in Architectural Engineering9. Internal flows

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1

Thermal and Fluids

in Architectural Engineering 9. Internal flows

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

Dept. of Architectural Engineering Hanyang Univ.

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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 Exchangers 15. Ideal Gas Mixtures

and Combustion

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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

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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

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Q  

ΔE 

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9.1 Introduction

□ Internal flows vs. external flows

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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

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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

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Q  

ΔE 

냉동기 온수/증기

발생기

열원설비 공기조화기

SA RA

EA OA

공기+물 중앙공조방식

Internal flows External flows

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9.2 Viscosity

□ To deal with flow frictional effect, the fundamental fluid property, viscosity has to be understood.

□ Shear stress in Solid and fluids

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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]

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9.2 Viscosity

□ Shear stress in fluids deforms the fluid, and makes velocity gradient

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-

Q  

ΔE 

Stationary plate

Moving plate

x y

δV δFt

δy

δl

δα

dy dV dt

dα y

V t

t V

y y

t



















radian) is

( )

tan(

rate deforminf







 

 



 







 



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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 F_t

dy dV dy dV











V

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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

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Q  

ΔE 

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□ No-slip on the wall

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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

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□ Velocity and Pressure difference in a pipe

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Q  

ΔE 

     









sin

0 sin

0 F

F F

0 F

ble) imcompresi state,

(steady Assumption

F

system in the

on conservati momentum

of Equation

g x, ,

x p x,

x

, ,

, x

























































 ^ ^

g m A A

P A P

g m A

A P A P

V m V

dt m dB

s e

e i i

s e

e i i

e x e i x i cv x

Fully developed flow in a inclined circle pipe

θ

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-

Q  

ΔE 

x e

i

x e

i

x x

s e

i e i

s e

e i i

dV dr g r

L P P

g r L

L dr P dV

P

dy R-y

d dy dr

dV dr dV

L r m

L r A

r A

A

g r L

P L P

g m A A

P A P









 







 



 













































































































2 sin 2

2 sin

) )

( y

- R r , (

) ,

2 ,

(

2 sin

sin

2 2



Fully developed flow in a inclined circle pipe

θ

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Q  

ΔE 

L)) P, , f(R, V

(

) P

R (

- r 1 L sin

P (r) 4

condition slip

- No introduce and

ion intergarat after

, difference pressure

and Velocity Finallly

2 sin 2

2 2













 











 



 











   









 







 



 





 









P P R g

V

dV dr

g r L

P P

i x

x e

i

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- The relation of average velocity is as below,

- The maximum velocity is at r=0,

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Q  

ΔE 

L

R gL

A V V

R g V

A x avg

x









 

8

) sin -

P ( (r)dA

R - r 1 L sin

P (r) 4

From,

2 2 2

 













 



 











 











 













 



 











 





 



 

L sin P 0) 4

(r

R - r 1 L sin

P (r) 4

From,

2 max

2 2

R g V

V

R g V

x x

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

-

Q  

ΔE 

2

; L sin

P 0) 4

(r

; 8

) sin -

P (

max

2 max

2

V V

R g V

V

L

R V gL

avg x avg











 



 



 







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□ Laminar vs. turbulent

M W

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Q  

ΔE 

9.4 Laminar and turbulent flow

• 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.

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□ 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

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Q  

ΔE 

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□ 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

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Q  

ΔE 

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□ Reynolds number, Re, is defined as below,

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Q  

ΔE 

Re L)

, , V, (

force viscosity

force inertial

Re

2 2



















f

VL VL

L

V _char

char char

DDG-51 Destroyer

1/20th scale model

출전: 대우건설기술연구소

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□ Nondimensionlization of flow equation in pipes, - Nondimension parameters

M W

-

Q  

ΔE 

]) [m unit same

are and

( [-]

L

pipe of

tices Charateris

onal Nondimensi

]) / [m unit same

2 are and 1 ( P

[-]

2

1 P P

Pressure onal

Nondimensi

*

2 2 2

2

*

D D L

L

s V

V







 

  

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□ Nondimensionlization of flow equation in pipes,

- Introduce nondimension parameters in the equation

M W

-

Q  

ΔE 

) Re

Re ( 64 64

P

) (

32 2

P 1

equation upper

the to L

and 2

1 P P

introduce

) 2 / 32 (

P

is equation flow

the case, a

in pipe) (horizonal

0 if

8

) sin -

P : (

equation Flow

*

2

*

* 2

2







 













V L L DV

D V V DL

D L V

D R D

LV

L

R V gL

char avg

avg avg

avg



 



 



 



 

 











 



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□ Darcy friction factor, f is defined as below

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Q  

ΔE 

f) of definition the

from 2 (

P Re ; 64

pipe horizonal

the of case In the

P ;

2

*

avg  V D f L f

f L

 









 

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□ 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

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ΔE 

9.5 Head loss

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□ Energy equation (first law) of a pipe system

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Q  

ΔE 

9.5 Head loss

 ₁ ₂

1 2

cv

2 2

2 1

2 1 1

cv

2 2

2 1

2 1 cv

0 q

2 q 2

0

2 q 2

0

mass) unit

per mean value characters

(small

newtonian) and

ible, imcompress

state, (steasy

case a

In

: law first the

from

z g z

P P g

u u

V gz u P

w

V gz h

w

e m e

m W

Q E

i

i cv

e i

cv

out

e e in

i i







 



 





 



  















   













   



















  













  















 ^ ^



^



^



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□ Energy equation (first law) of a pipe system

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ΔE 

9.5 Head loss

 

 ₁ ₂

cv 1 1

2

2 1

2 1 1

cv

q 0 q

z g z

P P g

u u

z g z

P P g

u u







 



 

 



 



  









 



 





 



  







Head loss, h_L [m]

Press. Head [m]

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□ 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

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ΔE 

9.5 Head loss



 



  

 g

u

h_L u² ¹ q^cv loss

Heat

(28)

□ Head loss and the Darcy friction factor, f

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ΔE 

9.5 Head loss

 

2 ) P

previous In the

(

h 2g h

system pipe

horizonal of

case In the

from q

2 2

L

1 L

2 1

1 cv

1 2

avg avg

V D f L V

D f L

g P g

P P

z g z

P P g

u u











 



 



 











 



 

 



 



  



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□ 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

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ΔE 

9.6 Fully developed turbulent flow in pipes

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□ Colebrook equation (Moody chart)

□ Modified Colebrook equation by Haaland

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Q  

ΔE 

flow nt in turbule

Re 51 . 2 7

. log 3 0 . 1 2













 







f D

f



flow nt in turbule Re

9 . 6 7

. log 3 8 . 1 1

11 . 1

















 













 



 D

f



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

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Q  

ΔE 

⁰^.⁷⁹^^ln ^Re^¹^.⁶⁴^² ^{in turbule}^nt^flow

 f

(32)

□ 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, L_ent,h is offered from experiments

- Lent,h ≈0.065ReD laminar Re<2100 - Lent,h ≈4.4(Re)^1/6D turbulent Re>4000

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Q  

ΔE 

⁰^.⁷⁹^^ln ^Re^¹^.⁶⁴^² ^{in turbule}^nt^flow

 f

9.7 Entrance Effect

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□ 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,

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-

Q  

ΔE 

9.8 Steady flow Energy Equation



 



  

























   













   







g u z u

g V g P g

z w g

V g P

w w

V gz u P

w

p i p

cv

i cv

cv 2

2 2

1 2

1 1

2 2

2 1

2 1 1

cv

q 2

2

working) is

(pump

system the

to working is

pump a

that case

In the

2 q 2

0



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□ The work efficiency of the pump as like the previous section, is defined as below

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Q  

ΔE 

9.8 Steady flow Energy Equation







p ideal ,

p

W W

m W

p s

wp

