Transition length

The transition length for deflagration to detonation is of the order of a meter for highly reactive fuels such as acetylene, hydrogen, and ethylene, but larger for most other hydrocarbon-air mixtures. Consequently, most laboratory... 

Langhaar, H. L. Steady flow in the transition length of a straight tube. I. Appl. Mech. 9 A55-A58, 1942. 

The K approach may also be used to define a transition crack length at, above which steady state applies. This transition length is given by31,83... 

Transition length for laminar and turbulent flow. The length of the entrance region of the tube necessary for the boundary layer to reach the center of the tube and for fully developed flow to be established is called the transition length. Since the velocity varies not only with length of tube but with radial distance from the center of the tube, flow in the entrance region is two dimensional. 

Thus for a 50-mm- (2-in.-) ID pipe and a Reynolds number of 1500 the transition length is 3.75 m (12.3 ft). If the fluid entering the pipe is turbulent and the velocity in the tube is above the critical, the transition length is nearly independent of the Reynolds number and is about 40 to 50 pipe diameters, with little difference between the distribution at 25 diameters and that at greater distances from the entrance, For a 50-mm-ID pipe, 2 to 3 m of straight pipe is sufficient when flow... 

Distance measured parallel with flow direction, m or ft x transition length... 

For this discrepancy explanation the relationship for kinetic scaling at condition R 4 is transition length scale) should be written [88] Eq. (51) ... 

If the velocity profile at the entrance region of a tube is flat, a certain length of the tube is necessary for the velocity profile to be fully established. This length for the establishment of fully developed flow is called the transition length or entry length. This is shown in Fig. 2.10-6 for laminar flow. At the entrance the velocity profile is flat i.e., the velocity is the same at all positions. As the fluid progresses down the tube, the boundary-layer thickness increases until finally they meet at the center of the pipe and the parabolic velocity profile is fully established. 

There exist several possibilities to generate such turbulent fluctuations at the inflow boundary [19]. Batten et al. [3] reformulated on the ideas of Kraichnan [14] and Smirnov et al. [21] for wall bounded flows. The velocity signal is generated by a sum of sines and cosines with random phases and amplitudes. The wave numbers are calculated from a three-dimensional spectrum and are scaled by the values of the Reynolds-stress tensor. A special wall treatment was applied to elongate near-wall structures. A transition length to physical turbulence of about ten channel half heights was obtained at low Reynolds number channel flow. 

According to the criterion given in [16, 21], the DDT in a smooth long tube can occur when the tube diameter is larger than the detonation cell size d> a). In. this case, the transition length exceeds the tube diameter by 10 times, thus, that criterion can be applied only for long tubes. The criterion needs to stress the difference between a minimum tube diameter which sustains detonation propagation (f = aln) and a minimum tube diameter which enables the DDT d = a). 

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