Influence of asymmetric blockage at flow exit on flow and heat transfer for an impinging slot jet on semi-concave surface

Paper presented at the 6th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 30 June - 2 July, 2008.Experimental studies of single slot jet impinging upon a concave surface are conducted by classical Particle Image Velocimetry (PIV) and infrared thermography, with nozzle exit Reynolds number (Re = 3200), dimensionless impinging height (H/b = 3 & 7) and relative curvature of the wall (Dc/b = 5). Results indicate that the oscillatory impinging jet generated a uniform and symmetric heat transfer area while the stabilized impinging jet caused an asymmetric heat transfer. This type of jet may be controlled by changing the outlet condition.vk201

Physical analysis of velocity and temperature cross-correlations in a plane mixing layer using variable temperature hot wire anemometry

International audienc

The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials

We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalised Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression

Etude expérimentale d'une couche de mélange anisotherme

Une couche de mélange anisotherme plane est étudiée dans différentes configurations de gradients forcés de vitesse et de température. L'écoulement est mis en oeuvre dans une soufflerie spécialement conçue pour générer des écoulements à basse vitesse avec génération séparée de deux courants à vitesses et températures contrôlées séparément. L'étude utilise une nouvelle technique d'anémométrie par fil chaud à surchauffe programmable dénommée PCTA. Le capteur permet de mesurer simultanément la vitesse et la température à haute fréquence en un même point. Les profils transversaux de vitesse et de température mesurés le long de la direction principale de l'écoulement donnent accès aux paramètres d'expansion de la couche de mélange. Les expansions de l'épaisseur de vorticité et de l'épaisseur de mélange thermique sont comparées, en fonction du paramètre de cisaillement dynamique et du nombre de Richardson. L'utilisation de l'anémomètre PCTA ouvre des perspectives d'analyse fine des interactions vitesse-température dans le mélange turbulent

{\phi}^4 Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics

We explore a {\phi}^4 model with an added external parabolic potential term. This term dramatically alters the spectral properties of the system. We identify single and multiple kink solutions and examine their stability features; importantly, all of the stationary structures turn out to be unstable. We complement these with a dynamical study of the evolution of a single kink in the trap, as well as of the scattering of kink and anti-kink solutions of the model. We see that some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, are sensitively dependent on the trap strength parameter, as well as the initial displacement of the kink and antikink

Homoclinic standing waves in focussing DNLS equations --Variational approach via constrained optimization

We study focussing discrete nonlinear Schr\"{o}dinger equations and present a new variational existence proof for homoclinic standing waves (bright solitons). Our approach relies on the constrained maximization of an energy functional and provides the existence of two one-parameter families of waves with unimodal and even profile function for a wide class of nonlinearities. Finally, we illustrate our results by numerical simulations.Comment: new version with revised introduction and improved condition (A3); 16 pages, several figure

Tunneling of quantum rotobreathers

We analyze the quantum properties of a system consisting of two nonlinearly coupled pendula. This non-integrable system exhibits two different symmetries: a permutational symmetry (permutation of the pendula) and another one related to the reversal of the total momentum of the system. Each of these symmetries is responsible for the existence of two kinds of quasi-degenerated states. At sufficiently high energy, pairs of symmetry-related states glue together to form quadruplets. We show that, starting from the anti-continuous limit, particular quadruplets allow us to construct quantum states whose properties are very similar to those of classical rotobreathers. By diagonalizing numerically the quantum Hamiltonian, we investigate their properties and show that such states are able to store the main part of the total energy on one of the pendula. Contrary to the classical situation, the coupling between pendula necessarily introduces a periodic exchange of energy between them with a frequency which is proportional to the energy splitting between quasi-degenerated states related to the permutation symmetry. This splitting may remain very small as the coupling strength increases and is a decreasing function of the pair energy. The energy may be therefore stored in one pendulum during a time period very long as compared to the inverse of the internal rotobreather frequency.Comment: 20 pages, 11 figures, REVTeX4 styl

Flow and heat transfer of a compressible impinging jet

International audienceThe influence of injection Mach number over the flow and heat transfer of an impinging air jet is investigated. For a given injection Reynolds number, jets with different injection diameters have been studied, decoupling the effects of injection Reynolds and Mach numbers. Three injection diameters were used, varying injection Mach number from 0.3 to 0.8. The effects of injection-to-plate distance were also studied. Flow was studied using Particle Image Velocimetry and infrared thermography was used to investigate both Nusselt number and adiabatic wall temperature (also called recuperation temperature) variations along the plate. The main effect of Mach number rise on the flow is a decrease in the number of Kelvin-Helmholtz vortices, reducing the amplitude of the secondary maximum of Nusselt number, particularly for low injection to plate spacing. Moreover, for Mach number low values, the adiabatic wall temperature is nearly constant whereas for higher values variations occur depending on injection-to-plate distance. For low distances, the mean radial velocity close to the wall, which presents relatively high values, reduces the temperature above the jet injection total temperature. For higher injection-to-plate distances, ambient air, with higher static temperature, is brought into the jet, increasing the static temperature of the jet and leading to adiabatic wall temperature superior to jet injection total temperature