Buoyancy-affected backward-facing step flow with heat transfer at low Prandtl number

Niemann, Martin; Fröhlich, Jochen

doi:10.1016/j.ijheatmasstransfer.2016.05.137

Cited by 43 publications

(18 citation statements)

References 25 publications

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“…For instance, it can be clearly seen that increasing the heat flux results in a decrease of the recirculation zone directly downstream of the step. This is also reported in [8] and [68].…”

Section: Resultssupporting

confidence: 80%

A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step

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Stabile

Rozza

et al. 2021

Applied Mathematical Modelling

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A Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier-Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreementwith the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about 10 5 times faster than the RANS simulations that are performed on eight cores.

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“…For instance, it can be clearly seen that increasing the heat flux results in a decrease of the recirculation zone directly downstream of the step. This is also reported in [8] and [68].…”

Section: Resultssupporting

confidence: 80%

A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step

Star

Stabile

Rozza

et al. 2021

Applied Mathematical Modelling

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show abstract

“…However, a detailed study of Vreman [4] shows that it takes several hundred thousand time steps to achieve that target even in channel flow, where the statistical uncertainty is reduced also with the spatial averaging in two homogeneous directions. The corresponding number of time steps for the flows with a single homogeneous direction [17] is larger, and must be even larger in the geometries without homogeneous directions, where the only available type of averaging is averaging in time or ensemble averaging with several independent DNS runs performed in the same geometry.…”

Section: Uncertainties In Channel Flowmentioning

confidence: 99%

Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021

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In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

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“…Then, we consider a more complex configuration, such as the flow over a backward-facing step in forced convection. Additionally, for this configuration, several studies are present in the literature and DNS data are available for Re = 9610 and Pr = 0.088 [21,22]. Both configurations have been tested with the isotropic four-parameter turbulence model.…”

Section: Introductionmentioning

confidence: 99%

A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids

Barbi

Giovacchini

Manservisi

2021

Fluids

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Due to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier–Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations.

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Buoyancy-affected backward-facing step flow with heat transfer at low Prandtl number

Cited by 43 publications

References 25 publications

A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step

A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step

Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids

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