Computational Fluid Dynamics : Basics Of Modelling
Computational Fluid Dynamics :Basics of modellingP. BACCHINProfessor Université de ToulouseUniversité Paul SabatierLaboratoire de génie Chimique31 062 TOULOUSE Cedex 9Tel : 05 61 55 81 63 Fax : 05 61 55 61 39Email : bacchin@chimie.ups-tlse.frWeb : http://lgc.inp-toulouse.frPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
What is Computational Fluid Dynamics ? Fluid (gas and liquid) flows are governed by partial differentialequations (PDE) which represent conservation laws for the mass,momentum, and energy Du p 2u gDt Computational Fluid Dynamics (CFD) consist in replacing PDE systemsby a set of algebraic equations which can be solved using computers.Patrice Bacchin - Bioart 6th network meeting, February 04, 20162
Why CFD ? To predict properties (velocities, concentration, temperature, electricalfield ) in the 3D and with time To compute fluid flows (meteorogical phenomena, transport ofcontaminant, combustion) but also : Human body (blood flow, breathing ) Biomedical devicesAfter validation, CFD simulations can be considered as « Numerical experiments »Patrice Bacchin - Bioart 6th network meeting, February 04, 20162
How to do CFD ?Commercial codesCan handle complex geometries and multiphysics problemCan produce accurate solutionsOpen source codePython (programming language) SciPy (eq. To Matlab) FiPy (finite volume PDE solver)Available on thecanopy yFrom 80’s the code evolves to easy to use softwareBut should be used with care by users (with a good knowledge and expertise)Patrice Bacchin - Bioart 6th network meeting, February 04, 20162
How to do virtual experimentsof the real world with CFD ?EngineeringReal worldMathematicsPhysics – essingNumerical recipes(discretization techniques)Cf Efrem course1 Pre-processingModel providingacceptable level ofcomplexity ?2ProcessingWill be presentedhere as a recipe(consider a preparationtime of 1 day) !Patrice Bacchin - Bioart 6th network meeting, February 04, 20163Post-ProcessingAccurate representationof reality ?2
1 Pre-processingFormulate the modelReal worldConceptualmodelPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Expertise for the model statementObjectives : Conceptual model providing acceptable depicting of the targeted applicationNeed an engineering approach of the problem What are the objectives (variable to determine) ? What is the simplest (but not simpler) way to describe the problem ? What is (are) the limiting phenomena ? What physical phenomena have to be accounted ? Coupling of fluid mechanics, heat transfer, mass transfer ? Simplification of the flow - Poiseuille flow Geometry of the domain Possible simplification Simplification of the geometry 3D- 1D What would be the way to progress from the simplest simulation to the final one ?Patrice Bacchin - Bioart 6th network meeting, February 04, 20162
Prerequisite on transport phenomenaTransportEnergymechanicalMassthermalFlux transported per time unit and sectional areaMomentum fluxHeat fluxMass fluxkg.m.s-1m2.sQNJm2.smol ou kgm2.st?Shear stressForce perareaPatriceBacchin - Bioart 6th network meeting, February 04, 20162
Fluid mechanicsHeat transferMass transferTransport by potential gradientShear rateNewton lawt yx duxdyviscosityDiffusionTemperature gradientFourier lawConcentration gradientFick lawd Q dxN DThermal conductivityTransport by advectionu * quantity/m3 u uQ uC p refdcdxdiffusionAdvection N ucTransportparduegradientto externalforcingTransfertde potentielPressure, GravityRadiationElectrical field Transformation : source or sink termChemical, electricalHomogeneous reaction1 dnmechnicalenergy kcth networkPatrice Bacchin - Bioart 6ormeeting,February 04, 2016 r V dt2
Fluid mechanicHeat transfert f (x,y,z,t)Q f (x,y,z,t)u f (x,y,z,t)t f (x,y,z,t)Mass transferc f (x,y,z,t)N f (x,y,z,t)Conservation law :accumulation inlet- outlet - source termContinuity equation div( u ) 0 d C p div(Q) sdt dc div( N ) rdtJ .m 3.s 1mol.m 3.s 1Momentum balanceDevelopment in 1D in Cartesian coordinates Du p t gDtNxS p 2u gkg.m.s 1m3 .s(Navier-Stokes)Nx dxdVdxAccumulation Inlet - outlet - reactiondV dc S Nx.dt - S Nx dx dt r S dxdcdN rdtdxPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Coordinates ?CartesianCylindrical SphericalDimension ?123Steady state ?Transient ?Source term (chemical reaction) ?YesNoTransfer mode ?DiffusionAdvectionMixPartial differential equation for the concentrationmax order 1 for time and order 2 for spatial directionInitial condition ?t t0c ciBoundary conditions ?x x0c c0N N0dc/dx 0Patrice Bacchin - Bioart 6th network meeting, February 04, 2016Concentration profileAnd mass flux2
Exemple of dialysis modeling1D cartesian model of dialysisDiffusion in the dialysis membraneDiffusionand advectionIn the concentratesideDiffusionand advectionIn the dialysatesideShould Be Made as Simple as Possible, But Not SimplerPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Diffusive transport in the membraneDiffusive transportSteady stateciCartesian Conservation lawcoordinate ?dcdN rdtdxcartesianDirection ?12NoSteady state?3Steady state?ce01NoYesdiffusionDiffusive transportd 2cdcD 0N Ddzdz 2Transport mode ?diffusionadvectionB.C. 1x 0c ciC.L. 2x ec cezc ciz ce ci ec cDNS S (ci ce ) i eeeDSTransient?Source term ?eDiffusion transport resistancePatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Diffusive-Advection at interfacedN y dNdc x Rdtdy dxDiffusion and advection atinterfaceSimplified tool for engineers d 2c d 2c dcdu y dcdc du D u y c x u x Rdtdy dxdy dx2 dy2 dxCoordinates ?cartesian div( u ) 0Direction ?123Steady stateuSouree term ?NocHydrodyanmicboundary layerduYesTransport mode ?diffusifm/sk DdDMass Boundary layerdDyN k ci cb Concentration at interfaceUTransientMass transfer coefficient, kDimensionless correlationconvectifxBoundary layer : thickness of fluid where the gradient is localisedPatrice Bacchin - Bioart 6th network meeting, February 04, 2016dSh 1,86( Re.Sc. H )0,33L2Re 2100
1D dialysis conceptual modelingDN cci cdi eN kc cc cci N N kd cdi cd cc cd 1 e 1 kd D kcDiffusion of creatinine 910-10 m2/sBoundary layer in concentrate 30 mBoundary layer in dialysate 200 mMembrane thickness 50 mDiffusionand advectionIn the concentratesideDiffusionand advectionIn the dialysatesideCreatinine concentration (mg/L)1210N 85,2 mg/(m2 .h)86The simplest but not simpler model420050100150200250300350400micrometersPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
The start point before CFDThe establishment of the conceptual model is a key point : to know the physics to inject in simulations to understand the mechanisms (and then to interpret the simulation results)The simplest model can then be refined :Cf Dmytro workMore complex physics : partition coefficient, reactive layers (adsorption, biological )More realistic : other geometries, 2D, 3D (need CFD)Patrice Bacchin - Bioart 6th network meeting, February 04, 20162
How to do virtual experimentsof the real world?EngineeringReal worldPhysics – ntsPost-processingNumerical recipes(discretization techniques)Cf Efrem course1 Pre-processingModel providingacceptable level ofcomplexity ?2ProcessingWill be presentedhere as a recipe(consider a preparationtime of 1 day) !Patrice Bacchin - Bioart 6th network meeting, February 04, 20163Post-ProcessingAccurate representationof reality ?2
2ProcessingPerform simulationConceptualmodelComputermodelPatrice Bacchin - Bioart 6th network meeting, February 04, 2016Post-processing2
The way to do :from an example Follow a complicated recipes(integrating sequentialy the ingredients)X 30 Perform simulation Change the ingredients and theoperating conditions –Redo simulationsTime scale for a superficial learning is daysPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
The way to do :from scratch with a software Apply KISS principles : Keep It as Simple as poSsible, Keep it small and simple,Keep it sober and significant Define the simplest physics, the smallest geometryPerform simulationsAdd new ingredients (one by one)Check simulations (save your work with a new file name)Be fair with computational timeYOU WILL DO ERRORSBUT ON SIMPLE AND RAPIDSIMULATIONSTime scale for this learning is monthsPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
The way to do :from scratch with a home codeTime scale for a deep learningis years !Patrice Bacchin - Bioart 6th network meeting, February 04, 20162
From an example :dialysis simulation with COMSOL MultiphysicsComsol multiphysics 7995 for a single-user license 1700 for academicsbut a lot of module in optionOptions needed for biomedical app.- CFD module 1700- Reaction eng. module 800Patrice Bacchin - Bioart 6th network meeting, February 04, 20162
Ingredients for dialysis Domain Meshing Physics model Fluid properties Boundary conditions Calculations Post processingPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Ingredients for dialysis Domain Meshing Physics model Fluid properties Boundary conditions Calculations Post processingEnough meshes to be accurateNot too much to save computational timePatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Ingredients for dialysis Domain Meshing Physics model Fluid properties Boundary conditions Calculations Post processingPartition coefficient (equilibrium)Diffusion in the membraneDiffusion and advection- description of the mass boundary layersPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Ingredients for dialysis Domain Meshing Physics model Fluid properties Boundary conditions Calculations Post processingPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Ingredients for dialysis Domain Meshing Physics model Fluid properties Boundary conditions Calculations Post processingPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Ingredients for dialysis Domain Meshing Physics model Fluid properties Boundary conditions Calculations Post-processingPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
How to do virtual experimentsof the real world?EngineeringReal worldPhysics – ntsPost-processingNumerical recipes(discretization techniques)Cf Efrem course1 Pre-processingModel providingacceptable level ofcomplexity ?2ProcessingWill be presentedhere as a recipe(consider a preparationtime of 1 day) !Patrice Bacchin - Bioart 6th network meeting, February 04, 20163Post-ProcessingAccurate representationof reality ?2
3ValidationRepresentation of the real world ?Post-processingValidationPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
Validation Computing accuracy ? Change mesh to smaller size should not change the solution Use the code for simple cases (having analytical solutions) By changing the geometry By changing the field equations by changing initial/boundary conditions Accurate representation of real world ? Compare the simulation results with available data Realise sensitivity analysis (often based on dimensionless number) and parametric studiesPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
CFD reliabilityWaterflowLaminarTurbulentNo couplingMomentum, Heat and MasscouplingIncompressibleOpen FlowIdeal phaseCompressibleConfinedTransfer inblood ortissueNon-ideal (interactions )Single phaseInertMutiphasic with phase changesMultiple chemical reactionStrong reliabilityPatrice Bacchin - Bioart 6th network meeting, February 04, 2016Weak reliability2
CFD and biological applicationsTaylor, C. A., Draney, M. T., Ku, J. P., Parker, D., Steele, B. N., Wang, K., & Zarins, C.K. (1999). Predictive medicine: computational techniques in therapeutic decisionmaking. Computer aided surgery, 4(5), 231-247.Blood flowKharboutly, Z., Fenech, M., Treutenaere, J. M., Claude, I., & Legallais, C. (2007). Investigationsinto the relationship between hemodynamics and vascular alterations in an establishedarteriovenous fistula. Medical engineering & physics, 29(9), 999-1007.Curcio, E., Macchiarini, P., & De Bartolo, L. (2010). Oxygen mass transfer in a humantissue-engineered trachea. Biomaterials, 31(19), 5131-5136.Oxygen transferPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
CFD and biomedical applications Heart pumping and blood flows Air flow in lungs and gases exchanges Mechanical properties, lubrification- cardiac valve design- Oxygenator designProthesis design Transfer in tissue- Bioartificial organ designPatrice Bacchin - Bioart 6th network meeting, February 04, 20162
CFD :a computer assisted by a human !EngineeringReal worldPhysics – ComputermodelPost-processingNumerical recipes(discretization techniques)Cf Efrem courseProvide acceptablelevel of complexity ?EngineeringValidationAccurate representationof reality ?A lot of questions can not be answered by the computer until now !Formulate the modelWhat should be solved ?Assumptions, limiting phenomena ?Check the resultsSolution valid ?Define the problemPatriceboundaryBacchin - Bioartconditions6th network meeting,Geometry,? February 04, 2016Analyse the resultsAnswer to initial questions?2
What is Computational Fluid Dynamics ? Fluid (gas and liquid) flows are governed by partial differential equations (PDE) which represent conservation laws for the mass, momentum, and energy Computational Fluid Dynamics (CFD) consist in replacing PDE systems by a set of algebraic equations which can be solved using computers. p u g Dt Du
1.1 What is computational fluid dynamics? 1.2 Basic principles of CFD 1.3 Stages in a CFD simulation 1.4 Fluid-flow equations 1.5 The main discretisation methods Appendices Examples 1.1 What is Computational Fluid Dynamics? Computational fluid dynamics (CFD) is the use of computers and
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