Simulations Involving Multiple Physics using Comsol Multiphysics Bruce A. Finlayson Professor Emeritus of Chemical Engineering University of Washington A&C Plenary Session, 2008 Structures Congress Vancouver, BC, April 24, 2008
The World is Flat: A Brief History of the Twenty-first CenturyThomas Friedman, NY Times • After the fall of the Berlin Wall, and the economic development in Southeast Asia, there are potentially 3 billion more knowledge workers. • The cost to transfer information is extremely low. • New requirements: creativity and innovation. • Having a good tool for multiphysics simulations is one way to allow creativity and innovation.
Pressure drop in orificeElissa Jacobsen and Febe Kusmanto Orifice diameters as small as 8 microns
Continuum mechanics can in fact explain data in devices as small as 8 microns. Dagan, et al., J. Fluid Mechanics, 1982, solved the Stokes problem analytically (straight lines). Our finite element simulations for Reynolds number = 0 agree with their solutions. The rest of the curve is numerical, solved for a range of parameters using the parametric solver with Re = 10^x, x=0:0.1:3.
Additional insights using Comsol Multiphysics • Does the temperature rise enough to cause the viscosity to change? • Solve the energy equation, too, with the viscous dissipation included using Comsol Multiphysics’ ability to put in equations. • Found the temperature rise was less than one degree for an adiabatic channel. • Work done with Yuli Tan
Mixing in the Dow reactor, Zach Tyree Entrance of Liquid A Entrance of Liquid B Exit Need geometry and flow rates, viscosity, but density is not very important at low Re. Relatively easy at low Reynolds numbers.
Good mixing won’t occur in laminar flow. Need to solve for flow and four concentration fields. The concentration distribution at the exit is very different from the velocity distribution and is quite irregular. Product concentration Axial velocity
Serpentine mixer is used to create good mixing in laminar flow in a short distance. Work with Chris Niels and Prof. Albert Folch
Serpentine mixer, Zach Tyree Used Comsol Multiphysics’ ability to solve the convective diffusion equation after the Navier-Stokes equation is solved, and on a different mesh, needed for Peclet number = 2200, 280,000 dof
Transient Thermal DiffusionThermal Field Flow Fractionation (TFFF), Nick Cox The temperature reaches a steady, linear profile in 0.0685 seconds. Solved in Comsol Multiphysics using the finite element method with 482 degrees of freedom. A key step is using boundary conditions on each side for zero total flux. Such boundary conditions are not sufficient to fully specify the problem. Thus, it is also necessary to add a condition that the average concentration (or mole fraction) remains constant. This is done in Comsol Multiphysics using Integration Coupling Variables. Otherwise the calculation will eventually become unstable.
Solutions for from zero to 10 seconds from zero to 100 seconds
Solutions for Final profile does not achieve as good separation; it takes 600 seconds to reach steady state instead of 100 seconds.
Mixing of polymer solution to make sludge flocculate A polymer solution is added to digested sludge in order to cause it to flocculate. The sludge is then sent to a centrifuge to separate the water from the sludge, which is used for fertilizer. This project began as a study of the incomplete mixing of the polymer. The goal of the Renton Wastewater Treatment Plant is to reduce the cost of the polymer by achieving good mixing with less polymer. Problem posed by Sharpe Mixers and the Renton Wastewater Treatment Plant: Is it in laminar flow?
Mixing with power law fluid I was willing to settle for a Newtonian solution; students wanted a full power-law model and succeeded.
Mixing in a Pharmaceutical Device(suggested by Dr. Mark Petrich, Rosetta Inpharmatics, Inc. work done by Nick Cox)
Electrochemical Printer -Nernst-Planck equation, Paul Roeter(diffusion with boundary change)
Surface binding of antigen Jennifer Foley/ Prof. Paul Yager • Solve N-S Velocity profile ~10,000 elements 2) Solve C-D/Surface Rxn ~13,000 elements Antibody binding region
Surface Equations Weak Boundary Mode Theta (# of available binding sites/area) C – bulk antigen concentration Cs – surface bound antigen concentration
Viscoelastic Polymer Flow Comsol Multiphysics can be used to solve the Navier-Stokes equations for a Newtonian fluid, and even a purely viscous non-Newtonian fluid when the viscosity depends upon shear rate (e.g. power law), but what about polymers? They exhibit elastic features as well.
Flows with Normal Stress Effects Elongational flow: Extrudate swell:
Equations Newtonian Fluid: Maxwell Model (h, l constant), White-Metzner Model (h, l vary with shear rate) : Phan-Thien-Tanner Model:
Differential-Elastic-Viscous-Split-Stress (DEVSS) Weighting funtions variables Ref: Guenette, R. and M. Fortin, J. Non-Newtonian Fluid Mech.60 27 (1995) R. G. Owens and T. N. Phillips, Computational Rheology, Imperial College Press (2002)
Comparison to Experiment Ref: D. G. Baird, J. Appl. Poly. Sci.20 3155 (1976) N. R. Jackson and B. A. Finlayson, J. Non-Newt. Fluid Mech.10 71 (1982)
Ferrofluid Applications • A ferrofluid is a stable colloidal suspension. • Composed of three main components • Solid magnetic particles (typical sizes are 5-10 nm) • Surfactant stabilizer (makes total sizes 25-30 nm) • Carrier fluid • Super-paramagnetic & non-electrically-conducting • Retains ability to flow in strong magnetic fields • Applications • Hermetic seals (computer hard drives, crystal growing apparatus) • Increased heat transfer in electrical devices (stereo speakers, electrical transformers) • Magnetic drug delivery
Insertion into Comsol - Rotating Magnetic Field Equations due to Rosensweig (1985) Use Navier-Stokes Equation with added terms and set LHS = 0. Spin equation: use diffusion equation (s) with added terms Magnetization: use convective diffusion equations with added terms but no diffusion Maxwell’s Equations for non-conducting fluid: use PDE General
Flow reversal at large H (relative H = 32) Spin viscosity 10x higher Relative spin viscosity = 1
Spin-up in 3D - at different heights when top surface is free but flat h = 0.1 h = 0.3 h = 0.59 Spin maximum = 0.214 in all cases Peak vorticity = .0012 .0034 .0047
Introduction to Chemical Engineering Computing • Philosophy - students can be good chemical engineers without understanding the details of the numerical analysis. • By using modern programs with good GUIs, the most important thing is to check your results. • Instead of teaching a small fraction of the class numerical methods, I now teach all the class to use the computer wisely.
Programs • Microsoft Excel ® • MATLAB® • Aspen Plus ® • FEMLAB ® Available, Dec., 2005
Chemical reactor models with radial dispersion, axial dispersion • Catalytic reaction and diffusion • One-dimensional transport problems in fluid mechanics, heat and mass transfer • Newtonian and non-Newtonian • Pipe flow, steady and start-up • adsorbtion • Two- and three-dimensional transport problems in fluid mechanics, heat and mass transfer • Entry flow • Laminar and turbulent • Microfludics, high Peclet number • Temperature effects (viscous dissipation) • Proper boundary conditions
Fluid-Solid Interactions(from Comsol 2007 CD) Object reenters the atmosphere at 3000 km/h. Does it deform or is it destroyed? Numerical Behavior of Different COMSOL Solution Methods for a Heat Transfer Problem Coupled with a Structural Mechanics Problem W. Joppich1, N. Kopp2 and D. Samokhvalov1 1University of Applied Sciences Bonn-Rhein-Sieg, Sankt Augustin, Germany 2Technisch Mathematische Studiengesellschaft GmbH, Bonn, Germany
Thermal-mechanical Analysis of Concrete Structure Exposed to High Temperature (in a fire)P. Kucera Faculty of Safety Engineering, VSB-Technical University of Ostrava, Ostrava-Vyskovice, Czech Republic
Multiphysics Approach to Model Solidification during EnamellingF. Van den Abeele and P. GoesArcelorMittal Research and Development, Ghent, Belgium
Coupled Heat and Water Flow in Variably-saturated Porous MediaT. Kamai and J. W. Hopmans Department of Land, Air and Water Resources, University of California, Davis, CA, USA Simultaneous measurement of coupled water and heat transport in variably saturated porous media is achieved with the heat pulse probe (HPP). The heat needle of the HPP generates a heat pulse, whereas at various strategically placed locations the temperature responses are measured at known distances from the heating element.
Fluid Structure Interactionwww.comsol.com/showroom/animations http://www.comsol.com/showroom/gallery/361.php
Contact Analysis of a Snap Hook Fastenerwww.comsol.com/showroom/animations http://www.comsol.com/showroom/gallery/366.php
Plastic Deformation During the Expansion of a Stent www.comsol.com/showroom/animations http://www.comsol.com/showroom/gallery/2197.php
Conclusions • The multiphysics capability of Comsol Multiphysics is very powerful. • Many times the students learn by induction - try something and explore, or see an anomaly and explore. • Comsol Multiphysics draws interest because • Color • Simulations are for real situations • If you think a phenomena is important, include it and see. • It provides and promotes: Motivation - Responsibility - Innovation - Creativity.