An adaptation of the low Mach number approximation for supercritical fluid buoyant flows

Accary, Gilbert; Raspo, Isabelle; Bontoux, Patrick; Zappoli, Bernard

doi:10.1016/j.crme.2005.03.004

Cited by 28 publications

(14 citation statements)

References 12 publications

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“…As the heat flux becomes infinite at a point source, we consider the heat flux to originate from a circular fluid region centered at (0.5H, 0.25H ) of In addition to the Navier-Stokes equations, a transport equation of a passive scalar Q is implemented with a diffusion coefficient that is one thousand times less than the thermal diffusivity of the fluid. This passive scalar Q is thus the additional tracer that is simply advected by the flow, as mentioned above (see also [3]). The same source term as given by Eq.…”

Section: Stationary Plume In a Supercritical Fluidmentioning

confidence: 96%

“…Two-dimensional numerical simulations have demonstrated [2] the interaction between convection and stratification in a supercritical fluid in configurations usually encountered in the atmosphere. An additional component was used as a tracer in the fluid flow (see below for details, and [3] for the numerical method).…”

Section: A Reduced Model Of Geophysical Flowsmentioning

confidence: 99%

“…The numerical method that has been used to perform the numerical experiment is accurate to second order in space and to third order in time. It was adapted from [20], with a vertically stratified initial density field being introduced [3]. It has been thoroughly validated [1], and the mesh size for a grid-independent solution depends on the heating of the bottom plate, with the finest being (100 × 140) nodes.…”

Section: Reverse Transition To Stability Through the Schwartzschild Linementioning

confidence: 99%

See 2 more Smart Citations

Rayleigh–Bénard and Rayleigh–Taylor Instabilities

Zappoli

Beysens

Garrabos

2014

Heat Transfers and Related Effects in Supercritical Fluids

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The stability of a near-critical fluid is studied in the Rayleigh-Bénard configuration: the fluid is heated from below or presents itself as a layer of a heavier fluid is on top a lighter one. The Rayleigh-Bénard instability is first addressed showing a double Rayleigh-Bénard situation thanks to the presence of the piston effect. The stability criterium is then discussed and some similarities with geophysical flows described. In the case of a warm fluid layer topped by a cooler one, it is shown that the thermal diffusion layer behaves as an interface and gives rise to a Rayleigh-Taylor like instability. Thermo-acoustic oscillations at the Rayleigh-Bénard threshold are described. They come from the interaction between thermal plumes with the thermostated, horizontal upper wall. Rayleigh-Bénard Instability Rayleigh and Schwarzschild CriteriaWhen a square cavity containing a fluid is initially heated from the side, there is fluid motion for any value of the thermal gradient; the configuration is said to be unconditionally unstable since a vanishingly slow motion exists for a vanishingly small temperature gradient. When the cavity is initially heated from below, the configuration is said to be conditionally stable: for small and steady temperature differences between the bottom and top plates, the fluid initially remains at rest, and heat is transported by diffusion; for increasing values of the temperature gradient, the fluid suddenly starts to move at a given threshold value of the temperature gradient. In this case, internal motion starts within the fluid due to buoyancy, which attempts to even out the temperature throughout the sample. However, this motion is hindered by the density and pressure stratification of the fluid and dissipative processes. Usually, the effect of one of these two factors on the onset of convection is analyzed, and this leads to either the Rayleigh criterion or the Schwarzschild criterion, both of which B. Zappoli et al., Heat Transfers and

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Section: Stationary Plume In a Supercritical Fluidmentioning

confidence: 96%

Section: A Reduced Model Of Geophysical Flowsmentioning

confidence: 99%

Section: Reverse Transition To Stability Through the Schwartzschild Linementioning

confidence: 99%

See 1 more Smart Citation

Rayleigh–Bénard and Rayleigh–Taylor Instabilities

Zappoli

Beysens

Garrabos

2014

Heat Transfers and Related Effects in Supercritical Fluids

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“…In the last decade, numerous numerical works have been devoted to the modeling of supercritical fluids (SCF) [1,2,3,4,5,6,7], especially near their gasliquid critical point. In fact, such fluids exhibit quite unusual properties, behaving as highly expandable gases with liquid-like density.…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Algorithm for Low Mach Number Supercritical Fluids

Ouazzani

Garrabos

2008

International Symposium on Advances in Computational Heat Transfer

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A new algorithm has been developed to compute low Mach Numbers supercritical fluid flows. The algorithm is applied using a finite volume method based on the SIMPLER algorithm. Its main advantages are to decrease significantly the CPU time, and the possibility for supercritical fluid flow modelisation to use other discretisation methods (such as spectral methods and/or finite differences) and other algorithms such as PISO or projection. It makes it possible to solve 3D problems within reasonable CPU time even when considering complex equations of state. The algorithm is given after first a brief description of the previously existing algorithm to solve for supercritical fluids. The side and bottom heated near critical carbon dioxide filled cavity problems are respectively solved and compared to the previously obtained results.

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“…To overcome the Boussinesq's approximation limitations in the case of perfect gas the key strategy has been to introduce an acoustic filtering of the compressible Navier-Stokes equations along with the Low-Mach-Number assumption [3,4,5]. This kind of algorithms has also been successful to compute natural convection flows of supercritical fluids close to critical point [6]. On the other hand for the liquid cases and more especially liquid water flows, up to the authors best knowledge there is no Low Mach Number approximation that has been convincingly combined to any liquid equation of state.…”

Section: Introductionmentioning

confidence: 99%