Annular flow droplet entrainment rate measuring method based on conical optical fiber probe

Abstract

The invention relates to an annular flow droplet entrainment rate measurement method based on a conical optical fiber probe. The method comprises the following steps: establishing an optical fiber probe measurement system; under the experimental condition of horizontal annular flow, respectively adjusting the sensitive tip of the optical fiber probe to different positions in the vertical radial direction of the horizontal pipeline, and continuously collecting output signals of at least 60 photoelectric detectors at each measurement position; processing an output signal of the photoelectric detector, positioning dispersed liquid drop signals in the output signal, and extracting the retention time and the liquid drop speed of each liquid drop; calculating a local droplet fraction and an average droplet velocity at each measurement position, and further calculating a local droplet mass flux; determining a gas phase circulation area; fitting the distribution of the mass flux of the liquid drops in the vertical direction of the pipeline by using an exponential function; integrating the distribution of the droplet mass flux in the gas phase circulation area, and calculating the total mass flow of the entrained droplets in the gas core; and dividing the entrained droplet mass flow by the liquid phase mass flow to calculate the droplet entrainment rate.

Description

Technical Field

[0001] The present invention belongs to the technical field of flow measurement and relates to a method for measuring the droplet entrainment rate in horizontal annular flow. Background Art

[0002] Gas-liquid annular flow widely exists in fields such as natural gas and oil transportation, steam generators, refrigeration systems, and the nuclear industry. Its characteristic is that the gas phase flows at high speed in the center of the pipeline, and the liquid phase forms a thin film along the pipe wall. Under the action of gas-phase shear, part of the liquid phase is stripped from the liquid film interface and entrained into the gas core to form high-speed flowing droplets. The droplet entrainment rate is defined as the ratio of the mass flow rate of the entrained droplets in the gas core to the total liquid mass flow rate. It significantly affects the heat transfer, pressure drop, and liquid holdup of the system, and is also related to the dryout phenomenon during the boiling process. It is an important parameter for fully developed annular flow [1]. In horizontal annular flow, gravity causes the distribution of the liquid film and droplets to exhibit complex asymmetry, making it difficult to measure the entrainment rate. Currently, there is no standard measurement technique for the droplet entrainment rate. In traditional research, mainly the liquid film extraction method and the constant-speed probe sampling method are used. These two techniques have large equipment volume, cumbersome operation, and high measurement costs. In contrast, the fiber optic probe technology has the advantages of being able to identify fluids with different refractive indices, high sensitivity, fast response, small disturbance to the flow field, and low cost, and is suitable for the detection of dense droplets [2]. In recent years, thanks to the development of manufacturing technology and sampling technology, a single fiber optic probe can independently measure the velocity and size of the discrete phase and has been used for the measurement of high-speed micron-scale droplet characteristics in industrial pipelines, including parameters such as droplet velocity, size, flux, and local liquid holdup [3], providing a new technical means for measuring the droplet entrainment rate in annular flow.

[0003] Related Literature

[0004] [1] WANG G, SAWANT P, ISHII M. A new entrainment rate model for annular two-phase flow [J]. International Journal of Multiphase Flow, 2020, 124: 103185.

[0005] [2] ALONZO M, LEFEBVRE A, HUANG Z, GLUCK S, CARTELLIER A. Doppler optical probe for drop size, velocity and flux measurements in assisted atomization [J]. Atomization and Sprays, 2023, 33.

[0006] [3] BAE B, KIM T, KIM K, JEONG J J, YUN B. Experimental investigation of droplet entrainment and deposition in horizontal stratified wavy flow[J]. International Journal of Heat and Mass Transfer, 2019, 144: 1186 - 13.

[0007] [4] Wang Maosen, Zheng Dandan, Xu Ying. A method for measuring droplet velocity based on a tapered optical fiber probe: 202311356594[P]. 2024 - 01 - 19.

[0008] [5] C. Berna, A. Escrivá, J. L. - Cobo, and L. E. Herranz. Review of droplet entrainment in annular flow: Characterization of the entrained droplets[J]. Progress in Nuclear Energy, 2015, 79: 64–86. Summary of the Invention

[0009] The present invention provides a method for measuring the droplet entrainment rate in horizontal annular flow. A tapered optical fiber probe is used to measure the droplet flux at different positions in the vertical radial direction of the pipe, and the distribution of the droplet flux is fitted. Considering the liquid film thickness, the droplet entrainment rate in horizontal annular flow is calculated. The technical solution of the present invention is as follows:

[0010] A method for measuring the droplet entrainment rate in annular flow based on a tapered optical fiber probe, comprising the following steps:

[0011] 1) Set up an optical fiber probe measurement system. Insert an optical fiber probe into the interior of the measurement pipe section through an L - shaped stainless - steel protective sleeve so that its sensitive tip faces the oncoming flow direction; Use a laser to emit infrared light, transmit the light to the tip of the optical fiber probe through a Y - shaped coupler, and the reflected light generated at the tip of the optical fiber probe is received by the other path of the coupler and converted into an electrical signal by a photodetector;

[0012] 2) Under the experimental conditions of horizontal annular flow, adjust the circumferential adjustment handle and radial adjustment handle on the measuring pipe section to control the measuring position of the optical fiber probe in the pipe cross-section; during the experiment, adjust the sensitive tip of the optical fiber probe to different positions in the vertical radial direction of the horizontal pipe respectively, and continuously collect the output signals of the photodetector for at least 60 s at each measuring position;

[0013] 3) Process the output signals of the photodetector, locate the scattered droplet signals therein, and extract the residence time Δt and droplet velocity u of each droplet;

[0014] 4) Calculate the local droplet fraction α and the average droplet velocity at each measuring position and then calculate the local droplet mass flux G d ;

[0015] 5) Determine the gas-phase flow region A g ;

[0016] 6) Use an exponential function to fit the distribution of the droplet mass flux in the vertical direction of the pipe G d (y / D);

[0017] In the gas-phase flow region A g Integrate the distribution of the droplet mass flux G d (y / D) to calculate the total entrained droplet mass flow rate W in the gas core LE ; S

[0018] 7) Divide the entrained droplet mass flow rate W LE by the liquid-phase mass flow rate W L to calculate the droplet entrainment rate f E .

[0019] Further, in step 3), the droplet velocity u is calculated by Equation (1):

[0020] S

[0021] where f is the oscillation frequency of the pre-signal, λ is the laser wavelength, and n is the air refractive index.

[0022] Further, in step 4), α, G d The calculation formulas are as follows:

[0023]

[0024] where T is the total measurement duration at a certain measurement point, N is the number of droplets, Δt i and u i represent the residence time and velocity of the i-th droplet, and ρ l represents the liquid-phase density.

[0025] Furthermore, the method of step 5) is as follows: determine the gas phase flow area A g The method is as follows: calculate the liquid film thickness h at the bottom of the pipe under the measurement condition through the empirical model, draw an auxiliary circle on the pipe flow cross section, the upper part of the auxiliary circle is tangent to the top of the pipe, and the lower part is set at the liquid film thickness h. Its diameter is equal to the difference between the pipe diameter D and the liquid film thickness h. The auxiliary circle is used as the gas phase flow area A. g .

[0026] Furthermore, in step 6), the distribution of the mass flux of the droplets in the vertical direction of the pipeline is G d The fitting formula for (y / D) is:

[0027] Where a and b are fitting coefficients, y is the vertical distance between a point on the pipe flow section and the bottom of the pipe, and y is 0 at the bottom of the pipe.

[0028] Furthermore, assuming the thickness of the liquid film at the bottom of the pipe is h, the total mass flow rate of the entrained droplets in the gas core is W LE :

[0029]

[0030] Furthermore, in step 7), the droplet entrainment rate f E :

[0031]

[0032] Where A represents the cross-sectional area of the pipe, V sl represents the liquid phase superficial velocity, ρ l Represents the liquid density. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 : Fiber optic probe measurement system.

[0034] Figure 2 : Fiber optic probe measuring tube section and L-shaped stainless steel protective sleeve.

[0035] Figure 3 : Fiber optic probe measurement position.

[0036] Figure 4 : Droplet signal diagram. (a) Droplet signal collected over a period of time; (b) A droplet signal and pre-signal magnification diagram.

[0037] Figure 5 : Schematic diagram of gas phase circulation area.

[0038] Figure 6 : Exponential function fitting droplet flux distribution diagram.

[0039] The description of the reference numerals is as follows:

[0040] 1. Guide screw; 2. Circumferential adjustment handle; 3. Inside the measuring tube; 4. Optical fiber probe

[0041] 5. Flange; 6. Bolt; 7. L-shaped stainless steel protective sleeve

[0042] 8. Radial adjustment handle; 9. Guide groove Specific implementation mode

[0043] The present invention will be further described below in conjunction with the accompanying drawings and examples. The measurement of the liquid droplet entrainment rate in horizontal annular flow includes the following steps:

[0044] 1) Set up an optical fiber probe measurement system.

[0045] The optical fiber probe measurement system is as Figure 1 shown. The optical fiber probe used is made of SMF-28e+ single-mode optical fiber produced by Corning Inc., with a core diameter of 8.2 μm and a cladding diameter of 125 μm. Its end is ground into a 35° taper angle for detecting liquid droplets. During the test, a laser generates infrared light with a power of 6 mW and a wavelength of 1550 nm, which is transmitted to the sensitive tip of the optical fiber probe through an optical fiber coupler. The reflected light generated at the sensitive tip is transmitted into a photodetector through the other path of the optical fiber coupler, converting the optical signal into an electrical signal and being collected by a computer equipped with a data acquisition board.

[0046] The optical fiber probe measuring tube section is as Figure 2 shown. This measuring tube section is connected to the test system through an external flange 5. The optical fiber probe is inserted into a horizontal measuring tube with an inner diameter of 50 mm through an L-shaped stainless steel protective sleeve 7, and its sensitive tip is facing the oncoming flow direction. A circumferential adjustment handle 2 is provided in the middle of the tube section, which can rotate the middle measuring tube section around the tube axis, thereby adjusting the circumferential measurement position of the optical fiber probe. The L-shaped stainless steel protective sleeve 7 is provided with a radial adjustment handle 8, which can adjust the radial measurement position of the optical fiber probe in the tube along the guide groove 9. The position of the optical fiber probe 4 is fixed by a guide screw 1 to achieve precise detection of different positions on the tube cross-section. During the experiment, it is necessary to control the gas-liquid flow rate in the pipeline to form a fully developed horizontal annular flow to ensure that the optical fiber probe can normally detect the liquid droplets in the gas core.

[0047] 2) Under the experimental conditions of horizontal annular flow, adjust the measurement position of the optical fiber probe and collect liquid droplet signals. The measurement positions are as Figure 3As shown in the figure, by adjusting the circumferential adjustment handle and the radial adjustment handle on the measuring pipe section, the sensitive tip of the optical fiber probe is fixed at five positions in the vertical radial direction of the horizontal pipe (including 0.2D, 0.4D, 0.5D, 0.6D, 0.8D. The bottom of the pipe is 0D, where D is the pipe diameter). At each measurement position, the output signal of the photodetector is continuously collected for at least 60 s.

[0048] 3) Process the output signal of the photodetector, locate a large number of scattered droplet signals therein, and extract the residence time Δt and droplet velocity u of each droplet. Figure 4 (a) shows the droplet signals collected over a period of time. Due to the difference in the refractive indices of the gas and liquid phases, when the sensitive tip of the optical fiber probe contacts the gas phase, the photodetector outputs a high level of about 700 mV. Whenever a droplet contacts the sensitive tip of the optical fiber probe, the photodetector outputs a low-level pulse of about 0 V. The amplified details of a certain droplet signal are as Figure 4 (b) shown, where the duration of the low level represents the duration of the droplet being punctured by the sensitive tip of the probe, which is defined as the droplet residence time Δt. Before the droplet contacts the probe, the reflected light from the droplet interface is received by the optical fiber probe and interferes with the reflected light from the interface of the sensitive tip of the probe in the core, forming an oscillating pre-signal. The oscillation frequency of the pre-signal is modulated by the droplet velocity. The droplet velocity u is calculated by Equation (1):

[0049]

[0050] where f is the oscillation frequency of the pre-signal, which can be extracted by performing synchronous compressed wavelet transform (WSST) on the pre-signal [4], λ is the laser wavelength, and n is the refractive index of air.

[0051] 4) Calculate the local droplet fraction α and the average droplet velocity at each measurement position Furthermore, calculate the local droplet mass flux G d . α, G d are calculated as:

[0052]

[0053] where T is the total measurement duration at a certain measurement point, N is the number of droplets collected within the duration T, Δt i and u i represent the residence time and velocity of the i-th droplet, and ρ l represents the liquid phase density.

[0054] 5) Determine the gas-phase flow region. Calculate the liquid film thickness h at the bottom of the pipe under the measurement conditions through an empirical model, as shown in Equation (5):

[0055]

[0056] Among them, V sg and V sl are the superficial gas velocity and superficial liquid velocity, and Fr g and Fr l are the gas-phase and liquid-phase Froude numbers, which can be expressed as:

[0057]

[0058] Among them, g is the acceleration due to gravity. Place a circle on the liquid film thickness h, and its diameter is equal to the difference between the pipe diameter D and the liquid film thickness h, as the gas-phase flow area A g , as Figure 5 shown.

[0059] 6) Use the exponential function of Equation (7) to fit the distribution of the mass flux of droplets in the vertical direction of the pipe G d (y / D), Figure 6 which shows the exponential distribution of the droplet flux fitted considering the liquid film thickness.

[0060]

[0061] Among them, a and b are fitting coefficients, y is the vertical distance from a point on the pipe flow cross-section to the bottom of the pipe, and y is 0 at the bottom of the pipe.

[0062] 7) Integrate the distribution of the droplet mass flux G g in the gas-phase flow area A d (y / D) to calculate the total entrained droplet mass flow rate W LE in the gas core.

[0063]

[0064] Among them, s is the horizontal chord length of A g at the vertical position y.

[0065] 8) Divide the entrained droplet mass flow rate W LE by the liquid-phase mass flow rate W L to calculate the droplet entrainment rate f E :

[0066]

[0067] Among them, A represents the pipe cross-sectional area.

[0068] To verify the effectiveness of the proposed measurement method for the droplet entrainment rate in horizontal annular flow, a full-flow experiment for measuring the droplet entrainment rate in horizontal annular flow was designed. The superficial gas velocity was set to 20 m / s, and the superficial liquid velocity was set to range from 0.04 m / s to 0.15 m / s. Under each working condition, a fully developed annular flow was formed in the test section. The droplet characteristics at five positions on the vertical centerline of the horizontal pipe were measured using the above-mentioned optical fiber probe. The sampling time at each position lasted for 60 s, and the sampling frequency was 125 MHz. Then, the droplet mass flux at each position was calculated, and the distribution of the droplet mass flux in the gas flow region was fitted using an exponential function. Finally, by integrating this exponential distribution, the mass flow rate of the droplets was obtained, and the droplet entrainment rate of the horizontal annular flow was calculated. The measured droplet entrainment rate was compared with the entrainment rate prediction model proposed by Berna et al. [5] in 2015 in Equation (10 - 12), and the results are shown in Table 1.

[0069]

[0070] where We sg is the gas-phase Weber number, Re sg and Re sl are the gas-phase and liquid-phase Reynolds numbers, ρ g and ρ l are the gas-phase and liquid-phase densities, μ g and μ l are the gas-phase and liquid-phase viscosities, and ρ is the surface tension.

[0071] Table 1 Comparison between the measured entrainment rate and the model prediction value

[0072]

[0073] In Table 1, it can be found that the errors between the droplet entrainment rate measured by the optical fiber probe and the model prediction values are all within 16%, verifying the reliability of the proposed measurement method.

Claims

1. A method for measuring the entrainment rate of liquid droplets in annular flow based on a conical optical fiber probe, comprising the following steps: 1) Set up an optical fiber probe measurement system. Insert an optical fiber probe into the interior of the measurement pipe section through an L-shaped stainless steel protective sleeve, with its sensitive tip facing the oncoming flow direction. Use a laser to emit infrared light, transmit the light to the tip of the optical fiber probe through a Y-shaped coupler, and the reflected light generated at the tip of the optical fiber probe is received by the other path of the coupler and converted into an electrical signal by a photodetector. 2) Under the experimental conditions of horizontal annular flow, adjust the circumferential adjustment handle and radial adjustment handle on the measurement pipe section to control the measurement position of the optical fiber probe in the pipe cross-section. During the experiment, adjust the sensitive tip of the optical fiber probe to different positions perpendicular to the radial direction of the horizontal pipe respectively, and continuously collect the output signals of the photodetector for at least 60 s at each measurement position. 3) Process the output signals of the photodetector, locate the scattered droplet signals therein, and extract the residence time Δt and droplet velocity u of each droplet. 4) Calculate the local droplet fraction α and the average droplet velocity at each measurement location and then calculate the local droplet mass flux G d ; 5) Determine the gas flow region A g ; 6) Use an exponential function to fit the distribution of the mass flux of the droplet in the vertical direction of the pipe G d (y / D); 7) In the gas-phase flow region A g Integrate the distribution G of the droplet mass flux d (y / D) to calculate the total entrained droplet mass flow rate W in the gas core LE ; 8) Divide the entrained droplet mass flow rate W LE by the liquid phase mass flow rate W L to calculate the droplet entrainment rate f E .

2. The method for measuring the entrainment rate of liquid droplets in annular flow based on a tapered optical fiber probe according to claim 1, wherein In step 3), the droplet velocity u is calculated by formula (1): where f is the oscillation frequency of the pre-signal, λ is the laser wavelength, and n is the refractive index of air.

3. A method for measuring the entrainment rate of liquid droplets in annular flow based on a conical optical fiber probe according to claim 1, characterized in that In step 4), α, G d The calculation formula is: where T is the total measurement duration at a certain measurement point, N is the number of droplets, and Δt i and u i represent the residence time and velocity of the i-th droplet, and ρ l represents the liquid-phase density.

4. A method for measuring the entrainment rate of liquid droplets in annular flow based on a tapered fiber optic probe according to claim 1, wherein The method of step 5) is as follows: Determine the gas-phase flow region A g , and the method is: Calculate the liquid film thickness h at the bottom of the pipeline under the measurement condition through an empirical model. Draw an auxiliary circle on the pipeline flow cross-section. The upper part of the auxiliary circle is tangent to the top of the pipeline, and the lower part is set at the liquid film thickness h. Its diameter is equal to the difference between the pipeline diameter D and the liquid film thickness h. Take the auxiliary circle as the gas-phase flow region A g .

5. A method for measuring the entrainment rate of liquid droplets in annular flow based on a tapered optical fiber probe according to claim 1, characterized in that, In step 6), the distribution G of the mass flux of the droplets in the vertical direction of the pipeline d (y / D) has a fitting formula as follows: where a and b are fitting coefficients, y is the distance in the vertical direction between a certain point in the pipe flow cross-section and the bottom of the pipe, y is 0 at the bottom of the pipe 9) A method for measuring the entrainment rate of liquid droplets in annular flow based on a tapered fiber optic probe according to claim 1, wherein, assuming the liquid film thickness at the bottom of the pipeline is h, the total mass flow rate W of the entrained liquid droplets in the gas core LE :

6. The method for measuring the entrainment rate of liquid droplets in annular flow based on a conical optical fiber probe according to claim 1, wherein The droplet entrainment rate f in step 7) E :[[]]END]] where A represents the cross-sectional area of the pipe, and V sl represents the apparent liquid velocity, and ρ l represents the liquid density.

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