This study of leakage and reverse flow reveals why pressure, speed and trapped volume shape volumetric efficiency pump performance.
Efficiency gains in modern hydraulic systems no longer come from mechanical tweaks alone. As motor-driven pumps operate at higher pressures and broader speed ranges, hidden inefficiencies, particularly those tied to fluid dynamics, are beginning to dominate the energy equation. A new study shines a spotlight on these underappreciated losses, revealing how pressure, flow behaviour, and chamber design interact in ways that could either cripple or optimise performance.
Dr Yong Chen, a researcher at the School of Mechanical Engineering at Zhejiang University of Technology, led a study into how internal leakage, reverse flow, and oil compressibility influence volumetric efficiency in high-pressure, motor-driven two-dimensional (2D) piston pumps. The results point to pressure as a far more damaging factor than speed, with practical implications for both pump design and predictive modelling.
The research introduces a comprehensive model that incorporates axial and circumferential leakage, turbulent reverse flow, and the compressibility of hydraulic oil. Verified through experimental testing and co-simulation using AMESim and Simulink, the model showed strong agreement with real-world data across a pressure range of 1 to 28 MPa and speeds from 500 to 3000 r/min. Engineers may find particular interest in the identification of trapped volume as a key variable in volumetric efficiency pump performance. The full study is available here via DOI for engineers seeking the complete analysis.
Reverse flow, not leakage, is the silent efficiency killer
While axial leakage has long been regarded as a primary loss factor, the simulations suggest that reverse flow, particularly at high pressures, is a far greater source of inefficiency. Under a test condition of 3000 r/min and 28 MPa, reverse flow accounted for 56.21 per cent of all volumetric losses. Circumferential leakage contributed 43.35 per cent, while axial leakage made up just 0.44 per cent by comparison.
“Pressure had the most significant impact on volumetric efficiency, mainly due to its influence on reverse flow,” Chen said. “Rotational speed, in contrast, actually improved efficiency by proportionally reducing the effect of leakage.”
Reverse flow occurs when the piston chamber reconnects with the discharge window during a rotation cycle, allowing high-pressure oil to surge back into the chamber. This not only lowers outlet pressure but also delays oil delivery to the discharge side, creating pronounced dips in output flow. Simulations showed these flow losses increased with pressure, even when the reverse flow window remained fixed.
Why speed helps and pressure hurts
At lower pressures and higher speeds, the relative contribution of leakage and reverse flow to overall flow volume decreases. This is because higher rotational speed increases the theoretical flow rate faster than the growth in losses. As a result, volumetric efficiency improves despite higher turbulence.
Experimental testing confirmed these dynamics. At 500 r/min and 28 MPa, volumetric efficiency dropped to 64.81 per cent. At 3000 r/min under the same pressure, it reached 89.53 per cent. The highest model error occurred under these low-speed, high-pressure conditions, suggesting a need for refined discharge flow coefficients during the reverse phase.
The co-simulation model incorporated the fluid’s compressibility, which had a pronounced effect at higher pressures. As oil compresses, even mechanically correct flow volumes deliver less actual fluid output. This insight reinforces the need to model energy losses across multiple parameters, not just flow geometry.
Trapped volume and design optimisation
Of the design variables tested, trapped volume had the most significant effect on volumetric efficiency. By reducing the volume of oil confined within the piston chamber during dead angles, the team was able to decrease the total reverse flow.
“When we reduced trapped volume, efficiency improved markedly,” Chen said. “At 28 MPa and 3000 r/min, the difference between high and low trapped volume conditions was nearly 10 per cent in volumetric efficiency.”
This finding has implications for pump engineers working in compact or lightweight applications. These include aerospace and robotics, where minimising dead space can both reduce energy losses and improve system responsiveness.
A model for further refinement
The model developed in this study integrates equations for Poiseuille and Couette flow, turbulence thresholds via Reynolds numbers, and the IFAS model for oil compressibility. While volumetric efficiency pump predictions aligned closely with experimental results, the researchers noted that further refinement of the discharge window flow coefficient could improve accuracy at extreme conditions.
“Additional experimental data under high-pressure reverse flow is needed to fine-tune the model,” Chen said.
For now, the findings offer practical guidance for system designers. Speed helps, pressure hurts, and reverse flow, not just leakage, is where energy loss hides.
Engineers interested in the full equations, modelling parameters, and simulation results can access the complete study here via DOI.
