A local lagrangian analysis of passive particle advection in a gas flow field

A local analysis is performed to study the departure from passive advection by small inertial particles based on a Lagrangian framework. The analysis considers heavy particles immersed in a gaseous flow and is restricted to short times, making it relevant to the PIV technique. A necessary (but not sufficient condition) for passive particle advection of inertial particles is that the quantity Λ_maxτ_p be much smaller than one, where Λ_max is the largest modulus of the eigenvalues corresponding to the velocity gradient tensor. This allows for the inertial and passive time scales to match beyond the initial transient, and consequently for the respective trajectories to remain relatively close. Due to this important role regarding advection behavior, Λ_maxτ_p is offered as a definition of a local Stokes number, St_Λ. Since this quantity is a field quantity, it directly provides indication of when and where passive advection by particles can be expected. A departure equation is obtained in one-dimension, where the influence of initial velocity and gravity are explicitly shown. If the flow is irrotational, the higher dimensional analysis reduces to a set of decoupled one-dimensional equations acting along each respective eigenvector of the velocity gradient tensor. A similar expression is found for the case of a purely temporal flow field.     

An advanced study of forced turbulent-flow film boiling for subcooled liquid with high velocity in a circular tube

A further advanced semi-empirical theory for the turbulent film boiling heat transfer of subcooled liquid flowing with high velocity in a circular tube is presented in this paper. A new analytical expression has been obtained theoretically and it is found that the exponent ofRe _D in the expression can be predicted analytically with an universal constant value of 4/5 for different fluids. Meanwhile, it is revealed that the coefficientk is correlated withk′, and thatk determined for flowing along plate can be extended to the case for flowing in a circular tube. The analyses show that new analytical expression concides really with the results presented before [5].     

A model for computer-based data acquisition and control

This paper describes the theory and ongoing development of a computer-based system for data acquisition and control termed theVIrtualDataAcquisition andControl (VIDAC) system. The VIDAC system has particular application to laboratory experimental research and is currently applied to the field of materials testing. A model is presented and intended to display the basic similarities of data-acquisition algorithms and forms the conceptual basis for the VIDAC system. A discussion of the implementation of this model in computer software is given and two experimental programs in materials testing are described which have used the VIDAC ideology.     

Multi-objective traction optimization of vehicles in loose dry sand using the generalized reduced gradient method

A work optimization strategy is combined with algorithms within the vehicle-terrain interface (VTI) model to maximize the traction of a four-wheel vehicle operating on loose dry sand. The optimization model distributes traction among the steered and non-steered wheels with the work optimum coefficient (WOC) of each wheel treated as an independent design objective. Drawbar pull (DBP), motion resistance (MR), longitudinal traction coefficient (LTC), lateral force coefficient (LFC), tire deflection, and wheel slip are key parameters that appear in the VTI model for traction performance analysis. The analysis includes wheels of different diameters, widths, heights, and inflation pressures, under variable wheel slips. A multi-objective optimization problem is formulated over a thirteen-dimensional search space bounded by eight design constraints. The generalized reduced gradient method is used to predict optimal values of the design variables as well as ground and traction parameters such as DBP, MR, LTC, and LFC for maximum slope climbing efficiency. The WOCs are maximized for lateral slip angles between 0° and 24° to find a set of Pareto optimal solutions over a wide range of weight factors. A method to apply the optimization results for predicting vehicle performance and traction control on dry sand is presented and discussed.     

Combined forced and natural convection in laminar film flow

A mathematical model for the flow and heat transfer in a gravity-driven liquid film is presented, in which the strict Boussinesq approximation is adopted to account for buoyancy. A similarity transformation reduces the governing equations to a coupled set of ordinary differential equations. The resulting two-parameter problem is solved numerically for Prandtl numbers ranging from 1 to 1000. Favourable buoyancy arises when the temperatureT _w of the isothermal surface is lower than the temperatureT ₀ of the incoming fluid, and the principal effects of the aiding buoyancy are to increase the wall shear and heat transfer rate. For unfavourable buoyancy (T _w>T ₀), the buoyancy force and gravity act in opposite directions and the flow in the film boundary layer decelerates, whereas the friction and heat transfer are reduced. The observed effects of buoyancy diminish appreciably for higher Prandtl numbers.     

The kinetic energy correction in viscometry

When calibratingU-tube capillary viscometers a kinetic energy correction is required for liquids in a certain viscosity range and in the past an unsatisfactory method has been used for its determination. This correction may be obtained with reasonable accuracy by least squares fitting flow time data to the corrected Poiseuille's law. The flow times of toluene (20°C and 25°C), benzene (25°C) and water (25°C), together with literature values of viscosity were used to determine the calibration constantC and the kinetic energy correctionB of a sizeA U-tube viscometer. The agreement with the manufacturer'sC and previously reportedB is very good. A modified kinetic energy correction of Cannon et al. does not appear to give better accuracy.     

A generalized formulation of the concept of nonhardening region

A stable hysteresis loop is realized under a cyclic loading between fixed strain limits for metals. To describe this phenomenon the idea of memory hypersphere was proposed by Chabocheet al. [1979] and it has been extended by Ohno [1982] as the concept of nonhardening (strain) region, which assumes that an isotropic hardening does not proceed when a plastic strain exists inside a hypersphere in the plastic strain space. A generalized formulation for this concept is presented in this article, which concerns isotropic-kinematic hardening materials, not limited to metals, undergoing a large deformation with a material rotation.     

The reflection of a symmetric Rayleigh-Lamb wave at the fixed or free edge of a plate

A semi-infinite plate of homogeneous isotropic, linearly elastic material occupies the region x≥0, |y|≤1, -∞<z<∞; the faces y=±1 are free of tractions, the end x=0 may be either fixed or traction free, and there are no body forces. A plane strain, time-harmonic, symmetric Rayleigh-Lamb wave propagates in the plate and is normally incident upon the end x=0. The problem of determining the resulting reflected wave field is solved by the “method of projection”, a method developed by the authors for solving corresponding problems in elastostatics. The solutions obtained for the dynamic problem fully satisfy the equations and boundary conditions of the linear theory, and (in the fixed-end case) proper account is taken of the singularities of the stress field at the corners x=0, y=±1. In each case the division of energy between the various reflected modes is found, and the dynamical stress intensity factors at the corners are determined in the fixed-end case. The existence of an “edge-mode” for the free-end case at a single isolated value of the frequency is confirmed, but a careful search revealed no similar phenomenon for the fixed-end case.     

Hyperbolic stress equations for compressible slabs

A constitutive law, chosen to model isotropic compressible slabs, is specialized for plane deformation and then substituted into the equations of motion. The resulting system is quasi-linear hyperbolic. Solutions depend on in situ measurements of a deformation-rate parameter, D. The characteristics of the hyperbolic system span a distance 2DH, where H is the penetration of the characteristics into the slab.     

The theory of elastic-plastic deformation at finite strain with induced anisotropy modeled as combined isotropic-kinematic hardening

A Theory of elastic-plastic deformation with strain induced anisotropy based on finite-deformation-valid continuum mechanics is presented. On the foundation of nonlinear kinematics which provides strict uncoupling of elastic and plastic deformation rate terms according to their physical origins, it introduces a basis for the modified plastic rate of deformation D̂^p suggested by G.J. Creus, A.G. Groehs and E.T. Onat in a report entitled “Constitutive Equations for Finite Deformations of Elastic-Plastic Solids,” 1984, in which this variable was suggested in order to give an elegant mathematical structure to the theory. D̂^p is shown to express the resultant rate of deformation in the current configuration of the elastically-plastically deforming material which is envisaged to be generated by the pure plastic flow and the anisotropy-caused spin, both considered to be occurring in the unstressed state.From this basis an elastic-plastic theory is developed in the case where the strain-induced anisotropy takes the form of combined isotropic-kinematic hardening, although the concepts involved also apply to more general anisotropic characteristics. A general evolution equation is adopted for the back stress α, the kinematic-hardening shift of the yield surface, its rate of growth being expressed as a general form-invariant function of α and D̂^p, including a general term expressing the influence of the spin of α because it is embedded in the deforming material.By providing an expression for the total strain rate as the sum of the strain rate D̂^p and an elastic term, linear in the Jaumann derivative of Kirchhoff stress, it is shown that (D̂^p dt) is the residual strain increment following a loading/unloading cycle imposed by a stress increment. By considering materials which obey the normality rule it is also shown that the instantaneous elastic-plastic moduli have the symmetries necessary for generating a rate potential function and hence can be incorporated into Hill's variational principle valid for solving problems involving finite deformation and convenient for finite-element exploitation.     

VIBRATION OF CAVITATING ELASTIC WING IN A PERIODICALLY PERTURBED FLOW: EXCITATION OF SUBHARMONICS

The vibration of an elastic wing with an attached cavity in periodically perturbed flows is analyzed. Because the cavity thickness and length L also are perturbed, an excitation with a fixed frequency ω leads to a parametric vibration of the wing, and the amplitudes and spectra of its vibration have nonlinear dependencies on the amplitude of the perturbation. Numerical analysis was carried out for a two-dimensional flow of ideal fluid. Wing vibration was described by means of the beam equation. As a result, two frequency bands of a significant vibration increase were found. A high-frequency band is associated mainly with an elastic resonance of the wing, and a cavity can add a certain damping. A low-frequency band is associated with cavity-volume oscillations. The governing parameter for the low-frequency vibration is the cavity length-based Strouhal number St_C=ωL/U, where U is the free-stream speed. The most significant vibration in the low-frequency band corresponds to approximately constant values of Sh_Cand has the most extensive subharmonics.     

Dynamic compressive strength properties of aluminium foams. Part II—‘shock’ theory and comparison with experimental data and numerical models

One-dimensional ‘steady-shock’ models based on a rate-independent, rigid, perfectly-plastic, locking (r-p-p-l) idealisation of the quasi-static stress-strain curves for aluminium foams are proposed for two different impact scenarios to provide a first-order understanding of the dynamic compaction process. A thermo-mechanical approach is used in the formulation of their governing equations. Predictions by the models are compared with experimental data presented in the companion paper (Part I) and with the results of finite-element simulations of two-dimensional Voronoi honeycombs.A kinematic existence condition for continuing ‘shock’ propagation in aluminium foams is established using thermodynamics arguments and its predictions compare well with the experimental data. The thermodynamics highlight the incorrect application of the global energy balance approach to describe ‘shock’ propagation in cellular solids which appears in some current literature.     

Duality in constitutive formulation of finite-strain elastoplasticity based on F=FeFp and F=FpFe decompositions

A constitutive theory for large elastic–plastic deformations is presented by employing F=F^pF^e decomposition of the total deformation gradient. A duality in constitutive formulation based on this and the well-known Lee's decomposition F=F_eF_p is established for isotropic polycrystalline and single crystal plasticity.     

A study on the determination of plastic properties of metals by instrumented indentation using two sharp indenters

An earlier optimisation approach proposed by Luo et al. [Luo, J., Lin, J., Dean, T. A., 2006. A Study on the Determination of Mechanical Properties of a power-law Material by Its Indentation Force-Depth Curve. Philosophical Magazine, 86(19), 2881-2905], which is based on the assumption that the instrumented indentation force-depth response of an elastic–plastic material is a linear combination of the corresponding elastic and elastic–perfect plastic materials, is extended in this work to extract mechanical properties of a power-law material from two given experimental indentation P–h curves for conical indenters of half included angles of 60° and 70.3°. It was found that the non-uniqueness problem encountered in the single P–h curve optimisation approach is effectively removed by the two P–h curves optimisation. The appropriateness of the use of second half included angle of 60° is discussed. For the five representative materials Al, Ti, Fe, Ni and steel, it was found that the maximum relative prediction errors for E, σ_y and n are 2%, 10.4% and 11.3%, respectively. The prediction accuracy of mechanical properties E, σ_y and n is generally better than other methods reported in the literature.     

A second order solution of the non-linear equations of conical shells

A second order asymptotic solution to the Donnell type non-linear equations of elastic homogeneous conical shells is presented. Closed form solutions for the displacements and stress resultants including twelve constants of integration are obtained by considering the lateral displacement to be of the order of kt where k is a geometric parameter and t is the shell thickness. Terms of order up tot/r in comparison to unity are omitted. The solutions are valid for asymmetric slowly varying edge or surface loads.     

Size-dependent coalescence kernel in fertilizer granulation-A comparative study

Granulation is a key process in several industries like pharmaceutical, food, fertilizer, agrochemicals, etc. Population balance modeling has been used extensively for modeling agglomeration in many systems such as crystallization, aerosols, pelletisation, etc. The key parameter is the coalescence kernel, β（ij） which dictates the overall rate of coalescence as well as the effect of granule size on coalescence rate. Adetayo, Litster, Pratsinis, and Ennis （1995） studied fertilizer granulation with a broad size distribution and modeled it with a two-stage kernel. A constant kernel can be applied to those granules which coalesce successfully. The coalescence model gives conditions for two types of coalescence, Type I and II. A twostage kernel, which is necessary to model granule size distribution over a wide size distribution, is applied in the present fluidized bed spray granulation process. The first stage is size-independent and non-inertial regime, and is followed by a size-dependent stage in which collisions between particles are non-random, i.e. inertial regime. The present work is focused on the second stage kernel where the feed particles of volume i and j collide and form final granule ij instead of i ＋j （Adetayo et al., 1995） which gives a wider particle size distribution of granules than proposed earlier.     

Stochastic poromechanical modeling of anthropogenic land subsidence

A key issue in poromechanical modeling, e.g. for predicting anthropogenic land subsidence due to fluid withdrawal, is the evaluation and use of representative mechanical properties for the deforming porous medium at a regional scale. One such property is the vertical uniaxial rock compressibility c_M which can be obtained through either laboratory oedometer tests or in situ measurements, and typically exhibits quite a marked scattering. This paper addresses the influence of the c_M uncertainty on the predicted land settlement using a stochastic simulation approach where c_M is regarded as a random variable and a large number of equally likely c_M realizations are generated and implemented into a poroelastic finite element model. A compressibility law, characterized by a log-normal distribution with depth-dependent mean, constant variance and exponential covariance, is assumed. The Monte Carlo simulation provides a set of responses which can be analyzed statistically. The results from a number of numerical experiments show how the c_M variance and covariance affect the reliability of the simulated land subsidence and provide a quantitative evaluation of the intrinsic uncertainty of the model prediction.     

Effect of residual stresses on the crack-tip constraint in a modified boundary layer model

Residual stresses play a crucial role in structural integrity assessment. In this study, a large cracked cylinder with a weld in the center is applied to investigate the effect of residual stresses on the crack-tip constraint. A modified boundary layer model with a remote displacement-controlled elastic K-field and T-stress under small scale yielding has been used to simulate the problem. A two-dimensional tensile residual stress field due to the weld is introduced into the model by the so-called eigenstrain method. It has been shown that the residual stresses can significantly elevate the crack-tip constraint and thus increase the probability for cleavage fracture. The constraint parameter R introduced by the authors can be used to rank the crack-tip constraint induced by the bi-axial residual stresses. The R value decreases with the increase in the applied J-integral. The residual stress-induced constraint is also coupled with the T-stress. The R value becomes smaller with larger T-stress.     

Numerical study of dispersing pollutant clouds in a built-up environment

In this paper, we study numerically the dispersion of a passive scalar released from an instantaneous point source in a built-up (urban) environment using a Reynolds-averaged Navier–Stokes method. A nonlinear k–? turbulence model [Speziale, C.G., 1987. On nonlinear k–l and k–? models of turbulence. J. Fluid Mech., 178, 459–475] was used for the closure of the mean momentum equations. A tensor diffusivity model [Yoshizawa, A., 1985. Statistical analysis of the anisotropy of scalar diffusion in turbulent shear flows. Phys. Fluids, 28, 3226–3231] was used for closure of the scalar transport equations. The concentration variance was also calculated from its transport equation, for which new values of Yoshizawa’s closure coefficients are used, in order to account for the instantaneous tracer release and the complex geometry. A new dissipation length-scale model, required for the modelling of the dissipation rate of concentration variance, is also proposed. The numerical results for the flow, the pollutant concentration and the concentration variance, are compared with experimental data. This data was obtained from a water-channel simulation of a full-scale field experiment of tracer dispersion through a large array of building-like obstacles known as the Mock Urban Setting Trial (MUST).     

A FENE-P k–ε turbulence model for low and intermediate regimes of polymer-induced drag reduction

A new low-Reynolds-number k–ε turbulence model is developed for flows of viscoelastic fluids described by the finitely extensible nonlinear elastic rheological constitutive equation with Peterlin approximation (FENE-P model). The model is validated against direct numerical simulations in the low and intermediate drag reduction (DR) regimes (DR up to 50%). The results obtained represent an improvement over the low DR model of Pinho et al. (2008) [A low Reynolds number k–ε turbulence model for FENE-P viscoelastic fluids, Journal of Non-Newtonian Fluid Mechanics, 154, 89–108]. In extending the range of application to higher values of drag reduction, three main improvements were incorporated: a modified eddy viscosity closure, the inclusion of direct viscoelastic contributions into the transport equations for turbulent kinetic energy (k) and its dissipation rate, and a new closure for the cross-correlations between the fluctuating components of the polymer conformation and rate of strain tensors (NLT_ij). The NLT_ij appears in the Reynolds-averaged evolution equation for the conformation tensor (RACE), which is required to calculate the average polymer stress, and in the viscoelastic stress work in the transport equation of k. It is shown that the predictions of mean velocity, turbulent kinetic energy, its rate of dissipation by the Newtonian solvent, conformation tensor and polymer and Reynolds shear stresses are improved compared to those obtained from the earlier model.