Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

Analysis of composite single lap joints using numerical and experimental approach

Adhesives are widely used to execute the assembly of aerospace and automotive structures due to their ability to join dissimilar materials, reduced stress concentration, and improved fatigue resistance. The mechanical behavior of adhesive joints can be studied either using analytical models or by conducting mechanical tests. However, the complexity owing to multiple interfaces, layers with different properties, material and geometric nonlinearity and its three-dimensional nature combine to increase the difficulty in obtaining an overall system of governing equations to predict the joint behavior. On the other hand, experiments are often time consuming and expensive due to a number of parameters involved. Finite element analysis (FEA) is profoundly used in recent years to overcome these limitations. The work presented in this paper involves the finite element modeling and analysis of a composite single lap joint where the adhesive-adherend interface region was modeled using connector elements. The computed stresses were compared with the experimental stresses obtained using digital image correlation technique. The results showed an agreement. Further, the failure load predicted using FEA was found to be closer to the actual failure load obtained by mechanical tests.

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I-3/I-1 shows a power-law behavior with strain amplitude. In addition, I-3/I-1 and the elastic component of stress amplitude sigma(E)(0) show a very prominent maximum at the strain value where the number density (n(v)) of the Taylor vortices is maximum. A subsequent increase in applied strain (gamma) results in the distortions of the vortices and a concomitant decrease in n(v), accompanied by a sharp drop in I-3 and sigma(E)(0). The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of gamma corresponding to the peak of I-3, similar to that observed for hard-sphere glasses.

Shear induced crystallization in different polymorphic forms of PVDF induced by surface functionalized MWNTs in PVDF/PMMA blends

Shear induced crystallization in PVDF/PMMA blends, especially at higher fractions of PMMA, can be quite interesting in understanding the structure-property correlation and processing of these blends. In a recent submission (Phys. Chem. Chem. Phys., 2014, 16, 2693-2704), we clearly demonstrated, using dielectric spectroscopy, that the origin of segmental relaxations concerning the crystalline segments of PVDF in PVDF/PMMA blends in the presence of MWNTs (multiwalled nanotubes) was strongly contingent on the size of the crystallite. We now understand that the fraction of PMMA in the blends governs the origin of polymorphism in PVDF. This motivated us to systematically study the effect of shear on the crystallization behavior of PVDF especially in blends with different polymorphic forms of PVDF. Two model blends were selected; one with a mixture of alpha and beta crystals and the other predominantly rich in alpha crystals. Initially, physical ageing, at different oscillation frequencies (1 rad s(-1) and 0.1 rad s(-1)), was monitored by melt rheology and subsequently, the effect of steady shear was probed in situ without changing the history of the samples. Intriguingly, the rate of crystallization was observed to be significantly higher for higher oscillation frequencies, which essentially suggest that shear has induced crystallization in the blends. More interestingly, the effect of steady shear was more pronounced in the blends rich in alpha crystals (bigger crystallites as observed from SAXS) and at lower oscillation frequencies.

Shear-imposed falling film

The study of a film falling down an inclined plane is revisited in the presence of imposed shear stress. Earlier studies regarding this topic (Smith, J. Fluid Mech., vol. 217, 1990, pp. 469-485; Wei, Phys. Fluids, vol. 17, 2005a, 012103), developed on the basis of a low Reynolds number, are extended up to moderate values of the Reynolds number. The mechanism of the primary instability is provided under the framework of a two-wave structure, which is normally a combination of kinematic and dynamic waves. In general, the primary instability appears when the kinematic wave speed exceeds the speed of dynamic waves. An equality criterion between their speeds yields the neutral stability condition. Similarly, it is revealed that the nonlinear travelling wave solutions also depend on the kinematic and dynamic wave speeds, and an equality criterion between the speeds leads to an analytical expression for the speed of a family of travelling waves as a function of the Froude number. This new analytical result is compared with numerical prediction, and an excellent agreement is achieved. Direct numerical simulations of the low-dimensional model have been performed in order to analyse the spatiotemporal behaviour of nonlinear waves by applying a constant shear stress in the upstream and downstream directions. It is noticed that the presence of imposed shear stress in the upstream (downstream) direction makes the evolution of spatially growing waves weaker (stronger).

Effect of hydrogen on the yielding behavior and shear transformation zone volume in metallic glass ribbons

The effect of hydrogen (H) charging on the shear yield strength (tau(max)) and shear transformation zone volume (Omega) of Ni-Nb-Zr metallic glass ribbons, with varying Zr content, were studied through the first pop-in loads during nanoindentation. Weight gain measurements after H charging and desorption studies were utilized to identify how the total H absorbed during charging is partitioned into mobile and immobile (or trapped) parts. These, in turn, indicate the significant role of H mobility in the amorphous structure on the yielding behavior. In high-Zr alloys, tau(max) increases significantly whereas Omega decreases. In low-Zr alloys, a slight decrease in tau(max) and increase in Omega were noted. These experimental observations are rationalized in terms of the mobility of the absorbed H in the amorphous structure and the possible role of it in the shear transformation zone dynamics during deformation of the metallic glass. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Dynamic Site Characterization and Correlation of Shear Wave Velocity with Standard Penetration Test `N' Values for the City of Agartala, Tripura State, India

Seismic site characterization is the basic requirement for seismic microzonation and site response studies of an area. Site characterization helps to gauge the average dynamic properties of soil deposits and thus helps to evaluate the surface level response. This paper presents a seismic site characterization of Agartala city, the capital of Tripura state, in the northeast of India. Seismically, Agartala city is situated in the Bengal Basin zone which is classified as a highly active seismic zone, assigned by Indian seismic code BIS-1893, Indian Standard Criteria for Earthquake Resistant Design of Structures, Part-1 General Provisions and Buildings. According to the Bureau of Indian Standards, New Delhi (2002), it is the highest seismic level (zone-V) in the country. The city is very close to the Sylhet fault (Bangladesh) where two major earthquakes (M (w) > 7) have occurred in the past and affected severely this city and the whole of northeast India. In order to perform site response evaluation, a series of geophysical tests at 27 locations were conducted using the multichannel analysis of surface waves (MASW) technique, which is an advanced method for obtaining shear wave velocity (V (s)) profiles from in situ measurements. Similarly, standard penetration test (SPT-N) bore log data sets have been obtained from the Urban Development Department, Govt. of Tripura. In the collected data sets, out of 50 bore logs, 27 were selected which are close to the MASW test locations and used for further study. Both the data sets (V (s) profiles with depth and SPT-N bore log profiles) have been used to calculate the average shear wave velocity (V (s)30) and average SPT-N values for the upper 30 m depth of the subsurface soil profiles. These were used for site classification of the study area recommended by the National Earthquake Hazard Reduction Program (NEHRP) manual. The average V (s)30 and SPT-N classified the study area as seismic site class D and E categories, indicating that the city is susceptible to site effects and liquefaction. Further, the different data set combinations between V (s) and SPT-N (corrected and uncorrected) values have been used to develop site-specific correlation equations by statistical regression, as `V (s)' is a function of SPT-N value (corrected and uncorrected), considered with or without depth. However, after considering the data set pairs, a probabilistic approach has also been presented to develop a correlation using a quantile-quantile (Q-Q) plot. A comparison has also been made with the well known published correlations (for all soils) available in the literature. The present correlations closely agree with the other equations, but, comparatively, the correlation of shear wave velocity with the variation of depth and uncorrected SPT-N values provides a more suitable predicting model. Also the Q-Q plot agrees with all the other equations. In the absence of in situ measurements, the present correlations could be used to measure V (s) profiles of the study area for site response studies.

Discussion of ``Atterberg Limits and Remolded Shear Strength-Water Content Relationships''

The present discussion tries to bring out the importance of clay mineralogical composition of fine-grained soils on their liquid limit behaviour. It reinforces the author's observation that the undrained shear strengths at liquid limit water content and at plastic limit water content are not unique.

The effect of gamma-gamma ` interface on the tensile and shear strengths of nickel-based superalloys: A first-principles study

First-principles density functional theory has been used to evaluate the shear and cleavage strength in terms of Griffith work and generalized stacking fault energy (GSF) of (001) plane for gamma, gamma' and gamma-gamma' system as a function of distance from the gamma/gamma' interface. Calculation of Griffith work suggests higher cleavage energy for bulk gamma as compared to gamma' while the GSF calculation suggests higher shear strength for bulk gamma' as compared to gamma. It has been found that the shear strength of the cubic plane of the gamma/gamma' interface is marginally lower than those of bulk gamma and gamma' phases. (C) 2014 Elsevier B.V. All rights reserved.

Hydrodynamic instability and shear layer effect on the response of an acoustically excited laminar premixed flame

Combustion instabilities can cause serious problems which limit the operating envelope of low-emission lean premixed combustion systems. Predicting the onset of combustion instability requires a description of the unsteady heat release driving the instability, i.e., the heat release response transfer function of the system. This study focuses on the analysis of fully coupled two-way interactions between a disturbance field and a laminar premixed flame that incorporates gas expansion effects by solving the conservation equations of a compressible fluid. Results of the minimum and maximum flame front deflections are presented to underline the impact of the hydrodynamic instability on the flame and the shear layer effect on the initial flame front wrinkling which is increased at decreasing gas expansion. These phenomena influence the magnitude of the burning area and burning area rate response of the flame at lower frequency excitation more drastically than reduced-order model (ROM) predictions even for low temperature ratios. It is shown that the general trend of the flame response magnitudes can be well captured at higher frequency excitation, where stretch effects are dominant. The phase response is influenced by the DL mechanism, which cannot be captured by the ROM, and by the resulting discrepancy in the flame pocket formation and annihilation process at the flame tip. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved,

Wave propagation analysis in adhesively bonded composite joints using the wavelet spectral finite element method

A wavelet spectral finite element (WSFE) model is developed for studying transient dynamics and wave propagation in adhesively bonded composite joints. The adherands are formulated as shear deformable beams using the first order shear deformation theory (FSDT) to obtain accurate results for high frequency wave propagation. Equations of motion governing wave motion in the bonded beams are derived using Hamilton's principle. The adhesive layer is modeled as a line of continuously distributed tension/compression and shear springs. Daubechies compactly supported wavelet scaling functions are used to transform the governing partial differential equations from time domain to frequency domain. The dynamic stiffness matrix is derived under the spectral finite element framework relating the nodal forces and displacements in the transformed frequency domain. Time domain results for wave propagation in a lap joint are validated with conventional finite element simulations using Abaqus. Frequency domain spectrum and dispersion relation results are presented and discussed. The developed WSFE model yields efficient and accurate analysis of wave propagation in adhesively-bonded composite joints. (C) 2014 Elsevier Ltd. All rights reserved.

Wall-mode instability in plane shear flow of viscoelastic fluid over a deformable solid

The linear stability analysis of a plane Couette flow of an Oldroyd-B viscoelastic fluid past a flexible solid medium is carried out to investigate the role of polymer addition in the stability behavior. The system consists of a viscoelastic fluid layer of thickness R, density rho, viscosity eta, relaxation time lambda, and retardation time beta lambda flowing past a linear elastic solid medium of thickness HR, density rho, and shear modulus G. The emphasis is on the high-Reynolds-number wall-mode instability, which has recently been shown in experiments to destabilize the laminar flow of Newtonian fluids in soft-walled tubes and channels at a significantly lower Reynolds number than that for flows in rigid conduits. For Newtonian fluids, the linear stability studies have shown that the wall modes become unstable when flow Reynolds number exceeds a certain critical value Re c which scales as Sigma(3/4), where Reynolds number Re = rho VR/eta, V is the top-plate velocity, and dimensionless parameter Sigma = rho GR(2)/eta(2) characterizes the fluid-solid system. For high-Reynolds-number flow, the addition of polymer tends to decrease the critical Reynolds number in comparison to that for the Newtonian fluid, indicating a destabilizing role for fluid viscoelasticity. Numerical calculations show that the critical Reynolds number could be decreased by up to a factor of 10 by the addition of small amount of polymer. The critical Reynolds number follows the same scaling Re-c similar to Sigma(3/4) as the wall modes for a Newtonian fluid for very high Reynolds number. However, for moderate Reynolds number, there exists a narrow region in beta-H parametric space, corresponding to very dilute polymer solution (0.9 less than or similar to beta < 1) and thin solids (H less than or similar to 1.1), in which the addition of polymer tends to increase the critical Reynolds number in comparison to the Newtonian fluid. Thus, Reynolds number and polymer properties can be tailored to either increase or decrease the critical Reynolds number for unstable modes, thus providing an additional degree of control over the laminar-turbulent transition.

Image-Segmentation Technique to Analyze Deformation Profiles in Different Direct Shear Tests

Results from interface shear tests on sand-geosynthetic interfaces are examined in light of surface roughness of the interacting geosynthetic material. Three different types of interface shear tests carried out in the frame of direct shear-test setup are compared to understand the effect of parameters like box fixity and symmetry on the interface shear characteristics. Formation of shear bands close to the interface is visualized in the tests and the bands are analyzed using image-segmentation techniques in MATLAB. A woven geotextile with moderate roughness and a geomembrane with minimal roughness are used in the tests. The effect of surface roughness of the geosynthetic material on the formation of shear bands, movement of sand particles, and interface shear parameters are studied and compared through visual observations, image analyses, and image-segmentation techniques.

Shear strength characteristics of mechanically biologically treated municipal solid waste (MBT-MSW) from Bangalore

Strength and stiffness properties of municipal solid waste (MSW) are important in landfill design. This paper presents the results of comprehensive testing of shear strength properties of mechanically biologically treated municipal solid waste (MBT-MSW) in laboratory. Changes in shear strength of MSW as a function of unit weight and particle size were investigated by performing laboratory studies on the MSW collected from Mavallipura landfill site in Bangalore. Direct shear tests, small scale and large scale consolidated undrained and drained triaxial tests were conducted on reconstituted compost reject MSW samples. The triaxial test results showed that the MSW samples exhibited a strain-hardening behaviour and the strength of MSW increased with increase in unit weight. Consolidated drained tests showed that the mobilized shear strength of the MSW increased by 40% for a unit weight increase from 7.3 kN/m(3) to 10.3 kN/m(3) at 20% strain levels. The mobilized cohesion and friction angle ranged from 5 to 9 kPa and 8 degrees to 33 degrees corresponding to a strain level of 20%. The consolidated undrained tests exhibited reduced friction angle values compared to the consolidated drained tests. The friction angle increased with increase in the unit weight from 8 degrees to 55 degrees in the consolidated undrained tests. Minor variations were found in the cohesion values. Relationships for strength and stiffness of MSW in terms of strength and stiffness ratios are developed and discussed. The stiffness ratio and the strength ratio of MSW were found to be 10 and 0.43. (c) 2015 Elsevier Ltd. All rights reserved.

Multi-transform based spectral element to include first order shear deformation in plates

For obtaining dynamic response of structure to high frequency shock excitation spectral elements have several advantages over conventional methods. At higher frequencies transverse shear and rotary inertia have a predominant role. These are represented by the First order Shear Deformation Theory (FSDT). But not much work is reported on spectral elements with FSDT. This work presents a new spectral element based on the FSDT/Mindlin Plate Theory which is essential for wave propagation analysis of sandwich plates. Multi-transformation method is used to solve the coupled partial differential equations, i.e., Laplace transforms for temporal approximation and wavelet transforms for spatial approximation. The formulation takes into account the axial-flexure and shear coupling. The ability of the element to represent different modes of wave motion is demonstrated. Impact on the derived wave motion characteristics in the absence of the developed spectral element is discussed. The transient response using the formulated element is validated by the results obtained using Finite Element Method (FEM) which needs significant computational effort. Experimental results are provided which confirms the need to having the developed spectral element for the high frequency response of structures. (C) 2015 Elsevier Ltd. All rights reserved.