3 years ago

Turbulent mixing of oil droplets in a round water jet

Turbulent mixing of oil droplets in a round water jet

Figure 4.2:

Figure 4.2: Visualisation of a jet with fluorescein at Re jet = 1000.Table 4.1: Jet characteristics at (z − z0) = 75 - 150 mm.Jet Reynolds number (Re jet ) 1000Jet diameter (d jet )0.83 mmWater density (ρ) 998kg/m 3Water viscosity (µ) 1.0· 10 −3 kg/ms (20 ◦ C)Initial flow rate (Φ jet )0.65 ml/sCentreline velocity (u s )97 - 49 mm/sMacro velocity scale (U)32 - 16 mm/sMacro length scale (L)0.5 - 1.1 mmMacro time scale (T )17 - 69 msDissipation rate (ɛ) 6.3·10 −2 - 4.1·10 −3 m 2 /s 3Kolmogorov length scale (η k ) 63 - 126 µmKolmogorov time scale (τ k )4 - 16 msKolmogorov velocity scale (v k ) 16 - 8 mm/smm/s. The macro scales are estimated with equations (2.41) and (2.42), whereas the Kolmogorovscales are estimated with equation (2.46). In table 4.1, the properties of the jet are summarized.4.1.2 Generation of oil-water mixtureInitially, the outlet of the micromixer was intended to be used as jet generator. In order to performa PIV-measurement, the number of oil droplets should be much smaller than the number of pixelsin the image field as the individual droplets would not be distinguishable anymore. The maximumratio of oil and water flow through the micromixer is, however, limited. If the oil flow dropsbelow 1/10 of the water flow, the pump stops. Now, assume an oil volume fraction of 0.1 in thereservoir. This concentration is diluted in the jet by entrainment of clean coflow liquid, accordingto equation (2.77). Then, a volume fraction of 0.1 leads to a centreline volume fraction in thejet (at (z − z0) = 90 mm, with Re jet = 1000 and κ = 1.4) of 0.004. The number of dropletsobserved by the camera is equal to the oil volume in the image field divided by the volume of adroplet of 20 µm. The volume of the image field is the thickness of the light sheet (d light =1.5mm), times the area of the camera view (1024 x 512 pixels of 61.3 x 61.3 µm = 20 cm 2 ), which isequal to 3 cm 3 . In this volume, the number of droplets would be 3 ·10 6 which is much more thanthe number of pixels (5·10 5 ). The other way around, aiming at a maximum of 100 droplets perinterrogation area of 32 x 32 pixels (c = 10 −4 ), the initial volume fraction must be below 1:500.The minimal volume fraction is 1:4000 which leads to an average of 15 droplets per interrogationarea, required for PIV (see section 3.2.2). With the combination of pumps and micromixer used,32

Table 4.2: Characteristics of droplets in a turbulent jet at (z − z0) = 75 - 150 mm and c 0 is 0.002.Droplet diameter (d d ) 20 µmOil density (ρ d ) 810kg/m 3Oil viscosity (µ d ) 2.6·10 −3 kg/ms (20 ◦ C)Interfacial tension (σ d )0.045 N/mResponse time (τ d ) 32 µsCentreline concentration (c s ) 9.8·10 −5 - 4.9·10 −5Droplet Weber number (W e d ) 4.2·10 −5 - 6.6·10 −6Collision frequency (ω col ) 2.5·10 −2 - 3.0·10 −3 s −1this concentration range can not be achieved. The mixture is therefore diluted in a water reservoirfrom which the jet is generated.The response time of the droplets is estimated according to equation (2.51): τ d = 32 µs. This ismuch smaller than the Kolmogorov time scale (see table 4.1) so the oil droplets are expected tofollow the fluid motion.To estimate the influence of buoyancy effects, at first the terminal velocity, U term , of a dropletof 20 µm is calculated with equation (2.54): U term = 45 µm/s. This is much smaller than theestimated centreline velocity. Secondly, the acceleration of a plume of oil droplets with volumefraction c = 10 −4 is considered: a plume = 0.2 mm/s 2 (see equation (2.55)). The mean decelerationof the jet between 75 and 150 mm is much larger: 50 mm/s 2 . Consequently, buoyancy effects arenegligible. If the volume fraction inside the jet is 10 −4 , two-phase effects may occur as describedin section 2.2. In this flow regime, droplets enhance the dissipation of turbulent kinetic energy(see figure 2.6).The droplet Weber number, W e d , varies between 4.2·10 −5 and 6.6·10 −6 ((z − z0) = 75 - 105 mm).As W e d ≪ 1, the droplets are assumed to remain spherical.To predict the possibility of coalescence, the collision frequency, ω col , is estimated according to2.60: ω col = 2.5·10 −2 - 3.0·10 −3 s −1 . It follows that c 2 (η k /d d ) 3 ≪ 1 (see section 2.2.3), so theeffects of coalescence in the self-similar region of the jet can be neglected. However, it should bekept in mind that it remains likely that coalescence will occur in the initial jet mixture and nearthe laminar-turbulent transition point. The experiments must point out whether coalescence is alarge disturbing factor. In table 4.2, the relevant droplet parameters are summarized.4.1.3 CoflowTo minimise disturbances of the jet by the coflow, a sponge is used as flow straightener. Thepressure drop over the sponge is quite small due to the large permeability. If an inhomogeneity,such as a leak, is present in the sponge, the resulting disturbance of the coflow is consequentlynot very large. The coflow is adjusted to compensate the entrained flow rate. In section 2.39, itis derived that the entrained flow at the top of the measurement section, (z − z0) = 200 mm, fora jet with Re jet = 1000, is equal to 57 ml/s. For a coflow rate of 60 ml/s (corresponding to 4mm/s), the mean vector field at the measurement position of z = 75 - 105 mm is depicted in figure4.3. Oil droplets are added to the coflow only to serve as seeding for the PIV-measurement.It can be noticed that, at the right side, the coflow reaches values of 1.5 times the coflow at the leftside. Besides, the mean value of the coflow in this area is around 10 mm/s, instead of the expected4 mm/s. Most of the coflow liquid is apparently flowing through the middle of the measurementsection. The centreline velocity near the measurement position is around 70 mm/s so this effectis expected to disturb the jet only at the edges. Improvement of the coflow field is not possible.Attempts to mount a more dense filter material did not succeed.33

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