Direct numerical and large eddy simulations are powerful tools for analyses of turbulent flows at low and large Reynolds or Rayleigh numbers in fundamental research. The current status of both methods and recent extensions are compiled. The progress achieved with subgrid scale models and numerics makes the method attractive for investigations in nuclear research and engineering. Applications of both methods of realistic technical flows are discussed. Open problems are mainly related to more general subgrid scale models for large complex containers, to the wall and inlet conditions for high Reynolds number and buoyant flows, and to discretisation schemes for local refinement of spatial resolution. As a classical example for the use of direct simulations, results are presented for a turbulent internally heated horizontal fluid layer. The analysis of the closure terms in the transport equation of the kinetic energy demonstrates major difficulties of the conventional statistical modelling for partially stably stratified convection.

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Direct numerical and large eddy simulations in nuclear applications

An in-house fully three-dimensional general-purpose finite element model is applied to solve the hydrodynamic structure in a periodic Kinoshita-generated meandering channel. The numerical model solves the incompressible Reynolds-averaged Navier–Stokes equations for mass and momentum, while solving the k − e equations for turbulence. The free surface is described by the rigid-lid approximation (using measured water surface data) for flat (smooth-bed) and self-formed (rough-bed) conditions. The model results are compared against experimental measurements in the ‘Kinoshita channel’, where three-dimensional flow velocities and turbulence parameters were measured. This validation was carried out for the upstream-valley meander bend orientation under smooth (flat bed) conditions. After validation, several simulations were carried out to predict the hydrodynamics in conditions where either it was not possible to perform measurements (e.g. applicability of the laboratory acoustic instruments) and to extrapolate the model to other planform configurations. For the flat smooth-bed case, a symmetric (no skewness) planform configuration was modeled and compared to the upstream-skewed case. For the self-formed rough-bed case, prediction of the hydrodynamics during the progression of bedforms was performed. It appears that the presence of bedforms on a bend has the following effects: (i) the natural secondary flow of the bend is disrupted by the presence of the bedforms, thus depending on the location of the dune, secondary flows might differ completely from the traditional orientation; (ii) an increment on both the bed and bank shear stresses is induced, having as much as 50% more fluvial erosion, and thus a potential increment on the migration rate of the bend. Implications on sediment transport and bend morphodynamics are also discussed in the paper. Copyright © 2013 John Wiley & Sons, Ltd.

Modulation of the flow structure by progressive bedforms in the Kinoshita meandering channel

Laminar flow through a two-dimensional square cavity in which internal (volumetric) heat generation takes place is analyzed numerically. The inflow is a horizontal jet at the bottom of the cavity, and the outlet is at the top, in a centered position. As the internal heat generation rate is increased, several flow patterns appear, in particular periodic and quasi-periodic in time flows. Two distinct regimes are identified, one dominated by inertia in which significant hot-fluid trapping occurs, and another, stratified regime, in which buoyancy effects are dominant. The effects of Reynolds number, Prandtl number, horizontal heat generation inhomogeneities, and wall boundary conditions are assessed. Of technological importance is the inertia-dominated regime, as temperatures much higher than the mean outflow temperature appear.

Numerical investigation of flow through a cavity with internal heat generation

En esta tesis se discute el modelado numerico del problema de lubricacion hidrodinamica en
los aros de piston de motores a explosion. Este modelado ha sido abordado con dos enfoques
bien distintos. Por un lado, se ha propuesto una formulacion numerica basada en el metodo
de volumenes finitos para resolver el modelo p–θ de Elrod–Adams, que no es otra cosa que
un modelo de orden reducido para el problema de lubricacion en presencia de cavitacion. Por
otro lado, se ha propuesto una formulacion numerica completa para la simulacion de flujos de
dos fases inmiscibles, es decir, un modelo de mayor orden para el problema fluido–dinamico
considerando la presencia por separado del lubricante y los gases.
Con respecto al primer enfoque considerado, la formulacion que proponemos permite resolver
la ecuacion de Reynolds e imponer las llamadas condiciones JFO, propuestas por Jacobson &
Floberg y Olsson, resultando en una formulacion estrictamente conservativa. El metodo esta basado
en un esquema de relajacion y permite resolver al mismo tiempo la dinamica de las partes
lubricadas. Luego de describir detalladamente el esquema, se aplica a varias situaciones practicas
y luego al problema de los aros de piston. Si bien el metodo es ampliamente usado, notamos
que debe ser modificado para estudiar esta clase especifica de dispositivos, por lo cual proponemos
una variacion del mismo. La evidencia numerica en este caso parece indicar que el modelo matem
atico, con esta modificacion, presenta multiplicidad de soluciones, lo cual motiva el estudio
del problema por medio de las ecuaciones de Navier–Stokes incompresibles.
En relacion con el segundo enfoque, en esta tesis se adopta una formulacion de elementos
finitos para las ecuaciones de Navier–Stokes, con un metodo de tipo level set para el seguimiento
de la interfase movil que separa las dos fases presentes en el sistema. La formulacion propuesta
utiliza interpolacion lineal para la velocidad, presion y funcion de level set. Se estudian varias
cuestiones particulares que deben ser tomadas en cuenta en una formulacion de este tipo. Por un
lado se estudia de manera exhaustiva un metodo de reinicializacion para mantener la regularidad
de la funcion de level set y se lo extiende al caso de mallas curvilineas. Ademas, proponemos
un nuevo espacio de elementos finitos, que no introduce incognitas adicionales y esta basado en
simples modificaciones del espacio P_1 conforme, para capturar las discontinuidades en el campo
de presiones debido a la presencia de la tension superficial, la cual es incluida mediante una
formulacion de Laplace–Beltrami. La formulaciodn propuesta es monolitica, es decir, se computan
simultaneamente todas las variables fluido–dinamicas (velocidad y presion) y la posicion de la
interfase (embebida en la funcion de level set), con un esquema iterativo de Newton–Raphson,
para lo cual se propone un computo mejorado del Jacobiano. Luego, se introduce un nuevo
metodo para acondicionar la velocidad de transporte en las cercanias de la interfase y mejorar
asi, en algunos casos, la precision de los calculos. El metodo esta basado en la resolucion de una
ecuacion a derivadas parciales y es por lo tanto mucho mas simple de implementar que otras
metodologias de tipo geometrico.
Finalmente, se aplica la formulacion numerica al problema fluido–dinamico en aros de piston
y los resultados son comparados con los correspondientes al modelo de lubricacion propuesto.

Simulación numérica en flujo de dos fases inmiscibles con aplicaciones en lubricación hidrodinámica

Thermal and mechanical characteristics of the moderator cell in a cold neutron source

A finite element simulation of flow and heat transfer in the moderator cell of a cold-neutron source (CNS), in which liquid deuterium subject to internal heat generation is flowing, is reported. The numerical scheme consists of a stabilized equal-order method. A time-accurate approach is adopted to resolve the large-scale eddies of the flow, with a Smagorinsky's model for the subgrid-scale effects. The thermal coupling follows a staggered strategy, with SUPG-type upwinding. A specific wall-law is developed that accounts for the correct partition of the heat deposited at the wall by radiation between the liquid deuterium and the helium gas flowing at the outer side of the wall. The average flow and thermal structure are presented. The turbulent fluctuations are both illustrated in physical space and decomposed into spectral components. The wavenumber spectrum suggests that adequate resolution of the large-scale eddies has been attained with just 200,000 nodes, while a DNS analysis would have required at le...

Daniela Arnica

Papers

Finite Element Modeling of Liquid Deuterium Flow and Heat Transfer in a Cold-neutron Source