Topics covered today include:

A brief review of the history of fluid dynamics.

An introductory overview of CFD.

I. A brief review of the history of fluid dynamics.

Fluid dynamics??? Fluid dynamics is the science of fluid motion. Fluid flow is commonly studied in one of three ways:

Experimental fluid dynamics(seventeenth century, laid in France and England)

An experimental investigation involving full-scale equipment can be used to predict how identical copies of the equipment (Full scale or small scale) would perform under the same conditions.

Theoretical fluid dynamics.(eighteenth and nineteenth centuries, again primarily in Europe). This works out the consequences of a mathematical model with set of equations

Numerically: computational fluid dynamics(CFD)..

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Antiquity Focus on waterworks: aqueducts,

canals, harbors, bathhouses. One key figure was Archimedes -

Greece (287-212 BC). He initiated the fields of static mechanics, hydrostatics, and pycnometry (how to measure densities and volumes of objects).

One of Archimedes’ inventions is the water screw, which can be used to lift and transport water and granular materials.

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Leonardo da Vinci -Italy (1452-1519) Leonardo set out to observe all

natural phenomena in the visible world, recognizing their form and structure, and describing them pictorially exactly as they are.

He planned and supervised canal and harbor works over a large part of middle Italy. In France he designed a canal that connected the Loire and Saone.

His contributions to fluid mechanics are presented in a nine part treatise (Del moto e misura dell’acqua) that covers the water surface, movement of water, water waves, eddies, falling water, free jets, interference of waves, and many other newly observed phenomena.

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Vinci’s “A Gigantic Explosion”

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Isaac Newton - England (1643-1727)

One of the most important figures in science. Most well known for his three laws of motion. His key contributions to fluid mechanics

include: The second law: F=m.a. The concept of Newtonian viscosity in which

stress and the rate of strain vary linearly. The reciprocity principle: the force applied

upon a stationary object by a moving fluid is equal to the change in momentum of the fluid as it deflects around the front of the object.

Relationship between the speed of waves at a liquid surface and the wavelength.

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18th and 19th century During this period, significant work was done trying to

mathematically describe the motion of fluids. Daniel Bernoulli (1700-1782) derived Bernoulli’s equation. Leonhard Euler (1707-1783) proposed the Euler equations,

which describe conservation of momentum for an inviscid fluid, and conservation of mass. He also proposed the velocity potential theory.

Claude Louis Marie Henry Navier (1785-1836) and George Gabriel Stokes (1819-1903) introduced viscous transport into the Euler equations, which resulted in the Navier-Stokes equation. This forms the basis of modern day CFD.

Other key figures were Jean Le Rond d’Alembert, Siméon-Denis Poisson, Joseph Louis Lagrange(Child prodigy became professor at the age19), Jean Louis Marie Poiseuille, John William Rayleigh, M. Maurice Couette, and Pierre Simon de Laplace.

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Osborne Reynolds – England (1842-1912) Reynolds was a prolific writer who

published almost 70 papers during his lifetime on a wide variety of science and engineering related topics.

He is most well-known for the Reynolds number, which is the ratio between inertial and viscous forces in a fluid. This governs the transition from laminar to turbulent flow.

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• Reynolds’ apparatus consisted of a long glass pipe through which water could flow at different rates, controlled by a valve at the pipe exit. The state of the flow was visualized by a streak of dye injected at the entrance to the pipe. The flow rate was monitored by measuring the rate at which the free surface of the tank fell during draining. The immersion of the pipe in the tank provided temperature control due to the large thermal mass of the fluid.

First part of the 20th century Much work was done on refining theories

of boundary layers and turbulence. Ludwig Prandtl (1875-1953): boundary

layer theory, the mixing length concept, compressible flows, the Prandtl number, and more.

Theodore von Karman (1881-1963) analyzed what is now known as the von Karman vortex street.

Geoffrey Ingram Taylor (1886-1975): statistical theory of turbulence and the Taylor microscale.

Andrey Nikolaevich Kolmogorov (1903-1987): the Kolmogorov scales and the universal energy spectrum.

George Keith Batchelor (1920-2000): contributions to the theory of homogeneous turbulence.

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Lewis Fry Richardson (1881-1953)

In 1922, Lewis Fry Richardson developed the first numerical weather prediction system. Division of space into grid cells and the finite difference

approximations of Bjerknes's "primitive differential equations.” His own attempt to calculate weather for a single eight-hour period

took six weeks and ended in failure. His model's enormous calculation requirements led Richardson to

propose a solution he called the “forecast-factory.” The "factory" would have filled a vast stadium with 64,000 people. Each one, armed with a mechanical calculator, would perform part

of the calculation. A leader in the center, using colored signal lights and telegraph

communication, would coordinate the forecast.

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1930s to 1950s Earliest numerical solution: for flow past a cylinder (1933).

○ A.Thom, ‘The Flow Past Circular Cylinders at Low Speeds’, Proc. Royal Society, A141, pp. 651-666, London, 1933

Kawaguti obtains a solution for flow around a cylinder, in 1953 by using a mechanical desk calculator, working 20 hours per week for 18 months, citing: “a considerable amount of labour and endurance.”

○ M. Kawaguti, ‘Numerical Solution of the NS Equations for the Flow Around a Circular Cylinder at Reynolds Number 40’, Journal of Phy. Soc. Japan, vol. 8, pp. 747-757, 1953.

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Flow transitions around a cylinder For flow around a cylinder, the flow starts separating at Re = 5.

For Re below 30, the flow is stable. Oscillations appear for higher Re.

The separation point moves upstream, increasing drag up to Re = 2000.

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Re = 9.6

Re = 13.1

Re = 30.2 Re = 2000

Re = 26

Re = 10,000

1960s and 1970s During the 1960s the theoretical division at Los Alamos contributed many numerical

methods that are still in use today, such as the following methods: Particle-In-Cell (PIC). Marker-and-Cell (MAC). Vorticity-Streamfunction Methods. Arbitrary Lagrangian-Eulerian (ALE). k- turbulence model.

During the 1970s a group working under D. Brian Spalding, at Imperial College, London, develop: Parabolic flow codes (GENMIX). Vorticity-Streamfunction based codes. The SIMPLE algorithm and the TEACH code. The form of the k- equations that are used today. Upwind differencing. ‘Eddy break-up’ and ‘presumed pdf’ combustion models.

In 1980 Suhas V. Patankar publishes Numerical Heat Transfer and Fluid Flow, probably the most influential book on CFD to date.

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Foundation stones:

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II. An introductory overview of CFD

Back Ground:

CFD, derived from different disciplines of fluid mechanics and heat transfer, is also finding its way into other important uncharted areas especially in process, chemical, civil, and environmental engineering.

Combination and approach:

Emergence of CFD Perhaps the most important reason for the growth of CFD

is that for much mainstream flow simulation, CFD is significantly cheaper than wind-tunnel testing and will become even more so in the future. Improvements in computer hardware performance have occurred hand in hand with a decreasing hardware cost.

Bird View:CFD is particularly dedicated to the fluids that are in motion

and how the fluid flow behaviour influences processes thatmay include heat transfer and possibly chemical reactions in combusting flows. Physical characteristics of the fluid motion described throughfundamental mathematical equations, usually in partial differentialform, and are often called governing equations. To solve these mathematical equations, they are converted Into computer programs or software packages using high Level computer programming languages

The computational part simply means the study of the fluid flow through numerical simulations, which involves employing computer programs or software packages performed on highspeed digital computers to attain the numerical solutions.

What is CFD?...Definition

Computational fluid dynamics is the art of replacing the integrals or the partial derivatives fundamental physical principle equations with discretized algebraic forms, which in turn are solved to obtain numbers for the flow field values at discrete points in time and/or space.

“No knowledge can be certain, if it is' not based upon mathematics

or upon some other knowledge which is' itself based upon the

mathematical Sciences”. ....Leonardo da Vinci (1425-1519)

“All the mathematical sciences are founded on relationsbetween physical laws and laws of numbers, so that the

aim ofexact science is to reduce the problems of nature to thedetermination of quantities by operations with numbers”.

.....James Clerk Maxwell, 1856

“When you measure what you are speaking about, and express it in

numbers, you know something about it,' but when you cannot

measure it, when you cannot express it in numbers, your knowledge

is of a meager and unsatisfactory kind.' it may be the beginning of

knowledge, but you have scarcely, in your thoughts, advanced to the

stage of science”. .....William Thomson, Lord Kelvin,1894

Applications of CFD I. AS A RESEARCH TOOL

CFD can employed to better understand the physical events or processes related to the action and interaction of phenomena associated with dissipation, diffusion, convection, boundary layers, and turbulence.

Nonlinearity phenomenon needs to seek numerical solutions for the partial differential equations, where CFD is at most necessary.

CFD, analogous to wind-tunnel tests, can be employed as a research tool to perform numerical experiments.

II. AS A DESIGN TOOL:

Optimization of product development and processes and/or to predict the performance of new designs even before they are manufactured or implemented.

CFD has assisted by providing significant and substantial insights into the flow characteristics within the equipment and processes required to increase production, improve longevity, and decrease waste.

III. IN AERO SPACE FIELD: CFD with its well-known application to aerodynamics

by the calculation of the lifting force on an aircraft wingspan.

CFD has been employed in resolving a number of complex operational problems in aircraft designs, such as studying the impact of trailing vortices on the safe operation of successive aircraft taking off and landing as well as enhancing the passenger and crew comfort by improving cabin ventilation, heating, and cooling.

Efforts to better understand and suppress the noise produced by heavy artillery and the safe operation of a military helicopter upon firing, CFD is increasingly being employed in military applications.

Aerospace

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Challenging problem!!...Governing flow equations are the Euler Equations. Same immaterial of region but their mathematical behaviour is different in the two regions. Between 1950-60, techniques were developed for just the subsonic portion, and for supersonic region(Method of characteristics). Unfortunately, the proper patching of these different techniques through the transonic region around the sonic line was extremely difficult.

After 1966, today assigned as a homework problem in a CFD graduate course!!!

Finally solved employing the concept of a time-dependent approach to the steady state, in 1966

IV. IN AUTOMOTIVE FIELD:

CFD is in forefront in the creation of innovative new internal systems that will better enhance the overall driving experience, improve driver and passenger comfort and safety, and advance fuel Economy.

Numerical simulations allow the ease of investigating different valve and port design that can lead to improved engine performance through better breathing and more

induction change distribution. Computational fluid dynamics has long been an

essential element in automotive design and manufacture.This technology has delivered the ability to shorten cycles, optimize existing engineering components and systems to improve energy efficiency and meet strict standards and specifications, improve in-car environment, and study the important external aerodynamics as illustrated in Fig.

Streamlines in a vehicle without (left) and with rear center and B-pillar ventilation (right)

V. IN BIOMEDICAL SCIENCES:

● With the breadth of physical models and advances in areas of fluid-structure interaction, particle tracking, turbulence modeling and better meshing facilities, rigorous CFD analysis is increasingly performed to study the fluid phenomena inside the human vascular system.

● CFD is being increasingly employed via virtual prototyping to recommend the best design for surgical reconstructions, such as carotid endarterectomy (fig 1) and to better understand the blood flow through an aneurysm in the abdominal artery.

● Fig 2 shows CFD in the biomedical area where the blood flow through an abnormal artery has been predicted.

Fig1 and 2

Biomedical

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Pressure Contours in Blood Pump

VI. IN CHEMICAL AND MINERAL PROCESSING:

● Improving the performance of gas-sparged stirred tank reactors in chemical industry by analyzing contours of different bubble size distribution within the stirred tank accompanied by the local flow behavior, indicated by velocity vectors, around one of the rotating blades Fig(1).

● Minerals processing involve complex fluid flow, heat, and mass transfer phenomena inside aggressive and hostile environments. By modeling, optimizing, and improving processes such as classification, separation, and filtration, CFD is at the forefront of providing designs with greater efficiencies and significant production outputs.

Fig1

VII. IN ENVIRONMENTAL ENGG.:

CFD has been used to predict the pollutant plume being dispersed from a cooling tower subject to wind conditions shown in below fig.

Environment

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For an architectural structure exposed to environmental elements have recently brought about an important study on the flow of air and water or any other fluid. Around the Itsukushima Torii (Gate),Hiroshima results we can see from the following sketch.

VIII. IN POWER GENERATION:

CFD to provide a technological edge through a better understanding of the equipment and processes.

CFD is being employed to optimize the turbine blades for generating constant power under varying wind conditions.

CFD has allowed the positioning of turbines throughout an area to achieve efficient wind capture and to minimize wake interaction.

Power generation systems

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CFD simulations have greatly assisted engineers to identifyareas where deficiencies in design occurred and in the causes of these ineffective operations can be established in order to reduce emissions in a cost-effective manner.

Example of CFD application to predicting the velocity field of a wind turbine

Electronics & Semi conductors

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IX. IN SPORTS:By applying CFD, steady-state lift and drag forces for the hand and arm are determined through applyingsophisticated turbulence model and adaptive meshing.

Industrial and Non-Industrial Application Areas

• aerodynamics of aircraft and vehicles: lift and drag • hydrodynamics of ships • power plant: combustion in IC engines and gas turbines • turbomachinery: flows inside rotating passages, diffusers etc. • electrical and electronic engineering: cooling of equipment including micro- circuits • chemical process engineering: mixing and separation, polymer moulding • external and internal environment of buildings: wind loading and heating/ ventilation • marine engineering: loads on off-shore structures • environmental engineering: distribution of pollutants and effluents • hydrology and oceanography: flows in rivers, estuaries, oceans • meteorology: weather prediction • biomedical engineering: blood flows through arteries and veins

Futures of CFD

● Significant advances in virtual technology and electronic reporting are allowing engineers to swiftly view and interrogate the CFD predictions and make necessary assessments and judgments on a given engineering design.

● With decreasing hardware costs and rapid computing times, engineers are increasingly relying on this reliable yet easy-to-use CFD tool for delivering accurate results as already described by the examples in the previous sections.

● Since all real-world flows are inherently unsteady, and for capturing the complex flame characteristics, LES provides the means of obtaining such solutions and is gradually replacing traditional two-equation models in academia research. The demand of LES Modelling is steadily growing.

● CFD will eventually be so entrenched in the design process that new product development will evolve toward "zero prototype engineering."

● Direct Numerical Simulation (DNS) of turbulent flows in academia research and possibly in some facets of industrial applications may well become a distinct certainty instead of a distinct impossibility.

Unique Advantages of CFD

1. The theoretical development of the computational sciences focuses on the construction and solution of the governing equations and the study of various approximations to these equations. CFD presents the perfect opportunity to study specific terms in the governing equations in a more detailed fashion. New paths of theoretical development are realized.

2. CFD complements experimental and analytical approaches by providing an alternative cost-effective means of Simulating real fluid flows and reduces lead time.

3. CFD has the capacity of simulating flow conditions that are not reproducible in experimental tests found in geophysical and biological fluid dynamics, such as nuclear accident scenarios or scenarios that are too huge or too remote to be simulated

experimentally.

4. CFD can provide rather unlimited detailed, visualized, and comprehensive information when compared to analytical and experimental fluid dynamics.

5. Ability to study systems where controlled experiments are difficult or impossible to perform(e.g. very large systems).

6. Ability to study systems under hazardous conditions at and beyond their normal performance limits(e.g. Safety studies and accident scenarios).

Limitations of CFD

1. Numerical errors exist in computations, therefore there will be differences between the computed results and reality.

2. Numerical results obtained must always be thoroughly examined before they are believed; therefore a CFD user needs to learn how to properly analyze and make critical judgment on the computed results.

3. Wonderfully bright color pictures may provide a sense of realism of the actual fluid mechanics inside the flow system, but they are worthless if they are not quantitatively correct.

4. CFD user needs to learn how to properly analyze and make critical judgment on the computed results.