Prediction Of Thermal Stratification Research Articles

Study of nuclear reactor external vessel passive cooling using computational fluid dynamics

Nuclear energy has recently re-gained support as a reliable source of carbon-free electricity. However, the safety of nuclear plants is still questioned, particularly in the wake of the tragic events in Fukushima. In response to this, the adoption of passive safety systems, providing cooling to the plant even in the absence of any active power, has been accelerated. However, the confident assessment of their effectiveness is still constrained by the large spatial scales involved, which makes experimental validation difficult and expensive. Additionally, the many complexities intrinsic to the prediction of natural convection makes the mathematical modelling of such systems problematic. In this paper, the development of computational fluid dynamics (CFD) as a reliable method to ultimately prove, and eventually improve, the passive safety features of reactors is described. The focus of the paper is external reactor vessel cooling. In the case of a reactor core melting, the core is kept inside the reactor vessel, which is cooled from the outside by natural convection after flooding the region of the containment that houses the vessel. More specifically, a recent experiment that simulates, at a reduced scale, cooling of the horizontal calandria vessel of a pressurized heavy water reactor, submerged in a water pool, is modelled using CFD. For this situation, of major relevance is the correct prediction of boiling on the external surface of the reactor vessel, and thermal stratification in the water pool, which could prevent lower regions of the pool from performing any heat transfer duty. Results from standard Reynolds-averaged Navier-Stokes based turbulent flow simulations demonstrate that more advanced models are needed for accurate simulation, specifically in view of the excessive mixing predicted by such approaches. In contrast, the development of a more advanced tool based on large eddy simulation (LES) is started from the prediction of thermal stratification in the water pool, for which good accuracy is demonstrated through comparisons with available data. Although further improvements are needed, and discussed, it is demonstrated that LES can provide a reliable tool for the analysis and design of passive safety systems and strategies, and the assessment of passive cooling effectiveness and reactor safety. Although computational effort remains the main constraint in using LES, computation times are not prohibitive, particularly given the continual increase in available computing resources.

Evolution of stratification in a cryogenic propellant tank at reduced gravity environment

The prediction of thermal stratification in a cryogenic storage tank is necessary for the successful execution of space mission. The working fluid may be stored in the sub-cooled conditions and possibility of heat infiltration may lead to the increase of temperature as well as the pressure of the cryogenic fluid. The rise in fluid pressure may also lead to cavitation in the turbo pump which has to be avoided. Commonly used stratification models are based on temperature and velocity correlation developed for flow over a flat plate. An experimental cryogenic test tank is designed, fabricated and stratification is studied using nitrogen as the model propellant. The effect of gravity on the evolution of stratification is studied by using a CFD model. The results show that the fluid velocity will be lesser at microgravity condition which causes the boundary layer fluid to absorb a large amount of heat and the nature of the heat transfer changes from convection to evaporation.

Prediction of thermal stratification in an engine-like geometry using a zero-dimensional stochastic reactor model

The prediction of local heat transfer and thermal stratification in the zero-dimensional stochastic reactor model is compared to direct numerical simulation published by Schmitt et al. in 2015. Direct numerical simulation solves the Navier–Stokes equations without incorporating model assumptions for turbulence and wall heat transfer. Therefore, it can be considered as numerical experiment and is suitable to validate approximations in low-dimensional models. The stochastic reactor model incorporates a modified version of the Euclidean Minimum Spanning Tree mixing model proposed by Subramaniam et al. in 1998. To capture the thermal stratification of the direct numerical simulation, the total enthalpy ( H) is used as the only mixing limiting scalar within the newly proposed H-Euclidean-Minimum-Spanning-Tree. Furthermore, a stochastic heat transfer model is incorporated to mimic turbulence effects on local heat transfer distribution to the walls. By adjusting the Cϕ mixing time and Ch stochastic heat transfer parameter, the stochastic reactor model predicts accurately the thermal stratification of the direct numerical simulation. Comparing the Woschni, Hohenberg and Heinle heat transfer model shows that the modified Heinle model matches accurately the direct numerical simulation results. Thereby, the Heinle model accounts for the influence of turbulent kinetic energy on the characteristic velocity in the heat transfer coefficient calculation. This highlights the importance of incorporating turbulence effects in low-dimensional heat transfer models. Overall, the zero-dimensional stochastic reactor model with the H-Euclidean-Minimum-Spanning-Tree mixing model, the stochastic heat transfer model and the modified Heinle correlation have proven successfully the prediction of mean quantities like temperature and heat transfer and thermal stratification of the direct numerical simulation.

Algebraic Turbulent Heat Flux Model for Prediction of Thermal Stratification in Piping Systems

The effect of stratification on the flow in bounded geometries is studied through computational fluid dynamics and two different modelings of the turbulent heat flux: constant turbulent Prandtl number and Algebraic Heat Flux Model (AHFM). The main feature of the work is evaluation of the effect of buoyancy on the thermal quantities, velocity field, and related pressure drop. For evaluation of the turbulent heat flux and temperature field, AHFM has been demonstrated to be superior to the simple eddy diffusivity approach. However, serious concerns remain for the prediction of the velocity field in both isothermal and nonisothermal conditions, since greater uncertainties for the obtained pressure drop and related Fanning friction factor can be introduced. Incremental pressure drop is also investigated in conditions deviating from fully developed flows, in order to study stratification effects qualitatively using an engineering method.

CFD analysis of thermal stratification and sensitivity study of model parameters for k–ɛ model in a cylindrical hot plenum

A sensitivity analysis of various numerical parameters on the prediction of thermal stratification in a 2D axi-symmetric domain has been carried out by using commercial code FLUENT 6.3. The analysis is carried out for both steady and unsteady flow conditions. The Reynolds number in all the cases has been considered as Re=19,200. The effect of under relaxation parameters, numerical schemes on convergence while solving mass, momentum and turbulence equations was first studied for steady state conditions. An optimal range for under relaxation parameters was found which ensures the stability of the numerical solutions and ensures faster convergence. Further, 1st order upwind scheme for convective terms of turbulent equations (k and ɛ) is found to give a better convergence in comparison with higher order schemes. The study was then extended to transient flow conditions and the stratification characteristics like rising of the stratification interface was studied. The turbulence model parameters of the standard k–ɛ model were changed and predictions were observed. It is observed that the values used for turbulence model parameters (Cμ, C1, C2) while solving the standard k–ɛ model for studying stratification characteristics are different than the model values used in k–ɛ equation. In the lower part of reactor vessel, k–ɛ model with standard value of model parameters have a very good agreement with the experimental observations of Moriya et al. (1987) while in the upper part the model parameters take different values than the standard values.

Forecasting Thermal Stratification of the Victoria Reservoir using a Hydrodynamic Model

Strong thermal stratification in a reservoir may result in oxygen depletion along the vertical profile downwards leading to its eutrophication. The paper is an investigation of thermal stratification behaviour of the Victoria reservoir in Sri Lanka, which experienced several water quality linked problems in the past. A one-dimensional reservoir hydrodynamics model is calibrated and validated for the Victoria reservoir. The calibration and validation are strengthened by calculating several goodness-of-fit statistics. The study further shows the possibility to change the strong thermal stratification of the Victoria reservoir by manipulating the releases from it. The model that ensures a reasonable prediction of thermal stratification enables taking precautionary measures to avoid adverse reservoir water quality conditions.

Prediction of thermal stratification in a curved duct with 3D body-fitted co-ordinates

SUMMARY This paper concerns a numerical prediction method for buoyancy-influenced flows using three-dimensional non-orthogonal curvilinear co-ordinates. The numerical analysis of the transformed governing equations for thermal hydraulics is based on a Lagrangian method, in which advected physical values are evaluated by local cubic spline interpolations with third-order accuracy in the three-dimensional computational domain. In addition, the buoyancy and diffusion terms are discretized in the Lagrangian scheme so as to have second-order accuracy with respect to time and space. The Neumann boundary conditions, which have been rather difficult for non-orthogonal co-ordinates to deal with, can be implemented by making use of normal vectors on the physical boundary surfaces and cubic spline interpolations. The developed numerical method is applied to the steady isothermal flow in a curved pipe and the unsteady stratified flow in a curved duct. Both of the predicted values are in good agreement with the experimental results and the validity of the prediction method is confirmed.

A prescriptive model of stratification induced by freshwater runoff

Stratification induced by freshwater buoyancy input constitutes a key determinant of the environment both in estuaries and adjacent regions of freshwater influence (ROFIs). Predicting the development and breakdown of estuarine stratification is inherently more difficult than the prediction of thermal stratification because the buoyancy input is localized at the lateral boundaries rather than being uniformly distributed over the surface. The primary processes responsible for controlling water column stability have been identified in a previous paper (Simpson et al., 1990 Estuaries 12, 125–132) as (i) the estuarine circulation driven by horizontal density gradients, (ii) stirring by tidal and wind stresses and (iii) straining of the density field by tidal shear. These processes are incorporated in a prescriptive model of the time evolution of stratification which utilizes analytical solutions for the tidal and density current profiles, specifies the mixing in terms of energy conditions previously used in the heating-stirring models and assumes a horizontal density gradient which is invariant with depth. The behaviour of this simple model is described and compared with recent time series observations of the variability of stratification in a tidally energetic ROFI which indicate the presence of strong semi-diurnal and semi-monthly cycles in water column stability. The model reproduces the main qualitative features of the observations but is restricted as a predictive tool by the constant density gradient assumption and the omission of the interaction between the tidal- and density-driven flows. The inclusion of this latter interaction, which occurs via the frictional stresses and the control of eddy viscosity by stratification and the turbulent energy intensity, requires a dynamically active model which specifies the feedback processes in terms of an appropriate closure scheme.