Numerical research on performance failure caused by gas blocking in multiphase mixed-transport pump under non-uniform inflow conditions

The helical-axial multiphase mixed-transport pump fails due to gas blocking caused by gas-liquid separation caused by cavitation under complex conditions with high gas volume fraction. This is an urgent engineering problem that needs to be addressed in the application of this pump. In order to simulate the flow structure characteristics in the channel, two types of non-uniform inflow boundary conditions were introduced. The bubble structure, velocity, and pressure under different inflow conditions were compared and analyzed, and the variation patterns affected by non-uniform boundary conditions were obtained. At the same time, the internal flow characteristics and mechanisms of multiphase mixed-transport pump are analyzed based on the velocity changes at the inlet of the impeller and the pressure fluctuations at the outlet of the guide vanes, leading to the intensification of gas-liquid separation and eventually the development of gas blocking. Research has shown that through programmatic control of the inlet boundary conditions, a linear change in inlet pressure has a more significant effect on the intensification of gas-liquid separation in the flow channel of the mixed-transport pump than a sinusoidal change, ultimately leading to significant performance failure when generating gas blocking. The research conclusion provides reference value for solving gas blocking in engineering applications of helical-axial multiphase mixed-transport pump.


Introduction
Spiral axial multiphase mixed transport pump has always been an ideal choice for oil and gas mixed transport equipment in deep sea and marginal oil fields due to its compact structure, large displacement, and insensitivity to solid particles in the fluid [1].When the inlet air content is high, the obtained cavity gradually increases from the cover to the hub in the cross-section after the impeller inlet, which is closely related to the experiment of the pump losing function due to inflation blockage [2].At present, many scholars at home and abroad have conducted extensive research on the impact of inlet conditions on pump performance.Shi Guangtai et al. [3] analyzed the turbulence intensity between stages of oil and gas mixed transport pump under different gas content through CFD numerical simulation, and found that the maximum turbulence intensity first decreases and then increases with the increase of gas content.Barrios L [4] carried out an experimental and theoretical study on the dynamic multiphase flow behavior in the mixed flow submersible electric pump (ESP).Through the mechanical model, the generation of stagnant bubbles at the inlet of the channel, the size of stagnant bubbles and the bubble Drag coefficient were predicted, and the bubble size was measured.Liu Zhengxian et al. [5] used Fluent to numerically simulate the effect of non-uniform inlet boundary conditions on the performance of the compressor stage, and obtained the results of changes in the internal flow field and stage performance of the compressor under the influence of non-uniform inlet velocity.Qiao yifei et al. [6] compared the performance curve of spent fuel cooling pump under different inflow conditions and the evolution of inflow flow field structure, and analyzed that non-uniform inflow led to obvious inflow distortion at the pump inlet, and the flow field velocity distribution was disordered.Long Yun et al. [7] studied the numerical simulation of the unsteady characteristics of pump under non-uniform inflow, and found that non-uniform inflow leads to the deviation of X radial force and Y radial force, which increases the degree of asymmetry of radial force.Van Esch [8] conducted an experimental study on the effect of non-uniform inflow on the performance and impeller load of a mixed flow pump, and observed that the rotor system was subjected to a very large and stable radial force.Huang R [9] conducted unsteady numerical simulation research on the transient cavitation flow of water jet pump under non-uniform inflow, predicted the hydrodynamic performance and cavitation performance well, and found that the occurrence of cavitation led to large fluctuations in hydrodynamic characteristics and non-uniformity of impeller inlet plane.Zhu D et al. [10] studied the effect of leading edge cavitation on the axial force of impeller blade in the reversible pump turbine pump mode, and found that from no cavitation to critical cavitation, the axial force first increases and then rapidly decreases; And as the flow rate increases, the flow separation and pressure drop gradually shift from the suction side to the pressure side.Liu X et al. [11] found that cavitation changes the inlet conditions of axial flow multiphase oil gas pump, aggregates unstable water flow, and generates significant pressure fluctuations.It also accelerates the frequency of axial force changes, exacerbating the uneven distribution of internal flow and circumferential pressure.
Due to the fact that gas-liquid separation is an important factor affecting the performance failure of oil gas mixed transport pump, non-uniform inflow intensifies the phenomenon of gas-liquid separation, making the pump prone to gas blocking and performance failure.However, the mechanism of the influence of non-uniform inflow on two-phase flow pump is currently not clear enough.Therefore, this article takes the helical-axial multiphase mixed-transport pump as the research object.Through numerical simulation of the flow field, it specifically describes the structural characteristics of non-uniform inflow, quantifies its impact on the external characteristics of the pump, and deeply analyzes the distribution characteristics and evolution mechanism of gas-liquid two-phase flow structure under non-uniform inflow, providing support for subsequent production and engineering applications.

Hydraulic design and 3D modeling
The main design parameters of a helical-axial multiphase mixed-transport pump (hereinafter referred to as a mixed-transport pump) with a specific speed of ns=289.455, a design flow rate of Qd=100m 3 /h, a design speed of n=4500rpm, and a head of H=25m are shown in Table Ⅰ 1 hydraulic design, mainly including the inlet section, impeller, diffuser, and outlet section.The key components of the mixed transport pump were modeled in 3D using Creo7.0software, as shown in Figure 2. To ensure the full development of flow at the inlet and outlet boundaries, the inlet and outlet were extended by 1.5 and 2.5 times the pipe diameter, respectively.In order to facilitate the flow field visualization test, both the diffuser and the housing are processed with transparent polymethyl methacrylate.The physical model is shown in Figure 2.

Grid partitioning and independence testing
During Fluent calculation, polyhedral meshes in Unstructured grid have better geometric adaptability and computational convergence.Firstly, use Workbench Mesh to perform tetrahedral meshing on the mixed transport pump.Perform expansion algorithm encryption on the impeller, diffusers, and inlet/outlet connections, and locally encrypt the impeller diffusers.Take 5 sets of grids and import them into Fluent under pure water conditions, and convert them into polyhedral grids for unrelated verification.The polyhedral grids are shown in Figure 3.After calculation, as the number of grids increases, the head and efficiency of the mixed transport pump continue to increase and tend to stabilize.The difference in pump performance parameters between the 4th and 5th grids is not significant, and the numerical simulation results can be ignored.Taking into account computing resources and efficiency, the fourth set of grids was selected for subsequent research.The final determination of the total number of unstructured grids in the computational domain is 7886802, and the grid independence test is shown in Figure 4. Final grid

Establishment of control equations
The multiphase flow Mixture model is used to calculate the cavitating flow in multiphase pump.The closed turbulence control equation adopts the standard k-e model.The standard wall function method was used to deal with near wall turbulence.It is suitable for situations where there is phase mixing or separation in the flow, or when the volume fraction of the dispersed phase is greater than 10%.In FLUENT, the control equations of the Mixture model mainly include the continuity equation, momentum equation, and energy equation of the mixture as follows [12]: Continuity equation: the continuity equation of the mixture is In the formula: ߩ is the density of the mixture; ‫ݑ‬ is the average speed of mass.
Momentum equation.The momentum equation of the Mixture model can be obtained by summing the momentum equations of all phases, and for incompressible fluids, it can be expressed as In the formula: g is the acceleration of gravity; F is physical strength; ‫ݑ‬ is the viscosity of hybrid power.
Energy equation.The energy equation of the mixture is as follows: In the formula, ݇ is the effective thermal conductivity, where ݇ ௧ is the turbulent thermal conductivity coefficient.The first item on the right represents the energy transfer caused by conduction.ܵ ா includes all other heat source energy.

Cavitation model
A cavitation model based on the Rayleigh-Plesset equation is used to describe the mass transfer process during phase transition using vapor or liquid volume fraction transport equations.The Rayleigh-Plesset equation is used to describe the speed of volume expansion or collapse of cavitation bubbles under the action of internal and external pressure differences.It ignores heat conduction and non-equilibrium phase transition effects, and uses the component transport method to describe the transport equation of vapor volume fraction as [13] డ In the formula: ߙ ௩ is the volume fraction of the vapor phase; ߙ ௩ is the vapor phase density; ‫ݑ‬ is the velocity of the mixed fluid; ݉̇ା is the rate of fluid evaporation; ݉̇ି is the rate of fluid condensation.
In order to construct ݉̇ା and ݉̇ି the Rayleigh-Plesset equation is introduced to describe the bubble dynamics equation of a cavitation bubble, which describes the volume expansion or collapse velocity of a cavitation bubble under the action of internal and external pressure differences.Its form is In the formula: ܴ is the radius of the bubble; ‫‬ ௩ is the pressure inside the cavity (saturated vapor pressure at ambient temperature); p is the liquid pressure; ߥ is the kinematic viscosity of the liquid; S is the surface tension coefficient; ߩ is the density of the liquid.
Ignoring the effects of second-order terms, surface tension, fluid viscosity, and non-condensable gas, the relationship between changes in bubble radius and pressure can be obtained: The Zwart Gerber Belamri model was proposed by Zwart et al. [14] which assumes that all bubbles in the system are of the same size.The mass transfer rate per unit volume is calculated using the density of bubbles and the rate of change per unit mass [15]: There is a relationship between the void number density and the vapor phase volume fraction, as well as the void radius, as follows From equation ( 9), it can be obtained that the main part of the interphase mass transfer rate (the left part of the root sign) is only related to the vapor phase density, and is not related to the liquid phase density.In order to solve the problem that equation ( 13) only applies to the initial stage of cavitation and the density of cavitation nucleons inevitably decreases with the increase of vapor volume fraction, Zwart et al. proposed using In the formula: ߙ ௨ is the volume fraction of cavitation nucleons, taken as 5 10 4 ‫ܨ‬ ௩ is the evaporation coefficient, which is an empirical constant used to correct the evaporation calculation results.In this simulation, 50 is taken; ‫ܨ‬ ௗ is the condensation coefficient and is also an empirical constant, taken as 0.01.The bubble radius is taken as ܴ = 1 × 10 ି m.

Implementation of non-uniform inflow
In practical engineering, it is difficult to ensure uniform flow at the inlet of the water pump.Therefore, in order to study the influence of non-uniform inflow on the helical-axial multiphase mixed-transport pump, equations ( 12) and ( 13) obtained using C language were loaded into Fluent using UDF for the nonuniform boundary conditions of pressure [16].The complex boundary conditions during the calculation process idealize the control of non-uniformly distributed wall pressure.When analyzing non-uniform inflow, in order to make the flow in the fluid domain affected by non-uniform inflow, a section of straight pipe is appropriately added in front of the impeller inlet to fully develop the non-uniform inflow.As shown in Figure 5, the vector distribution diagram of the non-uniform starting surface.Due to the negative gravity along the y-axis and the disturbance of internal flow, the inflow of the mixed transport pump during operation does not meet the principle of equal axial vectors.In order to simulate the imperfect inflow conditions during pump operation, this article defines two specific and non-uniform inlet conditions [17], which are similar to the actual operation of the pump.This article studies non-uniform inflow, taking the working condition with a gas content of 10% as an example, and calculates a critical cavitation pressure of 34000pa at the onset of cavitation.The pressure obtained by integrating radially on the yoz plane is equal, reducing the error of numerical simulation.For non-uniform inflow I, the pressure distribution curve on the yoz surface passes through points (-0.07,34000), (-0.035,18000), (0,34000), (0.035,50000), and (0.07,34000).Therefore, the curve equation is ܲ = ‫)ݕ758.44(݊݅ݏ77771‬+ 34000 12 The non-uniform inflow II is distributed on the yoz section with curve passing points (-0.07,30000), (0,34000), and (0.07,38000).Therefore, the curve equation is Compile the corresponding formulas into Fluent through UDF for subsequent numerical simulations.The pressure distribution at the inlet section of non-uniform inflow I is a Sine wave at the yoz section, which is symmetrical about the yoz plane along the axial direction.The hump points to the impeller inlet in the positive direction of the y-axis, and the hump points opposite to the impeller inlet in the negative direction of the y-axis; The pressure distribution at the inlet section of non-uniform inflow II follows a linear distribution, symmetrical about yoz along the axis, gradually increasing in the positive direction and decreasing in the negative direction.In order to ensure uniform flow in the impeller chamber, a straight tube rectifier is added in front of the moving blade, as shown in Figure 6 as the starting surface of the final fluid domain and non-uniform inflow.

Bubble generation and evolution process in helical axial multiphase mixed transport pump
Figure 7 shows the simulate the distribution of bubbles at different times in two non-uniform inflows, and compare the three moments of gas-liquid separation development after cavitation (T1 bubble initiation, T2 bubble development, and T3 gas generation blockage).From Figure 7, it can be seen that when bubbles are first generated at T1, the gas mainly appears in the impeller channel, and there are almost no bubbles generated in the diffuser channel.At this time, the forms of bubbles are mainly uniform bubbly flow and separated flow on the blade leading edge surface.At T2, as the flow develops, bubbles significantly increase throughout the entire flow channel.The separation flow at the leading and trailing edges of the blade continues to extend, and bubbles begin to aggregate and form a bubble like flow at the junction of the moving and stationary blade, with a local gas content of 100%.The gas inside the impeller also spreads through the diffuser channel, resulting in a large amount of uniform bubbly flow in the diffuser channel.At this time, the gas-liquid two-phase flow pattern in the impeller channel transitions from aggregated bubbly to gas blocking.At the final T3 moment, the bubbles fill the entire impeller channel, and the separated flow continues to extend; There is more aggregated bubbly flow at the junction of moving and stationary blade.Due to the pressure difference in the flow around the diffuser surface, the separated flow spreads from the leading edge of the diffuser concave surface, and the interaction with the separated flow at the trailing edge of the adjacent diffuser convex surface in the same flow channel blocks the flow channel.

Performance failure caused by gas blocking in helical-axial multiphase mixed-transport pump
From point 3 of this article, it can be seen that during numerical simulation, two specific inlet boundary conditions were obtained by programmatically controlling the inlet of a helical-axial multiphase mixed- transport pump, which can effectively simulate the process of non-uniform inflow causing bubbles to develop into air masses and block the flow channel.Figure 8 shows the head variation curve of a numerical simulation spiral axial multiphase mixed transport pump.Compared with the numerical simulation under pure water conditions, the head shows a downward trend under both non-uniform inflow conditions.When two non-uniform boundary conditions are applied, the head curve of the pump decreases with the increase of flow rate.At point a-a1, the bubbles flow in a bubble like manner in the impeller channel, and the head curve does not decrease significantly.As the flow rate increases, bubbles at point b-b1 fill the flow channel with a polymerized bubble like flow.From the head curve, it can be seen that the head of the pump decreases in a fractured manner, resulting in severe performance failure.Analyzing Figures 7 and 8, it is found that non-uniform inflow I and II can accurately simulate the evolution of bubbles at T1 bubble initiation and T3 gas generation blockage, and the proportion of nonuniform inflow II is longer when separated flow occurs on the blade surface.However, during the bubble development process at T2 time, non-uniform I and II have different effects on the intensification of bubbles in the flow channel.The separation flow on the blade surface is basically the same for both; As bubbles develop, the interaction between bubbles occurs earlier and more prominently at non-uniform time II.From this, it can be seen that the non-uniform II has a more pronounced effect on bubble activation in the flow channel under the two simulated specific inlet conditions.

Setting of monitoring points
In order to study the velocity and pressure disturbances in the impeller channel and inlet and outlet positions under two non-uniform inflow conditions during gas generation and blockage through numerical simulation.Set monitoring points on the 0.5-span surface of the impeller and diffuser for monitoring, as shown in Figure 9.Among them, 5 dynamic monitoring points yt1-yt5 are set along the flow direction on the convex surface of the impeller, and 5 dynamic monitoring points ya1-ya5 are set along the flow direction on the concave surface.Set four static monitoring points dt1-dt5 along the flow direction on the convex surface of the diffuser; Four monitoring points da1-da5 are set along the flow direction on the concave surface.From Figure 10, it can be seen that along the flow direction, the velocity at the monitoring point on the concave surface of the impeller blade shows a phenomenon of first increasing and then slowly decreasing.It reaches its maximum at the monitoring point ya5 at the trailing edge of the blade, and reaches its minimum when transitioning from the middle section of the moving and stationary blade to the inlet da1 of the diffusers, because there is energy loss in the middle section.The variation is not significant with different flow conditions.In the flow direction, the velocity change at the monitoring points on the convex surface of the blade is relatively stable, in a parabolic form.From Figure 11, it can be seen that along the flow direction, the speed at the monitoring point on the concave surface of the blade also shows a phenomenon of first increasing and then slowly decreasing, but the speed fluctuation at the inlet and outlet ends of the blade is relatively large under different flow conditions.The speed variation along the flow direction on the convex surface of the blade is relatively large, manifested as rising first and then stabilizing.The speed variation at the intersection of the moving and stationary blade under different working conditions fluctuates greatly.From this, it can be seen that the change in velocity at the beginning of bubble formation mainly occurs at the intersection of the concave surface of the blade and the moving and stationary blade.The non-uniform inlet flow changes the velocity field of the impeller, while the high-speed rotating impeller perturbs the non-uniform inlet flow.The combination of the two effects ultimately leads to the development of gas blocking.

The distribution of blade surface pressure during the development of gas blocking
According to the analysis of the monitoring point data set, it was found that the surface velocity of the impeller blade fluctuates significantly under two non-uniform inflow conditions, which is also the initial stage of bubbles.In order to further analyze the mechanism of gas blocking, Figure 12 qualitatively displays the pressure data at each monitoring point under two non-uniform inflow conditions, combined with a pressure cloud map.Analyzing Figure 12, it can be observed that the pressure data changes on the concave surface of the blade observed along the flow direction show that both non-uniform I and non-uniform II pressures first slowly decrease and then rapidly increase; Reaching the trough near point yo5 and reaching the peak near point do3.Presents a horizontally placed S with a difference of 12kPa between the maximum and minimum pressures.As the flow rate increases, the high-pressure points move to the left in sequence.However, as shown in Figure 12, under the rated operating conditions, the pressure changes at points yo1-yo3 are relatively large.The pressure cloud map of non-uniform I is uniform, while the pressure cloud map of non-uniform II is more chaotic, ultimately leading to flow intensification and more obvious gas blocking phenomenon.
Along the flow direction on the convex surface of the blade, the pressure near point yt1-dt2 is basically maintained at around 0-10kPa; The changes in pressure within this range also take the form of first decreasing, then increasing, and then decreasing.The trough appears near yt2 point, and the peak appears near yo5 point.From Figure 12, it can be seen that there is a sudden increase in pressure within the range of dt3-dt4 points, with non-uniform I appearing at low flow conditions and non-uniform II appearing at high flow conditions.From the pressure cloud map of 0.6Q, it can be seen that the high pressure zone of non-uniform I near the diffuser outlet covers a wider range than that of non-uniform II.

Conclusion
This article uses numerical simulation methods to idealize the inflow conditions using UDF, and studies the phenomenon of non-uniform inflow on bubble activation and ultimately developing into gas blocking in the flow channel of a helical-axial multiphase mixed-transport pump.The following conclusions are obtained: (1) In the stage of bubble development, the inflow conditions with linear pressure changes have a more obvious effect on gas-liquid activation in the flow channel, and the interaction between bubbles occurs earlier.During the development stage of bubbles, the head of the mixed transport pump decreases, which is not conducive to the efficient operation of the mixed transport pump.
(2) At the beginning of a bubble, the changes in velocity on the concave surface of both sine and linear transformations occur at the intersection of the moving and stationary blade, reaching a peak at the trailing edge of the impeller, while the velocity fluctuation on the convex surface is greater in the linear transformation.The linear transformation of the inflow conditions changes the velocity field of the impeller more significantly, while the high-speed rotating impeller perturbs the non-uniform inflow, and the two effects are superimposed.
(3) When generating gas blocking, the pressure on the concave surface of the blade first decreases and then increases, reaching a trough near the trailing edge of the impeller, and reaching a peak near the middle section of the diffuser flow channel.Under high flow conditions, the pressure at the impeller inlet becomes more chaotic during linear transformation, and the pressure on the convex surface of the blade suddenly increases within the middle range of the diffuser.The head of the mixed transport pump also decreases rapidly.It can be seen that linear transformation can effectively simulate the pressure fluctuation in the flow channel of a mixed transport pump when gas blocking occurs, thereby guiding the hydraulic design of the mixed transport pump and making it suitable for more complex incoming flow conditions.

Figure 2 .
Figure 2. Model of mixed transport pump.

Figure 3 .
Figure 3. Polyhedral mesh.After calculation, as the number of grids increases, the head and efficiency of the mixed transport pump continue to increase and tend to stabilize.The difference in pump performance parameters between the 4th and 5th grids is not significant, and the numerical simulation results can be ignored.Taking into account computing resources and efficiency, the fourth set of grids was selected for subsequent research.The final determination of the total number of unstructured grids in the computational domain is 7886802, and the grid independence test is shown in Figure4.

Figure 5 .
Figure 5. Two types of heterogeneous inlet section pressure distribution diagram.

Figure 7 .
Figure 7.Comparison of Bubble Evolution in Numerical Simulation.From Figure7, it can be seen that when bubbles are first generated at T1, the gas mainly appears in the impeller channel, and there are almost no bubbles generated in the diffuser channel.At this time, the forms of bubbles are mainly uniform bubbly flow and separated flow on the blade leading edge surface.At T2, as the flow develops, bubbles significantly increase throughout the entire flow channel.The separation flow at the leading and trailing edges of the blade continues to extend, and bubbles begin to aggregate and form a bubble like flow at the junction of the moving and stationary blade, with a local gas content of 100%.The gas inside the impeller also spreads through the diffuser channel, resulting in a large amount of uniform bubbly flow in the diffuser channel.At this time, the gas-liquid two-phase flow pattern in the impeller channel transitions from aggregated bubbly to gas blocking.At the final T3 moment, the bubbles fill the entire impeller channel, and the separated flow continues to extend; There is more aggregated bubbly flow at the junction of moving and stationary blade.Due to the pressure difference in the flow around the diffuser surface, the separated flow spreads from the leading edge of the diffuser concave surface, and the interaction with the separated flow at the trailing edge of the adjacent diffuser convex surface in the same flow channel blocks the flow channel.

Figure 8 .
Figure 8. Pump head curve when air blockage occurs.Analyzing Figures7 and 8, it is found that non-uniform inflow I and II can accurately simulate the evolution of bubbles at T1 bubble initiation and T3 gas generation blockage, and the proportion of nonuniform inflow II is longer when separated flow occurs on the blade surface.However, during the bubble development process at T2 time, non-uniform I and II have different effects on the intensification of bubbles in the flow channel.The separation flow on the blade surface is basically the same for both; As bubbles develop, the interaction between bubbles occurs earlier and more prominently at non-uniform time II.From this, it can be seen that the non-uniform II has a more pronounced effect on bubble activation in the flow channel under the two simulated specific inlet conditions.
Figures 10 and 11  show the variation of blade surface velocity along the flow channel under different flow conditions during bubble initiation under non-uniform inflow conditions I and II, respectively.

Figure 10 .
Figure 10.Non-uniform I velocity of the leaf surface at the beginning of bubbles.From Figure11, it can be seen that along the flow direction, the speed at the monitoring point on the concave surface of the blade also shows a phenomenon of first increasing and then slowly decreasing, but the speed fluctuation at the inlet and outlet ends of the blade is relatively large under different flow conditions.The speed variation along the flow direction on the convex surface of the blade is relatively large, manifested as rising first and then stabilizing.The speed variation at the intersection of the moving and stationary blade under different working conditions fluctuates greatly.From this, it can be seen that the change in velocity at the beginning of bubble formation mainly occurs at the intersection of the

Figure 11 .
Figure 11.Non-uniform Ⅱ velocity of the leaf surface at the beginning of bubbles.

Figure 12 .
Figure 12.Non-uniform pressure distribution of blade monitoring points under different working conditions I and II.

Table 1 .
. Geometric parameters of impeller and diffuser.