Showing papers on "K-epsilon turbulence model published in 2016"

High-Reynolds number Taylor-Couette turbulence.

Abstract: Taylor-Couette flow, the flow between two coaxial co- or counter-rotating cylinders, is one of the paradigmatic systems in the physics of fluids. The (dimensionless) control parameters are the Reynolds numbers of the inner and outer cylinders, the ratio of the cylinder radii, and the aspect ratio. One key response of the system is the torque required to retain constant angular velocities, which can be connected to the angular velocity transport through the gap. Whereas the low–Reynolds number regime was well explored in the 1980s and 1990s of the past century, in the fully turbulent regime major research activity developed only in the past decade. In this article, we review this recent progress in our understanding of fully developed Taylor-Couette turbulence from the experimental, numerical, and theoretical points of view. We focus on the parameter dependence of the global torque and on the local flow organization, including velocity profiles and boundary layers. Next, we discuss transitions between diff...

A Physics Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data

Abstract: Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally applicable RANS models with predictive capabilities are still lacking. Recently, data-driven methods have been proposed as a promising alternative to the traditional approaches of turbulence model development. In this work we propose a data-driven, physics-informed machine learning approach for predicting discrepancies in RANS modeled Reynolds stresses. The discrepancies are formulated as functions of the mean flow features. By using a modern machine learning technique based on random forests, the discrepancy functions are first trained with benchmark flow data and then used to predict Reynolds stresses discrepancies in new flows. The method is used to predict the Reynolds stresses in the flow over periodic hills by using two training flow scenarios of increasing difficulties: (1) the flow in the same periodic hills geometry yet at a lower Reynolds number, and (2) the flow in a different hill geometry with a similar recirculation zone. Excellent predictive performances were observed in both scenarios, demonstrating the merits of the proposed method. Improvement of RANS modeled Reynolds stresses enabled by the proposed method is an important step towards predictive turbulence modeling, where the ultimate goal is to predict the quantities of interest (e.g., velocity field, drag, lift) more accurately by solving RANS equations with the Reynolds stresses obtained therefrom.

Using field inversion to quantify functional errors in turbulence closures

Abstract: A data–informed approach is presented with the objective of quantifying errors and uncertainties in the functional forms of turbulence closure models. The approach creates modeling information from higher-fidelity simulations and experimental data. Specifically, a Bayesian formalism is adopted to infer discrepancies in the source terms of transport equations. A key enabling idea is the transformation of the functional inversion procedure (which is inherently infinite-dimensional) into a finite-dimensional problem in which the distribution of the unknown function is estimated at discrete mesh locations in the computational domain. This allows for the use of an efficient adjoint-driven inversion procedure. The output of the inversion is a full-field of discrepancy that provides hitherto inaccessible modeling information. The utility of the approach is demonstrated by applying it to a number of problems including channel flow, shock-boundary layer interactions, and flows with curvature and separation. In all these cases, the posterior model correlates well with the data. Furthermore, it is shown that even if limited data (such as surface pressures) are used, the accuracy of the inferred solution is improved over the entire computational domain. The results suggest that, by directly addressing the connection between physical data and model discrepancies, the field inversion approach materially enhances the value of computational and experimental data for model improvement. The resulting information can be used by the modeler as a guiding tool to design more accurate model forms, or serve as input to machine learning algorithms to directly replace deficient modeling terms.

Theoretical perspective on the route to turbulence in a pipe

Abstract: The route to turbulence in pipe flow is a complex, nonlinear, spatiotemporal process for which an increasingly clear theoretical understanding has emerged. This understanding is explained to the reader in several steps, exploiting analogies to co-existing thermodynamic phases and to excitable and bistable media. In the end, simple equations encapsulating the keys physical properties of pipe turbulence provide a comprehensive picture of all large-scale states and stages of the transition process. Important among these are metastable localized puffs, localized edge states, puff splitting and interactions between puffs, the critical point for the onset of sustained turbulence via spatiotemporal intermittency (directed percolation), and finally the rise of fully turbulent flow in the form of expanding weak and strong turbulent slugs.

Statistical models for spatial patterns of heavy particles in turbulence

Abstract: The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are ap...

A universal transition to turbulence in channel flow

Abstract: Experiments and simulations of the transition to turbulence in fluid flow through a quasi-2D channel reveal critical exponents consistent with directed percolation — long conjectured to be the universality class associated with the transition. Transition from laminar to turbulent flow drastically changes the mixing, transport, and drag properties of fluids, yet when and how turbulence emerges is elusive even for simple flow within pipes and rectangular channels1,2. Unlike the onset of temporal disorder, which is identified as the universal route to chaos in confined flows3,4, characterization of the onset of spatiotemporal disorder has been an outstanding challenge because turbulent domains irregularly decay or spread as they propagate downstream. Here, through extensive experimental investigation of channel flow, we identify a distinctive transition with critical behaviour. Turbulent domains continuously injected from an inlet ultimately decayed, or in contrast, spread depending on flow rates. Near a transition point, critical behaviour was observed. We investigate both spatial and temporal dynamics of turbulent clusters, measuring four critical exponents, a universal scaling function and a scaling relation, all in agreement with the (2 + 1)-dimensional directed percolation universality class.

Ecological collapse and the emergence of travelling waves at the onset of shear turbulence

Abstract: Simulated pipe flow is interpreted using an ecological model in which predatory zonal flow preys on turbulence, and laminar flows emulate nutrients — establishing a link between turbulence and the directed percolation universality class.

Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations

Abstract: We report results from direct numerical simulation (DNS) of stationary compressible isotropic turbulence at very-high resolutions and a range of parameters using a massively parallel code at Taylor Reynolds numbers ( ) ranging from to and turbulent Mach numbers ( ) ranging from 0.1 to 0.6 on up to grid resolutions. A stationary state is maintained by a stochastic solenoidal forcing at the largest scales. The focus is on the mechanisms of energy exchanges, namely, dissipation, pressure-dilatation correlation and the individual contributing variables. Compressibility effects are studied by decomposing velocity and pressure fields into solenoidal and dilatational components. We suggest a critical turbulent Mach number at about 0.3 that separate two different flow regimes – only at Mach numbers above this critical value do we observe dilatational effects to affect the flow behaviour in a qualitative manner. The equipartition of energy between the dilatational components of kinetic and potential energy, originally proposed for decaying flows at low , presents significant scatter at low , but appears to be valid at high for stationary flows, which is explained by the different role of dilatational pressure in decaying and stationary flows, and at low and high . While at low pressure possesses characteristics of solenoidal pressure, at high it behaves in similar ways to dilatational pressure, which results in significant changes in the dynamics of energy exchanges. This also helps explain the observed qualitative change in the skewness of pressure at high reported in the literature. Regions of high pressure are found to be correlated with regions of intense local expansions. In these regions, the density–temperature correlation is also seen to be relatively high. Classical scaling laws for low-order moments originally proposed for incompressible turbulence appear to be only weakly affected by compressibility for the range of and investigated.

The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence

Abstract: The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.

On the interaction of Taylor length scale size droplets and isotropic turbulence

Abstract: Droplets in turbulent flows behave differently from solid particles, e.g. droplets deform, break up, coalesce and have internal fluid circulation. Our objective is to gain a fundamental understanding of the physical mechanisms of droplet–turbulence interaction. We performed direct numerical simulations (DNS) of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor length scale and with 5 % droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number . In the droplet-laden cases, we varied one of the following three parameters: the droplet Weber number based on the r.m.s. velocity of turbulence ( ), the droplet- to carrier-fluid density ratio ( ) or the droplet- to carrier-fluid viscosity ratio ( ). In this work, we derive the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We also explain the role of the interfacial surface energy in the two-fluid TKE equation through the power of the surface tension. Furthermore, we derive the relationship between the power of surface tension and the rate of change of total droplet surface area. This link allows us to explain how droplet deformation, breakup and coalescence play roles in the temporal evolution of TKE. Our DNS results show that increasing , and increases the decay rate of the two-fluid TKE. The droplets enhance the dissipation rate of TKE by enhancing the local velocity gradients near the droplet interface. The power of the surface tension is a source or sink of the two-fluid TKE depending on the sign of the rate of change of the total droplet surface area. Thus, we show that, through the power of the surface tension, droplet coalescence is a source of TKE and breakup is a sink of TKE. For short times, the power of the surface tension is less than of the dissipation rate. For later times, the power of the surface tension is always a source of TKE, and its magnitude can be up to 50 % of the dissipation rate.

Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows

Abstract: Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are “minimal” in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx ≳ 2Lz, Ly ≳ Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx ≳ 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wall-bounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ∼20S−1, and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general.

A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing

Abstract: A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. The importance of using DNS to calibrate and assess RANS type turbulence models is also highlighted.

The role of large-coherent-eddy transport in the atmospheric surface layer based on CASES-99 observations

Abstract: The analysis of momentum and heat fluxes from the Cooperative Atmosphere-Surface Exchange Study 1999 (CASES-99) field experiment is extended throughout the diurnal cycle following the investigation of nighttime turbulence by Sun et al. (J Atmos Sci 69:338–351, 2012). Based on the observations, limitations of Monin–Obukhov similarity theory (MOST) are examined in detail. The analysis suggests that strong turbulent mixing is dominated by relatively large coherent eddies that are not related to local vertical gradients as assumed in MOST. The HOckey-Stick Transition (HOST) hypothesis is developed to explain the generation of observed large coherent eddies over a finite depth and the contribution of these eddies to vertical variations of turbulence intensity and atmospheric stratification throughout the diurnal cycle. The HOST hypothesis emphasizes the connection between dominant turbulent eddies and turbulence generation scales, and the coupling between the turbulence kinetic energy and the turbulence potential energy within the turbulence generation layer in determining turbulence intensity. For turbulence generation directly influenced by the surface, the HOST hypothesis recognizes the role of the surface both in the vertical variation of momentum and heat fluxes and its boundary effect on the size of the dominant turbulence eddies.

On the flux Richardson number in stably stratified turbulence

Abstract: The flux Richardson number (often referred to as the mixing efficiency) is a widely used parameter in stably stratified turbulence which is intended to provide a measure of the amount of turbulent kinetic energy that is irreversibly converted to background potential energy (which is by definition the minimum potential energy that a stratified fluid can attain that is not available for conversion back to kinetic energy) due to turbulent mixing. The flux Richardson number is traditionally defined as the ratio of the buoyancy flux to the production rate of turbulent kinetic energy . An alternative generalized definition for was proposed by Ivey & Imberger (J. Phys. Oceanogr., vol. 21, 1991, pp. 650–658), where the non-local transport terms as well as unsteady contributions were included as additional sources to the production rate of . While this definition precludes the need to assume that turbulence is statistically stationary, it does not properly account for countergradient fluxes that are typically present in more strongly stratified flows. Hence, a third definition that more rigorously accounts for only the irreversible conversions of energy has been defined, where only the irreversible fluxes of buoyancy and production (i.e. the dissipation rates of and turbulent potential energy ( )) are used. For stationary homogeneous shear flows, all of the three definitions produce identical results. However, because stationary and/or homogeneous flows are typically not found in realistic geophysical situations, clarification of the differences/similarities between these various definitions of is imperative. This is especially true given the critical role plays in inferring turbulent momentum and heat fluxes using indirect methods, as is commonly done in oceanography, and for turbulence closure parameterizations. To this end, a careful analysis of two existing direct numerical simulation (DNS) datasets of stably stratified homogeneous shear and channel flows was undertaken in the present study to compare and contrast these various definitions. We find that all three definitions are approximately equivalent when the gradient Richardson number . Here, , where is the buoyancy frequency and is the mean shear rate, provides a measure of the stability of the flow. However, when , significant differences are noticeable between the various definitions. In addition, the irreversible formulation of based on the dissipation rates of and is the only definition that is free from oscillations at higher gradient Richardson numbers. Both the traditional definition and the generalized definition of exhibit significant oscillations due to the persistence of linear internal wave motions and countergradient fluxes that result in reversible exchanges between and . Finally, we present a simple parameterization for the irreversible flux Richardson number based on that produces excellent agreement with the DNS results for .

Nonlinear Time-Varying Turbulence Signal Processing and Simulation Under Curvilinear Coordinate System

Abstract: In order to analyse the nature of the turbulence, the curvilinear coordinate system is established according to the relations of cartesian coordinate system. Aiming at this turbulence mechanism, the turbulence boundary equations were established, then all grid points of the coordinates can be got by the established equations. The dangerous degree measure (risk factor) was put forward. The mathematical model of risk factor was established as to quantitatively describe the danger level of turbulence. A turbulence signal processing algorithm is proposed combined with the Doppler effect and the computing grid. The simulation results show that the curvilinear coordinate system and three-dimensional turbulence field can reflect the characteristics of turbulence, and risk factor can reflect the danger level of turbulence, the proposed turbulence signal processing algorithm can detect and forecast the turbulence effectively.

Langmuir Turbulence Parameterization in Tropical Cyclone Conditions

Abstract: The Stokes drift of surface waves significantly modifies the upper-ocean turbulence because of the Craik–Leibovich vortex force (Langmuir turbulence). Under tropical cyclones the contribution of the surface waves varies significantly depending on complex wind and wave conditions. Therefore, turbulence closure models used in ocean models need to explicitly include the sea state–dependent impacts of the Langmuir turbulence. In this study, the K-profile parameterization (KPP) first-moment turbulence closure model is modified to include the explicit Langmuir turbulence effect, and its performance is tested against equivalent large-eddy simulation (LES) experiments under tropical cyclone conditions. First, the KPP model is retuned to reproduce LES results without Langmuir turbulence to eliminate implicit Langmuir turbulence effects included in the standard KPP model. Next, the Lagrangian currents are used in place of the Eulerian currents in the KPP equations that calculate the bulk Richardson number a...

Entropic multi-relaxation time lattice Boltzmann model for complex flows

Abstract: Entropic lattice Boltzmann methods were introduced to overcome the stability issues of lattice Boltzmann models for high Reynolds number turbulent flows. However, to date their validity has been investigated only for simple flows due to the lack of appropriate boundary conditions. We present here an extension of these models to complex flows involving curved and moving boundaries in three dimensions. Apart from a thorough investigation of resolved and under-resolved simulations for periodic flow and turbulent flow in a round pipe, we study in detail the set-up of a simplified internal combustion engine with a valve/piston arrangement. This arrangement allows us to probe the non-trivial interactions between various flow features such as jet breakup, jet–wall interaction, and formation and breakup of large vortical structures, among others. Besides an order of magnitude reduction in computational costs, when compared to state-of-the-art direct numerical simulations (DNS), these methods come with the additional advantage of using static Cartesian meshes also for moving objects, which reduces the complexity of the scheme. Going beyond first-order statistics, a detailed comparison of mean and root-mean-square velocity profiles with high-order spectral element DNS simulations and experimental data shows excellent agreement, highlighting the accuracy and reliability of the method for resolved simulations. Moreover, we show that the implicit subgrid features of the entropic lattice Boltzmann method can be utilized to further reduce the grid sizes and the computational costs, providing an alternative to modern modelling approaches such as large-eddy simulations for complex flows.

Turbulence attenuation in simultaneously heated and cooled annular flows at supercritical pressure

Abstract: Heated or cooled fluids at supercritical pressure show large variations in thermophysical properties, such as the density, dynamic viscosity and molecular Prandtl number, which strongly influence turbulence characteristics. To investigate this, direct numerical simulations were performed of a turbulent flow at supercritical pressure (CO2 at 8 MPa) in an annulus with a hot inner wall and a cold outer wall. The pseudo-critical temperature lies close to the inner wall, which results in strong thermophysical property variations in that region. The turbulent shear stress and the turbulent intensities significantly decrease near the hot inner wall, but increase near the cold outer wall, which can be partially attributed to the mean dynamic viscosity and density stratification. This leads to decreased production of turbulent kinetic energy near the inner wall and vice versa near the outer wall. However, by analysing a transport equation for the coherent streak flank strength, it was found that thermophysical property fluctuations significantly affect streak evolution. Near the hot wall, thermal expansion and buoyancy tend to decrease streak coherence, while the viscosity gradient that exists across the streaks interacts with mean shear to act as either a source or a sink in the evolution equation for the coherent streak flank strength. The formation of streamwise vortices on the other hand is hindered by the torque that is the result of the kinetic energy and density gradients. Near the cold wall, the results are reversed, i.e. the coherent streak flank strength and the streamwise vortices are enhanced due to the variable density and dynamic viscosity. The results show that not only the mean stratification but also the large instantaneous thermophysical property variations that occur in heated or cooled fluids at supercritical pressure have a significant effect on turbulent structures that are responsible for the self-regeneration process in near-wall turbulence. Thus, instantaneous density and dynamic viscosity fluctuations are responsible for decreased (or increased) turbulent motions in heated (or cooled) fluids at supercritical pressure.

Direct numerical simulation of a turbulent hydraulic jump: turbulence statistics and air entrainment

Abstract: We present direct numerical simulation (DNS) of a stationary turbulent hydraulic jump with inflow Froude number of 2, Weber number of 1820 and density ratio of 831, consistent with ambient water–air systems, all based on the inlet height and inlet velocity A non-dissipative geometric volume of fluid (VOF) method is used to track the detailed interactions between turbulent flow structures and the nonlinear interface dynamics Level set equations are also solved concurrent with VOF in order to calculate the interface curvature and surface tension forces The mesh resolution is set to resolve a wide range of interfacial scales including the Hinze scale Calculations are compared against experimental data of void fraction and interfacial scales indicating, reasonable agreement despite a Reynolds number mismatch Multiple calculations are performed confirming weak sensitivity of low-order statistics and void fraction on the Reynolds number The presented results provide, for the first time, a comprehensive quantitative data for a wide range of phenomena in a turbulent breaking wave using DNS These include mean velocity fields, Reynolds stresses, turbulence production and dissipation, velocity spectra and air entrainment data In addition, we present the energy budget as a function of streamwise location by keeping track of various energy exchange processes in the wake of the jump The kinetic energy is mostly transferred to pressure work, potential energy and dissipation while surface energy plays a less significant role Our results indicate that the rate associated with various energy exchange processes peak at different streamwise locations, with exchange to pressure work flux peaking first, followed by potential energy flux and then dissipation The energy exchange process spans a streamwise length of order jump heights Furthermore, we report statistics associated with bubble transport downstream of the jump The bubble formation is found to have a periodic nature Meaning that the bubbles are generated in patches with a specific frequency associated with the roll-up frequency of the roller at the toe of the jump, with its footprint apparent in the velocity energy spectrum Our study also provides the ensemble-averaged statistics of the flow which we present in this paper These results are useful for the development and validation of reduced-order models such as dissipation models in wave dynamics simulations, Reynolds-averaged Navier–Stokes models and air entrainment models

Effect of turbulence on the wake of a wall-mounted cube

Abstract: The influence of turbulence on the flow around a wall-mounted cube immersed in a turbulent boundary layer is investigated experimentally with particle image velocimetry and hot-wire anemometry. Free-stream turbulence is used to generate turbulent boundary layer profiles where the normalised shear at the cube height is fixed, but the turbulence intensity at the cube height is adjustable. The free-stream turbulence is generated with an active grid and the turbulent boundary layer is formed on an artificial floor in a wind tunnel. The boundary layer development Reynolds number ($Re_x$) and the ratio of the cube height ($h$) to the boundary layer thickness ($\delta$) are held constant at $Re_x = 1.8 \times 10^6$ and $h/\delta = 0.47$. It is demonstrated that the stagnation point on the upstream side of the cube and the reattachment length in the wake of the cube are independent of the incoming profile for the conditions investigated here. In contrast, the wake length monotonically decreases for increasing turbulence intensity but fixed normalised shear---both quantities measured at the cube height. The wake shortening is a result of heightened turbulence levels promoting wake recovery from high local velocities and the reduction in strength of a dominant shedding frequency.

Turbulence Model Selection for Low Reynolds Number Flows

Abstract: One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.

Microbubbles and Microparticles are Not Faithful Tracers of Turbulent Acceleration

Abstract: We report on the Lagrangian statistics of acceleration of small (sub-Kolmogorov) bubbles and tracer particles with Stokes number St≪1 in turbulent flow. At a decreasing Reynolds number, the bubble accelerations show deviations from that of tracer particles; i.e., they deviate from the Heisenberg-Yaglom prediction and show a quicker decorrelation despite their small size and minute St. Using direct numerical simulations, we show that these effects arise due the drift of these particles through the turbulent flow. We theoretically predict this gravity-driven effect for developed isotropic turbulence, with the ratio of Stokes to Froude number or equivalently the particle drift velocity governing the enhancement of acceleration variance and the reductions in correlation time and intermittency. Our predictions are in good agreement with experimental and numerical results. The present findings are relevant to a range of scenarios encompassing tiny bubbles and droplets that drift through the turbulent oceans and the atmosphere. They also question the common usage of microbubbles and microdroplets as tracers in turbulence research.

The creation and evolution of coherent structures in plant canopy flows and their role in turbulent transport

Abstract: In this paper we used simulation tools to study turbulent boundary-layer structures in the roughness sublayer. Of particular interest is the case of a neutrally-stratified atmospheric boundary layer in which the lower boundary is covered by a homogeneous plant canopy. The goal of this study was to formulate a consistent conceptual model for the creation and evolution of the dominant coherent structures associated with canopy roughness and how they link with features observed in the overlying inertial sublayer. First, coherent structures were examined using temporally developing flow where the full range of turbulent scales had not yet developed, which allowed for instantaneous visualizations. These visualizations were used to formulate a conceptual model, which was then further tested using composite-averaged structure realizations from fully-developed flow with a very large Reynolds number. This study concluded that quasi two-dimensional mixing-layer-like roller structures exist in the developed flow and give the largest contributions to mean Reynolds stresses near the canopy. This work fully acknowledges the presence of highly three-dimensional and localized vortex pairing processes. The primary argument is that, as in a mixing layer, the smaller three-dimensional vortex interactions do not destroy the larger two-dimensional structure. Because the flow has a very large Reynolds number, the roller-like structures are not well-defined vortices but rather are a conglomerate of a large range of smaller-scale vortex structures that create irregularities. Because of this, the larger-scale structure is more difficult to detect in correlation or conditional sampling analyses. The frequently reported ‘scalar microfronts’ and associated spikes in pressure occur in the slip-like region between adjacent rollers. As smaller vortices within roller structures stretch, they evolve to form arch- and hairpin-shaped structures. Blocking by the low-flux canopy creates vertical asymmetry, and tends to impede the vertical progression of head-down structures. Head-up hairpins are allowed to continually stretch upward into the overlying inertial sublayer, where they evolve into the hairpin structures commonly reported to populate wall-bounded flows. This process is thought to be modulated by boundary-layer-scale secondary instability, which enhances head-up hairpin formation along quasi-streamwise transects.

Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils

Abstract: A modeling paradigm is developed to augment predictive models of turbulence by effectively utilizing limited data generated from physical experiments. The key components of our approach involve inverse modeling to infer the spatial distribution of model discrepancies, and, machine learning to reconstruct discrepancy information from a large number of inverse problems into corrective model forms. We apply the methodology to turbulent flows over airfoils involving flow separation. Model augmentations are developed for the Spalart Allmaras (SA) model using adjoint-based full field inference on experimentally measured lift coefficient data. When these model forms are reconstructed using neural networks (NN) and embedded within a standard solver, we show that much improved predictions in lift can be obtained for geometries and flow conditions that were not used to train the model. The NN-augmented SA model also predicts surface pressures extremely well. Portability of this approach is demonstrated by confirming that predictive improvements are preserved when the augmentation is embedded in a different commercial finite-element solver. The broader vision is that by incorporating data that can reveal the form of the innate model discrepancy, the applicability of data-driven turbulence models can be extended to more general flows.

A Concept of Cross-Ferroic Plasma Turbulence

Abstract: The variety of scalar and vector fields in laboratory and nature plasmas is formed by plasma turbulence. Drift-wave fluctuations, driven by density gradients in magnetized plasmas, are known to relax the density gradient while they can generate flows. On the other hand, the sheared flow in the direction of magnetic fields causes Kelvin-Helmholtz type instabilities, which mix particle and momentum. These different types of fluctuations coexist in laboratory and nature, so that the multiple mechanisms for structural formation exist in extremely non-equilibrium plasmas. Here we report the discovery of a new order in plasma turbulence, in which chained structure formation is realized by cross-interaction between inhomogeneities of scalar and vector fields. The concept of cross-ferroic turbulence is developed, and the causal relation in the multiple mechanisms behind structural formation is identified, by measuring the relaxation rate and dissipation power caused by the complex turbulence-driven flux.

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Abstract: A statistically stationary homogeneous isotropic turbulent flow modified by 64 small fixed non-Stokesian spherical particles is considered. The particle diameter is approximately twice the Kolmogorov length scale, while the particle volume fraction is 0.001. The Taylor Reynolds number of the corresponding unladen flow is 32. The particle-laden flow has been obtained by a direct numerical simulation based on a discretization of the incompressible Navier–Stokes equations on 64 spherical grids overset on a Cartesian grid. The global (space- and time-averaged) turbulence kinetic energy is attenuated by approximately 9 %, which is less than expected. The turbulence dissipation rate on the surfaces of the particles is enhanced by two orders of magnitude. More than 5 % of the total dissipation occurs in only 0.1 % of the flow domain. The budget of the turbulence kinetic energy has been computed, as a function of the distance to the nearest particle centre. The budget illustrates how energy relatively far away from particles is transported towards the surfaces of the particles, where it is dissipated by the (locally enhanced) turbulence dissipation rate. The energy flux towards the particles is dominated by turbulent transport relatively far away from particles, by viscous diffusion very close to the particles, and by pressure diffusion in a significant region in between. The skewness and flatness factors of the pressure, velocity and velocity gradient have also been computed. The global flatness factor of the longitudinal velocity gradient, which characterizes the intermittency of small scales, is enhanced by a factor of six. In addition, several point-particle simulations based on the Schiller–Naumann drag correlation have been performed. A posteriori tests of the point-particle simulations, comparisons in which the particle-resolved results are regarded as the standard, show that, in this case, the point-particle model captures both the turbulence attenuation and the fraction of the turbulence dissipation rate due to particles reasonably well, provided the (arbitrary) size of the fluid volume over which each particle force is distributed is suitably chosen.