High Lift Devices

High Lift Devices

주요 명칭

동체

수직날개

Vertical Wing

수평날개

Rudder Elevator

Flap

방향전환(1)

Rolling

Yawing

Pitching

방향전환(2)

Rolling

Yawing

Pitching

PNU ME CFD LAB.

Potential Flow of Helicopter

=0^o =60^o

=90^o =120^o =150^o

헬리콥터 비행원리(1)

헬리콥터 비행원리(2)

Cobra

Bell 끄루크

부메랑의 원리

양력증가 양력감소

부메랑 (Boomerang)

형광부메랑

새와 비행기의 날개

새 날개

곤충 날개

박쥐 날개

Sketch by Leonardo da Vinci

Leonardo da Vinci

(1452-1519) Michelangelo di Lodovico Buonarroti Simoni

(1475-1564)

Leonardo da Vinci & Michelangelo

Works by Michelangelo

천지창조(1510)

아담의 창조이브의 창조

Works by Michelangelo

Works by Michelangelo

최후의 심판(Hymns of Advent) 1537-1541 다윗상

David(1501-1504)

designed by Michelangelo

Works by Leonardo da Vinci (1452-1519)

Mona Lisa (1503–1505/1507) Virgin and Child(1487?)

Works by Leonardo da Vinci (1452-1519)

The Last Supper (1498)

“da Vinci Code”

Leonardo da Vinci

Airplane

Helicopter

Automobile

Tank

Parachute

Machine Gun

Leonardo da Vinci

Leonardo da Vinci

Leonardo da Vinci

Leonardo da Vinci

날개이론의 응용(1)

날개이론의 응용(2)

수중 익선

골프공의 원리

항력증가, 비행거리 감소 항력감소, 비행거리 증가

수영의 원리(1)

부력

항력 증가

항력 감소

수영의 원리(2)

수영의 원리(3)

항력증가 항력감소

 For flows of liquids, the severe decrease in pressure may

result in cavitation, when the liquid pressure is reduced to the vapor pressure.

 The cavitation is a cause of severe noise and vibration, and erosion on the propeller surface.

Ex. 3.10

Gage Pressure

P₂ decreases as z₂ increases.

3.6.3 Flowrate Measurement

- Bernoulli Eq :

- Continuity Eq :

2 2 2

2 1

1

V

2 p 1

2 V

p

1

2 1 2

1 V

A V  A

Subst.

- Volume Flow Rate :

- Therefore, for a given flow geometry (A1 and A2) the flow rate can be determined if the pressure difference, pp1-p2, is measured.

 

 





2 1

2 1

2

A A

p V p



 



Ex. 3.11

2 2 2

2 1

1 V

2 p 1

2 V

p  1    

2 1 2

1 V

A V  A

- Bernoulli :

- Continuity :

 Sluice Gate:

Assume that the velocity profiles are uniform sufficiently upstream and downstream of the gate.

- Bernoulli :

- Continuity : Or,

Hence,

  ²

2 2 0

2 1

2 1 0

1 V z

2 p 1

z 2 V

p  1        





2 2 1

1

V A V

A

Q  

2 2 1

1

V bz V

bz 

 





2

1 z z

z z

g b 2

z

Q

 

- In the limit of ,

2

1

z

z 

 

   

  

1 2

2 1

2 1 2

2 1

2 1

2 1 2 1

2 2 1 2

2 1

2

2

2 2

1 2

2 1

gz b

z

z z

b gz z z

z z

z

z z z

b g z z

z

z z

b g z Q

z z 



 





 



 

 





2

1 z z

z z

g b 2

z

Q 

 

- This limiting result represents the fact that if , the kinetic energy of the fluid upstream of the gate is

negligible and the fluid velocity after it has fallen a distance is approximately .

- Because the fluid can not turn a sharp 90^o corner, the phenomena of vena contracta is generated and z₁a.

- The coefficient of contraction, C_c=z₂/a, is typically 0.62 for a/z₁<0.2.

2

1

z

z 

1 2

1

z z

z  

Ex. 3.12

Z₁=

a=

 Weir :

We would expect the average velocity across the top of the weir to be proportional to . 2gH

2 / 3 1

1

1

A 2 gH C Hb 2 gH C b 2 g H

C

Q   

where C₁ is constant, determined by the experiment.

Ex. 3.13

3.7 The Energy Line and the Hydraulic Grade Line

 For steady, inviscid, incompressible flow the total energy remains constant along a streamline.

  p z  H  constant on a streamline g

2 V

Head T otal

Head Piezometer

Head Elevation Head

Pressure Head

Velocity

2

  

 











- The difference between the energy line (EL) and the hydraulic grade line (HGL) is the velocity head.

3.8 Restriction on Use of the Bernoulli Equation

 Compressibility Effects:

- If assuming that the flow is isothermal along the streamline, .

const gz

2 V 1

dp  ₂  



streamline along

constant z

2 V

p  1 ²   

If the fluid is incompressible

const gz

2V 1 p

RT dp

gz 2 V

1 RT / p dp

gz 2V

1 dp

2 const

T

2 RT

p 2

















 













2 2

2 2

1 1

2

1 z

g 2 V p

ln p g z RT g

2

V   

 



  Thus, 

- If assuming that the flow is isentropic of a perfect gas, const

gz 2V

dp 1 p

C

gz 2V

1

dp ^p ₂

p

k / 1 1/k

p C

2 ²

k 1 / 1 k /

1   





 





const V gz

k p

C ^k  ^k   



 













2 1

/ 1

1 1/ 1 ² /

1

const 2 gz

p V 1 k C k

2 k

/ 1 1 k

/

1    



 









const 2 gz

p V 1 k

k

p ^1/k _{1 1/k} ²

k    



 





 



 









const 2 gz

V p 1 k

k  ²  





 







2 2

2 2

2 1

2 1 1

1 gz

2 V p

1 k gz k

2 V p

1 k

k  





 





 



 



 



 Thus, 

0.3 Incompressible

V = 335 ft/sec

= 228mph

= 102m/s

= 367km/h.

 Unsteady Effects:

Return to F=ma along the streamline

Thus,

By the way, since

 ^s

ds / dz

s Vol ( Vol)a

s sin p

F   

 







 













0 dz dp

ds

a_s    



s V V t V t

s s V t

t t V dt

) s , t ( a_s dV



 



 







 







 



0 2 dz

d V dp

t ds

V ²   

 



 



 



Therefore,

2 2

2 2

s 1 s

2 1

1 V z

2 p 1

t ds z V

2 V

p 1 ²

1









 

 













(along a streamline in the incompressible inviscid flows)

Ex. 3.16

2 2

2 2

s s

1 2

1 1

z 2 V

p 1 t ds

V

z 2 V

p 1

2

1









 

 













 Rotational Effects:

- Another restriction of the Bernoulli equation is that it is only applicable along the streamline.

- In general, the Bernoulli constant varies from streamline to streamline.

- However, under certain restrictions this constant is the same throughout the entire flow field

“Irrotational” Flow Field

 Viscous Effects:

  V gz  const.

2 1 p

Energy Potential

Energy Kinetic

2

potential.

of concept

in the elevation high

similar to is

pressure

high Because energy.

like - potential as

Acts

work.

flow to ude

Energy Pressure





 



effects viscous

the to due

loss energy

L 2

2 2 2

2 1

2 1 1

1

V gz gh

2 p 1

gz 2 V

p 1







 





 

(h_L:head loss)

(For viscous Flow)



2 2 2

2

input energy

mechanical in 1

2 1 1

1

V gz gh

2 p 1

E gz

2 V p 1





 







 