JP2014169995A - Measurement system of physical quantity and construction method of analytic model - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a measurement system of a physical quantity capable of highly accurately constructing an analytic model of a gas-liquid two-phase flow in a tube bundle.SOLUTION: In a case of constructing a basic equation to be an analytic model for analyzing a gas-liquid two-phase flow circulating through a tube bundle 5, a measurement system of a physical quantity measures a physical quantity used in the basic equation. The basic equation contains a constructive equation with a physical quantity to be each element of the analytic model as a function, and includes a physical quantity measurement unit 10 measuring a physical quantity, and an operation unit 20 acquiring correlation interpolating the physical quantity measured by the constructive equation with a physical quantity as a function and incorporating the acquired correlation in the constructive equation as a coefficient.

Description

  The present invention relates to a physical quantity measurement system and an analysis model construction method used for constructing an analysis model of a gas-liquid two-phase flow in a tube group.

  2. Description of the Related Art Conventionally, there is known a two-phase flow excitation force evaluation device that measures a void ratio of a two-phase flow that flows in a flow section where a plurality of pipes are arranged (see, for example, Patent Document 1). This two-phase flow excitation force evaluation device is formed of a conductive material on one surface of a tubular body, measures the displacement or stress of the tubular body in a state where the tubular body is vibrated, and determines the predetermined surface of the tubular body. Based on the potential difference between the potential at the position and the reference potential, the void fraction of the two-phase flow flowing in the vicinity of the tube is measured.

JP 2010-271074 A

  By the way, in order to simulate the behavior of the gas-liquid two-phase flow in the tube group, it has been attempted to construct an analysis model. An analysis model of a gas-liquid two-phase flow is constructed by appropriately incorporating constitutive equations having functions of physical quantities serving as elements in the tube group. However, the constitutive equation does not always simulate the actual behavior of physical quantities. For this reason, it is difficult to improve the accuracy of the constitutive equation, and it is difficult to accurately construct an analysis model in which the constitutive equation is incorporated.

  Therefore, an object of the present invention is to provide a physical quantity measurement system and an analysis model construction method capable of accurately constructing an analysis model of a gas-liquid two-phase flow in a tube group.

  The physical quantity measurement system according to the present invention is a physical quantity measurement system that measures a physical quantity used in the basic equation when constructing a basic equation serving as an analysis model for analyzing a gas-liquid two-phase flow flowing in a tube group. The basic equation includes a constitutive expression having the physical quantity as a function as each element of the analysis model as a function, and a physical quantity measuring unit for measuring the physical quantity and the constitutive expression having the physical quantity as a function are measured. And calculating a correlation for interpolating the physical quantity, and incorporating the calculated correlation as a coefficient into the constitutive equation.

  Further, another analytical model construction method of the present invention is an analytical model construction method for constructing a basic equation serving as an analytical model for analyzing a gas-liquid two-phase flow flowing in a tube group, wherein The equation includes a constitutive equation having a function of the physical quantity serving as each element of the analysis model, and a physical quantity measuring step for measuring a physical quantity used in the basic equation, and the constitutive equation having the physical quantity as a function are measured. A coefficient calculating step of calculating a correlation for interpolating the physical quantity, calculating the calculated correlation as a coefficient, and an analysis model building step of building the basic equation by incorporating the calculated coefficient into the constitutive equation It is characterized by.

  According to this configuration, it is possible to obtain a correlation that interpolates between a constitutive equation that uses a physical quantity as a function and a measured physical quantity, and to incorporate a coefficient related to the obtained correlation into the constitutive expression. Therefore, the constitutive equation can accurately simulate the behavior of the actual physical quantity, and an analysis model for analyzing the gas-liquid two-phase flow in which the constitutive equation is incorporated can be constructed with high accuracy.

  In this case, the constitutive equation is a constitutive equation of the space void ratio in the gas phase in the space of the tube group, and as the physical quantity as a function, the liquid film thickness of the liquid film formed on the outer peripheral surface of the tube And a ratio of the liquid droplets or liquid film contained in the gas phase in the space of the tube group, and the physical quantity measuring unit measures the liquid film thickness formed on the outer peripheral surface of the tube And a ratio measuring unit that measures a ratio of a droplet or a liquid film contained in a gas phase in the space of the tube group, and the arithmetic unit is configured such that the constitutive equation of the space void ratio is It is preferable that a correlation for interpolating the measured liquid film thickness and the ratio of the droplets or the liquid film is obtained, and the obtained correlation is incorporated as a coefficient into the constitutive equation.

  According to this configuration, a constitutive equation for the spatial void ratio can be constructed with high accuracy, and an analysis model in which this constitutive equation is incorporated can be constructed with high accuracy.

  In this case, the constitutive equation is a constitutive equation of the gas-liquid interface drag that is the drag at the interface between the gas phase and the liquid phase, and includes the gas-liquid interface velocity in the space of the tube group as the physical quantity as a function. The physical quantity measurement unit includes a gas-liquid interface velocity measurement unit that measures a gas-liquid interface velocity that is an interface velocity between a gas phase and a liquid phase in the space of the tube group, and the calculation unit includes the It is preferable that the constitutive equation of the gas-liquid interface drag obtains a correlation for interpolating the measured gas-liquid interface velocity and incorporates the obtained correlation into the constitutive equation as a coefficient.

  According to this configuration, a constitutive equation for the gas-liquid interface drag can be constructed with high accuracy, and an analysis model in which this constitutive equation is incorporated can be constructed with high accuracy.

  In this case, the constitutive equation is a constitutive equation of the gas-liquid interface area of the droplets contained in the gas phase in the space of the tube group, and includes the droplet diameter of the droplets as the physical quantity as a function. The physical quantity measuring unit has a droplet trapping unit that traps the droplets contained in the gas phase in the space of the tube group, and the arithmetic unit is a constitutive equation for the gas-liquid interface area of the droplets However, it is preferable that a correlation for interpolating the droplet diameter of the captured droplet is obtained, and the obtained correlation is incorporated as a coefficient in the constitutive equation.

  According to this configuration, the constitutive equation of the gas-liquid interface area of the droplet can be constructed with high accuracy, and an analysis model in which this constitutive equation is incorporated can be constructed with high accuracy.

  In this case, the constitutive equation is a constitutive equation of the gas-liquid interface area of the liquid film contained in the gas phase in the space of the tube group, and the liquid formed on the outer peripheral surface of the tube as the physical quantity as a function. The physical quantity measuring unit includes a liquid film measuring unit that measures the liquid film thickness formed on the outer peripheral surface of the pipe, and the arithmetic unit is a gas-liquid liquid of the liquid film. It is preferable that the constitutive equation for the interfacial area obtains a correlation for interpolating the measured liquid film thickness and incorporates the obtained correlation into the constitutive equation as a coefficient.

  According to this configuration, the constitutive equation of the gas-liquid interface area of the liquid film can be constructed with high accuracy, and an analysis model in which this constitutive equation is incorporated can be constructed with high accuracy.

  In this case, the constitutive equation is a constitutive equation of a gas phase flow velocity and a liquid phase flow velocity in the space of the tube group, and the physical quantity as a function is a space in the gas phase in the space of the tube group. The physical quantity measuring unit includes a void ratio and a differential pressure in the space of the tube group, and the physical quantity measuring unit is formed on each of the outer peripheral surfaces of the pair of opposed tubes, and the pair of electrodes disposed opposite to each other, and the tube group A differential pressure measuring unit that measures the differential pressure between the upstream side and the downstream side of the gas-liquid two-phase flow that circulates inside, and the arithmetic unit is based on the electrical characteristics between a pair of the electrodes Deriving the space void rate, and giving the derived space void rate and the differential pressure measured by the differential pressure measuring unit to the constitutive equation to calculate the flow velocity of the gas phase and the flow velocity of the liquid phase It is preferable to do.

  According to this configuration, the space void ratio in the space of the tube group can be derived by measuring electrical characteristics using a pair of electrodes. Here, the spatial void ratio has a correlation with the electrical characteristics, and the calculation unit calculates (converts) the spatial void ratio from the measured electrical characteristics based on the correlation equation between the spatial void ratio and the electrical characteristics. . Moreover, based on the derived space void ratio and the differential pressure measured by the differential pressure measuring unit, the gas phase flow rate and the liquid phase flow rate can be calculated from a predetermined constitutive equation. Therefore, the gas phase flow rate and the liquid phase flow rate can be derived from the calculated gas phase flow rate and liquid phase flow rate. Thereby, by arranging a pair of electrodes in the tube group, it is possible to simultaneously measure the gas phase flow rate and the liquid phase flow rate, shorten the time required for calculation, and improve calculation efficiency. be able to. The electrical characteristics include electrical resistance (conductance) or capacitance (capacitance). The space void ratio may be converted based on the electrical resistance between the pair of electrodes, or the electrostatic capacitance between the pair of electrodes. The space void ratio may be converted based on the capacity.

FIG. 1 is a schematic configuration diagram of a physical quantity measurement system according to the first embodiment. FIG. 2 is an explanatory diagram of a control block of the physical quantity measurement system according to the first embodiment. FIG. 3 is an explanatory diagram of a liquid film sensor. FIG. 4 is an explanatory diagram illustrating an example of a measured physical quantity. FIG. 5 is an explanatory diagram illustrating an example of a measured physical quantity. FIG. 6 is a flowchart regarding a method for constructing an analysis model according to the first embodiment. FIG. 7 is a schematic configuration diagram of a physical quantity measurement system according to the second embodiment. FIG. 8 is a schematic diagram of electrodes arranged in a tube of the physical quantity measurement system according to the second embodiment.

  Embodiments according to the present invention will be described below in detail with reference to the drawings. Note that the present invention is not limited to the embodiments. In addition, constituent elements in the following embodiments include those that can be easily replaced by those skilled in the art or those that are substantially the same.

  FIG. 1 is a schematic configuration diagram of a physical quantity measurement system according to the first embodiment. FIG. 2 is an explanatory diagram of a control block of the physical quantity measurement system according to the first embodiment. As shown in FIG. 1, the physical quantity measurement system 1 is used to measure a physical quantity used in a basic equation in order to construct a basic equation serving as an analysis model of a gas-liquid two-phase flow flowing in a tube group 5. System. Here, prior to the description of the measurement system 1, the tube group 5 in which the measurement system 1 is arranged will be described with reference to FIG.

  As shown in FIG. 1, the measurement system 1 is provided in the tube group 5. This tube group 5 is composed of a plurality of tubes 8 and simulates, for example, a heat transfer tube group provided inside a pressure generator of a pressurized water reactor. The plurality of tubes 8 are formed to have the same diameter, are arranged so that their axial directions are parallel, and have a staggered arrangement (so-called triangular arrangement). In the space D in which the tube group 5 is arranged, a gas-liquid two-phase flow that is an annular spray flow flows from one side (the lower side in the figure) to the other side (the upper side in the figure) of the space D. The annular spray flow is a state in which the ratio of the gas phase is larger than that of the liquid phase and the gas phase continues in the space D while the liquid phase exists as droplets L1 or liquid films L2.

  When the gas-liquid two-phase flow, which is an annular spray flow, flows through the space D in which the tube group 5 is arranged, the liquid phase becomes a droplet L1 formed in the space D, and the other part is a tube. 8 is a liquid film L2 formed on the outer peripheral surface.

  The measurement system 1 includes a high-speed camera 11, a droplet capture meter 12, a heat ray velocimeter 13, a liquid film sensor (liquid film measurement unit) 14, and a two-needle optical probe (ratio measurement unit, gas-liquid interface velocity measurement unit) 15. , A physical quantity measuring unit 10 including a pressure distribution meter 16 and a differential pressure meter 17, and a computing device (calculating unit) 20. Note that the physical quantity measuring unit 10 is not limited to the various measuring devices described above, and may include any measuring device as long as it measures physical quantities.

  The high-speed camera 11 images the flow state of the gas-liquid two-phase flow that circulates in the tube group 5. As shown in FIG. 1, the high-speed camera 11 is provided outside the space D of the tube group 5 with a transparent plate material such as an acrylic plate (not shown) sandwiched between the space D of the tube group 5 so as to take an image. The space D is imaged from outside D. The captured image captured by the high speed camera 11 is input to the arithmetic device 20. For this reason, the arithmetic unit 20 acquires a captured image captured by the high-speed camera 11. The captured image is used, for example, to specify the flow mode of the gas-liquid two-phase flow. Here, the flow mode is a mode representing a flow state of a gas-liquid two-phase flow, and examples thereof include a bubble flow, a slag flow, a churn flow, and an annular spray flow. Note that the high-speed camera 11 may be connected to the arithmetic device 20 and directly input a captured image to the arithmetic device 20, but is not limited to this configuration, and the arithmetic device 20 via a separate storage medium. May be entered indirectly.

  The droplet trapping meter 12 captures a gas-liquid two-phase droplet L1 flowing in the tube group 5. As shown in FIG. 1, the droplet trapping meter 12 is provided inside a predetermined tube 8 in the tube group 5. The droplet L1 captured by the droplet capture meter 12 is measured for the droplet diameter and the number (droplet diameter distribution) using a separate measuring device. The measured droplet diameter and number are input to the arithmetic unit 20. For this reason, the arithmetic unit 20 acquires the droplet diameter and the number of droplets L1 captured by the droplet capture meter 12. The droplet diameter of the droplet L1 is used, for example, as a physical quantity for calculating the gas-liquid interface area of the droplet L1, or used to specify the flow mode of the gas-liquid two-phase flow. The droplet capture meter 12 may be configured to directly measure the droplet diameter and number from the captured droplet L1. In this case, the droplet capturing meter 12 may also be connected to the computing device 20 and directly input the droplet diameter and the number of the captured droplet L1 to the computing device 20, but not limited to this configuration. You may input indirectly to the arithmetic unit 20 via a separate storage medium.

  The hot-wire anemometer 13 measures the flow velocity of the gas-liquid two-phase flow flowing through the tube group 5 and the passage frequency of the droplets L1. As shown in FIG. 1, the hot-wire anemometer 13 is located in the space D of the tube group 5. The gas phase flow velocity measured by the hot wire anemometer 13 and the passage frequency of the droplets L1 are input to the arithmetic unit 20. For this reason, the arithmetic unit 20 acquires the flow velocity of the gas phase measured by the hot-wire anemometer 13 and the passing frequency of the droplets L1. The gas phase flow velocity is used as a physical quantity for calculating the gas-liquid interface drag, for example. Moreover, the passage frequency of the droplet L1 is used, for example, to specify the flow mode of the gas-liquid two-phase flow. The hot-wire anemometer 13 is also connected to the computing device 20 and may directly input the gas phase flow velocity and the passage frequency of the droplets L1 to the computing device 20, but is not limited to this configuration. It may be indirectly input to the arithmetic unit 20 via the storage medium.

  FIG. 3 is an explanatory diagram of a liquid film sensor. The liquid film sensor 14 measures the liquid film thickness of the liquid film L2 formed on the outer peripheral surface of the predetermined pipe 8 in the tube group 5 and the flow velocity of the liquid film L2. As shown in FIG. 3, the liquid film sensor 14 is arranged with a predetermined interval in the circumferential direction of the insulating tube body 25 and an insulating tube body 25 constituting a part of the tube 8 using an insulator. And a pair of electrodes 26. The pair of electrodes 26 are arranged side by side in the axial direction. The liquid film sensor 14 measures a voltage generated by passing a current between the pair of electrodes 26. The liquid film sensor 14 derives the liquid film thickness from data in which the relationship between the liquid film thickness and the voltage is associated in advance based on the measured voltage. The liquid film sensor 14 measures the liquid film thickness at four locations in the circumferential direction of the insulating tube 25. The liquid film sensor 14 measures the flow velocity of the liquid film L2 based on the measured voltage. A plurality of the liquid film sensors 14 are provided at predetermined intervals in the axial direction of the tube 8. The liquid film thickness measured by the plurality of liquid film sensors 14 and the flow velocity of the liquid film L2 are input to the arithmetic unit 20. For this reason, the arithmetic unit 20 acquires the liquid film thickness measured by the liquid film sensor 14 and the flow velocity of the liquid film L2. The liquid film thickness is used as a physical quantity for calculating the gas-liquid interface area of the liquid film L2, for example. The flow rate of the liquid film L2 is used as a physical quantity for calculating the relative velocity between the flow rate of the gas phase and the flow rate of the liquid film L2. The liquid film sensor 14 is also connected to the arithmetic unit 20 and may directly input the liquid film thickness and the flow rate of the liquid film L2 to the arithmetic unit 20, but the present invention is not limited to this configuration. You may input indirectly to the arithmetic unit 20 via a storage medium.

  The two-needle optical probe 15 measures the gas-liquid interface velocity of the gas-liquid two-phase flow that circulates in the tube group 5 and the void fraction of the droplet L1 contained in the gas phase. Here, the gas-liquid interface velocity is the velocity at the interface between the gas phase and the liquid phase, and the void ratio of the droplets L1 is the ratio of the droplets L1 contained in the gas phase. As shown in FIG. 1, the tip of the two-needle optical probe 15 is located in the space D of the tube group 5. The gas-liquid interface velocity and the void ratio of the droplet L1 measured by the two-needle optical probe 15 are input to the arithmetic unit 20. For this reason, the arithmetic unit 20 acquires the gas-liquid interface velocity and the void ratio of the droplet L1 measured by the two-needle optical probe 15. The gas-liquid interface velocity is used as, for example, a physical quantity for calculating the gas-liquid interface drag. The void ratio of the droplet L1 is used as a physical quantity for calculating the gas-liquid interface area of the droplet L1, for example. Note that the two-needle optical probe 15 may also be connected to the computing device 20 and directly input the gas-liquid interface velocity and the void ratio of the droplet L1 to the computing device 20, but is not limited to this configuration. You may input indirectly to the arithmetic unit 20 via a separate storage medium.

  The pressure distribution meter 16 measures the pressure distribution in the circumferential direction of a predetermined tube 8 in the tube group 5. As shown in FIG. 1, the pressure distribution meter 16 has four pressure gauges 16 a arranged at predetermined intervals in the circumferential direction of the tube 8. For this reason, the pressure distribution meter 16 measures the pressure distribution in the circumferential direction by measuring the pressure at four locations in the circumferential direction of the pipe 8. The pressure distribution measured by the pressure distribution meter 16 is input to the arithmetic unit 20. For this reason, the arithmetic unit 20 acquires the pressure distribution measured by the pressure distribution meter 16. The pressure distribution is used as a physical quantity for constructing a gas-liquid two-phase flow analysis model. The pressure distribution meter 16 may also be connected to the arithmetic device 20 and the pressure distribution may be directly input to the arithmetic device 20, but the present invention is not limited to this configuration, and the arithmetic device 20 is provided via a separate storage medium. May be entered indirectly.

  The differential pressure gauge 17 measures the differential pressure between the upstream pressure and the downstream pressure of the gas-liquid two-phase flow flowing through the tube group 5. As shown in FIG. 1, the differential pressure gauge 17 includes an upstream pressure gauge 17a and a downstream pressure gauge 17b. The differential pressure measured by the differential pressure gauge 17 is input to the arithmetic unit 20. For this reason, the arithmetic unit 20 acquires the differential pressure measured by the differential pressure gauge 17. The differential pressure is used, for example, as a physical quantity for constructing a gas-liquid two-phase flow analysis model. The differential pressure gauge 17 may also be connected to the arithmetic device 20 and the differential pressure may be directly input to the arithmetic device 20, but the present invention is not limited to this configuration, and the arithmetic device 20 is connected to the arithmetic device 20 via a separate storage medium. You may enter it indirectly.

The physical quantity measured by the measurement system 1 configured as described above is used as a physical quantity that is an element of the analysis model in order to construct an analysis model of a gas-liquid two-phase flow. Here, with reference to FIG.4 and FIG.5, the physical quantity used when constructing | assembling an analysis model is demonstrated. 4 and 5 are explanatory diagrams illustrating examples of measured physical quantities. As shown in FIG. 4 and FIG. 5, the physical quantities include the void ratio α _d of the droplet L1, the liquid film thickness t _fm , the droplet diameter d _sm , the differential pressure ΔP, the pitch P _t , and the gas phase flow rate u _g. , site formed of the flow path cross-sectional area a _f, the liquid film L2 in the axial direction of the flow velocity u _f of the liquid _phase, the diameter d of the tube 8, the projected cross-sectional area a _d of the droplets _L1, the gas-liquid two-phase flow flows Wetting edge length L _t , wetting edge length L _{film of} the portion where the liquid film L2 is formed in the circumferential direction, average density ρ _m , flow path space V _flow , gas phase droplet V _drop , gas phase liquid film V _{film and the} like. The physical quantity described above is appropriately derived based on the measurement result of the measurement system 1.

The void ratio α _d of the droplet L1 is the ratio of the droplet L1 contained in the gas phase, and is measured by the two-needle optical probe 15. The liquid film thickness t _fm is the thickness in the radial direction of the liquid film L2 formed on the outer peripheral surface of the tube 8, and is measured by the liquid film sensor 14. The droplet diameter d _sm is the diameter of the droplet L1 in the gas phase, and is measured by the droplet capture meter 12 and the high-speed camera 11. The differential pressure ΔP is a pressure difference between the upstream side and the downstream side of the gas-liquid two-phase flow in the tube group 5, and is measured by the differential pressure gauge 17. The pitch P _t is a distance between the centers of adjacent tubes 8 in a triangular arrangement, and is a physical quantity defined in advance based on the triangular arrangement of the tube group 5. Velocity u _g in the gas phase is the flow rate of the gas phase of the gas-liquid two-phase flow is measured by hot-wire current meter 13. The liquid phase flow rate _uf is the liquid phase flow rate of the gas-liquid two-phase flow, and is measured by the liquid film sensor 14 when the liquid phase is the liquid film L2. When the liquid phase is the droplet L1, the flow velocity of the droplet L1 may be measured by the high speed camera 11.

The diameter d of the tube 8 is the diameter of the tube 8 constituting the tube group 5 and is a physical quantity that is defined in advance according to the tube 8 to be arranged. Projected cross-sectional area A _d of the droplets L1 is the cross-sectional area of the droplet L1 projected in a predetermined plane. The projection cross-sectional area A _d of the droplets L1 may be determined based on the captured image captured by the high speed camera 11. The channel cross-sectional area _Af is a cross-sectional area of a gas-liquid two-phase flow channel flowing through the tube group 5 and is a physical quantity defined in advance. Wetted perimeter L _t of the liquid film L2 in the axial direction is the length of the liquid film L2 formed in the axial direction of the tube 8, it is measured by a plurality of liquid film sensor 14 disposed in the axial direction of the tube 8 . The wetting edge length L _film of the liquid film L2 in the circumferential direction is the length of the liquid film L2 formed in the circumferential direction of the tube 8, and is measured by the liquid film sensor 14. The average density [rho _m is the density of the gas-liquid two-phase flow of liquid, a physical quantity defined in advance.

The flow path space _Vflow is a space (triangular dotted line shown in FIG. 4) formed by three adjacent tubes 8 in a triangular arrangement, and is a physical quantity defined in advance based on the triangular arrangement of the tube group 5. is there. The gas phase droplet V _drop is the volume of the droplet L1 in the gas phase in the _flow path space V _flow . The gas phase liquid film V _film is the volume of the liquid film L2 in the gas phase in the _flow path space V _flow .

The basic equation serving as the analysis model is constructed by appropriately incorporating a constitutive equation having the above physical quantity as a function. Examples of the constitutive equation having the physical quantity as a function include a constitutive equation of the spatial void ratio α, a constitutive equation of the gas-liquid interface drag F _b , a constitutive equation of the gas-liquid interface area a _{i_d} of the liquid droplet L1, and There are constitutive equations for the _interfacial area a _{i — f} . The constitutive equation is not limited to the above constitutive equation, and includes a constitutive equation having a function of the Reynolds number relating to the flow velocity of the gas phase and a constitutive equation having a function of the Reynolds number relating to the flow velocity of the droplet L1.

The constitutive equation of the spatial void ratio α includes the liquid film thickness t _fm of the liquid film L2 and the void ratio α _d (spatial liquid droplet ratio) of the liquid droplet L1 as a physical quantity as a function. Specifically, the constitutive formula of the space void ratio α is given by the following formula (1). In equation (1), η _drop is the liquid phase volume ratio (liquid ratio) of the droplet L1, and η _film is the liquid phase volume ratio (liquid ratio) of the liquid film L2.

Here, the relationship among the void ratio α _drop (α _d ) of the droplet L1, the liquid ratio η _drop of the droplet L1, the flow path space V _flow, and the gas phase droplet V _drop is given by the following equation (2). It is done.

Further, the relationship between the void ratio α _drop of the droplet L1, the apparent gas phase flow rate j _g , the apparent droplet flow velocity j _d , the gas phase drift velocity V _gj , and the distribution constant C ₀ is described below (3). It is given by the formula. Incidentally, the flow rate j _d of apparent gas phase is determined by the flow velocity u _f of the flow rate of the gas phase u _g and a liquid phase. Further, the gas phase drift velocity V _gj is measured by the two-needle optical probe 15. Further, the distribution constant C ₀ is a coefficient set for interpolating the measured physical quantity in the analytical model construction method described later.

Similarly, the relationship among the void ratio α _{film of} the liquid film L2, the liquid ratio η _film of the liquid film L2, the flow path space V _flow, and the liquid film V _{film in} the gas phase is given by the following equation (4).

In addition, the void ratio α _film of the liquid film L2 is obtained from the ratio of the liquid film L2 per unit volume based on the calculated average liquid film thickness (h / D). The average liquid film thickness is given by the following equation (5). Here, h is, the liquid film has a thickness of _{t fm,} is Re _f, is the Reynolds number of the liquid film L2, Re _g is the Reynolds number of the gas phase. Μ _f is the viscosity coefficient of the liquid film L 2, μ _g is the viscosity coefficient of the gas phase, ρ _f is the density of the liquid film L 2, and ρ _g is the density of the gas phase, σ is the surface tension. In the equation (5), the liquid film thickness h is measured by the liquid film sensor 14. In addition, the coefficient k, the coefficient a, and the coefficient b are coefficients that are set to interpolate the measured physical quantities in the analysis model construction method described later. Other physical quantities are predetermined (known) physical quantities.

Constitutive of the gas-liquid interface drag F _b as a physical quantity is a function, contains a gas-liquid interfacial velocity in the space D of the tube bundle 5. Here, the gas-liquid interface drag F _b is the force which acts on the interface between the gas and liquid phases. Further, the gas-liquid interface rate is determined by the relative velocity between the flow velocity u _f of the flow rate of the gas phase u _g and a liquid phase. Specifically, constitutive equation of the gas-liquid interface drag F _b is given by to the following equation (6). In the equation (6), _Cb is a gas-liquid interface drag coefficient, and is a coefficient set for interpolating the measured physical quantity in the analysis model construction method described later.

The constitutive equation of the gas-liquid _interfacial area a _{i_d} of the droplet L1 includes the space void ratio α _d and the droplet diameter d _{sm of the} droplet L1 as a physical quantity as a function. Specifically, the structural formula of the gas-liquid _interface area a _{i_d} of the droplet L1 is given by the following formula (7).

The constitutive equation of the gas-liquid _interface area a _{i_f} of the liquid film L2 includes the liquid film thickness t _fm as a physical quantity serving as a function. Specifically, the structural formula of the gas-liquid _interface area a _{i_f} of the liquid film L2 is given by the following formula (8).

  The constitutive equation configured in this manner incorporates a predetermined coefficient based on the measured physical quantity into the constitutive expression in order to simulate the behavior of each physical quantity with high accuracy. Next, a method for constructing an analysis model will be described with reference to FIG. FIG. 6 is a flowchart regarding a method for constructing an analysis model according to the first embodiment.

As shown in FIG. 6, in the analysis model construction method, a physical quantity measurement step S1, a coefficient calculation step S2, and an analysis model construction step S3 are performed in order. In the physical quantity measurement step S1, the measurement system 1 is used to measure the physical quantity used in the basic equation. In the coefficient calculation step S2, the arithmetic unit 20 obtains a correlation between the physical quantity measured in the physical quantity measurement step S1 and a constitutive expression using the physical quantity as a function, and calculates the obtained correlation as a coefficient. The coefficient, for example, is the above gas-liquid interface drag coefficient C _b. As a method for obtaining the correlation, for example, there is regression analysis or interpolation. In the analysis model construction step S3, the arithmetic device 20 incorporates the calculated coefficient into the constitutive equation, and constructs a basic equation including the constitutive equation in which the coefficient is incorporated. Thereby, the fundamental equation which is the constructed analysis model can be a basic equation in consideration of the actual flow state of the gas-liquid two-phase flow.

  As described above, according to the configuration of the first embodiment, it is possible to obtain a correlation that interpolates between a constitutive equation having a physical quantity as a function and a measured physical quantity, and to incorporate a coefficient relating to the obtained correlation into the constitutive expression. Therefore, the constitutive equation can accurately simulate the behavior of the actual physical quantity, and an analysis model for analyzing the gas-liquid two-phase flow in which the constitutive equation is incorporated can be constructed with high accuracy.

  In addition, according to the configuration of the first embodiment, the constitutive equation of the spatial void ratio α can be constructed with high accuracy, and an analysis model in which this constitutive equation is incorporated can be constructed with high accuracy.

Further, according to the configuration of Example 1, the constitutive equation of the gas-liquid interface drag F _b can be accurately built, an analysis model that this structure type is incorporated, it is possible to accurately build.

In addition, according to the configuration of the first embodiment, the constitutive equation of the gas-liquid _interface area a _{i_d} of the droplet L1 can be constructed with high accuracy, and the analysis model incorporating this constitutive equation can be constructed with high accuracy. It becomes.

Further, according to the configuration of the first embodiment, the constitutive equation of the gas-liquid _interface area a _{i_f} of the liquid film L2 can be constructed with high accuracy, and the analysis model in which this constitutive equation is incorporated can be constructed with high accuracy. It becomes.

  Next, a physical quantity measurement system 30 according to the second embodiment will be described with reference to FIGS. 7 and 8. FIG. 7 is a schematic configuration diagram of a physical quantity measurement system according to the second embodiment. FIG. 8 is a schematic diagram of electrodes arranged in a tube of the physical quantity measurement system according to the second embodiment. In the second embodiment, parts that are different from the first embodiment will be described in order to avoid redundant descriptions, and parts that have the same configuration as the first embodiment will be described with the same reference numerals. The measurement system 30 according to the second embodiment is provided with a pair of electrodes 31 instead of the two-needle optical probe 15 of the first embodiment.

By the way, the two-needle optical probe 15 of the first embodiment has a void ratio α at a predetermined measurement point of the gas-liquid two-phase flow that circulates in the tube group 5 (in the first embodiment, the droplet L1 contained in the gas phase). The void ratio α _d ) is measured. Here, in the case of measuring the distribution of the apparent gas phase flow velocity j _g and the apparent liquid phase (droplet) flow velocity j _d in the space D of the tube group 5, a two-needle optical probe is used in the space D. It is necessary to measure the void ratio α while moving 15. However, the void rate α is measured while moving the two-needle optical probe 15 in the space D, and the apparent gas phase flow rate j _g (hereinafter referred to as the gas phase flow rate j _g ) and the measured void rate α. If an attempt is made to calculate the distribution of the apparent liquid phase flow velocity j _d (hereinafter referred to as the liquid phase flow velocity j _d ), the time required for the calculation increases. For this reason, in Example 2, the space void ratio α in the space D of the tube group 5 is measured using a pair of electrodes 31.

  As shown in FIG. 7, the pair of electrodes 31 is provided on each of the pair of opposed tubes 8, and is disposed on the outer peripheral surface facing each tube 8. Further, as shown in FIG. 8, each electrode 31 is provided so as to extend along the axial direction of the tube 8. The pair of electrodes 31 is an electrostatic capacitance type, and the pair of electrodes 31 is in an insulated state. The pair of electrodes 31 is connected to the arithmetic device 20, and the arithmetic device 20 acquires the capacitance between the pair of electrodes 31.

  The arithmetic unit 20 derives the space void ratio α based on the capacitance between the pair of electrodes 31. Here, the space void ratio α has a correlation with the capacitance, and the arithmetic unit 20 calculates the space void ratio α from the measured capacitance based on the correlation equation between the space void ratio α and the capacitance. Calculated (converted).

Next, calculation of the gas phase flow rate and the liquid phase flow rate based on the calculated space void ratio α will be described. When calculating the gas phase flow rate and the liquid phase flow rate, the arithmetic unit 20 calculates the differential pressure dP _m (ΔP of Example 1) measured by the differential pressure gauge (differential pressure measurement unit) 17 of Example 1 and the gas phase. Is calculated based on the spatial void ratio α, which is information on the ratio between the flow rate of the liquid and the flow rate of the liquid phase. Specifically, the arithmetic unit 20 solves the differential pressure dP _m and the space void ratio α by simultaneously solving the following formulas (9) and (10), whereby the apparent gas phase flow rate j _g and the apparent gas flow rate j _g the seeking phase flow rate j _d liquid, by converting each of the flow rate of the gas phase flow and the liquid phase from the gas phase flow rate j _g and a liquid phase flow rate j _d determined, the flow rate of the gas phase flow and a liquid phase calculate.

Here, symbols and units included in the equation (9) will be described. Those whose unit is ND are dimensionless quantities.
j _g : Apparent gas phase flow velocity [m / s]
j _d : Apparent liquid phase flow velocity [m / s]
α: Void ratio (measured value) [ND]
C ₀ : Distribution constant V _gj : Drift speed [m / s]

Equation (9) shows the relationship between the space void ratio α, the apparent gas phase flow rate j _g , and the apparent liquid phase flow rate j _d . That is, the equation (9) is an equation in which the void ratio α _drop of the droplet L1 in the expression (3) of the first embodiment is replaced with the space void ratio α. At this time, the distribution constant C ₀ and the drift velocity V _gj are appropriately determined depending on the flow mode of the gas-liquid two-phase flow.

Next, symbols and units included in the expression (10) will be described. As described above, the unit of ND is a dimensionless quantity.
dP _m : differential pressure (measured value) [Pa]
φ _l ² : Two-phase multiplication coefficient [ND]
λ: friction coefficient [ND], λ = 0.3164Re1 / 4
D ₂ : equivalent diameter [m]
L: Differential pressure measurement section distance [m]
ρ _l : Liquid phase density [kg / m ³ ]

Equation (10) shows the relationship between the differential pressure dP _m , the apparent gas phase flow rate j _g , and the apparent liquid phase flow rate j _d . Note that the two-phase multiplication coefficient φ _l ² is obtained from a predetermined calculation formula, and the equivalent diameter D ₂ is, for example, an average value of equivalent diameters in the differential pressure measurement section.

Thus, (9) using the formula and (10), when obtaining the gas-phase flow rate j _g and the apparent liquid phase flow rate j _d apparent, other except the gas phase flow rate j _g and a liquid phase flow rate j _d The physical quantity of is known. Then, the arithmetic unit 20 obtains the spatial void ratio α by measuring the pair of electrodes 31 and obtains the differential pressure dP _m by measuring the differential pressure gauge 17 and gives it to the equations (9) and (10) and is known. Are given in the equations (9) and (10). Thereafter, computing device 20 (9), (10) by simultaneous equation, by solving for the gas phase flow rate _{j g} and a liquid phase flow rate _{j d,} we obtain both. Note that the void ratio α and the differential pressure dP _m vary with time t. Therefore, when solving the equations (9) and (10) simultaneously, it is preferable to use an average value in a predetermined period for the space void ratio α and the differential pressure dP _m rather than using an instantaneous value.

After obtaining the gas phase flow rate j _g and the liquid phase flow rate j _d , the arithmetic unit 20 obtains the respective flow rates and the total flow rate of the gas-liquid two-phase flow from the gas phase flow rate j _g and the liquid phase flow rate j _d . The conversion from the flow rate to the flow rate may be performed by multiplying the flow rate by the cross-sectional area of the flow path through which the gas-liquid two-phase flow passes, for example, if the flow rate is volumetric. In this case, according to the ratio between the gas phase and the liquid phase of the gas-liquid two-phase flow, the cross-sectional area of the flow path multiplied by the gas-phase flow velocity j _g and the cross-sectional area of the flow path multiplied by the liquid-phase flow velocity j _d can be divided. Good. The mass flow rate can be obtained by multiplying the volume flow rate by the density of the fluid.

As described above, according to the configuration of the second embodiment, the space void ratio α in the space D of the tube group 5 can be acquired by measuring the capacitance using the pair of electrodes 31. Then, based on the acquired space void ratio α and the differential pressure dP _m measured by the differential pressure gauge 17, the gas phase flow rate j _g and the liquid phase flow rate j _d are obtained from the equations (9) and (10), From the obtained gas phase flow rate j _g and liquid phase flow rate j _d , the gas phase flow rate and the liquid phase flow rate can be derived. For this reason, by arranging the pair of electrodes 31 in the tube group 5, it becomes possible to simultaneously measure the gas phase flow rate and the liquid phase flow rate, thereby shortening the time required for calculation and improving the calculation efficiency. Can be achieved.

  In the second embodiment, the pair of electrodes 31 is a capacitance type, but is not limited to this configuration, and a constant current type may be used. That is, the arithmetic unit 20 derives the space void ratio α based on the electrical resistance between the pair of electrodes 31. Here, the spatial void ratio α has a correlation with the electrical resistance, and the arithmetic unit 20 calculates (converts) the spatial void ratio α from the measured electrical resistance based on the correlation equation between the spatial void ratio α and the electrical resistance. )

DESCRIPTION OF SYMBOLS 1 Measurement system 5 Tube group 8 Tube 10 Physical quantity measurement part 11 High speed camera 12 Droplet capture meter 13 Heat ray velocimeter 14 Liquid film sensor 15 Two-needle type optical probe 16 Pressure distribution meter 17 Differential pressure meter 20 Arithmetic unit 25 Insulation tube 26 Electrode 30 measurement system (Example 2)
31 electrode D space L1 droplet L2 liquid film alpha spatial void fraction alpha _d droplets void fraction _{h, t fm} liquid film thickness d _sm droplet size ΔP differential pressure P _t pitch u _g vapor flow rate u _f liquid phase wetted perimeter of the projected cross-sectional area a _f gas-liquid two-phase flow flows flow path cross-sectional area L _t axis wetted perimeter of the liquid film in the direction length L _film circumferential liquid in the direction the film diameter a _d droplet flow rate d tubes ρ _g Gas-phase density ρ _f Liquid film density ρ _m Average density C _b Gas-liquid interface drag coefficient F _b Gas-liquid interface drag a _{i_d} Liquid-gas interface area a _{i_f} Liquid-gas interface area

Claims (7)

A physical quantity measurement system for measuring a physical quantity used in the basic equation in constructing a basic equation serving as an analysis model for analyzing a gas-liquid two-phase flow flowing in a tube group,
The basic equation includes a constitutive equation having a function of the physical quantity serving as each element of the analysis model,
A physical quantity measuring unit for measuring the physical quantity;
The constitutive equation that is a function of the physical quantity includes a calculation unit that interpolates the measured physical quantity and includes the calculated correlation as a coefficient to be incorporated into the constitutive equation. Measuring system. The constitutive equation is a constitutive equation of the space void ratio in the gas phase in the space of the tube group, and as the physical quantity as a function, the liquid film thickness of the liquid film formed on the outer peripheral surface of the tube, and the tube The proportion of droplets or liquid film contained in the gas phase in the group space,
The physical quantity measuring unit is
A liquid film measuring unit for measuring the liquid film thickness formed on the outer peripheral surface of the pipe;
A ratio measuring unit that measures the ratio of droplets or liquid film contained in the gas phase in the space of the tube group,
The calculation unit obtains a correlation in which the constitutive equation of the space void ratio interpolates the measured liquid film thickness and the ratio of the droplet or the liquid film, and the calculated correlation is used as a coefficient. The physical quantity measuring system according to claim 1, wherein the physical quantity measuring system is incorporated in a structural formula. The constitutive formula is a constitutive formula of a gas-liquid interface drag that is a drag at the interface between the gas phase and the liquid phase, and includes the gas-liquid interface velocity in the space of the tube group as the physical quantity as a function,
The physical quantity measuring unit is
A gas-liquid interface velocity measuring unit for measuring a gas-liquid interface velocity which is an interface velocity between a gas phase and a liquid phase in the space of the tube group,
The calculation unit obtains a correlation in which the constitutive equation of the gas-liquid interface drag interpolates the measured gas-liquid interface velocity, and incorporates the obtained correlation into the constitutive equation as a coefficient. The physical quantity measurement system according to claim 1 or 2. The constitutive equation is a constitutive equation of the gas-liquid interface area of the droplets contained in the gas phase in the space of the tube group, and includes the droplet diameter of the droplets as the physical quantity as a function,
The physical quantity measuring unit is
A droplet capturing section that captures the droplets contained in the gas phase in the space of the tube group;
The calculation unit obtains a correlation in which the constitutive equation of the gas-liquid interface area of the droplet interpolates the droplet diameter of the captured droplet, and incorporates the obtained correlation into the constitutive equation as a coefficient. The physical quantity measuring system according to any one of claims 1 to 3, wherein The constitutive equation is a constitutive equation of the gas-liquid interface area of the liquid film contained in the gas phase in the space of the tube group, and the physical quantity as a function of the liquid film formed on the outer peripheral surface of the tube. Including liquid film thickness,
The physical quantity measuring unit is
A liquid film measuring unit for measuring the liquid film thickness formed on the outer peripheral surface of the pipe;
The calculation unit obtains a correlation in which the constitutive equation of the gas-liquid interface area of the liquid film interpolates the measured liquid film thickness, and incorporates the obtained correlation into the constitutive equation as a coefficient. The physical quantity measurement system according to any one of claims 1 to 4. The constitutive equation is a constitutive equation of a gas phase flow rate and a liquid phase flow rate in the space of the tube group, and as a physical quantity as a function, a space void ratio in the gas phase in the space of the tube group and And differential pressure within the space of the tube group,
The physical quantity measuring unit is
A pair of electrodes formed on the outer peripheral surfaces of a pair of opposing tubes and disposed opposite to each other;
A differential pressure measuring unit that measures the differential pressure between the upstream side and the downstream side of the gas-liquid two-phase flow that circulates in the tube group, and
The calculation unit derives the spatial void ratio based on the electrical characteristics between the pair of electrodes, and the derived spatial void ratio and the differential pressure measured by the differential pressure measurement unit are expressed in the constitutive equation. The physical quantity measurement system according to claim 1, wherein the flow rate of the gas phase and the flow rate of the liquid phase are calculated. An analytical model construction method for constructing a basic equation as an analytical model for analyzing a gas-liquid two-phase flow flowing in a tube group,
The basic equation includes a constitutive equation having a function of the physical quantity serving as each element of the analysis model,
A physical quantity measuring step for measuring a physical quantity used in the basic equation;
A coefficient calculating step in which the constitutive equation having the physical quantity as a function calculates a correlation for interpolating the measured physical quantity, and calculates the calculated correlation as a coefficient;
An analytical model construction method comprising: an analytical model construction step of constructing the basic equation by incorporating the calculated coefficient into the constitutive equation.

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