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

Modèle de turbulence générique à deux équations de transport

ISRN : IRPHE/RS--2005-01--FRLes modèles de fermeture de turbulence à deux équations sont intéressants pour les applications industrielles dans lesquelles le détail du champ turbulent n'est pas recherché. Ces modèles sont encore très utiilsés dans les grands codes industriels en CFD. Les modèles à deux équations sont généralement basés sur le concept de viscosité de la turbulence et de ce fait peuvent être résolus numériquement de façon efficace alors que les modèles aux tensions de Reynolds nécessitent des techniques numériques spécifiques. Dans ces modèles de fermeture à deux équations, la première équation est généralement l'équation de l'énergie cinétique de la turbulence mais la deuxième équation peut porter sur diverses grandeurs caractéristiques et il existe une grande variété de formulations. Dans la pratique le choix se fait en fonction des types d'écoulements étudiés et aussi de la robustesse numérique de la formulation correspondante. Selon de choix de la variable caractéristique pour la deuxième équation, les propriétés du modèle qui en résulte peuvent être différentes. L'objet de la présente note est d'établir une formulation générique de cette équation qui englobe les principaux modèles existants. On utilisera pour cela la méthode du modelage invariant de J.L. Lumley selon une approche adaptée au présent problème. Le modèle générique présenté permet une formulation synthétique des divers modèles à deux équations et permet aussi de suggérer des termes nouveaux en vue de servir au développement de nouvelles formulations

Turbulence modeling of the Von Karman flow: viscous and inertial stirrings

International audienceThe present work considers the turbulent Von Karman flow generated by two counter-rotating smooth flat (viscous stirring) or bladed (inertial stirring) disks. Numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM model) are compared to velocity measurements performed at CEA (Commissariat à l'Energie Atomique, France). The main and significant novelty of this paper is the use of a drag force in the momentum equations to reproduce the effects of inertial stirring instead of modelling the blades themselves. The influences of the rotational Reynolds number, the aspect ratio of the cavity, the rotating disk speed ratio and of the presence or not of impellers are investigated to get a precise knowledge of both the dynamics and the turbulence properties in the Von Karman configuration. In particular, we highlighted the transition between the merged and separated boundary layer regimes and the one between the Batchelor (1951) and the Stewartson (1953) flow structures in the smooth disk case. We determined also the transition between the one cell and the two cell regimes for both viscous and inertial stirrings

Turbulent Von Karman Swirling Flows

International audienceWe investigate the turbulent Von Karman flow generated by two counter-rotating flat or bladed disks. Numerical predictions based on a Reynolds Stress Model (RSM) are compared to velocity measurements performed at CEA (Ravelet, 2005). This flow is of practical importance in many industrial devices such as in gas-turbine aeroengines. From an academic point of view, this configuration is often used for studying fundamental aspects of developed turbulence and especially of magneto-hydrodynamic turbulence

Turbulent Von Karman Swirling Flows

International audienceWe investigate the turbulent Von Karman flow generated by two counter-rotating flat or bladed disks. Numerical predictions based on a Reynolds Stress Model (RSM) are compared to velocity measurements performed at CEA (Ravelet, 2005). This flow is of practical importance in many industrial devices such as in gas-turbine aeroengines. From an academic point of view, this configuration is often used for studying fundamental aspects of developed turbulence and especially of magneto-hydrodynamic turbulence

Turbulent Von Kármán flow between two counter-rotating disks

National audienceThe present work considers the turbulent Von Kármán flow generated by two coaxial counter-rotating smooth (viscous stirring) or bladed (inertial stirring) disks enclosed by a cylindrical vessel. Numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM) are compared to velocity measurements performed at CEA. An efficient way to model the rule of straight blades is proposed. The influences of the rotational Reynolds number, the aspect ratio of the cavity, the rotating disk speed ratio and of the presence or not of impellers are investigated to get a precise knowledge of the dynamics and the turbulence properties in the Von Kármán configuration. In particular, we highlighted the transition be-tween the Batchelor and the Stewartson flow structures and the one between the merged and separated boundary layer regimes in the smooth disk case. We determined also the transition between the one cell and the two cell regimes for both viscous and inertial stirrings

Simulation of turbulent flows out of spectral equilibrium using the PITM method

The two main approaches to numerical prediction of turbulent flows that are the RANS method and the LES method have long been developed independently from each other and there is a need in practice to bridge these apparently different approaches. Relying upon the spectral theory background, it has been possible to develop continuous hybrid methods that allow seamless coupling between RANS and LES. The derivation of the PITM method is based on the dynamic equation of the two-point fluctuating velocity correlations with extension to nonhomogeneous turbulence. Indeed, the two-point velocity correlation equation embodies a detailed description of the turbulence field. Then, using Fourier transform and performing averaging on spherical shells on the dynamic equation, leads formally to the evolution equation of the one-dimensional spectral velocity correlation tensor. Exiled in one-dimensional space, the turbulence quantities are represented by functions of the scalar wave number rather than the wave vector. These spectral equations have also been the basis for developing one-dimensional non-isotropic spectral models [1, 2]. A partial integration over a split spectrum, with a given partitioning understood as spectral filtering, yields the partial integrated transport modeling (PITM) method that can be used for practical simulations of turbulent flows [3, 4]. As a result, new transport equations for the subfilter scale stresses and dissipation-rate have been obtained. In this formulation, the model is governed by a dimensionless parameter which involves the cutoff wave number and the turbulence length-scale. Previous simulations have shown that the PITM method is able to reproduce fairly well a large variety of internal and external flows out of spectral equilibrium in the energetic sense and spectral anisotropy sense. Because advanced closures can be used to model the subfilter range, then, large filter widths can be used without prejudice and as a result the computing time can be fairly reduced. The present paper considers various applications such as rotating flows encountered in turbomachinery [6], pulsed turbulent flows [3], flows with wall mass injection [4], flows with separation and reattachment of the boundary layer [7, 8] a mixing of two turbulent flows of different scales [9], airfoil flows [10], and a flow in a small axisymmetric contraction [11], while allowing a drastic reduction of the computational resources in comparison with the one required for highly resolved LES. [1] Cambon, C., Jeandel, D., Mathieu, J. 104, 247-262 (1981). [2] Chaouat, B., Schiestel, R. Theor. Comput. Fluid Dyn. 21, 201-229 (2007). [3] Schiestel, R., Dejoan, A. Theor. Comput. Fluid Dyn. 18, 443-468 (2005). [4] Chaouat, B., Schiestel, R. Phys. Fluids 17, 065106, 1-19 (2005). [5] Chaouat, B., Schiestel, R. Phys. Fluids 24, 085106, 1-34 (2012). [6] Chaouat, B. Phys. Fluids 24, 045108,1-35 (2012). [7] Chaouat, B. J. Turbul. 11, 1-30 (2010). [8] Chaouat, B., Schiestel, R. Computers and Fluids 84, 279-300 (2013). [9] Befeno, I., Schiestel, R. Flow, Turbul. Combust. 78, 129-151 (2007). [10] Stoellinger, M., Roy, R., Heinz, S. in Proceedings of the 9th Symposium on Turbulence Shear Flow Phenomena, edited by the University of Melbourne, 7B5, 1-6 (2015). [11] B. Chaouat. Flow, Turbul. Combust. In press (2016). [12] Uberoi M.S., Wallis, S. J. Fluid Mech. 24, 539-543 (1966)

Simulation d'écoulements transitionnels et turbulents en cavités rotor-stator avec transferts de chaleur.

National audienceOn étudie les écoulements non isothermes confinés entre un disque tournant (rotor) et un disque fixe (stator) par simulation numérique directe (DNS) dans le cas d'un écoulement de transition et par modélisation de la turbulence (Reynolds Stress Model noté RSM) pour des forts nombres de Reynolds. Sous l'approximation de Boussinesq, les résultats de la DNS montrent que les effets de variation de densité sont faibles. Les prévisions du modèle RSM sont ensuite comparées à des données disponibles dans la littérature et étendus pour une large gamme de nombre de Prandtl en conservant la densité constante