Initial Turbulence Research Articles

Mixing efficiency in decaying stably stratified turbulence

Mixing efficiency in stratified flows is a measure of the proportion of turbulent kinetic energy that goes into increasing the potential energy of the fluid by irreversible mixing. In this research direct numerical simulations (DNS) and rapid distortion theory (RDT) cal- culations of transient turbulent mixing events are carried out in order to study this aspect of mixing. In particular, DNS and RDT of decaying, homogeneous, stably-stratified turbulence are used to determine the mixing efficiency as a function of the initial turbu- lence Richardson number Rit0 = (NL0/u0) 2 , where N is the buoyancy frequency and L0 and u0 are initial length and velocity scales of the turbulence. The results show that the mixing efficiency increases with increasing Rit0 for small Rit0, but for larger Rit0 the mixing efficiency becomes approximately constant. These results are com- pared with data from towed grid experiments. There is qualitative agreement between the DNS results and the available experimental data, but significant quantitative discrepancies. The grid turbulence experiments suggest a maximum mixing efficiency (at large Rit0 )o f about 6%, while the DNS and RDT results give about 30%. We con- sider two possible reasons for this discrepancy: Prandtl number effects and non-matching initial conditions. We conclude that the main source of the disagreement probably is due to inaccuracy in determining the initial turbulence energy input in the case of the grid turbulence experiments.

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.

Moderate Reynolds number axisymmetric jet development downstream an extended conical diffuser: Influence of extension length

Low-velocity (bulk velocity of 4.4 m/s) and moderate Reynolds (7350) axisymmetrical jet development is studied by hot-film single sensor anemometry. The jet issues from a conical convergent-divergent diffuser with uniform extension (diameter 25 mm). Decreasing the length-to-diameter ratio of the extension tube from 20 down to 0.4 is shown to alter severely the mean velocity profile at the tube outlet from Blasius to top-hat whereas turbulence intensities increases from 6 up to 50%. Next, the influence of the initial velocity profile at the tube outlet on axisymmetrical jet development is assessed. The velocity development exhibits a self-similar far field characteristic for axisymmetrical jet development. Although, the jet centerline decay constant increases and the jet spreading rate decreases as length-to-diameter ratios are increased from 0.4 up to 7.2 for which the initial centerline velocity decreases. Therefore, scaling of the centerline decay constant and inverse scaling of the spreading rate with initial centerline velocity U 0 or initial velocity Reynolds number Re 0 reported for moderate Reynolds numbers and low initial turbulence levels [18,22] does not hold as the turbulence level exceeds a threshold value in the range 12–27%. In addition, the influence of initial conditions on near and far field turbulence properties is shown. A transition in near field behaviour is observed for length-to-diameters around 3.6. Flow and geometrical configurations under study are relevant to e.g. upper airway flow.

Combined effects of initial pressure and turbulence on explosions of hydrogen-enriched methane/air mixtures

Hydrogen-enrichment has been proposed as a useful method to overcome drawbacks (local flame extinction, combustion instabilities, lower power output, etc.) associated to turbulent premixed combustion of natural gas in both stationary and mobile systems. For the safe use of hydrogen-enriched hydrocarbon fuels, explosion data are needed. In this work, a comparative experimental study of the explosion behavior of stoichiometric hydrogen-enriched methane/air (with 10% of hydrogen molar content in the fuel) and pure methane/air mixtures is presented. Tests were carried out in a 5 l closed cylindrical vessel at different initial pressures (1, 3 and 6 bar), and starting from both quiescent and turbulent conditions. Results allow quantifying the combined effects of hydrogen substitution to methane, pressure and turbulence on maximum pressure, maximum rate of pressure rise, burning velocity and Markstein lengths.

Hurricane formation in diabatic Ekman turbulence

AbstractThis article investigates the emergence of hurricanes from chaotic swirling motions in a three‐layer model of the tropical troposphere that includes basic parametrizations of cumulus convection and air‐‐sea interaction. The chaotic flow is referred to as diabatic Ekman turbulence (DET), in order to emphasize that cumulus convection and Ekman pumping are critical to its behaviour. The time required for hurricane formation in DET is examined over a broad range of sea‐surface temperatures, tropical latitudes and surface exchange coefficients for moist entropy and momentum. The mean trends are sensible, but for a given set of parameters, the genesis time can vary significantly with subtle changes to the initial turbulence. Moreover, hurricanes do not always form. In the event that a tropical depression develops into a hurricane, the process is highly asymmetric. Intensification involves a shear‐flow instability, the production of mesovortices and contraction of the basic circulation. Despite the complex evolution, the intensification rate is largely consistent with the expectations of a quasi‐linear stability analysis. Properties of mature hurricanes and the nature of their fluctuations are discussed in the context of the model. Copyright © 2009 Royal Meteorological Society

Investigation on the turbulent stress anisotropy of axisymmetric turbulence under rapid rotation

The root cause of different oscillatory behavior of turbulent stress anisotropy under rapid rotation of initially axisymmetric turbulence is theoretically investigated. For this, based on the velocity spectral tensor of axisymmetric turbulence, the rapid part of the pressure-strain is determined and the equation of the turbulent stress anisotropy is solved for initial conditions generated by axisymmetric expansion and contraction of isotropic turbulence. As is well known, the damping of turbulent stress anisotropy under rapid rotation is observed for both initial conditions, and this feature is attributed to the linear rapid rotation effect on turbulence. On the other hand, the oscillatory development of turbulent stress anisotropy can be seen conspicuously only for the initial turbulence generated by axisymmetric expansion. This selective oscillatory feature is found to be strongly related to the total strain that is applied to the isotropic turbulence to generate the initial axisymmetric turbulence. And, through an asymptotic approach, it is also found that the material frame-indifference principle of two-dimensional turbulence is the underlying physics in this different oscillatory behavior.

DRIVING TURBULENCE AND TRIGGERING STAR FORMATION BY IONIZING RADIATION

We present high-resolution simulations on the impact of ionizing radiation of massive O stars on the surrounding turbulent interstellar medium (ISM). The simulations are performed with the newly developed software iVINE which combines ionization with smoothed particle hydrodynamics (SPH) and gravitational forces. We show that radiation from hot stars penetrates the ISM, efficiently heats cold low-density gas and amplifies overdensities seeded by the initial turbulence. The formation of observed pillar-like structures in star-forming regions (e.g. in M16) can be explained by this scenario. At the tip of the pillars gravitational collapse can be induced, eventually leading to the formation of low-mass stars. Detailed analysis of the evolution of the turbulence spectra shows that UV radiation of O stars indeed provides an excellent mechanism to sustain and even drive turbulence in the parental molecular cloud.

Turbulence-driven zonal flows in helical systems with radial electric fields

Collisionless long-time responses of the zonal-flow potential to the initial condition and turbulence source in helical systems having radial electric fields are derived theoretically. All classes of particles in passing, toroidally trapped, and helical-ripple-trapped states are considered. The transitions between the toroidally trapped and helical-ripple-trapped states are taken into account while solving the gyrokinetic equation analytically by taking its average along the particle orbits. When the radial displacements of helical-ripple-trapped particles are reduced either by neoclassical optimization of the helical geometry lowering the radial drift or by strengthening the radial electric field Er to boost the poloidal rotation, enhanced zonal-flow responses are obtained. Under the identical conditions on the magnitude of Er and the magnetic geometry, using ions with a heavier mass gives rise to a higher zonal-flow response, and therefore the turbulent transport is expected to show a more favorable ion-mass dependence than the conventional gyro-Bohm scaling.

The Emergence of Multiple Robust Zonal Jets from Freely Evolving, Three-Dimensional Stratified Geostrophic Turbulence with Applications to Jupiter

Abstract Three-dimensional numerical simulations of freely evolving stratified geostrophic turbulence on the β plane are presented as a simplified model of zonal jet formation on Jupiter. This study samples the parameter space that covers the low, middle, and high latitudes of Jupiter by varying the central latitude of the β plane. The results show that robust zonal jets can emerge from initial small-scale random turbulence through the upscale redistribution of the kinetic energy in the spectral space. The resulting flow’s sensitivities to the flow’s deformation radius LD and the two-dimensional Rhines length Lβ = U/β (U is the characteristic turbulence velocity and β is the meridional gradient of the planetary vorticity) are tested, revealing that whether the outcome of the upscale energy transfer becomes dominated by jets or vortices depends on the relative values of LD and Lβ. The values of Lβ and LD are varied by tuning the β-plane parameters, and it is found that the flow transitions from a jet-dominated regime in Lβ ≲ LD to a vortical flow in Lβ ≳ LD. A height-to-width ratio equal to f /N, the Coriolis parameter divided by the Brunt–Väisälä frequency, has previously been established for stable vortices, and this paper shows that this aspect ratio also applies to the zonal jets that emerge in these simulations.

Mixing efficiency in decaying stably stratified turbulence

Mixing efficiency in stratified flows is a measure of the proportion of turbulent kinetic energy that goes into increasing the potential energy of the fluid by irreversible mixing. In this research direct numerical simulations (DNS) and rapid distortion theory (RDT) calculations of transient turbulent mixing events are carried out in order to study this aspect of mixing. In particular, DNS and RDT of decaying, homogeneous, stably-stratified turbulence are used to determine the mixing efficiency as a function of the initial turbulence Richardson number R i t 0 = ( N L 0 / u 0 ) 2 , where N is the buoyancy frequency and L 0 and u 0 are initial length and velocity scales of the turbulence. The results show that the mixing efficiency increases with increasing R i t 0 for small R i t 0 , but for larger R i t 0 the mixing efficiency becomes approximately constant. These results are compared with data from towed grid experiments. There is qualitative agreement between the DNS results and the available experimental data, but significant quantitative discrepancies. The grid turbulence experiments suggest a maximum mixing efficiency (at large R i t 0 ) of about 6%, while the DNS and RDT results give about 30%. We consider two possible reasons for this discrepancy: Prandtl number effects and non-matching initial conditions. We conclude that the main source of the disagreement probably is due to inaccuracy in determining the initial turbulence energy input in the case of the grid turbulence experiments.

Stability and Convection in Impulsively Heated Porous Layers

Experiments are reported on initial instability, turbulence, and overall heat transfer in a porous medium heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height:diameter ratio of 1.9. Heating is with a constant flux lower surface and a constant temperature upper surface, and the stability criterion is determined for a step heat input. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac=83/(1.08η−0.08η2) for 0.02<η<0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is Nu=0.047Ra0.91Pr0.11(μ/μ0)0.72 for 100<Ra<5000. Time-averaged temperatures suggest the existence of a unicellular axisymmetric flow dominated by upflow over the central region of the heated surface. When turbulence is present, the magnitude and frequency of temperature fluctuations increase weakly with increasing Rayleigh number. Analysis of temperature fluctuations in the fluid provides an estimate of the speed of the upward moving thermals, which decreases with distance from the heated surface.

Characterization of low-temperature pyroclastic surges that occurred in the northeastern Japan arc during the late 19th century

Three eruption events occurring in the central part of the northeastern Japan arc were investigated and compared: Adatara AD1900, Zao AD1895, and Bandai AD1888. Producing low-temperature (LT) pyroclastic surges, these events are characterized by steam eruptions ejecting no juvenile material. These eruptions' well-preserved eruptive deposits and facies facilitated granulometric analyses of the beds, which revealed the transport and deposition mechanisms of LT surges. Combining these results with those of investigations of documents reporting the events, we correlated each eruption to the relevant individual bed and reconstructed the LT surge development sequence. Important findings related to the transport and deposition modes are the following. (1) Bed sets consisting of thin, laminated ash and its overlying thick massive tuff were recognized in the Adatara 1900 proximal deposits. The bed set was probably produced by a strong wind that discharged and propagated quickly from the vent (leading wind) and a gravitationally segregated, highly concentrated flow originated from the eruption column, within a discrete eruption episode. A similar combination might have occurred during the first surge of the Bandai 1888 event. (2) Comparison of the proximal and distal facies for the largest eruption of Adatara 1900 event indicates that the initial turbulence of the eruption cloud decreased rapidly, transforming into a density-stratified surge with a highly concentrated part near the base. Similar surges occurred in the climatic stage of Zao 1895. (3) Bandai 1888 ejecta indicate massive beds deposited preferentially at topographic lows. Co-occurring planar beds showed no topographic affection, as indicated by the topographic blocking of a stratified surge. The observed facies–massive tuffs, crudely stratified tuffs, and thin bedded tuffs–are compatible with those for high-temperature surges. At Bandai, absence of dune bedded tuffs and commonly poorer sorting in the LT surge deposits might be attributable to poor thermally induced turbulence of eruption columns. Condensation of vapor in the surges might have contributed to the poor sorting. The estimated explosion energies were 6 × 10 13 J for Adatara AD1900, 6.5 × 10 10 J for Zao AD1895, and 6.5 × 10 15 J for Bandai AD1888, implying that the three events were hydrothermal eruptions with distinctive eruptive mechanisms. Regarding eruption sources, the Adatara 1900 event was caused solely by thermal energy of the hydrothermal fluid, although magma intrusion likely triggered evolution of hydrothermal systems at Zao in 1895. Steam eruptions in the Bandai 1888 event occurred simultaneously with sudden exposure of the hydrothermal system, whose triggers require no internal energy.

Investigation of the grid and intake-generated tumble on the in-cylinder flow in a compression ignition direct-injection engine

The in-cylinder flow field was numerically investigated for a four-valve per cylinder Caterpillar diesel CAT3401 engine. The computer program used was the KIVA3V code developed by Los Alamos National Laboratory. To assess the effect of modelling assumptions made during the domain discretization, three grid models were developed. The first grid or the ‘complete’ grid was a full 360° mesh with moving valves, intake ports, exhaust ports, and runners. The second grid was a full 360° mesh without moving valves, intake ports, or exhaust ports. The third grid assumed that the in-cylinder flow field was periodic and a 60° mesh was generated to accommodate one of the six centrally located fuel injectors. It also neglected the valves and the intake and exhaust ports. The simplification of the grids is to reduce the massive computational and memory requirements to model these flows. For the complete grid, the computation was initiated when the piston was at the top dead centre location on the intake stroke. For the second and third grids, the computation was initiated after the intake valve had closed. Complex three-dimensional vortical flow structures or tumble is developed during the intake stroke. These structures were clearly shown when the complete grid was used. By comparing the solution of the complete grid with the solutions of the second and third grids, it was seen that important in-cylinder flow information is lost. To overcome this deficiency, a new parameter, namely the initial tumble ratio, was embedded into the standard KIVA3V code by the present authors. When the simplified second grid is used in conjunction with the initial tumble ratio option, an in-cylinder flow pattern similar to that which was computed with the complete grid was obtained. This indicates that the new option significantly improves the accuracy of in-cylinder flow prediction when the moving valves and intake or exhaust ports are not modelled. The effects of the values of the initial turbulence kinetic energy (TKEi) and the initial turbulence length scale (SCLi) were also studied. It is found that the suggested value of TKEi used in KIVA3V is too small to predict the actual turbulence kinetic energy in the cylinder when the second and third grids are used. Therefore, a larger value for TKEi is recommended. The effects of the different grids, the new initial tumble ratio, and the different values of SCLi and TKEi on important flow parameters, such as the swirl ratio, the tumble ratio, and the turbulence kinetic energy are compared in detail in this article.

Evaluation of high-velocity plunging jet-issuing characteristics as a basis for plunge pool analysis

This paper presents experimental work on the characteristics of jets issuing from water-releasing structures. Systematic experimental tests have been performed at near-prototype velocities of up to 30 m/s using a cylindrical jet nozzle. Dynamic pressures were measured along the diameter at the nozzle outlet with an acquisition rate of up to 2 kHz, for different upstream supply conditions. These measurements allowed assessing the mean and the fluctuating characteristics of the jet. The influence of supply circuit secondary currents, aeration and geometrical contraction on jet turbulence intensity and velocity profiles is discussed. The initial turbulence intensity varies from 2 to 8%, whereas the kinetic energy correction factor ranges from 1.0 to 1.1. Statistical analysis of pressure measurements shows that jet core pressures follow a Gaussian distribution fairly well for non-exceedence probabilities between 0.1 and 0.999. The experimental results and an extensive literature survey are used to define issuance parameters relevant for engineering practice.

Direct Computation of the Noise Generated by Subsonic Jets Originating from a Straight Pipe Nozzle

The noise generated by isothermal round jets at Mach number M = 0.9 and at the diameter-based Reynolds number ReD = 5 × 105, originating from a straight pipe nozzle, is computed directly using Large Eddy Simulation (LES), in order to highlight the potential influence of the inlet boundary conditions on the acoustic predictions. Two jets are simulated, displaying levels of fluctuating axial velocity at the nozzle exit respectively of 1.6% and 9% of the jet velocity, while the momentum thickness of the shear layers is nearly the same. The shear-layer development and the radiated sound fields obtained for the two jets are found to differ significantly. The shear layer of the jet with low initial turbulence levels develops for instance with higher turbulence intensities and a velocity flow field that is more correlated. In addition coherent annular vortices and pairings are clearly observed in this jet. Regarding the radiated noise, the jet with high initial turbulence levels provides sound levels and spectra in fairly good agreement with experimental data obtained for jets at Reynolds numbers ReD ≥ 5 × 105. The jet with low nozzle-exit turbulence levels is shown to generate more noise, which might result from vortex pairings in the shear layer as it was suggested by Zaman [1].

Manifestation of the stochastic resonance in submerged jets under an acoustic action

A phenomenon that is similar to the well-known stochastic resonance in nonlinear oscillators but is caused by the turbulence in a circular submerged jet under a harmonic acoustic action, rather than by noise, is considered. It is shown that, at a fixed distance from the nozzle, a variation of the initial turbulence level leads to a non-monotonic variation of the wave amplitude at the frequency of the acoustic action, namely, to the appearance of an amplitude maximum at a certain level of the initial turbulence. The qualitative explanation of the phenomenon consists in that the initial turbulence acts on the system in a way similar to that of external noise: it changes the effective parameters of the system and, in particular, shifts the spectral maxima, which is equivalent to a change in a certain “eigenfrequency.” Such a change in the effective parameters of the jet leads to a phenomenon similar to the stochastic resonance.

New dust explosion venting design requirements for turbulent operating conditions

The 2007 edition of the National Fire Protection Association Standard 68 for Explosion Protection by Deflagration Venting has a new provision to account for the turbulence level in combustible dust or powder processing equipment. This paper explains the development of this new provision for increased deflagration vent area requirements in highly turbulent combustible dust/powder processing equipment. The development includes a review of initial turbulence level effects on vented explosion pressures, and a review of turbulence levels measured in ASTM E1226 and ISO 6184/1 explosion test procedures to determine K st. A review of operating conditions in some representative spray dryer plant equipment suggests that most equipment of this type probably do not have high enough air flows to require increased explosion vent areas due to turbulence, but some types of equipment with high tangential entrance air flows may well need larger vent areas.

PIV measurements of a turbulent jet issuing from round sharp-edged plate

An experimental investigation is presented of a turbulent jet issuing from a round sharp-edged orifice plate (OP) into effectively unbounded surroundings. Planar measurements of velocity were conducted using Particle Image Velocimetry (PIV) in the near and transition regions. The Reynolds number, based on the jet initial diameter and velocity, is approximately 72,000. The instantaneous and mean velocities, Reynolds normal and shear stresses were obtained. The centerline velocity decay and the half-velocity radius were derived from the mean velocity. It is revealed that primary coherent structures occur in the near field of the OP jet and that they are typically distributed asymmetrically with respect to the nozzle axis. Comparison of the present PIV and previous hot-wire measurements for the OP jet suggests that high initial turbulence intensity leads to reduced rates of decay and spread of the mean flow field and moreover a lower rate of variation of the turbulence intensity. Results also show that self-similarity of the mean flow is well established from the transition region while the turbulent statistics are far from self-similar within the measured range to 16 diameters.

Rapid shear of initially anisotropic turbulence in a rotating frame

In the present study, we investigate, using inviscid rapid distortion theory, the evolution of sheared turbulence in a rotating frame as a function of the rotation rate (including stable, transitional, and unstable regimes), and examine the sensitivity of the results for various nonisotropic initial conditions. Analytical solutions are derived for the evolution of the stresses and the structure dimensionality tensor components for three one-dimensional and three two-dimensional initializations. From these solutions, we calculate the asymptotic states of the turbulence, which are compared to the exact numerical solution of the three-dimensional initially isotropic case. From the investigation it is shown that the qualitative characteristics of the isotropic solution in the unstable regime are represented quite accurately when the initial turbulence is dependent at least on the axis of the rotation of the frame. For the transitional and the stable regimes, though, the initial dependence of the turbulence on the axis of the mean flow is also crucial.

Numerical simulations of homogeneous charge compression ignition engines with high levels of residual gas

In order to account for the effect of mixture inhomogeneity in HCCI engines utilizing high levels of residual gas and to estimate accurate initial conditions, a sequential numerical procedure was devised. A one-dimensional (1D) engine cycle simulation and a three-dimensional (3D) CFD analysis were used to calculate the residual gas overall level and its spatial distribution. A Monte-Carlo method for the probability density function (PDF) of the mass fraction and temperature, assuming negligible spatial inhomogeneity in the mean quantities but including finite small-scale fluctuations, was used to allow for micro-mixing in the evolution of the chemical reactions. The computational fluid dynamics (CFD) analysis confirmed that substantial scalar inhomogeneity persists up to top dead centre (TDC). The result from the procedure showed a close prediction of the pressure profile from the experiment. However, the u HC level is underpredicted, attributed to the assumed spatial homogeneity of the mean quantities in the Monte-Carlo simulation, which causes an overprediction of the scalar fluctuation decay. Parametric studies of the initial mixture inhomogeneity and turbulence timescale showed that they affect both the ignition timing and combustion duration. A comparison of three mixing models (IEM, modified Curl, and EIEM) showed that the EIEM model predicts a later ignition. The results suggested that accurate prediction of pollutant emission in HCCI engines with high levels of residual gas can be achieved only by a fully 3D calculation incorporating turbulence-chemistry interactions, although combustion phasing and duration can be predicted with adequate accuracy with a volume-averaged representation of the initial residual gas fluctuations.