Local loss coefficients inside air cavity of ventilated pitched roofs

Abstract

Pitched roofs with a ventilated air cavity to avoid snow melt and ensure dry conditions beneath the roofing are a widely used construction in northern parts of Europe and America. The purpose of this study has been to determine pressure losses at the inlet (eaves) and inside the air cavity consisting of friction losses and passing of tile battens. These results are necessary to increase the accuracy of ventilation calculations of pitched roofs. Laboratory measurements, numerical analysis as well as calculations by use of empirical expressions have been used in the study. A large difference in the local loss coefficients depending on the edge design and height of the tile batten was found. The local loss coefficients of the round-edged tile battens were approximately 40% lower than the local loss coefficients of the sharp-edged tile battens. Furthermore, the local loss factor increased by increasing height of the tile batten. The numerical analysis was found to reliably reproduce the results from the measurements.

Full text

Local loss coefficients inside air cavity of ventilated
pitched roofs

Lars Gullbrekken1, Sivert Uvsløkk2, Stig Geving1 and Tore Kvande1
Abstract
Pitched roofs with a ventilated air cavity to avoid snow melt and ensure dry conditions
beneath the roofing is a widely used construction in northern parts of Europe and America.
The purpose of this study has been to determine pressure losses at the inlet (eaves) and
inside the air cavity consisting of friction losses and passing of tile battens. These results
are necessary to increase the accuracy of ventilation calculations of pitched roofs.
Laboratory measurements, numerical analysis as well as calculations by use of empirical
expressions have been used in the study.
A large difference in the local loss coefficients depending on the edge design and height of
the tile batten was found. The local loss coefficients of the round-edged tile battens was
approximately 40 % lower than the local loss coefficients of the sharp-edged tile battens.
Further, the local loss factor increased by increasing height of the tile batten. The numerical
analysis was found to reliably reproduce the results from the measurements.
Keywords
Laboratory measurements, local loss coefficients, COMSOL, roofing ventilation, air
cavity, tile batten
Introduction
Ventilated pitched roofs are currently a widely used construction for residential and non-
residential buildings in northern parts of Europe and America. The air cavity beneath the
roofing is ventilated to ensure dry conditions for the roof construction and keep the roofing
temperature low enough to avoid snow melt. The construction is of special interest
regarding the dry-out capacity in roofs with load-bearing systems of wood. When built in
line with the guidelines given by Roels and Langmans (2016), Uvsløkk (1996), and
Edvardsen and Ramstad (2014), ventilated pitched wooden roofs can be considered a
robust roof design. However, there are well-known degradation issues related to snow melt
and mould growth. Tobiasson et al. (1994) studied icing problems in northern America,

1Department of Civil and Environmental Engineering, Norwegian University of Science and Technology (NTNU),
Trondheim, Norway
2Department of Materials and Structures, SINTEF Building and Infrastructure, SINTEF, Trondheim, Norway.
Corresponding author:
Lars Gullbrekken, Norwegian University of Science and Technology (NTNU), Høgskoleringen 7 A 7046,
Trondheim, Norway.
Email: lars.gullbrekken@sintef.no

and they reported that the icing problems of several buildings in northern New York were
reduced by increasing the ventilation of the attics so that the temperature inside the attics
was below -1 °C when the external temperature was -5.5 °C. Measurements performed in
Canada by Walker and Forest (1995) showed that attic ventilation was mainly driven by
wind and that the ventilation increased by increasing wind speeds. The problem with snow
melt on roofs is reduced in modern well-insulated roofs with well-ventilated roofing
(Geving, 2011).
In the Nordic countries, the moisture conditions inside cold ventilated attics have
been studied. In Sweden, Samuelson (1998) found that a reduction in the ventilation of the
attics caused a drier climate inside the attic. However, the calculations assumed a totally
airtight ceiling structure beneath the attic. In Norway, Blom (2001) conducted field
measurements and calculations of ventilation of pitched wooden roofs with cold attics.
Blom found that a 48 mm high air cavity was appropriate in pitched, ventilated single-
family houses. Blom also pointed out that a key factor in moisture-safe constructions is to
ensure continuous thermal insulation and avoid air leakages through the insulation.
The current Norwegian guidelines for pitched roofs as given by Edvardsen and
Ramstad (2014) are too simplified. In particular, there are no common guidelines for roof
constructions with low angles, complicated roof design, roof spans longer than 7.5 m and
roofs with building-integrated photovoltaics (BIPV).
The driving forces given by wind and temperature differences (natural convection)
together with the calculated pressure losses in the air cavity below the roofing define the
ventilation rate of pitched wooden roofs. Important input parameters required to calculate
the wind-driven ventilation of pitched roofs include wind speed together with the
difference in wind pressure coefficient, cp, at the inlet and the outlet of the ventilation cavity
(see Figure 1). Pressure losses in the roof system including where the air passes (hereafter
called “passing”) the inlet and outlet, passing of tile battens and friction losses are
calculated based on the input data. The accuracy of these calculations obviously depends
on the accuracy of the local loss coefficients for the passing of the inlet, tile battens and
outlet.
The purpose of this study has been to determine pressure losses at the inlet (eaves)
and inside the air cavity consisting of friction losses and passing of tile battens.
Figure 1. Important input parameters to calculate the wind-driven ventilation of pitched
wooden roofs include wind speed together with the difference in wind pressure

coefficient, cp, at the inlet and outlet of the ventilation cavity as well as local losses inside
the air cavity.
Theoretical framework
The air flow through the air cavity system V
(m³/h) can be expressed by eq. (1), where the
air flow is proportional to the driving forces of roof ventilation, p

(Pa), given by the
driving forces of wind and buoyancy. The air flow is inversely proportional to the sum of
pressure losses through the air cavity system, R(Pa), in the following treated as friction
loss and local losses.
1
Vp
R


 (1)
Pressure losses and velocity profiles of pipes and air channels have previously been studied
both theoretically and experimentally. The extensive work has led to empirical expressions
for accurately calculating the pressure loss given well-defined flow situations, see e.g.
(Hansen et al., 2013).
The Reynolds number indicates whether a flow is laminar or turbulent: small
Reynolds numbers give laminar flow while large numbers give turbulent flow. The critical
Reynolds number gives the value of the Reynolds number for the transition from laminar
to turbulent flow. The size of the critical Reynolds number is dependent on the flow
characteristics, sharp edges and change in velocity. For most flows, the critical Reynolds
number is 2300 (Hansen et al., 2013).
Re h
uD


 (2)
Re is the Reynolds number (-), uis the average velocity (m/s), h
D is the hydraulic
diameter (m) of the flow channel and

is the kinematic viscosity (m²/s).
Friction loss
The pressure loss gradient (Pa/m),
p

inside a channel is dependent on the dynamic
pressure d
p
(Pa), the hydraulic diameter h
D (m) and the friction number

(-).
d
h
p
pD

 (3)
The dynamic pressure, d
p
(Pa), is given by:
2
1
2
dm
p
u

 (4)
Where

is the density of the air (kg/m³) and m
uis the average air velocity (m/s).
The hydraulic diameter, h
D(m), is given by:
2
h
ab
Dab

 (5)
Where a and bare the side lengths of the rectangular air channel (m).

For laminar flow, the friction number

(-) is inversely proportional with the Reynolds
number, Re.
64
Re

 (6)
Local losses
Pressure losses in components like valves and bends are called local losses. Flow
characteristics can be studied by applying established equations from fluid mechanics.
Local pressure loss is given by the local loss coefficient, see eq. (7) and (8). For

=0 the
local loss is zero and for

=1 the local loss is equal to the dynamic pressure. At steady
state, the driving forces are balanced by the pressure loss from friction and the pressure
loss of the different minor losses along the flow path.
2
2
m
u
P



 (7)
2
2
m
P
u


 (8)
Where Pis the pressure loss (Pa),

is the minor loss coefficient (-),

is the density of
the air (kg/m³), m
uis the average velocity (m/s). m
uis given by the airflow Q(m³/s) divided
by the area of the smallest cross-section of the flow path A(m²).
Narrowing of the flow channel
The pressure loss in a narrowing cross-sectional flow area is caused by a contraction of the
flow after the narrowing, given by the contraction factor

(see equation 10 (Hansen et al.,
2013) and Figure 2).
2
1
11





(9)
0
2


 (10)
Figure 2. Pressure loss when there is a sharp decrease in the cross-sectional flow area.

Contraction of the flow channel
Pressure loss when there is a sharp increase in the cross-sectional flow area can be
calculated using eq. 11, giving the local pressure loss as a function of the cross-sectional
area before and after the component (Hansen et al., 2013), see Figure 3.
1
2
2
1







(11)
Figure 3. Pressure loss when there is a sharp increase in the cross-sectional flow area.
The total local loss given by the local loss by contraction of the channel, 1

(-), and local
loss by narrowing of the channels, 2

(-), can be calculated using eq. (12).
12


 (12)
Previous research
In a laboratory study, Thiis et al. (2007) studied different roof eave designs and their inlet
geometry in order to specify the ability to reduce snow penetration into the roof. The
geometry and design of the ventilation openings was found to be the most important factor
in reducing snow penetration. An inlet position close to the wall was found to give
approximately 5 times more snow concentration of the air entering the roof cavity
compared to a position close to the end of the eave.
Idelchik (1994) contains a systematization and classification of data of hydraulic
resistances from a large number of experimental studies carried out and published at
different times in different countries.
Kronvall (1980) conducted measurements of airflow in building components and
showed how the concept of fluid mechanics could be applied to airflow in building
components. He also studied pressure losses at the entrance and bends in duct flows.
Later, Hofseth (2004) studied airflows in ventilated roof structures. As part of his
work, he performed laboratory measurements of local losses of building components
located inside the air cavity of the roof. He found that the local loss coefficient was
dependent on the mass flow.
Falk and Sandin (2013) also performed laboratory measurements to estimate loss
factors of metal battens inside ventilated wall cavities. They found that several of the loss
factors were dependent on the air velocity.

Methods
The method includes both a laboratory investigation on a large-scale test model of a pitched
wooden roof and numerical analysis using COMSOL software.
Laboratory test model
A large-scale test model of the ventilation air gap of a pitched roof was built in the SINTEF
and NTNU laboratory in Trondheim, Norway. The model consisted of an aluminium
profile with a length of 3550 mm and an internal width of 552 mm (see Figure 4). As shown
in Figure 4, the width of the box corresponds to the air gap between two counter battens
with a width of 48 mm and a centre-to-centre distance of 600 mm, which is a typical
situation in a ventilated wooden roof. As seen in Figure 5 and Figure 6, the total length of
the roof test model was 3550 mm and included a total of 11 tile battens with a centre-to-
centre distance of 350 mm. Nine air pressure nipples were positioned in the top of the box,
as seen in Figure 6.
a) b)
Figure 4. a) Cross-section of a typical roof construction with roofing tiles. b) A cross-
section of the test model consisting of an aluminium box corresponding to the air gap
between two counter battens with a width of 48 mm and a centre-to-centre distance of
600 mm. The center to center distance of the tile battens are 350 mm
The airflow through the roof structure is measured by a laminar flow meter which is
attached to a fan that sucks air through the ventilation gap system. In order to measure the
pressure differences, four pressure transmitters (Furness Controls FCO 352 Model 1) were
used. The pressure difference was recorded with a data logger (Delphin Technology Expert
Key 100C) with a logger interval of 1 Hz (see Figure 5). Each measuring step lasted
approximately 120 s. The accuracy and measuring range of the applied instruments are
given in Table 1.
Table 1: Accuracy and measuring range of applied sensors
Sensor Manufacturer Type Accuracy Range
Thermocouple Type T ±0.10 °C -20–+60 °C
Pressure transmitter
Folding rule
Furness Control FCO 352 Model 1
±0.25 % of
reading
±0.5 mm
0–+50 Pa
0–2000 mm

Figure 5. A large-scale test model of a pitched roof.
Positionofmeasuringequipment
Fan“Bypass system” Laminarflow
meter
Positionoffilter
Commutator
transformer
Pressuretransformers

Figure 6. Cross-section of the test model, with ten air pressure monitor positions. The
figures for the air pressure difference of the two points with circles, divided by the
number of tile batten passings, which is nine, are used as input in eq. (8).
Test procedure
The range of the air gap, height of the air cavity and center-to-center distance of the tile
batten was determined by an investigation into the Norwegian building traditions
described in Edvardsen and Ramstad (2014). In order to obtain as realistic measurements
as possible the results a field investigation of air velocity inside the air cavity of a roof
was studied (Gullbrekken 2017). He reported air velocity inside the air cavity for
different seasons/periods as a function of wind speed at 10 m above ground level. The
reported air velocity inside the air cavity was 0-1.2 m/s. The results were in line with a
previous and corresponding investigation reported by Blom (1990). In addition, an
important aspect was to choose air velocities that produced measurable static air pressure
difference when passing battens. Simple calculations by use of eq. (9-12) was performed
in order to predict the pressure difference.
The test procedure was performed by installation of tile battens in the measuring
rig, as showed in Figure 6. Then, the correct height of the air cavity beneath the tile
batten was adjusted (23, 36 or 48 mm). The air flow was adjusted in order to fit the
dynamic pressures of 0.05, 0.10, 0.20, 0.40 Pa. This implies an increasing airflow by
increasing height of the air cavity beneath the tile battens. A specific air flow was held
constant in 30 s and the data was logged with 1Hz logging interval. Then, a new air flow
was set and held constant in 30 s and so on.
Table 2 Test parameters, the chosen parameters and the reference to the chosen
parameters.
Test parameters Chosen parameters Reference
Height of the air gap 23, 36, 48 (mm) Edvardsen and Ramstad (2014)
Height of tile battens 30, 36, 48 (mm) Edvardsen and Ramstad (2014)
Center to center distance tile battens 350 (mm) Edvardsen and Ramstad (2014)
Air velocity below tile battens
(corresponding dynamic pressure) (Pa)
0.20, 0.40, 0.60, 0.80 (m/s) Gullbrekken (2017), Blom (1990)
Airflow

Different design of the eave
In order to study the local pressure loss coefficient at the inlet of the ventilation cavity,
we studied two different eave design solutions.
Classic design
A classic air inlet design in Norway has one or several air gaps in the horizontal part of
the eave construction (see Figure 7 a)). The laboratory investigation included
measurements of local loss coefficients given one air gap with a width of 50 mm with and
without installation of a fly net with an opening area of 67 % covering the gap opening.
Modern design
Stricter requirements regarding airtightness of buildings necessitates a continuous wind
barrier between wall and roof, as seen in Figure 7 b). In this case, the air inlet of the roof
ventilation system is a 25 mm wide air gap behind the gutter. The laboratory
investigation included measurements of local loss coefficients with and without a fly net
covering the gap opening. The fly net had an opening area of 67 %.
a) b)
Figure 7. The two different eaves designs. a) A classic solution with one air gap behind
the gutter board. b) a newer design with the air gap located between the gutter and the
gutter board.
Airtightness of the laboratory test model
Initially, the airtightness of the test model was measured. The joints between the aluminium
box and the rest of the test rig were sealed using tape. In addition, the inlet of the test rig
was sealed. The measurements showed that the airflow through the sealed test model was
less than 0.6 % of the smallest tested airflow. By adding the rafter detail, the airflow
through the sealed test model increased to 2.5 % compared to the smallest tested airflow.
Uncertainty assessment of the laboratory measurements
The root-mean square (RMS) method was used to derive the total uncertainty propagation
of the measured local loss coefficients,
p



, see eq. (16) and (17).

(12)
(13)
(14)
(15)
(16)
(17)
Where 1
P(Pa) and 2
P(Pa) is the static air pressure at the particular measuring positions. m
u
(m/s) is the average air velocity in the smallest cross section of the particular cross section.

is the density of the air (kg/m³),

is the temperature (K),qis the air flow (m³/h) and
A
is the area of the smallest cross section of the air cavity of the particular cross section.
Where, ()
()
pP
P

 is the uncertainty in the measured air pressure differences,
pT
T
is the
uncertainty in the air temperature measurements,
p
A
A
is the uncertainty in the cross
sectional area of the air cavity and the tile batten,
p
q
q

is the uncertainty of the measured
air flow through the air cavity.
No correlation between the various terms of the equation was found. The accuracy
and measuring range of the applied instruments are given by Table 1.
Numerical analysis
Laboratory measurements are expensive and takes a lot of time. Compared to laboratory
measurements numerical analysis implies a large reduction of time and the possibility to
investigate a larger span of design variation. Therefore, it is valuable to compare
measurements with simulations of the current study. In the current study, numerical
analysis includes simulation of airflow inside the air cavity between the underlayer roofing
and the roofing material. Conservation of mass, momentum and energy is based on the
assumption of a flowing media with constant properties. In the laminar regime, the flow of
the media can be predicted by solving the steady-state Navier–Stokes equations given in
eq. (18).
dv uu
f
dt


 

 (18)
2
12
293.15 293.15
2
2
22
2
2222
2
2 60000
()
()
m
KK
cavity
cavity
m
pp p p p
P
u
PPP
a
T
q
uA
PT A
aq
PTAq
PTAq








 





   


  





Where

denotes the density of the fluid (kg/m³), u is the velocity (m/s),

 denotes
shear stress and
f
being all other forces.
This can be rewritten assuming a Newtonian fluid:
2
dv uu p u
f
dt


  

 (19)
Where
p
is the pressure (Pa) and

(Pa s) is the dynamic viscosity.
2dv
p
uf u u
dt



   



 (20)
COMSOL Multiphysics software has been used for mesh generation and to solve the
system of partial differential equations.
The COMSOL Multiphysics software include eight built-in turbulence models. They
differ how they model the flow close to the wall, number of additional variables solved
for and what theses variables represent. Among them are the Low Re k-ε-model and Low
Re k-ω-model. The term "Low Reynolds number does not refer to the flow on a global
scale, but in the region close to the wall where viscous effects dominate. A low Reynolds
number model therefore more correctly reproduces the behaviour of different flows at
small distances from the wall. The Low Re k-ε-model solves for two variables: k, the
turbulence kinetic energy; and ε, the rate of dissipation of turbulence energy. A wall
function is used in the model. In that way the flow close to the surfaces is not simulated.
The Low Re k-ω-model is a model similar to the k-ε-model, but it solves for ω, the
specific rate of dissipation of kinetic energy. The model is more nonlinear and therefore
somewhat more difficult to converge. The model is useful in many cases when the k-ε-
model is not accurate. In this work we have used both models. The k-ε-model that is
more easily converging is used to find a prelimenary solution. Based on the solution the
k-ω-model is used to increase the accuracy of the solution. A coarse grid is used in the
solver in order to lower the period to perform the simulations, however even so one
calculation including four air velocities took several hours!
Calculation of the minor losses was performed according to eq. (8). The static
pressures of the simulations was read from the simulation model according to the
laboratory measurements. The position of the static pressure of the model is indicated by
red dots in Figure 8.
Simulation model
In order to simplify the model and thereby reduce the time needed for calculations, the
model only included passing of one tile batten (see Figure 8). The simulation model has
been used to calculate the loss in absolute pressure at different dynamic pressures inside
the air channel and thereby calculate the local singular loss coefficients according to eq.
(8). A parameter study including different dynamic pressures, dimensions of the tile batten
and height of the air channel below the tile batten was conducted.

Figure 8. Five cross sections of the air velocity distribution inside the air cavity given by
the COMSOL software. Higher air velocities are indicated in red color. Red dots indicate
the position of the static pressure measurements used in the calculations of the minor
losses
Results
Friction loss
Calculated and measured friction coefficients of the air cavity as a function of the Reynolds
number are shown in Figure 9. The theoretical friction coefficient is calculated according
to eq. (6) assuming that airflow inside the air channel is laminar.
Figure 9. Calculated and measured friction coefficients in the air channel at different
Reynolds numbers and counter batten thickness.
Tilebatten

Sharp-edged and round-edged tile battens
The local loss coefficients for 36 mm sharp-edged and 36 mm round-edged tile battens for
23 mm and 48 mm air gaps are shown in Figure 10 along with theoretical values as given
in the “Danvak" handbook by (Hansen et al., 2013).

Figure 10. Local loss coefficient for sharp-edged and rounded battens with different air
gaps and dynamic air pressure of the airflow passing the tile batten. “Danvak” means
values calculated from Hansen et al. (2013).
Different dimensions of tile and counter battens
Figure 11 shows local loss coefficients for tile battens that are 30 mm, 36 mm and 48 mm
high and air cavity heights of 23 mm, 36 mm and 48 mm below the tile batten as a function
of the dynamic pressure given by eq. (4). The width of the tile batten is kept constant at
48 mm. The open symbols represent the results of the measurements, the filled symbols
represent results from the COMSOL calculations, and the straight lines represent calculated
values according to equations 10, 11 and 12 given in the “Danvak" handbook (Hansen et
al., 2013).
Sharp‐
edgedtile
batten
Round‐
edgedtile
batten
r=3mm












Figure 11. Local loss coefficient as a function of dynamic pressure for tile battens that
are 30, 36 and 48 mm high. The filled symbols represent the results of the measurements,
the open symbols represent results from the COMSOL calculations, and the straight lines
represent theoretical values according to equations 10, 11 and 12 given in “Danvak"
handbook (Hansen et al., 2013).

In order to simplify the measuring results, eq. (21) and (22) describes the local
loss coefficient by passing of one sharp edged batten.

in eq. (22) is given by
1
A

and

2
A

in Figure 2. Equation 21 is derived by regression analysis and least square method. With
a starting point in eq. (9) the formulae was adjusted in order to obtain as small deviation
between the measuring results and the equation as possible. Figure 12 shows the
calculated results from eq. (21) compared to the measured results for the 36 mm air gap.


(21)


(22)


Figure 12. The filled symbols represent the results of the measurements, the open
symbols represent results from the COMSOL calculations, and the straight lines represent
values according to eq. (21).
Table 3 shows the average measured local loss coefficient by assuming a constant
relation between the local loss coefficient and the dynamic pressure. In the table, the
measured values are compared to the calculated values according to Hansen et al. (2013
and to results from eq. (21) which is a improved solution based on the laboratory
measurements.
3
1
2
11.375
A
A



 




Table 3 Average measured and calculated local loss coefficients.
Air
gap
Tile
batten
Average
measured
local loss
coefficient,

Standard
deviation,
measured
values
Calculated local
loss coefficient,
eq. (9-12)
% difference
compared to
measurements
Calculated local
loss coefficient
eq. (21)
% difference
compared to
measurements
(mm) (mm)
30 0.78 0.006 1.08 28 % 0.82 5 %
23 36 1 0.023 1.14 12 % 0.94 -6 %

48 1.19 0.04 1.22 2 % 1.14 -4 %
30 0.54 0.032 0.92 41 % 0.56 4 %
36 36 0.67 0.055 0.99 32 % 0.66 -2 %

48 0.8 0.025 1.09 27 % 0.83 4 %
30 0.42 0.003 0.81 48 % 0.43 2 %
48 36 0.5 0.013 0.88 43 % 0.51 2 %

48 0.67 0.028 0.99 32 % 0.66 -2 %
Uncertainty of the tile batten measurements
Each calculated local loss coefficients of the tile batten consist of three measurements; Two
friction loss measurements (the friction loss between and below the tile batten) and a
measurement of pressure loss including local losses by tile battens and friction. The
uncertainty has only been calculated for part of the measurements as given by Table 4.
Table 4 Average measured local loss coefficient and the calculated local loss and the
percentage difference between the two values.
23 mm cavity 48 mm cavity
Dynamic pressure 0.1 Pa 0.4 Pa 0.1 Pa 0.4 Pa
Tile batten height
(mm)


(%)


(%)


(%)


(%)
30 10.3 10.7 5.0 4.4
36 9.9 10.1 4.4 4.4
48 9.1 9.1 4.3 4.3
Air intake at eaves
Classic design
Figure 13 shows the local loss coefficient of the air intake design as a function of the
dynamic pressure in the air cavity beneath the tile battens. The pressure is measured at the
black dots in Figure 13. The figure shows results from one air gap of 50 mm with and
without a fly net. The different series in the diagram are related to measurements performed
with 23, 36 and 48 mm air gaps beneath the tile battens. The height of the tile batten is kept
constant at 36 mm.

a)
b)

Figure 13. Measuring results of local loss coefficient for the classic eaves design as a
function of dynamic pressure calculated for the air cavity beneath the tile batten. The
pressure is measured at the black dots.
Modern design
Figure 14 gives the minor loss coefficient of the detail as a function of the dynamic pressure
in the airflow beneath the tile batten. The pressure is measured at the black dots in Figure
14. The local loss coefficients in Figure 14 are corrected by subtracting the pressure loss
caused by the passing of one tile batten. The figure shows results from one air gap of 25 mm
with and without a fly net. The different series in the diagram are related to measurements
performed with 23, 36 and 48 mm air gaps beneath the tile battens. The height of the tile
batten is kept constant at 36 mm.

a)
b)
Figure 14. Measuring results of local loss coefficient for the modern eaves design as a
function of dynamic pressure calculated for the air cavity beneath the tile batten. The
pressure is measured at the black dots.
Discussion
The results show a good correspondence between the measured friction coefficient and the
calculated friction coefficient. The calculated Reynolds numbers of Figure 8 indicate
laminar flow. Therefore, the friction coefficient is inversely proportional to the Reynolds
number.
Laboratory measuring model compared to tile roofing
The design of the laboratory measurements can be directly compared to using membranes
on wooden boards for roofing. Use of metal sheeting or tiles implies an air gap between
the roofing and the tile batten. An air gap above the tile batten roofing will affect the flow
pattern of the airflow. It is likely that the increased cross-sectional area available for airflow

will reduce the local loss coefficient. Consequently, the measured local loss coefficients of
this study are conservative.
The effect of roof slope is not covered by this study. However, the slope will affect
the local loss at the eaves because the deflecting of the air flow entering the air cavity is
dependent of the roof slope.
The height of the tile batten
In general, both the measurements and COMSOL-simulations showed smaller local loss
coefficients compared to the calculations using the "Danvak" handbook (eq. (9-12)). Eq.
(9-12) are general values given a narrowing and contraction of the air flow. In this case
there is a small distance between the narrowing and contracting of the air flow possibly not
causing completely laminar and undisturbed air flow when the air passes the contraction.
Eq. (21) is an improvement of the eq. (9-12) and is specific for the passing of sharp edged
tile battens. According to Kronvall (1980), a short distance between two obstacles in an
airflow will cause a reduction of the total local loss coefficient given by the two obstacles.
The calculations, simulations and the measurements all showed increasing local loss
coefficients in line with increasing height of the tile batten. By assuming a constant relation
between the local loss coefficient and the dynamic pressure, a deviation between the
measured and calculated values of 3–80 % was found. The maximum deviation between
the average calculated local loss coefficient and average measured local loss coefficient
was 48 %. The equivalent number for eq. (21) was 9 %. Hence, a sufficient correspondence
between the calculated local loss coefficients for a batten passing given by eq. (21) and the
measurements was found. The smallest deviation was found for the smallest air cavity and
the largest height of the tile batten. The measurements of the smallest air gaps and largest
tile battens suggests a maximum 4 Pa pressure drop over nine tile battens. A larger
measured pressure difference reduces the errors from the resolution in the pressure
transmitter and fluctuations in the surrounding air.
The measurements and simulations of different dimensions of the tile batten
indicated a constant correlation between the local loss coefficient and the dynamic pressure
given a larger dynamic pressure than 0.10 Pa. However, both Hofseth (2004) and Falk and
Sandin (2013) found that the local loss coefficient was dependent on the air velocity and
hence the dynamic pressure. The air velocity of Hofseth’s results was 5–10 times larger
than the air velocity of the current study. This will of course influence the flow
characteristics inside the air cavity. The air velocity of Falk and Sandin (2013) was of the
same magnitude as the current study. Measurements at low dynamic pressures mean that
the measured pressure drop over the nine tile battens is very small, typically down to 0.1 Pa,
which could imply increased measuring error, both because of the resolution of the pressure
transmitter and fluctuations in the surrounding air.
However, the calculations of uncertainty do not interpret a correlation between the
dynamic pressure and the magnitude of the uncertainty. On the other hand, the magnitude
of uncertainty seems to increase by decreasing height of the air cavity below the tile batten.
One possible explanation is that the relative measuring error of the cross-sectional areas
increases by decreasing height of the air cavity. Based on this explanation and the constant
relation between the uncertainty and the tile batten height it is likely that the calculation of
uncertainty from the 36 mm air gap will be somewhere between the two calculated
uncertainties, i.e. somewhere between 5 and 10 %.

Sharp-edged and round-edged tile batten
The measurements showed a large difference in the local loss coefficients depending on
the edge design of the tile batten. The local loss coefficient of the rounded tile battens was
approx. 40 % lower than the local loss coefficients of the sharp-edged tile battens. Idelchik
(2005) also reported lowered local loss coefficients by use of rounded orifaces. There was
a larger difference between the sharp-edged and round-edged tile batten for the 48 mm air
gap compared to the 23 mm air gap. Almost all the measured values showed lower local
loss coefficients compared to the calculated values according to equations 9–12. The
smallest deviation was found for the 23 mm air gap and the sharp-edged tile batten.
Numerical analysis
It was found that the simplified COMSOL model shown in Figure 8 could reliably
reproduce the results from the measurements. The smallest deviation between the
simulations and the measurements was found for the smallest dynamic pressures. Many of
the measurements include low Reynolds-numbers, and the flow is laminar, but at the
highest dynamic pressures the flow are turbulent or in the transition zone. A possible
solution to lower the deviation at the highest Reynolds numbers is including of a different
model more adapted to high Reynolds numbers. However, a challenge is that the Reynolds
numbers are different in the different cross sections along the flow possibly changing
between laminar and turbulent flow. The Low Re k-ω-model was used in the COMSOL
simulations because of the geometry of the simulation model and the surface-position of
the static air pressure used in the calculation of the local losses. It was assumed that a more
accurate calculation of the flow characteristics close to the surface was important in order
to obtain a more correct static pressure at the surface.
A simplification of the model is the assumption of uniform flow at the inlet of the
model, below the tile batten. A close study into the second tile batten of Figure 8 shows
that the air velocity is somewhat higher in the middle of the cross section and close to the
lower surface compared to the air velocity close to the tile batten, also given in Figure 2.
The smallest difference between the measurements and the simulations was found for the
36 mm tile batten and the air gaps of 23, 36 and 48 mm. The simulation results indicates
that the tile batten height inflates less on the local loss coefficient compared to the
measurements and the calculations.
The results indicate that the COMSOL software can be used to produce local loss
coefficients where measurements of local loss coefficients of sharp-edged tile battens are
not available. Given a larger dynamic pressure than 0.10 Pa the COMSOL simulation
indicate a constant local loss coefficient. Some of the measuring results also indicate an
increasing local loss coefficient at lower dynamic pressures. This phenomena is not easy
to explain. The error by simplifying and calculating with a constant local loss coefficient
at these small dynamic pressures will, however, be small because of low air velocities
inside the cavity which, according to eq. 7, gives small pressure losses.
Eaves design
The local loss coefficient increases by increasing height of the air gap beneath the tile
batten. The explanation is the increasing airflow through the eaves construction by

increasing air gap beneath the tile batten because the dynamic pressure is calculated at the
passing of the tile battens. The measurements of the classic design show a large increase
in the local loss coefficient by introduction of a fly net inside the 50 mm air gap at the
eaves. The option without a fly net shows an increasing local loss coefficient by increasing
dynamic pressures. The measurements for the option with a fly net indicate a constant
relation between the dynamic pressure and the local loss coefficient for a dynamic pressure
larger than 0.2 Pa. The measurements and literature review conducted by Kronvall (1980)
also indicated a constant local loss coefficient independent of the Reynolds number. The
measurements include narrowing and contraction when the air enters the air space inside
the eaves construction. Further, the measurements include narrowing and contraction when
the air enters the air cavity below the roofing. The geometry of the eaves design makes it
difficult to compare the results to calculated results from equations in the literature.
The modern eaves design of Figure 13 shows increasing local loss coefficients
compared to the classic solution. This can partly be explained by the decreased gap in the
air cavity compared to the classic design. The measurements include pressure loss by
narrowing and friction loss in the 25 mm air cavity. Further, the measurements include a
bend and narrowing and contraction by passing of the lowest tile batten of the roof. As with
the classic solution, the local loss coefficient increases in line with the height of the air gap
and thereby increased mass flow through the air cavity. Installation of a fly net inside the
air cavity leads to approximately doubling of the local loss coefficients. The increase is
larges for the smallest dynamic pressures. The dynamic pressure is still calculated in the
cross section below the tile batten. Installation of fly net of course reduces the effective air
flow area and thereby increases the local loss coefficient.
The local loss coefficients with the classic design correspond to the local loss
coefficient given by four tile batten passings without a fly net and six tile batten passings
with a fly net. The local loss coefficient given by the modern design without a fly net
corresponds to approximately 16 tile batten passings. By installing a fly net, the local loss
coefficient corresponds approximately to 30 tile batten passings. Thiis et al. (2007) showed
that an increased local loss coefficient and thereby a reduction in the air velocity inside the
air cavity was effective to reduce snow penetration into the air cavity.
Measures to increase ventilation of pitched roofs
In order to increase the ventilation of a typical roof construction, a decrease in the height
of the tile batten is positive as well as an increase in the counter batten height. Use of round-
edged tile battens was also found to lower the local loss coefficient, by approx. 40 %, and
thereby increase the ventilation of the roof compared to a sharp-edged tile batten. To
increase the ventilation of pitched wooden roofs, the results show that a classic eaves
design without a fly net is the preferred eaves solution.
Conclusion
This study has found a large difference in the local loss coefficients depending on the edge
design of the tile batten. The local loss coefficients of the round-edged tile battens was
approximately 40 % lower than the local loss coefficients of the sharp-edged tile battens.
The measurements and simulations of different dimensions of the tile batten indicated a

constant correlation between the local loss coefficient and the dynamic pressure given a
larger dynamic pressure than 0.10 Pa. The COMSOL model used in the study could
reliably reproduce the results from the measurements. Increased height of the counter
batten as well as use of rounded tile battens was found to be effective at increasing the
ventilation of pitched wooden roofs. Further, the measurements showed considerably lower
local loss coefficients for the classic eaves design compared to the modern design.
Installation of fly net in the ventilation gap was found to approximately double the local
loss coefficient.
Acknowledgements
The authors gratefully acknowledge the financial support by the Research Council of
Norway and several partners through the Centre of Research-based Innovation "Klima
2050" (www.klima2050.no).
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