Understanding The Flow Dynamics Of An Aircraft

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section{The Road to Transition.} Understanding the flow dynamics of an aircraft in flight conditions is a very difficult task. The process that the flow undergoes is complicated and many factors are involved. The main understanding of this process is that it undergoes a transition from laminar flow (linear, parallel streamlines) to turbulent (chaotic, mixed) one. The region where this changes is called laminar-turbulent transition. It is important to understand the characteristics of the flow for prediction of this transition location. Laminar flows are sensitive to adverse pressure gradients and are inclined to separate, whereas turbulent flows create larger wall friction. \ Reynolds cite{Reynolds1883} assessed this laminar-turbulent transition by performing experiments in a pipe. He did this by injecting ink into a pipe with a water flow and observing the results. He noted that there were different regimes based on the speed of the flow, laminar and turbulent regions. A parameter, which is named after him, quantified this different behaviour of the fluid. The Reynolds number is the ratio of the inertia forces over the viscous ones and it dictates the transition process. We are interested in what caused this transition to occur and if there needs to be a critical value for this transition to happen. \ In aerodynamics many factors exist that contribute to the triggering of turbulence. In a three-dimensional boundary-layer on a swept wing, various instabilities are
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