3MS Multiphase Systems Problem Sheet 2024 Maximum THREE pages excluding cover page and references. The figures and table below present data from a study of a mixing vessel operated either with gas sparging or with solids. The details of the set up are shown in Figure 1 and Table 1. Experimental Setup and Data Air in Perspex Baffle Ring sparger Rushton 6-Blade Turbine ERT Linear Probe Electrode strip Figure 1. Experimental set up equipped with Linear Electrical Resistance Tomographic Apparatus. This geometry is different to the circumferential geometry used in 2nd year labs. The liquid is conductive (assume the density and viscosity are that of water and an interfacial tension of 0.04 N m¹), and the probe measures the distribution of conductivity in a 2-D radial slice from the impeller axis to close to the vessel wall. When a conductive aqueous solution is sparged with (non-conductive) gas bubbles, the conductivity distribution can be converted to a tomogram showing the distribution of voidage (air bubbles). Table 1. Tank Dimensions. Note: Liquid Fill Height = 3/2T Vessel Property Ratio with Tank Diameter, T Absolute Value (m) Tank Diameter, T 0.14 Impeller Diameter, D 2/5 0.056 Baffle width, B 1/10 0.014 Impeller clearance, C 4/14 0.04 Fluid Height, H 3/2 0.21 Ring sparger diameter 7/10 0.04 1 Exercise You will be asked to perform calculations for a permutation of particle size, particle density, solids mass fraction and gas volume rate based on YOUR University ID Number as shown in the table below: Parameter selection based on LAST 4 digits of ID 1st digit 2nd digit 3rd digit 4th digit Solids dp Pp Mass vvm (mm) (kg m-3) Fraction (-) (wt%) 0 0.20 3500 4.0 1.00 1 0.23 4000 4.5 1.25 2 0.25 4500 5.0 1.50 3 0.28 5000 5.5 1.75 4 0.30 5500 6.0 2.00 5 0.33 6000 6.5 2.25 6 0.35 6500 7.0 2.50 7 0.38 7000 7.5 2.75 8 0.40 7500 8.0 3.00 9 0.43 8000 8.5 3.25 For example, if your ID is 2013679 you would take the digits 3, 6, 7 and 9 to choose dp = 0.28 mm, pp = 6500 kg m‍³, mass fraction solids = 7.5wt% and air flow = 3.25 vvm. IMPORTANT: you must state your ID and the corresponding parameters on the cover page of the submission). Figures 2 and 3 show observations and measurements of gas distribution at various characteristic conditions as impeller speed increases for fixed gas volume rate. Figure 2 shows an image of the gas in the vessel and the corresponding tomogram of voidage (εg). (a) Flooding (b) Loading (c) Loading (d) Completely Dispersed/Recirculation (e) Completely Dispersed/Recirculation The average voidage vs depth has been determined from the tomograms and is shown in Figure 3. 2 70 (a) (b) (c) (d) (e) εg (%) 0.00 3.75 7.50 11.25 15.00 Figure 2: Vessel and tomogram images at increasing impeller speed (left to right) and constant gas volume rate. The tomogram shows voidage (gas holdup) in a radial slice. Relative height 1 0.9- 0.8 * * 0.7- Flooding Loading Loading * Recirculation + Recirculation 0.6 0.5 0.4 0.3 * + * + 0.2- 0.1- 0 0 5 10 15 20 ε (%) g Figure 3: Voidage vs height at increasing impeller speed (left to right). The voidage at each height is the average across the radius taken from the figure 2 tomograms. 3 1. Using your value for vvm, estimate the likely ranges of impeller speeds for each of the three conditions observed in Figures 2 and 3. [25%] 2. Pick a speed in each range (flooding, loading and complete dispersion/recirculation) and at each determine the power input, assuming no losses due to gassing. [15%] 3. Estimate the maximum bubble size at each of your three speeds [HINT - see UNIT 10 of Prof. Simmons' notes]. Compare qualitatively with Figure 2. [15%] 4. For ERT to work it is necessary that the liquid is conductive. If we are using water, then electrolytes must be added. Discuss the effect on bubble size versus a pure liquid. [15%] Stainless steel balls were added to the vessel and mixed without sparging. In this case the particles are conductive. Figure 4 shows mean conductivity in the radial plane vs height for three impeller speeds NJS, 2/3NJs and Njs. Relative height 0.9- 0.8- 0.7- 0.6- 0.5- 0.4- 0.3- 0.2- 0.1 2.725 2.73 2.735 2.74 2.745 Conductivity mS cm-1 Figure 4. Mean conductivity in the radial plane vs height for dispersion of stainless-steel spheres at different impeller speeds. 5. For your permutation of particle characteristics and loading, determine Njs. You can assume a Zwietering constant of 6 for the Rushton turbine. [10%] 6. The three impeller speeds in Figure 4 are NJS, NJs and NJs. Suggest which data curve corresponds to which speed. [10%] 7. With reference to Figure 4, comment on the suitability of ERT to determine Njs. [10%] 4