\section{Executive Summary}

Industry relevant heat treatment processes using ribbon burners (corrugated metal sheets pressed and spot welded together forming several small ports) are studied using large eddy simulations (LES) in this work. Experimental data from laser absorption spectroscopy is used to try and validate computational models. The initial simulations are modeled in an open-source CFD package, OpenFoam. A three dimensional section of a ribbon burner is simulated to characterize the temperature and water mole fraction profiles. \\

The chemistry in the simulations is a single-step global mechanism for the combustion of methane and boundary conditions are modeled to match the experimental setup, also at the University of Colorado, Boulder. There is some uncertainty about the initial conditions such as the inlet jet velocity and inlet temperature. In order to estimate those parameters, an inverse modeling approach is used wherein an open-source parameter optimization and calibration toolkit, Dakota, is used. A non-linear least squares algorithm approximates the hessian by making small perturbations in the inlet parameters (temperature and velocity) for this gradient based calibration approach. \\

Initial results show that this method can be useful to calibrate for parameters that might be hard to obtain experimentally. Using a gradient based approach reduces the number of total simulations that need to be performed and provides a better understanding of the sensitivity of each parameter to the centerline temperature profile. The chemistry modeling needs to be improved to get better results since the heat release is difficult to control and capture with an infinitely-fast, single-step chemistry model.

\newpage

\section{Introduction}

\subsection{Project Overview}

The improvement in the quality and availability of computational resources such as supercomputers and graphical processing units (GPUs) have increased the use of simulations in both academia and industry in the last few years. During the past four years, a gift from 3M has funded a project that is at the intersection of academia and industry at the University of Colorado, Boulder. The CU team, advised by Dr. Peter Hamlington and Dr. Greg Rieker, has designed and fabricated a burner/chilled-roller experimental platform, used advanced laser-based diagnostics for in situ measurements of temperature and $H_2O$ concentration above a catalytic burner, and performed computational simulations for a range of burner/chilled-roller operating conditions. Over the next two years, primary objectives of the project are to expand the laser diagnostic measurement suite to include OH concentration, experimentally characterize temperature and concentration fields in the region between the burner and chilled-roller for a range of conditions, accurately reproduce and supplement experimental measurements using computational simulations for a range of conditions, and computationally optimize the design and operating conditions of the burner/chilled-roller system for desired polymer film properties. \\

{} The overall objectives of this research are to characterize, optimize, and improve burner/chilled-roller systems for polymer film flame treatments. Through joint experimental and computational efforts, existing processes for polymer film treatments will be improved and new avenues of polymer treatment will be explored. Specific near- and long-term objectives of this project are to:

\begin{itemize}

\item Develop an experimental platform, high-speed in situ laser diagnostics, and high-resolution computational model to characterize and optimize burner/chilled-roller configurations, including those involving catalytic burners.

\item Use computational methods backed by experimental validation to rapidly explore a wide range of design and operational parameters and to improve the design and operation of burner/chilled-roller systems for the purpose of achieving specific flame treatment goals (e.g. increased speed, improved burner uniformity, and flame stability).

\item Use computational simulations to perform adjoint optimization of the burner/chilled-roller design and operating parameters in order to achieve desired temperature uniformity, radical concentrations, and heat transfer at the film surface.

\end{itemize}

\subsection{Experimental Setup}

{} Industry relevant heat treatment processes for films are tested using laser absorption spectroscopy. The use of corrugated stainless-steel sheets (called ribbons) create several small ports. Premixed fuel flows through these ports at a prescribed inlet temperature, velocity, and equivalence ratio. The combustion of this fuel mixture results in turbulent buoyant jets in the domain above the burner. The advantage to using such a ribbon pack as opposed to a single port inlet is that these ribbons provide higher flame stability and reduce the entrainment of cool ambient air. Several factors impact the burner performance such as the flow velocity, the gap between the burner and the impingement surface (roller), and the port angle. Therefore, it is important to move to the computational realm to study the design factors in a feasible manner.\\

{} The experimental setup for the ribbon burner is shown in Figure \ref{figribbonBurner}. A chilled cylindrical roller is placed above the ribbon burner and film is passed on the roller. The experimental team can estimate the temperature and certain species profiles using laser absorption spectroscopy. The initial simulations to validate the computational fluid dynamics (CFD) models are designed to study the domain above the burner without the roller, referred to as the open ribbon burner configuration. \\

\begin{figure}[htbp]

\begin{center}

\includegraphics[scale=1]{"/Users/sidnigam/Google Drive/Spring 2018/Reacting Flows/Project2/ribbonBurner"}

\caption{Schematic of ribbon burner experimental setup \cite{3Mpaper}}

\label{figribbonBurner}

\end{center}

\end{figure}

\subsection{Computational Setup}

{} The computational effort behind this project is to develop high fidelity simulations that can aid in the designing and optimization of these industrial burners. In order to test a change in the design experimentally, several labor hours and a lot of money needs to be spent. However, if there are well validated computational models, the client can save on both time and money. There are costs associated with acquiring the computational resources required to conduct such computationally intensive studies, but these costs are often orders of magnitude cheaper than their experimental counterparts. As 3M moves into design exploration and optimization using CFD, they will need validated models that accurately represent the interaction between the physics and the chemistry.\\

{} The computations are performed in an open-source, C++ package called OpenFOAM. It is one of the most popular open source codes for computational fluid dynamics. It is a community driven database of various solvers ranging from turbulent combustion to molecular gas dynamics. For simulating fires and buoyant jets, the most relevant solvers for OpenFOAM are FireFOAM, reactingFOAM, and XiFOAM. Of these solvers, only FireFOAM \cite{WangLES} incorporates radiation modeling thus prompting its use for our simulations. \\

{} The intent of FireFOAM was to augment the current engineering prediction tools for fires. Before FireFOAM, most of the computational work in fire based simulations were done using Fire Dynamics Simulator (FDS) code \cite{FDS} developed at the National Institute of Standards and Technology (NIST). FireFOAM is a relatively new solver in the OpenFOAM suite of combustion solvers. Using radiation modeling, chemical specie tracking, advanced chemistry mechanisms, higher order numerics, and pyrolysis modeling, FireFOAM has become a reliable solver for simulating fires and buoyant plumes. It is developed and used by the fire insurance company, FMGlobal as their main tool for computationally predicting the characteristics of fires and for studying effective ways of mitigating and extinguishing such fires. \\

{} There are some uncertainties in the experimental measurements, such as the inlet temperature and the inlet velocity. The inlet temperature of the premix stream can be affected by the burner ports which are narrow and tall (1.5 mm x 2.5 mm wide and 12 mm tall). The port walls are stainless steel and can heat up during the operation of the burner. The velocity is difficult to measure because the control system controls the overall flow rate of the premix stream, which comes out of the ports but can also seep through the ribbon walls that are pressed together resulting in a slow co-flow. Additionally, we use large eddy simulations (LES) that implicitly model the sub-grid scale eddies. All these factors require some sort of estimation for the experimental parameters. In this study, we use Dakota \cite{Dakota}, an open-source package of mathematical and statistical models that allows us to conduct a parameter estimation study on the ribbon burner simulations.\\

\section{Objectives}

This study is the first step towards developing high fidelity simulations for the open ribbon burner configuration. The main objective of this study is to accurately predict the temperature and water mole fraction profiles for the combustion of premixed methane and air mixture over a ribbon burner. The goals that will help reach the main objective of the study are:

\begin{itemize}

\item To test different meshes to study the grid convergence

\item To conduct parameter estimation studies in both two dimensions and three dimensions to estimate the experimental inlet velocity and temperature

\item To compare computational results to the experimental measurements from the laser absorption spectroscopy studies

\end{itemize}

\section{Questions/Hypotheses}

There are several hypotheses we are making in the initial run of the study.

\begin{itemize}

\item Single step chemistry is adequate in capturing the heat release and the water mole fraction

\item Exact geometry of the burner is not meshed; instead, a structured grid with the same area for each port is meshed

\item A small section of the ribbon burner is sufficient to capture the average temperature and water mole fraction profiles

\end{itemize}

We would also like to answer a few questions with this study.

\begin{itemize}

\item What is the best combustion model for this global chemical mechanism?

\item How many parameters should be varied to calibrate for temperature profiles?

\item What is the most appropriate calibration algorithm to use for this study?

\item What are the acceptable error margins in predicting the temperature and water mole fraction profiles?

\end{itemize}

\newpage

\section{Preliminary Research}

\subsection{Computational Method}

The numerical simulations have been performed using the software package OpenFOAM, which is a freely-available and open-source solver for computational fluid dynamics (CFD) simulations. OpenFOAM has many built-in physics modules, making it ideal for quickly simulating a broad range of problems. Since OpenFOAM is freely available, we anticipate that this choice of code will facilitate the transfer of simulation capabilities developed at CU to researchers at 3M. Eventually we would like to provide a computational tool that can be run by 3M researchers locally on their desktop workstations. \\

The computations performed are large-eddy simulations (LES), which allow 3D variations in the flow field to be resolved both temporally and spatially. LES directly resolves large-scale motions in the flow while modeling small scales, and thus strikes an ideal balance between computational efficiency and physical accuracy. The temporal and spatial accuracy of LES also makes it an ideal method for studying variations in temperature and chemical species fields above catalytic-type and ribbon-type burners. \\

{} FireFOAM is a fully compressible solver and uses the Favre filtered Navier-Stokes equations \cite{favre} to solve for the fluid flow. As with other reacting flow solvers, the total energy equation is in terms of total enthalpy. Species mixing is tracked using transport equations for the mixture fraction which is treated as a conserved scalar (Lewis number of unity). Since it is a large eddy simulation (LES) solver, closure is needed for the sub-grid scale stress. In case of FireFOAM, it is modeled by the eddy viscosity concept using a one-equation model. It should be noted that other models can be used for this closure as well such as the Smagorinsky model. Radiation modeling is also utilized in these simulations, and FireFOAM can use several different radiation models such as P1 (assumes a large optical thickness for flames) or fvDOM (finite volume discrete ordinate method). For the current study, we assumed an optically thin flame with a constant radiant fraction of 20\% which was estimated by McCaffrey \cite{firescience1}. The computational domain is shown in Figure \ref{figComputationalDomain}. Note that the domain shown is two dimensional, but the simulations are run in both two and three dimensional domains.\\

\begin{figure}[htbp]

\begin{center}

\includegraphics[scale=0.6]{"/Users/sidnigam/Google Drive/Spring 2018/Reacting Flows/Project2/2DComputationalDomain"}

\caption{Computational Domain}

\label{figComputationalDomain}

\end{center}

\end{figure}

\newpage{} In terms of the numerical methods applied, OpenFOAM uses the finite volume method on unstructured or structured mesh using pressure based solvers. This method is similar to the commercial CFD codes such as Ansys Fluent and Star CCM. Since OpenFOAM is open source and highly customizable, there are several numerical schemes that can be used for any simulation. The time stepping is adaptive and based on a stability metric called the courant number. A rule of thumb is to have the Courant number be below 0.5 in simulations for good convergence. Courant number is a dimensionless quantity defined below.

\bes{C = \frac{u_x\ \Delta t}{\Delta x}+ \frac{u_y \ \Delta t}{\Delta y}+ \frac{u_z \ \Delta t}{\Delta z}}

This value affects the convergence of a simulation. Physically, a Courant number greater than one implies that in certain parts of the simulation, the fluid flow spans more than a cell in the domain, implying that the said cell will be skipped in that iteration of the solver. This is why it should always be below 1. For these simulations, the courant number is set to 0.4 and PISO and SIMPLE algorithms are used to couple separate equations \cite{pisosimple}. Another important feature of OpenFOAM is the potential to scale these simulations. Since OpenFOAM is an object-oriented C++ code, one can use domain decomposition to make the simulations massively parallel \cite{parallelFOAM}. The authors estimate a linear scaling of up to 10,000 cells per processor. \\

\subsection{Parameter Estimation}

Since we are solving the Navier Stokes equations, the forward model is non-linear and complicated. We can leverage inverse modeling and use gradient based algorithms in order to estimate experimental parameters. In order to do that, we used Dakota. Using a non linear least squares solver, we can give Dakota a set of parameters to tweak in order to calibrate for the data we give it. Before we do that, we need to make sure we have the following prerequisites:

\begin{itemize}

\item A well refined domain with grid convergence testing

\item Proper representation of the chemistry and the combustion

\item Gradient based algorithm with a predetermined finite difference step size

\end{itemize}

We selected a non-linear least squares algorithm that adaptively estimates the Hessian through small perturbations to the parameters. The calibration parameters are given to Dakota with a range for their values and a vector is then given from the experimental dataset to act as the cost function to be minimized. After the initial simulation, the solver runs a couple of simulations with small perturbations to the initial parameter values and estimates the direction of steepest descent. The solver converged in 17 iterations. The results from the 3D calibration study are shown in Figure \ref{figDakota}.

\begin{figure}[htbp]

\begin{center}

\includegraphics[scale=0.37]{"/Users/sidnigam/Google Drive/Spring 2018/Reacting Flows/Project2/Dakota3DCalibration2"}

\caption{Parameter Estimation Using 3D Simulations}

\label{figDakota}

\end{center}

\end{figure}

\subsection{Accuracy}

There are some ways in which we can improve the accuracy of the model, which might improve the prediction of the temperature profiles that we observe. The main challenge would be to improve the chemistry modeling. Currently, these simulations are using the \emph{infinitelyfast} chemistry model which causes the combustion to occur as soon as the reactants are in contact with each other. Initial progress has been made to improve the fidelity of the chemistry by simulating a multi-step mechanism. However, these introduce emph{n} more equations to solve for where \emph{n} is the number of species modeled by the chemistry mechanism.\\

Some inaccuracies can be accounted for by the solver. As in our case, the fireFoam validation simulation also over-predicts the calculated peak temperature by $250-350$ K but that is attributed to the lack of correction of the experimental data for thermocouple radiation. According to McCaffrey, the flame temperatures estimated were under-predicted on the order of 20\% because of the thermocouple radiation \cite{WangLES}.\\

{} There are a few other drawbacks of this approach. FireFOAM solver's ability to predict fluid velocities, flame height, and entrainment of air are not the most reliable. The authors of the code show that the solver under-predicts the velocities compared to the experiments \cite{WangLES}. Predicting the flame height is difficult to measure experimentally because of the dependence on intermittency and the luminous flame burnout. \\

Finally, the mesh is not an exact representation of the geometry but is simplified to suit the calibration case.

\section{Research Approach}

{} While the initial results might not be the best, there is promise shown in this approach. In terms of the approach for the future, we would stick with fireFoam as the solver since it has improved with time. Almost once a year, OpenFOAM is updated based on new findings in literature and improvements to different algorithms. The developers of FireFOAM, FMGlobal, also update fireFoam frequently based on their research. Thus, it is always improving. A recent publication from 2018 \cite{fireapp1} shows the relevance of FireFOAM in fire simulations today. \\

One avenue for improvement for this study is how the chemistry is handled. When simulating chemical reactions (such as the combustion of a premixed methane jet), often times an advanced chemistry mechanism is used that tracks several species. Currently, the transport properties for all the species are assumed to be equal and it is non-trivial to change those values. Capturing those transport properties accurately is important for the species and temperature propagation in the domain. While look-up tables (another popular method of simulating chemical interactions in reacting flow simulations) are implemented in OpenFOAM v5, it is still not trivial to change the transport properties. The chemistry will be modeled differently and more accurately. Using an augmented reduced mechanism \cite{chemistry}, we can improve the accuracy of the simulation while still introducing a lot fewer species than the GRI 3.0 mechanism. This will strike a balance between the computational cost and the accuracy of the simulations. We also plan to use the supercomputers at CU for some of the more expensive simulations.\\

\section{Impact}

{} The overall impact of this research will be focused on the optimization and improvement of burner/ chilled-roller systems for polymer film flame treatments. Using the experimental and computational tools developed in this project, existing treatment processes will be improved and new avenues of technology innovation will be explored. This project builds on the respective experimental and computational strengths of the PIs, in addition to leveraging prior long-term research support from 3M. In the past two years, the experimental test stand has been designed and manufactured, the absorption laser diagnostics have been developed and validated, and the computational tool has been developed and used in preliminary studies to explore the effect of different system parameters on the temperature field at the film surface. \\

During the next two years, the experimental measurement library will be expanded, the physical fidelity of the computational tool will be increased, and the experimental and computational data will be used in a coupled, integrated approach to understanding catalytic burner operation and build upon the understanding of the ribbon burner operation. In all research, a specific emphasis has been placed on determining temperature uniformity and radical concentrations above the burner. In future years, this research platform may be used to examine optimization and control of the combined burner/chilled-roller system, as well as make detailed comparisons between catalytic and ribbon burners. In addition to providing valuable understanding and insight into combustion problems of interest to 3M, this project is also enabling the training of two students at CU in the areas of laser diagnostics, computational fluid dynamics, combustion, heat transfer, and industrial materials processing. \\

\section{Proposed Budget}

One of the advantages of using open-source softwares for computational work is that there are very few expenses. The relevant cost factors are:

\begin{itemize}

\item The meshing software, Pointwise, is commercial and a single-user floating license costs around \emph{\$2,000}

\item Supercomputer access varies in cost; it can be free if you are a part of the university (Summit \cite{summit} supercomputer at CU) or it can be pretty expensive to buy a node

\item A personal computer to run smaller simulations on can cost around \emph{\$2,500} \\

\end{itemize}

For a total of about \emph{\$5,000} and free access to Summit, the next set of simulations can be performed.

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