Constant-flow regulators are widely used in compact hydraulic systems to maintain stable flow rates under varying supply pressures. In elastomer-based regulators, pressure-induced deformation of a compliant element modifies the effective throttling area and thereby regulates hydraulic resistance. Predictive modeling of this behavior is challenging because the coupled deformation-flow process involves geometric nonlinearity, pressure-dependent contact conditions, and evolving flow restriction geometry. This study presents an experimentally calibrated reduced-order model for predicting the flow-pressure characteristics of elastomer-based constant-flow regulators used in solenoid inlet valves. The formulation combines an orifice-based hydraulic representation with a lumped-parameter energy model of elastomer deformation that determines discrete pillar loading configurations governing the effective throttling gap geometry. The deformation of the elastomer element is represented by equivalent indentation and tensile stiffness parameters identified through targeted experiments using a single adjustable regulator specimen. The modeling framework is applied to determine the pillar height configuration required to achieve a target flowrate of 7 L/min over an operating pressure range of 1-10 bar. Model predictions agree with experimental measurements within +/- 5% across the regulation regime. The proposed reduced-order formulation provides a computationally efficient alternative to detailed CFD-FEM simulations for engineering analysis and design of elastomer-based passive flow regulators.
This study aims to clarify the internal flow characteristics and mechanisms of stepped labyrinth seals and to accurately analyze the effects of structural parameters on the flow field and leakage characteristics. This paper conducts numerical simulations of the complex three-dimensional flow field and validates the results against experimental test data. Furthermore, the flow characteristics and sealing performance of stepped and straight-through labyrinth seals are compared. Based on an orthogonal design, a sensitivity analysis of the key structural parameters is conducted, and a predictive model for the leakage discharge coefficient is developed. The results show that the jet exiting the seal clearances is blocked as it impinges on the vertical step wall in stepped labyrinth seals. The resulting complex vortices, step-induced blockage, and flow detour collectively increase energy dissipation of the leakage flow. The distribution of flow losses is approximately uniform in the clearance regions of the stepped labyrinth seal. Under the design condition, the stepped labyrinth seal exhibits a 127.7% higher seal pressure drop and a 33% lower discharge coefficient compared with the straight-through labyrinth seal. In stepped labyrinth seals, the throttling effect of each clearance- chamber stage remains essentially uniform. Among the structural parameters of stepped labyrinth seals, the number of steps has the most significant influence on the leakage characteristics, with its effect being approximately twice that of the radial clearance. In contrast, the influence of the labyrinth chamber area is relatively minor. Within the investigated range, increasing the number of steps by one can result in at least a 20% increase in seal pressure drop and an 11%-24% decrease in the discharge coefficient. A discharge coefficient model for stepped labyrinth seals is developed in this study. Within the validation range, the maximum prediction error is 1.59%.
Enhancing compressor loading through unsteady mechanisms has long been of interest. Based on unsteady numerical simulations of the TA36 low-speed axial compressor stage, this study investigates wake vortex shedding to clarify the mechanism of unsteady aerodynamic effects under different rotor-stator spacing conditions. The results show that, at small rotor-stator spacings, wake vortex shedding occurs in both the spanwise and streamwise directions. Spanwise shedding is caused by the misalignment between the rotor trailing edge and stator leading edge, and it periodically influences the stator suction-side flow and suppresses corner separation. Streamwise shedding is induced by the stator leading-edge pressure potential, forming periodic vortices within the stator passage at the blade-passing frequency. To quantify their aerodynamic effects, two circulation-based correlations are established. One relates the relative circulation of the spanwise shedding vortex to the corner-loss coefficient, and the other links the circulation of the streamwise shedding vortex to the total pressure rise increment. These correlations provide a quantitative connection between instantaneous shed-vortex circulation and time-averaged compressor performance. Under the present conditions, the unsteady effects lead to a total pressure rise coefficient gain of up to 0.03 and an efficiency increase of up to 2.90 percentage points. This study provides a circulation-based quantitative framework for interpreting unsteady aerodynamic effects in axial compressor stages.
Impinging jet atomizers are essential in engineering applications, where two liquid jets collide to form a dynamic sheet that breaks into droplets, completing the atomization process. The sheet's properties (e.g., size, thickness, velocity, and geometry) are influenced by factors like impingement angle, jet velocity, and liquid properties. Since sheet formation occurs before droplet generation, modeling the sheet is critical for understanding the downstream atomization. The present work investigates the velocity distribution of a dynamic impinging sheet using experimental and theoretical approaches. Particle tracking velocimetry (PTV), combined with high-speed shadowgraph imaging, is used to measure the velocity. Experimental results of the velocity field, obtained for Reynolds numbers ranging from 362 to 430, show significant deviations from existing theoretical predictions. A revised model is proposed by incorporating friction effects at the air-sheet interface. Based on boundary layer theory in cylindrical coordinates, the new model adopts a unique boundary condition and a similarity variable to simplify and solve the governing equations numerically. The revised model predicts air boundary layer profiles and velocity distributions inside the sheet as functions of radial distance and azimuthal angle. The initial jet velocity profile, modeled as a free jet transitioning from Poiseuille flow, is also estimated. The revised model aligns more closely with experimental observations, identifying key parameters that influence sheet behavior. This study advances the understanding of impinging sheet dynamics, offering insights for improving atomization performance in practical applications.
This study investigates the hydrodynamic response of free-falling thick disks impacting a quiescent water surface, emphasizing how impact energy governs crown evolution, cavity dynamics, and energy dissipation. A systematic series of laboratory experiments was conducted with six disks of varying density ratios (rho d/rho w = 1.08-2.33), two aspect ratios (chi = 1.5 and 3), and four release heights (hr/do = 2.6-6.6), yielding a wide range of impact Froude numbers and dimensionless moments of inertia. High-speed imaging revealed that a distinct transition in flow regime occurs near hr/do = 4, where the morphology of the crown and the topology of the underwater cavity shift abruptly. Disks released below this threshold generated smooth, partially sealed crowns, while higher-energy impacts produced rough, fully sealed crowns accompanied by secondary jet formation and cavity oscillation. A critical normalized impact energy of Ei/Eo = 0.36 was identified as the minimum required for full crown sealing. Crown diameter and height at pinch-off scaled linearly with the impact Froude number, whereas crown height showed negligible dependence on release height. Gravity-driven disks exhibited shallower pinch-off depths and shorter collapse times than those of force-driven disks and spheres under equivalent conditions. Energy loss analysis indicated an inverse correlation between normalized dissipation and Froude number, with lower-energy impacts dissipating proportionally more energy. Different correlations were developed to relate the Froude number, dimensionless inertia, and energy dissipation to the observed crown and cavity characteristics, which can be utilized to enhance the current understanding of hydrodynamic impact behavior in finite-thickness bodies and provide predictive relationships useful for applications in marine, aerospace, and environmental engineering.
