EN 13384-2:2003

SLOVENSKI STANDARD
01-september-2003
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Chimneys - Thermal and fluid dynamic calculation methods - Part 2: Chimneys serving
more than one heating appliance
Abgasanlagen - Wärme- und strömungstechnische Berechnungsverfahren - Teil 2:
Abgasanlagen mit mehreren Feuerstätten
Conduits de fumée - Méthodes de calcul thermo-aéraulique - Partie 2: Conduits de
fumée desservant plus d'un appareil de chauffage
Ta slovenski standard je istoveten z: EN 13384-2:2003
ICS:
91.060.40 Dimniki, jaški, kanali Chimneys, shafts, ducts
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN 13384-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
May 2003
ICS 91.060.40
English version
Chimneys - Thermal and fluid dynamic calculation methods -
Part 2: Chimneys serving more than one heating appliance
Conduits de fumée - Méthodes de calcul thermo-aéraulique Abgasanlagen - Wärme- und strömungstechnische
- Partie 2: Conduits de fumée desservant plus d'un appareil Berechnungsverfahren - Teil 2: Abgasanlagen mit
de chauffage mehreren Feuerstätten
This European Standard was approved by CEN on 11 March 2003.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Management Centre has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, Slovak Republic, Spain, Sweden, Switzerland and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2003 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13384-2:2003 E
worldwide for CEN national Members.

Contents
page
Foreword .4
1 Scope .5
2 Normative references.5
3 Terms and definitions .6
3.1 chimney segment .6
3.2 collector segment.6
3.3 air-flue gas system .6
3.4 flue gas mass flow ( m) .6
3.4.1 declared flue gas mass flow ( m).6
W, j
3.4.2 calculated flue gas mass flow ( m) .6
Wc,j
3.5 calculated flue gas temperature (T ).6
Wc, j
3.6 calculated draught of the flue gas of the heating appliance (P ) .6
Wc,j
3.7 flue damper .6
3.8 balanced flue chimney .7
3.9 cascade arrangement.7
3.10 uulti inlet arrangement.7
3.11 air duct.7
3.12 pressure equalising opening.7
4 Symbols, terminology, units .7
5 Calculation method .9
5.1 General principles .9
5.2 Pressure equilibrium condition.10
5.3 Mass flow requirement.12
5.4 Pressure requirement.12
5.5 Temperature requirement .12
5.6 Calculation procedure.13
6 Flue gas data characterising the heating appliance.14
7 Data for chimney and connecting flue pipes.16
8 Basic data for the calculation.16
8.1 Air temperatures.16
8.1.1 External air temperature (T ).16
L
8.1.2 Ambient air temperature (T ) .16
u
8.2 External air pressure (p ) .16
L
8.3 Gas constant .16
8.3.1 Gas constant of the air (R ).16
L
8.3.2 Gas constant of flue gas (R) .16
8.4 Density of air () .16
L
8.5 Specific heat capacity of the flue gas (c ) .16
p
8.6 Water vapour content ((H O) ) and condensing temperature (T ) .16
2 ,j sp
8.7 Correction factor for temperature instability (S ).17
H
8.8 Flow safety coefficient (S ) .17
E
8.9 External coefficient of heat transfer .17
9 Determination of temperatures .17
10 Mixing calculations.19
( m)
10.1 Flue gas mass flow .19
, j
10.2 Flue gas temperature at the inlet of the chimney segment (T ).19
e,j
10.3 CO -content of the flue gas in the chimney segment ((CO ) ) .19
2 ,j
10.4 H O-content of the flue gas ((H O) ) .19
2 2 ,j
10.5 Gas constant of the flue gas (R ) .20
,j
10.6 Flue gas data.20
10.6.1 Specific heat capacity (c ), (c ) .20
pV,j p,j
10.6.2 Thermal conductivity of the flue gas (), () .20
AV,j A,j
10.6.3 Dynamic viscosity (), () .21
AV,j A,j
11 Density and velocity of the flue gas .21
12 Draught at the outlet of the connecting flue pipe and draught at the inlet of the chimney
segment .22
12.1 Draught at the inlet of the chimney segment.22
12.1.1 Draught due to chimney effect in the chimney segment (P ) .23
H,j
(P )
12.1.2 Pressure resistance in the chimney segment .23
R,j
12.2 Draught required at the outlet of the connecting flue pipe (P ) .25
Ze,j
12.2.1 Calculated pressure resistance of the connecting flue pipe (P ).26
V,j
12.2.2 Pressure resistance of the air supply (P ) .28
B,j
13 Inner wall temperature .29
14 Cascade installations.30
14.1 Principle of the calculation method.30
14.2 Pressure equilibrium condition.30
14.3 Mass flow requirement.32
14.4 Pressure requirement.32
14.5 Temperature requirement .32
14.6 Calculation procedure.32
14.7 Draught at the outlet of the connecting flue pipe and draught at the inlet of the collector
segment .33
14.7.1 Draught at the flue gas inlet into the collector segment (P ).33
ZC,j,l
14.7.2 Draught at the outlet of the connecting flue pipe (P ).35
ZeC,j,l
14.8 Inner wall temperature (T ) .37
iobC,j,l
15 Balanced flue chimney.37
15.1 Principle of the calculation method.37
15.2 Pressure equilibrium condition.37
15.3 Mass flow requirement.38
15.4 Pressure requirements.38
15.5 Temperature requirements .40
15.6 Calculation procedure for balanced flue chimneys .40
15.7 Mass flow of the supply air.41
15.8 Determination of the temperatures in balanced flue chimneys.42
15.8.1 Separate ducts .42
15.8.2 Concentric ducts .42
15.8.3 Concentric connection pipes .49
15.9 Pressure resistance of the air supply.55
15.9.1 Draught due to chimney effect at the outlet of the supply air duct.55
15.9.2 Draught due to chimney effect at the outlet of the air supply duct of connection pipes .55
15.9.3 Pressure resistance of the air supply duct of the chimney segment j (P ) .56
RB,j
15.10 Density and velocity of the supply air.59
15.10.1 Density and velocity of the supply air in the air supply duct averaged over the length of
the chimney segment.59
15.10.2 Density and velocity of the supply air averaged over the length of the connection pipes .60
Annex A (informative) Recommendations.61
A.1 Recommendations for the chimney and heating appliances:.61
A.2 Recommendations for connecting flue pipes:.61
Annex B (informative) Characteristics for the heating appliance .62
Foreword
This document EN 13384-2:2003 has been prepared by Technical Committee CEN /TC 166, "Chimneys",
the secretariat of which is held by UNI.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by November 2003, and conflicting national standards shall be
withdrawn at the latest by November 2003.
This draft is one of a series of standards prepared by CEN/TC 166 comprising product standards and
execution standards for chimneys.
Annexes A and B are informative.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Czech Republic, Denmark,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands,
Norway, Portugal, Slovakia, Spain, Sweden, Switzerland and the United Kingdom.
Introduction
The calculation described in this standard is complex and is intended to be solved by using a computer
programme. The general principles of this calculation method of EN 13384-1 also apply to this standard.
This standard is in support of the execution standards for a chimney installation serving more than one
heating appliance.
The execution standard identifies limitations and safety considerations associated with the design,
installation, commissioning and maintenance of a chimney serving more than one heating appliance (not
dealt within the calculation method).
1 Scope
This part of EN 13384 specifies methods for calculation of the thermal and fluid dynamic characteristics of
chimneys serving more than one heating appliance.
This part of EN 13384 covers both the cases, either
(1) where the chimney is connected with more than one connecting flue pipe from individual or several
appliances in a multi-inlet arrangement or
(2) where the chimney is connected with an individual connecting flue pipe connecting more than one
appliance in a cascade arrangement.
The case of multiple inlet cascade arrangement is covered by the case (1).
This part of EN 13384 deals with chimneys operating under negative pressure conditions (there can be
positive pressure condition in the connecting flue pipe) and is valid for chimneys serving heating appliances
for liquid, gaseous and solid fuels.
This part of EN 13384 does not apply to:
chimneys with different thermal resistance or different cross-section in the various chimney segments.
This part does not apply to calculate energy gain.
chimneys with open fire places, e.g. open fire chimneys or chimney inlets which are normally intended to
operate open to the room
chimneys which serve a mixture of fan assisted or forced draught burners or natural draught appliances.
Fan assisted appliances with draught diverter between the fan and the chimney are considered as
natural draught appliances.
chimneys with multiple inlets from more than 5 storeys. (This does not apply to balanced flue chimney.)
chimneys serving heating appliances with open air supply through ventilation openings or air ducts,
which are not installed in the same air supply pressure region (e.g. same side of building).
2 Normative references
This European Standard incorporates by dated or undated reference, provisions from other publications.
These normative references are cited at the appropriate places in the text, and the publications are listed
hereafter. For dated references, subsequent amendments to or revisions of any of these publications apply
to this European Standard only when incorporated in it by amendment or revision. For undated references
the latest edition of the publication referred to applies (including amendments).
EN 1443 Chimneys - General requirements.
prEN 12391-1 Chimneys - Metal chimneys – Part 1:Execution standard.
EN 13384-1:2002 Chimneys - Thermal and fluid dynamic calculation methods - Part 1: Chimneys serving
one appliance.
3 Terms and definitions
For the purposes of this European Standard, the terms and definitions given in EN 1443, EN 13384-1:2002
and prEN 12391-1 and the following apply.
3.1
chimney segment
part of a chimney between two consecutive flue gas connections or between the last flue gas connection
and the chimney outlet
3.2
collector segment
part of a connecting flue pipe between two consecutive flue gas connections or between the last flue gas
connection and the chimney inlet
3.3
air-flue gas system
system of concentric or non concentric ducts or parallel ducts for transport of combustion air from the open
air to the heating appliances and products of combustion from the heating appliances to the open air
3.4
flue gas mass flow ( m)
mass of the flue gas leaving the heating appliance through the connecting flue pipe per unit of time. In case
of a chimney serving more than one heating appliance, the air being transported through an appliance which
is out of action is also given the term flue gas mass flow.
3.4.1
declared flue gas mass flow ( m )
W, j
flue gas mass flow given by the manufacturer of the heating appliance j with respect to the heat output used
in the calculation
3.4.2
calculated flue gas mass flow ( m)
Wc,j
flue gas mass flow calculated with respect to calculated draught and the working conditions of the heating
appliance j
3.5
calculated flue gas temperature (T )
Wc, j
flue gas temperature at the outlet of the heating appliance j depending on the calculated flue gas mass flow
3.6
calculated draught of the flue gas of the heating appliance (P )
Wc,j
draught at the flue gas outlet of the heating appliance j depending on the calculated flue gas mass flow
3.7
flue damper
device to close or partially close the flue
3.8
balanced flue chimney
chimney where the point of air entry to the combustion air duct is adjacent to the point of discharge of
combustion products from the flue, the inlet and outlet being so positioned that wind effects are substantially
balanced
3.9
cascade arrangement
arrangement where two or more appliances situated in the same space are connected by a common
connecting flue pipe to the chimney
3.10
uulti inlet arrangement
arrangement where two or more appliances situated in different spaces are connected to the chimney by
individual connecting flue pipes
3.11
air duct
independent duct in a building or a structural part of a flue terminal conveying combustion air to a room-
sealed appliance
3.12
pressure equalising opening
opening or duct that directly connects the air duct with the flue at its base
4 Symbols, terminology, units
Symbols, terminology and units are given to make the text of this standard understandable, although a part
of them is already listed in part 1 of this standard series. Indices added to symbols for purposes of the
calculation method for chimneys serving more than one heating appliance relate to one chimney segment
and/or connection flue pipe section. An example of an indices numbering scheme is given in Figures 1 and
2. Indices numbering shall begin at the lowest, farthest appliance connection. For more than one cascade
system/connection, the indices numbering scheme for the calculation formula should be adopted in a similar
manner to that for a single cascade scheme. Symbols assigned to a specific section will be indicated by the
number of the section after the comma (e. g. H is the effective height of a section of a chimney segment
,1
between the outlet of the connecting flue pipe of the heating appliance in the lowest position and the outlet
of the connecting flue pipe of the next heating appliance).
Table 1 - Symbols, terminology, units
Symbols Terminology Units
A cross sectional area of the chimney m
c specific heat capacity of flue gas J/(kg·K)
p
D diameter m
hydraulic diameter m
D
h
g acceleration due to gravity = 9,81
m/s
H
effective height of the chimney segment j m
,j
H effective height of the connecting flue pipe j m
V,j
K, coefficient of cooling of the chimney segment j -
j
k coefficient of heat transmission of the chimney segment j
W/(m ·K)
j
k coefficient of heat transmission at upper end of the chimney segment j
W/(m ·K)
ob,j
coefficient of cooling of the connecting flue pipe j -
K
V,j
L length of the chimney segment j m
,j
mflue gas mass flow in the chimney segment j kg/s
, j
mflue gas mass flow in the connecting flue pipe j kg/s
V, j
mdeclared flue gas mass flow of the heating appliance j kg/s
W, j
mcalculated flue gas mass flow of the heating appliance j kg/s
Wc, j
N number of heating appliances serving the chimney -
Nu Nusselt number -
Q
minimum heat output of the heating appliance j kW
min,j
nominal heat output of the heating appliance j kW
Q
N,j
P pressure resistance of the air supply j of the heating appliance j Pa
B,j
P
calculated pressure resistance of the air supply of the heating appliance j Pa
Bc,j
P theoretical draught available due to chimney effect in chimney segment j Pa
H,j
wind velocity pressure Pa
P
L
p external air pressure Pa
L
P pressure resistance of the chimney segment j Pa
R,j
Pr Prandtl number -
P minimum draught for the heating appliance j Pa
W,j
calculated draught of the heating appliance j Pa
P
Wc,j
draught at the flue gas inlet into the chimney segment j Pa
P
Z,j
calculated pressure resistance of the connecting flue pipe j Pa
P
V,j
R gas constant of the flue gas J/(kg·K)
r mean value of roughness value of the inner wall m
Re
Reynolds number -
gas constant of the air J/(kg·K)
R
L
flow safety coefficient -
S
E
correction factor of temperature instability -
S
H
flue gas temperature at the inlet of the chimney segment j K
T
e,j
temperature limit of the chimney segment j K
T
g,j
T inner wall temperature at the outlet of chimney segment j at temperature K
iob,j
equilibrium
external air temperature K
T
L
mean temperature of the flue gas in the chimney segment j K
T
m,j
flue gas temperature at the outlet of the chimney segment j K
T
o,j
ambient air temperature of the chimney segment j K
T
u,j
declared flue gas temperature of the heating appliance j K
T
W,j
calculated flue gas temperature of the heating appliance j K
T
Wc,j
U internal circumference of the chimney m
w mean velocity over the length and over the cross section of the chimney m/s
m,j
segment j
internal coefficient of heat transfer of the flueW/(m ·K)
i
angle between flow directions e. g. between connecting flue pipe and the deg
chimney segment
dynamic viscosity of flue gasN·s/m
A
1 thermal resistance m ·K/W
coefficient of thermal conductivity of flue gas W/(m·K)A
density of flue gas averaged over the length and over the cross sectionkg/m
m,j
of the chimney segment j
coefficient of flow resistance due to friction of the flue -
coefficient of flow resistance due to a directional and/or cross sectional -
and/or mass flow change in the flue
5 Calculation method
5.1 General principles
The calculation is based upon determining the mass flow distribution in the chimney which fulfils the
pressure equilibrium condition (formula 1) at each flue gas inlet to the chimney (see Figure 1). After such a
distribution has been found three requirements shall be verified:
(1) the mass flow requirement (formulae 4 and 5)
(2) the pressure requirement (formula 6)
(3) the temperature requirement (formula 7)
NOTE The calculation is affected by the specific installation design. For recommendations for the installation of
appliance and connection flue pipes see annex A.
The validation of the mass flow requirement and pressure requirement shall be done at following working
conditions, using the external and ambient air temperatures specified in EN 13384-1.
All heating appliances are simultaneously operating at nominal heat output.
All heating appliances are simultaneously operating at minimum heat output
A single heating appliance operating at nominal heat output and all other appliances out of action (all
possible cases)
A single heating appliance operating at minimum heat output and all other appliances out of action (all
possible cases)
If the control of the installation guarantees that not all appliances will be in operation simultaneously, the
validation of the mass flow requirement and pressure requirement may be done with the maximum number
of appliances which will be in operation under the most adverse condition.
The validation for the mass flow requirement and pressure requirement for working conditions with heating
appliances at minimum heat output is not required in the following cases:
the heating appliances do not have any heat output range
the heating appliances have a heat output which is limited to a fixed value as specified on a label on the
appliance. In this case the nominal heat output is the given heat output on the label.
heating appliances heated with solid fuels without fan and appliances with regulated air supply.
The validation of the mass flow requirement for working conditions with appliances at nominal heat output is
not required in the following case:
the heating appliances have a flue gas mass flow at minimum heat output higher than or equal to the flue
gas mass flow at nominal heat output.
The temperature requirement shall be validated for the following relevant working condition, using the
ambient and external air temperatures as specified in EN 13384-1:
heating appliances for solid fuels without fan and heating appliances with regulated air supply are in
operation at nominal heat output,
heating appliances with a draught diverter which provide domestic hot water only are out of action.
These heating appliances operate with a considerable secondary air (These operate only a short time
and therefore it can be assumed that condensation will not cause damage or a lack in safety);
heating appliances with a fixed output range are in operation at this (nominal) heat output;
all other heating appliances are in operation at minimum heat output.
When chimneys suitable for operating under wet conditions are located inside a building the check of the
temperature requirement is necessary only for the top of the chimney.
The validation of the temperature requirement is not necessary when the chimney serves only domestic gas
fired water heaters with instantaneous production and domestic gas fired storage water heaters.
If the chimney system includes a draught regulator, the system is handled as a cascade system.
5.2 Pressure equilibrium condition
The following formulae shall be fulfilled for each chimney segment j at all relevant working conditions:
PP0,1
in Pa (1)
Z, j Ze, j
N
PP P P Z, j L H,k R,k
in Pa (2)
kj
PPPP
in Pa (3)
Ze,j Wc,j V,j Bc,j
Where:
P draught at the flue gas inlet to the chimney segment j in Pa
Z,j
P theoretical draught due to chimney effect in chimney segment k in Pa
H,k
P pressure resistance of the chimney segment k in Pa
R,k
P calculated draught of the heating appliance in Pa
Wc,j
P calculated pressure resistance of the connecting flue pipe of
V,j
chimney segment j in Pa
P calculated pressure resistance of the air supply for the
Bc,j
heating appliance j in Pa
P required draught at the flue gas inlet to the chimney segment j
Ze,j
P wind velocity pressure
L
N number of heating appliances
Key
1 Chimney
2 Connecting flue pipe j
3 Heating appliance j
4 Connecting flue pipe 2
5 Heating appliance 2
6 Connecting flue pipe 1
7 Heating appliance 1
8 Chimney segment 1
9 Chimney segment j
Figure 1 - Example of multiple inlet arrangement and numbering pressure values and temperature
values of a chimney serving more than one heating appliance
5.3 Mass flow requirement
Formulae 4 resp. 5 shall be verified for all relevant working conditions (see 5.6).
For each heating appliance in operation at nominal or minimum heat output :
mm
in kg/s (4)
Wc,j W,j
and for each heating appliance out of action:
m0
in kg/s (5)
Wc,j
Where:
m
calculated mass flow of the heating appliance in kg/s
Wc,j
m
declared mass flow of the heating appliance in kg/s
W, j
Where a damper is applied, flow resistance shall be taken as 0 unless additional data are available.
5.4 Pressure requirement
Additionally it has to be checked that the negative pressure (draught) in the chimney (P ) is more than or
Z,j
equal to the negative pressure in the room where the heating appliance is placed at calculated draught
conditions for air supply. The check on the pressure requirement shall be done using the same conditions
as specified for the check on the mass flow requirement (see 5.3 and 5.6). The following relations shall be
verified:
PP
in Pa (6)
Z,j Bc,j
Where:
P draught at the inlet to the chimney segment j in Pa
Z,j
P calculated pressure resistance of the air supply for
Bc,j
the heating appliance j in Pa
5.5 Temperature requirement
The relations (7) shall be verified for all relevant working conditions (see 5.6).
The check of the temperature requirement shall be done with a separate calculation using the newly
calculated flue mass flows that fulfil the pressure equilibrium conditions at an external air temperature of T
o,j
u
(see EN 13384-1)
T T in K (7)
iob,j g,j
Where:
T temperature of the inner wall of the chimney segment j at the
iob,j
end in K
T temperature limit for chimney segment j in K
g,j
The temperature limit T for chimneys suitable for operating under dry conditions is equal to the condensing
g,j
temperature T of the flue gas (see 8.6). T = T
sp,j g,j sp,j
The temperature limit T for chimneys suitable for operating under wet conditions is equal to the freezing
g,j
point of water: T = 273,15 K.
g,j
NOTE The following cases can be exempted from meeting the temperature requirement provided that it is accepted
that in case the requirement for temperature should be not fulfilled no guarantee can be given that no moisture appears.
In this cases insulation is recommended.
heating appliances which are substituted to a usual chimney which is already in operation and
the heat output of the heating appliances which are connected and/or substituted does not exceed 30 kW for each
and
the flue gas losses are not more or equal than 8 % and
an effective air conditioning of the chimney during standstill periods is given by draught diverters or dampers and
sufficient standstill periods are given (e. g. the minimum steady state heat output of the heating appliance is not
less than 20 % as the required heat).
5.6 Calculation procedure
For the calculation of the pressure and temperature values in a chimney serving more than one heating
appliance an iterative procedure is necessary. This calculation procedure is based on the application of
mass and energy conservation formulae under quasi steady state conditions.
In each point of connection between various ducts (at the end of connecting flue pipes, the begin and the
end of the chimney segments), all called nodes (see Figure 2), the following procedure shall be used:
Figure 2 - Designation of flow numbering for each node j (see formulae 8 and 9)
- The mass flow and the temperature shall be calculated with formulae 8 and 9.
mmm in kg/s (8)
, j-1 V, j , j
mcTmcTmcT in J/s (9)
, j-1 p,j-1 o, j-1 V, j pV,j oV,j , j p,j e,j
where:
mflue gas mass flow in chimney segment j-1 in kg/s
, j-1
mflue gas mass flow in connecting flue pipe in kg/s
V,j
mflue gas mass flow in chimney segment j in kg/s
, j
c specific heat capacity of flue gas in chimney segment j-1 in J/(kgK)
p,j-1
c specific heat capacity of flue gas in connecting flue pipe j in J/(kgK)
pV,j
c specific heat capacity of flue gas in chimney segment j in J/(kgK)
p,j
T temperature of the flue gas at the end of chimney segment j-1 in K
o,j-1
T temperature of the flue gas at the end of connecting flue pipe j in K
oV,j
T temperature of the flue gas at the inlet of chimney segment j in K
e,j
- The draught at the begin of the chimney segment (at point 3), is derived from the draught of this
chimney segments and all succeeding sections according to formula 2.
NOTE For certain fan assisted heating appliances according to the information of the manufacturer it can be
assumed that the mass flow is independent of the draught in the chimney. This information can be used to limit the
number of iterations.
For each iteration the following parameters shall be obtained:
- for each node j, the actual pressure (P , P ) and temperature values ( T at point 1, T at point 2,
Ze,j Z,j o,j-1 oV,j
T at point 3),
e,j
- for each section between two nodes, the average values of the actual temperature, mass flow and
velocity of the flue gas.
Before the first iteration an estimate of the calculated flue gas mass flow at the appliance outlet is
necessary. A possible starting value for the calculated mass flow is the declared flue gas mass flow of the
m.
appliance
W,j
Each iteration consists of the following two phases:
Phase 1: Calculate variables starting from the lowest node up to the outlet to the atmosphere as follows:
- calculated/estimated flue gas mass flow at the appliance outlet
- in each connecting flue pipe
calculated mass flow (formula 13);
average density of the flue gas (formula 29);
average velocity of the flue gas (formula 30);
flue gas temperature at the end (see EN 13384-1:2002, 5.8);
average flue gas temperature (see EN 13384-1:2002, 5.8).
- in each section of the flue
calculated mass flow after the confluence with the respective channels (formula 14);
temperature of the flue gas after the confluence (formula 15)
average density of the flue gas (formula 27);
average velocity of the flue gas (formula 28);
flue gas temperature at the end (see EN 13384-1:2002, 5.8);
average flue gas temperature (see EN 13384-1:2002, 5.8).
Phase 2: Calculate the draught values in each node tracking the flue duct backwards from the outlet into the
atmosphere down to the node that is at the greatest distance:
- draught required at the flue gas inlet into the chimney (formula 3)
- draught due to chimney effect at the inlet of the chimney segment (formula 31);
- pressure resistance in the chimney segment (using formula 32);
- draught at the inlet of the chimney segment (using formula 2);
The iteration described above (phase 1 and phase 2) at the working conditions under consideration (i.e.
nominal, minimum load and out of action) shall be continued until the pressure equilibrium condition is
fulfilled (formula 1).
When the pressure equilibrium condition is fulfilled, the values calculated at the last iteration can be
considered, for the purpose of this standard, to be those regarding the operation of the chimney.
If the pressure equilibrium condition is not fulfilled a new estimate of m based on the observed difference
W
between P and P and a new iteration shall be made.
Z,j Ze,j
6 Flue gas data characterising the heating appliance
For the calculation of the temperature and pressure values the relevant flue gas data characterising the
heating appliance shall be specified. This includes:
minimum, declared draught of the heating appliance (P )
W,j
declared flue gas temperature of the heating appliance (t )
W,j
Both values shall be given in relation to the flue gas mass flow at various working conditions of the heating
appliances (in operation, out of action). The calculated draught P of the heating appliance shall be given
Wc,j
th
for both working conditions in form of a 4 degree poly-nominal (formula 10).
2 3 4
mmmm
Wc,j Wc,j Wc,j Wc,j
P b b b b b
Wc,j o 1 2 3 4 in Pa (10)
mmmm
Wj Wj Wj Wj
y
m
Wc, j
tyy
Wc, j o 1
in °C (11)
m
W, j
Where:
b , b , b ,
0 1 2
b , b factors for the poly-nominal in the formula for calculated draught of heating appliance j
3 4
y , y , y factors for the exponential in the formula for calculated flue gas temperature heating
0 1 2
appliance j
m
calculated flue gas mass flow of heating appliance j in kg/s
Wc,j
m
declared flue gas mass flow of heating appliance j in kg/s
W,j
P calculated draught of the heating appliance in Pa
Wc,j
t calculated flue gas temperature of the heating appliance in °C
Wc,j
The values for b and y shall be obtained for both working conditions separately.
In case these values are not given, the flue gas data characterising the appliance are given in annex B.
In addition the declared volumetric concentration of CO of the flue gases at the relevant working conditions
(nominal heat output and minimum heat output for the appliances ) shall be specified. The declared
2 W,j
content of CO of the flue gases at the two working conditions can also be determined with Table B.1 and
Table B.2 of EN 13384-1:2002.
The calculated CO content of the flue gas of the heating appliance j (CO ) shall be determined for the
2 2 Wtat,j
two working conditions "in operation at nominal heat output" and ”in operation at minimum output” using the
following formula:
for heating appliances for liquid and gaseous fuels and heating appliances for solid fuels with automatic
feed
CO
Wc,j
in Vol.-% (12)mmf
Wc,j Wc,j
m2
mCO mf
W,j 2 W,j m1
W,j
in other cases
(CO ) = (CO ) in Vol.-%
2 Wc,j 2 W,j
Where:
(CO ) declared CO content of the flue gas of heating appliance j in Vol.-%
2 W,j 2
(CO ) calculated CO content of the flue gas of heating appliance j in Vol.-%
2 Wc,j 2
f , f coefficients according to EN 13384-1
m1 m2
m
calculated flue gas mass flow of heating appliance j in kg/s
Wc,j
m
declared flue gas mass flow of heating appliance j in kg/s
W, j
7 Data for chimney and connecting flue pipes
The mean roughness value for the inner wall (r resp. r ) and the thermal resistance ( resp. )
j V,j
, j V, j
for each connecting flue pipe and each chimney segment shall be identified (see EN 13384-1:2002, 5.6.2).
8 Basic data for the calculation
The basic data for the calculation shall be identified for each chimney segment unless otherwise specified in
this clause.
8.1 Air temperatures
8.1.1 External air temperature (T )
L
For the calculation of the external air temperature (T ) see EN 13384-1:2002, 5.7.1.2; a single value is
L
relevant for all chimney segments.
8.1.2 Ambient air temperature (T )
u
For the calculation of the ambient air temperature (T ) see EN 13384-1:2002, 5.7.1.3.
u
8.2 External air pressure (p )
L
For the calculation of the external air pressure (p ) see EN 13384-1:2002, 5.7.2, a single value is relevant
L
for all chimney segments.
8. 3 Gas constant
8.3.1 Gas constant of the air (R )
L
For the calculation of the gas constant of the air (R ) see EN 13384-1:2002, 5.7.3.1, a single value is
L
relevant for all chimney segments.
8.3.2 Gas constant of flue gas (R)
For the calculation of the gas constant of flue gas (R) see EN 13384-1:2002, 5.7.3.2.
For gas mixing use formula 19 in this standard.
8. 4 Density of air ()
L
For the calculation of the density of air () see EN 13384-1:2002, 5.7.4. A single value is relevant for all
L
chimney segments.
8. 5 Specific heat capacity of the flue gas (c )
p
For the calculation of the specific heat capacity of the flue gas (c ) see EN 13384-1:2002, 5.7.5.
p
For gas mixing use formulae 20, 21, 22 in this standard.
8.6 Water vapour content ((H O) ) and condensing temperature (T )
2 ,j sp
...