Large-scale Turbulent Flow Research Articles

The Basic k-ϵ Model and a New Model Based on General Statistical Descriptions of Anisotropic Inhomogeneous Turbulence Compared with DNS of Channel Flow at High Reynolds Number

Predictions are presented of mean values of statistical variables of large-scale turbulent flow of the widely used basic k-ϵ model, and of a new model, which is based on general statistical descriptions of turbulence. The predictions are verified against published results of direct numerical simulations (DNSs) of Navier–Stokes equations. The verification concerns turbulent channel flow at shear Reynolds numbers of 950, 2000, and 104. The basic k-ϵ model is largely based on empirical formulations accompanied by calibration constants. This contrasts with the new model, where descriptions of leading statistical quantities are based on the general principles of statistical turbulence at a large Reynolds number and stochastic theory. Predicted values of major output variables such as turbulent viscosity, diffusivity of passive admixture, temperature, and fluid velocities compare well with DNS for the new model. Significant differences are seen for the basic k-ϵ model.

Extinction of buoyant turbulent non-premixed flames under reduced oxygen concentrations

Local and global extinction of 10 kW buoyant turbulent non-premixed flames of methane from a 13.7 cm diameter burner under oxygen concentrations (OCs) from 20.9 % to 12 % are investigated using a combination of OH* chemiluminescence imaging and exhaust-gas sampling. Local flame extinction, indicated by holes or discontinuities in the OH* images, is only observed at OC lower than 17 %. For OC below 16 %, large-scale turbulent flow dynamics causes rapid creation of large extinction holes that do not reclose, and the overall combustion efficiency (η) decreases rapidly as local extinction becomes more probable. Direct observation of local extinction in buoyant turbulent flames provides important physical insights and validation data for models of extinction and re-ignition by distinguishing their respective contributions to η. We observe that local extinction events are associated with large-scale flow features, leading us to hypothesize that extinction behavior correlates with resolved-scale strain rates from large-eddy simulation (LES) in excess of the laminar extinction limit. This idea is investigated by performing LES for the target flame, extracting strain-rate statistics on the flame surface, and comparing these to both the extinction limits for canonical counterflow diffusion flames and to the experimentally observed extinction behavior. Results show that the cumulative distribution of turbulent flame strain rates up to the laminar extinction limit closely follows the measured OC dependence of η. This approach to η works well for different OCs and other fuels such as propane and ethylene, which suggests great potential for the development of computationally efficient extinction models for fire suppression.

Magnetogenesis in a Collisionless Plasma: From Weibel Instability to Turbulent Dynamo

We report on a first-principles numerical and theoretical study of plasma dynamo in a fully kinetic framework. By applying an external mechanical force to an initially unmagnetized plasma, we develop a self-consistent treatment of the generation of “seed” magnetic fields, the formation of turbulence, and the inductive amplification of fields by the fluctuation dynamo. Driven large-scale motions in an unmagnetized, weakly collisional plasma are subject to strong phase mixing, which leads to the development of thermal pressure anisotropy. This anisotropy triggers the Weibel instability, which produces filamentary “seed” magnetic fields on plasma-kinetic scales. The plasma is thereby magnetized, enabling efficient stretching and folding of the fields by the plasma motions and the development of Larmor-scale kinetic instabilities such as the firehose and mirror. The scattering of particles off the associated microscale magnetic fluctuations provides an effective viscosity, regulating the field morphology and turbulence. During this process, the seed field is further amplified by the fluctuation dynamo until energy equipartition with the turbulent flow is reached. By demonstrating that equipartition magnetic fields can be generated from an initially unmagnetized plasma through large-scale turbulent flows, this work has important implications for the origin and amplification of magnetic fields in the intracluster and intergalactic mediums.

Polymer-dominant drag reduction in turbulent channel flow over a superhydrophobic surface

In this study, we focused on the integration of a flexible polymer (polyacrylamide) and a (randomly patterned) superhydrophobic surface in a large-scale turbulent channel flow rig to investigate their combined drag reduction effectiveness. Experimental results indicate that, prior to degradation, polyacrylamide (at a 100-ppm concentration) and superhydrophobic surfaces individually manifest drag reductions of 35% and 7%, respectively. However, when combined, the influence of polymer additives remained consistent, with the introduction of superhydrophobic surfaces yielding negligible differences. A clear predominance was evidenced in our facility looking at realistic pressure for applications, with polymer additives overshadowing the impact of superhydrophobic surfaces.

Turbulent Flow through and over a Compact Three-Dimensional Model Porous Medium: An Experimental Study

There are several natural and industrial applications where turbulent flows over compact porous media are relevant. However, the study of such flows is rare. In this paper, an experimental investigation of turbulent flow through and over a compact model porous medium is presented to fill this gap in the literature. The objectives of this work were to measure the development of the flow over the porous boundary, the penetration of the turbulent flow into the porous domain, the attendant three-dimensional effects, and Reynolds number effects. These objectives were achieved by conducting particle image velocimetry measurements in a test section with turbulent flow through and over a compact model porous medium of porosity 85%, and filling fraction 21%. The bulk Reynolds numbers were 14,338 and 24,510. The results showed a large-scale anisotropic turbulent flow region over and within the porous medium. The overlying turbulent flow had a boundary layer that thickened along the stream by about 90% and infiltrated into the porous medium to a depth of about 7% of the porous medium rod diameter. The results presented here provide useful physical insight suited for the design and analyses of turbulent flows over compact porous media arrangements.

Investigation of numerical approaches to modeling large-scale turbulent vortex flows in the mode of vertical take-off and landing of an aircraft

The study considers the operation of an unmanned aerial vehicle in hovering mode over a flat landing platform. As a propulsion system, impellers are used, which are a system of a propeller rotating inside an air ring. The air ring is a body of revolution with an aerodynamic profile in cross section. The paper investigates the effect of unsteady interaction of vortex flows with the design of an aircraft by two alternative numerical methods, one of which is vortex-resolving. Numerical calculations are performed using the traditional turbulence modeling approach based on the averaged Navier–Stokes equations (RANS, Reynolds Averaged Navier–Stokes), where the turbulence is assumed to be isotropic, and the eddy-resolving Large Eddy Simulation method. The main feature of the latter is as follows: a turbulent flow is represented as the superposition of the motion of large-scale and small-scale turbulences. After discretizing the flow using a filtering operation, large-scale turbulence, which depends directly on the boundary conditions, is solved from the full Navier–Stokes equations. Small-scale turbulence has isotropic properties and is modeled similarly to semi-empirical RANS methods. The technique allows one to accurately calculate the vortex structure of any flow directly from the equations of motion using relatively low computing power, in contrast to the RANS models, which simulate the flow using a simplified mathematical model and can provide satisfactory accuracy only for a limited range of problems. The results indicate that eddy-resolving methods for modeling turbulence, in contrast to the methods based on averaged Navier–Stokes equations, make it possible to estimate the effect of aperiodic perturbations on the design of aircraft arising from the interaction of large eddies with each other and with the underlying surface. Such phenomena are accompanied by side impacts of a shock nature on the impeller rings, which can lead to loss of aircraft stability. Under conditions of a small propeller step, the use of an air ring results in a significant increase in the air flow passing through the rotor rotation loop, an increase in thrust due to the creation of flow circulation around the airfoil of the ring, and a decrease in the power on the propeller. Even though the effect of using an air ring disappears with a large incoming flow, this design is considered very promising for use on aircraft with vertical takeoff and landing. This mode of operation is the most energy-consuming and determines the greatest requirements for the lifting force of the power plant. The results of this work have demonstrated that numerical methods based on averaging the Navier–Stokes equations and the use of classical turbulence models of the k–ω or k–ε type, which are widely used in numerical modeling of propellers, in takeoff and landing modes fail to detect aperiodic unsteady phenomena associated with the interaction of large eddies, in contrast to eddy-resolving methods for modeling turbulence.

Comparative assessment of URANS, SAS and DES turbulence modeling in the predictions of massively separated ship airwake characteristics

An early assessment of the ship airwake characteristics is one of the most challenging tasks associated with the designing of vessels. The design of warship superstructures has traditionally followed the basic polyhedron shape (box type structures) to achieve the desired stealth capability. However, presence of such a box shape bluff superstructure generates massively separated airwake over the ship helodeck region. This airwake results into complex flow phenomena which carry strong velocity gradients in space and time, along with widely varying turbulence length scales. Under such conditions, the launch and recovery of a shipboard helicopter operations are very hazardous. Thus, an accurate assessment of the resultant ship airwake flow phenomena at early design stages is desirable.We present a comparative time-accurate assessment study in order to gain a better understanding of the capability of the Unsteady Reynolds-Averaged Navier-Stokes (URANS), the Scale-Adaptive Simulation (SAS) and the Detached Eddy Simulation (DES) turbulence models in predicting turbulent ship airwake characteristics. Detailed comparisons are conducted with respect to the in-house experimental data. Results show that the DES and SAS produce nearly similar trends of the mean flow properties when compared to the experimental results. However, comparisons of velocity spectra indicate that SAS can resolve the dominant large-scale turbulent flow structures with less computational burden. Further, this study also attempts to compare the variation of mean flow quantities with steady RANS approach in order to quantify the percentage variation between the predictions of the steady and unsteady turbulence modelling approach.

Superhydrophobic drag reduction in high-speed towing tank

Abstract

Comparative Analysis between Experimental and Numerical Model resultsof a Jetin a Shallow Water Tank

In this work a comparative analysis of a turbulent jet experiment produced by the injection of dyed water into a shallow tank filled with water of the same density and the results of a numerical modelare presented. Dye was injected with the source fluid as a tracer. The concentration of the dye in the shallow turbulent flow was determined using a video imaging technique.The present laboratory experiments were conducted in a tank of small depth, and it is significantly wide to avoid the effect of the side walls. The space between the parallel walls of the tank can be varied during the experiments. The large-scale turbulent flow in the water sheet between the walls of the tank is confined to essentially two-dimensional motion. The shear on the bottom of the tank is a momentum sink to be considered.A comparison of the numerical resultswith the experimental data showed a very good agreement in terms of the position reached by the jet at different times after injection is initialized. These findings are useful for turbulent modeling of the shallow shear flow and for application to the large scale heat and mass exchange processes in lagoons, lakes, the ocean and the atmosphere

Numerical Analysis of Non Contact Transportation System for Wafer Warping

In this work a comparative analysis of a turbulent jet experiment produced by the injection of dyed water into a shallow tank filled with water of the same density and the results of a numerical modelare presented. Dye was injected with the source fluid as a tracer. The concentration of the dye in the shallow turbulent flow was determined using a video imaging technique.The present laboratory experiments were conducted in a tank of small depth, and it is significantly wide to avoid the effect of the side walls. The space between the parallel walls of the tank can be varied during the experiments. The large-scale turbulent flow in the water sheet between the walls of the tank is confined to essentially two-dimensional motion. The shear on the bottom of the tank is a momentum sink to be considered.A comparison of the numerical resultswith the experimental data showed a very good agreement in terms of the position reached by the jet at different times after injection is initialized. These findings are useful for turbulent modeling of the shallow shear flow and for application to the large scale heat and mass exchange processes in lagoons, lakes, the ocean and the atmosphere.

Incorporation of turbulence in a nonlinear wake-oscillator model for the prediction of unsteady galloping response

The aeroelastic behavior of certain slender bluff bodies is known to be dominated in smooth flow by the interference of vortex-induced vibration and transverse galloping. In turbulent flow, wind tunnel experiments revealed a more complicated behavior, with some features that have not been fully understood yet. With the aim to explain the oscillation response observed for a sharp-edge rectangular cylinder with a side ratio of 1.5 and to make a step ahead in the simulation of the self-excited behavior of such bodies, a nonlinear wake-oscillator model that provided promising results in smooth flow is considered. The differential equations are randomized to account for the contribution of three-dimensional, partially-correlated, turbulent velocity fluctuations attacking the structure. Given the physical basis of the mathematical model, all the parameters but one are estimated based on wind tunnel tests on a stationary sectional model. In contrast, given the lack of wake measurements, one of the coupling coefficients in the equations is calibrated based on the cylinder response for a given value of the nondimensional mass-damping parameter (Scruton number). Then, the model is used to predict the vibrations recorded for very different values of the Scruton number, showing satisfactory accuracy. This fact highlights the key role played, even in turbulent flow, by vortex shedding and the importance of its nonlinear interaction with oncoming wind velocity fluctuations. The equations are also used to investigate the effect of turbulence intensity and integral length scale. In agreement with the experimental evidence, the response of the cylinder is found to be little sensitive to flow velocity fluctuations with small intensity (say, less than about 4%), but is remarkably affected by strong turbulence. The simulations also disclose a significant influence on the vibration amplitude of the integral length scale of turbulence. Finally, the proposed model might represent a useful engineering tool to estimate the unsteady galloping behavior of a slender structure immersed in a realistic large-scale turbulent flow, which seldom can be correctly reproduced in the wind tunnel.

DNS study of the global heat release rate during early flame kernel development under engine conditions

Despite the high technical relevance of early flame kernel development for the reduction of cycle-to-cycle variations in spark ignition engines, there is still a need for a better fundamental understanding of the governing in-cylinder phenomena in order to enable resilient early flame growth. To isolate the effects of small- and large-scale turbulent flow motion on the young flame kernel, a three-dimensional DNS database has been designed to be representative for engine part load conditions. The analysis is focussed on flame displacement speed and flame area in order to investigate effects of flame structure and flame geometry on the global burning rate evolution. It is shown that despite a Karlovitz number of up to 13, which is at the upper range of conventional engine operation, thickening of the averaged flame structure by small-scale turbulent mixing is not observed. After ignition effects have decayed, the flame normal displacement speed recovers the behavior of a laminar unstretched premixed flame under the considered unity-Lewis-number conditions. Run-to-run variations in the global heat release rate are shown to be primarily caused by flame kernel area dynamics. The analysis of the flame area balance equation shows that turbulence causes stochastic flame kernel area growth by affecting the curvature evolution, rather than by inducing variations in total flame area production by strain. Further, it is shown that in local segments of a fully-developed planar flame with similar surface area as the investigated flame kernels, temporal variations in flame area rate-of-change occur. Contrasting to early flame kernels, these effects can be exclusively attributed to curvature variations in negatively curved flame regions.

Analysis of premixed flame kernel/turbulence interactions under engine conditions based on direct numerical simulation data

Although the evolution of premixed flames in turbulence has been frequently studied, it is not well understood how small flames interact with large-scale turbulent flow motion. Since this question is of practical importance for the occurrence of cycle-to-cycle variations in spark ignition engines, the objective of the present work is to fundamentally differentiate early flame kernel development from well-established turbulent flame configurations. For this purpose, a DNS database consisting of three flames propagating in homogeneous isotropic turbulence (Falkenstein et al., Combust. Flame, 2019) is considered. The flames feature different ratios of the initially laminar flame diameter to the integral length scale. To quantify flame kernel development, the time evolution of flame topology and flame front geometry are analysed in detail. It is shown that some realizations of the early flame kernel are substantially influenced by high compressive strain caused by large-scale turbulent flow motion with characteristic length scales greater than the flame kernel size. As a result, the initial spherical kernel topology may become highly distorted, which is reflected in the stochastic occurrence of excessive curvature variance. Two mechanisms of curvature production resulting from early flame kernel/turbulence interactions are identified by analysis of the mean curvature balance equation. Further, it is shown that the curvature distribution of small flame kernels becomes strongly skewed towards positive curvatures, which is contrary to developed turbulent flames. Hence, the transition of ignition kernels to self-sustaining turbulent flames is very different in nature compared with the development of a statistically planar flame brush.

Epidermal biopolysaccharides from plant seeds enable biodegradable turbulent drag reduction

The high cost of synthetic polymers has been a key impediment limiting the widespread adoption of polymer drag reduction techniques in large-scale engineering applications, such as marine drag reduction. To address consumable cost constraints, we investigate the use of high molar mass biopolysaccharides, present in the mucilaginous epidermis of plant seeds, as inexpensive drag reducers in large Reynolds number turbulent flows. Specifically, we study the aqueous mucilage extracted from flax seeds (Linum usitatissimum) and compare its drag reduction efficacy to that of poly(ethylene oxide) or PEO, a common synthetic polymer widely used as a drag reducing agent in aqueous flows. Macromolecular and rheological characterisation confirm the presence of high molar mass (≥2 MDa) polysaccharides in the extracted mucilage, with an acidic fraction comprising negatively charged chains. Frictional drag measurements, performed inside a bespoke Taylor-Couette apparatus, show that the as-extracted mucilage has comparable drag reduction performance under turbulent flow conditions as aqueous PEO solutions, while concurrently offering advantages in terms of raw material cost, availability, and bio-compatibility. Our results indicate that plant-sourced mucilage can potentially serve as a cost-effective and eco-friendly substitute for synthetic drag reducing polymers in large scale turbulent flow applications.

Immersed boundary/solid method for the numerical simulation of particle-laden flows

An outlook of computational fluid dynamics methods based on the fixed Cartesian grid, especially the immersed boundary (IB) method and related techniques, is provided. The basic idea of IB methods and the improvements to maintain consistency of boundary condition and mass conservation, that is the consistent projection method, are discussed. Then, recent examples for particle-laden flows are introduced. To deal with many particles, the immersed solid method is picked up as an efficient alternative to the IB method. In particular, we place focus on the flow and heat transfer of dense mixture of particles and liquid. In such a condition, the flow in narrow gap in between solid interfaces is considered by the lubrication equation. Finally, for further development of application in large-scale turbulent flows laden with particles, the importance of explicitly-defined volume averaging is pointed out based on our recent progress.

A numerical model for the time-dependent wake of a pedalling cyclist

A method for computing the wake of a pedalling cyclist is detailed and assessed through comparison with experimental studies. The large-scale time-dependent turbulent flow is simulated using the Scale Adaptive Simulation approach based on the Shear Stress Transport Reynolds-averaged Navier–Stokes model. Importantly, the motion of the legs is modelled by joining the model at the hips and knees and imposing solid body rotation and translation to the lower and upper legs. Rapid distortion of the cyclist geometry during pedalling requires frequent interpolation of the flow solution onto new meshes. The impact of numerical errors, that are inherent to this remeshing technique, on the computed aerodynamic drag force is assessed. The dynamic leg simulation was successful in reproducing the oscillation in the drag force experienced by a rider over the pedalling cycle that results from variations in the large-scale wake flow structure. Aerodynamic drag and streamwise vorticity fields obtained for both static and dynamic leg simulations are compared with similar experimental results across the crank cycle. The new technique presented here for simulating pedalling leg cycling flows offers one pathway for improving the assessment of cycling aerodynamic performance compared to using isolated static leg simulations alone, a practice common in optimising the aerodynamics of cyclists through computational fluid dynamics.

Cryptographic hashing using chaotic hydrodynamics

Fluids may store and manipulate information, enabling complex applications ranging from digital logic gates to algorithmic self-assembly. While controllable hydrodynamic chaos has previously been observed in viscous fluids and harnessed for efficient mixing, its application to the manipulation of digital information has been sparsely investigated. We show that chaotic stirring of a viscous fluid naturally produces a characteristic signature of the stirring process in the arrangement of particles in the fluid, and that this signature directly satisfies the requirements for a cryptographic hash function. This includes strong divergence between similar stirring protocols' hashes and avoidance of collisions (identical hashes from distinct stirs), which are facilitated by noninvertibility and a broad chaotic attractor that samples many points in the fluid domain. The hashing ability of the chaotic fluidic map implicates several unexpected mechanisms, including incomplete mixing at short time scales that produces a hyperuniform hash distribution. We investigate the dynamics of hashing using interparticle winding statistics, and find that hashing starts with large-scale winding of kinetically disjoint regions of the chaotic attractor, which gradually gives way to smaller scale braiding of single-particle trajectories. In addition to providing a physically motivated approach to implementing and analyzing deterministic chaotic maps for cryptographic applications, we anticipate that our approach has applications in microfluidic proof-of-work systems and characterizing large-scale turbulent flows from sparse tracer data.

AFiD-GPU: A versatile Navier–Stokes solver for wall-bounded turbulent flows on GPU clusters

The AFiD code, an open source solver for the incompressible Navier–Stokes equations (http://www.afid.eu), has been ported to GPU clusters to tackle large-scale wall-bounded turbulent flow simulations. The GPU porting has been carried out in CUDA Fortran with the extensive use of kernel loop directives (CUF kernels) in order to have a source code as close as possible to the original CPU version; just a few routines have been manually rewritten. A new transpose scheme has been devised to improve the scaling of the Poisson solver, which is the main bottleneck of incompressible solvers. For large meshes the GPU version of the code shows good strong scaling characteristics, and the wall-clock time per step for the GPU version is an order of magnitude smaller than for the CPU version of the code. Due to the increased performance and efficient use of memory, the GPU version of AFiD can perform simulations in parameter ranges that are unprecedented in thermally-driven wall-bounded turbulence. To verify the accuracy of the code, turbulent Rayleigh–Bénard convection and plane Couette flow are simulated and the results are in excellent agreement with the experimental and computational data that have been published in literature. Program summaryProgram Title: AFiD-GPUProgram Files doi:http://dx.doi.org/10.17632/rwjdg7ry66.1Licensing provisions: MITProgramming language: Fortran 90, CUDA Fortran, MPIExternal routines: PGI, CUDA Toolkit, FFTW3, HDF5Nature of problem: Solving the three-dimensional Navier–Stokes equations coupled with a scalar field in a cubic box bounded between two walls and with periodic boundary conditions in the horizontal directions.Solution method: Second order finite difference method for spatial discretization, third order Runge–Kutta scheme in combination with Crank–Nicolson for the implicit terms for time advancement, two dimensional pencil distributed MPI parallelization, GPU accelerated routines.Additional comments including restrictions and unusual features: The code is available and supported on https://github.com/PhysicsofFluids/AFiD_GPU_opensource.

An approach for accelerating incompressible turbulent flow simulations based on simultaneous modelling of multiple ensembles

The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the constant growth of the supercomputers performance, however, they are still unattainable for lots of real-life problems. The key shortcoming of these methods is related to the need of simulating a long time integration interval to collect reliable statistics, while the time integration process is inherently sequential.The novel approach with modelling of multiple flow states is discussed in the paper. The suggested numerical procedure allows to parallelize the integration in time by the cost of additional computations. Multiple realizations of the same turbulent flow are performed simultaneously. This allows to use more efficient implementations of numerical methods for solving systems of linear algebraic equations with multiple right-hand sides, operating with blocks of vectors. The simple theoretical estimate for the expected simulation speedup, accounting the penalty of additional computations and the linear solver performance improvement, is presented. The two problems of modelling turbulent flows in a plain channel and in a channel with a matrix of wall-mounted cubes are used to demonstrate the correctness of the proposed estimates and efficiency of the suggested approach as a whole. The simulation speedup by a factor of 2 is shown.

The Possibility of Measuring Radial-Velocity Fluctuations in a Tokamak Plasma with the Aid of Enhanced Microwave-Scattering Diagnostics

We propose implementing the diagnostics of long-wavelength fluctuations of the radial velocity of tokamak plasma, which is based on Doppler-enhanced microwave scattering by short-wavelength fluctuations entrained by large-scale turbulent flow in the equatorial plane of a tokamak.