model, an additional damping function was introduced into the model of eddy viscosity, while the treatment of the turbulent kinetic energy (k) and its dissipation rate (ε) is an extension of the model for Newtonian fluids. For constructing the damping function, we considered the influence of viscoelasticity on the turbulent eddy motion and its dissipative scale and investigated the frequency response for the constitutive equation based on the Giesekus fluid model. Assessment of the proposed model’s performance in several rheological conditions for drag-reduced turbulent channel flows demonstrated good agreement with DNS (direct numerical simulation) data.

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Jovanović, Mihailo R. "From Bypass Transition to Flow Control and Data-Driven Turbulence Modeling: An Input–Output Viewpoint." Annual Review of Fluid Mechanics 53, no. 1 (January 5, 2021): 311–45. http://dx.doi.org/10.1146/annurev-fluid-010719-060244.

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Transient growth and resolvent analyses are routinely used to assess nonasymptotic properties of fluid flows. In particular, resolvent analysis can be interpreted as a special case of viewing flow dynamics as an open system in which free-stream turbulence, surface roughness, and other irregularities provide sources of input forcing. We offer a comprehensive summary of the tools that can be employed to probe the dynamics of fluctuations around a laminar or turbulent base flow in the presence of such stochastic or deterministic input forcing and describe how input–output techniques enhance resolvent analysis. Specifically, physical insights that may remain hidden in the resolvent analysis are gained by detailed examination of input–output responses between spatially localized body forces and selected linear combinations of state variables. This differentiating feature plays a key role in quantifying the importance of different mechanisms for bypass transition in wall-bounded shear flows and in explaining how turbulent jets generate noise. We highlight the utility of a stochastic framework, with white or colored inputs, in addressing a variety of open challenges including transition in complex fluids, flow control, and physics-aware data-driven turbulence modeling. Applications with temporally or spatially periodic base flows are discussed and future research directions are outlined.

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Fox, Rodney O. "On multiphase turbulence models for collisional fluid–particle flows." Journal of Fluid Mechanics 742 (February 21, 2014): 368–424. http://dx.doi.org/10.1017/jfm.2014.21.

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AbstractStarting from a kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-averaged (RA) equations are derived for the particle phase in a collisional fluid–particle flow. The corresponding equations for a constant-density fluid phase are derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled macroscale/hydrodynamic model, rigorously derived from a kinetic equation for the particles, is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). As derived from the hydrodynamic model, the RA turbulence model solves for the RA particle-phase volume fraction, the phase-averaged (PA) particle-phase velocity, the PA granular temperature and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of macroscale turbulence models for moderately dense granular flows, a clear distinction is made between the PA granular temperature $\Theta _\textit {p}$, which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy $k_\textit {p}$, which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model and we briefly discuss the available closures for these terms. Finally, we demonstrate by comparing model predictions with direct numerical simulation results that even for non-collisional fluid–particle flows it is necessary to provide separate models for $\Theta _\textit {p}$ and $k_\textit {p}$ in order to correctly account for the effect of the particle Stokes number and mass loading.

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Goncalves, Eric, and Dia Zeidan. "Numerical study of turbulent cavitating flows in thermal regime." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 7 (July 3, 2017): 1487–503. http://dx.doi.org/10.1108/hff-05-2016-0202.

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Purpose The aim of this work is to quantify the relative importance of the turbulence modelling for cavitating flows in thermal regime. A comparison of various transport-equation turbulence models and a study of the influence of the turbulent Prandtl number appearing in the formulation of the turbulent heat flux are proposed. Numerical simulations are performed on a cavitating Venturi flow for which the running fluid is freon R-114 and results are compared with experimental data. Design/methodology/approach A compressible, two-phase, one-fluid Navier–Stokes solver has been developed to investigate the behaviour of cavitation models including thermodynamic effects. The code is composed by three conservation laws for mixture variables (mass, momentum and total energy) and a supplementary transport equation for the volume fraction of gas. The mass transfer between phases is closed assuming its proportionality to the mixture velocity divergence. Findings The influence of turbulence model as regard to the cooling effect due to the vaporization is weak. Only the k – ε Jones–Launder model under-estimates the temperature drop. The amplitude of the wall temperature drop near the Venturi throat increases with the augmentation of the turbulent Prandtl number. Originality/value The interaction between Reynolds-averaged Navier–Stokes turbulence closure and non-isothermal phase transition is rarely studied. It is the first time such a study on the turbulent Prandtl number effect is reported in cavitating flows.

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Elghobashi, Said. "Direct Numerical Simulation of Turbulent Flows Laden with Droplets or Bubbles." Annual Review of Fluid Mechanics 51, no. 1 (January 5, 2019): 217–44. http://dx.doi.org/10.1146/annurev-fluid-010518-040401.

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This review focuses on direct numerical simulations (DNS) of turbulent flows laden with droplets or bubbles. DNS of these flows are more challenging than those of flows laden with solid particles due to the surface deformation in the former. The numerical methods discussed are classified by whether the initial diameter of the bubble/droplet is smaller or larger than the Kolmogorov length scale and whether the instantaneous surface deformation is fully resolved or obtained via a phenomenological model. Also discussed are numerical methods that account for the breakup of a single droplet or bubble, as well as multiple droplets or bubbles in canonical turbulent flows.

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Rao, B. K. "Turbulent Friction Factor for Two-Phase: Air-Powerlaw Fluid Flows Through Horizontal Tubes." Journal of Fluids Engineering 120, no. 1 (March 1, 1998): 136–39. http://dx.doi.org/10.1115/1.2819637.

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Turbulent experimental friction factors for air and power-law fluid flows through a horizontal tube are reported. The power-law fluids studied were aqueous solutions of Carbopol® (at concentrations 1000 and 2000 wppm). The two-phase friction factors were correlated in terms of the generalized Reynolds number (Re*). Over a range of the Re* from 6000 to 80,000, the simpler homogeneous model is accurate enough for engineering prediction of turbulent friction factor for air and power-law fluid flows through straight tubes.

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Vitale, Salvatore, Tim A. Albring, Matteo Pini, Nicolas R. Gauger, and Piero Colonna. "Fully turbulent discrete adjoint solver for non-ideal compressible flow applications." Journal of the Global Power and Propulsion Society 1 (November 22, 2017): Z1FVOI. http://dx.doi.org/10.22261/jgpps.z1fvoi.

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Abstract Non-Ideal Compressible Fluid-Dynamics (NICFD) has recently been established as a sector of fluid mechanics dealing with the flows of dense vapors, supercritical fluids, and two-phase fluids, whose properties significantly depart from those of the ideal gas. The flow through an Organic Rankine Cycle (ORC) turbine is an exemplary application, as stators often operate in the supersonic and transonic regime, and are affected by NICFD effects. Other applications are turbomachinery using supercritical CO2 as working fluid or other fluids typical of the oil and gas industry, and components of air conditioning and refrigeration systems. Due to the comparably lower level of experience in the design of this fluid machinery, and the lack of experimental information on NICFD flows, the design of the main components of these processes (i.e., turbomachinery and nozzles) may benefit from adjoint-based automated fluid-dynamic shape optimization. Hence, this work is related to the development and testing of a fully-turbulent adjoint method capable of treating NICFD flows. The method was implemented within the SU2 open-source software infrastructure. The adjoint solver was obtained by linearizing the discretized flow equations and the fluid thermodynamic models by means of advanced Automatic Differentiation (AD) techniques. The new adjoint solver was tested on exemplary turbomachinery cases. Results demonstrate the method effectiveness in improving simulated fluid-dynamic performance, and underline the importance of accurately modeling non-ideal thermodynamic and viscous effects when optimizing internal flows influenced by NICFD phenomena.

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Linden, P. F., and J. E. Simpson. "Gravity-driven flows in a turbulent fluid." Journal of Fluid Mechanics 172, no. -1 (November 1986): 481. http://dx.doi.org/10.1017/s0022112086001829.

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Caulfield, C. P. "Layering, Instabilities, and Mixing in Turbulent Stratified Flows." Annual Review of Fluid Mechanics 53, no. 1 (January 5, 2021): 113–45. http://dx.doi.org/10.1146/annurev-fluid-042320-100458.

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Understanding how turbulence leads to the enhanced irreversible transport of heat and other scalars such as salt and pollutants in density-stratified fluids is a fundamental and central problem in geophysical and environmental fluid dynamics. This review discusses recent research activity directed at improving community understanding, modeling, and parameterization of the subtle interplay between energy conversion pathways, instabilities, turbulence, external forcing, and irreversible mixing in density-stratified fluids. The conceptual significance of various length scales is highlighted, and in particular, the importance is stressed of overturning or scouring in the formation and maintenance of layered stratifications, i.e., robust density distributions with relatively deep and well-mixed regions separated by relatively thin interfaces of substantially enhanced density gradient.

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Westerweel, Jerry, Gerrit E. Elsinga, and Ronald J. Adrian. "Particle Image Velocimetry for Complex and Turbulent Flows." Annual Review of Fluid Mechanics 45, no. 1 (January 3, 2013): 409–36. http://dx.doi.org/10.1146/annurev-fluid-120710-101204.

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LLOR, ANTOINE. "Bulk turbulent transport and structure in Rayleigh–Taylor, Richtmyer–Meshkov, and variable acceleration instabilities." Laser and Particle Beams 21, no. 3 (July 2003): 305–10. http://dx.doi.org/10.1017/s0263034603213021.

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Directed energy and turbulence structure are shown to be crucial in understanding the growth of self-similar Rayleigh–Taylor and incompressible Richtmyer–Meshkov turbulent mixing zones. Averaging over the mixing zone is used to analyze the response of a modifiedk–ε model and a turbulent two-fluid model. Three different transport regimes are then identified by considering self-similar variable acceleration RT flows (SSVARTs), which appear as promising reference flows for model testing.

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Tian, Zhe, Ali Abdollahi, Mahmoud Shariati, Atefeh Amindoust, Hossein Arasteh, Arash Karimipour, Marjan Goodarzi, and Quang-Vu Bach. "Turbulent flows in a spiral double-pipe heat exchanger." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 1 (September 18, 2019): 39–53. http://dx.doi.org/10.1108/hff-04-2019-0287.

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Purpose This paper aims to study the fluid flow and heat transfer through a spiral double-pipe heat exchanger. Nowadays using spiral double-pipe heat exchangers has become popular in different industrial segments due to its complex and spiral structure, which causes an enhancement in heat transfer. Design/methodology/approach In these heat exchangers, by converting the fluid motion to the secondary motion, the heat transfer coefficient is greater than that of the straight double-pipe heat exchangers and cause increased heat transfer between fluids. Findings The present study, by using the Fluent software and nanofluid heat transfer simulation in a spiral double-tube heat exchanger, investigates the effects of operating parameters including fluid inlet velocity, volume fraction of nanoparticles, type of nanoparticles and fluid inlet temperature on heat transfer efficiency. Originality/value After presenting the results derived from the fluid numerical simulation and finding the optimal performance conditions using a genetic algorithm, it was found that water–Al2O3 and water–SiO2 nanofluids are the best choices for the Reynolds numbers ranging from 10,551 to 17,220 and 17,220 to 31,910, respectively.

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Mostafa, A. A. "Turbulent Diffusion of Heavy-Particles in Turbulent Jets." Journal of Fluids Engineering 114, no. 4 (December 1, 1992): 667–71. http://dx.doi.org/10.1115/1.2910083.

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The turbulent dispersion of heavy suspended particles in turbulent shear flows is analyzed when crossing trajectory effects are important. A semiempirical expression for particle diffusion coefficient is developed via a comparison with experimental data of two-phase turbulent jet flows. This expression gives the particle momentum diffusion coefficient in terms of the gas diffusion coefficient, mean relatively velocity, and root mean square of the fluctuating fluid velocity. The proposed expression is used in a two-phase flow mathematical model to predict different particle-laden jet flows. The good agreement between the predictions and data suggests that the developed expression for particle diffusion coefficient is reasonably accurate in predicting particle dispersion in turbulent free shear flows.

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Barkley, D. "Taming turbulent fronts by bending pipes." Journal of Fluid Mechanics 872 (June 4, 2019): 1–4. http://dx.doi.org/10.1017/jfm.2019.340.

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The flow of fluid through a pipe has been instrumental in illuminating the subcritical route to turbulence typical of many wall-bounded shear flows. Especially important in this process are the turbulent–laminar fronts that separate the turbulent and laminar flow. Four years ago Michael Graham (Nature, vol. 526, 2015, p. 508) wrote a commentary entitled ‘Turbulence spreads like wildfire’, which is a picturesque but also accurate characterisation of the way turbulence spreads through laminar flow in a straight pipe. In this spirit, the recent article by Rinaldi et al. (J. Fluid Mech., vol. 866, 2019, pp. 487–502) shows that turbulent wildfires are substantially tamed in bent pipes. These authors find that even at modest pipe curvature, the characteristic strong turbulent–laminar fronts of straight pipe flow vanish. As a result, the propagation of turbulent structures is modified and there are hints that the route to turbulence is fundamentally altered.

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Prakash, Vivek N., J. Martínez Mercado, Leen van Wijngaarden, E. Mancilla, Y. Tagawa, Detlef Lohse, and Chao Sun. "Energy spectra in turbulent bubbly flows." Journal of Fluid Mechanics 791 (February 15, 2016): 174–90. http://dx.doi.org/10.1017/jfm.2016.49.

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We conduct experiments in a turbulent bubbly flow to study the nature of the transition between the classical $-5/3$ energy spectrum scaling for a single-phase turbulent flow and the $-3$ scaling for a swarm of bubbles rising in a quiescent liquid and of bubble-dominated turbulence. The bubblance parameter (Lance & Bataille J. Fluid Mech., vol. 222, 1991, pp. 95–118; Rensen et al., J. Fluid Mech., vol. 538, 2005, pp. 153–187), which measures the ratio of the bubble-induced kinetic energy to the kinetic energy induced by the turbulent liquid fluctuations before bubble injection, is often used to characterise bubbly flow. We vary the bubblance parameter from $b=\infty$ (pseudoturbulence) to $b=0$ (single-phase flow) over 2–3 orders of magnitude (0.01–5) to study its effect on the turbulent energy spectrum and fluctuations in liquid velocity. The probability density functions (PDFs) of the fluctuations in liquid velocity show deviations from the Gaussian profile for $b>0$, i.e. when bubbles are present in the system. The PDFs are asymmetric with higher probability in the positive tails. The energy spectra are found to follow the $-3$ scaling at length scales smaller than the size of the bubbles for bubbly flows. This $-3$ spectrum scaling holds not only in the well-established case of pseudoturbulence, but surprisingly in all cases where bubbles are present in the system ($b>0$). Therefore, it is a generic feature of turbulent bubbly flows, and the bubblance parameter is probably not a suitable parameter to characterise the energy spectrum in bubbly turbulent flows. The physical reason is that the energy input by the bubbles passes over only to higher wavenumbers, and the energy production due to the bubbles can be directly balanced by the viscous dissipation in the bubble wakes as suggested by Lance & Bataille (1991). In addition, we provide an alternative explanation by balancing the energy production of the bubbles with viscous dissipation in the Fourier space.

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Anderson, William, Julio M. Barros, Kenneth T. Christensen, and Ankit Awasthi. "Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness." Journal of Fluid Mechanics 768 (March 6, 2015): 316–47. http://dx.doi.org/10.1017/jfm.2015.91.

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We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned ‘strips’). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl’s secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses – from above – and subsequent lateral ejection in order to preserve conservation of mass.

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30

Gauthier, S., and B. Le Creurer. "Compressibility effects in Rayleigh–Taylor instability-induced flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1916 (April 13, 2010): 1681–704. http://dx.doi.org/10.1098/rsta.2009.0139.

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We present a tentative review of compressibility effects in Rayleigh–Taylor instability-induced flows. The linear, nonlinear and turbulent regimes are considered. We first make the classical distinction between the static compressibility or stratification, and the dynamic compressibility owing to the finite speed of sound. We then discuss the quasi-incompressible limits of the Navier–Stokes equations (i.e. the low-Mach number, anelastic and Boussinesq approximations). We also review some results about stratified compressible flows for which instability criteria have been derived rigorously. Two types of modes, convective and acoustic, are possible in these flows. Linear stability results for perfect fluids obtained from an analytical approach, as well as viscous fluid results obtained from numerical approaches, are also reviewed. In the turbulent regime, we introduce Chandrasekhar’s observation that the largest structures in the density fluctuations are determined by the initial conditions. The effects of compressibility obtained by numerical simulations in both the nonlinear and turbulent regimes are discussed. The modifications made to statistical models of fully developed turbulence in order to account for compressibility effects are also treated briefly. We also point out the analogy with turbulent compressible Kelvin–Helmholtz mixing layers and we suggest some lines for further investigations.

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31

Lee, T. W. "Asymmetrical Order in Wall-Bounded Turbulent Flows." Fluids 6, no. 9 (September 14, 2021): 329. http://dx.doi.org/10.3390/fluids6090329.

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Scaling of turbulent wall-bounded flows is revealed in the gradient structures, for each of the Reynolds stress components. Within the “dissipation” structure, an asymmetrical order exists, which we can deploy to unify the scaling and transport dynamics within and across these flows. There are subtle differences in the outer boundary conditions between channel and flat-plate boundary-layer flows, which modify the turbulence structure far from the wall. The self-similarity exhibited in the gradient space and corresponding transport dynamics establish capabilities and encompassing knowledge of wall-bounded turbulent flows.

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32

Suga, Kazuhiko. "Modeling the Rapid Part of the Pressure-Diffusion Process in the Reynolds Stress Transport Equation." Journal of Fluids Engineering 126, no. 4 (July 1, 2004): 634–41. http://dx.doi.org/10.1115/1.1779660.

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Modeling the pressure-diffusion process is discussed to improve the prediction of turbulent recirculating flows by a second moment closure. Since the recent DNS research of a turbulent recirculating flow by Yao et al. [Theore. Comput. Fluid Dynamics 14 (2001) 337–358] suggested that the pressure-diffusion process of the turbulence energy was significant in the recirculating region, the present study focuses on the rapid part of the process consisting of the mean shear. This rapid pressure-diffusion model is developed for the Reynolds stress equation using the two-component-limit turbulence condition and added to a low Reynolds number two-component-limit full second moment closure for evaluation. Its effects are discussed through applications of turbulent recirculating flows such as a trailing-edge and a back-step flows. Encouraging results are obtained though some margins to be improved still remain.

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33

Meyer, Daniel W. "Modelling of turbulence modulation in particle- or droplet-laden flows." Journal of Fluid Mechanics 706 (July 12, 2012): 251–73. http://dx.doi.org/10.1017/jfm.2012.251.

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AbstractAddition of particles or droplets to turbulent liquid flows or addition of droplets to turbulent gas flows can lead to modulation of turbulence characteristics. Corresponding observations have been reported for very small particle or droplet volume loadings ${\Phi }_{v} $ and therefore may be important when simulating such flows. In this work, a modelling framework that accounts for preferential concentration and reproduces isotropic and anisotropic turbulence attenuation effects is presented. The framework is outlined for both Reynolds-averaged Navier–Stokes (RANS) and joint probability density function (p.d.f.) methods. Validations are performed involving a range of particle and flow-field parameters and are based on the direct numerical simulation (DNS) study of Boivin, Simonin & Squires (J. Fluid Mech., vol. 375, 1998, pp. 235–263) dealing with heavy particles suspended in homogeneous isotropic turbulence (Stokes number $\mathit{St}= O(1{\unicode{x2013}} 10)$, particle/fluid density ratio ${\rho }_{p} / \rho = 2000$, ${\Phi }_{v} = O(1{0}^{- 4} )$) and the experimental investigation of Poelma, Westerweel & Ooms (J. Fluid Mech., vol. 589, 2007, pp. 315–351) involving light particles ($\mathit{St}= O(0. 1)$, ${\rho }_{p} / \rho \gtrsim 1$, ${\Phi }_{v} = O(1{0}^{- 3} )$) settling in grid turbulence. The development in this work is restricted to volume loadings where particle or droplet collisions are negligible.

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34

WANG, LIPO. "On properties of fluid turbulence along streamlines." Journal of Fluid Mechanics 648 (April 7, 2010): 183–203. http://dx.doi.org/10.1017/s0022112009993041.

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Geometrical and dynamical properties of turbulent flows have been investigated by streamline segment analysis. Starting from each grid point, a streamline segment is defined as the part of its streamline bounded by the two adjacent extremal points of the velocity magnitude. Physically the streamline segments can be extended into a more meaningful concept, namely the streamtube segments, which are non-overlapping and space filling. This decomposition of the flow allows for new insights into vector-related statistics in turbulence. According to the variation of velocity, the streamline segments can be sorted into positive and negative segments. The overall properties of turbulent flows can be newly understood and explained from the statistics of these segments with simple structures; for instance, the negative skewness of the velocity derivative becomes naturally a kinematic outcome. Furthermore, from direct numerical simulations conditional statistics of pressure and kinetic energy dissipation along the streamline segments are evaluated and discussed.

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35

Voermans, J. J., M. Ghisalberti, and G. N. Ivey. "The variation of flow and turbulence across the sediment–water interface." Journal of Fluid Mechanics 824 (July 6, 2017): 413–37. http://dx.doi.org/10.1017/jfm.2017.345.

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A basic framework characterising the interaction between aquatic flows and permeable sediment beds is presented here. Through the permeability Reynolds number ($Re_{K}=\sqrt{K}u_{\ast }/\unicode[STIX]{x1D708}$, where$K$is the sediment permeability,$u_{\ast }$is the shear velocity and$\unicode[STIX]{x1D708}$is the fluid viscosity), the framework unifies two classical flow typologies, namely impermeable boundary layer flows ($Re_{K}\ll 1$) and highly permeable canopy flows ($Re_{K}\gg 1$). Within this range, the sediment–water interface (SWI) is identified as a transitional region, with$Re_{K}$in aquatic systems typically$O(0.001{-}10)$. As the sediments obstruct conventional measurement techniques, experimental observations of interfacial hydrodynamics remain extremely rare. The use of refractive index matching here allows measurement of the mean and turbulent flow across the SWI and thus direct validation of the proposed framework. This study demonstrates a strong relationship between the structure of the mean and turbulent flow at the SWI and$Re_{K}$. Hydrodynamic characteristics, such as the interfacial turbulent shear stress, velocity, turbulence intensities and turbulence anisotropy tend towards those observed in flows over impermeable boundaries as$Re_{K}\rightarrow 0$and towards those seen in flows over highly permeable boundaries as$Re_{K}\rightarrow \infty$. A value of$Re_{K}\approx 1{-}2$is seen to be an important threshold, above which the turbulent stress starts to dominate the fluid shear stress at the SWI, the penetration depths of turbulence and the mean flow into the sediment bed are comparable and similarity relationships developed for highly permeable boundaries hold. These results are used to provide a new perspective on the development of interfacial transport models at the SWI.

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36

Cvitanović, Predrag. "Recurrent flows: the clockwork behind turbulence." Journal of Fluid Mechanics 726 (June 6, 2013): 1–4. http://dx.doi.org/10.1017/jfm.2013.198.

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AbstractThe understanding of chaotic dynamics in high-dimensional systems that has emerged in the last decade offers a promising dynamical framework to study turbulence. Here turbulence is viewed as a walk through a forest of exact solutions in the infinite-dimensional state space of the governing equations. Recently, Chandler & Kerswell (J. Fluid Mech., vol. 722, 2013, pp. 554–595) carry out the most exhaustive study of this programme undertaken so far in fluid dynamics, a feat that requires every tool in the dynamicist’s toolbox: numerical searches for recurrent flows, computation of their stability, their symmetry classification, and estimating from these solutions statistical averages over the turbulent flow. In the long run this research promises to develop a quantitative, predictive description of moderate-Reynolds-number turbulence, and to use this description to control flows and explain their statistics.

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37

Luan, Zhaogao, and M. M. Khonsari. "Computational Fluid Dynamics Analysis of Turbulent Flow Within a Mechanical Seal Chamber." Journal of Tribology 129, no. 1 (June 27, 2006): 120–28. http://dx.doi.org/10.1115/1.2401220.

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Turbulent flow inside the seal chamber of a pump operating at high Reynolds number is investigated. The K−ε turbulence model posed in cylindrical coordinates was applied for this purpose. Simulations are performed using the fractional approach method. The results of the computer code are verified by using the FLUENT and by comparing to published results for turbulent Taylor Couette flow. Numerical results of four cases including two rotational speeds with four flush rates are reported. Significant difference between the laminar and the turbulence flow in the seal chamber is predicted. The behavior of the turbulent flows with very high Reynolds number was also investigated. The physical and practical implications of the results are discussed.

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38

Bai, L., M. Fiebig, and N. K. Mitra. "Numerical Analysis of Turbulent Flow in Fluid Couplings." Journal of Fluids Engineering 119, no. 3 (September 1, 1997): 569–76. http://dx.doi.org/10.1115/1.2819282.

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Numerical simulation of three-dimensional unsteady turbulent flows in fluid couplings was carried out by numerically solving Navier-Stokes equations in a rotating coordinate system. The standard k-ε model was used to take turbulence into account. A finite volume scheme with colocated body-fitted grids was used to solve the basic equations. Computed flow structures show the vortex generation and its effect on the torque transmission. Computed local velocity and torque flow compare well with measurements.

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39

Eggenhuisen, Joris T., Matthieu J. B. Cartigny, and Jan de Leeuw. "Physical theory for near-bed turbulent particle suspension capacity." Earth Surface Dynamics 5, no. 2 (May 17, 2017): 269–81. http://dx.doi.org/10.5194/esurf-5-269-2017.

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Abstract. The inability to capture the physics of solid-particle suspension in turbulent fluids in simple formulas is holding back the application of multiphase fluid dynamics techniques to many practical problems in nature and society involving particle suspension. We present a force balance approach to particle suspension in the region near no-slip frictional boundaries of turbulent flows. The force balance parameter Γ contains gravity and buoyancy acting on the sediment and vertical turbulent fluid forces; it includes universal turbulent flow scales and material properties of the fluid and particles only. Comparison to measurements shows that Γ = 1 gives the upper limit of observed suspended particle concentrations in a broad range of flume experiments and field settings. The condition of Γ > 1 coincides with the complete suppression of coherent turbulent structures near the boundary in direct numerical simulations of sediment-laden turbulent flow. Γ thus captures the maximum amount of sediment that can be contained in suspension at the base of turbulent flow, and it can be regarded as a suspension capacity parameter. It can be applied as a simple concentration boundary condition in modelling studies of the dispersion of particulates in environmental and man-made flows.

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40

He, Guowei, Guodong Jin, and Yue Yang. "Space-Time Correlations and Dynamic Coupling in Turbulent Flows." Annual Review of Fluid Mechanics 49, no. 1 (January 3, 2017): 51–70. http://dx.doi.org/10.1146/annurev-fluid-010816-060309.

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41

Kawahara, Genta, Markus Uhlmann, and Lennaert van Veen. "The Significance of Simple Invariant Solutions in Turbulent Flows." Annual Review of Fluid Mechanics 44, no. 1 (January 21, 2012): 203–25. http://dx.doi.org/10.1146/annurev-fluid-120710-101228.

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42

Yoo, Jung Yul. "The Turbulent Flows of Supercritical Fluids with Heat Transfer." Annual Review of Fluid Mechanics 45, no. 1 (January 3, 2013): 495–525. http://dx.doi.org/10.1146/annurev-fluid-120710-101234.

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43

Wallace, James M., and Petar V. Vukoslavčević. "Measurement of the Velocity Gradient Tensor in Turbulent Flows." Annual Review of Fluid Mechanics 42, no. 1 (January 2010): 157–81. http://dx.doi.org/10.1146/annurev-fluid-121108-145445.

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44

Launder, Brian, Sébastien Poncet, and Eric Serre. "Laminar, Transitional, and Turbulent Flows in Rotor-Stator Cavities." Annual Review of Fluid Mechanics 42, no. 1 (January 2010): 229–48. http://dx.doi.org/10.1146/annurev-fluid-121108-145514.

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45

Bose, Sanjeeb T., and George Ilhwan Park. "Wall-Modeled Large-Eddy Simulation for Complex Turbulent Flows." Annual Review of Fluid Mechanics 50, no. 1 (January 5, 2018): 535–61. http://dx.doi.org/10.1146/annurev-fluid-122316-045241.

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46

Ura, Masaru, and Nobuhiro Matsunaga. "ENTRAINMENT DUE TO MEAN FLOW IN TWO-LAYERED FLUID." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 189. http://dx.doi.org/10.9753/icce.v21.189.

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The entrainment phenomena have been investigated across an interface between two-layered stratified flow induced by wind shear stress. The velocities of mean flow, turbulence and entrainment have been measured under three different conditions of water surface by using a wind-wave tank. When the entrainment velocity ue is expressed on the basis of the turbulent quantities at the interface, the turbulent entrainment coefficient E ( = ue/u) is given by E = A-(egl/u2)-3I1 ( A = 0.7). Here Eg, u and 1 are the effective buoyancy, the turbulence intensity and the integral lengthscale of turbulence at the interface, respectively. This result coincides with the relationship of entrainment due to oscillating grid turbulence, in which the mean flow does not exist. When, for the practical purpose, the estimation of ue is made by using the mean velocity Um and the depth h of mixed layer, Em ( - Ue/Um ) = Am•(egh/Um 2)"3/2 is derived from the transformation of E = A-(egl/u2)-3/2. There holds Am = A-Tf between Am and Tf, Tf being a turbulence factor given by (u/Um)4•(1/h)-3/2. It has been found that this relationship is also valid in various types of two-layered stratified flows as well as the wind-induced two-layered flows.

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47

Eames, I., and J. B. Flor. "New developments in understanding interfacial processes in turbulent flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1937 (February 28, 2011): 702–5. http://dx.doi.org/10.1098/rsta.2010.0332.

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Interfaces, across which fluid and flow properties change significantly, are a ubiquitous feature of most turbulent flows and are present within jets, plumes, homogeneous turbulence, oceans and planetary atmospheres. Even when the interfaces occupy a small volume fraction of the entire flow, they largely control processes such as entrainment and dissipation and can act as barriers to transport. This Theme Issue brings together some of the leading recent developments on interfaces in turbulence, drawing in many methodologies, such as experiments, direct number simulations, inverse methods and analytical modelling.

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48

Lyu, Chaoyang, Wei Li, Mathieu Desbrun, and Xiaopei Liu. "Fast and versatile fluid-solid coupling for turbulent flow simulation." ACM Transactions on Graphics 40, no. 6 (December 2021): 1–18. http://dx.doi.org/10.1145/3478513.3480493.

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The intricate motions and complex vortical structures generated by the interaction between fluids and solids are visually fascinating. However, reproducing such a two-way coupling between thin objects and turbulent fluids numerically is notoriously challenging and computationally costly: existing approaches such as cut-cell or immersed-boundary methods have difficulty achieving physical accuracy, or even visual plausibility, of simulations involving fast-evolving flows with immersed objects of arbitrary shapes. In this paper, we propose an efficient and versatile approach for simulating two-way fluid-solid coupling within the kinetic (lattice-Boltzmann) fluid simulation framework, valid for both laminar and highly turbulent flows, and for both thick and thin objects. We introduce a novel hybrid approach to fluid-solid coupling which systematically involves a mesoscopic double-sided bounce-back scheme followed by a cut-cell velocity correction for a more robust and plausible treatment of turbulent flows near moving (thin) solids, preventing flow penetration and reducing boundary artifacts significantly. Coupled with an efficient approximation to simplify geometric computations, the whole boundary treatment method preserves the inherent massively parallel computational nature of the kinetic method. Moreover, we propose simple GPU optimizations of the core LBM algorithm which achieve an even higher computational efficiency than the state-of-the-art kinetic fluid solvers in graphics. We demonstrate the accuracy and efficacy of our two-way coupling through various challenging simulations involving a variety of rigid body solids and fluids at both high and low Reynolds numbers. Finally, comparisons to existing methods on benchmark data and real experiments further highlight the superiority of our method.

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Lopez de Bertodano, Martin, Xiaodong Sun, Mamoru Ishii, and Asim Ulke. "Phase Distribution in the Cap Bubble Regime in a Duct." Journal of Fluids Engineering 128, no. 4 (January 31, 2006): 811–18. http://dx.doi.org/10.1115/1.2201626.

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The lateral phase distribution in the cap-bubbly regime was analyzed with a three-dimensional three-field two-fluid computational fluid dynamics (CFD) model based on the turbulence model for bubbly flows developed by Lopez de Bertodano et al. [1994, “Phase Distribution in Bubbly Two-Phase Flow in Vertical Ducts,” Int. J. Multiphase Flow, 20(5), pp. 805–818]. The turbulent diffusion of the bubbles is the dominant phase distribution mechanism. A new analytic result is presented to support the development of the model for the bubble induced turbulent diffusion force. New experimental data obtained by Sun et al. [2005, “Interfacial Structure in an Air-Water Planar Bubble Jet,” Exp. Fluids, 38(4), pp. 426–439] with the state-of-the-art four-sensor miniature conductivity probe in a vertical duct is used to validate the three-field two-fluid model CFD simulations.

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50

Zhou, Xiao Lan, Cai Xi Liu, and Yu Hong Dong. "Turbulent Mass Transfer Simulations of Binary Electrolyte in Parallel-Plate Electrode Channel." Advanced Materials Research 550-553 (July 2012): 2014–18. http://dx.doi.org/10.4028/www.scientific.net/amr.550-553.2014.

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Electrochemical mass transfer in turbulent flows and binary electrolytes is investigated. The primary objective is to provide information about mass transfer in the near-wall region between a solid boundary and a turbulent fluid flow at different Schmidt numbers. Based on the computational fluid dynamics and electrochemistry theories, a model for turbulent electrodes channel flow is established. The turbulent mass transfer in electrolytic processes has been predicted by the direct numerical simulation method under limiting current and galvanostatic conditions, we investigate mean concentration and the structure of the concentration fluctuating filed for different Schmidt numbers from 0.1 to 100 .The effect of different concentration boundary conditions at the electrodes on the near-wall turbulence statistics is also discussed.

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Journal articles on the topic 'Turbulent fluid flows'

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