Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW (can’t have fully developed flow)

FLAT PLATE

Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW (can’t have fully developed flow)

BLUNT OBJECT

ParadoxesPipe Flow - hydraulic engineers knew p ~ Uavg

2

- theory and capillary tube showed p ~ Uavg

Drag - theory predict no drag (1744 –d’Alembert)

- several other paradoxes for external flows as well

Shape and Flow – Irvin Shapiro

http://web.mit.edu/fluids/www/Shapiro/ncfmf.html

Fluid Dynamics of dragParts I - IV

Air speeds up to 230 mph, drag forces object in jet upwards, causing spring to extend downwards

Pressurized settling chamber underneath desk

EXPERIMENTAL SET UP

Tubing leads air from settling chamber to U-tube manometer which is calibrated in mph, so can measure drag force and speed.

Can measure U and Drag

Question #1: sketch the graph of drag on sphere vs velocity

PARADOX #1

SPHERE

0 250 MPH 125 MPH

D ~ U2

D ~ UD = 6RU

Drag lower at higher speed!

250 mph125 mph

SPHERE

Question #2: if sphere is roughened,

what happens to drag?

PARADOX #2

If pipe walls are roughened, what happens to pressure drop?

PIPE

S

R

At “low” speeds, here 120 mph, the rough sphere on the left has more drag than the smooth sphere.

R

Above a certain critical speed, here 125 mph, the rough sphere has less drag than the smooth sphere.

R

S

Question #3a: What has moredrag at “high speeds”, a

sphere or streamlined bodywith the same diameter?

PARADOX #3a

At “high speeds”, a streamlined body has less drag than a sphere with the same diameter.

Question #3b: What has moredrag at “low speeds”, a

sphere or streamlined bodywith the same diameter?

PARADOX #3b

Equal weights in air and water, although in air at “high speeds” more drag on sphere, but in glycerin

at “low speeds” more drag on streamlined body

Equal weights in air and water, in air at “high speeds”more drag on sphere, but in glycerin at “low speeds”

more drag on streamlined body

Summary of Paradoxes

(1) In the first experiment we found that sometimes an increase of speed actually produces a decrease of drag.

(2) Sometime roughening increases drag and sometime it decreases drag.

(3) Sometime streamlining increases drag and sometime it decreases drag.

(1) In the first experiment we found that sometimes an increase of speed actually produces a decrease of drag.

Laminar Boundary Layer, bdy layer separates sooner on body, bigger wake

Turbulent Boundary Layer, bdy layer separates later on body, smaller wake

Components of pressure drag (P) and skin-friction drag (V) for laminar and turbulent flows past an unstreamlined body at high Reynolds number.

Viscous forces in turbulent flowgreater than laminar,but pressure forces may be reduced enough that totaldrag goes down!

IDEAL FLOW LAMINAR FLOW TURBULENT FLOW

S e p a r a t i o n

adverse pressure gradient Laminar bdy layer Turbulent bdy layer

Momentum of fluid near surface is significantly greater in turbulent flow than laminar flow, hence turbulent flow is more resistant to separation.

Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW (can’t have fully developed flow)

Re = UD/

CD = D/( ½ U2A)

Flow patterns around smooth cylinder for different Re

CYLINDER

(2) Sometime roughening increases drag and sometime it decreases drag. Roughness causes transition to turbulence sooner, turbulent flow allows boundary layer to remain attached longer; but roughness makes skin friction higher.

LAMINAR

TURBULENT

(2) Sometime roughening increases drag and sometime it decreases drag.

For U < A, both spheres have laminar bdy layer, greater drag on rough surface

due to skin friction

For B < U both spheres have turbulent bdy

layer, greater drag on rough surface

due to skin friction

Boundary layer becomes turbulent on roughened sphere soonerthan it does for smooth sphere. Turbulent boundary layer betterat mixing high momentum outer flow with flow in boundary layer. Thus energized by outer flow, turbulent boundary layer separates further back on sphere, resulting in a smaller wake and consequently less drag (1/5th as much at optimum speeds).

230 yds50 yds

SmoothDimpled

In the early days of golf , the balls were smooth, and it was only accidentally discovered that scarred balls travel further than smooth, unscarred ones. If today’s balls are driven, say, 230 yds, a smooth ball similarly struck would travel only 50 yards. Recently golf balls have been designed with randomly spaced hexagonals with the claim of an additional 6 yards.

Smooth

Trip Flow over a sphere.

Trip: Re = 30,000(with trip wireturbulent separation)

Smooth: Re = 15,000 (laminar separation)

From Van Dyke, Album of Fluid MotionParabolic Press, 1982Original photographs by

Werle, ONERA, 1980

PIPE

FLAT PLATE

CD = D/( ½ U2A)

f = (dp/dx)D/( ½ U2)

PIPEFLAT PLATE

SMOOTH CYLINDER

SMOOTH SPHERE

SMOOTH SPHERE

(3&4) Sometime streamlining increases drag and sometime it decreases drag.

At very low Reynolds numbers viscous effects extend far from body, really no boundary layer to speak of. At higher Reynolds number there is form drag due to a pronounced wake. Streamlining will reduce the size of the wake at higher Reynolds numbers.

Glycerin:Low Re

Water:High Re

From Visualized Flow – Japanese Society of Mechanical Engineers

Viscous flow around sphere

Viscous flow around stream-

lined body

Low Re – then friction drag important, want to decrease area

High Re – then pressure drag important, want to decrease wake

Small wake

Large wake

First flight of a powered aircraft 12/17/03 120ft in 12 secondsOrville Wright at the controls

Same drag at 210 mph

The End

D ~ U2

D ~ UD = 6RU

ASIDE: do you find it odd that viscous drag does not depend on density or pressure (p = RT)?

SPHERE

“The new law that he {Maxwell ~1862} predicted seemed to defy common sense. It was that the viscosity of a gas – the internal friction that causes drag on a body that moves through it – is independent of pressure. One might expect that a more compressed gas to exert a greater drag.”

Turns out that the effect of being surrounded by more molecules is exactly cancelled out by the fact that their mean free path is less.

The Man Who Changed Everything – Basil Mahon

When very small dust particles fall through one column of air at 1 atmospheric, they fall at the same terminal

velocity as if it was 0.01 atmosphere.

Most of the drag due to skin friction, very small wake.

Most of the drag due to pressure drop, largewake.