Buoyancy-driven flows beyond the Boussinesq approximation: A brief review

Mayeli, Peyman; Sheard, Gregory J.

doi:10.1016/j.icheatmasstransfer.2021.105316

Cited by 67 publications

(20 citation statements)

References 63 publications

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“…The mass and momentum conservation equations are, respectively:

\nabla \cdot \langle \mathbf{u}\rangle =0\

\frac{\partial \langle \mathbf{u}\rangle }{\partial t}+\nabla \cdot (\langle \mathbf{u}\rangle \otimes \langle \mathbf{u}\rangle )=-\nabla \left(\frac{\langle p\rangle }{{\rho }_{a}}\right)+\frac{1}{{\rho }_{a}}\nabla \cdot \left(\boldsymbol{\tau }+{\boldsymbol{\tau }}_{\mathbf{t}}\right)+(\langle R\rangle +1)\ \mathbf{g}\,

where 〈...〉 denotes the LES space scale filter, u the velocity vector, t time, p pressure, τ the resolved stress tensor, τ t the sub‐grid scale (SGS) turbulent stress tensor, ρ the local density, R = ( ρ − ρ a )/ ρ a the relative density difference, and g the gravitational acceleration. The momentum equation is based on the Boussinesq approximation, that is, density variations are considered only in the buoyancy term (e.g., Gray & Giorgini, 1976; Mayeli & Sheard, 2021). Transport of salt was computed using the incompressible mass diffusion equation (Cantero et al., 2007),

\frac{\partial R}{\partial t}+\mathbf{u}\cdot \nabla R={\nabla }^{2}\left({\alpha }_{\text{eff}}R\right)

where α eff = υ/ Sc + υ t /Sc t is the effective diffusivity with Sc = υ/D being the Schmidt number and Sc t = υ t /K the turbulent Schmidt number.…”

Section: Methodsmentioning

confidence: 99%

“…where 〈...〉 denotes the LES space scale filter, u the velocity vector, t time, p pressure, τ the resolved stress tensor, τ t the sub-grid scale (SGS) turbulent stress tensor, ρ the local density, R = (ρ − ρ a )/ρ a the relative density difference, and g the gravitational acceleration. The momentum equation is based on the Boussinesq approximation, that is, density variations are considered only in the buoyancy term (e.g., Gray & Giorgini, 1976;Mayeli & Sheard, 2021). Transport of salt was computed using the incompressible mass diffusion equation (Cantero et al, 2007),…”

Section: Numerical Modelmentioning

confidence: 99%

See 1 more Smart Citation

Unconfined Plunging of a Hyperpycnal River Plume Over a Sloping Bed and Its Lateral Spreading: Laboratory Experiments and Numerical Modeling

Shi

Negretti

Chauchat

et al. 2022

Water Resources Research

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show abstract

“…The mass and momentum conservation equations are, respectively:

\nabla \cdot \langle \mathbf{u}\rangle =0\

\frac{\partial \langle \mathbf{u}\rangle }{\partial t}+\nabla \cdot (\langle \mathbf{u}\rangle \otimes \langle \mathbf{u}\rangle )=-\nabla \left(\frac{\langle p\rangle }{{\rho }_{a}}\right)+\frac{1}{{\rho }_{a}}\nabla \cdot \left(\boldsymbol{\tau }+{\boldsymbol{\tau }}_{\mathbf{t}}\right)+(\langle R\rangle +1)\ \mathbf{g}\,

\frac{\partial R}{\partial t}+\mathbf{u}\cdot \nabla R={\nabla }^{2}\left({\alpha }_{\text{eff}}R\right)

where α eff = υ/ Sc + υ t /Sc t is the effective diffusivity with Sc = υ/D being the Schmidt number and Sc t = υ t /K the turbulent Schmidt number.…”

Section: Methodsmentioning

confidence: 99%

Section: Numerical Modelmentioning

confidence: 99%

Unconfined Plunging of a Hyperpycnal River Plume Over a Sloping Bed and Its Lateral Spreading: Laboratory Experiments and Numerical Modeling

Shi

Negretti

Chauchat

et al. 2022

Water Resources Research

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show abstract

“…According to the Boussinesq equation, 36 the flow through the crack per unit length is where q 1 is the gas flow of fracture, b is the fracture width, μ is the gas viscosity, and is the pressure gradient.…”

Section: Development Of the Experimental Instrument And Methodsmentioning

confidence: 99%

Experimental Study to Quantify Fracture Propagation in Hydraulic Fracturing Treatment

Pei

Pan

et al. 2022

ACS Omega

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Hydraulic fracturing plays an important role in the commercial development of unconventional oil and gas, which is directly related to the production of oil and gas wells. An accurate evaluation is critical for hydraulic fracturing, but it is urgent to propose a quantitative assessment of hydraulic fracturing fracture propagation for realizing hydraulic fracturing fracture propagation and multiposition permeability measurement under an in situ stress environment. Herein, a true triaxial stress loading and permeability testing device was designed and fabricated, and a permeability evaluation model was established under various states, which can realize the accurate measurement of multiple faces and the total permeability of tight specimens before and after hydraulic fracturing. It can directly measure permeability under the conditions of the true triaxial fracture propagation experiment. The comparative experimental result shows that the new technique can quantitatively evaluate the fracture propagation experiment of true triaxial hydraulic fracturing. The overall permeability and the directional permeability of the five faces were obtained, and the fracture propagation was evaluated by comparing the change in permeability. The test permeability error rate is within ±10%. Furthermore, a more refined evaluation of hydraulic fracturing fracture propagation can be carried out based on the fracture observation and AE event results. The research results provide a new strategy for a more quantitative and refined evaluation of fracture propagation and help to optimize the parameters of hydraulic fracturing.

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“…By utilizing Boussinesq's (Mayeli and Sheard, 2021) and Roseland approximations (Chu et al, 2020), the governed partial differential equations can be formulated as follows (Asjad et al, 2022):…”

Section: Description Of the Problemmentioning

confidence: 99%

Comparative investigation of fractional bioconvection and magnetohydrodynamic flow induced by hybrid nanofluids through a channel

et al. 2023

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The functional effects of medications, such as those that slow down and calm the body, have been investigated for the polarized diffusion coefficient based on the subsequent increase through magnetism. This study examines generalized Mittag–Lefer kernel-based fractional derivatives in MHD Brinkman-type fluids under bioconvection that contain hybrid titanium dioxide (TiO2) and silver (Ag) nanoparticles with water (H2O) and sodium alginate (NaC6H7O6) as the base fluids. Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) fractional derivatives, which are two contemporary definitions of fractional-order derivatives with a memory effect, were used to explore the modified fractional model utilizing the Laplace transformation and certain numerical algorithms. The impacts of restrictions on various nanoparticles were investigated and graphically displayed. We observed that the volumetric fraction improvement controls the fluid velocity by slowing it down. The water-based hybrid nanofluid has a greater influence on the temperature and momentum fields than the sodium alginate-based hybrid nanofluid due to the physical characteristics of the explored nanoparticles and base fluids. Additionally, the memory effect causes a higher substantial value for the AB-fractional derivative of the velocity profile than the CF-fractional derivative.

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Buoyancy-driven flows beyond the Boussinesq approximation: A brief review

Cited by 67 publications

References 63 publications

Unconfined Plunging of a Hyperpycnal River Plume Over a Sloping Bed and Its Lateral Spreading: Laboratory Experiments and Numerical Modeling

Unconfined Plunging of a Hyperpycnal River Plume Over a Sloping Bed and Its Lateral Spreading: Laboratory Experiments and Numerical Modeling

Experimental Study to Quantify Fracture Propagation in Hydraulic Fracturing Treatment

Comparative investigation of fractional bioconvection and magnetohydrodynamic flow induced by hybrid nanofluids through a channel

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