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1

Pendahuluan

Mekanika Fluida - TF 2204

CFDEFDAFD

2

0

1

Rei j

D p u u

Dt

∇• =

= −∇ + ∇ + ∇ •

U

UU

Dr. Suprijanto ST MTemail : [email protected]

Analytic Experiment Computational

2

THE DOs AND THE DON’Ts

• THE DO-s• Kerjakanlah pekerjaan rumah sebaik-baiknya karena

sumbangannya terhadap nilai akhir cukup besar.

• Pekerjaan rumah dapat dikerjakan bersama-sama namun jangan hanya sekedar menyalin pekerjaan kawan;pahamilah solusi setiap pekerjaan rumah karena denganitu sekurang-kurangnya Anda telah belajar memahamiperkuliahan ini.

• Peraturan umum mengenai kehadiran di kelas wajib

dipatuhi.



3

THE DOs AND THE DON’Ts

• THE DON’T-s• menggunakan telepon genggam (HP) di dalamkelas; 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.

4

Penilaian

Mid Term Test/Quizes ? %

Final Term Test ? %

Home Work/Take Home ? %



5

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 TEST

1 JAM KEGIATAN MANDIRI : MEMBACA LITERATUR

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

6

Satuan Acara Perkuliahan



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Satuan Acara Perkuliahan

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Fluid Mechanics• Fluids essential to life

• Human body 65% water

• Earth’s surface is 2/3 water

• Atmosphere extends 17km above the earth’s surface

• Affects every part of our lives



9

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)

10

Relevansi Mekanika Fluida dalam kehidupan

• Kehadiran fluida

• Cuaca dan musim

• Sistem Transportasi: mobil, KA, kapal,pesawat terbang

• Lingkungan

• Physiology dan kedokteran

• Olah raga



11

Cuaca dan Musim

Tornadoes

HurricanesGlobal Climate

Thunderstorm

12

KendaraanPesawat terbang

Kapal selamKA kecept. tinggi

Kapal laut



13

Lingkungan

Polusi udara Sungai

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WarmedFiltered

MoisturizedJutaan kantung

aveoli

Medik

Trachea Æbercabang dua

padabronchusÆdibagisekitar 15 bagian

berakhir padabronchioles Æ

yang mengirimkanudara pada jutaankantung kecil yang

disebut Alveoli



15

Medik

16

Olah raga

Water sports

Auto racing

Offshore racingCycling

Surfing



17

Fluids Engineering

Reality

Fluids Engineering System Components Idealized

EFD Mathematical Physics Problem Formulation

AFD CFD,

18

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)



19

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

p

u r R r xμ

∂= − −∂

Faktor gesekan:8

8 64Re2 2

w

du

dyw f V V

μ τ

ρ ρ

= = =

Asumsi: Fully developed, LowÆPendekatan: Penyederhanaan persmomentum, integrasi, penerapan syaratbatas untuk menentukan konstanta integrasidan menggunakan pers energi untuk menghitung head loss

xg y

u

x

u

x

p

Dt

Du+⎥

⎦

⎤⎢⎣

⎡

∂∂

+∂∂

+∂∂

−=2

2

2

2

μ

Head loss:1 2

1 2 f

p p z z h

γ γ + = + +

2

2

32

2 f

L V LV h f

D g D

μ

γ = =

UD2000Re

ρ <μ

=

00

0



21

22

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

0 5 y+< <

1lnu y B

κ

+ += + 520 10 y+< <

*

0

1U u r

f u r

⎛ ⎞−= −⎜ ⎟

⎝ ⎠

510 y

+ >

u y+ +=

( ) ( ) *0

*

1ln

u r r r u B

u κ ν

−= +

Re 3000>

* y yu ν

+ =*u u u

+ =*

wu τ ρ =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 212log Re .8 f

f = −

(R=0.41, B=5.5)



23

Analytical Fluid Dynamics• Example: turbulent flow in rough pipe

( )u u y k + +=

1ln

yu

k κ

+ = +

12log

3.7

k D

f = −( )

1ln 8.5 Re

yu f

k κ

+ = + ≠

Three regimes of flow depending on k +

1. K +<5, hydraulically smooth (no effect of roughness)2. 5 < K +< 70, transitional roughness (Re dependent)3. K +> 70, fully rough (independent Re)

Both laminar sublayer and overlap layer

are affected by roughnessInner layer:

Outer layer: unaffected

Overlap layer:

Friction factor :

For 3, using EFD data to adjust constants:

constant

24

Analytical Fluid Dynamics• Example: Moody diagram for turbulent pipe flow

1 1 22

1 2.512log

3.7 Re

k D

f f

⎡ ⎤= − +⎢ ⎥

⎣ ⎦

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



25

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

26

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



27

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

28

Applications of EFD (cont’d)

Example of industrial application

NASA's cryogenic wind tunnel simulates flight

conditions for scale models--a critical tool in

designing airplanes.

Application in teaching

Fluid dynamics laboratory



29

Full and model scale

• Scales: model, and full-scale

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

30

Measurement systems

• Instrumentation• Load cell to measure forces and moments

• Pressure transducers

• Pitot tubes

• Hotwire anemometry

• PIV, LDV

• Data acquisition• Serial port devices

• Desktop PC’s

• Plug-in data acquisition boards

• Data Acquisition software - Labview• Data analysis and data reduction

• Data reduction equations

• Spectral analysis



31

Instrumentation

Load cell

Pitot tube

Hotwire 3D - PIV

32

Data acquisition system

Hardware

Software - Labview



33

Dimensional analysis

• Definition : Dimensional analysis is a process of formulating fluid mechanics problems in

in terms of non-dimensional variables and parameters.• Why is it used :

• Reduction in variables ( If F(A1, A2, … , An) = 0, then f(Π1, Π2, … Πr < n) = 0,

where, F = functional form, Ai = dimensional variables, Π j = non-dimensional

parameters, m = number of important dimensions, n = number of dimensional variables, r

= n – m ). 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.

34

EFD – “hands on” experience

Lab1: Measurement of density and

kinematic 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

TapsTygonTubing

Load Cell

LoadCellL

D



35

Computational Fluid Dynamics

• CFD is use of computational methods forsolving 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

36

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).



37

Modeling

• Mathematical physics problem formulation of fluidengineering 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), andturbulent 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, ReynoldsNumber, and Mach Number, etc.

38

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)



39

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 around

NACA12 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 jet

centerline, Re=21,000 (D. Glaze).

40

Numerical methods• Finite difference methods:using numerical scheme toapproximate the exact derivativesin the PDEs

• Finite volume methods• Grid generation: conformal

mapping, algebraic methods anddifferential equation methods

• Grid types: structured,unstructured

• Solvers: direct methods (Cramer’srule, Gauss elimination, LUdecomposition) and iterativemethods (Jacobi, Gauss-Seidel,SOR)

Slice of 3D mesh of a fighter aircraft

o x

y

i i+1i-1

j+1

j

j-1

imax

jmaxxΔ

yΔ

2

1 1

2 2

2i i iP P PP

x x

+ −− +∂=

∂ Δ2

1 1

2 2

2 j j jP P PP

y y

+ −− +∂=

∂ Δ

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