- Text
- Velocity,
- Turbulent,
- Concentration,
- Droplets,
- Equation,
- Axial,
- Radial,
- Profiles,
- Droplet,
- Fluid,
- Mixing

Turbulent mixing of oil droplets in a round water jet

diameter **of** a 20 µm droplet is 4.7 µm which is smaller than the pixel size, thus peak-lock**in**g isexpected. The depth **of** field is, acccord**in**g to equation 3.3, equal to 2.7 mm so larger than thethickness **of** the light sheet.As the edges **of** the CCD are not illum**in**ated, the active pixel region is decreased to 1024 **in**the horizontal direction by 512 **in** the vertical direction. This decreases the read-out time **of** thecamera and **in**creases the number **of** images that can be stored **in** memory. In this configuration,a frequency **of** 4 Hz can be obta**in**ed and 200 double images can be stored **in** memory. Theexperiment has to wait while the s**of**tware (CamWare) writes data from memory to harddisk. Inorder to get the statistics **of** more than 200 double images, a number **of** equal experiments has tobe performed **in** sequence. Before the measurements are performed, a backg**round** greyvalue imageis recorded. The backg**round** is subtracted from every measured greyvalue image. To decrease thebackg**round** noise, multiple backg**round** images can be recorded and averaged before subtract**in**gfrom the measurements.Regard**in**g the size **of** the image field (6.3 cm x 3.15 cm) and the distance to the lens (60 cm), theangle **of** the **in**cident light beams on the camera, scattered by the **oil** **droplets**, varies between 87and 93 degrees. Accord**in**g to figure 3.5 this angle dependency **of** the scatter**in**g will be visible.The camera position is adjustable **in** every degree **of** freedom **in** order to po**in**t it straight at thelight sheet. The z-coord**in**ate measured from the **jet** outlet is read from a millimeter grid attachedto the measurement section.3.3.4 DisplacementTo calculate the displacement vectors **of** the double images the s**of**tware **of** DaVis, version 6.2,is used. It reads **in** the greyvalue images as stored by CamWare and applies a standard cyclicFFT-based algorithm to obta**in** the cross-correlation function [LaVision, 2001]. A multi-passalgorithm is applied, start**in**g at an **in**terrogation area **of** 64 x 64 pixels and end**in**g at 32 x 32with 50% overlap. It is possible with**in** the s**of**tware to try other algorithms to calculate thecorrelation function. Regard**in**g the size **of** an **in**terrogation area, the edges **of** 16 pixels width arenot calculated correctly. Therefore, they will be removed when the data are analysed. Outliersare def**in**ed as vectors hav**in**g a component with a difference with the median **of** its neighbourslarger than two times the rms **of** its neighbours.3.4 Mean velocity and turbulent statisticsIt is possible that the camera is slightly misaligned or the **jet** is not issued from the tube perfectlyvertically. To correct for a rotation **of** the **jet** **in** the image plane, the mean velocity data are fit to aGaussian curve on every height. If the middle **of** this curve, x0, is shifted as a function **of** the height,the camera is misaligned. The shift is calculated by fitt**in**g x0 to a l**in**ear function. Thereafter, therotational angle compensat**in**g this shift is applied to the velocity field and coord**in**ate system.The mean velocity field is calculated by averag**in**g over the velocity calculations **of** all N images.The fluctuations **in** the mean velocity, as a measure **of** the turbulence, are calculated accord**in**g to:u rms = √ 1 NN∑(u − u) 2 =1√u 2 − u 2 (3.6)**in** which the Reynolds condition uu = ūū is used (see section 2.1.1, N ≫ 1) From the mean axialvelocity, the mean centrel**in**e velocity, u s , and **jet** width, l, are obta**in**ed by fitt**in**g the mean velocityto a Gaussian curve on every axial position. For calculat**in**g the best fit, only the measurements**in**side the **jet** are used (-1 < η < 1), as the outer regions are disturbed by the c**of**low. The fitfunction has the follow**in**g form:( ) 2u = rp(3)e − x−rp(1)rp(2)(3.7)26

The regression parameter rp(1) is the position **of** the **jet** axis (x0), rp(2) the width **of** the **jet** (l)and rp(3) the centrel**in**e velocity (u s ). Subsequently, the spread**in**g rate, α, and virtual orig**in**, z0,can be calculated by impos**in**g the self-similarity conditions 2.16 and 2.17 to the **jet** width andcentrel**in**e velocity and fit a Gaussian curve to the velocity data **of** all positions (z, x) **in** the imagefield:( )u =r(4)2x−r(1)z − r(2) e−r(3) z−r(2)(3.8)The expression r(4)/(z − r(2)), is the centrel**in**e velocity for the **jet** with imposed self-similarity.The regression parameter r(2) is equal to the virtual orig**in**, z0, while r(3) determ**in**es the spread**in**grate by r(3) = 1/α 2 .The turbulent transport **of** momentum, the Reynolds shear stress, is calculated accord**in**g to:u ′ v ′ = 1 NN∑(u − u)(v − v) = uv − ū¯v (3.9)1F**in**ally, the uncerta**in**ty, due to the f**in**ite number **of** samples, **in** the mean velocity measurementsis determ**in**ed as follows:σ u = u rms√ (3.10)NThe velocity measurements are assumed to be **in**dependent, so the time **in**terval between twomeasurements (250 ms) is larger than the time scale **of** the flow. The theoretical pr**of**iles (seesection 2.1.3) will be compared to the experimental pr**of**iles. Besides, the boundary-layer equations(2.7) will be verified by substitut**in**g the self-similar pr**of**iles, as a function **of** the dimensionlessvariable (x − x0)/(z − z0).3.5 Mean concentration and turbulent statisticsThe first way to estimate the concentration **of** **oil** is to take the **in**tensity **of** the scattered light asa measure for the concentration **of** **droplets** present **in** the flow. This is allowed if the **droplets** aremonodisperse and their images do not overlap. Besides, it is necessary that the greyvalues **of** therecorded images are proportional to the amount **of** scattered light. By averag**in**g the greyvaluesover the area **of** N by N pixels sur**round****in**g a pixel, the s**in**gle droplet images are smeared out andan estimation **of** the concentration is acquired on every pixel position. The chosen number **of** pixels(N) **of** the averag**in**g area, depends on the concentration. The chance **of** f**in**d**in**g no **droplets** **in**this area, when **in** fact the concentration is non-zero, should be m**in**imal as it gives an unphysicalcontribution to the rms-values **of** the concentration field. On the other hand, enough **in**formation**of** the spatial development must be preserved. Therefore, N is chosen equal to the size **of** the**in**terrogation area **of** the PIV-measurements. An average **of** 15 **droplets** is observed **in** each **in**terrogationarea and it gives the highest possible spatial resolution for the comb**in**ed velocity andconcentration measurements.The estimation is not optimal because the light **in**tensity over the light sheet is not homogeneous.Light is absorbed by the **droplets**, scatter**in**g is angle dependent (forward scatter**in**g is higher thanbackward scatter**in**g) and the light **in**tensity **of** the light sheet itself is not distributed homogeneously:it has vertically a more or less Gaussian shape whereas it decreases from left to right dueto divergence **of** the light sheet. To compensate for these effects, a reference **in**tensity measurementis used to scale the greyvalue images. The reference **in**tensity is obta**in**ed by add**in**g **oil** **droplets**to the c**of**low and record the **in**tensity **of** the scattered light. However, the result will still not beoptimal: the droplet distribution dur**in**g the reference measurement differs from the distributiondur**in**g the measurements. As a consequence, the local absorption **in** the light sheet changes: the27

- Page 1: Turbulent mixing of oil dropletsin
- Page 4 and 5: ContentsSamenvattingSummaryviviii1
- Page 7 and 8: SamenvattingDit project richt zich
- Page 9: SummaryThis project focuses on the
- Page 12 and 13: measurements such as Hot Wire Anemo
- Page 14 and 15: 2.1.1 Boundary-layer equationsStart
- Page 16 and 17: Consequently, a self-similar soluti
- Page 18 and 19: is a function of z, so F must be eq
- Page 20 and 21: 0.020.015K−theoryPrandtlfrom Gaus
- Page 22 and 23: 2.1.6 Kolmogorov scalesVia a cascad
- Page 24 and 25: In order to find the response time,
- Page 26 and 27: If two droplets collide, during the
- Page 28 and 29: conserved.The centreline concentrat
- Page 30 and 31: Figure 3.1: Experimental set-up.3.1
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- Page 34 and 35: Figure 3.6: Composition of peaks in
- Page 38 and 39: presence of a highly seeded jet lea
- Page 41 and 42: Chapter 4ResultsThis chapter gives
- Page 43 and 44: Table 4.2: Characteristics of dropl
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- Page 61 and 62: 1measurementsGaussian fittheoretica
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90PIVWareDaVis8580U c[mm/s]75706590

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0.2PIVWareDaVis0.15V rms/U c0.10.05

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List of Figures2.1 A turbulent jet,

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List of SymbolsRomana - velocity of

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Greekα - spreading rate of the jet

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ReferencesAanen, L. (2002), Measure