Practice of two-phase flows with test cases of run_training_lbm

Introduction

Introduction

This section presents an overview of folder run_training_lbm to start practicing two-phase flows with LBM_Saclay. Those test cases are used in the LBM training session of 1) SMEMaG doctoral school ADUM and 2) Master of Sciences Sorbonne University SSU. Most of them appear in publications to validate new LBM numerical schemes or new two-phase models. Several examples of .ini files are contained in directory run_training_lbm. They run with the kernel NSAC_Comp which implements the Model of Navier-Stokes/Conservative Allen-Cahn (CAC)/Composition. Those input datafiles use several options or different values to help users for making their own test case. It is supposed that you run the test cases on ORCUS (see First simulations on ORCUS: example with GPU partition). Once the job is complete, the output files must be downloaded on your local computer and post-processed with paraview. Few examples of single-phase and two-phase flows are presented in Fig. 29.

Table of content

Direct access

Single-phase and two-phase without fluid flow

Run “Single phase test cases”

Run “Two-phase without fluid flows”

Two-phase flows

Run “Two-phase with fluid flows”

Run “Two-phase with fluid flows with composition effect”

Run “Two-phase fluid flows interacting with a solid phase”

../../../_images/Overview_NSAC_Comp.png

Fig. 29 Overview of two-phase simulations contained in folder run_training_lbm

List of test cases in run_training_lbm

List of test cases

The two-phase model can easily degenerate to single-phase flows. This is the reason why the first two test cases compare LBM_Saclay results with well-known solutions of “lid-driven cavity flows” and “Poiseuille flows”.

Table 6 Single-phase test cases

Name of test case

Equations

Comparisons

TestCase01_LidDrivenCavityFlow

Navier-Stokes

Benchmark with literature

TestCase02_Poiseuille_Water

Navier-Stokes

Analytical solution

Run “Single phase test cases”

Those test cases check the phase-field equation

Table 7 List of test cases of Two-phase without fluid flows

Name of test case

Equations

Comparisons

TestCase03_Zalesak-Disk2D

Phase-field

Initial condition

TestCase04_Deformation-Vortex2D

Phase-field

Benchmark Cahn-Hilliard & Allen-Cahn

TestCase05_Spinodal-Decomposition2D

Phase-field

–

TestCase06_Stefan-Problem

Phase-field/Composition

Analytical solution

Run “Two-phase without fluid flows”

Two-phase test cases with fluid flow
Table 8 List of test cases of Two-phase with fluid flows

Name of test case

Equations

Comparisons

TestCase07_Double-Poiseuille

Navier-Stokes/Phase-field

Analytical solution

TestCase08_Rayleigh-Taylor2D

Navier-Stokes/Phase-field

Benchmark with literature

TestCase09_Capillary-Wave2D

Navier-Stokes/Phase-field

Analytical solution

TestCase10_Falling-Droplet2D

Navier-Stokes/Phase-field

–

TestCase11_Rising-Bubble2D

Navier-Stokes/Phase-field

–

TestCase12_Taylor-Bubble2D

Navier-Stokes/Phase-field

–

TestCase13_Splashing-Droplet2D

Navier-Stokes/Phase-field

–

TestCase14_Dam-Break2D

Navier-Stokes/Phase-field

–

Run “Two-phase with fluid flows”

Two-phase with fluid flow & composition effect
Table 9 Test cases inside folder TestCase15_Surfactant

Name of test case

Equations

Comparisons

Analytical_Profile1

Navier-Stokes/Phase-field/Composition

Analytical solution

Analytical_Profile2

Navier-Stokes/Phase-field/Composition

Analytical solution

Coalescence

Navier-Stokes/Phase-field/Composition

–

Falling-Droplet

Navier-Stokes/Phase-field/Composition

–

Rising_Bubble

Navier-Stokes/Phase-field/Composition

–

Run “Two-phase with fluid flows with composition effect”

Two-phase interacting with a solid phase
Table 10 List of test cases of Two-phase interacting with a solid phase

Name of test case

Equations

Comparisons

TestCase16_Contact-Angle

Navier-Stokes/Phase-fields

–

TestCase17a_Hydrophobic-Solid

Navier-Stokes/Phase-fields

–

TestCase17b_Vertical-Wall

Navier-Stokes/Phase-fields

–

TestCase18_Container-Splash

Navier-Stokes/Phase-fields

–

TestCase19_Static-Container-Hole

Navier-Stokes/Phase-fields

–

TestCase20_Moving-Container-Hole

Navier-Stokes/Phase-fields

–

Run “Two-phase fluid flows interacting with a solid phase”

Parameters in S.I. units

Parameters in S.I. units

Most of input values in the .ini files correspond to dimensionless parameters of water-air or oil-air two-phase systems. Their parameters in SI units are presented in Tables Water – Air properties and Olive oil – Air properties below.

Table 11 Water – Air properties

Name

Symbol

Value

Dimension

Water density

\(\rho_{l}\)

\(998.29\)

kg/m \(^{3}\)

Kinematic viscosity

\(\nu_{l}\)

\(1.003\times10^{-6}\)

m \(^{2}\)/s

Air density

\(\rho_{a}\)

\(1.204\)

kg/m \(^{3}\)

Kinematic viscosity

\(\nu_{a}\)

\(1.56\times10^{-5}\)

m \(^{2}\)/s

Surface tension

\(\sigma\)

\(7.28\times10^{-2}\)

N/m

Gravity

\(g\)

\(9.81\)

m/s \(^{2}\)

Dynamic viscos water

\(\eta_{l}\)

\(10^{-3}\)

Pa.s

Dynamic viscos air

\(\eta_{a}\)

\(1.878\times10^{-5}\)

Pa.s

Density ratio

\(\rho_{l}/\rho_{a}\)

829.14

–

Dyn viscos ratio

\(\eta_{l}/\eta_{a}\)

53.33

–
Table 12 Olive oil – Air properties

Name

Symbol

Value

Dimension

Oil density

\(\rho_{l}\)

\(911.4\)

kg/m \(^{3}\)

Kinematic viscosity

\(\nu_{l}\)

\(9.216\times10^{-5}\)

m \(^{2}\)/s

Air density

\(\rho_{a}\)

\(1.225\)

kg/m \(^{3}\)

Kinematic viscosity

\(\nu_{a}\)

\(1.618\times10^{-5}\)

m \(^{2}\)/s

Surface tension

\(\sigma\)

\(0.032\)

N/m

Gravity

\(g\)

\(9.81\)

m/s \(^{2}\)

Dynamic viscos oil

\(\eta_{l}\)

\(0.08399988\)

Pa.s

Dynamic viscos air

\(\eta_{a}\)

\(1.983\times10^{-5}\)

Pa.s

Density ratio

\(\rho_{l}/\rho_{a}\)

744

–

Dyn viscos ratio

\(\eta_{l}/\eta_{a}\)

4236

–

Types of files in run_training_lbm

Types of files

The folder run_training_lbm contains several classical test cases of two-phase flows. They are all based on the Model of Navier-Stokes/Conservative Allen-Cahn (CAC)/Composition, but they differ by the use of different initial conditions, boundary conditions and values of parameters. The parameter values of those test cases are representative of various dimensionless numbers (Re, Bo, Mo, At, etc.) and for some of them, comparisons are performed with analytical solutions or well-known benchmarks.

Types of file inside the folder

Several types of files appear in the directory run_training_lbm. Besides the .ini input file of LBM_Saclay, several files are useful for 1) deriving the dimensionless input parameters, 2) post-processing the simulation outputs and 3) describing the test case.

The test case is described inside a “Readme” file with the suffix .txt. Sometimes a jupyter notebook (extension .ipynb) is present inside the directory. When the test case compares the numerical solution with one solution of reference (benchmark or analytical solution), one or several files with extensions .dat or .csv are used in a python script (extension .py) or in the jupyter file. Finally, when the post-processing with paraview requires many commands, a state file for paraview (suffix .pvsm) can be set in the directory. A summary of those files are presented in the Table below.

Table 13 Types of files

Extension

Description

Command

.ini

Input files for LBM_Saclay

LBM_saclay inputfilename.ini

.py

python scripts for Pre- & Post-Processing

python name.py

.ipynb

Jupyter notebook for validation sheets

jupyter notebook name.ipynb

.pvsm

State file for paraview

in paraview click “load state”

.txt

Readme text file

use your favorite editor

.csv or .dat

Ascii datafiles for comparisons

Used in .py & .ipynb scripts

Section author: Alain Cartalade