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Computational Fluid Dynamics - Fall 2013 The syllabus CFD references (Text books and papers) Course Tools Course Web Site: Computing Facilities available to the class (account info will be provided) OSCER (http://oscer.ou.edu) Boomer Linux Supercomputer Unix and Fortran Helps – Consult Links at CFD Home page

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CFD – An Introduction The physical aspects of any fluid flow are governed by three fundamental principles: Conservation of mass and energy, and Newton's second law of motion (F = m a). These fundamental principles can be expressed in terms of mathematical equations, usually as partial differential equations. Computational Fluid Dynamics (CFD) is the science of determining a numerical solution to the governing equations of fluid flow whilst advancing the solution through space or time to obtain a numerical description of the complete flow field of interest. Theoretical Fluid Dynamics. The governing equations for Newtonian fluid dynamics, the unsteady Navier-Stokes equations, have been known for over a century. However, the analytical investigation of reduced forms of these equations is still an active area of research. Experimental Fluid Dynamics has played an important role in validating and delineating the limits of the various approximations to the governing equations. The wind tunnel, for example, provides an effective means of simulating real flows. Traditionally this has provided a cost effective alternative to full scale measurement. However, in the design of equipment that depends critically on the flow behavior, for example the aerodynamic design of an aircraft, full scale measurement as part of the design process is economically impractical. This situation has led to an increasing interest in the development of a numerical wind tunnel. The steady improvement in the speed of computers and the available memory size since the 1950s has led to the emergence of computational fluid dynamics. This branch of fluid dynamics complements experimental and theoretical fluid dynamics by providing an alternative cost effective means of simulating real flows. As such it offers the means of testing theoretical advances for conditions unavailable on an experimental basis. The development of more powerful computers has furthered the advances being made in the field of computational fluid dynamics. Consequently CFD is now the preferred means of testing alternative designs in many engineering companies before final, if any, experimental testing takes place.

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Introduction – Principle of Fluid Motion 1.Mass Conservation 1.Conservation of air/water/fluid mass 2.Conservation for other material quantities (e.g., CO 2, water vapor in atmosphere, chemicals, pollutants, etc.) 2.Newton’s Second of Law (equations of motion) 3.Energy Conservation (e.g., heat energy, temperature equation) 4.Equation of State for Idealized Gas 5.Other equations These laws are expressed in terms of mathematical equations, usually as partial differential equations. Most important equations – the Navier-Stokes equations (T is the stress tenor and F the body force)

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Approaches for Understanding Fluid Motion Traditional Approaches Theoretical – find analytical solutions to the governing equations (often in simplified forms) Experimental – collect data from laboratory or field experiments Newer Approach Computational - CFD emerged as the primary tool for engineering design (e.g., automobile, aircraft, spacecraft), environmental modeling, weather prediction, oil reservoir simulation and prediction, nuclear weapon testing, among many others, thanks to the advent of digital computers

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Experimental FD Understanding fluid behavior using laboratory models and experiments. Important for validating theoretical solutions. E.g., Water tanks, wind tunnels

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Theoretical FD Science for finding usually analytical solutions of governing equations in different categories and studying the associated approximations / assumptions; h = d/2,

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Computational FD A science of finding numerical solutions of governing equations, using high-speed digital computers

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Why Computational Fluid Dynamics? Analytical solutions exist only for a handful of typically simple problems Much more flexible – easy change of configurations, parameters Can control numerical experiments and perform sensitivity studies, for both simple and complex systems or problems Can study something that is not directly observable (e.g., black holes of the universe or the future climate) because of the spatial and/or temporal scale/range of the problem. Computer solutions provide a more complete sets of data in time and space than observations of both real and laboratory phenomena (e.g., so far it’s not possible to directly observe 3D temperature and pressure inside tornadoes at high resolutions. Even harder inside nuclear bomb explosion.)

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Why Computational Fluid Dynamics? - Continued We can perform realistic experiments on phenomena that are not possible to reproduce in reality, e.g., the weather and climate Much cheaper than laboratory experiments (e.g., crash test of vehicles, experimental launches of spacecrafts) May be much more environment friendly (testing of nuclear arsenals) We can now use computers to DISCOVER new things (drugs, sub ‑ atomic particles, storm dynamics) much more quickly Computer models can predict, e.g., weather.

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An Example Case for CFD – Thunderstorm Outflow/Density Current Simulation

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Thunderstorm Outflow in the Form of Density Currents

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=1 =-1 Negative Internal Shear Positive Internal Shear

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=1 =-1 Negative Internal Shear Positive Internal Shear T=12 No Significant Circulation Induced by Cold Pool Xue (2010 QJ)

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Observation v.s. forecast of convection storms at 2 km grid spacing (June 6, 2008 case from CAPS realtime forecast) Radar observation of precipitation (reflectivity) at forecast initial time (initial condition)

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CONUS-Scale Realtime Forecast at 1 km grid spacing from spring 2009 (WRF with ARPS Radar DA) May 8, 2009 MCV/Derecho Case – 30 hour forecast Radar Observed Reflectivity Model Predicted Reflectivity

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Difficulties with CFD Typical equations of CFD are partial differential equations (PDEs) that requires high spatial and temporary resolutions to represent the originally continuous systems such as the ocean and atmosphere Most physically important problems are highly nonlinear ‑ true solution to the problem is often unknown therefore the correctness of the solution hard to ascertain – need careful validation (against theoretical understanding and limited measurement data)! It is often impossible to represent all relevant scales in a given problem – unresolved scales have to be ‘parameterized’ using ‘closure schemes’. There is often strong coupling between scales of flow for the atmospheric and most CFD problems. ENERGY TRANSFERS among scales.

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Difficulties with CFD The initial conditions of given problems often contain significant uncertainty – such as that of the atmosphere – because they can’t be measured with 100% accuracy. Errors and uncertainties with the numerical models can be significant because of inevitable approximations. We often have to parameterize processes which are not well understood (e.g., rain formation, chemical reactions, turbulence). We often have to impose nonphysical boundary conditions. Often a numerical experiment raises more questions than providing answers!!

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Positive Outlook More accurate numerical schemes / algorithms Bigger and faster computers (Petascale Computing Systems) Faster networks Better desktop computers Better programming tools and environment Better visualization tools Better understanding of dynamics / predictabilities etc.

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