Differential pressure sensors having non-smooth interior surfaces and uses thereof

Abstract

The present teachings relate to differential pressure sensors and methods for measuring the pressure difference across two pressure taps in fluid communication with the interior of a constant diameter throat having a non-uniform interior surface. The differential pressure sensor can enable the determination of flow rate as well as proxies for fluid viscosity and density. The internal surface of the throat is non-uniform, which improves the accuracy of pressure measurements across the laminar flow regime transitioning into the turbulent flow regime. The pressure taps enable the measurement of the differential pressure across the throat, either by measuring the absolute pressures at each tap or the pressure differential between the taps, facilitating a more accurate analysis of fluid properties.

Description

[0001] Attorney Docket No. WFU0023PCT

[0002] Differential Pressure Sensors Having Non-Smooth Interior Surfaces and Uses Thereof

[0003] CROSS REFERENCE TO RELATED APPLICATIONS

[0004] This patent application claims the benefit of and priority to U.S. Patent Application No. 63 / 788,417, filed on April 14, 2025, which application is incorporated by reference herein in its entirety for all purposes.

[0005] BACKGROUND

[0006] Differential pressure sensors are widely utilized across various industries to measure the pressure difference between two points in a system with many different applications. For example, differential pressure sensors are used in HVAC systems, in medical devices such as respirators, infusion pumps, and blood pressure monitors, in clean rooms and laboratories, in industrial processes, and in automotive applications.

[0007] Accurate pressure measurements are crucial for maintaining optimal system performance, detecting faults, and ensuring safety. In many fluid flow systems, the pressure differential is directly related to the flow rate of the fluid. However, as fluid flow conditions change, particularly during the transition from laminar to turbulent flow regimes, conventional differential pressure sensors often struggle to provide accurate readings.

[0008] Laminar flow, which occurs at lower velocities and is characterized by smooth, orderly fluid movement, is relatively easy to measure. In contrast, when the flow rate increases and transitions into the turbulent flow regime, the fluid flow becomes irregular and chaotic, introducing complex dynamics that can degrade the accuracy of conventional differential pressure sensors. This transition leads to unpredictable pressure losses and fluctuations, for which existing differential pressure sensors cannot effectively account.

[0009] Differential pressure flow sensors (or meters), which are commonly used to measure fluid flow and properties in situ, function by measuring pressure drops across constrictions such as orifice plates or Venturi tubes. These devices are particularly useful in uniform diameter tubes for simple and economical fluid flow measurements. Traditional differential pressure sensors typically assume a constant relationship between pressure differential and flow rate, a model that becomes unreliable during fluid flow transitions. As the fluid flow increases and transitions to becoming turbulent, pressure losses increase unpredictably, leading to measurement errors that affect system control, performance, and reliability.Attorney Docket No. WFU0023PCT

[0010] Further, the issues such as hydrodynamic entrance length and the transition to turbulent flow as flow rates vary can limit the effectiveness of these differential pressure sensors, making them only viable under carefully controlled conditions.

[0011] In-line viscometers can be integrated into the process fluid flow, offering continuous in situ viscosity monitoring without disrupting the fluid flow. Capillary rotational and acoustic viscometers can be adapted to be such in-line devices as well. Optical methods, such as laser-induced fluorescence and optical coherence tomography, can provide high-resolution, real-time viscosity data by examining how light interacts with the flowing fluid. In addition, electromagnetic viscometers use electromagnetic fields for viscosity measurement, which methods are particularly useful for conductive liquids. However, each of these methods has limitations and / or disadvantages. For example, capillary rotational meters introduce high pressure drops and include mechanical parts that are prone to wear. Optical, electromagnetic and acoustic methods are relatively expensive and can be disrupted by external factors such as system vibrations and electromagnetic fields induced by devices such as solenoid flow valves.

[0012] In situ methods for fluid density measurement include vibrating tube densitometers, pressure column differential sensors, and nuclear-based techniques. Vibrating tube densitometers can determine density by measuring the frequency shift of an oscillating tube filled with the fluid. Pressure column differential sensors can measure a pressure drop across a known vertical distance to infer density. Nuclear techniques, such as gamma-ray attenuation, can assess density based on the absorption of radiation as it passes through the fluid. These methodologies also have limitations and / or disadvantages. For example, vibrating tube densitometers are prone to be disrupted by system vibrations produced external to the device. Pressure column differential sensors depend on the device maintaining the precise horizontal orientation, which will differ for systems and devices deployed in the field. Nuclear techniques are highly technical and expensive.

[0013] Thus, there is a need for improved differential pressure sensors capable of providing accurate measurements across a wider range of fluid flow conditions, including the challenging transition from laminar to turbulent flow regimes. The present teachings address the challenges faced by conventional differential pressure sensors by incorporating advanced features and novel designs that can provide more precise and reliable differential pressure measurements, which in turn can lead to more accurate flow rate measurements andAttorney Docket No. WFU0023PCT

[0014] determination of fluid properties such as the viscosity and density.

[0015] SUMMARY

[0016] It has now been discovered that apparatus and methods can more accurately measure the flow rate of a fluid flowing through a constant cross-sectional area, e.g., constant diameter, tube (or throat) even as the flow rate changes from a laminar flow regime to a turbulent flow regime thereby providing differential pressure sensors with increased accuracy in determining flow rate of a fluid through the tube. In particular, a non-smooth surface, for example, a roughened surface, can be created in and / or added to the interior surface of a differential pressure sensor to regulate the velocity profiles through the tube and changes in flow rates. Regularizing the velocity profiles smooths the relationship between flow rate and pressure drop, mitigating unstable effects which occur during boundary layer development, turbulent transition and fully turbulent flow regimes. This effect allows for more regular relationships between the pressure drop and flow rate of a fluid through the device, which in turn allows for more accurate and regular in situ measurement of flow rates and fluid properties such as viscosity and / or density.

[0017] That is, if the flow rate and density of a fluid are known or measured elsewhere, the pressure differential can be used to determine or calculate the viscosity of the fluid. Similarly, if the flow rate (velocity) and viscosity of a fluid are known or measured elsewhere, the pressure differential can be used to determine or calculate the density of the fluid. In situ monitoring of these fluid properties can improve system operation and maintenance by guiding adjustments to the system to optimize performance.

[0018] Accordingly, in one aspect, the present teachings provide an improved differential pressure sensor designed to measure the pressure drop across a fluid flow system, particularly in applications where the flow can transition between laminar and turbulent regimes. The differential pressure sensor generally comprises a tube with an inlet, an outlet, and a throat located between the two, where the throat has a substantially constant internal diameter that is equal to or smaller in diameter than the inlet and outlet of the tube. An internal diameter of the throat typically is measured without consideration for any irregularities or protrusions from the internal surface of the throat or tube. A longitudinal axis through the tube and the throat from the inlet to the outlet of the tube defines a downstream direction. At least a portion of the internal surface of the throat is characterized by a non-smooth surface, whichAttorney Docket No. WFU0023PCT

[0019] plays a role in improving measurement accuracy of the sensor, especially during the transition of flow regimes.

[0020] The non-smooth surface of the throat can feature irregularities, protrusions, or grooves that can disrupt the flow and introduce controlled turbulence, allowing for a more accurate measurement of pressure differentials when flow conditions change. These surface irregularities may take various forms, including but not limited to an irregular distribution of protrusions, a pattern of protrusions (e.g., of polygons such as squares, rectangles, hexagons, octagons and combinations thereof), circumferential grooves (e.g., threads), or a roughened or an uneven texture. The non-smooth interior surface can be present on a portion of the throat (e.g., near the upstream end, in the middle, near the downstream end, and combinations thereof) or along the entire throat.

[0021] The differential pressure sensor also includes two pressure taps: a first pressure tap located near the upstream end of the throat and a second pressure tap located near the downstream end of the throat, to permit determination of the pressure differential within the throat between the two pressure taps. The pressure taps are in fluid communication with the interior of the throat.

[0022] The differential pressure sensor can include a pressure measurement assembly, such as a digital or an analog pressure measurement device. The pressure measurement assembly can include a digital pressure gauge, which can be connected to the pressure taps to measure the differential pressure. The pressure measurement assembly can communicate wirelessly and / or through a wired connection to a computer system and / or a central processing unit (CPU) for further analysis, recording, and action.

[0023] In another aspect, the present teachings provide methods of using a differential pressure sensor as described herein. In various embodiments, the methods include flowing a fluid through the throat at a constant or varying flow rate; measuring the pressure drop across the two pressure taps; and visualizing, recording, transmitting, reporting, analyzing, processing, actuating an action, integrating with other information, alerting, and / or archiving a measured pressure drop. The measured pressure drop can also be used to determine and / or calculate fluid properties such as viscosity and density, which can be further utilized for process control or to actuate specific actions based on the results. The fluid being measured can be a gas, such as a gaseous hydrocarbon (e.g., methane, propane, propylene, ethane, butane, and combinations thereof) or hydrogen (and combinations thereof with hydrocarbonAttorney Docket No. WFU0023PCT

[0024] gases). The differential pressure sensor can be used to optimize the performance of a fluid flow system, detect blockages, and / or monitor the condition of filtration systems.

[0025] DESCRIPTION OF THE DRAWINGS

[0026] It should be understood that the drawings described below are for illustration purposes only. Like numerals generally refer to like parts. The drawings are not necessarily to scale, with emphasis generally being placed upon illustrating the principles of the present teachings. The drawings are not intended to limit the scope of the present teachings in any way.

[0027] FIG. 1 is a schematic diagram of a differential pressure flow meter (sensor) using the Bernoulli effect.

[0028] FIG. 2 is a schematic diagram of a differential pressure flow sensor having a substantially constant internal diameter through its throat.

[0029] FIG. 3 is a schematic diagram of the development of a fluid flow profile inside a constant internal diameter tube (or throat).

[0030] FIG. 4A and 4B are schematic diagrams of the velocity profiles of a fluid in a tube (or throat) for laminar fluid flow (FIG. 4A) and turbulent fluid flow (FIG. 4B).

[0031] FIGS. 5A-5C are side cross-sectional schematic diagrams of embodiments of differential pressure sensors of the present teachings. FIG. 5A depicts an embodiment of a differential pressure sensor. FIG. 5B is an embodiment of a differential pressure sensor including a pressure measurement assembly in wired communication with a central processing unit (CPU) of a computer system. FIG. 5C is a differential pressure sensor including a pressure measurement assembly which includes a digital differential pressure gauge and wireless communication with the CPU of a computer system.

[0032] FIGS. 6A- 6E are cross-sectional perspective partial views of embodiments of throats of the present teachings. FIGS. 6F is an end cross-sectional view of the throat of FIG. 6B. FIG. 6G is a side cross-sectional view of an embodiment of a throat having an internal surface layer different from its external surface layer. These figures exemplify various nonsmooth interior surfaces of throats of the present teachings.

[0033] FIG. 7 is a graph of the experimental pressure drop measurements versus flow rate with the smooth and rough walled tubes of Example 1.

[0034] FIG. 8 is a graph of the experimental measurements of pressure drop slope versusAttorney Docket No. WFU0023PCT

[0035] flow rate with the smooth and rough walled tubes of Example 1.

[0036] FIGS. 9A-9C are perspective views of differential pressure sensors showing fluid domains for computational fluid dynamics modeling of threaded and smooth throats, where FIG. 9A is a fully threaded interior surface throat, FIG. 9B is a partially threaded interior surface throat with the distal and proximate ends include threading, and FIG. 9C is a smooth interior surface throat.

[0037] FIG. 10 is a graph of pressure drop versus flow rate data obtained by computational fluid dynamics modeling of the threaded and the smooth differential pressure measurement devices of FIGS. 9A-9C.

[0038] FIGS. 11A-11F are velocity profiles at flow rates of 0.25 normal liters per minute (NEPM) and 2 NEPM of gas phase propane at various locations along the sensor tube obtained by computational fluid dynamics modeling of the threaded and the smooth differential pressure measurement devices of FIGS. 9A-9C.

[0039] FIG. 12 is a graph of friction factor versus the inverse of the Reynolds number for tubes having a smooth interior surface throat and having a roughened interior surface throat.

[0040] FIG. 13 is a graph of density estimation versus Reynolds number for both laminar and turbulent parameters for the roughened walled throat tube.

[0041] FIG. 14 is graph of viscosity estimation versus Reynolds number for both laminar and turbulent parameters for the roughened walled throat tube.

[0042] FIG. 15 is a graph of density estimation versus Reynolds number using Equation 9 with data from FIG. 8 and parameters from Table 1 for both smooth and roughened walled throats (tubes).

[0043] FIG. 16 is a graph of density estimation versus Reynolds number using Equation 10 with data from FIG. 8 and parameters from Table 1 for both smooth and roughened walled throats (tubes).

[0044] DETAILED DESCRIPTION

[0045] As described herein, the present teachings generally provide improved differential pressure sensors having a non-uniform interior surface to regulate the velocity profiles across the length of two pressure taps, particularly with changes in fluid flow rates. Further, methods described herein using such differential pressure sensors can more accurately measure theAttorney Docket No. WFU0023PCT

[0046] flow rate of a fluid flowing through a constant cross-sectional area, e.g., constant diameter, tube even as the flow rate changes from a laminar flow regime to a turbulent flow regime. Accordingly, the differential pressure sensors of the present teachings can have increased accuracy in determining flow rate of a fluid through a tube or throat. In particular, without wishing to be bound to any particular theory, it is believed that regularizing the velocity profiles with the non-smooth interior surface smooths the relationship between flow rate and pressure drop, mitigating unstable effects which occur during boundary layer development, turbulent transition and fully turbulent flow regimes. This effect allows for more regular relationships between the pressure drop and flow rate of a fluid through the device, which in turn allows for more accurate and regular in situ measurement of flow rates and fluid properties such as viscosity and / or density.

[0047] That is, a differential pressure measurement sensor (or meter or device, which are used interchangeably herein) utilizing a constant diameter tube or throat between pressure taps is a simple and economical way to measure the flow rate, and determine or calculate density and / or viscosity of a fluid flow in situ. One drawback is the prevalence of turbulence and boundary layer development variability with flow rate, leading to inconsistent measurements. As a solution, it has been demonstrated through experiments and computational modeling that a non-uniform interior wall of the throat of a tube can regulate the flow distribution along the length of the throat and across a range of flow rates.

[0048] Experiments with smooth and rough walled throat tubes show that the devices with roughened or patterned interior surfaces yield more accurate and consistent measurements throughout the developing, laminar, turbulent transition, and fully turbulent flow regimes. In contrast, smooth interior surface throat tubes can typically only operate in certain regimes depending on what is being evaluated.

[0049] Differential pressure sensors are extensively used across various industries to measure the pressure difference between two points in a system. The differential pressure sensors of the present teachings can be used in any application where such a device is needed. More specifically, the differential pressure sensors of the present teachings can be useful to many applications in which there is a variable flow rate of a fluid, and where it may be important to monitor the fluid viscosity and / or density as it is changing with temperature, pressure and fluid species concentrations in real time. In HVAC systems, they can monitor air filters and detect blockages. In medical devices, such as respirators, infusion pumps, and blood pressureAttorney Docket No. WFU0023PCT

[0050] monitors, the devices can ensure accurate readings and patient safety. Differential pressure sensors can be crucial in clean rooms and laboratories for maintaining proper air flow and contamination-free environments. Additionally, in automotive applications, a differential pressure sensor can measure exhaust gas recirculation and monitor particle filters in engines. Finally, in various industrial processes, these sensors can monitor and control process flows, detect leaks, and measure liquid levels in tanks. For example, in fuel cell systems or combustion based devices such as internal combustion engines, water heaters and HVAC systems, a differential pressure sensor can be used in combination with other sensors to measure the species concentrations and flow rates of multiple gas species. See, e.g..

[0051] International Publication No. WO 2025 / [Application No. PCT / US2024 / 056858],

[0052] To facilitate an understanding of the present teachings, a number of terms and phrases are defined below.

[0053] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The abbreviations used herein have their conventional meaning within the chemical arts.

[0054] Throughout the description, where systems are described as having, including, or comprising specific components, or where processes and methods are described as having, including, or comprising specific steps, it is contemplated that, additionally, there are systems of the present invention that consist essentially of, or consist of, the recited components, and that there are processes and methods according to the present invention that consist essentially of, or consist of, the recited processing steps.

[0055] In the application, where an element or component is said to be included in and / or selected from a list of recited elements or components, it should be understood that the element or component can be any one of the recited elements or components, or the element or component can be selected from a group consisting of two or more of the recited elements or components.

[0056] Further, it should be understood that elements and / or features of an apparatus or a method described herein can be combined in a variety of ways without departing from the spirit and scope of the present invention, whether explicit or implicit herein. For example, where reference is made to a particular component of a system, that component can be usedAttorney Docket No. WFU0023PCT

[0057] in various embodiments of systems of the present invention and / or in methods of the present invention, unless otherwise understood from the context. In other words, within this application, embodiments have been described and depicted in a way that enables a clear and concise application to be written and drawn, but it is intended and will be appreciated that embodiments may be variously combined or separated without parting from the present teachings and invention(s). For example, it will be appreciated that all features described and depicted herein can be applicable to all aspects of the invention(s) described and depicted herein.

[0058] The articles “a” and “an” are used in this disclosure to refer to one or more than one (i.e., to at least one) of the grammatical object of the article, unless the context is inappropriate. By way of example, “an element” means one element or more than one element.

[0059] The term “and / or” is used in this disclosure to mean either “and” or “or” unless indicated otherwise.

[0060] It should be understood that the expression “at least one of’ includes individually each of the recited objects after the expression and the various combinations of two or more of the recited objects unless otherwise understood from the context and use. The expression “and / or” in connection with three or more recited objects should be understood to have the same meaning unless otherwise understood from the context.

[0061] The use of the term “include,” “includes,” “including,” “have,” “has,” “having,” “contain,” “contains,” or “containing,” including grammatical equivalents thereof, should be understood generally as open-ended and non-limiting, for example, not excluding additional unrecited elements or steps, unless otherwise specifically stated or understood from the context.

[0062] Where the use of the term “about” is before a quantitative value, the present invention also includes the specific quantitative value itself, unless specifically stated otherwise. As used herein, the term “about” refers to a ±10%, ±5%, ±3% or ±2% variation from the nominal value unless otherwise indicated or inferred from the context.

[0063] At various places in the present specification, variables or parameters are disclosed in groups or in ranges. It should be understood that the endpoints and each intervening integer value and each fraction thereof, as well as each subrange, between the recited endpointsAttorney Docket No. WFU0023PCT

[0064] (upper and lower limits) of that range are specifically disclosed. It is specifically intended that the description include each and every individual sub-combination of the members of such groups and ranges. For example, an integer in the range of 0 to 40 is specifically intended to individually disclose 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, and 40, and an integer in the range of 1 to 20 is specifically intended to individually disclose 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

[0065] The use of any and all examples, or exemplary language herein, for example, “such as” or “including,” is intended merely to illustrate better the present teachings and does not pose a limitation on the scope of the invention unless claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the present invention.

[0066] As a general matter, formulations specifying a percentage are by volume unless otherwise specified. Further, if a variable is not accompanied by a definition, then the previous definition of the variable controls.

[0067] Terms and expressions indicating spatial orientation or altitude such as “upper,” “lower,” “top,” “bottom,” horizontal,” “vertical,” and the like, unless their contextual usage indicates otherwise, are to be understood herein as having no structural, functional or operational significance and as merely reflecting the arbitrarily chosen orientation of the various views of apparatus, devices, components, and features of the present teachings that may be illustrated in certain of the accompanying figures.

[0068] Any particular embodiment of the present disclosure that falls within the prior art can be explicitly excluded from any one or more of the claims. Because such embodiments are deemed to be known to one of ordinary skill in the art, they can be excluded even if the exclusion is not set forth explicitly herein. Any particular embodiment of the disclosure can be excluded from any claim, for any reason, whether or not related to the existence of prior art.

[0069] The disclosure can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The foregoing embodiments are therefore to be considered in all respects illustrative rather than limiting the disclosure described herein. Scope of the disclosure is thus indicated by the appended claims rather than by the foregoingAttorney Docket No. WFU0023PCT

[0070] description, and all changes that come within the meaning and range of equivalency of the claims are intended to be embraced therein.

[0071] A “differential pressure sensor” or a “differential pressure meter” or a “differential pressure device” and similar descriptors used herein can refer to a device having two pressure taps that can measure either absolute pressure in (Pi and / or P2) (see FIG. 5B) or a pressure drop across (ZIP) (see FIG. 5C) a given fixed volume conduit, for example, a conduit having a fixed cross-sectional area perpendicular to the longitudinal axis of the conduit such as a constant diameter tube or throat. The pressure drop across the two pressure taps can be compared against different sensor data as a proxy for viscosity and / or density variation versus the baseline due to changes in gas composition.

[0072] Differential pressure flow sensors are widely used for in situ fluid flow and property measurement of both liquids and gases, leveraging their ability to measure pressure drops across constrictions such as orifice plates, Venturi tubes or simply along a constant diameter tube. For orifice plates and Venturi’s, the Bernoulli effect creates a strong dependence on the fluid density such that the flow rate Q can be calculated by the following equation:

[0073] Equation 1 Q = At[-P12P2

[0074]

[0075] fa- Where A, p and p are the cross-sectional area of the tube, and pressure and density of the fluid, respectively. The subscripts 1 and 2 denote the locations before and after the constriction of the flow, as illustrated in FIG 1.

[0076] For viscosity measurement, it is more useful to rely on the viscous pressure drop through a tube of uniform diameter, such that the Bernoulli effect does not occur between the pressure taps, as depicted in FIG. 2.

[0077] In such a device, the pressure differential along the tube is governed by the following equation:

[0078] Equation 2 p±— p2= Ap =

[0079]

[0080] Where V is the velocity of the fluid, L is the length between positions 1 and 2 of the tube, D is the tube diameter and f is the friction factor. The Reynolds number can be calculated as:Attorney Docket No. WFU0023PCT

[0081] r, ..

[0082] Equation 3n

[0083] Re = pVD

[0084] where / z is the dynamic viscosity.

[0085] 64

[0086] For laminar flow (Re <2000) the friction factor is defined as f = —

[0087]

[0088] , obtained from the Moody diagram (Moody, L. F. (1944) “Friction factors for pipe flow,” Transactions of the ASME, 66 (8): 671-684, which is incorporated by reference herein for its Moody diagram). For turbulent or non-ideal conditions f can also be treated as a calibration parameter related to the geometry and surface roughness. Substituting for f in Equation 2 assuming laminar flow yields:

[0089] Equation 4 P

[0090]

[0091] i — p2= 32 / zE

[0092] Therefore, pressure drop is proportional to the viscosity and velocity. If the velocity can be determined independently, the deviation of the pressure drop from the baseline value can be used as a proxy for the viscosity of the fluid.

[0093] In liquids, these devices offer the advantage of continuous, real-time viscosity and / or density monitoring without disrupting the flow, making them valuable for various industrial applications. They are well-established and versatile, adapting to different liquid types and flow conditions.

[0094] For gases, differential pressure flow meters function similarly but face unique challenges due to the lower density and viscosity along with different flow dynamics of gases. They are effective in providing immediate data and can be adapted to various gas types and flow setups. Nevertheless, gases are more susceptible to turbulence, which can significantly impact measurement accuracy. Within a single process with variable flow rates, the differential pressure measurement device might experience various stages of flow distribution development in laminar, turbulent transition and fully turbulent flow regimes. This invalidates underlying assumptions of the simple relations stated in the prior equations, as the relationship between the friction factor and the Reynolds number will differ based on the flow distribution in the channel for which the pressure drop is being measured. Therefore, a more sophisticated analysis is required to understand the relationship between pressure drop, density, viscosity and flow rate in differential pressure sensors for gases.

[0095] FIG. 3 shows a schematic diagram of the development of the velocity profile of a fluid in a substantially constant diameter tube. In the hydrodynamic entrance region, the shearAttorney Docket No. WFU0023PCT

[0096] stress due to viscous effects are highest at the inlet where the boundary layer is thinnest. This decreases as the flow transitions to a fully developed velocity profile, after which point the shear stress is constant.

[0097] The shape of this fully developed profile is determined by the Reynolds number (Re). For Reynolds number below approximately 2000, the flow will be in the laminar regime, and the velocity profile will develop with a parabolic shape as depicted in FIG. 4A. When the Reynolds number exceeds approximately 3000, the flow transitions to the turbulent regime, and the velocity profile will have a logarithmic shape as depicted in FIG. 4B. As shown in the Moody diagram, there is a discontinuous transition region highlighted between 2000 < Re < 3000 where the profile is less definitive, in which the transition from laminar to turbulent flow regimes takes place.

[0098] If it were the case that the friction factor decreased monotonically with increasing Reynolds number, the measurement of viscosity or density in transition between laminar and turbulent flow would be handled inherently. However, the discontinuity and sudden increase in friction factor which occurs in the transition regime makes measurement within and near this region inconsistent.

[0099] In sum, the pressure drop of a fluid across a constant diameter throat (tube) can be correlated to its flow rate, which in turn can be correlated to the viscosity and the density of the fluid. That is, with the pressure differential of a fluid flowing at a known flow rate along a known length of a constant diameter throat (length between two pressure taps), the viscosity of the fluid can be determined. Knowing the viscosity of a fluid along with the pressure differential of the fluid flowing at a known flow rate along a known length of a constant diameter throat permits determination of the density of the fluid. In the case of determining or calculating the viscosity or density, the flow rate often is determined independently using a flow meter upstream or downstream of the first pressure tap and the second pressure tap, respectively.

[0100] Accordingly, the present teachings provide differential pressure sensors having nonsmooth internal surfaces that can provide fluid flow distribution stabilization for more accurate in situ fluid property and flow rate measurements. The present teachings also include use of the differential pressure sensors as described herein.

[0101] In certain embodiments, the fluid is a gas. The differential pressure sensors andAttorney Docket No. WFU0023PCT

[0102] methods of the present teachings are applicable to any gases, e.g., a mixture of gases. In some embodiments, the gas comprises gaseous hydrocarbons, gaseous hydrocarbons mixtures, hydrogen, and combinations thereof. For example, gaseous hydrocarbons can include methane, ethane, propane, propylene, and butane. The differential pressure sensors and methods also can be used to help determine the flow rate, viscosity or density of any gas mixtures, including those containing uncertain species concentrations, for example, a contaminant.

[0103] In various embodiments, referring to FIG. 5A, the present teachings provide a differential pressure sensor 10 for a fluid comprising a tube 12 having an inlet 14, an outlet 16 and a throat 18 located between the inlet and the outlet. The longitudinal axis 20 through the tube and the throat from the inlet to the outlet defines a downstream direction. The throat comprises a substantially constant internal diameter (d) equal to or smaller than a diameter of the inlet (Di) and a diameter of the outlet (Do). It should be understood that in certain embodiments, the tube can have a diameter of its inlet and outlet, upstream and downstream of the throat, equal to the diameter of the throat, be made of the same material as the throat, and / or include a non-smooth interior surface.

[0104] Returning to FIG. 5A, the internal surface 22 of the throat comprises a non-smooth surface 24, here, grooves in or forming the internal surface. Here, the non-smooth surface is not present in the entire length of the throat. The differential pressure sensor also comprises a first pressure tap 26 located near an upstream end of the throat and in fluid communication with the interior of the throat; and a second pressure tap 28 located near a downstream end of the throat and in fluid communication with the interior of the throat.

[0105] In some embodiments, the non-smooth surface comprises irregularities at random positions along the internal surface of the throat. For example, as shown in FIG. 6A, the interior surface 22’ of the throat 18’ is a roughened surface, having irregularities at random positions 30. In various embodiments, the non-smooth surface is an uneven surfaces such as crumpled paper or a crumpled thin metallic sheet or similar textile or material. Such materials can be crimped or corrugated to create a non-uniform surface. FIG. 6A also shows the presence of a first pressure tap 26’ and the inlet 14’ of the tube 12’.

[0106] In some embodiments, the non-smooth surface comprises a pattern of protrusions on the internal surface of the throat. In certain embodiments, the non-smooth surface comprises a regularly patterned internal surface, for example, a regular surface roughness can be createdAttorney Docket No. WFU0023PCT

[0107] in or added to the interior surface of differential pressure sensor. In some embodiments, the pattern of protrusions is a regular pattern of one or more polygons. The one or more polygons can be squares, rectangles, hexagons, octagons, and combinations thereof. For example, as shown in FIG. 6B, the throat 18’ ’ includes a pattern of protrusions 34 of one or more polygons 32, here, rectangles in cross-sectional shape and flat topped pyramids in three-dimensions. FIG. 6B also depicts a first pressure tap 26”, which pressure tap has an opposing pressure tap 26”’. Further, FIG. 6F is an end cross-sectional view of the throat of FIG. 6B, showing the regular pattern of protrusions, which protrusions are polygons 32 in the crosssection viewed from the interior surface 22” of the throat 18”. The line de shows an internal diameter of throat 18”.

[0108] In particular embodiments, the non-smooth surface comprises grooves in the internal surface of the throat. The grooves can be in a pattern horizontally, vertically, or at any angle(s) in relation to the longitudinal axis of the tube or throat. In embodiments where the grooves intersect, the result can be an irregular or regular pattern of shapes, such as polygon shapes, for example, in patterns as disclosed herein. In some embodiments, the grooves are circumferential around the interior of the throat. FIG. 6C shows concentric non-overlapping grooves 36 in the interior surface of a throat 18’”. In certain embodiments, the grooves are threaded grooves 40 as shown in FIG. 6D for throat 18” ” . In various embodiments, the grooves are in a regular pattern along the longitudinal axis of the throat. In particular embodiments, the non-smooth surface includes or is a roughened surface. In certain embodiments, the non-smooth surface includes or is an uneven textured surface. As shown in FIG. 6E, the non-smooth surface can be a regular pattern of protrusion 34’ such as dimples 32’ in throat 18’””.

[0109] The non-uniform or non-smooth interior surface can be created using one or more of the following manufacturing processes: 3D printing (e.g., particularly of a pattern); threading a throat using, for example, a thread tap; roughing the interior surface with a coarse file, a sanding tool, or similar surface roughing tool or device; machining using Computer Numerical Control (CNC) (e.g., an O-ring groove cutter with custom tooling); chemical etching; chemical deposition; spray coating; injection molding with roughness pattern on the mold; casting with roughness pattern on the mold; and inserting a mesh sleeve or a spring into a throat (similar to an artery stent), and combinations thereof. Additional ways of creating a non-smooth surface in or on the interior surface of a throat include EDM (electricalAttorney Docket No. WFU0023PCT

[0110] discharge machining), waterjet and / or plasma cutting, shaping a thin walled throat from the outside such that a rough or patterned surface is present on the inside, and using corrugated tubing.

[0111] The throat composition includes at its exterior, a non-porous material to contain the fluid. The exterior throat material also should be rigid to maintain a straight constant diameter tubular section for the placement of the pressure taps. For example, a throat can be made of concentric layers of different materials, or can have an exterior layer that is non-porous and rigid. Examples of throat materials for the entire throat or for an exterior layer of a throat include, but are not limited to, any rigid, non-porous material such as silicone, rubber, plastic, metal, and ceramic, and combinations thereof.

[0112] The interior surface of the throat does not have such restrictions. That is, the interior wall and surface of a throat of the presend ng teachings for creating a roughness or pattern could be a porous material and / or a soft material opening up the possibility of using a textile or paper or wood product as the interior surface. For example, an internal layer could be made of a thin, pliable material that can be crimped, shaped, have a pattern applied to it (e.g., dimples or rings), or be compressed longitudinally to create a non-uniform surface such as a corrugated surface. The internal surface of the tube could be made of wood or paper or a textile whose circumference is surrounded by a non-porous material such as concentric “tubes,” with a wood tube sliding into a larger circumference metal one. That is, in certain embodiments, the differential pressure sensor can include a non-smooth surface that comprises a composition of matter different than a composition of matter of an outer circumference layer of the throat. Further, the interior surface could be made of materials adhered to the inner wall of the throat (e.g., the non-porous, rigid material) surface either covering the entire surface with an unevenly textured internal sleeve or creating a pattern on the internal surface of the throat by adhering the material in a patterned way. For example, as shown in FIG. 6G, the exterior layer 41 of the throat 18” ” ” is made of a non-porous, rigid material. The inner layer 43 of the throat, which in this embodiment forms the interior surface of the throat, is encompassed the exterior layer 41. The inner layer could be a paper or textile material which is able to be cut with a pattern, crimped, or roughened, then slid into the exterior layer or positioned by other means.

[0113] In addition, in certain embodiments, a throat can be made by bending and / or shaping a thin-walled sheet of non-porous material into a tubular structure (e.g., a tube or a throat) suchAttorney Docket No. WFU0023PCT

[0114] that a rough or a patterned surface is present on the inside surface. As with an internal layer as discussed above in conjunction with an exterior layer, a thin-walled tube or throat can have a non-uniform surface as its interior surface by crimping, shaping or applying a pattern of polygons, dimples or rings to the thin-walled material so that its interior surface is non-uniform or uneven. A thin-walled tube could also be compressing longitudinally (e.g., to be shaped like corrugated plastic pipe) to create a non-uniform interior surface. It should be understood that the exterior surface of the throat does not need to be smooth but can be of the inverse shape of the interior surface, for example, as with a corrugated structure or design.

[0115] In various embodiments, the non-smooth interior surface is present on a portion of the internal wall of the throat. For example, the non-smooth interior surface can be present on a portion of the throat near its upstream end, in the middle, and / or near its downstream end. FIG. 5A depicts an example where the non-smooth surface 42 is only on a portion of the interior surface in the middle between the two pressure taps. The non-smooth interior surface can be present in regular or irregular, and frequent or sporadic sections along the longitudinal axis of the throat. In certain embodiments, the non-smooth surface is present on substantially the entire or the entire internal wall of the throat. FIG. 5B depicts such an example of a non-smooth surface 44 spanning the entire or substantial! y the entire internal wall of the throat.

[0116] In some embodiments, the differential pressure sensor includes a throat that comprises a smaller internal diameter than an internal diameter of the tube. In certain embodiments, the internal diameter of the tube is constant upstream of and downstream of the throat. In particular embodiments, the internal diameter of the throat is determined without consideration of any irregularities or protrusions therefrom. In some embodiments, the substantially constant internal diameter is measured without consideration of any irregularities or protrusions therefrom. See, e.g., FIG. 6F, diameter de.

[0117] In various embodiments of the present teachings, a differential pressure sensor further comprises a pressure measurement assembly in fluid communication with the first pressure tap and in fluid communication with the second pressure tap. In some embodiments, the pressure measurement assembly is in electrical communication with a central processing unit (CPU) of a computer system. In certain embodiments, the electrical communication is wireless. In particular embodiments, the electrical communication is via wires, or a combination of wireless and wired communications. The pressure measurement assembly comprises a device for measuring the differential pressure between the first and secondAttorney Docket No. WFU0023PCT

[0118] pressure taps, which device can be a digital pressure transducer or an analogue pressure measurement device such as a water column. Further, either the pressure differential can be measured directly, or the two pressures at each pressure tap can be measured independently and the pressure differential calculated as the difference between the two independent measurements.

[0119] As shown in FIG. 5B, in some embodiments, the pressure measurement assembly 50 comprises a first pressure sensor or transmitter 56 in fluid communication with the first pressure tap; and a second pressure sensor or transmitter 56’ in fluid communication with the second pressure tap. The first and second pressure sensors are connected to a CPU 52 of a computer system 54 via hardwired connections 62, 62’.

[0120] In certain embodiments, as shown in FIG. 5C, the pressure measurement assembly comprises a digital differential pressure measurement device 58 such as a device comprising a digital differential pressure gauge 60. The digital differential pressure gauge can display, record, and / or transmit a differential pressure between the first pressure tap and the second pressure tap. The digital differential pressure measure measurement device is connected to a CPU 52 of a computer system 54 via wireless transmission 64. FIG. 5C also depicts a fluid flow sensor 66, upstream of the throat 18” ” ” ’ for determining the flow rate of fluid independent of the differential pressure sensor.

[0121] In various embodiments, the pressure measurement assembly comprises an analog differential pressure measurement device (not shown) such as a manometer, for example, a U-tube manometer or a dial type differential pressure gauge.

[0122] Another aspect of the present teachings includes methods of using the differential pressure sensors as described herein. The methods generally comprise flowing a fluid through the throat of a differential pressure sensor of the present teachings at a substantially constant flow rate; measuring and / or determining the pressure drop across the first pressure tap and the second pressure tap; and visualizing, recording, transmitting, reporting, analyzing, processing, actuating an action, integrating with other information, alerting, and / or archiving a measured pressure drop. In particular embodiments, the methods comprise actuating an action in response to the measured pressure drop, for example, determining the flow rate of the fluid through the throat.

[0123] In various embodiments, the methods further comprise calculating or determining aAttorney Docket No. WFU0023PCT

[0124] viscosity of the fluid, which can provide a measured viscosity of the fluid. In some embodiments, the methods include determining the flow rate of the fluid independent of the differential pressure sensor. In certain embodiments, the methods further comprise actuating an action in response to the measured viscosity of the fluid, for example, adjusting the flow rate of the fluid through the system and / or identifying the presence of an issue with and / or a contaminant in the fluid flow.

[0125] In certain embodiments, the methods further comprise calculating or determining a density of the fluid, which can be a measured density of the fluid. In some embodiments, the methods include determining the flow rate of the fluid independent of the differential pressure sensor. In particular embodiments, the methods further comprise actuating an action in response to the measured density of the fluid. As with a viscosity determination, determination or calculation of a density measurement of the flowing fluid can actuate adjusting the velocity of the fluid through the system and / or identifying the presence of an issue with or a contaminant in the fluid flow.

[0126] The actuated action will depend on the particular application to which the differential pressure sensor is being applied. For example, in an application where the differential pressure sensor is monitoring the flow of fluid downstream of a filter, the differential pressure sensor can alert an operator when the flow rate of the fluid downstream of the filter is below a threshold level indicating that the filter is getting filled and needs to be replaced.

[0127] In various embodiments, the methods further comprise measuring or determining the flow rate of the fluid upstream of or downstream of the throat to provide an independently measured fluid flow rate. In some embodiments, the methods further comprise calculating or determining a viscosity of the fluid using the independently measured flow rate. In certain embodiments, the methods further comprise actuating an action in response to the viscosity of the fluid using the independently measured flow rate. In particular embodiments, the methods further comprise calculating or determining a density of the fluid using the independently measured flow rate. In some embodiments, the methods further comprise actuating an action in response to the density of the fluid using the independently measured flow rate. For example, the viscosity and density derived differential pressure sensor data can be used to estimate the concentrations of constituent species and make corrections to flow rate measurements. Therefore, the fluid flow rate can be dynamically adjusted to compensate for variations in viscosity and density.Attorney Docket No. WFU0023PCT

[0128] In some embodiments, the methods of using the differential pressure sensors as described herein generally comprise flowing a fluid through the throat at a flow rate; measuring and / or determining the pressure drop across the first pressure tap and the second pressure tap; and visualizing, recording, transmitting, reporting, analyzing, processing, actuating an action, integrating with other information, alerting, and / or archiving a measured pressure drop. In certain embodiments, the methods further comprise calculating or determining the flow rate of the fluid.

[0129] Another application in which the differential pressure sensors of the present teachings are useful is in the detection of contaminant species. It has been discovered that a small amount of a contaminant which has different fluid properties than a primary, carrier gas can change the density and / or viscosity flow measurements relative to the flow rate of the fluid. Having real time, in situ calculation or determination of fluid flow properties can aid in the detection of contaminant species. That is, the estimated viscosity (or density) can be used to determine the presence of contaminant species. Accordingly, in certain embodiments, the methods further comprise determining the presence of a contaminant in the fluid based on variations in the viscosity and / or the density of the fluid.

[0130] EXAMPLES

[0131] In order that the disclosure described herein may be more fully understood, the following examples are set forth. The examples should not be construed in any way as limiting the scope of the invention.

[0132] Example 1. Flow in tubes with structured internal surface roughness Experimental measurements of pressure drop were taken for a gas flowing through a device such as the one illustrated in FIG. 2 for a range of flow rates. The diameter of the tube was 1.6 mm and the gas used was propane. In one instance, the device was made of a material with a relatively smooth surface whereas in the second instance the device was made with a material that had a rough surface containing regularly spaced artifacts resulting from the additive manufacturing method used to create the part. It was found that the relationship between the flow rate and pressure drop changed in terms of its power law dependence (increasing from approximately 1.4 to 1.7) as shown in FIG. 7.

[0133] Further data for the slope of the pressure drop versus flow rate was plotted in FIG. 8. The change in this slope correlates with the friction factor and indirectly to the ReynoldsAttorney Docket No. WFU0023PCT

[0134] number according to the Moody diagram. Reynolds number calculations estimate that the transition to turbulent flow should occur between 0.65 and 1 normal liters per minute (NLPM). In this range of flow rates, it was observed that the slope of the smooth wall data first goes down and then begins going up in an irregular fashion, corresponding to the behavior expected for a smooth walled tube according to the Moody diagram. The slope of the curve for the rough walled tube showed a similar discontinuity in this flow range, but the transition occurred in a more regular fashion.

[0135] From this data, without wishing to be bound to any particular theory, it is postulated that the rough surface acts in a beneficial way to regulate the velocity distribution inside the tube. However, the surface roughness which occurred in this tube was not intentional nor controllable. A better solution would be to create a uniform roughness pattern, such as a ribbed or threaded surface, to glean the same effect in a consistent and repeatable manner. Alternatively, a repeatable surface roughness could be achieved by any of the methods described herein such as 3D printing, chemical etching, or controlled substrate deposition.

[0136] Example 2. Computational Fluid Dynamics Simulations

[0137] To obtain further evidence and insights into this phenomena and the possible effectiveness of a device with such a feature, computational fluid dynamics simulations were performed for differential pressure sensors 10’, 10”, 10”’ having three different walls as depicted in FIGS. 9A-9C, respectively: (A) fully threaded 44’; (B) partly threaded 42’ (both with standard screw threads of M2x0.4); and (C) smooth 68. The small vertical tubes protruding from the main tube are representative of the pressure taps 26’, 28’. The inner diameter of the device is 1.7 mm and the gas properties for propane are applied to the fluid.

[0138] Pressure drop curves versus volumetric flow rate were plotted for all three cases in FIG. 10. As shown, the power dependence for the smooth tube is 1.4, very similar to the smooth tube measured experimentally (FIG. 7). The partly threaded tube shows a power dependence of 1.85 and the fully threaded tube is almost exactly 2.0. An exponent of 2 is indicative of a constant value for the friction factor in E uation 2.

[0139] Velocity profiles were compared at flow rates of 0.25 and 2 NLPM at various locations along the sensor tube as shown in FIGS. 11A-1 IF. For the smooth tube (FIGS. 11 A and 1 IB), there is a clear difference in the velocity profile shapes between the two different flow rates. A bias also occurs from top to bottom, such that there is a greater velocity towards the bottom of the tube away from the pressure taps. There is also evidence of under-Attorney Docket No. WFU0023PCT

[0140] developed velocity profile at the location of the first (left most) pressure port at 2 LPM. Overall, the shape of the profiles shift from parabolic at 0.25 LPM to the flattened shape more expected in turbulent flow at 2 LPM as depicted in FIGS. 4A and 4B, respectively.

[0141] For the partly threaded tube (FIGS. 11C and 1 ID), the velocity profiles are overall much more consistent between the two flow rates. They are also consistently parabolic, mimicking fully developed laminar flow. The only flow distribution showing signs of turbulence is the one occurring just before entering the threaded outlet portion at 2 LPM, which has a slightly flattened shape.

[0142] Finally, for the fully threaded tube (FIGS. 1 IE and 1 IF), a very consistent parabolic velocity profile occurs. The profile is consistent through the length of the tube and at each of the compared flow rates. This results in a velocity profile and pressure drop correlation which closely aligns with an ideal, fully developed laminar flow even when conditions are such that the flow would be under-developed or turbulent in nature. It is plausible that this is the mechanism that results in the smooth transition between laminar and turbulent regimes in the flow rate versus pressure drop relation found experimentally for the rough walled tube (FIG.

[0143] 8).

[0144] Example 3. Measuring Density and Viscosity Using Smooth and Roughened Differential Pressure Sensors

[0145] In this example, it is demonstrated how the pressure drop versus flow rate data plotted in FIG. 7 and FIG. 8 is used to estimate either the fluid viscosity or fluid density and how a smooth wall tube compares to a rough walled tube. First the friction factor was plotted versus the inverse of the Reynolds number as shown in FIG. 12, i.e., a plot of friction factor versus the inverse of the Reynolds number for smooth and roughened interior surface tubes.

[0146] It is found that in this particular instance a piecewise linear function, separated for laminar (Re < 2300) and turbulent (Re > 2300) regimes is adequate to fit the data as shown in Equation 5. This is not meant to be a limitation on the possible effective relationships between the friction factor and Reynolds number which might be better resolved by higher order functions or simple proportional factors depending on the situation.

[0147] fa (Re < 2300; a = aL; b = b Eq

[0148] 1uation s

[0149] 1f = - 1- b where: ,L

[0150] Re (Re > 2300; a = aT; b = bTAttorney Docket No. WFU0023PCT

[0151] Table 1. - Friction factor fitting parameters

[0152] FITTING PARAMETER SMOOTH TUBE ROUGH TUBE

[0153] « / . 1164 790

[0154] bL0.082 0.77

[0155] aT-243 -471

[0156]

[0157] bf 0.72 1.31

[0158] Substituting Equation 5 into Equation 2 yields:

[0159] > . , . ( a , , \ pV2L

[0160] Equation 6 Ap = I — + b I — -

[0161]

[0162] Substituting Equation 3 into Equation 6 and simplifying yields:

[0163] Equation 7 A

[0164]

[0165] p = cA- + b Z-- If the flow rate (velocity) and viscosity of the fluid are known or measured elsewhere, the pressure difference can be used to calculate the density as:

[0166] Equation s p

[0167]

[0168] =

[0169] Since the density is required to calculate the Reynolds number, it is not known during operation what the Reynolds number is and it is not possible to choose between the laminar and turbulent values of a and b. However, plotting the density estimation using both the laminar and turbulent parameters (FIG. 13) shows that at any Reynolds number the minimum of the two curves is closest to the real fluid density, with the two curves intersecting at about Re = 2300. Therefore, the density can be estimated as:

[0170] „ . / 2 Ap D di U 2 Ap D ar

[0171] Equation 9 p = mm — -7- - -7- -

[0172]

[0173] “ r \bLV2L b^ VD bf V2L bf VDj

[0174] Alternatively, if the flow rate and density of the fluid are known or measured elsewhere in the system, the pressure difference across the tube can be used to calculate the viscosity as:

[0175] Equation 10 p

[0176]

[0177] = — ~PVD

[0178] Similar to density, viscosity is required to estimate the Reynolds number and determine the correct parameters. The viscosity estimation for both parameter sets was plotted versus Reynolds number in FIG. 14. Unlike density, the two curves approach asymptotically at about Re = 2300, rather than crossing each other, in such a way that the Reynolds must be estimated to decide which parameter set should be used at any given flowAttorney Docket No. WFU0023PCT

[0179] rate. However, whereas density can vary by many orders of magnitude, the viscosity of gases tend to stay within a factor of ~ 10 of each other, so it is possible to have a close enough estimate of the Reynolds number using only the density and a reference value for the viscosity.

[0180] Using the parameters from Table 1 and Equation 9, the density estimate was plotted for both the smooth and rough tubes in FIG. 15. As shown, the rough tube flow data closely estimates the density for the entire flow range, whereas the smooth tube estimate varies greatly, particularly in the laminar regime (Re < 2300). This indicates that the rough tube is effective for measuring density, whereas a smooth tube is only effective in the turbulent regime.

[0181] Using the parameters from Table 1 and Equation 10, the viscosity estimate was plotted for both the smooth and rough tubes in FIG. 16. Note that the Reynolds number is estimated in situ by assuming a reference viscosity of ^ref = 1.0E — 5 [Pa-s], Such an assumption is particularly suitable for mixtures of gaseous hydrocarbons that have relati vely similar viscosides to one another. The assumption is also suitable in cases where a concentrated species of known viscosity is being diluted by small amounts of additional species. For gases where a reference viscosity cannot be estimated, this will have to be a calibration parameter that is adjusted until a stable viscosity measurement across the flow range is found. Similar to density, the rough tube flow data closely estimates the viscosity for the entire flow range. Meanwhile, the smooth tube estimate varies greatly, particularly in the turbulent transition and fully turbulent regimes (Re > 2300) and the under-developed flow regime (Re < 200). This indicates that the rough tube is effective at measuring the viscosity regardless of flow regime, whereas a smooth tube is only effective in the fully developed laminar flow regime

Claims

Attorney Docket No. WFU0023PCTCLAIMS1. A differential pressure sensor for a fluid, the differential pressure sensor comprising:a tube comprising an inlet, an outlet and a throat located between the inlet and the outlet, wherein the longitudinal axis through the tube and the throat from the inlet to the outlet defines a downstream direction, the throat comprises a substantially constant internal diameter equal to or smaller than a diameter of the inlet and a diameter of the outlet, and the internal surface of the throat comprises a non-smooth surface;a first pressure tap located on the throat near an upstream end of the throat and in fluid communication with the interior of the throat; anda second pressure tap located on the throat near a downstream end of the throat and in fluid communication with the interior of the throat.

2. The differential pressure sensor of claim 1, wherein the non-smooth surface comprises irregularities at random positions along the internal surface of the throat.

3. The differential pressure sensor of claim 1, wherein the non-smooth surface comprises a pattern of protrusions on the internal surface of the throat.

4. The differential pressure sensor of claim 3, wherein the pattern of protrusions is a regular pattern of one or more polygons.

5. The differential pressure sensor of claim 4, wherein the one or more polygons comprises squares, rectangles, hexagons, octagons, and combinations thereof.

6. The differential pressure senor of any one of claims 1-3, wherein the non-smooth surface comprises grooves in the internal surface.

7. The differential pressure sensor of claim 6 wherein the grooves are circumferential around the interior of the throat.

8. The differential pressure sensor of claim 6, wherein the grooves are threaded grooves.

9. The differential pressure sensor of any one of claims 6-8, wherein the grooves are in a regular pattern along the longitudinal axis of the throat.

10. The differential pressure sensor of claim 1, wherein the non-smooth surface comprisesAttorney Docket No. WFU0023PCTa roughened surface.

11. The differential pressure sensor of claim 1, wherein the non-smooth surface comprises a composition of matter different than a composition of matter of an outer circumference of the throat.

12. The differential pressure sensor of claim 12, wherein the composition of matter of the outer circumference of the throat is non-porous and rigid.

13. The differential pressure sensor of any one of claims 1-12, wherein the non-smooth surface is present on a portion of the internal wall of the throat.

14. The differential pressure sensor of any one of claims 1-12, wherein the non-smooth surface is present on substantially the entire internal wall of the throat.

15. The differential pressure sensor of any one of claims 1-14, wherein the throat comprises a smaller internal diameter than an internal diameter of the tube.

16. The differential pressure sensor of any one of claims 1-15, wherein the internal diameter of the tube is constant upstream of and downstream of the throat.

17. The differential pressure sensor of any one of claims 1-16, wherein the internal diameter of the throat is determined without consideration of any irregularities or protrusions therefrom.

18. The differential pressure sensor of any one of claims 1-17, wherein the substantially constant internal diameter of the throat is measured without consideration of any irregularities or protrusions therefrom.

19. The differential pressure sensor of any one of claims 1-18, further comprising a pressure measurement assembly in fluid communication with the first pressure tap and in fluid communication with the second pressure tap.

20. The differential pressure sensor of claim 19, wherein the pressure measurement assembly is in electrical communication with a central processing unit (CPU) of a computer system.Attorney Docket No. WFU0023PCT21. The differential pressure sensor of claim 20, wherein the electrical communication is wireless.

22. The differential pressure sensor of any one of claims 19-21, wherein the pressure measurement assembly comprises a first pressure sensor or transmitter in fluid communication with the first pressure tap; and a second pressure sensor or transmitter in fluid communication with the second pressure tap.

23. The differential pressure sensor of any one of claims 19-22, wherein the pressure measurement assembly comprises a digital differential pressure measurement device.

24. The differential pressure sensor of claim 23, wherein the digital differential pressure measurement device comprises a digital differential pressure gauge, wherein the digital differential pressure gauge displays, records, and / or transmits a differential pressure between the first pressure tap and the second pressure tap.

25. A method of using the differential pressure sensor of any one of claims 1-24, comprising:flowing a fluid through the throat at a substantially constant flow rate, measuring and / or determining the pressure drop across the first pressure tap and the second pressure tap; andvisualizing, recording, transmitting, reporting, analyzing, processing, actuating an action, integrating with other information, alerting, and / or archiving a measured pressure drop.

26. The method of claim 25, comprising actuating an action in response to the measured pressure drop.

27. The method of claim 25 or 26, further comprising calculating or determining a viscosity of the fluid.

28. The method of claim 27, further comprising actuating an action in response to the viscosity of the fluid.

29. The method of any one of claims 25-28, further comprising calculating or determining a density of the fluid.

30. The method of claim 29, further comprising actuating an action in response to theAttorney Docket No. WFU0023PCTdensity of the fluid.

31. A method of using the differential pressure sensor of any one of claims 1-24, comprising:flowing a fluid through the throat at a flow rate;measuring and / or determining the pressure drop across the first pressure tap and the second pressure tap; andvisualizing, recording, transmitting, reporting, analyzing, processing, actuating an action, integrating with other information, alerting, and / or archiving a measured pressure drop.

32. The method of claim 31 , further comprising calculating or determining the flow rate of the fluid.

33. The method of claim 31 or 32, further comprising measuring or determining the flow rate of the fluid upstream of or downstream of the throat to provide an independently measured fluid flow rate.

34. The method of claim 33, further comprising calculating or determining a viscosity of the fluid using the independently measured flow rate.

35. The method of claim 34, further comprising actuating an action in response to the viscosity of the fluid using the independently measured flow rate.

36. The method of any one of claims 33-36, further comprising calculating or determining a density of the fluid using the independently measured fluid flow rate.

37. The method of claim 36, further comprising actuating an action in response to the density of the fluid using the independently measured flow rate.

38. The method of any one of claims 26-29 and 33-36, further comprising determining the presence of a contaminant in the fluid based on variations in the viscosity and / or the density of the fluid.

39. The method of any one of claims 25-38, wherein the fluid is a gas.

40. The method of claim 39 wherein the gas comprises gaseous hydrocarbons, gaseous hydrocarbons mixtures, hydrogen, and combinations thereof.

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