Numerical study of expansion tube problems: Toward the simulation of cavitation

Goncalves, Éric

doi:10.1016/j.compfluid.2012.11.019

Cited by 46 publications

(49 citation statements)

References 66 publications

(100 reference statements)

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“…The authors additionally combined the blending function with the expressions of source terms of Zwartṁ Goncalves presented in 2014 [32] the first version of transport equation which has a form that includes two quantities not used before: the speed of sound, c, and the propagation of acoustic waves without mass transfer, c wallis . These are connected through a following relationship…”

Section: The Development Paths Of Numericalmentioning

confidence: 99%

Review of numerical models of cavitating flows with the use of the homogeneous approach

Niedźwiedzka¹,

Schnerr²,

Sobieski³

2016

Archives of Thermodynamics

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The focus of research works on cavitation has changed since the 1960s; the behaviour of a single bubble is no more the area of interest for most scientists. Its place was taken by the cavitating flow considered as a whole. Many numerical models of cavitating flows came into being within the space of the last fifty years. They can be divided into two groups: multifluid and homogeneous (i.e., single-fluid) models. The group of homogenous models contains two subgroups: models based on transport equation and pressure based models. Several works tried to order particular approaches and presented short reviews of selected studies. However, these classifications are too rough to be treated as sufficiently accurate. The aim of this paper is to present the development paths of numerical investigations of cavitating flows with the use of homogeneous approach in order of publication year and with relatively detailed description. Each of the presented model is accompanied by examples of the application area. This review focuses not only on the list of the most significant existing models to predict sheet and cloud cavitation, but also on presenting their advantages and disadvantages. Moreover, it shows the reasons which inspired present authors to look for new ways of more accurate numerical predictions and dimensions of cavitation. The article includes also the division of source terms of presented models based on the transport equation with the use of standardized symbols. Boldface lower-case letters refer to vectors while boldface capital letters and Greek lowercase letters refer to matrices.

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Section: The Development Paths Of Numericalmentioning

confidence: 99%

Review of numerical models of cavitating flows with the use of the homogeneous approach

Niedźwiedzka¹,

Schnerr²,

Sobieski³

2016

Archives of Thermodynamics

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“…The model consists in three conservation laws for mixture quantities and an additional equation for the void ratio (Goncalves 2013). We present below the inviscid one-dimensional equations, expressed with the vector of variables w = (ρ, ρu, ρE, α):…”

Section: A Four-equation Single-temperature Modelmentioning

confidence: 99%

“…Assuming the mass transfer is proportional to the divergence of the velocity, it is possible to develop a family of models (Goncalves 2013, Goncalves & Charriere 2014 in which the mass transfer is expressed as:ṁ…”

Section: Closure Relation For the Mass Transfermentioning

confidence: 99%

“…The number of variables to impose at boundaries is given by the number of positive characteristics. The characteristic relations obtained for the 4-equation system are (Goncalves 2013):…”

Section: Inlet and Outlet Boundary Conditionsmentioning

confidence: 99%

“…The vapour pressure is assumed to vary linearly with the temperature though the parameter dP vap /dT . Validations have shown the ability of such models to correctly simulate cavitation pockets in both water and freon R-114 (Goncalves 2013, Goncalves & Charriere 2014, Goncalves 2014, Charriere et al 2015, Goncalves & Zeidan 2015. In order to investigate thermal effects in LH 2 cryogenic cavitating flows, one-dimensional cavitation tube problems are proposed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical simulation of unsteady cavitation in liquid hydrogen flows

Goncalves

Zeidan

2017

IJESMS

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An unsteady cavitation model in liquid hydrogen flow is studied in the context of compressible, two-phase, one-fluid inviscid solver. This is accomplished by applying three conservation laws for mixture mass, mixture momentum and total energy along with gas volume fraction transport equation, with thermodynamic effects. Various mass transfers between phases are utilized to study the process under consideration. A numerical procedure is presented for the simulation of cavitation due to rarefaction and shock waves. Attention is focused on cavitation in which the simulated fluid is liquid hydrogen in cryogenic conditions. Numerical results are in close agreement with theoretical solutions for several test cases. The current numerical results show that liquid hydrogen flow can be accurately modeled using an accurate inviscid approach to describe the features of thermodynamic effects on cavitation.Keywords: Two-phase flow; heat and mass transfer; liquid and hydrogen, cavitation; homogeneous model; splitting techniques, inviscid simulation. Reference · · · Biographical notes: Eric Goncalvès is a Professor in the Aeronautical EngineeringSchool ISAE-ENSMA, Poitiers, France. Currently, he is the head of the Department Fluid Mechanics and Aerodynamics. His research interests are related to the modelling and the simulation of flows for which the density is variable such as compressible flow, two-phase flow and cavitation. Recent work include shock wave boundary layer interaction, thermal effects in cavitation and investigation of three-dimensional effects on cavitation pocket. Dia Zeidan is currently a Tenure-track Assistant Professor in the School of Basic Sciences and Humanities at the German Jordanian University, Amman, Jordan. His expertise is in the mathematical modelling and numerical simulations of multiphase fluid flow problems. Recent work also includes hyperbolicity and conservativity resolution related to two-phase flows equations in the context of the Riemann problem and simulations of such flows over a wide range of non-equilibrium behaviours.

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A compressible single‐temperature conservative two‐phase model with phase transitions

Spina

Vitturi

Romenski

2014

Numerical Methods in Fluids

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SUMMARYA model for multidimensional compressible two‐phase flow with pressure and velocity relaxations based on the theory of thermodynamically compatible system is extended to study liquid–gas flows with cavitation. The model assumes for each phase its own pressure and velocity, while a common temperature is considered. The governing equations form a hyperbolic system in conservative form and are derived through the theory of a thermodynamically compatible system. The phase pressure‐equalizing process and the interfacial friction are taken into account in the balance laws for the volume fractions of one phase and for the relative velocity by adding two relaxation source terms, while the phase transition is introduced into the model considering in the balance equation for the mass of one phase the relaxation of the Gibbs free energies of the two phases. A modification of the central finite‐volume Kurganov–Noelle–Petrova method is adopted in this work to solve the homogeneous hyperbolic part, while the relaxation source terms are treated implicitly. In order to investigate the effect of the mass transfer in the solution, a 1D cavitation tube problem is presented. In addition, two 2D numerical simulations regarding cavitation problem are also studied: a cavitating Richtmyer–Meshkov instability and a laser‐induced cavitation problem. Copyright © 2014 John Wiley & Sons, Ltd.

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Numerical study of expansion tube problems: Toward the simulation of cavitation

Cited by 46 publications

References 66 publications

Review of numerical models of cavitating flows with the use of the homogeneous approach

Review of numerical models of cavitating flows with the use of the homogeneous approach

Numerical simulation of unsteady cavitation in liquid hydrogen flows

A compressible single‐temperature conservative two‐phase model with phase transitions

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