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Turbulent mixing of oil droplets in a round water jet

Turbulent mixing of oil droplets in a round water jet

Figure 3.6: Composition

Figure 3.6: Composition of peaks in the cross-correlation function. From: Raffel (1998).• The velocity difference over the interrogation area should be at most 5% of the mean velocity.If the velocity gradient becomes too large, the correlation peak becomes too wide andconsequently hard to detect. Besides, there will be a bias towards small pixel displacementsas the probability of being double-exposed is larger for particles with smaller displacements.• The out-of-plane movement, which is the particle image displacement in the direction perpendicularto the light sheet, should be less than 1/4 the thickness of the light sheet. Particlesthat are exposed once inside the interrogation area add only noise to the correlation function.If the particle displacement, determined by the radial component of the turbulent intensities,is estimated at 0.3u s (see equation 2.41), the number of out-of-plane particles is smallenough if:∆t < 0.83 d lightu s(3.5)in which ∆t is the time interval in between the two exposures and d light the thickness of thelight sheet.• The in-plane movement should be 1/4 of the size of the interrogation area to minimise thenumber of particles that are exposed only once.• The accuracy of the PIV-measurement is optimal if the image diameter of the particle isabout 2 pixel units [Westerweel, 2000]. At smaller values, the displacement peak is no longerGaussian, whereas at larger values the curve becomes wider and more inaccurate to fit. Ifthe particle image is too small, peak-locking to integer pixel displacements may occur: thethree-point estimator in equation 3.4 needs the values of the correlation on the pixels next tothe peak. If these values are close to zero, due to a narrow peak, the subpixel displacementcan be biased towards the integer pixel position of the peak.• The flow must be seeded homogeneously. If not, a bias towards areas with higher concentrationoccurs, as they contribute more to the correlation function.The size of the interrogation area is commonly 32 x 32 pixels with 50% overlap with adjacent interrogationareas. If the number of particles is not large enough to do an accurate PIV-measurement,a multi-pass algorithm may be applied. As a first step, a large interrogation area is used to estimatethe displacement vector. This displacement is used to apply a shift to the images andcalculate a new cross-correlation with decreased interrogation area size. These steps can be repeatedif desirable.24

It is possible that calculated displacement vectors are spurious. For example due to fluctuationsin local seeding densities or presence of large particles. These vectors are called outliers. They canbe detected by comparing the value of each displacement with the median of the 8 surroundingvectors. If a certain threshold is exceeded they can be replaced by, for example, the median oftheir neighbours.3.3 PIV set-up3.3.1 Light sheetTo illuminate the oil droplets, a thin and non-diverging light sheet is constructed. A 50 mWcontinuous Argon-ion laser (λ = 488 nm) is used. This is a relatively weak source, so the exposuretime must be quite long to record a sufficient intensity of the scattered light. The maximal velocitythat may be measured accurately is therefore limited. The shortest exposure time for which thelight intensity is still high enough, will be determined experimentally.A Dantec prefabricated light sheet optics, consisting of a spherical and cylindrical lens, is used toconvert the laser beam into a light sheet. No complicated alignment procedures are involved butthe optics are hardly adjustable which might be a disadvantage. As the lens properties are notknown, the positioning of the sheet is optimised by observation. At a distance of 50 cm, the waistof the beam can be adjusted to the middle of the measurement section. The height of the sheet is5 cm and the thickness, measured on a millimeter grid, is 1.5 mm. It is possible to move the laserin the vertical direction with respect to the measurement section.3.3.2 SeedingThe oil droplets in the jet flow serve as tracer particles as they are supposed to be small enoughto follow the flow (see section 4.1.2). As the oil droplets are used as the seeding, a possible set-upwould be to connect the micromixing device directly to the jet capillary. The lowest possibleconcentration of oil droplets issued by the mixer, however, leads to a number of droplets whichis too large to perform a velocity measurement. So, direct injection is not an option. In section4.1.2, this will be verified quantitatively.In order to be able to measure the velocity of the region outside the jet, a low concentration of oildroplets is added also to the coflow. This seeding should be as low as possible as it contributes tothe concentration of oil droplets inside the jet, due to entrainment of the coflow liquid.Note, that it is inevitable that the seeding is not homogeneous. Large concentrations of oil dropletsare found inside and low concentrations are found outside the jet. One of the requirements toperform an accurate PIV-measurement is therefore not met. Especially at the boundaries of thejet, this may lead to errors in the velocity measurements.Before starting the two-phase jet experiment, two other experiments are performed to test thePIV set-up. At first, the seeding is added only to the coflow while a clean jet is generated by themicro annular gear pump. Secondly, the jet is seeded with the same amount of oil as the coflowand generated from the water reservoir (see section 4.1.4).3.3.3 Camera and image acquisition systemA Flowmaster 3s camera is used with a 1280 x 1024 pixels CCD chip. The size of a pixel is 6.7µm x 6.7 µm. For single-frame recording a frequency of 8 Hz can be reached. The camera isable to record two images within a short time interval in two different frames. The minimal timebetween these exposures, the interframing time, is 300 ns. The minimal distance between the lightsheet and the camera for which the images are in focus is 60 cm. In that case, one camera pixelcorresponds to 61.3 µm in the light sheet corresponding to a magnification factor, M, of 0.11 anda focal length, f, of 5.9 cm. A liquid crystal shutter, type Displaytech VS7500, is placed in frontof the camera in order to control the exposure of the camera. The response time of the shutteris 110 µs and it has a clear aperture of 1.9 cm. According to equation 3.1, the minimal image25

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