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Turbulent mixing of oil droplets in a round water jet

Turbulent mixing of oil droplets in a round water jet

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SummaryThis project focuses on the mixing of small oil droplets in a round turbulent jet. The aim is tosolve the terms in the turbulent transport equation. An experimental set-up is built to measurethe velocity and concentration field simultaneously. The velocity and concentration profiles areinspected on self-similarity properties and compared to the results of Fukushima & Aanen [Aanen,2002], who measured the turbulent transport of a real passive mixed quantity, namely a fluorescingdye. For the velocity measurements, Particle Image Velocimetry (PIV) is applied for which theoil droplets serve as tracer particles. From a theoretical approach it is verified that the dropletsare small enough to follow the fluid motion. The effects of buoyancy, break-up and coalescenceare negligible.The jet is issued from a capillary in a rectangular measurement section through which a constantcoflow is pumped. The jet flow is generated from a reservoir containing the oil-water mixture witha jet Reynolds number of about 1000. The droplets, generated by a commercial micro mixingdevice, are assumed to be monodisperse and have a diameter of approximately 20 µm. For thePIV-measurements the beam of an Argon-ion laser is converted into a light sheet at which a Flowmaster3s camera is pointed. From the cross-correlation of the double images, the displacementfield is calculated. The spreading rate of the velocity field (α = 0.099) is 10% smaller than thespreading rate found by Aanen. Moreover, the virtual origin is negative (-18d jet ), whereas Aanenfound z0 = 6.75d jet . The turbulent intensities of the velocity fluctuations are on the same levelas in the single-phase measurements performed during this project.The concentration field is calculated in two ways. First, the intensity of the scattered light istaken as a measure for the droplet concentration. A correction for the development of the lightintensity over the light sheet is applied. This scaling does not give a good result in the axial direction.Consequently, the measured centreline concentrations do not follow the expected 1/(z − z0)decay. On the other hand, the development of the width is linear and the concentration profiles,scaled with the measured centreline values, are symmetric. Secondly, the droplets are counted bysearching for local maxima in the greyvalue images. This is not a good alternative as, again, the1/(z − z0) decay is not followed. The spreading rate of the concentration field, α c , is 0.119 sothe ratio between the spreading of the concentration and velocity profiles, γ, is 1.20. This is inagreement with Aanen who found γ = 1.22. The position of the virtual origin for the self-similarconcentration profile is 3.98d jet .The self-similar mean axial velocity and concentration profiles are Gaussian and collapse whenscaled with the centreline values. The profiles agree with the theoretical profiles derived withK-theory, except for the outer regions. This is caused by intermittency, which leads to an overestimationof the eddy-viscosity. The fluctuations in the concentration field are 20% larger than inthe results of Aanen. This can be explained by shot-noise: oil droplets are small entities insteadof a real mixed quantity.The profiles of the turbulent fluxes are in good agreement with the profiles found for a passivescalar [Aanen, 2002]. The off-axis peak is clearly observed in the profile of the axial turbulent fluxand the profile of the radial flux follows the theoretical curve derived with K-theory quite well.Furthermore, the difference between the average and turbulent terms in the turbulent transportequation is considerably smaller than the order of magnitude of the individual terms. Therefore,it is concluded that the oil droplets fulfil this transport equation.viii

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