On the validity of the twofluid model for simulations of bubbly flow in nuclear reactors


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1 On the validity of the twofluid model for simulations of bubbly flow in nuclear reactors Henrik Ström 1, Srdjan Sasic 1, Klas Jareteg 2, Christophe Demazière 2 1 Division of Fluid Dynamics, Department of Applied Mechanics 2 Division of Nuclear Engineering, Department of Applied Physics Chalmers University of Technology SE Göteborg SWEDEN Corresponding author address:
2 Background Twophase simulations for a full core Coupling with heat transfer 3D Transient Use of new and innovative modelling strategies to contribute to the development of highfidelity simulations on a longer run DREAM4SAFER Development of Revolutionary and Accurate Methods for Safety Analyses of Future and Existing Reactors
3 Challenges The grid is too coarse Mesoscale structures cannot be resolved The governing equations must account for this In this project, the closures to the governing equations are to be derived from highly resolved numerical solutions to the microscopically correct governing equations
4 Scale terminology Twofluid model with coarse resolution macroscale Twofluid model with fine resolution microscale Bubbles in a continuous liquid Gasliquid interface INCREASING SPATIAL SCALE
5 The twofluid model Continuity equation for the dispersed (bubbly) phase: Volume fraction field of the continuous (liquid) phase: Momentum balance equations:
6 Computational setup Fully periodic 2D domain Aspect ratio = 4 Domain size: 0.1 x 0.4 (m) Mesh: 64 x 256 Gravity acts in the negative vertical direction A pressure drop is applied in the opposite direction of gravity to drive the flow at a relevant velocity Total simulation time is set to 4 s (corresponds to >40 flowthrough times)
7 Gassolid flow The setup is used to simulate an established gassolids case from Benyahia & Sundaresan (2012) Good agreement is found A timeresolved uniformity index is defined: Benyahia & Sundaresan, Powder Technology (2012)
8 Bubbly flow When the same case is rerun with only material properties changed (to a typical liquidgas flow), no mesoscale structures appear However: if the bubble size is changed to obtain the same terminal velocity as in the gassolids case (bubble diameter increases from 75 to 680 m), mesoscale structures appear (but seem to be of different character)
9 Mesh resolution Mesh resolution has a significant influence on the appearance of mesoscale structures x512 64x256 32x128 16x64 8x x512 64x256 32x128 16x64 8x
10 Influence of avg Mesoscale structures seem to appear only at high enough average bubble loading ( avg = 0.05 or higher) These results are consistent with literature investigations on the stability of uniformly bubbling suspensions (e.g. LBM w/ lift force by Sankaranarayanan & Sundaresan, CES 2002) where stability was lost at avg = avg = 0.1 avg = 0.05 avg =
11 Influence of walls Bounding the geometry with freeslip walls in the horizontal directions has a significant influence on the appearance of mesoscale structures cm 5 cm 1 cm
12 Inconsistencies with RANS Employing k together with the twofluid model suppresses the appearance of mesoscale structures cm 10 cm with k 1 cm 1 cm with k cm 10 cm with k 1 cm 1 cm with k In such a setup, there is an inconsistent mixing of scales over which averaging is performed
13 Conclusions Mesoscale structures can appear under conditions relevant to nuclear reactors if: The mesh resolution is fine enough The temporal resolution is fine enough The bubble size is large enough The steam void fraction is large enough Mesoscale structures are dampened/suppressed by: The presence of walls The modelling of turbulence via an eddy viscosity These results have been corroborated by comparisons with a different computational technique (MPPIC) and with two different CFD codes
14 Thank you for your attention! DREAM4SAFER Development of Revolutionary and Accurate Methods for Safety Analyses of Future and Existing Reactors The computations in this work were partially performed on C3SE computing resources.
15 Mesoscale phenomena The interphase momentum exchange is significantly affected by the subgrid homogeneity of the dispersed phase distribution The presence of mesoscale structures mean that: The subgrid distribution of the dispersed phase is inhomogeneous There are significant fluctuations in the local slip velocity The effective interphase momentum transfer is lower than in the uniform state The combined presence of mesoscale structures and unresolved geometry mean that: Phase segregation may be enhanced Effective interphase transfer terms are affected
16 The twofluid model Continuity equation for the dispersed (bubbly) phase: Volume fraction field of the continuous (liquid) phase: Momentum balance equations: No discrete phase pressure to avoid sensitivity to such model parameters The isotropic contribution to the discrete phase stresses comes from the shared pressure field The deviatoric contribution comes from the product of the discrete phase velocity gradients with the continuous phase viscosity
17 Mesh resolution Mesh resolution has a significant influence on the appearance of mesoscale structures x512 64x256 32x128 16x64 8x x512 64x256 32x128 16x64 8x Mesh d p / x x/d p x x x x x The Kolmogorov length scale is approximately 5d p
18 Temporal resolution Approximate magnitude and overall qualitative behavior of converged at a time step of 104 s t = 103 t = 104 t =
19 Influence of walls Bounding the geometry with freeslip walls in the horizontal directions has a significant influence on the appearance of mesoscale structures cm 5 cm 1 cm 1 Domain d p / x x/d p 10 cm cm cm
20 Influence of walls Noslip walls create steep gradients and cause (somewhat) different behavior Domain Liquid Bubbles Resolution 1 cm Free slip Free slip 64x256 1 cm No slip Free slip 128x512 6 x no slip free slip 4 Lift forces on bubbles in the nearwall region (currently not taken into account) are also known to affect phase separation
21 Scale terminology Twofluid model with coarse resolution macroscale The mesoscale structures: Arise due to local instabilities Characteristic sizes O(10100d p ) Can be captured by a transient twofluid model Twofluid model with fine resolution microscale Agrawal et al., J. Fluid Mech. 445 (2001) INCREASING SPATIAL SCALE
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