Chapter 11BW.ppt [호환 모드] - CNU FINCLfincl.cnu.ac.kr/lecture/shiphydrodynamics/Chapter_11BW.pdf · NACA2412 0.2524 L C = 0.0002 D C = 0.0003 D C = Chapter 11: Flow over bodies;

Chapter 11. Flow over bodies; Lift & Dragp ; g

Prof. Byoung-Kwon Ahn

bkahn@cnu ac kr http//fincl cnu ac [email protected] http//fincl.cnu.ac.kr

Dept. of Naval Architecture & Ocean EngineeringCollege of Engineering, Chungnam National University

11.1 Introduction

1) Flow over bodies (External flows): aircrafts, automobiles, buildings, ships, submarines, turbo-machines, etc. , ,

2) Fuel economy, speed, acceleration, maneuverability, stability, and control are directly related to the aerodynamic/hydrodynamic forces and moments.

3) General 6DOF motion of bodies is described by 6 equations for the linear3) General 6DOF motion of bodies is described by 6 equations for the linear (surge, heave, sway) and angular (roll, pitch, yaw) momentum.

4) Objects of this chapter: to understand the fundamentals of flow over bodies and calculate the drag and lift forces acting on bodies

pitch

bodies, and calculate the drag and lift forces acting on bodies.

ysway

x rollsurge h

yawShips in waves: 6DOF ti

Chapter 11: Flow over bodies; Lift & DragShip Hydrodynamics 2

zsurge heave 6DOF motion

11.1 Introduction

1) Classifications of the flow over bodies: ① 2D Flow: body is very long and of constant cross ① y y g

section and the flow is normal to the body.

② Axisymmetric Flow: body possesses rotational symmetry about an axis in the flow direction.

③ 3D Flow: body that cannot be modeled as above two cases.

④ Incompressible and Compressible Flows:

2) Streamlined body: align the body shape with the anticipated streamlines in the flow


11.2 Drag and Lift

1) Fluid dynamic forces are due to pressure and viscous forces acting on the body surfaceviscous forces acting on the body surface.

① Drag: component parallel to flow direction.

② Lift: component normal to flow direction.

2) Lift and drag forces can be found by integrating pressure and wall-shear stress.

( cos sin )F dF P dAθ τ θ+∫ ∫ ( cos sin )

( sin cos )

D D w

A A

F dF P dA

F dF P dA

θ τ θ

θ τ θ

= = − +

= = − −

∫ ∫

∫ ∫ ( sin cos )L L w

A A

F dF P dAθ τ θ= =∫ ∫


11.2 Drag and Lift

1) Drag and Lift forces are a function of velocity and density:and density:

& ( , )L DF F f V ρ=

2) Dimensional analysis gives 2 dimensionless parameters:

① Drag coefficient: 21/ 2D

D

FC

V Aρ=

0

1 SL

D DxC C dxL

= ∫

② Lift coefficient:2

1/ 2

1/ 2L

L

V A

FC

V A

ρ

ρ=

0

0

1 S

S

L

L LxS

L

C C dxL

=

∫

∫

Average

3) Area (A) can be frontal area (drag applications), planform area (wing aerodynamics), or wetted-surface area (ship hydrodynamics).

S

4) The Drag and Lift coefficients are primarily functions of the shape of the body, but in some cases they also depend on the Reynolds number and the surface roughness.


11.2 Drag and Lift: Example (Drag)

Blunt body (Scion xB) Streamlined body (Porsche 911)

21.0 2.25mDC A= =20.28 0.9mDC A= =

22.25mDC A =20.252mDC A =

1) Drag force for Scion is about 10 times larger th th t f P h b f l C

2(1/ 2 )D DF C A Vρ= ×than that of Porsche because of large CDand large projected area (A).

2) Power consumption is proportional to V3

( )D D ρ

31/ 2 ( )D DP F V V C Aρ= =


D D

11.3 Drag: Friction and Pressure Drag

1) Fluid dynamic drag forces are comprised of pressure and friction effectspressure and friction effects.① Skin Friction Drag (Viscous Drag)② Pressure Drag (Form Drag)

( ) ( )D D friction D pressureF F F

C C C

= +

( ) ( )D D friction D pressureC C C= +

Friction drag Pressure drag Friction & pressure drag


Friction drag Pressure drag Friction & pressure drag

11.3.1 Reducing Drag by Streamlining

1) Streamlining reduces drag by reducing FD(pressure) at the cost of increasing wetted D(pressure) gsurface area and FD(friction)

2) Goal is to eliminate flow separation and minimize total drag FDg D

3) Also improves structural acoustics since separation and vortex shedding can excite structural modes.excite structural modes.


11.3.1 Reducing Drag by Streamlining

The variation of friction pressure and total Th i i f h d ffi i fThe variation of friction, pressure and total drag coefficients of a streamlined airfoil with thickness-to-chord length ratio for Re=4x104

The variation of the drag coefficient of a long elliptical cylinder with aspect ratio.


11.3.2 Flow Separation

Separation point

Wake region The Location of the separation point depends on several factors such as Reynolds number, the surface roughness, and the level of fluctuations in the free stream.

Shedding vortex

At large angles of attack (usually larger than 15°), flow may separate completely from the top surface of an airfoil reducing lift drastically and causing the airfoil to stall.


11.4 CD of Common Geometries

1) For many geometries, total drag CD is constant for Re > 104

2) C can be very dependent upon orientation of body2) CD can be very dependent upon orientation of body.

3) 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

th ti l ( li PDE' ) f th f d i thimathematical reason (e.g., linear PDE's) for the success of doing this.


11.4 CD of Common Geometries


11.5 Flow over Flat Plate

5 =5 10ex

VxR

ν= × 63 10×ν

1) Boundary layer thickness (δ): 0.99u V=1) Boundary layer thickness (δ):

2) Viscous sub-layer: very thin layer next to the wall where viscous effects are dominant.

3) Drag on flat plate is solely due to friction created by laminar transitional

0.99u V

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

2( ) 1/ 2D D friction f D f fC C C F F C A Vρ= = → = =


( )D D friction f D f f ρ

11.5.2 Friction Coefficient

1) Local friction coefficient

① Laminar: ② Turbulent:

1/2 1/2

4.91 0.664 f x

xC

R Rδ = =

1/ 5 1/ 5

0.38 0.059 f x

xC

R Rδ = =

2) Average friction coefficient:

,1/2 1/2f xex exR R

, ,0

1 L

f x f xC C dxL

= ∫

,1/ 5 1/ 5f xex exR R

① Laminar: ② Turbulent:L

51/ 2

1.33 5 10f eLC R= < × 5 7

1/ 5

0.074 5 10 10f eLC R= × ≤ ≤

3) For some cases, plate is long enough for turbulent flow, but not long

1/ 2f eLeLR 1/ 5f eL

eLR

enough to neglect laminar portion

( ), ,lam , ,tur 1/ 50

1 0.074 1742

crx L

f f x f x fxC C dx C dx C

L R R= + → = −∫ ∫


( )0 crxeL eLL R R∫ ∫

11.6 Flow over Cylinders & Spheres

D

D

/R VD υ=


/eR VD υ=

11.6.1 Flow over Cylinders & Spheres

1) Flow is strong function of Re.

2) The delay of separation in turbulent flow enables the TBL (turbulent2) The delay of separation in turbulent flow enables the TBL (turbulent boundary layer) to travel father along the surface, resulting in a narrow wake and a smaller pressure drag (adverse pressure gradient).

3) Thi i i t t t t li d b di hi h i i i3) This is in contrast to streamlined bodies, which experience an increase in drag coefficient due to friction drag.

Re=15,000 (Laminar) θsep ≈ 80º Re=30,000 (Turbulent) θsep ≈ 140º


Re 15,000 (Laminar) θsep 80 Re 30,000 (Turbulent) θsep 140

11.6.2 Effect of Surface Roughness


11.7 Lift

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

2) Lift coefficient:

3) A=bc is the planform area

4) Aspect Ratio (AR) = b/c

Leading Edge

Trailing Edge


11.7.1 Wing Sections

1) NACA (National Advisory Committee for Aeronautics)

2) NACA 4 Digit Wing Section:2) NACA 4-Digit Wing Section:

Maximum Thickness (12% of the Chord)NACA4412

Maximum Thickness (12% of the Chord)Location of the maximum Camber (40% of the Chord)Maximum Camber (4% of the Chord)

NACA0012

Camber Line0.0

LE

1.0

TE

0.5

Suction side (Back)

NACA4412

Pressure side (Face)


Chord Line

11.7.3 Effect of Angle of Attack & Foil Shape

1) Thin-foil theory shows that CL≈2πα for α < αstall

2) Therefore lift increases linearly with α2) Therefore, lift increases linearly with α3) Objective for most applications is to achieve

maximum Lift-to-Drag ratio (CL/CD) ratio.

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

Thickness and camber influences pressure distribution and location of flow separation.


11.7.4 Irrotational & actual flow past airfoils

+ =+

1) Potential-Flow approximation gives accurate CL for angles of attack below stall: boundary layer can be neglected.

2) Kutta condition required at trailing edge: fixes stagnation pt at TE.


11.7.5 CL resulted from Potential Flow Theory

S1223

1.5236LC =NACA0012

0.0000LC =0.0026DC = −0.0003DC =

RONCZ

0.0298LC =NACA2412

0.2524LC =0.0002DC =0.0003DC =


11.7.6 Increasing Lift by using Flaps

A Flap airfoil with a slot can delay the separation and increase the liftp

NACA 5-Digit Wing SectionNACA 5 Digit Wing Section

NACA23012Max. Camber: 2%

D i C 0 3 (2 3/2 1/10)Design CL: 0.3 (2x3/2x1/10)

Max. Camber Location: 15%(30/2)

Maximum Thickness: 12%


Flaps extended (takeoff) Flaps retracted (cruising)

11.7.7 Increasing Lift by reducing Tip Vortices

1) Tip vortex created by leakage of flow from high-pressure side to low-pressure side of wing.g

2) Tip vortices from heavy aircraft persist far downstream and pose danger to light aircraft. Also sets takeoff and landing separation at busy airports.

3) Tip effects can be reduced by attaching endplates or winglets3) Tip effects can be reduced by attaching endplates or winglets.

Even though 0.1% reduction of the I d d DInduced Drag

2 2

A spect R atio:

b b bA R = = =

A bc c


A bc c

11.7.7 Wing In Ground effect (WIG) craft



NACA4412 NACA0012






11.7.8 Lift Generated by Spinning

1) Lift (CL) strongly depends on rate of rotation.

2) The effect of rate of rotation on CD is small.

3) Baseball, golf, soccer, tennis players utilize spin.

4) Magnus Effect: Lift generated by rotation.) g g y


Ex) Lift & Drag of a Commercial Airplane

• W=70,000kg, A=150m2, Altitute=1.2km, V=558km/h, NACA23012 Wing section• Assumption: no fuselage and other drags, no tip effectsD t iDetermine1) Minimum speed for takeoff & landing w/ and w/o extending the flaps.2) Angle of attack to cruise steadily.3) Power to thrust overcoming wing drag.

m1-safe m1

by FAA safety rule

w/o Flaps: 85.1m/s=306km/h1.2V V= =×

m2-safe

2

m2

2

w/ Flaps: 56.2m/s=202km/h

686,7001.22

1/ 2 1/ 2( )(155) (150)

1.2

0.312L

L

V

F

V

CV Aρ

= =

= = =

×

70,000 9.81 686.7kN

558/3 6 155m/s

W mg

V

= = × == =

2

1.22 2 11

1 1( ) (0.

2.03 3

20D

L

D C

C

F V A

πα α

ρ

= =

= =

→ ≈

212)(155) (150) 16.9kN

P Th t V l it (16 9)(155) 2 620kWF V

=

2m m

m1 m1

558/3.6 155m/s

1/ 2

w/o Flaps: 2 / 2(686,700) /(1.2)( )(150) 70.9m/s=255km/h1.52

L L

L

V

F W C V A

V W AC

ρ

ρ

= =

= =

= = =

Power=Thrust Velocity= (16.9)(155) 2,620kWDF V× = =


m2m2w/ Flaps: 2 / 2(686,700) /(1.2)( )(150) 46.8m/s=168km/h3.48LV W ACρ= = =

Documents

Chapter 11BW.ppt [호환 모드] - CNU FINCLfincl.cnu.ac.kr/lecture/shiphydrodynamics/Chapter_11BW.pdf · NACA2412 0.2524 L C = 0.0002 D C = 0.0003 D C = Chapter 11: Flow over bodies;