CFD verification of total pressure loss coefficient for gas-liquid two-phase flow

Traditionally, we design gas-liquid two-phase flow systems with pressure loss that is assumed by homogeneous flow. However, in real phenomena, the flow rate of water or air through a system cannot be correctly predicted unless we evaluate by the total pressure loss. there are currently few methods for measuring total pressure loss, and the value of total pressure loss is not yet clearly. Therefore, we devised a method to measure total pressure loss by pump Q-H characteristic and succeeded in measuring total pressure loss indirectly. We compared the test results with the analysis to clarify the prediction accuracy of the analysis using commercial codes. We apply three two-phase flow models for the simulation: a VOF model, a homogeneous flow model, and a two-fluid model. The simulation results of comparison between each fluid model indicated that the VOF model predicted with the best accuracy, with the error of 46% compared to the test results. This study provides a benchmark for the current commercial code, and the prediction accuracy of the different models provides a direction for future improvements in the analysis.


Introduction
Traditionally, designers in industry have used the loss of gas-liquid two-phase flow relative to the static pressure in designing and planning gas-liquid two-phase flow systems.In previous studies, many researchers have classified the gas-liquid two-phase flows in a system into homogeneous flow models and separated flow models and have proposed prediction equations [1][2][3][4][5][6][7][8][9] for pressure loss.For example, the relationship between parameters and two-phase friction multipliers proposed by Lockhart/Martelilli et al. [10] is used in industrial design.However, even with the many prediction equations that have been proposed, there is no equation that completely predicts the pressure drop in gas-liquid two-phase flows, and it requires verification by actual applications.The reason is that there are few cases in which the average dynamic pressure from a macroscopic viewpoint has been measured due to the complexity of gas-liquid two-phase flows, even though the total pressure loss including dynamic pressure is essentially necessary for the design and planning of fluid systems.Although there are fixed-point measurements of dynamic pressure in gas-liquid two-phase flow using a gas-phase suction-type total pressure probe and a wire mesh using electrical resistance, the total pressure difference at the inlet/outlet of the system, in other words, total pressure loss, has not yet been measured.Therefore, we designed a total pressure loss measurement of fluid systems using the QH characteristics of pumps and measured the total pressure loss of gas-liquid two-phase flows.The purpose of this paper is to compare the results of our total pressure loss measurements with those of gas-liquid two-phase flow analysis using current commercial codes and to benchmark our analysis.

Test apparatus
The test apparatus is the open-loop pump test facility indicated by figure 1, which is capable of flowing 360 L/min of liquid phase (water) and 180 L/min of gas phase (air) for each phase.The water flow rate was adjusted by the rotation speed of the pump.In this experiment, we installed a strain-type pressure measuring device at the pump inlet/outlet, a water tank for gravimetric flow measurement at the outlet end of the experimental apparatus, and strain-type pressure measuring devices and thermal flow measuring devices in the air piping system to measure the pump inlet/outlet pressure, pressure immediately before air injection, water volume flow rate, and air mass flow rate, respectively.Compressed air is injected downstream of the pump using a compressor, and a transparent plastic pipe is installed as part of the piping system to visualize the internal flow pattern with a high-speed camera.

The method of measuring two-phase flow's total pressure loss
In a system containing a pump, it is the total head characteristic of the pump and the resistance characteristic of the piping system that determine the operating point of the pump.As shown in figure 2, the total head and resistance characteristics of a pump have a certain intersection, and the pump works at the total head and flow rate at the intersection.In other words, by measuring the total head at a certain flow rate, It means to measure the resistance characteristics of the piping system.Therefore, by measuring the total pump head in a gas-liquid two-phase flow condition with air injection, we can obtain the resistance characteristics of the gas-liquid two-phase flow in the piping system.However, it is necessary to measure the pump head in a single-phase water flow with no gas phase inflow into the pump.In this test system, the gas phase is injected downstream of the pump.Therefore, it was necessary to subtract the total pressure loss in the liquid phase from the pump head to derive the total pressure loss in the gas-liquid two-phase flow.The total pressure loss in the gasliquid two-phase flow section is obtained by subtracting from the pump head the total pressure loss up to the pump inlet in the liquid phase section, the total pressure loss from the pump outlet to the gas phase inlet, and the height from the water surface at the inlet side to the outlet position.

The method of CFD analysis
In this paper, we compare test and CFD analysis results using the widely used commercial code STAR-CCM+ (ver.2021.1).There were Three gas-liquid two-phase flow models to apply for the fluid analysis: a VOF model, homogeneous flow model, and a two-fluid model.In this paper, the gas-liquid two-phase flow models, except for applying for the ideal fluid condition, consider a constant density condition.For the homogeneous flow model, slip velocity is considered or not, and population balance model (PBM) is used.The gas-liquid two-phase flow models used in this paper are shown table1 with respect to the setting of these conditions.

The model of CFD analysis
Figure 3 shows the analytical model used in this analysis.The model reproduces the pump outlet side of the test apparatus and includes valve elements in the piping system.The number of elements was determined by conducting a lattice dependency analysis.

The model of physics
The slip velocity, bubble resistance, surface tension, PBM were used as fluid models in this analysis.
The equations for each physical model are shown below.Since the PBM in this analysis also incorporates a model of coalescence and breakup, it is possible for bubble diameters to change due to coalescence and breakup among bubble diameters in the flow, and for bubbles to move from one bubble diameter cluster to another.

The calculation of two-phase flow's total pressure loss
In this analysis, as described in 3.1.we used two conditions for air: constant density and ideal gas.The variables to be considered in the conservation of energy are different under the two conditions, but in this analysis, the temperature change is as small as ±10 K, and the density change can be considered small.Therefore The total pressure loss was calculated using the following equation (7), referring to the basic equation described by Kataoka et al. [11].

The test result
In the test, we obtained data for water flow rate 360 L/min, varying the air flow rate every 20 L/min from 0 to 120 L/min.Since unsteady phenomena such as fluctuation of pump pressure and vibration of the piping system occurred due to the injection of gas phase, this paper uses the data for a water flow rate 360 L/min and air flow rate 60L/min, that the unsteady phenomena were relatively small.

Flow pattern in the pipe at visualized part
Figure 4 shows the flow pattern in the visualized piping, which was captured by a high-speed camera under the conditions of water flow rate of 360 L/min and air flow rate of 60 L/min.In figure 4, small bubbles of 3~4 mm in diameter flowed continuously in the upper half of the piping, and large bubbles flowed intermittently.The large bubbles had developed to a length of 50 mm in the flow direction.
The flow pattern is considered to be that of a flag flow with large bubbles accompanied by small bubbles.

Two-phase flow's total pressure loss
First, figure 5 shows the results of measuring the total pressure difference between the inlet and outlet of the pump when the quality is varied from 0 to 0.0005 by changing the air flow rate at a water flow rate of 360 L/min.The total pressure increases monotonically with increasing air flow rate compared to water single-phase flow (quality = 0).This indicates that the inflow of air increases the driving energy of the pump (i.e., the total pressure loss).
Figure 6 shows the value of each loss.For each loss, the losses at the pump inlet and the section from the pump outlet to the air inlet are due to the liquid single-phase flow.For the position loss due to the difference in height, the amount of loss depends on the density change to the change in gas phase injection.In this paper, the losses for a single phase of water flow are shown as representative values.
Using the results of figure 6, figure 7 shows the total pressure loss in the gas-liquid two-phase flow section after subtracting each loss from the total pump pressure.The gas-liquid two-phase flow loss increases steadily as the quality increases, and under the test conditions, the total pressure loss is also maximum at the maximum air flow rate.

The CFD analysis result 4.2.1. Effect of grid quality
Table 2 shows the results for the effect of grid quality.The results show that there is no grid quality in both the VOF model (No.1) and the homogeneous flow model (No.2).Therefore, in this analysis, the diameter of the air inlet is 3 mm, and the analysis is performed by selecting a mesh with a representative mesh size of 3 mm or less.

The result of total pressure loss
The results of the total pressure loss obtained from the analysis of each gas-liquid two-phase flow model are shown in table 3 and figure 7. The two-fluid model provides better feedback of the interfacial motion to the motion of each phase by analysis the equations of motion of each of the twophases compared to the other fluid models.This is expected to result in better prediction accuracy than other fluid models.8, figure 9 shows the internal flow conditions.Figure 8 shows the volume fraction contours for the VOF model, and figure 9 shows the volume fraction contours for the two-fluid model.Figure10(a), 10(b), 10(c), 10(d), 10(e) and 10(f) show volume fraction and Sauter mean diameter contours for the homogeneous flow model with PBM for each condition.These results capture the same trend as the test results.However, in the VOF model that tracks the interface, a continuous gas-phase region is created without the formation of small bubbles, which does not allow us to evaluate the real phenomena.This is due to it that a mesh with a representative length of 2.7 mm is used, which does not resolve bubbles with diameters of 3~4 mm.In figure 10(a), 10(b), 10(c) and 10(d) the gas phase tends to collect at the top of the pipe, but unlike the VOF model and the two-fluid model, its value is not 1.The volume fraction of air was around 0.4, indicating that the bubbles were more dispersed inside the pipe.Next, we discuss the Sauter mean diameter in figure.10.In the simplest model No. 2 and the model with slip No. 3, the Sauter mean diameter tended to increase once before the visualization pipe and then decrease from 8 mm to 7 mm until the bend located downstream of the visualization pipe.Since the diameter of bubbles passing through the visualization piping was 3~4 mm at the time of the test, the models No. 2 and 3 were not able to predict the bubble diameters.When the ideal gas condition in figure 10(e),10(f) was given, the bubble diameter passing through the visualization piping was 4~7 mm, which is a better result compared to the two homogeneous flow models.The bubble diameter tended to increase from the visualization pipe to the bend located downstream of the pipe, which is like the actual condition since coalescence and accumulation of gas phases are expected to occur at the bend located downstream of the pipe.
From these results, it represents that the VOF model is more accurate in predicting total pressure loss than other models, but it does not predict the gas phase distribution in terms of volume fractions.In addition, the VOF model is difficult to predict for this analysis with a large representative mesh size, because both the total pressure loss prediction and the bubble state are different from the test results.It should be noted that although the results obtained in this analysis showed that the VOF model gave the results most consistent with the test, we assume that the results obtained for the No1~5 fluid models.
Finally, in the homogeneous flow model, the prediction accuracy of total pressure loss was improved by adding velocity slip, and the bubble distribution was improved by considering the ideal gas condition.However, the accuracy of the prediction of total pressure loss was the worst compared to the other models.Considering the above, it indicates that whether to consider the motion at the interface has a significant impact on the accuracy of the analysis.To improve the prediction accuracy of total pressure loss in future gas-liquid two-phase flow analysis, a model that can solve the interfacial motion in more detail and the ideal fluid conditions, i.e., temperature and compressibility, can be considered.

Conclusion
We measured the total pressure loss of gas-liquid two-phase flow in tests and analysed with three fluid models VOF model, homogeneous flow model, and two-fluid model, constant density and ideal gas conditions using a general-commercial code.
1) The VOF model was the most accurate in predicting total pressure loss among the fluid models compared in this paper, estimating 46% lower than the test results.The two-fluid model was the second, and the homogeneous flow model was the worst.
2) we applied three different conditions (constant density, slip, and ideal gas conditions) for homogeneous flow model, and it indicated that the slip condition improved the prediction accuracy of total pressure loss, while the ideal gas condition improved the bubble diameter distribution.
3) The results of 1) and 2) indicate that it is important to capture the motion of the interface in predicting total pressure loss, and the importance of total pressure loss due to the motion of the interface has been recognized.In addition, since the bubble diameter distribution is affected by the ideal gas condition that takes temperature and compressibility into account, improving the prediction accuracy of the motion of the interface and bubble diameter can contribute to the improvement of total pressure loss.
This paper has established a benchmark for gas-liquid two-phase flow analysis using current commercial codes.The paper also confirms the policy needed to improve the accuracy of future analyses.the use of the VOF model for predicting total pressure loss in industry.

Figure 1 .
Figure 1.Test apparatus of pump loop for gas-liquid two-phase flow.

Figure 2 .
Figure 2. The diagram illustrating the method of measuring total pressure loss by pump Q-H curve and resistance curve.

Figure 5 .
Figure 5.The result of measuring pump head.

Figure 6 .
Figure 6.The values of total pressure loss at inlet side, position loss, total pressure loss between pump discharge side and injection point.

Figure 8 .
Figure 8. Contour results of volume fraction by VOF model.

Table 1 .
The condition of each fluid model.

Table 2 .
the results of the effect of grid quality.

Table 3 .
The error of two-phase flow's total pressure loss between CFD and test result.
Figure 7.Comparison with test result and CFD result about two-phase flow's total pressure loss.For each analysis result, figure