This study proposes a quadratic formulation for the head–flow relationship in centrifugal pumps based on Archimedean spiral kinematics and energy conservation principles. Conventional pump theory commonly relies on the Euler head equation, which predicts a linear dependence between head and flow rate. However, experimental observations often show systematic deviations from this linear trend, particularly at off-design operating conditions. In this work, the flow kinematics within the impeller are analyzed using simple physical models and a trajectory-based interpretation of fluid motion. The analysis reveals that the angular velocity of the fluid relative to the impeller decreases linearly with the flow ratio, leading to a slip relationship expressed as ω′/ω=1−q/Q. From this kinematic framework, a quadratic head–flow relationship emerges in which the pump head varies with the square of the term 1−q/Q. The model is supported by trajectory analysis of 11 representative flow paths within an Archimedean spiral impeller. The resulting formulation provides a physically intuitive description of pump behavior across the entire operating range and offers improved consistency with observed head–flow characteristics.
Magnetic liquid double suspension bearing (MLDSB) combines electromagnetic suspension with hydrostatic support to achieve high load capacity and stability under medium-speed, heavy-load conditions. When the electromagnetic system fails, the hydrostatic unit temporarily levitates the rotor, but its performance is governed by oil viscosity. This study is aimed at quantifying how viscosity influences rub-impact dynamics in MLDSB. A three-degree-of-freedom nonlinear model was established and solved by a fourth-order Runge-Kutta scheme. Parametric bifurcation analyses were performed over speed ratio 0.8-1.05, eccentricity ratio 0.15-0.40, initial pressure 0.1-1.6 bar, and bias current 0.5-2.0 A. Key dynamic features including bifurcation characteristics, phase path, and Poincare mapping were validated on a purpose-built MLDSB test bench. Results reveal a critical viscosity window (mu approximate to 3-4 & times; 10-3 Pa & centerdot; s) below which the first period-doubling bifurcation occurs, followed by alternating multiperiodic and chaotic motion. Higher eccentricity or speed ratio broadens the bifurcation interval, whereas increased initial pressure mitigates chaos. These findings provide design guidelines for viscosity selection and control strategies to enhance the fault-tolerant performance of MLDSB under rub-impact conditions.
Cylindrical hydrodynamic bearings are essential components of rotating machines used in applications ranging from small motors to large turbo generators. They operate based on the principle of a thin oil film that separates the rotating shaft from the bearing, preventing mechanical contact between the surfaces. Studies on cylindrical bearings usually consider an adequate supply of lubricant. However, it is crucial to analyze the phenomenon of oil starvation to understand the influence of lubrication conditions on bearing performance. Researchers have developed various numerical models to represent the behavior of hydrodynamic bearings; these models are able to determine the supporting pressure by solving the Reynolds equation. The present work used the so-called p - theta formulation and energy equation to represent the dynamic behavior of a cylindrical bearing. A journal bearing was designed and manufactured for experimental purposes, capable of being instrumented to monitor variables that will be compared with simulation results. Sixteen thermocouple sensors, equally spaced along the circumferential length of the bearing, were used to monitor the oil film temperature. A similar scheme was adopted for pressure data acquisition, with 16 pressure transducers. The obtained results demonstrated that the resulting thermohydrodynamic model accurately represents the dynamic behavior of the cylindrical bearing.
This work presents and validates a direct analytical methodology for the parametric hydrodynamic design of Pelton rotors. The proposed approach combines a one-dimensional theoretical framework for defining global geometric rotor parameters with an inductive method for generating bucket geometry, formalized from a comprehensive mapping of a high-efficiency commercial reference bucket. The reliability of this integrated design methodology is assessed via high-fidelity unsteady Reynolds-averaged Navier-Stokes (URANS) computational fluid dynamics (CFD) simulations, coupled with the volume of fluid (VOF) multiphase model and the k - omega SST turbulence model on a rotating five-bucket domain. A theoretical efficiency of 93.4% was estimated, closely aligning with the 91.4% total efficiency obtained from the CFD model. Furthermore, simulations under part-load conditions demonstrated the designed rotor ' s high performance, with efficiency remaining above 85% in all off-design scenarios. Finally, the proposed methodology provides a practical, reproducible, and computationally efficient tool for generating high-performance geometries, serving as a robust foundation for integrating into future optimization workflows, fluid-structure interaction analyses, and advanced research in Pelton turbine design.
Advanced gas turbines play a crucial role in power generation, operating at turbine inlet temperatures exceeding 1200 degrees C to maximize efficiency and output. While nickel-based superalloys provide structural integrity, their performance is limited at temperatures above 1250 degrees C, necessitating the use of advanced cooling strategies. This study employs response surface methodology (RSM) to systematically analyze and optimize cooling hole configurations, enhancing thermal management in high-temperature environments. Existing configurations prove inadequate for next-generation gas turbines operating at 1400 degrees C with cooling air at 400 degrees C. Through predictive modeling, an optimal configuration is identified, characterized by a blade height of 300 mm, 45 holes with a diameter of 2.0 mm, and a spacing of 4.75 mm, which effectively reduces metal temperatures to below 1250 degrees C. This optimized design significantly improves cooling efficiency and mitigates thermal hotspots, offering a viable solution for high-temperature turbine applications. The findings from this study offer a practical and scalable solution for thermal management in high-performance gas turbines, supporting the advancement of turbine technology capable of operating under more demanding thermal conditions.
