Ratio Of Length Scale Research Articles

Experiments on the merged vortex formation in a flapping plate

A two-dimensional flapping device was designed by consisting of a front flapping flat plate and a rear fixed horizontal plate in a rectangular tunnel. The flow characteristics near the plate and the downstream were studied under different flapping parameters. A high-speed camera was used to obtain the flow images to analyse the shedding vortex formation. Results show that a merged vortex is generated when the plate flaps and, relatively, an inertial vortex is generated when it stops. The vortex merger is in agreement with the Kovaznay model after the non-dimensional time / t T of 0.3, implying its non-equilibrium properties during energy transfer. The length-scale ratio of the merged vortex to the neighbour existing minor vortex is around 2, providing an experimental verification for the simulations of Cardesa et al. [Science 2017]. In addition, the most clear merged vortex is formed when the plate flaps between 30 and 60 degree at a tip flapping linear velocity 3 times bigger than the inlet flow velocity.

Effect of turbulence characteristics in the atmospheric surface layer on the peak wind loads on heliostats in stow position

This study investigates the dependence of peak wind load coefficients on a heliostat in stow position on turbulence characteristics in the atmospheric surface layer, such that the design wind loads, and thus the size and cost of heliostats, can be further optimised. Wind tunnel experiments were carried out to measure wind loads and pressure distributions on a heliostat in stow position exposed to gusty wind conditions in a simulated part-depth atmospheric boundary layer (ABL). Force measurements on different-sized heliostat mirrors at a range of heights found that both peak lift and hinge moment coefficients, which are at least 10 times their mean coefficients, could be optimised by stowing the heliostat at a height equal to or less than half that of the mirror facet chord length. Peak lift and hinge moment coefficients increased linearly and approximately doubled in magnitude as the turbulence intensity increased from 10% to 13% and as the ratio of integral length scale to mirror chord length Lux/c increased from 5 to 10, compared to a 25% increase with a 40% increase in freestream Reynolds number. Pressure distributions on the stowed heliostat showed the presence of a high-pressure region near the leading edge of the heliostat mirror that corresponds to the peak power spectra of the fluctuating pressures at low frequencies of around 2.4Hz. These high pressures caused by the break-up of large vortices at the leading edge are most likely responsible for the peak hinge moment coefficients and the resonance-induced deflections and stresses that can lead to structural failure during high-wind events.

A theoretical and computational framework for studying creep crack growth

In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the C^*-integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantity hat{C}_k needs to be determined from the Finite Element analysis in terms of a dimensionless quantity phi _0, which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack growth response in the limits of small and large phi _0, for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments.

Free Dry Vibration of Low-Aspect-Ratio Cantilever Wing: SemiAnalytical and Numerical Analysis With Experimental Verification

The free vibration of a low-aspect cantilever wing is studied by semianalytical, numerical, and experimental means. The wing is modeled as a two-way tapered, hollow Kirchhoff's plate, with the chord-wise section as symmetrical NACA0018 aerofoil. The chord length and the thickness taper from root to tip, over the span. The semianalytical approach is based on Galerkin's method, which includes the modal superposition of two orthogonal beam modeshapes (free-free beam in chord-wise direction and cantilever beam in span-wise direction). The free vibration is also studied numerically using ANSYS. The results have been compared with an experimental study, performing the dry impact hammer test. A model scale wing has been constructed from a 3-mm-thick metal sheet, with a length-scale ratio of 1:10. Comparative studies have been done among the three methods. The feasibility of modeling a low-aspect-ratio wing as a plate has been investigated. 1. Introduction Lifting surfaces commonly occur in engineering structures: fans, steam and gas turbine blades, impeller blades, wind turbine blades, helicopter fans, airplane wings, marine propeller blades, marine rudders and skegs, and other control surfaces like hydrofoils and wings in high-speed marine crafts. The lifting surface is typically a cantilever, with one edge welded to the main structure (root), and the other end free (tip). The span-wise geometry is tapered, for greater strength at the root and lighter weight at the tip. The chord-wise cross section is an aerofoil, which acts as a lifting surface to the incoming flow at varying angles of attack. The aspect ratio of the lifting surface, i.e., the ratio of the span length to the mean chord length, may vary from 0.4 to 0.6 in a turbine blade to 12 to 15 in an airplane wing/wind turbine. This work focuses on a low-aspect-ratio lifting surface, whose usual span-to-chord ratio is 1.5–2.

Rapid distortion of turbulence into an open turbine rotor

Rapid distortion of turbulence (RDT) theory is applied to homogeneous, isotropic turbulence incident on a horizontal axis turbine rotor such as a wind turbine or tidal-stream turbine. The mean flow field of the rotor which distorts the turbulence is represented by the commonly used axisymmetric actuator disc model due to Betz and Joukowski. The fluctuating streamwise component of the turbulence distorted by this field is calculated at the actuator disc plane. Turbulence velocity intensities and spectra are evaluated for general ratios of turbulence integral length scale to the rotor diameter, including the small-scale limit for which the original homogeneous strain analysis of Batchelor and Proudman may be applied. The distortion of the mean velocity profile of an incident rotor wake which may be considered a zero frequency disturbance relevant to wind and tidal turbine operation in large arrays is also analysed by the same method, treating it as a deterministic disturbance in the incident flow.

Generation of droplets via oscillations of a tapered capillary tube filled with low-viscosity liquids

Droplet formation via the oscillations of a tapered capillary tube is experimentally and numerically investigated using incompressible, low-viscosity Newtonian liquids. As in many other common methods of droplet generation, this technique features a transient flow that is directed out of a nozzle. However, due to the interactions of the oscillations, the tube, and the fluids, the flow rate upstream of the nozzle cannot be directly obtained. In this study, the motion of the tube is measured under the activation of a specific waveform, and the flow inside the tube and drop formation are further numerically studied using a non-inertial reference system in which the tube is stationary. The mechanism of ejection is quantitatively explained by analyzing the temporal variation in the velocity and pressure distributions inside the tube. The dynamics of drop formation, the drop velocity, and the drop radius are studied as functions of the dimensionless groups that govern the problem, including the Ohnesorge number Oh, the Weber number We, the gravitational Bond number G, and various length scale ratios. The results show that droplets are generated due to the inertia of the liquid and velocity amplification in the tapered section. By influencing the balance between the viscous effect and inertial effect of the liquid along the entire tube, the length scale ratios affect the evolution of the transient flow at the nozzle and eventually influence the drop radius and velocity. For liquids with viscosities close to that of pure water, the critical Reynolds number, at which a drop can be generated, linearly depends on the Z number (the reciprocal of Oh) at the nozzle.

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence.

A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U^{'} to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze=6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U^{'} is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.

Experimental investigation of the effect of droplet size on the vaporization process in ambient turbulence

This paper presents the results of an experimental investigation of the effect of droplet size on the fuel vaporization process in a turbulent atmosphere at standard ambient conditions. Single droplets of n-heptane and n-decane are formed and evaporated at the intersection point of two micro-fibers placed in the center of a fan-stirred spherical vessel which is maintained at room temperature and pressure. The droplet initial diameter varies in the range between 145 and 730µm. A controlled isotropic and homogeneous turbulent flow field with nearly zero mean velocity and intensity ranging between 0.25 and 1.5m/s is generated inside the vessel by means of eight axial fans. The results indicate that the droplet normalized squared diameter varies quasi-linearly with time, suggesting the applicability of the d2 law at all examined conditions. More importantly, the results reveal that the droplet initial diameter becomes a significant contributing factor in determining the evaporation rate in a turbulent environment, as the rate of vaporization is found to increase with both turbulent intensity and droplet size. However, droplet size produces no effect on the vaporization rate in quiescent (no flow) surroundings. The results also emphasize that as the ratio of the Kolmogorov length scale over droplet initial diameter approaches unity, the effect of turbulence becomes negligible, illustrating the importance of the small-scale eddies, and their relation to droplet size, in the transport/transfer of mass. The coupled effect of droplet size and turbulence on the vaporization rate is correlated in terms of either a turbulent Reynolds number or a vaporization Damköhler number.

Self-similar mixing in stratified plane Couette flow for varying Prandtl number

We investigate fully developed turbulence in stratified plane Couette flows using direct numerical simulations similar to those reported by Deusebioet al.(J. Fluid Mech., vol. 781, 2015, pp. 298–329) expanding the range of Prandtl number$Pr$examined by two orders of magnitude from 0.7 up to 70. Significant effects of$Pr$on the heat and momentum fluxes across the channel gap and on the mean temperature and velocity profile are observed. These effects can be described through a mixing length model coupling Monin–Obukhov (M–O) similarity theory and van Driest damping functions. We then employ M–O theory to formulate similarity scalings for various flow diagnostics for the stratified turbulence in the gap interior. The midchannel gap gradient Richardson number$Ri_{g}$is determined by the length scale ratio$h/L$, where$h$is the half-channel gap depth and$L$is the Obukhov length scale. As$h/L$approaches very large values,$Ri_{g}$asymptotes to a maximum characteristic value of approximately 0.2. The buoyancy Reynolds number$Re_{b}\equiv \unicode[STIX]{x1D700}/(\unicode[STIX]{x1D708}N^{2})$, where$\unicode[STIX]{x1D700}$is the dissipation,$\unicode[STIX]{x1D708}$is the kinematic viscosity and$N$is the buoyancy frequency defined in terms of the local mean density gradient, scales linearly with the length scale ratio$L^{+}\equiv L/\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$, where$\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$is the near-wall viscous scale. The flux Richardson number$Ri_{f}\equiv -B/P$, where$B$is the buoyancy flux and$P$is the shear production, is found to be proportional to$Ri_{g}$. This then leads to a turbulent Prandtl number$Pr_{t}\equiv \unicode[STIX]{x1D708}_{t}/\unicode[STIX]{x1D705}_{t}$of order unity, where$\unicode[STIX]{x1D708}_{t}$and$\unicode[STIX]{x1D705}_{t}$are the turbulent viscosity and diffusivity respectively, which is consistent with Reynolds analogy. The turbulent Froude number$Fr_{h}\equiv \unicode[STIX]{x1D700}/(NU^{\prime 2})$, where$U^{\prime }$is a turbulent horizontal velocity scale, is found to vary like$Ri_{g}^{-1/2}$. All these scalings are consistent with our numerical data and appear to be independent of$Pr$. The classical Osborn model based on turbulent kinetic energy balance in statistically stationary stratified sheared turbulence (Osborn,J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89), together with M–O scalings, results in a parameterization of$\unicode[STIX]{x1D705}_{t}/\unicode[STIX]{x1D708}\sim \unicode[STIX]{x1D708}_{t}/\unicode[STIX]{x1D708}\sim Re_{b}Ri_{g}/(1-Ri_{g})$. With this parameterization validated through direct numerical simulation data, we provide physical interpretations of these results in the context of M–O similarity theory. These results are also discussed and rationalized with respect to other parameterizations in the literature. This paper demonstrates the role of M–O similarity in setting the mixing efficiency of equilibrated constant-flux layers, and the effects of Prandtl number on mixing in wall-bounded stratified turbulent flows.

Spiralling liquid jets: verifiable mathematical framework, trajectories and peristaltic waves

The dynamics of a jet of an inviscid incompressible liquid spiralling out under the action of centrifugal forces is considered with both gravity and the surface tension taken into account. This problem is of direct relevance to a number of industrial applications, ranging from the spinning disc atomization process to nanofibre formation. The mathematical description of the flow by necessity requires the use of a local curvilinear non-orthogonal coordinate system centred around the jet’s baseline, and we present the general formulation of the problem without assuming that the jet is slender. To circumvent the inconvenience inherent in the non-orthogonality of the local coordinate system, the orthonormal Frenet basis is used in parallel with the local non-orthogonal basis, and the equation of motion, with the velocity considered with respect to the local coordinate system, is projected onto the Frenet basis. The variation of the latter along the baseline is then described by the Frenet equations which naturally brings the baseline’s curvature and torsion into the equations of motion. This technique allows one to handle different line-based non-orthogonal curvilinear coordinate systems in a straightforward and mathematically transparent way. An analysis of the slender-jet approximation that follows the general formulation shows how a set of ordinary differential equations describing the jet’s trajectory can be derived in two cases: $\mathit{We}=O(1)$ and $\unicode[STIX]{x1D716}\mathit{We}=O(1)$ as $\unicode[STIX]{x1D716}\rightarrow 0$, where $\unicode[STIX]{x1D716}$ is the ratio of characteristic length scales across and along the jet and $\mathit{We}$ is the Weber number. A one-dimensional model for the propagation of nonlinear peristaltic disturbances along the jet is derived in each of these cases. A critical review of the work published on this topic is presented showing where errors typically occur and how to identify and avoid them.

Experimental investigation of the effects of mean shear and scalar initial length scale on three-scalar mixing in turbulent coaxial jets

In a previous study we investigated three-scalar mixing in a turbulent coaxial jet (Caiet al.J. Fluid Mech., vol. 685, 2011, pp. 495–531). In this flow a centre jet and a co-flow are separated by an annular flow; therefore, the resulting mixing process approximates that in a turbulent non-premixed flame. In the present study, we investigate the effects of the velocity and length scale ratios of the annular flow to the centre jet, which determine the relative mean shear rates between the streams and the degree of separation between the centre jet and the co-flow, respectively. Simultaneous planar laser-induced fluorescence and Rayleigh scattering are employed to obtain the mass fractions of the centre jet scalar (acetone-doped air) and the annular flow scalar (ethylene). The results show that varying the velocity ratio and the annulus width modifies the scalar fields through mean-flow advection, turbulent transport and small-scale mixing. While the evolution of the mean scalar profiles is dominated by the mean-flow advection, the shape of the joint probability density function (JPDF) was found to be largely determined by the turbulent transport and molecular diffusion. Increasing the velocity ratio results in stronger turbulent transport, making the initial scalar evolution faster. However, further downstream the evolution is delayed due to slower small-scale mixing. The JPDF for the higher velocity ratio cases is bimodal at some locations while it is always unimodal for the lower velocity ratio cases. Increasing the annulus width delays the progression of mixing, and makes the effects of the velocity ratio more pronounced. For all cases the diffusion velocity streamlines in the scalar space representing the effects of molecular diffusion generally converge quickly to a curved manifold, whose curvature is reduced as mixing progresses. The curvature of the manifold increases significantly with the velocity and length scale ratios. Predicting the observed mixing path along the manifold as well as its dependence on the velocity and length scale ratios presents a challenge for mixing models. The results in the present study have implications for understanding and modelling multiscalar mixing in turbulent reactive flows.

Local turbulent energy dissipation rate in an agitated vessel: New approach to dimensionless definition

Using theory of turbulence, particularly using turbulence spectrum analysis, the relations e* = e/(u 4/ν) = const., vK/u = const. and Λ/ηK = const. were derived. Assuming that u ∝ (Nd) from this it follows that the widely used dimensionless local turbulent energy dissipation rate defined as e/((N 3 d 2) is directly proportional to impeller Reynolds number, i.e. e/((N 3 d 2) ∝ Re, and length scale ratio Λ/d is indirectly proportional to impeller Reynolds number, i.e. Λ/d ∝ Re–1, in an agitated vessel at high Reynolds number. The relations obtained by turbulence spectrum analysis were used for estimation of local turbulent energy dissipation rates experimentally measured by Stahl Wernersson and Tragardh (1998, 1999) covering the range of Re = 87600–910200 and own experimental data covering the range of Re = 50000–189000. The experiments have been performed in tanks of 300 mm and 400 mm in the inner diameter for three different viscosities and for various impeller rotational speeds.

Heat transfer in production and decay regions of grid-generated turbulence

Heat transfer measurements around the centreline circumference of a cylinder in crossflow are performed in a wind tunnel. The cylinder is placed at several stations downstream of three turbulence-generating grids with different geometries and different blockage ratios σg: a regular grid (RG60) with σg=32%, a fractal-square grid (FSG17) with σg=25% and a single-square grid (SSG) with σg=20%. Measurements are performed at 20 stations for 3 nominal Reynolds numbers (based on the diameter D of the cylinder) Re∞=11,100,24,500,37,900. Hot-wire measurements are performed along the centreline, without the cylinder in place, to characterise the flow downstream of the grids. The extent of the turbulence production region, where the turbulence intensity Tu increases with the streamwise distance x from the grid, is higher for SSG and more so for FSG17 than for RG60. The angular profiles of the Nusselt number Nu are measured in the production regions of these two grids and are compared to those obtained in the decay regions, where Tu decreases with x. This comparison is made at locations with approximately same Tu. It is found that, for SSG, Nu/Re0.5 on the front of the cylinder (boundary layer region) is lower in the production region than in the decay region. This is explained by the presence of clear and intense vortex shedding in the production region of SSG which reduces the turbulent fluctuations which are “effective” in enhancing the heat transfer across a laminar boundary layer. For higher Re∞, the values of Nu/Re0.5 on the front of the cylinder are higher in the production region of FSG17 than in that of SSG, despite Tu being higher for SSG. This is consistent with a lower intermittency of the flow for FSG17 caused by the presence of the fractal geometrical iterations. The recovery of Nu on the back of the cylinder (wake region) is appreciably higher in the production region than in the decay region for both FSG17 and for SSG. This can be due to the lower integral length scale ratio Lu/D in the production region and suggests, for the same Re∞, a reduction of the vortex formation length downstream of the cylinder, possibly promoted by the interaction between the wakes of the bars of the grid and the wake of the cylinder. At a large distance from the grids, the heat transfer enhancement is higher and it is more efficient for FSG17 and for SSG than for RG60. For high values of x in the turbulence decay region of the grids, the values of Nu‾ (circumferential average of Nu) are similar for FSG17 and for SSG and they are both appreciably higher than for RG60. This happens despite both FSG17 and SSG having a lower blockage ratio than RG60. The use of FSG17 has the practical advantage of combining high heat transfer rates on the cylinder with a weak vortex shedding from the grid.

Generating and controlling homogeneous air turbulence using random jet arrays

The use of random jet arrays, already employed in water tank facilities to generate zero-mean-flow homogeneous turbulence, is extended to air as a working fluid. A novel facility is introduced that uses two facing arrays of individually controlled jets (256 in total) to force steady homogeneous turbulence with negligible mean flow, shear, and strain. Quasi-synthetic jet pumps are created by expanding pressurized air through small straight nozzles and are actuated by fast-response low-voltage solenoid valves. Velocity fields, two-point correlations, energy spectra, and second-order structure functions are obtained from 2D PIV and are used to characterize the turbulence from the integral-to-the Kolmogorov scales. Several metrics are defined to quantify how well zero-mean-flow homogeneous turbulence is approximated for a wide range of forcing and geometric parameters. With increasing jet firing time duration, both the velocity fluctuations and the integral length scales are augmented and therefore the Reynolds number is increased. We reach a Taylor-microscale Reynolds number of 470, a large-scale Reynolds number of 74,000, and an integral-to-Kolmogorov length scale ratio of 680. The volume of the present homogeneous turbulence, the largest reported to date in a zero-mean-flow facility, is much larger than the integral length scale, allowing for the natural development of the energy cascade. The turbulence is found to be anisotropic irrespective of the distance between the jet arrays. Fine grids placed in front of the jets are effective at modulating the turbulence, reducing both velocity fluctuations and integral scales. Varying the jet-to-jet spacing within each array has no effect on the integral length scale, suggesting that this is dictated by the length scale of the jets.

Pulsatile electroosmotic flow in a microcapillary with the slip boundary condition

The pulsatile electroosmotic flow (PEOF) of a Newtonian fluid in a circular microchannel with slippage at the surface is theoretically analyzed. It is assumed that the electroosmotic flow is started from rest by the sudden imposition of a time-dependent external electric field. The PEOF is controlled by the following dimensionless parameters: the normalized slip length, δ, defined as the ratio of the Navier length to the microcapillary radius; the angular Reynolds number, Rω, which quantifies the competition between the time scale for the diffusion of momentum across the microcapillary and the externally imposed time scale due to the oscillatory electric field; the parameter ɛ, which characterizes the amplitude of the oscillating electric field; the electrokinetic parameter κ¯, defined as the ratio of the characteristic length scale to the Debye length; and the ionic energy parameter, α, which compares the electric potential at the surface to the thermal potential. The analysis is conducted for low and high zeta potentials; in the former case, an analytical solution is obtained, whereas in the latter, a numerical solution is found. The results reveal that the volumetric flow rate is notably increased in a microchannel with slippage at the wall surface.

A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory

The isogeometric analysis associated with a novel quasi-3D shear deformation theory is proposed to investigate size-dependent behaviours of functionally graded microplates. The modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The proposed approach is successfully applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions in which some benchmark numerical examples are presented. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and aspect ratios on the responses of the microplates.

Numerical investigation of the effect of pressure on heat release rate in iso-octane premixed turbulent flames under conditions relevant to SI engines

A series of direct numerical simulations (DNS) of iso-octane/air turbulent premixed flames in the thin reaction zones regime have been performed in order to investigate the effect of pressure on heat release rate under conditions relevant to spark-ignition (SI) engines (up to 20 bar and 800 K in the unburnt gas). Chemistry is represented by a reduced kinetics mechanism containing 74 species and 976 reactions (reduced from CaltechMech). The effect of pressure has been isolated by fixing the Karlovitz numbers, the Lewis numbers, and the ratio of integral length scale to laminar flame thickness. On one hand, the results suggest that pressure has very limited effect on the mean heat release rate, such that turbulent burning velocity is proportional to the turbulent surface area. In addition, while the chemical pathways are strongly affected by pressure in laminar flames, the global effect of turbulence on these pathways is negligible, independent of pressure. On the other hand, the local distribution of heat release rate was found to be significantly affected by pressure through differential diffusion-chemistry effects.

Vorticity isotropy in high Karlovitz number premixed flames

The isotropy of the smallest turbulent scales is investigated in premixed turbulent combustion by analyzing the vorticity vector in a series of high Karlovitz number premixed flame direct numerical simulations. It is found that increasing the Karlovitz number and the ratio of the integral length scale to the flame thickness both reduce the level of anisotropy. By analyzing the vorticity transport equation, it is determined that the vortex stretching term is primarily responsible for the development of any anisotropy. The local dynamics of the vortex stretching term and vorticity resemble that of homogeneous isotropic turbulence to a greater extent at higher Karlovitz numbers. This results in small scale isotropy at sufficiently high Karlovitz numbers and supports a fundamental similarity of the behavior of the smallest turbulent scales throughout the flame and in homogeneous isotropic turbulence. At lower Karlovitz numbers, the vortex stretching term and the vorticity alignment in the strain-rate tensor eigenframe are altered by the flame. The integral length scale has minimal impact on these local dynamics but promotes the effects of the flame to be equal in all directions. The resulting isotropy in vorticity does not reflect a fundamental similarity between the smallest turbulent scales in the flame and in homogeneous isotropic turbulence.

Effects of pressure waves on the stability of flames propagating in tubes

Numerical simulations were performed to study the effects of pressure waves on the evolution and stability of flames propagating in tubes. The model is the fully compressible reactive Navier–Stokes equations coupled to a calibrated one-step chemical-diffusive model for combustion in a stoichiometric hydrogen–air mixture. The numerical solution method is high order in space and time, and adaptive mesh refinement provides adequate resolution of flames, boundary layers, acoustic waves, and all of their interactions. The influence of tube length scale and aspect ratio was examined for a range of tube sizes that produce tulip flames (TFs) and series of distorted tulip flames (DTFs). The simulations show that pressure waves and acoustic properties of the tube play an important role in the flame evolution, specifically in the formation and evolution of the series of increasingly wrinkled DTFs. A time scale and pressure wave analysis of the results, combined with a linear analysis to give the growth rate of the Rayleigh–Taylor instability (RTI), shows that the RTI is a primary cause for the initiation of DTFs.

Characterization of aerosol Stokes number in 90° bends and idealized extrathoracic airways

Prediction of aerosol deposition in the respiratory system is important for improving the efficiency of inhaled drug delivery and for assessing the toxicity of airborne pollutants. Deposition is typically reported as a function of a global Stokes number which is based on a reference flow timescale, or the ratio of the characteristic flow length and velocity scales. In reality, however, particles experience varying flow timescales as they are advected through the airways, which motivates the use of an instantaneous Stokes number based on the local properties of the flow field. We then define the effective Stokes number as the time-average of the instantaneous value. This effective Stokes number thus encapsulates the flow history and geometric variability, and provides a more detailed account of the particle trajectory in the flow. Laminar and turbulent flows in a curved pipe are examined first and provide a simplified, or canonical, configuration of the flow in the upper airways. They are followed by a study of turbulent flow in an idealized mouth–throat geometry. Our results demonstrate that the effective Stokes number can deviate significantly from the traditional value based solely on the reference flow timescale. In addition, the effective Stokes number shows a clear correlation with deposition efficiency and can therefore be used to determine optimal aerosol release locations in order to minimize extrathoracic losses.