October 8, 015 COMSOL Conference 015 Boston Session: Optimiation and Simlation Methods Session Chair: Jeffre Fong, National Institte of Standards & echnolog Application of COMSOL Mltiphsics Software in ransport Phenomena Edcational Processes 1:00 PM :30 PM Mikhail Vasilev Pranav Sharma Patrick L. Mills* Department of Chemical and Natral Gas Engineering eas A & M Universit-Kingsville Kingsville-X 78363-80 USA *Patrick.Mills@tamk.ed Micro Heat Echanger (MHE) Application Anradha Nagaraj Department of Environmental Engineering
ransport Phenomena: Connecting heor to Practical Problems Graet-Nsselt Problem R Not constant bondar conditions? Fl specified onl for some region of the pipe? Imperfect thermal inslation? Electricall Heated Pipe Nonisothermal Flow Over a Clinder, c Comple arrangement of mltiple pipes? Viscos flow? Higher Renolds nmber? Sbsea Pipeline
Eamples of pical ransport Phenomena Corse Problems Momentm transport 1-D flid flow throgh a circlar pipe Energ transport Linear heat condction throgh a solid wall Mass transport Fickian diffsion in isothermal spherical catalst particle followed b a 1 st order reaction. (rr) = mmmmmm 1 rr RR = 1 LL 1 sinh(φφφφ) Ψ(λλ) = 1, λλ sinh(φφ) where Ψ = CC AA and λλ = rr CC AAAA RR CC AAAA L () 1 R Pros: Not ver complicated Straightforward to nderstand Eistence of analtical soltions Provides initial insight into more comple problems Cons: Lack of model response visaliation Limited applicabilit to real-world problems ransient soltions for 1-D problems are not simple to compte, e.g., infinite series of comple Eigenfnctions and Eigenvales
Motivation for Creating COMSOL Applications Desired Problem Attribtes Reinforce 1-D problems b etension to mltidimensions (-D or 3-D) and mlti-phsics. Contains varios phsico-chemical parameters that can be varied b the ser. Soltion can be generated within seconds to mintes with modern compting hardware. Abilit to readil modif the application to accont for problem variations and other derived qantities. Applications Developed Non-isothermal Flow Over a Clinder Graet-Nsselt Problem Flow hrogh a Dct Micro Heat Echanger Rotating Cone Pmp Cataltic Wall Microreactor -Micromier
Eample 1: Nonisothermal Flow Over a Heated Clinder Problem Statement,m COMSOL Geometr, c Model Eqations Eqation of Continit ρρ = 0 Navier-Stokes Eqations ρρ = ppii μμ FF Model Parameters,m Energ ransport Eqations ρρcc pp qq = QQ QQ vvvv qq = kk
Velocit, emperatre and Pressre Profiles at Varios Renolds Nmbers Gr = 10 8 Velocit Profiles (Re) emperatre Profiles (K) Pressre Profiles (Pa) Re =.5 Re = 5 Re = 50
COMSOL Application: Non-isothermal Flow over a Heated Clinder
Eample : Graet-Nsselt Problem (Constant Wall emperatre) Problem Statement,m COMSOL Geometr Model Eqations Eqation of Continit = 0 Navier-Stokes Eqations ρρ = ppii μμ Energ ransport Eqations ρρcc pp qq = QQ QQ vvvv qq = kk FF r,m
Velocit and emperatre Profiles Dimensionless Velocit for Varios Aial Positions 3-D Representation of Velocit Profiles Dimensionless emperatre for Varios Aial Positions 3-D Representation of emperatre Profiles V in =10-3 m/s V in =10-6 m/s ψψ(rr, ) = VV(rr, ) VV iiii θθ rr, = rr, iiii ww iiii
COMSOL Application: Graet-Nsselt Problem
Eample 3: Micro Heat Echanger Objectives: - Compare the heat echanger effectiveness factor b changing the flid flow. - Predict temperatre profiles b solving the copled momentm-energ transport eqations for a 3-D geometr. Model Geometr: 5 rectanglar dcts Cross-flow orientation Dimensions: Length of each slab 800 μm Width of each slab 800 μm Height of each slab 60 μm No. of Microchannels 5 Microchannel width 100 μm Microchannel height 30 μm Mat'l of Constrction Copper
Model Eqations: Momentm ransport Eqations - direction: -direction: -direction: Condction-Convection Eqation: Parameter Estimation: Effectiveness factor ρ is the flid densit, η is the flid viscosit, p is the flid pressre, K is flid condctivit, is temperatre, m mass flow rate, and Cp is the Specific heat capacit 0 = p t ρ µ ρ 0 = p t ρ µ ρ 0 = p t ρ µ ρ Q k k k t C p = ρ ) ( ) ( ) ( ) ( ma in cold in hot ot hot in hot in cold in hot p ot hot in hot p C m C m q q = = = ε Micro Heat Echanger Model Eqations & Effectiveness Factor
Micro Heat Echanger Velocit & emperatre Profiles Velocit Profile Slice Plot emperatre Profile Isosrface Plot Effectiveness Factor vs Flid Velocit
COMSOL Application: Micro Heat Echanger
COMSOL Application: Cataltic Wall Microreactor abs Inpt Model Description Reslts Panel Pressre Concentration of Reactant Concentration of Prodct
COMSOL Application: Rotating Cone Pmp
Conclsions COMSOL Mltiphsics : Provides robst representation of different mltiphsics problems that can be sed as a tool for teaching transport phenomena principles. Can be sed as an intermediate learning instrment between niversit edcation and real-world applications. Allows different cases of the same problem to be combined into a single application for parametric stdies. Allows more realistic simlation of real world problems for improved insight. he stdent can observe the effect of inpt parameters on an otpt variable.
hank o for or attention.