CaracterizaciĆ³n del flujo sobre vertederos escalonados con pendiente uniforme y peldaƱo variable
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2022
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es
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Universidad AndrƩs Bello
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Licencia CC
Licencia CC
Resumen
En la presente memoria se aborda el estudio numĆ©rico del flujo de agua en la regiĆ³n no aireada de tres vertederos escalonados de pendiente constante e igual a 51,34Ā°.Los tres casos modelados denominados Caso A, Caso Base y CaseB tienen escalones de geometrĆa variable con relaciones de altura/anchode10/8, 5/4 y 2,5/2, respectivamente. Estas relaciones corresponden a tamaƱos de cavidad(š¾š )de 6,26, 3,13 y 1,57 cm respectivamente, los cuales son indicativos del tamaƱo de la macro-rugosidad sobre el cual el flujo debe pasar. Con esto se busca dilucidar el efecto que tiene el tamaƱo de la cavidad sobre las variables medias del flujo tales como velocidad, altura de aguas, distribuciĆ³n de presiones, energĆa cinĆ©tica turbulenta y tasa de disipaciĆ³n de la energĆa cinĆ©tica turbulenta. Los tres modelos fueron implementados haciendo uso del software Open FOAM y considerando las ecuaciones promediadas de Navier-Stokes junto con el modelo de turbulencia k-ĪµestĆ”ndar.Los resultados numĆ©ricos indican que, a mayor tamaƱo de cavidad, mayor es tambiĆ©n la velocidad en la cavidad. Sin embargo, las velocidades fuera de la cavidad no parecieran estĆ”n influenciadas por el tamaƱo de la cavidad dada la similitud de la distribuciĆ³n de velocidades en la columna de agua entre los distintos vertederos. Para un vertedero escalonado dado, las distribuciones de energĆa cinĆ©tica y tasa de disipaciĆ³n de energĆa cinĆ©tica turbulenta en los vĆ©rtices de los peldaƱos pueden ser resumidas en una Ćŗnica curva, cuando la relaciĆ³n entre el tamaƱo de la cavidad y la altura de escurrimiento š¾š šāes menor a 0,8. Esto es, para los casos Base y B. Para el caso A, que tiene la rugosidad mayor, la auto similaridad en la distribuciĆ³n no es tan clara. TambiĆ©n se obtuvo, que los valores mĆ”ximos de estas estadĆsticas de la turbulencia crecen con el tamaƱo de la cavidad. Respecto a la distribuciĆ³n de presiones dentro de las cavidades, el Caso B es el Ćŗnico que tiene una distribuciĆ³n mayor a la hidrostĆ”tica, atribuible a lo pequeƱo de la cavidad. Los otros dos casos, presentan valores menores a la hidrostĆ”tica, con valores incluso negativos. Las presiones medidas en los vĆ©rtices de los escalones en la columna de agua siguen una distribuciĆ³n mayor a la hidrostĆ”tica para los tres casos estudiados. En los casos B y Base las presiones mĆ”ximas se ubican muy cerca del vĆ©rtice de los escalones. De manera diferente, se obtuvo que para el caso A, con mayor tamaƱo de cavidad, las presiones mĆ”ximas se ubican aproximadamente a un 20% de la altura de aguas.
This thesis discusses the numerical study of water flow in the non-aerated region of three stepped spillways havinga constant slope of51.34Ā°. The three modeled cases named Case A, Base and B have steps of variable geometry with height/width ratios of 10/8, 5/4 and 2.5/2, respectively. These ratios correspond to cavity sizes (š¾š ) of 6.26, 3.13 and 1.57 cm respectively, which are indicative of the size of the macro-roughness over which the flow must pass. This is to elucidatethe effect ofthe cavity size on the mean flow variables such as velocity, water depth, pressure distribution, turbulent kinetic energy, and dissipation rateof turbulent kinetic energy. The three models were implemented usingthe softwareOpenFOAM and considering the averaged Navier-Stokes equations together with the standard k-Īµ turbulence model.Numerical results indicate that, the larger the cavity size, the higher the velocity in the cavity. However, the velocities outside the cavity do not appear to be influenced by the cavity size given the similarity of the velocity distributionsin the water column amongthe different spillways. For a given steppedspillway,thedistributionsofturbulent kinetic energy andrate of dissipation of turbulent kinetic energy at the step edgescan be summarized in a single curve when the ratio of cavity size to water depthš¾š šāis smallerthan 0.8. Thisis, for Base and B cases. For case A, which has the higher roughness, a self-similardistribution is not so clear. It was also found that the maximum values of these turbulence statistics increase with the cavity size.Regarding pressuredistributionsinside the cavities, Case B is the only one that has a distribution higher than the hydrostaticdistribution, attributedto the small size of the cavity. The other two cases present values lower than hydrostaticdistribution, with even negative values. The pressures measured at the step edgesin the water column follow a distribution which is greater than the hydrostatic for the three cases studied. In cases B and Base, the maximum pressures are located very close to the step edges. Differently, for case A, with larger cavity size, the maximum values of pressureare located approximately at 20% of the water depth.
This thesis discusses the numerical study of water flow in the non-aerated region of three stepped spillways havinga constant slope of51.34Ā°. The three modeled cases named Case A, Base and B have steps of variable geometry with height/width ratios of 10/8, 5/4 and 2.5/2, respectively. These ratios correspond to cavity sizes (š¾š ) of 6.26, 3.13 and 1.57 cm respectively, which are indicative of the size of the macro-roughness over which the flow must pass. This is to elucidatethe effect ofthe cavity size on the mean flow variables such as velocity, water depth, pressure distribution, turbulent kinetic energy, and dissipation rateof turbulent kinetic energy. The three models were implemented usingthe softwareOpenFOAM and considering the averaged Navier-Stokes equations together with the standard k-Īµ turbulence model.Numerical results indicate that, the larger the cavity size, the higher the velocity in the cavity. However, the velocities outside the cavity do not appear to be influenced by the cavity size given the similarity of the velocity distributionsin the water column amongthe different spillways. For a given steppedspillway,thedistributionsofturbulent kinetic energy andrate of dissipation of turbulent kinetic energy at the step edgescan be summarized in a single curve when the ratio of cavity size to water depthš¾š šāis smallerthan 0.8. Thisis, for Base and B cases. For case A, which has the higher roughness, a self-similardistribution is not so clear. It was also found that the maximum values of these turbulence statistics increase with the cavity size.Regarding pressuredistributionsinside the cavities, Case B is the only one that has a distribution higher than the hydrostaticdistribution, attributedto the small size of the cavity. The other two cases present values lower than hydrostaticdistribution, with even negative values. The pressures measured at the step edgesin the water column follow a distribution which is greater than the hydrostatic for the three cases studied. In cases B and Base, the maximum pressures are located very close to the step edges. Differently, for case A, with larger cavity size, the maximum values of pressureare located approximately at 20% of the water depth.
Notas
Memoria (Ingeniero Civil)
Palabras clave
Vertederos Escalonados, Modelos MatemĆ”ticos, SimulaciĆ³n por Computador