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.     

A 1-D theory for extensional deformation of a viscoelastic filament under exponential stretching

We consider a viscoelastic filament placed between two coaxial discs, with the bottom plate fixed and the top plate pulled at an exponential rate. Using a slender rod approximation, we derive a one-dimensional (1-D) model which describes the deformation of a viscoelastic filament governed by the Oldroyd-B constitutive model. It is assumed that the flow is axisymmetric and that inertia and gravity are negligible. One solution of the model equations corresponds to ideal uniaxial elongation. A linear stability analysis shows that this solution is unstable for a Newtonian fluid and for viscoelastic filaments with small Deborah number (De ≤ 0.5). For Deborah number greater than 0.5, ideal uniaxial elongation is linearly stable. Numerical solution of the nonlinear equations confirms the result of the linear stability analysis. For initial conditions close to ideal uniaxial flow, our results show that if De > 0.5, the central portion of the filament undergoes considerable strain hardening. As a result, the sample remains almost cylindrical and the deformation approaches pure uniaxial extension as the Hencky strain increases. For De ≤ 0.5, the Trouton ratio based on the effective extension rate at the mid-plane radius gives a much better approximation to the true extensional viscosity than that based on the imposed stretch rate.     

Heat transfer and pressure drop studies in a circular tube fitted with straight full twist

Experimental investigation of heat transfer characteristics of circular tube fitted with straight full twist insert has been presented. The heat transfer coefficient increases with Reynolds number and decreasing spacer distance with maximum being 2 in. spacer distance for both the type of twist inserts. Also, there is no appreciable increase in heat transfer enhancement in straight full twist insert with 2 in. spacer distance. Experiments were carried out in turbulent flow using straight full twist insert with 4 in. spacer and similar trend of increasing Nusselt number with Reynolds number was observed. Performance evaluation analysis was made and the maximum performance ratio was obtained for each twist insert corresponding to the Reynolds number of 2550.     

Buckling behavior of Kelvin open-cell foams under [0 0 1], [0 1 1] and [1 1 1] compressive loads

This paper describes buckling modes and stresses of elastic Kelvin open-cell foams subjected to [0 0 1], [0 1 1] and [1 1 1] uniaxial compressions. Cubic unit cells and cell aggregates in model foams are analyzed using a homogenization theory of the updated Lagrangian type. The analysis is performed on the assumption that the struts in foams have a non-uniform distribution of cross-sectional areas as observed experimentally. The relative density is changed to range from 0.005 to 0.05. It is thus found that long wavelength buckling and macroscopic instability primarily occur under [0 0 1] and [0 1 1] compressions, with only short wavelength buckling under [1 1 1] compression. The primary buckling stresses under the three compressions are fairly close to one another and almost satisfy the Gibson–Ashby relation established to fit experiments. By also performing the analysis based on the uniformity of strut cross-sectional areas, it is shown that the non-uniformity of cross-sectional areas is an important factor for the buckling behavior of open-cell foams.     

Flow of a quasi-Newtonian fluid through a planar contraction

Flows through abrupt contractions are dominated by the rapid extension experienced in passing through the contraction. Thus, it is useful to employ a fluid model which considers the extensional viscosity explicitly in its constitutive equation. In this paper, the quasi-Newtonian fluid model, which admits shear thinning and extension thickening of the viscosity depending on the local type of flow as proposed by Schunk and Scriven [P. Schunk, L. Scriven, J, Rheol 34 (1990) 1085], is applied to the numerical simulation of the flow of a dilute polyacrylamide solution through a planar 4 : 1 contraction. In this theory the extra stress tensor does not only depend on the rate of strain tensor but also on the relative rate of rotation of the fluid. The material function – the viscosity function – is allowed to depend on the invariants of these two kinematic tensors yielding a local distinction between extensional, shear or rotation dominated flow. The governing equations are discretized using a finite volume method. Different model parameters are varied and the simulation results are compared with the generalized Newtonian fluid and experimental data.     

Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading

This paper describes an investigation into elastic buckling of an embedded multi-walled carbon nanotube under combined torsion and axial loading, which takes account of the radial constraint from the surrounding elastic medium and van der Waals force between two adjacent tube walls. Depending on the ratio of radius to thickness, the multi-walled carbon nanotubes discussed here are classified as thin, thick, and nearly solid. Critical buckling load with the corresponding mode is obtained for multi-walled carbon nanotubes under combined torsion and axial loading, with various values of the radius to thickness ratio and surrounded with different elastic media. The study indicates that the buckling mode (m, n) of an embedded multi-walled carbon nanotube under combined torsion and axial loading is unique and it is different from that with axial compression only. New features for the buckling of an embedded multi-walled carbon nanotube under combined torsion and axial loading and the meaningful numerical results are useful in the design of nanodrive device, nanotorsional oscillator and rotational actuators, where multi-walled carbon nanotubes act as basic elements.     

Nonlinear analysis of a SWCNT over a bundle of nanotubes

The deformation of a single wall carbon nanotube (SWCNT) interacting with a curved bundle of nanotubes is analyzed. The SWCNT is modeled as a straight elastic inextensible beam based on small deformation. The bundle of nanotubes is assumed rigid and the interaction is due to the van der Waals forces. An analytical solution is obtained using a bilinear approximation to the van der Waals forces. The analytical results are in good agreement with the results of two numerical methods. The results indicate that the SWCNT remains near the curved bundle provided that its curvature is below a critical value. For curvatures above this critical value the SWCNT breaks contact with the curved bundle and nearly returns to its straight position. A parameter study shows that the critical curvature depends on the stiffness of the SWCNT and the absolute minimum energy associated with the van der Waals forces but it is independent of the SWCNT's length in general. An analytical estimate of the critical curvature is developed. The results of this study may be applicable to composites of nanotubes where separation phenomena are suspected to occur.     

Rheological characterization of melt processed polycarbonate-multiwalled carbon nanotube composites

In this study polycarbonate/multiwalled carbon nanotube composites were produced with different compositions by diluting a masterbatch using melt mixing in a DACA-Micro-Compounder. The composites were rheologically characterized using an ARES-rheometer in the dynamic mode under nitrogen atmosphere at 280 °C and frequency varying from 100 to 0.056 rad/s.The results showed that the dynamic moduli and the viscosity increased with increasing MWNT content. At a concentration of 0.5 wt.% MWNT, a significant change in the frequency dependence of the moduli was observed which indicates a transition from a liquid like to a solid like behavior of the nanocomposites. This transition can be related to the formation of a combined network between the nanotubes and the polymer chains.     

Analytical modeling of synthetic fiber ropes. Part II: A linear elastic model for 1 + 6 fibrous structures

In part I of this study it was shown that, to model synthetic fiber ropes, two scale transition models can be used in sequence. The first model (continuum model) has been presented in the part I and the present paper examines the behavior of a fibrous structure consisting of 6 helicoidal strands around a central core (1 + 6 structure). An analytical model will be presented which enables the global elastic behavior of such a cable under tension–torsion loading to be predicted. In this model, first, the core and the strands are described as Kirchhoff–Love beams and then the traction–torsion coupling behavior is taken into account for both of them. By modeling the contact conditions between the strands and the core, with certain assumptions, it is possible to describe the behavior of the cable section as a function of the degrees of freedom of the core. The behavior of the cable can thus be deduced from the tension–torsion coupling behavior of its constituents. Tensile tests have been performed on the core, the strands and then on a full scale 205 ton failure load cable. Finally, predicted stiffness from the analytical models is compared to the test results.     

LES-based filter-matrix lattice Boltzmann model for simulating turbulent natural convection in a square cavity

In this paper, a novel thermal filter-matrix lattice Boltzmann model based on large eddy simulation (LES) is proposed for simulating turbulent natural convection. In this study, the Vreman subgrid-scale eddy-viscosity model is introduced into the present framework of LES to accurately predict the flow in near-wall region. Two dimensional numerical simulations of natural convection in a square cavity were performed at high Rayleigh number varying from 10⁷ to 10¹⁰ with a fixed Prandtl number of Pr = 0.71. The influences of the higher-order terms upon the present results at high Rayleigh numbers are examined, taking Ra = 10⁷ and 10⁸ as the example, revealing that the proper minimization of the higher-order terms can improve numerical accuracy of present model for high Rayleigh convective flow. For the turbulent convective flow, the time-averaged quantities in the median lines are presented and compared against those available results from previous studies. The general structure of turbulent boundary layers is well predicted. All numerical results exhibit good agreement with the benchmark solutions available in the previous literatures.     

Study of dynamic stability of the double-walled carbon nanotube under axial loading embedded in an elastic medium by the energy method

In this paper, the dynamic stability of single- and double-walled carbon nanotubes (SWCNT and DWCNT) under dynamic axial loading is investigated using the continuum mechanics model and the minimum total energy method. The natural frequencies of the SWCNT and the critical dynamic axial load of the SWCNT and DWCNT are obtained using the Rayleigh-Ritz method. The effects of the elastic medium and the van der Waals forces between the two layers in the DWCNT are taken into account using the Winkler model and Lennard-Jones theory, respectively. The effect of the small length scale is also considered using the Eringen Model. The critical dynamic axial load is increased by inserting an inner carbon nanotube (CNT) into an isolated CNT embedded in an elastic medium.     

Topological sensitivity to diagonal member flips of two-layered statically determinate trusses under worst loading

The paper deals with the topological sensitivity of free, unsupported, statically determinate plane trusses whose horizontal and vertical members form two horizontal layers of square cells and two or more vertical layers. The topology of a truss is decomposed into a form vector – the placement of cells containing diagonal members – and a binary vector describing the slopes of the diagonals. The construction of complete form and slope spaces is provided for any number of vertical layers. Using exhaustive search, forms with minimum and maximum sensitivity to slope change are found for trusses with 2 × 2 through 2 × 8 layers under worst static load condition, represented by the lowest eigenvalue of the least-squares equilibrium matrix. Typical features of the least and most sensitive forms and associated loads and internal forces are shown. Changes of absolute and relative topological sensitivities with increasing number of vertical layers are discussed.     

Numerical investigation of particle deposition inside aero-shielded solar cyclone reactor: A promising solution for reactor clogging

Solar cracking of methane is considered to be an attractive option due to its CO₂ free hydrogen production process. Carbon particle deposition on the reactor window, walls and exit is a major obstacle to achieve continuous operation of methane cracking solar reactors. As a solution to this problem a novel “aero-shielded solar cyclone reactor” was created. In this present study the prediction of particle deposition at various locations for the aero-shielded reactor is numerically investigated by a Lagrangian particle dispersion model. A detailed three dimensional computational fluid dynamic (CFD) analysis for carbon deposition at the reactor window, walls and exit is presented using a Discrete Phase Model (DPM). The flow field is based on a RNG k–ε model and species transport with methane as the main flow and argon/ hydrogen as window and wall screening fluid. Flow behavior and particle deposition have been observed with the variation of main flow rates from 10–20 L/min and with carbon particle mass flow rate of 7 × 10⁻⁶ and 1.75 × 10⁻⁵ kg/s. In this study the window and wall screening flow rates have been considered to be 1 L/min and 10 L/min by employing either argon or hydrogen. Also, to study the effect of particle size simulations have also been carried out (i) with a variation of particle diameter with a size distribution of 0.5–234 μm and (ii) by taking 40 μm mono sized particles which is the mean value for the considered size distribution. Results show that by appropriately selecting the above parameters, the concept of the aero-shielded reactor can be an attractive option to resolve the problem of carbon deposition at the window, walls and exit of the reactor.     

Particle deposition model for particulate flows at high temperatures in gas turbine components

This study proposes an improved physical model to predict sand deposition at high temperature in gas turbine components. This model differs from its predecessor (Sreedharan and Tafti, 2011) by improving the sticking probability by accounting for the energy losses during particle-wall collision based on our previous work (Singh and Tafti, 2013). This model predicts the probability of sticking based on the critical viscosity approach and collision losses during a particle–wall collision. The current model is novel in the sense that it predicts the sticking probability based on the impact velocity along with the particle temperature. To test the model, deposition from a sand particle laden jet impacting on a flat coupon geometry is computed and the results obtained from the numerical model are compared with experiments (Delimont et al., 2014) conducted at Virginia Tech, on a similar geometry and flow conditions, for jet temperatures of 950 °C, 1000 °C and 1050 °C. Large Eddy Simulations (LES) are used to model the flow field and heat transfer, and sand particles are modeled using a discrete Lagrangian framework. Results quantify the impingement and deposition for 20–40 μm sand particles. The stagnation region of the target coupon is found to experience most of the impingement and deposition. For 950 °C jet temperature, around 5% of the particle impacting the coupon deposit while the deposition for 1000 °C and 1050 °C is 17% and 28%, respectively. In general, the sticking efficiencies calculated from the model show good agreement with the experiments for the temperature range considered.     

Numerical simulation and analysis of the effect of rain and surface property on wind-turbine airfoil performance

The performance of wind turbines is significantly affected by the atmospheric condition of their operating environment. Because rain is a common phenomenon in many parts of the world, understanding its effect on the performance of wind turbines provides valuable information in determining the site for a new wind farm. We developed a multiphase computational fluid dynamics (CFD) model to estimate the effect of rain by simulating the actual physical process of rain droplets forming a water layer over the blades by coupling the Lagrangian Discrete Phase Model (DPM) and the Eulerian Volume of Fluid (VOF) models. We applied our model to a wind-turbine blade airfoil and studied the effect of rain for different rainfall rates in addition to the effect of surface tension and surface property of the airfoil. We observed that, at low rainfall rates, the performance of the airfoil is highly sensitive to the rainfall rate. However, if the rainfall rate is high enough to immerse most of the airfoil surface under water, a further increase in the rainfall rate does not have a substantial effect on the performance of the airfoil.     

CFD simulation of a gas–solid fluidized bed with two vertical jets

A computational fluid dynamics (CFD) model is used to investigate the hydrodynamics of a gas–solid fluidized bed with two vertical jets. Sand particles with a density of 2660 kg/m³ and a diameter of 5.0 × 10^?4 m are employed as the solid phase. Numerical computation is carried out in a 0.57 m × 1.00 m two-dimensional bed using a commercial CFD code, CFX 4.4, together with user-defined Fortran subroutines. The applicability of the CFD model is validated by predicting the bed pressure drop in a bubbling fluidized bed, and the jet detachment time and equivalent bubble diameter in a fluidized bed with a single jet. Subsequently, the model is used to explore the hydrodynamics of two vertical jets in a fluidized bed. The computational results reveal three flow patterns, isolated, merged and transitional jets, depending on the nozzle separation distance and jet gas velocity and influencing significantly the solid circulation pattern. The jet penetration depth is found to increase with increasing jet gas velocity, and can be predicted reasonably well by the correlations of Hong et al. (2003) for isolated jets and of Yang and Keairns (1979) for interacting jets.     

Experiments with a Wire-Mesh Sensor for stratified and dispersed oil-brine pipe flow

Two-phase oil–water flow was studied in a 15 m long horizontal steel pipe, with 8.28 cm internal diameter, using mineral oil (having 830 kg/m³ density and 7.5 mPa s viscosity) and brine (1073 kg/m³ density and of 0.8 mPa s viscosity). Measurements of the holdup and of the cross-sectional phase fraction distribution were obtained for stratified flow and for highly dispersed oil–water flows, applying a capacitive Wire-Mesh Sensor specially designed for that purpose. The applicability of this measurement technique, which uses a circuit for capacitive measurements that is adapted to conductive measurements, where one of the fluids is water with high salinity (mimicking sea water), was assessed. Values for the phase fraction values were derived from the raw data obtained by the Wire-Mesh Sensor using several mixture permittivity models. Two gamma-ray densitometers allowed the accurate measurement of the holdups, which was used to validate the data acquired with the capacitive Wire-Mesh Sensor. The measured time-averaged distribution of the phase fraction over the cross-sectional area was used to investigate the details of the observed two-phase flow patterns, including the interface shape and water height. The experiments were conducted in the multiphase-flow test facility of Shell Global International B.V. in the Netherlands.     

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.     

IR measurements of the thermodynamic effects in cavitating flow

The understanding of the thermodynamic effects of cavitating flow is crucial for applications like turbopumps for liquid hydrogen LH2 and oxygen LOx in space launcher engines. Experimental studies of this phenomenon are rare as most of them were performed in the 1960s and 1970s. The present study presents time resolved IR (Infra-Red) measurements of thermodynamic effects of cavitating flow in a Venturi nozzle.Developed cavitating flow of hot water (95 °C) was observed at different operating conditions – both conventional high speed visualization and high speed IR thermography were used to evaluate the flow parameters.Both the mean features of the temperature distributions and the dynamics of the temperature field were investigated. As a result of evaporation and consequent latent heat flow in the vicinity of the throat a temperature depression of approximately 0.4 K was measured. In the region of pressure recuperation, where the cavitation structures collapse, the temperature rise of up to 1.4 K was recorded. It was found that the temperature dynamics closely follows the dynamics of cavitation structures.Finally experimental results were compared against a simple model based on the Rayleigh–Plesset equation and the thermal delay theory and plausible agreement was achieved.Experimental data is most valuable for further development of numerical models which are, due to poor ensemble of existing experimental results, still at a very rudimentary level.     

A review of new wire arrays with open and closed magnetic configurations at the 1.6 MA Zebra generator for radiative properties and opacity effects

The studies emphasize investigation of plasma formation, implosion, and radiation features as a function of two load configurations: compact multi-planar and cylindrical wire arrays. Experiments with different Z-pinch loads were performed on 1.6 MA, 100 ns, Zebra generator at University of Nevada, Reno. The multi-planar wire arrays (PWAs) were studied in open and closed configurations with Al, Cu, brass, Mo and W wires. In the open magnetic configurations (single, double, triple PWAs) magnetic fields are present inside the arrays from the beginning of discharge, while in closed configurations (prism-like PWA) the global magnetic field is excluded inside before plasma flow occurs. The new prism-like PWA allows high flexibility in control of implosion dynamics and precursor formation. The spectral modeling, magneto-hydrodynamic (MHD) and wire ablation dynamic model (WADM) codes were used to describe the plasma evolution and plasma parameters. Experimentally observed electron temperature and density in multiple bright spots reached 1.4 keV and 5 × 10²¹ cm^?3, respectively. Two types of bright spots were observed. With peak currents up to 1.3 MA opacity effects became more pronounced and led to a limiting of the X-ray yields from compact cylindrical arrays. Despite different magnetic energy to plasma coupling mechanisms early in the implosion a comparison of compact double PWA and cylindrical WA results indicates that during the stagnation stage the same plasma heating mechanism may occur. The double PWA was found to be the best radiator tested at University scale 1 MA generator. It is characterized by a combination of larger yield and power, mm-scale size, and provides the possibility of radiation pulse shaping. Further, the newer configuration, the double PWA with skewed wires, was tested and showed the possibility of a more effective X-ray generation.