08-turb - Lecture 8 Turbulence Applied Computational Fluid...

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1 Lecture 8 - Turbulence Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org © André Bakker (2002-2006) © Fluent Inc. (2002)
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2 Turbulence What is turbulence? Effect of turbulence on Navier-Stokes equations. Reynolds averaging. Reynolds stresses.
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3 Instability All flows become unstable above a certain Reynolds number. At low Reynolds numbers flows are laminar. For high Reynolds numbers flows are turbulent. The transition occurs anywhere between 2000 and 1E6, depending on the flow. For laminar flow problems, flows can be solved using the conservation equations developed previously. For turbulent flows, the computational effort involved in solving those for all time and length scales is prohibitive. An engineering approach to calculate time-averaged flow fields for turbulent flows will be developed.
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4 Time What is turbulence? Unsteady, aperiodic motion in which all three velocity components fluctuate, mixing matter, momentum, and energy. Decompose velocity into mean and fluctuating parts: U i (t) U i + u i (t). Similar fluctuations for pressure, temperature, and species concentration values.
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5 Examples of simple turbulent flows jet mixing layer wake Some examples of simple turbulent flows are a jet entering a domain with stagnant fluid, a mixing layer, and the wake behind objects such as cylinders. Such flows are often used as test cases to validate the ability of computational fluid dynamics software to accurately predict fluid flows.
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6 Transition The photographs show the flow in a boundary layer. Below Re crit the flow is laminar and adjacent fluid layers slide past each other in an orderly fashion. The flow is stable. Viscous effects lead to small disturbances being dissipated. Above the transition point Re crit small disturbances in the flow start to grow. A complicated series of events takes place that eventually leads to the flow becoming fully turbulent.
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7 Transition in boundary layer flow over flat plate
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8 Transition in boundary layer flow over flat plate Turbulent spots Fully turbulent flow T-S waves
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9 Turbulent boundary layer Merging of turbulent spots and transition to turbulence in a natural flat plate boundary layer. Top view Side view
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10 Turbulent boundary layer Close-up view of the turbulent boundary layer.
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Transition in a channel flow Instability and turbulence is also seen in internal flows such as channels and ducts. The Reynolds number is constant throughout the pipe and is a function of flow rate, fluid properties and diameter. Three flow regimes are shown: Re < 2200 with laminar flow. Re = 2200 with a flow that alternates between turbulent and laminar. This is called transitional flow. Re > 2200 with fully
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08-turb - Lecture 8 Turbulence Applied Computational Fluid...

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