# Formulation and Validation of an Efficient Computational Model for a Dilute, Settling Suspension Undergoing Rotational Mixing

## Abstract

Designing processing equipment for the mixing of settling suspensions is a challenging problem. Achieving low-cost mixing is especially difficult for the application of slowly reacting suspended solids because the cost of impeller power consumption becomes quite high due to the long reaction times (batch mode) or due to large-volume reactors (continuous mode). Further, the usual scale-up metrics for mixing, e.g., constant tip speed and constant power per volume, do not apply well for mixing of suspensions. As an alternative, computational fluid dynamics (CFD) can be useful for analyzing mixing at multiple scales and determining appropriate mixer designs and operating parameters. We developed a mixture model to describe the hydrodynamics of a settling cellulose suspension. The suspension motion is represented as a single velocity field in a computationally efficient Eulerian framework. The solids are represented by a scalar volume-fraction field that undergoes transport due to particle diffusion, settling, fluid advection, and shear stress. A settling model and a viscosity model, both functions of volume fraction, were selected to fit experimental settling and viscosity data, respectively. Simulations were performed with the open-source Nek5000 CFD program, which is based on the high-order spectral-finite-element method. Simulations were performed for the cellulose suspension undergoing mixingmore »

- Authors:

- Publication Date:

- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE), Bioenergy Technologies Office (EE-3B)

- OSTI Identifier:
- 1352135

- Report Number(s):
- NREL/PO-5100-67519

- DOE Contract Number:
- AC36-08GO28308

- Resource Type:
- Conference

- Resource Relation:
- Conference: Presented at the 88th Annual Meeting of The Society of Rheology, 12-16 February 2017, Tampa, Florida

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 09 BIOMASS FUELS; settling suspensions; rotational mixing; large-volume reactors; computation fluid dynamics; CFD; cellulose suspension

### Citation Formats

```
Sprague, Michael A., Stickel, Jonathan J., Sitaraman, Hariswaran, Crawford, Nathan C., and Fischer, Paul F..
```*Formulation and Validation of an Efficient Computational Model for a Dilute, Settling Suspension Undergoing Rotational Mixing*. United States: N. p., 2017.
Web.

```
Sprague, Michael A., Stickel, Jonathan J., Sitaraman, Hariswaran, Crawford, Nathan C., & Fischer, Paul F..
```*Formulation and Validation of an Efficient Computational Model for a Dilute, Settling Suspension Undergoing Rotational Mixing*. United States.

```
Sprague, Michael A., Stickel, Jonathan J., Sitaraman, Hariswaran, Crawford, Nathan C., and Fischer, Paul F.. Tue .
"Formulation and Validation of an Efficient Computational Model for a Dilute, Settling Suspension Undergoing Rotational Mixing". United States.
doi:. https://www.osti.gov/servlets/purl/1352135.
```

```
@article{osti_1352135,
```

title = {Formulation and Validation of an Efficient Computational Model for a Dilute, Settling Suspension Undergoing Rotational Mixing},

author = {Sprague, Michael A. and Stickel, Jonathan J. and Sitaraman, Hariswaran and Crawford, Nathan C. and Fischer, Paul F.},

abstractNote = {Designing processing equipment for the mixing of settling suspensions is a challenging problem. Achieving low-cost mixing is especially difficult for the application of slowly reacting suspended solids because the cost of impeller power consumption becomes quite high due to the long reaction times (batch mode) or due to large-volume reactors (continuous mode). Further, the usual scale-up metrics for mixing, e.g., constant tip speed and constant power per volume, do not apply well for mixing of suspensions. As an alternative, computational fluid dynamics (CFD) can be useful for analyzing mixing at multiple scales and determining appropriate mixer designs and operating parameters. We developed a mixture model to describe the hydrodynamics of a settling cellulose suspension. The suspension motion is represented as a single velocity field in a computationally efficient Eulerian framework. The solids are represented by a scalar volume-fraction field that undergoes transport due to particle diffusion, settling, fluid advection, and shear stress. A settling model and a viscosity model, both functions of volume fraction, were selected to fit experimental settling and viscosity data, respectively. Simulations were performed with the open-source Nek5000 CFD program, which is based on the high-order spectral-finite-element method. Simulations were performed for the cellulose suspension undergoing mixing in a laboratory-scale vane mixer. The settled-bed heights predicted by the simulations were in semi-quantitative agreement with experimental observations. Further, the simulation results were in quantitative agreement with experimentally obtained torque and mixing-rate data, including a characteristic torque bifurcation. In future work, we plan to couple this CFD model with a reaction-kinetics model for the enzymatic digestion of cellulose, allowing us to predict enzymatic digestion performance for various mixing intensities and novel reactor designs.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Apr 11 00:00:00 EDT 2017},

month = {Tue Apr 11 00:00:00 EDT 2017}

}