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Computational Fluid Dynamics - Fall 2013
• The syllabus
• CFD references (Text books and papers)
• Course Tools
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Course Web Site: http://twister.ou.edu/CFD2013
http://ozone.ou.edu
Computing Facilities available to the class (account info will be
provided)
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OSCER (http://oscer.ou.edu) Boomer Linux Supercomputer
Unix and Fortran Helps – Consult Links at CFD Home page
CFD – An Introduction
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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.
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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.
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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.
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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.
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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.
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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.
Introduction – Principle of Fluid Motion
1. Mass Conservation
1.
2.
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3.
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5.
Conservation of air/water/fluid mass
Conservation for other material quantities (e.g., CO2, water vapor in
atmosphere, chemicals, pollutants, etc.)
Newton’s Second of Law (equations of motion)
Energy Conservation (e.g., heat energy, temperature equation)
Equation of State for Idealized Gas
Other equations
These laws are expressed in terms of mathematical equations,
usually as partial differential equations.
Most important equations – the Navier-Stokes equations
 V


 V V   p    T  F
 t

(T is the stress tenor and F the body force)
Approaches for Understanding Fluid Motion
• Traditional Approaches
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Theoretical – find analytical solutions to the governing
equations (often in simplified forms)
Experimental – collect data from laboratory or field
experiments
• Newer Approach
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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
Experimental FD
• Understanding fluid behavior using laboratory models and
experiments. Important for validating theoretical solutions.
• E.g., Water tanks, wind tunnels
Theoretical FD
• Science for finding usually analytical solutions of governing
equations in different categories and studying the associated
approximations / assumptions;
h = d/2,
c1  2gh / 0
Computational FD
• A science of finding numerical solutions of governing
equations, using high-speed digital computers
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.)
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.
An Example Case for CFD – Thunderstorm
Outflow/Density Current Simulation
Thunderstorm Outflow in the Form of Density
Currents
Positive Internal Shear
g=1
Negative Internal Shear
g=-1
T=12
Positive Internal Shear
g=1
Negative Internal Shear
g=-1
No Significant
Circulation Induced by
Cold Pool
Xue (2010 QJ) http://twister.ou.edu/papers/XueQJ2002.pdf
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)
CONUS-Scale Realtime Forecast at 1 km grid spacing
from spring 2009
(WRF with ARPS Radar DA)
Radar Observed Reflectivity
Model Predicted Reflectivity
May 8, 2009 MCV/Derecho Case – 30 hour forecast
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.
Difficulties with CFD
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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.
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Errors and uncertainties with the numerical models can be significant because of
inevitable approximations.
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We often have to parameterize processes which are not well understood (e.g., rain
formation, chemical reactions, turbulence).
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We often have to impose nonphysical boundary conditions.
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Often a numerical experiment raises more questions than providing answers!!
Positive Outlook
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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.