Ultrasonic physical property measuring device

Abstract

Provided is an ultrasonic physical property measuring device that can suppress the generation of secondary flow in a cylindrical body, and that seeks portability, and suppresses changes in physical properties. The ultrasonic physical property measuring device is an ultrasonic physical property measuring device 1 that uses ultrasonic waves to measure the flow velocity distribution of a liquid flowing in a cylindrical body 2 by reciprocally rotating the cylindrical body 2 in a fixed cycle, and that estimates the physical properties of the liquid from the aforementioned flow velocity distribution, and with respect to the aforementioned cylindrical body 2, an upper end surface 21 and a lower end surface 22 are both perforated in a flow-through manner, and a rotating mechanism 3 that supports and reciprocally rotates the cylindrical body 2 in a state in which a portion or the entirety of the cylindrical body 2 is immersed in the aforementioned liquid is provided.

Description

Technical Field

[0001] This invention relates to an ultrasonic property measuring device for determining the viscosity or elasticity of liquids. Background Technology

[0002] In the handling of liquids such as food, liquid materials, and chemicals, understanding the viscosity and elasticity of liquids is crucial for quality management of finished products, optimization of production processes, and maintenance of factory machinery and equipment. For example, in the food industry, not only does the mixing ratio of raw materials affect the taste or texture of the finished product, but changes in the physical properties of the liquids due to the mixing state of the raw materials or the controlled temperature also influence the taste or texture. Therefore, monitoring and managing changes in physical properties can greatly contribute to maintaining or improving the quality of the finished product.

[0003] Conventionally, rotary torque type apparatuses have been used for measuring the physical properties of liquids. These apparatuses involve placing the liquid to be measured into an open container, immersing a rod-shaped or plate-shaped rotating body in the liquid, rotating the rotating body, and measuring the torque applied to the rotating body to determine the viscosity of the liquid. This method is simple and easy to perform, and has been widely used as a physical property measuring device.

[0004] However, while the rotating torque type property measuring device is very effective for measuring the viscosity of Newtonian fluids with a fixed viscosity that is independent of shear rate (rotational speed), it cannot measure the correct properties for non-Newtonian fluids with viscosity that is dependent on shear rate, as the torque exerted on the liquid varies depending on the rotational speed of the rotating body.

[0005] Most liquids used in food, liquid materials, and chemicals are non-Newtonian fluids. Regarding this, a rotational rheometer employing two disks exists as an apparatus for measuring the properties of non-Newtonian fluids. This rotational rheometer forms a thin layer of the test fluid between two disks, which are then rotated relative to each other. By assuming a Couette flow pattern or similar velocity distribution within the test fluid layer, physical properties such as apparent viscosity or linear viscoelasticity are measured.

[0006] However, the actual flow within the test fluid layer does not conform to the velocity distribution assumed by Cuyet flow, resulting in a discrepancy between the assumed and actual velocity distribution. In other words, the determination of rheological properties using a rotational rheometer is subject to fundamental inaccuracies due to the assumed velocity distribution.

[0007] Therefore, Yoshida et al., the inventors of this application, proposed the following method: using ultrasound to measure the flow velocity distribution within a cylindrical container generated by adding liquid to the container and rotating it back and forth, and estimating the physical properties of the liquid within the rotating cylinder based on the flow velocity distribution (Non-Patent Document 1). That is, the method described in Non-Patent Document 1 is as follows: by comparing the theoretical value of the flow velocity distribution estimated based on the physical properties, such as the angular velocity or period of the cylindrical container's back and forth rotation, with the experimental value of the flow velocity distribution obtained through experiments conducted under the same conditions, the physical properties of the liquid used in the experiment are estimated. This method is a revolutionary approach that, in principle, does not require assumptions about the flow velocity distribution.

[0008] Prior art literature

[0009] Non-patent literature

[0010] Non-patent literature 1: Taiki Yoshida, Yuji Tasaka and Yuichi murai, “Rheological evaluation of complex fluids using ultrasonic spinning rheometry in an open container”, The Society of Rheology, Inc. J. Rheol. 61(3), pp. 537-549, May / June (2017). Summary of the Invention

[0011] The problem that the invention aims to solve

[0012] However, the accuracy of the property measurement in the method described in Non-Patent Document 1 depends in principle on the flow velocity distribution measured by ultrasound. Ideally, the flow within the cylindrical container should conform to the theoretical flow velocity distribution. Regarding this, as illustrated in the comparative example described later, it has been confirmed that in existing devices using cylindrical containers with a bottom surface, a flow other than the flow through the sidewalls of the cylinder is generated, resulting in what is known as a secondary flow. Therefore, the development of a device capable of suppressing secondary flows has become a research topic in order to further improve measurement accuracy.

[0013] Furthermore, the method described in Non-Patent Document 1 is very useful as it can determine physical properties that do not require assumptions about flow velocity distribution in principle, but the existing device is relatively large and difficult to move or transport. Therefore, there is an increasing demand for portable devices that can be moved or transported.

[0014] Furthermore, when using a bottomed cylindrical container, it is necessary to transfer the liquid to be measured from the storage tank or manufacturing pipeline into the cylindrical container, just like with a rotary torque type physical property measuring device. There is a concern that the physical properties may change with changes in temperature or the surrounding environment.

[0015] The present invention was made to solve the problems mentioned above, and its object is to provide an ultrasonic property measuring device that can suppress the generation of secondary flow in a cylindrical body, is portable, and suppresses changes in physical properties.

[0016] Solution for solving the problem

[0017] The ultrasonic property measuring device of the present invention addresses the problem of suppressing secondary flow caused by the upper and lower surfaces of a reciprocatingly rotating cylinder and achieving portability. It uses ultrasound to measure the velocity distribution of a liquid flowing within the cylinder by reciprocating the cylinder at a fixed cycle, and estimates the properties of the liquid based on the velocity distribution. The cylinder has both the upper and lower surfaces that are permeable, and includes a rotation mechanism that supports the cylinder and allows it to reciprocate while partially or completely immersed in the liquid.

[0018] In addition, as a solution of the present invention, in order to solve the problem of providing a support for a cylindrical body that can rotate the cylindrical body while suppressing secondary flow, the upper and lower end faces of the aforementioned cylindrical body may be fully open, and the aforementioned rotating mechanism, as a support for the aforementioned cylindrical body, has a rotating shaft supported by a power unit shaft above the axis of the aforementioned cylindrical body, a hub fixed to the lower end of the aforementioned rotating shaft, and multiple spokes extending radially from the aforementioned hub and fixed to the upper edge of the aforementioned cylindrical body.

[0019] Furthermore, as a solution of the present invention, in order to solve the problem of suppressing the influence on the velocity distribution of the flow generated by the rotating spokes in the cylindrical body by dispersing the flow in the radial and circumferential directions, it is also possible that each of the aforementioned spokes extends in a direction that is horizontally offset from the aforementioned axis position as its base end, and bends at a predetermined angle relative to the line connecting the aforementioned axis and the aforementioned base end.

[0020] In addition, as a solution of the present invention, in order to solve the problem of improving the measurement accuracy of the flow velocity distribution near the wall of the cylinder, an ultrasonic transducer that irradiates ultrasonic waves into the cylinder and receives ultrasonic waves reflected from the cylinder may be fixed to its outer surface in a manner that allows it to rotate integrally with the cylinder.

[0021] Invention Effects

[0022] According to the present invention, the generation of secondary flow in the cylindrical body can be suppressed, and portability is achieved while suppressing changes in physical properties. Attached Figure Description

[0023] Figure 1 This is a block diagram illustrating one embodiment of the ultrasonic property measuring device according to the present invention.

[0024] Figure 2 This is a perspective view showing the cylindrical body, support portion, and ultrasonic transducer in this embodiment.

[0025] Figure 3 This is a schematic diagram illustrating the secondary flow generated by a disk that becomes the bottom when a cylinder with a bottom surface is rotated.

[0026] Figure 4 This is a schematic diagram showing the positional relationship between the cylindrical body and the ultrasonic transducer that rotates integrally with the cylindrical body in this embodiment.

[0027] Figure 5 This is a top view showing the hub, spokes, and retaining ring in this embodiment.

[0028] Figure 6 This is a perspective view showing the support portion of the cylindrical body and the rotating mechanism in other embodiments.

[0029] Figure 7 This is a schematic diagram showing the state in which the cylindrical body and rotating mechanism of this embodiment are set in a storage tank for storing the liquid to be measured.

[0030] Figure 8 This is a schematic diagram showing the bending state of the spokes in this embodiment and the accompanying two-dimensional flow.

[0031] Figure 9 This is a schematic diagram of an apparatus (existing apparatus) fabricated in a comparative example for measuring the velocity distribution of a liquid flowing in a cylindrical body by existing methods using ultrasound.

[0032] Figure 10 This is a color map and vector diagram showing the flow velocity distribution and flow velocity vector within a cylindrical container in an existing apparatus in this comparative example.

[0033] Figure 11 This is a schematic diagram showing the ultrasonic property measuring device (the device of the present invention) manufactured in Example 1 and a tabletop container filled with the liquid to be measured.

[0034] Figure 12This is a coordinate graph showing the instantaneous flow velocity distribution and average flow velocity distribution inside the cylinder as measured by the device of the present invention in Embodiment 1.

[0035] Figure 13 It is a coordinate graph plotted on the instantaneous flow velocity distribution at the same phase as measured by the existing device and the device of the present invention in Example 2.

[0036] Figure 14 This is a coordinate graph showing the radius distribution of the shear strain velocity calculated based on the flow velocity distribution measured by the existing device and the device of the present invention in this embodiment 2.

[0037] Figure 15 This is a coordinate graph showing the radius distribution of the viscosity coefficient calculated based on the flow velocity distribution measured by the existing device and the device of the present invention in this embodiment 2.

[0038] Figure 16 This is a coordinate graph showing the viscosity curve calculated based on the flow velocity distribution measured by the existing device and the device of the present invention in this embodiment 2.

[0039] Figure 17 This is a coordinate graph showing the flow velocity curve calculated based on the flow velocity distribution measured by the existing device and the device of the present invention in this embodiment 2.

[0040] Figure 18 The following are schematic diagrams of (a) the measuring device, (b) the cylindrical body, (c) the support portion, and (d) a photograph of the support portion, used in Embodiment 3.

[0041] Figure 19 The results shown in Example 3 are (a) Doppler velocity distribution (measured value) including the moving speed of the ultrasonic transducer and (b) coordinate graph of the moving speed of the ultrasonic transducer, obtained from the measurement of an aqueous carboxymethyl cellulose solution at 15°C.

[0042] Figure 20 This is a coordinate graph showing the Doppler velocity distribution obtained from the measurement of a carboxymethyl cellulose aqueous solution at 15°C in Example 3, including the Doppler velocity distribution of the ultrasonic transducer's movement speed minus the ultrasonic transducer's movement speed.

[0043] Figure 21 This illustrates that in this embodiment 3, Figure 20 The graph shown is a coordinate diagram of the normalized circumferential velocity distribution of the calculated Doppler velocity distribution.

[0044] Figure 22This is a coordinate graph showing the viscosity curves calculated based on the measured temperatures of carboxymethyl cellulose aqueous solutions at 15°C, 20°C, and 25°C in Example 3. Detailed Implementation

[0045] Hereinafter, an embodiment of the ultrasonic property measuring device according to the present invention will be described using the accompanying drawings.

[0046] like Figure 1 As shown, the ultrasonic property measuring device 1 of this embodiment includes: a cylindrical body 2; a rotating mechanism 3 that supports the cylindrical body 2 and causes it to rotate in both directions; an ultrasonic flow velocity distribution measuring unit 4 that measures the flow velocity distribution of the liquid inside the cylindrical body 2; and a property calculation unit 5 that calculates the properties of the liquid based on the flow velocity distribution measured by the ultrasonic flow velocity distribution measuring unit 4. The components will be described below.

[0047] The cylindrical body 2 applies shear force to the liquid from its sidewall by reciprocating rotation, thereby causing the liquid to flow inside the cylindrical body 2. For example... Figure 2 As shown, the cylindrical body 2 is permeated in such a way that both the upper end face 21 and the lower end face 22 can flow through it. That is, the cylindrical body 2 allows the liquid to flow in and out of the upper end face 21 and the lower end face 22, which are permeated when the liquid is immersed, and allows the liquid to flow during the reciprocating rotation, thereby suppressing the generation of secondary flow.

[0048] In this embodiment, the secondary flow refers to the flow generated besides the circumferential flow (circumferential direction) of the cylinder that flows through the sidewalls of the cylinder when the cylinder 2 rotates in both directions. Figure 3 As shown, this refers to the flow in the radial direction (radial direction) from the axis toward the sidewall of the cylinder, or the circulating flow accompanying that radial direction. That is, when the lower end face 22 of the cylinder 2 has a bottom surface, as... Figure 3 As shown in (a), if the cylinder 2 rotates, the velocity near the cylinder sidewall is faster than the velocity near the axis at the bottom. The liquid near the bottom is stretched and flows by the shear force against the bottom. At this time, a velocity difference is generated near the axis and near the cylinder sidewall. Fluids have the property that the pressure decreases when the flow velocity increases; due to the aforementioned velocity difference, the pressure near the cylinder sidewall is lower than that near the axis. The liquid flows from the side with higher pressure to the side with lower pressure, thus generating a radial flow from the axis toward the cylinder sidewall. In addition, through this generated radial flow, such as... Figure 3 As shown in (b), a circulating flow is generated inside the cylindrical body 2 in a vortex-like manner, and an annular secondary flow is generated throughout the cylinder.

[0049] In this embodiment, to prevent the generation of such a secondary flow, the upper end face 21 and the lower end face 22 of the rotating body 2 are completely open, and each end face is only composed of the thickness of the cylindrical sidewall.

[0050] In addition, such as Figure 2 As shown, in this embodiment, the cylindrical body 2 has a transducer fixing part 23, which fixes the ultrasonic transducer 41 that transmits and receives ultrasonic waves in the ultrasonic flow velocity distribution measurement unit 4. Specifically, the transducer fixing part 23 is provided on the outer surface 24 of the cylindrical body 2, and is formed in a cylindrical shape with an inner diameter that allows the cylindrical rod-shaped ultrasonic transducer 41 to be embedded. Figure 4 As shown, the transducer fixing part 23 is positioned such that the measurement line (irradiation line) ξ of the ultrasonic wave caused by the ultrasonic transducer 41 passes through a distance Δy from the axis of the cylindrical body 2.

[0051] Furthermore, the support for the ultrasonic transducer 41 is not limited to a configuration that allows it to rotate integrally with the cylindrical body 2, such as... Figure 6 As shown in (a), it can also be supported by a support arm 42 that is fixed to a non-rotating part such as the power unit 32.

[0052] The rotating mechanism 3 is used to make the cylindrical body 2 rotate back and forth, and has a support part 31 that supports the cylindrical body 2 and a power part 32 that makes the cylindrical body supported by the aforementioned support part 31 rotate back and forth.

[0053] The support portion 31 is a component used to support the cylindrical body 2 when part or all of it is immersed in a liquid. For example... Figure 2 As shown, the support 31 in this embodiment is configured to support the cylindrical body 2 in a suspended manner from below, and has a rotating shaft 311, a hub 312 fixed to the lower end of the rotating shaft 311, multiple spokes 313 extending from the hub 312, and a fixing ring 314 for fixing the front end of each spoke 313 to the upper edge of the cylindrical body 2.

[0054] The rotating shaft 311 is also a component used for the following actions: supporting the cylinder 2 above its axis in a manner that allows part or all of the cylinder 2 to be immersed in the aforementioned liquid, and transmitting the rotational force caused by the power unit 32 to the cylinder 2. Figure 1 As shown, in this embodiment, the rotating shaft 311 is supported by the power unit 32. Unlike the rotating torque type property measuring device, this rotating shaft 311 does not measure torque, thus allowing for free selection of its length or the depth to which it is immersed in the liquid.

[0055] The hub 312 is used to connect the rotating shaft 311 to multiple spokes 313. In this embodiment, the hub 312 is formed in a generally square shape, and the spokes 313 can extend from the four corners. In addition, a connecting hole 315 for connecting the rotating shaft 311 is formed in the center of the hub 312.

[0056] Furthermore, the rotating shaft 311 and the hub 312 are not limited to being separate components as in this embodiment, such as... Figure 6 As shown in (b), it can also be integrally constructed in such a way that the lower end of the rotating shaft 311 functions as the hub 312.

[0057] Spokes 313 are components used to connect hub 312 to cylindrical body 2, extending radially from hub 312. In this embodiment, spokes 313 are obliquely arranged in a manner that allows the secondary flow generated in the radial direction, which is primarily caused by spokes 313, to be dispersed in the circumferential direction. Specifically, as... Figure 5 As shown, the base end is located at one of the four corners of the hub 312 and offset horizontally from the axle position by a predetermined distance, and extends horizontally and bends at a predetermined angle relative to the line connecting the axle and the base end.

[0058] The front end of the spoke 313 is fixed to the fixing ring 314, and is fixed to the upper edge of the cylindrical body 2 via the fixing ring 314.

[0059] In this embodiment, the upper edge of the cylindrical body 2 where the front end of the spoke 312 is fixed includes not only the upper end face 21 of the cylindrical body 2, but also a position that does not obstruct the measurement of the flow velocity distribution using ultrasonic waves. Therefore, in the aforementioned upper edge, as... Figure 6 As shown in (b), for the cylindrical body 2, it also includes the inner circumferential surface near the upper end face 21, or as shown in [the diagram]. Figure 6 As shown in (c), it also includes the outer surface 24 near the upper end face 21.

[0060] Furthermore, the fixing of the spokes 313 is not limited to the configuration of fixing them to the upper end via the fixing ring 314, such as... Figure 6 As shown in (b), the cylindrical body 2 can also be directly fixed without the fixing ring 314. Additionally, as... Figure 6 As shown in (d), spokes 313 can also be bent in the up and down directions.

[0061] The power unit 32 is used to make the cylindrical body 2 reciprocate in both directions within a predetermined angle range Θ at a fixed period f. In this embodiment, it is composed of an electric stepper motor that can control the rotation speed or angle range Θ. In addition, the power unit 32 is not limited to an electric stepper motor, and various electric motors can be appropriately selected. Furthermore, it may also be equipped with a gear mechanism or the like as needed.

[0062] The ultrasonic velocity distribution measurement unit 4 includes an ultrasonic transducer 41 that irradiates ultrasonic waves from the outside of the cylindrical body 2 toward the inside of the cylindrical body 2 and receives ultrasonic waves reflected from the inside of the cylindrical body 2 toward the outside of the cylindrical body 2. It analyzes the received ultrasonic waves and measures the velocity of the ultrasonic waves at multiple measurement points along the measurement line ξ in a time sequence. That is, the ultrasonic velocity distribution measurement unit 4 can measure the temporal and spatial velocity distribution uξ(ξ,t) on the measurement line ξ at time t.

[0063] The ultrasonic transducer 41 includes a small element that operates by applying a voltage. By applying a voltage with a fixed periodic amplitude, it vibrates and can irradiate approximately linear ultrasonic waves along the measurement line ξ. Furthermore, regarding the aforementioned element, if it vibrates due to reflected waves, it generates a voltage corresponding to that vibration, enabling it to receive reflected waves. In this embodiment, the ultrasonic transducer 41 is inserted into and fixed to the transducer fixing part 23 provided on the outer surface 24 of the cylindrical body 2 in a manner that allows it to rotate integrally with the cylindrical body 2. At this time, to suppress the effects of diffuse reflection of ultrasonic waves within the wall of the cylindrical body 2, the ultrasonic transducer 41 is preferably positioned such that the distance from the inner surface of the cylindrical body 2 to the front end is approximately equal to the diameter of the ultrasonic transducer 41. In this embodiment, this can be preset by integrating it with the cylindrical body 2.

[0064] The ultrasonic velocity distribution measurement unit 4 consists of a computer capable of computation and a program for performing computation. It converts the voltage based on the reflected wave received by the ultrasonic transducer 41 into a digital signal capable of computation and processes the digital signal, thereby calculating the temporal and spatial velocity distribution u. ξ (ξ,t). For calculating the temporal and spatial velocity distribution u ξ For example, the technology disclosed in Japanese Patent Application Publication No. 2003-344131 can be used for (ξ,t).

[0065] The property calculation unit 5 consists of a computer capable of computation and a program for performing computation, and is able to estimate the physical properties of the liquid based on the flow velocity distribution measured by the ultrasonic flow velocity distribution measurement unit 4. In this embodiment, the property calculation unit 5 is connected to the ultrasonic flow velocity distribution measurement unit 4 in a manner capable of data communication, and is configured to receive data on the flow velocity distribution measured by the ultrasonic flow velocity distribution measurement unit 4.

[0066] In addition, the property calculation unit 5 in this embodiment measures the temporal and spatial velocity distribution u along the measurement line ξ by fixing the ultrasonic transducer 41 to the outer surface 24 of the cylindrical body 2 and rotating it integrally. ξ (ξ,t) is transformed into the circumferential velocity distribution u inside the cylindrical body 2. θ (r,t).

[0067] First, the circumferential velocity of the ultrasonic transducer 41 is expressed by the following formula (1).

[0068] U wall (r, i) = ωRΘe -ωt

[0069] ...Formula (1)

[0070] Here, r is the distance from the axis in the radial direction, ω is the velocity, Θ is the range of rotation angles, and t is time.

[0071] In addition, the speed of the ultrasonic wave of the ultrasonic transducer 41 along the direction of the measurement line is expressed by the following formula (2).

[0072] U(ξ,t)=ωΘΔye -ωt

[0073] ...Formula (2)

[0074] Here, Δy is the distance from the axis.

[0075] If the velocity distribution u of the measurement line ξ measured by the ultrasonic velocity distribution measurement unit 4 is based on the above formulas (1) and (2), then... ξ (ξ,t) is transformed into a velocity distribution along the circumferential direction along the radial direction, which becomes the velocity distribution of the following formula (3).

[0076]

[0077] In this embodiment, the property calculation unit 5 calculates the circumferential velocity distribution u using formula (3). θ By comparing (r,t) with the theoretically calculated velocity distribution, the liquid's physical properties are estimated. Regarding the velocity distribution u in the circumferential direction in physical property calculation unit 5... θ (r,t) The method for estimating physical properties can use the technique disclosed in Non-Patent Document 1.

[0078] Furthermore, the ultrasonic flow velocity distribution measurement unit 4 and the physical property calculation unit 5 in this embodiment are configured as separate units, but they can also be configured using the same computer.

[0079] Next, the function of each component in the ultrasonic property measuring device 1 of this embodiment will be explained.

[0080] First, liquid is circulated by rotating the cylindrical body 2 back and forth at a fixed cycle. Specifically, part or all of the cylindrical body 2, supported by the support 31 of the rotating mechanism 3, is immersed in the liquid. For example, as Figure 7As shown, the cylindrical body 2 and the rotating mechanism 3 are transported to the storage tank 6, which stores the liquid to be measured, and are arranged to be immersed in the liquid at any depth and position from above the storage tank 6.

[0081] Both the upper end face 21 and the lower end face 22 of the cylindrical body 2 are open to flow, so the liquid flows into the cylindrical body 2 simply by sinking. The ultrasonic property measuring device 1 of this embodiment is not a torque measuring device like conventional rotary torque type property measuring devices, therefore the length of the rotating shaft 311 can be freely selected, and it can be positioned at a desired depth or location. Here, by setting the cylindrical body 2 to a state where it is completely immersed, the influence of changes in the free interface on the upper end face can be suppressed or eliminated. Furthermore, the installation of the storage tank 6 can be achieved simply by using the cylindrical body 2 and the rotating mechanism 3. In this embodiment, the ultrasonic transducer 41 is pre-fixed to the cylindrical body 2, making setup easy and highly portable.

[0082] Next, the power unit 32 of the rotating mechanism 3 causes the cylindrical body 2 to rotate back and forth at a fixed cycle. The liquid inside the cylindrical body 2 flows due to the shear force between its viscosity and the sidewall of the cylinder. At this time, the lower end face 22 of the cylindrical body 2 is completely open, and no secondary flow is generated. In addition, the rotating shaft 311 is positioned above the cylindrical body 2, so it does not affect the generation of secondary flow.

[0083] Furthermore, the hub 312 and each spoke 313 are formed in a manner that allows flow at the upper end face of the cylindrical body 2, thus significantly suppressing the generation of secondary flow compared to existing bottomed cylindrical containers that cover the entire bottom surface.

[0084] Furthermore, the secondary flow caused by each spoke 313 in this embodiment is generated along each spoke 313, and therefore dispersed not only in the radial direction but also in the circumferential direction. That is, as... Figure 8 As shown, if the spokes 313 are bent in a manner that is not arranged on a diagonal line passing through the axis, the flow a along the spokes 313 can also be dispersed into a flow b in the radial direction and a flow c in the circumferential direction, thus suppressing the generation of secondary flows.

[0085] The ultrasonic flow velocity distribution measurement unit 4 irradiates ultrasonic waves into the cylindrical body 2 via an ultrasonic transducer 41, and receives ultrasonic waves reflected from the cylindrical body 2, measuring the flow velocity of the ultrasonic waves at multiple measurement points along the measurement line ξ in a time sequence. Specifically, as... Figure 1As shown, a voltage used to generate ultrasonic waves is applied from the ultrasonic flow velocity distribution measuring unit 4 to the ultrasonic transducer 41. On the other hand, the ultrasonic transducer 41 receives ultrasonic waves reflected from inside the cylindrical body 2 and sends the voltage generated based on the reflected wave to the ultrasonic flow velocity distribution measuring unit 4. The ultrasonic flow velocity distribution measuring unit 4 converts the voltage received from the ultrasonic transducer 41 into the aforementioned digital signal and processes the aforementioned digital signal to calculate the temporal and spatial flow velocity distribution u of the liquid flowing within the cylindrical body 2, which rotates back and forth at a fixed period. ξ (ξ,t). Then, the calculated velocity distribution u ξ (ξ,t) is sent to the property calculation unit 5.

[0086] At this time, the ultrasonic transducer 41 is pre-fixed integrally to the outer surface 24 of the cylindrical body 2 in the optimal position, so the setting is easy and the error of each measurement can be suppressed.

[0087] The property calculation unit 5 receives the velocity distribution u sent from the ultrasonic velocity distribution measurement unit 4. ξ (ξ,t). Then, based on formula (3), the aforementioned velocity distribution u is... ξ (ξ,t) transformed into a circumferential velocity distribution u θ (r,t). Then, the circumferential velocity distribution u θ The physical properties are estimated by comparing (r,t) with the theoretically calculated velocity distribution (the velocity distribution in the same circumferential direction as the measured value).

[0088] The ultrasonic property measuring device 1 of this embodiment, as described above, can achieve the following effects.

[0089] 1. The upper end face 21 and the lower end face 22 of the cylindrical body 2 are both constructed in a flow-through manner, thereby enabling the flow of liquid that rotates back and forth and suppressing the generation of secondary flow.

[0090] 2. Both the upper end face 21 and the lower end face 22 of the cylindrical body 2 are constructed in a flow-through manner, so that liquid can be allowed to flow into the cylindrical body 2 by sinking into the liquid stored in the storage tank 6, etc., which can be easily set up, and there is no need to move it into other containers, etc., thus suppressing changes in the physical properties.

[0091] 3. The length of the rotating shaft 311 can be freely selected, so when measuring the physical properties of liquids stored in storage tanks 6, the differences in physical properties caused by different depths or positions can be measured.

[0092] 4. A support part 31, consisting of a rotating shaft 311, a hub 312, and spokes 313, supports the cylindrical body 2, thereby ensuring the flow of liquid and supporting the cylindrical body 2 in a manner that allows it to rotate back and forth.

[0093] 5. Bending each spoke 313 at a predetermined angle enables the secondary flow generated along the spokes 313 to be dispersed in both the radial and circumferential directions.

[0094] 6. The ultrasonic transducer 41 is pre-fixed in a manner that allows it to rotate integrally with the cylindrical body 2, or the upper end face 21 and lower end face 22 of the cylindrical body 2 are both connected in a flow-through manner. This makes setup easier, improves portability, and expands the measurement accuracy of the liquid flow velocity distribution or the range of space and velocity that can be measured. It also enables the measurement of the physical properties of liquids with various rheological characteristics.

[0095] Next, specific embodiments of the ultrasonic property measuring device according to the present invention will be described. Furthermore, the technical scope of the present invention is not limited to the features shown in the following embodiments.

[0096] Comparative example

[0097] <Regarding the secondary flow generated by the existing method disclosed in Non-Patent Document 1>

[0098] In this comparative example, the secondary flow generated when using the existing method disclosed in Non-Patent Document 1 is described. In the existing method, such as Figure 9 As shown, an experimental apparatus (hereinafter referred to as "the existing apparatus") is used to rotate a cylindrical container with a bottom surface back and forth at a fixed period. The aforementioned cylindrical container is made of propylene, with a thickness of 3 mm, a radius R = 77 mm, and a depth of 300 mm.

[0099] Additionally, a cylindrical container is placed inside a container that is slightly larger than the cylindrical container, and the cylindrical container is surrounded by water to allow ultrasonic waves from the ultrasonic transducer to penetrate into the cylindrical container. A rotating mechanism is located below the cylindrical container.

[0100] The liquid used for measurement had a kinematic viscosity of 1000 mM. 2 The silicone oil is a Newtonian fluid independent of shear rate. To improve the reflection of ultrasound, tiny particles (Mitsubishi Chemical Corporation, CHP20P, diameter 75-150 μm, specific gravity relative to silicone oil 1.03) are suspended in the silicone oil as reflectors. Then, the aforementioned silicone oil is filled with the silicone oil at a height z = 125 mm above the bottom of the cylindrical container to form a liquid surface.

[0101] The cylindrical container filled with the silicone oil is rotated back and forth at a frequency of 1 Hz with an angle range of Θ of 90 degrees (π / 2 rad).

[0102] The ultrasonic transducer has a frequency of 2 MHz and a diameter of 10 mm. This transducer is fixed to a mounting platform (not shown) that can move vertically (distance Δz from the bottom surface) and horizontally (distance Δy from the axis). In this comparative example, to monitor the overall flow in the cylindrical container, the ultrasonic transducer was moved at 10 mm intervals at distances Δy = 0 mm and Δy = 15 mm from the axis, within a height Δz = 10 mm to 110 mm from the bottom surface, and the flow velocity distribution was measured at each location.

[0103] Figure 10 This shows the measurement results of the effective viscosity (color mapping) calculated based on the flow velocity vector and flow velocity distribution within the cylindrical container. The horizontal axis shows the dimensionless position of the distance r from the axis of the cylindrical container to the side wall of the cylinder, using the inner diameter R of the cylindrical container. The vertical axis shows the height z above the bottom surface.

[0104] The velocity vector is a vector representation of the vertical velocity calculated using a continuous formula based on the radial velocity measured at a distance Δy = 0 mm. The direction of the arrow indicates the velocity direction, with longer arrows indicating faster velocity.

[0105] The color map shows the effective viscosity calculated based on the flow velocity distribution measured at a distance of Δy = 15 mm. The whiter the color, the lower the effective viscosity, and the darker the color, the higher the effective viscosity. Furthermore, since the ultrasonic transducer is positioned at a distance of Δy = 15 mm from the axis, flow velocity information (effective viscosity) cannot be obtained in the range r / R < Δy / R ≈ 0.2.

[0106] like Figure 10 As shown, the velocity vector illustrates flow not only in the radial direction but also in the vertical direction. At the bottom, a radial flow from the axis towards the cylinder wall is observed due to the velocity difference between the axis and the vicinity of the cylinder wall. Additionally, a descending flow is generated near the axis, and an ascending flow is generated near the wall, creating a secondary flow in a cyclical manner. Thus, an annular secondary flow is generated throughout the cylindrical container. This secondary flow has a velocity of approximately 10 to 50 mm / s.

[0107] Furthermore, the silicone oil used as the test fluid is a Newtonian fluid, and its viscosity is constant within the cylindrical container. However, as shown by the color mapping, the effective viscosity is calculated to be higher near the bottom of the cylindrical container than it is constant. This is because the flow near the bottom is considered to be close to a state of near-rigid rotation similar to the reciprocating rotation of the bottom surface, and the effective viscosity is overestimated.

[0108] From the above, it can be confirmed that in this comparative example, in the existing apparatus, the effective viscosity can be calculated based on the flow velocity distribution. On the other hand, by utilizing the radial flow generated near the bottom surface of the cylindrical container through rotation, an annular secondary flow is generated throughout the cylindrical container. Furthermore, the physical property values ​​cannot be accurately calculated based on the flow velocity distribution measured near the bottom surface.

[0109] Example 1

[0110] In this embodiment 1, an ultrasonic property measuring device (hereinafter referred to as "the device of the present invention") was fabricated to measure the flow velocity distribution inside a cylindrical body.

[0111] like Figure 11 As shown, the device of the present invention in this embodiment 1 has a cylindrical body with both the upper and lower ends fully open. The aforementioned cylindrical body is made of acrylic resin, with a thickness of 2 mm, a radius R = 77 mm, and a depth of 60 mm.

[0112] The support part has the following functions: Figure 2 and Figure 5 The diagram shows a rotating shaft, a hub located at the lower end of the rotating shaft, four spokes extending from the four corners of the hub, and a fixing ring connecting the front end of each spoke to the upper end of a cylindrical body. The rotating shaft has a diameter of 15 mm, and the hub is formed in a square shape with one side length of 45 mm. The spokes are formed in the shape of flat strips with a width of 10 mm and a thickness of 5.5 mm, bent relative to the line connecting the shaft center and the base end. The power unit provides shaft support for the rotating shaft at its upper end.

[0113] The ultrasonic transducer uses a frequency of 4MHz and a diameter of 8mm. This ultrasonic transducer is fixed to the outer surface of the cylindrical body at a distance Δy = 15mm from the axis and 20mm from the lower end face, in a manner that allows it to rotate integrally with the cylindrical body. Furthermore, to suppress noise caused by diffuse reflection within the cylindrical body's wall, the front end of the ultrasonic transducer is positioned approximately 8mm from the inner circumference of the cylindrical body (approximately 8mm in diameter).

[0114] The liquid used in the test was the same as the comparative example with a kinematic viscosity of 1000 mmHg. 2 / s of silicone oil allows tiny particles from Mitsubishi Chemical Corporation to be suspended as reflectors. For example... Figure 11 As shown, the silicone oil is filled into a container placed on a table. Then, the entire cylindrical body supported by the support is set to be immersed in the silicone oil in the container on the table, and, similar to the comparative example, it is rotated back and forth at 1 Hz with an angle range Θ of 90 degrees (π / 2 rad).

[0115] exist Figure 12 The figure shows the flow velocity distribution of silicone oil inside the cylinder as measured in Example 1. The horizontal axis represents the distance from the front end of the ultrasonic transducer. Here, the positional relationship between the axis of the cylinder and the sidewall of the cylinder is compared with that described in the comparative example. Figure 10 The left and right axes are reversed; the left side is near the sidewall of the cylinder, and the right side is near the axis. Additionally, the vertical axis represents the measured flow velocity (Doppler velocity) along the measurement line, which is the average of the instantaneous values ​​at four moments within one cycle of the reciprocating rotation and the flow velocity measured at fixed time intervals.

[0116] like Figure 12 As shown, the instantaneous velocity distribution varies symmetrically around a velocity of 0 mm / s, and the flow inside the cylinder reverses direction through reciprocating rotation. Furthermore, the average velocity distribution becomes approximately 0 mm / s. However, assuming a radial velocity component (secondary flow) is generated inside the cylinder, the measured velocity varies asymmetrically around 0 mm / s, and the average velocity will not be 0 mm / s.

[0117] From the above, it can be confirmed that the device of the present invention in this embodiment 1, compared with the existing device, can suppress secondary flow.

[0118] Example 2

[0119] Next, a comparison was made between the flow velocity distribution measured by the existing apparatus of the comparative example and the ultrasonic property measuring apparatus of the present invention according to Example 1, and the evaluable range that can be used for property calculation was studied.

[0120] Figure 13 This is a coordinate graph plotting the instantaneous velocity distribution at the same phase, measured by reciprocating rotation, and comparing the existing device with the device of the present invention. The left coordinate graph shows the results of the existing device, and the right coordinate graph shows the results of the device of the present invention. The horizontal and vertical axes are... Figure 13 Similarly, the horizontal axis represents the distance from the front end of the ultrasonic transducer, and the vertical axis represents the flow velocity along the measured line.

[0121] As shown in the left-hand graph, if existing equipment is used, noise is included in the flow velocity distribution if the distance from the ultrasonic transducer reaches approximately 75 mm. The primary reasons are: First, the silicone oil being measured has the property of attenuating ultrasonic waves; due to the distance, the received ultrasonic waves are insufficient for measuring the flow velocity, thus becoming noise. Second, the ultrasonic transducer is fixed at a position separated from the cylindrical container; therefore, as the ultrasonic waves are emitted in the water surrounding the cylindrical container and propagate through the container wall towards the silicone oil inside, diffuse reflection or attenuation occurs, resulting in noise. Third, the ultrasonic transducer and the cylindrical container have relative velocities; therefore, the greater the distance from the ultrasonic transducer, the slower the flow velocity in the measurement line direction, the fewer reflectors (microparticles) pass through the aforementioned measurement line, and the less sufficient the received ultrasonic waves become.

[0122] In contrast, as shown in the right-hand coordinate graph, in the apparatus of the present invention, noise is barely observed up to approximately 115 mm from the ultrasonic transducer. Even near the wall on the side opposite to where the ultrasonic transducer is located (around 150 mm away), the noise is minimal. Furthermore, noise that deviates significantly from the expected flow velocity distribution is rarely observed. This is believed to be because by fixing the ultrasonic transducer to the cylindrical body, diffuse reflection of ultrasonic waves is suppressed, and the closer the distance from the ultrasonic transducer is to the cylinder axis (the farther away), the faster the flow velocity in the direction of the liquid measurement line. Even at locations where ultrasonic waves tend to attenuate, sufficient ultrasonic waves can be received, suppressing noise generation. Therefore, the flow velocity can be measured up to near the wall, and it is expected that physical properties consistent with actual conditions can be calculated.

[0123] Therefore, the evaluable range for the radius of cylindrical containers and cylindrical bodies is studied. Here, the evaluable range refers to the range within which physical properties can be estimated.

[0124] Figure 14 This is a coordinate graph showing the shear strain rate at a radial position for a cylindrical container and a cylindrical body. The left coordinate graph shows the results of the device, and the right coordinate graph shows the results of the ultrasonic property measuring device according to the present invention. Figure 10 Similarly, the horizontal axis shows the dimensionless position of the distance r from the axis of the cylindrical container to the sidewall, represented by the inner diameter R of the cylindrical container (the positional relationship between the axis of the cylinder and the sidewall). Figure 12 and Figure 13 (The left and right sides are reversed.) The vertical axis represents the shear strain rate, and the colors indicate the probability density.

[0125] As shown in the left-hand coordinate graph, in the existing apparatus, there is a deviation in shear strain rate from the axis (r / R = 0) to r / R = 0.45. This is considered to be due to the small velocity gradient and low shear strain rate near the axis, resulting in the deviation. Furthermore, it can be confirmed that within the range exceeding r / R = 0.85, some values ​​showing a roughly linear pattern exhibit increases and decreases, indicating inaccurate measurements.

[0126] In contrast, as shown in the right-hand coordinate graph, in the device of the present invention, for the range exceeding r / R = 0.85, values ​​are also shown along a generally linear line, enabling accurate measurements.

[0127] Figure 15 This is a coordinate graph showing the viscosity coefficient calculated based on the radius and velocity distribution of the cylindrical container and body. Figure 14 Similarly, the horizontal axis represents the dimensionless position of the distance r from the center of the cylindrical container to the side wall of the cylinder, calculated using the inner diameter R of the cylindrical container. The vertical axis represents the viscosity coefficient, with colors indicating the probability density.

[0128] As shown in the left-hand graph, in existing devices, the viscosity coefficient in the range of r / R = 0.45 to 0.85, which is considered to enable accurate measurement of flow rate distribution, is consistent with the viscosity values ​​(catalog viscosity values) listed in the silicone oil catalog. On the other hand, the range beyond r / R = 0.85 deviates significantly from the catalog viscosity values, making it impossible to calculate the correct viscosity coefficient.

[0129] In contrast, as shown in the right-hand coordinate graph, in the apparatus of the present invention, the range from r / R = 0.45 to the cylindrical sidewall, i.e., r / R = 1, corresponds to the viscosity value in the catalog, and the correct viscosity coefficient can be obtained.

[0130] Such as these Figure 14 and Figure 15 As shown, the evaluable range of the existing device is from r / R = 0.45 to 0.85, while the evaluable range of the device of the present invention is expanded to be from r / R = 0.45 to 1. The flow caused by the reciprocating rotation of the cylinder is caused by shear force against the wall. By accurately measuring the velocity distribution near the wall, the accuracy of the calculated physical properties is improved. Therefore, it can be considered that the device of the present invention achieves improved accuracy compared to the existing device.

[0131] in addition, Figure 16 This is a coordinate graph showing the relationship between shear strain rate and viscosity coefficient. The left axis plots the results of the device, and the right axis plots the results of the device of the present invention. The horizontal axis is the shear strain rate, and the vertical axis is the viscosity coefficient. The colors indicate the probability density.

[0132] As shown in the left-hand graph, in the existing apparatus, the shear strain rate exceeds approximately 10 s. -1 The range cannot be measured. In contrast, as shown in the right-hand coordinate graph, in the ultrasonic property measuring device according to the present invention, the shear strain rate, even exceeding approximately 10 s... -1 Within this range, it is also roughly consistent with the viscosity value of the catalog, enabling accurate measurement.

[0133] in addition, Figure 17 This is a coordinate graph showing the relationship between shear strain rate and shear stress. The horizontal axis represents shear strain rate, and the vertical axis represents shear stress; the colors indicate probability density. Regarding the flow velocity curve, it shows the flow characteristics under constant-state (steady-state) viscosity measurements across multiple shear rate ranges, enabling estimation of shear stress (viscosity) in various processes with different shear rate ranges.

[0134] Results and Figure 16 Similarly, as shown in the left-hand graph, in the existing apparatus, the shear strain rate exceeds approximately 10 s. -1 The range cannot be measured. In contrast, as shown in the right-hand coordinate graph, in the device of the present invention, the shear strain rate is measured even when it exceeds approximately 10 s. -1 Measurements can also be performed within the specified range.

[0135] Therefore, such as Figure 16 and Figure 17 As shown, compared with existing devices, the device of the present invention can measure physical properties over a wider range of shear rates.

[0136] Based on the above, the device of the present invention has a wider evaluation range compared with existing devices, can calculate physical properties based on the flow velocity near the wall, and has a wider applicability range for shear strain rate, thus enabling the determination of physical properties of liquids with various rheological characteristics.

[0137] Example 3

[0138] Next, the temperature dependence of the viscous properties (velocity distribution) in a non-Newtonian fluid is measured using the apparatus of the present invention. For example... Figure 18 As shown in (a), the apparatus used in this embodiment 3 has a storage tank with a diameter of 430 mm and a depth of more than 350 mm for storing the test fluid. The sides and bottom of the storage tank are formed as two layers in a manner that allows circulating water to flow. In addition, a thermostat is connected to the storage tank to circulate the circulating water and maintain a fixed temperature.

[0139] like Figure 18 As shown in (b), the cylindrical body of the device of the present invention in this embodiment 3 is made of propylene, with a thickness of 2 mm, a radius R = 77 mm, and a depth of 100 mm. Additionally, if using... Figure 18(c) and Figure 18 (d) shows that the support has the same configuration as in Embodiment 2. Moreover, the cylindrical body is positioned at the center of the storage tank and its lower end is located 200 mm from the bottom surface of the storage tank.

[0140] The ultrasonic transducer is fixed on the outer side of the cylinder at a distance Δy = 18 mm from the axis and 400 mm from the lower end face in a manner that allows it to rotate integrally with the cylinder.

[0141] An aqueous solution of carboxymethyl cellulose was used as a non-Newtonian fluid in the test. The concentration of carboxymethyl cellulose in the aqueous solution used in Example 3 was 0.5 wt%. The aqueous solution of carboxymethyl cellulose was stored in a storage tank to a depth of 350 mm, with the cylindrical body completely submerged.

[0142] Then, a thermostat is used to circulate the water in the storage tank, maintaining a constant temperature for the carboxymethyl cellulose aqueous solution. In this Example 3, measurements were taken at temperatures of 15°C, 20°C, and 25°C.

[0143] exist Figure 19 The results of measuring an aqueous solution of carboxymethyl cellulose at 15°C using the apparatus of the present invention are shown. Figure 19 (a) Doppler velocity measured by an ultrasonic transducer. The vertical axis represents the distance from the ultrasonic transducer, and the horizontal axis represents the elapsed time. Additionally, the intensity of color and the contour lines indicate the strength of the Doppler velocity, showing that a darker color indicates a faster velocity. Figure 19 (b) is the moving speed of the ultrasonic transducer (cylindrical wall).

[0144] like Figure 19 As shown in (a), the velocity near the wall (around 0 mm and 150 mm along the longitudinal axis) and the velocity near the center of the cylinder (around 77 mm along the longitudinal axis) decrease. However, in Figure 19 The Doppler velocity in (a) includes the moving velocity of the ultrasonic transducer. Therefore, the calculation of... Figure 19 (b) The difference in the moving velocity of the ultrasonic transducer is used to extract the Doppler velocity generated by the reciprocating rotation of the cylinder. In addition, the circumferential velocity distribution of the calculated Doppler velocity is normalized.

[0145] exist Figure 20 The image shows the Doppler velocity distribution after subtracting the moving velocity of the ultrasonic transducer. Additionally, in... Figure 21 The image shows the circumferential velocity distribution of the flow after normalizing the Doppler velocity distribution. For example... Figure 20 and Figure 21As shown, the velocity is faster near the wall, and the repeated forward and reverse motion of the velocity manifests as a striped pattern. Furthermore, the striped pattern is tilted, indicating that the velocity gradually propagates along the central direction over time. This confirms that the apparatus of the present invention can measure the velocity distribution of an aqueous solution of carboxymethyl cellulose, used as a non-Newtonian fluid in the test.

[0146] Next, Doppler velocity measurements were performed by setting the temperature of the carboxymethyl cellulose aqueous solution to 15°C, 20°C, and 25°C, and the viscosity of the carboxymethyl cellulose aqueous solution at each temperature was calculated. Figure 22 It is a viscosity curve calculated under various temperature conditions, with the vertical axis representing viscosity and the horizontal axis representing shear rate.

[0147] like Figure 22 As shown, the viscosity decreases with increasing shear rate under various temperature conditions, exhibiting the characteristics of a non-Newtonian fluid whose viscosity depends on shear rate.

[0148] Furthermore, if the temperature of the carboxymethyl cellulose aqueous solution increases, its viscosity tends to decrease relative to the increase in shear rate. That is, the viscosity of the carboxymethyl cellulose aqueous solution changes with increasing temperature, decreasing from the stage of low shear rate onwards.

[0149] Based on the above, the device of the present invention can determine the physical properties of a non-Newtonian fluid that is temperature-dependent.

[0150] Furthermore, the ultrasonic property measuring device according to the present invention is not limited to the aforementioned embodiments and can be appropriately modified. For example, in order to improve the strength of the cylindrical body and prevent deformation due to reciprocating rotation, it may also have a reinforcing member mounted on the upper or lower end face to minimize the generation of secondary flow.

[0151] Symbol Explanation

[0152] 1. Ultrasonic property measuring device

[0153] 2. Cylindrical body

[0154] 3 Rotating mechanism

[0155] 4 Ultrasonic Flow Velocity Distribution Measurement Unit

[0156] 5. Property Calculation Unit

[0157] 6 Storage tanks

[0158] 21. Top surface

[0159] 22 Lower end face

[0160] 23 Transducer mounting part

[0161] 24. Outer surface

[0162] 31 Support section

[0163] 32 Power Department

[0164] 41 Ultrasonic transducer

[0165] 42 Support Arm

[0166] 311 Rotary Axis

[0167] 312 wheels

[0168] 313 spokes

[0169] 314 Fixing ring

[0170] 315 Connecting hole.

Claims

1. An ultrasonic property measuring device, which uses ultrasound to measure the velocity distribution of a liquid flowing within a cylinder by rotating the cylinder back and forth at a fixed cycle, and estimates the properties of the liquid based on the velocity distribution. In the ultrasonic property measuring device, the upper and lower ends of the cylinder are both permeable, and the device has a rotating mechanism that supports the cylinder and allows it to rotate back and forth while partially or completely immersed in the liquid.

2. The ultrasonic property measuring device according to claim 1, wherein, The upper and lower ends of the cylinder are completely open, and, The rotating mechanism, serving as a support for the cylindrical body, has a rotating shaft supported by a power unit shaft above the axis of the cylindrical body, a hub fixed to the lower end of the rotating shaft, and multiple spokes extending radially from the hub and fixed to the upper edge of the cylindrical body.

3. The ultrasonic property measuring device according to claim 2, wherein, Each spoke has a base end at a position horizontally offset from the axis position, and extends horizontally and bends at a predetermined angle relative to the line connecting the axis and the base end.

4. The ultrasonic property measuring device according to any one of claims 1 to 3, wherein, An ultrasonic transducer that irradiates ultrasonic waves into the cylindrical body and receives ultrasonic waves reflected from the cylindrical body is fixed to its outer surface in a manner that allows it to rotate integrally with the cylindrical body.

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