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Normalisation

# Normalisation - Testing velocity profiles in turbulent jets...

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Testing velocity profiles in turbulent jets for self- similarity -- a practical guide 1. Defining a coordinate system First, let us clearly define a sensible coordinate system for this flow. D y x U Fig. 1: Coordinate system (axes in blue) for turbulent jet flow. This is the usual way of doing it, and it is worth noting why this is so. First, in this model of the flow, only two spatial dimensions are considered. This includes both planar jets and axisymmetric jets. Whenever there is a mean flow, or most dominant flow component (in this case, the flow along the jet axis), it is common to assign the x coordinate, and corresponding u velocity component parallel to that direction. The flow measured is a time-averaged component (owing to the relatively large time constant of the pitot tube/manometer system), and so it is denoted U , rather than u . x is defined parallel to the mean flow and the long axis of the jet exit nozzle, beginning at the nozzle exit. Positive x moves in the direction of the flow, with positive U . The remaining coordinate, y , should be perpendicular to x . It has its origin at the centerline, which is the line of symmetry of the jet. Note how the coordinate system is fixed with respect to the jet flow itself, and not to some arbitrary laboratory reference. 2. The mean velocity profile in a turbulent jet The evolution of the jet flow at x > 5-6D is thought to occur in a self-similar fashion because turbulent velocity fluctuations have had sufficient time to re-arrange the initial flow that further flow evolution occurs with only pre-existing turbulence as its precursor.

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