Solid–Liquid Two-Phase Flowmeter Flow-Passage Wall Erosion Evolution Characteristics and Calibration of Measurement Accuracy

Abstract

Solid–liquid two-phase flowmeters are widely used in critical sectors, such as petrochemicals, energy, manufacturing, the environment, and various other fields. They are indispensable devices for measuring flow. Currently, research has primarily focused on gas–liquid two-phase flow within the flowmeter, giving limited attention to the impact of solid phases. In practical applications, crude oil frequently contains solid particles and other impurities, leading to equipment deformation and a subsequent reduction in measuring accuracy. This paper investigates how particle dynamic parameters affect the erosion evolution characteristics of flowmeters operating in solid–liquid two-phase conditions, employing the dynamic boundary erosion prediction method. The results indicate that the erosion range and peak erosion position on the overcurrent wall of the solid–liquid two-phase flowmeter vary with different particle dynamic parameters. Erosion mainly occurs at the contraction section of the solid–liquid two-phase flowmeter. When the particle inflow velocity increases, the erosion range shows no significant change, but the peak erosion position shifts to the right, primarily due to the evolution of the erosion process. With an increase in particle diameter, the erosion range expands along the inlet direction due to turbulent diffusion, as particles with lower kinetic energy exhibit better followability. There is no significant change in the erosion range and peak erosion position with an increase in particle volume fraction and particle sphericity. With a particle inflow velocity of 8.4 m/s, the maximum erosion depth reaches 750 μm. In contrast, at a particle sphericity of 0.58, the minimum erosion depth is 251 μm. Furthermore, a particle volume fraction of 0.5 results in a maximum flow coefficient increase of 1.99 × 10⁻³.

1. Introduction

In the current energy market, oil plays a crucial role. With the rapid global advancement of science, technology, and the economy, the demand for oil has escalated. The consequential surge in transactions, coupled with the depletion of onshore oil reserves, has become an inescapable reality. Exploiting submarine fields emerges as a developmental trend in the oil and gas sector to alleviate the growing disparity between supply and demand [1]. In the extraction, transport, and trading of sub-sea oil fields, the accuracy and performance of the solid–liquid two-phase flowmeter play a crucial role for various stakeholders [2,3,4,5,6]. However, deep-sea crude oil is a complex mixture containing natural gas, solid particles, impurities, and oil. Therefore, it is essential to ensure the measurement accuracy and performance of the solid–liquid two-phase flowmeter. The impact and abrasion of heavy-phase particles during the solid mixing and transport process in the flowmeter measurement channel cause the deformation of the flow coefficient [7,8,9,10,11]. Consequently, this decline in measurement performance and accuracy can lead to disputes and losses in the process of crude oil extraction and transport. Therefore, additional research on the erosion characteristics of solid–liquid two-phase flowmeters holds significant engineering importance [12,13,14,15]. It aims to safeguard solid–liquid two-phase flowmeters from erosion and enhance measurement accuracy in practical engineering applications.

Scholars from domestic and international institutions have researched erosion damage to the flow-passage walls in multiphase flowmeters with fixed boundaries. These factors encompass the material and shape of the flow-passage walls, particle properties, particle impact velocity, particle impact angle, and fluid properties [16,17,18,19,20,21]. Their interactions collectively contribute to the individual impact on the equipment. Li [22] designed an experimental setup to measure the impact of single particles and explored the influence of impact parameters on particle behaviour and material deformation. Their findings revealed that impact velocity significantly influences particle motion parameters, yet the shape of the erosion crater remains consistent across various impact velocities. Moreover, He [12] proposed a correlation equation for measuring the wet gas flow of the venturi flowmeter based on the two-phase mass flow coefficient. They discussed the factors influencing this coefficient and observed a linear increase with the Lockhart–Martinelli parameter, along with a decrease as the gas–liquid density ratio increased. Furthermore, various factors influence the erosion and damage to equipment operating in sandy conditions. Gajan [23] conducted high-pressure experiments on a venturi flowmeter in wet gas flow conditions. They analyzed the impact of water content on flow behaviour, comparing experimentally obtained flow coefficients with predictions derived from the flowmeter’s internal dynamics. Similarly, Dehkordi [24] employed the volume of fluid (VOF) model to investigate the two-phase flow of high-viscosity oil and water in a venturi flowmeter. They acquired data on two-phase pressure drops, instantaneous radial velocity, holding rate distributions, cross-section time-averaged holding rates, and slip rates. Lastly, Liu [25] conducted numerical calculations on a low-temperature venturi flowmeter. They observed a linear relationship between the flow coefficient and the root mean square of the reciprocal of the Reynolds number of the throat. The flow coefficient decreased with an increase in the diameter ratio of the throat and increased with a rise in the angle of constriction.

Currently, the primary focus in multiphase flowmeter research revolves around internal flow characteristics and cavitation. However, erosion factors have not been adequately considered in these studies. Furthermore, erosion-related research often relies on fixed boundaries, lacking a genuine representation of flow field conditions. This paper examines the impact of various particle dynamic parameters on the erosion characteristics and measurement accuracy of the solid–liquid two-phase flowmeter. It employs the dynamic boundary erosion prediction method along with the Oka erosion model to offer a theoretical reference for enhancing the measurement accuracy of solid–liquid two-phase flowmeters.

2. Numerical Model

2.1. Computational Domain Model

To comply with confidentiality requirements, the pertinent structural parameters of the solid–liquid two-phase flowmeter cannot be disclosed. The computational domain is established by SolidWorks 2010 3D modeling software, which includes the inlet straight section, tapered section, throat, expanding section, and the outlet straight section. Refer to Figure 1 for the profile of the solid–liquid two-phase flowmeter computational domain model.

2.2. Meshing of the Computational Domain

The erosion evolution characteristics of solid–liquid two-phase flowmeters are studied in this paper using dynamic mesh technology. The unstructured mesh deformation that occurs during movement is reconstructed better to enhance the mesh quality. Therefore, the computational domain model is divided into an unstructured mesh. Structured meshing of the computational domain was performed using the commercia software ICEM CFD 16.0 To better capture the near-wall surface flow, covering the boundary layer mesh near the wall surface, the computational domain mesh is displayed in Figure 2.

2.3. Oka Erosion Model

The process of particle collision with a material surface is highly complex; thus, the erosion model should attempt to encompass pertinent parameters that impact the degree of erosion. Oka [26,27] carried out an experiment that resulted in the development of an erosion rate calculation formula based on Oka’s model. The developed formula considered various parameters, such as particle diameter, target material density, and Vickers hardness, that influence the degree of erosion damage. The definition of erosion rate is as follows:

$$E_{\theta }=E_{90}f\left(\theta \right)$$

(1)

$$E_{90}=K{\left(H_v\right)}^{k_1}{\left(\frac{V}{V_{ref}}\right)}^{k_2}{\left(\frac{d_p}{d_{p_{ref}}}\right)}^{k_3}$$

(2)

$$f\left(\theta \right)={\left(\sin \theta \right)}^{n_1}{\left[1+H_v\left(1-\sin \theta \right)\right]}^{n_2}$$

(3)

The variable θ represents the collision angle; K denotes a constant associated with the particle properties; H_v denotes the Vickers hardness of the target material (Gpa); V stands for the collision velocity (m/s); V_ref is the reference velocity (m/s); d_p indicates the particle diameter (m); and d_pref represents the reference diameter of the particles (m). k₁, k₂, k₃, n₁, and n₂ are constants related to the characteristics of the particles and wall material, the values of the parameters are K = 65, d_pref = 0.326 mm, V_ref = 104 m/s, k₁ = −0.12, k₂ = 2.3H_v^0.038, k₃ = 0.19, n₁ = 0.71H_v^0.14, and n₂ = 2.4H_v^−0.94.

2.4. Erosion Depth Model Based on Dynamic Boundary

Material surface damage induced by erosion is a nonlinear, time-varying process with spatial characteristics. The parameters of particle dynamics also change during this process, which affects subsequent stages of erosion damage. The erosion depth obtained shows a dynamic nonlinear trend of accumulation. To accurately predict erosion damage, it is essential to account for the changes in the surface morphology of the flow-passage walls over time. Therefore, the dynamic boundary erosion prediction method is utilized to calculate the solid–liquid two-phase flow inside the solid–liquid two-phase flowmeter in Figure 3. The dynamic boundary erosion prediction method is used to dynamically calculate the wall erosion depth based on the mesh moving time step for the flow field. The deformation of unit surface (travelling distance) is shown in Equation (4):

$$\Delta x_{face}=\frac{E\times M_p\times \Delta t_{MM}}{A_{face}}$$

(4)

$$h={\displaystyle \sum _{t=0}^T\Delta x_{face,t}}$$

(5)

E represents the DPM erosion rate (m³/kg); M_p is the particle mass (kg); Δt_MM is the mesh travelling time step; A_face is the mesh area (m²); T is the total erosion time; and h is the total erosion depth.

3. Mesh Independence and Numerical Calculation Method

3.1. Mesh Independent Verification

To remove the impact of the mesh size on the calculation results, this paper confirmed the mesh independence of the solid–liquid two-phase flowmeter by measuring the differential pressure caused by pure oil flowing through the venturi flowmeter, as indicated in

Table 1. Mesh independent verification.

Mesh Scheme	Number of Mesh (106)	Pressure Difference (Pa)
1	0.77	59,325
2	1.21	59,246
3	1.55	59,181
4	1.64	59,177
5	1.75	59,176

. An increase in the number of mesh leads to a greater change in the differential pressure of pure oil flowing through the venturi flowmeter. However, when the mesh reaches a certain number, the change in differential pressure decreases. Hence, the total number of mesh cells used in the calculation is 1.55 × 10⁶.

3.2. Boundary Conditions

Based on ANSYS Fluent, the problem of degradation of measuring accuracy caused by erosion in solid–liquid two-phase flowmeters was calculated using the RNG k-ε to calculate the fluid phases and the discrete phase model (DPM) to track the particle trajectories. The velocity inlet was chosen for the inlet of the solid–liquid two-phase flowmeter, while the pressure outlet was chosen for the outlet. For the inlet of the turbulence term, the turbulence intensity and hydraulic diameter were selected, and for the outlet, the turbulence intensity and length scale were chosen. The flow-passage walls were defined as a no-slip wall, and the particles were set to escape at the inlet and outlet while rebounding from the wall.

Table 2. Physical parameters of wall materials, particles, and crude oils.

Items	Physical Parameters	Value
Wall materials	Density (kg/m3)	7510
	Vickers hardness (HV)	240
	Brinell hardness (HB)	195
Particles	Density (kg/m3)	2650
	Hardness	9
Crude Oils	Density (kg/m3)	753.8
	Dynamic Viscosity (kg/(m∙s))	20

displays the physical parameters of the wall materials, particles, and crude oil applied in the numerical simulation of the solid–liquid two-phase flowmeter’s erosion.

3.3. Numerical Calculation Method

The steady-state simulation of flowmeter flow field employs ANSYS FLUENT 2016. In solid–liquid two-phase flowmeter erosion studies, crude oil is considered an incompressible fluid, so a pressure-based solver is used. The RNG k-ε model was chosen for the turbulence model, as shown in Equations (6) and (7).

$$\frac{\partial }{\partial t}(\rho k)+\frac{\partial }{\partial x_i}(\rho k{u}_i)=\frac{\partial }{\partial x_j}\left(\left({\alpha }_{\kappa }{\mu }_{eff}\right)\frac{\partial k}{\partial x_j}\right)+G_k+G_b-\rho \epsilon -Y_{\mathrm{M}}$$

(6)

$$\frac{\partial }{\partial t}(\rho \epsilon )+\frac{\partial }{\partial x_i}(\rho \epsilon u_i)=\frac{\partial }{\partial x_j}\left(\left({\alpha }_{\epsilon }{\mu }_{eff}\right)\frac{\partial \epsilon }{\partial x_j}\right)+G_{1\epsilon }\frac{\epsilon }{k}\left(G_k+G_{3\epsilon }{G}_b\right)-G_{2\epsilon }\rho \frac{{\epsilon }^2}{k}-R$$

(7)

G_k denotes the production of turbulent kinetic energy due to the mean velocity gradient. G_b is the turbulent kinetic energy generated by the buoyancy force. Y_M denotes the contribution of fluctuating expansion to the total dissipation rate in compressible turbulence. A_k and α_ε are the inverse of the effective Prandtl numbers k and ε, respectively. G_1ε = 1.42, G_2ε = 1.68.

The control equations were discretized and solved using the SIMPLEC algorithm. The sub-relaxation factors were set to the default values provided by the system. These values were as follows: pressure (0.3), density (1), body forces (1), momentum (0.7), turbulent kinetic energy (0.8), turbulent dissipation rate (0.8), turbulent viscosity (1), and discrete phase sources (0.5). The pressure, momentum, turbulent kinetic energy, and other factors were set to the second-order windward format. The criterion for residual convergence is 1 × 10⁻⁸. The outcomes obtained from the numerical steady state simulation of the fluid-phase served as preliminary values for the erosion simulation of the multiphase flow. Then, the discrete phase model (DPM) was applied for calculating the particle erosion.

In the dynamic mesh setup for erosion prediction in solid–liquid two-phase flowmeters, the spring smoothing and mesh reconstruction techniques from the smoothing method were employed to smooth and reconstruct the mesh in the presence of substantial wall deformation, ensuring the quality of the mesh. After a trial calculation, the initial mesh movement time step was established as 24 h. In the spring smoothing process, the spring constant factor was set to 1, while the convergence accuracy and number of iterations were both left at their default system values, which were 0.001 and 20, respectively. The element method chose the Tri in Tri Zones. The mesh reconstruction method selected Local Cell and Local Face, with a minimum mesh size set to 0.4 and mesh size set to 0.9. The maximum mesh cell skewness was set at 0.8, and the maximum face skewness was set at 0.7. Additionally, the mesh reconstruction frequency was set to 5.

3.4. Experimental Verification

To validate the accuracy of the numerical simulations, this study conducted validation experiments using the Haimo Technology Group’s test bench, as illustrated in Figure 4. There is a water reservoir at the back of the test bench, into which prescreened sand with a volume fraction of 0.09 and diameter of 0.02 mm was introduced into the water reservoir.

Experiments were conducted on the flowmeter at an inlet flow velocity of 4.15 m/s in accordance with the designed flow rate. The experiments had varying durations of 12 h, 24 h, 36 h, 48 h, and 60 h. After each experiment, the flowmeter was subjected to ultrasonic cleaning and drying, followed by precise weighing using an electronic scale with an accuracy of 0.1 g. In this paper, a dynamic boundary erosion prediction method was employed in numerical simulations. The boundary mesh was reconfigured with erosion time and erosion rate, resulting in a change in mesh volume. The original mesh body minus the reconfigured mesh volume represents the lost volume. Finally, the volume multiplied by the density yields the lost mass. Combining these measurements with the numerical simulation results, a comparison was made, showing that the numerical results had an error of less than 3%, as illustrated in

Table 3. Comparison of calculated and experimental values.

Erosion Time (h)	Experimental Value (g)	Numerical Result (g)	Relative Error (%)
12	2.02	1.98	1.98
24	4.11	4.02	2.19
36	5.97	5.86	1.84
48	8.19	8.05	1.71
60	9.98	10.13	1.47

, affirming the reliability of the results presented in this study.

4. Analysis of Calculation Results

In accordance with the environmental and design requirements for the utilization of a solid–liquid two-phase flowmeter, the following working conditions have been established. The particle inflow velocity is 2.1 m/s, 4.2 m/s, 6.3 m/s, and 8.4 m/s. The particle volume fraction is 0.1, 0.2, 0.3, and 0.5. The particle diameter is 20 μm, 50 μm, 100 μm, and 150 μm. Experimentally, it was proven that the most serious erosion area of the solid–liquid two-phase flowmeter was at the tapering tube of the flowmeter, while the erosion area in other places was negligible. Therefore, the subsequent research will focus on the erosion problem at the tapering tube.

4.1. Influence of Particle Inflow Velocity on Erosion Evolution Characteristics and Measurement Accuracy

The erosion depth of flow-passage walls of the solid–liquid two-phase flowmeter for four particle inflow velocities are displayed in Figure 5 at 2, 4, 6, 8, and 10 years. The erosion depth curve indicates that the erosion pit depth increases significantly as the erosion time increases. At an erosion time of 10 years, the maximum erosion depth was 750 μm for a particle inflow velocity of 8.4 m/s; this depth was probably the maximum erosion depth for particles at a velocity of 2.1 m/s, which is 2.3 times greater. As the particle flow rate increases, the peak erosion position changes from 342 mm to 343 mm from the inlet, but there is no significant difference in the erosion range. Erosion progression leads to a rise in the quantity of erosion pits and a reduction in the flow velocity within them. Consequently, particle velocity decreases, reaching its nadir at the maximum depth of erosion. With decreasing erosion depth and an expanding follow-passage wall of the solid–liquid two-phase flowmeter, fluid velocity rises. Consequently, particles align with the fluid flow, resulting in an upsurge in particle velocity.

The flow coefficient is a dimensionless number utilized to characterize the fluid’s ability to flow through a specific device or channel under defined conditions. It represents the ratio between the volume of fluid passing through the device or channel per unit of time and the differential pressure generated during the fluid’s flow, as is shown in Equation (8):

$$K_v=10Q\sqrt{\frac{\rho /{\rho }_0}{\Delta P}}$$

(8)

In Figure 6, when the particle inflow velocity is less than 2.1 m/s, the flow coefficient increases from 0.9355 initially to 0.9363 over 10 years, reflecting a marginal rise of 8 × 10⁻⁴ with prolonged erosion time. Nevertheless, when the particle inflow velocity falls within the range of 4.2~8.4 m/s, the flow coefficient rises in conjunction with both erosion time and particle inflow velocity. The increase in the flow coefficient ranges from 1.56 × 10⁻³ to 1.97 × 10⁻³ over a span of 10 years. The flow coefficient shows a tendency to increase with both erosion time and an increase in particle inflow velocity.

4.2. Influence of Particle Volume Fraction on Erosion Evolution Characteristics and Measurement Accuracy

In Figure 7, with an increase in particle volume fraction, the erosion depth rises, reaching a maximum erosion depth of 758 μm after 10 years of erosion, with a particle volume fraction of 0.5. Compared to a particle volume fraction of 0.1, the maximum erosion depth is approximately twice as significant. However, the erosion range consistently falls within the region between approximately 330 mm to 355 mm from the inlet, with the peak erosion position consistently occurring at approximately 342 mm from the inlet. This occurs because as the particle volume fraction decreases, the number of particles in the flow channel also decreases, resulting in reduced erosion damage. Additionally, an increase in erosion depth elevates the roughness of the follow-passage walls, impeding fluid flow.

In Figure 8, as erosion time increases, the flow coefficient exhibits a consistent trend, namely, an increase in the flow coefficient with the passage of erosion time. With the particle volume fraction increased, there was a corresponding increase in the solid–liquid two-phase flowmeter flow coefficient, with increments of 1.04 × 10⁻³, 1.31 × 10⁻³, 1.56 × 10⁻³, and 1.99 × 10⁻³ over the course of 10 years.

4.3. Influence of Particle Diameter on Erosion Evolution Characteristics and Measurement Accuracy

In Figure 9, with an increase in particle diameter, the depth of the abrasion pit also increases. At the 10-year mark, the maximum abrasion depth reaches 748 μm when the particle diameter is 150 μm, which is approximately three times deeper than when the particle diameter is 20 μm. This is attributed to an escalation in the collision effect of particles on the wall as the particle diameter increases, resulting in a deeper erosion pit. With an increase in particle diameter, the abrasion range extends towards the inlet direction. The distance from the inlet to the flow-passage wall erosion area caused by the four particle diameters is 333 mm, 331 mm, 328 mm, and 327 mm, respectively. However, the peak erosion depth remains essentially consistent at approximately 343 mm from the inlet. This is attributable to the turbulent diffusion effect, where smaller particles, with lower kinetic energy, exhibit superior adherence to the fluid flow, resulting in a narrower erosion range. Conversely, larger particles, carrying a higher level of collision energy, generate a more extensive erosion area. This is primarily attributed to the turbulent diffusion effect: smaller particles, possessing lower kinetic energy, closely trail the fluid flow, leading to a limited extent of erosion damage. Conversely, larger particles carry significant collision energy, causing a more extensive area of erosion damage.

In Figure 10, when the particle diameter is 20 μm, the increase in the flow coefficient is the smallest over the course of erosion time, with a gain of 2.644 × 10⁻² over 10 years. For particle diameters in the range of 50~100 μm, the flow coefficient increases with larger increments, specifically 3.156 × 10⁻² and 3.161 × 10⁻², respectively. The most substantial increase in the flow coefficient occurs when the particle diameter is 150 μm, reaching a maximum increment of 3.196 × 10⁻².

4.4. Influence of Particle Sphericity on Erosion Evolution Characteristics and Measurement Accuracy

In practice, particles are seldom perfectly spherical. Therefore, investigating the sphericity of particles with varying shapes holds significant value for engineering applications. In this subsection, particle sphericity is employed as a variable to elucidate its impact on the erosion damage characteristics and flow coefficient of the solid–liquid two-phase flowmeter. Particle sphericity is defined as the ratio of the surface area of a sphere with a volume equal to that of the particle in question to the surface area of the particle itself, as shown in Equation (9):

$$\phi =\frac{s}{S}$$

(9)

In Equation (9), s is the surface area of a sphere of equal volume, and S is the surface area of the particle itself. In this paper, three particle sphericities, as proposed by Epstein [28], are employed, specifically 0.66, 0.76, and 0.86.

In Figure 11, as particle sphericity increases, the depth of erosion pits on the flow-passage wall of the solid–liquid two-phase flowmeter also increases. The most profound erosion was noted at 10 years of erosion time, with a particle sphericity of 1, resulting in a maximum erosion depth of 582 μm. In comparison to the maximum erosion depth at a particle sphericity of 0.58, this represents an approximately 2.3-fold increase. Nonetheless, the extent of erosion remains largely consistent, with the peak maximum erosion depth located at approximately 342 mm from the inlet. With increasing erosion time, the erosion depth of the solid–liquid two-phase flowmeter’s flow-passage wall consistently rises, indicating a cumulative effect on erosion depth over time. As erosion depth increases, particle velocity decreases initially due to the small resistance coefficient of large spherical particles; however, the gained kinetic energy results in a slight increase in particle velocity. Beyond the erosion peak position, approximately 348 mm from the inlet, as erosion time increases and the follow-passage wall decreases, fluid velocity rises. This prompts particles to follow the fluid flow, leading to an overall increase in particle velocity.

In Figure 12, as erosion time increases, the flow coefficient of the solid–liquid two-phase flowmeter exhibits a consistent pattern across different particle sphericities, demonstrating a gradual upward trend with increasing particle sphericity. Moreover, with a particle sphericity of 1, the flow coefficient experiences the most significant increase. As particle sphericity rises, the flow coefficient exhibits a gradual and consistent increase, with increases of 6.9 × 10⁻⁴, 1.01 × 10⁻³, 1.31 × 10⁻³, and 1.56 × 10⁻³ over the course of 10 years, respectively.

5. Conclusions

At present, numerical simulation is employed primarily to investigate the erosion of fixed boundary conditions or in conjunction with the PIV system, electron microscope scanner, and so forth to examine the multiphase flow and erosion morphology. However, these approaches are unable to accurately portray the evolution of erosion in multiphase flowmeter flow-passage walls. This paper presents a further study of the erosion characteristics of multiphase flowmeters through the dynamic boundary prediction method. The influence of erosion depth change on the average erosion rate and metering accuracy is analysed, with the results having significant implications for the protection of multiphase flowmeter erosion and improvement of the metering accuracy in practical engineering applications.

(1)

Erosion ranges and peak locations on the solid–liquid two-phase flowmeter flow-passage wall vary with distinct particle dynamic parameters. As the particle flow rate increases, the erosion range remains largely unchanged. Nevertheless, the erosion peak shifts to the right, mainly linked to the erosion evolution process. With an increase in particle diameter, the erosion range extends towards the inlet due to turbulent diffusion. Particles with lower kinetic energy closely follow the flow. The erosion range and peak position remained relatively stable despite increases in particle volume fraction and sphericity.

(2)

Erosion depth increases progressively with higher particle dynamic parameters. At a particle inflow velocity of 8.4 m/s, the maximum erosion depth is 750 μm. Conversely, at a particle sphericity of 0.58, the minimum erosion depth is 251 μm. Moreover, a particle volume fraction of 0.5 results in a maximum flow coefficient increase of 1.99 × 10⁻³.

This paper explores the influence of dynamic parameters on the multiphase flowmeter erosion characteristics and measurement accuracy in common working conditions. It is acknowledged that other conditions and different dynamic parameters may influence the multiphase flowmeter erosion characteristics and measurement accuracy. Therefore, further research is required to investigate these factors. In practical engineering, multiphase flowmeters may encounter two-phase cavitation and cavitation damage in gas–liquid conditions as well as three-phase abrasion damage in gas–solid–liquid scenarios. Currently, there is a paucity of research on these issues in multiphase flowmeters. Consequently, further investigation into the causes and effects of cavitation and erosion damage in multiphase flowmeters can be conducted at a later stage. Specifically, we will discuss the potential for future studies to extend our research to include bubbly flow [29] scenarios with water and solid particles, addressing slipping boundary issues [30] to enhance the applicability and relevance of our findings in practical settings.