Patent Document

BACKGROUND OF THE INVENTION 
     Motor vehicle manufacturers continue to study, improve and refine their products. Nearly every aspect of motor vehicle performance is under scrutiny. Passenger cars, sport utility vehicles and pickup trucks are significant objects of such study in areas of passenger comfort. One of the more esoteric areas under examination is cabin (passenger compartment) air infiltration and exfiltration. The flow of air into and out of the cabin affects not only noise levels and thus passenger comfort but also heating and cooling requirements. As permitted and average actual highway speeds again increase, proper understanding and quantitative analysis of air infiltration and exfiltration takes on added importance. 
     The infiltration/exfiltration of air during the forward motion of a “closed” vehicle is an undesirable but natural phenomena associated with the non-uniform pressure values at the external surface of the vehicle and the numerous small openings between various passenger compartment components such as doors and door openings. Such infiltration and the corresponding exfiltration is the result of the relative motion between the vehicle and the surrounding air which creates positive pressure on the forward region of the vehicle and negative pressure over the remainder of the vehicle&#39;s perimeter. Such positive and negative pressures exist with respect to the undisturbed ambient pressure. 
     Since the perimeter area that experiences negative pressure values is considerably larger than the area that experiences positive pressure, it can be expected that, in general, the passenger compartment will adopt a subatmospheric pressure condition at forward speeds. 
     The consequence of this is that the infiltration mass flow rate:                    m   .       i                 n       =            ∫     A     i                 n              ρ                     V   →     ·     n   ^                          A                ,           (   1   )                                
     will be non-zero. (By convention, {circumflex over (n)} is the outward drawn normal and, hence, the integral value is negative if the control surface surrounds the vehicle. The symbol “A in ” represents the total of the infiltration areas.) The ρ of equation (1) is that of the ambient air and, given the condition that V vehicle /a ambient &lt;0.2 where a=the speed of sound in the ambient, the entering ρ is safely assumed to be that of the atmosphere. In a steady state, the entering and exiting {dot over (m)} values are equal and this value ({dot over (m)} in ) will be referred to as the “infiltration rate” although it, of course, with equal accuracy quantitatively represents the exfiltration rate. 
     The fact that {dot over (m)} in  is distributed over the forward region of the motor vehicle makes its direct assessment quite difficult. A stratagem to measure and determine such infiltration rate would therefore be highly desirable to assist in the analysis and improve performance and comfort of motor vehicles and similar structures such as unpressurized airplane cabins, train passenger cars and the like. 
     SUMMARY OF THE INVENTION 
     An apparatus and method for measuring the infiltration flow rate into the passenger compartment of a moving motor vehicle includes a controlled source of a gas such as carbon dioxide (CO 2 ), a plurality of sensors disposed about the passenger compartment which provide data from which the concentration of such gas over time can be deduced and a multi-channel data storage device which discretely stores the concentration data from such plurality of sensors for later analysis and computation. The decay rate of the gas concentration within the passenger compartment is a function of the infiltration/exfiltration rate and the former rate can be deduced from the latter. Preferably, the vehicle will be stationary and disposed in a wind tunnel. However, testing with moving, remotely controlled vehicles on test tracks is also suitable. The apparatus and method have broad utility to determine infiltration/exfiltration rates of vehicular and non-vehicular compartments and containment structures such as unpressurized airplane cabins, train passenger cars, busses and the like subjected to an airstream. 
     Thus it is an object of the present invention to provide an apparatus for determining the infiltration/exfiltration rate of air into/out of a motor vehicle passenger compartment while in relative motion with respect to the approach air flow. 
     It is a further object of the present invention to provide a method of determining the infiltration/exfiltration of air into and or out of a motor vehicle passenger compartment while the vehicle is in motion. 
     It is a still further object of the present invention to provide an apparatus for measuring the concentration of a released quantity of a gas within a passenger compartment of a motor vehicle in actual or simulated motion to infer the infiltration/exfiltration rate. 
     It is a still further object of the present invention to provide a method for measuring the concentration of a released quantity of a gas within a passenger compartment of a motor vehicle in actual or simulated motion to infer the infiltration/exfiltration rate. 
     It is a still further object of the present invention to provide an apparatus for determining the infiltration/exfiltration rate of a compartment or containment structure subjected to an airstream. 
     It is a still further object of the present invention to provide a method for determining the infiltration/exfiltration rate of a compartment or containment structure subjected to an airstream. 
     Further objects and advantages of the present invention will become apparent by reference to the following description of the preferred embodiment and appended drawings wherein like reference numbers refer to the same assembly, element, component or feature. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a top plan view of a passenger car undergoing an air infiltration/exfiltration test according to the present invention; 
     FIG. 2 is a side elevational view of a passenger car undergoing an air infiltration/exfiltration test according to the present invention; 
     FIG. 3 is a fragmentary, side elevational view in partial section of a passenger car instrumented for an air infiltration/exfiltration test according to the present invention; 
     FIG. 4 is a fragmentary, top plan view in partial section of a passenger car instrumented for an air infiltration/exfiltration test according to the present invention; 
     FIG. 5 is an enlarged, side elevational view of an ultrasonic sound speed sensor assembly according to the present invention; 
     FIG. 6 is an enlarged, side elevational view of a first alternate embodiment ultrasonic sound speed sensor assembly according to the present invention; 
     FIG. 7 is a fragmentary, elevational view of a portion of a passenger car instrumented for an air infiltration/exfiltration test illustrating a first alternate embodiment test gas supply; 
     FIG. 8 is a side, elevational view of a portion of a first alternate embodiment test gas supply according to the present invention taken along line  8 — 8  of FIG. 7; 
     FIG. 9 is a fragmentary, elevational view of a portion of a passenger car instrumented for an air infiltration/exfiltration test illustrating a second alternate embodiment test gas supply; 
     FIG. 10 is a full, sectional view of a second alternate embodiment test gas supply according to the present invention taken along line  10 — 10  of FIG. 9; 
     FIG. 11 is an exploded, perspective view of a second alternate embodiment test gas supply according to the present invention; 
     FIG. 12 is a graph presenting pressure within the passenger compartment versus time wherein 0 is atmospheric pressure during a typical infiltration/exfiltration test run according to the present invention; 
     FIG. 13 is a graph of the mass of carbon dioxide (CO 2 ) within the passenger compartment versus time during a typical infiltration/exfiltration test run according to the present invention; 
     FIG. 14 is a graph of the infiltration mass flow rate versus time during a typical infiltration/exfiltration test run according to the present invention; and 
     FIG. 15 is a reference graph of the sound speed ratio (a m /a A ) for various mixtures of air and carbon dioxide (CO 2 ) mixtures. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring now to FIGS. 1,  2  and  3 , a motor vehicle  10  which may be a passenger car, sport utility vehicle, pickup truck or station wagon, for example, the motor vehicle  10  defines an interior or passenger compartment  12  which is accessible in conventional fashion through a plurality of hinged doors  14 . The motor vehicle  10  may be a mockup, prototype, shell or more typically, an actual vehicle in the mid to latter stages of development and may include passenger seats  16  and other interior components. Given such a motor vehicle  10 , the test and quantitative evaluation regarding infiltration and exfiltration of air will be utilized to assist final designs, particularly those relating to door and window seals, door and window moldings and other components and features which include openings or passages between the interior or passenger compartment  12  of the motor vehicle  10  and its exterior and environment. 
     The motor vehicle  10  is disposed in a wind tunnel  16  having a source of high velocity air such as one or a plurality of fans  18 . The fans  18  must be capable of providing air movement through the wind tunnel  16  at a speed generally in the upper range of motor vehicle speeds such as eighty miles per hour (128 kilometers per hour) and preferably in the range of from sixty miles per hour (96 kilometers per hour) to one hundred miles per hour (160 kilometers per hour). A multi-channel data storage device  22  which may be a multi-channel digital or analogue tape recorder or a properly configured computer having discrete multi-channel data storage capabilities is connected through a suitable multi-conductor cable  24  to instrumentation and sensors within the passenger compartment  12  of the motor vehicle  10  to be described directly below. 
     Turning now to FIGS. 3 and 4, the instrumentation within the interior or passenger compartment  12  of the motor vehicle  10  comprises a plurality of sensor assemblies  30  disposed thereabout. Each of the sensor assemblies  30  is mounted to a wall or floor member or panel  34  as illustrated in FIG. 5, and are disposed somewhat uniformly about the interior of the passenger compartment  12  as illustrated in FIGS. 3 and 4. Note that nine of the sensor assemblies  30  are disposed generally along each interior side wall of the passenger compartment  12 , three are disposed across the front and the rear, one is disposed in each of the left and right front and rear footwells and four are disposed generally centrally within the passenger compartment  12  adjacent the roof. 
     It should be understood that the use of thirty-two of the sensor assemblies  30  is generally illustrative and representative as are the specific locations illustrated. More or fewer of the sensor assemblies  30  may be utilized depending upon the size of the passenger compartment  12  and the size and configuration of components such as seats  16  within the passenger compartment  12  and other variables. It should be appreciated that the relatively large number of sensor assemblies  30  facilitates extensive post-test analysis of the recorded data. For example, all the data may be averaged together to provide a gross or average infiltration/exfiltration rate, they may be individually examined to pinpoint leaks and significant infiltration sources and exfiltration sinks or only data from certain sensors (e.g., those located along the lower left door seals) may be examined to focus on a certain area or problem. 
     As illustrated in FIG. 5, each of the sensor assemblies  30  preferably comprises a generally C-shaped bracket  32  which is attached to a member or panel  34  in the passenger compartment  12 . The bracket  32  rigidly mounts and maintains at a defined separation of, for example, 5.9 inches (15 cm) an ultrasonic transceiver transducer  36  which may be a piezoelectric device or similar transducer capable of both operation at ultrasonic frequencies and both transmitting and receiving, i.e., sensing, ultrasonic frequencies. Spaced from the transceiver transducer  36  the aforementioned known and fixed distance is a reflector  38 . The reflector  38  defines a smooth, hard, flat or spherically curved surface which reflects ultrasonic waves produced by the transceiver transducer  36  back to the transceiver transducer  36 . The transceiver transducer  36  is connected through conductors of the multiple conductor cable  24  to the data storage device  22 . As will be explained in more detail subsequently, the sensor assemblies  30  and more specifically the transceiver transducer  36  are provided with short bursts (packets) of high frequency energy and the time which the short burst of energy takes to travel the distance from the transceiver transducer  36  to the reflector  38  and return is recorded in the data storage device  22  for each of the sensor assemblies  30 . The transit time recorded reflects the composition of the gas through which the ultrasonic energy packet travels and such data may be utilized to compute the infiltration/exfiltration rate as more fully described below. 
     FIG. 6 illustrates a first alternate embodiment sensor assembly, each of the sensor assembly  30 ′. The first alternate embodiment sensor assembly  30 ′ preferably comprises a generally C-shaped bracket  32  which rigidly mounts an ultrasonic transmitter transducer  36 ′ at a defined separation of 5.9 inches (15 cm) from a complementary ultrasonic receiver transducer  40  disposed in opposed (facing) relationship therewith. The transmitter  36 ′ and the receiver  40  are connected through conductors of the multiple conductor cable  24  to the data storage device  22 . The transmitters  36 ′ of the sensor assemblies  30  are provided with short bursts (packets) of high frequency energy and the time which the short burst of energy takes to traverse the distance separating the transmitters  36 ′ and the receivers  40  is recorded in the data storage device  22  for each of the sensor assemblies  30  at its specific location. The transit time recorded reflects the composition of the gas through which the sound burst travels and such data may be utilized to compute the infiltration/exfiltration rate as more fully described below. 
     Returning briefly to FIG. 3, the determination of the infiltration/exfiltration flow rate is achieved by charging the interior or passenger compartment  12  of the motor vehicle  10  with a gas, preferably carbon dioxide (CO 2 ), and then monitoring the reduction over time of the concentration of the carbon dioxide and inferring that such reduction is the result of the replacement of the carbon dioxide with air that has infiltrated the passenger compartment  12 . Thus, it is necessary to provide a test gas charging assembly  42  which provides such carbon dioxide or other distinct and therefore identifiable gas. The carbon dioxide is preferably supplied to the passenger compartment  12  by two or more containers  44  which are preferably large flexible thin walled bladders placed upon the passenger seats  16  of the motor vehicle  10 . Such containers  44  preferably occupy or displace approximately 5 to 40 percent of the air within the compartment. The containers  44  are preferably filled with carbon dioxide (CO 2 ) and are at slight positive pressure. Each of the containers  44  includes one or more electromechanical valves  46  and/or a powered centrifugal blower  47  which may be activated remotely to allow the carbon dioxide (CO 2 ) within the container  44  to escape into the passenger compartment  12  at a preselected time. Two alternate embodiment test gas supply devices are described below. 
     Rigid walled containers such as metal tanks wherein the carbon dioxide (CO 2 ) is stored under significant pressure are not desirable inasmuch as release of the contents significantly cools the carbon dioxide and the containers and disturbs the thermal equilibrium of the air within the passenger compartment, thereby interfering with accurate measurements. 
     Referring now to FIGS. 6 and 7, a first alternate embodiment gas charging assembly  50  which may be used singly or in pairs is illustrated. The alternate embodiment gas charging assembly  50  which may be placed upon one or both of the passenger seats  16  of the motor vehicle  10  includes a lower horizontal planar member  52  which rests on the seat  16 . The lower planar member  52  is pivotally coupled to an upper planar member  54  by four single pantograph-like connector arms  56  which are pivotally secured at their respective ends to the lower planar member  52  and upper planar member  54  by appropriately disposed pivot pins  58 . A weight  62  having a mass of several pounds is placed upon the upper planar member  54 . A generally rectangular flexible walled container  64  which is similar to the containers  44  of the preferred embodiment is positioned between the lower planar member  52  and the upper planar member  54  and filled with a traceable gas such as carbon dioxide as described above. A plurality, preferably at least three, apertures  66  are formed in the vertical walls of the container  64  and are closed with an overlying flap  68  which functions as a one-way valve. A latch or release mechanism  70  includes a latch arm  72  which is pivotally secured to the lower planar member  58  by a pivot pin  68 . A solenoid  74  or similar electrically or pneumatically activated device includes a release plunger  76  which is received within a suitably disposed aperture  78  formed in one of the connector arms  56 . 
     To provide the necessary supply of carbon dioxide or other tracer gas to the interior  12  of the motor vehicle  10 , the container  64  is filled with carbon dioxide or similar gas and placed between the planar members  52  and  54  and the connector arms  56  and the latch arm  68  are disposed as illustrated. When the solenoid  74  is activated, the release plunger  76  is driven toward the bottom of the solenoid  74  and out of the aperture  76  in the pantograph-like connector arm  56 . The weight  62  is thus free to and does collapse the container  64  and drive the carbon dioxide or other tracer gas out the ports or apertures  66 . Through the first alternate embodiment gas charging assembly  50 , gas may also be dispersed within the interior  12  of the motor vehicle  10  which has not undergone significant expansion and cooling as would be the case if it were stored and released from a compact, pressurized container, as discussed above. 
     Referring now to FIGS. 9,  10  and  11  a second alternate embodiment gas charging assembly  80  is illustrated. The second alternate embodiment gas charging assembly  80  will preferably be utilized in multiples; three or four of the assemblies  80  provide a sufficient concentration of the test gas such as carbon dioxide within the interior  12  of the motor vehicle  10  to achieve excellent test results. The multiple gas charging assemblies  80  are, once again, preferably disposed on the front and rear seats  16  of the motor vehicle  10  as illustrated. Each of the second alternate embodiment gas charging assemblies  80  include an elongate cylindrical body  82  and a base  84 . The body  82  has circumferentially continuous side walls  86  whereas the base  84  defines a castellated bottom having circumferentially equal sized notches or apertures  88  and side wall portions  92 . 
     At the top of the gas charging assembly  80  is positioned a top cap  94  having open regions  96  and a center bar  98  defining an aperture  102  which receives an elongate rod  104  disposed concentrically about the center axis of the body  82 . The elongate rod  104  is received within a similar aperture  106  formed in a bottom cap  108  which is secured to the side wall portions  92  of the base  82 . Received upon the elongate rod  104  for bi-directional axial translation is a bearing sleeve  112 . The bearing sleeve  112  includes a pair of spaced apart linear bearing assemblies  114  which engage the exterior of the elongate rod  104 . The bearing sleeve  112  also includes a radially extending flange  116 . Secured to the radially extending flange  116  is a disc or piston  118  which has a diameter substantially equal to the inside diameter of the body  82  such that it may translate bi-directional therewithin while providing a reasonably gas tight seal thereagainst. Adjacent the top cap  94  of the body  82  is disposed a first solenoid  122  having a plunger  124  which interferes with the axial travel of the piston or disc  118 . If the disc  118  is positioned between the plunger  124  of the first solenoid  122  and the top cap  94  and the solenoid is then activated, the piston or disc  118  will be released to descend toward the base  84 . 
     Disposed between the body  82  and the base  84  of the second alternate embodiment gas charging assembly  80  are a pair of circular discs, one of which is fixed and the other of which is rotatable. A first fixed disc  126  defines a center aperture  128  and three equally spaced apart apertures  132  each occupying slightly less than 60° of arc. Disposed in sliding contact with the fixed disc  126  is a second rotatable disc  136  defining a center opening  138  and three equally spaced apart apertures  142  each extending over slightly less that 60° of arc. The fixed disc  126  and the rotatable disc  136  are, as noted above, disposed adjacent one another and it will be appreciated that from a position in which the apertures  132  and  142  are aligned such that fluid passage therethrough is achieved, rotation of the rotatable disc  136  through approximately 60° of arc will fully close off the apertures  132  and thus terminate fluid flow or communication. The fixed disc  126  is supported by a cylindrical inlet member  144  which extends from the fixed disc  126  to the bottom cap  108  and includes a fill port  146 . A reinforcing or bearing member  148  may be secured to the rotatable disc  136  to facilitate its rotation about the inlet member  146 . 
     To achieve rotation of the rotatable disc  136  relative to the fixed disc  126 , a watch spring  150  or similar circular spring may be wrapped about the inlet member  144  and one end secured to it and the other end secured to the rotatable disc  136 . Suitable interfering stops  152  are mounted upon the rotatable disc  136  and the base  84  to define a limit of rotation driven by the watch spring  150  such that the apertures  132  and  142  are aligned and therefore open. A second solenoid  154  is secured to the base  84  and includes a plunger  156  which interferes with one of the stops  152  on the rotatable disc  136  in its closed position and restrains motion of the disc  136  against the force of the spring  150 . When the second solenoid  154  is activated, retraction of the plunger  156  permits the rotatable disc  136  to rotate approximately 60° and open the apertures  132  in the fixed disc  126 . 
     To charge the second alternate embodiment assembly  80 , the rotatable disc  136  is rotated such that the apertures  132  are closed and it is restrained by the plunger  156  of the second solenoid  154 . At this time, the piston or disc  118  will be at its lowermost position, adjacent the fixed disc  126 . The first solenoid  122  may be activated at this time. Carbon dioxide or other gas is then supplied through the fill port  146  in the inlet member  144  and the interior of the body  82  is filled with carbon dioxide as the piston or disc  118  rises. When the piston or disc  118  is driven to its uppermost limit of travel, adjacent the top cap  94 , the first solenoid  122  is deactivated such that the plunger  124  restrains the disc or piston assembly  118  against downward motion. When it is desired to discharge the carbon dioxide from the charging assembly  80 , both of the solenoids  122  and  154  are activated, releasing the piston or disc  118  and opening the apertures  132  thereby releasing the carbon dioxide. 
     As a further alternative, the carbon dioxide may be provided to the passenger compartment  12  of the motor vehicle  10  through pipes, conduits or the like (not illustrated). However, the use of the self-contained internal containers  44  or  64  has the advantage of eliminating piping or conduits from the exterior of the motor vehicle  10  to its interior as well as the need to create openings in the body of the vehicle  10  to accept such conduits thereby permitting more accurate simulation of the vehicle and its operating conditions. 
     Finally, the instrumentation in the passenger compartment includes at least one sensor assembly  48  which provides data to the data storage device  22  over the multi-conductor cable  24 . Preferably, the sensor assembly  48  includes an electric air pressure (barometric) sensor and temperature sensor such as a thermistor which provide signals and information regarding the instantaneous air or mixture pressure with respect to the static pressure of the approach air and the temperature of the air within the passenger compartment  12  of the motor vehicle  10 . 
     Test Operation 
     Referring now to FIG. 6, the motor vehicle  10  whose {dot over (m)} i  value at a given relative flow speed (i.e., the speed of the approach air with respect to the vehicle) is desired, is placed in the wind tunnel  16 , outfitted with the appropriate sensor assemblies  30  as described above and connected to the data storage device  22 . Once the fans  18  of the tunnel have started and the interior pressure of the passenger compartment  12  comes to equilibrium: (p(U o )&lt;p atm ), this pressure value will be sensed by the air pressure sensor  48  and recorded on the data storage device  22  and used as a reference condition for subsequent measurements. Note, if the vehicle is aerodynamically bluff, then p(U o ) may be larger than P atm . 
     The large, flexible wall containers  44  filled with CO 2  will have been placed in the passenger compartment prior to the initiation of the test and will have reached temperature equilibrium with the surroundings  12 . 
     Following the establishment of P(U o )&lt;P atm , the electromechanical valves  46  will be energized and the CO 2  will be released from the containers  44  with the consequence of a slight pressure rise within the passenger compartment  12 . The time of this release will be designated as t r  and the symbols (t CO     2   =0) and M CO     2   (0) will designate the time at which the initial mass of the CO 2  in the compartment is established. 
     The corresponding pressure at the time of t CO     2   (0) will be larger than p(U o ) as a result of the introduction of CO 2  from the containers  44  into the passenger compartment  12 . It is assumed that the excess CO 2 , that is, the CO 2  that leads to a pressurization of the passenger compartment  12 , will leak to the surroundings in a relatively short time. A smaller, residual over-pressure will remain in the passenger compartment  12  as a result of the larger molecular weight of the CO 2  as described below. 
     The natural infiltration and exit leakage of the (air+CO 2 ) mixture will cause the CO 2  to be displaced by fresh air. However, since the outflow is delivering a mixture of density greater than pure air, the driving pressure [p(t)−p exterior ] will necessarily be larger than [p(U o )−p exterior ]. Hence, there will be a decay process in which p(t)→p(U o ). 
     By monitoring p(t), it is inferred that the condition for which {dot over (m)} i (t)→{dot over (m)} i (∞) can be identified given p(t)→p(U o ). Also, it will be possible to infer {dot over (m)} i (t)→{dot over (m)} i (∞) by observing the time for which the CO 2  concentration approaches zero. 
     FIGS. 1 and 2 illustrate a control volume (CV) that has been placed around the motor vehicle  10 . The external surface of the CV is the external surface of the motor vehicle  12 . 
     The conservation of mass for this CV can be expressed as (from, e.g., Potter, M. C. and Foss, J. F.  Fluid Mechanics  (1975))              0   =               t              ∫   cv          ρ                        ∀     +       ∫   cs          ρ                     V   →     ·     n   ^                            A     .                             (   2   )                                
     Per the above discussion, the symbol {dot over (m)} i  represents the desired quantity: the infiltration mass flow rate of air into the passenger compartment  12  of the motor vehicle  10 . Equation (2) can be written in terms of {dot over (m)} i  as                0                t            ∫     ρ                        ∀       +       ∫     A   exit            ρ                     V   →     ·   n                        A           -       m   .     i                      
                             (   I   )                          (   II   )                          (   III   )                     (   3   )                                
     where A exit  is defined as the sum of the area segments at which mass leaves the motor vehicle  10 . The ρ values in equation (3) represent, in general, the density, ρ m , of the gas mixture: air plus CO 2 . 
     As noted above, term I of equation (3) is zero when p=p(U o ) before the released carbon dioxide is flushed from the passenger compartment  12  of the motor vehicle  10 . However, during the transient period: t CO     2     =0 ≦t≦t 28 , measurements—which can be used to approximate term I and an inferred time dependent history for ρ m (t) at the exiting locations—can be combined to infer {dot over (m)} i (t). 
     As illustrated in FIG. 14, since {dot over (m)} i (t) will increase to {dot over (m)} i (∞) as the interior pressure is decreased to p(U o ), an extrapolation of the {dot over (m)} i (t) magnitudes will yield the desired infiltration rate. 
     Equation (2) can be equivalently written for carbon dioxide as well as the air/carbon dioxide mixture that is described by equation (2). That is,                    0   =                          t                         ∫   cv            ρ     CO   2                 ∀     +                  ∫   cx            ρ     CO   2              V   →     ·   n             A                                 =                          t                         ∫   cv            ρ     CO   2                 ∀     +                  ∫     A   exit              ρ     CO   2              V   →     ·     n   ^               A                                                (     I   c     )                     (     II   c     )                                (   4   )                                
     Note that there is (effectively) no influx of carbon dioxide; hence, term I c  is simply balanced by the efflux of carbon dioxide as described by II c . 
     Consider that experimental techniques to evaluate term I of equation (3) and term I c  of equation (4) are available. Specifically, 
     
       
         ρ m ( x   j   ,y   j   ,z   j   ,t ) and ρ CO     2   ( x   j   ,y   j   ,z   j   ,t ) 
       
     
     will be determined at a sufficient number of locations within the passenger compartment  12  that the integral values of I and I c  will be adequately approximated. The spatial average of p CO     2    in the interior (i.e., &lt;ρ CO     2   &gt;) will be assumed to exist at the exiting areas such that (4) can be written as              0   =     ∀                 t            〈     ρ     CO   2       〉       +       〈     ρ     CO   2       〉            q   exit     .     
                             (     I   c     )                          (     II   c   ′     )                             (5a)                                
     The symbol ∀, which represents the volume of the passenger compartment  12 , times the time derivative in equation (5) is equal to I c  in equation (4) by definition. The central assumption of the present method is contained in the presumed equality of II c  and II c ′ where q exit  is the volume flow rate of the exiting gas. Namely,                q   exit     =       ∫     A   exit                V   →     ·     n   ^                          A                 (5b)                                
     As stated above, I c  can be approximated by measurements. Hence, q exit  will be inferred from equation (5a). 
     The symbol I c ″ is now introduced to differentiate between the mathematically defined &lt;ρ CO     2   &gt; in equation (5a) and the experimentally defined &lt;ρ″ CO     2   &gt; that will be determined by the procedures in the next section. The resulting equation, which can be balanced experimentally, is                0   ≈     ∀                 t            〈     ρ     CO   2     ″     〉       +       〈     ρ     CO   2     ″     〉          q   exit                  
                             I   c   ″                          II   c   ″                     (5c)                                
     The approximate equality represents both the assumption regarding the density in II c ″ and the measurement uncertainty between I c ″ and the mathematical quantity I c . 
     Returning to equation (3) for the time period between t CO     2     =0  and t ∞ , and using the symbol ( ) m  to denote properties of the CO 2 +air mixture and ( )″ to denote measured quantities, the equivalent of equation (3) becomes                0   ≈     ∀                 t            〈     ρ   m   ″     〉       +       〈     ρ   m   ″     〉          q   exit       -       m   .     i                
                             I   m   ″                          II   m   ″                     (6)                                
     where the approximate equality is as described for equation (5c) above. 
     Equation (6) has the same integrity as equation (5c). Terms I m ″ and II m ″ can, therefore, be determined in equation (6) and the desired {dot over (m)} i (t) can be inferred as the sum of these two terms. (Note that I m ″&lt;0 and II m ″&gt;0). 
     It can be expected that {dot over (m)} i (t) will gradually approach {dot over (m)} i (∞) as indicated in FIG.  14 . It is important to note that the discrete measurements to be used for the evaluation of I m ″ in equation (6) can be expected to exhibit scatter about a smooth distribution that would represent the behavior of I in equation (3). This scatter, however, will be a result of random processes and a smoothed representation of the terms in equation (6) should be readily extracted from the data. This expectation has been confirmed by measurement at Michigan State University in January, 1999. 
     The following section defines the strategy to infer &lt;ρ″ CO     2   &gt; and &lt;ρ″ air &gt; that are required to implement the above described {dot over (m)} i (t) evaluation. For convenience, these designations are changed to: ( ) c  for ( ) CO     2    and ( ) A  for ( ) air . 
     Experimental Technique 
     Thermodynamic Considerations 
     Consider that the CO 2  and the air temperatures and pressures are in equilibrium for all relevant times of this analysis. Hence, for ρ m  as the mixture density: 
     
       
         ρ m =ρ c +ρ a   (7a) 
       
     
     and 
     
       
         1=ρ′ c +ρ′ a   (7b) 
       
     
     where all terms in equation (7) are evaluated at (x j , y j , z j , t) which represents a discrete position in space for the specified instant (t). The ρ′ c  and ρ′ a  quantities are equivalent to the concentrations of CO 2  and air, respectively. 
     A speed-of-sound technique will be used to infer ρ m  at an adequate number of locations within the passenger compartment  12 . The sound speed (a) can be described as 
     
       
         α={square root over (γRT)}  (8) 
       
     
     where γ=ratio of specific heats (γ=c p /c v ), and R=gas constant. For this binary mixture 
      γ m =ρ′ c γ c +ρ′ α γ A   
     and 
     
       
           R   m =ρ′ c   R   c +ρ′ α   R   A . 
       
     
     Using the thermodynamic quantities:                R   C     =     0.189        kJ       Kg   o        K                   γ   C     =   1.289                 R   A     =     0.287        kJ       Kg   o        K                     γ   A     =   1.4     ,                                
     and developing a relationship for the sound speed of the mixture (a m ) in terms of the sound speed for air alone (a A ), the following equation can be developed. Specifically,                      a   m       a   A       =       {         [     1   -     ρ   a   ′       )          c   1       +     ρ   a   ′       ]          [         (     1   -     ρ   a   ′       )          c   2       +     ρ   a   ′       ]         }       1   /   2             (9a)                                
     where 
     
       
           c   1 =γ c /γ A =(1.289/1.4)=0.921  (9b) 
       
     
     and 
     
       
           c   2   =R   c   /R   A =(0.189/0.287)=0.659  (9c) 
       
     
     Equations (9a), (9b) and (9c) are represented in graphical form in FIG.  15 . 
     The magnitude of ρ″ CO     2    that is required for the evaluation of q exit  in (5c), can be obtained using the following steps. 
     i) The sound speed, in pure air, can be solved for explicitly from 
     
       
         α A ( t →∞)={square root over (γ A   R   A   T   A +L )}. 
       
     
     Hence, the left hand side denominator of (9a) is known for each of the sensor assemblies  30  once the CO 2  has been completely flushed from the compartment  12 . 
     ii) The time dependent a M (t) values, between the release of the CO 2  and its complete extraction from the compartment  12 , are known from                  a   M          (   t   )       =       [       a   M       a   A       ]            a   A     .               (9d)                                
     iii) Since α M   2 (t) can be expressed as 
     
       
         α M   2 ( t )=γ M   P   M /ρ M   (9e) 
       
     
     and since the (absolute) magnitude of the pressure in the compartment  12  can be measured as a function of time during the depletion of the CO 2 , the unknown values in (9e) can be expressed as                    ρ   M       γ   M            (   t   )       =           P   M       a   M   2            (   t   )       =     λ        (   t   )                 (9f)                                
     where λ(t) is an experimentally known coefficient. 
     iv) The desired mixture density, ρ M (t), can therefore be written as                        ρ   M          (   t   )       =                  λ        (   t   )              γ   M          (   t   )                     =                  λ        (   t   )            [           ρ   A          γ   A       +       ρ   c          γ   c           ρ   M       ]                   =                  γ   A            λ        (   t   )            [       ρ   a   ′     +       c   1          (     1   -     ρ   a   ′       )         ]                       (9i)                                
     v) The required CO 2  concentration can then be evaluated from 
     
       
         ρ c ( t )=(ρ c /ρ M )ρ M =(1−ρ′ α )ρ M .  (9j) 
       
     
     The (9a) function: ρ′ α =ρ′ α (α m /α A ) can be expressed as a second order polynomial; namely,                ρ   a   ′     =       β   0     +       β   1          (       a   m       a   A       )       +         β   2          (       a   m       a   A       )       2               (   10   )                                
     If equation (10) is evaluated over the range: 0.9≦ρ′ α ≦1.0, then β 0 =−2.8174, β 1 =2.8728 and β 2 =0.9446. As noted, the second order fit is quite adequate for the indicated range of ρ a ′ values and this function permits ρ α ′ to be inferred if the ratio of sound speeds is known. 
     Equations (9) and (10) shows that a direct measurement of the sound speed (in a given spatial domain of the compartment  12 ) will permit the local values of ρ′ a  to be determined. With these values at a sufficient number of points in space, {dot over (m)} i (∞) can be computed as described above. 
     Determination of {dot over (m)} i (t)→{dot over (m)} i (∞) 
     It is envisioned that thirty-two sensor assemblies  30  may be utilized to determine the “semi-local” values of (a m /a A ) and hence the concentration of air (i.e., ρ a ′) at the measurement locations. 
     Several viable methods to determine the a m  value along the length of the measurement path exist. Specifically, over the burst duration of N cycles where, for example, N=4, the ultrasonic output for each pair of transmitters  36 ′ and receivers  40  can be processed to evaluate the time-of-flight of the wave packet. 
     Specifically, consider that the frequency of the four-cycle burst is 40 KHz and that the distance traveled is nominally 15 cm. The burst duration: 
     
       
         Δ t   B =4 cycles/40 KHz= 10   −4  sec 
       
     
     whereas the transit time (Δt T ) will be nominally 
     
       
         Δ t   T =15 cm/3.4×10 4  cm/sec=4.4×10 −4  sec. 
       
     
     Hence, the responding receiver  40  can be “blanked” for the duration of the “send” pulse (thereby eliminating noise effects related to vibration modes in the support member) and the receiver  40  can then be interrogated to identify the passage of a “pulse train.” This will obviate the need to respond to a particular or detailed feature of the transmitted signal which will simplify the time-of-flight evaluation. Alternatively, the receiver  40  can be replaced by a spherical reflector cap such that the emitter “receives” the chirp. In this case the transit length would be 30 cm. 
     The received signal can be processed with a high speed (e.g., 10 MHz) A/D converter. It is estimated that the uncertainty in the processed signal will be ca ±2 “aperture times” or ±0.2 microsec. Hence, the time-of-flight will be resolved to            2   ×     10     -   4                     m                   sec        (   resolution   )           0.882  msec(time-of-flight)       ≈     1                 part                 in                 4   ,   385                            
     More importantly, the capacity to resolve the ρ′ A  value given that ρ′ A  is of order 0.99 can be assessed.                δρ   a   ′     =                           ∂     ρ   a   ′         ∂     (       a   m     /     a   A       )         ]         ρ   A   ′     →   1            ∂     (       a   m     /     a   A       )                     =                  [       1.8892        (       a   m       a   A       )       +   2.8728     ]          1     4   ,   385                     =                  [         (   1.8892   )            (       0.027        ρ   a   ′2       +     0.366        ρ   a   ′       +   0.607     )       1   /   2         +   2.8728     ]          1     4   ,   385                     =                  1.09   ×     10     -   3                     at                   ρ   a   ′       =   0.99                            and               =                  1.08   ×     10     -   3                     at                   ρ   a   ′       =   0.9                                  
     This resolution is quite adequate for the present purpose. Note that these thirty-two discrete measurements will be combined to approximate the integral value of the concentration in the passenger compartment  12 . The uncertainty of the integration, i.e., the approximation of the integral value from the discrete measurements, will dominate the evaluation of &lt;ρ a &gt;. Hence, the available resolution in the determination of the discrete ρ α ′ values is quite satisfactory. 
     Given that the analysis is referenced to the magnitude of (a m /a A ), the measurement system can also be self-calibrated by recording the transit time of a pulse in the air environment either prior to the initiation of the CO 2 discharge or after ρ′ c →0. Test experience suggests the latter is the preferred technique. 
     The determination of the spatially averaged ρ α ′ value in the space occupied by each of the N sensor assemblies  30  or  30 ′ will contribute to the integrand of II m ″ in equation (3). It can be expected that each measurement will exhibit random fluctuations. However, by summing the N values to approximate the integral and by identifying the “smooth” representation of term I (as it experiences an “exponential decay”) in equation (3), one can infer {dot over (m)} i (t) from that equation. 
     Hence, the stated objective, of determining the {dot over (m)} i (∞)value, will be met by recording the limiting value of {dot over (m)} i (t) as the CO 2  is flushed from the passenger compartment  12 . 
     Additional information regarding the location of the leaks can be expected in terms of the records from the individual sensor assemblies  30  or  30 ′ that are placed at the perimeter of the passenger compartment  12 . 
     The foregoing disclosure is the best mode devised by the inventor for practicing this invention. It is apparent, however, that apparatus incorporating modifications and variations will be obvious to one skilled in the art of air infiltration testing. Inasmuch as the foregoing disclosure presents the best mode contemplated by the inventor for carrying out the invention and is intended to enable any person skilled in the pertinent art to practice this invention, it should not be construed to be limited thereby but should be construed to include such aforementioned obvious variations and be limited only by the spirit and scope of the following claims.

Technology Category: b