Steady Turbulence Research Articles

Transfer Efficiency and Organization in Turbulent Transport over Alpine Tundra

The exchange of momentum, heat and trace gases between atmosphere and surface is mainly controlled by turbulent fluxes. Turbulent mixing is usually parametrized using Monin–Obukhov similarity theory (MOST), which was derived for steady turbulence over homogeneous and flat surfaces, but is nevertheless routinely applied to unsteady turbulence over non-homogeneous surfaces. We study four years of eddy-covariance measurements at a highly heterogeneous alpine valley site in Finse, Norway, to gain insights into the validity of MOST, the turbulent transport mechanisms and the contributing coherent structures. The site exhibits a bimodal topography-following flux footprint, with the two dominant wind sectors characterized by organized and strongly negative momentum flux, but different anisotropy and contributions of submeso-scale motions, leading to a failure of eddy-diffusivity closures and different transfer efficiencies for different scalars. The quadrant analysis of the momentum flux reveals that under stable conditions sweeps transport more momentum than the more frequently occurring ejections, while the opposite is observed under unstable stratification. From quadrant analysis, we derive the ratio of the amount of disorganized to organized structures, that we refer to as organization ratio (OR). We find an invertible relation between transfer efficiency and corresponding organization ratio with an algebraic sigmoid function. The organization ratio further explains the scatter around scaling functions used in MOST and thus indicates that coherent structures modify MOST. Our results highlight the critical role of coherent structures in turbulent transport in heterogeneous tundra environments and may help to find new parametrizations for numerical weather prediction or climate models.

Attempt to compensate for effects of energy conservation error on static pressure fluctuation using sub-grid scale components with the Reynolds number dependence of isotropic/anisotropic steady turbulence

Attempt to compensate for effects of energy conservation error on static pressure fluctuation using sub-grid scale components with the Reynolds number dependence of isotropic/anisotropic steady turbulence

Mixed Averaging Procedures

The statistical operators typically applied in postprocessing numerical databases for statistically steady turbulence are a mixture of physical averages in homogeneous spatial directions and in time. Alternative averaging operators may involve phase or ensemble averages over different simulations of the same flow. In this paper, we propose straightforward metrics to assess the relative importance of these averages, employing a mixed averaging analysis of the variance. We apply our novel indicators to two statistically steady turbulent flows that are homogeneous in the spanwise direction. In addition, this study highlights the local effectiveness of the averaging operator, which can vary significantly depending on the mean flow velocity and turbulent length scales. The work can be utilized to identify the most effective averaging procedure in flow configurations featuring at least two homogeneous directions. Thus, this will contribute to achieving better statistics for turbulent flow predictions or reducing computing time.

Transient power dynamics in nematic electroconvection.

We have observed the transient dynamics in nematic electroconvection during a sudden change in the driving voltage. The steady state dynamics of nematic electroconvection during a constant driving voltage are well characterized examples of spatiotemporal chaos, and thus are useful for the study of chaotic transients. For a set of starting conditions, we were able to show that the system can enter a long-lived transient state with a larger power dissipation rate. This transient state decays through the skew varicose instabilities into steady state defect turbulence. We observed the onset of both Eckhaus and skew varicose instabilities, interpret this transition in the framework of dynamical crisis, and quantify the transition through the evolution of the information entropy in the images as well as the power dissipated by the sample. We identify this long-lived but transient state as originating from the structure of the convective rolls in the initial state and hypothesize that the exploitation of transient states such as these may occur in natural systems and could be leveraged for industrial processing.

Observing Planetesimal Formation under Streaming Instability in the Rings of HD 163296

We introduce a new technique to determine the gas turbulence and surface density in bright disk rings, under the assumption that dust growth is limited by turbulent fragmentation at the ring center. We benchmark this prescription in HD 163296, showing that our measurements are consistent with available turbulence upper limits and agree with independent estimates of the gas surface density within a factor of 2. We combine our results with literature measurements of the dust surface density and grain size to determine the dust-to-gas ratio and Stokes number in the 67 and 100 au rings. Our estimates suggest that particle clumping is taking place under the effect of streaming instability (SI) in the 100 au ring. Even though in the presence of external isotropic turbulence this process might be hindered, we provide evidence that turbulence is nonisotropic in both rings and likely originates from mechanisms (such as ambipolar diffusion) that could ease particle clumping under SI. Finally, we determine the mass accretion rate under the assumption that the disk is in steady state and turbulence regulates angular momentum transport. Our results are in tension with spectroscopic measurements and suggest that other mechanisms might be responsible for accretion, in qualitative agreement with the detection of a magnetocentrifugal wind in this system. Applying our method to larger samples can be used to statistically assess if SI is a viable mechanism to form planetesimals in bright rings.

Energy transfer and vortex structures: visualizing the incompressible turbulent energy cascade

The transfer of kinetic energy from large to small scales is a hallmark of turbulent flows. Yet, a precise mechanistic description of this transfer, which is expected to occur via an energy cascade, is still missing. Several conceptually simple configurations with vortex tubes have been proposed as a testing ground to understand the energy cascade. Here, we focus on incompressible flows and compare the energy transfer occurring in a statistically steady homogeneous isotropic turbulent (HIT) flow with the generation of fine-scale motions in configurations involving vortex tubes. We start by filtering the velocity field in bands of wavenumbers distributed logarithmically, which allows us to study energy transfer in Fourier space and also visualize the energy cascade in real space. In the case of a statistically steady HIT flow at a moderate Reynolds number, our numerical results do not reveal any significant correlation between regions of intense energy transfers and vorticity or strain, filtered in corresponding wavenumber bands, nor any simple self-similar process. In comparison, in the transient turbulent flow obtained from the interaction between two antiparallel vortex tubes, we observe a qualitatively simpler organization of the intense structures, as well as of the energy transfer. However, the correlations between energy transfer and strain are small, and point to complicated dynamics of energy transfer. By imposing a structure at large scales consisting of antiparallel vortex tubes in a statistically steady flow, we observed a picture qualitatively similar to what was observed for the transient flow, but the energy transfer statistics do not reproduce the type of triadic interactions seen in HIT. These results indicate that the specific properties of the large-scale vortical structures affect the way energy is transferred, and may not be fully representative of HIT.

EXPERIMENTAL STUDY OF LAGRANGIAN MIXING IN WEAKLY DISSIPATIVE TIDAL CHANNELS

Estuaries are extremely dynamic environments, allowing wildlife to grow in a wide variety of ecosystems because of the interaction of masses of water with different characteristics. In particular, coastal bays and estuaries are characterized by flows driven by hydraulic unbalance such as baroclinic pressure gradients, river inflows and wind stresses, and tidal waves. Here, following a reductionist approach, we examine dispersion processes in a physical model of a tidal channel bounded by an inlet mouth, with tides as the dominant forcing. The presence of a tidal inlet can generate macro-vortices that during a tidal cycle may influence the momentum and mass transport on relatively large distances (Awaji et al. (1980), Awaji (1982), Branyon et al. (2022)). Moreover, tides tend to produce non-monotonic particle velocity correlation leading to possible particle looping trajectories that also reflect on a looping character of the Lagrangian integral time scales, differently from the classical statistically steady or homogeneous turbulence (Enrile et al. (2019)). Our goal is to examine the dispersion regimes by means of two-dimensional velocity measurements at the free surface reproduced in a large-scale physical model as a starting point for Lagrangian analysis. We show how the presence of a tidal inlet generates complex flow patterns depending on the character of the forcing tides. Furthermore, the mixed nature of tides may be crucial to dispersion processes, as it enhances the ability of the flow to transport mass in the direction of the main flow.

A characterization of unsteady effects for transonic turbine airfoil limit loading

To better understand the effect of vortex shedding on the nature of the trailing edge shock system during airfoil limit loading a computational fluid dynamic investigation was performed for a transonic turbine airfoil at sublimit, limit and supercritical conditions. Four modeling strategies were employed: steady state RANS, unsteady RANS, DDES, and turbulence model free. The influence of transient modeling approaches on the predicted mass-flow averaged total pressure loss coefficient, mass-flow averaged flow angles, and on the limit loading pressure ratio were found to be insignificant with the exception of the URANS model during critical loading. It was found that the URANS modeling approach failed to predict the transition from near trailing edge dominated vortex formation to base pressure vortex formation resulting in a drastic rise in predicted total pressure loss. Surface isentropic Mach distributions were predicted similarly for all modeling strategies, with the exception of the trailing edge base pressure region and points of shock impingement along the suction surface. A detailed review of the boundary layer states at the trailing edge was performed. It was found that all of the modeling approaches predicted laminar boundary layer profiles along the pressure surface trailing edge and turbulent profiles along the suction surface. The predicted base pressure distributions were also reviewed, showing the base pressure to decrease with increasing pressure ratio. The unsteady simulation approaches consistently predicted lower average surface pressures than the steady state RANS simulations. Qualitative images of the numerical Schlieren contours were presented and reviewed showing large differences in the prediction of vortex shape, size, and subsequent shock influence.

LES analysis clarifying the response of static pressure fluctuation characteristics in isotropic/anisotropic steady turbulence field to reducing isotropic small-scale spatial resolution

This study aims to clarify the effects of an isotropic reduction in spatial resolution on the characteristics of the static pressure fluctuation in isotropic/anisotropic statistically steady state turbulence. Although previous direct numerical analyses have investigated the static pressure fluctuation, this study considers it as a quantity that could be more straightforwardly obtained from experimental measurements and numerical analyses. To address this issue, a large-eddy simulation is used in this study. The Smagorinsky model, the Vreman model and the implicit LES model are used in this study to model sub-grid scale fluctuations. The influence of isotropic spatial resolution reduction is set by changing the accuracy order for the discretisation of the viscous terms from second to eighth order, based on a three-dimensional cubic computational domain with spatially uniform computational grid width. The accuracy order for the convection terms is also set to second and fourth order in this study. When the discretisation accuracy order of the viscous terms is second order, there is a significant reduction in the accuracy of the implicit LES. The discretisation accuracy order of the viscous terms should be set to fourth order or higher, as seen in this study. In addition, unlike the turbulent kinetic energy, different discretisation accuracy orders for the viscous and convective terms also have a non-negligible effect on the static pressure fluctuation analysis.

Random Walk Particle Tracking to Model Dispersion in Steady Laminar and Turbulent Pipe Flow.

To accurately model a two-dimensional solute transport in drinking water pipes and determine the effective dispersion coefficients for one-dimensional water quality models of water distribution systems, a random walk particle tracking approach was developed to analyze the advection and dispersion processes in circular pipes. The approach considers a solute particle's two-dimensional random movement caused by molecular or turbulent diffusion and associated velocity profile, and can simulate any mixing time and accurately model the longitudinal distribution of the solute concentration. For long mixing times, the simulation results agreed with a previous analytically derived solution. For turbulent flow conditions, simulations showed that the longitudinal dispersion of the solute is very sensitive to the utilized cross-sectional velocity profiles. This approach is easy to implement programmatically and unconditionally stable. It can predict the mixing characteristics of a pipe under various initial and boundary conditions.

Universal scaling regimes in rotating fluid turbulence

Scaling arguments for steady turbulence in a rotating fluid are set up. These are used to show that it displays dual scaling regimes: a rotation-dominated regime for the largest scales and a Kolmogorov scaling regime for intermediate scales. For decaying rotating turbulence, it is speculated that the energy spectrum, while carrying a decaying amplitude, contains a large-scale rotation-dominated regime that increases in size over time, and an intermediate-scale Kolmogorov scaling regime that shrinks in time.

Numerical study of transient convective turbulent boundary layer flow along a vertical plate: analysis of kinetic energy and its dissipation rate

ABSTRACT The present article numerically investigates the turbulent buoyancy-driven (natural convection) flow along a vertical plate with a low Reynolds turbulence two-equation k-ϵ model. The deployed turbulence model is appropriate for low Reynolds number (LRN) turbulent flow adjacent to a solid boundary, and the turbulence kinetic energy (TKE) and dissipation rate of TKE are estimated using the momentum equations and are solved simultaneously with the mean flow conservation equations. Two-dimensional time-dependent viscous incompressible turbulent flow is simulated. This flow domain is governed by a highly non-linear group of partial differential equations, namely the time-averaged continuity, momentum, and energy, and also the flow property is determined through TKE, and dissipation rate of TKE equations. Since these equations are not solvable using analytical methods, an implicit second-order finite difference method is employed to solve the governing turbulent flow equations numerically. The simulated time-averaged velocity, temperature, TKE, and dissipation rate of TKE profiles along with friction factor and heat transfer rate are computed for different values of turbulent Reynolds and Prandtl numbers. Average velocity, temperature, turbulence energy, and dissipation rate under both transient and steady-state conditions are decreased with increment in . There is a decrement in average transient velocity and turbulence energy rates with increasing values, whereas the average temperature profile increases. Average steady temperature and turbulence energy profiles are also enhanced with rising values of . The majority of researchers focus on laminar flow and thus far turbulent flow has mainly been addressed through experiments only. To better elucidate the flow in this condition, the novelty of the present study is to utilize a numerical FDM procedure to probe more deeply into the turbulence characteristics in buoyancy-driven (natural convection) flow along a vertical plate with a low Reynolds turbulence two-equation k-ϵ model, as this topic is fundamental to many applications in science and engineering. Furthermore, the results of the turbulent flow simulations obtained from the current model are corroborated with existing results for the special case of laminar flow and a good correlation is achieved.

An EDQNM study of the dissipation rate in isotropic non-equilibrium turbulence

The energy cascade from large to small scales is a robust feature of three-dimensional turbulence. In statistically steady turbulence, the average dissipation is in equilibrium with the energy injected in the system. A global quantity measuring the deviations from such a flux equilibrium is the normalised dissipation rate , corresponding to the viscous dissipation, normalised by quantities associated with the largest scales of the system. Recent investigations have pointed out how this normalised dissipation rate varies in unsteady flows. We focus on two test-cases to assess non-equilibrium in isotropic turbulence. These cases are, respectively, turbulence in the presence of a large-scale periodic forcing and turbulence with reversed initial conditions. We show, using the Eddy-Damped Quasi-Normal Markovian closure, that for turbulence in the presence of periodic forcing, a scaling is reproduced ( indicating the Taylor-scale Reynolds number) when the forcing-frequency is adjusted to be of the order of the inverse of the integral time-scale. It is shown that the spectrum can be decomposed into an equilibrium spectrum, governed by Kolmogorov scaling in the inertial range, and a perturbation spectrum, proportional to , k being the wavenumber. For reversed turbulence, a novel procedure is introduced to prescribe initial conditions for the nonlinear transfer. Subsequently a clear transient with a scaling is observed in the dynamics.

Dynamics of inertial spheroids in a decaying Taylor–Green vortex flow

Inertial spheroids, prolates and oblates, are studied in a decaying Taylor–Green vortex (TGV) flow, wherein the flow gradually evolves from laminar anisotropic large-scale structures to turbulence-like isotropic Kolmogorov-type vortices. Along with particle clustering and its mechanisms, preferential rotation and alignment of the spheroids with the local fluid vorticity are examined. Particle inertia is classified by a nominal Stokes number St, which to first-order aims to eliminate the shape effect. The clustering varies with time and peaks when the physically relevant flow and particle time scales are of the same order. Low inertial (St<1) spheroids are subjected to the centrifuging mechanism, thereby residing in stronger strain-rate regions, while high inertial (St≫1) spheroids lag the flow evolution and modestly sample strain-rate regions. Contrary to the expectations, however, spheroids reside in high strain-rate regions when the particle and flow time scales are comparable due to the dynamic interactions between the particles and the evolving flow scales. Moderately inertial (St≤1) prolates preferentially spin and oblates tumble throughout the qualitatively different stages of the TGV flow. These preferential modes of rotation correlate with parallel and perpendicular alignments of prolate and oblate spheroids, respectively, with the local fluid vorticity. However, for high inertial spheroids preferential rotation and alignment are decorrelated due to a memory effect, i.e., inertial particles require longer time to adjust to the local fluid flow. This memory effect is not only due to high particle inertia, as in statistically steady turbulence, but also caused by the continuously evolving TGV flow scales.

Prediction of Self-Sustained Oscillations of an Isothermal Impinging Slot Jet

The present results are focused on the self-sustained oscillations of a confined impinging slot jet and their role in the flow structure and modeling requirements. Unsteady laminar, large-eddy simulation (LES), and Reynolds-averaged Navier–Stokes (RANS) predictions of an isothermal confined impinging jet were validated for several nozzle-to-plate ratios (H/B=4–15) and for laminar (Re=340 and 480) and turbulent (Re=104–2.7×104) conditions. The impinging flow structure was found to be highly influenced by the H/B ratio. For high ratios (H/B>5), the studied steady RANS turbulence models could not satisfactorily predict the high diffusion reported experimentally in the jet-impinging influence zone. The failure of these models has been attributed to the modeling issues of turbulence closures. However, for H/B=8, unsteady laminar 3D and LES calculations were verified, and a sinuous oscillation mode was developed, revealing self-sustained oscillations and the display of periodic flapping of the impinging jet in good agreement with the experiments. The predicted flapping oscillation is one of the reasons for the higher diffusion near the impingement wall, which was verified in several time-averaged experimental studies. The presence of jet flapping matters for clarifying the already long discussion on the RANS model’s validation in predicting impinging jets with high H/B ratios, adding justification to the failure of these turbulence models. This unsteady behavior is correctly computed through LES.

Development of a single-scale initial flow field into steady homogeneous turbulence with validating a constructed Fourier spectral analysis

This study presents the development of a single-scale initial velocity field into steady homogeneous isotropic turbulence. Here, we verify a constructed Fourier spectral analysis, which is then used to approach the present issue. The present homogeneous isotropic turbulence is maintained steady by using a linear forcing scheme of Lundgren (2003). Here, two values of the primary coefficient are set here for this scheme. The initial velocity field is also set to maintain the flow globally isotropic. Temporal developments of turbulence statistics, visualization results and structure functions are examined in this study. As shown in a previous study, Rosales and Meneveau (2005), the turbulence length scale at a steady-state could remain independent of a value used for the linear forcing coefficient. The turbulence fields needed 10 to 15 times longer than the turbulence time scale to achieve this steady-state. A larger amount of time was needed for the structure functions to reach their steady-state profiles than for the turbulence statistics.

Experimental and numerical investigation of compressibility effects on velocity derivative flatness in turbulence

Compressibility effects on the velocity derivative flatness F∂u′/∂x are investigated by experiments with opposing arrays of piston-driven synthetic jet actuators (PSJAs) and direct numerical simulations (DNS) of statistically steady compressible isotropic turbulence and temporally evolving turbulent planar jets with subsonic or supersonic jet velocities. Experiments using particle image velocimetry show that nearly homogeneous isotropic turbulence is generated at the center of a closed box from interactions between supersonic synthetic jets. The dependencies of F∂u′/∂x on the turbulent Reynolds number Reλ and the turbulent Mach number MT are examined both experimentally and using DNS. Previous studies of incompressible turbulence indicate a universal relationship between F∂u′/∂x and Reλ. However, both experiments and DNS confirm that F∂u′/∂x increases relative to the incompressible turbulence via compressibility effects. Although F∂u′/∂x tends to be larger with MT in each flow, the F∂u′/∂x in the turbulent jets and the turbulence generated from PSJAs deviate from those in incompressible turbulence at lower MT compared with isotropic turbulence sustained by a solenoidal forcing. The PSJAs and supersonic planar jets generate strong pressure waves, and the wave propagation can cause an increased F∂u′/∂x, even at low MT. These results suggest that the compressibility effects on F∂u′/∂x are not solely determined from a local value of MT and depend on the turbulence generation process.

A comparison of major steady RANS approaches to engineering ABL simulations

Engineering atmospheric boundary layer (EABL) simulations performed using Computational Fluid Dynamics (CFD) can give key insights in successfully addressing a variety of topics in environmental and structural aerodynamics. To improve understanding of this complex topic, a computational evaluation of the shear stress-driven (SSD), pressure-driven (PD) and body-force-driven (BFD) EABL flows was performed using the open-source CFD code OpenFOAM®. The EABL simulations were computationally evaluated by using the successor domain technique (SDT) and precursor domain technique (PDT). The boundary conditions applied in the CFD algorithm using OpenFOAM® to computationally model the SSD, PD, and BFD EABL flows were reported and discussed. A developed CFD approach may also be satisfactorily used in other relevant CFD codes, including but not limited to Ansys CFX®, Ansys Fluent®, STAR−CCM+®. The impact of the EABL models on surface pressure distribution on a low-rise cubic building, the total building drag force and the wind velocities in pedestrian-level areas was computationally evaluated by using major Reynolds-averaged Navier-Stokes (RANS) turbulence models, i.e., the standard k−ε, re-normalization group (RNG) k−ε, realizable k−ε, Wilcox's k−ω, and Menter's k−ω shear stress transport (SST) turbulence models. The obtained computational results indicate that the SSD and PD EABL flows may be successfully modeled in cases where additional modifications of the officially released CFD code are not required in regard to the PDT. The PD EABL flow may be successfully modeled by using all studied RANS turbulence models in combination with the PDT. The EABL flow throughout an empty computational domain is homogeneous even without using a body force because the employed CFD code is capable of creating the required pressure gradient that drives the flow along the computational domain. While the surface pressure estimation on the windward body surface and in the recirculation zones was generally proven to be an issue when using steady RANS two-equation turbulence models, surface pressures in the stagnation zone on the windward cubic building surface and pressures on the top and the side building surfaces in the present study agree well with the experiments when using the RNG k−ε and Menter's k−ω SST turbulence models. The pressure distribution on the building surfaces, the total building drag force and wind characteristics in the vicinity of a lift-up building are not considerably affected by the choice of the EABL model, while they are substantially affected by the type of RANS turbulence model. The best agreement with the experiments was achieved when using the RNG k−ε and Menter's k−ω SST turbulence models, so these models may be recommended for future applications.

A numerical study on natural ventilation promotion and control in experimental house with fluid diode window

The objective of this study is to investigate the effects of installing a fluid diode window (FDW) in buildings to promote natural ventilation by controlling ventilation paths. An FDW is a porous plate with an internal structure that provides varying resistance to airflow depending on the flow direction. An FDW was installed in the bathroom of an experimental house to prevent polluted air from flowing into the adjacent multipurpose room during ventilation. Computational fluid dynamics simulations with a steady Reynoldsaveraged turbulence model and tracer gas method were performed to evaluate the performance of the FDW. The results show that an open window or FDW in the bathroom reduced the concentration and increased the ventilation rate. In the same wind direction at which the airflow exits through the window or FDW, it flows out at almost the same volumetric flow rate. In the cases where the airflow enters the bathroom through the window or FDW, the effect of preventing backflow from the bathroom window to the multipurpose room can be observed when the FDW was utilised, resulting in a reduction or even prevention of the gas entering the multipurpose room.

Advanced approach for oxygen transport and crystallization front calculation in Cz silicon crystal growth

Modeling of oxygen transport during Czochralski (Cz) silicon crystal growth still is a big challenge due to oxygen evacuation from the melt free surface, affected by strong anisotropy of turbulent mass transport. To predict the crystal oxygen concentration and crystallization front geometry with reasonable accuracy usually a 3D unsteady LES or DNS approach is required which demands significant computation resources and time. We present a new steady turbulence model using the extended hypothesis for modeling the Reynolds stress tensor, which accounts for different mechanisms of Reynolds stresses anisotropy and can be used in fast 2D engineering calculations. Several 8″ silicon crystals were grown in EKZ 3500 furnace with varying operating parameters. Wafers have been cut from different parts of the crystals and analyzed using the Fourier-transform infrared spectroscopy (FTIR) for oxygen concentration in facilities of Fraunhofer CSP and iTechSolar. The comparison between experimental and calculated results, which include oxygen concentration and interface deflection, is discussed in details. Time-averaged Reynolds stress tensor components as well as the turbulent heat fluxes components are compared between unsteady LES and steady RANS approaches.