Unsteady gravity-driven slender rivulets of a power-law fluid

Unsteady gravity-driven flow of a thin slender rivulet of a non-Newtonian power-law fluid on a plane inclined at an angle α to the horizontal is considered. Unsteady similarity solutions are obtained for both converging sessile rivulets (when 0 < α < π/2) in the case x < 0 with t < 0, and diverging pendent rivulets (when π/2 < α < π) in the case x > 0 with t > 0, where x denotes a coordinate measured down the plane and t denotes time. Numerical and asymptotic methods are used to show that for each value of the power-law index N there are two physically realisable solutions, with cross-sectional profiles that are ‘single-humped’ and ‘double-humped’, respectively. Each solution predicts that at any time t the rivulet widens or narrows according to |x | ^{(2N+1)/2(N+1)} and thickens or thins according to |x | ^N/(N+1) as it flows down the plane; moreover, at any station x, it widens or narrows according to |t | ^?N/2(N+1) and thickens or thins according to |t | ^?N/(N+1). The length of a truncated rivulet of fixed volume is found to behave according to |t | ^N/(2N+1).     

Evaluation of subgrid-scale models in large-eddy simulation of flow past a two-dimensional block

Large-eddy simulations of flow past a two-dimensional (2D) block were performed to evaluate four subgrid-scale (SGS) models: (i) the traditional Smagorinsky model, (ii) the Lagrangian dynamic model, (iii) the Lagrangian scale-dependent dynamic model, and (iv) the modulated gradient model. An immersed boundary method was employed to simulate the 2D block boundaries on a uniform Cartesian grid. The sensitivity of the simulation results to grid refinement was investigated by using four different grid resolutions. The velocity streamlines and the vertical profiles of the mean velocities and variances were compared with experimental results. The modulated gradient model shows the best overall agreement with the experimental results among the four SGS models. In particular, the flow recirculation, the reattachment position and the vertical profiles are accurately reproduced with a relative coarse grid resolution of (N_x × N_y × N_z=) 160 × 40 × 160 (n_x × n_z = 13 × 16 covering the block). Besides the modulated gradient model, the Lagrangian scale-dependent dynamic model is also able to give reasonable prediction of the flow statistics with some discrepancies compared with the experimental results. Relatively poor performance by the Lagrangian dynamic model and the Smagorinsky model is observed, with simulated recirculating patterns that differ from the measured ones. Analysis of the turbulence kinetic energy (TKE) budget in this flow shows evidence of a strong production of TKE in the shear layer that forms as the flow is deflected around the block.     

Some C0-continuous mixed formulations for general dipolar linear gradient elasticity boundary value problems and the associated energy theorems

The goal of this work is a systematic presentation of some classes of mixed weak formulations, for general multi-dimensional dipolar gradient elasticity (fourth order) boundary value problems. The displacement field main variable is accompanied by the double stress tensor and the Cauchy stress tensor (case 1 or μ ? τ ? u formulation), the double stress tensor alone (case 2 or μ ? u formulation), the double stress, the Cauchy stress, the displacement second gradient and the standard strain field (case 3 or μ ? τ ? κ ? ε ? u formulation) and the displacement first gradient, along with the equilibrium stress (case 4 or u ? θ ? γ formulation). In all formulations, the respective essential conditions are built in the structure of the solution spaces. For cases 1, 2 and 4, one-dimensional analogues are presented for the purpose of numerical comparison. Moreover, the standard Galerkin formulation is depicted. It is noted that the standard Galerkin weak form demands C¹-continuous conforming basis functions. On the other hand, up to first order derivatives appear in the bilinear forms of the current mixed formulations. Hence, standard C⁰-continuous conforming basis functions may be employed in the finite element approximations. The main purpose of this work is to provide a reference base for future numerical applications of this type of mixed methods. In all cases, the associated quadratic energy functionals are formed for the purpose of completeness.     

Static wall layers in plane channel displacement flows

We study steady and pulsating displacement flows of a Bingham fluid by a Newtonian fluid, along a plane channel. For sufficiently large yield stress a static residual wall layer can result during the displacement. The flow is parameterised by the Reynolds number (Re), the Bingham number (B) and the viscosity ratio (M). Perhaps intuitively, thicker layers are found with larger M and at lower Re. The residual layer is formed on the advective timescale of the displacement but drains on a slower timescale governed by M. For larger M truly stationary layers are only found for large t when the layer has thinned sufficiently to become static. Increased Re results in increased energy production locally around the finger. For large enough Re the energy production can play a significant role in yielding the fluid. As the energy production rate increases it also becomes focused around the corner or shoulder region of the front, and spreads axially along the initial part of the residual layer. This causes fluid to yield increasingly far behind the front and allows for the layer to thin. As B increases the static layer tends to decrease (see also [1], [2]). At small Re the static layer thickness appears to be independent of M. At large Re the layer thickness is dependent on M and decreases asymptotically to a constant value as B → ∞.For pulsating displacement flow rates, Q(t) = 2(1 + Asin  ωt) : A ∈ [0, 1) we study two ranges: ωRe ? 2π and ωRe ? 2π. For the viscous regime (ωRe ? 2π) a pseudo-steady 1D model predicts that the residual layer should remain static for 3(1 + Asin  ωt) < MB. In practice we find that partial mobilisation of the residual layer occurs even when this inequality is satisfied, but not if MB becomes significantly larger than 3(1 + A). For ωRe ? 2π we mobilise the layer for significantly larger values of MB and at smaller A, than in the viscous regime. This effect is traced to the occurrence of out-of-phase velocity fluctuations in the displacing fluid within a wall layer close to the interface.     

Bow shocks formed by plasma collisions in laser irradiated semi-cylindrical cavities

The formation of shocks in plasmas created by short pulse laser irradiation (λ = 800 nm, I ≈ 1 × 10¹² W cm^?2) of semi-cylindrical cavities of different materials was studied combining visible and soft X-ray laser interferometry with simulations. The plasma rapidly converges near the axis to form a dense bright plasma focus. Later in time a long lasting bow shock is observed to develop outside the cavity, that is shown to arise from the collision of plasmas originating from within the cavity and the surrounding flat walls of the target. The shock is sustained for tens of nanoseconds by the continuous arrival of plasma ablated from the target walls. The plasmas created from the heavier target materials evolve more slowly, resulting in increased shock lifetimes.     

Neutrality in the case of N-phase elliptical inclusions with internal uniform hydrostatic stresses

A novel method is proposed to design neutral N-phase (N ? 3) elliptical inclusions with internal uniform hydrostatic stresses. We focus on the study of the internal and external stress states of an N-phase elliptical inclusion which is bonded to an infinite matrix through (N ? 2) interphase layers. The interfaces of the N-phase elliptical inclusion are (N ? 1) confocal ellipses. The design of the resulting overall composite material consists of four stages: (i) an inner perfectly bonded interphase/inclusion interface which is necessary to make the internal uniform stress state hydrostatic; (ii) outer imperfect interphase layers properly designed to make the coated inclusion harmonic (i.e., the uniform mean stress of the original field within the matrix is unperturbed); (iii) the aspect ratio of the elliptic inclusion uniquely chosen for a given material and thickness parameters to make the resulting coated inclusion neutral (i.e., the prescribed uniform stress field in the matrix remains undisturbed); and finally (iv) the derivation of a simple condition relating the remote uniform stresses and the thickness parameters of the (N ? 2) interphase layers for given material parameters which lead to internal uniform hydrostatic stresses. We note that another interesting feature of the present results is that the mean stress is found to be constant within each interphase layer, and the hoop stress in the innermost interphase layer is uniform along the entire interphase/inclusion interface.     

LES of turbulent flow in a concentric annulus with rotating outer wall

Fully-developed turbulent flow in a concentric annulus, r₁/r₂ = 0.5, Re_h = 12,500, with the outer wall rotating at a range of rotation rates N = U_θ,wall/U_b from 0.5 up to 4 is studied by large-eddy simulations. The focus is on the effects of moderate to very high rotation rates on the mean flow, turbulence statistics and eddy structure. For N up to ∼2, an increase in the rotation rate dampens progressively the turbulence near the rotating outer wall, while affecting only mildly the inner-wall region. At higher rotation rates this trend is reversed: for N = 2.8 close to the inner wall turbulence is dramatically reduced while the outer wall region remains turbulent with discernible helical vortices as the dominant turbulent structure. The turbulence parameters and eddy structures differ significantly for N = 2 and 2.8. This switch is attributed to the centrifuged turbulence (generated near the inner wall) prevailing over the axial inertial force as well as over the counteracting laminarizing effects of the rotating outer wall. At still higher rotation, N = 4, the flow gets laminarized but with distinct spiralling vortices akin to the Taylor–Couette rolls found between the two counter-rotating cylinders without axial flow, which is the limiting case when N approaches to infinity. The ratio of the centrifugal to axial inertial forces, Ta/Re² ∝ N² (where Ta is the Taylor number) is considered as a possible criterion for defining the conditions for the above regime change.     

The effect of incidence angle on the mean wake of surface-mounted finite-height square prisms

The mean wake of a surface-mounted finite-height square prism was studied experimentally in a low-speed wind tunnel to explore the combined effects of incidence angle (α) and aspect ratio (AR). Measurements of the mean wake velocity field were made with a seven-hole pressure probe for finite square prisms of AR = 9, 7, 5 and 3, at a Reynolds number of Re = 3.7 × 10⁴, for incidence angles from α = 0° to 45°. The relative thickness of the boundary layer on the ground plane, compared to the prism width, was δ/D = 1.5. As the incidence angle increases from α = 0° to 15°, the mean recirculation zone shortens and the mean wake shifts in the direction opposite to that of the mean lift force. The downwash is also deflected to this side of the wake and the mean streamwise vortex structures in the upper part of the wake become strongly asymmetric. The shortest mean recirculation zone, and the greatest asymmetry in the mean wake, is found at the critical incidence angle of α_critical ≈ 15°. As the incidence angle increases from α = 15° to 45°, the mean recirculation zone lengthens and the mean streamwise vortex structures regain their symmetry. These vortices also elongate in the wall-normal direction and become contiguous with the horseshoe vortex trailing arms. The mean wake of the prism of AR = 3 has some differences, such as an absence of induced streamwise vorticity near the ground plane, which support its classification as lying below the critical aspect ratio for the present flow conditions.     

Theoretical stress analysis of intersecting cylindrical shells subjected to external loads transmitted through branch pipes

A thin shell theoretical solution of two normally intersecting cylindrical shells subjected to thrust-out force and three kinds of moments transmitted through branch pipes is presented in this paper. The solutions of modified Morley equation, which can be applicable up to ρ₀ = d/D ⩽ 0.8 and λ = d/(DT)^1/2 ⩽ 8 and the order of accuracy is raised to O(T/D), for the four loading cases are given. The accurate continuity conditions of generalized forces and displacements at the intersecting curve of two cylindrical shells for the four loading cases and the condition of the uniqueness of displacements are derived in this paper. The presented results are verified by experimental and numerical results successfully. They are in agreement with WRC Bulletin 297 when d/D is small.     

CFD modelling and wind tunnel validation of airflow through plant canopies using 3D canopy architecture

The efficiency of pesticide application to agricultural fields and the resulting environmental contamination highly depend on atmospheric airflow. A computational fluid dynamics (CFD) modelling of airflow within plant canopies using 3D canopy architecture was developed to understand the effect of the canopy to airflow. The model average air velocity was validated using experimental results in a wind tunnel with two artificial model trees of 24 cm height. Mean air velocities and their root mean square (RMS) values were measured on a vertical plane upstream and downstream sides of the trees in the tunnel using 2D hotwire anemometer after imposing a uniform air velocity of 10 m s^?1 at the inlet. 3D virtual canopy geometries of the artificial trees were modelled and introduced into a computational fluid domain whereby airflow through the trees was simulated using Reynolds-Averaged Navier–Stokes (RANS) equations and k-ε turbulence model. There was good agreement of the average longitudinal velocity, U between the measurements and the simulation results with relative errors less than 2% for upstream and 8% for downstream sides of the trees. The accuracy of the model prediction for turbulence kinetic energy k and turbulence intensity I was acceptable within the tree height when using a roughness length (y₀ = 0.02 mm) for the surface roughness of the tree branches and by applying a source model in a porous sub-domain created around the trees. The approach was applied for full scale orchard trees in the atmospheric boundary layer (ABL) and was compared with previous approaches and works. The simulation in the ABL was made using two groups of full scale orchard trees; short (h = 3 m) with wider branching and long (h = 4 m) with narrow branching. This comparison showed good qualitative agreements on the vertical profiles of U with small local differences as expected due to the spatial disparities in tree architecture. This work was able to show airflow within and above the canopy in 3D in more details.     

Some exact solutions for rotating flows of a generalized Burgers’ fluid in cylindrical domains

The velocity field and the adequate shear stress corresponding to the flow of a generalized Burgers’ fluid model, between two infinite co-axial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is due to the inner cylinder that applies a time dependent torsional shear to the fluid. The solutions that have been obtained, presented in series form in terms of usual Bessel functions J₁( ? ), J₂( ? ), Y₁( ? ) and Y₂( ? ), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for Burgers’, Oldroyd-B, Maxwell, second grade, Newtonian fluids and large-time transient solutions for generalized Burgers’ fluid are also obtained as special cases of the present general solutions. The effect of various parameters on large-time and transient solutions of generalized Burgers’ fluid is also discussed. Furthermore, for small values of the material parameters, λ₂ and λ₄ or λ₁, λ₂, λ₃ and λ₄, the general solutions corresponding to generalized Burgers’ fluids are going to those for Oldroyd-B and Newtonian fluids, respectively. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.     

Flow fields and packing states in the discharge flow of noncircular particles—A SIPHPM simulation

Although the discharge flow of spherical materials has been extensively explored, the effect of particle shape on discharge is still poorly understood. The present work explores the two-dimensional discharge flow fields of noncircular particles using the soft-sphere-imbedded pseudo-hard particle model method. Rectangular particles having different aspect ratios (R_a = 1, 1.5, 2–5) and regular polygonal particles having different numbers of sides (N_s = 3–8, 10) are discharged through hopper beds having different orifice widths (D_i = 40, 70.77, 99.13, 125.74, 151.13 mm). The discharge rates of differently shaped particles in different beds are consistent with Beverloo’s relation. Moreover, the flow fields are computed and evaluated to study the effects of R_a, N_s, and D_i on particle discharge. The characteristics of particle–particle connections in the discharge process are evaluated according to the temporal evolution and spatial distribution of the contact points. Additionally, the effect of the initial packing on the discharge profile is investigated. The findings help clarify the discharge of noncircular particles.     

Synthesis of mesoporous γ-AlOOH@Fe3O4 magnetic nanomicrospheres

Mesoporous γ-AlOOH@Fe₃O₄ magnetic nanomicrospheres were synthesized using superparamagnetic Fe₃O₄ nanoparticles as the core and aluminum isopropoxide (AIP) as the aluminum source. The obtained magnetic nanomicrospheres were characterized by X-ray powder diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), N₂ adsorption–desorption and vibrating sample magnetometry (VSM). The effects of preparation parameters such as hydrolysis time of AIP, concentration of AIP and coating layer number on microspheres were investigated. The results indicated that the mesoporous γ-AlOOH@Fe₃O₄ magnetic nanomicrospheres consisted of a mesoporous γ-AlOOH shell and a Fe₃O₄ magnetic core. The diameter of γ-AlOOH@Fe₃O₄ nanomicrospheres was about 200 nm, the thickness of mesoporous γ-AlOOH shell was about 5 nm and the average pore size was 3.8 nm. The thickness of the mesoporous γ-AlOOH shell could be controlled via layer-by-layer coating times. The formation mechanism of the mesoporous γ-AlOOH shell involved a “chemisorption–hydrolysis” process.     

Analytical and numerical techniques to predict carbon nanotubes properties

In this paper, two different approaches for modeling the behaviour of carbon nanotubes are presented. The first method models carbon nanotubes as an inhomogeneous cylindrical network shell using the asymptotic homogenization method. Explicit formulae are derived representing Young’s and shear moduli of single-walled nanotubes in terms of pertinent material and geometric parameters. As an example, assuming certain values for these parameters, the Young’s modulus was found to be 1.71 TPa, while the shear modulus was 0.32 TPa. The second method is based on finite element models. The inter-atomic interactions due to covalent and non-covalent bonds are replaced by beam and spring elements, respectively, in the structural model. Correlations between classical molecular mechanics and structural mechanics are used to effectively model the physics governing the nanotubes. Finite element models are developed for single-, double- and multi-walled carbon nanotubes. The deformations from the finite element simulations are subsequently used to predict the elastic and shear moduli of the nanotubes. The variation of mechanical properties with tube diameter is investigated for both zig-zag and armchair configurations. Furthermore, the dependence of mechanical properties on the number of nanotubules in multi-walled structures is also examined. Based on the finite element model, the value for the elastic modulus varied from 0.9 to 1.05 TPa for single and 1.32 to 1.58 TPa for double/multi-walled nanotubes. The shear modulus was found to vary from 0.14 to 0.47 TPa for single-walled nanotubes and 0.37 to 0.62 for double/multi-walled nanotubes.     

Experimental study of single bubble motion in a liquid metal column exposed to a DC magnetic field

The motion of single Argon bubbles rising in the eutectic alloy GaInSn under the influence of a DC longitudinal magnetic field (parallel to the direction of bubble motion) was examined. The magnetic field strength was varied up to 0.3 T corresponding to a magnetic interaction parameter N (which measures the ratio of electromagnetic forces to inertial forces) slightly greater than 1. The liquid metal was at rest in a cylindrical container. Bubble and liquid velocities were measured using ultrasound Doppler velocimetry (UDV). The measured bubble terminal velocity showed oscillations indicating a zigzag movement of ellipsoidal bubbles. For small bubbles (d_e ⩽ 4.6 mm) an increase of the drag coefficient with increasing magnetic interaction parameter N was observed, whereas for larger bubbles (d_e ⩾ 5.4 mm) the application of the magnetic field reduces the drag coefficient. The measurements revealed a distinct electromagnetic damping of the bubble induced liquid velocity leading to more rectilinear bubble trajectories when the magnetic field is applied. Moreover, significant modifications of the bubble wake structure were observed. Raising of the magnetic field strength caused an enlargement of the eddies in the wake. The Strouhal number decreases with increasing magnetic interaction parameter N.     

Influence of temperature on a carbon–fibre epoxy composite subjected to static and fatigue loading under mode-I delamination

In this paper, interlaminar crack initiation and propagation under mode-I with static and fatigue loading of a composite material are experimentally assessed for different test temperatures. The material under study is made of a 3501-6 epoxy matrix reinforced with AS4 unidirectional carbon fibres, with a symmetric laminate configuration [0°]_16/S. In the experimental programme, DCB specimens were tested under static and fatigue loading. Based on the results obtained from static tests, fatigue tests were programmed to analyse the mode-I fatigue behaviour, so the necessary number of cycles was calculated for initiation and propagation of the crack at the different temperatures. G–N curves were determined under fatigue loading, N being the number of cycles at which delamination begins for a given energy release rate. G_ICmax–a, a–N and da/dN–a curves were also determined for different G_cr rates (90%, 85%, 75%, etc.) and different test temperatures: 90 °C, 50 °C, 20 °C, 0 °C, ?30 °C and ?60 °C.     

Image decomposition method for the analysis of a mixed dislocation in a general multilayer

The elastic solutions for a mixed dislocation in a general multilayer with N dissimilar anisotropic layers are obtained via a generalized image decomposition method. The original problem is decomposed into N homogeneous subproblems with strategically placed continuously distributed image (virtual) dislocations which satisfy the consistency conditions for degenerate N − M (M < N) layer problems. The image dislocations are used to satisfy the interface or free surface conditions, and represent the unknowns of the problem. The resulting singular Cauchy integral equations are transformed into non-singular Fredholm integral equations of the second kind using certain H- and I-integral transforms. The Fredholm integral equations are then solved via the classical Nyström method. The general decomposition and the elimination of all singular integrals yield an exact formulation of the problem; the approximation arises only in the Nyström method. The dislocation mixity and the number of layers dissimilar in thickness and elastic anisotropy can be handled without difficulty, constrained only by the number of linear algebraic equations in the Nyström method for large N. For the numerical study, image forces on a dislocation in two- and three-layer systems are calculated. The accuracy of the results is verified by checking the boundary conditions and by comparison with previous results. The dependence of the image force on the dislocation position and mixity, and on the layer thicknesses and elastic anisotropies, is also illustrated via numerical investigations.     

Numerical analysis of turbulent convection heat transfer from an array of perforated fins

Numerical investigation is made for three-dimensional fluid flow and convective heat transfer from an array of solid and perforated fins that are mounted on a flat plate. Incompressible air as working fluid is modeled using Navier–Stokes equations and RNG based k ? ? turbulent model is used to predict turbulent flow parameters. Temperature field inside the fins is obtained by solving Fourier’s conduction equation. The conjugate differential equations for both solid and gas phase are solved simultaneously by finite volume procedure using SIMPLE algorithm. Perforations such as small channels with square cross section are arranged streamwise along the fin’s length and their numbers varied from 1 to 3. Flow and heat transfer characteristics are presented for Reynolds numbers from 2 × 10⁴ to 4 × 10⁴ based on the fin length and Prandtl number is taken Pr = 0.71. Numerical computations are validated with experimental studies of the previous investigators and good agreements were observed. Results show that fins with longitudinal pores, have remarkable heat transfer enhancement in addition to the considerable reduction in weight by comparison with solid fins.     

Solvent-less synthesis of zinc oxide nanostructures from Zn(salen) as precursor and their optical properties

ZnO nanoparticles, 10–20 nm in size, were synthesized by heat treatment in air at 500 °C for 5 h., using [N,N′-bis(salicylaldehydo) ethylene diamine]zinc(II), i.e., Zn(salen), as precursor, which was obtained by a solvent-free solid–solid reaction. Heat-treated products were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy, and transmission electron microscopy. Room temperature photoluminescence spectra of ZnO nanostructures are dominated by green emission attributed to oxygen vacancy related donor–acceptor transition.