Method, System, and Computer-Readable Medium for Compensating Ultrasonic Flow Measurement Error due to Elliptical Deformation of a Fluid Transport Pipe
The method and system address the inaccuracy of flow rate calculations in deformed pipes by calculating the deformation ratio coefficient (K) and adjusting sensor positions to derive the appropriate distance (Z) between ultrasonic sensors, enhancing measurement accuracy and reliability.
Patent Information
- Authority / Receiving Office
- KR · KR
- Patent Type
- Patents
- Current Assignee / Owner
- HS CMT CO LTD
- Filing Date
- 2025-12-02
- Publication Date
- 2026-07-27
AI Technical Summary
Existing flow rate calculation methods for ultrasonic flowmeters are inaccurate and unreliable when the circular cross-section of pipes deforms into an elliptical shape due to aging or ground subsidence, as they assume a circular pipe and do not account for changes in cross-sectional area and ultrasonic angles.
A method and system that corrects flow rate calculations by calculating the deformation ratio coefficient (K) using external measurements of the deformed pipe's dimensions, adjusting sensor positions, and deriving the appropriate distance (Z) between ultrasonic sensors based on elliptical deformation, ensuring accurate flow rate measurement without cutting the pipe.
Improves the reliability and accuracy of flow rate calculations in deformed pipes by accounting for elliptical deformation, reducing time and cost while maintaining measurement precision.
Smart Images

Figure 112025135550370-PAT00023_ABST
Abstract
Description
Technology Field
[0001] The present application relates to a method for calculating (correcting) a flow rate when elliptical deformation occurs in a circular pipe transporting a fluid. Specifically, the present application relates to a method for calculating (correcting) a flow rate to ensure the accuracy and reliability of flow rate measurement when the circular cross-section of the pipe is deformed into an elliptical cross-section, a flow meter system for performing said method, and a recording medium on which a related algorithm is recorded. Background Technology
[0002] Piping used for fluid transport (e.g., pipes transporting gases such as carbon dioxide or ammonia, and water and sewage pipes transporting liquids) is designed to have a circular cross-section considering hydraulic pressure distribution, fluid transport efficiency, ease of maintenance (e.g., prevention of sediment), economic feasibility, or constructability. However, since pipes are intended for long-term use once installed, aging is unavoidable; consequently, the cross-section deforms from a circular shape to an elliptical shape due to changes in the ground where the pipes are buried (e.g., subsidence) or external pressures not anticipated at the time of design.
[0003] However, ultrasonic flowmeters used to calculate pipe flow rates operate by assuming the pipe is a perfect circle. Therefore, if the pipe cross-section changes from a circular shape to an elliptical one, not only does it cause errors in the cross-sectional area that forms the basis of flow rate calculations, but it also poses problems such as reduced reliability and measurement errors resulting from changes in the angles of incidence and reflection of the ultrasound.
[0004] Several techniques regarding the correction of flow rate calculations passing through pipes are presented in patent literature. For example, Patent Document 1 presents a method for calculating the total flow rate by using a flow velocity distribution curve to correct the flow rate in an unmeasured area (near the wall) in order to correct the deviation between the inner diameter specified in the pipe standard and the actual inner diameter, such as in cases of ellipticity. However, this document merely assumes the pipe is circular and compensates for the radius (R) error through a correction formula. Since this technique does not reflect changes in reality (e.g., actual deformed pipe size and the resetting of the flow meter settings itself considering this) but merely introduces a correction coefficient based on a circular cross-section, there are limitations in improving accuracy. In other words, the technique disclosed in Patent Document 1 has limitations in improving the accuracy and reliability of flow rate calculations in response to situations where the pipe is deformed into an ellipse. Furthermore, the flow rate correction of Patent Document 2 corresponds to temperature changes, the flow rate calculation of Patent Document 3 is a signal processing approach that utilizes the difference in arrival times of ultrasonic signals along the ultrasonic travel path, and the flow rate correction of Patent Document 4 merely adopts a method of correcting sound speed and flow rate using the difference between the theoretical sensor distance and the distance measured by the actual ultrasonic signal; therefore, these patent documents are also insufficient as direct responses to pipe deformation into an ellipse. Prior art literature
[0005] Republic of Korea Published Patent No. 특2002-0021560 (Publication Date: March 21, 2002) Republic of Korea Registered Patent No. 10-1022407 (Publication Date: March 15, 2011) Republic of Korea Registered Patent No. 10-1302645 (Publication Date: September 3, 2013) Republic of Korea Registered Patent No. 10-1324574 (Publication Date: November 1, 2013) The problem to be solved
[0006] One objective of the present application is to provide a method for correcting an error related to flow rate calculation that occurs during elliptical deformation of a circular cross-section of a pipe, a system for performing said method, and a recording medium having said algorithm recorded thereon.
[0007] Another objective of the present application is to provide a flow rate calculation (correction) method, a related system, and a recording medium on which an algorithm is recorded, which improves the reliability and accuracy of flow rate calculations.
[0008] The above-mentioned purpose of this application and other purposes can all be resolved by the invention of this application described below. means of solving the problem
[0009] According to one embodiment of the present application, a flow rate measurement correction method corresponding to elliptical deformation of a fluid transport pipe equipped with at least one pair of ultrasonic sensors is provided.
[0010] The above method is,
[0011] The cross-sectional area (S) of the pipe material calculated from the diameter information of the fluid transport pipe in a circular state before deformation pipe ), and the outer diameter cross-sectional area of the elliptical cross-section pipe calculated from the elliptical outer diameter information measured after deformation of the fluid transport pipe (A out Based on ), the inner diameter cross-sectional area (A) of an elliptical cross-section pipe plastically deformed into an ellipse in a garden in Step (A) for calculating )
[0012] Step (B) of calculating the deformation ratio coefficient K according to [Equation 2] below;
[0013] According to [Equation 3-1] and [Equation 3-2] below, the deformation ratio coefficient K is used to determine the outer diameter of the major axis of the elliptical cross-section (OD') of the deformed pipe. L ) and shortened outer diameter (OD' S By applying to each of the ) the inner diameter of the major axis of the elliptical cross-section (ID') of the elliptically deformed pipe L ) and shortened inner diameter (ID' S Step (C) for estimating )
[0014] According to [Equation 4-1], [Equation 4-2] and [Equation 4-3] below, the estimated inner diameter of the major axis of the elliptical cross-section (ID') L ) and shortened inner diameter (ID' S From the value, the outer diameter length (OD') of the elliptical cross-section at the design angle (θ) where the ultrasonic sensor is attached, relative to the center of the pipe cross-section. θ ), elliptical cross-section inner diameter length (ID' θ ) and pipe thickness (t' θ Step (D) for calculating )
[0015] The above calculated elliptical cross-sectional inner diameter length (ID' θ ) and pipe thickness (t' θ A step (E) of deriving an appropriate distance (Z) between sensors based on the elliptical deformation of the ultrasonic sensor;
[0016] The method may include a step (F) of adjusting the attachment position of the sensor or the distance between sensors according to the derived appropriate distance (Z). At this time, the design angle (θ) is the angle of the sensor attachment position specified when installing a flow meter on a pipe, and is defined as an acute angle with respect to the diameter of the deformation circle perpendicular to the direction of gravity as 0°.
[0017] [Equation 2]
[0018]
[0019] [Equation 3-1]
[0020] Long axis inner diameter (ID' L ) = K x Major axis outer diameter (OD' L )
[0021] [Equation 3-2]
[0022] Shortened inner diameter (ID') S ) = K x Shortest Outer Diameter (OD') S )
[0023] [Equation 4-1]
[0024] The outer diameter (OD') of the elliptical cross-section at a specific design angle (θ) θ ) =
[0025]
[0026] [Equation 4-2]
[0027] Elliptical cross-section inner diameter length (ID') at a specific design angle (θ) θ ) =
[0028]
[0029] [Equation 4-3]
[0030] Pipe thickness (t' at a specific design angle (θ) θ ) =
[0031] The outer diameter of the elliptical cross-section (OD') at a specific design angle (θ) θ ) - Elliptical cross-section inner diameter length (ID') at a specific design angle (θ) θ )} ÷ 2
[0033] According to another embodiment of the present application, an ultrasonic flow measurement system corresponding to elliptical deformation of a fluid transport pipe is provided. The system comprises
[0034] A memory unit storing information on the outer diameter (OD) and inner diameter (ID) of a circular cross-section pipe before deformation; and the actual measured major axis outer diameter (OD') of the deformed pipe. L ) and shortened outer diameter (OD' S It includes an input unit that receives ) input; a calculation unit that calculates an appropriate distance (Z) between sensors based on elliptical deformation; and a display unit that displays the attachment position of the sensors or the distance between sensors according to the appropriate distance (Z) between the sensors,
[0035] The above operation unit is,
[0036] Assuming plastic deformation where the cross-sectional area of the pipe material remains the same before and after deformation, the measured outer diameter of the major axis (OD') after deformation L ) and shortened outer diameter (OD' S Calculate the deformation ratio coefficient (K) using the outer diameter (OD) and inner diameter (ID) information of the pipe before deformation, and
[0037] Based on the above coefficient (K), the inner diameter of the major axis of the elliptical cross-section of the deformed pipe (ID' L ), shortened inner diameter (ID' S ), outer diameter length of the elliptical cross-section (OD') at a specific design angle (θ) θ ), elliptical cross-section inner diameter length (ID' θ ) and pipe thickness (t' θ It produces ),
[0038] The above calculated inner diameter length of the elliptical cross-section (ID' θ ) and pipe thickness (t' θ It can be configured to calculate the appropriate distance (Z) between sensors according to elliptical deformation based on ).
[0040] According to another embodiment of the present application, an ultrasonic flow measurement system corresponding to elliptical deformation of a fluid transport pipe is provided. The system comprises:
[0041] A memory unit storing information on the outer diameter (OD) and inner diameter (ID) of a circular cross-section pipe before deformation; and the actual measured major axis outer diameter (OD') of the deformed pipe. L ) and shortened outer diameter (OD' S It includes an input unit that receives ) input; a calculation unit that calculates an appropriate distance (Z) between sensors based on elliptical deformation; and a control unit that adjusts the attachment position of the sensors or the distance between sensors according to the appropriate distance (Z) between sensors,
[0042] The above operation unit
[0043] Assuming plastic deformation where the cross-sectional area of the pipe material remains the same before and after deformation, the measured outer diameter of the major axis (OD') after deformation L ) and shortened outer diameter (OD' S Calculate the deformation ratio coefficient (K) using the outer diameter (OD) and inner diameter (ID) information of the pipe before deformation, and
[0044] Based on the above coefficient (K), the inner diameter of the major axis of the elliptical cross-section of the deformed pipe (ID' L ), shortened inner diameter (ID' S), outer diameter length of the elliptical cross-section (OD') at a specific design angle (θ) θ ), elliptical cross-section inner diameter length (ID' θ ) and pipe thickness (t' θ It produces ),
[0045] The above calculated inner diameter length of the elliptical cross-section (ID' θ ) and pipe thickness (t' θ It can be configured to calculate the appropriate distance (Z) between sensors according to elliptical deformation based on ).
[0047] According to another embodiment of the present application, a computer-readable recording medium is provided that records an algorithm for performing the above method. Effects of the invention
[0049] According to a specific embodiment of the present application, a method for correcting errors related to flow rate calculations occurring during elliptical deformation of a circular cross-section of a pipe, a system for performing said method, and a recording medium having said algorithm recorded thereon are provided. Accordingly, the present invention provides the effect of increasing the reliability and accuracy of flow rate calculations.
[0050] Furthermore, the present application provides a highly reliable method for calculating flow rates in a pipe in which a circular cross-section is deformed into an elliptical shape, by verifying the internal dimensions of the deformed section based on external measurements without cutting the pipe or directly inspecting the interior, thereby enabling the reduction of time and cost while satisfying the requirements of actual field conditions. Brief explanation of the drawing
[0052] Figure 1 is a schematic diagram illustrating the change in distance due to the elliptical deformation of a circular cross-sectional pipe and the occurrence of errors in ultrasonic transmission and reception. Specifically, Figure 1a is a cross-sectional view illustrating the deformation of the pipe, and Figure 1b is a top view illustrating the deformation of the pipe in which an ultrasonic flow sensor is installed externally. In these figures, the shape indicated in black illustrates the state before deformation, and the shape indicated in red illustrates the state after deformation. For reference, looking at Figure 1b, which is the top view, it can be seen that as the circular pipe deforms into an ellipse due to gravity, a distance correction of Δd is required compared to the initially set sensor separation distance. FIG. 2 illustrates the dimensions of the pipe cross-section after deformation. Specifically, FIG. 2a illustrates the circular cross-sectional dimensions of the pipe before deformation. FIG. 2b illustrates the elliptical cross-sectional dimensions of the pipe after deformation, and FIG. 2c illustrates the outer diameter (OD') at the angle (θ) at which the ultrasound travels relative to the center of the pipe cross-section (the angle at which the ultrasound is transmitted and received) (θ) during the initial design (or initial ultrasonic sensor setting), based on the angle (θ) at which the ultrasound travels. θ ) and inner diameter (ID' θ ) and pipe thickness (t' θ Explains ). In Figures 2b and 2c, the red circle indicates the circular cross-section of the piping before deformation. Figure 3 illustrates a method for calculating the appropriate distance (Z) between sensors after elliptical deformation of the piping. Specifically, Figure 3a shows the path (reverse / path) for transmitting and receiving ultrasound and the direction of fluid flow (shaded arrow) between sensors (shaded rectangles) facing each other in a diagonal shape. The calculation of the appropriate distance (Z) (distance between ultrasonic sensors) after deformation is based on the projected distance (X) relative to the direction of fluid flow (pipe axis direction) along the path of ultrasound travel. pipe and X fluid It explains that it is calculated through ). Fig. 3b shows the projected distance (X pipe , X fluid In calculating ), according to the law of refraction, the angle of incidence (Φ i ) and angle of refraction (Φ r Explains that ) is considered. Specific details for implementing the invention
[0053] Hereinafter, the invention according to a specific embodiment of the present application will be described in detail with reference to the attached drawings. For convenience of explanation, the size or shape of each illustrated component may be exaggerated or reduced. Furthermore, to clearly explain the present invention, specific descriptions regarding known components and their functions have been omitted, and some notations for components repeated in each drawing have also been omitted.
[0054] Unless specifically defined otherwise, all terms used in this specification may be used in a meaning that is commonly understood by those skilled in the art to which the present invention pertains. Furthermore, explanations regarding content or universal content that is commonly understood by those skilled in the art to which the present invention pertains have been omitted.
[0055] Unless specifically defined otherwise, the term “comprising” as used in this specification is interpreted as not excluding one or more other configurations or steps with respect to the configurations or steps mentioned in relation to said term.
[0056] Unless otherwise specifically defined, singular expressions used in this specification include the meaning of the plural form.
[0057] Unless otherwise specifically defined, the term “piping” as used herein may be used for transporting fluids, and the material (material) forming the pipe may be, for example, metal, plastic, and / or concrete.
[0058] Unless otherwise specifically defined, the term "fluid transported by piping" in this specification is used to include gases and liquids. Although not specifically limited, liquids may be used to include tap water, sewage, wastewater, domestic water, industrial water, and other substances that are in a liquid state when transported by piping. Additionally, gases may be used to include not only air required for domestic ventilation, but also gases related to the energy industry (e.g., natural gas, oil gas, hydrogen, etc.), special gases for general industrial use (e.g., oxygen, nitrogen, and argon), carbon dioxide or hydrogen receiving attention in relation to green technologies such as CCUS, and other substances that are in a gaseous state when transported by piping.
[0060] The inventor of the present application has diligently researched the problem of reduced accuracy and reliability in flow rate calculations due to changes in pipe cross-sectional shape and related technologies, and has completed the invention of the present application.
[0061] Specifically, when a pipe is deformed from a circular shape to an elliptical shape, not only are major and minor axes formed, but the inner and outer diameters of the pipe also differ in dimension, which causes problems with ultrasonic transmission and reception between sensors attached at designated locations. Taking this into consideration, the inventor of the present application ellipse Based on the assumption that the deformation is plastic deformation (the thickness in the major axis direction increases and the thickness in the minor axis direction decreases), that is, a physical assumption based on plastic deformation such as 'even if the original circular cross-section of the pipe is compressed into an ellipse, there is no change in the volume of the pipe material itself and the total cross-sectional area corresponding to the thickness of the pipe material itself does not change,' a method for inversely calculating the internal deformed shape (inner diameter of the ellipse, internal area of the ellipse (fluid flow area), thickness of the ellipse pipe at a specific design angle, etc.) using only external actual measurements, and a recording medium containing a related system and a related algorithm for ensuring the accuracy and reliability of flow rate calculation based on this, was completed.
[0062] Specific examples of the present application will be described in detail below.
[0064] Flow rate calculation (correction) method
[0065] In one example relating to the present application, the present application relates to a method for calculating (correcting) flow rate according to elliptical deformation of a circular pipe. Specifically, the method is a flow rate measurement correction method corresponding to elliptical deformation of a fluid transport pipe equipped with at least one pair of ultrasonic sensors, and may be performed by including at least steps A to F described below.
[0066] Step A: Inner diameter cross-sectional area (A in Calculation of )
[0067] In a specific embodiment of the present application, the method is a cross-sectional area (S) of the piping material calculated from the diameter information of the circle state before deformation of the fluid transport piping. pipe ); and the outer diameter cross-sectional area of the elliptical cross-section pipe calculated from the elliptical outer diameter information measured after deformation of the fluid transport pipe (A out Based on ), the inner diameter cross-sectional area (A) of an elliptical cross-section pipe plastically deformed into an ellipse in a garden in It may include a step (A) of calculating ).
[0068] In one example, the diameter information of the circle state before deformation may include the outer diameter (OD) and inner diameter (ID) values of the circular cross-section of the circle pipe. Such circle diameter information of the pipe before deformation is already determined as a design parameter when designing the pipe or the ultrasonic flow meter for measuring the flow rate passing through the pipe.
[0069] In one example, the outer diameter information of the ellipse state measured after the above deformation is the major axis outer diameter (OD' L ) and shortened outer diameter (OD' SIt may include actual measured values for ). As such, the present invention records the degree of physical shape change for a pipe whose cross-section has been deformed from a circle to an ellipse, corrects the flow rate measurement method by reflecting the change in the geometric path (distance, thickness) from the actual amount of physical change as described below, and corrects the ultrasonic path itself in the deformed ellipse. The outer diameter information of the ellipse in the deformed ellipse state can be measured not only by a jig but also by known equipment such as a laser measuring device (laser micrometer), imaging equipment, etc.
[0070] In one example, step (A) is based on the outer diameter (OD) and inner diameter (ID) information of the fluid transport pipe before deformation in its original circle state, and the cross-sectional area (S) of the pipe material. pipe It may include a step (a1) of calculating ) according to [Equation 1]. At this time, the cross-sectional area (S) of the piping material pipe ) can be calculated according to [Equation 1].
[0071] [Equation 1]
[0072]
[0073] When a circular cross-section of a pipe is deformed into an ellipse, the internal dimensions (major axis inner diameter, minor axis inner diameter) cannot be determined without cutting the pipe. However, even if the pipe is crushed and deformed, the volume of the material forming the pipe itself does not change; as the pipe deformation causes the thickness of the major axis section to increase and the thickness of the minor axis section to decrease, the cross-sectional area (S) of the pipe-forming material pipeIt is possible to make an assumption regarding plastic deformation that the value is the same both before and after deformation. Based on this assumption, the area of the internal space (i.e., the fluid flow area) can be calculated using only the external dimensions of the pipe deformed into an ellipse as shown below. For reference, the internal cross-sectional area of the deformed pipe material can be obtained by subtracting the internal area of the ellipse, calculated by the internal major axis and the internal minor axis, from the external area of the ellipse, calculated by the external major axis and the external minor axis, even in the deformed ellipse.
[0074] In one example, step (A) is the elliptical state major axis outer diameter (OD') of the pipe after deformation. L ) and shortened outer diameter (OD' S Based on actual measurement information regarding ), the outer diameter area (A) of the modified elliptical cross-section pipe above out It may include a step (a2) of calculating ). The outer diameter area (A) of the elliptical cross-section pipe. out ) is the major axis outer diameter (OD' L ) and shortened outer diameter (OD' S ) The information is obtained by applying it to the formula for calculating the announced elliptical cross-sectional area.
[0075] In one example, the above step (A) is the inner diameter area (A) of the modified elliptical cross-section pipe. in ), that is, the step (a3) of obtaining the fluid flow cross-sectional area may be included. At this time, the inner diameter cross-sectional area (A) of the elliptical cross-section pipe. in ) is the outer diameter area (A) of the elliptical cross-section pipe. out In ), the cross-sectional area (S) of the above piping material pipe It can be obtained by subtracting ).
[0076] Step B: Calculate deformation ratio coefficient K
[0077] In a specific embodiment of the present application, the method may include a step (B) of calculating a deformation ratio coefficient K according to [Equation 2] below.
[0078] [Equation 2]
[0079] or
[0080] In the above [Equation 2], the above A out is the outer diameter area of the elliptical cross-section pipe, and the above A in represents the inner diameter area of a modified elliptical cross-section pipe.
[0081] As mentioned above, the inner elliptical dimensions of the deformed pipe cannot be determined without cutting the pipe. However, as mentioned above, assuming plastic deformation of the pipe, the change in each diameter in the major axis direction (or minor axis direction) can be considered identical, and in a situation where the internal elliptical dimensions of the pipe cannot be determined, information regarding the deformed elliptical area as described above (A out , A in Since ) can be secured, the above 'area' ratio (A in / A out By applying the square root to ), a deformation ratio coefficient K, which is a clue regarding the degree of 'length' deformation, can be derived. Based on this K value, the inner dimensions of the deformed ellipse can be calculated as described below without actual measurement.
[0082] Step C: Estimation of the inner dimensions of the deformed ellipse
[0083] In a specific embodiment of the present application, the method determines the deformation ratio coefficient K value (see [Equation 2]) according to [Equation 3-1] and [Equation 3-2] below, the outer diameter of the major axis of the elliptical cross-section (OD') of the deformed pipe. L ) and shortened outer diameter (OD' S By applying to each of the ) the inner diameter of the major axis of the elliptical cross-section (ID') of the elliptically deformed pipe L ) and shortened inner diameter (ID' S It may include a step (C) of estimating ).
[0084] [Equation 3-1]
[0085] Long axis inner diameter (ID' L ) = K x Major axis outer diameter (OD' L )
[0086] [Equation 3-2]
[0087] Shortened inner diameter (ID') S ) = K x Shortest Outer Diameter (OD') S )
[0088] As such, in this application, since the deformation of the cross-sectional shape of the pipe is assumed to be plastic deformation, the inner dimensions of the elliptical pipe can be derived from the outer information without cutting the pipe.
[0089] Step D: Calculate dimensions at the design angle (θ)
[0090] In a specific embodiment of the present application, the method, according to [Equation 4-1], [Equation 4-2] and [Equation 4-3] below, [Equation 4-3], [Equation 4-2], and [Equation 4-3], L ) and shortened inner diameter (ID' S From the value, the outer diameter length (OD') of the elliptical cross-section at a specific design angle (θ) where the ultrasonic sensor is attached, relative to the center of the pipe cross-section θ ), elliptical cross-section inner diameter length (ID' θ ) and pipe thickness (t' θ It may include a step (D) of calculating ) (see FIG. 2c).
[0091] The above design angle (θ) is the angle of the sensor attachment position, which is one of the design specifications designated by the user when installing a flow meter in a pipe. It is defined as an acute angle with respect to the diameter of the circle before deformation, which is perpendicular to the direction of gravity, as 0°. Depending on the design value θ, it is determined where in the pipe the ultrasonic sensor will be attached. After the pipe is deformed, the above design angle (θ) can be defined as an acute angle set with respect to the major axis of the ellipse, which is perpendicular to the direction of gravity, as 0°.
[0092] [Equation 4-1]
[0093] The outer diameter (OD') of the elliptical cross-section at a specific design angle (θ) θ ) =
[0094]
[0095] [Equation 4-2]
[0096] Elliptical cross-section inner diameter length (ID') at a specific design angle (θ) θ ) =
[0097]
[0098] [Equation 4-3]
[0099] Pipe thickness (t' at a specific design angle (θ) θ ) =
[0100] The outer diameter of the elliptical cross-section (OD') at a specific design angle (θ) θ ) - Elliptical cross-section inner diameter length (ID') at a specific design angle (θ) θ )} ÷ 2
[0101] The above [Equation 4-1] and [Equation 4-2] are elliptic equations (x) relating to the radius (r) expressed in an orthogonal coordinate system (x, y). 2 / a 2 + y 2 / b 2 = 1) is converted to polar coordinates (x=r·cosθ, y= r·sinθ), and this is the radius (major axis radius=ID' L / 2, short radius=ID' s / 2, r ID =ID' θ It can be obtained by organizing it into an expression regarding / 2).
[0102] The values obtained through the above process are used to verify the appropriate distance between sensors after elliptical deformation and to adjust the attachment positions of the sensors, as described below.
[0103] Step E: Derivation of the optimal distance (Z) between sensors
[0104] In one example, the above method is the calculated elliptical cross-sectional inner diameter length (ID' θ ) and pipe thickness (t' θ Based on ), it may include a step (E) of deriving an appropriate distance (Z) between sensors according to the elliptical deformation of the ultrasonic sensor. Snell's law regarding refraction may be used in this process.
[0105] In one example, the step (E) of deriving the appropriate distance (Z) above is such that, according to [Equation 5-1] below, the ultrasound thickness (t' θ Horizontal (projected) distance (X) passing through a pipe wall that moves in a direction horizontal to the fluid flow (or pipe axis direction) while passing through the pipe wall. pipe It may include a step (e1) of calculating ) (see FIG. 3a and 3b).
[0106] [Equation 5-1]
[0107]
[0108] However, in the above [Equation 5-1], Φ i θ represents the angle formed by the direction of propagation of ultrasound within the pipe with the normal to the fluid flow. The above Φ i is the ultrasonic incidence angle from the sensor, which is a value already known (or determined) when setting up (designing) the piping and ultrasonic sensor.
[0109] In one example, the step (E) of deriving the appropriate distance (Z) above is a fluid passage horizontal (projection) distance (X) where the ultrasound passes through the fluid along a specific design angle (θ) according to [Equation 5-2] below and moves in a direction horizontal to the fluid flow. fluid It may include a step (e2) of calculating ) (see FIG. 3a and 3b).
[0110] [Equation 5-2]
[0111]
[0112] However, in the above [Equation 5-2], Φ r represents the angle formed by the direction of propagation of ultrasound traveling from the pipe to the fluid with the normal to the fluid flow. The above Φ r θ is the angle at which the ultrasound penetrates the fluid after passing through the pipe wall, and it is a value already known (or determined) when setting up (designing) the pipe and ultrasonic sensor. For example, Φ r It can be calculated as follows.
[0113]
[0114] In one example, the step (E) of deriving the appropriate distance (Z) may include the step (e3) of calculating the sensor attachment distance (Z) modified according to [Equation 5-3] below (see FIGS. 3a and 3b).
[0115] [Equation 5-3]
[0116]
[0117] In the above [Equation 5-3], N is a natural number determined by the ultrasonic path, and is the number of directions of propagation (in the fluid) changed after the ultrasonic waves traveling in the fluid are reflected from the inner wall of the pipe.
[0118] For example, when ultrasonic transmission and reception occur between a pair of ultrasonic sensors, the ultrasonic travel paths between the sensors include an upward straight ( / ) path, a downward straight (inverse / ) path, a V path, N There may be a path or a W path, etc. In this case, the number of times (N) the ultrasound changes its path within the fluid as it is refracted and reflected may vary depending on the entire designed ultrasound path, and N is the number of directions of travel that the ultrasound moving within the fluid changes after being reflected from the inner wall of the pipe (limited to movement within the fluid). Also, since transmission and reception occur between a pair of ultrasonic sensors, there may be 2 instances where the ultrasound passes through the pipe wall.
[0119] Although not specifically limited, if the ultrasonic sensors are facing each other in a downward straight path (reverse / path) as in FIG. 3a, the adjustment distance (Z) may be as shown in [Equation 5-3-1] below.
[0120] [Equation 5-3-1]
[0121]
[0122] Step F: Adjust sensor position (distance between sensors) based on appropriate distance (Z).
[0123] In one example, the method may include a step (F) of adjusting the attachment position of the sensor or the distance between sensors according to the derived appropriate distance (Z).
[0124] Generally, ultrasonic flowmeters are designed so that the ultrasonic waves emitted from the transmitter pass through the pipe wall, travel through the fluid, pass through the opposite pipe wall, and accurately reach the receiver at a predetermined set (design) distance (Z). norm Depending on the fluid flow direction (pipe axis direction), it is attached to the pipe at a predetermined distance. However, if the pipe is deformed into an ellipse, the initial pipe and sensor settings (design) values change. For example, as can be seen in the concept illustrated in Fig. 1b, if the circular cross-section of the pipe is deformed into an ellipse due to gravity or the like, accurate ultrasonic transmission and reception with the other ultrasonic sensor paired with it cannot be achieved at the ultrasonic sensor position placed at the initial setting (design) position. Therefore, it is necessary to adjust the existing sensor spacing distance initially set (designed) to match the appropriate distance (Z) described above.
[0125] Such distance adjustment can be achieved, for example, by moving one of the pair of ultrasonic sensors located further back in the direction of fluid flow (or pipe axis). This distance adjustment may be performed manually by the user or automatically via a rail. In the latter case, the ultrasonic sensor may be equipped to be movable and fixed on a rail provided on the pipe wall.
[0126] As such, in the present invention, by adjusting (modifying or correcting) the installation position of the sensors (or the distance between sensors) to match the modified reality, the accuracy of sensor transmission and reception can be increased, and the accuracy and reliability of flow rate measurement can be improved.
[0127] Flow rate calculation after correction reflecting physical deformation
[0128] After undergoing the aforementioned steps, since the flow rate measurement or correction of the method based on elliptical deformation has been performed, ultrasonic transmission and reception can subsequently be performed at the adjusted installation location according to a known method. Furthermore, when the flow velocity (V) is calculated according to a known method such as the time difference method or the Doppler method, the flow rate (Q=V·A) can be calculated based on the corresponding flow velocity and the pipe cross-sectional area (A).
[0129] According to a specific embodiment of the present application in relation thereto, the present application performs the calculation of the flow rate by excluding the assumption that the pipe cross-sectional area is circular. Specifically, the method of the present application, instead of using a circular cross-sectional area derived based on the inner diameter (ID) of a circular cross-sectional pipe before deformation, uses the inner diameter cross-sectional area (A) of an elliptical cross-sectional pipe calculated as above. in The flow rate can be calculated using ) as the fluid flow cross-sectional area. Accordingly, the actual deformed fluid flow area can be taken into account in the calculation of the flow rate.
[0131] Flow rate calculation (correction) system
[0132] In another example relating to the present application, the present application relates to a system capable of performing a method for calculating (correcting) the flow rate according to the elliptical deformation of a circular pipe. That is, the system is an ultrasonic flow rate measuring system equipped with a correction function regarding the flow rate or the method of measuring the flow rate when the pipe undergoes elliptical deformation.
[0133] In one example, the above-described system may be a system configured to perform the method described above. Therefore, the meanings of the terms used to describe the system described below refer to those explained in relation to the method described above, and a detailed explanation thereof is omitted.
[0134] In one example, the system may be equipped with at least one pair of ultrasonic sensors. And, the ultrasonic sensors, the ultrasonic transmission and reception between the at least one pair of ultrasonic sensors, an upward straight ( / ) path, a downward straight (inverse / ) path, a V path, N It can be attached to the outer wall of the fluid transport piping to form a path or a W path.
[0135] The above system may be composed of two suns, for example, as follows.
[0136] First aspect of the system
[0137] According to one example relating to the present application, the system comprises: a memory unit storing information on the outer diameter (OD) and inner diameter (ID) of a circular cross-section pipe before deformation; and the actual long axis outer diameter (OD') of the deformed pipe. L ) and shortened outer diameter (OD' S The ultrasonic flow measurement system corresponding to the elliptical deformation of a fluid transport pipe may include: an input unit receiving input; a calculation unit calculating an appropriate distance (Z) between sensors according to the elliptical deformation; and a display unit displaying the attachment position of the sensors or the distance between sensors according to the appropriate distance (Z) between sensors.
[0138] At this time, the above-mentioned operation unit,
[0139] Assuming plastic deformation where the cross-sectional area of the pipe material remains the same before and after deformation, the measured outer diameter of the major axis (OD') after deformation L ) and shortened outer diameter (OD' S Calculate the deformation ratio coefficient (K) using the outer diameter (OD) and inner diameter (ID) information of the pipe before deformation, and
[0140] Based on the above deformation ratio coefficient (K), the inner diameter of the major axis of the elliptical cross-section of the deformed pipe (ID' L ), shortened inner diameter (ID' S ), outer diameter length of the elliptical cross-section (OD') at a specific design angle (θ) θ ), elliptical cross-section inner diameter length (ID' θ) and pipe thickness (t' θ It produces ),
[0141] The above calculated inner diameter length of the elliptical cross-section (ID' θ ) and pipe thickness (t' θ Based on ), the appropriate distance (Z) between sensors according to elliptical deformation can be calculated.
[0142] In one example, the above operation unit,
[0143] When calculating the flow rate, instead of calculating the cross-sectional area based on the inner diameter (ID) of the original circular cross-section pipe, the inner diameter cross-sectional area (A) of the deformed elliptical cross-section pipe is used. in )second Calculate the flow rate using the fluid flow cross-sectional area, and
[0144] The inner diameter cross-sectional area (A) of the above modified elliptical cross-section pipe in ) is the outer diameter area (A) of the elliptical cross-section pipe. out The cross-sectional area of the piping material (S) in ) pipe It can be calculated by subtracting ).
[0145] Although not specifically limited, in a specific embodiment of the system of the first sun described above, a manager or operator manually sets the initial distance (Z) by referring to the appropriate distance (Z) displayed on the display unit. norm The position of the sensor or the distance between sensors can be adjusted from ).
[0146] Second sun regarding the system
[0147] According to another example relating to the present application, the system comprises: a memory unit storing information on the outer diameter (OD) and inner diameter (ID) of a circular cross-section pipe before deformation; and the actual long axis outer diameter (OD') of the deformed pipe. L ) and shortened outer diameter (OD' SThe ultrasonic flow measurement system corresponding to the elliptical deformation of a fluid transport pipe may include: an input unit receiving input; a calculation unit calculating an appropriate distance (Z) between sensors according to the elliptical deformation; and a control unit adjusting the attachment position of the sensors or the distance between sensors according to the appropriate distance (Z) between sensors.
[0148] At this time, the above operation unit
[0149] Assuming plastic deformation where the cross-sectional area of the pipe material remains the same before and after deformation, the measured outer diameter of the major axis (OD') after deformation L ) and shortened outer diameter (OD' S Calculate the deformation ratio coefficient (K) using the outer diameter (OD) and inner diameter (ID) information of the pipe before deformation, and
[0150] Based on the above coefficient (K), the inner diameter of the major axis of the elliptical cross-section of the deformed pipe (ID' L ), shortened inner diameter (ID' S ), outer diameter length of the elliptical cross-section (OD') at a specific design angle (θ) θ ), elliptical cross-section inner diameter length (ID' θ ) and pipe thickness (t' θ It produces ),
[0151] The above calculated inner diameter length of the elliptical cross-section (ID' θ ) and pipe thickness (t' θ Based on ), the appropriate distance (Z) between sensors according to elliptical deformation can be calculated.
[0152] In one example, the above operation unit,
[0153] When calculating the flow rate, instead of calculating the cross-sectional area based on the inner diameter (ID) of the original circular cross-section pipe, the inner diameter cross-sectional area (A) of the deformed elliptical cross-section pipe is used. in )second Calculate the flow rate using the fluid flow cross-sectional area, and
[0154] The inner diameter cross-sectional area (A) of the above modified elliptical cross-section pipe in ) is the outer diameter area (A) of the elliptical cross-section pipe. outThe cross-sectional area of the piping material (S) in ) pipe It can be calculated by subtracting ).
[0155] In a specific embodiment regarding the second solar system described above, the ultrasonic sensor may be configured such that its position or distance is adjusted by a control unit to match an appropriate distance (Z). For example, the ultrasonic sensor may be positioned on a rail that enables position adjustment of the sensor, and the rail may be formed on the surface of the outer wall of a pipe, extending for a predetermined length in a direction identical to or horizontal to the direction of fluid flow, and the system and related components may be configured such that the control unit automatically adjusts the attachment position of the sensor or the distance between sensors in the direction of extension of the rail according to the calculated appropriate distance (Z) between sensors.
[0156] Functions and configuration of other systems
[0157] In relation to the configuration and function of the first and second solar systems described above, in addition to what has been described above, the memory unit may perform the function of storing (recording) various information related to flow rate management, such as setting (design) information regarding pipes and ultrasonic sensors, and calculation information by the calculation unit, as well as calculation (computation) results. Furthermore, the input unit may perform the function of receiving information stored (recorded) by the memory unit, information required for calculation by the calculation unit, and / or setting (design) information regarding pipes and ultrasonic sensors from the memory unit. Additionally, the calculation unit may be configured to perform all calculations necessary for the execution of the method described above.
[0158] The control unit included in the second solar system is configured so that the adjustment of the sensor's attachment position or distance can be automated instead of manual adjustment by a user or manager.
[0159] In addition, the display unit included in the first solar system may also be included in the second solar system and may be configured to check management matters such as status information or user manuals related to the memory unit, input unit, operation unit, and control unit described above.
[0160] Each component of these systems can be configured (equipped) to be electrically connected or wired / wireless connected to one another within a single physical device or within multiple physical devices so that each function can be organically performed to correct the flow rate calculation based on the elliptical deformation described above.
[0161] Furthermore, any description not specifically mentioned regarding the configuration and function of the first and second solar systems may be replaced by the content described regarding the method described above.
[0162] recording media
[0163] In another example relating to the present application, the present application relates to a computer-readable recording medium having an algorithm recorded therein that can perform a method for calculating (correcting) a flow rate according to the elliptical deformation of a circular pipe.
[0165] The foregoing description is merely one of several aspects of the present invention, and the present invention may include various embodiments in which various modifications may be made. For example, differences such as changes in formulas based on the setting of the reference position of the angle are one of the various modifications according to the embodiments of the present invention. As such, the present invention should be understood to include all modifications, equivalents, or substitutions that fall within the technical spirit or scope of the claimed rights of the present invention. Explanation of the symbols
[0166] OD: Outer diameter of the circular cross-section before deformation ID: Inner diameter of the circular cross-section before deformation OD' L : Outer diameter of the major axis of the elliptical cross-section after deformation OD' S: Shortest outer diameter of the elliptical cross-section after deformation ID' L : Inner diameter of the major axis of the elliptical cross-section after deformation ID' S : Shortest axis inner diameter of the elliptical cross-section after deformation t'(L): Pipe (material) thickness along the major axis of the ellipse after deformation t'(S): Pipe (material) thickness in the direction of the minor axis of the ellipse after deformation OD' θ : The outer diameter having a specific angle θ from the center of the ellipse after deformation ID' θ : Inner diameter length having a specific angle θ from the center of the ellipse after deformation t' θ : Pipe (material) thickness at a specific angle θ from the center of the ellipse after deformation X pipe : Ultrasound thickness (t' θ Horizontal projected distance moving along the pipe wall (in a direction horizontal to the fluid flow or along the pipe axis) X fluid : The horizontal projected distance that ultrasound travels as it passes through the fluid (in a direction parallel to the fluid flow or along the pipe axis). Z: Appropriate distance between sensors (in modified elliptical piping, refers to the distance in the direction horizontal to the fluid flow or along the pipe axis)
Claims
Claim 1 A flow rate measurement correction method corresponding to elliptical deformation of a fluid transport pipeline equipped with at least one pair of ultrasonic sensors, wherein the method comprises the cross-sectional area (S) of the pipeline material calculated from the diameter information of the fluid transport pipeline in a circular state prior to deformation. pipe ), and the outer diameter cross-sectional area of the elliptical cross-section pipe calculated from the elliptical outer diameter information measured after deformation of the fluid transport pipe (A out Based on ), the inner diameter cross-sectional area (A) of an elliptical cross-section pipe plastically deformed into an ellipse in a garden in Step (A) for calculating ); Step (B) for calculating the deformation ratio coefficient K according to [Equation 2] below; and Step (D) for calculating the deformation ratio coefficient K value according to [Equation 3-1] and [Equation 3-2] below for the outer diameter of the major axis of the elliptical cross-section (OD' of the deformed pipe). L ) and shortened outer diameter (OD' S By applying to each of the ) the inner diameter of the major axis of the elliptical cross-section (ID') of the elliptically deformed pipe L ) and shortened inner diameter (ID' S Step (C) for estimating ); according to [Equation 4-1], [Equation 4-2] and [Equation 4-3] below, the estimated inner diameter of the major axis of the elliptical cross-section (ID' L ) and shortened inner diameter (ID' S From the value, the outer diameter length (OD') of the elliptical cross-section at the design angle (θ) where the ultrasonic sensor is attached, relative to the center of the pipe cross-section θ ), elliptical cross-section inner diameter length (ID' θ ) and pipe thickness (t' θ Step (D) of calculating ); the calculated inner diameter length (ID' of the elliptical cross-section above θ ) and pipe thickness (t' θ A flow rate measurement correction method corresponding to elliptical deformation of a fluid transport pipeline, comprising: a step (E) of deriving an appropriate distance (Z) between sensors based on the elliptical deformation of the ultrasonic sensor based on ); and a step (F) of adjusting the attachment position of the sensor or the distance between sensors according to the derived appropriate distance (Z) (wherein the design angle (θ) is the sensor attachment position angle specified when installing a flow meter on the pipeline, and is defined as an acute angle with respect to the diameter of the deformation circle perpendicular to the direction of gravity as 0°): [Equation 2] [Equation 3-1] Long axis inner diameter (ID' L ) = K x Major axis outer diameter (OD' L )[Equation 3-2] Shortened inner diameter (ID' S ) = K x Shortest Outer Diameter (OD') S )[Equation 4-1] Length of the outer diameter of the elliptical cross-section (OD') at a specific design angle (θ) θ ) = [Equation 4-2] Length of the inner diameter of the elliptical section (ID') at a specific design angle (θ) θ ) = [Equation 4-3] Pipe thickness (t') at a specific design angle (θ) θ ) = {Outer diameter length of the elliptical cross-section (OD' at a specific design angle (θ)} θ ) - Elliptical cross-section inner diameter length (ID') at a specific design angle (θ) θ )} ÷ 2 Claim 2 In claim 1, the diameter information in the circle state before deformation includes the outer diameter (OD) and inner diameter (ID) values of the circular cross-section of the circle pipe, and the outer diameter information in the ellipse state measured after deformation includes the major axis outer diameter (OD' L ) and shortened outer diameter (OD' S Includes actual measured values for ), and the cross-sectional area (S) of the piping material. pipe ) is calculated according to [Equation 1], and the inner diameter cross-sectional area (A) of the elliptical cross-section pipe is in ) is the outer diameter area (A) of the elliptical cross-section pipe. out In ), the cross-sectional area (S) of the above piping material pipe A flow rate measurement correction method corresponding to elliptical deformation of a fluid transport pipe equipped with at least one pair of ultrasonic sensors, obtained by subtracting ): [Equation 1] Claim 3 In claim 1, the step (E) of deriving the appropriate distance (Z) is such that, according to [Equation 5-1] below, the ultrasound thickness (t' θ Horizontal projected distance through a pipe wall (X) moving in a direction horizontal to the fluid flow while passing through a pipe wall that is ) pipe Calculate ), and according to [Equation 5-2] below, the horizontal projection distance (X) through which the ultrasound passes through the fluid and moves in a direction horizontal to the fluid flow along a specific design angle (θ). fluid A method for measuring ultrasonic flow of an elliptically deformed pipe, which is performed by calculating ) and calculating the sensor attachment distance (Z) modified according to [Equation 5-3] below: [Equation 5-1] (wherein in [Equation 5-1], Φ i θ represents the angle formed by the direction of propagation of the ultrasound within the pipe with the normal to the fluid flow [Equation 5-2] (wherein in [Equation 5-2], Φ r θ represents the angle formed by the direction of propagation of the ultrasound moving from the pipe to the fluid with the normal to the fluid flow [Equation 5-3] (wherein in [Equation 5-3], N is a natural number determined by the ultrasonic path, representing the number of changes in the direction of travel of the ultrasonic waves moving within the fluid after they are reflected from the inner wall of the pipe.) Claim 4 In claim 1, the above method, when calculating the flow rate, instead of using the circular cross-sectional area derived based on the inner diameter (ID) of the circular cross-sectional pipe before deformation, uses the inner diameter cross-sectional area (A) of the elliptical cross-sectional pipe calculated as above. in )second Ultrasonic flow measurement method for elliptically deformed pipes, calculating flow rate using fluid flow cross-sectional area. Claim 5 A system for performing the method according to claim 1, wherein the system comprises: a memory unit for storing information on the outer diameter (OD) and inner diameter (ID) of a circular cross-section pipe before deformation; and the actual measured major axis outer diameter (OD') of the deformed pipe. L ) and shortened outer diameter (OD' S It includes an input unit that receives ) input; a calculation unit that calculates an appropriate distance (Z) between sensors according to elliptical deformation; and a display unit that displays the attachment position of the sensors or the distance between sensors according to the appropriate distance (Z) between the sensors, wherein the calculation unit, based on plastic deformation in which the cross-sectional area of the pipe material is the same before and after the deformation of the piping, calculates the measured major axis outer diameter (OD') after deformation L ) and shortened outer diameter (OD' S A deformation ratio coefficient (K) is calculated using the outer diameter (OD) and inner diameter (ID) information of the pipe before deformation, and based on the coefficient (K), the inner diameter of the major axis of the elliptical cross-section (ID') of the deformed pipe L ), shortened inner diameter (ID' S ), outer diameter length of the elliptical cross-section (OD') at a specific design angle (θ) θ ), elliptical cross-section inner diameter length (ID' θ ) and pipe thickness (t' θ Calculates ) and the inner diameter length (ID' of the elliptical cross-section calculated above θ ) and pipe thickness (t' θ An ultrasonic flow measurement system corresponding to the elliptical deformation of a fluid transport pipeline, which calculates the appropriate distance (Z) between sensors according to the elliptical deformation based on ). Claim 6 A system for performing the method according to claim 1, wherein the system comprises: a memory unit for storing information on the outer diameter (OD) and inner diameter (ID) of a circular cross-section pipe before deformation; and the actual measured major axis outer diameter (OD') of the deformed pipe. L ) and shortened outer diameter (OD' S It includes an input unit that receives ) input; a calculation unit that calculates an appropriate distance (Z) between sensors based on elliptical deformation; and a control unit that adjusts the attachment position of the sensors or the distance between sensors according to the appropriate distance (Z) between the sensors, wherein the calculation unit, based on plastic deformation in which the cross-sectional area of the pipe material is the same before and after the deformation of the piping, calculates the measured major axis outer diameter (OD') after deformation L ) and shortened outer diameter (OD' S A deformation ratio coefficient (K) is calculated using the outer diameter (OD) and inner diameter (ID) information of the pipe before deformation, and based on the coefficient (K), the inner diameter of the major axis of the elliptical cross-section (ID') of the deformed pipe L ), shortened inner diameter (ID' S ), outer diameter length of the elliptical cross-section (OD') at a specific design angle (θ) θ ), elliptical cross-section inner diameter length (ID' θ ) and pipe thickness (t' θ Calculates ) and the inner diameter length (ID' of the elliptical cross-section calculated above θ ) and pipe thickness (t' θ An ultrasonic flow measurement system corresponding to the elliptical deformation of a fluid transport pipeline, which calculates the appropriate distance (Z) between sensors according to the elliptical deformation based on ). Claim 7 An ultrasonic flow measurement system corresponding to elliptical deformation of a fluid transport pipe, wherein, in claim 5 or 6, the system comprises at least one pair of ultrasonic sensors, and the ultrasonic movement between the pair of ultrasonic sensors is formed along a straight path or includes a straight path and a reflection path along the inner wall of the pipe. Claim 8 An ultrasonic flow measurement system corresponding to elliptical deformation of a fluid transport pipe, wherein, in claim 6, the ultrasonic sensor is positioned on a rail that enables position adjustment of the sensor, and the rail is formed on the outer wall surface of the pipe and extends for a predetermined length in a direction equal to or horizontal to the direction of fluid flow, and the control unit adjusts the attachment position of the sensor or the distance between sensors in the extension direction of the rail according to the calculated appropriate distance (Z) between sensors. Claim 9 In claim 5 or 6, the above calculation unit, instead of calculating the cross-sectional area based on the inner diameter (ID) of the original circular cross-section pipe before deformation when calculating the flow rate, calculates the inner diameter cross-sectional area (A) of the deformed elliptical cross-section pipe. in )second Calculate the flow rate using the fluid flow cross-sectional area, and the inner diameter cross-sectional area (A) of the modified elliptical cross-section pipe. in ) is the outer diameter area (A) of the elliptical cross-section pipe. out The cross-sectional area of the piping material (S) calculated according to Equation 1 below in ) pipe Ultrasonic flow measurement system corresponding to the elliptical deformation of a fluid transport pipe, calculated by subtracting ): [Equation 1] Claim 10 A computer-readable recording medium having an algorithm for performing the method according to paragraph 1.