Simulation of Two Phase Flow in FLUENT

ANSYS konference 2008 16. ANSYS FEM Users‘ Meeting & 14. ANSYS CFD Users’ Meeting

Luhačovice 5. - 7. listopadu 2008 1

SIMULATIONS OF TWO-PHASE FLOW IN FLUENT

Ing. Václav Dostal Ph.D., Fakulta strojní ČVUT v Praze, [email protected] Ing. Václav Železný, Fakulta strojní ČVUT v Praze, [email protected] Ing. Pavel Zacha, Ing. Fakulta strojní ČVUT v Praze, [email protected]

ABSTRACT This paper presents the recent efforts on simulating two-phase flow of Pb-Bi and steam

in 2D using the CFD code Fluent. The study was performed in support of the Pb-Bi cooled direct contact steam generation fast reactor in which water is injected directly above the core; the produced steam is separated at the top and is send to the turbine. The simulation used volume of fluid explicit model and set the other important simulation parameters as follows: pressure velocity relation PISO, discretization scheme body force weighted for pressure and the second order upwind for momentum. For void fraction the donor-acceptor model appears to perform the best, CISCAM gives similar results, but finer mesh is required. The mass flow boundary condition was used at the inlet and the mass flows were set 0 kg/s for Pb-Bi and 0.07 kg/s for steam. At the outlet the pressure outlet boundary condition was used. The use of a turbulent model (the k-ε realizable) was necessary in order to properly model the slug flow.

1 INTRODUCTION The two-phase flow simulations in CFD are a relatively new issue, which requires a lot of attention should the future application of such codes be attractive for the nuclear reactor simulations. It is necessary first to establish the procedure for the two phase-flow simulations, before one may model directly the experimental setups and verify the obtained data. While the most interesting cases for such simulations would be for the pressurized water reactors and for the boiling water reactors, it was decided to perform the analysis for one of the generation IV reactors – a Pb-Bi cooled direct contact steam generation fast reactor [1]. This interesting reactor concept realizes cost savings from the fact that it does not require steam generators and primary coolant pumps as water is injected and boils directly above the reactor and drives Pb-Bi coolant flow around the reactor. Produced steam is separated at the top of the reactor and then drives the turbine. Several experiments in support of this reactor have been performed [2, 3]. However, as will be shown later, the current capabilities are not sufficient enough to model them completely. This work is the continuation of [4]. First, the past achievements are summarized and then the new results are presented.

2 TWO PHASE FLOW SIMULATIONS In the CFD code fluent the two-phase flow phenomenon can be modeled in several ways. The two-phase flow models used in Fluent are Euler-Euler models. These models treat the different phases as interpenetrating continua. Since the volume of a phase cannot be occupied by the other phases, the concept of phase’s volume fraction is introduced. These volume fractions are assumed to be continuous functions of space and time and their sum equals to one. The conservation equations for each phase are derived to obtain a set of equations, which have a similar structure for all phases. Constitutive relations that are obtained from empirical information are used to close these equations. Three different Euler-Euler multiphase models are available in FLUENT: the volume of fluid (VOF) model, the mixture model, and the



Eulerian model [5]. For the higher void fraction cases, such as slug flows it is recommended to use the VOF model. The performed experiments used high void fraction therefore the VOF is used as a primary model throughout the paper. This paper presents the results of the two-phase flow simulations of Pb-Bi and steam with different mesh size and with and without the turbulence models. All the simulations were performed in 2D. While it is understood that two-phase flow strongly depends on all three dimensions. However, using the 2D has a big advantage in the reduced computational time, which as will be shown later is quite long. Using 2D thus allowed running more simulations and get better feeling which mathematical models are good for modeling the two-phase flow phenomenon. Hopefully, using this knowledge it will be possible to run successfully a 3D case in the future.

2.1 Modeling of phase interface

The reconstruction based schemes available in FLUENT are Geo-Reconstruct and Donor-Acceptor. The discretization schemes available with explicit scheme for VOF are First Order Upwind, Second Order Upwind, CICSAM, Modified HRIC and QUICK. Geo-reconstruct - the geometric reconstruction scheme represents the interface between fluids using a piecewise-linear approach. In FLUENT this scheme is the most accurate and is applicable for general unstructured meshes. The first step in this scheme is calculating the position of the linear interface relative to the centre of each partially-filled cell, based on information about the volume fraction and its derivatives in the cell. The second step is calculating the advecting amount of fluid through each face using the computed linear interface representation and information about the normal and tangential velocity distribution on the face. The third step is calculating the volume fraction in each cell using the balance of fluxes calculated during the previous step. Donor-acceptor – approach uses the FLUENT standard interpolation whenever a cell is completely filled with one phase or another. When the cell is near the interface between two phases, a "donor-acceptor" scheme is used to determine the amount of fluid advected through the face. This scheme identifies one cell as a donor of an amount of fluid from one phase and another (neighbour) cell as the acceptor of that same amount of fluid, and is used to prevent numerical diffusion at the interface. The amount of fluid from one phase that can be convected across a cell boundary is limited by the minimum of two values: the filled volume in the donor cell or the free volume in the acceptor cell.

Figure 1: Examples of interphase interface calculation

Compressive interface capturing scheme for arbitrary meshes (CICSAM) – this scheme is a high resolution differencing scheme and is particularly suitable for flows with high ratios of viscosities between the phases. CICSAM is implemented in FLUENT as an explicit



scheme and o offers the advantage of producing an interface that is almost as sharp as the geometric reconstruction scheme. Modified HRIC - for simulations using the VOF multiphase model, upwind schemes are generally unsuitable for interface tracking because of their overly diffusive nature. Central differencing schemes, while generally able to retain the sharpness of the interface, are unbounded and often give unphysical results. In order to overcome these deficiencies, FLUENT uses a modified version of the High Resolution Interface Capturing (HRIC) scheme. The modified HRIC scheme is a composite Normalized Variable Diagram (NVD) scheme that consists of a non-linear blend of upwind and downwind differencing. The modified HRIC scheme provides improved accuracy for VOF calculations when compared to QUICK and second-order schemes, and is less computationally expensive than the Geo-Reconstruct scheme.

2.2 Laminar modeling

Due to the expected difficulties in the modeling the first simulations were performed without any turbulent model. The results of the simulation are shown in Figs. 2 and 3. Figure 2 is for the coarse mesh with the cell size of 0.5 mm, except for the boundary layer, where 0.2 mm in the was used. Results in Fig. 3 were obtained for a finer mesh with 0.2 mm cell size. The meshes were formed by 990000 quads and 164178 quads respectively. The other simulation parameters were: laminar flow, explicit VOF, pressure velocity relation PISO, discretization scheme body force weighted for pressure, second order upwind for momentum and CISCAM for void fraction. Boundary conditions were mass flow inlet (Pb-Bi 0 kg/s and steam 0.07 kg/s) and pressure outlet. The difference in simulation time arises from the difference of time step, which has to be reduced for better convergence of the finer mesh. The running time for these cases was on the order of 0.3 s/day for the 0.5 mm mesh and 0.1 s/day for the 0.2 mm mesh. As was already described in [4], from Figs. 1 and 2 it is apparent that the finer mesh gives results, which are closer to the slug flow regime. The void fraction in the coarse mesh deviated more from the expected 0 or 1 behavior. This indicated that the significant number of the calculated bubbles were smaller than the used cell size. The large bubbles did not form at all and the results are far from the slug flow, which is against the experimental results as well as the expectations. The finer mesh gives better results as far as void fraction is concerned. The bubbles are of larger dimension, but still smaller that in the slug flow. They have more of a spherical shape than the typical slug flow bullet shape. The gas lift pump effect was observed in both cases.

2.3 Turbulent modeling

In order ro obtain better results the turbulent model was used for the same analysis. The same operating, boundary and simulation conditions were used. The k-ε realizable turbulent model was used. The discretization scheme for the turbulent kinetic energy and the turbulent dissipation rate was the second order upwind scheme. The running time for these cases was about the same as for the laminar cases. Figures 4 and 5 show the results of the simulations (these were also already describe in [4]. The benefit of using the turbulent model is clearly visible. The bullet shaped bubble with smaller bubbles in the wake is formed. However, there is still a significant amount of cells with the void fraction between 0 and 1 indicating the amount of smaller bubbles than the cell size is still large. Nevertheless, the results are much better than in the case of laminar flow. The best results were achieved for the fine mesh with turbulent modeling. The bullet shape first bubble development is clearly visible as well as the formation of small bubbles in the



wake of the large bubble. The coalescence of smaller bubbles can be observed as well. The second slug-flow bubble is not as large as the first one, however the train of larger bubbles followed by the smaller bubbles in the wake is formed.

Figure 2: Steam bubbling in Pb-Bi, cell size 0.5 mm, laminar flow, 0 – 3 s after injection



Figure 3: Steam bubbling in Pb-Bi, cell size 0.2 mm, laminar flow, 0 – 1.9 s after injection



Figure 4: Steam bubbling in Pb-Bi, cell size 0.5 mm, turbulent flow, 0 – 2 s after injection



Figure 5: Steam bubbling in Pb-Bi, cell size 0.2 mm, turbulent flow, 0 – 2 s after injection



Figure 6: X and Y velocity contours, cell size 0.2 mm, turbulent flow, at 0.9 s after injection



Figure 7 Steam bubbling in Pb-Bi, cell size 0.5 mm, turbulent flow, 0 – 3 s after injection, donor-acceptor

For the case shown in Fig. 5 the velocity contours are show in Fig. 6. The x axis is horizontal and the y axis is vertical. From the contours of the x-component of the mixture velocity one may observe the beginning of the circulation, but more importantly one may see the s-shaped direction of flow behind the first bullet shaped bubble. It is indicated by the alternating regions of the positive and negative x-component of the mixture velocity, which suggest the alternation of the flow direction. The y-component of the mixture velocity, i.e. the vertical mixture velocity component, is more interesting. It shows the flow paths of the rising steam and the downward flow of Pb-Bi around the bubbles, especially close to the wall. The results with the different volume fraction dicretization scheme are shown in Fig. 7. In this simulation the donor-acceptor dicretization scheme was used. The results are similar to what was seen in Fig. 5 for CISCAM and 0.2mm cell size mesh. However, for the donor-acceptor scheme the coarser mesh was used and therefore the computational time was significantly reduced. This case was run for longer time and therefore also the under carry of the bubbles in



the downcomer could be observed. Even though not many bubbles actually reached the bottom this phenomenon could bring the problem of core voiding and associated reactivity feedbacks in the real nuclear reactor case.

3 CONCLUSIONS A two-phase flow simulation of Pb-Bi and steam using a CFD code Fluent was performed. The incorporation of the turbulent model (k-ε realizable), when compared to the laminar flow, resulted in larger bubbles and formation of the bullet shaped first bubble typical for the slug flow, which was observed in the experiments. The incorporation of the turbulent model did not result in the significant increase in the simulations’ computational time. When the CISCAM void fraction discretization scheme was used, the results of the simulations revealed that a very fine mesh with cell size on the order of 0.2 mm is necessary. Such mesh produced results close to the slug flow. It resulted in larger bubbles and reduced the amount of bubbles smaller that the cell size. The simulations using such a fine mesh turned out to be computationally quite intense. The donor-acceptor void fraction discretization scheme with the cell size of 0.5 mm achieved even better results than the CISCAM discretization scheme with finer mesh at much shorter times and therefore appears to be more favorable.

ACKNOWLEDGEMENTS

This work was funded from the Research Plan: Safety of Nuclear Installations MSM6840770020. The support is gratefully acknowledged.

REFERENCES [1] Takahashi M., Obara T., Iguchi T., et al. (2004), Design and Experimental Study for

Development of Pb-Bi Cooled Direct Contact Boiling Water Small Fast Reactor (PBWFR). Proc. of Int. Conf. on Advanced Power Plants (ICAPP), p.4058 Pittsburgh, 13-17 Jun.

[2] Akashi T., Takahashi M., “Study on Pb-Bi-Steam Two-Phase Flow for Evaluation of Lift Pump Performance in PBWFR,” 12th International Conference on Nuclear Engineering (ICONE12), Arlington, Virginia, USA, April 25-29, (2004).

[3] M. Takahashi, et al., “Study on Pb-Bi-Water Direct Contact Boiling Two-Phase Flow and Heat Transfer”, Progress in Nucl. Energy, Vol.47, No.1-4, January-April 2005. pp. 569-576

[4] Dostal V., Zelezny V., Zacha P.,” CFD Simulations of Pb-Bi Two-Phase Flow”, International Youth Nuclear Congress 2008 (IYNC 2008), Interlaken , Switzerland, September 20 – 26, (2008), paper no. 249

[5] Fluent 6.3 User’s Guide, September, (2006)

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Simulation of Two Phase Flow in FLUENT