The unsteady flow within a centrifugal pump, particularly the pressure distribution on rotating impeller blades, is fundamental to its performance and stability. Direct, high-fidelity measurement of this pressure field remains a significant technical challenge due to the complexity of transmitting data from a high-speed rotating frame. In response, this study develops and validates a novel wireless measurement system designed to acquire dynamic pressure data directly from rotating pump blades. The objective is to use this system to conduct a detailed experimental investigation of the spatiotemporal characteristics of blade surface pressure under various operating conditions. This approach provides crucial data for validating computational fluid dynamics (CFD) models, optimizing hydraulic design, and understanding the root causes of pump vibration and noise.

The study was conducted on a centrifugal pump with a design flow rate (Q_d) of 18 m³/h, a rotational speed of 1 450 rpm, and an eight-blade impeller. A wireless measurement system was custom-designed, integrating four miniature pressure sensors (0–200 kPa range, 0.5% accuracy) flush-mounted on the blade surface to minimize flow disturbance. A specially machined main shaft with internal grooves routed the sensor wires to a compact shaft-mounted module containing signal amplifiers, a multi-channel data acquisition (DAQ) card, and a Wi-Fi transmitter. The DAQ system synchronously sampled data from all four channels at 1 024 Hz. Measurement points were located on the pressure side at 30% (PA) and 70% (PB) of the chord length, with corresponding locations on the suction side (SA and SB). Experiments were conducted over a range of flow rates, and nonstationary signal processing techniques, including time-domain analysis and Fast Fourier Transform, were applied.

The experiments provided detailed insights into time-averaged and unsteady pressure characteristics. Time-averaged results confirmed that on both the pressure and suction sides, the pressure at the trailing edge was higher than that at the leading edge. The pressure difference between the pressure and suction sides increased linearly with flow rate. Notably, the leading edge exhibited greater sensitivity to flow rate variations compared with the trailing edge, indicating that improvements in inlet flow conditions more significantly impact the loading at the blade front. The dynamic pressure signals showed strong periodicity driven by rotor–stator interaction (RSI) with the volute tongue. Frequency-domain analysis revealed that the dominant pulsation frequency at all locations was the shaft rotation frequency (F_i≈24.17 Hz), followed by the blade passing frequency (F_b≈193.36 Hz) and the third harmonic of the shaft rotation (≈72.5 Hz). The amplitude of the dominant frequency varied non-monotonically with flow rate, decreasing initially, then increasing, and finally decreasing again. Furthermore, the dimensionless peak-to-peak value (97% confidence level) exhibited a monotonic trend with increasing flow rate.

A stable and reliable wireless measurement system for acquiring dynamic surface pressure on a rotating centrifugal pump impeller was successfully developed and validated. The system enables multi-point, synchronized, high-fidelity data acquisition, overcoming the limitations of conventional methods. The results offer direct quantitative insights into the effects of RSI and flow rate on blade loading and pressure pulsation, providing a valuable experimental database for CFD validation and a key foundation for the design of high-performance centrifugal pumps.

Centrifugal pumps are a common type of hydraulic machinery widely used in water transfer, energy storage, agricultural irrigation, oil production, and more. Owing to system regulation demands, these pumps often need to switch operating conditions and, therefore, operate for long periods in off-design states. This requires a wide efficient operating range and the development of advanced design methods. To address the issues of low precision in load control design methods and narrow efficient operating ranges, this paper proposes a centrifugal pump impeller design method based on the three-segment quadratic function controlling blade load distribution.

The proposed method divides the blade load from the impeller inlet to the outlet into three segments: the inlet segment, the intermediate segment, and the outlet segment. Each segment is given a quadratic function-type load distribution to construct the impeller design method based on three-segment quadratic function load control. By assigning values to 13 independent control parameters, the specific form of load distribution is determined, resulting in the final structure of the impeller. Using this design method, a centrifugal pump with a specific speed of 102 is designed and numerically simulated to analyze its energy and flow-field characteristics. This study also establishes a comprehensive test bench for closed centrifugal pump hydraulic model testing, which consists of the test pump, pipeline system, and sensors that measure inlet pressure, outlet pressure, flow rate, rotational speed, and torque. The designed pump is manufactured and tested on this bench.

The simulation results demonstrate that the optimized impeller achieves a 4.11% increase in efficiency at the designed point Q_d and a 5.35% increase in the average efficiency under multiple operating conditions ranging from 0.7 Q_d to 1.3 Q_d, with an almost unchanged flow-head curve. The energy characteristics indicate that the optimized impeller has a wide efficient operating range. Internal flow-field analysis reveals a decrease in the area and strength of vortex and flow separation at off-design points. At the 50% span of the blades, the pressure distribution from the impeller inlet to the outlet is more uniform, and the streamline distribution is more reasonable. Furthermore, changing the blade load in the inlet section from a fast rise to a slow increase improves pressure distribution on the blade surface, reduces local pressure gradients, and achieves a uniform variation. The tested results show that the maximum efficiency of the designed pump is 78.20%, which meets the design requirements. Meanwhile, the simulated results are compared with experimental results. The error between the simulated and experimental results is lower than 5%, validating the accuracy of the simulation method.

Both simulated and experimental results confirm that the centrifugal pump impeller design method based on the three-segment quadratic function load control significantly enhances pump efficiency, improves flow patterns, and provides a reference for the development of high-efficiency and wide-operating-condition impellers.

The Yarlung Zangbo River contains numerous hydropower resources, with high head and large flow rates in the downstream region, which is conducive to power generation by Pelton turbines. Pelton turbines convert the kinetic energy generated from the water potential energy into mechanical energy for rotating a runner. The runner is the core component for the flow and work of the Pelton turbine, and the shape of its bucket is crucial for the runner's performance, which is uniformly arranged along the hub of the runner. As the surface shape of the bucket is complex, several parameters are required to determine its geometry model, undoubtedly posing a huge obstacle to work.

In this paper, a design method is proposed to address the problem of designing and improving the bucket based on the Bézier curve. The design space is simplified as much as possible based on geometry, and the Bézier curves are utilized for designing the bucket shape. An orthogonal analysis is applied for the optimization of bucket parameters, while the computational fluid dynamics method is employed for analyzing the energy characteristics and three-dimensional flow field of the Pelton turbine. In the bucket design method, the three-dimensional geometry of the bucket can be divided into contour, flow profile, and guidelines, and several characteristic parameters can be determined for those lines. Each type of line includes several biquadratic Bézier curve connections. The number of characteristic line parameters is decreased by establishing a connection between five control points of the Bézier curves. Thus, a three-dimensional design method for the bucket of the Pelton turbine is proposed based on the five controlled characteristic parameters. The main optimization parameters are chosen by the geometry. Subsequently, bucket depth, width increment, outflow angle, splitter angle, and cutout diameter are chosen to conduct orthogonal optimization for the Pelton turbine bucket. For further analysis of the flow characteristics of the optimized bucket, the runner is modeled based on the optimum parameters. In the computational fluid dynamics method, grids are meshed by ICEM, and computational fluid dynamics is performed with ANSYS FLUENT.

The results of the polar analysis and three-dimensional unsteady flow field revealed that width had the maximum influence on runner efficiency; outflow angle, cutout diameter, and bucket depth had a smaller influence; and splitting angle had the minimum influence. After optimization, the hydraulic efficiency of the Pelton turbine was increased by 6.71%. The optimized bucket demonstrated a larger torque peak than the prototype bucket. The bucket always showed large torque when its torque decreased to zero and exhibited smoother curve transition and longer work time. Thus, the optimized bucket demonstrated greater total torque than the prototype bucket; furthermore, the former's high-pressure area was larger, making the energy conversion of water from the nozzle to the bucket more effective.

This paper proposes a three-dimensional design method for the Pelton turbine bucket based on the controlled characteristic parameters. The energy performance of the Pelton turbine was enhanced by the orthogonal optimization and three-dimensional flow simulation.