Abstract:
A vehicle exhaust measurement system is provided includes that a conduit having a conduit inlet and a conduit outlet. A make-up air tube is connected to and is in fluid communication with the conduit inlet. The make-up air tube provides make-up air for mixing an exhaust gas. A mixed gas tube is connected to and is in fluid communication with the conduit outlet. The mixed gas tube conveys a mixture of make-up air and exhaust gas to analysis equipment. In the preferred embodiment, the exhaust gas tube extends through an outer wall of the conduit. A mixing plate is arranged in either the conduit or the mixed gas tube with the exhaust gas tube extending to a position adjacent to the mixing plate. The exhaust gas tube conveys the exhaust gas to the mixing plate to mix the exhaust gas and the make-up air at the mixing plate. A correction factor may be applied to the measurements taken by a differential pressure based fluid flow measurement device such as a smooth approach orifice (SAO) to provide an adjusted flow of measurement at the flow measurement device to correct for the pressure pulsations. The correction factor is calculated based upon the intensity of the pulsations of the differential pressure signal, which indicates the flow through the SAO. A correction factor is calculated to account for the changes in density in the diluted exhaust gas during the test as the dilution ratio changes.

Description:
[0001]     This application is a continuation-in-part of U.S. patent application Ser. No. 10/981,235, which is a divisional of U.S. patent application Ser. No. 10/310,524, filed on Dec. 5, 2002, issued as U.S. Pat. No. 6,973,818 on Dec. 13, 2005. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     This invention relates to an engine or vehicle exhaust measurement device, and more particularly, the invention relates to a compact direct vehicle exhaust flow measurement device (DVE), which may be easily packaged within a test cell while providing compensation for engine exhaust pulsations when needed.  
         [0003]     The determination of engine or vehicle exhaust emissions during a test cycle is necessary to verify compliance with emission standards. To quantify the products of combustion correctly either the exhaust flow has to be known or an alternative method has to be used. A common method is the CVS (Constant Volume Sampling) principle, which has been used for many years in the industry and is a widely used standard. A CVS system samples the total amount of exhaust gas expelled by the engine or vehicle and dilutes it with air. The total flow as a sum of exhaust gas and dilution air is kept virtually constant. A constant sample is taken at a point far enough downstream of the mixing zone where the mixture is homogenous. CVS systems are quite large and costly, especially when they are designed for large flow rates.  
         [0004]     The raw modal and partial flow sampling methods have proven to be adequate, but especially for transient test cycles they require a fast and accurate exhaust flow measurement system to control the proportionality of gaseous and particulate sampling. International standards like ISO 8178 or ISO 16183 specify exhaust gas flow measurement methods and accuracy requirements. The preferred type of system that may be employed to gather and test the exhaust is a direct vehicle exhaust flow measurement device (DVE). A DVE receives the entire volume of exhaust gases and measures the exhaust flow directly at the tailpipe. A wide variety of measurement principles has been applied, i.e. ultrasonic flow meters or differential pressure devices, like flow nozzles. An additional requirement for vehicle testing is a low pressure change at the exit of the tailpipe, which can only be achieved with a low flow restriction of the flow metering device.  
         [0005]     Internal combustion engines utilize poppet valves to release the spent exhaust gases from the combustion cylinder to the tailpipe. As the exhaust valves open and close pressure pulsations are created within the exhaust gas stream. Emissions standards have become more stringent, and therefore, measurement accuracy has become increasingly important. The pressure pulsations within the exhaust gases may introduce an error into the flow measurement and may result in an inaccuracy in the emissions test. Precautions have to be taken or an active correction has to be employed to minimize the impact of these pressure pulsations on the flow measurement.  
         [0006]     One embodiment of a DVE based on differential pressure devices is described in the prior art. This embodiment mixes the total amount of exhaust with make-up air and measures the mixed exhaust flow rate as well as the flow of make-up gas such as ambient air. The exhaust flow is calculated by subtracting the make-up air flow into the system measured by a subsonic venturi from the total flow of make-up air and exhaust gases through the system measured by a critical flow venturi. A correction factor might be generated by comparing the flow of make-up air through the subsonic venturi and the critical flow venturi during a calibration process in which the tailpipe is closed. However, an inaccuracy results with such a calibration procedure because of the nonlinear relationship between the differential pressure across the subsonic venturi and the flow rate through this device. Other inaccuracies are introduced by the presence of engine pulsations. Further, inaccuracies are caused in the temperature measurement from inhomogeneous mixing of make-up air and hot exhaust gases.  
         [0007]     The composition of the make-up air used to dilute the sample exhaust gas is constant. However, the amount the sample exhaust gas is diluted during a given test varies. As a result, the density of the diluted exhaust gas varies throughout the test, which introduces an error in the measurements.  
         [0008]     Typically, the emissions test takes place in a rather confined cell in which space is limited. As a result, the exhaust gas flow measurement system must be rather compact but without compromising the high level of accuracy needed to comply with the increasingly stringent emissions test standards. Therefore, what is needed is an exhaust flow measurement device with low flow restriction that may be packaged within a cell while providing an accurate flow measurement with reduced sensitivity to exhaust gas pressure pulsations.  
       SUMMARY OF THE INVENTION AND ADVANTAGES  
       [0009]     The present invention provides a vehicle exhaust measurement system that receives the entire volume of exhaust gases and mixes it with a make-up gas such as ambient air. The system includes a conduit having a conduit inlet and a conduit outlet. A make-up air tube and a flow meter are connected to and are in fluid communication with the conduit inlet. The make-up air tube provides make-up air for mixing with the exhaust gas from the vehicle or engine. In the preferred embodiment the make-up air flow meter measures a pressure differential across a head type flow meter indicative of make-up airflow. A mixed gas tube is connected to and is in fluid communication with the conduit outlet. The mixed gas tube conveys a mixture of make-up air and exhaust gas to a critical flow venturi. A blower is connected to the outlet of the critical flow venturi and provides sufficient suction to maintain critical flow throughout its operation. The exhaust gas tube, which conveys the total exhaust gas of the engine or vehicle to the U-shaped conduit, extends through an outer wall of the conduit. A mixing plate is arranged in either of the conduit or the mixed gas tube. The exhaust gas tube extends to a position near the mixing plate. The exhaust gas tube conveys the exhaust gas to the mixing plate, where the make-up air and exhaust gas are homogeneously mixed. A section of the exhaust gas tube that is inside the conduit may be perforated to reduce the suction on the exhaust gas tube.  
         [0010]     The flow of make-up air and exhaust through the system is determined minus the flow of make-up air into the system to determine the flow of the total volume of exhaust gases. The flow through the DVE is calibrated by comparing the flow rates at a smooth approach orifice and critical flow venturi. A calibration factor is determined based upon the comparison and is applied to a differential pressure transducer associated with the smooth approach orifice to obtain accurate measurements at the smooth approach orifice throughout the range of flow rates there through.  
         [0011]     A correction factor is also determined for the type of exhaust gas used in the particular test. This correction factor accounts for the difference in density of the diluted exhaust gas and make-up air during the test.  
         [0012]     The intensity and frequency of the exhaust gas pulsations is determined and a correction factor is calculated based upon the intensity of the exhaust gas pulsations. This correction factor may be applied to the measurements taken by the make-up air flow meter to provide an adjusted flow of measurement at the flow measurement device to correct for the pressure pulsations.  
         [0013]     Accordingly, the above invention provides an exhaust volume measurement device that may be packaged within a cell while maintaining a homogeneous mixture and provides an accurate measurement of the flow.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0014]     Other advantages of the present invention can be understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:  
         [0015]      FIG. 1  is a schematic view of the present invention vehicle exhaust measurement system;  
         [0016]      FIG. 2A  is a perspective view of one tubing arrangement for a test cell having exhaust gas collection tubing at the floor;  
         [0017]      FIG. 2B  is a perspective view of the vehicle exhaust measurement system for a test cell having exhaust gas collection tubing at the ceiling;  
         [0018]      FIG. 3  is a cross-sectional view of a flow measurement system incorporating a mixing plate;  
         [0019]      FIG. 4  is a perspective view of the conduit shown in  FIG. 3 ;  
         [0020]      FIG. 5  is a graph of corrections factors for pressure pulsations; and  
         [0021]      FIG. 6  is a flow diagram depicting a method of correcting the pressure measurements for exhaust gas pressure pulsations. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0022]     The exhaust flow measurement system  10  is shown schematically in  FIG. 1 . The system  10  is attached to a tailpipe  12  from an engine or vehicle that contains exhaust gases having the products of combustion. Example fuels combusted during a test procedure are gasoline, diesel, methane, propane, methanol, ethanol and mixtures thereof. Since the flow measurement system  10  must typically be packaged within the spatial constraints of an emissions test cell, the tubing in the system must be arranged in such a manner to fit within the test cell. Similarly, it is desirable to have the flow measurement devices and sensors packaged compactly relative to one another so that they and the associated controllers may be packaged as a unit within the test cell along with the tubing.  
         [0023]     The exhaust gases from the tailpipe  12  are mixed with a make-up gas such as ambient air. The flow of the exhaust (Q ex ) is determined by taking the total flow of the exhaust gases mixed with make-up air (Q tot ) and subtracting the flow of the make-up air (Q dil ). The calculation without correction is represented by equation 1 below. 
 
 Q   ex   =Q   tot   −Q   dil   (Equation 1) 
 
         [0024]     Referring to  FIGS. 1 and 3 , the flow measurement system  10  includes a conduit  22  having a conduit inlet  24  and a conduit outlet  26 . Preferably, the conduit is U-shaped, which enables the system to be packages more compactly. A make-up air tube  28  is connected to the conduit inlet  24 . The make-up air flows through a flow meter such as a smooth approach orifice (SAO)  31  to measure the flow of make-up air to determine Q dil . It is to be understood that various types of flow meters, such as other head type flow meters or ultrasonic flow meters, may be used to measure the flow of the make-up gas. In this application, “SAO” is used to denote a flowmeter generally, although some of the example equations may be specific to a subsonic venturi, which may have a smooth approach orifice, for example. In one example, an internal body flow meter can be used. In one example, an internal body flow meter (IBF) is a teardrop shaped member suspended in a cylindrical tube by multiple support members. An annular groove is provided in the cylindrical tube at an annulus. Multiple taps are arranged circumferentially about the annulus to provide an average pressure reading at the annulus.  
         [0025]     Returning now to  FIG. 1 , a temperature sensor  32  and an absolute pressure sensor  34  are arranged at the inlet of the SAO  31 . A pressure sensor  36  measures the differential pressure between the throat of the SAO  31  and the inlet. The sensors  32 ,  34 ,  36  are used to calculate the flow through the SAO  31 , as it is well known in the art.  
         [0026]     Prior art configurations may share pressure sensor connections and use unbalanced conduits, which introduces errors into the pressure pulsation intensity measurement on either side of the sensor. The error introduced in the prior art may be up to several percent of the measured flow. In the present invention the pressure sensor  34  is preferably connected to the tube  28  by conduit  27  independently from pressure sensor  36 . Furthermore, the conduits  33  and  35 , which connect pressure sensor  36 , are acoustically balanced. Providing separate connections for the sensors  34  and  36  and using acoustically balanced conduits ensures more accurate pressure pulsation intensity measurements. For best results, each of the differential pressure sensors must be acoustically balanced for the DVE at the initial setup of the system to account for the variations between the sensors.  
         [0027]     The procedure of acoustical balancing of the pressure transducers contains the following steps: The conduits  33  and  35 , which connect the differential pressure sensor  36  at one end, have to be connected at the other end to one point and pressure pulsations have to be introduced there. The length of either the conduit  33  or  35  has to be varied until the pressure sensor  36  is not able detect the pressure pulsations. Specifically, a tee is connected to the DVE where it will be subject to pressure pulsations. The pressure sensor is connected to either side of the tee with substantially equal lengths of conduits in an effort to obtain the same transport time and magnitude of the pressure pulsations on either side of the sensor. The lengths are adjusted to account for the variation in the sensor and the conduits, which typically results in conduits of substantially the same length assuming conduits of the same internal diameter. The sensor may then be reattached to the DVE in the normal manner for testing with the length-adjusted conduits. The acoustic balancing procedure must be repeated if the sensor is replaced.  
         [0028]     While the acoustic balancing is discussed in terms of adjusting length of the conduits, it is to be understood that any factor may be adjusted that contributes to the imbalance of pressure pulsations on either side of the sensor. In a broader sense, the volume of the conduits is adjusted to balance the sensor. In the case small diameter tubing, such as 1/16″ inner diameter, the sensor may be easily balanced by trimming the length of the tubing.  
         [0029]     An exhaust gas tube  37  conveys the exhaust gases from the tailpipe  12  to the conduit  22 . A mixed gas tube  38  is connected to the conduit outlet  26 . The exhaust gas and make-up air are mixed in the mixed gas tube  38 . A critical flow venturi (CFV)  40  regulates and measures the flow of the mixture of exhaust gas and make-up air. It is to be understood that various types of flow meters, such as other head type flow meters, may be used to measure the flow of the mixture of exhaust gas and make-up air. In this application, “CFV” is used to denote a flowmeter generally, although some of the example equations may be specific to a critical flow venturi.  
         [0030]     A fast response temperature sensor  42  and an absolute pressure sensor  44  are arranged at the inlet of the CFV. To obtain the desired flow meter accuracy, the reading of the temperature sensor is preferably within about ±6° C. (±12° F.) after about 0.3 s, while the repeatability of the sensor is preferably better than about ±0.3° C. (±0.6° F.). The fast response time of the temperature sensor is required for transient operation of the DVE. An absolute pressure sensor  46  may be arranged at the outlet of the CFV  40  to verify that the flow remains critical during the test.  
         [0031]     The sensors  42  and  44  are used to calculate the flow of diluted exhaust gas through the CFV  40 , as is well known in the art. The exhaust and make-up gases are preferably homogeneously mixed prior to entering the CFV and temperature measurement of the gases to ensure accurate results. Use of a mixing plate enables the gases to be mixed over a shorter length of tube so that a more compact system may be used. This, in turn, also enables the flow meters and sensors to be located more closely to one another. The measurement taken at the SAO  31  is subtracted from the measurement taken at the CFV  40  to determine the flow of exhaust gases entering the flow measurement system  10  from the exhaust gas tube  37 , as indicated by equation 1 above.  
         [0032]     A blower  48  maintains critical flow through the CFV  40  to ensure that the measurement at the CFV is accurate. A heated blanket  50  may be wrapped about the exposed portion of the exhaust gas tube  30  and the conduit  22  up to the CFV  40  to ensure that the gases within the flow measurement system  10  do not condense prior to reaching the CFV  40 . Condensation of the gases would introduce an error into the results calculated using the measurement taken by the CFV  40 .  
         [0033]      FIGS. 2A and 2B  depict tubing  53  that may carry the mixed exhaust gases to the blower. If the tubing is arranged at the floor of the test cell a tubing arrangement, as shown by reference number  53  in  FIG. 2A , may be used. If the tubing is at the ceiling of the test cell the tube  53 , as shown in  FIG. 2B , may be used.  
         [0034]     Referring to  FIGS. 3 and 4 , the conduit  22  includes an outer radius  55 . Conduit  22  includes an apex  56 , which may be defined by the midpoint of the curvature of the outer radius. The exhaust gas tube  37  extends through the outer wall of the conduit  22  to one side of the apex  56  and is curved in a manner similar to the curvature of the conduit  22 . A mixing plate  58  is disposed within the conduit  22  or the mixed gas tube  38 . Preferably, the mixing plate  58  is arranged after the curvature of the conduit  22 . The exhaust gas tube  37  includes a terminal end  60  that is arranged proximate to the mixing plate  58 . A section  57  of the exhaust gas tube  37  may be perforated once the tube  37  enters the conduit  22  to reduce the suction on the tailpipe. Mixing of the exhaust gas from the exhaust gas tube  37  and the make-up air from the conduit  22  substantially begins at the mixing plate  58 . Preferably, the length of the mixed gas tube  38  is sufficient to permit homogeneous mixing of the gases prior to measurement of the diluted gases at the CFV  40 . Homogeneous mixing is required to ensure proper operation of the CFV and accurate temperature measurement.  
         [0035]     The flow measurement system  10  must be calibrated to ensure accurate flow measurement through the flow devices. This calibration procedure is performed in two steps. At first the three-way valves  49  and  51  are switched to disconnect the conduits  33  and  35  of the pressure transducer  36  from the SAO  31 . The ends of the conduits are now open to atmosphere. After an appropriate stabilization time a new zero offset B is calculated for the differential pressure transducer  36 . After completing the first step the conduits  33  and  35  are reconnected to the SAO  31 , the valve  52  is closed and the blower  48  draws ambient air through the SAO  31  and CFV  40 . The flow measurements taken at the SAO  31  and CFV  40  should be in agreement with one another. A correction factor A is calculated using equation 2 below. The correction factor A is coincident with the ratio of the flow through the SAO  31  and the flow through the CFV  40  and has to be applied to the reading of the differential pressure sensor  36 .  
               Q   CFV     =       C   D     ·   Y   ·     π   4     ·     d   2     ·         2   ·   A   ·     (       Δ   ⁢           ⁢   p     +   B     )         ρ   ·     (     1   -     β   4       )                     (     Equation   ⁢           ⁢   2     )             
 
         [0036]     C D  discharge coefficient  
         [0037]     d throat diameter  
         [0038]     ρ gas density  
         [0039]     β=d THROAT /D INLET    
         [0040]     Y is the adiabatic expansion factor:  
             Y   =         τ     2   κ       ·     κ     κ   -   1       ·       1   -     τ       κ   -   1     κ           1   -   τ       ·       1   -     β   4           1   -       β   4     ·     τ     2   κ           ⁣                   (     Equation   ⁢           ⁢   3     )             
 
         [0041]     τ=p THROAT /p INLET    
         [0042]     κ=C p /C v    
         [0043]     C p , C v  are the specific heat capacities  
         [0044]     This calibration method differs from the calibration described in the prior art, where a correction factor is simply multiplied with the flow rate through the subsonic venturi. However, inaccuracy results with such a calibration procedure because of the nonlinear relationship between the differential pressure across the subsonic venturi and the flow rate through this device, the calibration method is only accurate for one specific flow rate. In contrast, the present invention calibration method ensures the accuracy of the calibrated SAO readings over the complete flow range of the device.  
         [0045]     The effects of the undesired exhaust gas pressure pulsations may be minimized by applying a correction factor to the flow measurement. With reference to  FIGS. 5 and 6 , this correction factor is calculated from the differential pressure measurement of the pressure transducer  36  and depends on the pulsation intensity of the pressure signal. The frequency f of the pulsations varies depending on engine parameters and operation and is measured with a signal processing circuit (see block  72 ). The signal processing circuit processes the pressure signal to generate a filtered signal ΔP μ  (see block  72 ) at a cutoff frequency of approximately half of the minimum frequency of the pressure pulsations. The magnitude of the pressure pulsations is determined by the signal processing circuit as ΔP σ  (see block  72 ). The pulsation intensity I p  (see block  74 ) is calculated as:  
               I   p     =         Δ   ⁢           ⁢     P   σ         Δ   ⁢           ⁢     P   μ         ·       c   *       (       c   *     +       10.64   ·     f   4     ·   Δ     ⁢           ⁢   x       )                 (     Equation   ⁢           ⁢   4     )                 with   ⁢           ⁢     c   *       =     c   -         Q   dil     /   π     ⁢           ⁢         d   th   2     4     .                 (     Equation   ⁢           ⁢   5     )             
 
 c speed of sound 
 
 Δx distance between the pressure transducer taps 
 
 Q dil  volumetric make-up air flow 
 
 d th  SAO throat diameter 
 
         [0046]     The constant 10.64 is a unit conversion constant. The combined correction factor is represented by F p (I p ) (see block  76 ) and is graphically depicted in  FIG. 5 .  
                 F   p     ⁡     (     I   p     )       =       1     2   ·   π       ·       ∫   0     2   ⁢   π       ⁢       (           I   p     ·     sin   ⁡     (   θ   )         +   1       )     ⁢           ⁢     ⅆ   θ                   (     Equation   ⁢           ⁢   6     )             
 
         [0047]     The calibrated and corrected exhaust gas flow may be represented by equation 7. The flow measurement correction provides increased accuracy of the tests results. 
 
 Q   ex   =Q   CFV   −F   p ( I   p (Δ P   μ   ,ΔP   σ   ,f ))· Q   dil   (Equation 7) 
 
 The correction factor is applied to the flow measurement system  10  as schematically depicted in  FIG. 6  (see block  78 ). 
 
         [0048]     Make-up air with a uniform composition flows through the flow meter  31  (e.g. SAO or IBF), but diluted exhaust flows through the flow meter  40  (e.g. CFV). The composition, and therefore the density, of diluted exhaust changes as the relative amount of exhaust in the mixture that passes through the CFV changes. This effect is illustrated in Equations 8-28. The error of the computed exhaust flow turns out to be small and nearly constant. As a result, it can be easily corrected.  
         [0049]     The flow through the CFV is given by:  
               Q   CFV     =           K   v     ·   P       T       .             (     Equation   ⁢           ⁢   8     )             
 
 The factor K v  is composed of several parameters, including the density, which corresponds to the molecular weight of the gas passing through the CVF. The parameters P and T are the pressure and temperature, respectively, at the CFV.  
             ρ   =         P   s     ·   M         T   s     ·   R               (     Equation   ⁢           ⁢   9     )             
 
         [0050]     P s =pressure at standard conditions  
         [0051]     T s =temperature at standard conditions  
               K   v     =         C   d     ·   Y   ·   π   ·       d   2     4     ·       T   s       P   s         ⁢         R       M       .               (     Equation   ⁢           ⁢   10     )             
 
         [0052]     Here, R is the universal gas constant and M is the molecular weight of the gas. Y is the adiabatic expansion factor. Since K v  is normally calculated for moist air, it can be converted to a value for diluted exhaust. Using familiar subscripts, where air is the make-up gas, one can show that  
               K   v   tot     =       K   v   air     ·           M   air       M   tot         .               (     Equation   ⁢           ⁢   11     )             
 
 Where tot designates diluted exhaust, therefore, Equation 8 can be written:  
               Q   CFV   tot     =       Q   CFV   air     ·         M   air       M   tot                   (     Equation   ⁢           ⁢   12     )             
 
 and, from Equations 1 and 12, the following is obtained:  
               Q   ex     =         Q   CFV   air     ·         M   air       M   tot           -       Q   dil     .               (     Equation   ⁢           ⁢   13     )             
 
 Rearranging Equation 13 to obtain the expression for M tot :  
               M   tot     =             Q   ex     ⁢     M   ex       +       Q   dil     ⁢     M   air           Q   CFV   tot       .             (     Equation   ⁢           ⁢   14     )             
 
 Since Q ex =Q CFV −Q dil , then:  
                     ⁢         M   tot     =             (       Q   CFV     -     Q   dil       )     ⁢     M   ex       +       Q   dil     ⁢     M   air           Q   CFV       .     
     ⁢   So       ,             (     Equation   ⁢           ⁢   15     )                       ⁢         (       M   air       M   tot       )       1   2       =       (         M   air           (       Q   CFV     -     Q   dil       )     ⁢     M   ex       +       Q   dil     ·     M   air             Q   CFV       )       1   2                 (     Equation   ⁢           ⁢   16     )                       ⁢     =       (           (       Q   CFV     -     Q   dil       )     ⁢     M   ex       +       Q   dil     ·     M   air             Q   CFV     ·     M   air         )       -     1   2                   (     Equation   ⁢           ⁢   17     )                       ⁢     =       (                 Q             ⁢   CFV       ⁢     M             ⁢   air         +       Q             ⁢   CFV       ⁢     M             ⁢   ex         -       Q             ⁢   CFV       ⁢     M   air       -                   Q   dil     ⁢     M   ex       +       Q   dil     ⁢     M   air                   Q   CFV     ·     M   air         )       -     1   2                   (     Equation   ⁢           ⁢   18     )                       ⁢         (       M   air       M   tot       )       1   2       =         (     1   +       (         M   ex     -     M   air         M   air       )     ⁢     (         Q   CFV     -     Q   dil         Q   CFV       )         )       -     1   2         .               (     Equation   ⁢           ⁢   19     )             
 
         [0053]     Substituting this into Equation 13 at this point leads to a complex expression. Equation 19 can be simplified by assuming 1) that Q CFV   air ≈Q CFV   tot , and 2) that:  
                 (     1   +   α     )       -     1   2         ≈     1   -       α   2     ⁢           ⁢   when   ⁢           ⁢   α   ⁢     &lt;&lt;   1                 (     Equation   ⁢           ⁢   20     )             
 
 As a result,  
                 (       M   air       M   tot       )       1   2       ≈     (     1   -       1   2     ·         M   ex     -     M   air         M   air       ·         Q   CFV     -     Q   dil         Q   CFV           )             (     Equation   ⁢           ⁢   21     )             
 
 so that  
             a   =           M   ex     -     M   air         M   air       ·       1   2     .               (     Equation   ⁢           ⁢   22     )             
 
 Making the appropriate substitutions:  
               Q   ex     =         Q   CFV   air     ⁡     (     1   -     a   ⁢       (       Q   CFV     -     Q   dil           Q   CFV           )       -     Q   dil               (     Equation   ⁢           ⁢   23     )                       ⁢     =       Q   CFV   air     -     a   ⁢           ⁢     Q   CFV       +     a   ⁢           ⁢     Q   dil       -     Q   dil                 (     Equation   ⁢           ⁢   24     )                       ⁢     =       (       Q   CFV   air     -     Q   dil       )     ⁢     (     1   -   a     )                 (     Equation   ⁢           ⁢   25     )             
 
 or, more completely:  
               Q   ex     =       (       Q   CFV   air     -     Q   dil       )     ⁢       (     1   -         M   ex     -     M   air         2   ⁢     M   air           )     .               (     Equation   ⁢           ⁢   26     )             
 
         [0054]     This is a relatively simple expression to account for the systematic error resulting from changes in the density of the diluted exhaust during the test. The correction is remarkably useful since the correction is constant, i.e. independent of exhaust flow. For gasoline, M ex =29.02 and moist air is M air =28.85, so we have:  
               1   -         M   ex     -     M   air         2   ⁢     M   air           =       1   -       29.02   -   28.85       2   ·   28.85         =   0.9970             (     Equation   ⁢           ⁢   27     )             
 
 Thus:  
               Q   ex     =       (       Q   CFV   air     -     Q   dil       )     ·   0.9970             (     Equation   ⁢           ⁢   28     )             
 
         [0055]     When exhaust gas is flowing, the air based calculation by the DVE underestimates exhaust flow by a constant 0.3%. The correction factor can be manipulated and applied to any variable expressed in Equation 28, for example. The correction for other fuels varies according to the following table:  
                                                     TABLE 1                                   M ex     Measured Exhaust   Correction Factor                                        Gasoline   29.02   0.997   1.003           Methane   27.73   1.019   0.981           Propane   28.41   1.008   0.992           Methanol   27.64   1.021   0.979                      
 
         [0056]     The invention has been described in an illustrative manner, and it is to be understood that the terminology that has been used is intended to be in the nature of words of description rather than of limitation. Several corrections to a DVE have been described. Of course, more or fewer corrections may be used, and the correction may be applicable to other exhaust measurement devices. Obviously, many modifications and variations of the present invention are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the appended claims the invention may be practiced otherwise than as specifically described.