thermal and fluids in architectural engineering 9...

1

Thermal and Fluids

in Architectural Engineering

9. Internal 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

9.1 Introduction

9.2 Viscosity

9.3 Fully developed laminar flow in pipes

9.4 Laminar and turbulent flow

9.5 Head loss

9.6 Fully developed turbulent flow in pipes

9.7 Entrance Effects

9.8 Steady-flow energy equation

9. Internal flows

9.1 Introduction

□ The design of flow systems requires, - a means to move the fluid from one to other place

- determination of pressure, flow rate, and velocity

□ The fluid friction causes- Pressure drop, change of velocity, profile of flows

- loss of flow energy

□ The friction effect is an important factor that decides

the flow of fluids

M W - Q ΔE

9.1 Introduction

□ Internal flows vs. external flows

M W - Q ΔE

• Internal flows are dominated

by the influence of friction

of the fluid throughout the

flow field

• In external flows, friction

effects are limited to the

boundary layer and wake.

Source: Fluid mechanics, McGraw-hill, pp325

Source: Fundamentals of Thermal-Fluid

Sciences, McGraw-hill, pp377

9.1 Introduction

□ The fluid systems in buildings - Internal flows: supply water, HVAC system, heating

- External flows: wind effect on tall building,

flows of air in buildings

M W - Q ΔE

냉동기

온수/증기발생기

열원설비 공기조화기

SARA

EA OA

공기+물중앙공조방식

Internal flows External flows

9.2 Viscosity

□ To deal with flow frictional effect, the fundamental

fluid property, viscosity has to be understood.

□ Shear stress in Solid and fluids

M W - Q ΔE

Rubber

-deforming

> tear or break

-Need strong force

Stationary plate

Moving plate

[Solids]

Water

- continuously deformed

> No tear or No break

-Need weak force

Stationary plate

Moving plate

[fluids]

9.2 Viscosity

□ Shear stress in fluids deforms the fluid, and makes

velocity gradient

M W - Q ΔE

Stationary plate

Moving plate

x

y

δV

δFt

δy

δl

δα

dy

dV

dt

dα

y

V

t

tV

yy

t

radian) is ( )tan(

rate deforminf

9.2 Viscosity

□ Shear stress and viscosity

- Viscosity is a property of the fluid, and it indicates that

how much internal friction in the fluid is present

- Most of the fluids operated in buildings are Newtonian fluids

M W - Q ΔE

Stationary plate

Moving plate

x

y

δFt

δy

δl

fluids)(Nwtonian

gradient)(velocity

A

Ft

dy

dV

dy

dV

V

9.3 Fully developed laminar flows in pipes

□ Flow in pipes

- The fluid near the wall slows down (y=0 > V=0; No slip)

- The fully developed flow region is where the velocity of

profile is independent of the distance, x

M W - Q ΔE

Source: Fluid mechanics, McGraw-hill, pp325


□ No-slip on the wall

M W - Q ΔE

[Example No-slip]

• No-slip condition: A fluid in direct contact with a solid ``sticks'‘ to the surface due to viscous effects

• The fluid property responsible for the no-slip condition is viscosity



□ Velocity and Pressure difference in a pipe

M W - Q ΔE

sin

0sin

0FFF

0F

ble)imcompresi state,(steady Assumption

F

system in theon conservati momentum ofEquation

gx,,xpx,

x

,,,

x

gmAAPAP

gmAAPAP

VmVmdt

dB

seeii

seeii

exeixicvx

Fully developed flow in

a inclined circle pipe

θ



M W - Q ΔE

xei

xei

x

x

sei

ei

seeii

dVdrrg

L

PP

gLr

L

dr

dVPP

dyR-yddrdy

dV

dr

dV

LrmLrArAA

gLr

LPP

gmAAPAP

2

sin

2

sin2

))(y-Rr ,(

) ,2 , (

sin2

sin

22

Fully developed flow in

a inclined circle pipe

θ



M W - Q ΔE

L))P,,f(R,V(

)P ( R

r-1sin

L

P

4(r)

condition slip-No introduce and

ionintergaratafter ,difference pressure andVelocity Finallly

2

sin

2

22

PPgR

V

dVdrrg

L

PP

ix

xei



- The relation of average velocity is as below,

- The maximum velocity is at r=0,

M W - Q ΔE


L

RgL

A

V

V

gR

V

A

x

avg

x

8

)sin-P((r)dA

R

r-1sin

L

P

4(r) From,

2

22

sinL

P

40)(r

R

r-1sin

L

P

4(r) From,

2

max

22

gR

VV

gR

V

x

x


- The relation of average and maximum velocity is as below,

M W - Q ΔE


2

;sinL

P

40)(r

; 8

)sin-P(

max

2

max

2

VV

gR

VV

L

RgLV

avg

x

avg

□ Laminar vs. turbulent

M W - Q ΔE


• Laminar: highly ordered fluid motion with smooth streamlines.

• Transitional: a flow that contains both laminar and turbulent regions

• Turbulent: highly disordered fluid motion characterized by velocity fluctuations and eddies.



□ The flow, ether laminar or turbulent, depends on

the velocity of the fluid

□ Small disturbances are damped out in low velocity

□As the velocity increases, the flow becomes unstable,

and the disturbances grow and become random

□ The analysis of turbulent flow is very difficult

- simplifying, experiments, and numerical methods

M W - Q ΔE


□ Reynolds number, Re, (Non dimension unit) is very

useful to analysis the flow of the fluid, either laminar

or, turbulent

□ Nondimensionalization has advantages as below

- Increases insight about key parameters

- Decreases number of parameters in the problem

- Easier communication

- Fewer experiments and simulations

M W - Q ΔE


□ Reynolds number, Re, is defined as below,

M W - Q ΔE


ReL),, V,(

forceviscosity

force inertialRe

22

f

VL

VL

LV char

char

char

DDG-51 Destroyer

1/20th scale model

출전: 대우건설기술연구소

Source: Fluid mechanics,

McGraw-hill, pp279

□ Nondimensionlization of flow equation in pipes,

- Nondimension parameters

M W - Q ΔE


])[munit same are and ( [-] L

pipe of ticesCharateris onalNondimensi

])/[munit same are 2

1 and

P( [-]

2

1

PP

Pressure onalNondimensi

*

222

2

*

DLD

L

sV

V

□ Nondimensionlization of flow equation in pipes,

- Introduce nondimension parameters in the equation

M W - Q ΔE


)Re( Re

6464P

)(32

2

1P

equationupper the toL and

2

1

PP introduce

)2/( 32

P

isequation flow thecase, ain pipe) (horizonal 0 if

8

)sin-P( :equation Flow

*

*

2

*2*

*

2

*

2

2

VL

DVL

D

VDLV

D

L

V

DRD

LV

L

RgLV

char

avg

avg

avg

avg

avg

avg

□ Darcy friction factor, f is defined as below

M W - Q ΔE


f) of definition thefrom( 2

P

;Re

64

pipe horizonal theof case In the

;P

2

*

*

avgV

D

Lf

f

Lf

□ The previous sections, the friction effect are

described using the conservation of momentum

□ The other expression of the friction effect is Head loss

using the first law

□ Head loss presented by distance unit [m], is very

useful to design pipe system

M W - Q ΔE

9.5 Head loss

□ Energy equation (first law) of a pipe system

M W - Q ΔE

9.5 Head loss

2112cv

2

222

21

211

cv

2

22

1

21

cv

q0

22q0

22q0

mass)unit per mean value characters (small

newtonian) and ible,imcompress state,(steasy case aIn

: lawfirst thefrom

zzg

PP

g

uu

gzVP

ugzVP

uw

gzV

hgzV

hw

ememWQE

i

icv

eicv

out

ee

in

ii

□ Energy equation (first law) of a pipe system

M W - Q ΔE

9.5 Head loss

211cv12

21121cv

q

q0

zzg

PP

g

uu

zzg

PP

g

uu

Head loss, hL

[m]Press. Head

[m]

□ Head loss includes dissipated energy within the fluid

due to friction effect

□ This causes a rise in internal energy of the fluid, and

there may be a heat transfer between the pipe and

surrounding

M W - Q ΔE

9.5 Head loss

g

uuhL

cv12 q lossHeat

□ Head loss and the Darcy friction factor, f

M W - Q ΔE

9.5 Head loss

)2

P previous In the(

2gh

h

system pipe horizonal of case In the

q from

2

2

L

1L

211cv12

avg

avg

V

D

Lf

V

D

Lf

g

P

g

PP

zzg

PP

g

uu

□Analytical solution for turbulent flows are impossible

- simplifying assumptions, numerical methods, experiments

□ There are results of experiments that can be used in

building system

□ Examples

- Colebrook equation (Moody chart)

- Petuhov equation for the smooth pipes

M W - Q ΔE


□ Colebrook equation (Moody chart)

□Modified Colebrook equation by Haaland

M W - Q ΔE

flownt in turbule Re

51.2

7.3log0.2

1

f

D

f


flownt in turbule Re

9.6

7.3log8.1

111.1

D

f

□ For the smooth pipes (ε=0) by Petkhov

M W - Q ΔE

flownt in turbule 64.1Reln79.02

f


□ In the fully developed flows (laminar or turbulent),

the friction factor, f, is constant

□ But, friction factor varies in the entrance region

□ The useful information on the entrance length, Lent,h

is offered from experiments

- Lent,h ≈0.065ReD laminar Re<2100

- Lent,h ≈4.4(Re)1/6D turbulent Re>4000

M W - Q ΔE

flownt in turbule 64.1Reln79.02

f

9.7 Entrance Effect

□ If, the components, such as pumps, fans, turbines,

and other devises, are added to the pipe system,

the first law of the pipe system is defined as below,

M W - Q ΔE

9.8 Steady flow Energy Equation

g

uuz

g

V

g

P

g

wz

g

V

g

P

ww

gzVP

ugzVP

uw

ip

pcv

icv

cv22

222

1

211

2

222

21

211

cv

q

22

working)is (pump

system the to workingis pump a that case In the

22q0

□ The work efficiency of the pump as like the previous

section, is defined as below

M W - Q ΔE

9.8 Steady flow Energy Equation

p

ideal,

p

W

W

mW

ps

pw

thermal and fluids in architectural engineering 9...

Documents