Wall velocity

Imposition of no-slip velocity conditions at solid walls is based on the assumption that the shear stress at these surfaces always remains below a critical value to allow a complete welting of the wall by the fluid. This iraplie.s that the fluid is constantly sticking to the wall and is moving with a velocity exactly equal to the wall velocity. It is well known that in polymer flow processes the shear stress at the domain walls frequently surpasses the critical threshold and fluid slippage at the solid surfaces occurs. Wall-slip phenomenon is described by Navier s slip condition, which is a relationship between the tangential component of the momentum flux at the wall and the local slip velocity (Sillrman and Scriven, 1980). In a two-dimensional domain this relationship is expressed as... 

Equations (3.59) and (3.60) are recast in terms of their components and solved together. After algebraic manipulations and making use of relations (3.61) slip-wall velocity components are found as... 

Fig. 31. Bubble wall velocity vs time during cavitational collapse for different values of the parameter X defined as X ss 0.4 c iTl] p./fri/2 (Ph — Pv)i/2). X permits us to account for the viscous and inertia effects of the polymer solution (redrawn according to Ref. [122]) ...

The arrow indicates the inner wall velocity. The double peaks indicate a bimodal behavior associated with velocity fluctuations (adapted from reference [23]). 

X component of velocity of the screw flight at the barrel wall z component of velocity of the screw flight at the barrel wall velocity of barrel as observed in the Lagrangian frame X component of velocity of the barrel as observed in the Lagrangian frame z component of velocity of the barrel as observed in the Lagrangian frame velocity component in the x direction... 

Table 2, p 5 of Ref 7, entitled "Cylinder Test Results , shows density, detonation velocities and cylinder wall velocities for various pure and mixed HE s. Our table 2 gives some selected values... 

Explosive Density g/cc Detonation Velocity Cylinder Wall Velocity (mm/psec) ... 

I. Since Kury et al did not explain, how they deed cylinder wall velocity, it was assumed by senior author BTF that it was obtd for Comp B, for example... 

II. If brisance is judged by wall velocity, then HMX has the highest brisance, while that of TNT is the lowest... 

The success of the ID fluid dynamic model to describe the flow field in the DPF channel (Konstandopoulos and Johnson, 1989 Konstandopoulos et al., 1999, 2003) is an indication for the existence of a (nearly) self-similar flow field. A necessary condition for the application of the ID model for the heat transfer problem as well, is that the wall velocity ww variation must be small along the characteristic channel length required for establishment of a steady heat transfer pattern (i.e. a length of a2ftz/y.lh). In transferring the above to the case of flow and heat transfer in a DPF channel we may formally write the heat balance as... 

Fig. 3.11 The cylinder on the left is filled with a gas at pressure p and bounded by two pistons that can move with velocity u. The long cylindrical annulus on the left is filled with a fluid. The center rod is fixed, but the outer cylindrical shell moves upward at a constant velocity. Under these circumstances a steady state-velocity distribution will develop in the fluid as illustrated u(r), with the zero velocity at the inner-rod wall and the wall velocity at the shell surface. A cylindrical control volume with its zrz shear stresses is illustrated.

Consider a long cylindrical shell whose interior is filled with an incompressible fluid. If the fluid is initially at rest when the cylinder begins to rotate, a boundary layer develops as the momentum diffuses inward toward the center of the cylinder. The fluid s circumferential velocity vu comes to the cylinder-wall velocity immediately, owing to the no-slip condition. At very early time, however, the interior fluid will be only weakly affected by the rotation, with the influence increasing as the boundary layer diffuses inward. If the shell continues to rotate at a constant angular velocity, the fluid inside will eventually come to rotate as a solid body. 

The cylinder-wall circumferential velocity can be an arbitrary function of time, with the fluid velocity still subject to parallel-flow assumptions. The cylindrical analog of Stokes Second problem is to let the cylinder-wall velocity oscillate in a periodic manner. The wall velocity is specified as... 

For a nondimensional oscillation period of tp = 0.1, Fig. 4.15 shows the circumferential velocity profiles at four instants in the period. The wall velocity follows the specified rotation rate exactly, which it must by boundary-condition specification. The center velocity r — 0 is constrained by boundary condition to be exactly zero, incenter = 0. The interior velocities are seen to lag the wall velocity, owing to fluid inertia and the time required for the wall s influence to be diffused inward by fluid shearing action. 

There is a single parameter that governs this system, the Reynolds number based on the wall-velocity difference A V,... 

Fig. 5.14 Nondimensional velocity profiles for selected values of Rey, where both the lower wall and upper wall velocities are equal at V.

B5 - B6 These cells are the specified values (in m/s) of the inner and outer wall velocities. The values are assigned to the names in A5-A6 using the INSERT NAME DEFINE command. 

A7-B7 The maximum wall velocity was used as the scaling factor in the nondimension-alization of the problem. Cell B7 contains =MAX(ABS(U in), ABS(U.out)) and A7 contains the name U max, which is defined to represent the contents of B7. 

Step 1 is purely hydrodynamic and relates the perturbation Q to the velocity near the wall which is the only relevant quantity for the mass transfer response. at are either wall velocity gradients or coefficients involved in the velocity expansion near the wall. This step requires the use of Navier-Stokes equations and will be treated in Chapter 2. 

Cathodic walls velocity v = velocity in the porous electrode... 

We describe herein the first analysis of copper cylinder expansion tests with pressed ETN. We discuss the detonation behavior for the material, along with wall velocity and diameter effect information. All data is compared to PETN tested under similar conditions. 

Figure 2. (a) Shorting switch data used to determine detonation velocities, (b) PDV wall velocities for ETN and PETN cylinder shots. Each line is an average from 4 PDV probes. 

Explosive Composition Density g/cc Deton Vel mm/ysec Cylinder Wall Velocity mm/ftsec at R—Ro =5 mm R—R0=19mm ... 

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