Analysis of the Internal Flow Characteristics and Impeller Strength of the Stay Vane Mixed Flow Chemical Pump

Abstract

To improve the energy conversion performance and long-term structural stability of stay vane mixed-flow chemical pumps used for industrial residual pressure recovery, this paper establishes a coupled numerical framework of computational fluid dynamics (CFD) and finite element structural analysis (FEA). The internal flow evolution, radial hydraulic excitation, transient pressure oscillation and impeller mechanical bearing capacity are systematically investigated under three typical flow states: partial load 0.7 Q_d, design condition 1.0 Q_d and overload 1.2 Q_d. The results show that the flow inside the pump is smooth and there is no obvious backflow or separation under the rated working condition, and the energy conversion efficiency is the best. When operating under partial discharge, boundary layer separation and recirculating secondary vortices easily emerge inside the pump passage, which drastically elevates hydraulic energy dissipation. Meanwhile, operating load exerts a remarkable influence on the impeller’s radial hydraulic load and transient pressure oscillation intensity. The radial force and the pressure pulsation amplitude at the impeller outlet are the largest under the small flow condition, and the force is the most stable under the rated working condition. Blade passing frequency dominates the frequency components of transient pressure fluctuations. The maximum von-Mises stress on the impeller concentrates at the filet where blade roots connect with the hub, and this peak value hits 86.3 MPa under partial-load low-flow operating status. Calculated stress values for all three flow rates satisfy the structural safety criteria. The outcomes of this numerical investigation can offer reliable technical support for hydraulic performance optimization and structural dimension design of this type of mixed-flow chemical pump.

1. Introduction

Under the strategic background of global energy structure transformation and industrial energy conservation and emission reduction, the upgrading of energy recovery and efficient fluid conveying equipment has become the core path for achieving low-carbon development in the fields of chemical engineering, metallurgy, thermal power, and water conservancy [1,2]. In chemical processes, industrial circulating water systems, municipal flood control and drainage, and energy power station supporting systems, a large amount of residual pressure energy in pressurized fluids is not fully utilized. Traditional pump equipment has high energy consumption and low energy utilization rate, which significantly deviates from the development requirements of green, low-carbon, and energy-efficient [3]. Mixed-flow pumps, as key equipment connecting low-pressure conveying and high-pressure energy conversion, possess the advantages of high head of centrifugal pumps and large flow rate of axial-flow pumps, and play an irreplaceable role in fluid conveying and residual pressure energy recovery systems. Their hydraulic performance, operational stability, and structural safety directly determine the energy recovery efficiency and overall economy of the system [4,5].

Equipped with stay vanes, the mixed-flow chemical pump realizes efficient mutual transformation between fluid dynamic and static pressure energy relying on the rotating impeller’s work input and the flow straightening function of stay vanes. It has broad application prospects in scenarios such as industrial residual pressure recovery, energy cascade utilization in circulating water systems, and energy optimization in chemical processes [6,7,8,9]. As the equipment develops towards larger size, higher rotational speed, higher efficiency, and long-term reliable operation, the complex three-dimensional turbulent flow inside the pump, pressure pulsation caused by the dynamic interference between the impeller and the stay vanes, and the structural strength and fatigue safety issues of the impeller under the combined action of centrifugal force and fluid load, have become the key bottlenecks restricting the improvement of energy recovery efficiency and the stable operation of the equipment. Flow separation, secondary flow, vortex structure, and unsteady pressure pulsation will cause local hydraulic losses and reduce the efficiency of energy conversion; blade stress concentration and excessive deformation may lead to structural failure and threaten system safety. Plenty of researchers have carried out in-depth explorations into the internal flow mechanisms inside various pump devices. Ye et al. [10] adopted CFD with a 3D transient dynamic mesh to compare the inner flow of single and double helical pumps. Their work proved the double helical pump boasts better volumetric efficiency and sealing performance. Its outlet flow drops with rising pressure difference, while higher medium viscosity can mitigate such flow reduction. Konishi et al. [11] put forward a novel impeller with radial and annular passages for stable wide-range operation. This design outperforms conventional impellers, delivering identical flow parameters at a lower specific speed. The study also verified that pump head declines monotonically with flow rate, as friction-free hydraulic losses inside the impeller grow linearly with discharge. Cai et al. [12] combined numerical simulations and experimental tests to investigate flow pattern variations in an axial-flow nuclear main pump across various flow rates, uncovering the evolution laws of its internal flow structures. Heng et al. [13] investigated gas–liquid two-phase performance of disk pumps. They captured internal two-phase flow structures via high-speed photography and adopted multiple test methods to characterize the pump’s hydraulic behaviors with visualized flow fields. The results show that at the nominal initial condition, at 1500 revolutions per minute, the disc pump reaches 34% (maximum inlet gas void fraction), and at 2000 revolutions per minute, 49%, while the corresponding pump performance drop point’s IGVFc (critical inlet gas void fraction) is close to 9%.

In recent years, the collaborative simulation technology of CFD and FEA has provided a reliable means for accurately revealing the flow field patterns within pumps, optimizing hydraulic structures, and evaluating structural strength. In the numerical calculation of the flow field, the full-channel simulation based on the Reynolds-averaged N-S equations and the SST k − ω turbulence model can accurately capture the velocity distribution, pressure characteristics, and dynamic interference effects within the pump, providing theoretical support for reducing hydraulic losses and improving energy recovery efficiency; in the structural strength analysis, the finite element method coupled with the flow field pressure load and centrifugal load, and based on the fourth strength theory (von-Mises stress) to evaluate the stress and deformation of the blades, can ensure the structural safety of the impeller under high-energy conditions. Some scholars have analyzed the strength of the impeller. Chen et al. [14] simulated fatigue crack growth by the extended finite element method (XFEM) coupled with the Walker equation, and validated this method on circular tensile specimens under load ratios R = 0.1, 0.5 and 0.85. They also performed crack propagation calculations at two distinct positions of a vertical centrifugal pump-turbine in turbine mode. This XFEM-based numerical approach can effectively predict crack geometries and component fatigue life. Yan et al. [15] adopted FSI finite element simulations to quantify pipeline vibration induced by fluid pressure oscillation, discussing the influences of internal pressure, pipe length, and clamp layout. Their numerical outcomes reveal that structural displacement rises with fluid pressure, yet the growth rate gradually slows down. Lu et al. [16] numerically investigated unsteady flow behaviors and fluid force effects on the rotor system of a vortex-type mixed-flow circulating pump at 0.8 Q_d, 1.0 Q_d and 1.2 Q_d. Simulated flow fields indicate disordered vortex structures and substantial energy losses under partial loads, whereas overload conditions produce steep velocity gradients inside the impeller and aggravate hydraulic dissipation. Zhang et al. [17] adopted a scale-adaptive hybrid RANS-LES model to analyze the flow behaviors of a propulsion pump. They further put forward an indirect acoustic characterization approach relying on Lamb vector divergence to quantify turbulent noise sources. Validated against acoustic finite element predictions and test data, this novel method proves reliable for quantitatively evaluating turbulence-induced acoustic excitation.

Currently, systematic research on the internal flow mechanism, energy loss characteristics, pressure pulsation control, and rotor structure strength of the stay vane type mixed-flow chemical pump for energy recovery requirements is still relatively lacking. Most existing mixed-flow pump FSI studies focus on water supply pumps, nuclear main pumps and circulation pumps; few systematically target stay vane mixed-flow chemical pumps for industrial residual pressure energy recovery. Previous work only separately analyzed internal flow, pressure pulsation or impeller strength, without coupling three working conditions (0.7/1.0/1.2 Q_d) to reveal the correlation between flow separation, radial force pulsation, blade stress concentration and energy recovery efficiency. This paper fills this gap. This paper takes a circular pump chamber stay vane type mixed-flow chemical pump as the research object, focusing on the goal of efficient fluid transportation and energy recovery enhancement. It analyzes the pump’s internal flow characteristics, radial force distribution, and pressure pulsation patterns, reveals the stress and deformation characteristics of the blades, aiming to clarify the energy conversion and fluid–solid coupling mechanism within the pump, and providing theoretical basis and technical reference for the hydraulic optimization, structural improvement, and efficient and reliable application of the stay vane type mixed-flow chemical pump in energy recovery systems.

2. Numerical Simulations

2.1. Governing Equations

Full-flow CFD simulations are performed for the pump with 25 °C clean water as the working medium, which is simplified as a single-phase, incompressible Newtonian fluid for single-flow modeling. The incompressible continuity equation and Reynolds-averaged Navier–Stokes (RANS) equations are solved to capture the internal flow field distribution. The following equations are:

$${\displaystyle \frac{\partial u_j}{\partial x_j}}=0$$

(1)

$$\rho u_j{\displaystyle \frac{\partial u_i}{\partial x_j}}=\rho F_i-{\displaystyle \frac{\partial p^{\ast }}{\partial x_i}}+{\mu }_{eff}{\displaystyle \frac{\partial }{\partial x_j}}({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}})$$

(2)

In the above formulas, ρ denotes fluid density, μ_eff refers to the effective fluid viscosity, and p* stands for transformed pressure containing turbulent kinetic energy k.

Solving the fundamental flow equations requires addressing two core problems: the coupling of continuity and momentum equations, as well as the proper selection of turbulence models. The fluid inside the pump is incompressible liquid, and the continuity equation does not contain the pressure term. When solving simultaneously, singularities may occur, and some algorithms applicable to compressible flows cannot be directly applied. Therefore, the incompressible N-S equations mainly address the problem of coupling between velocity and pressure. There are many solutions for the N-S equations, and the most widely used method in the calculation of hydraulic mechanical flow fields is the pressure correction method. If this method predicts the pressure field inaccurately, it will violate the continuity equation. Thus, based on the continuity equation, a pressure correction equation is derived to correct the predicted pressure and velocity fields, and this process repeats until a convergent solution for the pressure field and velocity field is obtained.

Numerical prediction of 3D turbulent flow within pumps generally relies on Reynolds-averaged N-S turbulence theories, which fall into two categories: Reynolds stress models and eddy-viscosity models. Existing literature confirms the standard SST k − ω model delivers reliable pump performance predictions and enjoys extensive engineering adoption. Accordingly, the SST k − ω model is adopted herein, with transport equations for turbulent kinetic energy k and specific dissipation rate ω presented below [18]:

$${\displaystyle \frac{\partial (\rho k)}{\partial t}}+{\displaystyle \frac{\partial (\rho u_{i}k)}{x_i}}=P-{\displaystyle \frac{\rho k^{3/2}}{l_{k-w}}}+{\displaystyle \frac{\partial (\rho k)}{\partial x_i}}\left[(\mu +{\sigma }_k{\mu }_i){\displaystyle \frac{\partial k}{\partial x_i}}\right]$$

(3)

$${\displaystyle \frac{\partial (\rho \omega )}{\partial t}}+{\displaystyle \frac{\partial (\rho u_i\omega )}{x_i}}=C_{\omega }P-\beta \rho {\omega }^2+{\displaystyle \frac{\partial }{\partial x_i}}\left[({\mu }_l+{\sigma }_{\omega }{\mu }_t){\displaystyle \frac{\partial \omega }{\partial x_i}}\right]+2(1-F_1){\displaystyle \frac{\rho {\sigma }_{\omega 2}}{\omega }}{\displaystyle \frac{\partial k}{\partial x_i}}{\displaystyle \frac{\partial \omega }{\partial x_i}}$$

(4)

In these equations, ρ denotes fluid density, P stands for the turbulence production term, μ is dynamic viscosity, μ_t represents turbulent eddy viscosity, σ refers to a model constant, C_ω is the dissipation coefficient, F1 is the blending function, and l_k−ω denotes the turbulence length scale. The turbulence scale l_k−ω within the term ρk^3/2/l_k−ω is defined in Equation (5).

$$l_{k-\omega }=k^{1/2}{\beta }_k\omega$$

(5)

The finite element method is utilized to evaluate the structural strength of the impeller in this work. Displacement-based finite element analysis discretizes the solid domain into multiple interconnected elements sharing discrete nodes. Once the element-level force–displacement relation is derived, matrix assembly techniques can be employed to construct the global structural equilibrium relation for numerical solving. For linear steady structural analysis, inertial and damping effects other than steady acceleration fields are neglected, leading to the following global equilibrium equation:

[K]{u} = {F}

(6)

where [K] denotes the stiffness matrix, {u} represents nodal displacement, and {F} is the total nodal external load including gravity, impeller-induced centrifugal force and fluid pressure on FSI interfaces. The pressure load data is extracted from full-passage CFD results of the pump.

By solving, the node displacements {u} are obtained, and thus the stresses {σ} at each node can be calculated:

[σ] = [D] [B]{u}

(7)

where [B] is the strain matrix derived from element shape functions, and [D] is the elastic matrix determined by the material elastic modulus and Poisson’s ratio. The equivalent von Mises stress is further calculated following the fourth strength criterion as expressed below:

$${\sigma }_e=\sqrt{{\displaystyle \frac{1}{2}}\left[{\left({\sigma }_x-{\sigma }_y\right)}^2+{\left({\sigma }_y-{\sigma }_z\right)}^2+{\left({\sigma }_z-{\sigma }_x\right)}^2+6({\sigma }_{xy}^2+{\sigma }_{yz}^2+{\sigma }_{xz}^2)\right]}$$

(8)

2.2. Geometric Model and Grid Generation

The research object in this paper is a mixed-flow pump with an annular pump chamber. It is widely applied in urban flood control and drainage, as well as circulating water systems for power, water supply, chemical and metallurgical enterprises. The main components of the pump structure include the inlet pipe, impeller, stay vanes, and ring-shaped volute. The detailed three-dimensional model is shown in Figure 1. The inlet diameter of the impeller D₁ is 550 mm, the outlet adopts an inclined outlet, the diameter of the outlet close to the rim D₂ is 662 mm, the diameter of the outlet close to the hub D₃ is 530 mm, and the outlet height of the stay vanes H₂ is 225 mm. Specific details can be found in Figure 2. The rated rotational speed of the impeller n_r is 1465 rpm, the rated flow rate Q_r is 12,000 m³/h, the rated head H_r is 56.3 m, and the rated efficiency is 80%. The number of impeller blades Z_imp is 5, and the number of stay vanes Z_sv is 13. Detailed information can be found in

Table 1. Pump unit detailed parameter table.

Components	Value	Unit
The diameter of Inlet D1	550	[mm]
The diameter near the shroud outlet edge D2	662	[mm]
The diameter near the hub outlet edge D3	530	[mm]
The height of the stay vanes outlet H2	225	[mm]
Rated impeller speed nr	1465	[rpm]
Design flow Qd	12,000	[m3/h]
Rated head Hr	56.3	[m]
Number of impeller blades Zimp	5	[−]
Number of stay vane blades Zsv	13	[−]

.

Prior to numerical simulation, mesh generation is required for the established 3D geometric model. In this paper, Ansys mesh is chosen for meshing. The inlet pipe section adopts hexahedral meshes, while the other components use tetrahedral meshes. Regarding the grid sensitivity, this paper selected five grid schemes to calculate the head. As shown in Figure 3, after the number of grids reached 4.3 million, the head remained basically stable with no significant changes. Therefore, considering the calculation cost and accuracy, this study chose the grid scheme of 5.5 million. The total number of meshes is 5,504,111. The detailed mesh diagram is shown in Figure 4, and the number of meshes for each component is presented in

Table 2. Grid detailed parameter table.

Component	Mesh Type	Element Count
Inlet pipe	Hexahedral	281,088
Impeller	Tetrahedral	1,965,011
Stay vane	Tetrahedral	1,376,869
Volute	Tetrahedral	1,881,143
Total		5,504,111

.

2.3. Boundary Conditions and CFD Setup

This study utilized the commercial software Ansys CFX 2024 R2 and the Static Structural module to conduct flow field calculations and rotor strength analysis. Detailed flow field boundary conditions are specified as follows: standard atmospheric pressure (101,325 Pa) is set as the reference pressure. The inlet of the water pipeline is defined as the fluid domain inlet with a mass flow inlet boundary condition. The flow value is set to the corresponding flow rate under the corresponding working conditions. This study focuses on analyzing three working conditions: 0.7 Q_d, 1.0 Q_d, and 1.2 Q_d. The volute outlet acts as the fluid domain outlet with a static pressure boundary condition of 0 Pa. The multi-reference frame (MRF) approach is adopted here, where only the impeller rotor rotates at a speed of 1465 r/min. The other components are all stationary. Interfaces between the inlet and the rotor, between the rotor and the stay vanes, and between other components are all dynamic–static interfaces. Interfaces between different components use the General Grid Interface (GGI) model. All solid surfaces are set as wall boundaries, with no-slip shear conditions applied, and the wall real flow characteristics are simulated using the standard roughness model. Wall functions are adopted to approximate near-wall turbulent flow via empirical correlations, and the SST k − ω turbulence model is selected. Steady-state computations run for 3000 iterations, whose outcomes serve as the initial flow field for subsequent unsteady simulations. Transient calculations cover 10 full rotor revolutions, discretized into 180 time steps per revolution with 10 inner iterations for each step. The time step size is 2.2753 × 10⁻⁴ s, leading to a total simulation duration of 0.409558 s. Calculations are considered converged once the RMS residuals of continuity and momentum equations drop below 10⁻⁵ [19,20,21].

3. Experimental Testing and Validation

This study obtained the hydraulic performance through model tests, as shown in Figure 5. It can be clearly seen from Figure 5a that the overall trend of the efficiency curve is highly consistent. CFD can accurately predict the change pattern of efficiency. Near the peak (8000–12,000 m³/h), the two almost overlap, with extremely small errors, about 5%; there is a slight deviation in the small flow ranges, but it is still within the acceptable range. The maximum error is less than 15%. From Figure 5b, it can be seen that the overall downward trend is consistent. CFD can accurately capture the change pattern of head with flow rate. In the medium flow range (8000–15,000 m³/h), the two are closely matched, and the error is approximately 5%. In the small flow range (<8000 m³/h), CFD is slightly higher than the test value; the maximum error is less than 20%. This indicates that the numerical simulation method is reliable in predicting the efficiency characteristics of the pump, especially near the optimal operating condition, with higher accuracy.

4. Results and Discussion

4.1. Flow Field Characteristics

The internal flow behaviors of the impeller and guide vanes at 0.5 span are analyzed in this paper, with the corresponding cross-section illustrated in Figure 6. Three operating points, namely partial flow, design and overload conditions, are discussed in terms of velocity and pressure distributions. The internal flow lines and velocity distribution within the stay vane type mixed-flow chemical pump under different conditions are shown in Figure 7. From the perspective of Blade to Blade, at the small flow condition of 0.7 Q_d, there are obvious low-speed zones and local recirculation in the flow channel of the impeller outlet and stay vanes, and flow separation occurs near the blade wall, with enhanced secondary flow. At the rated condition of 1.0 Q_d, the internal flow of the impeller and stay vanes is smooth, without obvious recirculation or separation, and the velocity distribution in the main flow area is uniform, with a higher energy conversion efficiency. Under the overload condition of 1.2 Q_d, the flow velocity rises throughout the flow passage, accompanied by localized high-speed regions at the impeller outlet and within the volute. The velocity gradient increases, and local turbulence dissipation enhances, resulting in a decrease in flow stability. For all three operating conditions, fluid pressure gradually increases from the impeller inlet to the impeller outlet and the stay vane passage as fluid flows through the rotating impeller. There are obvious high-pressure areas at the rotor outlet and stay vanes region, but there are some uneven pressure phenomena in the stay vanes’ flow channels [22,23,24,25,26].

4.2. Radial Force Analysis

Figure 8 presents the time-domain radial force curves of the impeller under various working conditions, and fast Fourier transform (FFT) is implemented to derive the corresponding frequency-domain spectra. Only the stable 0–0.2 s (five full rotations) segment of the full 0.4096 s simulation (10 full rotations) is displayed for clear observation of periodic signals. The first five revolutions are discarded to eliminate transient startup effects. For the 0.7 Q_d low-flow condition, the amplitude of the radial force of the impeller is the largest, with intense fluctuations. The dominant frequency of the resultant radial force is 4.4 times the rotational frequency f_n, and the average radial force is approximately 5500 N, while the radial force pulsation amplitude is around 9000 N, which is greater than the average radial force; for the 1.0 Q_d rated condition, the amplitude of the radial force is the smallest, with stable fluctuations. The main frequency of the radial resultant force is 5 f_n, and the average radial force is approximately 4200 N, while the radial force pulsation amplitude is around 2300 N; for the 1.2 Q_d high-flow condition, the amplitude of the radial force is between the low-flow and rated conditions, with a fluctuation amplitude slightly higher than that of the rated condition. The main frequencies of the radial resultant force are 5 f_n (f_n = n/60) and 5 f_b (f_b = f_n × Z_imp), and the average radial force is approximately 4500 N, while the radial force pulsation amplitude is around 2500 N. The resultant radial force F is shown in Equation (9).

$$F=\sqrt{F_x^2+F_y^2}$$

(9)

4.3. Pressure Pulsation Signal Analysis

Figure 9 illustrates the layout of pressure fluctuation monitoring points for analyzing pressure pulsation inside the pump. Three measuring points are arranged separately at the impeller inlet, volute and volute outlet, and numerical simulations are carried out under three flow rates: 0.7 Q_d, 1.0 Q_d, and 1.2 Q_d. The formula for calculating pressure pulsation is as follows:

$$\mathsf{\Delta }H=(P_{\max }-P_{\min })/\rho g$$

(10)

where P_max represents the maximum pressure value, Pa; P_min represents the minimum pressure value, Pa.

As Figure 10, Figure 11 and Figure 12 show, for the monitoring point JK at the inlet of the impeller, the maximum pulsation amplitude is 0.7 Q_d, with a relative pulsation value of △H/H_d = 7.62%; 1.0 Q_d has the minimum value, at 4.83%; 1.2 Q_d has a value of 6.49%, and the dynamic and static interference is the strongest at low flow rates. From the monitoring point WK in the volute area, the pulsation amplitude of 1.0 Q_d is the largest, at 7.09%; 0.7 Q_d and 1.2 Q_d are 5.13% and 5.42%, respectively, and the stay vane’s rectification effect is more significant in the rated condition, with more prominent pressure fluctuations. For the monitoring point CK in the volute outlet area, the overall pressure pulsation amplitude is the lowest, and it increases with the increase in flow rate. 0.7 Q_d is only 1.88%, 1.0 Q_d is 3.13%, and 1.2 Q_d reaches 6.27%. The pressure pulsation in the volute is most significantly affected by the flow rate. The detailed results are shown in

Table 3. Table of pressure fluctuation amplitudes at monitoring points for different operating conditions.

Monitoring Points	Condition	△H	△H/Hd
JK	0.7 Qd	4.297	7.62
	1.0 Qd	2.725	4.83
	1.2 Qd	3.661	6.49
WK	0.7 Qd	2.891	5.13
	1.0 Qd	3.998	7.09
	1.2 Qd	3.058	5.42
CK	0.7 Qd	1.062	1.88
	1.0 Qd	1.762	3.13
	1.2 Qd	3.535	6.27

. From the frequency domain results, the main frequencies of the inlet and volute pressure pulsations are both the blade passage frequency (f_b), and there are low-frequency pressure pulsation components. In addition, the volute also has harmonic components; The dominant frequency of pressure pulsation at the outlet is a low frequency of 0.2 f_n.

Under 1.0 Q_d, the inflow angle of the impeller outlet perfectly matches the stay vane inlet angle; the mainstream flow is concentrated through the stay vane channel without separation, and the rotor–stator interference effect between five blades and 13 stay vanes is fully excited without flow separation damping, leading to the maximum pressure fluctuation amplitude at the stay vane monitoring point. Under off-design conditions, flow separation forms a low-speed wake to suppress partial pulsation amplitude.

Low-frequency dominant component at impeller outlet 0.2 f_n: This low frequency originates from the periodic asymmetric vortex shedding at the impeller outlet shroud under rotating action, which is a large-scale vortex unsteady characteristic frequency, independent of blade passing frequency. A detailed vortex evolution nephogram is supplemented to support this explanation.

4.4. Analysis of the Strength of the Impeller

Separate three-dimensional geometric models are constructed for the flow field and impeller structural field calculations in this work. The computational domains for the impeller body structure field and the internal flow field of the impeller are simultaneously meshed, ensuring that the grid nodes at the interface between fluid and solid correspond one-to-one, thereby guaranteeing the accurate transfer of pressure loads at the fluid–solid interface. The meshes and computational domains for flow field calculation and structure field calculation are shown in Figure 13.

The fluid–structure interaction setup for impeller strength evaluation is detailed as follows. The structural domain model consists solely of the pump impeller. A fixed constraint is imposed on the hub-shaft joint surface as the structural boundary condition. Two types of loads are applied to the impeller: inertial loads and surface loads. Inertial loads include impeller self-weight and rotational inertial effects corresponding to a rotational speed of 1465 rpm. Surface loads refer to fluid pressure distributed on FSI interfaces, which are extracted and mapped from preceding CFD flow field solutions.

In the calculation of the impeller structure field, the material property of the impeller is set as steel, and its impeller material parameters are as shown in

Table 4. Impeller material parameter table.

Name	Materials	Elasticity Modulus (N/mm2)	Density (kg/m3)	Poisson Ratio
Shroud	Steel	2.1 × 105	7.85 × 10−6	0.3
Blade	Steel	2.1 × 105	7.85 × 10−6	0.3
Hub	Steel	2.1 × 105	7.85 × 10−6	0.3

.

The strength of the impeller was evaluated through fluid–solid coupling, and the result is shown in Figure 14. It can be observed from the figure that the maximum equivalent stress reaches 86.3 MPa under the low-flow condition, emerging at the junction of blade roots and the hub where severe stress concentration occurs. Under the design flow condition, the maximum equivalent stress decreases to 67.1 MPa, accompanied by uniform stress distribution without prominent high-stress regions, which corresponds to the optimal structural safety performance. At the high flow rate condition, the maximum equivalent stress is 68.6 MPa, slightly higher than the rated condition, and the range of high-stress areas expands slightly. Overall, the maximum stress of the impeller is all less than 100 MPa, meeting the requirements of engineering applications. Detailed data can be found in

Table 5. Impeller strength result parameters table.

Conditions	Flowrate (m3/h)	Maximum Equivalent Stress (Mpa)
0.7 Qd	8400	86.3
1.0 Qd	12,000	67.1
1.2 Qd	14,400	68.6

.

The material yield strength of steel is supplemented (σs = 235 MPa); the safety factor under each working condition is calculated (n0.7 Q_d = 2.72, n1.0 Q_d = 3.50, n1.2 Q_d = 3.43). The formula for calculating the safety factor is as follows:

$$n={\sigma }_s/S_{\max }$$

(11)

where σs is the material yield strength of steel, S_max is the maximum equivalent stress.

All safety factors exceed the minimum allowable value of 1.5 for pump impellers. The maximum stress occurs at the blade root; the low-flow condition has the highest stress and pulsation amplitude, which is the critical fatigue control condition for long-term operation;

This paper adopts one-way fluid–structure coupling, i.e., CFD flow field pressure load is transmitted to the structural solver, and structural deformation feedback to the flow field is ignored. From a large number of studies on unidirectional and bidirectional fluid–solid coupling, it can be known that the deformation of the structural steel impeller blades has a very weak impact on the flow field. Therefore, using unidirectional fluid–solid coupling can meet the engineering requirements.

5. Conclusions

This paper mainly investigates the internal flow characteristics of a mixed-flow chemical pump equipped with guide vanes and conducts strength analysis on its impeller. The three main conclusions are summarized as follows:

• Under the rated operating condition of 1.0 Q_d, the internal flow presents uniform streamlines without flow separation or backflow. The velocity and pressure distribution are uniform, and the energy conversion efficiency is the highest. At a low flow rate of 0.7 Q_d, backflow, flow separation and secondary flow are prone to occur, resulting in a significant increase in hydraulic loss. At a high flow rate of 1.2 Q_d, the flow velocity is too high and local turbulence dissipation is enhanced. The rated operating condition is the optimal operating range for this pump.
• Flow rate exerts a remarkable impact on impeller radial force and pressure pulsation. The impeller radial force and outlet pressure fluctuation reach the maximum under low-flow conditions, while the force remains the most stable with minimal pulsation at the design operating point. The dominant frequency of pressure pulsation is primarily governed by the blade passing frequency. Pressure fluctuation intensity peaks at the impeller outlet and attains the minimum within the volute. The amplitude of pressure pulsation in the volute rises considerably under large-flow conditions.
• The maximum equivalent stress of the blade appears at the junction of the blade root and hub. The stress is the highest under the low-flow condition (86.3 MPa) and the lowest under the rated condition (67.1 MPa). The maximum stress in all three conditions is less than the allowable stress, meeting the structural safety requirements. The low-flow condition is the key control condition for the strength and fatigue design of the impeller.

Some suggestions are proposed for the design of the energy recovery vane-type chemical pump to avoid long-term operation at low flow rates, and to reduce stress concentration at the root of the blades and pressure pulsation. Reasonably match the number of impeller blades and stay vanes to suppress the vibration caused by dynamic-static interference. Optimize the round corners at the root of the blades to reduce the stress concentration coefficient.