Study on Distribution Characteristics of Gas-Liquid Two-Phase Flow in Pitot tube Sampler

Gas-liquid two-phase current systems are widely existed in the petroleum, the chemical industry, the metallurgy, the nuclear power and many industrial fields. Two-phase’s phase distribution and measurement can’t be avoided in two phase current system. And it is also a difficult problem that has not been solved. In this paper, we designed a pitot-distributor. Experimental measurement and theory analysis were carried out to study the distribution data and situation of the distributor in gas-liquid two-phase flow. Firstly, a special experimental device for pitot-distributor was designed and experiments were carried out at air-water two-phase flow loop. The main text pipeline’s diameter is 50mm, the system pressure is 0.24∼0.28MPa, there are five branches in the pitot-distributor, each branch’s diameter is 8mm. The paper has first analyzed the influencing factors of gas extraction ratios and liquid extraction ratios, which were effected by four different types of pitot-separator. Next, it analyzed different efforts under two kind of pressure. Then, we established the math model and calculated the coefficients. Last, we analyzed the erroneous. The experimental result indicated that the tube-12345 structure is the perfect one which can keep extraction ratios more stable in a quite wide rang. Liquid extraction ratios (KL) mainly are affecting by the pressure and its structure. The gas extraction ratios (KG) mainly are affecting by the pressure.


Pitot sampler structure
The pitot tube sampler designed in this paper can transform four different sampling structures by opening or closing the ball valve. The sampling sections are shown in Figure 1-1a, 1-1b, 1-1c and 1-1d, which are represented as "branch tube-12345", "branch tube-234", "branch tube-1234" and "branch tube-2345" respectively.    When the laminar flow, the gas-liquid flow rate is slow, the liquid phase is mainly in the lower part of the pipeline due to gravity, and the uppermost branch tube 1 can hardly receive liquid, so the tube-12345 is basically the same as the tube-2345 (1,4), the tube-234 and the tube-1234 is basically the same (2, 3), and when the same four branches, the tube-2345 has a larger split coefficient than the tube-1234. Comparing Figure 1-2 a and b, it can be seen that the pressure has little effect on K L , and the liquid phase split coefficient under laminar flow mainly depends on the position of the branch pipe in the cross section. There is no absolute division criterion for wave flow and laminar flow. The two flow patterns are also classified as wave laminar flow when dividing the flow pattern. Therefore, similar to laminar flow, the upper part of the pipe is gas and the lower part is liquid. Therefore, tube-12345 is basically the same as tube-2345; wave flow is different from laminar flow in that the flow pattern has volatility, and the gas-liquid interface is wavy line, so even in a relatively stable flow pattern (assuming that the gas content of the cross section is equal to the liquid content of the cross section), the sample bodies of the branch tubes 1, 2, and 3 may be a gas-liquid mixture. Therefore, the shunt coefficient of tube-12345 is greater than tube-2345 and tube-234, and tube-12345 is slightly larger than tube-2345. The tube-2345, which is also the same, has a larger split coefficient than the tube-1234. Comparing Figure 1-2a and b, it can be seen that the pressure has an influence on K L , the greater the pressure, the greater the volatility of the wave current and the slightly different shunt coefficients.
Slug flow is an intermittent flow in which long bubbles and liquid plugs alternately flow through the distribution tube section. Taitel et al. suggest that the flow structure of the slug flow can be simplified to a unit body composed of long bubbles and liquid plugs. The distribution under the slug flow can be seen as a superposition of the two parts of the liquid membrane zone distribution and the liquid plug zone distribution. When there is no liquid plug, similar to the laminar flow condition, when the liquid plug comes, the pressure in the distribution pipe suddenly increases, and the spoiler installed in front of the sampling distributor rotates to form a symmetrical annular flow. Therefore, branch tube-12345 has the largest liquid phase split coefficient, tube-234 is the least, and tube-2345 is larger than tube-1234 because of the similar laminar flow when there is no liquid plug. Comparing Figures 1-2 a and b, it can be seen that the pressure has an effect on K L , the greater the pressure, the smaller the shunt coefficient. Basically, under the pressure of 1 industrial and mining, the liquid phase splitting coefficient is proportional to the branch pipe occupying the cross-sectional area of the pipe.
In the case of annular flow, the amount of liquid is very small, the middle three branches are located in the gas concentration area, and the upper and lower branches are facing the annular liquid film. As can be seen from the figure, the tube-1234 is slightly larger than the tube-2345, this is because the liquid film is uneven and the lower liquid film is thick. Tube-234 is located in the gas concentration zone, the amount of liquid taken is very small, and the value of the shunt coefficient of tube-12345 is the largest. Comparing Figure 1-2 a and b, it can be seen that the pressure has little effect on K L , because the pressure of the annular flow itself is very large, and the difference of 0.05MPa is not obvious.

1.2.2.
Influence of pitot tube structure on gas phase splitting coefficient. Figure 1-2 shows the gas phase splitting coefficient of the four pitot tube samplers. The X axis is the four pitot tube sampler structures. 1, 2, 3 and 4 represent tube-12345, tube-234, tube-1234, tube-2345, respectively, and the ordinate is the gas phase splitting coefficient. Now analyze Figure 1-2: In the laminar flow, the gas phase splitting coefficient is stable under the structure of the four pitot tube samplers. This is because the gas phase and the liquid phase have obvious boundaries when laminar flow, so the tube-12345 and tube-1234 structures in the gas concentration zone have many branches. The gas is the most, the tube-1234 split coefficient is larger; The wave flow is similar to the laminar flow, but due to the large fluctuation of the wave flow, when the gas slug flow is also carried in the branch tube located in the liquid concentration zone, the gas phase split coefficient of the tube-1234 is the largest; In the case of slug flow, when there is no liquid plug, similar to the laminar flow and the wave flow, the gas is mainly obtained in the gas concentration zone, and when the liquid plug is present, the pressure inside the tube increases to cause the spoiler to rotate (see the first section of Chapter 4). Forming an annular flow, the intermediate gas concentration zone can take gas. In the upper and lower liquid concentration zone, since the liquid film thickness is smaller than the inner diameter of the sampling tube, the gas-liquid mixture can also be obtained, and the pipe-12345 takes the most gas; In the case of annular flow, the gas-phase splitting coefficients of the other four structures are the most stable except for tube-12345, which is maintained between 0.04 and 0.05.  Figure 1-3 a and b, it can be seen that the pressure has an influence on the gas phase shunt coefficient. The larger the pressure, the more gas is taken, and the shunt coefficient is larger.  Table 1-2 shows the comparison of the four structures and sampling characteristics of the pitot tube sampler. For the tube-12345 type with evenly distributed branch pipes, it can be ensured that the branch pipes are located in the gas phase concentration zone and the liquid phase concentration zone simultaneously in each flow mode, and the split fluid entering the split circuit has both gas and single phase liquid, or a two-phase fluid having a constant gas-bearing gas rate. The sampling representative can be improved by using a plurality of sampling branches to uniformly distribute the sampling in the main section. However, the volatility of different flow patterns is very different and cannot be generalized. It requires a split-type discussion (see Chapter 4). However, it can be determined that under the two flow patterns of laminar flow and wave flow, the gas phase split coefficient is not affected by the sampling tube distribution.  Table 1-3 shows the gas phase and liquid phase volume flow in the main road in the experiment. Since the tube-12345 takes more gas and liquid phase and is uniform, therefore, tube-12345 is taken as an example to study the effect of gas/liquid flow on the splitting coefficient.  It can be seen from the analysis of Figure 1-4 that the liquid-phase splitting coefficient decreases with the increase of the liquid volume flow rate, and the larger the flow rate, the more the liquid is taken; the gas-phase splitting coefficient increases with the increase of the liquid volume flow rate, but the change is not obvious. This is due to the different volatility of different flow patterns, and also requires split analysis.
It can be seen from the analysis of Figure 1-5 that the liquid phase splitting coefficient decreases with the increase of gas volume flow rate, and the larger the gas volume is, the smaller the liquid is taken; the gas phase splitting coefficient is not obvious with the increase of gas volume flow.  When the gas-liquid two-phase fluid flows in the pipeline, various flow structure forms will be traveled due to different pressure, flow, heat load and pipe geometry, which is referred to as flow pattern. The more common horizontal flow patterns currently recognized include stratified flow, wave flow, slug flow, bubble flow, annular flow and the like. Since different gas-liquid two-phase flow patterns have different hydrodynamic and heat transfer characteristics [17], it is necessary to divide the flow pattern to study the flow pattern control when studying the gas-liquid two-phase flow problem. Here, do not make more statements.

Establishment of mathematical model
The sample body is in parallel relationship with the main fluid, so the split coefficients K G , K L mainly depend on the relative resistance characteristics of the main fluid circuit and the sample body circuit. In addition, the number and position of the sampling tubes also have a large influence on the characteristics of the shunt coefficient. The phase separation model in the two-phase flow theory can be used to write the calculation formula of the total pressure difference ΔP 1 of the main fluid circuit and the total pressure difference ΔP 2 of the sample body loop: In the formula, and are the total resistance coefficients of the main fluid circuit and the sample body circuit respectively. And are the density of the gas phase and the liquid phase, respectively. A2 A3 is the flow cross-sectional area of the main fluid circuit and the sample body circuit respectively, and 1  is the primary fluid circuit phase separation model correction coefficient, and 2  is the sample body loop phase separation model correction coefficient. In the experiment, the upstream pressure is the mixing pressure, and the final end of the main fluid and the sample body are at atmospheric pressure, so the pressure difference between the two stages is equal, that is, ΔP 1 =ΔP 2 , and the following relationship can be derived from the formulas (2-1) and formula (2-2): Equation (2-3) comprehensively reflects the relationship between the gas phase splitting coefficient K G , the liquid phase splitting coefficient K and the two-phase fluid density, the structural parameters, and the gas phase and liquid phase of the two-phase fluid to be measured. When the gas-liquid twophase fluid and structural parameters are known, both the gas phase splitting coefficient K G and the liquid phase splitting coefficient K L are unknown, and therefore K G and K L cannot be obtained according to the formula (2-3). Therefore, it is necessary to add another complementary equation relation about K G and K L in order to solve its value. After the summary of the predecessors, it is found that the gas-liquid two-phase fluid can improve the kinetic energy through the flow type intervention, and the liquid film on the wall will be torn and pulverized. As the air flow is dispensed, a small amount of liquid film will also be killed and also low. The spray is told from the mixer mouth, but a small amount of liquid film remains on the wall; the spray from the spoiler tells the droplet that its movement has a certain independence due to inertia and is basically unaffected by the gas phase. Therefore, the liquid phase flow into the sampling tube is equal to the total droplet flow [100] of the cross section of the sampling tube port. This is: Where ΔM LF represents the residual liquid film flow rate, is a coefficient related to the distribution pattern of the droplet on the pipe flow cross section and the sampling tube structure. The calculation formula of the liquid phase split coefficient K L can be obtained: It can be seen from equation (2)(3)(4)(5) that K L gradually increases as the liquid sample flow rate increases. When M L2 increases to a certain value, the latter phase b/ M L3 in parentheses will be small  10 relative to 1, can be ignored, at this time K L is equal to the constant a. After determining the liquid phase splitting coefficient, the calculation formula of the gas phase splitting coefficient K G can be obtained according to the formula (2-3): Where K G1 is the value of the shunt coefficient when the dryness is equal to 1, and ΔK G is the influence of K L and other factors on K G . Can be calculated separately using the formula below

Determination of the coefficient of the mathematical model
Equations (2-5) ~ (2-8) are formula models of pitot-type samplers derived from the formula, where the coefficients a, b are unknown and need to be calibrated using measured data. Table 2 According to the empirical formula (2-5), we can see that the liquid phase split coefficient K L is proportional to the sampled liquid mass flow M L3 and tends to be stable with the increase of M L3 .  When there is no liquid plug, it is similar to laminar flow and wave flow. The concentrated area mainly obtains gas. When there is liquid plug, the pressure inside the tube increases to make the spoiler rotate, forming a symmetrical annular flow and the middle gas concentration area can take gas. In the upper and lower liquid concentration area, since the liquid film thickness is smaller than the inner diameter of the sampling tube, obtaining a gas-liquid mixture; Analysis Figure 2-8: The gas phase splitting coefficient is the most stable when the annular flow is used.
Comparing the measured maps under the two pressures in Figure 2-5 ~ Figure 2-8, it can be found that the pressure at the laminar flow has a greater influence on the gas-phase splitting coefficient. The greater the pressure, the more gas is taken. When comparing the flow patterns longitudinally, it can be found that the gas phase splitting coefficient K G is greatly affected by the liquid phase flow rate, while  11 the gas phase flow rate (gas phase conversion speed) has little effect on the K G . ΔK G is small, K G and K G1 are very close, and the difference between the two is basically not affected by the gas phase flow rate and the liquid phase flow rate.         Table 2-3 shows the error analysis of the liquid phase splitting coefficient and the gas phase splitting coefficient. Since the gas measurement accuracy is low in the experiment, the value of the gas phase split coefficient below 0.01 is not considered. The absolute error is the absolute value of the calculated value and the measured value difference. The standard deviation is equal to the sum of the squares of n (calculated valuemeasured value), then divided by (n-1), and finally squared.

Conclusion
Regarding the distribution characteristics of the pitot tube sampler, the following conclusions were obtained: ① The liquid phase split coefficient (K L ) is mainly affected by the position and pressure of the main section of the branch pipe. If the branch pipe is in the liquid phase concentration zone, K L is larger; as the pressure increases, the K L decreases, laminar and annular flow, and no effect on pressure.
② The gas phase splitting coefficient (K G ) is mainly affected by pressure. The higher the pressure, the more gas is taken. At the same time, the position of the main pipe in which the branch pipe is located also has an effect on K G , but it is not obvious.  18 ③ K L decreases with the increase of liquid volume flow rate, but not the larger the flow rate, the more liquid is taken; K G increases with the increase of liquid volume flow, but the change is not obvious.
④ Under various flow patterns, K L gradually increases with the increase of liquid phase sampling flow rate, and finally tends to be stable.
⑤ The gas phase flow rate (gas phase conversion rate) has little effect on K G , and its size is mainly determined by the distributor characteristics and system resistance.