Fractional Model to estimate the turbulence index in pipelines

Abstract

Turbulence is a phenomenon whose description is still an open question, despite presenting itself in nature and many industrial processes. While in the laminar regime, the flow behavior is described successfully through the phenomenological equations of conservation of the moment. In a turbulent regime, this approach fails since the fluctuations around the average speed are magnified and cannot neglect. Pressure drop determinations are essential in pipelines since they are related to an oil country's production and economy. This paper proposes a model to estimate the turbulence speed profile for flows in tubes as a function of the Reynolds number. The moment's conservation equations are fractional differential equations, where the hypothesis established that the order of the derivative depends on the intensity of the fluctuations. The theoretical results by our Model correspond qualitatively with those expected, allowing hypothesis acceptance.