Post on 14-Apr-2018
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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 : supri@tf.itb.ac.id
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.html7/27/2019 Bagian 1 Introduction-2011
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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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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.gif7/27/2019 Bagian 1 Introduction-2011
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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