Air Release and Cavitation Modeling with a Lumped Parameter Approach Based on the Rayleigh–Plesset Equation: The Case of an External Gear Pump

Abstract

In this paper, a novel approach for the simulation of cavitation and aeration in hydraulic systems using the lumped parameter method is presented. The presented approach called the Hybrid Rayleigh–Plesset Equation model is derived from the Rayleigh–Plesset Equation representative of bubble dynamics and overcomes several shortcomings present in existing lumped parameter based cavitation modeling approaches. Models based on static approximations do not consider the non-equilibrium effects of phase change on the system and incorrectly predict the system dynamics. On the other hand, the existing dynamic cavitation modeling strategies account for the non-equilibrium effects of phase change but express the evolution of phases through approximations of the Rayleigh–Plesset Equation (such as exclusion of nonlinear interactions in bubble dynamics), which often lead to physically unrealistic time-scales of bubble growth or dissolution. This paper presents a dynamic model for cavitation which is capable of predicting cavitation in hydraulic systems while preserving the nonlinear dynamics arising from the Rayleigh–Plesset Equation. The derived model determines the evolution of phases in terms of physically realizable parameters such as the bubble radius and the nuclei density, which can be estimated or determined experimentally. The paper demonstrates the effectiveness of the derived modeling approach with the help of numerical simulations of an External Gear Machine. Results from the simulations employing the proposed model are compared with an existing dynamic cavitation modeling approach and validated with experimental results over a range of dynamic parameters.

First attempt to determine the critical inlet pressure for aircraft pumps with a numerical approach that considers vapor cavitation and air aeration

“…Normally, the fluid is not chemically pure; thus, this boiling occurs over a range of pressures. According to Casoli et al 19 and Shah et al, 21 this study refers to the pressure at which cavitation begins as the ''high saturated vapor pressure'' (p hvap ) and the pressure at which it is complete as the ''low saturated vapor pressure'' (p lvap ). All air and gas is assumed to be released when the pressure decreases to less than p hvap .…”

“…The lumped parameter of continuum modeling methods can be used for producing sufficiently accurate results, and a careful study of the overall features of hydraulic machines or components can reduce computational costs. In this category, numerical solutions have been proposed by Edge and coworkers, 16,17 Berta et al, 18 Casoli et al, 19 Vacca and coworkers, 20,21 and SA Imagine. 22 However, in these classic lumped parameter approaches, the dynamic nature of the gaseous cavitation process has not been considered.…”

Анализ Особенностей Моделирования Процессов В Топливных Шестеренных Насосах Гтд

“…В классических методиках [1 -3] рекомендуется принимать линейное или гиперболическое распределение давления. Но, как показывают предварительные расчеты и анализ последних работ [4,5], первое предположение (линейное распределение) неверно. Такое распределение возможно лишь в том случае, когда шестерня находится концентрично с корпусом и по всей длине рабочего участка сохраняется постоянный зазор.…”

Modeling the Meshing Procedure of the External Gear Fuel Pump Using a CFD Tool

“…Several approaches exist today [3] for external gear pump modeling but the most commonly used are computational fluid dynamics (CFD) and lumped parameters models. Results of simulation using modeling with lumped parameters for external gear pump have been shown in article [4][5][6][7][8][9]. This approach uses the division of pump volume for control volumes in which fluid properties are assumed uniform and dependent on time only.…”