The Swedish defence agency (FOI) has developed a particle model (called Pello) that simulates the dispersion of aerosols and gases. At the boundaries, such as the ground, the particles can either reflect back into the domain (the atmosphere) or be absorbed. Which of the events that occurs is decided by a certain probability, which in the present model depends on mere physical properties. In this thesis we have investigated a newly proposed boundary behaviour which also depends on the time step used in the numerical simulations. We verified the accuracy of the new model by using a dispersion model with an explicit solution. To gain a better understanding of how important parameters at the boundary influence each other, we performed a sensitivity analysis. Simulations showed an overall improving concentration profile as the time step became smaller and the new model working well. The convergence order of the simulations was found to be close to 0.5. In this thesis we have shown that there exist an upper limit for the time step, which depends on the specific model. The present used time step at FOI does not have this versatile property. But having this upper limit for the time step close to the boundary, and a uniform time step can be time demanding. This lead us to the conclusion that an adaptive time step should be implemented.

The use of hazardous toxic substances is very common in the industrial sector. The substances are often stored in tanks in storage compartments or transported between industrial premises. In case of an accident involving these substances, severe harm can affect both population and the environment. This leaves a demand for an accurate prediction of the substance concentration distribution to mitigate the risks as much as possible and in advance create suitable safety measures. Toxic gases and vapors are often denser than air making it affected by negative buoyancy forces. This will make the gas descend and spread horizontally when reaching the ground. Swedish Defence Research Agency (FOI) carries today a model called LillPello for simulating the dispersion of gases, yet it does not account for the specific case of a dense gas. Therefore, this thesis aims to implement the necessary effects needed to accurately simulate the dispersion of a dense gas. These effects were implemented in Fortran 90 by solving five conservation equations for energy, momentum (vertical and horizontal) and mass. The model was compared against experimental data of a leak of ammonia (NH3). By analyzing the result of the simulations in this thesis, we can conclude that the overall result is satisfactory. We can notice a small concentration underestimation at all measurement points and the model produced a concentration power law coefficient which lands inside the expected range. Two out of the three statistical quantities Geometric Mean (MG), Geometric Variance (VG) and Factor of 2 (FA2) produced values within the ranges of acceptable values. The drawback of the model as it is implemented today is its efficiency, so the main priority for the future of this thesis is to improve this. The model should also be analyzed on more experiments to further validate its accuracy. / Användandet av giftiga ämnen är vanligt inom den industriella sektorn. Ämnena är oftast lagrade i behållare positionerade i lagringsutrymmen eller så transporteras ämnena mellan industrilokaler. I samband med en olycka innehållande dessa substanser kan stora skador drabba både befolkning och miljön. Detta leder till ett behov av att noggrant kunna förutspå koncentrationsfördelningen för att minska riskerna, samt i förväg kunna skapa lämpliga säkerhetsåtgärder. Giftiga gaser och ångor är oftast tyngre än luft vilket gör att gasen blir påverkad av negativ bärkraft. Detta gör att gasen sjunker och sprids horisontalt när den når marken. Totalförsvarets Forskningsinstitut (FOI) besitter idag en modell kallad LillPello som simulerar spridning av gaser, men den hanterar inte det specifika fallet av en tunggas. Därför siktar detta projekt på att, in i LillPello, implementera de nödvändiga effekterna som behövs för att korrekt kunna simulera spridningen av en tunggas. Dessa effekter är implementerad i Fortran 90 genom att lösa fem konserveringsekvationer för energi, momentum (vertikal och horisontell) samt massa. Modellen jämfördes mot data från ett fältexperiment där ammoniak (NH3) släpptes ut. Genom att analysera resultatet från simuleringar kan vi dra slutsatsen att det övergripande resultatet är tillfredsställande. Vi kan notera en underskattning för alla koncentrationsmätningar i simuleringarna och modellen producerade en potenslagsexponent vars värde hamnade innanför den accepterade gränsen. Två utav de tre beräknade statistiska kvantiteterna: Geometriskt medelvärde (MG), Geometrisk varians (VG) och Faktor av 2 (FA2) producerade värden inom de acceptabla gränserna. Största nackdelen med modellen är dess effektivitet och därför är största prioritet för det fortsatta arbetet inom detta projekt att effektivisera implementeringen. Modellen ska även bli vidare analyserad mot fler experiment för att validera dess noggrannhet.

Made available in DSpace on 2014-08-20T14:25:46Z (GMT). No. of bitstreams: 1 dissertacao_marieli_sallet.pdf: 231023 bytes, checksum: f445526b62fbfcde40fb1bc5ca90923a (MD5) Previous issue date: 2007-02-23 / Currently, the search for analytical solutions for the dispersion problems is one of the main research subjects in the pollutant dispersion modeling. These solutions become important due to the intention to obtain dispersion models that generate reliable results in a small computational time, which are of great interest for regulatory air quality applications. Lagrangian particle models are an important and effective tool to simulate the atmospheric dispersion of airborne pollutants. These models are based on the Langevin equation, which is derived from the hypothesis that the velocity is given by the combination between a deterministic term and a stochastic term. In this work is presented a new Lagrangian particle model to simulate the pollutant dispersion in low wind speed conditions. During low wind speed, the diffusion of a pollutant in the planetary boundary layer (PBL) is indefinite and it has been observed that the plume is subject to a great deal of horizontal undulations, which are called plume meandering. The method proposed leads to a stochastic integral equation whose solution has been obtained through the Method of Successive Approximations or Picard s Iteration Method. The integral equation is written in terms of the real and imaginary parts of the complex function before performing the multiplication of the integrating factor, expressed by the Euler formula, inside and outside of the integral solution. To take account the meandering effect, the Frenkiel s Eulerian autocorrelation functions for low wind conditions is included naturally in the model. The new approach has been evaluated through the comparison with experimental data and other different dispersion models. Particularly, the results obtained by the model agree very well with the experimental data, indicating the model represents the dispersion process correctly in low wind speed conditions. It is also possible to verify that the new model results are better than ones obtained by the other models. The analytical feature of the technique and the natural inclusion of the Frenkiel s Eulerian autocorrelation function become the model more accurate than other models. / Atualmente, a busca por soluções analíticas para os problemas de dispersão é um dos principais assuntos de pesquisa na modelagem da dispersão de poluentes. Estas soluções tornam-se importantes devido à intenção de obter modelos de dispersão que geram resultados confiáveis em um tempo computacional pequeno, que são de grande interesse para aplicações no controle da qualidade do ar. Modelos de partícula Lagrangeano são uma ferramenta importante e eficaz para simular a dispersão atmosférica de poluentes do ar. Esses modelos são baseados na equação de Langevin, que é derivada da hipótese que a velocidade é dada por uma combinação entre um termo determinístico e um termo estocástico. Neste trabalho é apresentado um novo modelo de partícula Lagrangeano para simular a dispersão de poluentes em condições de velocidade de vento fraco. Durante a velocidade de vento fraco, a difusão de um poluente na Camada Limite Planetária (CLP) é indefinida e tem sido observado que a pluma está sujeita a grandes ondulações horizontais, que são chamadas meandro do vento. O método proposto leva a uma equação integral estocástica cuja solução é obtida através do Método das Aproximações Sucessivas ou Método Iterativo de Picard. A equação integral é escrita em termos das partes real e imaginária da função complexa antes de realizar a multiplicação do fator integrante, expresso pela fórmula de Euler, dentro e fora da solução integral. Para considerar o efeito do meandro, as funções de autocorrelação Euleriana de Frenkiel para condições de vento fraco são incluídas naturalmente no modelo. A nova aproximação foi avaliada através da comparação com dados experimentais e outros diferentes modelos de dispersão. Particularmente, os resultados obtidos pelo modelo concordam muito bem com os dados experimentais, indicando que o modelo representa o processo de dispersão corretamente em condições de velocidade de vento fraco. Também é possível verificar que os resultados do novo modelo são melhores do que os obtidos pelos outros modelos. A característica analítica da técnica e a inclusão natural da função de autocorrelação Euleriana de Frenkiel tornam o modelo mais exato que os outros modelos.