On higher‐order mixed FEM for low Mach number flows: application to a natural convection benchmark problem

Heuveline, Vincent

doi:10.1002/fld.454

Cited by 52 publications

(50 citation statements)

References 32 publications

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“…1 shows the Mach number isolines (color shading) along with the streamline contours for a Raleigh number of 10 6 . This agrees very closely with the results obtained by (Heuveline, 2003) as well as those obtained assuming strictly incompressible flow with the Boussinesq approximation. Note, however, that if we changed the temperatures, e.g.…”

Section: Strictly Incompressible Examplesupporting

confidence: 92%

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Progress in the Development of Compressible, Multiphase Flow Modeling Capability for Nuclear Reactor Flow Applications

Berry¹,

Saurel²,

Petitpas³

et al. 2008

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8 MotivationIn nuclear reactor safety and optimization there are key issues that rely on in-depth understanding of basic two-phase flow phenomena with heat and mass transfer. Within the context of multiphase flows, two bubble-dynamic phenomena -boiling (heterogeneous) and flashing or cavitation (homogeneous boiling), with bubble collapse, are technologically very important to nuclear reactor systems. The main difference between boiling and flashing is that bubble growth (and collapse) in boiling is inhibited by limitations on the heat transfer at the interface, whereas bubble growth (and collapse) in flashing is limited primarily by inertial effects in the surrounding liquid. The flashing process tends to be far more explosive (and implosive), and is more violent and damaging (at least in the near term) than the bubble dynamics of boiling. However, other problematic phenomena, such as crud deposition, appear to be intimately connecting with the boiling process. In reality, these two processes share many details.Flashing occurs in flowing liquid systems when the pressure falls sufficiently low in some region of the flow, reaching a metastable state where the temperature is higher than the saturated one at the reduced pressure of this expanded state. Then the superheated liquid releases its metastable energy (stored as internal energy) very quickly, even explosively, producing either pure vapor (bubble) or liquid-vapor mixture at high velocity, [2]. Expansion effects in nuclear reactor systems are often due to geometrical effects, as for example in nozzles where flashing appears at locations where the pressure is relatively low and the liquid superheated. In the case of twophase blowdown (from the superheated liquid state), bubble collapse is usually not important, but the flashing of superheated liquid strongly influences critical flow rates. In other cases, besides the performance limitations which this cavitation may cause in flow systems, subsequent bubble collapse may be responsible for damage to nearby solid surfaces.Many nuclear reactor applications rely on convective nucleate boiling to efficiently remove high heat fluxes from heated surfaces. Nucleate boiling is a very effective heat transfer mechanism, however it is well known that there exists a critical value of the heat flux at which nucleate boiling transitions to film boiling (departure from nucleate boiling (DNB) and boiling crisis), a very poor heat transfer mechanism. In most practical applications it is imperative to maintain the operating heat flux below such critical value, which is called the Critical Heat Flux (CHF). In this case, the presence of a nearby solid surface is necessary for the rapid supply of the latent heat inherent in the phase change. The presence of these surfaces is known to modify the flow patterns and other characteristics of these multiphase flows, and therefore must be interactively coupled with analyses of these phenomena. And again, as mentioned above, DNB is believed to play an integral role in performance degradatio...

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Section: Strictly Incompressible Examplesupporting

confidence: 92%

“…We consider the thermally driven, circulatory flow of air in an upright square domain (Heuveline, 2003). The two horizontal walls are defined as no-slip, adiabatic solid walls and the two vertical walls are defined as no-slip isothermal walls, 606 K on the left wall and 594 K on the right.…”

Section: Strictly Incompressible Examplementioning

confidence: 99%

Progress in the Development of Compressible, Multiphase Flow Modeling Capability for Nuclear Reactor Flow Applications

Berry¹,

Saurel²,

Petitpas³

et al. 2008

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“…The flow solver used in this work is an academic high-order code based on the low Mach number approximation [17,18]. This code (SAILOR) may be used for solving a wide range of flows under various conditions, varying from isothermal and constant density to situations with considerable density and temperature variations.…”

Section: Les Solvermentioning

confidence: 99%

Parametric Analysis of Excited Round Jets - Numerical Study

Tyliszczak

Geurts

2014

Flow Turbulence Combust

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A computational analysis of excited round jets is presented with emphasis on jet bifurcation phenomenon due to superposition of axial and flapping forcing terms. Various excitation parameters are examined including the amplitudes of the forcing, their frequencies and phase shift. It is shown that alteration of these parameters significantly influences the spatial jet evolution. This dependence may be used to control the jet behaviour in a wide range of qualitatively different flow structures, starting from a modification of the spreading rate of a single connected jet, through large scale deformation of an asymmetric jet, onto jet bifurcation leading to a doubly and even triply split time-averaged jet, displaying different strengths and locations of the branches. We establish that: (i) jet splitting is possible only when the amplitudes of the forcing terms are comparable to or larger than the level of natural turbulence; (ii) the angle between the developing jet branches can be directly controlled by the frequency of the axial forcing and the phase shift between axial and flapping forcing. An optimum forcing frequency is determined, leading to the largest spreading rate.

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“…A duality-based a posteriori error analysis is developed for the conforming hp Galerkin finite element approximation [4]. …”

Section: Heuveline Heidelberg University Germanymentioning

confidence: 99%

Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 2. Contributions to the June 2004 conference

et al. 2005

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Abstract. In the second part of the paper, we compare the solutions produced in the framework of the conference "Mathematical and numerical aspects of low Mach number flows" organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.Mathematics Subject Classification. 65M50, 76M10, 76M12, 76M20, 76M22, 76R10.

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On higher‐order mixed FEM for low Mach number flows: application to a natural convection benchmark problem

Cited by 52 publications

References 32 publications

Progress in the Development of Compressible, Multiphase Flow Modeling Capability for Nuclear Reactor Flow Applications

Progress in the Development of Compressible, Multiphase Flow Modeling Capability for Nuclear Reactor Flow Applications

Parametric Analysis of Excited Round Jets - Numerical Study

Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 2. Contributions to the June 2004 conference

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