Effective flow of a viscous liquid through a helical pipe

We study the flow of a viscous fluid through a pipe with helical shape parameterized with , where the small parameter stands for the distance between two coils of the helix. The pipe has small cross-section of size . Using the asymptotic analysis of the microscopic flow described by the Navier–Stokes system, with respect to the small parameter that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe. To cite this article: E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).

Résumé

On considère un écoulement dans un tube de section circulaire et de forme hélicoïdale paramétré par , où est la distance entre deux tours de la spirale. Le rayon de la section du tube est lui aussi supposé égal à . A partir de l'écoulement microscopique décrit par le système de Navier–Stokes et en utilisant l'analyse asymptotique par rapport à ce petit paramètre on obtient l'écoulemment effectif décrit par une formule explicite de type Poiseuille associée à une petite déviation due à la géometrie du tube. Pour citer cet article : E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).     

Dynamical stability of the response of oscillators with discontinuous or steep first derivative of restoring characteristic

The influence of factors which can lead to incorrect prediction of dynamical stability of the periodic response of oscillators which contain a non-linear restoring characteristic with discontinuous or steep first derivative is considered in this paper. For that purpose, a simple one degree-of-freedom system with a piecewise-linear force-displacement relationship subjected to a harmonic excitation is analysed. Stability of the periodic response obtained in the frequency domain by the incremental harmonic balance method is determined by using the Floquet–Liapounov theorem. Responses in the time domain are obtained by digital simulation. The accuracy of determining the eigenvalues of the monodromy matrix (in the considered example) significantly depend on the corrective vector norm r , the accuracy of numerical determination of the times when the system undergoes a stiffness change, and on the number of step functions M (used in the Hsu's procedure), only for r >1×10⁻⁵,>1×10⁻⁵ and M<2000. Otherwise, except if the maximum modulus of the eigenvalues of the monodromy matrix is very close to unity, their influence on estimation of dynamical stability is minor. On the contrary, neglecting very small harmonic terms of the actual time domain response can cause a very large error in the evaluation of the eigenvalues of the monodromy matrix, and so they can lead to incorrect prediction of the dynamical stability of the solution, regardless of whether the maximum modulus of the eigenvalues of the monodromy matrix is close to unity or not.     

Domain perturbation method and shape of a bubble in a uniform flow of an inviscid liquid

In many problems with a free boundary there is defined a small parameter, , for which the solution is sometimes known for a particular value, =0, and the general solution is obtained as a series in the parameter. To find this solution, the equations can be written on a reference configuration and solved in a fixed domain. The purpose of this study is to show that this method of domain perturbation is a good one. The range of validity of this method will be studied on the model example of the irrotational flow of a perfect fluid around a bubble. The radius of convergence of the series solution will be determined, as will the nature of the solution in the neighbourhood of the first real singularity.     

Radiation and hot electron temperature measurements of short-pulselaser driven hohlraums

We have performed measurements of the radiation and the hot electron temperature in sub-millimetre size hohlraums driven by a high intensity short-pulse laser. The results indicate that radiation temperatures 80 eV can be obtained with 20 J of laser energy delivered on target. Radiation-hydrodynamics simulations indicate an absorption into thermal X-rays of 1–2%, with peak temperatures similar to those measured experimentally.     

Evolution of the E structural unit during uniaxial and constrained tensile deformation

Molecular dynamics simulations are used to study the mechanisms by which Shockley partial dislocations are nucleated from 1 1 0 copper grain boundaries which contain the E structural unit. Simulations in this work indicate that the natural conformation of the interface porosity with respect to the primary dislocation slip systems is responsible for the easy emission of Shockley partial dislocations during a tensile deformation. Furthermore, it is found that tensile stresses parallel to the interface plane can diminish the severity of the E structural unit on the dislocation nucleation process.     

Near-critical CO2 liquid--vapor flow in a sub-microchannel. Part II: Flow regimes

The mean-field free-energy LBM is used to investigate the liquid--vapor flow regimes in a two-dimensional 200 nm channel with near-critical CO₂ at temperature 25 ^oC and pressure 6.434 MPa as the working fluid. Flow regimes over vapor qualities ranging from 0.01x0.90, Weber numbers O(10⁻²)WeO(10³), and capillary numbers O(10⁻²)CaO(10) are investigated. Three major types of flow regimes are encountered -- dispersed flow, bubble/plug flow, and liquid strip flow, each of which encompasses variations of the basic flow regime. The three major flow regimes with all their variations can be further classified into two major categories – regular and irregular. Irregular flow regimes are characterized by a distorted interface, including distorted bubble/slug flow, intermittent strip flow, wavy strip flow, and wispy-strip flow. Flows in which the interface is ordered and symmetric such as bubble/plug and strip flows are classified as regular flow regimes. It is found that the transition from regular to irregular flow regimes occurs at Weber number between 500 and 1000, independent of the vapor quality. Although no experiments exist at the same conditions, comparison of the predicted transition between regular and irregular regimes shows the same qualitative trends as experiments found in the literature.     

High-order LES of turbulent heat transfer in a rotor–stator cavity

The present work examines the turbulent flow in an enclosed rotor–stator system subjected to heat transfer effects. Besides their fundamental importance as three-dimensional prototype flows, such flows arise in many industrial applications but also in many geophysical and astrophysical settings. Large eddy simulations (LES) are here performed using a spectral vanishing viscosity technique. The LES results have already been favorably compared to velocity measurements in the isothermal case (Séverac, E., Poncet, S., Serre, E., Chauve, M.P., 2007. Large eddy simulation and measurements of turbulent enclosed rotor–stator flows. Phys. Fluids, 19, 085113) for a large range of Reynolds numbers 10⁵Re=Ωb²/ν10⁶, in an annular cavity of large aspect ratio G=(b-a)/H=5 and weak curvature parameter R_m=(b-a)/(b+a)=1.8 (a,b the inner and outer radii of the rotor and H the interdisk spacing). The purpose of this paper is to extend these previous results in the non-isothermal case using the Boussinesq approximation to take into account the buoyancy effects. Thus, the effects of thermal convection have been examined for a turbulent flow Re=10⁶ of air in the same rotor–stator system for Rayleigh numbers up to Ra=10⁸. These LES results provide accurate, instantaneous quantities which are of interest in understanding the physics of turbulent flows and heat transfers in an interdisk cavity. Even at high Rayleigh numbers, the structure of the iso-values of the instantaneous normal temperature gradient at the disk surfaces resembles the one of the iso-values of the tangential velocity with large spiral arms along the rotor and more thin structures along the stator. The averaged results show small effects of density variation on the mean and turbulent fields. The turbulent Prandtl number is a decreasing function of the distance to the wall with 1.4 close to the disks and about 0.3 in the outer layers. The local Nusselt number is found to be proportional to the local Reynolds number to the power 0.7. The evolution of the averaged Bolgiano length scale L_B with the Rayleigh number indicates that temperature fluctuations may have a large influence on the dynamics only at the largest scales of the system for Ra10⁷, since L_B remains lower than the thermal boundary layer thicknesses.     

CFD-simulation of a circulating fluidized bed riser

In the current work, a model of the fluid mechanics in the riser of a circulating fluidized bed （CFB） has been implemented using computational fluid dynamics （CFD）. The model developed shall be used in future as the basis of 3D-reactor model for the simulation of large scale CFB combustors. The two-fluid model （TFM） approach is used to represent the fluid mechanics involved in the flow. The computational implementation is accomplished by the commercial software FLUENT. Different closure formulations are tested on a simplified geometry. Two different turbulence formulations, namely the swirl modified RNG k-e model and the Realizable k-e model, are tested in combination with two different approaches to solid phase turbulence, namely the dispersion and per phase approach. One focus of the current work is put on the study of different drag correlations. Besides the drag correlations by Syamlal et al. [Syamlal, M., Rogers, W., ＆ O＇Brien, T. J. （1993）. MFIX documentation theory guide. Technical Report DOE/METC-9411004, U.S. Department of Energy （DOE）. Morgantown Energy Technology Center： Morgantown, WV] and Gidaspow [Gidaspow, D. （1994）. Multiphaseflow andfluidization. New York： Academic Press] the EMMS model has been used to determine the momentum exchange between the two phases. The resulting formulation is then used to simulate a 1-m × 0.3-m cold CFB setup and is validated by experimental results [Schlichtharle, P. （2000）. Fluid dynamics and mixing of solids and gas in the bottom zone of circulating fluidized beds. Unoublished doctoral dissertation, Technische Universitaet Hamburg-Harburg, Shaker Verlag： Aachen].     

Effects of variable viscosity and thermal conductivity of Al2O3–water nanofluid on heat transfer enhancement in natural convection

Heat transfer enhancement in horizontal annuli using variable properties of Al₂O₃–water nanofluid is investigated. Different viscosity and thermal conductivity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Chon et al. expression for conductivity and the Nguyen et al. experimental data for viscosity which take into account the dependence of these properties on temperature and nanoparticle volume fraction. It was observed that for Ra  10⁴, the average Nusselt number was reduced by increasing the volume fraction of nanoparticles. However, for Ra = 10³, the average Nusselt number increased by increasing the volume fraction of nanoparticles. For Ra  10⁴, the Nusselt number was deteriorated every where around the cylinder surface especially at high expansion ratio. However, this reduction is only restricted to certain regions around the cylinder surface at Ra = 10³. For Ra  10⁴, the difference in Nusselt number between the Maxwell Garnett and Chon et al. model prediction is small. But, there was a deviation in prediction at Ra = 10³ and this deviation becomes more significant at high volume fraction of nanoparticles. The Nguyen et al. data and Brinkman model gives completely different predictions for Ra  10⁴ where the difference in prediction of Nusselt number reached 30%. However, this difference was less than 10% at Ra = 10³.     

On the rheology of a dilute suspension of rigid spheres in a weakly viscoelastic matrix fluid

The complete solution for the pressure and the velocity field up to O(De) of a dilute suspension of neutrally buoyant, non-Brownian rigid spheres suspended in an unbounded, weakly viscoelastic matrix fluid, where is the solid volume fraction and De is the Deborah number of the matrix fluid, is presented. The spheres are subjected to an arbitrary linear velocity profile at infinity. The analytical solution is used for the prediction of the bulk stress, and specifically for the calculation of the first and the second normal stress differences in simple shear and uniaxial elongational flows. A comparison of the results with available values reported in the literature is also offered. The final expressions for the bulk normal stress differences in shear and uniaxial elongational flow fully agree with those reported earlier by Greco et al., J. Non-Newton. Fluid Mech., 147 (2007) 1–10.     

Molecular dynamics simulation of deformation and failure of nanocrystals of bcc metals

Simulations of uniaxial and hydrostatic tension of Fe and Mo nanocrystal are made by molecular dynamics method. Stress versus strain are obtained while regularities of lattice rearrangement during nanocrystal plastic deformation are considered. Local instability of nanocrystal lattice, which is the cause for transition from elastic to plastic deformation of nanocrystal, is found. It is shown that local shear stresses is a driving force of nanocrystal lattice rearrangements under the conditions of both uniaxial and hydrostatic tension, so, local instability of nanocrystal of bcc metals should be considered as shear instability. Realization of “orthorhombic” path of deformation at 1 0 0 tension of Mo nanocrystal is specific case of above effect. It is demonstrated that unlike covalent nanocrystal, metallic nanocrystals display “heterogeneous” mechanism of crack nucleation, which essence is that cracks nucleate not in homogeneous elastically deformed lattice but in shear bands or near their boundaries, i.e., after non-homogeneous plastic deformation of nanocrystal.     

Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid

Effects of inclination angle on natural convection heat transfer and fluid flow in a two-dimensional enclosure filled with Cu-nanofluid has been analyzed numerically. The performance of nanofluids is tested inside an enclosure by taking into account the solid particle dispersion. The angle of inclination is used as a control parameter for flow and heat transfer. It was varied from  = 0° to  = 120°. The governing equations are solved with finite-volume technique for the range of Rayleigh numbers as 10³  Ra  10⁵. It is found that the effect of nanoparticles concentration on Nusselt number is more pronounced at low volume fraction than at high volume fraction. Inclination angle can be a control parameter for nanofluid filled enclosure. Percentage of heat transfer enhancement using nanoparticles decreases for higher Rayleigh numbers.     

Collision operator including large-angle scattering for moderately coupled plasma

A new approach has been developed to treat the large-angle as well as the small-angle binary collisions in high temperature and high density plasmas when the test particle distribution function f_α is even function about the test velocity and the relations of the mass and the velocity between the test particles and the field particles are satisfied with m_αm_β (such as electron–ion collision or Lorentz-gas model) and . With the approach, the Boltzmann collision operator is derived to be suitable for the plasma considered as weakly coupled (Coulomb logarithm ) and moderately coupled , i.e., for the electron–ion coupling constant Γ_ei<0.1. The modified collision operator has a direct and practical connection to the Rosenbluth potentials, the new reduced electron–ion collision operator differs from the original Fokker–Planck operator for Coulomb collisions by terms of order . Moreover, some calculations of relaxation rate and transport properties are given for new reduced electron–ion collision operator that shows corrections.     

Explicit conditions for the existence of exceptional body waves and subsonic surface waves in anisotropic elastic solids

It is known that a subsonic surface (Rayleigh) wave exists in an anisotropic elastic half-space x₂  0 if the first transonic state is not of Type 1. If the first transonic state is of Type 1 but the limiting wave is not exceptional, a subsonic surface wave exists. If the first transonic state is of Type 1 and the limiting wave is exceptional, a subsonic surface wave exists when . It is shown that an exceptional body wave is necessarily an exceptional transonic wave, and could be an exceptional limiting wave. Only two wave speeds are possible for an exceptional body wave. We present explicit conditions in terms of the reduced elastic compliances for the existence of an exceptional body wave. If an exceptional body wave exists, conditions are given for identifying whether the transonic state is of Type 1. Hence, through the existence of an exceptional body wave we provide explicit conditions for the existence of a subsonic surface wave with the exception when needs to be computed.     

Accurate heat transfer measurements using thermochromic liquid crystal. Part 1: Calibration and characteristics of crystals

Encapsulated thermochromic liquid crystal (TLC) can accurately measure surface temperature in a variety of heat transfer and fluid flow experiments. Narrow-band TLC, where the colour changes over a temperature range of 1 °C, can be used to determine surface temperature within an uncertainty of 0.1 °C. Wide-band TLC, typically active over 5–20 °C, allow the possibility of mapping surface temperature distributions. In part 1 of this two-part paper, an extensive set of calibrations for narrow-band and wide-band TLC is reported. This generic study provides insight into the importance and influence of the various factors governing the colour–temperature relationship. These governing effects include the variation in optical path, the spectrum of the illumination source, the lighting and viewing angles, the differences between cooling or heating cycles (hysteresis), the variation with the number of heating or cooling cycles (aging) and how this varies with TLC film thickness. Two narrow-band crystals are also specifically calibrated for application to experiments on a transparent disc rotating at high speed (5000 rpm). Part 2 of this paper describes how these accurately-calibrated crystals were used to measure the transient surface temperature on, and heat transfer to, a rotating disc.     

Regularity criteria for the 3D MHD equations in terms of the pressure

In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition b being in the Serrin's regularity class, if the pressure p belongs to L^α,γ with or the gradient field of pressure p belongs to L^α,γ with on [0,T], then the solution remains smooth on [0,T].     

Whole-body vibration: Evaluation of emission and exposure levels arising from agricultural tractors

A study was conducted to quantify whole-body vibration (WBV) emission and estimated exposure levels found upon a range of modern, state-of-the-art agricultural tractors, when operated in controlled conditions (traversing ISO ride vibration test tracks and performing selected agricultural operations) and whilst performing identical tasks during ‘on-farm’ use. The potential consequences of operator WBV exposure limitations, as prescribed by the European Physical Agents (Vibration) Directive:2002 (PA(V)D), upon tractor usage patterns were considered. Tractor WBV emission levels were found to be very dependent upon the nature of field operation performed, but largely independent of vehicle suspension system capability (due to the dominance of horizontal vibration). However, this trend was reversed during on-road transport. Few examples (9%) of tractor field operations approached or exceeded the PA(V)D Exposure Limit Value (ELV) during 8 h operation, but this figure increased (to 27%) during longer working days. However virtually all (95%) ‘on-farm’ vehicles exceeded the Exposure Action Value (EAV) during an 8-h day. The PA(V)D is not likely to restrict the operation of large, state-of-the-art tractors during an 8-h day, but will become a limitation if the working day lengthens significantly. Further ‘on-farm’ WBV data collection is required to enable creation of a robust, generic WBV emission database for agricultural tractor operations, to enable estimation of likely WBV exposure by employers.     

Plasticity of metal wires in torsion: Molecular dynamics and dislocation dynamics simulations

The orientation dependent plasticity in metal nanowires is investigated using molecular dynamics and dislocation dynamics simulations. Molecular dynamics simulations show that the orientation of single crystal metal wires controls the mechanisms of plastic deformation. For wires oriented along , dislocations nucleate along the axis of the wire, making the deformation homogeneous. These wires also maintain most of their strength after yield. In contrast, wires oriented along and directions deform through the formation of twist boundaries and tend not to recover when high angle twist boundaries are formed. The stability of the dislocation structures observed in molecular dynamics simulations are investigated using analytical and dislocation dynamics models.     

Comparison of two- and three-dimensional modeling of invert trap for sewer solid management

In the present study, five different invert trap configurations （rectangular with and without lids on both sides; trapezoidal, trapezoidal with rectangular base and rectangular with trapezoidal base with lids on both sides） were simulated for both two-dimensional （2D） and three-dimensional （3D） flow conditions for three sediment types （sand, styrocell and plastic beads） at six flow rates （0.35, 0.70, 1.05, 1.35, 4.55 and 9.95 L/s） for each trap. Computational fluid dynamics （CFD）-based modeling using FLUENT software with Renormalization Group （RNG） k-e model along with discrete phase model （DPM） were used in the simulations. A hexagonal/tetrahedral and map-type non-uniform grid was chosen to discretize the entire computational domain and a control volume finite difference method was used to solve the governing equations. The flow rates selected in the present study cover the entire range of flow rate expected for dry weather and monsoon. The simulation is capable of differentiating between 2D and 3D modeling of particle trajectories, the effects of flow rate and trap geometry on flow patterns developed in the trap. The sediment retention ratio for 2D is higher than that for 3D modeling for all flow conditions, particle types and model geometry due to inclusion of lateral effects in 3D modeling. The invert trap having rectangular shape with trapezoidal base is found to be the most efficient configuration in both 2D and 3D modeling.