Numerical simulation of gas-liquid two-phase flow in a disc pump under different inlet bubble diameters

Visual investigation and numerical simulation were utilized to analyze the internal flow pattern transformation and bubble diameter variation of a gas-liquid two-phase flow disc pump. The results reveal that increasing the intake volume fraction (IGVF) from 1.12% to 27.67% changes the flow pattern in the suction chamber from bubbly to agglomerate bubbly, slug flow, and separated flow. Due to the particularity of the impeller structure of the disc pump, the blades in the leaf area of the front and rear cover plates play a barrier role. The gas phase gathers most violently at the edge of the blade in the leaf area, while the flow channel in the middle leafless area is wider and has higher permeability. At 1500r/min and 7.11% inlet volume void fraction, the local void fraction extreme value of the front edge of the blade in the blade area of the front cover plate increases to three times the initial void fraction, while the void fraction extreme value of the middle section of the bladeless area decreases to two-thirds of the initial void fraction. This research can be used to analyze the gas phase distribution and migration law in the disc pump impeller.


Introduction
The disc pump is a kind of special fluid-conveying pump with special impeller structure.The impeller blades are discontinuous along the axial direction, and the impeller passage is divided into a blade flow zone and a bladeless flow zone.When conveying high gas content fluid, the traditional centrifugal pump impeller flow channel is prone to gas blockage, resulting in impeller idling, while the disc pump impeller flow channel is wider, and the gas medium is not easy to gather locally in the impeller to form an airbag, which can carry and transport high gas content liquid while operating stably.Therefore, at present, the transportation problems under the conditions of high viscosity, high gas content and multiphase flow in petrochemical, metallurgical machinery, medical and other fields have ushered in new solutions [1].
Through tests and numerical simulations, domestic and foreign researchers have conducted a large amount of research and study on the gas-liquid two-phase flow process in centrifugal pumps in recent years.Verde et.Al [2] carried out a visual inspection of the inside of the impeller of the centrifugal pump, and determined the relationship between the input voidage and the change of the flow pattern inside the impeller.He et.Al [3] studied the surge characteristics of a centrifugal pump with air bubble inflow and found that the change of air content at the inlet and outlet changed the flow pattern in the impeller.Wei et.Al [4] studied the flow pattern changes caused by bubbles entering the impeller, and identified three main flow patterns in the impeller: condensation bubble flow, airbag flow, and gas-liquid separation flow.The phase slip between gas and liquid will be exacerbated by the airbag flow and gas-liquid separation flow.He et.Al [5][6][7] used the PBM group equilibrium model to study the coalescency and fragmentation behavior of bubbles in a centrifugal pump.The research reveals that as the inlet void fraction increases, tiny cavitation builds in the impeller and generates air mass surrounding the impeller inlet, resulting in the pump's surge.Zhang et.Al [8][9][10] saw the inlet pipe of a centrifugal pump using high-speed photography technology, and hypothesized that the average bubble diameter at the impeller inlet increased with increasing inlet void fraction and dropped with increasing rotating speed.According to Tabib et.Al [11], the proper beginning bubble width should be chosen to ensure that the numerical simulation process is compatible with the actual gas-liquid two-phase flow process.Caridad et.Al [12] investigated the link between the head of the centrifugal pump and the average diameter of the bubble and discovered that the head reduces as the average diameter of the bubble increases.Li et.Al [13] discovered that as the incoming gas content of a centrifugal pump increases, the gas phase distribution in the impeller changes dramatically.Zakem et.Al [14] studied the movement of a single bubble in the stirring paddle and found that the uneven force of the bubble in the stirring paddle resulted in gas accumulation.Si et.Al [15] studied the internal flow characteristics of gas-liquid two-phase flow in centrifugal pumps.When the gas concentration of the incoming flow reaches 4.6%, the flow pattern in the impeller splits, and the bubbles at the impeller's outflow aggregate at the tongue to form a blockage, causing the pump to idle.The gap between the predicted and experimental results of the Euler multiphase flow model used by academics at home and abroad [16][17] is less than 10%, and the computed macroscopic physical quantities of multiphase pump performance have great accuracy.It can be utilized to aid in the experimental investigation of multiphase pumps.
There have been few research on the gas-liquid two-phase flow of the disc pump in the past, and they have primarily concentrated on the analysis of the disc pump's exterior properties.The internal flow law of the disc pump was not thoroughly studied, and the gas phase distribution law within the disc pump could not be adequately described.As a result, visualization research and numerical simulation methods [18] are employed to investigate the force and motion law of bubbles with varying inlet diameters in the flow field, as well as to explain the gas phase distribution and flow field fluctuation law in the disc pump.

Physical model and meshes generation
Figure 1 depicts the impeller solid model for the radial straight blade disc pump, and Table 1 lists the important parameters.To eliminate the effect of reflux on simulation results, the inlet and output pipe portions of the model pump are extended to 6 times the pipe diameter.Figure 2 shows the geometric model of the fluid domain of the disc pump, while Figure 3 shows the computational fluid domain grid.The impeller and volute employ a tetrahedral grid with a common node, whereas the inlet and outlet extension sections use hexahedral grids.

Grid independence verification
Grid independence verification of pure water condition (liquid phase flow Q = 41.15m 3 /h, rotational speed n = 1500r/min) and gas-liquid two-phase condition (liquid phase flow Q = 41.15m 3 /h, n = 1500 r/min, IGVF = 2.98%) is performed to ensure calculation accuracy and reduce calculation cost, as shown in Table 2.The fluctuation is within 1% when the grid number hits 3.28 million, and the final computation grid number is 3.28 million.Furthermore, as shown in Figure 4, the Y-plus values of the produced rotor grid are generally around 15, which fits the calculation requirements of the SST k- turbulence model.

Gas-liquid two-phase flow model and control equation
The three-dimensional flow field of the disc pump is solved using Fluent software.The three-dimensional viscous fluid Navier-Stokes equation is as follows [19]: Continuity equation is defined as Equation (1).
The momentum equation is defined as Equation (2).
In the equation : l and g are liquid water and gas phase air, respectively. , i  and i u are the phase density, volume fraction and the velocity components in the three directions of xyz respectively, i  symbolizes the i phase strain force tensor, as shown in Equation (3).i F represents the volume force.Only drag force, pressure gradient force and buoyancy are considered in this paper, The following equation can be used to express i F .
(4) Where P F  , D F and B F are the pressure gradient and drag force and the buoyancy of the bubble， respectively, D F is calculated by Equation (5) [19][20][21].
Where G V and L V are the liquid and gas local velocities, respectively.d is the diameter of the bubble, and D C is the drag coefficient.Equation ( 6) [22] defines the drag coefficient D C :   0.687 24 1 0.15 1000 0.44 1000 the Reynold's number can be calculated as [19,23]: where L  is the liquid viscosity.
The force caused by the pressure gradient within the impeller channel denotes the pressure gradient along the stream line.
Buoyancy of the fluid on the bubble B F is calculated by Equation (9) .
where f  and s  are the liquid and gas local densities, respectively.g is the gavity.

Boundary conditions and solution control set
Fluent employs the heterogeneous Euler-Euler model.The turbulence model adopts SST k- model, while the Gidaspow model is used in the drag force model of gas-liquid two-phase flow [13,24].The drag force model of gas-liquid two-phase flow is Gidaspow model.The inlet adopts velocity boundary condition and the outlet adopts pressure boundary condition.There is no wall slip.
To solve the pressure-velocity coupling, the Phase Coupled SIMPLE algorithm is employed.The multi-coordinate MRF approach is utilized to control the fluid and impeller motion directions.The calculation residual's convergence accuracy is set to 10 -5 , and the calculation process's convergence is checked by monitoring the mass conservation of the intake and outflow.Without addressing deformation and phase change, and neglecting mass and heat transmission between the two phases, it is assumed that the bubbles are homogeneous spheres of the same diameter.
Previous visualization tests reveal that the bubble diameter in the disc pump ranges between 0.1mm and 1.5mm [15][16], and the initial inlet bubble diameter is selected as stated in Table 3.The simulation scheme of Table 4 is intended to investigate the effect of inlet bubble diameter on gas phase distribution in the pump.

Experimental method
The disc pump test bench at Xihua University's Key Laboratory of Fluid and Power Machinery of the Ministry of Education boasts excellent precision, simple operation, safety, and reliability.The test bench is made up of a disc pump, a variable frequency motor, a data gathering system, a water tank, an electromagnetic flowmeter, a valve, a sensor, and a torque meter, among other things.

Analysis of the experimental result
Water circulates through the entrance pipe, disc pump, water storage tank, and outlet pipe.The gas-liquid mixing device mixes the gas through the gas injection pipe into the inlet pipe section, and the water is fully mixed before entering the disc pump, flowing into the water storage tank along the pipe, and discharging from the water storage tank's top.An electromagnetic flowmeter (uncertainty 0.5%) measures the liquid flow rate, which is regulated by an outlet valve, and a pressure sensor (uncertainty ±0.2%)measures the inlet and outlet pressures.A gas mass flowmeter (uncertainty of ± 0.1%) measures the flow of gas and an intake valve controls it.The pump's speed can be adjusted using the electrical control cabinet.
During the test, the electrical control cabinet adjusts the pump speed to 1500r/min and the beginning flow rate of the liquid phase to 41.15m 3 /h.The gas valve is progressively opened without altering the outlet valve, reducing the liquid phase flow naturally.Following a smooth run, the high-speed camera captures the flow conditions at various void fractions in turn.
Due to the influence of cross-sectional shape, medium surface tension, local gravity field, wall roughness and other factors, the flow pattern identification becomes complicated.At present, the flow pattern diagram is a simple method to comprehensively express the transition relationship between flow patterns.The widely used flow pattern diagram is Baker flow pattern diagram [25].Based on a significant number of visual experimental tests, four types of centrifugal pump flow patterns-bubble flow, agglomerated bubble flow, slug flow, and separated flow -can be distinguished based on the difference in gas-liquid apparent mass flow rate.Shao et.Al [26] investigated how the internal flow pattern of the horizontal tube and the impeller changed as the void fraction in the input increased.It has been discovered that the flow pattern shifts from bubbly flow to agglomeration bubbly flow, slug flow, and segregated flow as the gas content increases.
According to the previous research [1], the disc pump is tested at the initial liquid phase flow rate Q = 50m 3 /h at 1500r/min speed.The pipeline's liquid flow rate will gradually drop as the gas content rises.The water flow was maintained constant during the test while the valve was gradually opened.The gas content progressively rises while the water flow gradually declines.Figure 7 displays the test outcomes.
(1) The fluid in the inlet pipe is a bubble flow when the intake void fraction is low (IGVF≤5%), as shown in Figure 7(a).The gas is scattered throughout the flow channel, and the gaps between the bubbles are substantial.
(2) The input pipe forms an agglomerated bubble flow when the inlet void fraction approaches 5%, which worsens the flow instability in the disc pump.As indicated in Figure 7(b), the gas builds up in the upper portion of the inlet pipe, the gas and liquid are not mixed evenly, and the degree of separation increases.
(3) When the inlet gas content rises above 15%, the bubbles combine, a substantial volume of gas collects at the top of the pipeline, the degree of gas-liquid separation increases, and a slug flow forms in the pipeline space, as seen in Figure 7(c).( 4) When the input gas content reaches a crucial amount (IGVF≥ 20%), the pump operation process becomes unstable, and it is easy for idling to generate a cutoff occurrence.In the intake pipe, the gas and liquid phases are entirely separated.As illustrated in Figure 7(d), the gas phase is dispersed in the top portion of the input pipe and the liquid phase is distributed in the lower part of the inlet pipe, generating a separate phase flow in the pipe.The variation of flow pattern in the suction chamber under changing incoming gas content is complex, according to the aforementioned test results.When the inlet gas content is low, the bubble diameter is small, and the aggregation phenomena is not readily apparent.The bubble diameter grows as the inlet void fraction increases.In the process of reaching the critical unstable void fraction, the test bench produces vibration and noise, and finally the flow is cut off.In summary, in order to explore the influence of the size of the inlet bubble diameter on the gas phase aggregation, the simulated inflow is selected as the operating condition under the aggregated bubble flow state, so that a relatively stable and obvious bubble aggregation phenomenon can be observed.

Comparisons with experimental results
An open test bench of a disc pump validates the correctness of numerical simulation findings of gas-liquid two-phase flow.The pump speed is 1500 revolutions per minute, and the starting liquid flow rate is 41.15m 3 /h.To maintain water flow, the valve is not adjusted, and the valve gas content gradually increases.Figure 8 displays the connection between disc pump head and air content.An open test bench with a disc pump is used to validate the correctness of numerical simulation results for gas-liquid two-phase flow.The starting liquid flow rate is 41.15m 3 /h, and the pump speed is 1500r/min.To sustain water flow, the valve is not adjusted, and the air content of the valve is progressively raised.Figure 8 displays the association between the head of the disc pump and the air content.The visualization test of the horizontal inlet pipe of the disc pump was carried out by high-speed photography technology.The gas phase distribution in the inlet pipe of the disc pump is shown in Figure 8.It is worth noting that due to gravity, bubbles gradually gather into bubble clusters from the injection hole into the inlet pipe to the impeller inlet, and distribute in the upper part of the pipe.When the bubble clusters enter the impeller, they first flow into the flow channel at the top of the pipe near the front pump chamber.The impeller of traditional centrifugal pump has continuous blades.The blade shear force of the inlet large bubbles is large and easy to be broken by the impeller, so it can be assumed that the bubbles enter the flow channels of the impeller evenly [14].Because the flow channel in the impeller of the disc pump is wide and the blade is discontinuous, the shear force of the bubble in the flow channel is small [27], which is not easy to be broken by the impeller blade, and cannot be regarded as the bubble entering the flow channel of the impeller evenly.Therefore, the gas phase distribution at the inlet section of the impeller must be corrected by the lifting force of the bubble, so that the simulation process is consistent with the test.It is assumed that the bubble is a uniform sphere of equal diameter, without considering deformation and phase transition.Since the local gravity field and fluid medium density are constant, the buoyancy force on the bubble correlates to its cubic diameter.Equation (9) defines buoyancy.Figure 9 depicts the gas phase distribution at the impeller's intake section before and after the change.The variability of the gas phase distribution rises dramatically in the changed portion.The top of the pipe near the front pump chamber has the highest gas content, and local accumulation produces bubble clusters.The test findings in Figure 10 demonstrate that the head steadily decreases as the intake void percentage increases.In the numerical simulation, the head steadily drops as the input bubble diameter increases at the same void %.When the initial bubble diameter is constant, the error of setting a small diameter inlet bubble (d = 0.1mm) is small, but as the void fraction increases, the error between the numerical simulation results and the experimental results grows significantly.As a result, the proper beginning bubble diameter should be chosen to ensure that the numerical simulation process matches the real physical process of gas-liquid two-phase flow.
The test findings in Figure 10 demonstrate that the head steadily lowers as the incoming gas concentration increases.Under the same gas composition, numerical modeling shows that the head drops as the input bubble diameter increases.When the initial bubble diameter is constant, the error of setting the inlet bubble with a small diameter (d = 0.1mm) is small under low gas content conditions, but as the gas content increases, the error between the numerical simulation results and the experimental results increases significantly.As a result, an adequate beginning bubble width should be chosen to ensure that the numerical simulation process matches the real physical process of gas-liquid two-phase flow.
In this paper, the inlet bubble diameter is modified, and the inlet initial bubble diameter is set to be smaller (d=0.1mm) at low gas content (IGVF=1.12%).As the void fraction increases, the initial bubble diameter at the inlet also increases accordingly.
As can be seen from Figure 8, under different gas content conditions, the inlet bubble diameter correction effect is better, and the water head error between numerical simulation and test is significantly reduced.A large number of numerical simulation and experimental results were compared and analyzed, and the initial bubble diameter d and IGVF were modified and fitted by Matlab software.The R-square value 0.9684 fitted by Weibull function was close to 1, and the fitting effect was good.The relationship between IGVF and initial bubble diameter d is shown in Equation (10).The modified inlet bubble diameter formula presented in this paper is only suitable for flow prediction when large scale coalescence of bubbles does not occur under low gas holdup.When the inlet gas content increases to a certain extent, the fixed-size Euler two-fluid model is not accurate enough to simulate the gas-liquid two-phase flow.The dynamic process of bubble size change and the coalescence and fragmentation between bubbles can be further considered.

Theoretical analysis of bubble motion
The variation law of bubble motion and the impact of void percentage on bubble motion are elucidated using a theoretical force analysis of a single bubble in the impeller.Because the disc pump's impeller blades are discontinuous and the flow channel is relatively large, the shear force of the bubble at the impeller's inlet is minimal, and it is not easily split by the blade.As a result, it differs from a traditional centrifugal pump in terms of assessing the force of the bubble movement process.The flow of bubbles in a disc pump's impeller path is primarily regulated by three forces: drag force D F , pressure gradient P F  and buoyancy B F .The main motion of the bubble calculated by Newton 's second law is shown in Equation (11).The schematic diagram for force analysis of bubbles in impeller.The movement of the bubble in the impeller channel was measured by analyzing a single bubble in the blade region of the front sealing plate.Because the inertial effects of the gas phase and the liquid phase differ, the crowding impact of the liquid phase over the gas phase promotes the accumulation of gas on the suction surface of the impeller blade, so the volume fraction of gas in the impeller blade is greater than that on the pressure surface.The gas content of the input influences the pressure gradient force and buoyancy of the bubble since it directly defines the diameter of the bubble in the impeller.With growing inlet gas concentration, the pressure gradient force and buoyancy force of the liquid rise dramatically, enhancing the movement trend of bubbles towards the suction area of the blade and intensifying gas phase accumulation on the suction surface.

The streamline distribution in the flow channel under different inflow bubble diameters
The rotational speed of the simulation is 1500r/min, the liquid flow rate was 41.15m 3 /h, IGVF was 7.11%, and the effect of bubble diameter on the numerical simulation internal flow was investigated.The gas phase is specified as the inlet bubble diameter of 0.1mm, 0.4mm, 0.9mm, and 1.5mm in the computation of gas-liquid two-phase flow.To examine the axial distribution of fluid in the impeller and volute, the axial portion of the pump is removed.Figure 12 displays the flow line distribution velocity cloud diagram in the axial part of the pump for various inlet bubble diameters.
When the fluid flows from the impeller inlet to the impeller outlet, the fluid is bound by the wall of the front pump chamber.Most of the fluid flows along the wall towards the impeller outlet in the blade area of the front and rear cover plates, and a small part of the fluid flows to the impeller outlet through the gap of the ring.At the intersection of the impeller outlet and the volute, most of the fluid flows out along the volute to the outlet direction, and a small part of the fluid flows back along the front cover plate to the ring gap, forming a vortex at the ring gap.Due to the influence of the asymmetric structure of the volute, there is a vortex structure in the flow disorder of the fluid in the front and rear cavities.With the increase of the inlet bubble diameter, the number of vortices in the front cavity and the rear cavity increases continuously.
Regardless of the effect of other forces on the bubble, the bubble in the flow field is primarily affected by the three forces of drag force (force caused by gas-liquid phase), buoyancy (force caused by gravity of the earth), and pressure gradient force (force caused by the difference in pressure on both sides of the wall).The drag force is related to the square of the bubble diameter, the buoyancy to the cube of the bubble diameter, and the pressure gradient force to the cube of the drag force [13].Bubbles in the flow field are primarily affected by drag force (force caused by gas and liquid phase), buoyancy force (force caused by earth gravity), and pressure gradient force (force caused by pressure difference on both sides of the wall), without taking other forces into account.The drag force is related to the square of the bubble diameter, the buoyancy force to the cube of the bubble diameter, and the pressure gradient force to the cube of the drag force [13].When the bubble's diameter is small, the fluid's tractive and drag forces are dominating, the bubble's following is strong, and the gas-liquid mixture is uniform.When the bubble's diameter is high, the buoyancy effect grows substantially, and the slip between the two phases causes a local concentration of bubbles in the front and rear cavities.Therefore, large bubbles are more likely to block at the impeller outlet and the front cavity ring, resulting in an increase in local void fraction, and vortices are more likely to be generated in this area.At the same time, due to the generation of vortices, the retention of gas in this region is aggravated, resulting in the accumulation of local gas, which increases the intensity of vortices and reduces the efficiency of energy transfer in the impeller.

The influence of bubble diameter change on pressure distribution in impeller
In general, the pressure in the impeller blade area gradually decreases with the increase of the inlet bubble diameter, and the suction surface of the impeller blade and the area near the impeller inlet are low pressure areas, and the pressure surface of the impeller blade and the area near the impeller outlet are high pressure areas, as shown in Figure 13 and Figure 14.During the operation of the disc pump, energy is transmitted to the fluid in the pump owing to the spinning of the impeller, and the pressure along the entrance of the impeller is the lowest.As the radius rises, so does the pressure.The kinetic energy of the fluid is progressively turned into pressure energy during the whole process of fluid flowing to the volute outlet due to the rise in the cross-sectional area of the volute, thus the pressure of the volute flowing to the outlet direction is gradually raised.The pressure differential between the impeller's intake and output diminishes as the inlet bubble diameter increases, reducing the pump's operating capacity and performance.The pressure in the impeller channel is symmetrical when the inflow bubble diameter is 0.1mm.As the breadth of the inflow bubble increases, the local pressure in the top half of the impeller channel falls, resulting in an imbalanced distribution.The distribution of the impeller's bladeless area is comparable to that of the impeller's bladeless area, as illustrated in Figure 15.The pressure in the impeller's bladeless zone reduces continuously as the intake bubble diameter increases, and the pressure on the pressure surface of the blade is larger than the pressure on the suction surface of the blade.

The influence of bubble diameter change on gas volume distribution in impeller
The wall of the front cover plate of the impeller is the relative position (Z = 0mm), and the wall of the rear cover plate is the relative position (Z = 16mm).It can be seen from the structure of the disc pump impeller that when Z = 0 ~4mm is the bladed area of the front cover plate, Z = 12 ~16mm is the bladed area of the rear cover plate, and Z = 4 ~12mm is the bladeless area.Each interval of 1mm set a impeller runner shaft section, a total of 15 shaft sections, define Z = 2 for the front cover plate with blade area middle section, Z = 8 for the bladeless area middle section, Z = 14 for the back cover plate with blade area middle section, the shaft section position is shown in Figure 16, the average void fraction distribution curve of the shaft section at different positions of the impeller is shown in Figure 17.When the intake bubble diameter is small (d = 0.1mm), the average void fraction distribution of the axial section at different points is quite uniform, remaining at around 7.11%, which is nearly identical to the initial inlet void fraction.When the input bubble diameter is increased to 0.9mm, the void fraction near the impeller's blade area increases dramatically, and the void fraction of the blade area and the bladeless area of the front and rear cover plates both reach extreme values.It is clear from a comparison of the experimental head findings with those from the prior numerical simulation that using a bubble inlet diameter of 0.9mm is more accurate at this void fraction.The extreme gas content in the front cover plate's leaf area is approximately three times the initial inlet gas content, the extreme gas content in the back cover plate's leaf area is approximately twice the initial inlet gas content, and the gas content in the middle of the leafless area is reduced to two-thirds of the initial gas content.The phenomena of bubbles accumulating in the bladed area of the impeller becomes more visible as the inflow bubble diameter increases.The gas is primarily distributed in the bladed areas of the impeller's front and rear cover plates, with less gas distributed in the bladeless area.
According to the logic of Figure 17, there is no interphase slip between the gas and liquid phases because of the strong follow-up of the liquid drag force to the small bubbles at the intake, so the bubbles are evenly distributed in the leaf area and the leafless area.Due to gravity, when the inlet bubble diameter is large, the huge bubbles eventually gather into bubble clusters, which are dispersed on the top of the blade near the front pump chamber.After entering the impeller, the majority of the gas flows to the impeller outlet along the blade area of the front sealing plate, with only a minor portion flowing through the bladeless area of the rear sealing plate.Interphase slide occurs between the gas and liquid phases due to the poor followability of large bubbles.At the same time, bubbles form air sacs in the bladed area due to the barrier effect of the impeller blade, resulting in an increase in local air content.The research reveals that the extreme value of the void percentage in the bladed area is found at the impeller blade's edge (the interface between the bladed and bladeless areas).Because the pressure in the bladeless area is higher than in the bladed area, the pressure gradient force makes it difficult for large bubbles to cross the edge of the blade, hence aggregation is most intense at the blade's edge.
Figures 18 and 19 show the contours of the gas phase volume fractions of 7% and 25% in the disc pump's impeller and volute under the condition of IGVF = 7.11%.The gas phase distribution in the flow channel can be intuitively observed with varying inlet bubble diameters.In general, as the inflow bubble diameter grows, so does the volume of local high void fraction gas in the impeller.As can be observed in the previous article, gas phase aggregation has happened when the initial inlet gas content is 7.11%.According to a comparison of numerical simulation and experimental head findings, an inlet bubble diameter of 0.9mm is more accurate.At this point, the gas volume with the higher gas content occupies nearly the whole impeller flow channel, and the gas volume on the suction surface of the blade is greater than the gas volume on the pressure surface.
At the same time, the high air content gas is disseminated in the impeller flow channel away from the volute tongue due to volute tongue interference.The obvious gas phase aggregation phenomena, however, cannot be obtained if the inlet bubble diameter is tiny (0.1mm ~0.4mm), and the numerical simulation head is substantially higher than the experimental head.The numerical simulation head is lower than the test head when the input bubble diameter is too large (1.5mm), resulting in a substantial inaccuracy.As a result, the initial bubble diameter must be rectified for varied void fraction situations.

Conclusion
In order to study the internal flow pattern transformation and the change law of bubble diameter of gas-liquid two-phase flow disc pump, this paper uses visual research and numerical simulation methods to analyze.When the rotational speed is 1500 r/min, the flow pattern in the suction chamber changes from bubble flow to agglomerated bubble flow, slug flow and segregated flow as the inlet void fraction increases from 1.12% to 27.67%, and the degree of gas-liquid separation increases as the void fraction increases.
The gas phase accumulation at the edge of the blade in the leaf area is the most intense due to the disc pump's impeller blades' discontinuous characteristics, and because the blades in the leaf area of the front and rear cover plates act as a barrier.When the rotational speed is 1500r/min and the inlet volume void fraction is 7.11%, the local void fraction extreme value of the blade edge section in the blade area of the front cover plate increases to 3 times of the initial void fraction, and the void fraction extreme value of the middle section in the bladeless area decreases to 2/3 of the initial void fraction.
Under the circumstance of intake gas content, the discrepancy between numerical simulation and experimental findings of constant intake bubble diameter grows as inlet gas content increases.When large scale bubble coalescence does not occur at low gas concentration, the initial bubble diameter adjustment approach can make the numerical simulation findings compatible with the experimental data.

Figure 4 .
Figure 4. Y plus distribution on impeller walls.
Figure 5 depicts the schematic diagram of the disc pump open cycle experimental system, whereas Figure 6 depicts the physical diagram of the disc pump experimental platform.

Figure 5 .
Figure 5. Open-cycle experimental system of the disc pump.

Figure 7 .
Flow pattern in the inlet pipe.

Figure 8 .
Figure 8. Numerical simulation of gas-liquid two-phase flow and comparison of experimental results.

Figure 9 .
Figure 9. Gas phase distribution in inlet pipe of disc pump by experiment and numerical simulation .The visualization test of the horizontal inlet pipe of the disc pump was carried out by high-speed photography technology.The gas phase distribution in the inlet pipe of the disc pump is shown in Figure8.It is worth noting that due to gravity, bubbles gradually gather into bubble clusters from the injection hole into the inlet pipe to the impeller inlet, and distribute in the upper part of the pipe.When the bubble clusters enter the impeller, they first flow into the flow channel at the top of the pipe near the front pump chamber.The impeller of traditional centrifugal pump has continuous blades.The blade shear force of the inlet large bubbles is large and easy to be broken by the impeller, so it can be assumed that the bubbles enter the flow channels of the impeller evenly[14].Because the flow channel in the impeller of the disc pump is wide and the blade is discontinuous, the shear force of the bubble in the flow channel is small[27], which is not easy to be broken by the impeller blade, and cannot be regarded as the bubble entering the flow channel of the impeller evenly.Therefore, the gas phase distribution at the inlet section of the impeller must be corrected by the lifting force of the bubble, so that the simulation process is consistent with the test.It is assumed that the bubble is a uniform sphere of equal diameter, without considering deformation and phase transition.Since the local gravity field and fluid medium density are constant, the buoyancy force on the bubble correlates to its cubic diameter.Equation (9) defines buoyancy.Figure9depicts the gas phase distribution at the impeller's intake section before and after the change.The variability of the gas phase distribution rises dramatically in the changed portion.The top of the pipe near the front pump chamber has the highest gas content, and local accumulation produces bubble clusters.

Figure 10 .
Figure10.Gas phase distribution at the inlet section of impeller before and after correction.The test findings in Figure10demonstrate that the head steadily decreases as the intake void percentage increases.In the numerical simulation, the head steadily drops as the input bubble diameter increases at the same void %.When the initial bubble diameter is constant, the error of setting a small diameter inlet bubble (d = 0.1mm) is small, but as the void fraction increases, the error between the numerical simulation results and the experimental results grows significantly.As a result, the proper beginning bubble diameter should be chosen to ensure that the numerical simulation process matches the real physical process of gas-liquid two-phase flow.The test findings in Figure10demonstrate that the head steadily lowers as the incoming gas concentration increases.Under the same gas composition, numerical modeling shows that the head drops as the input bubble diameter increases.When the initial bubble diameter is constant, the error of setting the inlet bubble with a small diameter (d = 0.1mm) is small under low gas content conditions, but as the gas content increases, the error between the numerical simulation results and the experimental results increases significantly.As a result, an adequate beginning bubble width should be chosen to ensure that the numerical simulation process matches the real physical process of gas-liquid two-phase flow.In this paper, the inlet bubble diameter is modified, and the inlet initial bubble diameter is set to be smaller (d=0.1mm) at low gas content (IGVF=1.12%).As the void fraction increases, the initial bubble diameter at the inlet also increases accordingly.As can be seen from Figure8, under different gas content conditions, the inlet bubble diameter correction effect is better, and the water head error between numerical simulation and test is significantly reduced.A large number of numerical simulation and experimental results were compared and analyzed, and the initial bubble diameter d and IGVF were modified and fitted by Matlab software.The R-square value 0.9684 fitted by Weibull function was close to 1, and the fitting effect was good.The relationship between IGVF and initial bubble diameter d is shown in Equation(10).The modified inlet bubble diameter formula presented in this paper is only suitable for flow prediction when large scale coalescence of bubbles does not occur under low gas holdup.When the inlet gas content increases to a certain extent, the fixed-size Euler two-fluid model is not accurate enough to simulate the gas-liquid two-phase flow.The dynamic process of bubble size change and the coalescence and fragmentation between bubbles can be further considered.
mass of the bubble, and P v is the velocity of the bubble.As shown in Figure 11 the force diagram of the bubble in the impeller is shown, in which R F is the resultant force of three forces.The drag force D F , the pressure gradient force P F  and the buoyancy force B F are defined as shown in (5) (8) (9).

Figure 11 .
Figure 11.The schematic diagram for force analysis of bubbles in impeller.The movement of the bubble in the impeller channel was measured by analyzing a single bubble in the blade region of the front sealing plate.Because the inertial effects of the gas phase and the liquid phase differ, the crowding impact of the liquid phase over the gas phase promotes the accumulation of gas on the suction surface of the impeller blade, so the volume fraction of gas in the impeller blade is greater than that on the pressure surface.The gas content of the input influences the pressure gradient force and buoyancy of the bubble since it directly defines the diameter of the bubble in the impeller.With growing inlet gas concentration, the pressure gradient force and buoyancy force of the liquid rise dramatically, enhancing the movement trend of bubbles towards the suction area of the blade and intensifying gas phase accumulation on the suction surface.

Figure 12 .
Liquid flow line and velocity distribution in flow passage with different inlet bubble diameters.

Figure 13 .Figure 14 .Figure 15 .
Figure 13.Pressure distribution in the driven blade area of the shroud.

Figure 17 .
Figure 17.Distribution of gas void fraction in axial section.When the intake bubble diameter is small (d = 0.1mm), the average void fraction distribution of the axial section at different points is quite uniform, remaining at around 7.11%, which is nearly identical to the initial inlet void fraction.When the input bubble diameter is increased to 0.9mm, the void fraction near the impeller's blade area increases dramatically, and the void fraction of the blade area and the bladeless area of the front and rear cover plates both reach extreme values.It is clear from a comparison of the experimental head findings with those from the prior numerical simulation that using a bubble inlet diameter of 0.9mm is more accurate at this void fraction.The extreme gas content in the front cover plate's leaf area is approximately three times the initial inlet gas content, the extreme gas content in the back cover plate's leaf area is approximately twice the initial inlet gas content, and the gas content in the middle of the leafless area is reduced to two-thirds of the initial gas content.The phenomena of bubbles accumulating in the bladed area of the impeller becomes more visible as the inflow bubble diameter increases.The gas is primarily distributed in the bladed areas of the impeller's front and rear cover plates, with less gas distributed in the bladeless area.According to the logic of Figure17, there is no interphase slip between the gas and liquid phases because of the strong follow-up of the liquid drag force to the small bubbles at the intake, so the bubbles are evenly distributed in the leaf area and the leafless area.Due to gravity, when the inlet bubble diameter is large, the huge bubbles eventually gather into bubble clusters, which are dispersed on the top of the blade near the front pump chamber.After entering the impeller, the majority of the

Figure 18 .Figure 19 .
Figure 18.contour distribution cloud map of 7 % gas volume fraction in impeller and volute.

Table 1 .
Parameters of the disc pump impeller.

Table 2 .
Head of the disc pump under different grid numbers.