This article was co-written by Spiros-Foivos Mallios & Georgios Giannakouros.

Abstract

In this article, we will discuss how to speed up CFD simulations leveraging AI-Enabled Reduced-Order Modeling. More specifically we will focus on the mixing process of an industrial tank.

The goal is to enable fast predictions of the required time to achieve uniform mixing (mixing time), based on various operational and design parameters of the mixer. For this purpose, a dynamic non-linear reduced-order model (ROM) is created using Altair® romAITM. To generate the training data, high-fidelity simulations are carried out using Altair’s Navier-Stokes CFD solver, AcuSolveTM.

The trained ROM can estimate the transient response of mixing metrics ~ 20.000 times faster than the original CFD simulation enabling much faster optimization.

Optimizing mixing processes in industrial tanks is essential for enhancing product quality, reducing production time, and ensuring energy efficiency across various industries, including pharmaceuticals, chemicals, and food processing.

Computational Fluid Dynamics has been long established as a powerful tool for designing and improving industrial mixing tanks, allowing engineers to simulate fluid behavior, predict performance, and make data-driven decisions to enhance mixing efficiency.

So, what is the challenge here?

When designing such systems, several operational and design parameters play a role , such as the Blade Pitch Angle, the Impeller Speed and the Viscosity of the Liquid in use. These three variables are common parameters in an industrial mixing case and significantly affect the behavior of the system.

The process of selecting the optimal combination of those parameters can become a quite tedious process, since traditionally even though CFD simulations give great accuracy, they require a considerable amount of solving time. Just to consider, for a medium sized mixing tank, more than 10 million elements are typically needed for an correct representation of the model!

This is where Reduced-Order modelling comes into place. A model can be trained to predict only the needed (of interest) metrics. In this case the ROM focuses on predicting the uniformity of the mixing over time.

The workflow that we follow here is quite common among many applications. Creating a ROM requires data, we can get them from either simulation results or even from real measurements (sensors), in this case it’s Simulation. Then we feed this data into romAI Director and train a romAI model that can be then used to optimize the mixing.

In other applications, it is common that the romAI model is integrated into a larger system simulation, enabling to connect multiple disciplines together and thus opens the road for Digital Twins creation.

CFD Setup

AcuSolve is a Navier-Stokes CFD solver based on the FEM, making it ideal for mixing simulations. Its advanced modeling capabilities, along with the intuitive SimLab pre-processing interface, make it perfectly suited for capturing complex fluid behavior in industrial mixing processes.

The geometry of the model is presented in the following image. The driving force of the flow field is a pitch blade turbine impeller with 4 blades.

The mesh includes a total of more than 12 million elements and 3 million computational nodes. Additionally, local mesh refinement techniques were applied in areas requiring higher computational accuracy. A mix of tetrahedral and hexahedral elements was used to capture accurately the different flow effects on each region.

The modeling of the mixing phenomena was conducted using Frozen Flow simulations with the species method. Specifically, two separate simulations were performed.

• First, the steady-state flow field is calculated, and the Moving Reference Frame (MRF) method is used for the rotation of the impeller. With this technique, we define a volume around the rotating geometry in which we numerically specify the rotational phenomena without the physical rotation of the geometry.
• In the second simulation, the flow equations are deactivated, and only the species equation is solved involving convection and diffusion. A common example is injecting dye into water, where the dye spreads with the flow and diffusion, visualizing mixing without affecting the water’s behavior. The cylindrical volume (blue color) at the top of the mixing tank also serves as the initial condition for the species, where the maximum initial concentration is defined at the start

Overall, this technique allows us to model the transient mixing behavior within a steady-state flow field. With this setup each CFD run requires around 6h of CPU time for a total of 30s simulation time.

For the calculation of the mixing uniformity, the Coefficient of Variation metric was selected.

The coefficient of variation quantifies the relative variability of species concentrations in the fluid by expressing the standard deviation relative to the average concentration of the homogeneous mix. Full homogenization is achieved when CοV is less than 0.01, indicating a highly consistent mixture.

Design of Exploration

For the present study, three design variables were selected:

• Viscosity: Affects diffusion and flow resistance
• Impeller Speed: Drives fluid motion, creating vortices and shear layers.
• Blade Pitch Angle: Adjust flow direction and intensity, controlling turbulence and circulation.

A fractional factorial DoE was performed with a total of 13 combinations of the design variables with the levels shown on the image above.

Each combination produces a different transient response on the mixing index, the results from the AcuSolve runs are plotted bellow:

Each transient AcuSolve run generates hundreds of valid training points that can be used during the training process. The generated data was stored in a csv format and was fed into romAI Director.(accessible from Altair Twin ActivateTM).

We start with the Pre-processor tab where we filter the responses to remove any numerical noise from the simulation. Next, we move on to the Builder tab where we set up the system structure and define the hyper-parameters used during the training. On this example we set the 3 corresponding Inputs and 1 Output & State Variable. (State Variable must be selected in order to create a dynamic rom model)

But how do we make sure that our romAI model is trained properly?

A first indication can be given by the Loss Curve. The Training Loss (blue line) should converge after the given amount of epochs and also the error calculated on the Test dataset (green ‘x’) should be close to the training loss.

Moreover, a dynamic ROM model should be tested by performing a time simulation on completely unfamiliar combination of inputs, to asses the good generalization capability of the ROM generated.

To quickly simulate it, we leverage the Post-Processor tab inside the romAI Director GUI. Alternatively, one can deploy the model in TwinActivate, or on your choice in 3rd party platform that supports the FMI standard or can run C Code.

To validate it, we run 2 more AcuSolve simulations, with unfamiliar combination and values on the design variables. On the Table below are the results of romAI related to the time required to complete the mixing.

The mixing time is calculated based on where the Coefficient of Variation (CoV) reaches the threshold (target) of 0.01, indicating a near homogeneous fluid.

Below are the transient responses of the CoV tested on the 2 unfamiliar cases (No 14 & 15).

Conclusions

• Relatively few AcuSolve transient simulations are needed compared to traditional ML approaches.
• Gain Factor > 20.000 enabling Real Time applications & Optimization
• ROM Able to predict the dynamic response, not just the final steady state value
• Very good generalization capabilities making the model trustworthy on new predictions