# Abstr:Buoyancy-opposed wall jet

## Application Area 3: Chemical & Process, Thermal Hydraulics & Nuclear Safety

### Application Challenge AC3-01

#### Abstract

The topic chosen for study as the Application Challenge is that of 2-dimensional buoyancy-opposed plane wall jet penetrating into a slowly moving, counter-current uniform flow. Buoyancy-influenced flows are commonly encountered in nuclear power plants, and these can present particular challenges both to modellers and to experimentalists. One example is found within the side-core region of the steel pressure vessel in magnox gas-cooled reactor systems. In this case, a downward-flowing wall jet of hot gas meets a slow upward flow of cool gas. The downward extent of the penetration of hot gas has a significant influence on the temperature distribution in the side-core region of the reactor pressure vessel.

Experimental study of this flow has been performed at the University of Manchester by Jackson et al (2000) using a water rig. Particle Image Velocimetry (PIV) and Laser Doppler Anemometry (LDA) systems were used to study the mean flow and turbulence fields. Laser light sheet flow visualisation and PIV were used to obtain pictures of the instantaneous flow structure. Detailed measurements of local mean velocity, turbulence and temperature were then made using an LDA system incorporating a fibre optic probe and a traversable rake of thermocouples.

Following the preliminary computations of Dr Kidger, reported in Issue 1, a more extensive set of computations has been undertaken at UMIST, under the direction of Prof. Launder, Dr Iacovides and Dr Craft. The work was carried out by Mr Gerasimov, who continued to use the two-dimensional finite-volume TEAM code, developed by Huang and Leschziner (1983), with a Cartesian geometry for the flow field with a staggered grid storage arrangement. For this particular flow study, convective transport in equations for mean quantities was approximated via the QUICK scheme of Leonard (1979), but with the first order upwind scheme of Patankar (1980) in the turbulence equations. The SIMPLE pressure coupling algorithm of Patankar and Spalding (1972) was employed. As in the preliminary study, four models of turbulence have been considered. Two of these are variants of an eddy-viscosity scheme where the turbulent stresses <uiuj> are approximated by means of an isotropic apparent viscosity mt . The other two use second-moment-closure, where the turbulent stresses are evaluated by means of their own transport equations:

- Model 1: Eddy-Viscosity scheme with wall functions (KEWF)
- Model 2: Low-Reynolds-number Eddy-Viscosity scheme (LRKE)
- Model 3: Basic Second Moment Closure (Basic2mc)
- Model 4: Two-Component Limit Second Moment Closure (TCL2mc)

The modelling of near-wall turbulence within the computationally efficient High-Reynolds-number models (models 1, 3 and 4) received particular attention, because of the important role of the near-wall flow in the overall flow development and of the impracticality (and perhaps impossibility) of adopting a low-Reynolds-number approach for handling the sub-layer. In addition to the conventional wall-function strategy, a novel approach has been developed and introduced. As in the conventional approach, the near-wall control volume is large enough for the near-wall node to lie outside the viscosity-dominated sub-layer. In contrast to the conventional wall-function, the log-law, and the other associated assumptions, are no longer used to provide the wall shear stress to the integral form of the momentum equation and the modifications to the turbulent kinetic energy equation over the near-wall control volume. These are instead obtained from the analytical solution of the near-wall form of the momentum equation, using a prescribed variation of the turbulent viscosity. This novel wall-function strategy has been extended to take into account effects of buoyancy, changes in molecular viscosity due to temperature, streamwise velocity change and high Prandtl number.

During the final stages of this test flow, LES predictions, carried out under the direction of Professor Laurence, have also become available, Addad et al (2003). The objective of these simulations is to supplement the experimental data by providing more extensive data against which to assess the effectiveness of the RANS computations.

The relative simplicity in the particular flow geometry coupled with the complexity of the flow phenomena will, hopefully, enable useful evaluations to be made of turbulence models and computational formulations that are used in the study of buoyancy influenced thermal convection.

Buoyancy-influenced flows are commonly encountered in nuclear reactor systems. One example is a buoyancy-opposed plane wall jet flow which is found within the side-core region of the steel pressure vessel in magnox gas-cooled reactor systems.

The reactor pressure-vessel temperatures form part of the input to the structural integrity assessment of the vessel, upon which the safety case for continued operation of the plant is based. Modelling is often used in nuclear plant applications such as this to supplement sparse plant measurements, and quantification of the uncertainties associated with the calculated thermofluid loading of structures is generally needed.

The preliminary computational experiments performed have raised several numerical and modelling issues. The two main problems encountered so far are the choice (and calibration) of the most appropriate turbulence model as well as an issue of sensitivity of convergence relative to the boundary conditions. For that reason it is flow topology parameters rather than heat transfer parameters that are chosen to assess the quality of the numerical simulations at this initial stage, namely:

- The jet spreading rate (distance from the wall where the mean velocity becomes half the local maximum velocity)
- The jet penetration depth

*Contributors: Jeremy Noyce - Magnox Electric*