On the applicability of Stokes’ hypothesis to low-Mach-number flows

Papalexandris, Miltiadis

doi:10.1007/s00161-019-00785-z

Cited by 14 publications

(8 citation statements)

References 20 publications

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“…The Stokes' hypothesis is assumed. See Papalexandris for further details on the applicability of the Stokes' hypothesis to low Mach number flows 39 . The solved equations are presented below.…”

Section: Filtered Low-mach Number Equationsmentioning

confidence: 99%

Investigation of thermal large-eddy simulation approaches in a highly turbulent channel flow submitted to strong asymmetric heating

2021

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Section: Filtered Low-mach Number Equationsmentioning

confidence: 99%

Investigation of thermal large-eddy simulation approaches in a highly turbulent channel flow submitted to strong asymmetric heating

2021

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“…2),p stands for the sum of the second-order term of the low-Mach-number expansion of the pressure and the bulk viscous pressure [23,24]. The deviatoric part of the viscous stress tensor,τ , is given below where I is the identity matrix andμ the dynamic viscosity:…”

Section: Governing Equations and Numerical Set-upmentioning

confidence: 99%

Numerical simulations of turbulent thermal convection with a free-slip upper boundary

Hay

Papalexandris

2019

Proc. R. Soc. A.

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In this paper, we report on direct numerical and large-eddy simulations of turbulent thermal convection without invoking the Oberbeck–Boussinesq approximation. The working medium is liquid water and we employ a free-slip upper boundary condition. This flow is a simplified model of thermal convection of water in a cavity heated from below with heat loss at its free surface. Analysis of the flow statistics suggests similarities in spatial structures to classical turbulent Rayleigh–Bénard convection but with turbulent fluctuations near the free-slip boundary. One important observation is the asymmetry in the thermal boundary layer heights at the lower and upper boundaries. Similarly, the budget of the turbulent kinetic energy shows different behaviour at the free-slip and at the lower wall. Interestingly, the work of the mean pressure is dominant due to the hydrostatic component of the mean-pressure gradient but also depends on the density fluctuations which are small but, critically, non-zero. As expected the boundary-layer heights decrease with the Rayleigh number, due to increased turbulence intensity. However, independent of the Rayleigh number, the height of the thermal boundary layer at the upper boundary is always smaller than that on the lower wall.

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“…The reader is referred to Ref. 60 for precise explanations on the applicability of the Stokes' hypothesis to low Mach number flows. A source term is introduced in the energy equation to allow the study of different axial locations in a solar receiver by modifying the fluid temperature.…”

Section: Filtered Low-mach Number Equationsmentioning

confidence: 99%

Direct simulations and subgrid modeling of turbulent channel flows asymmetrically heated from both walls

2021

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Thermal Large-Eddy Simulations (T-LES) and a Direct Numerical Simulation (DNS) are carried out in a bi-periodical channel with hot and cold wall temperatures of respectively 900 K and 1300 K. The mean fluid temperature is lowered below the cold wall temperature thanks to a heat source, resulting in a both walls heating of the fluid. The hot and cold wall friction Reynolds numbers are respectively 640 and 1000. These conditions are representative of the working conditions of gas-pressurized solar receiver of solar power tower. The Low Mach number Navier-Stokes equations are solved. The coupling between the dynamic and the temperature effects is considered. In the T-LES, both the momentum convection and the density-velocity correlation subgrid terms are modeled. Functional models, structural models, and mixed models are considered. A tensorial version of the Anisotropic Minimum-Dissipation (AMD) model is also investigated. The Quick and the second-order centered schemes are tested for the discretization of the mass convection term. Firstly, an overview of the results of 17 T-LES on first-and second-order statistics is proposed. It permits selecting 6 of these simulations for a detailed analysis consisting in the investigation of profiles of mean quantities and turbulent correlations. A particular attention is given to the wall heat fluxes because it is a critical point for the design and the optimization of solar receivers. Overall, the first-order statistics are better predicted than the second-order's. The tensorial AMD model takes advantage of the classical AMD model properties and better reproduces the anisotropy of the flow thanks to its formulation. The tensorial AMD model produces the most reliable and efficient results among the considered models.

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On the applicability of Stokes’ hypothesis to low-Mach-number flows

Cited by 14 publications

References 20 publications

Investigation of thermal large-eddy simulation approaches in a highly turbulent channel flow submitted to strong asymmetric heating

Investigation of thermal large-eddy simulation approaches in a highly turbulent channel flow submitted to strong asymmetric heating

Numerical simulations of turbulent thermal convection with a free-slip upper boundary

Direct simulations and subgrid modeling of turbulent channel flows asymmetrically heated from both walls

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