Forced Turbulence Research Articles

Data-driven model for Lagrangian evolution of velocity gradients in incompressible turbulent flows

Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$ , in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ( $A = \sqrt {A_{ij}A_{ij}}$ ) from that of the more universal normalised velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$ . The boundedness and compactness of the $b_{ij}$ -space along with its universal dynamics allow for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein–Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation data over a wide range of velocity-gradient features and Reynolds numbers.

Diffusive-convection staircases in the polar oceans: the interplay between double diffusion and turbulence

Numerical simulations have been conducted to examine the structure of diffusive-convection staircases in the presence of vortical-mode-induced turbulent forcing. By modulating the input power $P$ and the background density ratio $R_\rho$ , we have identified three distinct types of staircase structures in these simulations: namely staircases maintained in the system driven by double-diffusion, by turbulence or by a combination of both double-diffusion and turbulence. While we showed that staircases maintained in the double-diffusion-dominated system are accurately characterised by the existing model originally proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, no. 3, 1978, pp. 417–432), we introduced new physical models to describe the staircase structures maintained in the turbulence-dominated system and the system driven by both turbulence and double-diffusion. Our integrated model reveals that turbulence fundamentally governs the entire life cycle of the diffusive-convection staircases, encompassing their formation, maintenance and eventual disruption in the Arctic Ocean's thermohaline staircases. While our previous work of Ma & Peltier (J. Fluid Mech., vol. 931, 2022b) demonstrated that turbulence could initiate the formation of Arctic staircases, these staircases are sustained by both turbulence and double-diffusion acting together after formation has occurred. Strong turbulence may disrupt staircase structures; however, the presence of weak turbulence could lead to unstable stratification within mixed layers of the staircases, as well as enhancing vertical heat and salt fluxes. Turbulence can even sustain a stable staircase structure factor when $R_\rho$ is relatively large, following a similar mechanism to the density staircases observed in laboratory experiments. Consequently, previous parameterisations (e.g. Kelley, J. Geophys. Res.: Oceans, vol. 95, no. C3, 1990, pp. 3365–3371) on the vertical heat flux across the diffusive-convection staircases may provide a significant underestimation of the heat transport by ignoring the influences of turbulence.

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .

Budget equations and astrophysical nonlinear mean-field dynamos

Abstract Solar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, nonlinear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence) for (i) a forced turbulence, (ii) a shear-produced turbulence and (iii) a convective turbulence. As the result of this effect, a nonlinear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field αΩ, α2 and α2Ω dynamo instabilities are always saturated by the strong large-scale magnetic field.

Velocity gradient analysis of a head-on vortex ring collision

We simulate the head-on collision between vortex rings with circulation Reynolds numbers of 4000 using an adaptive, multiresolution solver based on the lattice Green's function. The simulation fidelity is established with integral metrics representing symmetries and discretization errors. Using the velocity gradient tensor and structural features of local streamlines, we characterize the evolution of the flow with a particular focus on its transition and turbulent decay. Transition is excited by the development of the elliptic instability, which grows during the mutual interaction of the rings as they expand radially at the collision plane. The development of antiparallel secondary vortex filaments along the circumference mediates the proliferation of small-scale turbulence. During turbulent decay, the partitioning of the velocity gradients approaches an equilibrium that is dominated by shearing and agrees well with previous results for forced isotropic turbulence. We also introduce new phase spaces for the velocity gradients that reflect the interplay between shearing and rigid rotation and highlight geometric features of local streamlines. In conjunction with our other analyses, these phase spaces suggest that, while the elliptic instability is the predominant mechanism driving the initial transition, its interplay with other mechanisms, e.g. the Crow instability, becomes more important during turbulent decay. Our analysis also suggests that the geometry-based phase space may be promising for identifying the effects of the elliptic instability and other mechanisms using the structure of local streamlines. Moving forward, characterizing the organization of these mechanisms within vortices and universal features of velocity gradients may aid in modelling turbulent flows.

The influence of turbulence and inertia in radial fracture flow

Industrial applications of flow through fractures such as geothermal energy or hydraulic stimulation involve forcing large flow rates through small fractures, thereby inducing inertial fluid behaviours and turbulence. The most common fracture flow model, Poiseuille flow (the cubic law), is incapable of capturing these phenomena and thus the impact of inertial and turbulent forces in fracture flow has remained relatively unexplored. The GG22 flow model is a newly derived fracture flow model that is capable of capturing inertial, transient and turbulent forces. In this article, we apply the GG22 flow model to hydraulic stimulation of radial fractures for the first time to determine how these phenomena manifest. We show that inertia and turbulence only manifest near the wellbore (within 30 radii) and lead to changes in fracture shape and injection pressure but have little impact on tip behaviour. Turbulence increases wellbore pressure and aperture while inertia decreases wellbore pressure and aperture. The majority of the pressure loss along the fracture occurs near the wellbore and is captured by turbulence where entrance correction factors would otherwise be needed. Using water, turbulence is the dominant mechanism that causes departures from Poiseuille flow at high $Re$ . The solution departs immediately upon the manifestation of turbulence ( $Re\geq 2\times 10^3$ ), while inertial effects manifest at higher flow rates ( $Re\geq 2\times 10^4$ ). Using slickwater, the opposite trend is observed: inertial effects manifest first ( $Re\geq 5\times 10^3$ ), while turbulent effects are delayed ( $Re\geq 10^4$ ). In both cases, the threshold for departures from the Poiseuille flow solution are low and the differences are large.

Unidirectional and combined transitional flow bedforms: Controls on process and distribution in submarine slope settings

ABSTRACTMixed grain‐size bedforms comprise alternating sand‐rich and poorly sorted mud‐rich laminae and bands. These bedforms have been identified in distal submarine settings formed underneath unidirectional flows. This study documents mixed grain‐size bedforms in a proximal submarine slope setting formed beneath both unidirectional and combined flows. Core and outcrop data with well‐constrained palaeogeographical context are used to describe two types of mixed grain‐size bedform. Type A bedforms comprise mud‐rich current ripples and low‐amplitude bed‐waves with alternating concave and planar sandstone–mudstone foresets that pass into mud‐rich troughs, and aggradational sinusoidal laminasets. Type B bedforms consist of sandstone–mudstone laminasets that comprise rounded, biconvex ripples with sigmoidal‐shaped foresets and swale and hummock‐like laminasets and banded sets. These bedforms occur in channel‐margin, internal‐levée and external‐levée, intraslope and disconnected lobe environments, and represent 27 to 63% by stratigraphic thickness of the studied successions. They are interpreted as deposits of clay‐rich transitional flows, whose depositional style is governed by the balance of cohesive and turbulent forces, and the rate of flow deceleration. Type B bedforms are further interpreted as combined transitional flow deposits, resulting from flow deflection and ponding processes by seabed topography. Upward and lateral transitions between different bedforms create distinct bedform sequences, demonstrating progressive spatio‐temporal transformations in flow properties and their topographic interactions. By using a well‐constrained palaeogeographical setting, mixed grain‐size bedforms are shown to be situated close to sites of erosion into muddy substrates, abrupt losses in confinement, and/or changes in slope gradient. These bedforms demonstrate that flow transformation and transitional flow behaviour are not restricted to distal submarine settings. Furthermore, mixed grain‐size bedforms are not a diagnostic criterion for bottom currents, because such flows cannot account for the high mud content in laminasets, or the interlamination of sand and mud.

소용돌이 속에서 만난 엘리엇과 포우

This paper delves into the works of two influential literary figures, Edgar Allan Poe and T. S. Eliot, to explore their notion of vortex. While Poe’s “A Descent into the Maelström” presents a harrowing tale of a man’s encounter with a natural vortex, Eliot’s The Waste Land explores the destructive power of natural elements and their symbolic implications. Through a comparative analysis of these works, this paper aims to uncover the thematic and symbolic connections between Poe and Eliot’s vortex, shedding light on the psychological and existential aspects of human experience. While these works belong to different literary traditions and styles, they share certain thematic resonances in their treatment of the vortex as a metaphor for the turbulent forces that shape human existence.

Steady-State Supersaturation Distributions for Clouds under Turbulent Forcing

Abstract The supersaturation equation for a vertically moving adiabatic cloud parcel is analyzed. The effects of turbulent updrafts are incorporated in the shape of a stochastic Lagrangian model, with spatial and time correlations expressed in terms of turbulent kinetic energy. Using the Fokker–Planck equation, the steady-state probability distributions of supersaturation are analytically computed for a number of approximations involving the time-scale separation between updraft fluctuations and phase relaxation, and droplet or ice particle size fluctuations. While the analytical results are presented in general for single-phase clouds, the calculated distributions are used to compute mixed-phase cloud properties—mixed fraction and mean liquid water content in an initially icy cloud—and are argued to be useful for generalizing and constructing new parameterization schemes. Significance Statement Supersaturation is the fuel for the development of clouds in the atmosphere. In this paper, our goal is to better understand the supersaturation budget of clouds embedded in a turbulent environment by analyzing the basic equations of cloud microphysics. It is found that the turbulent characteristics of an air parcel substantially affect the cloud’s supersaturation budget and hence its life cycle. This is also shown in the context of mixed-phase clouds where, depending on the turbulent regime, different liquid-to-ice ratios are found. Consequently, the theoretical approach of this paper is crucial to develop tools to parameterize small-scale atmospheric features, like clouds, into global circulation models to improve climate projections for the future.

Comparison of forcing schemes to sustain homogeneous isotropic turbulence

Studies of forced homogeneous isotropic turbulence (HIT) of multiphase systems rely on a comprehensive understanding of the single-phase HIT flow to quantify any turbulence modifications due to injection of the dispersed phase. Here, we compare external forcing schemes to generate and sustain single-phase HIT. The considered forcing schemes, Lundgren, Arnold–Beltrami–Childress, and Mallouppas, are based on the application of the body force in physical space to inject energy into the flow at large length scales. Direct numerical simulations are performed in cubic periodic domains of 1283 and 2563 size using a lattice Boltzmann method. The range of the Taylor's Reynolds number achieved is ReλT=24.4–75.4. The Lundgren force takes the longest time to generate turbulence and produces significant fluctuations in the turbulence properties in the statistically stationary state. Additionally, this force interacts with the velocity field in the entire range of wavenumbers, which is not the case for the other two forces. However, the scale-by-scale analysis shows that for the considered forces, the behavior of the non-linear energy transfer, dissipation, and energy injection terms differs only within the initial 16% of the wavenumbers that represent large length scales. After that, all terms behave consistently among each other for different forcing schemes. We conclude that the three considered large-scale forcing schemes do not affect the generated turbulent flow fields at small scales and can be used to study turbulence modification by the dispersed phase.

From Internal Waves to Turbulence in a Stably Stratified Fluid.

We report on the statistical analysis of stratified turbulence forced by large-scale waves. The setup mimics some features of the tidal forcing of turbulence in the ocean interior at submesoscales. Our experiments are performed in the large-scale Coriolis facility in Grenoble which is 13m in diameter and 1m deep. Four wave makers excite large-scale waves of moderate amplitude. In addition to weak internal wave turbulence at large scales, we observe strongly nonlinear waves, the breaking of which triggers intermittently strong turbulence at small scales. A transition to strongly nonlinear turbulence is observed at smaller scales. Our measurements are reminiscent of oceanic observations. Despite similarities with the empirical Garrett and Munk spectrum that assumes weak wave turbulence, our observed energy spectra are rather to be attributed to strongly nonlinear internal waves.

Numerical Simulation of the Two-Phase Flow Dynamics in an Alkaline Water Electrolyzer Considering Difference in Bubble Diameter

For more efficient hydrogen production, predicting the characteristics of bubble flow inside a water electrolyzer is critical since bubbles affect ion transport, and electrode coverage by bubbles influence overpotentials and the entire electrolysis performance. Transport of bubble significantly depends on its size. In this study, a CFD model of an alkaline water electrolyzer which considers difference in sizes of generated bubbles was developed. The model treats bubbles of different sizes as different gas phases, which are independent of each other. The total bubble mass source for a given current density is divided into phases of each bubble size according to experimental visualizations. Drag, virtual mass, lift, wall lubrication, and turbulent dispersion forces are considered as interaction between gas and liquid phase.The following three sizes of bubbles were considered: diameters d = 36 μm (small), 75 μm (medium), and 208 μm (large). The entire calculation domain represents the anode side of a zero-gap monopolar alkaline water electrolyzer. Figure 1 shows the volume fraction fields of the three gas phases (i.e., bubble sizes) at a constant current density of 0.6 A/cm2. The bubbles are generated on the electrode surface at the z=0 plane. As the liquid phase forms a circulating flow inside the electrolyzer, small bubbles are transported along the circulating downstream flow due to smaller buoyancy force compared to their viscous drag. In contrast, large bubbles flow out directly to the upper outlet because buoyancy force dominates. This result points out the need to consider the difference in bubble diameter for designing flow field inside alkaline water electrolyzer.[Acknowledgements]This study was based on results obtained from the Development of Fundamental Technology for Advancement of Water Electrolysis Hydrogen Production in Advancement of Hydrogen Technologies and Utilization Project (P14021) commissioned by the New Energy and Industrial Technology Development Organization (NEDO).Fig. 1. Total gas phase volume fraction field obtained from the sum of the volume fraction field for each size bubble, and its experimental visualization. Figure 1

Particle Clustering in Turbulence: Prediction of Spatial and Statistical Properties with Deep Learning

We investigate the utility of deep learning for modeling the clustering of particles that are aerodynamically coupled to turbulent fluids. Using a Lagrangian particle module within the Athena++ hydrodynamics code, we simulate the dynamics of particles in the Epstein drag regime within a periodic domain of isotropic forced hydrodynamic turbulence. This setup is an idealized model relevant to the collisional growth of micron- to millimeter-sized dust particles in early-stage planet formation. The simulation data are used to train a U-Net deep-learning model to predict gridded three-dimensional representations of the particle density and velocity fields, given as input the corresponding fluid fields. The trained model qualitatively captures the filamentary structure of clustered particles in a highly nonlinear regime. We assess model fidelity by calculating metrics of the density field (the radial distribution function) and of the velocity field (the relative velocity and the relative radial velocity between particles). Although trained only on the spatial fields, the model predicts these statistical quantities with errors that are typically <10%. Our results suggest that, given appropriately expanded training data, deep learning could complement direct numerical simulations in predicting particle clustering within turbulent flows.

The structure and dynamics of massive high-z cosmic-web filaments: three radial zones in filament cross-sections

ABSTRACT We analyse the internal structure and dynamics of cosmic-web filaments connecting massive high-z haloes. Our analysis is based on a high-resolution arepo cosmological simulation zooming-in on three Mpc-scale filaments feeding three massive haloes of $\sim 10^{12}\, \text{M}_\odot$ at z ∼ 4, embedded in a large-scale sheet. Each filament is surrounded by a cylindrical accretion shock of radius $r_{\rm shock} \sim 50 \, {\rm kpc}$. The post-shock gas is in virial equilibrium within the potential well set by an isothermal dark-matter filament. The filament line-mass is $\sim 9\times 10^8\, \text{M}_\odot \, {\rm kpc}^{-1}$, the gas fraction within rshock is the universal baryon fraction, and the virial temperature is ∼7 × 105 K. These all match expectations from analytical models for filament properties as a function of halo mass and redshift. The filament cross-section has three radial zones. In the outer ‘thermal’ (T) zone, $r \ge 0.65 \, r_{\rm shock}$, inward gravity, and ram-pressure forces are overbalanced by outward thermal pressure forces, decelerating the inflowing gas and expanding the shock outwards. In the intermediate ‘vortex’ (V) zone, 0.25 ≤ r/rshock ≤ 0.65, the velocity field is dominated by a quadrupolar vortex structure due to offset inflow along the sheet through the post-shock gas. The outward force is dominated by centrifugal forces associated with these vortices, with additional contributions from global rotation and thermal pressure. Shear and turbulent forces associated with the vortices act inwards. The inner ‘stream’ (S) zone, $r \lt 0.25 \, r_{\rm shock}$, is a dense isothermal core, $T\sim 3 \times 10^4 \, {\rm K}$ and $n_{\rm H}\sim 0.01 \, {\rm cm^{-3}}$, defining the cold streams that feed galaxies. The core is formed by an isobaric cooling flow and is associated with a decrease in outward forces, though exhibiting both inflows and outflows.

Turbulent energy transfers in physical and scale spaces at dissipative length scales

In statistically stationary homogeneous incompressible turbulence, the average energy transfer rate balance which exists at diffusion/dissipation-dominated length scales does not reflect what actually happens locally in space and time. We use a highly resolved direct numerical simulation of forced periodic turbulence to shed some light on the actual fluctuating dynamics which occur at these very small scales and which are rubbed off by averaging. Even though the viscous diffusion in physical space averages to zero and fluctuates less intensely than all other terms (except the energy input rate) in the local (in space–time) two-point energy balance, it fundamentally cannot be neglected. The local unsteadiness and the interspace turbulence transport terms cannot be ignored either in the interscale energy dynamics in spite of the fact that they also average to zero.

Numerical study on flow-induced vibration and radiated noise of tube bundle in a shell-and-tube heat exchanger

This paper presents a numerical study of the flow-induced vibration and radiated noise characteristics of the heat exchange tube under external transverse turbulence excitation. A three-dimensional numerical model of the densely packed staggered tube bundles was established, the large eddy simulation (LES) was used to simulate the flow field around the tube bundle, and the analyses of the lift and drag forces on the surface of the tube bundle are performed in the time and frequency domains. Then, the turbulent exciting force on the surface of the tube was extracted and used as fluid load, the dynamic mode decomposition (DMD) method was used to reduce the order of the high-dimensional turbulent exciting force, the vibration of the bundle induced by the turbulent distribution force was obtained. Finally, the displacement of the bundle was extracted as noise source, and the boundary element method (BEM) was used to calculate the radiated noise characteristics of the bundle. The results show that the prediction of the flow induced vibration and radiated noise of the heat exchange tube using the simplified method is quite accurate, but greatly reduces computational consumption.

A two-dimensional void fraction distribution fast prediction model and application to a rod bundle

Accurate prediction of void fraction distribution is essential for system optimization, design, and safety analysis which involves gas-liquid two-phase flow. This paper introduces a novel conceptual two-dimensional Void Fraction Distribution Fast Prediction model (VDFP) designed to rapidly predict the void fraction distribution of fully developed two-phase pipe flow. By achieving this, the N-S equations were simplified into a readily solvable Laplacian form. The simplification was based on two assumptions: 1) For the steady simulation of fully developed pipe flow, the convective and axial diffusion terms in the time-averaged N-S equations are negligible; 2) The pressure field can be predefined as linearly decreasing along the axial direction while ignoring the radial pressure difference. After determining the axial velocity distribution, the void fraction distribution can be calculated through the balance of interfacial forces (lift force, wall lubrication force, and turbulent dispersion force) in the radial direction, which has a solid physical foundation and is applicable across a wide range of operating conditions. The feasibility of the VDFP model was validated by comparing the predicted results with experimental data of air-water two-phase flow in a rod bundle channel with a rod diameter of 25 mm and a rod pitch of 34 mm. Additionally, considering the constraints imposed by the rod bundle subchannel, the impact of bubble geometric restrictions on void fraction prediction was also evaluated. The validation results indicate that the VDFP model predicts the wall peak and core peak void fraction distribution results with satisfactory accuracy, and its solving time is <3 s, showing considerable potential for further reduction.

Euler-Euler LES of bubble column bubbly flows by considering sub-grid scale turbulent dispersion effect on modulating bubble transport

It has now been recognised and generally accepted that turbulent dispersion may be modelled using the time average of the fluctuating part of the interphase momentum, employing the drag the Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. As the turbulent eddies in the surrounding of bubbles interact strongly with the bubbles in bubbly flow, the bubble trajectories and bubble oscillation take place accordingly as the consequence of continuous deformation of the bubble surfaces. When using large eddy simulation for modelling bubbly flow, the sub-grid scale (SGS) filtered velocity fluctuations of liquid phase can be interpreted as many small eddies that may act on the surface of bubbles, consequently giving rise to bubble shape variations and the dispersion of bubbles. This study employs Euler/Euler large-eddy simulation (LES) modelling to demonstrate that the turbulent dispersion force model can be used to effectively indicate the influence of turbulent eddies on bubble dynamics, in particular the bubble cluster oscillations, which leads to remarkable improvements in the prediction of bubble lateral dispersion behaviour. The use of spatial filtering to model the SGS bubble dispersion is proposed with a modification on SGS eddy viscosity to reflect turbulent dispersion due to bubble induced turbulence. The results of the time-averaged LES modelled bubble velocities and bubble volume fraction profiles are in good agreement with the experimental data while the turbulent kinetic energy spectrum obtained at different locations on the centreline of the bubble column still exhibits the conventional −5/3 scaling for shear induced turbulence and a −3 scaling for bubble induced turbulence.

Transition from turbulence-dominated to instability-dominated combustion regime in lean hydrogen-air flames

To explore the importance of thermodiffusive and hydrodynamic instabilities of laminar flames in turbulent flows, previously generated direct numerical simulations of statistically one-dimensional complex-chemistry lean hydrogen-air flames in forced turbulence were continued by switching-off turbulence forcing. Three sets of flames characterized by different ratios of initial root-mean-square velocity to laminar flame speed, i.e., (A) u′/SL=2.2, (B) u′/SL=4.0, and (C) u′/SL=8.3, were addressed. Moreover, new complementary simulations of unstable laminar flames were performed. Analyses from the obtained numerical results indicate (but do not prove) that laminar flame instabilities play a minor role at sufficiently high Karlovitz numbers Ka. This supposition is supported, first, in cases B and C, where the initial value of turbulent burning velocity UT is significantly higher than burning velocity evaluated during non-linear stage of laminar flame instability development in the same computational domain. Second, regular large-scale perturbations of instantaneous flame surface are prominent in the unstable laminar flame but are not observed at high Ka. Third, Karlovitz numbers associated with appearance of such perturbations as the turbulence decays are scattered between 4 and 10 and are consistent within an order of magnitude to a recently proposed criterion (Chomiak and Lipatnikov, Phys. Rev. E 107: 015102, 2023) of importance for laminar flame instabilities in turbulent flows. Fourth, at such transition instants, a ratio of potential and solenoidal turbulent kinetic energies, averaged over the flame-brush leading edge, is close to 2.0 in 11 studied cases and a ratio of UT/SL varies between 3.0 and 3.5. Fifth, the maximum fuel consumption rate (over the computational domain) decreases as the turbulence decays. Thus, the initial maximum rates are significantly higher than the counterpart rate in the unstable laminar flame. Together these results show that the hypothesis that laminar flame instabilities play only a minor role at high Ka deserves further study.

Effects of different working parameters on the turbulent drag reduction regulated by annular plasma synthetic jet actuators

Reduction of turbulent drag force is one of important works in the design of airplanes and hypersonic aircrafts. The annular plasma synthetic jet (APSJ) has become an interesting and popular flow control method in reducing the drag of turbulent boundary layers. In this paper, a comprehensive experimental study is carried out on the turbulent drag reduction regulated by an array of annular plasma synthetic jet actuators. The effects of the operating parameters such as the actuation voltage, the pulse frequency and the incoming wind speed on the drag reduction rate are studied and discussed in detail. The performances of the plasma actuator array are evaluated and summarized at multiple working conditions. Finally, the coherent structures of turbulence and the hairpin-like vortices are depicted and discussed. The results show that the optimal drag reduction rate is achieved, as the actuation voltage, pulse frequency and incoming wind speed are Vpp = 7 kV, fp= 50 Hz, and U∞ = 7 m/s, respectively. A resonant coupling phenomenon is observed when the pulse frequency of the actuators approaches the characteristic frequency of the coherent structure. The upward sweep flow induced by APSJ actuators may lead to a reduction of the turbulent drag force, but the downward wash flow leads to an increase in the drag. Present study could provide solid experimental data and a helpful guidance for the drag reduction of an airplane.