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Title 40 → Chapter I → Subchapter U → Part 1066 → Subpart G |

Title 40: Protection of Environment

PART 1066—VEHICLE-TESTING PROCEDURES

Contents

§1066.601 Overview.

§1066.605 Mass-based and molar-based exhaust emission calculations.

§1066.610 Dilution air background correction.

§1066.615 NOX intake-air humidity correction.

§1066.620 Removed water correction.

§1066.625 Flow meter calibration calculations.

§1066.630 PDP, SSV, and CFV flow rate calculations.

§1066.635 NMOG determination.

§1066.695 Data requirements.

(a) This subpart describes calculations used to determine emission rates. See the standard-setting part and the other provisions of this part to determine which equations apply for your testing. This subpart describes how to—

(1) Use the signals recorded before, during, and after an emission test to calculate distance-specific emissions of each regulated pollutant.

(2) Perform calculations for calibrations and performance checks.

(3) Determine statistical values.

(b) You may use data from multiple systems to calculate test results for a single emission test, consistent with good engineering judgment. You may also make multiple measurements from a single batch sample, such as multiple weighing of a PM filter or multiple readings from a bag sample. Although you may use an average of multiple measurements from a single test, you may not use test results from multiple emission tests to report emissions. We allow weighted means where appropriate, such as for sampling onto a PM filter over the FTP. You may discard statistical outliers, but you must report all results.

(a) Calculate your total mass of emissions over a test cycle as specified in paragraph (c) of this section or in 40 CFR part 1065, subpart G, as applicable.

(b) See the standard-setting part for composite emission calculations over multiple test intervals and the corresponding weighting factors.

(c) Perform the following sequence of preliminary calculations to correct recorded concentration measurements before calculating mass emissions in paragraphs (e) and (f) of this section:

(1) For vehicles above 14,000 pounds GVWR, correct all THC and CH4 concentrations for initial contamination as described in 40 CFR 1065.660(a), including continuous readings, sample bag readings, and dilution air background readings. This correction is optional for vehicles at or below 14,000 pounds GVWR.

(2) Correct all concentrations measured on a “dry” basis to a “wet” basis, including dilution air background concentrations.

(3) Calculate all NMHC and CH4 concentrations, including dilution air background concentrations, as described in 40 CFR 1065.660.

(4) For vehicles at or below 14,000 pounds GVWR, calculate HC concentrations, including dilution air background concentrations, as described in this section, and as described in §1066.635 for NMOG. For emission testing of vehicles above 14,000 pounds GVWR, with fuels that contain 25% or more oxygenated compounds by volume, calculate THCE and NMHC concentrations, including dilution air background concentrations, as described in 40 CFR part 1065, subpart I.

(5) Correct all gaseous concentrations for dilution air background as described in §1066.610.

(6) Correct NOX emission values for intake-air humidity as described in §1066.615.

(7) Correct all PM filter masses for sample media buoyancy as described in 40 CFR 1065.690.

(d) Calculate g/mile emission rates using the following equation unless the standard-setting part specifies otherwise:

Where:

e[emission] = emission rate over the test interval.

m[emission] = emission mass over the test interval.

D = the measured driving distance over the test interval.

(e) Calculate the emission mass of each gaseous pollutant using the following equation:

Where:

m[emission] = emission mass over the test interval.

Vmix = total dilute exhaust volume over the test interval, corrected to standard reference conditions, and corrected for any volume removed for emission sampling and for any volume change from adding secondary dilution air.

p[emission] = density of the appropriate chemical species as given in §1066.1005(f).

x[emission] = measured emission concentration in the sample, after dry-to-wet and background corrections.

c = 10−2 for emission concentrations in %, and 10−6 for emission concentrations in ppm.

Example:

Vmix = 170.878 m3 (from paragraph (f) of this section)

ρNOx = 1913 g/m3

xNOx = 0.9721 ppm

c = 10−6

mNOx = 170.878·1913·0.9721·10−6 = 0.3177 g

(f) Calculation of the emission mass of PM, mPM, is dependent on how many PM filters you use, as follows:

(1) Except as otherwise specified in this paragraph (f), calculate mPM using the following equation:

Where:

mPM = mass of particulate matter emissions over the test interval, as described in §1066.815(b)(1), (2), and (3).

Vmix = total dilute exhaust volume over the test interval, corrected to standard reference conditions, and corrected for any volume removed for emission sampling and for any volume change from adding secondary dilution air. For partial-flow dilution systems, set Vmix equal to the total exhaust volume over the test interval, corrected to standard reference conditions.

VPMstd = total volume of dilute exhaust sampled through the filter over the test interval, corrected to standard reference conditions.

Vsdastd = total volume of secondary dilution air sampled through the filter over the test interval, corrected to standard reference conditions. For partial-flow dilution systems, set Vsdastd equal to total dilution air volume over the test interval, corrected to standard reference conditions.

mPMfil = mass of particulate matter emissions on the filter over the test interval.

mPMbkgnd = mass of particulate matter on the background filter.

Example:

Vmix = 170.878 m3 (from paragraph (g) of this section)

VPMstd = 0.925 m3 (from paragraph (g) of this section)

Vsdastd = 0.527 m3 (from paragraph (g) of this section)

mPMfil = 0.0000045 g

mPMbkgnd = 0.0000014 g

(2) If you sample PM onto a single filter as described in §1066.815(b)(4)(i) or (b)(4)(ii) (for constant volume samplers), calculate mPM using the following equation:

Where:

mPM = mass of particulate matter emissions over the entire FTP.

Vmix = total dilute exhaust volume over the test interval, corrected to standard reference conditions, and corrected for any volume removed for emission sampling and for any volume change from adding secondary dilution air.

V[interval]-PMstd = total volume of dilute exhaust sampled through the filter over the test interval (ct = cold transient, s = stabilized, ht = hot transient), corrected to standard reference conditions.

V[interval]-sdastd = total volume of secondary dilution air sampled through the filter over the test interval (ct = cold transient, s = stabilized, ht = hot transient), corrected to standard reference conditions.

mPMfil = mass of particulate matter emissions on the filter over the test interval.

mPMbkgnd = mass of particulate matter on the background filter over the test interval.

Example:

Vmix = 633.691 m3

Vct-PMstd = 0.925 m3

Vct-sdastd = 0.527 m3

Vs-PMstd = 1.967 m3

Vs-sdastd = 1.121 m3

Vht-PMstd = 1.122 m3

Vht-sdastd = 0.639 m3

mPMfil = 0.0000106 g

mPMbkgnd = 0.0000014 g

mPM = 0.00222 g

(3) If you sample PM onto a single filter as described in §1066.815(b)(4)(ii) (for partial flow dilution systems), calculate mPM using the following equation:

Where:

mPM = mass of particulate matter emissions over the entire FTP.

V[interval]-exhstd = total engine exhaust volume over the test interval (ct = cold transient, s = stabilized, ht = hot transient), corrected to standard reference conditions, and corrected for any volume removed for emission sampling.

V[interval]-PMstd = total volume of dilute exhaust sampled through the filter over the test interval (ct = cold transient, s = stabilized, ht = hot transient), corrected to standard reference conditions.

V[interval]-dilstd = total volume of dilution air over the test interval (ct = cold transient, s = stabilized, ht = hot transient), corrected to standard reference conditions and for any volume removed for emission sampling.

mPMfil = mass of particulate matter emissions on the filter over the test interval.

mPMbkgnd = mass of particulate matter on the background filter over the test interval.

Example:

Vct-exhstd = 5.55 m3

Vct-PMstd = 0.526 m3

Vct-dilstd = 0.481 m3

Vs-exhstd = 9.53 m3

Vs-PMstd = 0.903 m3

Vs-dilstd = 0.857 m3

Vht-exhstd = 5.54 m3

Vht-PMstd = 0.527 m3

Vht-dilstd = 0.489 m3

mPMfil = 0.0000106 g

mPMbkgnd = 0.0000014 g

mPM = 0.00269 g

(4) If you sample PM onto a single filter as described in §1066.815(b)(5)(i) or (b)(5)(ii) (for constant volume samplers), calculate mPM using the following equation:

Where:

mPM = mass of particulate matter emissions over the entire FTP.

Vmix = total dilute exhaust volume over the test interval, corrected to standard reference conditions, and corrected for any volume removed for emission sampling and for any volume change from secondary dilution air.

V[interval]-PMstd = total volume of dilute exhaust sampled through the filter over the test interval (ct = cold transient, cs = cold stabilized, ht = hot transient, hs = hot stabilized), corrected to standard reference conditions.

V[interval]-sdastd = total volume of secondary dilution air sampled through the filter over the test interval (ct = cold transient, cs = cold stabilized, ht = hot transient, hs = hot stabilized), corrected to standard reference conditions.

mPMfil = mass of particulate matter emissions on the filter over the test interval.

mPMbkgnd = mass of particulate matter on the background filter over the test interval.

Example:

Vmix = 972.121 m3

Vct-PMstd = 0.925 m3

Vct-sdastd = 0.529 m3

Vcs-PMstd = 1.968 m3

Vcs-sdastd = 1.123 m3

Vht-PMstd = 1.122 m3

Vht-sdastd = 0.641 m3

Vhs-PMstd = 1.967 m3

Vhs-sdastd = 1.121 m3

mPMfil = 0.0000229 g

mPMbkgnd = 0.0000014 g

mPM = 0.00401 g

(5) If you sample PM onto a single filter as described in §1066.815(b)(5)(ii) (for partial flow dilution systems), calculate mPM using the following equation:

Where:

mPM = mass of particulate matter emissions over the entire FTP.

V[interval]-exhstd = total engine exhaust volume over the test interval (ct = cold transient, cs = cold stabilized, ht = hot transient, hs = hot stabilized), corrected to standard reference conditions, and corrected for any volume removed for emission sampling.

V[interval]-PMstd = total volume of dilute exhaust sampled through the filter over the test interval (ct = cold transient, cs = cold stabilized, ht = hot transient, hs = hot stabilized), corrected to standard reference conditions.

V[interval]-dilstd = total volume of dilution air over the test interval (ct = cold transient, cs = cold stabilized, ht = hot transient, hs = hot stabilized), corrected to standard reference conditions and for any volume removed for emission sampling.

mPMfil = mass of particulate matter emissions on the filter over the test interval.

mPMbkgnd = mass of particulate matter on the background filter over the test interval.

Example:

Vct-exhstd = 5.55 m3

Vct-PMstd = 0.526 m3

Vct-dilstd = 0.481 m3

Vcs-exhstd = 9.53 m3

Vcs-PMstd = 0.903 m3

Vcs-dilstd = 0.857 m3

Vht-exhstd = 5.54 m3

Vht-PMstd = 0.527 m3

Vht-dilstd = 0.489 m3

Vhs-exhstd = 9.54 m3

Vhs-PMstd = 0.902 m3

Vhs-dilstd = 0.856 m3

mPMfil = 0.0000229 g

mPMbkgnd = 0.0000014 g

mPM = 0.00266 g

(g) This paragraph (g) describes how to correct flow and flow rates to standard reference conditions and provides an example for determining Vmix based on CVS total flow and the removal of sample flow from the dilute exhaust gas. You may use predetermined nominal values for removed sample volumes, except for flows used for batch sampling.

(1) Correct flow and flow rates to standard reference conditions as needed using the following equation:

Where:

V[flow]std = total flow volume at the flow meter, corrected to standard reference conditions.

V[flow]act = total flow volume at the flow meter at test conditions.

pin = absolute static pressure at the flow meter inlet, measured directly or calculated as the sum of atmospheric pressure plus a differential pressure referenced to atmospheric pressure.

Tstd = standard temperature.

pstd = standard pressure.

Tin = temperature of the dilute exhaust sample at the flow meter inlet.

Example:

VPMact = 1.071 m3

pin = 101.7 kPa

Tstd = 293.15 K

pstd = 101.325 kPa

Tin = 340.5 K

(2) The following example provides a determination of Vmix based on CVS total flow and the removal of sample flow from one dilute exhaust gas analyzer and one PM sampling system that is utilizing secondary dilution. Note that your Vmix determination may vary from Eq. 1066.605-7 based on the number of flows that are removed from your dilute exhaust gas and whether your PM sampling system is using secondary dilution. For this example, Vmix is governed by the following equation:

Where:

VCVSstd = total dilute exhaust volume over the test interval at the flow meter, corrected to standard reference conditions.

Vgasstd = total volume of sample flow through the gaseous emission bench over the test interval, corrected to standard reference conditions.

VPMstd = total volume of dilute exhaust sampled through the filter over the test interval, corrected to standard reference conditions.

Vsdastd = total volume of secondary dilution air flow sampled through the filter over the test interval, corrected to standard reference conditions.

Example:

Using Eq. 1066.605-8:

VCVSstd = 170.451 m3, where VCVSact = 170.721 m3, pin = 101.7 kPa, and Tin = 294.7 K

Using Eq. 1066.605-8:

Vgasstd = 0.028 m3, where Vgasact = 0.033 m3, pin = 101.7 kPa, and Tin = 340.5 K

Using Eq. 1066.605-8:

VPMstd = 0.925 m3, where VPMact = 1.071 m3, pin = 101.7 kPa, and Tin = 340.5 K

Using Eq. 1066.605-8:

Vsdastd = 0.527 m3, where Vsdaact = 0.531 m3, pin = 101.7 kPa, and Tin = 296.3 K

Vmix = 170.451 + 0.028 + 0.925 − 0.527 = 170.878 m3

(h) Calculate total flow volume over a test interval, V[flow], for a CVS or exhaust gas sampler as follows:

(1) Varying versus constant flow rates. The calculation methods depend on differentiating varying and constant flow, as follows:

(i) We consider the following to be examples of varying flows that require a continuous multiplication of concentration times flow rate: raw exhaust, exhaust diluted with a constant flow rate of dilution air, and CVS dilution with a CVS flow meter that does not have an upstream heat exchanger or electronic flow control.

(ii) We consider the following to be examples of constant exhaust flows: CVS diluted exhaust with a CVS flow meter that has an upstream heat exchanger, an electronic flow control, or both.

(2) Continuous sampling. For continuous sampling, you must frequently record a continuously updated flow signal. This recording requirement applies for both varying and constant flow rates.

(i) Varying flow rate. If you continuously sample from a varying exhaust flow rate, calculate V[flow] using the following equation:

Where:

Example:

N = 505

Q̇CVS1 = 0.276 m3/s

Q̇CVS2 = 0.294 m3/s

frecord = 1 Hz

Using Eq. 1066.605-11,

Δt = 1/1 = 1 s

VCVS = (0.276 + 0.294 + ... + Q̇CVS505)·1

VCVS = 170.721 m3

(ii) Constant flow rate. If you continuously sample from a constant exhaust flow rate, use the same calculation described in paragraph (h)(2)(i) of this section or calculate the mean flow recorded over the test interval and treat the mean as a batch sample, as described in paragraph (h)(3)(ii) of this section.

(3) Batch sampling. For batch sampling, calculate total flow by integrating a varying flow rate or by determining the mean of a constant flow rate, as follows:

(i) Varying flow rate. If you proportionally collect a batch sample from a varying exhaust flow rate, integrate the flow rate over the test interval to determine the total flow from which you extracted the proportional sample, as described in paragraph (h)(2)(i) of this section.

(ii) Constant flow rate. If you batch sample from a constant exhaust flow rate, extract a sample at a proportional or constant flow rate and calculate V[flow] from the flow from which you extract the sample by multiplying the mean flow rate by the time of the test interval using the following equation:

Example:

Q̇̅CVS = 0.338 m3/s

Δt = 505 s

VCVS = 0.338·505

VCVS = 170.69 m3

[79 FR 23823, Apr. 28, 2014, as amended at 80 FR 9121, Feb. 19, 2015; 81 FR 74203, Oct. 25, 2016]

(a) Correct the emissions in a gaseous sample for background using the following equation:

Where:

x[emission]dexh = measured emission concentration in dilute exhaust (after dry-to-wet correction, if applicable).

x[emission]bkgnd = measured emission concentration in the dilution air (after dry-to-wet correction, if applicable).

DF = dilution factor, as determined in paragraph (b) of this section.

Where:

xCO2 = amount of CO2 measured in the sample over the test interval.

xNMHC = amount of C1-equivalent NMHC measured in the sample over the test interval.

xCH4 = amount of CH4 measured in the sample over the test interval.

xCO = amount of CO measured in the sample over the test interval.

α = atomic hydrogen-to-carbon ratio of the test fuel. You may measure α or use default values from Table 1 of 40 CFR 1065.655.

β = atomic oxygen-to-carbon ratio of the test fuel. You may measure β or use default values from Table 1 of 40 CFR 1065.655.

(c) Determine the dilution factor, DF, over the test interval for partial-flow dilution sample systems using the following equation:

Where:

Vdexhstd = total dilute exhaust volume sampled over the test interval, corrected to standard reference conditions.

Vexhstd = total exhaust volume sampled from the vehicle, corrected to standard reference conditions.

(d) Determine the time-weighted dilution factor, DFw, over the duty cycle using the following equation:

Where:

N = number of test intervals.

i = test interval number

t = duration of the test interval.

DF = dilution factor over the test interval.

Example:

You may correct NOX emissions for intake-air humidity as described in this section if the standard-setting part allows it. See §1066.605(c) for the proper sequence for applying the NOX intake-air humidity correction.

(a) For vehicles at or below 14,000 pounds GVWR, apply a correction for vehicles with reciprocating engines operating over specific test cycles as follows:

(1) Calculate a humidity correction using a time-weighted mean value for ambient humidity over the test interval. Calculate absolute ambient humidity, H, using the following equation:

Where:

MH2O = molar mass of H2O.

pd = saturated vapor pressure at the ambient dry bulb temperature.

RH = relative humidity of ambient air

Mair = molar mass of air.

patmos = atmospheric pressure.

Example:

MH2O = 18.01528 g/mol

pd = 2.93 kPa

RH = 37.5% = 0.375

Mair = 28.96559 g/mol

patmos = 96.71 kPa

(2) Use the following equation to correct measured concentrations to a reference condition of 10.71 grams H2O vapor per kilogram of dry air for the FTP, US06, LA-92, SC03, and HFET test cycles:

Where:

χNOx = measured NOX emission concentration in the sample, after dry-to-wet and background corrections.

Hs = humidity scale. Set = 1 for FTP, US06, LA-92, and HFET test cycles. Set = 0.8825 for the SC03 test cycle.

H = ambient humidity, as determined in paragraph (a)(1) of this section.

Example:

H = 7.14741 g H2O vapor/kg dry air time weighted over the FTP test cycle

χNOx = 1.21 ppm

(b) For vehicles above 14,000 pounds GVWR, apply correction factors as described in 40 CFR 1065.670.

[80 FR 9121, Feb. 19, 2015, as amended at 81 FR 74207, Oct. 25, 2016]

Correct for removed water if water removal occurs upstream of a concentration measurement and downstream of a flow meter used to determine mass emissions over a test interval. Perform this correction based on the amount of water at the concentration measurement and on the amount of water at the flow meter.

This section describes the calculations for calibrating various flow meters based on mass flow rates. Calibrate your flow meter according to 40 CFR 1065.640 instead if you calculate emissions based on molar flow rates.

(a) PDP calibration. Perform the following steps to calibrate a PDP flow meter:

(1) Calculate PDP volume pumped per revolution, Vrev, for each restrictor position from the mean values determined in §1066.140:

Where:

V̇̅ref = mean flow rate of the reference flow meter.

Tin = mean temperature at the PDP inlet.

pstd = standard pressure = 101.325 kPa.

f̅nPDP = mean PDP speed.

Pin = mean static absolute pressure at the PDP inlet.

Tstd = standard temperature = 293.15 K.

Example:

V̇̅ref = 0.1651 m3/s

Tin = 299.5 K

pstd = 101.325 kPa

f̅nPDP = 1205.1 r/min = 20.085 r/s

Pin = 98.290 kPa

Tstd = 293.15 K

Vrev = 0.00866 m3/r

(2) Calculate a PDP slip correction factor, Ks for each restrictor position from the mean values determined in §1066.140:

Where:

f̅mPDP = mean PDP speed.

p̅out = mean static absolute pressure at the PDP outlet.

p̅in = mean static absolute pressure at the PDP inlet.

(3) Perform a least-squares regression of Vrev, versus Ks, by calculating slope, a1, and intercept, a0, as described in 40 CFR 1065.602.

(4) Repeat the procedure in paragraphs (a)(1) through (3) of this section for every speed that you run your PDP.

(5) The following example illustrates a range of typical values for different PDP speeds:

Table 1 of §1066.625—Example of PDP Calibration Data

f̅nPDP (revolution/s) | a1 (m ^{3}/s) | a0 (m ^{3}/revolution) |
---|---|---|

12.6 | 0.841 | 0.056 |

16.5 | 0.831 | −0.013 |

20.9 | 0.809 | 0.028 |

23.4 | 0.788 | −0.061 |

(6) For each speed at which you operate the PDP, use the appropriate regression equation from this paragraph (a) to calculate flow rate during emission testing as described in §1066.630.

(b) SSV calibration. The equations governing SSV flow assume one-dimensional isentropic inviscid flow of an ideal gas. Paragraph (b)(2)(iv) of this section describes other assumptions that may apply. If good engineering judgment dictates that you account for gas compressibility, you may either use an appropriate equation of state to determine values of Z as a function of measured pressure and temperature, or you may develop your own calibration equations based on good engineering judgment. Note that the equation for the flow coefficient, Cf, 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, you may either use an appropriate equation of state to determine values of γ as a function of measured pressure and temperature, or you may develop your own calibration equations based on good engineering judgment.

(1) Calculate volume flow rate at standard reference conditions, V̇̅std, as follows

Where:

Cd = discharge coefficient, as determined in paragraph (b)(2)(i) of this section.

Cf = flow coefficient, as determined in paragraph (b)(2)(ii) of this section.

At = cross-sectional area at the venturi throat.

R = molar gas constant.

pin = static absolute pressure at the venturi inlet.

Tstd = standard temperature.

pstd = standard pressure.

Z = compressibility factor.

Mmix = molar mass of gas mixture.

Tin = absolute temperature at the venturi inlet.

(2) Perform the following steps to calibrate an SSV flow meter:

(i) Using the data collected in §1066.140, calculate Cd for each flow rate using the following equation:

Where:

V̇̅ref = measured volume flow rate from the reference flow meter.

(ii) Use the following equation to calculate Cf for each flow rate:

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 (b)(2)(iii) of this section.

β = ratio of venturi throat diameter to inlet diameter.

(iii) Calculate r using the following equation:

Where:

Δp = differential static pressure, calculated as venturi inlet pressure minus venturi throat pressure.

(iv) You may apply any of the following simplifying assumptions or develop other values as appropriate for your test configuration, consistent with good engineering judgment:

(A) For raw exhaust, diluted exhaust, and dilution air, you may assume that the gas mixture behaves as an ideal gas (Z = 1).

(B) For raw exhaust, you may assume γ = 1.385.

(C) For diluted exhaust and dilution air, you may assume γ = 1.399.

(D) For diluted exhaust and dilution air, you may assume the molar mass of the mixture, Mmix, is a function only of the amount of water in the dilution air or calibration air, as follows:

Where:

Mair = molar mass of dry air.xH2O = amount of H2O in the dilution air or calibration air, determined as described in 40 CFR 1065.645.

MH2O = molar mass of water.

Example:

Mair = 28.96559 g/mol

xH2O = 0.0169 mol/mol

MH2O = 18.01528 g/mol

Mmix = 28.96559 · (1 − 0.0169) + 18.01528 · 0.0169 Mmix = 28.7805 g/mol

(E) For diluted exhaust and dilution air, you may assume a constant molar mass of the mixture, Mmix, for all calibration and all testing if you control the amount of water in dilution air and in calibration air, as illustrated in the following table:

Table 2 of §1066.625—Examples of Dilution Air and Calibration Air Dewpoints at Which You May Assume a Constant Mmix

If calibration Tdew ( °C) is . . . | assume the following constant Mmix (g/mol) . . . | for the following ranges of Tdew ( °C) during emission tests^{a} |
---|---|---|

≤0 | 28.96559 | ≤18 |

0 | 28.89263 | ≤21 |

5 | 28.86148 | ≤22 |

10 | 28.81911 | ≤24 |

15 | 28.76224 | ≤26 |

20 | 28.68685 | −8 to 28 |

25 | 28.58806 | 12 to 31 |

30 | 28.46005 | 23 to 34 |

^{a}The specified ranges are valid for all calibration and emission testing over the atmospheric pressure range (80.000 to 103.325) kPa.

(v) The following example illustrates the use of the governing equations to calculate Cd of an SSV flow meter at one reference flow meter value:

V̇̅ref = 2.395 m3/s

Z = 1

Mmix = 28.7805 g/mol = 0.0287805 kg/mol

R = 8.314472 J/(mol·K) = 8.314472 (m2·kg)/(s2·mol·K)

Tin = 298.15 K

At = 0.01824 m2

pin = 99.132 kPa = 99132 Pa = 99132 kg/(m·s2)

γ = 1.399

β = 0.8

Δp = 7.653 kPa

Cf = 0.472

Cd = 0.985

(vi) Calculate the Reynolds number, Re#, for each reference flow rate at standard conditions, V̇̅refstd, using the throat diameter of the venturi, dt, and the air density at standard conditions, ρstd. Because the dynamic viscosity, μ, is needed to compute Re#, you may use your own fluid viscosity model to determine μ for your calibration gas (usually air), using good engineering judgment. Alternatively, you may use the Sutherland three-coefficient viscosity model to approximate μ, as shown in the following sample calculation for Re#:

Where, using the Sutherland three-coefficient viscosity model:

Where:

μ0 = Sutherland reference viscosity.

T0 = Sutherland reference temperature.

S = Sutherland constant.

Table 3 of §1066.625—Sutherland Three-Coefficient Viscosity Model Parameters

Gas^{1} | μ0 | T0 | S | Temperature range within ±2% error^{2} | Pressure limit^{2} |
---|---|---|---|---|---|

kg/(m·s) | K | K | K | kPa | |

Air | 1.716·10−5 | 273 | 111 | 170 to 1900 | ≤1800. |

CO2 | 1.370·10−5 | 273 | 222 | 190 to 1700 | ≤3600. |

H2O | 1.12·10−5 | 350 | 1064 | 360 to 1500 | ≤10000. |

O2 | 1.919·10−5 | 273 | 139 | 190 to 2000 | ≤2500. |

N2 | 1.663·10−5 | 273 | 107 | 100 to 1500 | ≤1600. |

^{1}Use tabulated parameters only for the pure gases, as listed. Do not combine parameters in calculations to calculate viscosities of gas mixtures.

^{2}The model results are valid only for ambient conditions in the specified ranges.

Example:

μ0 = 1.716·10−5 kg/(m·s)

T0 = 273 K

S = 111 K

Tin = 298.15 K

dt = 152.4 mm = 0.1524 m

ρstd = 1.1509 kg/m3

Re# = 1.3027·106

(vii) Calculate ρ using the following equation:

(viii) Create an equation for Cd as a function of Re#, using paired values of the two quantities. The equation may involve any mathematical expression, including a polynomial or a power series. The following equation is an example of a commonly used mathematical expression for relating Cd and Re#:

(ix) Perform a least-squares regression analysis to determine the best-fit coefficients for the equation and calculate SEE as described in 40 CFR 1065.602.

(x) If the equation meets the criterion of SEE ≤0.5% ⋅ Cdmax, you may use the equation for the corresponding range of Re#, as described in §1066.630(b).

(xi) If the equation does not meet the specified statistical criteria, you may use good engineering judgment to omit calibration data points; however, you must use at least seven calibration data points to demonstrate that you meet the criterion. For example, this may involve narrowing the range of flow rates for a better curve fit.

(xii) Take corrective action if the equation does not meet the specified statistical criterion even after omitting calibration data points. For example, select another mathematical expression for the Cd versus Re# equation, check for leaks, or repeat the calibration process. If you must repeat the calibration process, we recommend applying tighter tolerances to measurements and allowing more time for flows to stabilize.

(xiii) Once you have an equation that meets the specified statistical criterion, you may use the equation only for the corresponding range of Re#.

(c) CFV calibration. 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 calibrate each venturi independently to determine a separate calibration coefficient, Kv, for each venturi, or calibrate each combination of venturis as one venturi by determining Kv for the system.

(1) To determine Kv for a single venturi or a combination of venturis, perform the following steps:

(i) Calculate an individual Kv for each calibration set point for each restrictor position using the following equation:

Where:

V̇̅refstd= mean flow rate from the reference flow meter, corrected to standard reference conditions.

T̅in= mean temperature at the venturi inlet.

P̅in= mean static absolute pressure at the venturi inlet.

(ii) Calculate the mean and standard deviation of all the Kv values (see 40 CFR 1065.602). Verify choked flow by plotting Kv as a function of pin. Kv will have a relatively constant value for choked flow; as vacuum pressure increases, the venturi will become unchoked and Kv will decrease. Paragraphs (c)(1)(iii) through (viii) of this section describe how to verify your range of choked flow.

(iii) If the standard deviation of all the Kv values is less than or equal to 0.3% of the mean Kv, use the mean Kv in Eq. 1066.630-7, and use the CFV only up to the highest venturi pressure ratio, r, measured during calibration using the following equation:

Where:

ΔpCFV = differential static pressure; venturi inlet minus venturi outlet.

pin = mean static absolute pressure at the venturi inlet.

(iv) If the standard deviation of all the Kv values exceeds 0.3% of the mean Kv, omit the Kv value corresponding to the data point collected at the highest r measured during calibration.

(v) If the number of remaining data points is less than seven, take corrective action by checking your calibration data or repeating the calibration process. If you repeat the calibration process, we recommend checking for leaks, applying tighter tolerances to measurements and allowing more time for flows to stabilize.

(vi) If the number of remaining Kv values is seven or greater, recalculate the mean and standard deviation of the remaining Kv values.

(vii) If the standard deviation of the remaining Kv values is less than or equal to 0.3% of the mean of the remaining Kv, use that mean Kv in Eq 1066.630-7, and use the CFV values only up to the highest r associated with the remaining Kv.

(viii) If the standard deviation of the remaining Kv still exceeds 0.3% of the mean of the remaining Kv values, repeat the steps in paragraph (c)(1)(iv) through (vii) of this section.

(2) During exhaust emission tests, monitor sonic flow in the CFV by monitoring r. Based on the calibration data selected to meet the standard deviation criterion in paragraphs (c)(1)(iv) and (vii) of this section, in which Kv is constant, select the data values associated with the calibration point with the lowest absolute venturi inlet pressure to determine the r limit. Calculate r during the exhaust emission test using Eq. 1066.625-8 to demonstrate that the value of r during all emission tests is less than or equal to the r limit derived from the CFV calibration data.

[79 FR 23823, Apr. 28, 2016, as amended at 81 FR 74208, Oct. 25, 2016]

This section describes the equations for calculating flow rates from various flow meters. After you calibrate a flow meter according to §1066.625, use the calculations described in this section to calculate flow during an emission test. Calculate flow according to 40 CFR 1065.642 instead if you calculate emissions based on molar flow rates.

(a) PDP. (1) Based on the speed at which you operate the PDP for a test interval, select the corresponding slope, a1, and intercept, a0, as determined in §1066.625(a), to calculate PDP flow rate, v̇, as follows:

Where:

fnPDP = pump speed.

Vrev = PDP volume pumped per revolution, as determined in paragraph (a)(2) of this section.

Tstd = standard temperature = 293.15 K.

pin = static absolute pressure at the PDP inlet.

Tin = absolute temperature at the PDP inlet.

pstd = standard pressure = 101.325 kPa.

(2) Calculate Vrev using the following equation:

pout = static absolute pressure at the PDP outlet.

Example:

a1 = 0.8405 m3/s

fnPDP = 12.58 r/s

pout = 99.950 kPa

pin = 98.575 kPa

a0 = 0.056 m3/r

Tin = 323.5 K

Vrev = 0.063 m3/r

v̇= 0.7079 m3/s

(b) SSV. Calculate SSV flow rate, v̇, as follows:

Where:

Cd = discharge coefficient, as determined based on the Cd versus Re# equation in §1066.625(b)(2)(viii).

Cf = flow coefficient, as determined in §1066.625(b)(2)(ii).

At = venturi throat cross-sectional area.

R = molar gas constant.

pin = static absolute pressure at the venturi inlet.

Tstd = standard temperature.

pstd = standard pressure.

Z = compressibility factor.

Mmix = molar mass of gas mixture.

Tin = absolute temperature at the venturi inlet.

Example:

Cd = 0.890

Cf = 0.472

At = 0.01824 m2

R = 8.314472 J/(mol·K) = 8.314472 (m2·kg)/(s2·mol·K)

pin = 98.496 kPa

Tstd = 293.15 K

pstd = 101.325 kPa

Z = 1

Mmix = 28.7789 g/mol = 0.0287789 kg/mol

Tin = 296.85 K

V̇ = 2.155 m3/s

(c) CFV. If you use multiple venturis and you calibrated each venturi independently to determine a separate calibration coefficient, Kv, for each venturi, calculate the individual volume flow rates through each venturi and sum all their flow rates to determine CFV flow rate, V̇. If you use multiple venturis and you calibrated venturis in combination, calculate V̇ using the Kv that was determined for that combination of venturis.

(1) To calculate V̇ through one venturi or a combination of venturis, use the mean Kv you determined in §1066.625(c) and calculate V̇ as follows:

Where:

Kv = flow meter calibration coefficient.

Tin = temperature at the venturi inlet.

pin = absolute static pressure at the venturi inlet.

Example:

Kv = 0.074954 m3·K0.5/(kPa·s)

pin = 99.654 kPa

Tin = 353.15 K

V̇= 0.39748 m3/s

(2) [Reserved]

[81 FR 74211, Oct. 25, 2016]

For vehicles subject to an NMOG standard, determine NMOG as described in paragraph (a) of this section. Except as specified in the standard-setting part, you may alternatively calculate NMOG results based on measured NMHC emissions as described in paragraphs (c) through (f) of this section.

(a) Determine NMOG by independently measuring alcohols and carbonyls as described in 40 CFR 1065.805 and 1065.845. Use good engineering judgment to determine which alcohols and carbonyls you need to measure. This would typically require you to measure all alcohols and carbonyls that you expect to contribute 1% or more of total NMOG. Calculate the mass of NMOG in the exhaust, mNMOG, with the following equation, using density values specified in §1066.1005(f):

Where:

mNMHC = the mass of NMHC and all oxygenated hydrocarbon (OHC) in the exhaust, as determined using Eq. 1066.605-2. Calculate NMHC mass based on ρNMHC.

ρNMHC = the effective C1-equivalent density of NMHC as specified in §1066.1005(f).

mOHCi = the mass of oxygenated species i in the exhaust calculated using Eq. 1066.605-2.

ρOCHi = the C1-equivalent density of oxygenated species i.

RFOHCi[THC-FID] = the response factor of a THC-FID to oxygenated species i relative to propane on a C1-equivalent basis as determined in 40 CFR 1065.845.

(b) The following example shows how to determine NMOG as described in paragraph (a) of this section for (OHC) compounds including ethanol (C2H5OH), methanol (CH3OH), acetaldehyde (C2H4O), and formaldehyde (CH2O) as C1-equivalent concentrations:

mNMHC = 0.0125 g

mCH3OH = 0.0002 g

mC2H5OH = 0.0009 g

mCH2O = 0.0001 g

mC2H4O = 0.00005 g

RFCH3OH[THC-FID] = 0.63

RFC2H5OH[THC-FID] = 0.75

RFCH2O[THC-FID] = 0.00

RFC2H4O[THC-FID] = 0.50

ρNMHC-liq = 576.816 g/m3

ρCH3OH = 1332.02 g/m3

ρC2H5OH = 957.559 g/m3

ρCH2O = 1248.21 g/m3

ρC2H4O = 915.658 g/m3

(c) For gasoline containing less than 25% ethanol by volume, you may calculate NMOG from measured NMHC emissions as follows:

(1) For hot-start and hot-running test cycles or intervals other than the FTP, you may determine NMOG based on the NMHC emission rate using the following equation:

Where:

eNMOGh = mass emission rate of NMOG from the hot-running test cycle.

eNMHCh = mass emission rate of NMHC from the hot-running test cycle, calculated using ρNMHC-liq.

Example:

eNMHCh = 0.025 g/mi

eNMOGh = 0.025 · 1.03 = 0.026 g/mi

(2) You may determine weighted composite NMOG for FTP testing based on the weighted composite NMHC emission rate and the volume percent of ethanol in the fuel using the following equation:

Where:

eNMOGcomp = weighted FTP composite mass emission rate of NMOG.

eNMHCcomp = weighted FTP composite mass emission rate of NMHC, calculated using ρNMHC-liq.

VPEtOH = volume percentage of ethanol in the test fuel. Use good engineering judgment to determine this value either as specified in 40 CFR 1065.710 or based on blending volumes, taking into account any denaturant.

Example:

eNMHCcomp = 0.025 g/mi

VPEtOH = 10.1%

eNMOGcomp = 0.025 · (1.0302 + 0.0071 · 10.1) = 0.0275 g/mi

(3) You may determine NMOG for the transient portion of the FTP cold-start test for use in fuel economy and CREE calculations based on the NMHC emission rate for the test interval and the volume percent of ethanol in the fuel using the following equation:

Where:

eNMOG-FTPct = mass emission rate of NMOG from the transient portion of the FTP cold-start test (generally known as bag 1).

eNMHC-FTPct = mass emission rate of NMHC from the transient portion of the FTP cold-start test (bag 1), calculated using ρNMHC-liq.

Example:

eNMHC-FTPct = 0.052 g/mi

VPEtOH = 10.1%

eNMOG-FTPct = 0.052 · (1.0246 + 0.0079 · 10.1) = 0.0574 g/mi

(4) You may determine NMOG for the stabilized portion of the FTP test for either the cold-start test or the hot-start test (bag 2 or bag 4) for use in fuel economy and CREE calculations based on the corresponding NMHC emission rate and the volume percent of ethanol in the fuel using the following equation:

Where:

eNMOG-FTPcs-hs = mass emission rate of NMOG from the stabilized portion of the FTP test (bag 2 or bag 4).

eNMHC-FTPcs-hs = mass emission rate of NMHC from the stabilized portion of the FTP test (bag 2 or bag 4), calculated using ρNMHC-liq.

(5) You may determine NMOG for the transient portion of the FTP hot-start test for use in fuel economy and CREE calculations based on the NMHC emission rate for the test interval and the volume percent of ethanol in the fuel using the following equation:

Where:

eNMOG-FTPht = mass emission rate of NMOG from the transient portion of the FTP hot-start test (bag 3).

eNMHC-FTPht = mass emission rate of NMHC from the transient portion of the FTP hot-start test (bag 3), calculated using ρNMHC-liq.

(6) For PHEVs, you may determine NMOG based on testing over one full UDDS using Eq. 1066.635-3.

(d) You may take the following alternative steps when determining fuel economy and CREE under 40 CFR part 600 for testing with ethanol-gasoline blends that have up to 25% ethanol by volume:

(1) Calculate NMOG by test interval using Eq. 1066.635-3 for individual bag measurements from the FTP.

(2) For HEVs, calculate NMOG for two-bag FTPs using Eq. 1066.635-3 as described in 40 CFR 600.114.

(e) We consider NMOG values for diesel-fueled vehicles, CNG-fueled vehicles, LNG-fueled vehicles, and LPG-fueled vehicles to be equivalent to NMHC emission values for all test cycles.

(f) For all fuels not covered by paragraphs (c) and (e) of this section, manufacturers may propose a methodology to calculate NMOG results from measured NMHC emissions. We will approve adjustments based on comparative testing that demonstrates how to properly represent NMOG based on measured NMHC emissions.

[79 FR 23823, Apr. 28, 2014, as amended at 80 FR 9122, Feb. 19, 2015; 81 FR 74212, Oct. 25, 2016]

Record information for each test as follows:

(a) Test number.

(b) A brief description of the test vehicle (or other system/device tested).

(c) Date and time of day for each part of the test sequence.

(d) Test results. Also include a validation of driver accuracy as described in §1066.425(j).

(e) Driver and equipment operators.

(f) Vehicle information as applicable, including identification number, model year, applicable emission standards (including bin standards or family emission limits, as applicable), vehicle model, vehicle class, test group, durability group, engine family, evaporative/refueling emission family, basic engine description (including displacement, number of cylinders, turbocharger/supercharger used, and catalyst type), fuel system (type of fuel injection and fuel tank capacity and location), engine code, GVWR, applicable test weight, inertia weight class, actual curb weight at zero miles, actual road load at 50 mi/hr, transmission class and configuration, axle ratio, odometer reading, idle rpm, and measured drive wheel tire pressure.

(g) Dynamometer identification, inertia weight setting, indicated power absorption setting, and records to verify compliance with the driving distance and cycle-validation criteria as calculated from measured roll or shaft revolutions.

(h) Analyzer bench identification, analyzer ranges, recordings of analyzer output during zero, span, and sample readings.

(i) Associate the following information with the test record: test number, date, vehicle identification, vehicle and equipment operators, and identification of the measurements recorded.

(j) Test cell barometric pressure and humidity. You may use a central laboratory barometer if the barometric pressure in each test cell is shown to be within ±0.1% of the barometric pressure at the central barometer location.

(k) Records to verify compliance with the ambient temperature requirements throughout the test procedure and records of fuel temperatures during the running loss test.

(l) [Reserved]

(m) For CVS systems, record dilution factor for each test interval and the following additional information:

(1) For CFV and SSV testing, Vmix for each interval of the exhaust test.

(2) For PDP testing, test measurements required to calculate Vmix for each test interval.

(n) The humidity of the dilution air, if you remove H2O from an emission sample before measurement.

(o) Temperature of the dilute exhaust mixture and secondary dilution air (in the case of a double-dilution system) at the inlet to the respective gas meter or flow instrumentation used for PM sampling. Determine minimum values, maximum values, mean values, and percent of time outside of the tolerance over each test interval.

(p) The maximum exhaust gas temperature over the course of the test interval within 20 cm upstream or downstream of PM sample media.

(q) If applicable, the temperatures of the heated FID, the gas in the heated sample line, and the heated filter. Determine minimum values, maximum values, average values, and percent of time outside of the tolerance over each test interval.

(r) Gas meter or flow measurement instrumentation readings used for batch sampling over each test interval. Determine minimum, maximum, and average values over each test interval.

(s) The stabilized pre-test weight and post-test weight of each particulate sample media (e.g., filter).

(t) Continuous temperature and humidity of the ambient air in which the PM sample media are stabilized. Determine minimum values, maximum values, average values, and percent of time outside of the tolerance over each test interval.

(u) For vehicles fueled by natural gas, the test fuel composition, including all carbon-containing compounds (including CO2, but excluding CO). Record C1 and C2 compounds individually. You may record C3 through C5 hydrocarbons together, and you may record C6 and heavier hydrocarbon compounds together.

(v) For vehicles fueled by liquefied petroleum gas, the test fuel composition, including all carbon-containing compounds (including CO2, but excluding CO). Record C1 through C4 compounds individually. You may record C5 and heavier hydrocarbons together.

(w) For the AC17 test in §1066.845, interior volume, climate control system type and characteristics, refrigerant used, compressor type, and evaporator/condenser characteristics.

(x) Additional information related to evaporative emissions. [Reserved]

(y) Additional information related to refueling emissions. [Reserved]

[[79 FR 23823, Apr. 28, 2016, as amended at 81 FR 74213, Oct. 25, 2016]