CFD for multiphase flow in vertical risers

Frank Bos Dynaflow Research Group (DRG), The Netherlands

Francesco Tocci Politecnico di Milano, Italy Ruud Henkes Shell Projects & Technology, The Netherlands Delft University of Technology, The Netherlands

Agenda

• Introduction, background and objectives • Overview of common CFD methods • Description of the hybrid CFD model • CFD simulation results for two test cases

– Case 1 – Case 2

• Conclusions

Who are we? • Dynaflow Research Group is an engineering consulting

firm – Trainings (Flow assurance, piping, pressure vessels, CFD,

FEA, etc.) – Software: BOSfluids/BOSpulse (Surge and Pulsation

analysis for single phase piping/pipelines) – Engineering Consulting (Vibrations, surge analysis,

multiphase flows, etc.) • Wide range of clients and applications

– From upstream to downstream – From process piping to cooling water and from LNG on/off-

loading to engineering of Fiberglass piping

Why are we doing this CFD research?

• DRG encounters quite often multiphase flow problems on commercial projects – Vibration due to slug flow – Separation in large scale flow separators (slug

catchers) – Multiphase flow in dredging and drilling

• DRG is good at software development

– Improve existing Open-Source CFD tools for multiphase flow in components and piping

What is our objective? • Current CFD methods works quite well for laminar and

stratified separation/mixing processes, but for liquid entrainment and complex flow regimes more sophisticated CFD methods are required

• Objective - To study the feasibility and improve hybrid CFD models. Application to flow in pipelines and risers

• Multiphase research collaboration – Shell Global Solutions International – Delft University of Technology (i.e. MSc projects)

Agenda

• Introduction • Background and objectives • Overview of common CFD methods • Description of the hybrid CFD model • CFD simulation results for two test cases

– Case 1 – Case 2

• Conclusions

Different flow regimes in vertical pipes like risers

Different flow regimes can be distinguished depending on geometrical, operational and physical parameters. (Rosa et al., 2012)

a) Bubbly

b) Spherical cap

c) Stable slug

d) Unstable slug

e) Semi-annular

f) Annular

CFD models are applicable to only one specific class of flows

• Different length scales are present in the flow depending on the flow regime. Do they all need to be captures?

• Annular flow, slugs or bubble entrainment?

Volume of fluid (VOF) versus two-fluid (Eulerian) approaches

CFD of multiphase systems tends to be regime-dependent: Length scale of flow that is resolved ( ̴mesh): l Interfacial length scale (droplet or bubble size): d l << d Segregated/free surface flow: Volume of Fluid (VOF) • All immiscible fluids are considered as one effective fluid throughout the domain • Physical properties are calculated as weighted averages based on the liquid

volume fraction l >> d Dispersed flow: Eulerian-Eulerian (two-fluid) • Momentum equation for each of the phases • Exchange terms to account for interphase momentum transfer and turbulence Coupling of the VOF model and the two-fluid model can overcome the issue of flow regime selection

Agenda

• Introduction • Background and objectives • Overview of common CFD methods • Description of the hybrid CFD model • CFD simulation results for two test cases

– Case 1 – Case 2

• Conclusions

Hybrid model description • Eulerian framework with interface sharpening in segregated zones • Conditionally phase-averaged equations for continuity and

momentum conservation for incompressible and isothermal flow, for each of the phases k:

𝜕𝜕𝛼𝛼𝑘𝑘𝜕𝜕𝜕𝜕 + 𝒖𝒖𝑘𝑘 ∙ 𝛻𝛻𝛼𝛼𝑘𝑘 = 0

𝜕𝜕(𝜌𝜌𝑘𝑘𝛼𝛼𝑘𝑘𝒖𝒖𝑘𝑘)

𝜕𝜕𝜕𝜕 + 𝜌𝜌𝑘𝑘𝛼𝛼𝑘𝑘𝒖𝒖𝑘𝑘 ∙ 𝛻𝛻 𝒖𝒖𝑘𝑘 = −𝛼𝛼𝑘𝑘𝛻𝛻𝑝𝑝 + 𝛻𝛻 ∙ 𝜇𝜇𝑘𝑘𝛼𝛼𝑘𝑘𝛻𝛻𝒖𝒖𝑘𝑘 + 𝜌𝜌𝑘𝑘𝛼𝛼𝑘𝑘𝒈𝒈 + 𝑭𝑭𝐷𝐷,𝑘𝑘 + 𝑭𝑭𝑠𝑠,𝑘𝑘

• Closure relations for forces due to gravity, drag and surface tension • Implemented in OpenFOAM and comparisons were made with

commercial CFD software (Fluent and StarCCM) and experiments

Additional forces required when resolving dispersed phases

• Surface tension force 𝐹𝐹𝑠𝑠,𝑘𝑘 = 𝜎𝜎𝜎𝜎𝛻𝛻𝛼𝛼 , 𝜎𝜎 = −𝛻𝛻 ∙ 𝛻𝛻𝛻𝛻

|𝛻𝛻𝛻𝛻|

• Drag force 𝐹𝐹𝐷𝐷,𝑘𝑘 = 𝛼𝛼𝑐𝑐𝛼𝛼𝑑𝑑𝐾𝐾 𝒖𝒖𝑑𝑑 − 𝒖𝒖𝑐𝑐 , 𝐾𝐾 = 3

4𝜌𝜌𝑐𝑐𝐶𝐶𝐷𝐷

|𝒖𝒖𝑑𝑑−𝒖𝒖𝑐𝑐|𝑑𝑑𝑑𝑑

,

𝐶𝐶𝐷𝐷 = �24(1 + 0.15𝑅𝑅𝑅𝑅0.683

𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅 < 1000

0.44 𝑅𝑅𝑅𝑅 ≥ 1000

Interface sharpening between the distinct fluids

• Interfacial sharpening in an Eulerian framework:

𝜕𝜕𝛼𝛼𝑘𝑘𝜕𝜕𝜕𝜕 + 𝒖𝒖𝑘𝑘 ∙ 𝛻𝛻𝛼𝛼𝑘𝑘 + 𝛻𝛻 ∙ 𝒖𝒖𝑐𝑐𝛼𝛼𝑘𝑘 1 − 𝛼𝛼𝑘𝑘 = 0

𝒖𝒖𝑐𝑐 = 𝐶𝐶𝛻𝛻 𝒖𝒖𝛻𝛻𝛼𝛼𝛻𝛻𝛼𝛼

• Interfacial compression velocity introduced to compress the interface when large variations of alpha occurs (two segregated phases)

• This hybrid implementation resolves for – Sharp interfaces between segregated phases (VOF) and – Dispersed phases using the Eulerian approach (two-fluid)

Summary of the hybrid model (VOF combined with two-fluid)

• Volume of Fluid (VOF) resolves one momentum equation shared by all phases – Fails to predict the slippage velocity reducing the model

accuracy drastically at higher flow rates (large slippage) • Eulerian (two-fluid) method can only be applied to

dispersed flows • Hybrid solver

– Includes numerical interface sharpening within the Eulerian framework (per-phase momentum equations)

– Capable to resolve both segregated AND dispersed phases

Agenda

• Introduction • Background and objectives • Overview of common CFD methods • Description of the hybrid CFD model • CFD simulation results for two test cases

– Case 1 – Case 2

• Conclusions

Case 1 Present results with OpenFOAM are compared with Fluent results by Worthen and Henkes ( 2015) • Vertical pipe with a diameter of 50.8 mm and length of 2.54 m (50D) at

atmospheric pressure with a flow of air and water. • Inlet flow rates: 𝑄𝑄𝑎𝑎𝑎𝑎𝑎𝑎 = 31.1 𝑚𝑚3/ℎ and 𝑄𝑄𝑤𝑤𝑎𝑎𝑤𝑤𝑤𝑤𝑎𝑎 = 1 𝑚𝑚3/ℎ • Annular flow at the inlet with liquid holdup fraction = 0.18 • Turbulence model: SST k- ω • Grid independence study showed a minimum required grid size of 560k

cells

Flow field analysis shows churn flow characteristics similar to experiments

Blue: Water volume fraction > 0.5

Time variation in total liquid holdup

• Both VOF models (OpenFOAM and Fluent) converges to similar liquid holdup values (good agreement)

• VOF models are not able to predict slug flow in risers due, since the (breaking) interface cannot be resolve sufficiently accurate

• Hybrid model needs more time to converge, but better approximates the experiment

Time-averaged liquid holdup fraction and pressure drop

• Both VOF solvers (OpenFOAM and Fluent) over predicts the dispersion between phases, leading to a under prediction of the liquid holdup and consequent lower pressure drop

• The Hybrid model is able to capture the churn flow characteristics well such that the pressure drop and liquid holdup are closely matched with the experiments

Agenda

• Introduction • Background and objectives • Overview of common CFD methods • Description of the hybrid CFD model • CFD simulation results for two test cases

– Case 1 – Case 2

• Conclusions

• 6 m vertical (transparent) pipe with a 67 mm internal diameter using air and silicone oil

• At the inlet: Us,air = 0.344 m/s Us,silicone oil = 0.05 m/s

• Turbulence model: k- ε model • Grid converged solution 1 million cells

Case 2 Present results with OpenFOAM are compared with Star CCM+ (VOF) results by Abdulkadir et al. (2015)

Flow field analysis shows slug flow (Taylor bubbles followed by liquid slug bodies with dispersed smaller bubbles

Time traces of void fraction compared

Void fraction averaged on cross-sectional planes

• Good agreement for void

fraction at three monitoring planes

• Reasonably good agreement of alternating periods of high and low void fractions, indicating gas bubble passage (travelling slugs)

WMS Plane 3

ECT Plane 2

ECT Plane 1

Probability Density Functions compared

• Reasonably good agreement of the PDFs between CFD and experiments

• Twin-peaked PDF depicting the liquid slug body and the Taylor bubble

• The void fraction in the liquid slug body showed lower values in the CFD compared to experiments

WMS Plane 3

ECT Plane 2

ECT Plane 1

ECT Plane 1 ECT Plane 2

Formation of leading Taylor bubble (Taylor bubble, liquid film and wake)

Agenda

• Introduction • Background and objectives • Overview of common CFD methods • Description of the hybrid CFD model • CFD simulation results for two test cases

– Case 1 – Case 2

• Conclusions

Conclusions • The VOF method (both in OpenFOAM and Fluent) is not suitable for

the flow conditions leading to slug or churn flow because of the large slippage between the two phases (at large flow rates)

• The hybrid multiphase solver combines the Euler-Euler two-fluid method with VOF-type interface capturing: it keeps a sharp interface between segregated flow structures and is able to represent dispersed regions

• Due to the flexibility of the hybrid solver there is no need to have a priori knowledge on the flow pattern

• The comparison for two test cases shows that there is close agreement between the OpenFOAM Hybrid model results and the predictions with Star CCM+ and with experiments

Thanks for your attention