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(continued)
(1) First transform normalized speed values into reference speed values. For a given speed point, multiply the corresponding % power by the maximum test power defined in the standard-setting part. The result is the reference power for each speed point. You may calculate a corresponding reference torque for each point and command that reference torque instead of a reference power.
(2) If your engine does not operate below a certain power under normal in-use conditions, you may use a declared minimum power as the reference value instead of any value denormalized to be less than the declared value. For example, if your engine is directly connected to a propeller, it may have a minimum power called idle power. In this case, at idle conditions (i.e., 0% speed, 0% power), you may use a corresponding idle power as a reference power instead of 0 kW.
§ 1065.630 1980 international gravity formula.
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The acceleration of Earth's gravity, ag, varies depending on your location. Calculate ag at your latitude, as follows:
Where:
T = Degrees north or south latitude.
Example:
T = 45°
ag = 9.7803267715 · (1+
5.2790414 · 10-3 · sin 2 (45) +
2.32718 · 10-5 ·sin 4 (45) +
1.262 · 10-7 ·sin 6 (45) +
7 · 10-10 ·sin 8 (45)
ag = 9.8178291229 m/s 2
§ 1065.640 Flow meter calibration calculations.
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This section describes the calculations for calibrating various flow meters. After you calibrate a flow meter using these calculations, use the calculations described in §1065.642 to calculate flow during an emission test. Paragraph (a) of this section first describes how to convert reference flow meter outputs for use in the calibration equations, which are presented on a molar basis. The remaining paragraphs describe the calibration calculations that are specific to certain types of flow meters.
(a) Reference meter conversions. The calibration equations in this section use molar flow rate, n ref, as a reference quantity. If your reference meter outputs a flow rate in a different quantity, such as standard volume rate, V stdref, actual volume rate, V actref, or mass rate, m ref, convert your reference meter output to a molar flow rate using the following equations, noting that while values for volume rate, mass rate, pressure, temperature, and molar mass may change during an emission test, you should ensure that they are as constant as practical for each individual set point during a flow meter calibration:
Where:
n ref = reference molar flow rate.
V stdref = reference volume flow rate, corrected to a standard pressure and a standard temperature.
V actref = reference volume flow rate at the actual pressure and temperature of the flow rate.
m ref = reference mass flow.
Pstd = standard pressure.
Pact = actual pressure of the flow rate.
Tstd = standard temperature.
Tact = actual temperature of the flow rate.
R = molar gas constant.
Mmix = molar mass of the flow rate.
Example 1:
V stdref = 1000.00 ft 3 /min = 0.471948 m/s
P = 29.9213 in Hg @ 32 °F = 101325 Pa
T = 68.0 °F = 293.15 K
R = 8.314472 J/(mol·K)
n ref = 19.169 mol/s
Example 2:
m ref = 17.2683 kg/min = 287.805 g/s
Mmix = 28.7805 g/mol
n ref =10.0000 mol/s
(b) PDP calibration calculations. For each restrictor position, calculate the following values from the mean values determined in §1065.340, as follows:
(1) PDP volume pumped per revolution, Vrev (m 3 /rev):
Example:
n ref = 25.096 mol/s
R = 8.314472 J/(mo·lK)
T in = 299.5 K
P in = 98290 Pa
f nPDP = 1205.1 rev/min = 20.085 rev/s
Vrev = 0.03166 m 3 /rev
(2) PDP slip correction factor, Ks (s/rev):
Example:
f nPDP = 1205.1 rev/min = 20.085 rev/s
P out = 100.103 kPa
P in= 98.290 kPa
Ks = 0.006700 s/rev
(3) Perform a least-squares regression of PDP volume pumped per revolution, Vrev, versus PDP slip correction factor, Ks, by calculating slope, a1, and intercept, a0, as described in §1065.602.
(4) Repeat the procedure in paragraphs (b)(1) through (3) of this section for every speed that you run your PDP.
(5) The following example illustrates these calculations:
Table 1 of § 1065.640_Example of PDP Calibration Data
------------------------------------------------------------------------
f8nPDP a1 a0
------------------------------------------------------------------------
755.0............................................. 50.43 0.056
987.6............................................. 49.86 -0.013
1254.5............................................ 48.54 0.028
1401.3............................................ 47.30 -0.061
------------------------------------------------------------------------
(6) For each speed at which you operate the PDP, use the corresponding slope, a1, and intercept, a0, to calculate flow rate during emission testing as described in §1065.642.
(c) Venturi governing equations and permissible assumptions. 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., rSSV versus rCFV). These governing equations assume one-dimensional isentropic inviscid compressible flow of an ideal gas. In paragraph (c)(4) of this section, we describe other assumptions that you may make, depending upon how you conduct your emission tests. If we do not allow you to assume that the measured flow is an ideal gas, the governing equations include a first-order correction for the behavior of a real gas; namely, the compressibility factor, Z. If good engineering judgment dictates using a value other than Z=1, you may either use an appropriate equation of state to determine values of Z as a function of measured pressures and temperatures, 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, ?, 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 ? as a function of measured pressures and temperatures, or you may develop your own calibration equations based on good engineering judgment. Calculate molar flow rate, n , as follows:
Where:
Cd = Discharge coefficient, as determined in paragraph (c)(1) of this section.
Cf = Flow coefficient, as determined in paragraph (c)(2) of this section.
At = Venturi throat cross-sectional area.
pin = Venturi inlet absolute static pressure.
Z = Compressibility factor.
Mmix = Molar mass of gas mixture.
R = Molar gas constant.
Tin = Venturi inlet absolute temperature.
(1) Using the data collected in §1065.340, calculate Cd using the following equation:
Where:
n ref = A reference molar flow rate.
(2) Determine Cf using one of the following methods:
(i) For CFV flow meters only, determine CfCFV from the following table based on your values for ß and ?, using linear interpolation to find intermediate values:
Table 2 of § 1065.640_CfCFV versus ß and ? for CFV Flow
Meters
------------------------------------------------------------------------
CfCFV
-------------------------------------------------------------------------
?dexh
?exh =
ß = 1.385 ?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, you may use the following equation to calculate Cf:
Where:
? = 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 section.
ß = Ratio of venturi throat to inlet diameters.
(3) Calculate r as follows:
(i) For SSV systems only, calculate rSSV using the following equation:
Where:
?pSSV = Differential static pressure; venturi inlet minus venturi throat.
(ii) For CFV systems only, calculate rCFV iteratively using the following equation:
(4) You may make any of the following simplifying assumptions of the governing equations, or you may use good engineering judgment to develop more appropriate values for your testing:
(i) For emission testing over the full ranges of raw exhaust, diluted exhaust and dilution air, you may assume that the gas mixture behaves as an ideal gas: Z=1.
(ii) For the full range of raw exhaust you may assume a constant ratio of specific heats of ? =1.385.
(iii) For the full range of diluted exhaust and air (e.g., calibration air or dilution air), you may assume a constant ratio of specific heats of ? = 1.399.
(iv) For the full range of diluted exhaust and air, you may assume the molar mass of the mixture is a function only of the amount of water in the dilution air or calibration air, xH2O, determined as described in §1065.645, as follows:
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
(v) For the full range of diluted exhaust and air, you may assume a constant molar mass of the mixture, Mmix, for all calibration and all testing as long as your assumed molar mass differs no more than ±1% from the estimated minimum and maximum molar mass during calibration and testing. You may assume this, using good engineering judgment, if you sufficiently control the amount of water in calibration air and in dilution air or if you remove sufficient water from both calibration air and dilution air. The following table gives examples of permissible ranges of dilution air dewpoint versus calibration air dewpoint:
Table 3 of § 1065.640_Examples of Dilution Air and Calibration Air
Dewpoints at Which you May Assume a Constant Mmix.
------------------------------------------------------------------------
assume the for the following
following ranges of Tdew
If calibration Tdew (°C) is... constant Mmix (°C) during
(g/mol)... emission tests \a\
------------------------------------------------------------------------
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.
------------------------------------------------------------------------
\a\ Range valid for all calibration and emission testing over the
atmospheric pressure range (80.000 to 103.325) kPa.
(5) The following example illustrates the use of the governing equations to calculate the discharge coefficient, Cd of an SSV flow meter at one reference flow meter value. Note that calculating Cd for a CFV flow meter would be similar, except that Cf would be determined from Table 1 of this section or calculated iteratively using values of ß and ? as described in paragraph (c)(2) of this section.
Example:
n ref = 57.625 mol/s
Z = 1
Mmix = 28.7805 g/mol = 0.0287805 kg/mol
R = 8.314472 J/(mol·K)
Tin = 298.15 K
At = 0.01824 m 2
pin = 99132.0 Pa
? = 1.399
ß = 0.8
?p = 2.312 kPa
Cf = 0.274
Cd = 0.981
(d) SSV calibration. Perform the following steps to calibrate an SSV flow meter:
(1) Calculate the Reynolds number, Re#, for each reference molar flow rate, using the throat diameter of the venturi, dt. 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:
µ = Dynamic viscosity of calibration gas.
µ0 = Sutherland reference viscosity.
T0 = Sutherland reference temperature.
S = Sutherland constant.
Table 3 of § 1065.640_Sutherland Three-Coefficient Viscosity Model Parameters
--------------------------------------------------------------------------------------------------------------------------------------------------------
µ0 kg/(m · Temp range within
Gas \a\ s) T0 K S K ±2% error K Pressure limit kPa
--------------------------------------------------------------------------------------------------------------------------------------------------------
Air........................................................ 1.716 · 10-5 273 111 170 to 1900 [le] 1800
CO2........................................................ 1.370 · 10-5 273 222 190 to 1700 [le] 3600
H2O........................................................ 1.12 · 10-5 350 1064 360 to 1500 [le] 10000
O2......................................................... 1.919 · 10-5 273 139 190 to 2000 [le] 2500
N2......................................................... 1.663 · 10-5 273 107 100 to 1500 [le] 1600
--------------------------------------------------------------------------------------------------------------------------------------------------------
\a\ Use tabulated parameters only for the pure gases, as listed. Do not combine parameters in calculations to calculate viscosities of gas mixtures.
Example:
µ0 = 1.7894 · 10-5 kg/(m·s)
T0 = 273.11 K
S = 110.56 K
µ = 1.916 · 10-5 kg/(m·s)
Mmix = 28.7805 g/mol
n ref = 57.625 mol/s
dt = 152.4 mm
Tin = 298.15 K
Re# = 7.2317 · 10 5
(2) Create an equation for Cd versus Re#, using paired values of (Re#, Cd). For the equation, you may use 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#:
(3) Perform a least-squares regression analysis to determine the best-fit coefficients to the equation and calculate the equation's regression statistics, SEE and r 2 , according to §1065.602.
(4) If the equation meets the criteria of SEE = 0.5% · n refmax and r 2 = 0.995, you may use the equation to determine Cd for emission tests, as described in §1065.642.
(5) If the SEE and r 2 criteria are not met, you may use good engineering judgment to omit calibration data points to meet the regression statistics. You must use at least seven calibration data points to meet the criteria.
(6) If omitting points does not resolve outliers, take corrective action. 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 process, we recommend applying tighter tolerances to measurements and allowing more time for flows to stabilize.
(7) Once you have an equation that meets the regression criteria, you may use the equation only to determine flow rates that are within the range of the reference flow rates used to meet the Cd versus Re# equation's regression criteria.
(e) 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 discharge coefficient, Cd, for each venturi, or calibrate each combination of venturis as one venturi. In the case where you calibrate a combination of venturis, use the sum of the active venturi throat areas as At, the sum of the active venturi throat diameters as dt, and the ratio of venturi throat to inlet diameters as the ratio of the sum of the active venturi throat diameters to the diameter of the common entrance to all of the venturis. To determine the Cd for a single venturi or a single combination of venturis, perform the following steps:
(1) Use the data collected at each calibration set point to calculate an individual Cd for each point using Eq. 1065.640–4.
(2) Calculate the mean and standard deviation of all the Cd values according to Eqs. 1065.602–1 and 1065.602–2.
(3) If the standard deviation of all the Cd values is less than or equal to 0.3% of the mean Cd, then use the mean Cd in Eq 1065.642–6, and use the CFV only down to the lowest ?pCFV measured during calibration.
(4) If the standard deviation of all the Cd values exceeds 0.3% of the mean Cd, omit the Cd values corresponding to the data point collected at the lowest ?pCFV measured during calibration.
(5) 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.
(6) If the number of remaining Cd values is seven or greater, recalculate the mean and standard deviation of the remaining Cd values.
(7) If the standard deviation of the remaining Cd values is less than or equal to 0.3 % of the mean of the remaining Cd, use that mean Cd in Eq 1065.642–6, and use the CFV values only down to the lowest ?pCFV associated with the remaining Cd.
(8) If the standard deviation of the remaining Cd still exceeds 0.3% of the mean of the remaining Cd values, repeat the steps in paragraph (e) (4) through (8) of this section.
§ 1065.642 SSV, CFV, and PDP molar flow rate calculations.
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This section describes the equations for calculating molar flow rates from various flow meters. After you calibrate a flow meter according to §1065.640, use the calculations described in this section to calculate flow during an emission test.
(a) PDP molar flow rate. Based upon the speed at which you operate the PDP for a test interval, select the corresponding slope, a1, and intercept, a0, as calculated in §1065.640, to calculate molar flow rate, n , as follows:
Where:
Example:
a1 = 50.43
f nPDP = 755.0 rev/min = 12.58 rev/s
pout = 99950 Pa
pin = 98575 Pa
a0 = 0.056
R = 8.314472 J/(mol·K)
Tin = 323.5 K
Cp = 1000 (J/m 3 )/kPa
Ct = 60 s/min
Vrev = 0.06389 m 3 /rev
n = 29.464 mol/s
(b) SSV molar flow rate. Based on the Cd versus Re# equation you determined according to §1065.640, calculate SSV molar flow rate, n during an emission test as follows:
Example:
At = 0.01824 m 2
pin = 99132 Pa
Z = 1
Mmix = 28.7805 g/mol = 0.0287805 kg/mol
R = 8.314472 J/(mol·K)
Tin = 298.15 K
Re# = 7.232·10 5
? = 1.399
ß = 0.8
?p = 2.312 kPa
Using Eq. 1065.640–6,
rssv = 0.997
Using Eq. 1065.640–5,
Cf = 0.274
Using Eq. 1065.640–4,
Cd = 0.990
n = 58.173 mol/s
(c) CFV molar flow rate. 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. If you use multiple venturis and you calibrated each venturi independently to determine a separate discharge coefficient, Cd, for each venturi, calculate the individual molar flow rates through each venturi and sum all their flow rates to determine n . If you use multiple venturis and you calibrated each combination of venturis, calculate n using the sum of the active venturi throat areas as At, the sum of the active venturi throat diameters as dt, and the ratio of venturi throat to inlet diameters as the ratio of the sum of the active venturi throat diameters to the diameter of the common entrance to all of the venturis. To calculate the molar flow rate through one venturi or one combination of venturis, use its respective mean Cd and other constants you determined according to §1065.640 and calculate its molar flow rate n during an emission test, as follows:
Example:
Cd = 0.985
Cf = 0.7219
At = 0.00456 m 2
pin = 98836 Pa
Z = 1
Mmix = 28.7805 g/mol = 0.0287805 kg/mol
R = 8.314472 J/(mol·K)
Tin = 378.15 K
n = 0.985·0.712
n = 33.690 mol/s
§ 1065.645 Amount of water in an ideal gas.
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This section describes how to determine the amount of water in an ideal gas, which you need for various performance verifications and emission calculations. Use the equation for the vapor pressure of water in paragraph (a) of this section or another appropriate equation and, depending on whether you measure dewpoint or relative humidity, perform one of the calculations in paragraph (b) or (c) of this section.
(a) Vapor pressure of water. Calculate the vapor pressure of water for a given saturation temperature condition, Tsat, as follows, or use good engineering judgment to use a different relationship of the vapor pressure of water to a given saturation temperature condition:
(1) For humidity measurements made at ambient temperatures from (0 to 100) °C, or for humidity measurements made over super-cooled water at ambient temperatures from (-50 to 0) °C, use the following equation:
Where:
pH20 = vapor pressure of water at saturation temperature condition, kPa.
Tsat = saturation temperature of water at measured conditions, K.
Example:
Tsat = 9.5 °C
Tdsat= 9.5 + 273.15 = 282.65 K
-log10(PH20) = -0.074297
pH20 = 10 0.074297 = 1.1866 kPa
(2) For humidity measurements over ice at ambient temperatures from (-100 to 0) °C, use the following equation:
Example:
Tice = -15.4 °C
Tice = -15.4 + 273.15 = 257.75 K
-log10(pH20) = -0.79821
PH20 = 10 0.074297 = 0.15941 kPa
(b) Dewpoint. If you measure humidity as a dewpoint, determine the amount of water in an ideal gas, xH20, as follows:
Where:
xH20 = amount of water in an ideal gas.
pH20 = water vapor pressure at the measured dewpoint, Tsat = Tdew.
pabs = wet static absolute pressure at the location of your dewpoint measurement.
Example:
Pabs = 99.980 kPa
Tsat = Tdew = 9.5 °C
Using Eq. 1065.645–2,
PH20 = 1.1866 kPa
xH2O = 1.1866/99.980
xH2O = 0.011868 mol/mol
(c) Relative humidity. If you measure humidity as a relative humidity, RH%, determine the amount of water in an ideal gas, xH20, as follows:
Where:
xH20 = amount of water in an ideal gas.
RH% = relative humidity.
PH20 = water vapor pressure at 100% relative humidity at the location of your relative humidity measurement, Tsat = Tamb.
Pabs = wet static absolute pressure at the location of your relative humidity measurement.
Example:
RH% = 50.77%
Pabs = 99.980 kPa
Tsat = Tamb = 20 °C
Using Eq. 1065.645–2,
PH20 = 2.3371 kPa
xH2O = (50.77% · 2.3371)/99.980
xH2O = 0.011868 mol/mol
§ 1065.650 Emission calculations.
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(a) General. Calculate brake-specific emissions over each test interval in a duty cycle. Refer to the standard-setting part for any calculations you might need to determine a composite result, such as a calculation that weights and sums the results of individual test intervals in a duty cycle. We specify three alternative ways to calculate brake-specific emissions, as follows:
(1) For any testing, you may calculate the total mass of emissions, as described in paragraph (b) of this section, and divide it by the total work generated over the test interval, as described in paragraph (c) of this section, using the following equation:
Example:
mNOX = 64.975 g
W = 25.783 kW·hr
eNOX = 64.975/25.783
eNOX = 2.520 g/(kW·hr)
(2) For discrete-mode steady-state testing, you may calculate the ratio of emission mass rate to power, as described in paragraph (d) of this section, using the following equation:
(3) For field testing, you may calculate the ratio of total mass to total work, where these individual values are determined as described in paragraph (e) of this section. You may also use this approach for laboratory testing, consistent with good engineering judgment. This is a special case in which you use a signal linearly proportional to raw exhaust molar flow rate to determine a value proportional to total emissions. You then use the same linearly proportional signal to determine total work using a chemical balance of fuel, intake air, and exhaust as described in §1065.655, plus information about your engine's brake-specific fuel consumption. Under this method, flow meters need not meet accuracy specifications, but they must meet the applicable linearity and repeatability specifications in subpart D or subpart J of this part. The result is a brake-specific emission value calculated as follows:
Example:
m = 805.5 ~ g
w = 52.102 ~ kW·hr
eCO = 805.5/52.102
eCO = 2.520 g/(kW·hr)
(b) Total mass of emissions. To calculate the total mass of an emission, multiply a concentration by its respective flow. For all systems, make preliminary calculations as described in paragraph (b)(1) of this section, then use the method in paragraphs (b)(2) through (4) of this section that is appropriate for your system. Calculate the total mass of emissions as follows:
(1) Concentration corrections. Perform the following sequence of preliminary calculations on recorded concentrations:
(i) Correct all concentrations measured on a “dry” basis to a “wet” basis, including dilution air background concentrations, as described in §1065.659.
(ii) Calculate all HC concentrations, including dilution air background concentrations, as described in §1065.660.
(iii) For emission testing with an oxygenated fuel, calculate any HC concentrations, including dilution air background concentrations, as described in §1065.665. See subpart I of this part for testing with oxygenated fuels.
(iv) Correct the total mass of NOX based on intake-air humidity as described in §1065.670.
(v) Calculate brake-specific emissions before and after correcting for drift, including dilution air background concentrations, according to §1065.672.
(2) Continuous sampling. For continuous sampling, you must frequently record a continuously updated concentration signal. You may measure this concentration from a changing flow rate or a constant flow rate (including discrete-mode steady-state testing), as follows:
(i) Varying flow rate. If you continuously sample from a changing exhaust flow rate, synchronously multiply it by the flow rate of the flow from which you extracted it. We consider the following to be examples of changing flows that require a continuous multiplication of concentration times molar 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. Account for dispersion and time alignment as described in §1065.201. This multiplication results in the flow rate of the emission itself. Integrate the emission flow rate over a test interval to determine the total emission. If the total emission is a molar quantity, convert this quantity to a mass by multiplying it by its molar mass, M. The result is the mass of the emission, m. Calculate m for continuous sampling with variable flow using the following equations:
Example:
MNMHC = 13.875389 g/mol
N = 1200
xNMHC1 = 84.5 µmol/mol = 84.5 · 10-6 mol/mol
xNMHC2 = 86.0 µmol/mol = 86.0 · 10-6 mol/mol
n exh1 = 2.876 mol/s
n exh2 = 2.224 mol/s
frecord = 1 Hz
Using Eq. 1065.650-5,
?t = 1/1 = 1 s
mNMHC = 13.875389 · (84.5 · 10-6 · 2.876 + 86.0 · 10-6 ·2.224 + ... + xNMHC1200 · n exh) · 1
mNMHC = 25.23 g
(ii) Constant flow rate. If you continuously sample from a constant exhaust flow rate, calculate the mean concentration recorded over the test interval and treat the mean as a batch sample, as described in paragraph (b)(3)(ii) of this section. We consider the following to be examples of constant exhaust flows: CVS diluted exhaust with a CVS flow meter that has either an upstream heat exchanger, electronic flow control, or both.
(3) Batch sampling. For batch sampling, the concentration is a single value from a proportionally extracted batch sample (such as a bag, filter, impinger, or cartridge). In this case, multiply the mean concentration of the batch sample by the total flow from which the sample was extracted. You may calculate total flow by integrating a changing flow rate or by determining the mean of a constant flow rate, as follows:
(i) Varying flow rate. If you collect a batch sample from a changing exhaust flow rate, extract a sample proportional to the changing exhaust flow rate. We consider the following to be examples of changing flows that require proportional sampling: 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. Integrate the flow rate over a test interval to determine the total flow from which you extracted the proportional sample. Multiply the mean concentration of the batch sample by the total flow from which the sample was extracted. If the total emission is a molar quantity, convert this quantity to a mass by multiplying it by its molar mass, M. The result is the mass of the emission, m. In the case of PM emissions, where the mean PM concentration is already in units of mass per mole of sample, M PM, simply multiply it by the total flow. The result is the total mass of PM, mPM. Calculate m for batch sampling with variable flow using the following equation:
Example:
MNOX = 46.0055 g/mol
N = 9000
x NOX = 85.6 µmol/mol = 85.6 · 10-6 mol/mol
n dexhl = 25.534 mol/s
n dexh2 = 26.950 mol/s
frecord = 5 Hz
Using Eq. 1065.650–5,
?t = 1/5 = 0.2
mNOX = 46.0055 · 85.6 · 10-6 · (25.534 + 26.950 + ... +n exh9000) · 0.2
mNOX = 4.201 g
(ii) Constant flow rate. If you batch sample from a constant exhaust flow rate, extract a sample at a constant flow rate. We consider the following to be examples of constant exhaust flows: CVS diluted exhaust with a CVS flow meter that has either an upstream heat exchanger, electronic flow control, or both. Determine the mean molar flow rate from which you extracted the constant flow rate sample. Multiply the mean concentration of the batch sample by the mean molar flow rate of the exhaust from which the sample was extracted, and multiply the result by the time of the test interval. If the total emission is a molar quantity, convert this quantity to a mass by multiplying it by its molar mass, M. The result is the mass of the emission, m. In the case of PM emissions, where the mean PM concentration is already in units of mass per mole of sample M PM, simply multiply it by the total flow, and the result is the total mass of PM, mPM, Calculate m for sampling with constant flow using the following equations:
and for PM or any other analysis of a batch sample that yields a mass per mole of sample,
Example:
M PM = 144.0 µg/mol = 144.0 · 10-6 g/mol
n dexh = 57.692 mol/s
?t = 1200 s
mPM = 144.0 · 10-6 · 57.692 · 1200
mPM = 9.9692 g
(4) Additional provisions for diluted exhaust sampling; continuous or batch. The following additional provisions apply for sampling emissions from diluted exhaust:
(i) For sampling with a constant dilution ratio (DR) of air flow versus exhaust flow (e.g., secondary dilution for PM sampling), calculate m using the following equation:
Example:
mPMdil = 6.853 g
DR = 5:1
mPM = 6.853 · (5 + 1)
mPM = 41.118 g
(ii) For continuous or batch sampling, you may measure background emissions in the dilution air. You may then subtract the measured background emissions, as described in §1065.667.
(c) Total work. To calculate total work, multiply the feedback engine speed by its respective feedback torque. Integrate the resulting value for power over a test interval. Calculate total work as follows:
Example:
N = 9000
fn1 = 1800.2 rev/min
fn2 = 1805.8 rev/min
T1 = 177.23 N·m
T2 = 175.00 N·m
Crev = 2 · p rad/rev
Ct1 = 60 s/min
Cp = 1000 (N·m)/kW
frecord = 5 Hz
Ct2 = 3600 s/hr
P1 = 33.41 kW
P2 = 33.09 kW
Using Eq. 1065.650–5,
?t = 1/5 = 0.2 s
W = 16.875 kW·hr
(d) Steady-state mass rate divided by power. To determine steady-state brake-specific emissions for a test interval as described in paragraph (a)(2) of this section, calculate the mean steady-state mass rate of the emission, m , and the mean steady-state power, P , as follows:
(1) To calculate, m , multiply its mean concentration, x , by its corresponding mean molar flow rate, n . If the result is a molar flow rate, convert this quantity to a mass rate by multiplying it by its molar mass, M. The result is the mean mass rate of the emission, m PM. In the case of PM emissions, where the mean PM concentration is already in units of mass per mole of sample, M PM, simply multiply it by the mean molar flow rate, n . The result is the mass rate of PM, m PM. Calculate m using the following equation:
(2) Calculate P using the following equation:
(3) Ratio of mass and work. Divide emission mass rate by power to calculate a brake-specific emission result as described in paragraph (a)(2) of this section.
(4) Example. The following example shows how to calculate mass of emissions using mean mass rate and mean power:
MCO = 28.0101 g/mol
x CO = 12.00 mmol/mol = 0.01200 mol/mol
n = 1.530 mol/s
f n = 3584.5 rev/min = 375.37 rad/s
T = 121.50 N·m
m = 28.0101·0.01200·1.530
m = 0.514 g/s
P = 121.5·375.37
P = 45607 W = 45.607 kW
eCO = 0.514/45.61
eCO = 0.0113 g/(kW·hr)
(e) Ratio of total mass of emissions to total work. To determine brake-specific emissions for a test interval as described in paragraph (a)(3) of this section, calculate a value proportional to the total mass of each emission. Divide each proportional value by a value that is similarly proportional to total work.
(1) Total mass. To determine a value proportional to the total mass of an emission, determine total mass as described in paragraph (b) of this section, except substitute for the molar flow rate, n , or the total flow, n, with a signal that is linearly proportional to molar flow rate, n , or linearly proportional to total flow, n , as follows:
(2) Total work. To calculate a value proportional to total work over a test interval, integrate a value that is proportional to power. Use information about the brake-specific fuel consumption of your engine, efuel, to convert a signal proportional to fuel flow rate to a signal proportional to power. To determine a signal proportional to fuel flow rate, divide a signal that is proportional to the mass rate of carbon products by the fraction of carbon in your fuel, wc. For your fuel, you may use a measured wc or you may use the default values in Table 1 of §1065.655. Calculate the mass rate of carbon from the amount of carbon and water in the exhaust, which you determine with a chemical balance of fuel, intake air, and exhaust as described in §1065.655. In the chemical balance, you must use concentrations from the flow that generated the signal proportional to molar flow rate, n , in paragraph (e)(1) of this section. Calculate a value proportional to total work as follows:
Where:
(3) Divide the value proportional to total mass by the value proportional to total work to determine brake-specific emissions, as described in paragraph (a)(3) of this section.
(4) The following example shows how to calculate mass of emissions using proportional values:
N = 3000
frecord = 5 Hz
efuel = 285 g/(kW·hr)
wfuel = 0.869 g/g
Mc = 12.0107 g/mol
n 1 = 3.922 ~mol/s = 14119.2 mol/hr
xCproddry1 = 91.634 mmol/mol = 0.091634 mol/mol
xH2O1 = 27.21 mmol/mol = 0.02721 mol/mol
Using 1065.650–5,
?t = 0.2 s
W = 5.09 ~ (kW·hr)
(f) Rounding. Round emission values only after all calculations are complete and the result is in g/(kW·hr) or units equivalent to the units of the standard, such as g/(hp·hr). See the definition of “Round” in §1065.1001.
§ 1065.655 Chemical balances of fuel, intake air, and exhaust.
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(a) General. Chemical balances of fuel, intake air, and exhaust may be used to calculate flows, the amount of water in their flows, and the wet concentration of constituents in their flows. With one flow rate of either fuel, intake air, or exhaust, you may use chemical balances to determine the flows of the other two. For example, you may use chemical balances along with either intake air or fuel flow to determine raw exhaust flow.
(b) Procedures that require chemical balances. We require chemical balances when you determine the following:
(1) A value proportional to total work, W , when you choose to determine brake-specific emissions as described in §1065.650(e).
(2) The amount of water in a raw or diluted exhaust flow, xH2O, when you do not measure the amount of water to correct for the amount of water removed by a sampling system. Correct for removed water according to §1065.659(c)(2).
(3) The flow-weighted mean fraction of dilution air in diluted exhaust x dil, when you do not measure dilution air flow to correct for background emissions as described in§1065.667(c). Note that if you use chemical balances for this purpose, you are assuming that your exhaust is stoichiometric, even if it is not.
(c) Chemical balance procedure. The calculations for a chemical balance involve a system of equations that require iteration. We recommend using a computer to solve this system of equations. You must guess the initial values of up to three quantities: the amount of water in the measured flow, xH2O, fraction of dilution air in diluted exhaust, xdil, and the amount of products on a C1 basis per dry mole of dry measured flow, xCproddry. For each emission concentration, x, and amount of water xH2O, you must determine their completely dry concentrations. xdry and xH2Odry. You must also use your fuel's atomic hydrogen-to-carbon ratio, a, and oxygen-to-carbon ratio, ß. For your fuel, you may measure a and ß or you may use the default values in Table 1 of §1065.650. Use the following steps to complete a chemical balance:
(1) Convert your measured concentrations such as, xCO2meas, xNOmeas, and xH2Oint, to dry concentrations by dividing them by one minus the amount of water present during their respective measurements; for example: xH2OxCO2, xH2OxNO, and xH2Oint. If the amount of water present during a “wet” measurement is the same as the unknown amount of water in the exhaust flow, xH2O, iteratively solve for that value in the system of equations. If you measure only total NOX and not NO and NO2 separately, use good engineering judgement to estimate a split in your total NOX concentration between NO and NO2 for the chemical balances. For example, if you measure emissions from a stoichiometric spark-ignition engine, you may assume all NOX is NO. For a compression-ignition engine, you may assume that your molar concentration of NOX, xNOX, is 75% NO and 25% NO2 For NO2 storage aftertreatment systems, you may assume xNOX is 25% NO and 75% NO2. Note that for calculating the mass of NOX emissions, you must use the molar mass of NO2 for the effective molar mass of all NOX species, regardless of the actual NO2 fraction of NOX.
(2) Enter the equations in paragraph (c)(4) of this section into a computer program to iteratively solve for xH2O and xCproddry. If you measure raw exhaust flow, set xdil equal to zero. If you measure diluted exhaust flow, iteratively solve for xdil. Use good engineering judgment to guess initial values for xH2O, xCproddry, and xdil. We recommend guessing an initial amount of water that is about twice the amount of water in your intake or dilution air. We recommend guessing an initial value of xCproddry as the sum of your measured CO2, CO, and THC values. If you measure diluted exhaust, we also recommend guessing an initial xdil between 0.75 and 0.95, such as 0.8. Iterate values in the system of equations until the most recently updated guesses are all within ±1% of their respective most recently calculated values.
(3) Use the following symbols and subscripts in the equations for this paragraph (c):
xH2O = Amount of water in measured flow.
xH2Odry = Amount of water per dry mole of measured flow.
xCproddry = Amount of carbon products on a C1 basis per dry mole of measured flow.
xdil = Fraction of dilution air in measured flow, assuming stoichiometric exhaust; or xdil = excess air for raw exhaust.
xprod/intdry = Amount of dry stoichiometric products per dry mole of intake air.
xO2proddry = Amount of oxygen products on an O2 basis per dry mole of measured flow.
x[emission]dry = Amount of emission per dry mole of measured flow.
x[emission]meas = Amount of emission in measured flow.
xH2O[emission]meas = Amount of water at emission-detection location. Measure or estimate these values according to §1065.145(d)(2).
xH2Oint = Amount of water in the intake air, based on a humidity measurement of intake air.
xH2Odil = Amount of water in dilution air, based on a humidity measurement of intake air.
xO2airdry = Amount of oxygen per dry mole of air. Use xO2airdry= 0.209445 mol/mol.
xCO2airdry = Amount of carbon dioxide per dry mole of air. Use xCO2airdry = 375 µmol/mol.
a = Atomic hydrogen-to-carbon ratio in fuel.
ß = Atomic oxygen-to-carbon ratio in fuel.
(4) Use the following equations to iteratively solve for xH2O and xCproddry:
(5) The following example is a solution for xH2O and xCproddry using the equations in paragraph (c)(4) of this section:
Table 1 of § 1065.655_Default values of atomic hydrogen-to-carbon ratio, a, atomic oxygen-to-carbon
ratio, ß and carbon mass fraction of fuel, WC, for various fuels
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Carbon mass
Fuel Atomic hydrogen and oxygen-to-carbon ratios concentration,
CHa Oß WCg/g
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Gasoline................................... CH1.85O0 0.866
#2 Diesel.................................. CH1.80O0 0.869
#1 Diesel.................................. CH1.93O0 0.861
Liquified Petroleum Gas.................... CH2.64O0 0.819
Natural gas................................ CH3.78O0.016 0.747
Ethanol.................................... CH3O0.5 0.521
Methanol................................... CH4O1 0.375
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(d) Calculated raw exhaust molar flow rate from measured intake air molar flow rate or fuel mass flow rate. You may calculate the raw exhaust molar flow rate from which you sampled emissions, n exh, based on the measured intake air molar flow rate, n int, or the measured fuel mass flow rate, m fuel, and the values calculated using the chemical balance in paragraph (c) of this section. Solve for the chemical balance in paragraph (c) of this section at the same frequency that you update and record n int or m fuel.
(1) Crankcase flow rate. You may calculate raw exhaust flow based on n int or m fuel only if at least one of the following is true about your crankcase emission flow rate:
(i) Your test engine has a production emission-control system with a closed crankcase that routes crankcase flow back to the intake air, downstream of your intake air flow meter.
(ii) During emission testing you route open crankcase flow to the exhaust according to §1065.130(g).
(iii) You measure open crankcase emissions and flow, and you add the masses of crankcase emissions to your brake-specific emission calculations.
(iv) Using emission data or an engineering analysis, you can show that neglecting the flow rate of open crankcase emissions does not adversely affect your ability to demonstrate compliance with the applicable standards.
(2) Intake air molar flow rate calculation. Based on n int, calculate n exh as follows:
Where:
n exh= raw exhaust molar flow rate from which you measured emissions.
n int =intake air molar flow rate including humidity in intake air.
Example:
n int= 3.780 mol/s
xH20int = 16.930 mmol/mol = 0.016930 mol/mol
xprod/intdry = 0.93382 mol/mol
xH20dry = 130.16 mmol/mol = 0.13016 mol/mol
xdil = 0.20278 mol/mol
n exh = 4.919 mol/s
(3) Fuel mass flow rate calculation. Based on m fuel, calculate n exh as follows:
Where:
n exh= raw exhaust molar flow rate from which you measured emissions.
m fuel= intake air molar flow rate including humidity in intake air.
Example:
m fuel= 6.023 g/s
wC = 0.869 g/g
MC = 12.0107 g/mol
xCproddry = 125.58 mmol/mol = 0.12558 mol/mol
xH20dry = 130.16 mmol/mol = 0.13016 mol/mol
xdil = 0.20278 mol/mol
n exh = 4.919 mol/s
§ 1065.659 Removed water correction.
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(a) If you remove water upstream of a concentration measurement, x, or upstream of a flow measurement, n, correct for the removed water. Perform this correction based on the amount of water at the concentration measurement, xH2O[emission]meas, and at the flow meter, xH2O, whose flow is used to determine the concentration's total mass over a test interval.
(b) Downstream of where you removed water, you may determine the amount of water remaining by any of the following:
(1) Measure the dewpoint and absolute pressure downstream of the water removal location and calculate the amount of water remaining as described in §1065.645.
(2) When saturated water vapor conditions exist at a given location, you may use the measured temperature at that location as the dewpoint for the downstream flow. If we ask, you must demonstrate how you know that saturated water vapor conditions exist. Use good engineering judgment to measure the temperature at the appropriate location to accurately reflect the dewpoint of the flow.
(3) You may also use a nominal value of absolute pressure based on an alarm setpoint, a pressure regulator setpoint, or good engineering judgment.
(c) For a corresponding concentration or flow measurement where you did not remove water, you may determine the amount of initial water by any of the following:
(1) Use any of the techniques described in paragraph (b) of this section.
(2) If the measurement comes from raw exhaust, you may determine the amount of water based on intake-air humidity, plus a chemical balance of fuel, intake air and exhaust as described in §1065.655.
(3) If the measurement comes from diluted exhaust, you may determine the amount of water based on intake-air humidity, dilution air humidity, and a chemical balance of fuel, intake air, and exhaust as described in §1065.655.
(d) Perform a removed water correction to the concentration measurement using the following equation:
Example:
xCOmeas = 29.0µmol/mol (continued)