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Turbulent mixing of oil droplets in a round water jet

Turbulent mixing of oil droplets in a round water jet

conserved.The

conserved.The centreline concentration is obtained by substituting the expressions for the concentration andthe velocity in the equation for conservation of solute matter flux (2.67).∫ ∞Q = 2πu s c s l 2 1η0 (1 + η 2 /8B) 2k+2kdη = c 0 Φ jet ⇒ c s =(κ + 2)c 0d jet8 √ 2Bκα(z − z 0 )(2.77)Finally, the equation for the radial turbulent flux, v ′ c ′ , can be derived by substituting the expressionsfor F (η) and h(η) in the integrated equation of transport (2.71):v ′ c ′ ≡ UCk(η) = UCc 3F (η)h(η)η= αu s c sη/2(1 + η 2 /8B) 2/κ+1 (2.78)In figure 2.7b the theoretical profile of the radial turbulent flux is plotted for two values of κ.1Concentration profileκ=1κ=1.40.2Radial turbulent fluxκ=1κ=1.40.80.10.60.4()/(α u sc s)00.2−0.10−2 −1.5 −1 −0.5 0 0.5 1 1.5 2η(a)−0.2−2 −1.5 −1 −0.5 0 0.5 1 1.5 2η(b)Figure 2.7: Theoretical profile of the concentration (a) and radial turbulentflux (b).18

Chapter 3Measurement techniqueIn order to obtain quantitative data describing the turbulent mixing of oil droplets in a round jet,the instantaneous velocity and concentration fields need to be measured. The set-up of the waterjet and the generation of the oil-water emulsion is described in section 3.1. A description of thevelocity measurement technique (particle image velocimetry (PIV)) and the built PIV set-up aregiven in section 3.2 and 3.3 respectively. Sections 3.4 and 3.5 go into the acquisition of the meanvelocity and concentration fields and the corresponding turbulent statistics. The last section isdedicated to the correlation of the concentration and velocity measurements, which describes themixing process.3.1 Flow facility3.1.1 JetA schematic drawing of the flow facility is shown in figure 3.1. A capillary with an inner diameterof 0.83 mm, measured with a microscope, is mounted in a rectangular measurement section (11x 11 x 30 cm 3 ) through which a constant water flow can be pumped. This water flow will bereferred to as the coflow. The measurement section consists of four glass plates, mounted in astainless steel frame. PVC plugs with tube connections are fitted into the top and the bottom ofthe section.The outlet of the capillary is at 8 cm above the bottom of the measurement section. A tubeconnects the capillary to a reservoir containing the oil-water mixture. The water level in thereservoir is kept at a level ∆h above the outlet of the outflow tube. This causes a pressuredifference between the capillary outlet and the fluid in the measurement section which is thedriving force for the jet flow.By adding fluorescein to the water, the jet can be visualised to get a first impression of thebehaviour of the jet for different Reynolds numbers. The height of the water reservoir whichcorresponds to a sufficient value of the Reynolds number must be determined experimentally bymeasuring the centreline velocity at different values of ∆h. Equation 2.40 estimates the initialvolumetric flow rate, and consequently the Reynolds number, for the measured centreline velocities(see section 4.1.1).The coflow is applied to avoid back flow in the measurement section as oil droplets would fill it upand block the view of the camera. Consequently, the flow rate is chosen such that it compensatesfor the entrained jet flow, according to equation 2.39. To achieve a homogeneous coflow field, a 7mm thick sponge fixed between plastic frames is inserted in the measurement section to serve asa flow straightener.It might appear to be reasonable to create a jet using a pump. However, this would alter thecharacteristics of the mixture. Therefore, a less accurate flow rate is accepted using a reservoirtank.19

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