Convective Time Scale Research Articles

TURBULENT CHEMICAL DIFFUSION IN CONVECTIVELY BOUNDED CARBON FLAMES

ABSTRACT It has been proposed that mixing induced by convective overshoot can disrupt the inward propagation of carbon deflagrations in super-asymptotic giant branch stars. To test this theory, we study an idealized model of convectively bounded carbon flames with 3D hydrodynamic simulations of the Boussinesq equations using the pseudo-spectral code Dedalus. Because the flame propagation timescale is much longer than the convection timescale, we approximate the flame as fixed in space, and only consider its effects on the buoyancy of the fluid. By evolving a passive scalar field, we derive a turbulent chemical diffusivity produced by the convection as a function of height, . Convection can stall a flame if the chemical mixing timescale, set by the turbulent chemical diffusivity, , is shorter than the flame propagation timescale, set by the thermal diffusivity, κ, i.e., when . However, we find for most of the flame because convective plumes are not dense enough to penetrate into the flame. Extrapolating to realistic stellar conditions, this implies that convective mixing cannot stall a carbon flame and that “hybrid carbon–oxygen–neon” white dwarfs are not a typical product of stellar evolution.

Convective moisture adjustment time scale as a key factor in regulating model amplitude of the Madden‐Julian Oscillation

AbstractDespite its pronounced impacts on weather extremes worldwide, the Madden‐Julian Oscillation (MJO) remains poorly represented in climate models. Here we present findings that point to some necessary ingredients to produce a strong MJO amplitude in a large set of model simulations from a recent model intercomparison project. While surface flux and radiative heating anomalies are considered important for amplifying the MJO, their strength per unit MJO precipitation anomaly is found to be negatively correlated to MJO amplitude across these multimodel simulations. However, model MJO amplitude is found to be closely tied to a model's convective moisture adjustment time scale, a measure of how rapidly precipitation must increase to remove excess column water vapor, or alternately the efficiency of surface precipitation generation per unit column water vapor anomaly. These findings provide critical insights into key model processes for the MJO and pinpoint a direction for improved model representation of the MJO.

Effects of internal circulation and particle mobility during nanofluid droplet evaporation

The effect of internal circulation on evaporation of fluid droplets containing nano-sized particles is analytically investigated, where internal circulation is caused by viscous effects at the liquid–gas interface in the convective environment. The competing time scales of liquid diffusion, convection, and particle diffusion are first analyzed as influenced by gas phase velocity, relative viscosities of gas and liquid phases, and the droplet size. The results reveal the importance of internal recirculation for droplets of practical sizes. To demonstrate the role of internal circulation plays on particle distribution and shell formation during the evaporation process, a symmetric Hill vortex and strong circulation are assumed for solving a one-dimensional governing equation, which to yield (i) the particle redistribution during the evaporation process, (ii) the time and the size upon shell formation (i.e., the end of the first-stage evaporation/drying) due to inclusion of particles at the droplet surface, and (iii) internal particle distribution that forecast possible morphologies of particle aggregates once the drying process is complete. These results are found to be dependent upon (a) the relative time scales of liquid diffusion and particle mobility (the effect of Lewis number, Le), and (b) the relative importance or evaporation rate (K) and particle mobility (the effect of Peclet number, Pe). Comparisons with previous results without internal circulation are made, as related to the time for shell formation and possible morphologies. Such comparisons reveal some distinctly different, and surprising, phenomena during and at the end of the first-stage evaporation.

Pulsed Actuation Control of Flow Separation on a ROBIN Rotorcraft Fuselage

Separation control of the three-dimensional flow over the aft segment of a NASA Rotor-Body-Interaction (ROBIN) rotorcraft fuselage is investigated in wind-tunnel experiments using arrays of miniature combustion-based actuators. Successive pulsed actuation is effected by momentary jets each having a characteristic time scale that is an order of magnitude shorter than the convective time scale of the flow. The actuators are placed upstream of the transition ramp between the ROBIN’s fuselage and the tail boom. The jet-induced interactions with the massively separated crossflow over the ramp and their effects on the global aerodynamic forces and moments are investigated using high-resolution particle image velocimetry that is acquired phase-locked to the actuation waveform in conjunction with simultaneous force and moment measurements using an onboard load cell. The present investigations show that symmetric actuation about the model’s centerline can significantly mitigate separation, lead to a reduction in drag and lift, and alter the pitching moment. Asymmetric actuation, and consequently nonuniform attachment, can induce significant side forces as well as roll and yaw moments that may be exploited for steering and improved flight maneuverability.

Study on air ingress of the 200 MWe pebble-bed modular high temperature gas-cooled reactor

Air ingress, one of the beyond design basis accidents (BDBA) for high temperature gas-cooled reactors (HTR), receives high attention during the design of the 200MWe pebble-bed modular high temperature gas-cooled reactor (HTR-PM), because it may result in severe consequence including the corrosion of the fuel elements and graphite reflector. A hypothetical air ingress accident, caused by the double-ended guillotine break (DEGB) of the horizontal coaxial hot-gas duct, is studied in this paper.After the rupture of the hot-gas duct, the following accident developing progress can be divided into three stages: (1) depressurization, (2) slow air ingress via diffusion and local convection, (3) onset of the overall, stable natural circulation and the consequent continuous air ingress. Based on the design of the HTR-PM, the time scale of diffusion and convection in the second stage is studied to evaluate the onset time of the stable natural circulation. Furthermore, the TINTE model of the HTR-PM is then established to simulate the hot-gas duct DEGB accident, including the flow rate of natural circulation, the corrosion of the fuel elements and the graphite reflector, the feasibility of the mitigation measures. The results show that due to the high pebble bed core with large flow resistance, as well as the complicated flow structure of the HTR-PM, it would take long time to obtain stable natural circulation. The results also indicate that, the bottom reflector graphite could consume most of the oxygen before it reaches the core and the injection of the nitrogen can effectively mitigate the corrosion of the graphite.

Effect of equivalence ratio on the modal dynamics of azimuthal combustion instabilities

The present paper investigates the effect of equivalence ratio on the modal dynamics of self-excited azimuthal combustion instabilities in a laboratory-scale annular combustor. It is shown that operating at different equivalence ratios not only affects the mode of oscillation (whether the instabilities are mixed, or predominantly spinning or standing modes), but also the way in which mode switching between these states occurs. Using pressure time-series data obtained at multiple locations around the annulus the phenomenon of mode switching is investigated through the spin ratio, the orientation of the nodal lines and the envelope of the pressure oscillations. These three parameters all suggest that mode switching events occur almost periodically, and over azimuthal convective time scales. Moreover, analysis of the spin ratio and orientation of the nodal lines show that these parameters are correlated, and that their mean rates of change or trajectories also have a preferred direction. Therefore, these quantities were found to oscillate backwards and forwards in-phase with each other, as opposed to the mode simply rotating in one direction, providing new insight into the nature of modal dynamics of self-excited azimuthal modes.

Design and Scaling of Plasma Streamwise Vortex Generators for Flow Separation Control

The design and scaling of plasma streamwise vortex generators in a variable pressure gradient environment are presented. This involves measurements in the boundary layer on the suction surface of a V-22 wing model which provided a generic flowfield that undergoes trailing-edge flow separation as a precursor to lift stall. Experiments were performed at freestream Mach numbers from 0.1 to 0.2, which resulted in chord Reynolds numbers of to . Different streamwise pressure gradients were examined by changing the airfoil angle of attack. Three components of the mean velocity in the boundary layer on the suction side of the wing model were measured using a five-hole pitot probe. These measurements were used to quantify the plasma streamwise vortex generator generated mean streamwise vorticity and the magnitude of the vorticity reorientation term in the vorticity transport equation that was used in the scaling analysis of the plasma streamwise vortex generator performance. The results validate the prediction of the streamwise vorticity production associated with the reorientation of the boundary-layer mean vorticity to scale as , where is the streamwise length of the plasma streamwise vortex generator array, is the external velocity at the crest of the airfoil, is the characteristic mean velocity of the flow over the plasma streamwise vortex generator array, is the change in the streamwise velocity produced by the plasma actuator, and is the spanwise spacing between the plasma streamwise vortex generator electrodes. The criteria for is that the convective timescale be greater than the timescale for vorticity reorientation in the boundary layer, namely, . Both the plasma streamwise vortex generator generated and were found to scale with . An optimally scaled plasma streamwise vortex generator array on the V-22 wing model produced as much as a 40 point drag count reduction at poststall angles of attack.

Storm time dynamics of ring current protons: Implications for the long‐term energy budget in the inner magnetosphere

AbstractOur investigation of the long‐term ring current proton pressure evolution in Earth's inner magnetosphere based on Van Allen Probes data shows drastically different behavior of the low‐ and high‐ energy components of the ring current proton population with respect to the SYM‐H index variation. We found that while the low‐energy component of the protons (<80 keV) is strongly governed by convective timescales and is very well correlated with the absolute value of SYM‐H index, the high‐energy component (>100 keV) varies on much longer timescales and shows either no correlation or anticorrelation with the absolute value of SYM‐H index. Our study also shows that the contributions of the low‐ and high‐ energy protons to the inner magnetosphere energy content are comparable. Thus, our results conclusively demonstrate that proton dynamics, and as a result the energy budget in the inner magnetosphere, do not vary strictly on storm time timescales as those are defined by the SYM‐H index.

MEMS flexible thermal flow sensors for measurement of unsteady flow above a pitching wind turbine blade

MEMS (Micro-Electro-Mechanical System) thermal flow sensors have been applied widely in boundary-layer studies and aerodynamic flow sensing due to high spatial resolutions and fast response times as well as minimal interference with fluid flow. In this study, self-made MEMS thermal flow sensors were designed and fabricated on a flexible skin. The steady laminar separation was investigated on two-dimensional LS (1) 0417 airfoil by using thermal flow sensors at various angles of attack with validation by hot wires and flow visualization. The unsteady flow on the pitching airfoil was experimentally investigated to simulate the dynamic stall condition of VAWT (Vertical Axis Wind Turbine). Based on variations of the mean value and standard deviation of the thermal flow sensor signals, nine stages of unsteady flow developing events are identified with further evidence from flow visualization. As the reduced frequency (k) increases, the incipient transition is delayed to higher angles of attack during the pitch-up motion; the re-laminarization is postponed to lower angles of attack during the pitch-down motion. The hysteresis is more pronounced at higher k where the oscillating time scale plays a more significant role in determining the unsteady flow pattern than the convective time scale. The phase difference between transition and re-laminarization was enlarged from Δα≈4.9° for k=0.009 to Δα≈13.5° for k=0.027 at Re=6.3×104.

Effect of surface charge convection and shape deformation on the dielectrophoretic motion of a liquid drop.

The dielectrophoretic motion and shape deformation of a Newtonian liquid drop in an otherwise quiescent Newtonian liquid medium in the presence of an axisymmetric nonuniform dc electric field consisting of uniform and quadrupole components is investigated. The theory put forward by Feng [J. Q. Feng, Phys. Rev. E 54, 4438 (1996)10.1103/PhysRevE.54.4438] is generalized by incorporating the following two nonlinear effects-surface charge convection and shape deformation-towards determining the drop velocity. This two-way coupled moving boundary problem is solved analytically by considering small values of electric Reynolds number (ratio of charge relaxation time scale to the convection time scale) and electric capillary number (ratio of electrical stress to the surface tension) under the framework of the leaky dielectric model. We focus on investigating the effects of charge convection and shape deformation for different drop-medium combinations. A perfectly conducting drop suspended in a leaky (or perfectly) dielectric medium always deforms to a prolate shape and this kind of shape deformation always augments the dielectrophoretic drop velocity. For a perfectly dielectric drop suspended in a perfectly dielectric medium, the shape deformation leads to either increase (for prolate shape) or decrease (for oblate shape) in the dielectrophoretic drop velocity. Both surface charge convection and shape deformation affect the drop motion for leaky dielectric drops. The combined effect of these can significantly increase or decrease the dielectrophoretic drop velocity depending on the electrohydrodynamic properties of both the liquids and the relative strength of the electric Reynolds number and electric capillary number. Finally, comparison with the existing experiments reveals better agreement with the present theory.

A Simple Stochastic Model for Dipole Moment Fluctuations in Numerical Dynamo Simulations

Earth's axial dipole field changes in a complex fashion on many different time scales ranging from less than a year to tens of million years. Documenting, analysing, and replicating this intricate signal is a challenge for data acquisition, theoretical interpretation, and dynamo modelling alike. Here we explore whether axial dipole variations can be described by the superposition of a slow deterministic drift and fast stochastic fluctuations, i.e. by a Langevin-type system. The drift term describes the time averaged behaviour of the axial dipole variations, whereas the stochastic part mimics complex flow interactions over convective time scales. The statistical behaviour of the system is described by a Fokker-Planck equation which allows useful predictions, including the average rates of dipole reversals and excursions. We analyse several numerical dynamo simulations, most of which have been integrated particularly long in time, and also the palaeomagnetic model PADM2M which covers the past 2 Myr. The results show that the Langevin description provides a viable statistical model of the axial dipole variations on time scales longer than about 1 kyr. For example, the axial dipole probability distribution and the average reversal rate are successfully predicted. The exception is PADM2M where the stochastic model reversal rate seems too low. The dependence of the drift on the axial dipole moment reveals the nonlinear interactions that establish the dynamo balance. A separate analysis of inductive and diffusive magnetic effects in three dynamo simulations suggests that the classical quadratic quenching of induction predicted by mean-field theory seems at work.

Stochastic fluid structure interaction of three-dimensional plates facing a uniform flow

An experiment on a flat rectangular plate facing a uniform flow at $Re=264\,000$ shows the importance of the base pressure loading on the asymmetric static modes of the turbulent wake. The plate is free to rotate around its short symmetry axis. For plates with aspect ratio ${\it\kappa}<6$, the angular position exhibits strong random discontinuities between steady states of non-zero angles. The steady states have long time durations, more than one order of magnitude greater than the convective time scale. The discontinuities, comparable to rare and violent events, are due to strong fluid forces associated with a drastic global change of the three-dimensional wake – mainly the switching between the static asymmetric modes. A clear transition occurs at ${\it\kappa}=6$, for which the angular fluctuations are minimum, leading for ${\it\kappa}>6$ to a classical fluid structure interaction with periodic fluctuations. The transition is supported by a recent global stability analysis of rectangular fixed plates in the laminar regime.

Characterisation of convective regimes over the British Isles

Convection‐permitting modelling has led to a step change in forecasting convective events. However, convection occurs within different regimes which exhibit different forecast behaviour. A convective adjustment timescale can be used to distinguish between these regimes and examine their associated predictability. The convective adjustment timescale is calculated from radiosonde ascents and found to be consistent with that derived from convection‐permitting model forecasts. The model‐derived convective adjustment timescale is then examined for three summers in the British Isles to determine characteristics of the convective regimes for this maritime region. Convection in the British Isles is predominantly in convective quasi‐equilibrium, with 85% of convection having a timescale less than or equal to 3 h. This percentage varies spatially with more non‐equilibrium events occurring in the south and southwest. The convective adjustment timescale exhibits a diurnal cycle over land. The non‐equilibrium regime occurs more frequently at mid‐range wind speeds and with winds from southerly to westerly sectors. Most non‐equilibrium convective events in the British Isles are initiated near large coastal orographic gradients or on the European continent. Thus, the convective adjustment timescale is greatest when the location being examined is immediately downstream of large orographic gradients and decreases with distance from the convective initiation region. The dominance of convective quasi‐equilibrium conditions over the British Isles argues for the use of large‐member ensembles in probabilistic forecasts for this region.

Numerical study of driven flows of shear thinning viscoelastic fluids in rectangular cavities

In this work, we present a numerical study of flow of shear thinning viscoelastic fluids in rectangular lid driven cavities for a wide range of aspect ratios (depth to width ratio) varying from 1/16 to 4. In particular, the effect of elasticity, inertia, model parameters and polymer concentration on flow features in rectangular driven cavity has been studied for two shear thinning viscoelastic fluids, namely, Giesekus and linear PTT. We perform numerical simulations using the symmetric square root representation of the conformation tensor to stabilize the numerical scheme against the high Weissenberg number problem. The variation in flow structures associated with merging and splitting of elongated vortices in shallow cavities and coalescence of corner eddies to yield a second primary vortex in deep cavities with respect to the variation in flow parameters is discussed. We discuss the effect of the dominant eigenvalues and the corresponding eigenvectors on the location of the primary eddy in the cavity. We also demonstrate, by performing numerical simulations for shallow and deep cavities, that where the Deborah number (based on convective time scale) characterizes the elastic behaviour of the fluid in deep cavities, Weissenberg number (based on shear rate) should be used for shallow cavities.

Acceleration of convective dissolution by chemical reaction in a Hele-Shaw cell.

New laboratory experiments quantify the destabilising effect of a second-order chemical reaction on the fingering instability of a diffusive boundary layer in a Hele-Shaw cell. We show that, for a given chemical system, the dynamics of such a reactive boundary layer is fully determined by two dimensionless groups, Da/Ra(2), which measures the timescale for convection compared to those for reaction and diffusion, and CBo', which reflects the excess of the environmental reactant species relative to the diffusing solute. Results of a systematic study varying CBo' in the range 0-0.1 are presented. It is shown that the chemical reaction increases the growth rate of a perturbation and favours small wavelengths compared to the inert system. A higher concentration of CBo' not only accelerates the onset of convection, but crucially also increases the transport of the solute by up to 150% compared to the inert system. This increase in solute transfer has important practical implications, such as in the storage of carbon dioxide in saline aquifers.

Flow regime mapping of high inertial gas–liquid droplet microflows in flow-focusing geometries

Confined gas–liquid droplet microflows present a lot of new perspectives for microfluidic systems that require the presence of a gaseous phase. In addition to the benefits associated with the discretization of reactive and sensing processes, the highly inertial droplets generated in these systems can enable fast efficient mixing by pair collisions as well as high system throughput due to the short convective timescales involved in the droplet transport. Presented herein is mapping of the geometry-specific droplet generation from a binary gas–liquid flow for different flow-focusing configurations. The dynamic interactions of inertia, shear stress, viscous and surface tension forces create three unique regimes in the gas–liquid flow rate space, providing adaptable flow configuration to specific applications. Analytical investigation and numerical analyses involving governing forces are also introduced to predict the effective droplet diameter versus gas flow rate. We found that the experimental results were well matched to the analytical predictions within 10 % of uncertainty.

Rotational evolution of slow-rotator sequence stars

The observed mass-age-rotation relationship in open clusters shows the progressive development of a slow-rotators sequence. The observed clustering on this sequence suggests that it corresponds to some equilibrium or asymptotic condition that still lacks a complete theoretical interpretation, crucial to our understanding of the stellar angular momentum evolution. We couple a rotational evolution model, which takes into account internal differential rotation, with classical and new proposals for the wind braking law, and fit models to the data using a MCMC method. The description of the evolution of the slow-rotators sequence requires taking into account the transfer of angular momentum from the radiative core to the convective envelope; we find that, in the mass range 0.85-1.10 $M_{\odot}$, the core-envelope coupling time-scale for stars in the slow-rotators sequence scales as $M^{-7.28}$. Quasi-solid body rotation is achieved only after 1-2 Gyr, depending on stellar mass, which implies that observing small deviations from the Skumanich law ($P \propto \sqrt{t}$) would require period data of older open clusters than available to date. The observed evolution in the 0.1-2.5 Gyr age range and in the 0.85-1.10 $M_{\odot}$ mass range is best reproduced by assuming an empirical mass dependence of the wind angular momentum loss proportional to the convective turnover time-scale and to the stellar moment of inertia. Period isochrones based on our MCMC fit provide a tool for inferring stellar ages of solar-like main-sequence stars from their mass and rotation period largely independent from the wind braking model adopted. These effectively represent gyro-chronology relationships that take into account the physics of the two-zone model for the stellar angular momentum evolution.

Substrate degradation in high-Rayleigh-number reactive convection

We study buoyancy-induced convection of a solute in an ideal two-dimensional fluid-saturated porous medium, where the solute undergoes a second-order reaction with a chemical substrate that is fixed in the underlying matrix. Numerical simulations at high Rayleigh number show how a flow is established in which a thin dynamic boundary layer beneath the solute source feeds slender vertical plumes beneath. We examine how the substrate is reactively degraded, at a rate enhanced by convective mixing. For the case when the substrate is abundant, we derive a reduced-order model describing the slow degradation of the substrate, which is formulated as a novel one-dimensional free-boundary problem. Numerical simulations and the reduced model reveal how, when the reaction is rapid compared to the convective time scale, the plumes propagate deep into the flow domain with reaction confined to a narrow region at their base. In contrast, slow reaction allows plumes to fill the domain before degradation of the substrate proceeds homogeneously. An alternative model with a thin reaction front captures the rapid degradation of the substrate when the solute concentration is relatively high.

Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions.

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O(1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.

Instabilities in unsteady boundary layers with reverse flow

Instabilities arising in unsteady boundary layers with reverse flow have been investigated experimentally. Experiments are conducted in a piston driven unsteady water tunnel with a shallow angle diffuser placed in the test section. The ratio of temporal (Πt) to spatial (Πx) component of the pressure gradient can be varied by a controlled motion of the piston. In all the experiments, the piston velocity variation with time is trapezoidal consisting of three phases: constant acceleration from rest, constant velocity and constant deceleration to rest. The adverse pressure gradient (and reverse flow) are due to a combination of spatial deceleration of the free stream in the diffuser and temporal deceleration of the free stream caused by the piston deceleration. The instability is usually initiated with the formation of one or more vortices. The onset of reverse flow in the boundary layer, location and time of formation of the first vortex and the subsequent flow evolution are studied for various values of the ratio Πx/(Πx+Πt) for the bottom and the top walls. Instability is due to the inflectional velocity profiles of the unsteady boundary layer. The instability is localized and spreads to the other regions at later times. At higher Reynolds numbers growth rate of instability is higher and localized transition to turbulence is observed. Scalings have been proposed for initial vortex formation time and wavelength of the instability vortices. Initial vortex formation time scales with convective time, δ/ΔU, where δ is the boundary layer thickness and ΔU is the difference of maximum and minimum velocities in the boundary layer. Non-dimensional vortex formation time based on convective time scale for the bottom and the top walls are found to be 23 and 30 respectively. Wavelength of instability vortices scales with the time averaged boundary layer thickness.