Bagian 1 Introduction-2011

7/27/2019 Bagian 1 Introduction-2011

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Pendahuluan

Mekanika Fluida - TF 2204

CFDEFDAFD

2

0

1

Rei j

Dp u u

Dt

U

UU

Dr. Suprijanto ST MTemail : [email protected]

Analytic Experiment Computational


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THE DOs AND THE DONTs

THE DO-s Kerjakanlah pekerjaan rumah sebaik-baiknya karena

sumbangannya terhadap nilai akhir cukup besar.

Pekerjaan rumah dapat dikerjakan bersama-sama namunjangan hanya sekedar menyalin pekerjaan kawan;pahamilah solusi setiap pekerjaan rumah karena dengan

itu sekurang-kurangnya Anda telah belajar memahamiperkuliahan ini.

Peraturan umum mengenai kehadiran di kelas wajibdipatuhi.


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THE DOs AND THE DONTs

THE DONT-s menggunakan telepon genggam (HP) di dalam

kelas; pelanggaran terhadap hal ini dikenakandenda : Rp 100.000,- dan dana terkumpul akanmenjadi milik seluruh peserta kelas.

menggunakan sandal selama mengikutiperkuliahan ini.

hadir lebih lambat dari dosen.


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Penilaian

Mid Term Test/Quizes ? %

Final Term Test ? %

Home Work/Take Home ? %


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Pustaka

Fox and McDonald, P.J. Pritchard,Introduction to Fluid Mechanics, John Wiley, 2004

S.W. Yuan, Foundation of Fluid Mechanics, Prentice-Hall,

3 SKS BERARTI AKTIVITAS PER MINGGU TERDIRI DARI :

PER MINGGU:1 JAM TATAP MUKA

1 JAM KEGIATAN TERSTRUKTUR : HOME WORK, TAKE HOME TEST1 JAM KEGIATAN MANDIRI : MEMBACA LITERATUR

BERARTI : 3 SKS --> BEBAN DILUAR KELAS 6 JAM PER MINGGU !


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Satuan Acara Perkuliahan


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Satuan Acara Perkuliahan


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Fluid Mechanics

Fluids essential to life Human body 65% water

Earths surface is 2/3 water

Atmosphere extends 17km above the earths surface

Affects every part of our lives


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History

Faces of Fluid Mechanics

Archimedes(C. 287-212 BC)

Newton(1642-1727)

Leibniz(1646-1716)

Euler(1707-1783)

Navier(1785-1836)

Stokes(1819-1903)

Reynolds(1842-1912)

Prandtl(1875-1953)

Bernoulli(1667-1748)

Taylor(1886-1975)
http://www-gap.dcs.st-and.ac.uk/~history/PictDisplay/Taylor_Geoffrey.html


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Relevansi Mekanika Fluida dalam kehidupan

Kehadiran fluida Cuaca dan musim

Sistem Transportasi: mobil, KA, kapal,pesawat terbang

Lingkungan

Physiology dan kedokteran

Olah raga


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Cuaca dan Musim

Tornadoes

HurricanesGlobal Climate

Thunderstorm


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Kendaraan

Pesawat terbang

Kapal selamKA kecept. tinggi

Kapal laut


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Lingkungan

Polusi udara Sungai


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WarmedFiltered

MoisturizedJutaan kantung

aveoli

Medik

Trachea bercabang dua

padabronchusdibagi

sekitar 15 bagianberakhir padabronchioles

yang mengirimkanudara pada jutaankantung kecil yang

disebut Alveoli


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Medik


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Olah raga

Water sports

Auto racing

Offshore racingCycling

Surfing


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Fluids Engineering

Reality

Fluids Engineering System Components Idealized

EFD Mathematical Physics Problem Formulation

AFD CFD,


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Analytical Fluid Dynamics (AFD)

Teori formulasi masalah fisika matematik Control volume & differential analysis

Solusi eksak untuk kondisi dan geometri sederhana

Solusi aproksimasi pada aplikasi praktis

Linear

Hubungan empiris dengan menggunakan data EFD(eng. Fluid dynamics)


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Analytical Fluid Dynamics

Pokok bahasan Definisi dan sifat-sifat fluida

Statika fluida

Gerak fluida

Kontinuitas, momentum, dan prinsip energy

Analisis dimensional dan keserupaan

Tahanan permukaan

Aliran dalam conduits Hambatan dan gaya angkat


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Analytical Fluid Dynamics

Schematic

Contoh: aliran laminar pada pipa

Solusi pasti :

2 21( ) ( )( )

4

pu r R r

x

Faktor gesekan:8

8 64Re2 2

w

du

dywfV V

Asumsi: Fully developed, Low

Pendekatan: Penyederhanaan persmomentum, integrasi, penerapan syaratbatas untuk menentukan konstanta integrasidan menggunakan pers energi untuk

menghitung head loss

xgy

u

x

u

x

p

Dt

Du

2

2

2

2

Head loss:1 2

1 2 f

p pz z h

2

2

32

2f

L V LVh f

D g D

UD2000Re

00

0


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21


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Analytical Fluid Dynamics Contoh: aliran turbulent flow pada pipa smooth (

)

0 5y

1lnu y B

520 10y

*

0

1U u r

fu r

510y

u y

*

0*

1 lnu r r r u Bu

Re 3000

*y yu *u u u *

wu Three layer concept (using dimensional analysis)

1. Laminar sub-layer (viscous shear dominates)

2. Overlap layer (viscous and turbulent shear important)

3. Outer layer (turbulent shear dominates)

Assume log-law is valid across entire pipe:

Integration for average velocity and using EFD data to adjust constants:

1 21

2 log Re .8ff

(k=0.41, B=5.5)


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Analytical Fluid Dynamics Example: turbulent flow in rough pipe

u u y k

1 ln yuk

12log

3.7

k D

f

1ln 8.5 Re

yu f

k

Three regimes of flow depending on k+1. K+ 70, fully rough (independent Re)

Both laminar sublayer and overlap layerare affected by roughnessInner layer:

Outer layer: unaffected

Overlap layer:

Friction factor:

For 3, using EFD data to adjust constants:

constant


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Analytical Fluid Dynamics Example: Moody diagram for turbulent pipe flow

1 1 22

1 2.512log

3.7 Re

k D

ff

Composite Log-Law for smooth and rough pipes is given by the Moody diagram:


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Experimental Fluid Dynamics (EFD)

Definition:

Use of experimental methodology and procedures for solving fluidsengineering systems, including full and model scales, large and tabletop facilities, measurement systems (instrumentation, data acquisitionand data reduction), uncertainty analysis, and dimensional analysis andsimilarity.

EFD philosophy:

Decisions on conducting experiments are governed by the ability of theexpected test outcome, to achieve the test objectives within allowableuncertainties.

Integration of UA into all test phases should be a key part of entireexperimental program

test design determination of error sources estimation of uncertainty documentation of the results


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Purpose

Science & Technology: understand and investigate aphenomenon/process, substantiate and validate a theory(hypothesis)

Research & Development: document a process/system,provide benchmark data (standard procedures,validations), calibrate instruments, equipment, andfacilities

Industry: design optimization and analysis, provide datafor direct use, product liability, and acceptance

Teaching: instruction/demonstration


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Applications of EFD

Application in research & development

Tropic Wind Tunnel has the ability to create

temperatures ranging from 0 to 165 degrees

Fahrenheit and simulate rain

Application in science & technology

Picture of Karman vortex shedding
http://www.damtp.cam.ac.uk/user/turbmix/Biagio/images/vortex-small.gif


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Applications of EFD (contd)

Example of industrial application

NASA's cryogenic wind tunnel simulates flightconditions for scale models--a critical tool in

designing airplanes.

Application in teaching

Fluid dynamics laboratory


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Full and model scale

Scales: model, and full-scale

Selection of the model scale: governed by dimensional analysis and similarity


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Measurement systems

Instrumentation

Load cell to measure forces and moments Pressure transducers

Pitot tubes

Hotwire anemometry

PIV, LDV

Data acquisition Serial port devices

Desktop PCs

Plug-in data acquisition boards

Data Acquisition software - Labview

Data analysis and data reduction Data reduction equations

Spectral analysis


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Instrumentation

Load cell

Pitot tube

Hotwire3D - PIV


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Data acquisition system

Hardware

Software - Labview

Di i l l i


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Dimensional analysis

Definition : Dimensional analysis is a process of formulating fluid mechanics problems inin terms of non-dimensional variables and parameters.

Why is it used :

Reduction in variables ( If F(A1, A2, , An) = 0, then f(P1, P2, Pr < n) = 0,where, F = functional form, Ai = dimensional variables, Pj = non-dimensionalparameters, m = number of important dimensions, n = number of dimensional variables, r

= nm ). Thereby the number of experiments required to determine f vs. F is reduced.

Helps in understanding physics

Useful in data analysis and modeling

Enables scaling of different physical dimensions and fluid properties

Example

Vortex shedding behind cylinder

Drag = f(V, L, r, m, c, t, e, T, etc.)

From dimensional analysis,

Examples of dimensionless quantities : Reynolds number, Froude

Number, Strouhal number, Euler number, etc.

EFD h d i


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EFDhands on experience

Lab1: Measurement of density andkinematic viscosity of a fluid

Lab2: Measurement of

flow rate, friction factor and

velocity profiles in smooth and

rough pipes.

Lab3: Measurement of surface pressure

Distribution, lift and drag coefficient for an airfoil

ToScanivalve

Chord-wisePressure

Taps

TygonTubing

Load Cell

Load CellL

D


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Computational Fluid Dynamics CFD is use of computational methods for

solving fluid engineering systems, includingmodeling (mathematical & Physics) andnumerical methods (solvers, finite differences,and grid generations, etc.).

Rapid growth in CFD technology since adventof computer

ENIAC 1, 1946 IBM WorkStation


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Purpose The objective of CFD is to model the continuous fluids

with Partial Differential Equations (PDEs) anddiscretize PDEs into an algebra problem, solve it,validate it and achieve simulation based designinstead of build & test

Simulation of physical fluid phenomena that aredifficult to be measured by experiments: scalesimulations (full-scale ships, airplanes), hazards

(explosions,radiations,pollution), physics (weatherprediction, planetary boundary layer, stellarevolution).


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Modeling

Mathematical physics problem formulation of fluid

engineering system Governing equations: Navier-Stokes equations (momentum),

continuity equation, pressure Poisson equation, energyequation, ideal gas law, combustions (chemical reactionequation), multi-phase flows(e.g. Rayleigh equation), and

turbulent models (RANS, LES, DES). Coordinates: Cartesian, cylindrical and spherical coordinatesresult in different form of governing equations

Initial conditions(initial guess of the solution) and BoundaryConditions (no-slip wall, free-surface, zero-gradient,

symmetry, velocity/pressure inlet/outlet) Flow conditions: Geometry approximation, domain, Reynolds

Number, and Mach Number, etc.

M d li ( l )


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Modeling (examples)

Free surface animation for ship inregular waves

Developing flame surface (Bell et al., 2001)

Evolution of a 2D mixing layer laden with particles of Stokes

Number 0.3 with respect to the vortex time scale (C.Narayanan)

Modeling (examples contd)


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Modeling (examples, cont d)

3D vortex shedding behind a circular cylinder(Re=100,DNS,J.Dijkstra)

DES,Re=105, Iso-

surface of Q

criterion (0.4)

for turbulent

flow aroundNACA12 with

angle of attack

60 degrees

LES of a turbulent jet. Back wall shows a slice of the dissipation rate and the

bottom wall shows a carpet plot of the mixture fraction in a slice through the jetcenterline, Re=21,000 (D. Glaze).


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Numerical methods Finite difference methods:

using numerical scheme to

approximate the exact derivativesin the PDEs

Finite volume methods Grid generation: conformal

mapping, algebraic methods anddifferential equation methods

Grid types: structured,

unstructured Solvers: direct methods(Cramersrule, Gauss elimination, LUdecomposition) and iterativemethods (Jacobi, Gauss-Seidel,SOR)

Slice of 3D mesh of a fighter aircraft

ox

y

i i+1i-1

j+1

j

j-1

imax

jmaxx

y

2

1 1

2 2

2i i iP P PP

x x

2

1 1

2 2

2j j jP P PP

y y

Bagian 1 Introduction-2011

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