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Modeling Multi-Phase Flow Using CFD with Related Applications

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Modeling Multi-Phase Flow Using CFD with Related Applications Computational Methods in Multiphase Flow III 251 Modeling multi-phase flow using CFD with related applications D. Lin, P. Diwakar, V. Mehrotra, B. Rosendall & J. Berkoe Bechtel Corporation, USA Abstract Concurrent liquid-gas flow manifests itself into different flow regimes depending on fluid properties, flow rates, heat inputs and geometry. The Baker chart has identified at least seven flow regimes, viz. stratified, wavy, plug, slug, annular, dispersed and bubbly flow. Each flow regime exhibits a unique flow pattern and may transition from one to another depending on the flow conditions in the pipe. Computational Fluid Dynamics (CFD) with multiphase flow equations add a capability by which these flow regimes can be visualized and understood. In this paper stratified and slug flow regimes are studied by using CFD modeling. The modeling results are validated by comparison with published experimental data. The benchmark comparison shows that CFD is successful in predicting the following aspects in two-phase flow: • Quantitative prediction of stream-wise velocities in both phases. • Qualitative prediction of flow regime, phase distribution and pressure distribution. • Transition between certain, but not all, flow regimes. On the other hand, more research and development is needed to accurately predict pressure drop and vapor/liquid interface location when the velocity difference between phases is relatively large. The application of the validated CFD model is extended to the same flow regime in a tee joint distributor system. The results demonstrate that the mal-distribution of flow can occur in complex piping systems with sudden transition. Keywords: validation, transition, stratified flow, slug flow, CFD. 1 Introduction Two-phase flow is a challenging problem because the interaction of liquid and vapor phase can generate different flow patterns depending on properties of the WIT Transactions on Engineering Sciences, Vol 50, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) 252 Computational Methods in Multiphase Flow III fluids, flow rates, heat inputs and geometry. Baker [1] has identified seven flow regimes for concurrent flows in a horizontal pipe: stratified, wavy, plug, slug, annular, dispersed, and bubbly flow. Some of the flow regimes are transient and migrate from one regime to another. Slug flow is intrinsically unsteady and is characterized by a succession of slugs of liquid separated by large gas bubbles whose diameter approaches that of a pipe. It is considered one of the most challenging flow types to model because of its intermittent nature and lack of understanding in the mechanism. Stratified flow is characterized by liquid running at the bottom and vapor at the top of a pipe due to gravity effects. It is considered the simplest flow regime. This study focuses on modeling these two flow regimes. CFD employs different mechanistic models to predict different flow regimes. It is very important to choose the correct modeling approach that captures the physics of the application. The best mechanistic multi-phase CFD model for predicting the behavior in stratified and slug flows is the VOF (Volume of Fluid) approach (Fluent Manual). The Eulerian-Granular model can successfully predict the level of solid-liquid mixing when compared to experimental tests (Rosendall and Berkoe [5]). Due to the complex nature of two-phase flows, it is necessary to validate the CFD model with experimental data before applying the analysis to more complex systems. Validation with experimental results for stratified and slug flow regime is covered in Section 3. More complex geometry and some results (flow pattern, velocity and pressure) are presented in Section 4. Finally, some concluding remarks about using CFD to two-phase flow problems are presented in Section 5. 2 CFD multiphase model description 2.1 Governing equations The Volume of Fluid (VOF) model is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. In addition to solving the continuity and momentum equations, VOF model solves one additional set of equation for the volume fractions. These equations are listed below (Fluent Manual): ∂ρ G + ∇ •(ρv ) = 0 ∂t ∂ G GG G G G ()()ρv+ ∇ • ρ vv = −∇ p + ∇ •[(µ ∇v + ∇ vT )] + ρ g ∂t ∂α q G +v • ∇α = 0 ∂t q WIT Transactions on Engineering Sciences, Vol 50, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) Computational Methods in Multiphase Flow III 253 G where ρ = density for each phase, v = velocity vector that is shared for all the 2 phases, µ = viscosity of each phase, g = gravitation = 9.81 m/s , and αq = the volume fraction for the qth phase of fluid. 2.2 Assumptions The following assumptions were made for all calculations in this study: • No phase changes were considered in liquid and vapor. • Both phases were considered incompressible. The compressibility of the gas phase is not expected to have a significant effect on the results. • The air and water were assumed of constant density and viscosity. • The surface tension for the air-water interaction was assumed constant. 3 Validation of CFD Model for various flow regimes 3.1 Slug flow validation The CFD results presented in this section are compared with experimental results on slug flow in a horizontal 2” pipe (Lewis et al. [2]). This paper provides average velocity profile measurements for comparison. In the initial CFD testing, it was observed that the generation of small bubbles and the latter regrouping phenomenon are very important in predicting slug flow. These require: 1. High velocity differential and mixing (between vapor and liquid) at the inlet. This can be achieved by using very small injection or impingement (on fences that provide sufficient restriction), which enhances liquid and vapor mixing and ensures the generation of small bubbles. 2. A fine grid throughout so that shear stress is not smeared or smoothed out. This will ensure proper break up and coalesce of bubbles downstream of the inlet. 3.1.1 Geometry, mesh and boundary conditions: To create a 3D pipe flow model of 200 diameters long with a vapor injection zone of 100mm pores will require millions of calculation cells and take a long time to converge. Based on this consideration, a 2D CFD model was used for this study. Nine air and water inlets were created along with slots downstream of the inlets to enhance mixing. The fence also creates vapor bubbles in the pipe. It is expected that the simplified CFD model may have a different transition length for a fully developed slug flow and the different pressure drop through the pipe length. These two aspects were not investigated in the experiment, however. The VOF time-dependent segregated solver was used for tracking the break up and coalesces of the vapor bubbles. For a slug flow, the larger bubbles are of interest. The air inlet velocity is 3.3 m/s, and the water inlet velocity was 2.5 m/s. This translates to air superficial velocity of 1.1 m/s and water superficial velocity WIT Transactions on Engineering Sciences, Vol 50, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) 254 Computational Methods in Multiphase Flow III of 1.65 m/s, which corresponds to case (b) in Lewis et al. [2]. The average air volume fraction was calculated to be 0.4. The outlet was specified as outflow boundary condition. The walls were specified as stationary walls. The maximum aspect ratio of the computational cells was about 2 and the total grid was about 210,000 in this calculation. 3.1.2 Analysis and discussion 3.1.2.1 Generation of air and water bubbles The formation of air bubbles is represented by contours of volume fraction as illustrated in Fig. 1. Red color indicates air and blue represents water. As can be seen, air bubbles of different sizes were generated immediately downstream of the slots. Some air accumulated and broke off behind the slots. As the air bubbles traveled downstream, they coalesced and broke again. Influenced by gravity, air bubbles rose up to the top portion of the pipe and water settled towards the bottom of the pipe. Some eventually formed bigger bubbles that resembled the flow pattern shown in Fig. 2. Air Inlet slots Flow 2 in direction Water Inlet walls 200 in. Figure 1: Slug flow creation using slotted inlets and fences. Figure 2: Tracking large bubbles in slug flow. 3.1.2.2 Slug flow downstream of developing zone Fig. 3 shows a snap shot of air and water distribution in the whole length of pipe. Fig. 3(a) shows the first 50 diameters of pipe and 3(b) from 50 to 100 diameters. Starting from about 40 diameters downstream, the air accumulates at the top of the pipe. The water exhibited wavy pattern with small air bubbles trapped inside. WIT Transactions on Engineering Sciences, Vol 50, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) Computational Methods in Multiphase Flow III 255 (a) (b) Figure 3: (a) Flow pattern in the first 50 diameters; (b) Flow patterns from 50 diameters to 100 diameters. 3.1.2.3 Velocity profile The velocity profile at x/D=75 is shown in Fig. 4 (right), where x is measured along the length of the pipe and D=2”. Fig. 4 shows that the calculated air speed is higher than the water speed by about 10%. A similar trend was also observed in the experiment (Lewis et al. [2]). 4.00 4 2 vel@x/D=75 3.50 3.5 experiment 3.00 3 vof@x/D=75 1.5 2.50 2.5 2.00 2 1 Uave(m/s) 1.50 1.5 1.00 velocity (m/s) CFD 1 0.5 volume ofair fraction 0.50 Experiment 0.5 0.00 -1 -0.5 0 0.5 1 0 0 r/R -1 -0.5 0 0.5 1 r/R Figure 4: Comparison of calculated time-averaged velocity profile with measurements at x/D=100 and x/D=75.
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