# computational fluid dynamics

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Computational fluid dynamics (CFD) is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the millions of calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. Even with high-speed supercomputers only approximate solutions can be achieved in many cases. Ongoing research, however, may yield software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is often performed using a wind tunnel with the final validation coming in flight test.

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Computational Tools for Aircraft DesignITA Aircraft Design Department

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Contents

CFD What It is? Overview on Mesh Technology Turbulence Modeling

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Chapter 15: Computational Fluid Dynamics

CFD What It Is?

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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) is the art of replacing such PDE systems by a set of algebraic equations which can be solved using digital computers. The object under study is also represented computationally in an approximate discretized form.

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Introduction

Why use CFD?

Numerical simulations of fluid flow (will) enable architects to design comfortable and safe living environments designers of vehicles to improve the aerodynamic characteristics chemical engineers to maximize the yield from their equipment petroleum engineers to devise optimal oil recovery strategies surgeons to cure arterial diseases (computational hemodynamics) meteorologists to forecast the weather and warn of natural disasters safety experts to reduce health risks from radiation and other hazards military organizations to develop weapons and estimate the damage CFD practitioners to make big bucks by selling colorful pictures :-)ME33 : Fluid Flow 5 Chapter 15: Computational Fluid Dynamics

Introduction

What is?

Practice of engineering and science has been dramatically altered by the development ofScientific computing Mathematics of numerical analysis Tools like neural networks The Internet

Computational Fluid Dynamics is based upon the logic of applied mathematicsprovides tools to unlock previously unsolved problems is used in nearly all fields of science and engineeringAerodynamics, acoustics, bio-systems, cosmology, geology, heat transfer, hydrodynamics, river hydraulics, etc

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Chapter 15: Computational Fluid Dynamics

Introduction What It is?CFD is the simulation of fluids engineering systems using modeling (mathematical physical problem formulation) and numerical methods (discretization methods, solvers, numerical parameters, and grid generations, etc.) CFD made possible by the advent of digital computer and advancing with improvements of computer resources (500 flops, 194720 teraflops, 2003)

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Chapter 15: Computational Fluid Dynamics

Introduction Why Use CFD?Analysis and Design1. Simulation-based design instead of build & testMore cost effective and more rapid than EFD* CFD provides high-fidelity database for diagnosing flow field

2. Simulation of physical fluid phenomena that are difficult for experimentsFull scale simulations (e.g., ships and airplanes) Environmental effects (wind, weather, etc.) Hazards (e.g., explosions, radiation, pollution) Physics (e.g., planetary boundary layer, stellar evolution)

Knowledge and exploration of flow physics* Experimental Fluid DynamicsME33 : Fluid Flow 8 Chapter 15: Computational Fluid Dynamics

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 physics Modern 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 designME33 : Fluid Flow 9 Chapter 15: Computational Fluid Dynamics

IntroductionScientific methodAristotle (384-322 BCE)Greek philosopher, student of Plato Logic and reasoning was the chief instrument of scientific investigation; Posterior Analytics To possess scientific knowledge, we need to know the cause of which we observeThrough their senses humans encounter facts or data Through inductive means, principles created which will explain the data Then, from the principles, work back down to the factsExample: Demonstration of the fact (Demonstratio quia) The planets do not twinkle What does not twinkle is near the earth Therefore the planets are near the earth Knowledge of Aristotles work lost to Europe during Dark Ages. Preserved by Mesopotamian (modern day Iraq) libraries.ME33 : Fluid Flow 10 Chapter 15: Computational Fluid Dynamics

IntroductionScientific methodGalileo Galilei (1564-1642)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.

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Chapter 15: Computational Fluid Dynamics

IntroductionMathematics Isaac Newton (1643 1727)Laid the foundation (along with Leibniz) for differential and integral calculus It has been claimed that the Principia is the greatest work in the history of the physical sciences. Book I: general dynamics from a mathematical standpoint Book II: treatise on fluid mechanics Book 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.12 Chapter 15: Computational Fluid Dynamics

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IntroductionFluid MechanicsFaces of Fluid Mechanics : some of the greatest minds of history have tried to solve the mysteries of fluid mechanics

Archimedes

Da Vinci

Newton

Leibniz

Euler

BernoulliME33 : Fluid Flow

Navier13

Stokes

Reynolds

Prandtl

Chapter 15: Computational Fluid Dynamics

IntroductionFluid MechanicsFrom mid-1800s to 1960s, research in fluid mechanics focused uponAnalytical methodsExact solution to Navier-Stokes equations (~80 known for simple problems, e.g., laminar pipe flow) Approximate methods, e.g., Ideal flow, Boundary layer theory

Experimental methodsScale models: wind tunnels, water tunnels, towing-tanks, flumes,... Measurement techniques: pitot probes; hot-wire probes; anemometers; laser-doppler velocimetry; particle-image velocimetry Most man-made systems (e.g., airplane) engineered using buildand-test iteration.

1950s present : rise of computational fluid dynamics (CFD)ME33 : Fluid Flow 14 Chapter 15: Computational Fluid Dynamics

IntroductionHistory of computing

Computing, 1945-1960Early computer engineers thought that only a few dozen computers required worldwide Applications: cryptography (code breaking), fluid dynamics, artillery firing tables, atomic weapons ENIAC, 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 1945ME33 : Fluid Flow 15 Chapter 15: Computational Fluid Dynamics

IntroductionHistory of computing

Ultra Project

Left. The Colossus computer at Bletchley Park, Buckinghamshire, England, c. 1943. Funding for this code-breaking machine came from the Ultra project.

In the early 1930s Polish cryptographers first broke the code of Germany's cipher machine Enigma. They were led by mathematician Marian Rejewski and assisted by material provided to them by agents of French intelligence. For much of the decade, the Poles were able to decipher their neighbour's radio traffic, but in 1939, faced with possible invasion and difficulties decoding messages because of changes in Enigma's operating procedures, they turned their information over to the Allies. Early in 1939 Britain's secret service set up the Ultra project at Bletchley Park, 50 miles (80 km) north of London, for the purpose of intercepting the Enigma signals, deciphering the messages, and controlling the distribution of the resultant secret information. Strict rules were established to restrict the number of people who knew about the existence of the Ultra information and to ensure that no actions would alert the Axis powers that the Allies possessed knowledge of their plans. The incoming signals from the German war machine (more than 2,000 daily at the war's height) were of the highest level, even from Adolf Hitler himself. Such information enabled the Allies to build an accurate picture of enemy plans and orders of battle, forming the basis of war plans both strategic and tactical. Ultra intercepts of signals helped the Royal Air Force to win the Battle of Britain. Intercepted signals between Hitler and General Gnther von Kluge led to the destruction of a large part of the German forces in Normandy in 1944 after the Allied landing. ME33 : Fluid Flow 16 Chapter 15: Computational Fluid Dynamics

IntroductionHigh-performance computingTop 500 computers in the world compiled: www.top500.org Computers located at major centers connected to researchers via Internet

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Chapter 15: Computational Fluid Dynamics

Outline CFD What It is?CFD ProcessModel Equations Discretization Grid Generation Boundary Conditions Solve Post-Processing Uncertainty Assessment

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Chapter 15