convection - eth zconvection 1. convection 1. flow type 2. reynolds number 3. free and forced...

78
Convection Dr. Jonas Allegrini

Upload: others

Post on 11-Mar-2020

19 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

Dr. Jonas Allegrini

Page 2: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

2

Page 3: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary layers and the convective heat transfer coefficient 7. Relations for heat transfer coefficients

2. Air transport

1. Driving forces 2. Air permeance 3. Air transport, airtightness

3

Page 4: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

Flow type

4

Page 5: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow

Smoke rising from a cigarette. For the first few centimeters, the flow remains laminar, and then becomes unstable and turbulent as the rising hot air accelerates upwards.

5

Page 6: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow

This figure shows the flow in a street with a pollutant source.

What type of flow is this?

6

Page 7: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow

These images show the transition from laminar to turbulent flow

7

Page 8: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow

Laminar flow = flow in “laminae”; layers. Smooth flow where only molecules are exchanged between the

different fluid layers

Laminar flow occurs when a fluid flows in parallel layers, with no disruption between the layers.

8

Page 9: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow

Turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes, and rapid variation of pressure and velocity in space and time.

Turbulent flow = Chaotic flow where fluid particles are exchanged between different fluid layers

9

Page 10: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow

Turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes, and rapid variation of pressure and velocity in space and time.

time

v velocity

time

10

Page 11: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow

In laminar flow viscous forces are dominant, producing a smooth, constant fluid motion

In turbulent flow inertial forces are dominant, which tend to produce random eddies, vortices and other flow instabilities.

11

Page 12: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

Flow type Reynolds number

12

Page 13: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Reynolds number

Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.

νVRe L

=

kinematic viscosity (m²/s)

mean fluid velocity (m/s)

Characteristic length (m)

13

Page 14: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Reynolds number: flow in a pipe

For pipes the characteristic length equals the hydraulic diameter equal to 4 times the surface divided by the perimeter

Consider a pipe with radius r

νVRe L

=

r2r2r4L

2

=⋅

=ππ

14

Page 15: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Reynolds number

Reynolds number is connected to the type of flow:

Re < 2000 laminar

Re > 20000 turbulent 2000 < Re < 20000 transitional

νVRe L

=

15

Page 16: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

16

Page 17: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Turbulent flow around a building

Vortex shedding.

Vortices are created at the back of the body and detach periodically from either side of the body.

17

Page 18: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Horns Rev, Denmark

Panama city, Florida

© Panhandle Helicopter/ JR Hott

© Christian Steiness 18

Page 19: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

Flow type The Reynolds number Free and Forced convection

19

Page 20: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow: forced and free convection

When the flow of gas or liquid comes from differences in density and temperature, it is called free or natural convection. The forces involved are called buoyancy forces.

When the flow of gas or liquid is

circulated by pumps or fans it is called forced convection.

20

Page 21: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

Flow type Reynolds number Free and Forced convection

Grashof number

21

Page 22: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Type of flow: forced and free convection

Grashof number Gr is a dimensionless number which gives the ratio of the buoyancy to viscous force acting on a fluid. It is used in situations involving natural convection.

22

Page 23: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

Flow type Reynolds number Free and Forced convection Nusselt number

23

Page 24: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Nusselt number

Nusselt number is the ratio of convective to conductive heat transfer across (normal to) the boundary

The convection and conduction heat

flows are perpendicular to the mean fluid flow

The conductive component is

measured under the same conditions as the heat convection but with a (hypothetically) stagnant (or motionless) fluid.

conduction

convection

qqNu =

Conductive heat flow rate W/m2K

Convective heat flow rate W/m2K

24

Page 25: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

The Nusselt number

A Nusselt number close to unity, namely convection and conduction of similar magnitude, is characteristic of laminar flow. A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100-1000 range.

conductive

convective

hhNu =

Conductive heat transfer

coefficientv

Convective heat transfer

coefficient

25

Page 26: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

Flow type Reynolds number Free and Forced convection Nusselt number Convective thermal resistance of a cavity

26

Page 27: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

The convective thermal resistance of a cavity

A cavity with a width d and filled with a gas with a thermal conductivity λ shows a Nusselt number 1.2. Determine the convective thermal resistance.

d Determine the conductive heat flow rate:

θλθ

∆=∆

=dR

qconductive

The convective heat flow rate is the given by:

θλ∆⋅=⋅=

dNuqNuq conductiveconvective

Assume Nu=1.2, λ=0.025 W/mK, d=0.05 m

27

Page 28: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

The convective thermal resistance of a cavity

The convective thermal resistance is given by

cconvective R

q θ∆=

or

λ⋅=

NudRc

Assume Nu=1.2, λ=0.025 W/mK, d=0.05 m

WKmRc /67.1025.02.1

05.0 2=⋅

=28

Page 29: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convection

Flow type Reynolds number Free and Forced convection Nusselt number The convective thermal resistance of a cavity Boundary layers and the convective heat transfer coefficient

29

Page 30: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Boundary layers and convective heat transfer coefficient

Suppose a plate is heated with a constant heat flow. We let flow air over the plate with initial temperature θfl. A boundary

layer develops and the velocity profile of the developed boundary layer is given below:

y

y=0

Velocity Profile

Flow direction

Heat flux

30

Page 31: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Boundary layer

A boundary layer is that layer of fluid in the immediate vicinity of a bounding surface.

outer layer

(fully turbulent)

inner layer (viscous effects present)

Log-law layer

Buffer layer

Linear sub-layer (viscous layer)

Linear sub-layer (viscous layer): very close to the wall: viscous effects dominate the flow

Buffer layer: intermediate layer between the linear sub-layer and the log-law layer where the viscous and turbulent effects are about equally important

Log-law layer: inertial effects are dominant over viscous effects 31

Page 32: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Boundary layers and convective heat transfer coefficient

The temperature profile in the developed boundary layer is given below and goes from a surface temperature θs to the fluid temperature θfl taken as a reference temperature

y

y=0

Temperature Profile Velocity Profile

Flow direction

Heat flux

θfl

θs 32

Page 33: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

The convective heat flow between surface and fluid

Definition of the heat transfer coefficient

)( flscc hq θθ −=

Heat flow rate W/m2

Heat transfer coefficient W/m2K

Reference temperature

fluid Surface

temperature

33

Page 34: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Convetion

Flow type The Reynolds number Free and Forced convection The Nusselt number The convective thermal resistance of a cavity Boundary layers and the convective heat transfer coefficient Relations for heat transfer coefficients

34

Page 35: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Relation between heat transfer coefficient and Nusselt number

The definition of the Nusselt number gives:

)( flscc hq θθ −= The definition of the heat transfer coefficient gives:

θλ∆⋅=

dNuqc

which gives:

dNuhc

λ⋅=

35

Page 36: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Relations for heat transfer coefficients

Forced convection

meteorological windspeed (m/s)

0

10

20

30

40

50

60

0 5 10 15 20 25

heat

tran

sfer

coe

ffic

ient

(W

/(m2 ·

K))

Ito et al. [1972] Sharples [1984] Loveday and Taki [1996]

windward side leeward side

smvvh

smvvh

c

c

/52.7

/59.36.5

78.0 >=

≤+=

36

Page 37: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

Relations for heat transfer coefficients

Free convection b

c Lah

∆=

θ

0.0

2.0

4.0

6.0

8.0

0 3 6 9 12 15 temperature difference (K)

heat

tran

sfer

coe

ffic

ient

(W

/(m2 ·

K))

Alamdari and Hammond [Eq. 4.71] Khalifa walls + radiator [Eq. 4.72]

Khalifa walls + fan [Eq. 4.73]

standard value: h c = 3.5 W/(m?·K) [NBN B62-002]

37

Page 38: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

38

Air transport 1. Driving forces

2. Air permeance

• porous materials

• cracks

3. Air transport, airtightness

Page 39: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

39

1. Driving forces 1.1 wind

all slides with blue titles by Prof. Dr. Bert Blocken

1.2 stack effect

1.3 mechanical equipment

Page 40: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

40

Wind velocity Wind velocity is a three-dimensional vector quantity (magnitude and direction).

v = v(x,y,z,t)

u = u(x,y,z,t)

v = v(x,y,z,t)

w = w(x,y,z,t)

x

y

z

v

u w

v

Wind speed and wind direction Wind speed is a scalar; the magnitude of the wind velocity vector. .

Wind direction is a scalar; the direction of the wind velocity vector.

ATMOSPHERIC BOUNDARY LAYER FLOW

Definitions

Page 41: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

41

The instantaneous wind speed is a function of space and time. It can be decomposed into a mean and a fluctuating component.

u = U + u’

v = V + v’

w = W + w’ time

u

U

u’

The mean wind speed is the average over a certain time interval.

The fluctuating component can be called “turbulence” or “turbulent fluctuation”.

A measure of the turbulence in the flow is the root mean square of the turbulent fluctuations:

u’2 ó u = Turbulent fluctuations in x-direction

Turbulent fluctuations in y-direction

Turbulent fluctuations in z-direction

v’2 ó v =

w’2 ó w =

ATMOSPHERIC BOUNDARY LAYER FLOW

Definitions

Page 42: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

42

The most often used measure for turbulence is the “turbulence intensity”, defined as:

U u’2 I u =

V v’2 I v =

W w’2 I w =

Turbulence intensity in x-direction

Turbulence intensity in y-direction

Turbulence intensity in z-direction

Definitions

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 43: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

43

-The layer where the wind is influenced by the earth’s roughness.

-The roughness causes turbulence in this layer and the typical increase of wind speed with height in the ABL

Atmospheric boundary layer

Definitions

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 44: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

44

Atmospheric boundary layer

-The layer where the wind is influenced by the earth’s roughness.

- The roughness causes turbulence in this layer and the typical increase of wind speed with height in the ABL

y

x

- Low heights: low wind speed, high turbulence intensity

- Larger heights: higher wind speed, lower turbulence intensity

wind speed

turbulence intensity

Definitions

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 45: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

45

Atmospheric boundary layer

y

x

geostrophic wind speed turbulence intensity

- ABL height is not constant: depends on the thermal conditions in the atmosphere • During the day: earth surface is heated → strong (vertical) thermal mixing occurs → the ABL height can

easily exceed 1000 m.

* During night: earth surface cools down → a stable thermal stratification results with little vertical motion, less turbulence → ABL height can be as low as 100 m. * In cloudy conditions and in strong winds, during day as well as during night, the ABL height is about 1000 m. In these situations, the thermal effects are negligible compared to the mechanical production of turbulence (due to surface friction) and the ABL is called “(thermally) neutrally stable”.

- The height where the wind speed is no longer influenced by the surface roughness = gradient height

- Wind speed at this height = gradient wind speed or geostrophic wind

Definitions

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 46: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

46

ABL flow over a uniformly rough, level surface

Vertical wind speed profile is given by log law or power law:

( )

+=

0

0ABL

yyy

lnκ

uyU

Logarithmic law U(y) is wind speed at height y u*ABL is friction “velocity”

κ is the Von Karman constant (= 0.42)

y0 is the aerodynamic roughness length

y0 = aerodynamic roughness length: a measure of the roughness of the surface. - y0 depends on the nature of the roughness elements on the surface: size, shape, orientation and spacing. - not a real height; rather an “equivalent roughness that is felt by the flow”. - “a measure of the size of the eddies at the surface”.

y

x

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 47: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

47

( )

+=

0

0ABL

yyy

lnκ

uyU

roughness classification

ABL flow over a uniformly rough, level surface

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 48: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

48

ABL flow over a uniformly rough, level surface

y0 (m) Landscape description

1 0.0002 Sea

Open sea or lake (irrespective of the wave size), tidal flat, snow-covered flat plain, featureless desert, tarmac, concrete, with a free fetch of several kilometres.

2 0.005 Smooth

Featureless land surface without any noticeable obstacles and with negligible vegetation; e.g. beaches, pack ice without large ridges, morass, and snow-covered or fallow open country.

3 0.03 Open

Level country with low vegetation (e.g. grass) and isolated obstacles with separations of at least 50 obstacle heights; e.g. grazing land without windbreaks, heather, moor and tundra, runway area of airports.

4 0.10 Roughly open

Cultivated area with regular cover of low crops, or moderately open country with occasional obstacles (e.g. low hedges, single rows of trees, isolated farms) at relative horizontal distances of at least 20 obstacle heights.

5 0.25 Rough

Recently-developed “young” landscape with high crops or crops of varying height, and scattered obstacles (e.g. dense shelterbelts, vineyards) at relative distances of about 15 obstacle heights.

6 0.50 Very rough

“Old” cultivated landscape with many rather large obstacle groups (large farms, clumps of forest) separated by open spaces of about 10 obstacle heights. Also low large vegetation with small interspaces such as bush land, orchards, young densely-planted forest.

7 1.0 Closed

Landscape totally and quite regularly covered with similar-size large obstacles, with open spaces comparable to the obstacle heights; e.g. mature regular forests, homogeneous cities or villages.

8 ≥ 2.0 Chaotic

Centres of large towns with mixture of low-rise and high-rise buildings. Also irregular large forests with many clearings.

Roughness classification by Davenport, updated by Wieringa (1992):

Fetch (upstream distance): at least 5 to 10 km !

Allows visual determination of aerodynamic roughness length

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 49: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

49

ABL flow over a uniformly rough, level surface

Log law with different values of y0

0

10

20

30

40

50

0 2 4 6 8 10

horizontal wind speed (m/s)

heig

ht a

bove

gro

und

(m) Yo = 0.0002 m

Yo = 0.005 mYo = 0.03 mYo = 0.10 mYo = 0.25 mYo = 0.50 mYo = 1.0 mYo = 2.0 m

y0

y0 y0 y0 y0 y0 y0 y0 y0

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 50: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

50

Vertical wind speed profile is given by log law or power law:

( )

+=

0

0ABL

yyy

lnκ

uyU

Log law

Power law α

refref yy

UU(y)

=

U(y) is wind speed at height y

Uref is the reference wind speed at height yref

α is the power-law exponent

A direct relation exists between y0 and α, e.g.:

y0 (m) α

_________________

0.03 0.17

1 0.28

0

10

20

30

40

50

0 5 10 15

horizontal wind speed (m/s)

heig

ht a

bove

gro

und

(m)

log lawpower law

ABL flow over a uniformly rough, level surface

ATMOSPHERIC BOUNDARY LAYER FLOW

Page 51: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

51

y

x

Wind flow around a single building

BUILDING AERODYNAMICS

Page 52: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

52

1. Flow over building

2. Oncoming flow

3. Flow from stagnation point over building

4. Flow from stagnation point around vertical building edges

5. Downflow from stagnation point

6. Standing vortex, base vortex or horseshoe vortex

7. Stagnation flow in front of building near ground level

8. Corner streams (vortex wrapping around corners)

9. Flow around building sides at ground level (adding to corner streams)

10. Recirculation flow

11. Stagnation region behind building at ground level.

12. Restored flow direction

13. Large vortices behind building

16. Small vortices in shear layer

Wind flow around a single building

BUILDING AERODYNAMICS

Page 53: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

53

1. Driving forces

1.1 wind

2

2vCP apwρ

=

0.4

-0.3

-0.2

-0.3

-0.3 2

)(2vCCP a

pipewρ

−=∆

Cp Values

Page 54: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

54

1. Driving forces 1.1 wind

αhkvv m= h

mh

ksmvm

625.035.0

/10

====

α

smv /5.5= PaPw 7.12=∆

mv

10

2)(

2vCCP apipew

ρ−=∆

Page 55: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

55

1. Driving forces Kkg

JRTR

Pa

a

aa 287, ==ρ

1.2 Stack effect

)( ieT zgP ρρ −=∆

−=∆

ia

a

ea

aT TR

PTR

PzgP

−=∆

iea

aT TTR

PzgP 11

z

( )eim

aT TzgP θθρ −=∆

1

Page 56: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

56

1. Driving forces

KkgJR

TRP

aa

aa 287, ==ρ

1.2 Stack effect

( )eim

aT TzgP θθρ −=∆

1

( ) mzmkgC aei 250³/2.120 ==°=− ρθθ

PaPT 215=∆

( ) mzmkgC aei 5.2³/2.120 ==°=− ρθθ

PaPT 15.2=∆

Page 57: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

57

ΔP

Neutral plane

Effect of stack effect

Page 58: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

58

ΔP

Neutral plane

Page 59: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

59

Compartment

ΔP

Neutral plane ΔP

Neutral plane

Page 60: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

60

1. Driving forces 1.1 wind

2)(

2vCCP apipew

ρ−=∆

KkgJR

TRP

aa

aa 287, ==ρ

1.2 Stack effect

)(1ei

maT T

zgP θθρ −=∆

MP∆

1.3 Mechanical equipment

MTWa PPPP ∆+∆+∆=∆

Page 61: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

61

Air transport 1. Driving forces

2. Air permeance

• porous materials

• cracks

3. Air transport, airtightness

Page 62: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

62

2. Air permeance 2.1 Porous materials

aaa Pkg ∇−=

Poiseuille’s law

ga air flow

ka air permeability

Page 63: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

63

poreVV

matV

VVpore=0φ

open porosity

2. Air permeance 2.1 Porous materials

Air permeability

flow under pressure differential

aP∆

Page 64: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

64

Some materials and their air permeance gypsum board with aluminum foil 12,7 mm negligible plywood, 6,4 mm 0.0084 L/s m2 at 75 Pa gypsum board, 12,7 mm 0.0091 L/s m2 at 75 Pa fiber board 11 mm 0.83 L/s m2 at 75 Pa polyurethane in panel with aluminum foil, 25 mm negligible extruded polystyrene board, 25 mm negligible foamed in place polyurethane, 25 mm negligible expansed polystyrene board, 25 mm 0.021 L/s m2 at 75 Pa fibrous insulation very high metal sheet negligible polyethylene 0.15 mm negligible spun bonded polyolefin membrane 0.96 L/s m2 at 75 Pa

Page 65: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

65

2. Air permeance 2.1 Porous materials

aaa Pkg ∇−= Poiseuille’s law

mass conservation t

wgdiv aa ∂

∂−=)(

0=∇∇ aa Pk

steady state

for many materials, ka is function of ΔPa

Page 66: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

66

exfiltration aus

infiltration ein 0

5

10

15

20

25

0 0.02 0.04 0.06 0.08 0.1

x-as (m)

tem

pera

tuur

(°C

)

Impact of air transport on temperature gradient

Page 67: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

67

-1.5

-1

-0.5

0

0.5 1

-0.001 -0.0005 0 0.0005 0.001

luchtstroomdichtheid (kg/m2s)

war

mte

stro

omdi

chth

eid

(W/m

2 s)

Conduction

Convection

total

exfiltration infiltration θ1=0°C θ2=1°C

heat

flow

air flow

Page 68: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

68

2.2 Cracks

aaa PKg ∆=

1−∆= baa PaK laminar b=1

turbulent b=0.5

2

2aa

ha

vdLfP ρ

=∆

baab

perimeterAdh 22

44+

==

a

b

L

Page 69: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

69

Air transport 1. Driving forces

2. Air permeance

• porous materials

• cracks

3. Air transport, airtightness

Page 70: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

70

3. Envelope airtightness

Airtightness of whole envelope cannot be evaluated at design stage On site evaluation only Blower door test

to evaluate airtightness at 50 Pa differential

Page 71: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

71

3. Envelope airtightness Blower door test

Series ∆P [Pa] and Q [m3/s]

ΔPa=50 Pa

Page 72: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

72

Blower door test With ΔP and Q, determination of C and n

( )nCQ 5050 =

Air flow to maintain 50Pa differential

npCQ ∆=

Q

Δp

Indication small (=1) or large (=0.5) cracks !! !

Page 73: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

73

Airtightness

Calculation

5050 ACH

volumeQ

=

House of 15 m x 15 m x 5 m = 1125 m3 air Measured air flux (Q) = 937,5 liter/second

ACH3 m 1125 x l 1000

m 1 x s/h 3600 x l/s 937,5503

3

=

Page 74: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

74

For example, due to stack effect Cracks above neutral plane exfiltration Cracks below neutral plane infiltration

Air leakage sites

74

Page 75: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

75

Hot and humid indoor air leaking out may lead to interstitial condensation

Air leakage

Page 76: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

76

Localisation of air leakage sites with infrared thermography and blower door

aP∆

76

Page 77: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

77

Infiltration at floor-wall junction

77

Page 78: Convection - ETH ZConvection 1. Convection 1. Flow type 2. Reynolds number 3. Free and forced convection 4. Nusselt number 5. The convective thermal resistance of a cavity 6. Boundary

78

Air leakage control: sealing cracks

2

1

4

3