On the Eulerian Large Eddy Simulation of disperse phase flows: an asymptotic preserving scheme for small Stokes number flows

In the present work, the Eulerian Large Eddy Simulation of dilute disperse phase flows is investigated. By highlighting the main advantages and drawbacks of the available approaches in the literature, a choice is made in terms of modelling: a Fokker-Planck-like filtered kinetic equation proposed by Zaichik et al. 2009 and a Kinetic-Based Moment Method (KBMM) based on a Gaussian closure for the NDF proposed by Vie et al. 2014. The resulting Euler-like system of equations is able to reproduce the dynamics of particles for small to moderate Stokes number flows, given a LES model for the gaseous phase, and is representative of the generic difficulties of such models. Indeed, it encounters strong constraints in terms of numerics in the small Stokes number limit, which can lead to a degeneracy of the accuracy of standard numerical methods. These constraints are: 1/as the resulting sound speed is inversely proportional to the Stokes number, it is highly CFL-constraining, and 2/the system tends to an advection-diffusion limit equation on the number density that has to be properly approximated by the designed scheme used for the whole range of Stokes numbers. Then, the present work proposes a numerical scheme that is able to handle both. Relying on the ideas introduced in a different context by Chalons et al. 2013: a Lagrange-Projection, a relaxation formulation and a HLLC scheme with source terms, we extend the approach to a singular flux as well as properly handle the energy equation. The final scheme is proven to be Asymptotic-Preserving on 1D cases comparing to either converged or analytical solutions and can easily be extended to multidimensional configurations, thus setting the path for realistic applications

Modelling particle collisions in moderately dense curtain impacted by an incident shock wave

The interactions between an incident shock and moderately dense particle curtain are simulated with the Eulerian-Lagrangian method. A customized solver based on OpenFOAM is extended with an improved drag model and collision model, and then validated against two benchmark experiments. In this work, parametric studies are performed considering different particle sizes, volume fractions, and curtain thicknesses. It is found that smaller particle size and larger volume fractions lead to stronger reflected shock and weaker transmitted shock. Different expansion stages of the curtain fronts are also studied in detail. Attention is paid to the particle collision effects on the curtain evolution behaviours. According to our results, for the mono-dispersed particle curtain, the collision effects on curtain front behaviors are small, even when the initial particle volume fraction is as high as 20%. This is due to the positive velocity gradient across the curtain after the shock wave passage, leading to faster motion of downstream particles than the upstream ones and hence no collision occurs. For the bi-dispersed particle curtain, the collision effects become important in the mixing region of different-size particles. Collisions decelerate small particles while accelerate large ones and cause velocity scattering. Moreover, increasing the bi-dispersed curtain thickness leads to multiple collision force peaks due to the local particle accumulations, which is the result of the delayed separation of different particle groups. Our results indicate that the collision model may be unnecessary to predict curtain fronts in mono-dispersed particles, but in bi-dispersed particles, the collision effects are important and therefore must be modelled

Modelling of spray-wall impingement

When a drop collides with an interposed surface, three phases are usually involved: liquid (the drop), solid (the substrate) and gas (the surrounding environment). Such an event involves a number of parameters associated with the physical characteristics of the incident particles, the properties of the target surface, and the natural features of the air flow. Each occurrence leads to a singular outcome, since each particle experiences a different reality throughout the injection cycle. Therefore, the development of appropriate modelling strategies of this complex multi-phase flow requires a thorough understanding of the mechanisms underlying the spray impingement process. Several computational models have been reported in the open literature, although not always successfully. From these, only a few have attempted to replicate the more intricate scenarios that include the formation and development of a liquid film over the surface due to the deposition of previously injected particles, the presence of a high velocity cross-flowing gas, and the thermal effects promoted by the existence of hot walls. Even though these elements are some of the more influential parameters affecting the final outcome of spray-wall impacts, most of the simulations still neglect some of them in their formulation. Therefore, in order to capture the majority of the physical phenomena observed in experimental studies, CFD codes must be equipped with superior mathematical formulations. During the present doctoral research, three independent computational extensions have been devised and integrated into the model used by our research group to simulate spray-wall interactions. The upgrades — that have been proposed over the course of the study — have been denominated as the liquid film, evaporation and breakup sub-models. They are intended to complement the basic mathematical formulation adopted in the original simulation procedure. This approach has contributed to enhance the prediction capabilities of the model, since it is now capable of capturing some phenomena that were not considered previously. On the other hand, it has also extended the range of applicability of the CFD code to a new set of impact conditions (i.e., in hot environments and with a high velocity crossflow). Furthermore, the present work provides a detailed analysis of the results obtained, with major emphasis given to the disintegration mechanisms and secondary droplet characteristics. Both quantitative and qualitative comparisons between computational and experimental results are presented. When pertinent, the impact of a particular sub-model onto the outcome predicted is also evaluated by comparing the versions of the model with and without the corresponding computational extension. Moreover, a systematic approach is adopted at each section to infer the influence of different parameters on the final outcome. This methodology has been decisive to better understand the factors affecting the phenomena occurring during impact.Quando uma gota colide com uma superfície interposta, estão normalmente envolvidas três fases: líquida (a gota), sólida (o substrato) e gasosa (o ambiente circundante). Este evento envolve um determinado número de parômetros associados com as características físicas das partículas incidentes, as propriedades da superfície alvo, e as características naturais do escoamento de ar. Cada ocorrência conduz a um desfecho singular, uma vez que cada partícula experimenta uma realidade diferente ao longo do ciclo de injeção. Por conseguinte, a elaboração de estratégias de modelação adequadas deste escoamento multifásico complexo requer um conhecimento profundo dos mecanismos subjacentes ao processo relativo ao impacto de spray. Foram propostos vários modelos computacionais na literatura, embora nem sempre com sucesso. Destes, apenas alguns tentaram reproduzir os cenários mais intrincados que incluem a formação e desenvolvimento de um filme líquido sobre a superfície devido à acumulação de partículas anteriormente injetadas, a presença de um escoamento transversal com elevada velocidade, e os efeitos térmicos promovidos pela existência de paredes quentes. Embora estes sejam alguns dos parâmetros que mais influenciam o resultado final do impacto de sprays em paredes, a maioria dos modelos ainda negligenciam alguns deles na sua formulação. Assim, de modo a capturar a maioria dos fenómenos físicos observados em estudos experimentais, os códigos de CFD devem ser equipados com uma formulação matemática mais desenvolvida. Durante esta investigação, foram concebidas três extensões computacionais independentes. Estes desenvolvimentos foram, posteriormente, integrados no modelo utilizado para simular as interações spray-parede. Estes sub-modelos — que foram propostos ao longo do estudo — foram denominados de filme líquido, evaporação e breakup, e eram destinados a complementar a formulação matemática de base adotada na simulação original. Esta abordagem contribuiu para aumentar a capacidade de previsão do modelo uma vez que este é agora capaz de capturar alguns fenómenos que não eram considerados anteriormente. Por outro lado, permitiu alargar a gama de aplicabilidade do código de CFD para um novo conjunto de condições de impacto (isto é, em ambientes quentes e com escoamentos cruzados de alta velocidade). Além disso, este trabalho apresenta uma análise detalhada dos resultados obtidos, sendo que é atribuída grande ênfase aos mecanismos de desintegração e características de gotas secundárias. São recorrentemente apresentadas comparações entre os resultados computacionais e experimentais tanto de forma quantitativa como qualitativa. Quando pertinente, o impacto de um determinado sub-modelo para o resultado previsto na simulação é também avaliado através da comparação das versões do código de CFD com e sem o respetivo sub-modelo. Além disso, uma abordagem sistemática é adotada em cada secção para inferir acerca da influência de diferentes parâmetros sobre o resultado final. Esta metodologia revelou-se decisiva para compreender melhor os fatores que afetam os fenómenos decorrentes do impacto