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
This section describes the calculations for calibrating various flow meters. Point 3.9.1 first describes how to convert reference flow meter outputs for use in the calibration equations, which are presented on a molar basis. The remaining points describe the calibration calculations that are specific to certain types of flow meters.
The calibration equations in this section use molar flow rate, ṅ ref, as a reference quantity. If the adopted reference meter outputs a flow rate in a different quantity, such as standard volume rate, V̇ stdref actual volume rate, V̇ actdref, or mass rate, ṁ ref, the reference meter output shall be converted to a molar flow rate by means of equations (7-136), (7-137) and (7-138), noting that while values for volume rate, mass rate, pressure, temperature, and molar mass may change during an emission test, they should be kept as constant as practical for each individual set point during a flow meter calibration:
| (7-136) | |
|---|---|
where:
For each restrictor position, the following values shall be calculated from the mean values determined in point 8.1.8.4 of Annex VI, as follows:
(a) PDP volume pumped per revolution, V rev (m3/rev): (7-137) where: = mean value of reference molar flow rate [mol/s] R = molar gas constant [J/(mol · K)] = mean inlet temperature [K] = mean inlet pressure [Pa] = mean rotational speed [rev/s]
(b) PDP slip correction factor, K s [s/rev]: (7-138) Where: = mean reference molar flow rate [mol/s] = mean inlet temperature [K] = mean inlet pressure [Pa] = mean outlet pressure [Pa] = mean PDP revolution speed [rev/s] R = molar gas constant [J/(mol · K)]
(c) A least-squares regression of PDP volume pumped per revolution, V rev, versus PDP slip correction factor, K s, shall be performed by calculating slope, a 1, and intercept, a 0, as described in Appendix 4;
(d) The procedure in subparagraphs (a) to (c) of this point shall be repeated for every speed that PDP is operated;
(e) Table 7.4 Example of PDP calibration data [rev/min] [rev/s] a 1 [m3/min] a 1 [m3/s] a 0 [m3/rev] 755,0 12,58 50,43 0,8405 0,056 987,6 16,46 49,86 0,831 – 0,013 1 254,5 20,9 48,54 0,809 0,028 1 401,3 23,355 47,30 0,7883 – 0,061
(f) For each speed at which the PDP is operated, the corresponding slope, a 1, and intercept, a 0, shall be used to calculate flow rate during emission testing as described in point 3.6.3(b).
This section describes the governing equations and permissible assumptions for calibrating a venturi and calculating flow using a venturi. Because a subsonic venturi (SSV) and a critical-flow venturi (CFV) both operate similarly, their governing equations are nearly the same, except for the equation describing their pressure ratio, r (i.e., r SSV versus r CFV). These governing equations assume one-dimensional isentropic inviscid compressible flow of an ideal gas. In point 3.9.3(d), other assumptions that may be made are described. If the assumption of an ideal gas for the measured flow is not allowed, the governing equations include a first-order correction for the behaviour of a real gas; namely, the compressibility factor, Z. If good engineering judgment dictates using a value other than Z = 1, an appropriate equation of state to determine values of Z as a function of measured pressures and temperatures may be used, or specific calibration equations may be developed based on good engineering judgment. It shall be noted that the equation for the flow coefficient, C f, is based on the ideal gas assumption that the isentropic exponent, γ, is equal to the ratio of specific heats, cp/cV. If good engineering judgment dictates using a real gas isentropic exponent, an appropriate equation of state to determine values of γ as a function of measured pressures and temperatures may be used, or specific calibration equations may be developed. Molar flow rate, ṅ [mol/s], shall be calculated by means of equation (7-139):
| (7-139) | |
|---|---|
Where:
(a) Using the data collected in point 8.1.8.4 of Annex VI, C d is calculated by means of equation (7-140): (7-140) Where: ṅ ref = reference molar flow rate [mol/s] Other symbols as per equation (7-139).
(b) C f shall be determined using one of the following methods: (i) For CFV flow meters only, C fCFV is derived from Table 7.5 based on values for β (ratio of venturi throat to inlet diameters) and γ (ratio of specific heats of the gas mixture), using linear interpolation to find intermediate values: Table 7.5 C fCFV versus β and γ for CFV flow meters C fCFV β γ exh = 1,385 γ dexh = γ air = 1,399 0,000 0,6822 0,6846 0,400 0,6857 0,6881 0,500 0,6910 0,6934 0,550 0,6953 0,6977 0,600 0,7011 0,7036 0,625 0,7047 0,7072 0,650 0,7089 0,7114 0,675 0,7137 0,7163 0,700 0,7193 0,7219 0,720 0,7245 0,7271 0,740 0,7303 0,7329 0,760 0,7368 0,7395 0,770 0,7404 0,7431 0,780 0,7442 0,7470 0,790 0,7483 0,7511 0,800 0,7527 0,7555 0,810 0,7573 0,7602 0,820 0,7624 0,7652 0,830 0,7677 0,7707 0,840 0,7735 0,7765 0,850 0,7798 0,7828 (ii) For any CFV or SSV flow meter, equation (7-141) may be used to calculate C f: (7-141) Where: γ = isentropic exponent [-]. For an ideal gas, this is the ratio of specific heats of the gas mixture, cp/cV r = pressure ratio, as determined in paragraph (c)(3) of this point β = ratio of venturi throat to inlet diameters
(c) The pressure ratio r shall be calculated as follows: (i) For SSV systems only, r SSV shall be calculated by means of equation (7-142): (7-142) Where: Δp ssv = differential static pressure; venturi inlet minus venturi throat [Pa] (ii) For CFV systems only, r CFV shall be calculated iteratively by means of equation (7-143): (7-143)
(d) Any of the following simplifying assumptions of the governing equations may be made, or good engineering judgment may be used to develop more appropriate values for testing:
(i) For emission testing over the full ranges of raw exhaust gas, diluted exhaust gas and dilution air, the gas mixture may be assumed to behave as an ideal gas: Z = 1; (ii) For the full range of raw exhaust gas a constant ratio of specific heats of γ = 1,385 may be assumed; (iii) For the full range of diluted exhaust gas and air (e.g., calibration air or dilution air), a constant ratio of specific heats of γ = 1,399 may be assumed; (iv) For the full range of diluted exhaust gas and air, the molar mass of the mixture, M mix [g/mol], may be considered as a function only of the amount of water in the dilution air or calibration air, x H2O, determined as described in point 3.3.2 and shall be calculated by means of equation (7-144): M mix = M air· (1 –x H2O) +M H2O· (x H2O) (7-144) Where: M air = 28,96559 g/mol M H2O = 18,01528 g/mol x H2O = amount of water in the dilution or calibration air [mol/mol] (v) For the full range of diluted exhaust gas and air, a constant molar mass of the mixture, M mix, may be assumed for all calibration and all testing as long as assumed molar mass differs no more than ± 1 % from the estimated minimum and maximum molar mass during calibration and testing. This assumption may be made if sufficient control of the amount of water in calibration air and in dilution air is ensured, or if sufficient water is removed from both calibration air and dilution air. Table 7.6 provides for examples of permissible ranges of dilution air dew point versus calibration air dew point: Table 7.6 Examples of dilution air and calibration air dew points at which a constant M mix may be assumed If calibration T dew (°C) is ... the following constant M mix (g/mol) is assumed for the following ranges of T dew (°C) during emission tests () dry 28,96559 dry to 18 0 28,89263 dry to 21 5 28,86148 dry to 22 10 28,81911 dry to 24 15 28,76224 dry to 26 20 28,68685 – 8 to 28 25 28,58806 12 to 31 30 28,46005 23 to 34 (1) Range valid for all calibration and emission testing over the atmospheric pressure range (80,000 to 103,325) kPa.
| (a) | Molar based approach. To calibrate an SSV flow meter the following steps shall be performed: (i) The Reynolds number, Re #, for each reference molar flow rate, shall be calculated using the throat diameter of the venturi, d t [equation (7-145)]. Because the dynamic viscosity, μ, is needed to compute Re#, a specific viscosity model may be used to determine μ for calibration gas (usually air), using good engineering judgment [equation (7-146)]. Alternatively, the Sutherland three-coefficient viscosity model may be used to approximate μ (see Table 7.7): (7-145) Where: d t = diameter of the SSV throat [m] M mix = mixture molar mass [kg/mol] ṅ ref = reference molar flow rate [mol/s] and, using the Sutherland three-coefficient viscosity model: (7-146) Where: μ = Dynamic viscosity of calibration gas [kg /(m · s)] μ 0 = Sutherland reference viscosity [kg /(m · s)] S = Sutherland constant [K] T 0 = Sutherland reference temperature [K] T in = Absolute temperature at the venturi inlet [K] Table 7.7 Sutherland three-coefficient viscosity model parameters Gas () μ 0 T0 S Temp range within ± 2 % error Pressure limit kg /(m · s) K K K kPa Air 1,716 × 10– 5 273 111 170 to 1 900 ≤ 1 800 CO2 1,370 × 10– 5 273 222 190 to 1 700 ≤ 3 600 H2O 1,12 × 10– 5 350 1,064 360 to 1 500 ≤ 10 000 O2 1,919 × 10– 5 273 139 190 to 2 000 ≤ 2 500 N2 1,663 × 10– 5 273 107 100 to 1 500 ≤ 1 600 (1) Tabulated parameters only for the pure gases, as listed, shall be used. Parameters to calculate viscosities of gas mixtures shall not be combined. (ii) An equation for C d versus Re# shall be created, using paired values of (Re#, C d). C d is calculated according to equation (7-140), with C f obtained from equation (7-141), or any mathematical expression may be used, including a polynomial or a power series. Equation (7-147) is an example of a commonly used mathematical expression for relating C d and Re#; (7-147) (iii) A least-squares regression analysis shall be performed to determine the best-fit coefficients to the equation and calculate the equation's regression statistics, the standard estimate error SEE and the coefficient of determination r 2, in accordance with Appendix 3; (iv) If the equation meets the criteria of SEE < 0,5 % n ref max (or ṁ refmax) and r 2 ≥ 0,995, the equation may be used to determine C d for emission tests, as described in point 3.6.3(b); (v) If the SEE and r 2 criteria are not met, good engineering judgment may be used to omit calibration data points to meet the regression statistics. At least seven calibration data points shall be used to meet the criteria; (vi) If omitting points does not resolve outliers, corrective action shall be taken. For example, another mathematical expression for the C d versus Re# equation shall be selected, leaks are to be checked, or the calibration process has to be repeated. If the process shall be repeated, tighter tolerances shall be applied to measurements and more time for flows to stabilize shall be allowed; (vii) Once the equation meets the regression criteria, the equation may be used only to determine flow rates that are within the range of the reference flow rates used to meet the C d versus Re# equation's regression criteria. | | | | |
| --- | --- | --- | --- | --- | --- | | | (7-145) | | | | | | d t | = | diameter of the SSV throat [m] | | | | | M mix | = | mixture molar mass [kg/mol] | | | | | ṅ ref | = | reference molar flow rate [mol/s] | | | | | | (7-146) | | | | | | μ | = | Dynamic viscosity of calibration gas [kg /(m · s)] | | | | | μ 0 | = | Sutherland reference viscosity [kg /(m · s)] | | | | | S | = | Sutherland constant [K] | | | | | T 0 | = | Sutherland reference temperature [K] | | | | | T in | = | Absolute temperature at the venturi inlet [K] | | | | | Gas () | μ 0 | T0 | S | Temp range within ± 2 % error | Pressure limit | | kg /(m · s) | K | K | K | kPa | | | Air | 1,716 × 10– 5 | 273 | 111 | 170 to 1 900 | ≤ 1 800 | | CO2 | 1,370 × 10– 5 | 273 | 222 | 190 to 1 700 | ≤ 3 600 | | H2O | 1,12 × 10– 5 | 350 | 1,064 | 360 to 1 500 | ≤ 10 000 | | O2 | 1,919 × 10– 5 | 273 | 139 | 190 to 2 000 | ≤ 2 500 | | N2 | 1,663 × 10– 5 | 273 | 107 | 100 to 1 500 | ≤ 1 600 | | (1) Tabulated parameters only for the pure gases, as listed, shall be used. Parameters to calculate viscosities of gas mixtures shall not be combined. | | | | | | | | (7-147) | | | | |
Some CFV flow meters consist of a single venturi and some consist of multiple venturis, where different combinations of venturis are used to meter different flow rates. For CFV flow meters that consist of multiple venturis, either calibration of each venturi independently to determine a separate discharge coefficient, C
d, for each venturi, or calibration of each combination of venturis as one venturi may be performed. In the case where a combination of venturis is calibrated, the sum of the active venturi throat areas is used as A t, the square root of the sum of the squares of the active venturi throat diameters as d t, and the ratio of the venturi throat to inlet diameters is the ratio of the square root of the sum of the active venturi throat diameters (d
to the diameter of the common entrance to all of the venturis (D). To determine the C
d for a single venturi or a single combination of venturis, the following steps shall be performed:
(a) With the data collected at each calibration set point an individual C d for each point shall be calculated using equation (7-140);
(b) The mean and standard deviation of all the C
d values shall be calculated in accordance with equations (7-155) and (7-156);
(c) If the standard deviation of all the C d values is less than or equal to 0,3 % of the mean C d, then the mean C d shall be used in equation (7-120), and the CFV shall be used only down to the lowest r measured during calibration; r = 1 – (Δp/pin) (7-148)
(d) If the standard deviation of all the C
d values exceeds 0,3 % of the mean C d, the C d values corresponding to the data point collected at the lowest r measured during calibration shall be omitted;
(e) If the number of remaining data points is less than seven, corrective action shall be taken by checking calibration data or repeating the calibration process. If the calibration process is repeated, checking for leaks, applying tighter tolerances to measurements and allowing more time for flows to stabilize, is recommended;
(f) If the number of remaining C
d values is seven or greater, the mean and standard deviation of the remaining C d values shall be recalculated;
(g) If the standard deviation of the remaining C d values is less than or equal to 0,3 % of the mean of the remaining C d, that mean C d shall be used in equation (7-120) and the CFV values only down to the lowest r associated with the remaining C d shall be used;
(h) If the standard deviation of the remaining C d still exceeds 0,3 % of the mean of the remaining C d values, the steps set out in points (d) to (g) shall be repeated.
Appendix 1
Drift Correction
Scope and frequency
The calculations in this Appendix 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 according to this Appendix. 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.
Correction principles
The calculations in this Appendix utilize a gas analyzer's responses to reference zero and span concentrations of analytical gases, as determined sometime before and after a test interval. The calculations correct the gas analyzer's responses that were recorded during a test interval. The correction is based on an analyzer's mean responses to reference zero and span gases, and it is based on the reference concentrations of the zero and span gases themselves. Validation and correction for drift shall be performed as follows:
3. Drift validation
After applying all the other corrections–except drift correction–to all the gas analyzer signals, brake-specific emissions shall be calculated in accordance with point 3.8. Then all gas analyzer signals shall be corrected for drift according to this Appendix. Brake-specific emissions shall be recalculated using all of the drift-corrected gas analyzer signals. The brake-specific emission results shall be validated and reported before and after drift correction according to point 8.2.2.2 of Annex VI.
4. Drift correction
All gas analyzer signals shall be corrected as follows:
(a) Each recorded concentration, xi, shall be corrected for continuous sampling or for batch sampling,
;
(b) Correction for drift shall be calculated by means of equation (7-149): (7-149) Where: xi driftcor = concentration corrected for drift [μmol/mol] x refzero = reference concentration of the zero gas, which is usually zero unless known to be otherwise [μmol/mol] x refspan = reference concentration of the span gas [μmol/mol] x prespan = pre-test interval gas analyzer response to the span gas concentration [μmol/mol] x postspan = post-test interval gas analyzer response to the span gas concentration [μmol/mol] xi or = concentration recorded, i.e. measured, during test, before drift correction [μmol/mol] x prezero = pre-test interval gas analyzer response to the zero gas concentration [μmol/mol] x postzero = post-test interval gas analyzer response to the zero gas concentration [μmol/mol]
(c) For any pre-test interval concentrations, concentrations determined most recently before the test interval shall be used. For some test intervals, the most recent pre-zero or pre-span might have occurred before one or more previous test intervals;
(d) For any post-test interval concentrations, concentrations determined most recently after the test interval shall be used. For some test intervals, the most recent post-zero or post-span might have occurred after one or more subsequent test intervals;
(e) If any pre-test interval analyzer response to the span gas concentration, x prespan, is not recorded, x prespan shall be set equal to the reference concentration of the span gas: x prespan = x refspan;
(f) If any pre-test interval analyzer response to the zero gas concentration, x prezero, is not recorded, x prezero shall be set equal to the reference concentration of the zero gas: x prezero = x refzero;
(g) Usually the reference concentration of the zero gas, x
refzero, is zero: x refzero = 0 μmol/mol. However, in some cases it might be known that x refzero has a non-zero concentration. For example, if a CO2 analyzer is zeroed using ambient air, the default ambient air concentration of CO2, which is 375 μmol/mol, may be used. In this case, x refzero = 375 μmol/mol. When an analyzer is zeroed using a non-zero x refzero, the analyzer shall be set to output the actual xrefzero concentration. For example, if x refzero = 375 μmol/mol, the analyzer shall be set to output a value of 375 μmol/mol when the zero gas is flowing to the analyzer.
Appendix 2
Carbon Flow Check
Introduction
All but a tiny part of the carbon in the exhaust gas comes from the fuel, and all but a minimal part of this is manifest in the exhaust gas as CO2. This is the basis for a system verification check based on CO2 measurements. In the case of SI engines without control of excess air ratio λ or SI engines operating outside the range 0,97 ≤ λ ≤ 1,03, the procedure shall additionally include measurement of HC and CO.
The flow of carbon into the exhaust gas measurement systems is determined from the fuel flow rate. The flow of carbon at various sampling points in the emissions and particulate sampling systems is determined from the CO2 (or CO2, HC and CO) concentrations and gas flow rates at those points.
In this sense, the engine provides a known source of carbon flow, and observing the same carbon flow in the exhaust pipe and at the outlet of the partial flow PM sampling system verifies leak integrity and flow measurement accuracy. This check has the advantage that the components are operating under actual engine test conditions of temperature and flow.
Figure 7.1 shows the sampling points at which the carbon flows shall be checked. The specific equations for the carbon flows at each of the sample points are given in the following points.
Carbon flow rate into the engine (location 1)
The carbon mass flow rate into the engine qm
Cf [kg/s] for a fuel CHαOε shall be calculated by means of equation (7-150):
| (7-150) | |
|---|---|
Where:
Carbon flow rate in the raw exhaust gas (location 2)
The carbon mass flow rate in the exhaust pipe of the engine qm Ce [kg/s] shall be determined from the raw CO2 concentration and the exhaust gas mass flow rate by means of equation (7-151):
| (7-151) | |
|---|---|
where:
If CO2 is measured on a dry basis it shall be converted to a wet basis in accordance with point 2.1.3 or point 3.5.2.
As an alternative to performing the calculation solely based upon CO2 in point 3.1, the carbon mass flow rate in the exhaust pipe of the engine qm Ce [kg/s] shall be determined from the raw CO2, HC and CO concentration and the exhaust gas mass flow rate by means of equation (7-152):
| | (7-152) |
| --- | --- |
Where:
If CO2 or CO are measured on a dry basis they shall be converted to a wet basis in accordance with point 2.1.3 or point 3.5.2.
Carbon flow rate in the dilution system (location 3)
For the partial flow dilution system, the splitting ratio also needs to be taken into account. The carbon flow rate in an equivalent dilution system qm Cp [kg/s] (with equivalent meaning equivalent to a full flow system where the total flow is diluted) shall be determined from the dilute CO2 concentration, the exhaust gas mass flow rate and the sample flow rate; the new equation (7-153) is identical to equation (7-151), being only supplemented by the dilution factor qm dew/qm p.
| (7-153) | |
|---|---|
Where:
If CO2 is measured on a dry basis it shall be converted to a wet basis in accordance with point 2.1.3 or point 3.5.2.
For the partial flow dilution system, the splitting ratio also needs to be taken into account. As an alternative to performing the calculation solely based upon CO2 in point 4.1, the carbon flow rate in an equivalent dilution system qm
Cp [kg/s] (with equivalent meaning equivalent to a full flow system where the total flow is diluted) shall be determined from the dilute CO2, HC and CO concentrations, the exhaust gas mass flow rate and the sample flow rate; the new equation (7-154) is identical to equation (7-152), being only supplemented by the dilution factor qm dew/qm p.
| | (7-154) |
| --- | --- |
Where:
If CO2 or CO are measured on a dry basis they shall be converted to a wet basis in accordance with point 2.1.3 or point 3.5.2 of this Annex.
Calculation of the molar mass of the exhaust gas
The molar mass of the exhaust gas shall be calculated by means of equation (7-13) (see point 2.1.5.2.of this Annex).
Alternatively, the following exhaust gas molar masses may be used:
M e (diesel) = 28,9 g/mol
M
e (LPG) = 28,6 g/mol
M e (Natural gas/biomethane) = 28,3 g/mol
M e (Petrol) = 29,0 g/mol
Appendix 3
Statistics
Arithmetic mean
The arithmetic mean,
, shall be calculated by means of equation (7-155):
| (7-155) | |
|---|---|
2. Standard deviation
The standard deviation for a non-biased (e.g., N–1) sample, σ, shall be calculated by means of equation (7-156):
| (7-156) | |
|---|---|
Root mean square
The root mean square, rmsy, shall be calculated by means of equation (7-157):
| (7-157) | |
|---|---|
t-test
It shall be determined if the data passes a t-test by means of the following equations and Table 7.8:
(a) For an unpaired t-test, the t statistic and its number of degrees of freedom, v, shall be calculated by means of equations (7-158) and (7-159): (7-158) (7-159)
(b) For a paired t-test, the t statistic and its number of degrees of freedom, v, shall be calculated by means of equation (7-160), noting that the εi are the errors (e.g., differences) between each pair of y ref i and yi: v= N – 1 (7-160)
(c) Table 7.8 shall be used to compare t to the t
crit values tabulated versus the number of degrees of freedom. If t is less than t crit, then t passes the t-test. Table 7.8 Critical t values versus number of degrees of freedom, v v Confidence 90 % 95 % 1 6,314 12,706 2 2,920 4,303 3 2,353 3,182 4 2,132 2,776 5 2,015 2,571 6 1,943 2,447 7 1,895 2,365 8 1,860 2,306 9 1,833 2,262 10 1,812 2,228 11 1,796 2,201 12 1,782 2,179 13 1,771 2,160 14 1,761 2,145 15 1,753 2,131 16 1,746 2,120 18 1,734 2,101 20 1,725 2,086 22 1,717 2,074 24 1,711 2,064 26 1,706 2,056 28 1,701 2,048 30 1,697 2,042 35 1,690 2,030 40 1,684 2,021 50 1,676 2,009 70 1,667 1,994 100 1,660 1,984 1 000 + 1,645 1,960
Linear interpolation shall be used to establish values not shown here.
F-test
The F statistic shall be calculated by means of equation (7-161):
| (7-161) | |
|---|---|
(a) For a 90 % confidence F-test, Table 7.9 is used to compare F to the F crit90 values tabulated versus (N–1) and (N ref–1). If F is less than F crit90, then F passes the F-test at 90 % confidence;
(b) For a 95 % confidence F-test, Table 7.10 is used to compare F to the F
crit95 values tabulated versus (N–1) and (N ref–1). If F is less than F crit95, then F passes the F-test at 95 % confidence.
| N – 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | 1000+ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| N ref – 1 | |||||||||||||||||||
| 1 | 39,86 | 49,50 | 53,59 | 55,83 | 57,24 | 58,20 | 58,90 | 59,43 | 59,85 | 60,19 | 60,70 | 61,22 | 61,74 | 62,00 | 62,26 | 62,52 | 62,79 | 63,06 | 63,32 |
| 2 | 8,526 | 9,000 | 9,162 | 9,243 | 9,293 | 9,326 | 9,349 | 9,367 | 9,381 | 9,392 | 9,408 | 9,425 | 9,441 | 9,450 | 9,458 | 9,466 | 9,475 | 9,483 | 9,491 |
| 3 | 5,538 | 5,462 | 5,391 | 5,343 | 5,309 | 5,285 | 5,266 | 5,252 | 5,240 | 5,230 | 5,216 | 5,200 | 5,184 | 5,176 | 5,168 | 5,160 | 5,151 | 5,143 | 5,134 |
| 4 | 4,545 | 4,325 | 4,191 | 4,107 | 4,051 | 4,010 | 3,979 | 3,955 | 3,936 | 3,920 | 3,896 | 3,870 | 3,844 | 3,831 | 3,817 | 3,804 | 3,790 | 3,775 | 3,761 |
| 5 | 4,060 | 3,780 | 3,619 | 3,520 | 3,453 | 3,405 | 3,368 | 3,339 | 3,316 | 3,297 | 3,268 | 3,238 | 3,207 | 3,191 | 3,174 | 3,157 | 3,140 | 3,123 | 3,105 |
| 6 | 3,776 | 3,463 | 3,289 | 3,181 | 3,108 | 3,055 | 3,014 | 2,983 | 2,958 | 2,937 | 2,905 | 2,871 | 2,836 | 2,818 | 2,800 | 2,781 | 2,762 | 2,742 | 2,722 |
| 7 | 3,589 | 3,257 | 3,074 | 2,961 | 2,883 | 2,827 | 2,785 | 2,752 | 2,725 | 2,703 | 2,668 | 2,632 | 2,595 | 2,575 | 2,555 | 2,535 | 2,514 | 2,493 | 2,471 |
| 8 | 3,458 | 3,113 | 2,924 | 2,806 | 2,726 | 2,668 | 2,624 | 2,589 | 2,561 | 2,538 | 2,502 | 2,464 | 2,425 | 2,404 | 2,383 | 2,361 | 2,339 | 2,316 | 2,293 |
| 9 | 3,360 | 3,006 | 2,813 | 2,693 | 2,611 | 2,551 | 2,505 | 2,469 | 2,440 | 2,416 | 2,379 | 2,340 | 2,298 | 2,277 | 2,255 | 2,232 | 2,208 | 2,184 | 2,159 |
| 10 | 3,285 | 2,924 | 2,728 | 2,605 | 2,522 | 2,461 | 2,414 | 2,377 | 2,347 | 2,323 | 2,284 | 2,244 | 2,201 | 2,178 | 2,155 | 2,132 | 2,107 | 2,082 | 2,055 |
| 11 | 3,225 | 2,860 | 2,660 | 2,536 | 2,451 | 2,389 | 2,342 | 2,304 | 2,274 | 2,248 | 2,209 | 2,167 | 2,123 | 2,100 | 2,076 | 2,052 | 2,026 | 2,000 | 1,972 |
| 12 | 3,177 | 2,807 | 2,606 | 2,480 | 2,394 | 2,331 | 2,283 | 2,245 | 2,214 | 2,188 | 2,147 | 2,105 | 2,060 | 2,036 | 2,011 | 1,986 | 1,960 | 1,932 | 1,904 |
| 13 | 3,136 | 2,763 | 2,560 | 2,434 | 2,347 | 2,283 | 2,234 | 2,195 | 2,164 | 2,138 | 2,097 | 2,053 | 2,007 | 1,983 | 1,958 | 1,931 | 1,904 | 1,876 | 1,846 |
| 14 | 3,102 | 2,726 | 2,522 | 2,395 | 2,307 | 2,243 | 2,193 | 2,154 | 2,122 | 2,095 | 2,054 | 2,010 | 1,962 | 1,938 | 1,912 | 1,885 | 1,857 | 1,828 | 1,797 |
| 15 | 3,073 | 2,695 | 2,490 | 2,361 | 2,273 | 2,208 | 2,158 | 2,119 | 2,086 | 2,059 | 2,017 | 1,972 | 1,924 | 1,899 | 1,873 | 1,845 | 1,817 | 1,787 | 1,755 |
| 16 | 3,048 | 2,668 | 2,462 | 2,333 | 2,244 | 2,178 | 2,128 | 2,088 | 2,055 | 2,028 | 1,985 | 1,940 | 1,891 | 1,866 | 1,839 | 1,811 | 1,782 | 1,751 | 1,718 |
| 17 | 3,026 | 2,645 | 2,437 | 2,308 | 2,218 | 2,152 | 2,102 | 2,061 | 2,028 | 2,001 | 1,958 | 1,912 | 1,862 | 1,836 | 1,809 | 1,781 | 1,751 | 1,719 | 1,686 |
| 18 | 3,007 | 2,624 | 2,416 | 2,286 | 2,196 | 2,130 | 2,079 | 2,038 | 2,005 | 1,977 | 1,933 | 1,887 | 1,837 | 1,810 | 1,783 | 1,754 | 1,723 | 1,691 | 1,657 |
| 19 | 2,990 | 2,606 | 2,397 | 2,266 | 2,176 | 2,109 | 2,058 | 2,017 | 1,984 | 1,956 | 1,912 | 1,865 | 1,814 | 1,787 | 1,759 | 1,730 | 1,699 | 1,666 | 1,631 |
| 20 | 2,975 | 2,589 | 2,380 | 2,249 | 2,158 | 2,091 | 2,040 | 1,999 | 1,965 | 1,937 | 1,892 | 1,845 | 1,794 | 1,767 | 1,738 | 1,708 | 1,677 | 1,643 | 1,607 |
| 21 | 2,961 | 2,575 | 2,365 | 2,233 | 2,142 | 2,075 | 2,023 | 1,982 | 1,948 | 1,920 | 1,875 | 1,827 | 1,776 | 1,748 | 1,719 | 1,689 | 1,657 | 1,623 | 1,586 |
| 20 | 2,949 | 2,561 | 2,351 | 2,219 | 2,128 | 2,061 | 2,008 | 1,967 | 1,933 | 1,904 | 1,859 | 1,811 | 1,759 | 1,731 | 1,702 | 1,671 | 1,639 | 1,604 | 1,567 |
| 23 | 2,937 | 2,549 | 2,339 | 2,207 | 2,115 | 2,047 | 1,995 | 1,953 | 1,919 | 1,890 | 1,845 | 1,796 | 1,744 | 1,716 | 1,686 | 1,655 | 1,622 | 1,587 | 1,549 |
| 24 | 2,927 | 2,538 | 2,327 | 2,195 | 2,103 | 2,035 | 1,983 | 1,941 | 1,906 | 1,877 | 1,832 | 1,783 | 1,730 | 1,702 | 1,672 | 1,641 | 1,607 | 1,571 | 1,533 |
| 25 | 2,918 | 2,528 | 2,317 | 2,184 | 2,092 | 2,024 | 1,971 | 1,929 | 1,895 | 1,866 | 1,820 | 1,771 | 1,718 | 1,689 | 1,659 | 1,627 | 1,593 | 1,557 | 1,518 |
| 26 | 2,909 | 2,519 | 2,307 | 2,174 | 2,082 | 2,014 | 1,961 | 1,919 | 1,884 | 1,855 | 1,809 | 1,760 | 1,706 | 1,677 | 1,647 | 1,615 | 1,581 | 1,544 | 1,504 |
| 27 | 2,901 | 2,511 | 2,299 | 2,165 | 2,073 | 2,005 | 1,952 | 1,909 | 1,874 | 1,845 | 1,799 | 1,749 | 1,695 | 1,666 | 1,636 | 1,603 | 1,569 | 1,531 | 1,491 |
| 28 | 2,894 | 2,503 | 2,291 | 2,157 | 2,064 | 1,996 | 1,943 | 1,900 | 1,865 | 1,836 | 1,790 | 1,740 | 1,685 | 1,656 | 1,625 | 1,593 | 1,558 | 1,520 | 1,478 |
| 29 | 2,887 | 2,495 | 2,283 | 2,149 | 2,057 | 1,988 | 1,935 | 1,892 | 1,857 | 1,827 | 1,781 | 1,731 | 1,676 | 1,647 | 1,616 | 1,583 | 1,547 | 1,509 | 1,467 |
| 30 | 2,881 | 2,489 | 2,276 | 2,142 | 2,049 | 1,980 | 1,927 | 1,884 | 1,849 | 1,819 | 1,773 | 1,722 | 1,667 | 1,638 | 1,606 | 1,573 | 1,538 | 1,499 | 1,456 |
| 40 | 2,835 | 2,440 | 2,226 | 2,091 | 1,997 | 1,927 | 1,873 | 1,829 | 1,793 | 1,763 | 1,715 | 1,662 | 1,605 | 1,574 | 1,541 | 1,506 | 1,467 | 1,425 | 1,377 |
| 60 | 2,791 | 2,393 | 2,177 | 2,041 | 1,946 | 1,875 | 1,819 | 1,775 | 1,738 | 1,707 | 1,657 | 1,603 | 1,543 | 1,511 | 1,476 | 1,437 | 1,395 | 1,348 | 1,291 |
| 120 | 2,748 | 2,347 | 2,130 | 1,992 | 1,896 | 1,824 | 1,767 | 1,722 | 1,684 | 1,652 | 1,601 | 1,545 | 1,482 | 1,447 | 1,409 | 1,368 | 1,320 | 1,265 | 1,193 |
| 1000+ | 2,706 | 2,303 | 2,084 | 1,945 | 1,847 | 1,774 | 1,717 | 1,670 | 1,632 | 1,599 | 1,546 | 1,487 | 1,421 | 1,383 | 1,342 | 1,295 | 1,240 | 1,169 | 1,000 |
| N – 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | 1000+ |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| N ref – 1 | |||||||||||||||||||
| 1 | 161,4 | 199,5 | 215,7 | 224,5 | 230,1 | 233,9 | 236,7 | 238,8 | 240,5 | 241,8 | 243,9 | 245,9 | 248,0 | 249,0 | 250,1 | 251,1 | 252,2 | 253,2 | 254,3 |
| 2 | 18,51 | 19,00 | 19,16 | 19,24 | 19,29 | 19,33 | 19,35 | 19,37 | 19,38 | 19,39 | 19,41 | 19,42 | 19,44 | 19,45 | 19,46 | 19,47 | 19,47 | 19,48 | 19,49 |
| 3 | 10,12 | 9,552 | 9,277 | 9,117 | 9,014 | 8,941 | 8,887 | 8,845 | 8,812 | 8,786 | 8,745 | 8,703 | 8,660 | 8,639 | 8,617 | 8,594 | 8,572 | 8,549 | 8,526 |
| 4 | 7,709 | 6,944 | 6,591 | 6,388 | 6,256 | 6,163 | 6,094 | 6,041 | 5,999 | 5,964 | 5,912 | 5,858 | 5,803 | 5,774 | 5,746 | 5,717 | 5,688 | 5,658 | 5,628 |
| 5 | 6,608 | 5,786 | 5,410 | 5,192 | 5,050 | 4,950 | 4,876 | 4,818 | 4,773 | 4,735 | 4,678 | 4,619 | 4,558 | 4,527 | 4,496 | 4,464 | 4,431 | 4,399 | 4,365 |
| 6 | 5,987 | 5,143 | 4,757 | 4,534 | 4,387 | 4,284 | 4,207 | 4,147 | 4,099 | 4,060 | 4,000 | 3,938 | 3,874 | 3,842 | 3,808 | 3,774 | 3,740 | 3,705 | 3,669 |
| 7 | 5,591 | 4,737 | 4,347 | 4,120 | 3,972 | 3,866 | 3,787 | 3,726 | 3,677 | 3,637 | 3,575 | 3,511 | 3,445 | 3,411 | 3,376 | 3,340 | 3,304 | 3,267 | 3,230 |
| 8 | 5,318 | 4,459 | 4,066 | 3,838 | 3,688 | 3,581 | 3,501 | 3,438 | 3,388 | 3,347 | 3,284 | 3,218 | 3,150 | 3,115 | 3,079 | 3,043 | 3,005 | 2,967 | 2,928 |
| 9 | 5,117 | 4,257 | 3,863 | 3,633 | 3,482 | 3,374 | 3,293 | 3,230 | 3,179 | 3,137 | 3,073 | 3,006 | 2,937 | 2,901 | 2,864 | 2,826 | 2,787 | 2,748 | 2,707 |
| 10 | 4,965 | 4,103 | 3,708 | 3,478 | 3,326 | 3,217 | 3,136 | 3,072 | 3,020 | 2,978 | 2,913 | 2,845 | 2,774 | 2,737 | 2,700 | 2,661 | 2,621 | 2,580 | 2,538 |
| 11 | 4,844 | 3,982 | 3,587 | 3,357 | 3,204 | 3,095 | 3,012 | 2,948 | 2,896 | 2,854 | 2,788 | 2,719 | 2,646 | 2,609 | 2,571 | 2,531 | 2,490 | 2,448 | 2,405 |
| 12 | 4,747 | 3,885 | 3,490 | 3,259 | 3,106 | 2,996 | 2,913 | 2,849 | 2,796 | 2,753 | 2,687 | 2,617 | 2,544 | 2,506 | 2,466 | 2,426 | 2,384 | 2,341 | 2,296 |
| 13 | 4,667 | 3,806 | 3,411 | 3,179 | 3,025 | 2,915 | 2,832 | 2,767 | 2,714 | 2,671 | 2,604 | 2,533 | 2,459 | 2,420 | 2,380 | 2,339 | 2,297 | 2,252 | 2,206 |
| 14 | 4,600 | 3,739 | 3,344 | 3,112 | 2,958 | 2,848 | 2,764 | 2,699 | 2,646 | 2,602 | 2,534 | 2,463 | 2,388 | 2,349 | 2,308 | 2,266 | 2,223 | 2,178 | 2,131 |
| 15 | 4,543 | 3,682 | 3,287 | 3,056 | 2,901 | 2,791 | 2,707 | 2,641 | 2,588 | 2,544 | 2,475 | 2,403 | 2,328 | 2,288 | 2,247 | 2,204 | 2,160 | 2,114 | 2,066 |
| 16 | 4,494 | 3,634 | 3,239 | 3,007 | 2,852 | 2,741 | 2,657 | 2,591 | 2,538 | 2,494 | 2,425 | 2,352 | 2,276 | 2,235 | 2,194 | 2,151 | 2,106 | 2,059 | 2,010 |
| 17 | 4,451 | 3,592 | 3,197 | 2,965 | 2,810 | 2,699 | 2,614 | 2,548 | 2,494 | 2,450 | 2,381 | 2,308 | 2,230 | 2,190 | 2,148 | 2,104 | 2,058 | 2,011 | 1,960 |
| 18 | 4,414 | 3,555 | 3,160 | 2,928 | 2,773 | 2,661 | 2,577 | 2,510 | 2,456 | 2,412 | 2,342 | 2,269 | 2,191 | 2,150 | 2,107 | 2,063 | 2,017 | 1,968 | 1,917 |
| 19 | 4,381 | 3,522 | 3,127 | 2,895 | 2,740 | 2,628 | 2,544 | 2,477 | 2,423 | 2,378 | 2,308 | 2,234 | 2,156 | 2,114 | 2,071 | 2,026 | 1,980 | 1,930 | 1,878 |
| 20 | 4,351 | 3,493 | 3,098 | 2,866 | 2,711 | 2,599 | 2,514 | 2,447 | 2,393 | 2,348 | 2,278 | 2,203 | 2,124 | 2,083 | 2,039 | 1,994 | 1,946 | 1,896 | 1,843 |
| 21 | 4,325 | 3,467 | 3,073 | 2,840 | 2,685 | 2,573 | 2,488 | 2,421 | 2,366 | 2,321 | 2,250 | 2,176 | 2,096 | 2,054 | 2,010 | 1,965 | 1,917 | 1,866 | 1,812 |
| 22 | 4,301 | 3,443 | 3,049 | 2,817 | 2,661 | 2,549 | 2,464 | 2,397 | 2,342 | 2,297 | 2,226 | 2,151 | 2,071 | 2,028 | 1,984 | 1,938 | 1,889 | 1,838 | 1,783 |
| 23 | 4,279 | 3,422 | 3,028 | 2,796 | 2,640 | 2,528 | 2,442 | 2,375 | 2,320 | 2,275 | 2,204 | 2,128 | 2,048 | 2,005 | 1,961 | 1,914 | 1,865 | 1,813 | 1,757 |
| 24 | 4,260 | 3,403 | 3,009 | 2,776 | 2,621 | 2,508 | 2,423 | 2,355 | 2,300 | 2,255 | 2,183 | 2,108 | 2,027 | 1,984 | 1,939 | 1,892 | 1,842 | 1,790 | 1,733 |
| 25 | 4,242 | 3,385 | 2,991 | 2,759 | 2,603 | 2,490 | 2,405 | 2,337 | 2,282 | 2,237 | 2,165 | 2,089 | 2,008 | 1,964 | 1,919 | 1,872 | 1,822 | 1,768 | 1,711 |
| 26 | 4,225 | 3,369 | 2,975 | 2,743 | 2,587 | 2,474 | 2,388 | 2,321 | 2,266 | 2,220 | 2,148 | 2,072 | 1,990 | 1,946 | 1,901 | 1,853 | 1,803 | 1,749 | 1,691 |
| 27 | 4,210 | 3,354 | 2,960 | 2,728 | 2,572 | 2,459 | 2,373 | 2,305 | 2,250 | 2,204 | 2,132 | 2,056 | 1,974 | 1,930 | 1,884 | 1,836 | 1,785 | 1,731 | 1,672 |
| 28 | 4,196 | 3,340 | 2,947 | 2,714 | 2,558 | 2,445 | 2,359 | 2,291 | 2,236 | 2,190 | 2,118 | 2,041 | 1,959 | 1,915 | 1,869 | 1,820 | 1,769 | 1,714 | 1,654 |
| 29 | 4,183 | 3,328 | 2,934 | 2,701 | 2,545 | 2,432 | 2,346 | 2,278 | 2,223 | 2,177 | 2,105 | 2,028 | 1,945 | 1,901 | 1,854 | 1,806 | 1,754 | 1,698 | 1,638 |
| 30 | 4,171 | 3,316 | 2,922 | 2,690 | 2,534 | 2,421 | 2,334 | 2,266 | 2,211 | 2,165 | 2,092 | 2,015 | 1,932 | 1,887 | 1,841 | 1,792 | 1,740 | 1,684 | 1,622 |
| 40 | 4,085 | 3,232 | 2,839 | 2,606 | 2,450 | 2,336 | 2,249 | 2,180 | 2,124 | 2,077 | 2,004 | 1,925 | 1,839 | 1,793 | 1,744 | 1,693 | 1,637 | 1,577 | 1,509 |
| 60 | 4,001 | 3,150 | 2,758 | 2,525 | 2,368 | 2,254 | 2,167 | 2,097 | 2,040 | 1,993 | 1,917 | 1,836 | 1,748 | 1,700 | 1,649 | 1,594 | 1,534 | 1,467 | 1,389 |
| 120 | 3,920 | 3,072 | 2,680 | 2,447 | 2,290 | 2,175 | 2,087 | 2,016 | 1,959 | 1,911 | 1,834 | 1,751 | 1,659 | 1,608 | 1,554 | 1,495 | 1,429 | 1,352 | 1,254 |
| 1000+ | 3,842 | 2,996 | 2,605 | 2,372 | 2,214 | 2,099 | 2,010 | 1,938 | 1,880 | 1,831 | 1,752 | 1,666 | 1,571 | 1,517 | 1,459 | 1,394 | 1,318 | 1,221 | 1,000 |
6. Slope
The least-squares regression slope, a
1y, shall be calculated by means of equation (7-162):
| (7-162) | |
|---|---|
Intercept
The least-squares regression intercept, a 0y, shall be calculated by means of equation (7-163):
| | (7-163) |
| --- | --- |
8. Standard estimate of error
The standard estimate of error, SEE, shall be calculated by means of equation (7-164):
| (7-164) | |
|---|---|
Coefficient of determination
The coefficient of determination, r 2, shall be calculated by means of equation (7-165):
| (7-165) | |
|---|---|
Appendix 4
1980 INTERNATIONAL GRAVITY FORMULA
The acceleration of Earth's gravity, a g, varies depending on the location and a g shall be calculated for a respective latitude, by means of equation (7-166):
| ag = 9,7803267715 [1 + 5,2790414 × 10– 3 sin2 θ + 2,32718 × 10– 5 sin4 θ + 1,262 × 10– 7 sin6 θ + 7 × 10– 10 sin8 θ] | (7-166) |
|---|---|
Where:
Appendix 5
Particle number calculation
Determination of particle numbers
For partial flow dilution systems residence time in the particle number sampling and measurement system shall be accounted for by time aligning the particle number signal with the test cycle and the exhaust gas mass flow rate according to the procedure in point 8.2.1.2 of Annex VI. The transformation time of the particle number sampling and measurement system shall be determined in accordance with point 2.1.3.7 of Appendix 1 of Annex VI.
Where particle numbers are sampled using a partial flow dilution system according to the specifications set out in point 9.2.3 of Annex VI, the number of particles emitted over the test cycle shall be calculated by means of equation (7-167):
| (7-167) | |
|---|---|
Where:
N is the number of particles emitted over the test cycle, [#/test],
medf is the mass of equivalent diluted exhaust gas over the cycle, determined by means of equation (7-45) (point 2.3.1.1.2), [kg/test],
k is the calibration factor to correct the particle number counter measurements to the level of the reference instrument where this is not applied internally within the particle number counter. Where the calibration factor is applied internally within the particle number counter, a value of 1 shall be used for k in equation (7-167),
is the average concentration of particles from the diluted exhaust gas corrected to standard conditions (273,2 K and 101,33 kPa), particles per cubic centimetre,
is the mean particle concentration reduction factor of the volatile particle remover specific to the dilution settings used for the test.
with
| (7-168) | |
|---|---|
Where:
cs,i is a discrete measurement of particle concentration in the diluted exhaust gas from the particle counter, corrected for coincidence and to standard conditions (273,2 K and 101,33 kPa), particles per cubic centimetre,
n is the number of particle concentration measurements taken over the duration of the test.
Where particle numbers are sampled using a full flow dilution system according to the specifications set out in point 9.2.2 of Annex VI, the number of particles emitted over the test cycle shall be calculated by means of equation (7-169):
| (7-169) | |
|---|---|
Where:
N is the number of particles emitted over the test cycle, [#/test],
med is the total diluted exhaust gas flow over the cycle calculated according to any one of the methods described in points 2.2.4.1 to 2.2.4.3, of Annex VII, kg/test,
k is the calibration factor to correct the particle number counter measurements to the level of the reference instrument where this is not applied internally within the particle number counter. Where the calibration factor is applied internally within the particle number counter, a value of 1 shall be used for k in equation (7-169),
is the average corrected concentration of particles from the diluted exhaust gas corrected to standard conditions (273,2 K and 101,33 kPa), particles per cubic centimetre,
is the mean particle concentration reduction factor of the volatile particle remover specific to the dilution settings used for the test.
with
| (7-170) | |
|---|---|
Where:
cs,i is a discrete measurement of particle concentration in the diluted gas exhaust from the particle counter, corrected for coincidence and to standard conditions (273,2 K and 101,33 kPa), particles per cubic centimetre,
n is the number of particle concentration measurements taken over the duration of the test
Where particle numbers are sampled using a partial flow dilution system according to the specifications set out in point 9.2.3 of Annex VI, the rate of emission of particles during each individual discrete-mode shall be calculated by means of equation (7-171) using the average values for the mode:
| (7-171) | |
|---|---|
Where:
Ṅ is the rate of emission of particles during the individual discrete-mode, [#/h],
qmedf is the equivalent diluted exhaust mass flow rate on a wet basis during the individual discrete-mode, determined in accordance with equation (7-51) (point 2.3.2.1), [kg/s],
k is the calibration factor to correct the particle number counter measurements to the level of the reference instrument where this is not applied internally within the particle number counter. Where the calibration factor is applied internally within the particle number counter, a value of 1 shall be used for k in the equation (1-171),
is the average concentration of particles from the diluted exhaust gas during the individual discrete-mode corrected to standard conditions (273,2 K and 101,33 kPa), particles per cubic centimetre,
is the mean particle concentration reduction factor of the volatile particle remover specific to the dilution settings used for the test.
with
| (7-172) | |
|---|---|
Where:
cs,i is a discrete measurement of particle concentration in the diluted gas exhaust from the particle counter, corrected for coincidence and to standard conditions (273,2 K and 101,33 kPa), particles per cubic centimetre,
n is the number of particle concentration measurements taken during the individual discrete-mode sampling period
Where particle numbers are sampled using a full flow dilution system according to the specifications set out in point 9.2.2 of Annex VI, the rate of emission of particles during each individual discrete-mode shall be calculated by means of equation (7-173) using the average values for the mode:
| | (7-173) |
| --- | --- |
Where:
Ṅ is the rate of emission of particles during the individual discrete-mode, [#/h],
qmdew is the total diluted exhaust mass flow rate on a wet basis during the individual discrete-mode, [kg/s],
k is the calibration factor to correct the particle number counter measurements to the level of the reference instrument where this is not applied internally within the particle number counter. Where the calibration factor is applied internally within the particle number counter, a value of 1 shall be used for k in equation (7-173),
is the average concentration of particles from the diluted exhaust gas during the individual discrete-mode corrected to standard conditions (273,2 K and 101,33 kPa), particles per cubic centimetre,
is the mean particle concentration reduction factor of the volatile particle remover specific to the dilution settings used for the test.
with
| (7-174) | |
|---|---|
Where:
cs,i is a discrete measurement of particle concentration in the diluted gas exhaust from the particle counter, corrected for coincidence and to standard conditions (273,2 K and 101,33 kPa), particles per cubic centimetre,
n is the number of particle concentration measurements taken during the individual discrete-mode sampling period.
Test result
For each applicable individual RMC, hot-start NRTC and cold-start NRTC the specific emissions in number of particles/kWh shall be calculated by means of equation (7-175):
| (7-175) | |
|---|---|
Where:
N is the number of particles emitted over the applicable RMC, hot-start run of the NRTC or cold-start NRTC,
Wact is the actual cycle work in accordance with point 7.8.3.4 of Annex VI, [kWh].
For an RMC, in case of an engine with infrequent (periodic) exhaust after-treatment system regeneration (see point 6.6.2 of Annex VI), the specific emissions shall be corrected with either the applicable multiplicative adjustment factor or with the applicable adjustment additive 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).
For an RMC the final result shall also be adjusted with the applicable multiplicative or additive deterioration factor established according to the requirements of Annex III.
For the NRTC, the final test result shall be a weighted average from cold-start run and hot-start run (including infrequent regeneration where relevant) shall be calculated by means of equation (7-176) or (7-177):
(a) In the case of multiplicative regeneration adjustment, or engines without infrequently regenerating exhaust after-treatment system (7-176)
In the case of additive regeneration adjustment
| (7-177) | |
|---|---|
Where:
Ncold is the total number of particles emitted over the NRTC cold-start run of the NRTC,
Nhot is the total number of particles emitted over the NRTC hot-start run of the NRTC,
Wact,cold is the actual cycle work over the cold-start NRTC in accordance with point 7.8.3.4 of Annex VI, [kWh],
Wact, hot is the actual cycle work over the hot-start NRTC in accordance with point 7.8.3.4 of Annex VI, [kWh],
kr is the regeneration adjustment, according to point 6.6.2 of Annex VI, or in the case of engines without infrequently regenerating exhaust after-treatment system kr = 1
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).
The result, where applicable inclusive of infrequent regeneration adjustment factor, shall also be adjusted by the applicable multiplicative or additive deterioration factor established according to the requirements of Annex III.
The specific emissions e [#/kWh] shall be calculated by means of equation (7-178):
| | (7-178) |
| --- | --- |
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 is the weighting factor for the mode i [-]
Ṅi is the mean emission number flow rate for the mode i [#/h] from equation (7-171) or (7-173) depending upon the dilution method
In case of an engine with infrequent (periodic) exhaust after-treatment system regeneration (see point 6.6.2 of Annex VI), the specific emissions shall be corrected with either the applicable multiplicative adjustment factor or with the applicable adjustment additive 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). 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 at equation (7-178).
The result, where applicable inclusive of infrequent regeneration adjustment factor, shall also be adjusted by the applicable multiplicative or additive deterioration factor established according to the requirements of Annex III.
The final NRSC and weighted average NRTC test results shall be rounded in one step to three significant figures in accordance with ASTM E 29–06B. No rounding of intermediate values leading to the final brake specific emission result is permissible.
2.4.1. At the engine manufacturer's request, dilution tunnel background particle number concentrations may be sampled, prior to or after the test, from a point downstream of the particle and hydrocarbon filters into the particle number measurement system, to determine the tunnel background particle concentrations.
2.4.2. Subtraction of particle number tunnel background concentrations shall not be allowed for type-approval, but may be used at the manufacturer's request, with the prior approval of the approval authority, for conformity of production testing, if it can be demonstrated that tunnel background contribution is significant, which can then be subtracted from the values measured in the diluted exhaust gas.
Appendix 6
Ammonia emission calculation
Calculation of the mean concentration for transient (NRTC and LSI-NRTC) test cycles and RMC
The mean NH3 concentration in the exhaust gas over the test cycle cNH3 [ppm] shall be determined by integrating the instantaneous values over the cycle. Equation (7-179) shall be applied:
| (7-179) | |
|---|---|
Where:
cNH3,i is the instantaneous NH3 concentration in the exhaust gas [ppm]
n is the number of measurements
For the NRTC, the final test result shall be calculated by means of equation (7-180):
| cNH3 = (0,1 × cNH3,cold) + (0,9 × cNH3,hot) | (7-180) |
| --- | --- |
Where:
cNH3,cold is the mean NH3 concentration of the cold-start NRTC [ppm]
cNH3,hot is the mean NH3 concentration of the hot-start NRTC [ppm]
Calculation of the mean concentration for discrete-mode NRSC
The mean NH3 concentration in the exhaust gas over the test cycle cNH3 [ppm] shall be determined by measuring the mean concentration for each mode and weighting the result in accordance with the weighting factors applicable to the test cycle. Equation (7-181) shall be applied:
| (7-181) | |
|---|---|
Where:
is the mean NH3 concentration in the exhaust gas for mode i [ppm]
Nmode is the number of modes in the test cycle
WFi is the weighting factor for the mode i [-]
ANNEX VIII
Performance requirements and test procedures for dual-fuel engines
Scope
This Annex shall apply for dual-fuel engines as defined in Article 3(18) of Regulation (EU) 2016/1628 when they are being operated simultaneously on both a liquid and a gaseous fuel (dual-fuel mode).
This Annex shall not apply for testing engines, including dual-fuel engines, when they are being operated solely on liquid or solely on gaseous fuels (i.e. when the GER is either 1 or 0 according to the type of fuel). In this case the requirements are the same as for any single-fuel engine.
Type approval of engines operated simultaneously on a combination of more than one liquid fuel and a gaseous fuel or a liquid fuel and more than one gaseous fuel shall follow the procedure for new technologies or new concepts given in Article 33 of Regulation (EU) 2016/1628.
Definitions and abbreviations
For the purposes of this Annex the following definitions shall apply:
2.1. ‘GER (Gas Energy Ratio)’ has the meaning defined in Article 3(20) of Regulation (EU) 2016/1628 based on the lower heating value;
2.2. ‘GERcycle’ means the average GER when operating the engine on the applicable engine test cycle;
2.3. ‘Dual-fuel Type 1A engine’ means either: (a) a dual-fuel engine of a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the hot-start NRTC test-cycle with an average gas energy ratio that is not lower than 90 % (GERNRTC, hot ≥ 0,9) and that does not idle using exclusively liquid fuel, and that has no liquid-fuel mode, or; (b) a dual-fuel engine of any (sub-) category other than a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the NRSC with an average gas energy ratio that is not lower than 90 % (GERNRSC ≥ 0,9) and that does not idle using exclusively liquid fuel, and that has no liquid-fuel mode;
2.4. ‘Dual-Fuel Type 1B engine’ means either: (a) a dual-fuel engine of a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the hot-start NRTC test-cycle with an average gas energy ratio that is not lower than 90 % (GERNRTC, hot ≥ 0,9) and that does not idle using exclusively liquid fuel in dual-fuel mode, and that has a liquid-fuel mode, or; (b) a dual-fuel engine of any (sub-) category other than a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the NRSC with an average gas energy ratio that is not lower than 90 % (GERNRSC ≥ 0,9) and that does not idle using exclusively liquid fuel in dual-fuel mode, and that has a liquid-fuel mode;
2.5. ‘Dual-Fuel Type 2A engine’ means either: (a) a dual-fuel engine of a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the hot-start NRTC test-cycle with an average gas energy ratio between 10 % and 90 % (0,1 < GERNRTC, hot < 0,9) and that has no liquid-fuel mode or that operates over the hot-start NRTC test-cycle with an average gas energy ratio that is not lower than 90 % (GERNRTC, hot ≥ 0,9), but that idles using exclusively liquid fuel, and that has no liquid-fuel mode, or; (b) a dual-fuel engine of any (sub-) category other than a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the NRSC with an average gas energy ratio between 10 % and 90 % (0,1 < GERNRSC < 0,9), and that has no liquid-fuel mode or that operates over the NRSC with an average gas energy ratio that is not lower than 90 % (GERNRSC ≥ 0,9), but that idles using exclusively liquid fuel, and that has no liquid-fuel mode;
2.6. ‘Dual-Fuel Type 2B engine’ means either: (a) a dual-fuel engine of a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the hot-start NRTC test-cycle with an average gas energy ratio between 10 % and 90 % (0,1 < GERNRTC, hot < 0,9) and that has a liquid-fuel mode or that operates over the hot-start NRTC test-cycle with an average gas energy ratio that is not lower than 90 % (GERNRTC, hot ≥ 0,9), and that has a liquid-fuel mode but that can idle using exclusively liquid fuel in dual-fuel mode, or; (b) a dual-fuel engine of any (sub-) category other than a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the NRSC with an average gas energy ratio between 10 % and 90 % (0,1 < GERNRSC < 0,9), and that has no liquid-fuel mode or that operates over the NRSC with an average gas energy ratio that is not lower than 90 % (GERNRSC ≥ 0,9), and that has a liquid-fuel mode but that can idle using exclusively liquid fuel in dual-fuel mode;
2.7. ‘Dual-Fuel Type 3B engine’ means either: (a) a dual-fuel engine of a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the hot-start NRTC test-cycle with an average gas energy ratio that does not exceed 10 % (GERNRTC, hot ≤ 0,1) and that has a liquid-fuel mode, or: (b) a dual-fuel engine of any (sub-) category other than a sub-category of NRE 19 ≤ kW ≤ 560, that operates over the NRSC with an average gas energy ratio that does not exceed 10 % (GERNRSC ≤ 0,1) and that has a liquid-fuel mode;
Dual-fuel specific additional approval requirements
In the case for a given engine type the value of GERcycle can be reduced from the maximum by an operator-adjustable control, the minimum GERcycle shall not be limited but the engine shall be capable of meeting the emission limit values at any value of GERcycle permitted by the manufacturer.
General requirements
A dual-fuel engine may only operate in liquid-fuel mode if, when operating in liquid-fuel mode, it has been certified according to all the requirements of this Regulation concerning operation solely on the specified liquid fuel.
When a dual-fuel engine is developed from an already certified liquid-fuel engine, then a new EU type approval certificate is required in the liquid-fuel mode.
4.1.2.1. Dual-fuel Type 1A engines shall not idle using liquid fuel exclusively except under the conditions defined in point 4.1.3 for warm-up and start.
4.1.2.2. Dual-fuel Type 1B engines shall not idle using liquid fuel exclusively in dual-fuel mode.
4.1.2.3. Dual-fuel Types 2A, 2B and 3B engines may idle using liquid fuel exclusively.
4.1.3.1. A Type 1B, Type 2B, or Type 3B dual-fuel engine may warm-up or start using liquid fuel solely. In the case that the emission control strategy during warm-up or start-up in dual-fuel mode is the same as the corresponding emission control strategy in liquid-fuel mode the engine may operate in dual-fuel mode during warm-up or start-up. If this condition is not met the engine shall only warm-up or start-up using liquid fuel solely when in liquid-fuel mode.
When an engine is operating in service mode it is subject to an operability restriction and is temporarily exempted from complying with the requirements related to exhaust emissions and NOx control described in this Regulation.
The operability restriction applicable to non-road mobile machinery fitted with a dual-fuel engine of engine categories other than IWP, IWA, RLL and RLR operated in service mode is the one activated by the ‘severe inducement system’ specified in point 5.4 of Appendix 1 of Annex IV.
In order to account for safety concerns and to allow for self-healing diagnostics, use of an inducement override function for releasing full engine power is permitted according to point 5.5 of Appendix 1 of Annex IV.
The operability restriction shall not otherwise be deactivated by either the activation or deactivation of the warning and inducement systems specified in Annex IV.
The activation and the deactivation of the service mode shall not activate or deactivate the warning and inducement systems specified in Annex IV.
For engines of category IWP, IWA, RLL and RLR, in order to account for safety concerns operation in service mode shall be permitted without limitation on engine torque or speed. In this case whenever an operability restriction would have been active according to point 4.2.2.3 the on-board computer log shall record in non-volatile computer memory all incidents of engine operation where the service mode is active in a manner to ensure that the information cannot be intentionally deleted.
It shall be possible for national inspection authorities to read these records with a scan tool. A description of the connection for, and method to read, those records shall be included in the information folder as set out in Part A of Annex I of Implementing Regulation (EU) 2017/656.
The operability restriction shall be automatically activated when the service mode is activated.
In the case where the service mode is activated according to point 4.2.3 because of a malfunction of the gas supply system, the operability restriction shall become active within 30 minutes operating time after the service mode is activated.
In the case where the service mode is activated because of an empty gaseous fuel tank, the operability restriction shall become active as soon as the service mode is activated.
The operability restriction system shall be deactivated when the engine no longer operates in service mode.
In order to permit the non-road mobile machinery to move to a position of safety, upon detection of an empty gaseous fuel tank, or of a malfunctioning gas supply system:
(a) Dual-fuel engines of Types 1A and 2A shall activate the service mode;
(b) Dual-fuel engines of Types 1B, 2B and 3B shall operate in liquid mode.
In the case of an empty gaseous fuel tank, the service mode or, as appropriate according to point 4.2.3, the liquid fuel mode shall be activated as soon as the engine system has detected that the tank is empty.
When the gas availability in the tank again reaches the level that justified the activation of the empty tank warning system specified in point 4.3.2, the service mode may be deactivated, or, when appropriate, the dual-fuel mode may be reactivated.
In the case of a malfunctioning gas supply system that causes the unavailability of gaseous fuel, the service mode or, as appropriate according to point 4.2.3, the liquid fuel mode shall be activated when gaseous fuel supply is not available.
As soon as the gaseous fuel supply becomes available the service mode may be deactivated, or, when appropriate, the dual-fuel mode may be reactivated.
The non-road mobile machinery shall provide to the operator a visual indication of the mode under which the engine operates (dual-fuel mode, liquid mode, or service mode).
The characteristics and the location of this indicator shall be left to the discretion of the OEM and may be part of an already existing visual indication system.
This indicator may be completed by a message display. The system used for displaying the messages referred to in this point may be the same as the ones used for NOx control diagnostics, or other maintenance purposes.
The visual element of the dual-fuel operating mode indicator shall not be the same as the one used for the purpose of NOx control diagnostics, or for other engine maintenance purposes.
Safety alerts always have display priority over the operating mode indication.
4.3.1.1. The dual-fuel mode indicator shall be set to service mode as soon as the service mode is activated (i.e. before it becomes actually active) and the indication shall remain as long as the service mode is active.
4.3.1.2. The dual-fuel mode indicator shall be set for at least one minute on dual-fuel mode or liquid-fuel mode as soon as the engine operating mode is changed from liquid fuel to dual-fuel mode or vice-versa. This indication is also required for at least one minute at key-on, or at the request of the manufacturer at engine cranking. The indication shall also be given upon the operator's request.
Non-road mobile machinery fitted with a dual-fuel engine shall be equipped with a dual-fuel warning system that alerts the operator that the gaseous fuel tank will soon become empty.
The dual-fuel warning system shall remain active until the tank is refuelled to a level above which the warning system is activated.
The dual-fuel warning system may be temporarily interrupted by other warning signals providing important safety-related messages.
It shall not be possible to turn off the dual-fuel warning system by means of a scan-tool as long as the cause of the warning activation has not been rectified.
The dual-fuel warning system shall consist of a visual alert system (icon, pictogram, etc.) left to the choice of the manufacturer.
It may include, at the choice of the manufacturer, an audible component. In that case, the cancelling of that component by the operator is permitted.
The visual element of the dual-fuel warning system shall not be the same as the one used for the purpose of NOx control diagnostics, or for other engine maintenance purposes.
In addition the dual-fuel warning system may display short messages, including messages indicating clearly the remaining distance or time before the activation of the operability restriction.
The system used for displaying the warning or messages referred to in this point may be the same as the one used for displaying the warning or messages related the NOx control diagnostics, or warning or messages for other maintenance purposes.
A facility to permit the operator to dim the visual alarms provided by the warning system may be provided on non-road mobile machinery for use by the rescue services or on non-road mobile machinery designed and constructed for use by the armed services, civil defense, fire services and forces responsible for maintaining public order.
When a dual-fuel engine operates in dual-fuel mode:
(a) The reference torque curve retrievable shall be the one obtained when that engine is tested on an engine test bench in the dual-fuel mode;
(b) The recorded actual torques (indicated torque and friction torque) shall be the result of the dual-fuel combustion and not the one obtained when operating with liquid fuel exclusively.
When a dual-fuel engine operates in liquid-fuel mode, the reference torque curve retrievable shall be the one obtained when the engine is tested on an engine test bench in liquid-fuel mode.
4.5.1. Where used for a dual-fuel engine, adaptive strategies shall, in addition to satisfying the requirements of Annex IV, additionally comply with the following requirements:
4.6 The type-approval shall be conditional upon providing to the OEM and end-users, ————— in accordance with Annexes XIV and XV, instructions for installation and operation of the dual-fuel engine including the service mode set out in point 4.2 and the dual-fuel indicator system set out in point 4.3.
5. Performance requirements
5.1. The performance requirements, including emission limit values, and the requirements for EU type-approval applicable to dual-fuel engines are identical to those of any other engine of the respective engine category as set out in this Regulation and in Regulation (EU) 2016/1628, except as set out in this Annex.
5.2 The hydrocarbon (HC) limit for operation in dual-fuel mode shall be determined using the average gas energy ratio (GER) over the specified test cycle as set out in Annex II to Regulation (EU) 2016/1628.
5.3 The technical requirements on emission control strategies, including documentation required to demonstrate these strategies, technical provisions to resist tampering and the prohibition of defeat devices are identical to those of any other engine of the respective engine category as set out in Annex IV.
5.4 The detailed technical requirements on the area associated with the relevant NRSC, within which there is control of the amount that the emissions shall be permitted to exceed the limit values set out in Annex II to Regulation (EU) 2016/1628 are identical to those of any other engine of the respective engine category as set out in Annex IV.
Demonstration requirements
6.1. The demonstration requirements applicable to dual-fuel engines are identical to those of any other engine of the respective engine category as set out in this Regulation and in Regulation (EU) 2016/1628, except as set out in section 6.
6.2. Compliance with the applicable limit values shall be demonstrated in dual-fuel mode.
6.3. For dual-fuel engine types with a liquid-fuel mode (i.e. types 1B, 2B, 3B) compliance with the applicable limit values shall additionally be demonstrated in liquid-fuel mode.
6.8. A demonstration report shall document the demonstration conducted pursuant to points 6.1 to 6.7.1 The report shall:
Requirements to ensure the correct operation of NOx control measures
7.1. Annex IV (technical requirements on NOx control measures) shall apply to dual-fuel engines, whether operating in dual-fuel or liquid mode.
Appendix 1
Dual-fuel engine dual-fuel indicator, warning system, operability restriction — Demonstration requirements
1. Dual-fuel indicators
The ability of the engine to command the activation of the dual-fuel mode indicator when operating in dual-fuel mode shall be demonstrated at EU type-approval.
In the case of a Type 1B, Type 2B, or Type 3B dual-fuel engine the ability of the engine to command the activation of the liquid-fuel mode indicator when operating in liquid-fuel mode shall be demonstrated at EU type-approval.
The ability of the engine to command the activation of the service mode indicator when operating in service mode shall be demonstrated at EU type-approval.
1.3.1. When so-equipped it is sufficient to perform the demonstration related to the service mode indicator by activating a service mode activation switch and to present the approval authority with evidence showing that the activation occurs when the service mode is commanded by the engine system itself (for example, through algorithms, simulations, result of in-house tests, etc. …).
2. Warning system
The ability of the engine to command the activation of the warning system in the case that the amount of gaseous fuel in the gaseous fuel tank is below the warning level, shall be demonstrated at EU type-approval. For that purpose the actual amount of gaseous fuel may be simulated.
3. Operability restriction
In the case of a Type 1A or Type 2A dual-fuel engine the ability of the engine to command the activation of the operability restriction upon detection of an empty gaseous fuel tank and of a malfunctioning gas supply system shall be demonstrated at EU type-approval. For that purpose the empty gaseous fuel tank and the malfunctioning of the gas supply may be simulated.
3.1. It is sufficient to perform the demonstration in a typical use-case selected with the agreement of the approval authority and to present that authority with evidence showing that the operability restriction occurs in the other possible use-cases (for example, through algorithms, simulations, result of in-house tests, etc.).
Appendix 2
Emission test procedure requirements for dual-fuel engines
1. General
This point defines the additional requirements and exceptions of this Annex to enable emission testing of dual-fuel engines independent whether these emissions are solely exhaust emissions or also crankcase emissions added to the exhaust emissions according to point 6.10 of Annex VI. In the case that no additional requirement or exception is listed, the requirements of this Regulation shall apply to dual-fuel engines in the same way as they apply to any other approved engine types or engine families under Regulation (EU) 2016/1628.
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