Measurement of the first and second normal stress differences: Correlation of four experiments on a polyisobutylene/decalin solution “D1”

Pressure distribution measurements for a polyisobutylene/decalin solution D1 in the Truncated Cone-and-Plate (TCP) apparatus are combined with elastic hole pressures obtained for the same solution on the Lodge Stressmeter^® in order to provide two independent estimates of the second normal-stress difference (N ₂). The values ofN ₂ from the TCP apparatus, obtained by numerical differentiation of a function of the center-hole pressure and the pressure gradient, are in good agreement with measurements made on the same sample by Tanner et al. with a direct method, namely the Tilted Trough Experiment, and by Christiansen et al. with a method that requires an extrapolation to the pressure at the free surface of coneand-plate rheogoniometer data obtained with flush-mounted pressure transducers. The viscosities from the modified Stressmeter for low shear rates extend over five decades of shear rate, including a zero-shear-rate region, and agree with the data of Christiansen on a torque-driven flow. The Higashitani-Pritchard-Baird-Lodge (HPBL) equation relatingN ₁–N ₂ to the hole pressure gives good agreement with the data over a certain range of shear stress. The Newtonian hole pressures for several liquids at 20 and 46 °C compare well with a finite-element calculation for a two-dimensional Poiseuille flow. When the elastic hole pressures from the Stressmeter are combined with the extrapolated rim pressures from the TCP Apparatus in order to extract the value ofN ₂, an agreement betweenN ₂ from the center-hole pressure andN ₂ from the rim pressure can only be obtained up to a shear rate of about 40 s^–1, beyond which the value of –N ₂ from the rim pressure diverges abruptly to negative values. It is possible that this constitutes the first quantitative estimate of an edge effect in cone-and-plate rheometry. Alternatively, the elastic hole pressure in cone-and-plate flow is not equivalent to the elastic hole pressure in Poiseuille flow, at least at high shear rates. The data of Christiansen et al. with flush-mounted pressure transducers appear to confirm this second possibility. Finally, a single set of shift factors obeying the Williams, Landel and Ferry equation superposes the viscosity, the first and the second normal-stress difference within experimental scatter, which can be less than 1% for a certain combination of normal-stress differences. The data were recorded at 3, 20, 30, and 46 °C in the shear rate range 1–260 s^–1.     

“Thermal layer” effect in MHD: Interaction of a parallel shock with a layer of decreased density

Interaction of a parallel fast MHD shock with a layer of decreased density is discussed using ideal MHD approach. This is an extrapolation of gas dynamic thermal layer effect on ideal MHD. Computer simulations show that a magnetic field of a moderate intensity ( 1) may change the character of the flow for intermediate Mach numbers (M 5) and a new raking regime may occur which is not observed in the absence of a magnetic field. Self similar precursor analogous to that in gas dynamics may develop in the case of highM and low density in the layer but magnetic forces essentially decrease its growth rate. This problem appears in connection with cosmical shock propagation where planetary magnetic tails play the role of the thermal layer, and it may also be observed in the laboratory when the shock is strong enough to heat the walls ahead of it.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

A double-superposition global–local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach

A higher-order global–local theory is proposed based on the double-superposition concept for free vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied. Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account. Some dynamic buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time. Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm.     

Further Comments on “Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work”

This note is concerned with the assertion of Barletta and Nield (2009a) that “a fluid with a thermal expansion coefficient greater than that of a perfect gas (β > β _perfect gas) is of marginal or no interest in the framework of convection in porous media”, and that for a remark of Magyari (Transp. Porous Media, 2009) about the forced convection eigenflow solutions, the circumstance β > β _perfect gas does not represent “a sound physical basis”. Here, it is shown, however, that these assertions are in contradiction with the experimentally measured values of β for important technical fluids as e.g., air, nitrogen, carbon dioxide, and ammonia where, in the temperature range between −20 and +100°C, just the inequality β > β _perfect gas holds.     

3D reconstruction of the flow and vortical field in a rotating sharp “U” turn channel

Particle image velocimetry experiments have been carried out to obtain visualizations and measurements of the main and secondary flow fields in a square channel with a sharp “U” turn. Both the main and the secondary flow fields have been used to perform a 3D reconstruction of the mean flow and vortical fields in the turn region and in the outlet duct. In order to study the influence of the rotation, tests both in stationary (absence of rotation, Re = 20,000) and in rotating (Re = 20,000 and Ro = 0.3) conditions have been performed. The results show that the Coriolis and centrifugal forces, caused by the rotation, yield strong modifications to the symmetrical flow and vortical fields that are generated, in the static case, only by the abrupt inversion of the flow direction.     

Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part II. Application to InxGa1−xAs/InP system

Cracking phenomena in tensile-strained In_xGa_1?xAs epitaxial film on an InP substrate are analyzed via the formulation given in Part I [Lee, S., Choi, S.T., Earmme, Y.Y., 2006. Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part I. Mathematical formulation. International Journal of Solids and Structures 43, 3401–3413], where the solution for a dislocation in an anisotropic trimaterial is used as a fundamental solution and the crack is modeled by the continuous distribution of dislocations. Misfit strains and stresses are evaluated as a function of indium content x in an In_xGa_1?xAs/InP system. A single crack and periodic cracks, respectively, induced by the misfit stresses are considered. The crack opening profile, the crack mouth displacement, and the energy release rate as a function of the crack length are obtained. The critical conditions for a single crack and periodic cracks, respectively, are thus obtained, and are found to depend on the film thickness, the crack length, and the period of the cracks. The results of these analyses are also compared with published data obtained from experiments.     

“Non-free” interaction of plane shock waves and the boundary layer in the neighborhood of the leading edge of a plate with slip

The interaction between a normally impinging shock wave and the boundary layer on a plate with slip is studied in the neighborhood of the leading edge using various experimental methods, including special laser technology, to visualize the supersonic conical gas flows. It is found that in the “non-free” interaction, when the leading edge impedes the propagation of the boundary layer separation line upstream, the structure of the disturbed flow is largely identical to that in the developed “free” interaction, but with higher parameter values and gradients in the leading part of the separation zone. The fundamental property of developed separation flows, namely, coincidence of the values of the pressure “plateau” in the separation zone and the pressure behind the oblique shock above the separation zone of the turbulent boundary layer, is conserved. Moscow. e-mail: ostap@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 57–69, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00099).     

Numerical Simulation of Diesel Spray Evaporation in a “Stabilized Cool Flame” Reactor: A Comparative Study

The major objective of this work is to numerically investigate the interacting physical and chemical phenomena that characterize the flow in a stabilized cool flame diesel fuel spray evaporation system. A two-phase RANS computational fluid dynamics code has been developed and used to predict the characteristics of the developing turbulent, multiphase, multi-component, reactive flow-field. The code employs a Eulerian–Lagrangian approach, taking into account the mass, momentum, thermal and turbulent energy exchange between the phases. A variety of physical phenomena, such as turbulent dispersion, droplet evaporation, droplet-wall collision, conjugate heat transfer, drift correction, two-way coupling are taken into account by implementing respective sub-models. Two alternative modelling approaches for the simulation of cool flame reactions have been validated and evaluated by comparing numerical predictions with experimental data from two atmospheric pressure, evaporating Diesel spray, Stabilized Cool Flame reactors. Both models have achieved good quantitative agreement in the majority of the considered test cases. The results have been used to estimate the local physical and chemical characteristic time scales of the occurring phenomena, thus allowing, for the first time, the classification of stabilized cool flames.     

Corrigendum to “Solution of a crack in an electrostrictive solid” [International Journal of Solids and Structures 47 (2010) 444–453]

In our previous work [Gao, C.F., Mai, Y.W., Zhang, N., 2010. Solution of a crack in an electrostrictive solid. International Journal of Solids and Structures 47, 444–453.] the intensity factor of the total stress for an impermeable crack is directly written by using the corresponding result of a permeable crack. This is based on the fact that an impermeable crack can be considered as a special case of a permeable crack where the electric field is not zero. However, the singularity of total stresses for the impermeable crack can also be analyzed directly from the complex potentials. In this Corrigendum, the singularity of the total stresses is further studied for the impermeable crack, and the intensity factors are re-derived by using the obtained complex potentials. It is shown that for an impermeable crack, the total stresses still have an inverse square-root singularity but their intensity factor is different from that obtained by the solution of a permeable crack. Therefore, it is concluded that solutions for impermeable cracks cannot be obtained directly from those of permeable cracks, since the assumption of the electric boundary condition has not only influenced the electric fields on the crack-faces but also on the electric body force inside the material.     

Detailed experimental study of a highly compressible supersonic turbulent plane mixing layer and comparison with most recent DNS results: “Towards an accurate description of compressibility effects in supersonic free shear flows”

A compressible supersonic mixing layer at convective Mach number (Mc) equal to 1 has been studied experimentally in a dual stream supersonic/subsonic wind-tunnel. Laser Doppler Velocimetry (L.D.V.) measurements were performed making possible a full estimation of the mean and turbulent 3D velocity fields in the mixing layer. The Reynolds stress tensor was described. In particular, some anisotropy coefficients were obtained. It appears that the structure of the Reynolds tensor is almost not affected by compressibility at least up to Mc = 1.The turbulent kinetic energy budget was also experimentally estimated. Reynolds analogies assumptions were used to obtain density/velocity correlations in order to build the turbulent kinetic energy budget from LDV measurements. Results have been compared to other experimental and numerical results. Compressibility effects on the turbulent kinetic energy budget have been detected and commented. A study about thermodynamics flow properties was also performed using most recent DNS results experimentally validated by the present data. A non-dimensional number is then introduced in order to quantify the real effect of pressure fluctuations on the thermodynamics quantities fluctuations.     

Comments on the Paper “Non-Darcian Forced-Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium” by O. Aydin and A. Kaya,Transport in Porous Media,doi:10.1007/s11242-007-9200-x, 2008

In a very recent paper by Aydin and Kaya (Transp. Porous Media (to appear), 2008) the combined effects of viscous dissipation and surface mass flux on the forced-convection boundary-layer flow was considered. However, as the present Note shows, the thermal boundary condition imposed at the outer edge of the boundary-layer by Aydin and Kaya is incompatible with the energy equation, and thus the results of their paper are in error.     

Comment on “Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work” by A. Barletta and D. A. Nield,Transport in Porous Media,DOI 10.1007/s11242-008-9320-y, 2009

In a recent article by Barletta and Nield (Transport in Porous Media, DOI , 2009), the title problem for the fully developed parallel flow regime was considered assuming isoflux/isothermal wall conditions. For the limiting cases of the forced and the free convection, analytical solutions were reported; for the general case, numerical solutions were reported. The aim of the present note is (i) to give an analytical solution for the full problem in terms of the Weierstrass elliptic P-function, (ii) to illustrate this general approach by two easily manageable examples, and (iii) to rise a couple of questions of basic physical interest concerning the interplay between the viscous dissipation and the pressure work. In this context, the concept of “eigenflow” introduced by Barletta and Nield is discussed in some detail.     

Comment on “New method to obtain periodic solutions of period two and three of a rational difference equation” [Nonlinear Dyn 79:241–250]

In this paper, we discuss the results of Elsayed (Nonlinear Dyn 79:241–250, 2015) for periodic solution of period two and three of rational difference equation. Also, we study the existence of periodic solutions of some difference equation by using old method and new method and comparison of results. The results obtained here correct and improve some known results in Elsayed (Nonlinear Dyn 79:241–250, 2015). Some numerical examples will be given to illustrate our results.     

The onset of gas entrainment from a flowing stratified gas–liquid regime in dual discharging branches: Part II: Critical conditions at low to moderate branch Froude numbers

This is the second of a two part investigation. Experiments were performed in a 50.8 mm diameter horizontal pipe with three 6.35 mm diameter branches located at the test section mid-span. The inlet length was 1.8 m, and three branch orientations were tested at 0° (side), 45° (inclined), and 90° (bottom) from horizontal. Water and air, operating at 206 kPa, were used and both fluids flowed co-currently within the inlet in the smooth-stratified regime. The inlet superficial velocity of the liquid phase ranged between 0.04 and 0.15 m/s while in the gas phase values of 0.3, 0.4, and 1 m/s were tested. Three different dual discharge combinations were tested and included side-inclined, side-bottom, and inclined-bottom. The tested branch flow Froude numbers were limited between low to moderate values which ranged between 1 and 23. Extensive experimental data are reported for the critical conditions at the onset of gas entrainment during dual discharge. A novel map was developed for the inclined-bottom branch configuration showing the relationship between the inlet superficial liquid velocity and branch Froude numbers. This map was used to quantify the three observed modes of gas entrainment during dual discharge. These modes were classified as onset of gas entrainment in the inclined branch only, in the bottom branch only, or both the inclined and bottom branches simultaneously. The critical height at the onset of gas entrainment results are compared to published models and data sets and poor agreement was found with studies conducted in stratified gas–liquid reservoirs.     

Corrigendum of “Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate” [International Journal of Non-Linear Mechanics 38 (2003) 513–520]

The problem of steady, laminar mixed convection heat and mass transfer past a semi-infinite vertical plate in the presence of Hall current has been studied. The governing partial differential equations describing the problem are transformed to a system of non-linear ordinary differential equations with appropriate boundary conditions using Lie's method of infinitesimal transformation groups. The non-linear ordinary differential equations are solved numerically using Chebyshev spectral method. The effects of various parameters on the velocity profiles, temperature and concentration profiles are presented and discussed. This work is an extension and correction for the paper by Megahed et al. [1], published in International Journal of Non-Linear Mechanics 38 (2003) 513–520.