Experimental velocity study of non-Boussinesq Rayleigh-Bénard convection

Valori, Valentina; Elsinga, Gerrit E.; Rohde, M.; Tummers, M.J.; Westerweel, J.; Hagen, Tim van der

doi:10.1103/physreve.95.053113

Cited by 18 publications

(10 citation statements)

References 17 publications

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“…We use the correlation µ(cP) = 0.02141 × 10 247.8/(T (K)−140) ∼ 0.3654 [25]. The Boussinesq approximation originally expresses that (i ) density fluctuations result principally from thermal effects-analogous to dissolution here-rather than pressure effects, and (ii ) density variations are neglected except when they are coupled to gravity (i.e., in the buoyancy force, −ρ g) [38,39]. Under this approximation, density variations are small compared to velocity gradients and a divergence-free flow (∇ · v = 0) can be assumed.…”

Section: Formulationmentioning

confidence: 99%

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

2018

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We numerically examine solutal convection in porous media, driven by the dissolution of carbon dioxide (CO2) into water-an effective mechanism for CO2 storage in saline aquifers. Dissolution is associated with slow diffusion of free-phase CO2 into the underlying aqueous phase followed by density-driven convective mixing of CO2 throughout the water-saturated layer. We study the fluid dynamics of CO2 convection in the single aqueous-phase region. A comparison is made between two different boundary conditions in the top of the formation: (i) a constant, maximum aqueous-phase concentration of CO2, and (ii) a constant, low injection-rate of CO2, such that all CO2 dissolves instantly and the system remains in single phase. The latter model is found to involve a nonlinear evolution of CO2 composition and associated aqueous-phase density, which depend on the formation permeability. We model the full nonlinear phase behavior of water-CO2 mixtures in a confined domain, consider dissolution and fluid compressibility, and relax the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characteristics of spreading, mixing, and a dissolution flux in two-and three-dimensional media for both boundary conditions. We also revisit the scaling behavior of Sherwood number (Sh) with Rayleigh number (Ra), which has been under debate for porous-media convection. Our measurements from the solutal convection in the range 1, 500 Ra 135, 000 show that the classical linear scaling Sh ∼ Ra is attained asymptotically for the constant-concentration case. Similarly linear scaling is recovered for the constant-flux model problem. The results provide a new perspective into how boundary conditions may affect the predictive powers of numerical models, e.g., for both the short-term and long-term dynamics of convective mixing rate and dissolution flux in porous media at a wide range of Rayleigh numbers.

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Section: Formulationmentioning

confidence: 99%

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

2018

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“…(i) The characteristic velocity becomes asymmetric, as found in previous numerical [13,16,17] and experimental studies [25,26], and (ii) the shape of the velocity and temperature profiles inside the boundary layers changes due to temperature-dependent fluid properties.…”

Section: A Derivationmentioning

confidence: 56%

“…This is nontrivial and has so far not been done experimentally because Pr m andX are both intrinsic properties of a fluid. Previous experiments and simulations have been conducted at fixed T m with varyingX by changing and P m , thus causing also changes in Ra m and Pr m [11,14,17,19,25,26]. Manipulating the degree of the NOB effect in such a way always results also in a change of Ra m , which also changes the heat flux.…”

Section: Experimental Program and The Description Of The Setupmentioning

confidence: 99%

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Turbulent Rayleigh-Bénard convection under strong non-Oberbeck-Boussinesq conditions

2020

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We report on Rayleigh-Bénard convection with strongly varying fluid properties experimentally and theoretically. Using pressurized sulfur-hexafluoride (SF 6) above its critical point, we are able to make measurements at mean temperatures (T m) and pressures (P m) along Prandtl-number isolines in the (T, P) parameter space. This allows us to keep the mean Rayleigh-(Ra m) and Prandtl number (Pr m) constant while changing the temperature dependences of the fluid properties independently, e.g., probing the liquidlike or gaslike region that are left and right of the supercritical isochore. Hence, non-Oberbeck-Boussinesq (NOB) effects can be measured and analyzed cleanly. We measure the temperature at midheight (T c) as well as the global vertical heat flux. We observe a significant heat transport enhancement of up to 112% under strong NOB conditions. Furthermore, we develop a theoretical model for the global vertical heat flux based on ideas of Grossmann and Lohse (GL) in OB systems, adjusted for nonconstant fluid properties. In this model, the NOB effects influence the boundary layer and hence T c , but the change of the heat flux is predominantly due to a change of the fluid properties in the bulk, in particular the heat capacity c p and density ρ. Predictions from our model are consistent with our experimental results as well as with previous measurements carried out in pressurized ethane and cryogenic helium.

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“…For liquid working fluid cases, having large temperature differences between hot and cold surfaces and its effect on the viscosity along with applying the Boussinesq approximation for non‐gaseous mixtures may result in inaccurate results. For instance, Valori et al 25 used water and methanol as their working fluid beyond the validity of the Boussinesq approximation in a cubical Rayleigh‐Bénard convection cell. They found that the non‐Boussinesq effect manifests itself as an increase of time‐averaged horizontal velocity component close to the bottom wall of the cell and as a global top‐bottom asymmetry of the velocity field.…”

Section: Introductionmentioning

confidence: 99%

A centrifugal buoyancy formulation for Boussinesq‐type natural convection flows applied to the annulus cavity problem

Mayeli

Sheard

2020

Numerical Methods in Fluids

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Summary Traditionally, the Boussinesq approximation is adopted for numerical simulation of natural convection phenomena where density variations are supposed negligible except through the gravity term of the momentum equation. In this study, a recently developed formulation based on a Boussinesq approximation is presented in which the density variations are also considered in the advection terms. Extending density‐variations to the advection terms captures centrifugal effects arising from both bulk enclosure rotation and within individual vortices, and thus more accurate results are expected. In this respect, the results of the proposed formulation are compared against the conventional Boussinesq simulations and weakly compressible approximation in the concentric horizontal annulus cavity. A new relation is established which maps the magnitude of the non‐Boussinesq parameter of incompressible flow to the corresponding relative temperature difference of a compressible flow simulation which is in agreement with the maximum allowed Gay‐Lussac number to avoid unphysical density values. For comparison purposes, variations of different thermo‐fluid parameters including average and local Nusselt number, entropy generation, and skin friction up to Ra = 105 are computed. Results obtained under the proposed approximation agree with the classical Boussinesq approximation up to Ra = 103 for large non‐Boussinesq parameter corresponding to the large relative temperature difference, but at Ra = 105, computed thermo‐fluid parameters via the two approaches are not identical which justifies the inclusion of large Gay‐Lussac number for convection dominated regime in natural convection problems.

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Experimental velocity study of non-Boussinesq Rayleigh-Bénard convection

Cited by 18 publications

References 17 publications

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

Turbulent Rayleigh-Bénard convection under strong non-Oberbeck-Boussinesq conditions

A centrifugal buoyancy formulation for Boussinesq‐type natural convection flows applied to the annulus cavity problem

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