March 13, 2018
Mixing quality optimization of static helix mixer
Static helix mixers are widely used in chemical industry for in-line blending of high viscous liquids under laminar flow conditions. They consist of a cylindrical pipe containing a sequence of fixed helically twisted blades, with the twist direction of every blade being inverted with respect to preceding one. The specific geometry of helix mixer provides repetitive stretching, folding and stacking back of inflowing unmixed materials known as Baker’s transformation and provides efficient exponential mixing. However, mixing quality is known to depend upon the blades geometry and could be significantly improved by the right choice of blades length, thickness and twist angle.
The objective of the project was to determine optimal geometry of static helix mixer blades for Sulzer Mixpac company, to obtain the best attainable mixing performance with minimal pressure drop for the mixer of given constant length (number of sections).
We consider helix mixer of fixed diameter with the geometry of each blade being determined by the following parameters:
- Number of convolutions t
- Length of one total rotation h
- Blade thickness s
- Angle α is fixed
Static helix mixer geometry and parameters
The main challenges of this problem are as follows:
- Multi-objective problem
- Numerical diffusion effects
- Huge CPU time
Three geometry constraints and five global parameters are to be taken into account.
Two different modeling approaches supplemented with automated numerical optimization methods were used to determine mixing quality: straight-forward two-fluid CFD and mapping approach with adaptive sampling developed by DATADVANCE.
The first approach (simulation of two-fluid mixing in FlowVision software), though characterized by an easy setup, physical diffusion modeling and no additional post-processing, still is notorious for being computationally heavy, and numerical diffusion effects are known to be so strong that they may completely squash all the details of the real flow in a static mixer.
The mapping approach included the following stages:
- Flow simulation (obtain the flow pattern with CFD tool on proper mesh)
- Flow transformation (track evolution between inlet and outlet, particle tracking is used)
- Transfer matrix (get the quantitative definition of transfer matrix)
- Mixing measure (calculate mixing quality criterion)
Mapping approach, in its turn, has its technical difficulties, such as the necessity to generate a large number of tracks, no physical diffusion and the need to post-process particle tracking. Introduced adaptive sampling allowed reducing total required number of particle tracks without affecting accuracy. It helped to overcome the main problem, which is a small number of tracking particles leading to empty cells at the outlet and slow simulation due to a uniformly distributed large number of particles.
Mapping approach illustration
Since mapping approach requires sophisticated pre- and post-processing, ANSYS Fluent was used for single-fluid flow simulation and for DPM particle tracking. Meshing was performed in ANSYS ICEM CFD.
DPM particle tracks in ANSYS Fluent
Then, the two-objective optimization problem with computationally expensive objectives was solved using Multi-Objective Surrogate-Based Optimization (MOSBO) method in pSeven, algorithm selected automatically thanks to SmartSelection technique.
Optimization workflow in pSeven
Mapping approach with adaptive sampling was introduced, which requires no upstream tracking and guarantees smart tracking particles injection. Automatically selected best suitable optimization method in pSeven – MOSBO – allowed to successfully solve the Multi-objective helix optimization problem with just 70 evaluations of expensive CFD model. The Pareto frontier (mixing quality vs pressure drop) was discovered, its’ analysis revealing essentially a single optimal design.
Optimal parameters were confirmed by the comparison of the straight-forward study results with those of the suggested approach: different methods and different definitions led to the same design.
Results of two approaches led to the same design
By Anton Saratov, Application Engineer, DATADVANCE