Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition

International audienceNon-Newtonian boundary layer flow and heat transfer over an exponentially stretching sheet with partial slip boundary condition has been studied in this paper. The flow is subject to a uniform transverse magnetic field. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST), and (ii) prescribed heat flux (PHF). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. An effective second order numerical scheme has been adopted to solve the obtained differen- tial equations. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameters on the velocity, skin-friction coefficient and the temperature boundary layer. It is found that the third grade fluid parameter increases the momentum boundary layer thickness and decreases the thermal boundary layer thickness

Numerical modeling of heat transfer and fluid flow in rotor-stator cavities with throughflow

International audienceThe present study considers the numerical modeling of the turbulent flow in a rotor-stator cavity subjected to a superimposed throughflow with heat transfer. Numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure are compared with experimental data available in the literature. Considering small temperature differences, density variations can be here neglected which leads to dissociate the dynamical effects from the heat transfer process. The fluid flow in an enclosed disk system with axial throughflow is well predicted compared to the velocity measurements performed at IRPHE (Poncet 2005) under isothermal conditions. When the shroud is heated, the effects of rotation and coolant outward throughflow on the heat transfer have been investigated and the numerical results are found to be in good agreement with the data of Sparrow and Goldstein (1976). Their results have been extended for a wide range of the Prandtl numbers. We have also considered the case of an open rotor-stator cavity with a radial inward throughflow with heat transfer along the stator, which corresponds to the experiment of Djaoui et al. (2001). Our results have been compared to both their temperature measurements and their asymptotic model with a close agreement between the different approaches, showing the efficiency of the second order modeling. An empirical correlation law is given to predict the averaged Nusselt number depending on the Reynolds and Prandtl numbers and on the coolant flowrate

Numerical modeling of heat transfer and fluid flow in rotor-stator cavities with throughflow

The present study considers the numerical modeling of the turbulent flow in a rotor-stator cavity subjected to a superimposed throughflow with heat transfer. Numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM) are compared with experimental data available in the literature. Considering small temperature differences, density variations can be here neglected which leads to dissociate the dynamical flow field from the heat transfer process. The turbulent flux is approximated by a gradient hypothesis with tensorial eddy diffusivity coefficient

Turbulence Modeling of Torsional Couette Flows

International audienceThe present study considers the numerical modeling of the turbulent flow inside a rotor-stator cavity subjected or not to a superimposed throughflow. Extensive numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM model) are performed mainly in the case of turbulent flows with merged boundary layers known as turbulent torsional Couette flows and belonging to the regime III of Daily and Nece (1960). The RSM model has already shown its capability of predicting accurately the mean and turbulent fields in various rotating disk configurations. For the first time, a detailed mapping of the hydrodynamic flow over a wide range of rotational Reynolds numbers, aspect ratios of the cavity and flow rate coefficients is here provided in the turbulent torsional Couette flow regime

Large Eddy Simulation of Non-Isothermal Turbulent Rotor-Stator Flows

Non-isothermal turbulent flows in an enclosed rotorstator cavity are here investigated using large eddy simulation (LES). Besides their fundamental importance as three-dimensional prototype flows, such flows arise in many industrial applications and especially in turbomachineries. The LES is performed using a Spectral Vanishing Viscosity technique, which is shown leading to stable discretizations without sacrificing the formal accuracy of the spectral approximation. The LES results have been favorably compared to velocity measurements in the isothermal case. The Boussinesq approximation is then used to take into account the centrifugal-buoyancy effects. The thermal effects have been examined for Re equal to 1 million in a rotor-stator cavity of aspect ratio G=(b-a)/h=5 and curvature parameter Rm=(b-a)/(b+a)=1.8 (a, b the inner and outer radii of the rotor and h the interdisk spacing) and 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. The averaged results show small effects of density variation on the mean and turbulent fields

Turbulence characteristics of the Bödewadt layer in a large shrouded rotor-stator system

4 pagesA three-dimensional direct numerical simulation (3D DNS) is performed to describe the turbulent flow in an enclosed rotor-stator cavity characterized by a large aspect ratio $G=(b-a)/h=18.32$ and a small radius ratio $a/b=0.15$ ($a$ and $b$ the inner and outer radii of the rotating disk and $h$ the interdisk spacing). Recent comparisons with velocity measurements have shown that, for the rotational Reynolds number $Re=\Omega b^2/\nu=95000$ ($\Omega$ the rate of rotation of the rotating disk and $\nu$ the kinematic viscosity of water) under consideration, the stator boundary layer is 3D turbulent and the rotor one is still laminar. Budgets for the turbulence kinetic energy are here presented and highlight some characteristic features of the effect of rotation on turbulence. A quadrant analysis of conditionally averaged velocities is also performed to identify the contributions of different events (ejections and sweeps) on the Reynolds shear stress

The legacy of Henri Victor Regnault in the arts and sciences

International audienceThe 21st of July 2010 marked the bicentennial of the birth of Henri Victor Regnault, a famous French chemist and physicist and a pioneer of paper photography. During his lifetime, he received many honours and distinctions for his invaluable scientific contributions, especially to experimental thermodynamics. Colleague of the celebrated chemist Louis-Joseph Gay-Lussac (1778-1850) at the École des Mines and mentor of William Thomson (1824-1907) at the École Polytechnique, he is nowadays conspicuously absent from all the textbooks and reviews (Hertz, 2004) dealing with thermodynamics. This paper is thus the opportunity to recall his major contributions to the field of experimental thermodynamics but also to the nascent field, in those days, of organic chemistry. Avid amateur of photography, he devoted more than twenty years of his life to his second passion. Having initially taken up photography in the 1840s as a potential tool for scientific research, he ultimately made many more photographs for artistic and self-expressive purposes than scientific ones. He was a founding member of the Société Héliographique in 1851 and of the Société Française de Photographie in 1854. Like his scientific work, his photography was quickly forgotten upon his death, but has begun to attract new respect and recognition

Blasius flow and heat transfer of fourth-grade fluid with slip

International audienceThis investigation deals with the effects of slip, magnetic field, and non-Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness

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

International audienceThe 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 et al. 2007) for a large range of Reynolds numbers in an annular cavity of large aspect ratio and weak curvature parameter. 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 of air in the same rotor–stator system for Rayleigh numbers up to 100 millions. 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 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 Ra larger than 10 millions, since the averaged Bolgiano length scale remains lower than the thermal boundary layer thicknesses

Transport efficiency of metachronal waves in 3d cilia arrays immersed in a two-phase flow

The present work reports the formation and the characterization of antipleptic and symplectic metachronal waves in 3D cilia arrays immersed in a two-fluid environment, with a viscosity ratio of 20. A coupled lattice-Boltzmann-Immersed-Boundary solver is used. The periciliary layer is confined between the epithelial surface and the mucus. Its thickness is chosen such that the tips of the cilia can penetrate the mucus. A purely hydrodynamical feedback of the fluid is taken into account and a coupling parameter $\alpha$ is introduced allowing the tuning of both the direction of the wave propagation, and the strength of the fluid feedback. A comparative study of both antipleptic and symplectic waves, mapping a cilia inter-spacing ranging from 1.67 up to 5 cilia length, is performed by imposing the metachrony. Antipleptic waves are found to systematically outperform sympletic waves. They are shown to be more efficient for transporting and mixing the fluids, while spending less energy than symplectic, random, or synchronized motions