Implementation and Demonstration of a Boundary Condition Wall Function for Industrial Scale Particulate Fouling CFD Modeling Sverre G. Johnsen, Magnus Åberg and Stein Tore Johansen SINTEF Materials and Chemistry y
N-7465 Trondheim, Norway
[email protected]
Introduction Modeling of mass transfer of particles from a gas/liquid bulk flow to solid surfaces is a considerable challenge in most industrial processes, including heat exchanger applications. Using computational fluid dynamics (CFD) directly on these applications is very challenging and costly due to the grid refinement required to capture the complex physical processes that dominate in the near-wall region. In two previous papers, Johnsen and Johansen (2009a) and (2009b), a mass transfer wall function, for coarse grid CFD models, was proposed. The model can be employed to calculate particle phase masstransfer coefficients, for the turbulent boundary layer, by coupling the detailed physics of the nearwall region with the external flow. It can thus be employed as a boundary condition mass sink in industrial scale CFD models, at reasonable computational costs.
Figure 1: The developed wall function resolves subgrid length scales to capture the fine-scale particle dynamics close to the wall.
Implementation CFD Model ybulk ,bulk , ux,bulk ,Tbulk
Wall BC
y
Wall function:
km
Figure 2: Schematic of the flow of a cold suspension along a hot wall. Particles are affected by inter particle interactions, hydrodynamic, thermal and particle-wall forces.
f ( ybulk ,bulk , ux,bulk ,Tbulk ,Twall )
Twall
Figure 3: The wall function is implemented in the commercial CFD software Ansys Fluent as a mass sink in cells at the wall. The wall function takes input (bulk) values from the CFD model and returns a mass transfer rate.
The mass-transfer wall function is implemented as a user-defined function (UDF) in the commercial CFD software Ansys Fluent. This enables us, in principle, to model fouling in any complex heat-exchanger geometry in two or three dimensions. We have demonstrated how the fouling model performs in two different heat-exchanger geometries, a pipe with heated wall and a heated/cooled cylinder in transversal flow. We model a two-phase system consisting of liquid water and 30 vol-% CaCO3 particles. Both demonstrations are performed on a coarse grid with y 50 , using the standard k-ε turbulence model.
7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010
Figure 7: Deposition rate along the surface of a cylinder (counterclockwise starting in the down-stream stagnation point) in transversal flow. Due to the model formulation, stagnation point deposition rates are under estimated.
industrial applications experiencing fouling problems. Currently the fouling model does not handle stagnation points correctly, as it was developed for flow parallel to the wall. Mending this stagnation point deficiency is imperative to taking on complex geometries where normal-to-wall bulk particle inertia is non-zero. The model is currently in lack of validation due to the difficulties in finding good experimental results citing all necessary input parameters (thermophoretic strength, DLVO parameters).
Discussion
Acknowledgements
0
Figure 4: 2D (1mx0.1m) axisymmetric pipe geometry consisting of 900 cells. The fluid enters from the left. Symmetry axis at the bottom, fouling occurs along the top wall.
Deposition Rate, [kg/m2s]
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-1.5
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-2.5
-3 0
0
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-0.16
Deposition Rate, [kg/m2s]
0.0157
0.0314
0.0471
0.0628
Position, [m]
Axial Position, [m]
-0.18 -0.2 -0.22 -0.24 -0.26 -0.28 -0.3
Figure 5: Deposition rate along the length of a pipe.
Figure 6: 2D model of a cylinder in transversal flow consisting of 2180 cells. The cylinder diameter is 2cm and there are 60 cells along the cylinder surface. Fluid enters from the left and particles are deposited on the cylinder surface.
In previous works a one-dimensional model has been developed for particle transport and deposition, in the turbulent boundary-layer, including Brownian diffusion, thermophoresis, XDLVO near-wall forces, granular stress and shear induced re-entrainment. The model can be employed to calculate mass-transfer coefficients for the particle phase, and has been implemented as a mass transfer boundary wall-function for coarse grid CFD simulations using UDFs in Ansys Fluent. The UDF resolves sub-grid length scales necessary to resolve the fine-scale particle dynamics near the wall, and calculates a mass sink for the grid cells residing at the wall. The mass deposition wall function shows promising results and is, in principle, applicable to most
This work was funded by The Research council of Norway and Sintef.
References Johnsen S.G. and Johansen S.T. (2009a), Deposition Modeling from Multi-Phase Dispersed Flow - A Boundary Layer Wall Function Approach, Heat Exchanger Fouling and Cleaning - 2009, Schladming, Austria, June 2009. Johnsen S.G. and Johansen S.T. (2009b), Development of a Boundary Condition Wall Function for Particulate Fouling CFD Modeling, 7th International Conference on CFD in the Minerals and Process Industries, Melbourne, Australia, December 2009.
