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.     

Effect of dislocation structure on fracture toughness of strained BCC-metals

Mechanical properties of materials depend on their structure. Examined are the effects of dislocation structure on fracture toughness and mechanisms of fracture of BCC-metals. Fracture toughness was determined by depending specimens with cracks introduced into the plane perpendicular to the plane of rolling. Fracture toughness increases with decreasing yield stress (for =15–25%). This is due to instability of slightly misoriented cell structure under repeated loading. The peak of fracture toughness at the temperature 77 K was not observed. The increase of fracture toughness for high strained metals (>60% for Mo, and >85% for Cr) corresponds to cell size reduction and the change of fracture mechanisms.     

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.     

A two-dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation

We derive a closed system of effective equations describing a time-dependent flow of a viscous incompressible Newtonian fluid through a long and narrow elastic tube. The 3D axially symmetric incompressible Navier–Stokes equations are used to model the flow. Two models are used to describe the tube wall: the linear membrane shell model and the linearly elastic membrane and the curved, linearly elastic Koiter shell model. We study the behavior of the coupled fluid–structure interaction problem in the limit when the ratio between the radius and the length of the tube, , tends to zero. We obtain the reduced equations that are of Biot type with memory. An interesting feature of the reduced equations is that the memory term explicitly captures the viscoelastic nature of the coupled problem. Our model provides significant improvement over the standard 1D approximations of the fluid–structure interaction problem, all of which assume an ad hoc closure assumption for the velocity profile. We performed experimental validation of the reduced model using a mock circulatory flow loop assembled at the Cardiovascular Research Laboratory at the Texas Heart Institute. Experimental results show excellent agreement with the numerically calculated solution. Major applications include blood flow through large human arteries. To cite this article: S. Čanić et al., C. R. Mecanique 333 (2005).     

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.     

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.     

Progress in subgrid-scale transport modelling for continuous hybrid non-zonal RANS/LES simulations

The partially integrated transport modelling (PITM) method can be viewed as a continuous approach for hybrid RANS/LES modelling allowing seamless coupling between the RANS and the LES regions. The subgrid turbulence quantities are thus calculated from spectral equations depending on the varying spectral cutoff location [Schiestel, R., Dejoan, A., 2005. Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theoretical and Computational Fluid Dynamics 18, 443–468; Chaouat, B., Schiestel, R., 2005. A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Physics of Fluids, 17 (6)] The PITM method can be applied to almost all statistical models to derive its hybrid LES counterpart. In the present work, the PITM version based on the transport equations for the turbulent Reynolds stresses together with the dissipation transport rate equation is now developed in a general formulation based on a new accurate energy spectrum function E(κ) valid in both large and small eddy ranges that allows to calibrate more precisely the c_sgs2 function involved in the subgrid dissipation rate _sgs transport equation. The model is also proposed here in an extended form which remains valid in low Reynolds number turbulent flows. This is achieved by considering a characteristic turbulence length-scale based on the total turbulent energy and the total dissipation rate taking into account the subgrid and resolved parts of the dissipation rate. These improvements allow to consider a large range of flows including various free flows as well as bounded flows. The present model is first tested on the decay of homogeneous isotropic turbulence by referring to the well known experiment of Comte-Bellot and Corrsin. Then, initial perturbed spectra E(κ) with a peak or a defect of energy are considered for analysing the model capabilities in strong non-equilibrium flow situations. The second test case is the classical fully turbulent channel flow that allows to assess the performance of the model in non-homogeneous flows characterised by important anisotropy effects. Different simulations are performed on coarse and refined meshes for checking the grid independence of solutions as well as the consistency of the subgrid-scale model when the filter width is changed. A special attention is devoted to the sharing out of the energy between the subgrid-scales and the resolved scales. Both the mean velocity and the turbulent stress computations are compared with data from direct numerical simulations.     

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.     

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.     

A model for film-forming with Newtonian and shear-thinning fluids

The formation of a thin film by (i) the slow penetration of a gas bubble into a liquid filled tube, (ii) the withdrawal of a planar substrate from a liquid filled gap, is investigated theoretically for the cases of both Newtonian and shear-thinning liquids; the latter conforming to either a power–law or Ellis model. Formulated as a boundary value problem underpinned by lubrication theory, the analysis gives rise to a system of ordinary differential equations which are solved numerically subject to appropriate boundary conditions. For Newtonian liquids comparison of the predicted residual film thickness for a wide range of capillary number, Ca  (10⁻⁴, 10), is made with others obtained using existing expressions, including the classical one of Bretherton, in the region of parameter space over which they apply. In the case of (i), prediction of the behaviour of the residual fluid fraction and gap-to-film thickness ratio, for a Newtonian liquid and one that is shear-thinning and modelled via a power–law, is found to be in particularly good agreement with experimental data for Ca < 0.2. For (ii), both shear-thinning models are utilized and contour plots of residual film thickness generated as a function of Ca and the defining parameters characteristic of each model.     

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.     

Flow structure of wake behind a rotationally oscillating circular cylinder

Flow around a circular cylinder oscillating rotationally with a relatively high forcing frequency has been investigated experimentally. The dominant parameters affecting this experiment are the Reynolds number (Re), oscillation amplitude (θ_A), and frequency ratio F_R=f_f/f_n, where f_f is the forcing frequency and f_n is the natural frequency of vortex shedding. Experiments were carried out under conditions of Re=4.14×10³, 0°θ_A60° and 0.0F_R2.0. Rotational oscillation of the cylinder significantly modified the flow structure in the near-wake. Depending on the frequency ratio F_R, the cylinder wake showed five different flow regimes, each with a distinct wake structure. The vortex formation length and the vortex shedding frequency were greatly changed before and after the lock-on regime where vortices shed at the same frequency as the forcing frequency. The lock-on phenomenon always occurred at F_R=1.0 and the frequency range of the lock-on regime expanded with increasing oscillation amplitude θ_A. In addition, the drag coefficient was reduced when the frequency ratio F_R was less than 1.0 (F_R<1.0) while fixing the oscillation amplitude at θ_A=30°. When the oscillation amplitude θ_A was used as a control parameter at a fixed frequency ratio F_R=1.0 (lock-on regime), the drag reduction effect was observed at all oscillation amplitudes except for the case of θ_A=30°. This type of active flow control method can be used effectively in aerodynamic applications while optimizing the forcing parameters.     

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.     

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.     

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].     

Limitation on crack speed for a strip-craze model applied to PMMA

A strip-craze model is proposed to study crack propagation in polymers. A nonlinear differential equation is derived to govern the dynamic process of crack propagation. The viscous feature of the material in the craze zone is taken into account by means of an experimentally determined relationship between the craze stress and crack speed. By fitting experimental data of PMMA into the model, some parameters including the strip-craze length are deduced. A non-singular stress is introduced to control the crack propagation with a strip craze at its tip. Variations of the crack length and the crack speed with time are computed and their dependence on the non-singular stress is investigated. For PMMA, three stages of crack propagation are identified in terms of initial non-singular stress σ_ns0. When σ_ns0<60 MPa, the crack speed mm/s and the crack is basically stationary; when 60 <σ_ns0<95 MPa, then mm/s the crack is in slow propagation; when σ_ns0>95 MPa, then mm/s and the crack is in rapid propagation. The proposed model is applicable only in slow crack propagation.     

Turbulent wake and vortex shedding for a stack partially immersed in a turbulent boundary layer

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake and Kármán vortex shedding for a cylindrical stack of aspect ratio AR=9 was investigated in a low-speed wind tunnel using thermal anemometry. The cross-flow Reynolds number was Re_D=2.3×10⁴, the jet Reynolds number ranged from Re_d=7.6×10³ to 4.7×10⁴, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-stack-height ratio of δ/H=0.5 at the location of the stack. From the behaviour of the turbulent wake and the vortex shedding, the flow around the stack could be classified into three regimes depending on the value of R, which were the downwash (R<0.7), cross-wind-dominated (0.7R<1.5), and jet-dominated (R1.5) flow regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields, as well as the variation of the Strouhal number and the power spectrum along the stack height.