Mathematics Behind CFD applied to modeling slot die

Key Fields for CFD • Mathematics • Physics • Software Engineering The goal of the training- turn the ferocious 3 headed dog into a cute puppy Credits : 1. https: //en. wikipedia. org/wiki/Cerberus © 2018 Carestream 2. https: //www. deviantart. com/lorenzolivrieri/art/12 -Cerberus-12 -Labours-of-Hercules-583392360

3 Key Fields Mathematics • Each of these three fields deserve equal respect when setting out to develop Simulations to drive product and process development in industry Physics /Engineering Computational /Software Eng © 2018 Carestream

Key Fields: Mathematics • Tensor Calculus • Partial Differential Equations in Tensor form • Coupled & non-coupled • Linear & non linear • Different notation then most engineers are used to • Finite Methods • Finite Differences Methods • Finite Element Methods • Finite Volume Methods • • Fourier Transforms Specific Algorithms for Finite Methods Solvers and Matrix Solver Linear Algebra Solving Systems of Linear and Nonlinear Matrices Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream • Discretization must be evaluated for each problem • Balancing underconvergance versus over convergance • Stability analysis

Key Fields: Physics • Fluid Dynamics • Navier Stokes Equations • Simplifications for specific sections of modeling: • Ie: 1 d lubrication model for die/web fluid interface (the coating bead) • Solids Dynamics • Fluid solids interactions due to bar deflection and deformation during operation • Heat and Mass Transfer • Fluid properties and composition may be temperature dependent • Heat transfer from coating die to fluid • Heat transfer due to reaction of fluid Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream • All of these can be combined into Multiphysics Simulations

Key Fields: Computational/Software Engineering • Software Engineering • Designing code that meets needs while being sustainable and maintainable • HPC Engineering • Building hardware tailored to fit the computational demand • Standard equipment not up to the task • due to high IO requirements & big data needs • Special High Performance Requirements • • Static and Dynamic Memory Management Parallel computing Gpu computing Asynchronous Simulation computing • Special hardware and networking requirements • Isolated equipment Mathematics Physics /Engineering Computational /Software Eng • “low Level programming languages” © 2018 Carestream

Tensor Calculus Applied to Slot Die Modeling …time to shake off the rust…. Mathematics

Key Mathematics • Tensor Calculus • Partial differential equations • Differential Equations in Tensor form • Finite Methods • Finite Differences Methods (FDM) • Finite Element Method (FEM) • Finite Volume Method (FVM) • Fourier Transforms • Specific Algorithms for Finite Methods Solvers and Matrix Solvers Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

Fundamental Theorem of Tensor Calculus 1. Key Concepts to Refresh on 1. 2. 3. 4. 5. Line integrals Green’s Theorem Stokes Theorem Divergence Theorem Leibniz Integral Rule Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

• Line Integral & Gradient of a Curve in Tensor Calculus Mathematics Physics

Gradient of a Line • Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

Computational Engineering and Software Design © 2018 Carestream

Key Fields: Software Engineering • memory management: • • How the computer stores data When it stored that data Volume of data generation Velocity of data IO to different devices • Ie Disk, Ram, CPU • Parallel processing: • Breaking up the computing job across multiple • Servers, CPUs, Cores on CPUs • GPU Computing • What we will all be talking about in 12 years • HPC job scheduling • Management of large data sets • Commanding servers to compute jobs and analyze data sets • MPI communication • Communication language upon which both, parallel processes and HPC management operates Mathematics Physics /Engineering Computational /Software Eng http: //www. advancedclustering. com/products/hpc-clusters/# © 2018 Carestream

100 s of jobs Is this Overkill? Maybe for academic research, but when industry needs to accelerate the development process a high priority project needs to generate results faster. Need to deliver information to engineering as fast as industry moves Physics /Engineering Computational /Software Eng 1 day turn around Hundred s of gb’s of data Mathematics © 2018 Carestream Lots of simulations to organize to meet customers needs One simulation weighs over [3 -6] gb …This is “Big Data”

Big Data • Highly trending in the tech sector • Multiple Definitions • Simplest definition: • any data management where each file >2 gb • Real Definition: • Data which is not able to be handled by standard methods based on regular database management • 3 V’s of Big Data • Volume, Variety Velocity Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

High Performance Computing Engineering Big Data Management High Performance Computing Mathematics High Performance Code Physics /Engineering Computational /Software Eng © 2018 Carestream High Performance Hardware

Memory Management In essence how the computer stores information which is not being written to disk Is is being written to the HEAP or the Stack These are critical pieces of information to successfully understand how to write high performance programs. Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

Physical Phenomena: Applied to Slot Die Modeling …time to shake of the rust…. ©

Key Fields: Physics • Fluid Dynamics • Naiver Stokes Equations • Simplifications for specific sections of modeling: • Ie: 1 d lubrication model for die/web fluid interface (the coating bead) • Solids Dynamics • Fluid solids interactions due to bar deflection and deformation during operation • Heat and Mass Transfer • Fluid properties and composition may be temperature dependent • Heat transfer from coating die to fluid • Heat transfer due to reaction of fluid Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

Fundamental Physics For FVM • Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

Coordinate Transformation • Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

How to Numerically Solve PDE’s Finite Methods Finite Differences Method (FDM) Finite Element Method (FEM) Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream Finite Volume Method (FVM)

Finite Volume Methods • Basic concept • Partial differential equation (PDE) is evaluated into a modified differential equation • Navier Stokes equation for Slot die modeling internal to the cavity and slot geometry • (if only accounting for fluid flows) Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

Bringing it All together © 2018 Carestream

Steps in CFD Process Geometry Mathematics Redesign Mesh Validate Solve Analyze Physics /Engineering Computational

There is a lot going on Between each of these 3 fields the researcher must remain patient and have a clear identification of what they plan to perform with FVM or FEM take small steps … develop mathematics … develop physics Ref: https: //www. ossila. c om/pages/slot-diecoating-theory … develop code Repeat and Add Capabilities to the modeling with Each iteration Mathematics Physics /Engineering Computational /Software Eng © 2018 Carestream

Carestream R+D Developing Custom Modeling and Process/Product Development © 2018 Carestream

Additional Modeling Capabilities from CFD (1/2) • Ability to test Modifications to existing dies • Approximate shim dimensions, optimize control on wet thickness (downweb and crossweb) • Model different inlets, different manifold designs, non newtonian fluids (this may be future? ) • Waste and cost reduction, better quality, faster time to market • Improved models will reduce the number of trials required to establish coating configuration • Error reduction, root cause analysis • Computational Models have more control over error. • Simulate Different formulations and compare results directly against each other, knowing that there was not some unknown variable that could have caused poor coating conditions • Improved communication with Customer • Use 3 d simulations to identify and share opportunities for equipment improvement • Deliver results faster through in-house resources • Research in Coating Field has made clear agreement on viability of coating design through Multiphysics Simulations p. 29 © 2018 Carestream

Additional Modeling Capabilities from CFD • Ability to Visualize the Coating Problem: • See Flow inside of the die • where recirculation's are forming • where are particles settling or agglomerating • where stagnation may result in unwanted changes in coating fluid over time • Parametric Studies: to determine how variables impact overall performance • Parametric studies to evaluate: • Perturbations in delivery rate • Perturbations in fluid homogeneity • Errors in die construction, pressure driven deformation, warping (temperature gradients) © 2018 Carestream

Evaluating Value to Business Cons Pros Integration Speed Initial Delay Short Term $ ©

Additional Modeling Capabilities from CFD • Ability to Visualize the Coating Problem: • See Flow inside of the die • where recirculation's are forming • where are particles settling or agglomerating • Parametric Studies: to determine how variables impact overall performance • Parametric studies to evaluate: • Perturbations in delivery rate • Perturbations in fluid homogeneity • Errors in die construction p. 32 © 2018 Carestream

Using Simulation to break down the problem Whether or not the ability to simulate just the cavity is critical, the flexibility is what is important to understand. example: • If you wanted to test a • new shim or new inlet • Determine if the flow is caused by: • Bad inlet geometry triggering turbulence that causes shear thinning • Rough interface between slot and cavity • Optimize Individual sections then determine the impact on the overall geometry https: //www. ossila. com/pages/slot-die-coating-theory © 2018 Carestream Ex: simplify and isolate sections of the geometry for analysis

Applications for Shape Optimization Case: Vw Audi Group • These same modeling methods can

Bad simulations happen, so make sure to learn from them! When modeling for products we must understand physics in the real system and how it is being transformed and modified through the model mathematically. Then understand how that is being executed through code. This enables the engineer ensure that the correct solution can be scaled to fit the business needs. …results are unclear fall back on the math, and re-trace the code © 2018 Carestream

Case Study Comparison of different non-newtonain polymeric solutions and their performance in an end

Comparison of Two Non Newtonian Solutions © 2018 Carestream

Testing a Series of Different Boundary Conditions © 2018 Carestream

Insight into developing better geometries If our customers have a solution that cannot be modified the Modeling software can be re -developed to design a new die which does generate a distribution that is acceptable. Maybe Modify an Inlet? © 2018 Carestream

Case Study 2 Delivering Best Knowledge to Product Development -> as Fast as possible!

Use your Software Skills to speed up your work and others. Develop The development cycles can be automated by writing programs that generate multiple case simulations, varying geometries and flow conditions The test cycles can also be automated to generate clear flags for simulations that are well outside of acceptable Automate Test Validation process can be automated by writing programs which generate reports and analyze those against structured data. Deploy Good Developer look for all opportunities. We all know automation of our work is coming. It is better to be on the side performing the automation and save ourselves some stress. © 2018 Carestream Automate

scale up to iteratively run hundreds of cases © 2018 Carestream

Reapplying Programming knowledge from writing CFD code, to Programming Intelligent Software © 2018 Carestream

Summary • There is enough information to fill multiple lifetimes • Must strive to balance three fields equally • Do not underestimate the Fields most Coating Engineers are unfamiliar with (Software Eng) Special thanks to Carestream to Funding the development of this research • And thanks to my family for supporting me while I write code with my headphones on in a large portion of my free time © 2018 Carestream Visit us at our booth to learn more about how Carestream can accelerate coating product development through Contract Manufacturing and Growth Development