Simulação das Grandes Escalas de Escoamentos de Camada Limite Turbulenta
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Data
2007
Autores
Borges, Amadeu Duarte da Silva
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O objectivo principal deste trabalho foi contribuir para a melhoria da simulação computacional de escoamentos sobre geometrias complexas com o método da simulação das grandes escalas da turbulência (LES { Large Eddy Simulation), integrando novos modelos submalha e aperfeiçoando as condiçõeses de fronteira, especialmente na vizinhança do solo. Na tentativa de previsão da relaminarização foi ainda usada a metodologia da simulação dos turbilhões destacados (DES { Detached Eddy Simulation).
Utilizando os modelos de Smagorinsky, dinâmico, dinâmico Lagrangeano e de similaridade de escala de Bardina, estudou-se o escoamento turbulento num canal plano, com número de Reynolds Re¿ = 395. Após comparação com resultados obtidos anteriormente com o método da simulação numérica directa (DNS { Direct Numerical Simulation),conclui-se que os perfis de velocidade média e as flutuações da velocidade longitudinal foram bem reproduzidos por todas as simulações, destacando-se especialmente o modelo dinâmico Lagrangeano com similaridade de escala na previsão da flutuação. Já as flutuações das componentes vertical e transversal apresentaram uma concordância pior com os resultados de DNS, apresentado um défice de, aproximadamente, 40% no valor máximo. A tensão de corte foi bem prevista por todas as simulações, com destaque para a que usou o modelo dinâmico. Um estudo sobre o valor da constante do modelo de Smagorinsky permitiu concluir que, para a malha utilizada, o valor CS = 0:064 produzia resultados consideravelmente melhores que o valor inicial, melhorando nomeadamente a previsão da dissipação.
A simulação das grandes escalas da turbulência e o método dos turbilhões destacados foram usados no estudo do escoamento de uma camada limite sobre uma lomba, com número de Reynolds Reµ = 4030, utilizando uma malha curvilínea e não ortogonal. Em LES, as tensões submalha foram modeladas com recurso ao modelo dinâmico Lagrangeano. O escoamento experimenta um forte gradiente de pressão adverso a jusante do topo da lomba, que causou separação intermitente, mas sem separação do escoamento médio. A análise dos resultados mostrou que ambos os métodos foram capazes de prever a formação de camadas internas, assim como o rápido retorno ao equilíbrio após o fim da lomba. No entanto, o LES foi incapaz de reproduzir a tendência dos valores experimentais do coeficiente de fricção (Cf ) no topo da lomba, atribuída no trabalho experimental á relaminarização. Todavia, alguns parâmetros utilizados para medir a aceleração da camada limite sugeriram que não existiam condições para a ocorrência deste fenómeno. Os resultados de LES apresentaram boa concordãncia com os valores experimentais da velocidade longitudinal e tensões de Reynolds. As previsões de LES para o escoamento médio foram pouco sensíveis á formulaçãoo das condições de parede, mas apresentaram grande sensibilidade á resolução espacial. As previsões obtidas por DES apresentaram pior concordância com os valores experimentais que os resultados obtidos por LES, verificando-se, por exemplo, diferenças na ordem dos 30% na zona compreendida entre o topo e o final da lomba, nas proximidades da parede
Rodando a lomba de 45º relativamente ao escoamento incidente, introduziu-se uma característica tridimensional, que não existia no caso anterior. O escoamento á entrada do domínio computacional é caracterizado pelo número de Reynolds Reµ = 3800 e gradiente de pressão nulo. Os perfiss do escoamento médio desviaram-se do comportamento típico da lei logarítmica, mas não houve separação. A evolução das componentes do tensor de Reynolds foi explicada pelo crescimento de duas camadas internas, provocadas pelas descontinuidades na curvatura da superfície nas proximidades do início e do fim da lomba. Os coeficientes de pressão e de fricção mostraram-se indiferente ás características particulares de cada simulação (metodologia e malha). Na previsão da velocidade média, os resultados LES e DES produziram um comportamento muito semelhante. No que diz respeito ás tensões normais, as previsões LES apresentaram melhores resultados que os obtidos por DES, principalmente na região próxima da parede (nas duas posições a montante do fim da lomba e para y=µ = 1 verificaram-se diferenças de 80% para o DES). O mesmo aconteceu relativamente ás tensões de corte.
The main objective of this work was to contribute to the improvement of the computational simulation of flows over complex geometries using the Large Eddy Simulation (LES) method, integrating new subgrid models and improving the boundary conditions, especially in the near wall zone. The Detached Eddy Simulation (DES) methodology was also The turbulent flow in a flat channel with Reynolds number Re¿ = 395 was studied using the Smagorinsky, dynamic, dynamic Lagrangian and Bardina scale-similarity models. After comparison with available results of a Direct Numerical Simulation, we concluded that the average velocity profiles and the streamwise fluctuation were correctly predicted in all simulations, particularly with the dynamic Lagrangian model with Bardina scale-similarity stresses. However, the wall-normal and spanwise fluctuations presented a poor agreement with the DNS values, with a 40% de¯cit at the maximum value. The shear stress was correctly predicted in all simulations, specially in that with the dynamic model. A study about the Smagorinsky model constant leaded to CS = 0:064, with the adopted mesh and produced better results than the initial value, improving the dissipation predictionused, attempting to improved the prediction of the relaminarisation. The Large Eddy and the Detached Eddy Simulation methods were used in the study of a boundary layer flow over a bump, with Reynolds number Reµ = 4030, using a curvilinear and non-orthogonal grid mesh. The LES subgrid stresses were modelled with the dynamic Lagrangian model. The flow experiences a strong adverse pressure gradient after the summit of the bump, which causes an intermittent separation, but not mean-flow separation. The analysis of the results showed that both methods were able to predict the formation of internal layers, as well as a quick return to equilibrium after the bump. Nevertheless, the LES was unable to reproduce the tendency of the experimental values of the friction coefficient (Cf ) in the summit of the bump, attributed in the experimental work to the relaminarisation. The LES results are in good agreement with the measurements of the stream wise velocity and the Reynolds stresses. The LES predictions for the mean flow are little sensitive to the formulation of the wall conditions, but they present larger sensitivity to the spatial resolution. The results obtained using DES showed worse agreement with the measurements than the results obtained using LES, with, for instance, differences around 30% between the top and the end of the hill and near the wall. Turning the bump of 45o relatively to the incoming flow introduced a three-dimensional characteristic, absent in the previous case. The flow at the inlet of the computational domain is characterized by the Reynolds number of Reµ = 3800 and no pressure gradient. The mean velocity profile deviated significantly from the log-law, but without separation. The evolution of the Reynolds tensor components is explained by the growth of two internal layers forced by discontinuities in the surface curvature near the beginning and the end of the bump. The pressure and friction coefficients were not affected by particular features of each simulation (methodology and grid resolution). In the prediction of the mean velocity, both LES and DES showed a very similar behaviour. Regarding the normal stresses, better results were obtained with LES than with DES, especially in the region near the wall (in the two positions downstream of the hill and for y=µ = 1 differences of 80% for the DES were verified). The same was verified relatively to the shear stresses.
The main objective of this work was to contribute to the improvement of the computational simulation of flows over complex geometries using the Large Eddy Simulation (LES) method, integrating new subgrid models and improving the boundary conditions, especially in the near wall zone. The Detached Eddy Simulation (DES) methodology was also The turbulent flow in a flat channel with Reynolds number Re¿ = 395 was studied using the Smagorinsky, dynamic, dynamic Lagrangian and Bardina scale-similarity models. After comparison with available results of a Direct Numerical Simulation, we concluded that the average velocity profiles and the streamwise fluctuation were correctly predicted in all simulations, particularly with the dynamic Lagrangian model with Bardina scale-similarity stresses. However, the wall-normal and spanwise fluctuations presented a poor agreement with the DNS values, with a 40% de¯cit at the maximum value. The shear stress was correctly predicted in all simulations, specially in that with the dynamic model. A study about the Smagorinsky model constant leaded to CS = 0:064, with the adopted mesh and produced better results than the initial value, improving the dissipation predictionused, attempting to improved the prediction of the relaminarisation. The Large Eddy and the Detached Eddy Simulation methods were used in the study of a boundary layer flow over a bump, with Reynolds number Reµ = 4030, using a curvilinear and non-orthogonal grid mesh. The LES subgrid stresses were modelled with the dynamic Lagrangian model. The flow experiences a strong adverse pressure gradient after the summit of the bump, which causes an intermittent separation, but not mean-flow separation. The analysis of the results showed that both methods were able to predict the formation of internal layers, as well as a quick return to equilibrium after the bump. Nevertheless, the LES was unable to reproduce the tendency of the experimental values of the friction coefficient (Cf ) in the summit of the bump, attributed in the experimental work to the relaminarisation. The LES results are in good agreement with the measurements of the stream wise velocity and the Reynolds stresses. The LES predictions for the mean flow are little sensitive to the formulation of the wall conditions, but they present larger sensitivity to the spatial resolution. The results obtained using DES showed worse agreement with the measurements than the results obtained using LES, with, for instance, differences around 30% between the top and the end of the hill and near the wall. Turning the bump of 45o relatively to the incoming flow introduced a three-dimensional characteristic, absent in the previous case. The flow at the inlet of the computational domain is characterized by the Reynolds number of Reµ = 3800 and no pressure gradient. The mean velocity profile deviated significantly from the log-law, but without separation. The evolution of the Reynolds tensor components is explained by the growth of two internal layers forced by discontinuities in the surface curvature near the beginning and the end of the bump. The pressure and friction coefficients were not affected by particular features of each simulation (methodology and grid resolution). In the prediction of the mean velocity, both LES and DES showed a very similar behaviour. Regarding the normal stresses, better results were obtained with LES than with DES, especially in the region near the wall (in the two positions downstream of the hill and for y=µ = 1 differences of 80% for the DES were verified). The same was verified relatively to the shear stresses.
Descrição
Tese de Doutoramento em Ciências de Engenharia
Palavras-chave
Mecânica dos fluidos , Turbulência , Escoamentos , Camada-limite