Transitional Boundary Layers

Liu, X. and Rodi, W. (1991). Experiments on transitional boundary layers with wake induced unsteadiness. J. Fluid Mech. 231, 229-256. 

Poll, D.I.A., Danks, M. and Yardley, M. (1996). The effects of suction and blowing on stability and transition at a swept attachment-line. In Transitional Boundary Layers in Aeronautics (Eds. R. Henkes J. Van Ingen), Elsevier, Amsterdam, Holland. 

Transitional Boundary Layers for Uniform Free-Stream Velocity... 

Fig. 3. An overview of atomistic mechanisms involved in electroceramic components and the corresponding uses (a) ferroelectric domains capacitors and piezoelectrics, PTC thermistors (b) electronic conduction NTC thermistor (c) insulators and substrates (d) surface conduction humidity sensors (e) ferrimagnetic domains ferrite hard and soft magnets, magnetic tape (f) metal—semiconductor transition critical temperature NTC thermistor (g) ionic conduction gas sensors and batteries and (h) grain boundary phenomena varistors, boundary layer capacitors, PTC thermistors.

However, the transition Reynolds number depends on free-stream turbulence and may range from 3 X 10 to 3 X lO ". The laminar boundary layer thickness 8 is a function of distance from the leading edge ... 

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... 

Between about Rop = 350,000 and 1 X 10 , the drag coefficient drops dramatically in a drag crisis owing to the transition to turbulent flow in the boundary layer around the particle, which delays aft separation, resulting in a smaller wake and less drag. Beyond Re = 1 X 10 , the drag coefficient may be estimated from (Clift, Grace, and Weber) ... 

The boundary layers, or interphases as they are also called, form the mesophase with properties different from those of the bulk matrix and result from the long-range effects of the solid phase on the ambient matrix regions. Even for low-molecular liquids the effects of this kind spread to liquid layers as thick as tens or hundreds or Angstrom [57, 58], As a result the liquid layers at interphases acquire properties different from properties in the bulk, e.g., higher shear strength, modified thermophysical characteristics, etc. [58, 59], The transition from the properties prevalent in the boundary layers to those in the bulk may be sharp enough and very similar in a way to the first-order phase transition [59]. 

Moreover, in many cases, a shift of Tg to lower values of temperature has been detected, but in these cases the quality of adhesion between phases may be the main reason for the reversing of this attitude 11,14). If calorimetric measurements are executed in the neighbourhood of the glass transition zone, it is easy to show that jumps of energies appear in this neighbourhood. These jumps are very sensitive to the amount of filler added to the matrix polymer and they were used for the evaluation of the boundary layers developed around fillers. 

Indeed, the multi-layered model, applied to fiber reinforced composites, presented a basic inconsistency, as it appeared in previous publications17). This was its incompatibility with the assumption that the boundary layer, constituting the mesophase between inclusions and matrix, should extent to a thickness well defined by thermodynamic measurements, yielding jumps in the heat capacity values at the glass-transition temperature region of the composites. By leaving this layer in the first models to extent freely and tend, in an asymptotic manner, to its limiting value of Em, it was allowed to the mesophase layer to extend several times further, than the peel anticipated from thermodynamic measurements, fact which does not happen in its new versions. 

The novel element in these models is the introduction of a third phase in the Hashin-Rosen model, which lies between the two main phases (inclusions and matrix) and contributes to the progressive unfolding of the properties of the inclusions to those of the matrix, without discontinuities. Then, these models incoporate all transition properties of a thin boundary-layer of the matrix near the inclusions. Thus, this pseudo-phase characterizes the effectiveness of the bonding between phases and defines a adhesion factor of the composite. 

By using Lipatov s theory, interrelating the abrupt jumps in the specific heat of composites at their respective glass transition temperatures with the values of the extents of these boundary layers, the thickness of the mesophase was accurately calculated. 

When a fluid flowing at a uniform velocity enters a pipe, the layers of fluid adjacent to the walls are slowed down as they are on a plane surface and a boundary layer forms at the entrance. This builds up in thickness as the fluid passes into the pipe. At some distance downstream from the entrance, the boundary layer thickness equals the pipe radius, after which conditions remain constant and fully developed flow exists. If the flow in the boundary layers is streamline where they meet, laminar flow exists in the pipe. If the transition has already taken place before they meet, turbulent flow will persist in the... 

Putting the constant equal to zero, implies that <5 = 0 when x = 0, that is that the turbulent boundary layer extends to the leading edge of the surface. An error is introduced by this assumption, but it is found to be small except where the surface is only slightly longer than the critical distance xc for the laminar-turbulent transition. 

It is of interest to compare the rates of thickening of the streamline and turbulent boundary layers at the transition point. Taking a typical value of Rexc — 105, then ... 

Thus the turbulent boundary layer is thickening at about four times the rate of the streamline boundary layer at the transition point. 

Water flows at a velocity of 1 m/s over a plane surface 0.6 m wide and 1 m long. Calculate the total drag force acting on the surface if the transition from streamline to turbulent flow in the boundary layer occurs when the Reynolds group ReXc = 105. 

For the inlet length of a pipe in which the boundary layers are forming, the equations in the previous section will give an approximate value for the heat transfer coefficient. It should be remembered, however, that the flow in the boundary layer at the entrance to the pipe may be streamline and the point of transition to turbulent flow is not easily defined. The results therefore are, at best, approximate. 

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