Numerical calculation of particle and bubble dispersion in a fluid-phase resonance mixer

在初步研究中，可以证明，流体相共振混合器（FPR混合器）是适合实现有效的流体混合。为此，进行了数值计算（使用OpenFOAM）和实验。在本提案中，旨在证明FPR混合器适用于颗粒和气泡分散。应再次使用OpenFOAM通过欧拉（LES）/拉格朗日方法进行数值计算。然而，为了对液相中的颗粒和气泡分散进行真实的数值计算，应考虑所有相关的流体力对分散相的动力学进行分析。这意味着考虑阻力、重力/浮力、压力项、附加质量、巴塞力和滑移剪切升力的运动方程的扩展。附加质量和巴塞特项的系数应根据Odar &汉密尔顿（1964）以及Michaelides & Roig（2011）最近提出的建议来确定，巴塞特项取决于Strouhal数。将比较使用两种系数获得的结果。此外，不同的非定常力的重要性将进行详细分析，并将模拟结果与FPR混合器中的测量结果进行比较。这些研究将在斯托克斯数的依赖（取决于颗粒和气泡的尺寸、密度比和脉动频率），并就不稳定力的重要性提供相应的建议。为了优化几何形状，计划对颗粒和气泡的分散进行数值计算（例如沉管直径和底部间隙）和FPR混合器的操作条件（例如振荡频率）。目标是尽可能实现颗粒或气泡的均匀分布。为了确定这些条件，斯托克斯数应在相关范围内变化。此外，还首次详细分析了工艺过程中非定常力对分散效果的影响，并对选定的工艺条件进行了实验验证。连续相和分散相的速度场的同时测量将通过使用荧光示踪粒子结合PIV（粒子图像测速）以及PTV（粒子跟踪测速）的应用来实现。通过使用两个CCD相机与适当的光学滤波器，两个阶段可靠地区分。此外，瞬时分散相浓度场将被估计。

In preliminary investigations it could be demonstrated that the fluid-phase resonance mixer (FPR-mixer) is suitable for realising effective fluid mixing. For this purpose, both numerical calculations (with OpenFOAM) as well as experiments were conducted. In the present proposal it is intended to prove the suitability of the FPR-mixer for particle and bubble dispersion. The numerical calculations shall be conducted by the Euler (LES)/Lagrange approach using again OpenFOAM.For allowing a realistic numerical calculation of particle and bubble dispersion in a liquid phase, however, the dynamics of the dispersed phase shall be analysed considering all relevant fluid forces. This implies an extension of the equation of motion accounting for drag, gravity/buoyancy, pressure term, added mass, basset-force and slip-shear lift. The coefficients for added mass and Basset term shall be taken according to Odar & Hamilton (1964) as well as those recently suggested by Michaelides & Roig (2011), which depends for the Basset term on the Strouhal number. Results obtained with both coefficients will be compared. Moreover, the importance of the different unsteady forces will be analyzed in detail and the simulation results will be compared with measurements in the FPR-mixer. These studies will be done in dependence of the Stokes-number (depending on particle- and bubble-size, density ratio and pulsation frequency) and provide corresponding recommendations regarding the importance of the unsteady forces.On the basis of these developments, numerical calculations of the dispersion of particles and bubbles are planned in order to optimise geometry (e.g. diameter of immersed pipe and bottom clearance) and operational conditions (e.g. oscillation frequency) of the FPR-mixer. The objective is achieving a homogeneous distribution of particles or bubbles as much as possible. For identifying these conditions the Stokes-number shall be varied over the relevant range. In addition the effect of the unsteady forces on the dispersion result in a technical process will be analysed in detail for the first time.For validating the numerical calculations, experiments for selected conditions will be conducted. The simultaneous measurement of the velocity fields for continuous and dispersed phase will be realised by using fluorescing tracer particles in conjunction with the application of PIV (particle image velocimetry) as well as PTV (particle tracking velocimetry). By using two CCD-cameras with appropriate optical filters both phases are reliably distinguished. In addition instantaneous dispersed phase concentration fields will be estimated.