Application of the maximum entropy technique in tomographic reconstruction from laser diffraction data to determine local spray drop size distribution

This work proposes a new deconvolution technique to obtain local drop size distributions from line-of-sight intensity data measured by laser diffraction technique. The tomographic reconstruction, based on the maximum entropy (ME) technique, is applied to forward scattered light signal from a laser beam scanning horizontally through the spray on each plane from the center to the edge of spray, resulting in the reconstructed scattered light intensities at particular points in the spray. These reconstructed intensities are in turn converted to local drop size distributions. Unlike the classical method of the onion peeling technique or other mathematical transformation techniques that yield unrealistic negative scattered light intensity solutions, the maximum entropy constraints ensure positive light intensity. Experimental validations to the reconstructed results are achieved by using phase Doppler particle analyzer (PDPA). The results from the PDPA measurements agree very well with the proposed ME tomographic reconstruction.     

Model validation image data for breakup of a liquid jet in crossflow: part I

We have applied three different imaging diagnostics: particle imaging velocimetry, high-speed shadowgraphy, and ballistic imaging, to observe the breakup of a liquid jet in a crossflow of air under a variety of conditions. The experimental system was designed to provide well-controlled conditions with minimal amounts of turbulence in the liquid jet and the gaseous crossflow. A variety of Weber numbers and momentum flux ratios were studied in order to provide a sizable data set for the validation of computational models. This paper briefly describes the three spray imaging techniques, outlines the results obtained to-date, and tabulates image statistics for each of ten spray conditions at varying distances from the spray nozzle orifice. The end result is a first installment in what will become a comprehensive model validation data set for jets in crossflow for use by computational fluid dynamics modelers.     

An experimental method for studying the high speed impact of a liquid drop on a liquid surface

Summary An experimental method for studying the high speed impact of a liquid drop on a liquid surface is described in which the liquid surface is moved against the stationary drop. Photographs are presented of the impact of a water surface at 47,7 m/sec on a stationary water drop 0,175 cm diameter. Proposals are made for further work to resolve certain discrepancies between results obtained using this method and those derived from earlier work in which drops fall freely onto a standing surface.Übersicht Es wird eine experimentelle Methode zur Untersuchung des Aufprallens von Flüssigkeitstropfen auf eine Flüssigkeitsoberfläche beschrieben, bei der die flüssige Fläche mit hoher Geschwindigkeit gegen einen stationären Tropfen bewegt wird. Fotos des Aufprallvorgangs bei Geschwindigkeiten von 47,7 m/s mit Tropfen von 0,175 cm Durchmesser werden gezeigt. Weiterhin werden Vorschläge gemacht, wie bei künftigen Untersuchungen ] gewisse Unterschiede in den Ergebnissen nach der hier beschriebenen Methode und bei frei fallenden Tropfen aufgeklärt werden könnten.Acknowledgment is made to Mr. M. J. B. Nash for his assistance in doing the experimental work. This work was carried out at the Royal Aircraft Establishment, Farnborough, Hampshire, England.     

Use of lagrangian methods to describe drop deposition and distribution in horizontal gas—liquid annular flows

Drop distribution and deposition in horizontal gas—liquid annular flow is described by a diffusion model, which views the concentration field as the result of dispersion from a distribution of sources. Drops originating from a wall source are considered to diffuse in a field of homogeneous turbulence, while simultaneously being swept downward by the gravitational field. Deposition is assumed to be controlled by two mechanisms operating in parallel, and boundary conditions are derived which correctly satisfy conservation of mass. This analysis for an instantaneous source is shown to be equivalent to considering diffusion in a coordinate system moving with the settling velocity of the particles. The results are found to be useful for understanding droplet distribution and deposition.     

On the breakup of slender liquid bridges: Experiments and a 1-D numerical analysis

Slender axisymmetric dielectric liquid bridges are made stable by the action of an axial electric field. In this paper, the subsequent dynamics of a slender liquid bridge after turning off the electric field is considered. The evolution in time of the bridge profile is investigated both theoretically and experimentally. A one-dimensional model is used to simulate the dynamic response of the system. Experiments are performed applying an axial electric field to a liquid bridge of 1 mm of diameter, and turning-off the electric field. The evolution of the liquid bridge is recorded using a video camera, and the digitized images are analysed. Good agreement between computations and experiments is found.     

Numerical study of a single drop impact onto a liquid film up to the consequent formation of a crown

In this paper, the whole dynamic process of a single drop impact onto a thin liquid surface up to the consequent formation of a thin crown is numerically studied using the smoothed particle hydrodynamics (SPH) method. Especially, the gravity, artificial viscosity, and surface tension are introduced into the model. The obtained SPH numerical results are compared with experimental results. The numerical model of the SPH method is valid for simulating the dynamic process of a single drop impact onto a liquid surface. Meanwhile, it is found that the whole dynamic process mainly depends on the depth of the liquid pool and the initial velocity of the droplet.     

The response of the level of a liquid fluidized bed to a sudden change in the fluidizing velocity

Summary When the fluidizing velocity in a liquid fluidized bed of solid particles is suddenly changed, a discontinuity in the porosity is introduced at the bottom of the bed. This discontinuity is propagated upwards through the bed. The boundary between the old and the new porosity broadens or remains sharp depending on whether the porosity is increased or decreased. This behaviour is reflected in the way in which the bed level changes as a function of time. For a few different systems such response curves have been measured by means of a specially designed follow-up system. On the basis of the above mechanism a quantitative theory was developed for the response of the bed level to a step-wise change in the fluidizing velocity. This theory proved to give a satisfactory agreement with the observed facts.List of symbols m.k.s. units have been used for the purpose of calculation - d _p diameter of particle - h instantaneous height of the fluidized bed - n constant in eq. (2) - t time - u average velocity of the fluidized particles with respect to the wall, positive in the direction of the liquid flow - U _s settling velocity of single particle in tube; constant in eq. (2) - v average liquid velocity with respect to the wall - w() velocity of propagation of a disturbance d at a porosity - x coordinate in the direction of flow - porosity, void fraction - _p particle density - liquid velocity in region above particles, volumetric flow per unit area of empty tube - index 0 refers to the steady situation for t 0 - index 1 refers to the steady state situation state reached after t = t ₁     

Group theoretic analysis and similarity solution for a nonlinear viscous rod subjected to time dependent velocity impact

Unidirectional wave motion in a nonlinear viscous rod obeying Norton's law in creep, subjected to time dependent velocity impact is considered. From the basic equations of the problem and the four parameter dimensional group of transformations, absolute invariants of the group are constructed to obtain similarity transformations. Similarity representation of the original system of partial differentiation equations is formulated as a system of nonlinear ordinary differential equations with auxiliary conditions. Closed form solutions are obtained for a linear rod, for a nonlinear rod subjected to constant velocity impact and a weekly nonlinear rod. Nonlinear case is solved by a numerical approach based on the quasilinearization method.     

The relation of the threshold velocity of coal dust to its size and humidity

On the ground of wharf and a station where coal is piled up,the sources polluting theatmosphere are mainly the raised coal dust.According to the principle of mechanics,withthe consideration of the gravities of coal dust particles and liquid droplets,coal dust size andhumidity,under the condition of force balance when the coal dust was raised,the authorsobtained a theoretical formula for the threshold velocity of coal dust with humidity.Finally,the theoretical values from the formula gave a good agreement with the experimental datafrom some wind tunnels.     

Visualization of the impact of water drops on a hot surface: effect of drop velocity and surface inclination

The behaviour of one drop impinging on a hot surface by varying the surface temperature, the drop velocity and the position of the surface (horizontal and a inclined 45°) both at a temperature below and above the Leidenfrost temperature has been experimentally evaluated, estimating the temperature at which the drop rebounds. A large influence on the drop velocity has been evidenced. The inclination of the surface decreases the critical value of the temperature above which the surface is not rewetted.     

Probing the velocity fields of gas and liquid phase simultaneously in a two-phase flow

The feasibility of simultaneous measurements of the instantaneous velocity fields of gaseous and liquid phase is demonstrated in a laminar, unsteady two-phase flow. Thus, the instantaneous relative velocity field can be measured in such media. This is achieved by combining Particle Image Velocimetry (PIV) and a gas-phase velocimetry technique, which is based on laser-induced fluorescence (LIF) from a gaseous tracer. The wavelength shift of LIF is exploited to separate it from Mie scattering from the liquid phase. The new technique and the PIV measurement system work independently in this approach. Thus, the measurement accuracy and precision of the new technique can be validated by comparing it to the PIV results in regions of the flow field where the relative velocity vanishes. Received: 18 October 1998/Accepted: 16 October 1999     

A novel fuzzy-logic based method for determination of individual bubble velocity and size from dual-plane ultrafast X-ray tomography data of two-phase flow

Ultrafast X-ray tomography enables non-invasive imaging of gas-liquid flows with high spatial and temporal resolution. While it is relatively straightforward to extract e.g. gas fraction profiles from cross-sectional tomographic images, the extraction of bubble and gas-liquid interface information requires advanced image processing techniques. Thereby it is an important necessity to transform the temporal scale in the scanned sequences into a corresponding length scale for obtaining correct volumetric information. For bubbly flows this means that the velocity of the dispersed phase, e.g. the gas bubbles, has to be determined from dual-plane scans. A common and widely applied method to obtain gas phase velocities is cross-correlating the image sequences of the two scanning planes. This gives an averaged velocity for each position in the cross-section. In the present work, a new method is introduced, which determines the velocity of individual gas bubbles. This new method is termed as “bubble twinning method”, because it tries to identify twin-bubbles in both scanning planes. The developed algorithm compares essential bubble parameters, that is, volume, position and residence time in the slice, by applying a fuzzy-logic based membership function approach. The algorithm was tested for bubbly flow as well as slug flow conditions. Results are compared with established theoretical predictions as well as the cross-correlation method.     

A theoretical correlation for the Nusselt number in direct contact evaporation of a moving drop in an immiscible liquid

Numerical solutions for the Nusselt number during the direct contact evaporation of a moving drop in a stagnant column of immiscible liquid are presented. The effect of bubble growth rate on the radial component of drop velocity is taken into account in the analysis and the Nusselt number is found to be a function of Peclet number, Jakob number and vapour open angle. A comparison of theoretical and experimental correlations for the Nusselt number shows good agreement. The analysis also yields information on the temperature profile and the thickness of the thermal boundary layer surrounding the evaporating drop.

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Eine theoretische Beziehung für die Nusselt- Zahl bei Verdunstung eines bewegten Tropfens, der in direktem Kontakt zu einer unmischbaren Flüssigkeit steht

Zusammenfassung Es werden numerische Lösungen für die Nusselt-Zahl während der Verdunstung eines bewegten Tropfens, der in direktem Kontakt mit der umgebenden ruhenden Säule aus unmischbarer Flüssigkeit steht, mitgeteilt. In der Berechnung wird der Einfluß der Blasenwachstumsrate auf die radiale Komponente der Tropfengeschwindigkeit berücksichtigt. Es wird festgestellt, daß die Nusselt-Zahl eine Funktion der Peclet-Zahl, der Jakobs-Zahl und des Öffnungswinkels des Dampfes ist. Ein Vergleich der theoretischen und experimentellen Beziehungen für die Nusselt-Zahl zeigt gute Übereinstimmung. Die Berechnung enthält auch Informationen über das Temperaturprofil und die Dicke der thermischen Grenzschicht um den verdampfenden Tropfen.

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Nomenclature A constant in Eq. (4) - B diameter ratio - C _p specific heat of continuous liquid phase - h instantaneous heat transfer coefficient - h _fg latent heat of evaporation of dispersed phase - Ja system Jakob number, C_p t/(_v h_fg) - k thermal conductivity of continuous liquid phase - m mass of liquid fraction in the evaporating drop - m ₀ total mass of evaporating drop - Nu Nusselt number, 2hR/k - Pe Peclet number, 2UR/ - Pr Prandtl number,/ - q heat transfer rate per unit surface area of evaporating drop - r radial coordinate - R instantaneous radius of evaporating drop - Re Reynolds number, 2UR/ - t time - T temperature - T _c temperature of continuous liquid phase - T _d saturation temperature of dispersed phase - U _r radial component ofU - U tangential component ofU - U bubble translational velocity - x exponent in Eq. (4) - y transformed coordinate, (r–R)/R Greek letters thermal diffusivity of continuous liquid phase - half vapour open angle - non-dimensional bubble growth rate, - T temperature difference, (T _c –T _d ) - density of continuous liquid phase - _v density of dispersed vapour phase - non-dimensional temperature,(T– T _c )/(T _p -T _c ) - spherical polar coordinate - dimensionless time, t/R² - transformed coordinate, (–cos) - kinematic viscosity of continuous liquid phase     

Numerical simulation of a Trombe wall to predict the energy storage rate and time duration of room heating during the non-sunny periods

In this paper, 2D numerical simulation of the Trombe wall performance and indoor air environment under unsteady state condition for a room located in Yazd, Iran are studied. The governing equations involve mass, momentum and energy conservation, which are discretized by the finite volume method after non-dimensionalization. The SIMPLER algorithm is used for coupling the velocity and pressure. The average absorbed solar radiation on the Trombe wall has been defined for different hours of the coldest period of the year (21 January–19 February) in Yazd. All equations have been solved together using a FORTAN code. The main aim of this research is to investigate the time duration of room heating during the non-sunny periods. The stored energy of the wall being delivered to the inside room was defined for different materials of the Trombe wall. The results show that the Trombe wall made of paraffin wax can keep the room warmer in comparison with other materials for about 9 h.