Corresponding author: Aleksandra V. Voronina (AVVoronina@mephi.ru)

Academic editor: Boris Balakin

The paper considers the problem of selecting a turbulence model to simulate natural convection near the surface of a VVER-1000 fuel assembly unloaded from the reactor by computational fluid dynamics (^{13} to 3.28∙10^{14}. It has been shown that the best agreement with experimental data, with an average deviation not exceeding ~ 8%, is provided by the RNG

A long-term experience in testing fuel assemblies (

A repair and inspection bench for the VVER-1000 reactor FAs has been developed and is deployed at NPPs which makes it possible to examine closely the FAs, identify their form change, detect and remove leaky fuel elements, and perform eddy-current radioscopy of the fuel cladding (

Right after the VVER-1000

The convective layer formed near the

Numerical simulation based on

Hundreds of turbulence models have currently been developed of which none is however versatile. When there is a new item to be numerically simulated for convection, a problem therefore arises as to what particular turbulence model to select and how to estimate the confidence of the results obtained by simulation.

As a rule, the rationale for the turbulence model selection is provided through comparing the calculated data obtained using different models with experimental results. And the experiment can be conducted using the tested item as such or its model or the item’s convection processes which are physically close (identical) to same.

Literature does not contain experimental data on the parameters of natural convection near the surface of a VVER-1000

The paper presents the results of a

There is a great number of theoretical and experimental studies dealing with investigating the natural convection near a vertical heated surface. Since the phenomenon of natural convection is of most interest to scientists in calculation of structural elements and utility systems regarding the removal or supply of heat, many papers are concerned with studying the natural convection near a vertical surface uniformly heated in an air environment. Studies to investigate convection near a non-isothermal surface are much fewer. One of the earliest papers with published results from experiments to study laminar convection near a vertical surface with a constant heat flux in water is that by Lock and Trotter (

The experiments published in (

In a general form, the flow of a viscous liquid is described by a system of Navier-Stokes equations consisting of a mass conservation equation and the law of conservation of momentum (

where

There are three approaches to simulation of turbulent flows:

direct numerical simulation (DNS);

solution of systems of Reynolds-averaged equations (RANS);

large eddy simulation (LES) method.

Many studies were undertaken to simulate a free convective flow near a vertical heating surface for isothermal conditions (

The problem was simulated numerically in an unsteady two-dimensional statement. A flow was studied along a heat emitting plate of the height 1.5 m immersed in a static liquid (water) with the constant temperature _{∞}. The diagram of the computational region is presented in Fig.

Diagram of the computational region.

The initial conditions have the following form:

_{∞},

where ^{2}/s^{2}; ε is the dissipation rate of the turbulence kinetic energy, m^{2}/s^{3}; ω is the specific dissipation rate of the turbulence energy, s^{–1}; and _{∞} is the water temperature, °С.

Temperature conditions of the second kind were defined as the boundary conditions on the plate surface

as well as no-slip and impermeability conditions for the velocity

where λ is the wall material’s thermal conductivity; ^{2}; and

A symmetry condition meaning the equality to zero of the boundary-normal liquid motion velocity component and of the temperature and pressure gradients has been defined for areas

The following boundary conditions are defined on boundaries

_{∞},

_{∞}.

where _{∞} and _{∞} are the water pressure and temperature respectively.

The following

Models of the

Boussinesq approximation is used not infrequently to describe convective motion (

An equation solver, called Pressure-Based Solver, was used for solving. The Simple (Semi-Implicit Method for Pressure-Linked Equations) algorithm was used to calculate the velocity field coupling with pressure involving a counter-flow pattern of the second order accuracy (Second Order Up-wind) for the convective members in the momentum conservation equation, for the kinetic turbulent energy equation, and for the turbulent energy dissipation equation. The convergence of the solution was regarded to be achieved in events when the difference between iterations in solving continuity, momentum, energy, turbulent kinetic energy, and dissipation rate equations reached 1×10^{–6}.

Regular meshes condensing towards the heated wall were used for the calculations. Ansys Meshing was used as the mesh generator. The mesh model was built with regard for the key criteria that characterize its quality (ANSYS Fluent).

Convection was simulated for the conditions of two experiments the results of which are published in (^{2}; the water temperature was _{∞} = 33 °С; and the temperature profile in the boundary layer was recorded at a height of ^{2}; _{∞} = 23 °С; ^{2}, _{∞} = 23 °С;

Figs _{w} – _{∞} (where _{w} is the plate surface temperature) along the plate height for experiments 1 and 2 in (^{12} and for the full turbulence onset, Ra = 4∙10^{13}.

Excessive wall temperature in conditions of the experiment in (^{2}.

It can be seen from the figures that the results for all of the turbulence models used are close to the experimental results in the laminar region and predict satisfactorily the laminar-turbulent transition region (3∙10^{12} < Ra < 4∙10^{13}). In the developed turbulence region, Ra > 4∙10^{13}, the results of the calculations based on the Standard

Excessive wall temperature in conditions of the experiment in (^{2}.

Fig.

Temperature profile in the boundary layer in conditions of the experiment in (^{2}.

The greatest discrepancies between the experimental and calculated data fall on the region near the plate wall being in the limits of ~ 0.1 mm. Here, the calculated data exceeds that obtained in the experiment. The possible reason for such discrepancies is that the water temperature is hard to measure correctly in the immediate vicinity of the plate, since the temperature sensors perturb the structure of the convective flow viscous sublayer.

Table

Deviations of numerical simulation results from experimental data

Turbulence model | Average deviation of calculated data, % | Maximum deviation of calculated data, % |
---|---|---|

Standard k-ε | 11.64 | 26.38 |

RNG k-ε | 8.07 | 22.16 |

Realizable k-ε | 14.70 | 26.44 |

SST k-ω | 14.32 | 26.34 |

It can be seen from the table that the best result is achieved in the event of the RNG

Temperature profile in the boundary layer in conditions of the experiment in (^{2}.

Temperature profile in the boundary layer in conditions of the experiment in (^{2}.

The Ansys Fluent code was used for the

The simulation results were compared with the experimental data obtained earlier for the excessive temperature of the plate surface and the water temperature profiles in the turbulent boundary layer for the three heat flux density values: ~ 4.5, 19.5, and 28.7 kW/m^{2}. The comparison results have shown the following.

All turbulence models used give the calculation results which are close to the experimental values in the laminar region and predict satisfactorily the laminar-turbulent transition region.

To the exception of Standard

Therefore, it is recommended to use a two-parameter semi-empirical turbulence model, RNG

* Russian text published:Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2021, n. 1, pp. 83–94.