PREDICTION OF TWO-PHASE FLOW IN SMALL TUBES - CiteSeerX

5th European Thermal-Sciences Conference, The Netherlands, 2008

PREDICTION OF TWO-PHASE FLOW IN SMALL TUBES: A SYSTEMATIC COMPARISON OF STATE-OF-THE-ART CMFD CODES A. Carlson1 , P. Kudinov1 , C. Narayanan2 1

Division of Nuclear Power Safety, The Royal Institute of Technology, Stockholm, Sweden 2 ASCOMP GmbH, Technoparkstrasse 1, 8005 Z¨ urich, Switzerland

Abstract Multiphase dynamics and its characteristics for two-phase gas-liquid flow have been investigated by means of advanced numerical simulations. Although important in many engineering applications, methods for robust and accurate simulations for high density and viscosity ratios remain elusive. A comprehensive comparison of two state-of-the-art Computational Multi–Fluid Dynamics (CMFD) codes, Fluent and TransAT, have been performed. The two commonly used methods for two–phase flow simulations, namely Volume of Fluid implemented in Fluent and Level Set implemented in TransAT, could be compared as a result. Significant differences were observed between the two flow topologies predicted by the two codes. For the bubbly flow case, a recirculating flow was predicted inside the bubbles by TransAT, meanwhile no significant recirculation was observed in the solution with Fluent. For the slug flow case a significant deviation was observed between the results from Fluent and TransAT on the slug formation and frequency. Periodic slug formation was observed with TransAT, in agreement with the experimental result of Chen et al. [4]. A periodic slug formation was not obtained with Fluent.

1

Introduction

Industry is simultaneously pushing performance and miniaturization of components for micro– fluidic engineering applications such as Lab-on-chip, bio-MEMS and micro cooling electronics. In their micro channels, heat and mass transfer processes take place, which can be increased by the use of multi–phase flow. A detailed knowledge of the two-phase flow characteristics, such as the interfacial topology and pressure drop, is an essential and controlling parameter for performance enhancement. This has a direct affect on micro-fluidic design strategies. Computational Multi–Fluid Dynamics (CMFD) is a tool, making it possible to study multiphase flow phenomena, aiming to be applicable for micro-fluidic design. Micro channels inherit features that make them feasible for direct numerical simulations in contrast to larger channels. The flow patterns are more stable, due to the dominating capillary force, with a modest separation of length scales. The computational domain is substantially reduced, with the same mesh resolution. This enables use of, otherwise computationally expensive, CMFD simulations. CMFD is increasing in use (in both industry and science), and interface-tracking methods are today an asset in commercially available codes. It is therefore important to recognize the application areas where codes or models fail to deliver physically sound results. It is also necessary to depict and eliminate numerical shortcomings to obtain trustworthy simulation results. Our motivation is the prospect of deterministic knowledge-based development strategies originating from numerical experiments, with the goal to go beyond the present empiricism governing micro–fluidic design. In this study, characteristics of gas-liquid two-phase flow in a miniature channel have been investigated with two state-of-the-art CMFD codes, Fluent and TransAT. They have different Interface Tracking (IT) capabilities; Fluent with the Volume of Fluid (VOF) method and

5th European Thermal-Sciences Conference, The Netherlands, 2008

TransAT with the Level Set (LS) method. VOF and LS are two of the most widely applied IT methods and have been applied with success for multi–fluid simulations. Taha et al. [13, 12] investigated rising Taylor bubbles with Fluent–VOF, and reported strong recirculation patterns within the gas phase. Akbar and Ghiaasiaan [1] and Quian and Lawal [10] investigated twophase flow in horizontal channels with Fluent–VOF. The flow direction of the gas bubbles were parallel to the motion of the liquid, co-flowing streams. No recirculation flow field was displayed within the bubbles. A similar investigation was performed by Lakehal et al. [8] (TransAT) and Fukagata [5], with different LS codes. Both reported significant enhancement of heat transfer due to the flow surrounding the bubbles. VOF and LS should, with adequate implementation, generate qualitatively coherent results. However, there seems to be a discrepancy in the literature between reported results, for twophase flow patterns in horizontal pipes, with VOF and Level Set. We scrutinizing the performance of Fluent and TransAT and aim to answer the following issues: Do the codes reproduce the expected flow regime change with the increase of gas volume fraction? Which differences in modelling could account for the deviations observed in the numerical results? How sensitive is the generation of interfacial instabilities, which induce the breakup of the inlet gas jet, to the numerical implementation of the interface tracking method? A detailed comparison depict deficiency for the numerical method in Fluent–VOF for the prediction of the slug flow pattern. As it fail to predict the formation of the growing interfacial instability and eventual slug formation of the injected gas. Mitigative strategies are suggested to improve the modelling of this class of problems.

2 2.1

Simulation framework Description of the CMFD codes

Two different CMFD codes have been used for the simulations. Fluent is a commercial code with the VOF method [7] and TransAT developed at ASCOMP GmbH has the LS method [11]. VOF and Level Set inherit some well-documented, positive and negative features summarized in the figure below. Our focus is not to cure these ”illnesses”, but they are noted in the evaluation of VOF and LS performance. Both codes solve the multi-fluid Navier Stokes equations based

Method:

POSITIVE:

NEGATIVE: Spurious currents

VOF

Conserving mass

”Sharp” interface

Level Set Reduced spurious currents

Smearing of material properties (min 2 cells) CPU expensive Mass loss Smearing of material properties (min 1 cell) CPU expensive

Figure 1: Positive and negative features with the VOF and LS method. on a finite volume method and a pressure–based solver. The codes use different discretization schemes and time integration methods; the ones applied in the simulations are listed in the table

5th European Thermal-Sciences Conference, The Netherlands, 2008

below. The reconstruction of the interface in VOF (c) is performed with a CISAM scheme 2nd order, and the LS function (φ) is advected using the QUICK linear upwind scheme. Scheme description

Fluent

TransAT

MUSCL (3nd order) QUICK(3rd order) Euler (1st order) Runge–Kutta (3rd order) PISO SIMPLE PRESTO Standard CISAM QUICK – WENO (3rd order)

Convection scheme Time integration P-V coupling P interpolation Colour function Reinitialization

Table 1: Discretization schemes and time integration methods applied.

2.2

Problem description

2D axis–symmetric simulations have been performed based on the experiments by Chen et al. [4]. Air (ρg = 1.22kg/m3 , µg = 1.78 · 10−5 kg/ms) and water (ρl = 998kg/m3 , µl = 0.001kg/ms) are injected into a pipe of co-flowing water. The outer annulus is feeding water, and the small concentric pipe is feeding air. We make the assumption that there is at t=0 no fully developed velocity profile in the domain and that entrance edge effects can be ignored. Gravitational effects have been neglected based on the limit derived by Bretherton [3], Bo