A Hybrid Model for Simulation of Cavitating Flows (original) (raw)
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Discrete Bubble Modeling of Unsteady Cavitating Flow
International Journal for Multiscale Computational Engineering, 2006
A discrete vapor bubble model is developed to simulate unsteady cavitating flows. In this model, the mixed vapor-liquid mixture is modeled as a system of pure phase domains (vapor and liquid) separated by free interfaces. On the phase boundary, a numerical solution for the phase transition is developed for compressible flows. This model is used to study the effect of cavitation bubbles on atomization, i.e., the breakup of a high-speed jet and spray formation. The major conclusion is that a multiscale (three-scale) model is sufficient to achieve agreement with quantitative macroscale flow parameters, such as spray opening angle and spray volume fraction or density, or as a qualitative measure, the occurrence of spray formation. The authors believe this to be the first numerical study of the atomization process at such a level of detail in modeling of the related physics.
2020
Der Hauptzweck dieser Studie ist es, ein profundes Wissen über die Wechselwirkung zwischen Kavitation und Luftfreisetzung zu erlangen, indem das komplexe Feld der Blasendynamik und die damit verbundenen Dampf- und Luftflüsse unter Nichtgleichgewichtsbedingungen untersucht werden. Um dieses Ziel zu erreichen, werden die maßgeblichen Differentialgleichungen numerisch gelöst, einschließlich der Erhaltung von Masse, Impuls und Energie innerhalb und außerhalb der Blase. Die gesamte Thermodynamik wurde auf der Grundlage validierter experimenteller Datensätze in das Modell implementiert, sodass das Modell für verschiedene Flüssigkeiten und Flüssigkeitsgemische verwendet werden kann. Dieses Modell mit detaillierter Erklärung der Transportprozesse und der hohen Genauigkeit kann auf die CFD-Codes angewendet und als geeignetes Kavitationsmodell verwendet werden.
A compressible multi-scale model to simulate cavitating flows
Journal of Fluid Mechanics
We propose a compressible multi-scale model that (i) captures the dynamics of both large vapour cavities (resolved vapour) and micro-bubbles (unresolved vapour), and (ii) accounts for medium compressibility. The vapour mass, momentum and energy in the compressible homogeneous mixture equations are explicitly decomposed into constituent resolved and unresolved components that are independently treated. The homogeneous mixture of liquid and resolved vapour is tracked as a continuum in an Eulerian sense. The unresolved vapour terms are expressed in terms of subgrid bubble velocities and radii that are tracked in a Lagrangian sense using a novel ‘ kRkRkR - RPRPRP equation’ (k, constant multiple; R, bubble size; RP, Rayleigh-Plesset). The kRkRkR - RPRPRP equation is formally derived in terms of the pressure at a finite distance ( kRkRkR ) from the bubble while accounting for the effects of neighbouring bubbles; p(kR)p(kR)p(kR) may therefore be either a near-field or far-field pressure. The equation exactl...
Realizability improvements to a hybrid mixture-bubble model for simulation of cavitating flows
Computers & Fluids, 2018
Cavitating multi-phase flows include an extensive range of cavity structures with different length scales, from micro bubbles to large sheet cavities that may fully cover the surface of a device. To avoid high computational expenses, incompressible transport equation models are considered a practical option for simulation of large scale cavitating flows, normally with limited representation of the small scale vapour structures. To improve the resolution of all scales of cavity structures in these models at a moderate additional computational cost, a possible approach is to develop a hybrid Eulerian mixture-Lagrangian bubble solver in which the larger cavities are considered in the Eulerian framework and the small (subgrid) structures are tracked as Lagrangian bubbles. A critical step in developing such hybrid models is the correct transition of the cavity structures from the Eulerian mixture to a Lagrangian discrete bubble framework. In this paper, such a multi-scale model for numerical simulation of cavitating flows is described and some encountered numerical issues for Eulerian-Lagrangian transition are presented. To address these issues, a new improved formulation is developed, and simulation results are presented that show the issues are overcome in the new model.
A comparative study between numerical methods in simulation of cavitating bubbles
International Journal of Multiphase Flow, 2018
In this paper, the performance of three different numerical approaches in cavitation modelling are compared by studying two benchmark test cases to understand the capabilities and limitations of each method. Two of the methods are the well established compressible thermodynamic equilibrium mixture model and the incompressible transport equation finite mass transfer mixture model, which are compared with a third method, a recently developed Lagrangian discrete bubble model. In the Lagrangian model, the continuum flow field is treated similar to the finite mass transfer approach, however the cavities are represented by individual bubbles. Further, for the Lagrangian model, different ways to consider how the fluid pressure influences bubble dynamics are studied, including a novel way by considering the local pressure effect in the Rayleigh-Plesset equation. The first case studied is the Rayleigh collapse of a single bubble, which helps to understand each model behaviour in capturing the cavity interface and the surrounding pressure variations. The special differences between the Lagrangian and finite mass transfer models in this case clarify some possible origin for some limitations of the latter method. The second investigated case is the collapse of a cluster of bubbles, where the collapse of each bubble is affected by the dynamics of surrounding bubbles. This case confirms the importance of considering local pressure in the improved form of the Rayleigh-Plesset equation and illustrates the influence of the liquid compressibility for cavity modelling and appropriate capturing of the collapse pressure.
Numerical simulation and analysis of multi-scale cavitating flows
Journal of Fluid Mechanics, 2021
Cavitating flows include vapour structures with a wide range of different length scales, from micro-bubbles to large cavities. The correct estimation of small-scale cavities can be as important as that of large-scale structures, because cavitation inception as well as the resulting noise, erosion and strong vibrations occur at small time and length scales. In this study, a multi-scale cavitating flow around a sharp-edged bluff body is investigated. For numerical analysis, while popular homogeneous mixture models are practical options for large-scale applications, they are normally limited in the representation of small-scale cavities. Therefore, a hybrid cavitation model is developed by coupling a mixture model with a Lagrangian bubble model. The Lagrangian model is based on a four-way coupling approach, which includes new submodels, to consider various small-scale phenomena in cavitation dynamics. Additionally, the coupling of the mixture and the Lagrangian models is based on an improved algorithm that is compatible with the flow physics. The numerical analysis provides a detailed description of the multi-scale dynamics of cavities as well as the interactions between vapour structures of various scales and the continuous flow. The results, among others, show that small-scale cavities not only are important at the inception and collapse steps, but also influence the development of large-scale structures. Furthermore, a comparison of the results with those from experiment shows considerable improvements in both predicting the large cavities and capturing the small-scale structures using the hybrid model. More accurate results (compared with the traditional mixture model) can be achieved even with a lower mesh resolution.
Euler-Euler and Euler-Lagrange approaches to cavitation modelling in marine applications
CIMNE, 2011
Two different approaches to cavitation modelling are investigated in the paper. With the Euler-Euler approach vapour-volume fraction is computed based on a volume of fluid method in combination with a simple mass-transfer model for cavitation. Using an Euler-Lagrange approach, separate equations for bubble size and motion are solved for each of the bubbles/nuclei. Computed bubbles are subsequently mapped to an Eulerian field to obtain vapour-volume fraction of the Eulerian mixture field. Numerical results of a 2D hydrofoil and a propeller flow demonstrate strong parameter dependency for the Euler-Euler approach. Providing the correct (measured) initial bubble distribution, Euler-Lagrange techniques display a fair amount of predictive accuracy as demonstrated for a 2D hydrofoil.
Numerical Simulation of Cavitation Flows Based on Their Hydrodynamic Similarity
International Journal of Engine Research, 2006
Hydrodynamic similarity of cavitation flows in nozzles of different scales has been observed experimentally. In this paper a model of cavitation has been developed, taking into account the bubbly nature of cavitation and assuming local homogeneity of the vapour-liquid flow. The model of cavitation is built from correlations for evaporation and condensation, based on bubble dynamics theory, and an equation for the number density of cavitation bubbles, derived by assuming hydrodynamic similarity of cavitation flows. Compared with conventional models of cavitation, which fix the number density of cavitation bubbles, the present model takes into account the effect of liquid tension on the number density of active cavitation nuclei. The model has been implemented within the VECTIS computational fluid dynamics code and applied to the simulation of cavitating flows in nozzles.