Patent Publication Number: US-2022221380-A1

Title: Duct sensor with duct probe for sampling a fluid from a duct and method of operation

Description:
TECHNICAL FIELD 
     The present invention relates to a duct probe for sampling a fluid from a main fluid flow in a duct, to a duct sensor equipped with such a duct probe, and to a method of operating such a duct sensor. 
     PRIOR ART 
     From the prior art, duct probes are known for diverting a partial flow from a main fluid flow in a duct, passing the partial flow to a sensing element that is arranged outside the duct, and returning the partial flow to the duct after it has passed the sensing element. A duct probe typically has tubular shape, defining a longitudinal axis that extends perpendicular to the main fluid flow in the duct. The duct probe defines two channels: a supply channel for passing the partial flow from the duct to the sensing element outside the duct, and a discharge channel for returning the partial flow from the sensing element back to the duct. Each of the supply channel and the discharge channel is typically closed at the end that is located inside the duct, and open at the other end, which is located outside the duct. The open ends are in fluid communication with the sensing element. For diverting the partial flow from the duct into the supply channel, one or more inflow openings are provided in a wall of the supply channel. Often, but not necessarily, these inflow openings face the fluid flow in the duct. Similarly, for returning the partial flow to the main fluid flow, one or more outflow openings are provided in a wall of the discharge channel. 
     Examples of duct probes in various shapes and configurations are disclosed in US 2006/0027353 A1, US 2008/0257011 A1, US 2013/0160571 A1, US 2013/0255357 A1, 
     EP 2 835 592 A1, and DE 10 2014 010 719 A1. 
     In operation, the duct probe is arranged in the duct such that the main fluid flow hits the duct probe laterally and passes around the duct probe. The resulting deflection of the main fluid flow will typically lead to a positive back pressure at the inflow openings and to a negative pressure at the outflow openings due to the Bernoulli/Venturi effect. Thereby a pressure difference results between the supply channel and the discharge channel, the magnitude of the pressure difference depending on the flow rate of the main fluid flow in the duct. This pressure difference will in turn drive the partial flow through the duct probe, the flow rate of the partial flow strongly depending on the flow rate of the main fluid flow. 
     In some applications, it is desired to minimize the pressure difference between the supply channel and the discharge channel or at least its dependence on the flow rate of the main fluid flow. This is true, in particular, if the sensing element implements a particle counter, since variations of the flow rate of the partial flow inevitably cause undesired variations of the number of particles that pass the particulate matter sensor per unit time. It may therefore be desirable to keep variations of the pressure difference between the inflow and outflow openings at a minimum. 
     US 2005/0097947 A1 discloses a duct probe forming a first passage extending from an air inlet to an air outlet. A second passage extends around a shunt plate, forming a bypass of the first passage. An air flow measuring element is arranged in the second passage for measuring a flow velocity or flow rate of air passing through the second passage. If an air flow that enters the duct probe contains dust or liquid matter, the dust or liquid matter passes through the first passage and is prevented from entering the second passage. 
     Thereby the dust or liquid matter is prevented from contaminating the air flow measurement device in the second passage. In an embodiment, a step portion is formed at the meeting point of the first passage and the second passage, increasing the cross-section of the first passage there. As a result, dust or liquid matter contained in the air flow are temporarily trapped at the step portion. In another embodiment, the shunt plate has an inclined portion that projects into the first passage and is inclined towards the air outlet. In yet another embodiment, the shunt plate has an inclined portion that projects into the first passage and is inclined towards the air inlet. The inclined portion has a through-hole. EP 3 258 241 A2 discloses a particulate matter sensor device comprising a flow channel extending between a flow inlet and a flow outlet, a radiation source, and a radiation detector. A flow modifying device is provided for reducing particulate matter precipitation onto the radiation source, the radiation detector, or channel walls in their close proximity. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a duct probe that exhibits a reduced pressure difference between the supply channel and the discharge channel in the presence of a main fluid flow and/or a reduced dependence of the pressure difference on the flow rate of the main fluid flow. 
     This object is achieved by a duct probe according to claim  1 . Further embodiments of the invention are laid down in the dependent claims. 
     Accordingly, a duct probe is provided for sampling a fluid from a main fluid flow in a duct. The duct probe defines an elongated supply channel and an elongated discharge channel, the supply channel and the discharge channel extending substantially along a longitudinal axis of the duct probe. In operation, the longitudinal axis of the duct probe will advantageously extend across the main fluid flow, preferably perpendicular to the main fluid flow. Each of the supply channel and the discharge channel has a closed end and an open end, the open end being configured for direct or indirect connection to an environmental sensor. The supply channel has at least one inflow opening, which is preferably formed in a lateral peripheral surface of the supply channel (the term “lateral” being used with respect to the longitudinal axis of the duct probe), for diverting a partial flow from the main fluid flow into the supply channel. Likewise, the discharge channel has at least one outflow opening, which is preferably formed in a lateral peripheral surface of the discharge channel, for returning the partial flow from the discharge channel into the main fluid flow after it has passed the environmental sensor. According to the present invention, the duct probe comprises at least one compensation channel that connects the supply channel and the discharge channel in a region that is located between the closed ends and the open ends of the supply channel and the discharge channel, respectively, in order to reduce a pressure difference between the supply channel and the discharge channel when the duct probe is exposed to a main fluid flow. 
     The inflow opening and the compensation channel are arranged and sized to cause a jet flow through the inflow opening, the jet flow being directed towards the compensation channel. The jet flow is generated when the duct probe is exposed to the main fluid flow, the inflow opening facing the main flow or being oriented relative to the main flow in some other manner such that a portion of the main fluid flow will enter the supply channel through the inflow opening. The portion of the main fluid flow that passes through the inflow opening is accelerated to form the jet flow. The jet flow is decelerated when it passes through the compensation channel. In other words, the maximum flow velocity of the jet flow is higher upstream of the compensation channel (i.e., on the side of the supply channel) than downstream of the compensation channel (i.e., on the side of the discharge channel). The deceleration causes a negative pressure difference between the upstream and downstream sides of the compensation channel, which counteracts the positive pressure difference caused by the backpressure at the inflow opening and by the negative pressure due to the Bernoulli/Venturi effect at the outflow opening. By choosing the dimensions of the inflow opening and compensation channel appropriately, the jet flow can be tailored such that the negative pressure difference compensates the positive pressure difference to such a degree that both the value of the resulting pressure difference between the supply channel and the discharge channel as well as its dependence on the flow rate of the main fluid flow are massively reduced. 
     In order to ensure that the jet flow is directed towards the compensation channel, the inflow opening and the compensation channel are preferably aligned along a common jet axis. The jet axis preferably extends across the longitudinal axis of the duct probe, in particular, perpendicular to the longitudinal axis. In use, the jet axis can advantageously be arranged along the direction of the main fluid flow. In some embodiments, also the outflow opening is arranged along the same jet axis. This may simplify manufacture of the duct probe. 
     In order to decelerate the jet flow when it passes through the compensation channel, it is preferred that the free cross-sectional area of the compensation channel is greater than the free cross-sectional area of the inflow opening. In addition, it is preferred that the outflow opening has a free cross-sectional area that is greater than or equal to the free cross-sectional area of the compensation channel so as to avoid excessive flow resistance at the outflow opening. 
     In particular, assuming that the inflow opening and the compensation channel have circular cross-sectional shape, a first geometric diameter D 1  can be defined for the inflow opening, and a second geometric diameter D 2  can be defined for the compensation opening. Further assuming that the downstream end of the inflow opening and the upstream end of the compensation opening are spaced by a distance W, an opening angle a can be defined by the following equation: 
     
       
         
           
             
               tan 
               ⁢ 
               α 
             
             = 
             
               
                 
                   
                     D 
                     ⁢ 
                     2 
                   
                   - 
                   
                     D 
                     ⁢ 
                     1 
                   
                 
                 
                   2 
                   ⁢ 
                   W 
                 
               
               . 
             
           
         
       
     
     The above definition of the opening angle can be readily generalized to situations where the inflow opening and the compensation channel do not have circular cross-sectional shape by replacing the geometric diameters D 1 , D 2  of the inflow opening and of the compensation channel by their corresponding hydraulic diameters, the hydraulic diameter D of an opening or channel being defined as D=4A/P, where A is the cross-sectional area and P is the perimeter of the opening/channel. For a circular cross-section, the hydraulic diameter is identical to the geometric diameter. It is advantageous if the thus-defined opening angle is in the range of 2° to 4°. This finding is independent of the exact cross-sectional shapes of the inflow opening and the compensation channel, at least as long as the aspect ratio of each opening or channel is not too large. In the context of the present disclosure, the term “aspect ratio” is to be understood as relating to the ratio between the longest diametral dimension and the shortest diametral dimension of the clear cross section of an opening or channel, the term “diametral dimension” relating to a distance between two points on opposite sides of the perimeter of the clear cross section, a straight line through these points passing through the geometric center (centroid) of the clear cross section. For instance, under this definition of the term “aspect ratio”, the aspect ratio of a circle is 1:1; for a square, it is √{square root over (2)}:1, etc. In particular, the above-mentioned preferred range of the opening angle of 2° to 4° is expected to be valid at least as long as the aspect ratio is below approximately 2.5:1, such as for a rectangle with a ratio between its long and short edges below about 2:1, a trapezoid with a ratio of average length to height between about 1:2 and about 2:1, an ellipse with a ratio between major and minor axis below 2.5:1, etc. Ideally, the cross-sectional areas of the inflow opening and of the compensation channel are chosen and oriented such that the cross-sectional area of the compensation channel fully covers the cross-sectional area of the inflow opening in a projection along the jet axis. 
     For larger aspect ratios, different opening angles might be optimal. 
     In some embodiments, the compensation channel is formed by a compensation opening in a separating wall that is common to both the supply channel and the discharge channel. In particular, the duct probe can have tubular shape, preferably cylindrical shape, and comprise a straight, flat separating wall that separates the discharge channel from the supply channel inside the duct probe. In other embodiments, the compensation channel can be formed in a different manner, e.g., by a short pipe between the supply channel and the discharge channel if these channels are formed by separate tubes. 
     The duct probe can be complemented by an environmental sensor to form a complete duct sensor. The environmental sensor can comprise a measurement channel and a sensing element inside or adjacent to the measurement channel, the measurement channel being directly or indirectly connected to the open ends of the supply channel and the discharge channel of the duct probe. In this manner, a partial flow that enters the supply channel through the inflow opening flows through the supply channel into the measurement channel, passes the sensing element, and flows from the measurement channel through the discharge channel into the outflow opening. The connection between the duct probe and the environmental sensor can be direct, e.g., by directly mounting a sensor housing of the environmental sensor on the duct probe, or it can be indirect, e.g., via rigid or flexible tubing. 
     In particular, the environmental sensor can be a particulate matter sensor. In order to create the partial flow at a defined flow rate, the environmental sensor can comprise a fan. 
     A method of operating such a duct sensor can comprise:
         arranging the duct probe in a duct, the longitudinal axis of the duct probe extending across a main flow direction of the duct;   generating a main fluid flow through the duct along the main flow direction, thereby causing a jet flow through the inflow opening towards the compensation channel; and   diverting a partial flow from the inflow opening into the supply channel, passing the partial flow through the measurement channel past the sensing element, and passing the partial flow through the discharge channel to the outflow opening.       

     In particular, the duct sensor is operated under such conditions that the jet flow is decelerated when it passes through the compensation channel, i.e., the jet flow has a higher maximum velocity upstream from the compensation channel than downstream from it, in order to efficiently reduce the pressure difference between the supply channel and the discharge channel. The jet flow is generated by accelerating the fluid that passes through the inflow opening. Specifically, the jet flow advantageously has a maximum velocity in the supply channel downstream from the inflow opening and upstream from the compensation channel that exceeds an average velocity of the main fluid flow at the same location that would be present in the absence of the duct probe. 
     Advantageously, the fluid of the main fluid flow is a compressible fluid. Preferably the fluid is a gas, in particular, air, or an aerosol, i.e., a suspension of fine solid particles or liquid droplets in a gas such as air. 
     As already discussed, the environmental sensor can be a particulate matter sensor, and the method can comprise determining a particle concentration and/or size distribution in the partial flow, using the particulate matter sensor. However, the environmental sensor can also be any other type of sensor for determining at least one property of the partial flow, such as a gas sensor for determining a composition and/or concentration of one or more analyte gases in the partial flow, a humidity sensor, a temperature sensor etc. 
     The environmental sensor can comprise a fan, and the method can comprise sustaining the partial flow using the fan. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Preferred embodiments of the invention are described in the following with reference to the drawings, which are for the purpose of illustrating the present preferred embodiments of the invention and not for the purpose of limiting the same. In the drawings, 
         FIG. 1  shows, in a highly schematic manner, a longitudinal sectional view of a duct sensor comprising a duct probe according to the prior art: 
         FIG. 2  shows a two-dimensional diagram that illustrates a simulated pressure distribution inside and outside the duct probe in  FIG. 1 ; 
         FIG. 3  shows a diagram illustrating the pressure difference between the supply channel and the discharge channel of the duct probe in  FIG. 1  as a function of the flow velocity of the main fluid flow in the duct; 
         FIG. 4  shows, in a highly schematic manner, a longitudinal sectional view of a duct sensor comprising a duct probe according to the present invention; 
         FIG. 5  shows a diagram illustrating the relative sizes of the inflow opening, the compensation opening, and the outflow opening; 
         FIG. 6  shows a two-dimensional diagram that illustrates a simulated pressure distribution inside and outside the duct probe in  FIG. 4 ; 
         FIG. 7  shows a diagram illustrating the pressure difference between the supply channel and the discharge channel of the duct probe in  FIG. 4  as a function of the flow velocity of the main fluid flow in the duct; 
         FIG. 8  shows, in a highly schematic manner, a front view of a portion of a duct probe that has two inflow openings of different sizes and two associated compensation openings; 
         FIG. 9  shows, in a highly schematic manner, a front view of a portion of a duct probe that has a slit-like inflow opening and an associated slit-like compensation opening; 
         FIG. 10  shows, in a highly schematic manner, a cross-sectional view of a duct probe having circular-cylindrical shape and having a separating wall that separates the interior of the duct probe into a supply channel and a discharge channel; and having an oval outer boundary and two separate tubes inside, which form a supply channel and a discharge channel. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG. 1  illustrates, in a highly schematic manner and not to scale, a duct sensor that includes a duct probe  20  according to the prior art. 
     An environmental sensor  30  comprises a sensor element  31  that is housed in a sensor housing  32 . The sensor housing  32  defines a measurement channel  33 , the sensor element  31  being arranged in or adjacent to the measurement channel  33 . 
     The environmental sensor  30  is arranged outside a duct  10  that carries a main fluid flow Fm. The duct  10  is delimited by a duct wall  11 . An elongated duct probe  20  extends from the sensor housing  32  through a probe opening of the duct wall  11  into the inside of the duct  10 . The duct probe  20  defines a longitudinal axis L that extends perpendicular to the main fluid flow Fm. Inside the duct probe  20 , two parallel channels extend along the longitudinal axis L: a supply channel  21  and a discharge channel  22 . The channels are separated by a separating wall  25 . Each channel is closed at its respective end that is located inside the duct  10 , while it is open at its respective end that is connected to the environmental sensor  30  outside the duct  10 . A lateral inflow opening  23  is present in the circumferential side wall of the supply channel  21 , facing the main fluid flow Fm. A lateral outflow opening  24  is present in the circumferential side wall of the discharge channel  22 . The outflow opening  24  is arranged downstream from the inflow opening  23  with respect to the main fluid flow Fm, facing away from the main fluid flow Fm. 
     At its open end, the supply channel  21  opens out into the measurement channel  33 . The measurement channel  33  in turn opens out into the discharge channel  22 . The measurement channel  33  forms the only connection between the supply channel  21  and the discharge channel  22 . In particular, the supply channel  21  and the discharge channel  22  are not connected anywhere along the length of the duct probe  20  between their closed and open ends, i.e., the separating wall  25  does not have any openings. 
     In operation, the main fluid flow Fm in the duct  10  hits the duct probe laterally. The main fluid flow Fm creates a positive backpressure at the inflow opening  23  and a negative pressure at the outflow opening  24  due to the Venturi/Bernoulli effect. The resulting pressure difference between the inflow opening  23  and the outflow opening  24  depends on the flow rate of the main fluid flow Fm. 
     As a result of the pressure difference, a partial flow Fp is created through the duct sensor. The partial flow enters the supply channel  21  through the inflow opening  23 . The partial flow Fp flows upwards through the supply channel  21  into the measurement channel  33 , past the sensor element  31 , and downwards through the discharge channel  22 , before leaving the duct probe  20  at the outflow opening  24 . The sensor element  31  detects one or more properties of the partial flow Fp. The flow rate of the partial flow Fp strongly depends on the pressure difference between the supply channel  21  and the discharge channel  22 , which in turn strongly depends on the flow rate of the main fluid flow Fm. 
       FIG. 2  illustrates a simulated pressure distribution inside and outside the duct probe  10 . The data shown in this figure were created through a numerical simulation of fluid dynamics, using the software COMSOL Multiphysics, Version  5 . 4 . The following assumptions were made in the simulation: The duct  10  has a square cross section with a clear width of 120 mm and a height of 100 mm. The duct probe  20  has a circular cross section with an outer diameter of 15 mm and a wall thickness of 1.5 mm. Inside the duct probe, a straight, flat separating wall  25  of thickness 1.5 mm separates the supply channel  21  from the discharge channel  22 . The length of the portion of the duct probe  20  that extends inside the duct is 50 mm. The inflow opening  23  has circular shape with a diameter of 2.0 mm. Its centre is located at a distance of 30 mm from the duct wall. 
     Likewise, the outflow opening  24  has circular shape with a diameter of 2.0 mm; its centre is also located at a distance of 30 mm from the duct wall. The fluid used for the simulations was air at standard conditions (1013 hPa, 20° C.). A main fluid flow Fm having a homogeneous flow velocity distribution with a flow velocity of 12 m/s at the entrance of the duct was assumed. A k-epsilon turbulence model was used. The flow resistance of the environmental sensor was assumed to be essentially infinite, resulting in a negligible flow rate of the partial flow Fp. 
     The simulation results in  FIG. 2  demonstrate the presence of a considerable pressure difference dp between the supply channel  21  and the discharge channel  22 . 
     The simulation was repeated for different flow rates of the main fluid flow Fm, with flow velocities at the duct entrance in the range between 0 and 12 m/s.  FIG. 3  illustrates that the pressure difference dp strongly depends on the flow velocity v of the main fluid flow Fm in the duct  10 , rising continuously and monotonically with increasing flow velocity and following approximately a quadratic function. At a flow velocity of 6 m/s, the pressure difference is approximately 32 Pa. At a flow velocity of 12 m/s, the pressure difference is almost 130 Pa. 
     Such a strong dependence of the pressure difference on the flow rate of the main fluid flow Fm may be undesirable. This is true, in particular, in applications where the environmental sensor  30  is a particulate matter sensor for determining a concentration and/or size distribution of particulate matter in the main fluid flow. A well-known type of particulate matter sensor acts as a particle counter, comprising a radiation source and a radiation detector. The radiation source, typically a laser, creates radiation in a measurement zone. The radiation is scattered by particles that enter the measurement zone. The radiation detector, typically a photodetector, registers single scattering events from individual particles. From the frequency of the scattering events and the flow rate through the measurement zone, the number concentration of the particles can be inferred. From the intensity of each scattering event, the size of each particle can be inferred. By combining both quantities, a measure for the mass concentration of the particles can be obtained. Since the flow rate enters the determination of the number density, it is desirable to closely control the flow rate through the environmental sensor  30 . However, the presence of a considerable and strongly varying pressure difference between the supply channel  21  and the discharge channel  22  makes it difficult to control this flow rate. 
       FIG. 4  illustrates, in a highly schematic manner and not to scale, a duct sensor according to an embodiment of the present invention. The general setup of the duct sensor is similar to the prior-art duct sensor in  FIG. 1 . Again, the duct sensor comprises an environmental sensor  30  that includes a sensor element  31  and a sensor housing  32  that defines a measurement channel  33  for a partial flow Fp. In the present example, the environmental sensor  30  further includes a fan  34  for actively sustaining the partial flow Fp through the measurement channel  33 . However, in other embodiments, the fan can be omitted. Furthermore, in the present example, the sensor element  31  is arranged in the measurement channel  33  in such a manner that the partial flow Fp passes through the sensor element  31 . However, in other embodiments, the sensor element  31  may be arranged adjacent the measurement channel  33  such that the partial flow flows over the sensor element  31 , as in the embodiment in  FIG. 1 . 
     As in the prior-art embodiment in  FIG. 1 , a supply channel  21  and a discharge channel  22  extend inside the duct probe  20  along its longitudinal axis L, the channels being parallel to each other and being separated by a straight, flat, elongated separating wall  25 . As in the prior-art embodiment in  FIG. 1 , each channel is closed at its respective end that is located inside the duct  10 , while it is open at its respective end that is connected to the sensor housing  30  outside the duct  10 . As in the prior-art embodiment in  FIG. 1 , a lateral inflow opening  23  is present in the circumferential side wall of the supply channel  21 , facing the main fluid flow Fm, and a lateral outflow opening  24  is present in the circumferential side wall of the discharge channel  22  downstream from the inflow opening  23 . 
     In contrast to the prior-art embodiment in  FIG. 1 , a compensation channel  26  is present between the supply channel  21  and the discharge channel  22  in a region between their respective closed and open ends. The compensation channel  26  is formed by a . compensation opening in the separating wall  25  that separates the supply channel  21  and the discharge channel  22 . The inflow opening  23  and the compensation channel  26  are aligned along a common jet axis. The jet axis extends perpendicular to the longitudinal axis L of the duct probe, along the flow direction of the main fluid flow Fm. In the present example, also the outflow opening  24  is aligned with the jet axis. 
     Because of the presence of the compensation channel  26 , a jet flow Fj is created through the inflow opening  23 , the jet flow being directed towards the compensation channel  26 . The jet flow is decelerated when it passes through the compensation channel  26 , thereby causing a negative pressure difference between the supply channel  21  and the discharge channel  22 . This negative pressure difference counteracts the positive pressure difference that is caused by the main fluid flow Fm when it hits the duct probe  20  and is deflected around it. Thereby the jet flow Fj acts to reduce the pressure difference between the supply channel  21  and the discharge channel  22  that would be present in the absence of the compensation channel  26 . At the same time, the jet flow Fj reduces the dependence of this pressure difference on the flow rate of the main fluid flow Fm. 
     Simulations were carried out to determine the expected velocity distribution inside and around a duct probe as illustrated in  FIG. 4 . The same assumptions were made in the simulation as described above in conjunction with  FIG. 2 . The simulations showed that the jet flow Fj is significantly accelerated when it passes through the inflow opening  23  and decelerated again when it passes through the compensation channel  26 . The maximum flow velocity of the jet flow Fj was much larger in the supply channel  21  upstream from the compensation channel  26  than in the discharge channel  22  downstream from the compensation channel  26 . The maximum flow velocity of the jet flow Fj was also significantly larger than the average flow velocity of the main fluid flow Fm that would be present at the same location in the absence of the duct probe and at the same total flow rate through the duct. 
     In order to ensure that the flow velocity of the jet flow Fj is larger at the upstream side of the compensation channel  26  than at its downstream side, the cross-sectional area of the compensation channel  26  is advantageously larger than the cross-sectional area of the inflow opening  23 . In addition, in order to avoid that the outflow opening forms a bottleneck with excessive flow resistance, the cross-sectional area of the outflow opening  24  is advantageously larger than or equal to the cross-sectional area of the compensation channel  26 . This is illustrated by the way of example in  FIG. 5 . In this example, the inflow opening  23 , the compensation channel  26 , and the outflow opening  24  are assumed to have circular shape. The inflow opening  23  and the outflow opening  24  are each formed in a circumferential wall  27  of the duct probe; the compensation channe 126  is formed in the separating wall  25 . The diameter of the inflow opening  23  is designated as D 1 , the diameter of the compensation channe 126  is designated as D 2 , and the diameter of the outflow opening  24  is designated as D 3 . The corresponding cross-sectional areas are designated as A 1 , A 2 , and A 3 , respectively. The width of the supply channel  21 , measured along the jet axis N between the inflow opening  23  and the compensation channel  26 , is designated as W. In the present example, the discharge channel  22  has the same width W between the compensation channel  26  and the outflow opening  24 . In order to decelerate the jet flow when it passes through the compensation channel  26 , the cross-sectional area of the compensation channe 126  is somewhat larger than the cross-sectional area of the inflow opening  23 , i.e., D 2 &gt;D 1 . In the present example, the cross-sectional area of the outflow opening  24  is the same as the cross-sectional area of the compensation channe 126 , i.e., D 3 =D 2 . 
     Generally speaking, the parameters D 1 , D 2 , D 3 , and W, among others, can be tuned to optimize the dependence of the pressure difference between the supply channel  21  and the discharge channel  22  on the flow rate of the main fluid flow Fm. In order to more easily quantify the difference between the sizes of the inflow opening  23  and the compensation channe 126  independent of absolute dimensions, a dimensionless opening angle a can be introduced, which is defined by the following relationship: 
     
       
         
           
             
               tan 
               ⁢ 
               α 
             
             = 
             
               
                 
                   D 
                   ⁢ 
                   2 
                 
                 - 
                 
                   D 
                   ⁢ 
                   1 
                 
               
               
                 2 
                 ⁢ 
                 W 
               
             
           
         
       
     
     Instead of using the geometric diameters D 1 , and D 2 , the corresponding hydraulic diameters may be used. 
     In order to evaluate the effects of the jet flow Fj on the pressure difference between the supply channel  21  and the discharge channel  22 , simulations of the pressure distribution inside and around the duct probe in  FIG. 4  were carried out, again with the same assumptions as described above in conjunction with the simulations shown in  FIG. 2 . The opening angle a was varied, and the dependence of the pressure difference between the supply channel  21  and the discharge channel  22  on the flow velocity of the main fluid flow Fm upstream from the duct probe was evaluated for each opening angle. It was found that the optimum value for the opening angle α was (2.7±0.3)°, leading to the smallest variation of the pressure difference for flow velocities between 0 and 12 m/s. While this result was achieved for the specific probe dimensions discussed above in conjunction with  FIG. 2 , the result is expected to depend only weakly on the absolute dimensions of the probe, on the exact shape of the probe, or on the shape of the openings as long as these variations are within reasonable bounds. Of course, for a completely different geometry of the duct probe or for completely different shapes of the openings (e.g., narrow slits having a large aspect ratio), different opening angles might be optimal. 
       FIG. 6  shows a two-dimensional diagram that illustrates the resulting pressure distribution at the optimum opening angle of 2.7° for a flow velocity of 12 m/s. As expected, the pressure distribution is almost unchanged as compared to the diagram in  FIG. 2  outside the duct probe. However, as a result of the jet flow Fj, pressure is dramatically reduced (from almost +100 Pa to approximately −10 Pa) inside the inflow opening. The pressure inside the supply channel  21  is reduced from approximately +100 Pa to approximately −6 Pa. On the other hand, the pressure in the discharge channel  22  has risen from approximately −27 Pa to approximately −6 Pa, again, which again is due to the jet flow Fj. The resulting total pressure difference between the supply channel  21  and the discharge channel  22  is almost zero. 
       FIG. 7  shows the dependence of the simulated pressure difference dp between the supply channel  21  and the discharge channel  22  on the flow velocity of the main fluid flow Fm upstream from the duct probe for the optimized opening angle of 2.7°. For flow velocities between 0 and 12 m/s, the pressure difference never exceeds 1.7 Pa, having a maximum at a flow velocity of approximately 6 m/s and being close to zero at a flow velocity of 12 m/s. This is in contrast to the simulated pressure difference for a conventional duct probe in  FIG. 3 , which sharply rises with increasing flow velocity and exceeds 120 Pa at a flow velocity of 12 m/s. These simulation results show that the present invention can achieve a massive reduction of the pressure difference and of its dependence on the flow rate of the main fluid flow Fm. 
     While the simulations were carried out for a single inflow opening  23 , a single outflow opening  24 , and a compensation channel  26  in the form of a single compensation opening, each of these openings having circular shape, different numbers and geometries of these openings are conceivable. This illustrated by way of example in  FIGS. 8 and 9 . 
       FIG. 8  illustrates that more than one set of inflow openings and compensation channels can be provided. These sets may have different dimensions. Thereby, the dependence of the pressure difference on the flow velocity of the main fluid flow Fm can be further optimized. In the example of  FIG. 8 , a first jet flow is created through a first inflow opening  23  and a first compensation channel  26 . A second jet flow is created through a second inflow opening  23 ′ and a second compensation channel  26 ′. Due to the different dimensions of the inflow openings and compensation channels, the negative pressure difference that is caused by each jet flow will be different for the two jet flows. By tailoring the dimensions of the inflow openings and compensation channels, the dependence of the pressure difference between the supply and discharge channels on the flow velocity of the main fluid flow Fm can be optimized. The outflow openings are not illustrated in  FIG. 8 . Instead of providing separate outflow openings for each set of first and second inflow openings and compensation channels, it is conceivable to provide a single common outflow opening. 
       FIG. 9  illustrates that the inflow opening, the outflow opening and the compensation channel can each have a cross-sectional shape that is different from circular. In the present example, the cross-sectional shape of the inflow opening and of the compensation channel is slit-like and trapezoidal, the cross-sectional area of the compensation channel fully covering the inflow opening in a projection along the common jet axis. By optimizing shape and size of the inflow opening and the compensation channel, again the dependence of the pressure difference between the supply and discharge channels on the flow velocity of the main fluid flow Fm can be optimized. 
     Of course, many other shapes of the inflow opening(s) and compensation channel(s) are conceivable. 
     While the simulations in the above-described examples were carried out for a circular-cylindrical duct probe having a straight, flat separating wall, different probe designs may be used. This is illustrated in  FIGS. 10 and 11 . In the embodiment of  FIG. 10 , the duct probe has circular cross section and a straight, flat separating wall  25 , in which a compensation channel  26  in the form of a simple compensation opening is formed. The partial flow Fp through the supply channel  21  and the discharge channel  22  is indicated by dots and crosses within a small circle, a dot indicating a flow direction out of the drawing plane, and a cross indicating a flow direction into the drawing plane. The jet flow Fj is indicated by an arrow drawn in a broken line. In the embodiment of  FIG. 11 , the duct probe has an oval cross section. Two parallel tubes are arranged within the duct probe. forming the supply channel  21  and the discharge channel  22 . A compensation channel  26  is formed by a short pipe  28  between the tubes. Many other probe designs are conceivable, including designs with more than one supply channel and/or more than one discharge channel. 
     While in the embodiment of  FIG. 4  the environmental sensor  30  is directly connected to the open ends of the supply channel  21  and discharge channels  22 , it is also conceivable to connect the environmental sensor  30  to the duct probe  20  via rigid or flexible tubing. 
     The present invention is of particular advantage if the environmental sensor  30  is a particulate matter sensor for determining a concentration and/or size distribution of particulate matter in the main fluid flow. However, the environmental sensor  30  does not need to be a particulate matter sensor. In other embodiments, the environmental sensor may be a gas sensor for determining a composition and/or concentration of one or more analyte gases in the main fluid flow, a humidity sensor, a temperature sensor etc. 
     The present invention makes it possible to closely control the flow rate through the environmental sensor  30 , e.g., by using an integrated fan, without the need to compensate for a pressure difference inside the duct probe that is created by the main fluid flow. 
     
       
         
           
               
             
               
                   
               
               
                 LIST OF REFERENCE SIGNS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 10 
                 duct 
               
               
                   
                 11 
                 duct wall 
               
               
                   
                 20 
                 duct probe 
               
               
                   
                 21 
                 supply channel 
               
               
                   
                 22 
                 discharge channel 
               
               
                   
                 23, 23′ 
                 inflow opening 
               
               
                   
                 24, 24′ 
                 outflow opening 
               
               
                   
                 25 
                 separating wall 
               
               
                   
                 26, 26′ 
                 compensation channel 
               
               
                   
                 27 
                 circumferential wall 
               
               
                   
                 28 
                 pipe 
               
               
                   
                 30 
                 environmental sensor 
               
               
                   
                 31 
                 sensing element 
               
               
                   
                 32 
                 sensor housing 
               
               
                   
                 33 
                 measurement channel 
               
               
                   
                 34 
                 fan 
               
               
                   
                 Fm 
                 main fluid flow 
               
               
                   
                 Fp 
                 partial flow 
               
               
                   
                 Fj 
                 jet flow 
               
               
                   
                 L 
                 longitudinal axis 
               
               
                   
                 N 
                 jet axis 
               
               
                   
                 A1, A2, A3 
                 cross-sectional area 
               
               
                   
                 D1, D2, D3 
                 diameter 
               
               
                   
                 W 
                 width 
               
               
                   
                 α 
                 opening angle