Conference Agenda

Direct Numerical Simulation (DNS) is regarded as an accurate and reliable approach to generate high-resolution data. However, due to the high computational costs involved, DNS investigations are typically limited to simple geometries and scaled-down conditions. In addition to providing an insight into the flow physics, fully-resolved DNS data is often used as a valuable reference for development, validation and improvement of Computational Fluid Dynamics (CFD) models. It is shown in this study, Under-resolved DNS (UDNS) based on spectral element methods (SEM) offers a more cost-effective alternative for generating high-quality reference data, while still providing sufficiently accurate flow statistics with significantly fewer degrees-of-freedom. Moreover, calculating the statistical quantities of the flow using UDNS does not require the additional effort involved in including sub-grid modeling contributions.

The resolution and accuracy of DNS and UDNS simulations are evaluated for an internally-heated natural convection flow at Rayleigh number of 10¹¹. Three UDNS simulations are performed at progressively coarser grid resolutions, thereby reducing the computational costs. It is shown that high-accuracy DNS can only be achieved at a grid resolution criteria of Δ/η_k ~ π. The UDNS approach is shown to achieve sufficiently accurate results for the mean and RMS velocity and temperature fields, as well as the turbulent kinetic energy budgets. Such UDNS statistical data can serve as a cost-effective alternative for reference for the validation of engineering CFD models. Furthermore, high-quality reference data can be obtained at more realistic flow conditions at higher Reynolds or Rayleigh numbers, where fully-resolved DNS may be infeasible.

Direct Numerical Simulations (DNS) are considered an accurate and reliable approach to generate high-resolution data. However, due to higher computational costs involved, DNS is generally performed in scaled and/or simpler geometry, which is representative of the real industrial-scale scenario. In order to represent the flow and heat transport between an array of fuel rods in a reactor core, simulations are conventionally performed in a smaller computational domain with periodic boundaries – often limited to a single interstitial subchannel space or domain around a single pin.

The present study examines DNS results for several different configurations – a periodic domain around a single pin, a single subchannel space, and arrays of 2×1 and 2×2 subchannels. It is shown quantitatively that the proximity of the periodic boundaries in the smaller domains significantly alters the flow physics. The periodic boundaries of the smaller domains, being highly-correlated, cannot faithfully represent the large-scale flow interaction across subchannels. Higher-order flow statistics, which may be used for development and validation of lower order models, are shown to be significantly affected by the periodic boundaries of the smaller domain. The distribution of wall shear stress and Nusselt number around the pin are also seen to be affected. A comparison of secondary flows in the different geometry representations is also presented. Flow pulsations in the narrow gap, typically associated with low P/D ratios, are also observed for the present P/D ratio of 1.326. The frequency of these pulsations is also shown to be affected by the size of the domain.

The supercritical water-cooled reactor is one of the proposed designs under further
study and development by the Generation IV International Forum (GIF). Like any
emerging technology, it presents technical challenges that must be resolved and better
understood. This paper addresses one of these challenges, from a thermal hydraulics
perspective, by focusing on the effect of idealised surface roughness on flow and heat
transfer in mixed convection of supercritical water.
To investigate this phenomenon, we perform six DNS simulations for fully developed,
asymmetrically heated channel flows. Three cases feature channel walls (top and
bottom) tiled with pyramids to represent an idealized surface roughness of Rt (peak-to-
valley height) 0.05δ (where δ is the half-channel height), while the remaining three have
smooth walls for comparison. We examine three flow conditions: (i) vertical flow with
mixed convection, (ii) stably-stratified mixed convection horizontal flow, and (iii) forced
convection. Constant temperature boundary conditions are applied at the channel walls,
with the hot side having a temperature greater than the pseudocritical temperature and
the cold wall temperature smaller than it. The temperature difference between the walls
is kept at 15 K. The aim of this work is to study the impact of roughness on heat transfer
deterioration and enhancement. Comparisons are made between mixed and forced
convection flows in both vertical and horizontal orientations, and the DNS data provided
will be useful for benchmarking.
The simulations employ the open-source DNS solver CHAPSim 2.0, with the prescribed
surface roughness modelled using an Immersed Boundary Method (IBM). This method
allows for the modelling of complex geometries by introducing a body force to the solid
nodes.

CFD codes used in the nuclear industry require an extensive validation, over a large range of thermal hydraulic conditions. In the context of PWR scenarios with shutdown of the primary pumps, buoyancy-affected flows in the core rod bundle can be encountered at low flow rate. However, scarce experimental data are available for this type of flow.

To address this issue, a Wall-Resolved LES (quasi-DNS using high-order schemes) of an upward flow within a heated rod bundle subjected to lateral power skews has been performed by Vicente Cruz et al.[1]. This numerical experiment of a complex turbulent mixed convection flow using a Boussinesq approximation, exhibiting cross flows, a mixing layer and a local re-laminarization, provides a highly accurate database for code validation.

In the present work, following the recommendations by Benhamadouche[2], the same configuration is investigated using code_saturne[3]. The predictions show good agreement with the reference database which demonstrates the capability of this in-house industrial code to carry out high-fidelity LES computations for this type of configuration.

[1] R. Vicente Cruz et al., “Numerical investigation of the mainly axial flow in mixed convection regime within tube bundles”, Proceedings of the 18th UK Heat Transfer Conference (2024)

[2] S. Benhamadouche, “On the use of (U)RANS and LES approaches for turbulent incompressible single phase flows in nuclear engineering applications”, Nuclear Engineering and Design, 312, pp. 2–11 (2017)

[3] code_saturne is an open-source incompressible CFD code developed by EDF (https://www.code-saturne.org/cms/web/).

Twisted elliptical tubes are a proposed heat transfer enhancement (HTE) for use in Molten Salt Reactors (MSRs) due to their enhanced thermal performance compared to plain tubes. The twisting ellipsoid geometry causes the fluid to swirl as it passes over the tubes, enhancing mixing and inducing turbulence at lower Reynolds numbers. This effect increases the overall convective heat transfer; however, this is at the cost of increased frictional pressure losses. In this study, the Nek5000 computational fluid dynamics (CFD) code is used to perform Large Eddy Simulations (LES) of external flow around twisted elliptical tube bundles. Simulations were performed for three different tube cross-sectional aspect ratios (maximum versus minimum diameter), Reynolds numbers of 1,000 and 7,000, and Prandtl numbers ranging from 1-25. The aim of this study is to further characterize the heat transfer phenomena seen around twisted elliptical tubes when varying the tube aspect ratio, which is a dependency that has not been historically accounted for. Previous work by the authors has investigated the dependency of cross-sectional aspect ratio (AR=1.1 – 2.1) and below unity Prandtl numbers (Pr=0.001 – 1) for this geometry, and this study aims to extend this work by investigating above unity Prandtl numbers and varying Reynolds numbers.