thermal and fluids in architectural engineering 10...

1

Thermal and Fluids

in Architectural Engineering

10. External flows

Jun-Seok Park, Dr. Eng., Prof.

Dept. of Architectural Engineering

Hanyang Univ.

Where do we learn in this chaper

1. Introduction

2.The first law

3.Thermal resistances

4. Fundamentals of fluid mechanics

5. Thermodynamics

6. Application

7.Second law

8. Refrigeration,

heat pump, and

power cycle

9. Internal flow

10. External flow

11. Conduction

12. Convection

14. Radiation

13. Heat Exchangers15. Ideal Gas Mixtures

and Combustion

10.1 Introduction

10.2 Boundary Layer Concepts

10.3 Differential Equations of fluid flows

10.4 Drag and Lift concepts

10.5 Drag force

10.6 Lift force

10. External flows

10.1 Introduction

□ External flow- flows around a body

- flows far away a body

□ Drag force- The force that acts parallel to the direction of the fluid flow

- Pressure + Viscous forces

□ Lift force- The force that acts perpendicular to the direction of the

fluid flow

- Pressure + Viscous forces

10.2 Boundary Layer Concepts

Source: Introduction to Thermal and Fluid engineering,Wiely, pp448

10.2 Boundary Layer Concepts

□ inviscid flow (free stream)- a outside of viscous influenced region

- no viscous stresses

□ viscous flow (boundary layer)- a inside of viscous influenced region

- viscous stresses act

□ Boundary layer thickness- boundary layer velocity reaches 99% of the free stream

velocity

- laminar region, transition region, turbulent region

M W - Q ΔE

□ Differential Equations of fluid flows

) (c.s) (c.v

..

유출입량통한를질량변화에서의

SCVC

dAVdVt

)() () (

)()()(...

내부운동량변화유출입량운동량힘주어지는외부에서

VCSCVC

tp dVVt

dAVVdVbFF

) () ( ) (

)(..

변화량내부에너지유출입물질의일에너지와

VCSC

dVet

dAVedWdQ

질량보존방정식(연속방정식)

운동량보존방정식(Euler/Bernoulli/

N-S)

에너지보존방정식

10.3 Differential Equations of fluid flows

10.3 Differential Equations of fluid flows

M W - Q ΔE

□Mass conservation equation

c.s)on flows (mass)c.vin changes (mass

..

SCVC

dAVdVt

c.v

c.s

M W - Q ΔE

))()()(

(

))((

) theory Gauss(

)(

(

..

..

z

w

y

v

x

u

t

Vt

dAVdVV

dVVdVt

dAVdVt

SV

VCVC

SCVC

10.3 Differential Equations of fluid flows

□Mass conservation equation

M W - Q ΔE

□Momentum conservation equation

• 응력(Stress) : 유체의 임의의 체적 요소에 작용하는 힘

-Body force : 체적요소의 표면에 작용하지 않고체적 전체의 질량에 분포되는 힘 (중력, 자력 등), Fb

-Surface force : 체적요소의 표면이 주위와 접촉하여 발생하는 힘, Fs

체적요소 표면에서의 유체 정압(P), Fp>표면에 수직으로 작용하는 힘

점성(Viscous)에 따른 전단응력(τ), Ft> 표면의 접선방향으로 작용하는 힘

Fp

FtFs

10.3 Differential Equations of fluid flows

M W - Q ΔE

VCSCVCtp

VCSCbs

dVVt

dAVVdVbFF

dVVt

dAVVFF

...

..

)()()(

)(

Surface force

Body force Momentum flows

on c.s

Momentum

changes in c.v.

VCVCVCtp dVV

tdVVVdVbFF

...)()()(

10.3 Differential Equations of fluid flows

□Momentum conservation equation

M W - Q ΔE

Surface force (Ft and Fp)

10.3 Differential Equations of fluid flows

□Momentum conservation equation

M W - Q ΔE

- Surface force in each direction

)(3

2)(2

)(3

2)(2

)(3

2)(2

)( ),( ),(

z

w

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v

x

u

y

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x

w

z

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yy

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xzzxzyyzyxxy

10.3 Differential Equations of fluid flows

□Momentum conservation equation

M W - Q ΔE

VCSCtp dVV

tdAVVFF

..)()(

Surface force

)(z

ww

y

vv

x

uu

t

wvu

),,(

Momentum flows

on c.s

Momentum

changes in c.v.

10.3 Differential Equations of fluid flows

□Momentum conservation equation

M W - Q ΔE

t

w

z

ww

y

vv

x

uu

Yz

w

y

v

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u

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zz

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pz

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py

t

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px

)(

)(3

2)(2)()(- :

)(

)()(3

2)(2)(- :

)(

)()()(3

2)(2(- :

Navier-Stokes Equation

10.3 Differential Equations of fluid flows

□Momentum conservation equation

M W - Q ΔE

□ Energy conservation equation

(1) kinetic Energy: V2/2

(2) Potential Energy: b, body force

(3) Internal Energy:e

10.3 Differential Equations of fluid flows

M W - Q ΔE

) (

)2

()2

()2

())(

n)(Conductioflow) mass fromenergy and convextion())((

)(

222

.

.

..

z

Tk

zy

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yx

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x

Vew

z

Vev

y

Veu

xdAVedQ

dAVedQ

dVet

dAVedWdQ

SC

SC

VCSC

열전달전도

10.3 Differential Equations of fluid flows

□ Energy conservation equation

M W - Q ΔE

t

edVe

t

wvuz

wvuy

wvu

z

pw

y

pv

x

puZwYuXudW

dVet

dAVedWdQ

VC

zzzyzxyzyyyxxzxyxx

VCSC

)(

)()()(x

)()()()(

)(

.

..

10.3 Differential Equations of fluid flows

□ Energy conservation equation

M W - Q ΔE

t

e

wvuz

wvuy

wvu

z

pw

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pv

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puZwYuXu

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zzzyzxyzyyyxxzxyxx

)(

)()()(x

)()()()(

)2

()2

()2

(222

-Energy including Kinetic energy

10.3 Differential Equations of fluid flows

□ Energy conservation equation

M W - Q ΔE

t

e

z

w

y

v

x

up

z

Tk

zy

Tk

yx

Tk

xz

ew

y

ev

x

eu

)(

-Energy exclude Kinetic energy

10.3 Differential Equations of fluid flows

□ Energy conservation equation

10.4 Drag and Lift Force

• Fluid dynamic forces are

due to pressure and

viscous forces

acting on the body surface.

• Drag: component parallel

to flow direction.

• Lift: component normal to

flow direction.

Source: Fundamentals of Thermal-Fluid

Sciences, McGraw-hill, pp592

10.4 Drag and Lift Concept

□ Lift and drag forces can be found by integrating

pressure and wall-shear stress.

Source: Fundamentals of Thermal-Fluid

Sciences, McGraw-hill, pp592

10.4 Drag and Lift Concept

□ Lift FL and drag FD forces are a function of

density and velocity V.

□ Dimensional analysis gives 2 dimensionless

parameters: lift and drag coefficients.

□Area A can be frontal area (drag applications),

planform area (wing aerodynamics), or wetted-

surface area (ship hydrodynamics).

10.4 Drag and Lift Concept

□ Example : lift and drag coefficients.

Scion XB Porsche 911

CD = 1.0, A = 25 ft2, CDA = 25ft2 CD = 0.28, A = 10 ft2, CDA = 2.8ft2

• Drag force FD=1/2V2(CDA) will be ~ 10 times larger for Scion XB

• Source is large CD and large projected area

• Power consumption P = FDV =1/2V3(CDA) for both scales with V3!

10.4 Drag and Lift Concept

□ For applications such as tapered wings, CL and

CD may be a function of span location.

□ For these applications, a local CL,x and CD,x are

introduced and the total lift and drag is determined

by integration over the span L

10.5 Drag force

□Analytic solutions are not possible for external flows- Experiments, numerical analysis, CFD

□ Drag force- drag force on a body is the sum of the pressure and

shear forces acting parallel to the flow velocity

□ In a flat plate- drag force is caused only by shear stress (P=0)

10.5 Drag force

• Fluid dynamic forces are comprised of pressure and friction effects.

• Often useful to decompose,

– FD = FD,friction + FD,pressure

– CD = CD,friction + CD,pressure

• This forms the basis of ship model testing where it is assumed that

– CD,pressure = f(Fr)

– CD,friction = f(Re)

Friction drag

Pressure drag

Friction & pressure dragSource: Fundamentals of Thermal-Fluid

Sciences, McGraw-hill, pp594

10.5 Drag force

• Streamlining reduces drag

by reducing FD,pressure, at the

cost of increasing wetted

surface area and FD,friction.

• Goal is to eliminate flow

separation and minimize

total drag FD

• Also improves structural

acoustics since separation

and vortex shedding can

excite structural modes.

10.5 Drag force

□ Example

10.5 Drag force

• For many geometries, total drag

CD is constant for Re > 104

• CD can be very dependent upon

orientation of body.

• As a crude approximation,

superposition can be used to add

CD from various components of a

system to obtain overall drag.

However, there is no

mathematical reason (e.g., linear

PDE's) for the success of doing

this. Source: Fundamentals of Thermal-Fluid

Sciences, McGraw-hill, pp598

10.5 Drag force

Source: Fundamentals of Thermal-Fluid Sciences, McGraw-hill, pp600

10.5 Drag force

□ Drag on flat plate is solely due to friction created by laminar, transitional, and turbulent boundary layers.

Source: Fundamentals of Thermal-Fluid Sciences, McGraw-hill, pp605

10.5 Drag force

• Local friction coefficient

– Laminar:

– Turbulent:

• Average friction coefficient

– Laminar:

– Turbulent:

For some cases, plate is long enough for turbulent flow,

but not long enough to neglect laminar portion

Source: Fundamentals of Thermal-Fluid

Sciences, McGraw-hill, pp607

10.6 Lift force

• Lift is the net force (due to pressure and viscous forces) perpendicular to flow direction.

• Lift coefficient

• A=bc is the planform area

Source: Fundamentals of Thermal-Fluid Sciences,

McGraw-hill, pp614

10.6 Lift force

• Thin-foil theory shows that CL≈2 for < stall

• Therefore, lift increases linearly with

• Objective for most applications is to achieve maximum CL/CD

ratio.

• CD determined from wind-tunnel or CFD (BLE or NSE).

• CL/CD increases (up to order 100) until stall.

Source: Fundamentals of Thermal-

Fluid Sciences, McGraw-hill, pp616