Subfilter-scale Stress Modelling for Large Eddy Simulations

A subfilter-scale (SFS) stress model is developed for large-eddy simulations (LES) and is tested on various benchmark problems in both wall-resolved and wall-modelled LES. The basic ingredients of the proposed model are the model length-scale, and the model parameter. The model length-scale is defined as a fraction of the integral scale of the flow, decoupled from the grid. The portion of the resolved scales (LES resolution) appears as a user-defined model parameter, an advantage that the user decides the LES resolution. The model parameter is determined based on a measure of LES resolution, the SFS activity. The user decides a value for the SFS activity (based on the affordable computational budget and expected accuracy), and the model parameter is calculated dynamically. Depending on how the SFS activity is enforced, two SFS models are proposed. In one approach the user assigns the global (volume averaged) contribution of SFS to the transport (global model), while in the second model (local model), SFS activity is decided locally (locally averaged). The models are tested on isotropic turbulence, channel flow, backward-facing step and separating boundary layer. In wall-resolved LES, both global and local models perform quite accurately. Due to their near-wall behaviour, they result in accurate prediction of the flow on coarse grids. The backward-facing step also highlights the advantage of decoupling the model length-scale from the mesh. Despite the sharply refined grid near the step, the proposed SFS models yield a smooth, while physically consistent filter-width distribution, which minimizes errors when grid discontinuity is present. Finally the model application is extended to wall-modelled LES and is tested on channel flow and separating boundary layer. Given the coarse resolution used in wall-modelled LES, near the wall most of the eddies become SFS and SFS activity is required to be locally increased. The results are in very good agreement with the data for the channel. Errors in the prediction of separation and reattachment are observed in the separated flow, that are somewhat improved with some modifications to the wall-layer model.

On the approximation of the subgrid scale for systems of equations

Postprint (published version)

Turbulent shallow-water model for orographic subgrid-scale perturbations

A parallel pseudo-spectral method for the simulation in distributed memory computers of the shallow-water equations in primitive form was developed and used on the study of turbulent shallow-waters LES models for orographic subgrid-scale perturbations. The main characteristics of the code are: momentum equations integrated in time using an accurate pseudo-spectral technique; Eulerian treatment of advective terms; and parallelization of the code based on a domain decomposition technique. The parallel pseudo-spectral code is efficient on various architectures. It gives high performance onvector computers and good speedup on distributed memory systems. The code is being used for the study of the interaction mechanisms in shallow-water ows with regular as well as random orography with a prescribed spectrum of elevations. Simulations show the evolution of small scale vortical motions from the interaction of the large scale flow and the small-scale orographic perturbations. These interactions transfer energy from the large-scale motions to the small (usually unresolved) scales. The possibility of including the parametrization of this effects in turbulent LES subgrid-stress models for the shallow-water equations is addressed.

Catchment-scale modelling of flow and nutrient transport in the Chalk unsaturated zone

The unsaturated zone exerts a major control on the delivery of nutrients to Chalk streams, yet flow and transport processes in this complex, dual-porosity medium have remained controversial. A major challenge arises in characterising these processes, both at the detailed mechanistic level and at an appropriate level for inclusion within catchment-scale models for nutrient management. The lowland catchment research (LOCAR) programme in the UK has provided a unique set of comprehensively instrumented groundwater-dominated catchments. Of these, the Pang and Lambourn, tributaries of the Thames near Reading, have been a particular focus for research into subsurface processes and surface water-groundwater interactions. Data from LOCAR and other sources, along with a new dual permeability numerical model of the Chalk, have been used to explore the relative roles of matrix and fracture flow within the unsaturated zone and resolve conflicting hypotheses of response. From the improved understanding gained through these explorations, a parsimonious conceptualisation of the general response of flow and transport within the Chalk unsaturated zone was formulated. This paper summarises the modelling and data findings of these explorations, and describes the integration of the new simplified unsaturated zone representation with a catchment-scale model of nutrients (INCA), resulting in a new model for catchment-scale flow and transport within Chalk systems: INCA-Chalk. This model is applied to the Lambourn, and results, including hindcast and forecast simulations, are presented. These clearly illustrate the decadal time-scales that need to be considered in the context of nutrient management and the EU Water Framework Directive. (C) 2007 Elsevier B.V. All rights reserved.

A theoretical framework for energy and momentum consistency in subgrid-scale parameterization for climate models

A theoretical framework for the joint conservation of energy and momentum in the parameterization of subgrid-scale processes in climate models is presented. The framework couples a hydrostatic resolved (planetary scale) flow to a nonhydrostatic subgrid-scale (mesoscale) flow. The temporal and horizontal spatial scale separation between the planetary scale and mesoscale is imposed using multiple-scale asymptotics. Energy and momentum are exchanged through subgrid-scale flux convergences of heat, pressure, and momentum. The generation and dissipation of subgrid-scale energy and momentum is understood using wave-activity conservation laws that are derived by exploiting the (mesoscale) temporal and horizontal spatial homogeneities in the planetary-scale flow. The relations between these conservation laws and the planetary-scale dynamics represent generalized nonacceleration theorems. A derived relationship between the wave-activity fluxes-which represents a generalization of the second Eliassen-Palm theorem-is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

MEGAPOLI: concept of multi-scale modelling of megacity impact on air quality and climate

The EU FP7 Project MEGAPOLI: "Megacities: Emissions, urban, regional and Global Atmospheric POLlution and climate effects, and Integrated tools for assessment and mitigation" (http://megapoli.info) brings together leading European research groups, state-of-the-art scientific tools and key players from non-European countries to investigate the interactions among megacities, air quality and climate. MEGAPOLI bridges the spatial and temporal scales that connect local emissions, air quality and weather with global atmospheric chemistry and climate. The suggested concept of multi-scale integrated modelling of megacity impact on air quality and climate and vice versa is discussed in the paper. It requires considering different spatial and temporal dimensions: time scales from seconds and hours (to understand the interaction mechanisms) up to years and decades (to consider the climate effects); spatial resolutions: with model down- and up-scaling from street- to global-scale; and two-way interactions between meteorological and chemical processes.

A regime-dependent parametrization of subgrid-scale cloud water content variability

The subgrid-scale spatial variability in cloud water content can be described by a parameter f called the fractional standard deviation. This is equal to the standard deviation of the cloud water content divided by the mean. This parameter is an input to schemes that calculate the impact of subgrid-scale cloud inhomogeneity on gridbox-mean radiative fluxes and microphysical process rates. A new regime-dependent parametrization of the spatial variability of cloud water content is derived from CloudSat observations of ice clouds. In addition to the dependencies on horizontal and vertical resolution and cloud fraction included in previous parametrizations, the new parametrization includes an explicit dependence on cloud type. The new parametrization is then implemented in the Global Atmosphere 6 (GA6) configuration of the Met Office Unified Model and used to model the effects of subgrid variability of both ice and liquid water content on radiative fluxes and autoconversion and accretion rates in three 20-year atmosphere-only climate simulations. These simulations show the impact of the new regime-dependent parametrization on diagnostic radiation calculations, interactive radiation calculations and both interactive radiation calculations and in a new warm microphysics scheme. The control simulation uses a globally constant f value of 0.75 to model the effect of cloud water content variability on radiative fluxes. The use of the new regime-dependent parametrization in the model results in a global mean which is higher than the control's fixed value and a global distribution of f which is closer to CloudSat observations. When the new regime-dependent parametrization is used in radiative transfer calculations only, the magnitudes of short-wave and long-wave top of atmosphere cloud radiative forcing are reduced, increasing the existing global mean biases in the control. When also applied in a new warm microphysics scheme, the short-wave global mean bias is reduced.

Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow

Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, by means of LES of a channel flow, with friction Reynolds numbers $Re_\tau=590$ up to $Re_\tau=5200$, with relatively coarse resolutions. Data from each simulation will be compared to baseline DNS data. Results have shown that, in contrast to the DEVM, the EASSM has promising potentials for flow predictions at high friction Reynolds numbers: the higher the friction Reynolds number is the better the EASSM will behave and the worse the performances of the DEVM will be. The better performance of the EASSM is contributed to the ability to capture flow anisotropy at the small scales through a correct formulation for the SGS stresses. Moreover, a considerable reduction in the required computational resources can be achieved using the EASSM compared to DEVM. Therefore, the EASSM combines accuracy and computational efficiency, implying that it has a clear potential for industrial CFD usage.

Modelagem da dispersão de odores em ambientes urbanos

O presente trabalho investigou o problema da modelagem da dispersão de compostos odorantes em presença de obstáculos (cúbicos e com forma complexa) sob condição de estabilidade atmosférica neutra. Foi empregada modelagem numérica baseada nas equações de transporte (CFD1) bem como em modelos algébricos baseados na pluma Gausseana (AERMOD2, CALPUFF3 e FPM4). Para a validação dos resultados dos modelos e a avaliação do seu desempenho foram empregados dados de experimentos em túnel de vento e em campo. A fim de incluir os efeitos da turbulência atmosférica na dispersão, dois diferentes modelos de sub-malha associados à Simulação das Grandes Escalas (LES5) foram investigados (Smagorinsky dinâmico e WALE6) e, para a inclusão dos efeitos de obstáculos na dispersão nos modelos Gausseanos, foi empregado o modelo PRIME7. O uso do PRIME também foi proposto para o FPM como uma inovação. De forma geral, os resultados indicam que o uso de CFD/LES é uma ferramenta útil para a investigação da dispersão e o impacto de compostos odorantes em presença de obstáculos e também para desenvolvimento dos modelos Gausseanos. Os resultados também indicam que o modelo FPM proposto, com a inclusão dos efeitos do obstáculo baseado no PRIME também é uma ferramenta muito útil em modelagem da dispersão de odores devido à sua simplicidade e fácil configuração quando comparado a modelos mais complexos como CFD e mesmo os modelos regulatórios AERMOD e CALPUFF. A grande vantagem do FPM é a possibilidade de estimar-se o fator de intermitência e a relação pico-média (P/M), parâmetros úteis para a avaliação do impacto de odores. Os resultados obtidos no presente trabalho indicam que a determinação dos parâmetros de dispersão para os segmentos de pluma, bem como os parâmetros de tempo longo nas proximidades da fonte e do obstáculo no modelo FPM pode ser melhorada e simulações CFD podem ser usadas como uma ferramenta de desenvolvimento para este propósito. Palavras chave: controle de odor, dispersão, fluidodinâmica computacional, modelagem matemática, modelagem gaussiana de pluma flutuante, simulação de grandes vórtices (LES).

Modelling of combustion and sorbent reactions in three-dimensional flow environment of a circulating fluidized bed furnace

This thesis presents a three-dimensional, semi-empirical, steady state model for simulating the combustion, gasification, and formation of emissions in circulating fluidized bed (CFB) processes. In a large-scale CFB furnace, the local feeding of fuel, air, and other input materials, as well as the limited mixing rate of different reactants produce inhomogeneous process conditions. To simulate the real conditions, the furnace should be modelled three-dimensionally or the three-dimensional effects should be taken into account. The only available methods for simulating the large CFB furnaces three-dimensionally are semi-empirical models, which apply a relatively coarse calculation mesh and a combination of fundamental conservation equations, theoretical models and empirical correlations. The number of such models is extremely small. The main objective of this work was to achieve a model which can be applied to calculating industrial scale CFB boilers and which can simulate all the essential sub-phenomena: fluid dynamics, reactions, the attrition of particles, and heat transfer. The core of the work was to develop the model frame and the required sub-models for determining the combustion and sorbent reactions. The objective was reached, and the developed model was successfully used for studying various industrial scale CFB boilers combusting different types of fuel. The model for sorbent reactions, which includes the main reactions for calcitic limestones, was applied for studying the new possible phenomena occurring in the oxygen-fired combustion. The presented combustion and sorbent models and principles can be utilized in other model approaches as well, including other empirical and semi-empirical model approaches, and CFD based simulations. The main achievement is the overall model frame which can be utilized for the further development and testing of new sub-models and theories, and for concentrating the knowledge gathered from the experimental work carried out at bench scale, pilot scale and industrial scale apparatus, and from the computational work performed by other modelling methods.

A multi-scale framework for strategic management of diffuse pollution

A multi-scale framework for decision support is presented that uses a combination of experiments, models, communication, education and decision support tools to arrive at a realistic strategy to minimise diffuse pollution. Effective partnerships between researchers and stakeholders play a key part in successful implementation of this strategy. The Decision Support Matrix (DSM) is introduced as a set of visualisations that can be used at all scales, both to inform decision making and as a communication tool in stakeholder workshops. A demonstration farm is presented and one of its fields is taken as a case study. Hydrological and nutrient flow path models are used for event based simulation (TOPCAT), catchment scale modelling (INCA) and field scale flow visualisation (TopManage). One of the DSMs; The Phosphorus Export Risk Matrix (PERM) is discussed in detail. The PERM was developed iteratively as a point of discussion in stakeholder workshops, as a decision support and education tool. The resulting interactive PERM contains a set of questions and proposed remediation measures that reflect both expert and local knowledge. Education and visualisation tools such as GIS, risk indicators, TopManage and the PERM are found to be invaluable in communicating improved farming practice to stakeholders. (C) 2008 Elsevier Ltd. All rights reserved.

Probabilistic simulations of crop yield over western India using the DEMETER seasonal hindcast ensembles

Process-based integrated modelling of weather and crop yield over large areas is becoming an important research topic. The production of the DEMETER ensemble hindcasts of weather allows this work to be carried out in a probabilistic framework. In this study, ensembles of crop yield (groundnut, Arachis hypogaea L.) were produced for 10 2.5 degrees x 2.5 degrees grid cells in western India using the DEMETER ensembles and the general large-area model (GLAM) for annual crops. Four key issues are addressed by this study. First, crop model calibration methods for use with weather ensemble data are assessed. Calibration using yield ensembles was more successful than calibration using reanalysis data (the European Centre for Medium-Range Weather Forecasts 40-yr reanalysis, ERA40). Secondly, the potential for probabilistic forecasting of crop failure is examined. The hindcasts show skill in the prediction of crop failure, with more severe failures being more predictable. Thirdly, the use of yield ensemble means to predict interannual variability in crop yield is examined and their skill assessed relative to baseline simulations using ERA40. The accuracy of multi-model yield ensemble means is equal to or greater than the accuracy using ERA40. Fourthly, the impact of two key uncertainties, sowing window and spatial scale, is briefly examined. The impact of uncertainty in the sowing window is greater with ERA40 than with the multi-model yield ensemble mean. Subgrid heterogeneity affects model accuracy: where correlations are low on the grid scale, they may be significantly positive on the subgrid scale. The implications of the results of this study for yield forecasting on seasonal time-scales are as follows. (i) There is the potential for probabilistic forecasting of crop failure (defined by a threshold yield value); forecasting of yield terciles shows less potential. (ii) Any improvement in the skill of climate models has the potential to translate into improved deterministic yield prediction. (iii) Whilst model input uncertainties are important, uncertainty in the sowing window may not require specific modelling. The implications of the results of this study for yield forecasting on multidecadal (climate change) time-scales are as follows. (i) The skill in the ensemble mean suggests that the perturbation, within uncertainty bounds, of crop and climate parameters, could potentially average out some of the errors associated with mean yield prediction. (ii) For a given technology trend, decadal fluctuations in the yield-gap parameter used by GLAM may be relatively small, implying some predictability on those time-scales.

Dissolution-Precipitation in Porous Media: Experiments and Modelling

The evolution of porosity due to dissolution/precipitation processes of minerals and the associated change of transport parameters are of major interest for natural geological environments and engineered underground structures. We designed a reproducible and fast to conduct 2D experiment, which is flexible enough to investigate several process couplings implemented in the numerical code OpenGeosys-GEM (OGS-GEM). We investigated advective-diffusive transport of solutes, effect of liquid phase density on advective transport, and kinetically controlled dissolution/precipitation reactions causing porosity changes. In addition, the system allowed to investigate the influence of microscopic (pore scale) processes on macroscopic (continuum scale) transport. A Plexiglas tank of dimension 10 × 10 cm was filled with a 1 cm thick reactive layer consisting of a bimodal grain size distribution of celestite (SrSO4) crystals, sandwiched between two layers of sand. A barium chloride solution was injected into the tank causing an asymmetric flow field to develop. As the barium chloride reached the celestite region, dissolution of celestite was initiated and barite precipitated. Due to the higher molar volume of barite, its precipitation caused a porosity decrease and thus also a decrease in the permeability of the porous medium. The change of flow in space and time was observed via injection of conservative tracers and analysis of effluents. In addition, an extensive post-mortem analysis of the reacted medium was conducted. We could successfully model the flow (with and without fluid density effects) and the transport of conservative tracers with a (continuum scale) reactive transport model. The prediction of the reactive experiments initially failed. Only the inclusion of information from post-mortem analysis gave a satisfactory match for the case where the flow field changed due to dissolution/precipitation reactions. We concentrated on the refinement of post-mortem analysis and the investigation of the dissolution/precipitation mechanisms at the pore scale. Our analytical techniques combined scanning electron microscopy (SEM) and synchrotron X-ray micro-diffraction/micro-fluorescence performed at the XAS beamline (Swiss Light Source). The newly formed phases include an epitaxial growth of barite micro-crystals on large celestite crystals (epitaxial growth) and a nano-crystalline barite phase (resulting from the dissolution of small celestite crystals) with residues of celestite crystals in the pore interstices. Classical nucleation theory, using well-established and estimated parameters describing barite precipitation, was applied to explain the mineralogical changes occurring in our system. Our pore scale investigation showed limits of the continuum scale reactive transport model. Although kinetic effects were implemented by fixing two distinct rates for the dissolution of large and small celestite crystals, instantaneous precipitation of barite was assumed as soon as oversaturation occurred. Precipitation kinetics, passivation of large celestite crystals and metastability of supersaturated solutions, i.e. the conditions under which nucleation cannot occur despite high supersaturation, were neglected. These results will be used to develop a pore scale model that describes precipitation and dissolution of crystals at the pore scale for various transport and chemical conditions. Pore scale modelling can be used to parameterize constitutive equations to introduce pore-scale corrections into macroscopic (continuum) reactive transport models. Microscopic understanding of the system is fundamental for modelling from the pore to the continuum scale.