Structure of the temperature field in a flow over heated waves

Liquid crystal thermometry (LCT) was used to quantify temperature fields in a flow over resistively heated waves and assess the effect of the large-scale longitudinal structures that were previously obtained in the velocity field for an isothermal flow (A. Günther and P. Rudolf von Rohr, submitted article, 2002). The wavelength 6 was 10 times larger than the amplitude, and the considered Reynolds numbers were 725 and 3300, defined with the bulk velocity and the half-channel height. A constant heat flux was imposed at the wavy bottom wall. For the first time, LCT was used to determine the fluid temperature in a wall-bounded flow with heat transfer. The dominant spanwise scale obtained from a proper orthogonal decomposition (POD) of the fluid temperature field above an uphill location of the wavy wall was 1.56. It agrees well with the one previously obtained for a decomposition of the streamwise velocity.     

Occurrence of caustics for high-frequency acoustic waves propagating through turbulent fields

A numerical technique for simulating the propagation of high-frequency acoustic waves through turbulent fields is introduced. The technique involves two elements: the generation of a random isotropic scalar or vectorial field in terms of a superposition of discrete random Fourier modes; and the integration of the ray-trace equations of geometrical acoustics to describe the trajectories of rays and their distortion. For each realization we compute the ray trajectories and the evolution of the cross section of an elementary ray tube. We then accumulate statistics over an ensemble of realizations to estimate the probability of occurrence of the first caustic. Our results demonstrate that the position of caustics is governed by universal parameters related to the derivatives of the correlation function of the fluctuating components of the turbulent medium.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.     

Théorie des effets rhéo-optiques dans un continu polarisable et magnétisable

Summary The total momentum-energy tensor describing the interaction of a polarizable and magnetizable continuum with an electromagnetic field is constructed on the basis ofLorentz invariance. The equations of balance of energy and momentum are deduced and applied to the study of the magnetooptical, electrooptical and photoelastic behavior of an elastic polarizable and magnetizable isotropic continuum. This model exhibits theCotton-Mouton andKerr effects but thePockels andFaraday rotations don't appear.     

Particular aspects of the forced response of finite-dimensional modular structures

Summary The paper analyzes, from an engineering point of view, a problem strictly connected to the Large Space Structures dynamics, precisely the dynamics of modular structures of arbitrary length, arbitrarily constrained at either end and arbitrarily subject to external loads at the boundaries of each repetitive element. In particular the attention is focused on the relation between the propagation characteristics of an indefinite structure and the forced response of a finite-dimensional one; this relation is established in closed form for a periodic beam in transverse vibration. A detailed numerical investigation on the same structure confirms the analytical results and shows the peculiar dynamic properties of finite-dimensional modular structures.

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Sommario Viene presentata una analisi ingegneristica di un problema estremamente attuale delle grandi strutture spaziali, ovvero lo studio della dinamica di strutture modulari di lunghezza arbitraria, soggette ad arbitrary vincoli alle estremità e ad arbitrari carichi esterni applicati in corrispondenza delle giunzioni tra due moduli adiacenti. In particolare l'interesse del lavoro è rivolto alla determinazione di una relazione tra le caratteristiche di propagazione di una struttura indefinita e la risposta forzata della omologa struttura di lunghezza finita; tale relazione viene ricavata in forma chiusa per una trave periodica. Una serie di simulazioni numeriche sulla medesima struttura conferma i risultati analitici, mostrando le peculiarità del comportamento dinamico di strutture periodiche di lunghezza finita.

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Paper presented as Particular Aspects of the Dynamics of Finite-Dimensional Modular Structures at the ESA Workshop on Modal Representation of Flexible Structures by Continuum Methods, ESTEC, Noordwijk, The Netherlands, June 1989.     

Dynamics of two-phase bubble-droplets in immiscible liquids

This paper describes an experimental study of two-phase bubble-droplets of butane in distilled water. In the process of direct-contact heat transfer between two immiscible liquids, and with change of phase, evaporation occurs within a liquid droplet to form an interior bubble which ultimately may expand to absorb the entire droplet. The so-called stopped-evaporation two-phase bubble-droplets were formed by such evaporating droplets of butane rising in a column of water by application of pressure on the surface of the water to stop the evaporation. The configurations of such bubble-droplets, which depend on the ratio of mass of the vapor to mass of the liquid, are discussed. Results are also given for the rise velocity, and comparisons are made between the rise velocity of stopped-evaporation droplets and those of evaporating droplets.

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Dynamik zweiphasiger Blasen-Tropfen in unmischbaren Flüssigkeiten

Zusammenfassung Die experimentelle Untersuchung von zweiphasigen Blasen-Tropfen aus Butan in destilliertem Wasser wird beschrieben. Bei direktem Wärmeaustausch mit Phasenänderung zwischen zwei unmischbaren Flüssigkeiten beginnt die Verdampfung innerhalb eines Flüssigkeitstropfens und bildet eine innere Blase, die sich schließlich ausdehnt und den Tropfen absorbiert. Ein Ende der Verdampfung konnte beim Aufsteigen von Butantropfen in eine Wassersäule durch Anlegen von Druck an der Wasseroberfläche erreicht werden. Die Struktur dieser Blasen-Tropfen, die abhängt vom Verhältnis der Massen des Dampfes und der Flüssigkeit, wird diskutiert. Außerdem werden Ergebnisse für die Aufstiegsgeschwindigkeit gegeben und die Aufstiegsgeschwindigkeiten der verdampfenden Tropfen mit denen bei beendeter Verdampfung verglichen.

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Nomenclature d Equivalent spherical diameter of initial droplet (mm) - D Equivalent spherical diameter of bubble-droplet (mm) - m₀₀ Initial mass of droplet (kg) - m _v Mass of vapour (kg) - Re _c Reynolds number based on water properties (Re_c=UD/) - t Time (s) - T _c Temperature of water (°C) - U Rise velocity (m/s) - Z Position of bubble-droplet (mm) - t ₀ Overall temperature difference (C deg) - Density (kg/m³) - Viscosity (kg/m s)     

Influence of the optical configuration on temperature measurements with fluid-dispersed TLCs

An accurate temperature calibration of fluid-dispersed thermochromic liquid crystal (TLC) particles is an important prerequisite for quantitative liquid crystal thermometry (LCT) measurements in flows. Encapsulated TLCs are subjected to uniform and linear temperature fields and are illuminated with a sheet of white light. A digital camera records the color distribution reflected by the particles. For the first time, a telecentric objective is used to eliminate the angular dependence of the color within the image plane. The paper systematically assesses how the temperature calibration is affected by the angle between the camera axis and the light-sheet plane, and by the properties of the working fluid. The obtained results provide design criteria for quantitative LCT measurements in situations where small spatial variations of the fluid temperature need to be resolved, namely for turbulent heat transfer problems in wall-bounded flows. Received: 22 January 2001/Accepted: 16 October 2001     

Integral treatment of subcooled forced convection film boiling on a flat plate

Subcooled forced convection film boiling on a flat plate has been analysed by means of an integral method. Following the two phase boundary layer theory, the momentum and energy equations for both liquid and vapor layers are considered along with the compatibility conditions on the liquid-vapor interface. Subsequently, the governing equations are reduced to a set of algebraic equations which can readily be solved for given parameters. Comparison of the present solution with the Cess and Sparrow solution reveals an excellent performance of the present solution procedure. The effects of superheating, subcooling and liquid Prandtl number on the hydrodynamic and heat transfer characteristics are fully discussed. Furthermore, the asymptotic formulas are derived for the local Nusselt number and skin friction coefficient through a careful examination of the physical limiting conditions.     

An analysis of turbulent free convection about bodies of arbitrary geometrical configurations

A general solution method is suggested for the prediction of the turbulent free convection heat transfer from curved surfaces. The method which may be viewed as a generalized version of the Eckert-Jackson method for the isothermal plate, is designed to deal with bodies of arbitrary geometrical configurations. The surface wall temperature is also allowed to vary in the streamwise direction in an arbitrary fashion. For the illustrative purpose, the calculations are carried out for the turbulent free convection about the horizontal circular cylinder, and the results are compared with the existing empirical formula. The flow transition from laminar to turbulent is also predicted by matching the laminar and turbulent solutions.     

Influence of the volume fraction on the electrokinetic properties of maghemite nanoparticles in suspension

We used several complementary experimental and theoretical tools to characterise the charge properties of well-defined maghemite nanoparticles in solution as a function of the volume fraction. The radius of the nanoparticles is equal to 6 nm. The structural charge was measured from chemical titration and was found high enough to expect some counterions to be electrostatically attracted to the surface, decreasing the apparent charge of the nanoparticle. Direct-current conductivity measurements were interpreted by an analytical transport theory to deduce the value of this apparent charge, denoted here by ‘dynamic effective charge’. This dynamic effective charge is found to decrease strongly with the volume fraction. In contrast, the ‘static’ effective charge, defined thanks to the Bjerrum criterion and computed from Monte Carlo simulations turns out to be almost independent of the volume fraction. In the range of Debye screening length and volume fraction investigated here, double layers around nanoparticles actually interact with each other. This strong interaction between nanocolloidal maghemite particles is probably responsible for the experimental dependence of the electrokinetic properties with the volume fraction.     

Flame retardant polypropylene through the joint action of sepiolite and polyamide 6

The influence of the incorporation of polyamide-6 (PA) and natural sepiolite nanoparticles on both the thermal degradation and fire behaviour of polypropylene (PP) matrix has been investigated by thermogravimetric analysis (TGA) and mass loss calorimetry. For that purpose, PP/PA blends and nanocomposites thereof were prepared by melt processing. TGA results evidenced that the use of maleic anhydride grafted-polypropylene (MA-g-PP) as compatibilizer led to a significant improvement in thermal stability under air. Such improvement was linked to the formation of a char layer preventing the thermo-oxidative degradation of PP. Interestingly, the thermal resistance of this char layer was further improved by adding 5 wt% of natural sepiolite leading to important increase of time to ignition and reduction of peak of heat release rate (pHRR) during mass loss calorimeter test.