Transition from laminar to turbulent

It commonly assumed that the flow is turbulent in the shot sleeve, runner system, and the duration of the filling of the cavity. Further, it also assumed that the model can reasonably represent the turbulence structure. These assumptions are examined herein. We examine the flow in 1) the shot sleeve, 2) the runner system, and 3) the mold cavity. Note, that even if the turbulence is exist in some regions it doesn't necessarily mean that all the flow field is turbulent.

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Figure: Transition to turbulent flow in circular pipe for instantaneous flow after Wygnanski and others by interpolation

Figure exhibits the transition to a turbulent flow for instantaneous starting flow in a circular pipe. The abscissa represents time and the y-axis represents the number at which transition to turbulence occurs. The points on the graphs show the transition to a turbulence. This figure demonstrates that a large time is required to turn the flow pattern to a turbulent which measured in several seconds. The figure demonstrates that the transition does not occur below a certain critical number (known as the critical number for steady state). It also shows that a considerable time has to elapse before transition to turbulence occurs even for a relatively large Reynolds number. The geometry in die casting however is different and therefore it is expected that the transition occurs at different times. Our present knowledge of this area is very limited. Yet, a similar transition delay is expected to occur after the ``instantaneous'' start-up which probably will be measured in seconds. The flow in die casting in many situations is very short (in order of milliseconds) and therefore it is expected that the transition to a turbulent flow does not occur.

After the liquid metal is poured, it is normally repose for sometime in a range of 10's seconds. This fact is known in the scientific literature as the quieting time for which the existed turbulence (if exist) is reduced and after enough time (measured in seconds) is illuminated. Hence, if turbulence was created during the filling process of the shot sleeve is ``disappeared''. Now we can examine the question, is the flow in the duration of the slow plunger velocity is turbulent (see Figure ).

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Figure: Flow pattern in the shot sleeve

Clearly, the flow in the substrate (a head the wave) is still (almost zero velocity) and therefore the turbulence does not exist. The number behind the wave is above the critical number (which is in the range of 2000-3000). The typical time for the wave to travel to the end of the shot sleeve are in the range of a second. At present there are no experiments on the flow behind the wave¹⁰. To discuss the free interface as oppose to solid interface. The estimation can be done by looking at what is known in the literature about the transition to turbulence in instantaneous starting pipe flow. It has been shown [#!flow:wygy!#] that the flow changes from a laminar flow to turbulent flow occurs in an abrupt meaner for a flow with supercritical number.

A typical velocity of the propagating front (transition between laminar to turbulent) is about at same velocity as the mean velocity of the flow. Hence, it is reasonable to assume that the turbulence is confined to a small zone in the wave front since the wave is traveling in a faster velocity than the mean velocity. should we insert a graph about the relation between the mean velocity and wave velocity in the shot sleeve Note that the thickness of the transition layer is a monotone increase function of time (traveling distance). The number in the shot sleeve based on the diameter is in a range of which means that the boundary layer has not developed much. Therefore, the flow can be assumed as almost a plug flow with the exception of the front region. what about the solid layer the skimmed to ``increase'' the plunger head and effects on the flow.