Commission Delegated Regulation (EU) 2017/654 of 19 December 2016 supplementing Regulation (EU) 2016/1628 of the European Parliament and of the Council with regard to technical and general requirements relating to emission limits and type-approval for internal combustion engines for non-road mobile machinery

If the emissions are measured on a dry basis, the measured concentration c d on dry basis shall be converted to the concentration c w on a wet basis by means of equation (7-3):

Image omitted; see official source	(7-3)

where:

k w	=	dry-to-wet conversion factor [-]
---	---	---
c d	=	emission concentration on a dry basis [ppm] or [% vol]

For complete combustion, the dry-to-wet conversion factor for raw exhaust gas is written as k w,a [-] and shall be calculated by means of equation (7-4):

Image omitted; see official source	(7-4)

where:

H a	=	intake air humidity [g H2O/kg dry air]
---	---	---
qm f, i	=	instantaneous fuel flow rate [kg/s]
---	---	---
qm ad, i	=	instantaneous dry intake air flow rate [kg/s]
---	---	---
p r	=	water pressure after cooler [kPa]
---	---	---
p b	=	total barometric pressure [kPa]
---	---	---
w H	=	hydrogen content of the fuel [% mass]
---	---	---
k f	=	combustion additional volume [m3/kg fuel]

with:

Image omitted; see official source	(7-5)

where:

w H	=	hydrogen content of fuel [% mass]
---	---	---
w N	=	nitrogen content of fuel [% mass]
---	---	---
w O	=	oxygen content of fuel [% mass]

In equation (7-4), the ratio p r/p b may be assumed:

Image omitted; see official source	(7-6)

For incomplete combustion (rich fuel air mixtures) and also for emission tests without direct air flow measurements, a second method of k w,a calculation is preferred:

Image omitted; see official source	(7-7)

where:

| | | |

| --- | --- | --- | | c CO2 | = | concentration of CO2 in the raw exhaust gas, on a dry basis [per cent vol] | | | | | | --- | --- | --- | | c CO | = | concentration of CO in the raw exhaust gas, on a dry basis [ppm] | | | | | | --- | --- | --- | | p r | = | water pressure after cooler [kPa] | | | | | | --- | --- | --- | | p b | = | total barometric pressure [kPa] | | | | | | --- | --- | --- | | α | = | molar to carbon hydrogen ratio [-] | | | | | | --- | --- | --- | | k w1 | = | intake air moisture [-] |

| | |

| --- | --- | | Image omitted; see official source | (7-8) |

2.1.4.   NOx correction for humidity and temperature

As the NOx emission depends on ambient air conditions, the NOx concentration shall be corrected for ambient air temperature and humidity with the factors kh,D or kh,G [-] given in equations (7-9) and (7-10). These factors are valid for a humidity range between 0 and 25 g H2O/kg dry air.

• (a) for compression-ignition engines Image omitted; see official source (7-9)

- (b) for spark ignition engines

kh.G = 0,6272 + 44,030 × 10^{– 3} × Ha – 0,862 × 10^{– 3} × Ha ² (7-10)

where:

H a	=	humidity of the intake air [g H2O/kg dry air]

2.1.5.   Component specific factor u

Two calculation procedures are described in points 2.1.5.1 and 2.1.5.2. The procedure set out in point 2.1.5.1 is more straightforward, since it uses tabulated u values for the ratio between component and exhaust gas density. The procedure set out in point 2.1.5.2 is more accurate for fuel qualities that deviate from the specifications in Annex VIII, but requires elementary analysis of the fuel composition.

2.1.5.1.   Tabulated values

Applying some simplifications (assumption on the λ value and on intake air conditions as shown in Table 7.1) to the equations set out in point 2.1.5.2, the resulting values for u gas are given in Table 7.1.

Table 7.1

Raw exhaust gas u and component densities (for emission concentration expressed in ppm)

Fuel	ρe			Gas
Fuel	ρe	NOx	CO	HC	CO2	O2	CH4
Fuel	ρe			ρgas [kg/m3]
Fuel	ρe	2,053	1,250	[^E0034]	1,9636	1,4277	0,716
Fuel	ρe			ugas [^E0035]
Diesel (non-road gas-oil)	1,2943	0,001586	0,000966	0,000482	0,001517	0,001103	0,000553
Ethanol for dedicated compression ignition engines (ED95)	1,2768	0,001609	0,000980	0,000780	0,001539	0,001119	0,000561
Natural gas / bio-methane [^E0036]	1,2661	0,001621	0,000987	0,000528 [^E0037]	0,001551	0,001128	0,000565
Propane	1,2805	0,001603	0,000976	0,000512	0,001533	0,001115	0,000559
Butane	1,2832	0,001600	0,000974	0,000505	0,001530	0,001113	0,000558
LPG [^E0038]	1,2811	0,001602	0,000976	0,000510	0,001533	0,001115	0,000559
Petrol (E10)	1,2931	0,001587	0,000966	0,000499	0,001518	0,001104	0,000553
Ethanol (E85)	1,2797	0,001604	0,000977	0,000730	0,001534	0,001116	0,000559

Depending on fuel

At λ = 2, dry air, 273 K, 101,3 kPa

u accurate within 0,2 % for mass composition of: C = 66 – 76 %; H = 22 – 25 %; N = 0 – 12 %.

NMHC on the basis of CH2,93 (for total HC the u gas coefficient of CH4 shall be used).

u accurate within 0,2 % for mass composition of: C3 = 70 – 90 %; C4 = 10 – 30 %.

2.1.5.2.   Calculated values

The component specific factor, u gas,i, may be calculated by the density ratio of the component and the exhaust gas or alternatively by the corresponding ratio of molar masses [equations (7-11) or (7-12)]:

Image omitted; see official source	(7-11)

or

Image omitted; see official source	(7-12)

where:

M gas	=	molar mass of the gas component [g/mol]
---	---	---
M e, i	=	instantaneous molar mass of the wet raw exhaust gas [g/mol]
---	---	---
ρ gas	=	density of the gas component [kg/m3]
---	---	---
ρ e,i	=	instantaneous density of the wet raw exhaust gas [kg/m3]

The molar mass of the exhaust gas, M e,i shall be derived for a general fuel composition CHαOεNδSγ under the assumption of complete combustion, and shall be calculated by means of equation (7-13):

Image omitted; see official source

(7-13)

Where:

qm f, i	=	instantaneous fuel mass flow rate on wet basis [kg/s]
---	---	---
qm aw, i	=	instantaneous intake air mass flow rate on wet basis [kg/s]
---	---	---
α	=	molar hydrogen-to-carbon ratio [-]
---	---	---
δ	=	molar nitrogen-to-carbon ratio [-]
---	---	---
ε	=	molar oxygen-to-carbon ratio [-]
---	---	---
γ	=	atomic sulphur-to-carbon ratio [-]
---	---	---
H a	=	intake air humidity [g H2O/kg dry air]
---	---	---
M a	=	dry intake air molecular mass = 28,965 g/mol

The instantaneous raw exhaust gas density ρ

e, i [kg/m³] shall be calculated by means of equation (7-14):

Image omitted; see official source	(7-14)

where:

qm f, i	=	instantaneous fuel mass flow rate [kg/s]
---	---	---
qm ad, i	=	instantaneous dry intake air mass flow rate [kg/s]
---	---	---
H a	=	intake air humidity [g H2O/kg dry air]
---	---	---
k f	=	combustion additional volume [m3/kg fuel] [see equation (7-5)]

2.1.6.   Mass flow rate of the exhaust gas

2.1.6.1.   Air and fuel measurement method

The method involves measurement of the air flow and the fuel flow with suitable flowmeters. The instantaneous exhaust gas flow qm ew, i [kg/s] shall be calculated by means of equation (7-15):

qm ew, i = qm aw, i + qm f, i	(7-15)

where:

qm aw, i	=	instantaneous intake air mass flow rate [kg/s]
---	---	---
qm f, i	=	instantaneous fuel mass flow rate [kg/s]

2.1.6.2.   Tracer measurement method

This involves measurement of the concentration of a tracer gas in the exhaust gas. The instantaneous exhaust gas flow q mew,i [kg/s] shall be calculated by means of equation (7-16):

Image omitted; see official source	(7-16)

where:

qV t	=	tracer gas flow rate [m3/s]
---	---	---
c mix, i	=	instantaneous concentration of the tracer gas after mixing [ppm]
---	---	---
ρ e	=	density of the raw exhaust gas [kg/m3]
---	---	---
c b	=	background concentration of the tracer gas in the intake air [ppm]

The background concentration of the tracer gas c b may be determined by averaging the background concentration measured immediately before the test run and after the test run. When the background concentration is less than 1 % of the concentration of the tracer gas after mixing c mix, i at maximum exhaust gas flow, the background concentration may be neglected.

2.1.6.3.   Air flow and air to fuel ratio measurement method

This involves exhaust gas mass calculation from the air flow and the air to fuel ratio. The instantaneous exhaust gas mass flow q mew, i [kg/s] shall be calculated by means of equation (7-17):

Image omitted; see official source	(7-17)

with:

Image omitted; see official source	(7-18)
Image omitted; see official source	(7-19)

where:

qm aw, i	=	wet intake air mass flow rate [kg/s]
---	---	---
A/F st	=	stoichiometric air-to-fuel ratio [-]
---	---	---
λi	=	instantaneous excess air ratio [-]
---	---	---
c COd	=	concentration of CO in the raw exhaust gas on a dry basis [ppm]
---	---	---
c CO2d	=	concentration of CO2 in the raw exhaust gas on a dry basis [per cent]
---	---	---
c HCw	=	concentration of HC in the raw exhaust gas on a wet basis [ppm C1]
---	---	---
α	=	molar hydrogen-to-carbon ratio [-]
---	---	---
δ	=	molar nitrogen-to-carbon ratio [-]
---	---	---
ε	=	molar oxygen-to-carbon ratio [-]
---	---	---
γ	=	atomic sulphur-to-carbon ratio [-]

2.1.6.4.   Carbon balance method, 1-step procedure

The following 1-step formula set out in equation (7-20) can be used for the calculation of the wet exhaust gas mass flow rate qm ew, i [kg/s]:

Image omitted; see official source	(7-20)

with the carbon factor f c [-] given by:

Image omitted; see official source	(7-21)

Where:

qm f, i	=	instantaneous fuel mass flow rate [kg/s]
---	---	---
w C	=	carbon content of fuel [% mass] (see equation (7-82) of point 3.3.3.1 or table 7.3)
---	---	---
H a	=	intake air humidity [g H2O/kg dry air]
---	---	---
k fd	=	combustion additional volume on a dry basis [m3/kg fuel]
---	---	---
c CO2d	=	dry CO2 concentration in the raw exhaust gas [%]
---	---	---
c CO2d,a	=	dry CO2 concentration in the ambient air [%]

| | | |

| --- | --- | --- | | c COd | = | dry CO concentration in the raw exhaust gas [ppm] |

| | | |

| --- | --- | --- | | c HCw | = | wet HC concentration in the raw exhaust gas [ppm] |

and factor k fd [m³/kg fuel] that is calculated by means of equation (7-22) on a dry basis by subtracting the water formed by combustion from k f:

k fd = k f – 0,11118 · w H	(7-22)

where:

k f	=	fuel specific factor of equation (7-5) [m3/kg fuel]
---	---	---
w H	=	hydrogen content of fuel [% mass]

2.2.   Diluted gaseous emissions

2.2.1.   Mass of the gaseous emissions

The exhaust gas mass flow rate shall be measured with a constant volume sampling (CVS) system, which may use a positive displacement pump (PDP), a critical flow venturi (CFV) or a subsonic venturi (SSV).

For systems with constant mass flow (i.e. with heat exchanger), the mass of the pollutants m gas [g/test] shall be determined by means of equation (7-23):

m gas = k h · k · u gas · c gas · m ed	(7-23)

where:

u gas is the ratio between density of exhaust gas component and density of air, as given in Table 7.2 or calculated by means of equation (7-34) [-]

c gas = mean background corrected concentration of the component on a wet basis [ppm] or [% vol] respectively

k h = NOx correction factor [-], only to be applied for the NOx emission calculation

k = 1 for c gasr,w, i in [ppm], k = 10 000 for c gasr,w, i in [% vol]

m ed = total diluted exhaust gas mass over the cycle [kg/test]

For systems with flow compensation (without heat exchanger), the mass of the pollutants m gas [g/test] shall be determined by calculation of the instantaneous mass emissions, by integration and by background correction by means of equation (7-24):

Image omitted; see official source	(7-24)

Where:

c e	=	emission concentration in the diluted exhaust gas, on a wet basis [ppm] or [% vol]
---	---	---
c d	=	emission concentration in the dilution air, on a wet basis [ppm] or [% vol]
---	---	---
m ed, i	=	mass of the diluted exhaust gas during time interval i [kg]

| | | |

| --- | --- | --- | | m ed | = | total mass of diluted exhaust gas over the cycle [kg] | | | | | | --- | --- | --- | | u gas | = | tabulated value from Table 7.2 [-] | | | | | | --- | --- | --- | | D | = | dilution factor [see equation (7-28) of point 2.2.2.2] [-] | | | | | | --- | --- | --- | | k h | = | NOx correction factor [-], only to be applied for the NOx emission calculation | | | | | | --- | --- | --- | | k | = | 1 for c in [ppm], k = 10 000 for c in [% vol] |

The concentrations c gas, c e and c d can be either values measured in a batch sample (bag, but not allowed for NOx and HC) or be averaged by integration from continuous measurements. Also m ed, i has to be averaged by integration over the test cycle.

The following equations show how the needed quantities (c e, u gas and m ed) shall be calculated.

2.2.2.   Dry-to-wet concentration conversion

All concentrations set out in point 2.2.1 measured dry shall be converted to a wet basis by means of equation (7-3).

2.2.2.1.   Diluted exhaust gas

Dry concentrations shall be converted to wet concentrations by means of one of the following two equations [(7-25) or (7-26)] applied to equation:

Image omitted; see official source	(7-25)

or

Image omitted; see official source	(7-26)

where:

α	=	molar hydrogen to carbon ratio of the fuel [-]
---	---	---
c CO2w	=	concentration of CO2 in the diluted exhaust gas on a wet basis [per cent vol]
---	---	---
c CO2d	=	concentration of CO2 in the diluted exhaust gas on a dry basis [per cent vol]

The dry to wet correction factor k w2 takes into consideration the water content of both intake air and dilution air and shall be calculated by means of equation (7-27):

Image omitted; see official source	(7-27)

where:

H a	=	intake air humidity [g H2O/kg dry air]
---	---	---
H d	=	dilution air humidity [g H2O/kg dry air]
---	---	---
D	=	dilution factor [see equation (7-28) of point 2.2.2.2] [-]

2.2.2.2.   Dilution factor

The dilution factor D [-] (which is necessary for the background correction and the k w2 calculation) shall be calculated by means of equation (7-28):

Image omitted; see official source	(7-28)

where:

F S	=	stoichiometric factor [-]
---	---	---
c CO2,e	=	concentration of CO2 in the diluted exhaust gas on a wet basis [per cent vol]
---	---	---
c HC,e	=	concentration of HC in the diluted exhaust gas on a wet basis [ppm C1]
---	---	---
c CO,e	=	concentration of CO in the diluted exhaust gas on a wet basis [ppm]

The stoichiometric factor shall be calculated by means of equation (7-29):

Image omitted; see official source	(7-29)

Where:

α	=	molar hydrogen to carbon ratio in the fuel [-]

Alternatively, if the fuel composition is not known, the following stoichiometric factors may be used:

F S (diesel) = 13,4

FS (LPG) = 11,6

FS (NG) = 9,5

FS (E10) = 13,3

FS (E85) = 11,5

If a direct measurement is made of the exhaust gas flow, the dilution factor D [-] may be calculated by means of equation (7-30):

Image omitted; see official source	(7-30)

Where:

qV CVS is the volumetric flow rate of diluted exhaust gas [m³/s]

qV ew = volumetric flow rate of raw exhaust gas [m³/s]

2.2.2.3.   Dilution air

k w,d = (1 – k w3) · 1,008	(7-31)

with

Image omitted; see official source	(7-32)

where:

H d	=	dilution air humidity [g H2O/kg dry air]

2.2.2.4.   Determination of the background corrected concentration

The average background concentration of the gaseous pollutants in the dilution air shall be subtracted from measured concentrations to get the net concentrations of the pollutants. The average values of the background concentrations can be determined by the sample bag method or by continuous measurement with integration. Equation (7-33) shall be used:

Image omitted; see official source	(7-33)

Where:

c gas	=	net concentration of the gaseous pollutant [ppm] or [% vol]
---	---	---
c gas,e	=	emission concentration in the diluted exhaust gas, on a wet basis [ppm] or [% vol]
---	---	---
c d	=	emission concentration in the dilution air, on a wet basis [ppm] or [% vol]
---	---	---
D	=	dilution factor [see equation (7-28) of point 2.2.2.2] [-]

2.2.3.   Component specific factor u

The component specific factor u gas of diluted gas can either be calculated by means of equation (7-34) or be taken from Table 7.2; in Table 7.2 the density of the diluted exhaust gas has been assumed equal to air density.

| | |

| --- | --- | | Image omitted; see official source | (7-34) |

Where:

M gas	=	molar mass of the gas component [g/mol]
---	---	---
M d,w	=	molar mass of diluted exhaust gas [g/mol]
---	---	---
M da,w	=	molar mass of dilution air [g/mol] (see equation (7-144) of point 3.9.3)
---	---	---
M r,w	=	molar mass of raw exhaust gas [g/mol] (see Appendix 2 point (5)
---	---	---
D	=	dilution factor [see equation (7-28) of point 2.2.2.2] [-]

Table 7.2

Diluted exhaust gas u values (for emission concentration expressed in ppm) and component densities

Fuel	ρe			Gas
Fuel	ρe	NOx	CO	HC	CO2	O2	CH4
Fuel	ρe			ρgas [kg/m3]
Fuel	ρe	2,053	1,250	[^E0039]	1,9636	1,4277	0,716
Fuel	ρe			ugas [^E0040]
Diesel (non-road gas-oil)	1,2943	0,001586	0,000966	0,000482	0,001517	0,001103	0,000553
Ethanol for dedicated compression ignition engines (ED95)	1,2768	0,001609	0,000980	0,000780	0,001539	0,001119	0,000561
Natural gas / bio-methane [^E0041]	1,2661	0,001621	0,000987	0,000528 [^E0042]	0,001551	0,001128	0,000565
Propane	1,2805	0,001603	0,000976	0,000512	0,001533	0,001115	0,000559
Butane	1,2832	0,001600	0,000974	0,000505	0,001530	0,001113	0,000558
LPG [^E0043]	1,2811	0,001602	0,000976	0,000510	0,001533	0,001115	0,000559
Petrol (E10)	1,2931	0,001587	0,000966	0,000499	0,001518	0,001104	0,000553
Ethanol (E85)	1,2797	0,001604	0,000977	0,000730	0,001534	0,001116	0,000559

Depending on fuel.

At λ = 2, dry air, 273 K, 101,3 kPa.

u accurate within 0,2 % for mass composition of: C = 66 – 76 %; H = 22 – 25 %; N = 0 – 12 %.

NMHC on the basis of CH2,93 (for total HC the u gas coefficient of CH4 shall be used).

u accurate within 0,2 % for mass composition of: C3 = 70 – 90 %; C4 = 10 – 30 %.

2.2.4.   Exhaust gas mass flow calculation

2.2.4.1.   PDP-CVS system

The mass of the diluted exhaust gas [kg/test] over the cycle shall be calculated by means of equation (7-35), if the temperature of the diluted exhaust gas m ed is kept within ± 6 K over the cycle by using a heat exchanger:

Image omitted; see official source	(7-35)

where:

V 0	=	volume of gas pumped per revolution under test conditions [m3/rev]
---	---	---
n P	=	total revolutions of pump per test [rev/test]
---	---	---
p p	=	absolute pressure at pump inlet [kPa]
---	---	---
Image omitted; see official source	=	average temperature of the diluted exhaust gas at pump inlet [K]
---	---	---
1,293 kg/m3	=	air density at 273,15 K and 101,325 kPa

If a system with flow compensation is used (i.e. without heat exchanger), the mass of the diluted exhaust gas m ed, i [kg] during the time interval shall be calculated by means of equation (7-36):

Image omitted; see official source	(7-36)

where:

V 0	=	volume of gas pumped per revolution under test conditions [m3/rev]
---	---	---
p p	=	absolute pressure at pump inlet [kPa]
---	---	---
n P, i	=	total revolutions of pump per time interval i [rev/Δt]
---	---	---
Image omitted; see official source	=	average temperature of the diluted exhaust gas at pump inlet [K]
---	---	---
1,293 kg/m3	=	air density at 273,15 K and 101,325 kPa

2.2.4.2.   CFV-CVS system

The mass flow over the cycle m ed [g/test] shall be calculated by means of equation (7-37), if the temperature of the diluted exhaust gas is kept within ± 11 K over the cycle by using a heat exchanger:

Image omitted; see official source	(7-37)

Where:

t	=	cycle time [s]
---	---	---
K V	=	calibration coefficient of the critical flow venturi for standard conditions Image omitted; see official source
---	---	---
p p	=	absolute pressure at venturi inlet [kPa]
---	---	---
T	=	absolute temperature at venturi inlet [K]
---	---	---
1,293 kg/m3	=	air density at 273,15 K and 101,325 kPa

If a system with flow compensation is used (i.e. without heat exchanger), the mass of the diluted exhaust gas m ed, i [kg] during the time interval shall be calculated by means of equation (7-38):

Image omitted; see official source	(7-38)

where:

Δti	=	time interval of the test [s]
---	---	---
K V	=	calibration coefficient of the critical flow venturi for standard conditions Image omitted; see official source
---	---	---
p p	=	absolute pressure at venturi inlet [kPa]
---	---	---
T	=	absolute temperature at venturi inlet [K]
---	---	---
1,293 kg/m3	=	air density at 273,15 K and 101,325 kPa

2.2.4.3.   SSV-CVS system

The diluted exhaust gas mass over the cycle m ed [kg/test] shall be calculated by means of equation (7-39), if the temperature of the diluted exhaust gas is kept within ± 11 K over the cycle by using a heat exchanger:

m ed = 1,293 · qV SSV · Δt	(7-39)

Where:

1,293 kg/m3	=	air density at 273,15 K and 101,325 kPa
---	---	---
Δt	=	cycle time [s]
---	---	---
qV SSV	=	air flow rate at standard conditions (101,325 kPa, 273,15 K) [m3/s]

with

Image omitted; see official source	(7-40)

Where:

A 0	=	collection of constants and units conversions = 0,0056940 Image omitted; see official source
---	---	---
d V	=	diameter of the SSV throat [mm]
---	---	---
C d	=	discharge coefficient of the SSV [-]
---	---	---
p p	=	absolute pressure at venturi inlet [kPa]
---	---	---
T in	=	temperature at the venturi inlet [K]
---	---	---
r p	=	ratio of the SSV throat to inlet absolute static pressure, Image omitted; see official source [-]

| | | |

| --- | --- | --- | | r D | = | ratio of the SSV throat diameter to the inlet pipe inner diameter Image omitted; see official source [-] |

If a system with flow compensation is used (i.e. without heat exchanger), the mass of the diluted exhaust gas m

ed, i [kg] during the time interval shall be calculated by means of equation (7-41):

m ed, i = 1,293 · qV SSV · Δt i	(7-41)

Where:

1,293 kg/m3	=	air density at 273,15 K and 101,325 kPa
---	---	---
Δti	=	time interval [s]
---	---	---
qV SSV	=	volumetric flow rate of the SSV [m3/s]

2.3.   Calculation of particulate emission

2.3.1.   Transient (NRTC and LSI-NRTC) test cycles and RMC

The particulate mass shall be calculated after buoyancy correction of the particulate sample mass in accordance with point 8.1.13.2.5 of Annex VI.

2.3.1.1.   Partial flow dilution system

2.3.1.1.1.   Calculation based on sample ratio

The particulate emission over the cycle m PM [g] shall be calculated by means of equation (7-42):

Image omitted; see official source	(7-42)

where:

m f	=	particulate mass sampled over the cycle [mg]
---	---	---
r s	=	average sample ratio over the test cycle [-]

with:

Image omitted; see official source	(7-43)

Where:

m se	=	sample mass of raw exhaust gas over the cycle [kg]
---	---	---
m ew	=	total mass of raw exhaust gas over the cycle [kg]
---	---	---
m sep	=	mass of diluted exhaust gas passing the particulate collection filters [kg]
---	---	---
m sed	=	mass of diluted exhaust gas passing the dilution tunnel [kg]

In case of the total sampling type system, m sep and m sed are identical.

2.3.1.1.2.   Calculation based on dilution ratio

The particulate emission over the cycle m PM [g] shall be calculated by means of equation (7-44):

Image omitted; see official source	(7-44)

Where:

m f	=	particulate mass sampled over the cycle [mg]
---	---	---
m sep	=	mass of diluted exhaust gas passing the particulate collection filters [kg]
---	---	---
m edf	=	mass of equivalent diluted exhaust gas over the cycle [kg]

The total mass of equivalent diluted exhaust gas mass over the cycle m edf [kg] shall be determined by means of equation (7-45):

Image omitted; see official source	(7-45)

With:

Image omitted; see official source	(7-46)
Image omitted; see official source	(7-47)

Where:

qm edf, i	=	instantaneous equivalent diluted exhaust gas mass flow rate [kg/s]
---	---	---
qm ew, i	=	instantaneous exhaust gas mass flow rate on a wet basis [kg/s]
---	---	---
r d, i	=	instantaneous dilution ratio [-]
---	---	---
qm dew, i	=	instantaneous diluted exhaust gas mass flow rate on a wet basis [kg/s]
---	---	---
qm dw,i	=	instantaneous dilution air mass flow rate [kg/s]
---	---	---
ƒ	=	data sampling rate [Hz]
---	---	---
N	=	number of measurements [-]

2.3.1.2.   Full flow dilution system

The mass emission shall be calculated by means of equation (7-48):

Image omitted; see official source	(7-48)

where:

m f	=	is the particulate mass sampled over the cycle [mg]
---	---	---
m sep	=	is the mass of diluted exhaust gas passing the particulate collection filters [kg]
---	---	---
m ed	=	is the mass of diluted exhaust gas over the cycle [kg]

with

m sep = m set – m ssd	(7-49)

Where:

m set	=	mass of double diluted exhaust gas through particulate filter [kg]
---	---	---
m ssd	=	mass of secondary dilution air [kg]

2.3.1.2.1.   Background correction

The particulate mass m PM,c [g] may be background corrected by means of equation (7-50):

Image omitted; see official source	(7-50)

Where:

m f	=	particulate mass sampled over the cycle [mg]
---	---	---
m sep	=	mass of diluted exhaust gas passing the particulate collection filters [kg]
---	---	---
m sd	=	mass of dilution air sampled by background particulate sampler [kg]
---	---	---
m b	=	mass of collected background particulates of dilution air [mg]
---	---	---
m ed	=	mass of diluted exhaust gas over the cycle [kg]
---	---	---
D	=	dilution factor [see equation (7-28) of point 2.2.2.2] [-]

2.3.2.   Calculation for discrete-mode NRSC

2.3.2.1.   Dilution system

All calculations shall be based upon the average values of the individual modes i during the sampling period.

• (a) For partial-flow dilution, the equivalent mass flow of diluted exhaust gas shall be determined by means of equation (7-51) and the system with flow measurement shown in Figure 9.2: Image omitted; see official source (7-51) Image omitted; see official source (7-52) Where: qm edf = equivalent diluted exhaust gas mass flow rate [kg/s] qm ew = exhaust gas mass flow rate on a wet basis [kg/s] r d = dilution ratio [-] qm dew = diluted exhaust gas mass flow rate on a wet basis [kg/s] qm dw = dilution air mass flow rate [kg/s]

- (b) For full-flow dilution systems qm

dew is used as qm edf.

2.3.2.2.   Calculation of the particulate mass flow rate

The particulate emission flow rate over the cycle q mPM [g/h] shall be calculated by means of equations (7-53), (7-56), (7-57) or (7-58):

• (a) For the single-filter method Image omitted; see official source (7-53) Image omitted; see official source (7-54) Image omitted; see official source (7-55) Where: qm PM = particulate mass flow rate [g/h] m f = particulate mass sampled over the cycle [mg] Image omitted; see official source = average equivalent diluted exhaust gas mass flow rate on wet basis [kg/s] qm edf i = equivalent diluted exhaust gas mass flow rate on wet basis at mode i [kg/s] WFi = weighting factor for the mode i [-] m sep = mass of diluted exhaust gas passing the particulate collection filters [kg] m sep i = mass of diluted exhaust gas sample passed through the particulate sampling filter at mode i [kg] N = number of measurements [-]

• (b) For the multiple-filter method Image omitted; see official source (7-56) Where: qm PM i = particulate mass flow rate for the mode i [g/h] m f i = particulate sample mass collected at mode i [mg] qm edf i = equivalent diluted exhaust gas mass flow rate on wet basis at mode i [kg/s] m sep i = mass of diluted exhaust gas sample passed through the particulate sampling filter at mode i [kg] The PM mass is determined over the test cycle by summation of the average values of the individual modes i during the sampling period. The particulate mass flow rate qm PM [g/h] or qm PM i [g/h] may be background corrected as follows:

• (c) For the single-filter method Image omitted; see official source (7-57) Where: qm PM = particulate mass flow rate [g/h] m f = particulate sample mass collected [mg] m sep = mass of diluted exhaust gas sample passed through the particulate sampling filter [kg] m f,d = particulate sample mass of the dilution air collected [mg] m d = mass of the dilution air sample passed through the particulate sampling filters [kg] Di = dilution factor at mode i [see equation (7-28) of point 2.2.2.2] [-] WFi = weighting factor for the mode i [-] Image omitted; see official source = average equivalent diluted exhaust gas mass flow rate on wet basis [kg/s]

• (d) For the multiple-filter method Image omitted; see official source (7-58) Where: qm PM i = particulate mass flow rate at mode i [g/h] m f i = particulate sample mass collected at mode i [mg] m sep i = mass of diluted exhaust gas sample passed through the particulate sampling filter at mode i [kg] m f,d = particulate sample mass of the dilution air collected [mg] m d = mass of the dilution air sample passed through the particulate sampling filters [kg] D = dilution factor [see equation (7-28) of point 2.2.2.2] [-] q medf i = equivalent diluted exhaust gas mass flow rate on wet basis at mode i [kg/s] If more than one measurement is made, m f,d/m d shall be replaced with

Image omitted; see official source .

2.4.   Cycle work and specific emissions

2.4.1.   Gaseous emissions

2.4.1.1.   Transient (NRTC and LSI-NRTC) test cycles and RMC

Reference is made to points 2.1 and 2.2 for raw and diluted exhaust gas respectively. The resulting values for power P [kW] shall be integrated over a test interval. The total work W act [kWh] is calculated by means of equation (7-59):

Image omitted; see official source	(7-59)

Where:

Pi	=	instantaneous engine power [kW]
---	---	---
ni	=	instantaneous engine speed [rpm]
---	---	---
Ti	=	instantaneous engine torque [Nm]
---	---	---
W act	=	actual cycle work [kWh]
---	---	---
ƒ	=	data sampling rate [Hz]
---	---	---
N	=	number of measurements [-]
---	---	---
Δti	=	the measurement interval [s]

Where auxiliaries were fitted in accordance with Appendix 2 of Annex VI there shall be no adjustment to the instantaneous engine torque in equation (7-59). Where, according to points 6.3.2 or 6.3.3 of Annex VI to this regulation necessary auxiliaries that should have been fitted for the test are not installed, or auxiliaries that should have been removed for the test are installed, the value of Ti used in equation (7-59) shall be adjusted by means of equation (7-60):

T i = T i ,meas + T i, AUX	(7-60)

Where:

Ti ,meas	=	measured value of instantaneous engine torque
---	---	---
Ti, AUX	=	corresponding value of torque required to drive auxiliaries determined in accordance with equation (6-18) of Annex VI.

The specific emissions e gas [g/kWh] shall be calculated in the following ways depending on the type of test cycle.

Image omitted; see official source	(7-61)

Where:

m gas	=	total mass of emission [g/test]
---	---	---
W act	=	cycle work [kWh]

In case of the NRTC, for gaseous emissions other than CO2 the final test result e gas [g/kWh] shall be a weighted average from cold-start run and hot-start run by means of equation (7-62):

Image omitted; see official source	(7-62)

Where:

m cold is the gas mass emissions of the cold-start NRTC [g]

W act, cold is the actual cycle work of the cold-start NRTC [kWh]

m hot is the gas mass emissions of the hot-start NRTC [g]

W act, hot is the actual cycle work of the hot-start NRTC [kWh]

In case of the NRTC, for CO2 the final test result e CO2 [g/kWh] shall be calculated from the hot-start NRTC by means of equation (7-63):

Image omitted; see official source	(7-63)

Where:

m CO2, hot is the CO2 mass emissions of the hot-start NRTC [g]

W act, hot is the actual cycle work of the hot-start NRTC [kWh]

2.4.1.2.   Discrete-mode NRSC

The specific emissions e gas [g/kWh] are calculated by means of equation (7-64):

Image omitted; see official source	(7-64)

where:

qm gas, i	=	mean emission mass flow rate for the mode i [g/h]
---	---	---
Pi	=	engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX)
---	---	---
WFi	=	weighting factor for the mode i [-]
---	---	---
Nmode	=	number of modes in applicable discrete-mode NRSC

2.4.2.   Particulate emissions

2.4.2.1.   Transient (NRTC and LSI-NRTC) test cycles and RMC

The particulate specific emissions shall be calculated with equation (7-61) where e gas [g/kWh] and m gas [g/test] are substituted by e PM [g/kWh] and m PM [g/test] respectively:

Image omitted; see official source	(7-65)

where:

m PM	=	total mass of particulates emission, calculated in accordance with point 2.3.1.1 or 2.3.1.2 [g/test]
---	---	---
W act	=	cycle work [kWh]

The emissions on the transient composite cycle (i.e. cold-start NRTC and hot-start NRTC) shall be calculated as shown in point 2.4.1.1.

2.4.2.2.   Discrete-mode NRSC

The particulate specific emission e PM [g/kWh] shall be calculated by means of equations (7-66) or (7-67):

• (a) For the single-filter method Image omitted; see official source (7-66) where: Pi = engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX) WFi = weighting factor for the mode i [-] qm PM = particulate mass flow rate [g/h] Nmode = number of modes in applicable discrete-mode NRSC

• (b) For the multiple-filter method Image omitted; see official source (7-67) Where: Pi = engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX) WFi = weighting factor for the mode i [-] qm PM i = particulate mass flow rate at mode i [g/h] Nmode = number of modes in applicable discrete-mode NRSC

For the single-filter method, the effective weighting factor, WF

e i, for each mode shall be calculated by means of equation (7-68):

Image omitted; see official source	(7-68)

Where:

m sep i	=	mass of the diluted exhaust gas sample passed through the particulate sampling filters at mode i [kg]

| | | |

| --- | --- | --- | | Image omitted; see official source | = | average equivalent diluted exhaust gas mass flow rate [kg/s] | | | | | | --- | --- | --- | | qm edf i | = | equivalent diluted exhaust gas mass flow rate at mode i [kg/s] | | | | | | --- | --- | --- | | m sep | = | mass of the diluted exhaust gas sample passed through the particulate sampling filters [kg] |

The value of the effective weighting factors shall be within 0,005 (absolute value) of the weighting factors listed in Appendix 1 of Annex XVII.

2.4.3.   Adjustment for emission controls that are regenerated on an infrequent (periodic) basis

In case of engines, other than those of category RLL, equipped with exhaust after-treatment systems that are regenerated on an infrequent (periodic) basis (see point 6.6.2 of Annex VI), the specific emissions of gaseous and particulate pollutants calculated according to points 2.4.1 and 2.4.2 shall be corrected with either the applicable multiplicative adjustment factor or with the applicable additive adjustment factor. In the case that infrequent regeneration did not take place during the test the upward factor shall be applied (k ru,m or k ru,a). In the case that infrequent regeneration took place during the test the downward factor shall be applied (k rd,m or k rd,a). In the case of the discrete-mode NRSC, where the adjustment factors have been determined for each mode they shall be applied to each mode during the calculation of the weighted emission result.

2.4.4.   Adjustment for deterioration factor

The specific emissions of gaseous and particulate pollutants calculated according to points 2.4.1 and 2.4.2, where applicable inclusive of the infrequent regeneration adjustment factor according to point 2.4.3, shall also be adjusted by the applicable multiplicative or additive deterioration factor established according to the requirements of Annex III.

2.5.   Diluted Exhaust Flow (CVS) Calibration and Related Calculations

The CVS system shall be calibrated by using an accurate flowmeter and a restricting device. The flow through the system shall be measured at different restriction settings, and the control parameters of the system shall be measured and related to the flow.

Various types of flowmeters may be used, e.g. calibrated venturi, calibrated laminar flowmeter, calibrated turbine meter.

2.5.1.   Positive displacement pump (PDP)

All the parameters related to the pump shall be simultaneously measured along with the parameters related to a calibration venturi which is connected in series with the pump. The calculated flow rate (in m³/s at pump inlet, absolute pressure and temperature) shall be plotted versus a correlation function which is the value of a specific combination of pump parameters. The linear equation which relates the pump flow and the correlation function shall be determined. If a CVS has a multiple speed drive, the calibration shall be performed for each range used.

Temperature stability shall be maintained during calibration.

Leaks in all the connections and ducting between the calibration venturi and the CVS pump shall be maintained lower than 0,3 % of the lowest flow point (highest restriction and lowest PDP speed point).

The airflow rate (qV CVS) at each restriction setting (minimum 6 settings) shall be calculated in standard m³/s from the flowmeter data using the manufacturer's prescribed method. The airflow rate shall then be converted to pump flow (V 0) in m³/rev at absolute pump inlet temperature and pressure by means of equation (7-69):

Image omitted; see official source	(7-69)

where:

qV CVS	=	airflow rate at standard conditions (101,325 kPa, 273,15 K) [m3/s]
---	---	---
T	=	temperature at pump inlet [K]
---	---	---
p p	=	absolute pressure at pump inlet [kPa]
---	---	---
n	=	pump speed [rev/s]

To account for the interaction of pressure variations at the pump and the pump slip rate, the correlation function (X 0) [s/rev] between pump speed, pressure differential from pump inlet to pump outlet and absolute pump outlet pressure shall be calculated by means of equation (7-70):

Image omitted; see official source	(7-70)

Where:

| | | |

| --- | --- | --- | | Δp p | = | pressure differential from pump inlet to pump outlet [kPa] | | | | | | --- | --- | --- | | p p | = | absolute outlet pressure at pump outlet [kPa] | | | | | | --- | --- | --- | | n | = | pump speed [rev/s] |

A linear least-square fit shall be performed to generate the calibration by means of equation (7-71):

V 0 = D 0 –m · X 0	(7-71)

with D 0 [m³/rev] and m [m³/s], intercept and slope respectively, describing the regression line.

For a CVS system with multiple speeds, the calibration curves generated for the different pump flow ranges shall be approximately parallel, and the intercept values (D 0) shall increase as the pump flow range decreases.

The calculated values from the equation shall be within ± 0,5 % of the measured value of V

2.5.2.   Critical flow venturi (CFV)

Calibration of the CFV is based upon the flow equation for a critical venturi. Gas flow is a function of venturi inlet pressure and temperature.

To determine the range of critical flow, K

V shall be plotted as a function of venturi inlet pressure. For critical (choked) flow, K V will have a relatively constant value. As pressure decreases (vacuum increases), the venturi becomes unchoked and K V decreases, which indicates that the CFV is operated outside the permissible range.

The airflow rate (qV CVS) at each restriction setting (minimum 8 settings) shall be calculated in standard m³/s from the flowmeter data using the manufacturer's prescribed method. The calibration coefficient K V

Image omitted; see official source shall be calculated from the calibration data for each setting by means of equation (7-72):

Image omitted; see official source	(7-72)

Where:

qV SSV	=	air flow rate at standard conditions (101,325 kPa, 273,15 K) [m3/s]
---	---	---
T	=	temperature at the venturi inlet [K]
---	---	---
p p	=	absolute pressure at venturi inlet [kPa]

The average K V and the standard deviation shall be calculated. The standard deviation shall not exceed ± 0,3 % of the average K V.

2.5.3.   Subsonic venturi (SSV)

Calibration of the SSV is based upon the flow equation for a subsonic venturi. Gas flow is a function of inlet pressure and temperature, pressure drop between the SSV inlet and throat, as shown in equation (7-40).

The airflow rate (qV SSV) at each restriction setting (minimum 16 settings) shall be calculated in standard m³/s from the flowmeter data using the manufacturer's prescribed method. The discharge coefficient shall be calculated from the calibration data for each setting by means of equation (7-73):

Image omitted; see official source	(7-73)

Where:

A 0	=	collection of constants and units conversions Image omitted; see official source
---	---	---
qV SSV	=	air flow rate at standard conditions (101,325 kPa, 273,15 K) [m3/s]
---	---	---
T in,V	=	temperature at the venturi inlet [K]
---	---	---
d V	=	diameter of the SSV throat [mm]
---	---	---
r p	=	ratio of the SSV throat to inlet absolute static pressure = 1 – Δp/p p [-]
---	---	---
r D	=	ratio of the SSV throat diameter, d V, to the inlet pipe inner diameter D [-]

To determine the range of subsonic flow, C d shall be plotted as a function of Reynolds number Re, at the SSV throat. The Re at the SSV throat shall be calculated by means of equation (7-74):

Image omitted; see official source	(7-74)

with

Image omitted; see official source	(7-75)

Where:

| | | |

| --- | --- | --- | | A1 | = | collection of constants and units conversions = 27,43831 Image omitted; see official source |

| | | |

| --- | --- | --- | | qV SSV | = | air flow rate at standard conditions (101,325 kPa, 273,15 K) [m³/s] | | | | | | --- | --- | --- | | d V | = | diameter of the SSV throat [mm] | | | | | | --- | --- | --- | | μ | = | absolute or dynamic viscosity of the gas [kg/(m · s)] |

| | | |

| --- | --- | --- | | b | = | 1,458 × 10⁶ (empirical constant) [kg/(m · s · K^0,5)] | | | | | | --- | --- | --- | | S | = | 110,4 (empirical constant) [K] |

Because qV SSV is an input to the Re equation, the calculations shall be started with an initial guess for qV SSV or C d of the calibration venturi, and repeated until qV SSV converges. The convergence method shall be accurate to 0,1 % of point or better.

For a minimum of sixteen points in the region of subsonic flow, the calculated values of C d from the resulting calibration curve fit equation shall be within ± 0,5 % of the measured C d for each calibration point.

2.6.   Drift Correction

2.6.1.   General procedure

The calculations in this section shall be performed to determine if gas analyzer drift invalidates the results of a test interval. If drift does not invalidate the results of a test interval, the test interval's gas analyzer responses shall be corrected for drift in accordance with point 2.6.2. The drift-corrected gas analyzer responses shall be used in all subsequent emission calculations. The acceptable threshold for gas analyzer drift over a test interval is specified in point 8.2.2.2 of Annex VI.

The general test procedure shall follow the provisions specified in Appendix 1 with concentrations xi or

Image omitted; see official source being replaced by concentrations ci or

Image omitted; see official source .

2.6.2.   Calculation procedure

The drift correction shall be calculated by means of equation (7-76):

Image omitted; see official source	(7-76)

Where:

| | | |

| --- | --- | --- | | ci driftcor | = | concentration corrected for drift [ppm] |

| | | |

| --- | --- | --- | | c refzero | = | reference concentration of the zero gas, which is usually zero unless known to be otherwise [ppm] | | | | | | --- | --- | --- | | c refspan | = | reference concentration of the span gas [ppm] |

| | | |

| --- | --- | --- | | c prespan | = | pre-test interval gas analyzer response to the span gas concentration [ppm] | | | | | | --- | --- | --- | | c postspan | = | post-test interval gas analyzer response to the span gas concentration [ppm] | | | | | | --- | --- | --- | | ci or Image omitted; see official source | = | concentration recorded, i.e. measured, during test, before drift correction [ppm] | | | | | | --- | --- | --- | | c prezero | = | pre-test interval gas analyzer response to the zero gas concentration [ppm] | | | | | | --- | --- | --- | | c postzero | = | post-test interval gas analyzer response to the zero gas concentration [ppm] |

3.1.   Subscripts

	Quantity
abs	Absolute quantity
act	Actual quantity
air	Air, dry
atmos	Atmospheric
bkgnd	Background
C	Carbon
cal	Calibration quantity
CFV	Critical flow venturi
cor	Corrected quantity
dil	Dilution air
dexh	Diluted exhaust gas
dry	Dry quantity
exh	Raw exhaust gas
exp	Expected quantity
eq	Equivalent quantity
fuel	Fuel
	Instantaneous measurement (e.g.: 1 Hz)
i	An individual of a series
idle	Condition at idle
in	Quantity in
init	Initial quantity, typically before an emission test
max	Maximum (i.e. peak) value
meas	Measured quantity
min	Minimum value
mix	Molar mass of air
out	Quantity out
part	Partial quantity
PDP	Positive displacement pump
raw	Raw exhaust
ref	Reference quantity
rev	Revolution
sat	Saturated condition
slip	PDP slip
smpl	Sampling
span	Span quantity
SSV	Subsonic venturi
std	Standard quantity
test	Test quantity
total	Total quantity
uncor	Uncorrected quantity
vac	Vacuum quantity
weight	Calibration weight
wet	Wet quantity
zero	Zero quantity

3.2.   Symbols for chemical balance

x dil/exh = Amount of dilution gas or excess air per mole of exhaust gas

x H2Oexh = Amount of water in exhaust per mole of exhaust gas

x Ccombdry = Amount of carbon from fuel in the exhaust per mole of dry exhaust gas

x H2Oexhdry = Amount of water in exhaust per dry mole of dry exhaust gas

x prod/intdry = Amount of dry stoichiometric products per dry mole of intake air

x dil/exhdry = Amount of dilution gas and/or excess air per mole of dry exhaust gas

x int/exhdry = Amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust gas

x raw/exhdry = Amount of undiluted exhaust gas, without excess air, per mole of dry (raw or diluted) exhaust gas

x O2intdry = Amount of intake air O2 per mole of dry intake air

x CO2intdry = Amount of intake air CO2 per mole of dry intake air

x H2Ointdry = Amount of intake air H2O per mole of dry intake air

x CO2int = Amount of intake air CO2 per mole of intake air

x

CO2dil = Amount of dilution gas CO2 per mole of dilution gas

x

CO2dildry = Amount of dilution gas CO2 per mole of dry dilution gas

x H2Odildry = Amount of dilution gas H2O per mole of dry dilution gas

x H2Odil = Amount of dilution gas H2O per mole of dilution gas

x [emission]meas = Amount of measured emission in the sample at the respective gas analyzer

x [emission]dry = Amount of emission per dry mole of dry sample

x H2O[emission]meas = Amount of water in sample at emission-detection location

x H2Oint = Amount of water in the intake air, based on a humidity measurement of intake air

3.3.   Basic parameters and relationships

3.3.1.   Dry air and chemical species

This section uses the following values for dry air composition:

x O2airdry = 0,209445 mol/mol

x Arairdry = 0,00934 mol/mol

x N2airdry = 0,78084 mol/mol

x CO2airdry = 375 μmol/mol

This section uses the following molar masses or effective molar masses of chemical species:

M air = 28,96559 g/mol (dry air)

M Ar = 39,948 g/mol (argon)

M C = 12,0107 g/mol (carbon)

M CO = 28,0101 g/mol (carbon monoxide)

M CO2 = 44,0095 g/mol (carbon dioxide)

M H = 1,00794 g/mol (atomic hydrogen)

M H2 = 2,01588 g/mol (molecular hydrogen)

M H2O = 18,01528 g/mol (water)

M He = 4,002602 g/mol (helium)

M N = 14,0067 g/mol (atomic nitrogen)

M N2 = 28,0134 g/mol (molecular nitrogen)

M NOx = 46,0055 g/mol (oxides of nitrogen (*))

M O = 15,9994 g/mol (atomic oxygen)

M O2 = 31,9988 g/mol (molecular oxygen)

M C3H8 = 44,09562 g/mol (propane)

M S = 32,065 g/mol (sulphur)

M HC = 13,875389 g/mol (total hydrocarbon (**))

- (**)The effective molar mass of HC is defined by an atomic hydrogen-to-carbon ratio, α, of 1,85;

• (*)The effective molar mass of NOx is defined by the molar mass of nitrogen dioxide, NO2.

This section uses the following molar gas constant R for ideal gases:

R = 8,314472J (mol · K)

This section uses the following ratios of specific heats γ [J/(kg · K)]/[J/(kg · K)] for dilution air and diluted exhaust:

γ air = 1,399 (ratio of specific heats for intake air or dilution air)

γ dil = 1,399 (ratio of specific heats for diluted exhaust gas)

γ exh = 1,385 (ratio of specific heats for raw exhaust gas)

3.3.2.   Wet air

This section describes how to determine the amount of water in an ideal gas:

3.3.2.1.   Vapour pressure of water

The vapour pressure of water p H2O [kPa] for a given saturation temperature condition, T sat [K], shall be calculated by means of equations (7-77) or (7-78):

• (a) For humidity measurements made at ambient temperatures from 0 to 100 °C or for humidity measurements made over super-cooled water at ambient temperatures from – 50 to 0 °C: Image omitted; see official source (7-77) Where: p H2O = vapour pressure of water at saturation temperature condition [kPa] T sat = saturation temperature of water at measured condition [K]

• (b) For humidity measurements made over ice at ambient temperatures from (– 100 to 0) °C: Image omitted; see official source (7-78) Where: T sat = saturation temperature of water at measured condition [K]

3.3.2.2.   Dew point

If humidity is measured as a dew point, the amount of water in an ideal gas x H2O [mol/mol] shall be obtained by means of equation (7-79):

Image omitted; see official source	(7-79)

Where:

x H2O = amount of water in an ideal gas [mol/mol]

p H2O = vapour pressure of water at the measured dew point, T sat=T dew [kPa]

p abs = wet static absolute pressure at the location of dew point measurement [kPa]

3.3.2.3.   Relative humidity

If humidity is measured as a relative humidity RH %, the amount of water of an ideal gas x H2O [mol/mol] is calculated by means of equation (7-80):

Image omitted; see official source	(7-80)

Where:

RH % = relative humidity [%]

p H2O = water vapour pressure at 100 % relative humidity at the location of relative humidity measurement, T sat=T amb [kPa]

p

abs = wet static absolute pressure at the location of relative humidity measurement [kPa]

3.3.2.4.   Dew point determination from relative humidity and dry bulb temperature

If humidity is measured as a relative humidity, RH %, the dew point, T

dew, shall be determined from RH % and dry bulb temperature by means of equation (7-81):

Image omitted; see official source

(7-81)

Where

p H2O = water vapor pressure scaled to the relative humidity at the location of relative humidity measurement, T sat = T amb

T dew = dew point as determined from relative humidity and dry bulb temperature measurements

3.3.3.   Fuel properties

The general chemical formula of fuel is CHαOβSγNδ with α atomic hydrogen-to-carbon ratio (H/C), β atomic oxygen-to-carbon ratio (O/C), γ atomic sulphur-to-carbon ratio (S/C) and δ atomic nitrogen-to-carbon ratio (N/C). Based on this formula the carbon mass fraction of fuel w C can be calculated. In case of diesel fuel the simple formula CHαOβ may be used. Default values for fuel composition may be derived from Table 7.3:

Table 7.3

Default values of atomic hydrogen-to-carbon ratio, α, atomic oxygen-to-carbon ratio, β, atomic sulphur-to-carbon ratio, γ, atomic nitrogen-to-carbon ratio, δ, and carbon mass fraction of fuel, w C for reference fuels

Fuel	Atomic hydrogen, oxygen, sulphur and nitrogen-to-carbon ratios CHαOβSγNδ	Carbon mass concentration, w C [g/g]
Diesel (non-road gas-oil)	CH1,80O0S0N0	0,869
Ethanol for dedicated compression ignition engines (ED95)	CH2,92O0,46S0N0	0,538
Petrol (E10)	CH1,92O0,03S0N0	0,833
Petrol (E0)	CH1,85O0S0N0	0,866
Ethanol (E85)	CH2,73O0,36S0N0	0,576
LPG	CH2,64O0S0N0	0,819
Natural Gas/Biomethane	CH3,78O0,016S0N0	0,747

3.3.3.1.   Calculation of carbon mass concentration wC

As an alternative to the default values in Table 7.3, or where default values are not given for the reference fuel being used, the carbon mass concentration w C may be calculated from measured fuel properties by means of equation (7-82). Values for α and β shall be determined for the fuel and inserted into the equation in all cases, but γ and δ may optionally be set to zero if they are zero in the corresponding line of Table 7.3:

Image omitted; see official source	(7-82)

where:

M C = molar mass of carbon.

α = atomic hydrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

M H = molar mass of hydrogen.

β = atomic oxygen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

M O = molar mass of oxygen.

γ = atomic sulphur-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

M S = molar mass of sulphur.

δ = atomic nitrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

M

N = molar mass of nitrogen.