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

初步研究表明，液相共振混合器（fpr -混合器）适合实现流体的有效混合。为此，进行了数值计算（用OpenFOAM软件）和实验。在本提案中，旨在证明fpr混合器对颗粒和气泡分散的适用性。数值计算采用欧拉(LES)/拉格朗日方法，再次使用OpenFOAM。然而，为了对颗粒和气泡在液相中的分散进行真实的数值计算，必须考虑所有相关的流体力来分析分散相的动力学。这意味着考虑到阻力、重力/浮力、压力项、附加质量、基础力和滑移剪切升力的运动方程的扩展。附加质量和Basset项的系数应根据Odar & Hamilton（1964）以及Michaelides & Roig（2011）最近提出的建议，其中Basset项取决于Strouhal数。用两个系数得到的结果将进行比较。此外，还详细分析了不同非定常力的重要性，并将模拟结果与fpr混合器中的测量结果进行了比较。这些研究将根据斯托克斯数（取决于颗粒和气泡的大小、密度比和脉动频率）进行，并就非定常力的重要性提供相应的建议。在这些发展的基础上，计划对颗粒和气泡的分散进行数值计算，以优化fpr混合器的几何形状（例如浸入管的直径和底部间隙）和操作条件（例如振荡频率）。目标是尽可能实现粒子或气泡的均匀分布。为确定这些条件，斯托克数应在相关范围内变化。此外，本文还首次详细分析了非定常力对工艺过程中分散结果的影响。为了验证数值计算，将在选定的条件下进行实验。通过荧光示踪粒子结合PIV（粒子图像测速）和PTV（粒子跟踪测速）的应用，可以实现连续相和分散相速度场的同时测量。通过使用两个带有适当滤光片的ccd相机，可以可靠地区分两个相位。此外，还将估计瞬时分散相浓度场。

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.