Direct numerical simulation of a turbulent boundary layer up to Reθ = 2500

Direct numerical simulations (DNSs) of a turbulent boundary layer (TBL) with Re_θ = 570-2560 were performed to investigate the spatial development of its turbulence characteristics. The inflow simulation was conducted in the range Re_θ = 570-1600 by using Lund’s method. To resolve the numerical periodicity induced by the recycling method, we adopted a sufficiently long streamwise domain of x/θ_in,i = 1000 (=125δ_0,i), where θ_in,i is the inlet momentum thickness and δ_0,i is the inlet boundary layer thickness in the inflow simulation. Furthermore, the main simulation with a length greater than 50δ₀ was carried out independently by using the inflow data, where δ₀ is the inlet boundary layer thickness of the main simulation. The integral quantities and the first-, second- and higher-order turbulence statistics were compared with those of previous data, and good agreement was found. The present study provides a useful database for the turbulence statistics of TBLs. In addition, instantaneous field and two-point correlation of the streamwise velocity fluctuations displayed the existence of the very large-scale motions (VLSMs) with the characteristic widths of 0.1-0.2δ and that the flow structure for a length of approximately ∼6δ fully occupies the streamwise domain statistically.     

Moiré interferometry at VPI & SU

A relatively easy technique for producing high-frequency gratings on specimens extends moiré techniques into the high-sensitivity domain. Whole-field patterns of inplane displacement components are obtained with grating frequencies of 1200, 2400 and 4000 l/mm (30,480, 60,960 and 101,600 l/in.). Moiré interferometry is a case of two-beam interference, characterized by extensive range, excellent fringe contrast and fringe localization on the specimen surface. It is a reflection technique, compatible with opaque specimens and live observation of deformation.     

Electromechanical response of (3–0, 3–1) particulate,fibrous, and porous piezoelectric composites with anisotropic constituents: A model based on the homogenization method

An analytical framework based on the homogenization method has been developed to predict the effective electromechanical properties of periodic, particulate and porous, piezoelectric composites with anisotropic constituents. Expressions are provided for the effective moduli tensors of n-phase composites based on the respective strain and electric field concentration tensors. By taking into account the shape and distribution of the inclusion and by invoking a simple numerical procedure, solutions for the electromechanical properties of a general anisotropic inclusion in an anisotropic matrix are obtained. While analytical forms are provided for predicting the electroelastic moduli of composites with spherical and cylindrical inclusions, numerical evaluation of integrals over the composite microstructure is required in order to obtain the corresponding expressions for a general ellipsoidal particle in a piezoelectric matrix. The electroelastic moduli of piezoelectric composites predicted by the analytical model developed in the present study demonstrate excellent agreement with results obtained from three-dimensional finite-element models for several piezoelectric systems that exhibit varying degrees of elastic anisotropy.     

Two-phase flow simulations at 0−4o inclination in an eccentric annulus

Co-current two-phase simulations of gas-liquid flow with mixture velocities from 1.2 to 4.2 m/s were run in a partially eccentric annulus and compared with entirely eccentric and concentric experimental data collected at the Institute for Energy Technology in Norway. The gas-phase was sulphur hexafluoride (SF₆) for all cases, while the liquid-phase was Exxsol D60 for the horizontal cases and a mixture of Exxsol D60 and Marcol 82 for the inclined case. The outer diameter of the annulus was 0.1 m for all cases, while the inner diameter was 0.05 m in the horizontal configuration and 0.04 m for the inclined configuration. The purpose of this paper is to explore the effect of the holdup fraction, mixture velocity, and interior pipe’s position on the pressure gradient and flow regime, in effect a study of the pressure gradient and holdup fraction transients. The comparisons between simulations and experiments indicate that moving the pipe from an entirely eccentric to the partially eccentric configuration has a drastic impact on the pressure gradient. In all 4 cases where the inner pipe was changed from a completely eccentric geometry in the experiments to a less eccentric configuration in the simulations, we notice an increase of 48–303% of the mean pressure gradient. Comparatively, the 4 cases where the pipe was moved from a concentric experimental configuration to a more eccentric configuration in the simulations result in less drastic pressure gradient changes. Two cases were within 22% of the experimental results for mean, maximum, and minimum pressure gradient, while the last two cases exceeded the minimum and mean pressure gradients by 25–250%, respectively. The flow regime is rarely significantly affected by a change in eccentricity; 2 out of the 8 horizontal cases indicate either a transition from wavy flow to slug flow or significantly larger waves. The most prominent and frequent discrepancies identified were altered slug and wave frequencies. The last case, a 4^o inclined, partially eccentric simulation was compared to an entirely eccentric experiment and results in a 0.2 Hz increase in wave frequency, up from the experimental 0.56 Hz and a 49% increase in the mean pressure gradient.     

Multivalued penalty method for evolution variational inequalities with <Emphasis Type="Italic">λ</Emphasis><Subscript>0</Subscript>-pseudomonotone multivalued maps

We consider evolution variational inequalities with λ ₀-pseudomonotone maps. The main properties of these maps are investigated. By using the finite-difference method, we prove the property of strong solvability for the class of evolution variational inequalities with λ ₀-pseudomonotone maps. Using the penalty method for multivalued maps, we show the existence of weak solutions of evolution variational inequalities on closed convex sets. The class of multivalued penalty operators is constructed. We also consider a model example to illustrate this theory.     

A Phase-Partitioning Model for CO<Subscript>2</Subscript>–Brine Mixtures at Elevated Temperatures and Pressures: Application to CO<Subscript>2</Subscript>-Enhanced Geothermal Systems

Correlations are presented to compute the mutual solubilities of CO₂ and chloride brines at temperatures 12–300°C, pressures 1–600 bar (0.1–60 MPa), and salinities 0–6 m NaCl. The formulation is computationally efficient and primarily intended for numerical simulations of CO₂-water flow in carbon sequestration and geothermal studies. The phase-partitioning model relies on experimental data from literature for phase partitioning between CO₂ and NaCl brines, and extends the previously published correlations to higher temperatures. The model relies on activity coefficients for the H₂O-rich (aqueous) phase and fugacity coefficients for the CO₂-rich phase. Activity coefficients are treated using a Margules expression for CO₂ in pure water, and a Pitzer expression for salting-out effects. Fugacity coefficients are computed using a modified Redlich–Kwong equation of state and mixing rules that incorporate asymmetric binary interaction parameters. Parameters for the calculation of activity and fugacity coefficients were fitted to published solubility data over the P–T range of interest. In doing so, mutual solubilities and gas-phase volumetric data are typically reproduced within the scatter of the available data. An example of multiphase flow simulation implementing the mutual solubility model is presented for the case of a hypothetical, enhanced geothermal system where CO₂ is used as the heat extraction fluid. In this simulation, dry supercritical CO₂ at 20°C is injected into a 200°C hot-water reservoir. Results show that the injected CO₂ displaces the formation water relatively quickly, but that the produced CO₂ contains significant water for long periods of time. The amount of water in the CO₂ could have implications for reactivity with reservoir rocks and engineered materials.     

A C<Superscript>0</Superscript>-type zig–zag theory and finite element for laminated composite and sandwich plates with general configurations

In order to conveniently develop C⁰ continuous element for the accurate analysis of laminated composite and sandwich plates with general configurations, this paper develops a C⁰-type zig–zag theory in which the interlaminar continuity of transverse shear stresses is a priori satisfied and the number of unknowns is independent of the number of layers. The present theory is applicable not only to the cross-ply but also to the angle-ply laminated composite and sandwich plates. On the premise of retaining the merit of previous zig–zag theories, the derivatives of transverse displacement have been taken out from the displacement fields. Therefore, based on the proposed zig–zag theory, it is very easy to construct the C⁰ continuous element. To assess the performance of the proposed model, the classical quadratic six-node triangular element with seven degrees of freedom at each node is presented for the static analysis of laminated composite and sandwich plates. The typical examples are taken into account to assess the performance of finite element based on the proposed zig–zag theory by comparing the present results with the three-dimensional elasticity solutions. Numerical results show that the present model can produce the more accurate deformations and stresses compared with the previous zig–zag theories.     

EDIT0RIAL B0ARD 0F “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in chief: Yeh, Kai-yuan (叶开源) Executive Editors: Wang, Zhi-zhong (王志忠) ; Xu, Yin-ge (徐尹格) Zhang, Lu-kun (张录坤)     

EDIT0RIAL B0ARD 0F “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in-chief: Yeh, Kal-yuan (叶开沅)     

Unsteady PTV velocity field past an airfoil solved with DNS: Part 1. Algorithm of hybrid simulation and hybrid velocity field at <Emphasis Type="Italic">Re</Emphasis> ≈ 10<Superscript>3</Superscript>

We develop a hybrid unsteady-flow simulation technique combining direct numerical simulation (DNS) and particle tracking velocimetry (PTV) and demonstrate its capabilities by investigating flows past an airfoil. We rectify instantaneous PTV velocity fields in a least-squares sense so that they satisfy the equation of continuity, and feed them to the DNS by equating the computational time step with the frame rate of the time-resolved PTV system. As a result, we can reconstruct unsteady velocity fields that satisfy the governing equations based on experimental data, with the resolution comparable to numerical simulation. In addition, unsteady pressure distribution can be solved simultaneously. In this study, particle velocities are acquired on a laser-light sheet in a water tunnel, and unsteady flow fields are reconstructed with the hybrid algorithm solving the incompressible Navier–Stokes equations in two dimensions. By performing the hybrid simulation, we investigate nominally two-dimensional flows past the NACA0012 airfoil at low Reynolds numbers. In part 1, we introduce the algorithm of the proposed technique and discuss the characteristics of hybrid velocity fields. In particular, we focus on a vortex shedding phenomenon under a deep stall condition (α = 15°) at Reynolds numbers of Re = 1000 and 1300, and compare the hybrid velocity fields with those computed with two-dimensional DNS. In part 2, the extension to higher Reynolds numbers is considered. The accuracy of the hybrid simulation is evaluated by comparing with independent experimental results at various angles of attack and Reynolds numbers up to Re = 10⁴. The capabilities of the hybrid simulation are also compared with two-dimensional unsteady Reynolds-Averaged Navier–Stokes (URANS) solutions in part 2. In the first part of these twin papers, we demonstrate that the hybrid velocity field approaches the PTV velocity field over time. We find that intensive alternate vortex shedding past the airfoil, which is predicted by the two-dimensional DNS, is substantially suppressed in the hybrid simulation and the resultant flow field is similar to the PTV velocity field, which is projection of the three-dimensional velocity field on the streamwise plane. We attempt to identify the motion that originates three-dimensional flow patterns by highlighting the deviation of the PTV velocity field from the two-dimensional governing equations at each snapshot. The results indicate that the intensive spots of the deviation appear in the regions in which three-dimensional instabilities are induced in the shear layer separated from the pressure side.     

Measurement of Strain Localization Resulting from Monotonic and Cyclic Loading at 650 <Superscript>∘</Superscript>C in Nickel Base Superalloys

A methodology is presented for the use of the oxide scale that develops in polycrystalline Ni-base superalloys at service temperature, as a speckle pattern for μm-scale resolution strain measurements. Quantitative assessment of the heterogeneous strain field at the grain scale is performed by high-resolution SEM digital image correlation under monotonic and cyclic loading in polycrystalline Ni-base superalloys up to 650 ^°C. In the René 88DT superalloy, strain localization is observed near twin boundaries during low cycle fatigue (LCF) at intermediate temperatures, correlating with activation of {111} 〈110〉 and {111} 〈112〉 slip systems. A strong correlation between the microstructural configuration that promotes strain localization during monotonic loading and crack initiation at 650 ^°C in low cycle fatigue was observed.     

Magnetic and electrochemical behavior of rhombohedral α-Fe2O3 nanoparticles with (1 0 4) dominant facets

Uniform rhombohedral α-Fe₂O₃ nanoparticles, ～60 nm in size, were synthesized via a triphenylphosphine-assisted hydrothermal method. Scanning electron micrograph (SEM) and transmission electron micrograph (TEM) analyses showed that the as-synthesized rhombohedral nanoparticles were enclosed by six (1 0 4) planes. The concentration of triphenylphosphine played an important role in morphological evolution of the α-Fe₂O₃ nanoparticles. The as-prepared rhombohedral nanoparticles possessed remanent magnetization M_r of 2.6 × 10^?3 emu/g and coercivity H_C of 2.05 Oe, both lower than those of other α-Fe₂O₃ particles with similar size, indicating their potential applications as superparamagnetic precursor materials. Furthermore, these rhombohedral α-Fe₂O₃ nanoparticles exhibited good sensor capability toward H₂O₂ with a linear response in the concentration range of 2–20 mM.     

Effect of perforation on flow past a conic cylinder at <Emphasis Type="Italic">Re</Emphasis> = 100: vortex-shedding pattern and force history

The flow past a circular-section cylinder with a conic shroud perforated with four holes at the peak was simulated numerically at \(Re=100\), considering two factors, viz. the angle of attack and the diameter of the holes. The effects of the perforated conic shroud on the vortex shedding pattern in the near wake was mainly investigated, as well as the time history of the drag and lift forces. In the investigated parameter space, three flow regimes were generally identified, corresponding to weak, moderate, and strong disturbance effects. In regime I, the wake can mainly be described by alternately shedding Kármán or Kármán-like vortices. In regime II, the spanwise vortices are obviously disturbed along the span due to the appearance of additional vorticity components and their interactions with the spanwise vortices, but still shed in synchronization along the spanwise direction. In regime III, the typical Kármán vortices partially or totally disappear, and some new vortex shedding patterns appear, such as \(\Omega \)-type, obliquely shedding, and crossed spanwise vortices with opposite sign. Corresponding to these complex vortex shedding patterns in the near wake, the fluid forces no longer oscillate regularly at a single vortex shedding frequency, but rather with a lower modulation frequency and multiple amplitudes. An overview of these flow regimes is presented.     

Unsteady PTV velocity field past an airfoil solved with DNS: Part 2. Validation and application at Reynolds numbers up to <Emphasis Type="Italic">Re</Emphasis> ≤ 10<Superscript>4</Superscript>

Hybrid unsteady-flow simulation combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS) is introduced in the series of two papers. Particle velocities on a laser-light sheet acquired with time-resolved PTV in a water tunnel are supplied to two-dimensional DNS with time intervals corresponding to the frame rate of the PTV. Hybrid velocity fields then approach those representing the PTV data in the course of time, and the reconstructed velocity fields satisfy the governing equations with the resolution comparable to numerical simulation. In part 2, by extending the capabilities of the hybrid simulation to higher Reynolds numbers, we simulate flows past the NACA0012 airfoil over ranges of Reynolds numbers (Re ≤ 10⁴) and angles of attack (−5° ≤ α ≤ 20°) and validate the proposed technique by comparing with experimental results in terms of the lift and drag coefficients. We also compare the results with unsteady Reynolds-averaged Navier–Stokes (URANS) simulation in two-dimensions and show the advantages of the hybrid simulation against two-dimensional URANS.     

Possibility of impulsive gas transport through a capillary at high initial pressure in the system (P 0≥100 MPa)

The possibility of impulsive (using a chemical explosive) gas transport at high initial pressure from a secondary into a primary vessel in times 100t175sec has been experimentally demonstrated. In the first 90sec the proposed device is insensitive to the high internal gas pressure. Whent90sec the strength properties of its elements must be taken into account. By this time the amount of gas in the primary vessel has increased by approximately 43% relative to the initial amount. The use of lightweight pistons (titanium, aluminum or magnesium instead of steel) makes it possible to bring the piston travel time within the range insensitive to the strength properties.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–9, September–October, 1993.     

The viscosity of water at high pressures – especially at subzero degrees centigrade

New experimental data for the viscosity of water at high pressures up to 700 MPa in the temperature range of −13 °C to 20 °C are presented. The measurements were carried out with two different types of viscometer, both gravity driven. The set-up of the viscometers and the pressure-dependent corrections are briefly described. The viscosity data are compared with available literature data. Reasons for the deviations are discussed. Models to describe pressure-viscosity behavior of water are applied to the data. The applicability to the moderate temperature viscosity data is discussed and it is checked whether the range of validity of the models can be extended to subzero temperatures. Received: 8 March 2000 Accepted: 28 June 2000     

Experiments on the Flow Field and Acoustic Properties of a Mach number 0·75 Turbulent Air Jet at a Low Reynolds Number

In this paper we present the experimental results of a detailed investigation of the flow and acoustic properties of a turbulent jet with Mach number 0·75 and Reynolds number 3·5 10³. We describe the methods and experimental procedures followed during the measurements, and subsequently present the flow field and acoustic field. The experiment presented here is designed to provide accurate and reliable data for validation of Direct Numerical Simulations of the same flow. Mean Mach number surveys provide detailed information on the centreline mean Mach number distribution, radial development of the mean Mach number and the evolution of the jet mixing layer thickness both downstream and in the early stages of jet development. Exit conditions are documented by measuring the mean Mach number profile immediately above the nozzle exit. The fluctuating flow field is characterised by means of a hot-wire, which produced radial profiles of axial turbulence at several stations along the jet axis and the development of flow fluctuations through the jet mixing layer. The axial growth rate of the jet instabilities are determined as function of Strouhal number, and the axial development of several spectral components is documented. The directivity of the overall sound pressure level and several spectral components were investigated. The spectral content of the acoustic far field is shown to be compatible with findings of hot-wire experiments in the mixing layer of the jet. In addition, the measured acoustic spectra agree with Tam’s large-scale similarity and fine-scale similarity spectra (Tam et al., AIAA Pap 96, 1996).     

A N0TE ON THE EXPRESSION FOR THE ROTATI0N TENS0R IN TERMS OF EULER·ANGLES

It is pointed out in this paper that the deri-vation of the expression for the rotation tensor interms of Euler angles by N.E.Kochin is errone-ous.To point out Kochin′s deficit on this problemis advantageous for perfecting the concept of therotation tensor and its method of expression.