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The modeling of interphase forces plays a significant role in the numerical simulation of gas–liquid flow in a rotodynamic multiphase pump, which deserves detailed study.

Numerical analysis is conducted to estimate the influence of interphase forces, including drag force, lift force, virtual mass force, wall lubrication force and turbulent dispersion force.

The results show that the magnitude of the interphase forces can be sorted by: drag force > virtual mass force > lift force > turbulent dispersion force > wall lubrication force. The relations between interphase forces and velocity difference of gas–liquid flow and also the interphase forces and gas volume fraction are revealed. The distribution characteristics of interphase forces in the passages from impeller inlet to diffuser outlet are illustrated and analyzed. According to the results, apart from the drag force, the virtual mass force, lift force and turbulent dispersion force are required, whereas wall lubrication force can be neglected for numerical simulation of gas–liquid flow in a rotodynamic multiphase pump. Compared with the conventional numerical method which considers drag force only, the relative errors of predicted pressure rise and efficiency based on the proposed numerical method in account of four major forces can be reduced by 4.95 per cent and 3.00 per cent, respectively.

The numerical analysis reveals the magnitude and distribution of interphase forces inside multiphase pump, which is meaningful for the simulation and design of multiphase pump.

Interphase forces between the gas and liquid phases determine many phenomena in bubbly flow. For the interphase forces in a multiphase rotodynamic pump, the magnitude analysis was carried out within the framework of two-fluid model. The purpose of this paper is to clarify the relative importance of various interphase forces on the mixed transport process, and the findings herein will be a base for the future study on the mechanism of the gas blockage phenomenon, which is the most challenging issue for such pumps.

Four types of interphase forces, i.e. drag force, lift force, virtual mass force and turbulent dispersion force (TDF) were taken into account. By comparing with the experiment in the respect of the head performance, the effectiveness of the numerical model was validated. In conditions of different inlet gas void fractions, bubble diameters and rotational speeds, the magnitude analyses were made for the interphase forces.

The results demonstrate that the TDF can be neglected in the running of the multiphase rotodynamic pump; the drag force is dominant in the impeller region and the outlet extended region. The sensitivity analyses of the bubble diameter and the rotational speed were also performed. It is found that larger bubble size is accompanied by smaller predicted drag but larger predicted lift and virtual mass, while the increase of the rotational speed can raise all the interphase forces mentioned above.

This paper has revealed the magnitude information and the relative importance of the interphase forces in a multiphase rotodynamic pump.

Numerical simulations of a multistage multiphase pump at different operating conditions were performed to study the variational characteristics of flow parameters for each impeller. The simulation results were verified against the experimented results. Because of the compressibility of the gas, inlet volume flow rate qi and inlet flow angle ß_i for each impeller decrease gradually from the first to the last stage. The volume flow rate at the entrance of the pump q, rotational speed n and inlet gas volume fraction (IGVF) affect the characteristics of qi and ß_i.

The hydraulic design features of the impellers in the multistage multiphase pump are obtained based on the flow parameter characteristics of the pump. Using the hydraulic setup features, stage-by-stage design of the multistage multiphase pump for a nominal IGVF has been conducted.

The numerical simulation results show that hydraulic loss in impellers of the optimized pump is substantially reduced. Furthermore, the hydraulic efficiency of the optimized pump increases by 3.29 per cent, which verifies the validation of the method of stage-by-stage design.

Under various operating conditions, q_i and ß_i decrease gradually from the first to the fifth stage because of the compressibility of the gas. For this characteristic, the fluid behavior varies at each stage of the pump. As such, it is necessary to design impellers stage by stage in a multistage rotodynamic multiphase pump.

These results will have substantial effect on various practical operations in the industry. For example, in the development of subsea oilfields, the conventional conveying equipment, which contains liquid-phase pumps, compressors and separators, is replaced by multiphase pumps. Multiphase pumps directly transport the mixture of oil, gas and water from subsea oilwells through a single pipeline, which can simplify equipment usage, decrease backpressure of the wellhead and save capital costs.

Characteristics of a multistage multiphase pump under different operating conditions were investigated along with features of the inlet flow parameters for every impeller at each compression stage. Our simulation results have established that the change in the inlet flow parameters of every impeller is mainly because of the compressibility of the gas. The operational parameters q, n and IGVF all affect the characteristics of qi and ß_i. However, the IGVF has the most prominent effect. Lower values of IGVF have an insignificant effect on the gas compressibility. Higher values of IGVF have a significant effect on the gas compressibility. All these characteristics affect the hydraulic design of the impellers for a multistage multiphase pump. In addition, the machining precision should also be considered. Considering all these factors, when IGVF is lower than 10 per cent, all the impellers in the pump can be designed uniformly. When IGVF varies from 10 to 30 per cent, the first two stages should be designed separately, and the latter stages are uniform starting with the second stage. When IGVF varies from 30 to 50 per cent, the first three stages should be designed separately, and the latter stages are going to be similar to the third stage. An additional increase in IGVF results in degeneration of the differential pressure of the pump, which will reduce the compressibility of the gas. As such, it can be deduced that only the first three stages should be designed separately, and the latter stages will be similar to the third stage. In addition, for the pump working under a lower volume flow rate than 25 m³/h, the first three stages should be designed individually while keeping the geometrical structure of the subsequent stages the same as the third stage.

This paper aims to present a novel numerical technique for solving the incompressible multiphase mixture model.

The multiphase mixture model contains a set of momentum and continuity equations for the mixture phase, a second phase continuity equation and the algebraic equation for the relative velocity. For solving continuity equation for the second phase and advection term of momentum, an improved approach fine grid advection-multiphase mixture flow (FGA-MMF) is developed. In the FGA-MMF method, the continuity equation for the second phase is solved with higher-order schemes in a two times finer grid. To solve the advection term of the momentum equation, the advection fluxes of the volume fraction in the continuity equation for the second phase are used.

This approach has been used in various tests to simulate unsteady flow problems. Comparison between numerical results and experimental data demonstrates a satisfactory performance. Numerical examples show that this approach increases the accuracy and stability of the solution and decreases non-monotonic results.

The solver for the multi-phase mixture model can only be adopted to solve the incompressible fluid flow.

The paper developed an innovative solution (FGA-MMF) to find multi-phase flow field value in the multi-phase mixture model. Advantages of the FGA-MMF technique are the ability to accurately determine the phases interpenetrating, decreasing the numerical diffusion of the interface and preventing instability and non-monotonicity in solution of large density variation problems.

The purpose of this paper is to study the dimensionless characteristics of a molten salt pump and propose an approach to carry out the modeling experiment by using water instead of molten salts.

External characteristics of the pump were estimated by using the steady flow model and compared with the experimental results. By taking water as the working fluid, the pathlines in the volute of the model pump were validated by the results obtained of high-speed photography. According to the derived dimensionless characteristics of the molten salt pump, the modeling experimental schemes were proposed. Adopting the validated numerical simulation model, the performance of the molten salt pump was studied in detail.

The modeling experimental schemes designed according to the dimensionless characteristics are theoretically feasible. However, to carry out the experiment successfully, factors such as rotational speed, geometric size, flow rate and head should be taken into account. The flow in the pumps is similar under the similar operating condition and the external characteristics of the similar pump can be converted to each other. Compared with transporting water, the decline of the head and efficiency is within 5 per cent when the viscosity is lower than 0.01453 Pa · s. The pump is not suitable for running under the critical Reynolds number of 1.0 × 10⁷.

The current work revealed the relationships among the dimensionless performances of a molten salt pump and proposed a critical Reynolds number Re_Qcr for the pump running.

The purpose of this paper is to propose a prediction method of gas-liquid two-phase flow patterns and reveal the flow characteristics in the suction chamber of a centrifugal pump.

A transparent model pump was experimentally studied, and the gas-liquid two-phase flow in the pump was numerically simulated based on the Eulerian–Eulerian heterogeneous flow model. The numerical simulation method was verified from three aspects: the flow pattern in the suction chamber, the gas spiral length and the external characteristics of the pump. The two-phase flow in the suction chamber was studied in detail by using the numerical simulation method.

There are up to eight flow patterns in the suction chamber. However, at a certain rotational speed, only six flow patterns are observed at the most. At some rotational speeds, only four flow patterns appear. The gas spiral length has little relationship with the gas flow rate. It decreases with the increase of the liquid flow rate and increases with the increase of the rotational speed. The spiral flow greatly increases the turbulence intensity in the suction chamber.

A method for predicting the flow pattern was proposed. Eight flow patterns in the suction chamber were identified. The mechanism of gas-liquid two-phase flow in the suction chamber was revealed. The research results have reference values for the stable operation of two-phase flow pumps and the optimization of suction chambers.

The purpose of this study is to suppress secondary flows and improve aerodynamic performance of a centrifugal impeller.

A multi-objective optimisation design system was described. The optimization design system was composed of a three-dimensional (3D) inverse design, multi-objective optimisation and computational fluid dynamics (CFD) analysis. First, the control parameter ΔCp for the secondary flows was derived and selected as the optimisation objective. Then, aimed at minimising ΔCp, a 3D inverse design for impellers with different blade loading distributions and blade lean angles was completed and multi-objective optimisation was conducted. Lastly, the improvement in the distribution of secondary flows and aerodynamic performance of the optimal impeller was demonstrated by CFD analysis.

The study derived the control parameter ΔCp for the secondary flows. ΔCp can indicate the distribution of secondary flows both near the blade pressure and suction surfaces. As ΔCp decreased, secondary flows decreased. The blade loading distribution with fore maximum blade loading at the shroud and aft maximum blade loading at the hub, coupled with a small negative blade lean angle, could help suppress secondary flows and improve aerodynamic efficiency.

A direct control method on internal flow field characteristic-secondary flows by optimisation design was proposed for a centrifugal impeller. The impeller optimisation design process saves time by avoiding substantial CFD sample calculations.

This study aims to complete the optimization design of a centrifugal impeller with both high aerodynamic efficiency and good structural machinability.

First, the design parameters were derived from the blade loading distribution and the meridional geometry in the impeller three-dimensional (3D) inverse design. The blade wrap angle at the middle span surface and the spanwise averaged blade angle at the blade leading edge obtained from inverse design were chosen as the machinability objectives. The aerodynamic efficiency obtained by computational fluid dynamics was selected as the aerodynamic performance objective. Then, using multi-objective optimization with the optimal Latin hypercube method, quadratic response surface methodology and the non-dominated sorting genetic algorithm, the trade-off optimum impellers with small blade wrap angles, large blade angles and high aerodynamic efficiency were obtained. Finally, computational fluid dynamics and computer-aided manufacturing were performed to verify the aerodynamic performance and structural machinability of the optimum impellers.

Providing the fore maximum blade loading distribution at both the hub and shroud for the 3D inverse design helped to promote the structural machinability of the designed impeller. A straighter hub coupled with a more curved shroud also facilitated improvement of the impeller’s structural machinability. The preferred impeller was designed by providing both the fore maximum blade loading distribution at a relatively straight hub and a curved shroud for 3D inverse design.

The machining difficulties of the designed high-efficiency impeller can be reduced by reducing blade wrap angle and enlarging blade angle at the beginning of impeller design. It is of practical value in engineering by avoiding the follow-up failure for the machining of the designed impeller.