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

Convection

Dr. Jonas Allegrini

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

Convection

Flow type

4

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

Type of flow

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

What type of flow is this?

6

Type of flow

These images show the transition from laminar to turbulent flow

7

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

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

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

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

Convection

Flow type Reynolds number

12

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

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

Reynolds number

Reynolds number is connected to the type of flow:

Re < 2000 laminar

Re > 20000 turbulent 2000 < Re < 20000 transitional

νVRe L

=

15

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

Horns Rev, Denmark

Panama city, Florida

© Panhandle Helicopter/ JR Hott

© Christian Steiness 18

Convection

Flow type The Reynolds number Free and Forced convection

19

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

Convection

Flow type Reynolds number Free and Forced convection

Grashof number

21

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

Convection

Flow type Reynolds number Free and Forced convection Nusselt number

23

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

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

Convection

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

26

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

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

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

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

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

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

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

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

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

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

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

38

Air transport 1. Driving forces

2. Air permeance

• porous materials

• cracks

3. Air transport, airtightness

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

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

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 =


Definitions

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


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


44


-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


45


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


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


47

( )

+=

∗

0

0ABL

yyy

lnκ

uyU

roughness classification



48


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


49


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


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



51

y

x

Wind flow around a single building

BUILDING AERODYNAMICS

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

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

54


αhkvv m= h

mh

ksmvm

625.035.0

/10

====

α

smv /5.5= PaPw 7.12=∆

mv

10

2)(

2vCCP apipew

ρ−=∆

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

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=∆

57

ΔP

Neutral plane

Effect of stack effect

58

ΔP

Neutral plane

59

Compartment

ΔP

Neutral plane ΔP

Neutral plane

60


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 ∆+∆+∆=∆

61


2. Air permeance


• cracks


62

2. Air permeance 2.1 Porous materials

aaa Pkg ∇−=

Poiseuille’s law

ga air flow

ka air permeability

63

poreVV

matV

VVpore=0φ

open porosity


Air permeability

flow under pressure differential

aP∆

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

65


aaa Pkg ∇−= Poiseuille’s law

mass conservation t

wgdiv aa ∂

∂−=)(

0=∇∇ aa Pk

steady state

for many materials, ka is function of ΔPa

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

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

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

69


2. Air permeance


• cracks


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

71

3. Envelope airtightness Blower door test

Series ∆P [Pa] and Q [m3/s]

ΔPa=50 Pa

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 !! !

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

=

74

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

Air leakage sites

74

75

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

Air leakage

76

Localisation of air leakage sites with infrared thermography and blower door

aP∆

76

77

Infiltration at floor-wall junction

77

78

Air leakage control: sealing cracks

2

1

4

3

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

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