From f9bb5685b853aa2eee8ceb8ce1eaf4ae18976bd8 Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Mon, 14 Feb 2022 14:51:02 +0100 Subject: [PATCH] Biblio: VOF models --- biblio/chapters/literature.tex | 122 +++++++++++++++++++++++++++------ biblio/library.bib | 39 +++++++++++ biblio/main.tex | 1 - 3 files changed, 140 insertions(+), 22 deletions(-) diff --git a/biblio/chapters/literature.tex b/biblio/chapters/literature.tex index da5de39..cf05bc6 100644 --- a/biblio/chapters/literature.tex +++ b/biblio/chapters/literature.tex @@ -202,30 +202,110 @@ representation of the fluid. \cite{altomare2017long} \cite{wen2018non} -\subsection{VARANS models} +\subsection{VOF models} -\cite{van1995wave,troch1999development} +\subsubsection{Introduction} -COBRAS \parencite{liu1999numerical}: spatially averaged RANS -with $k-\varepsilon$ turbulence model. Drag forces modeled by empirical linear -and non-linear friction terms; \cite{hsu2002numerical}: introduced VARANS in -order to account for small scale turbulence inside the porous media. --> -COBRAS-UC/IH2VOF \parencite{losada2008numerical,lara2008wave}: VOF VARANS (2D); -refactor of COBRAS code, with improved wave generation, improvement of input -and output data. --> -IH3VOF \parencite{del2011three}: 3D VOF VARANS, updated porous media equations, -optimization of accuracy vs computation requirements, specific boundary -conditions, validation. Adding SST model. --> -IHFOAM/olaFlow \parencite{higuera2015application}: Rederivation of -\cite{del2011three}, add time-varying porosity; Improvement to wave generation -and absorption; implementation in OpenFOAM; extensive validation; application -to real coastal structures. +Contrary to SPH models, the volume of fluid (VOF) method relies on a Eulerian +representation of the fluid \parencite{hirt1981volume}. This method uses a +marker function, the value of which represents the fraction of fluid in a cell. -\cite{vieira2021novel}: Use of artificial neural networks to determine porosity -parameter for VOF VARANS model. +\subsubsection{2D models} + +Using the VOF method along with Navier-Stokes equations, several models have +been developed in order to model fluid dynamics around porous structures. +\textcite{van1995wave} first implemented 2D-V incompressible Navier-Stokes +equations using the VOF method while accounting for porous media. The results +of the numerical model were validated with analytical solutions for simple +cases, as well as physical model tests. The model yielded acceptable results, +but the representation of turbulence and air-extrusion still required +improvement. + +\textcite{troch1999development} developed the VOFbreak\textsuperscript{2} model +in order to provide improvements. The Forchheimer theory +\parencite{burcharth1995one} is used in order to model the behavior of the flow +inside porous media. The hydraulic gradient generated in porous media is +decomposed as a linear term, a quadratic term, and an inertia term. Those terms +are ponderated by three coefficients that need to be calibrated. Several +attempts have been made to obtain analytical formulas for those +\parencite{burcharth1995one,van1995wave}, but no universal result has been +provided. \textcite{vieira2021novel} additionnaly proposed using artificial +neural networks in order to calibrate those values, which are generally +calibrated using experimental results. + +Parallely, \textcite{liu1999numerical} created a new model (COBRAS) that used +the VOF method. The model is based on the combination of Reynolds averaged +Navier-Stokes (RANS) equations and a $k-\varepsilon$ turbulence model. The +porous media is modelled similarly to \textcite{troch1999development}. The +offered results were improved compared to earlier models as more a more +accurate consideration of turbulence outside porous media was added. This model +was further improved by \textcite{hsu2002numerical} in order to account for +small scale turbulence inside the porous media thanks to volume averaged RANS +(VARANS) equations. + +The COBRAS model was then reworked by +\textcite{losada2008numerical,lara2008wave} to add improvements to wave +generation and usability. The main difference between this new code (COBRAS-UC) +and COBRAS is the addition of irregular waves generation. The code was also +optimized to reduce the number of iterations. The improvements allowed for +longer simulations to be computed. The predictions for free surface elevation +and pressure in front of a porous breakwater were accurate, but improvements +were still needed, in particular considering computation time. + +\subsubsection{3D models} + +The combination of VARANS equations and the VOF method was then brought to 3D +domains by \textcite{del2011three} in IH3VOF. Specific boundary conditions were +also added for several wave theories. Additionnaly, an improved turbulence +model was used ($\omega$-SST model, \cite{menter1994two}), which provides +strongly improved results in zones where strong pressure gradients appear. +Strong agreement between IH3VOF and experimental results was obtained, but the +need for accurate boundary conditions limited the applicability of the model. + +\textcite{higuera2015application} reworked the equations from +\textcite{del2011three} as discrepancies were observed with earlier literature +and added several improvements to the model. Notably, time-varying porosity was +added in order to account for eventual sediment displacement. New boundary +conditions were added, with static and dynamic boundary wave generators as well +as passive and acive wave absorption being implemented. The resulting model +(IHFOAM/olaFlow, \cite{olaFlow}) was implemented in the OpenFOAM toolbox. + +\subsubsection{Conclusion} + +VOF models have been developped to provide accurate results for the study of +wave impact on porous structures. The validation results from +\textcite{higuera2015application} show the capabilities of such models in +accurately representing rubble-mound breakwaters subject to irregular +three-dimensional wave fields. + +Nonetheless, the representation of porosity in those models is still mainly +based on experimental calibration, particularly for the inertia term of +porosity induced friction. + +%\paragraph{Notes} +% +%\cite{van1995wave,troch1999development} +% +%COBRAS \parencite{liu1999numerical}: spatially averaged RANS +%with $k-\varepsilon$ turbulence model. Drag forces modeled by empirical linear +%and non-linear friction terms; \cite{hsu2002numerical}: introduced VARANS in +%order to account for small scale turbulence inside the porous media. +%-> +%COBRAS-UC/IH2VOF \parencite{losada2008numerical,lara2008wave}: VOF VARANS (2D); +%refactor of COBRAS code, with improved wave generation, improvement of input +%and output data. +%-> +%IH3VOF \parencite{del2011three}: 3D VOF VARANS, updated porous media equations, +%optimization of accuracy vs computation requirements, specific boundary +%conditions, validation. Adding SST model. +%-> +%IHFOAM/olaFlow \parencite{higuera2015application}: Rederivation of +%\cite{del2011three}, add time-varying porosity; Improvement to wave generation +%and absorption; implementation in OpenFOAM; extensive validation; application +%to real coastal structures. +% +%\cite{vieira2021novel}: Use of artificial neural networks to determine porosity +%parameter for VOF VARANS model. \subsection{Other} diff --git a/biblio/library.bib b/biblio/library.bib index e95497c..b0adaa9 100644 --- a/biblio/library.bib +++ b/biblio/library.bib @@ -915,3 +915,42 @@ publisher={Molecular Diversity Preservation International} } +@article{hirt1981volume, + title={Volume of fluid (VOF) method for the dynamics of free boundaries}, + author={Hirt, Cyril W and Nichols, Billy D}, + journal={Journal of computational physics}, + volume={39}, + number={1}, + pages={201--225}, + year={1981}, + publisher={Elsevier} +} + +@incollection{van1993numerical, + title={Numerical simulation of wave motion on and in coastal structures}, + author={Van der Meer, JW and Petit, HAH and Van den Bosch, P and Klopman, G and Broekens, RD}, + booktitle={Coastal Engineering 1992}, + pages={1772--1784}, + year={1993} +} + +@article{burcharth1995one, + title={On the one-dimensional steady and unsteady porous flow equations}, + author={Burcharth, HF and Andersen, OK}, + journal={Coastal engineering}, + volume={24}, + number={3-4}, + pages={233--257}, + year={1995}, + publisher={Elsevier} +} + +@article{menter1994two, + title={Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications}, + author={Menter, FR}, + journal={AIA A JOURNAL}, + volume={32}, + number={8}, + year={1994} +} + diff --git a/biblio/main.tex b/biblio/main.tex index 914c489..7cc6a29 100644 --- a/biblio/main.tex +++ b/biblio/main.tex @@ -4,7 +4,6 @@ \usepackage[ backend=biber, - sorting=ynt, style=iso-authoryear, sorting=nyt, ]{biblatex}