Mean Strain Rate Research Articles

The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions

Strong turbulence at a water–air free surface can lead to splashing and a disconnected surface as in a breaking wave. Averaging to obtain boundary conditions for such flows first requires equations of motion for the two-phase region. These are derived using an integral method, then averaged conservation equations for mass and momentum are obtained along with an equation for the turbulent kinetic energy in which extra work terms appear. These extra terms include both the mean pressure and the mean rate of strain and have similarities to those for a compressible fluid. Boundary conditions appropriate for use with averaged equations in the body of the water are obtained by integrating across the two-phase surface layer.A number of ‘new’ terms arise for which closure expressions must be found for practical use. Our knowledge of the properties of strong turbulence at a free surface is insufficient to make such closures. However, preliminary discussions are given for two simplified cases in order to stimulate further experimental and theoretical studies.Much of the turbulence in a spilling breaker originates from its foot where turbulent water meets undisturbed water. A discussion of averaging at the foot of a breaker gives parameters that may serve to measure the ‘strength’ of a breaker.

Taylor impact test for ductile porous materials—Part 1: theory

Taylor tests have been commonly employed to determine dynamic yield stress of solids at a high strain rate. In this paper, the original Taylor model is extended in order to provide a theoretical basis for testing ductile porous materials. The key difference between solids and porous materials in this respect is that porous materials are compressible and their density changes with the compressive strain. Calculations have been made for porous materials with a relative density that is a linear function of compressive strain e, i.e., ρ/ ρ 0=1+ ae. The final length of the projectile after impact, L 1/ L, is plotted against parameter ρ 0 U 2/ Y (see Fig. 9) and this plot is used in a Taylor test to determine the dynamic yield stress. The mean strain rate of the test can be estimated from Eqs. (21) or (22). In a companion paper (Int J Impact Eng), experiments for dynamic yield stress of porous materials will be reported based on the present theoretical analysis.

Opposed jets with small separations and their implications for the extinction of opposed flames

Profiles of static pressure and the mean and rms of velocity fluctuations in opposed isothermal jets were measured with a combination of static-pressure probes, hot-wire and laser-Doppler velocimetry. The static pressures close to the axis at the outlet planes of the two jets increased as the separation was reduced below three diameters, with measurable and increasing radial flow below 0.8 diameters. This, in turn, reduced the mean axial velocity on the axis of symmetry. The mean strain rate along the stagnation plane was near constant over much of the impingement region for separations greater than 1.0 diameter and a maximum occurred at radial distances which increased as the jet separation was reduced below this value. The maximum values stemmed from the exit-plane profiles and were larger than the bulk strain rate by a factor which increased with radial distance from 2 to 5 for separations of 0.8 and 0.2 diameters.

Strain rates measured along the wrinkled flame contour within turbulent non-premixed jet flames

The thin, wrinkled CH reaction layers within moderate- (Re = 9,100) and high- (18,600) Reynolds-number turbulent non-premixed jet flames were identified by using planar laser-induced fluorescence, and the in-plane strain rates on these reaction layers were measured using simultaneous Particle Imaging Velocimetry (PIV). The PIV diagnostics resolved the Taylor scale; the strain-limited diffusion length scale was fully resolved for half the cases studied and nearly resolved for the others. In the high-Reynolds-number jet, instantaneous strain rates on the flame surface are highly intermittent, with peak values exceeding 10,000 s −1. Mean strain rates, conditioned on the CH-peak contour, are relatively constant (150 s −1) in the Re = 9100 flame and increase (650–1700 s −1) with axial location in the Re = 18,600 flame, resulting from the flame wrinkling process. The CH-layer thickness does not appear to respond in amplitude or in phase with the strain field, indicating that quasi-steady conditions do not occur. The strain field apparently oscillates at frequencies as high as 5–10 kHz—which is the inverse of the crossing time of integral-scale eddies—perhaps because only the low-frequency component of strain effectively acts on the flame. Mean axial velocities, conditioned on the CH-peak contour, were found to remain constant from the flame base to tip and to approximately equal the product of the stoichiometric mixture fraction and the fuel-exit velocity, in agreement with prediction.

Mechanical and hydraulic properties of till beneath Bakaninbreen, Svalbard

AbstractBakaninbreen, Svalbard, was in the late phase of a prolonged surge during 1995–96. In order to investigate the nature of the basal mechanical and hydraulic regime, sets of tilt sensors equipped with pore-pressure sensors were installed into the basal till layer. Water-pressure transducers were also installed in the boreholes above the ice–till interface. During 1995, the measured mean strain rate in the till was 0.44 a−1 up-glacier of the surge front, while down-glacier the rate was 0.04 a−1. Our interpretation indicates that deformation was the dominant component of basal motion. Strain rates fluctuated strongly, and periods of both positive (down-glacier) and negative (up-glacier) strain occurred. No consistent relationship was apparent between effective pressure and strain rate within the basal till layer. The viscosity of the basal sediments ranged from 1.3 × 1012 to 3.4 × 1012 Pa s. Such high values suggest that the till layer beneath Bakaninbreen may be partially frozen. Analysis of simultaneous measurements of pore-water and borehole water pressure suggests the hydraulic diffusivity of the till layer ranges from 1.2 to 5.0 × 10−6 m2 s−1, and the hydraulic conductivity from 3.2 × 10−7 to 7.7 × 10−8 m s−1.

A Numerical Study of Transient Ignition in a Counterflow Nonpremixed Methane-Air Flame Using Adaptive Time Integration

This paper presents a computational algorithm to predict highly-transient flame behavior in counter-flow situations. The first objective of the paper is to extend the transient counterflow problem to incorporate some gasdynamic compressibility effects, yet retain the desirable similarity structure. By relaxing assumptions in earlier formulations, the computational algorithms can deliver high accuracy even in periods of extremely rapid transients, like combustion ignition. The algorithms are demonstrated on two combustion-ignition problems for methane-air, counterflow, nonpremixed flames. The first concerns the ignition transient in a steady strain field. The second concerns the effects of a high-frequency oscillatory strain field on the ignition process. The results reveal that, when the mean strain rate is near the steady ignition limit, the ignition process is highly sensitive to the details of the strain-rate fluctuations.

Dynamic materials modelling concepts applied to analysis of hot rolling of commercial aluminium alloys

A typical industrial hot rolling operation applied to a commercial Al–1%Mg alloy has been analysed in terms of some concepts from dynamic materials modelling (DMM), particularly the so called dissipator co-content J and the efficiency of power dissipation through microstructural changes η. The calculation of the parameter η for every deformation condition of the hot rolling schedule has been conducted assuming that this variable depends not only on the mean deformation temperature and strain rate but also on the strain applied to the material. All the analysis has been conducted on the basis of a constitutive equation previously determined for this material on a rational basis, which is capable of describing the strain, strain rate, and temperature dependence of the flow stress. It has been determined that, for this material, η can be significantly dependent on strain under certain deformation conditions, particularly low deformation temperatures and relatively high strain rates. It has also been shown that for the materials analysed, η is much more dependent on deformation temperature than on strain rate. A comparative analysis carried out with aluminium of various purities indicates that η is much lower for the alloy when it is deformed under similar conditions. In this sense, it has been suggested that such results could be interpreted in terms of the impurity content of the material and the interaction of the alloying atoms with the dislocation structure developed during high temperature deformation. However, this is only possible if the hypothesis advanced by Prasad and co-workers, that the power dissipation efficiency is associated with the dynamic microstructural processes that occur during deformation, is considered valid. The present results indicate that, contrary to previous findings, in terms of DMM concepts there are no specific conditions of temperature and strain rate for the optimum processing of the materials investigated.

Influence of Curvature-Driven Favorable Pressure Gradient on Supersonic Turbulent Boundary Layer

The influence of a wall curvature-driven favorable pressure gradient on the turbulent and mean flow properties of a Mach 2.9 boundary layer (Re x = 1.23 × 10 7 ) were investigated using laser Doppler velocimetry. A zero-pressure-gradient boundary layer (Re x = 1.35 x 10 7 ) was also mapped for comparative purposes. In addition to the typical mean and turbulent statistical properties, the data in this study were acquired with the specific goal of resolving the mean strain rates in all three coordinate directions; these data allowed for measurement of the extra Reynolds shear-stress production terms. The maximum magnitude of the distortion was 0.1, which indicated that the pressure gradient was strong. The expected stabilizing effect on the turbulence intensities was observed. Near the wall, the kinematic Reynolds shear stresses were reduced by approximately 75%. Above y/δ 0.4 the favorable pressure gradient induced a negative Reynolds shear stress, whereas the main strain rate remained positive. The reduced shear-stress levels were attributed to negative overall production and the use of a body-intrinsic coordinate system for data collection

Extinction Limits of Opposed Jet Turbulent Premixed Methane Air Flames with Sprays of Water and NaCI-Water Solution

An experimental study on water mist extinction of turbulent premixed flames is described. The aim of the study is to compare the extinction limits of opposed jet turbulent methane/air flames with and without the addition of water mist, and to study the influence of several parameters including the structure of water mist in terms of droplet size and mass fraction of the condensed phase, mean strain rate and equivalence ratio. The effect of NaCI water solution on premixed flame extinction is also presented. An air assisted atomizer is developed to produce and control the water mist. The structure of the water mist is characterized by a Phase Doppler Anemometer. Water mist interaction with three different configurations of the opposed jet premixed flames is explored and the results arc discussed by introducing a parameter representing the water mist efficiency.

磁性材料の化学 ＭｎＡｌＣ磁石の異方性化のメカニズム

Effect of powder particle size, extrusion temperature and mean strain rate on anisotropy of MnAlC alloy was investigated. The anisotropy proceeding mechanism of MnAlC alloy was considered by anisotropy investigation with specimens during exrusion.MnAlC powder was made by Ar gas atomizing process, classified fixed particle sizes and was compacted by extrusion at extrusion temperature: 853-993K and mean strain rate: 0.005-0.05/s.Anisotropy of MnAlC formed was found to improve at lower temperature, finer particle size and lower strain rate. It was considered to be related to the homogeneity of τ phase and the crystal grain size. It was found that anisotropy of MnAlC magnet was increased as deformation right after the start of extrusion and saturated at the part on the way of extrusion.This phenomenon can be explained by the two deformation areas, one is that dynamic recrystallization proceeds as keeping the former crystal orientation according to the strain induced grain boundary migration mechanism, the other is that dynamic recrystallization proceeds with no relation to the former crystal orientation according to the nucleation and growth mechanism.

Measurements of the turbulent burning velocity and the structure of premixed flames on a low-swirl burner

A method has been developed to accurately determine the turbulent burning velocity in planar turbulent premixed flames stabilized by a low swirl. Six lean methane/air flames have been investigated covering the flamelet as well as the thin reaction zones regime. The probability of finding the instantaneous flame front is measured together with the velocity field by combining simultaneously OH–laser-induced predissociative fluorescence with either Rayleigh thermometry or particle image velocimetry (PIV). It is demonstrated that the turbulent flame brush thickness is independent of v� /sL and that the turbulent burning velocity agrees with predictions from a model equation for the flame surface area ratio using the level set approach. The measurements of the two-dimensional flowfield show a recirculation zone downstream of the flame stabilization area. This exhibits a comparable flow pattern to stagnation point flames. However, mean strain rates are much lower since the flames stabilize close to the burner exit, and the flame is not influenced by the recirculation zone. A comparison of the root-mean-square velocities obtained from Laser-Doppler Amemometry measurements to those determined by PIV show a good agreement. It can be shown that turbulence is attenuated in the flame zone and only moderately increased behind it.

Extinction Limits Of Opposed Jet Turbulent Premixed Methane Air Flames With Water Mist

An experimental study on water mist extinction of turbulent premixed tlames is described. The aim of the study is to compare the extinction limits of opposed jet turbulent methanelair flames with and without the addition of water mist, and to study the influence of several parameters including the structure of water mist in tenns of droplet size and mass fraction of the condensed phase, mean strain rate, equivalence ratio and turbulence. An existing opposed jet turbulent premixed flame experimenta! set-up is moditied to include a water mist production system. An air assisted atomizer is developed to produce and control the water mist. The structure of the water mist is characterized by a Phase Doppler Anemometer. Water mist interaction with three different configurations of opposed jet premixed tlames is explored and the results arc discussed by introducing a parameter representing the water mist efficiency.

On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence

The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]

Approach to isotropy in a smooth wall turbulent boundary layer

The approach to local isotropy in a smooth wall turbulent boundary layer is examined using measurements of velocity spectra and moments, up to order 4, of velocity increments. The ratio of the measured spectrum of the wall normal velocity fluctuation v to that calculated using isotropy from the measured spectrum of the longitudinal velocity fluctuation u, depends mainly on the Kolmogorov-normalized local mean strain rate and the Taylor microscale Reynolds number. These parameters also affect in a systematic way the departure from isotropy of the u− v spectral correlation coefficient and of the v increment moments.

Experimental investigation of turbulence generated by breaking waves in water of intermediate depth

This paper reports a set of laboratory data for breaking waves in the water of intermediate depth. A monochromatic wave train with a wave height of 14.5 cm and a wavelength of 121 cm was generated in a water depth, h, of 20 cm. The wave train breaks consistently at a distance of about 2h from the wave generator. The instantaneous velocity fields under the breaking waves on a two-dimensional vertical plane were measured by using the particle image velocimetry (PIV) technique. By repeating the same experiments twenty times and performing the ensemble average, mean velocity, mean vorticity, turbulence intensity, and other flow properties such as the Reynolds stress and the mean strain rate were calculated. Outside the aerated region, where the density of air bubbles is high, the experimental data show that the mean vorticity was of the same order of magnitude as (C/h) (≈6 s−1) with C being the phase speed. The maximum turbulence intensity outside the aerated region was in the order of magnitude of 0.1 C (≈11 cm/s). The time-averaged (over one wave period) turbulence intensity under the wave trough level was one order of magnitude smaller, i.e., it was about 0.04 C (≈4.8 cm/s). Based the experimental data, the transport equation for turbulent kinetic energy was further examined. The turbulence dissipation rate and its time scale were also estimated. Under the trough level at the measurement section, which was about 3h downstream from the breaking point, the turbulence production, and dissipation were of the same order of magnitude, but not identical. The turbulence advection, production, and dissipation were equally important, while the turbulence diffusion was almost negligible.

Assessment of Taylor's hypothesis and local isotropy due to strain applied to a nearly homogeneous and isotropic flow

The effect of variation of the integral length scale on the accuracy of Taylor’s hypothesis and the assumption of local isotropy when a mean strain is applied to a nearly homogeneous and isotropic, heated turbulent flow is investigated. The mean strain is produced by placing one of two cylinders downstream of the heated wire mesh. Results show, the mean strain rate where the directly measured variance of the streamwise spatial gradient differs by less than ten percent from the corresponding value computed using Taylor’s hypothesis and temporal derivative decreases with increasing the ratio of the integral length scale to the cylinder diameter.

Analyses of slow high-concentration flows of granular materials

A theory intended for slow, dense flows of cohesionless granular materials is developed for the case of planar deformations. By considering granular flows on very fine scales, one can conveniently split the individual particle velocities into fluctuating and mean transport components, and employ the notion of granular temperature that plays a central role in rapid granular flows. On somewhat larger scales, one can think of analogous fluctuations in strain rates. Both kinds of fluctuations are utilized in the present paper. Following the standard continuum approach, the conservation equations for mass, momentum and particle translational fluctuation energy are presented. The latter two equations involve constitutive coefficients, whose determination is one of the main concerns of the present paper. We begin with an associated flow rule for the case of a compressible, frictional, plastic continuum. The functional dependence of the flow rule is chosen so that the limiting behaviours of the resulting constitutive relations are consistent with the results of the kinetic theories developed for rapid flow regimes. Following Hibler (1977) and assuming that there are fluctuations in the strain rates that have, for example, a Gaussian distribution function, it is possible to obtain a relationship between the mean stress and the mean strain rate. It turns out, perhaps surprisingly, that this relationship has a viscous-like character. For low shear rates, the constitutive behaviour is similar to that of a liquid in the sense that the effective viscosity decreases with increasing granular temperature, whereas for rapid granular flows, the viscosity increases with increasing granular temperature as in a gas. The rate of energy dissipation can be determined in a manner similar to that used to derive the viscosity coefficients. After assuming that the magnitude of the strain-rate fluctuations can be related to the granular temperature, we obtain a closed system of equations that can be used to solve boundary value problems. The theory is used to consider the case of a simple shear flow. The resulting expressions for the stress components are similar to models previously proposed on a more ad hoc basis in which quasi-static stress contributions were directly patched to rate-dependent stresses. The problem of slow granular flow in rough-walled vertical chutes is then considered and the velocity, concentration and granular temperature profiles are determined. Thin boundary layers next to the vertical sidewalls arise with the concentration boundary layer being thicker than the velocity boundary layer. This kind of behaviour is observed in both laboratory experiments and in granular dynamics simulations of vertical chute flows.

A New Approach to Characterizing the Equilibrium States of the Reynolds Stress Anisotropy in Homogeneous Turbulence

Using representation theory, a system of three scalar invariant relationships for homogeneous turbulence is developed which is equivalent to the general algebraic relationship for the Reynolds stress anisotropy tensor at equilibrium. From these three relations, which account for any additional anisotropy effect, a single scalar, algebraic relationship between three state variables, the turbulent production-to-dissipation rate ratio, a scaled turbulent time scale, and a ratio of mean rotation rate and strain rate invariants, is derived. This provides a unique characterization for all planar homogeneous turbulent flows. With this result, equilibrium can be predicted based solely on the form of the pressure-strain rate closure model, including both linear and nonlinear models. Consequences of this formulation to the description of two-dimensional inhomogeneous flows and their prediction are also deduced.

Viscoelastic response of fibroblasts to tension transmitted through adherens junctions

Cytoplasmic deformation was monitored by observing the displacements of 200-nm green fluorescent beads microinjected into the cytoplasm of Swiss 3T3 fibroblasts. We noted a novel protrusion of nonruffling cell margins that was accompanied by axial flow of beads and cytoplasmic vesicles as far as 50 microm behind the protruding plasma membrane. Fluorescent analog cytochemistry and immunofluorescence localization of F-actin, alpha-actinin, N-cadherin, and beta-catenin showed that the protruding margins of deforming cells were mechanically coupled to neighboring cells by adherens junctions. Observations suggested that protrusion resulted from passive linear deformation in response to tensile stress exerted by centripetal contraction of the neighboring cell. The time dependence of cytoplasmic strain calculated from the displacements of beads and vesicles was fit quantitatively by a Kelvin-Voight model for a viscoelastic solid with a mean limiting strain of 0.58 and a mean strain rate of 4.3 x 10(-3) s(-1). In rare instances, the deforming cell and its neighbor spontaneously became uncoupled, and recoil of the protruding margin was observed. The time dependence of strain during recoil also fit a Kelvin-Voight model with similar parameters, suggesting that the kinetics of deformation primarily reflect the mechanical properties of the deformed cell rather than the contractile properties of its neighbor. The existence of mechanical coupling between adjacent fibroblasts through adherens junctions and the viscoelastic responses of cells to tension transmitted directly from cell to cell are factors that must be taken into account to fully understand the role of fibroblasts in such biological processes as wound closure and extracellular matrix remodeling during tissue development.

Slow Transients and Metastability in Wormlike Micelle Rheology

The steady-state nonlinear rheology of wormlike micellar systems is thought to be subject to shear banding (the underlying shear stress vs. strain rate curve σ(γ) is nonmonotonic). Shear banding may result in a plateau (σ(γ) = σp) in the measured flow curve (at controlled mean strain rate γ). We present new rheological data for aqueous CPyCl/NaSal (100 mM /60 mM). Steady-state flow curves published previously for this system (Rehage H. and Hoffmann H., Mol. Phys. 74 (1991) 933) have since been interpreted as shear-banded flow with top-jumping, in which the steady-state shear rate γ1 in the low shear band is the largest possible (γ 1 = γ 1 max , σ p = σ max ). That would rule out the existence of a metastable branch with a stress larger than σp. We show that such a branch does, however, exist (for temperatures in the range 20 - 25 °C). Similar results are found for a 100 mM/75 mM system. The time scale for relaxation of a metastable state onto true steady state flow, τ ss , is far longer than the Maxwell time of the fluid; this is consistent with shear banding. We observe τ ss ∼ (γ - γ c ) -P in the metastable regime (γ > γ 1 ), with p an exponent that depends on composition and temperature. The critical shear rate γ c is in some cases less than γ 1 so that no actual divergence of τ ss occurs. In at least one case, though, there is evidence for a physical divergence (γ c > γ 1 ) accompanied by a small window of shear rates, γ 1 < γ < γ c , for which τ ss is effectively infinite. In some respects the observed behaviour resembles that reported previously (Berret J.-F., Roux D.C. and Porte G., J. Phys. II Prance 4 (1994) 1261) for equimolar CPyCl/NaSal in 0.5 M NaCl. Those results were interpreted in terms of nucleation and growth of a shear-induced nematic phase. However the same explanation is unlikely for the low weight fractions (Φ ≤ 5%) used in our study.