Presentation on theme: "Chapter 15: Computational Fluid Dynamics"— Presentation transcript:
1 Chapter 15: Computational Fluid Dynamics Eric G. PatersonDepartment of Mechanical and Nuclear EngineeringThe Pennsylvania State UniversitySpring 2005
2 IntroductionPractice of engineering and science has been dramatically altered by the development ofScientific computingMathematics of numerical analysisThe InternetComputational Fluid Dynamics is based upon the logic of applied mathematicsprovides tools to unlock previously unsolved problemsis used in nearly all fields of science and engineeringAerodynamics, acoustics, bio-systems, cosmology, geology, heat transfer, hydrodynamics, river hydraulics, etc…
3 IntroductionWe are in the midst of a new Scientific Revolution as significant as that of the 16th and 17th centuries when Galilean methods of systematic experiments and observation supplanted the logic-based methods of Aristotelian physicsModern tools, i.e., computational mechanics, are enabling scientists and engineers to return to logic-based methods for discovery and invention, research and development, and analysis and design
4 Introduction Scientific method Aristotle ( BCE)Greek philosopher, student of PlatoLogic and reasoning was the chief instrument of scientific investigation; Posterior AnalyticsTo possess scientific knowledge, we need to know the cause of which we observeThrough their senses humans encounter facts or dataThrough inductive means, principles created which will explain the dataThen, from the principles, work back down to the factsExample: Demonstration of the fact (Demonstratio quia)The planets do not twinkleWhat does not twinkle is near the earthTherefore the planets are near the earthKnowledge of Aristotle’s work lost to Europe during Dark Ages. Preserved by Mesopotamian (modern day Iraq) libraries.
5 Introduction Scientific method Galileo Galilei ( )Formulated the basic law of falling bodies, which he verified by careful measurements.He constructed a telescope with which he studied lunar craters, and discovered four moons revolving around Jupiter.Observation-based experimental methods: required instruments & tools ; e.g., telescope, clocks.Scientific Revolution took place in the sixteenth and seventeenth centuries, its first victories involved the overthrow of Aristotelian physicsConvicted of heresy by Catholic Church for belief that the Earth rotates round the sun. In 1992, 350 years after Galileo's death, Pope John Paul II admitted that errors had been made by the theological advisors in the case of Galileo.
6 Introduction Mathematics Isaac Newton (1643 – 1727)Laid the foundation (along with Leibniz) for differential and integral calculusIt has been claimed that the Principia is the greatest work in the history of the physical sciences.Book I: general dynamics from a mathematical standpointBook II: treatise on fluid mechanicsBook III: devoted to astronomical and physical problems. Newton addressed and resolved a number of issues including the motions of comets and the influence of gravitation.For the first time, he demonstrated that the same laws of motion and gravitation ruled everywhere under a single mathematical law.
7 Introduction Fluid Mechanics Faces of Fluid Mechanics : some of the greatest minds of history have tried to solve the mysteries of fluid mechanicsArchimedesDa VinciNewtonLeibnizEulerBernoulliNavierStokesReynoldsPrandtl
8 Introduction Fluid Mechanics From mid-1800’s to 1960’s, research in fluid mechanics focused uponAnalytical methods (Primary focus of ME33)Exact solution to Navier-Stokes equations (~80 known for simple problems, e.g., laminar pipe flow)Approximate methods, e.g., Ideal flow, Boundary layer theoryExperimental methodsScale models: wind tunnels, water tunnels, towing-tanks, flumes,...Measurement techniques: pitot probes; hot-wire probes; anemometers; laser-doppler velocimetry; particle-image velocimetryMost man-made systems (e.g., airplane) engineered using build-and-test iteration.1950’s – present : rise of computational fluid dynamics (CFD)
9 Introduction History of computing Mastodons of computing,Early computer engineers thought that only a few dozen computers required worldwideApplications: cryptography (code breaking), fluid dynamics, artillery firing tables, atomic weaponsENIAC, or Electronic Numerical Integrator Analyzor and Computer, was developed by the Ballistics Research Laboratory in Maryland and was built at the University of Pennsylvania's Moore School of Electrical Engineering and completed in November 1945
10 Introduction High-performance computing Top 500 computers in the world compiled:Computers located at major centers connected to researchers via Internet
11 OutlineCFD ProcessModel EquationsDiscretizationGrid GenerationBoundary ConditionsSolvePost-ProcessingUncertainty AssessmentExamples (note to instructors: this section has been removed. When I taught ME33 at PSU, I showed examples of my personal research)ConclusionsFLOWLAB
12 Model EquationsMost commercial CFD codes solve the continuity, Navier-Stokes, and energy equationsCoupled, non-linear, partial differential equationsFor example, incompressible form
13 Discretization Grid Generation Flow field must be treated as a discrete set of points (or volumes) where the governing equations are solved.Many types of grid generation: type is usually related to capability of flow solver.Structured gridsUnstructured gridsHybrid grids: some portions of flow field are structured (viscous regions) and others are unstructuredOverset (Chimera) grids
16 Unstructured Grids Structured-Unstructured Nozzle Grid Branches in Human Lung
17 Discretization Algebraic equations To solve NSE, we must convert governing PDE’s to algebraic equationsFinite difference methods (FDM)Each term in NSE approximated using Taylor series, e.g.,Finite volume methods (FVM)Use CV form of NSE equations on each grid cell ! ME 33 students already know the fundamentals !Most popular approach, especially for commercial codesFinite element methods (FEM)Solve PDE’s by replacing continuous functions by piecewise approximations defined on polygons, which are referred to as elements. Similar to FDM.
18 Boundary Conditions Typical conditions WallNo-slip (u = v = w = 0)Slip (tangential stress = 0, normal velocity = 0)With specified suction or blowingWith specified temperature or heat fluxInflowOutflowInterface Condition, e.g., Air-water free surfaceSymmetry and PeriodicityUsually set through the use of a graphical user interface (GUI) – click & set
19 Solve Run CFD code on computer Monitor Residuals 2D and small 3D simulations can be run on desktop computers (e.g., FlowLab)Unsteady 3D simulations still require large parallel computersMonitor ResidualsDefined two waysChange in flow variables between iterationsError in discrete algebraic equation
20 Uncertainty Assessment Process of estimating errors due to numerics and modelingNumerical errorsIterative non-convergence: monitor residualsSpatial errors: grid studies and Richardson extrapolationTemporal errors: time-step studies and Richardson extrapolationModeling errors (Turbulence modeling, multi-phase physics, closure of viscous stress tensor for non-Newtonian fluids)Only way to assess is through comparison with benchmark data which includes EFD uncertainty assessment.
21 Conclusions Capabilities of Current Technology Complex real-world problems solved using Scientific ComputingCommercial software available for certain problemsSimulation-based design (i.e., logic-based) is being realized.Ability to study problems that are either expensive, too small, too large, or too dangerous to study in laboratoryVery small : nano- and micro-fluidicsVery large : cosmology (study of the origin, current state, and future of our Universe)Expensive : engineering prototypes (ships, aircraft)Dangerous : explosions, response to weapons of mass destruction
22 Conclusions Limitations of Current Technology For fluid mechanics, many problems not adequately described by Navier-Stokes equations or are beyond current generation computers.TurbulenceMulti-phase physics: solid-gas (pollution, soot), liquid-gas (bubbles, cavitation); solid-liquid (sediment transport)Combustion and chemical reactionsNon-Newtonian fluids (blood; polymers)Similar modeling challenges in other branches of engineering and the sciences
23 ConclusionsBecause of limitations, need for experimental research is greatHowever, focus has changedFromResearch based solely upon experimental observationsBuild and test (although this is still done)ToHigh-fidelity measurements in support of validation and building new computational models.Currently, the best approach to solving engineering problems often uses simulation and experimentation
24 FlowLab FlowLab (http://www.flowlab.fluent.com/) Educational software that uses the power of flow visualization through CFD to teach basic fluid mechanics principles in the engineering classroom.Runs Fluent's general purpose CFD code, FLUENT, and pre-processor, GAMBIT, in the background, with a user-friendly, student-specific graphical user interface (GUI) on its front end.Based on ready-to-use exercises, FlowLab eliminates the long learning curve associated with general fluid flow modeling packages, making it easy to deploy as part of the undergraduate or masters-level curriculum.Templates for Problems – in Cengel and Cimbala.
25 FlowLab Templates are Nearly self-guided Designed to teach specific lessonsEffect of grid resolutionEffect of domain sizeFlow physics and sensitivity to parameters, e.g., diffuser angle, airfoil angle of attack, etc.GUI for post-processing is easy to learnContoursStreamlinesVector Plots
26 FlowLabStep 1: Select template from startup menu (Example: Creep Domain template)
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