convection - eth zconvection 1. convection 1. flow type 2. reynolds number 3. free and forced...
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Convection
Dr. Jonas Allegrini
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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
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Convection
Flow type
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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.
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Type of flow
This figure shows the flow in a street with a pollutant source.
What type of flow is this?
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Type of flow
These images show the transition from laminar to turbulent flow
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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.
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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
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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
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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.
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Convection
Flow type Reynolds number
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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)
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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
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Reynolds number
Reynolds number is connected to the type of flow:
Re < 2000 laminar
Re > 20000 turbulent 2000 < Re < 20000 transitional
νVRe L
=
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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.
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Horns Rev, Denmark
Panama city, Florida
© Panhandle Helicopter/ JR Hott
© Christian Steiness 18
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Convection
Flow type The Reynolds number Free and Forced convection
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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.
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Convection
Flow type Reynolds number Free and Forced convection
Grashof number
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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.
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Convection
Flow type Reynolds number Free and Forced convection Nusselt number
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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
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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
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Convection
Flow type Reynolds number Free and Forced convection Nusselt number Convective thermal resistance of a cavity
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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
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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
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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
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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
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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
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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
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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
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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
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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⋅=
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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 >=
≤+=
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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]
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Air transport 1. Driving forces
2. Air permeance
• porous materials
• cracks
3. Air transport, airtightness
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1. Driving forces 1.1 wind
all slides with blue titles by Prof. Dr. Bert Blocken
1.2 stack effect
1.3 mechanical equipment
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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
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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
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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
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-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
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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
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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
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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
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( )
+=
∗
0
0ABL
yyy
lnκ
uyU
roughness classification
ABL flow over a uniformly rough, level surface
ATMOSPHERIC BOUNDARY LAYER FLOW
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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
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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
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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
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y
x
Wind flow around a single building
BUILDING AERODYNAMICS
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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
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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
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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−=∆
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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
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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=∆
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ΔP
Neutral plane
Effect of stack effect
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ΔP
Neutral plane
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Compartment
ΔP
Neutral plane ΔP
Neutral plane
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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 ∆+∆+∆=∆
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Air transport 1. Driving forces
2. Air permeance
• porous materials
• cracks
3. Air transport, airtightness
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2. Air permeance 2.1 Porous materials
aaa Pkg ∇−=
Poiseuille’s law
ga air flow
ka air permeability
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poreVV
matV
VVpore=0φ
open porosity
2. Air permeance 2.1 Porous materials
Air permeability
flow under pressure differential
aP∆
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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
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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
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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
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-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
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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
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Air transport 1. Driving forces
2. Air permeance
• porous materials
• cracks
3. Air transport, airtightness
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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
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3. Envelope airtightness Blower door test
Series ∆P [Pa] and Q [m3/s]
ΔPa=50 Pa
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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 !! !
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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
=
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For example, due to stack effect Cracks above neutral plane exfiltration Cracks below neutral plane infiltration
Air leakage sites
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Hot and humid indoor air leaking out may lead to interstitial condensation
Air leakage
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Localisation of air leakage sites with infrared thermography and blower door
aP∆
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Infiltration at floor-wall junction
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Air leakage control: sealing cracks
2
1
4
3