Nonequilibrium vibration-dissociation phenomena behind a propagating shock wave: Vibrational population calculation

An analysis of nonequilibrium phenomena behind a plane shock is presented concerning the vibrational relaxation and the dissociation of a pure diatomic gas. In the first part, the temperature range is 600 K–2500 K and the dissociation processes are neglected. The population of each vibrational level is computed by solving relaxation and conservation equations. The relaxation process is described by the master equations of each vibrational level. The vibrational transition probabilities appearing in the relaxation equations are calculated analytically and take into account the anharmonicity of molecular vibration and the potential angular dependence. The populations obtained are compared to those calculated using a Treanor model and to those calculated with a nonequilibrium Boltzmann distribution. For moderately high levels significant differences may be observed. The importance of the V-V process is found to be weak for the transitions involving the lowest levels. In the second part, the temperature range is 2500 K–5500K and the dissociation process is taken into account as well as the gas dynamic behavior which did not appear in several recent works. The kinetic equations are transformed to obtain a first order differential system and the resolution of such a system coupled with the conservation equations leads to the population of each vibrational level. The vibrational transition probabilities associated with the atom-molecule interaction are deduced from the cross section calculation used in the first part. The bound-free transition probabilities are obtained, following Marrone and Treanor, assuming that dissociation must occur preferentially from the higher vibrational states: the Marrone and Treanor probability model is extended and employed with an anharmonic oscillator. In the present investigation, behind the shock wave, the evolution of the population distribution expressed as a function of the distance is not monotonous: a lag time appears as shown experimentally in previous works for the macroscopic parameters. For moderately high levels the influence of the anharmonicity and those of the V-V processes appear significant and strongly related. In a general way, in both temperature ranges investigated, the V-V processes reduce the effects of the T-V transfer. Finally the influence of thecharacteristic probability temperature U of Marrone and Treanor is analyzed and a method of determination of local varying U is proposed.     

Uniqueness of Positive Solutions of Δu+f(u)=0 in ℝN, N≦3

We study the uniqueness of radial ground states for the semilinear elliptic partial differential equation in ℝ ^N . We assume that the function f has two zeros, the origin and u ₀>0. Above u ₀ the function f is positive, is locally Lipschitz continuous and satisfies convexity and growth conditions of a superlinear nature. Below u ₀, f is assumed to be non-positive, non-identically zero and merely continuous. Our results are obtained through a careful analysis of the solutions of an associated initial‐value problem, and the use of a monotone separation theorem. It is known that, for a large class of functions f, the ground states of (*) are radially symmetric. In these cases our result implies that (*) possesses at most one ground state. (Accepted July 3, 1996)     

On multiple-path sonic anemometer measurement theory

In this paper, a model of the measuring process of sonic anemometers with more than one measuring path is presented. The main hypothesis of the work is that the time variation of the turbulent speed field during the sequence of pulses that produces a measure of the wind speed vector affects the measurement. Therefore, the previously considered frozen flow, or instantaneous averaging, condition is relaxed. This time variation, quantified by the mean Mach number of the flow and the time delay between consecutive pulses firings, in combination with both the full geometry of sensors (acoustic path location and orientation) and the incidence angles of the mean with speed vector, give rise to significant errors in the measurement of turbulence which are not considered by models based on the hypothesis of instantaneous line averaging. The additional corrections (relative to the ones proposed by instantaneous line-averaging models) are strongly dependent on the wave number component parallel to the mean wind speed, the time delay between consecutive pulses, the Mach number of the flow, the geometry of the sensor and the incidence angles of mean wind speed vector. Kaimal´s limit k_W1=1/l (where k_W1 is the wave number component parallel to mean wind speed and l is the path length) for the maximum wave numbers from which the sonic process affects the measurement of turbulence is here generalized as k_W1=C_l/l, where C_l is usually lesser than unity and depends on all the new parameters taken into account by the present model.     

Evaluation of temperature gradients within combusting droplets in linear stream using two colors laser-induced fluorescence

The scope of this paper concerns the heating process of fuel droplets injected in a hot gaseous environment. The two colors laser-induced fluorescence technique allows measuring the temperature distribution within a droplet by scanning the droplet volume by a sufficiently small probe volume compared to the droplet volume itself. The temperature field is reconstructed using two approaches which have been compared. One is based on a geometrical optics model and the other is based on the 3D calculation of the internal excitation field within the droplet, using the generalized Lorenz-Mie theory. Experimental results have been obtained on a combusting monodisperse ethanol droplet stream (diameter around 200 m).     

Nonlinear Stability of a One-Dimensional Boussinesq Equation

We study nonlinear orbital stability and instability of the set of ground state solitary wave solutions of a one-dimensional Boussinesq equation or one-dimensional Benney–Luke equation. It is shown that a solitary wave (traveling wave with finite energy) may be orbitally stable or unstable depending on the range of the wave's speed of propagation.     

Fully three-dimensional direct numerical simulation of a plunging breakerSimulation numérique directe tridimensionnelle du déferlement plongeant

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier–Stokes equations in air and water. The interface tracking is achieved by a Lax–Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed. To cite this article: P. Lubin et al., C. R. Mecanique 331 (2003).     

The effects of displacement induced by thermal perturbations on the structure and stability of boundary-layer flows

The free-interaction influence of a thermal expansion process in boundary-layer gas flow is analyzed using the formalism of triple-deck theory. The physical model considered is the forced convection of a gas flowing over a flat plate subject to a heated slab. Both linearized and full nonlinear solutions are obtained using Fourier transform methods and spectral numerical techniques. The influence of monochromatic thermal perturbation on boundary-layer stability (lower branch) is studied and first-order correction of the lower branch neutral stability curve for the boundary-layer flow has been obtained. The shift of neutral stability is then computed for different values of the thermal perturbation wave number, making unstable some otherwise stable modes.This work has been supported by the Cray Research Inc. through a grant on supercomputing.     

The Hungarian periconceptional service as a model for community genetics

OBJECTIVES: This review describes the methods and results of the Hungarian periconceptional service consisting of counselling, examinations and medical interventions. (The term periconceptional is used instead of preconceptional because the early postconceptional period is also involved to this service.) METHODS: The service was based on three steps: check-up examination of reproductive health (i.e., preconceptional screenings), a 3-month preparation for conception, dispensed and/or supervised by qualified nurses, and a better protection in early pregnancy for the most sensitive early development of the embryo for voluntary and eligible couples. RESULTS: Experiences from the coordinating centre of the Hungarian periconceptional service are summarized between February 1, 1984, and January 31, 1999, thus 15 years. Participants with positive family histories, case histories and subjects with genito-urinary infections had a more effective flow towards secondary care. Infertile couples were diagnosed and treated sooner. The periconceptional service is effective for the introduction of periconceptional folic acid-containing multivitamin supplementation and for the reduction of smoking and alcohol consumption in females in the preconceptional period. The rate of major congenital abnormalities (20.6 per 1,000) was significantly lower than expected. CONCLUSIONS: The periconceptional service is feasible and has many benefits. Thus, proper preparation for conception is the earliest and probably the most important effort to prevent genetic diseases.     

A Slender Chisel-Like Body in a Supersonic Stream

The wave drag of a chisel-tike slender ruled body in a supersonic stream is considered. The dependence of the drag on the body geometry is studied. A comparison with axisymmetric bodies and the von Karman ogive is drawn.     

Slipping zone location in squeeze flow

In squeeze flow rheometry, the main problem is the boundary condition between the squeezed material and the plates. Therefore, the crucial assumption is to know the location and the shape of the sample part where wall slip may or may not occur. This question is investigated from experimental results. For this, squeeze flow experiments are carried out to visualize the flow pattern at the walls. Influence of boundary conditions is particularly studied using different plate surface condition. As a result, with wall slipping conditions, we propose a flow modelling divided into two zones: a circular central zone of the sample sticks on the plates and, beyond that zone, the sample slips at the plates with friction.