Acceleration boundary layer

Fig. 19. Kays MTEN calculation for the heat transfer to an accelerating boundary layer (St = Stanton number).

When a fluid flowing with a uniform velocity enters a pipe, a boundary layer forms at the walls and gradually thickens with distance from the entry point. Since the fluid in the boundary layer is retarded and the total flow remains constant, the fluid in the central stream is accelerated. At a certain distance from the inlet, the boundary layers, which have formed in contact with the walls, join at the axis of the pipe, and, from that point onwards, occupy the whole cross-section and consequently remain of a constant thickness. Fulty developed flow then exists. If the boundary layers are still streamline when fully developed flow commences, the flow in the pipe remains streamline. On the other hand, if the boundary layers are already turbulent, turbulent flow will persist, as shown in Figure 11.8. 

At the inlet to the pipe the velocity across the whole section is constant. The velocity at the pipe axis will progressively increase in the direction of flow and reach a maximum value when the boundary layers join. Beyond this point the velocity profile, and the velocity at the axis, will not change. Since the fluid at the axis has been accelerated, its kinetic energy per unit mass will increase and therefore there must be a corresponding all in its pressure energy. 

This chapter presents a physical description of the interaction of flames with fluids in rotating vessels. It covers the interplay of the flame with viscous boundary layers, secondary flows, vorticity, and angular momentum and focuses on the changes in the flame speed and quenching. There is also a short discussion of issues requiring further studies, in particular Coriolis acceleration effects, which remain a totally unknown territory on the map of flame studies. 

Kuznetsov, M. et al.. Effect of boundary layer on flame acceleration and DDT, Proceedings of the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems on CD, Montreal, 2005. 

The favourable properties which mark out vesicles as protocell models were confirmed by computer simulation (Pohorill and Wilson, 1995). These researchers studied the molecular dynamics of simple membrane/water boundary layers the bilayer surface fluctuated in time and space. The model membrane consisted of glycerine-1-monooleate defects were present which allowed ion transport to occur, whereby negative ions passed through the bilayer more easily than positive ions. The membrane-water boundary layer should be particularly suited to reactions which are accelerated by heterogeneous catalysis. Thus, the authors believe that these vesicles fulfil almost all the conditions required for the first protocells on earth ... 

Although the velocity right at the wall is zero, the boundary layer at the wall is quite small, so this equation applies up to the boundary layer very near the wall. Setting the sum of the forces equal to the particle acceleration and... 

At Re = 20, Cn increased sharply to pass through a maximum of approximately 0.22 at Re = 40, declining to be very small for Re > 150. Large normal drag is probably related to wake development, and similar effects may be expected whenever the flow pattern changes markedly with Re. In the critical range, lateral acceleration would tend to produce asymmetric boundary layer transition, so that significant lift can be anticipated. 

In his supplement to Syllabus, Dunkle remarked (Ref 22, p lid) that schlieren photography of deton waves in 40/60 C2H2/O2 initially at 1/4 atm showed a wavy pattern of criss-crossing dark diffuse lines behind the front. Fay Opel (Ref 17) calculated that if these lines are a weak wake of Mach waves in supersonic flow, the flow of the burnt gases with respect to the front is Mach 1.14 rather than Mach 1.00 as in a C-J process. However, at this pressure the reaction is complete within a fraction of a millimeter behind the front, and the flow could very well accelerate to Mach 1.14 with density decrease below the C-J value. Fay Opel traced the effect to the boundary layer. 

The entry-length region is characterized by a diffusive process wherein the flow must adjust to the zero-velocity no-slip condition on the wall. A momentum boundary layer grows out from the wall, with velocities near the wall being retarded relative to the uniform inlet velocity and velocities near the centerline being accelerated to maintain mass continuity. In steady state, this behavior is described by the coupled effects of the mass continuity and axial momentum equations. For a constant-viscosity fluid,... 

For laminar airflow in a tube, when 8 approaches the tube radius, Poiseuille flow or a parabolic flow profile is fully developed. This is accomplished by the acceleration of the central portion of the flow. However, when Re exceeds a value lying somewhere between 104 and 106, the laminar boundary layer becomes so thick that it is no longer stable, and a turbulent boundary layer develops. 

It is evident in Figures 30.18 and 30.19 that, after the accelerated adhesion test, the primer-coated air LPCAT treated TPOs showed poor adhesion performance as compared to argon and methane LPCAT-treated TPOs. This is a clear indication that air-plasma treatment can achieve the paintable surface but cannot provide the treated surface that can be painted in a durable manner. The poor durability can be attributed to (1) the water-sensitive nature of adhesion and (2) the excessive degradation of polypropylene that causes weaker boundary layer. 

The i ITE methods include a calculation of the turbulence energy, and hence one may study the effects of variable free stream turbulence. Kearney et al. (K3) have compared such predictions with their data, and Fig. 22 shows a typical result for strongly accelerated turbulent boundary layer. 

One of the functions of mechanical abrasion is to break up these boundary layers and assist in the transport of reactants to and products from the surface. During polishing, abrasive particles penetrate through the boundary layers bringing fresh chemical reactants to the surface. Chemical reactants may be adsorbed onto the abrasive or simply be able to diffuse to the surface more readily by virtue of the disruption of the boundary layers. In addition, reaction products can adsorb onto the abrasive particle to be transported from the surface with the particle (see, for example, Section 5.1.3). By assisting in the transport of reactants and products, abrasion serves to accelerate the chemical component of CMP as well as providing the mechanical component. 

The differential forms of the equations of motion in the velocity boundary layer are obtained by applying Newton s second law of motion to a differential conlrol volume element in the boundary layer. Newton s second law is an expression for momenluin balance and can be slated as the net force acting on the control volume is equal to the mass times the acceleration of the fluid element wilhht the control volume, which is also equal to the net rate of momentum outflow from the control volume. 

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