Circular Channels

The data of Triplett et al. (1999a) were obtained with air and water at near-atmospheric pressure and room temperature. 

The flow regimes in the test sections were identified visually with the aid of a strobe and a digital camera. The camera was always targeted at the test section center. No systematic attempt was made to assess and eliminate the test section entrance effects on the flow regimes. However, the distance between the point pictured by the camera and the test section inlet was well over 100 channel diameters everywhere. Thus, although the possibility exists that the reported flow regimes are influenced by the test section entrance conditions, this influence may not be significant. 

At relatively low liquid superficial velocities, increasing the mixture volumetric flux led to longer bubbles and shorter liquid slugs, eventually leading to the merging of elongated bubbles, and the development of the slug-annular flow pattern, repre- 

---

Hartnett, S. P. and Kostic, M. /nr. Comm. Heat Mass Transfer 17 (1990) 59. Turbulent friction factor correlations for power law fluids in circular and non-circular channels. 

Before describing the transition prediction methods, it is instructive to describe how a diabatic map is used. One chooses a desired mass flux and sets the heat flux to be dissipated (assumed uniform along and around the circular channel) up to the desired local length from the inlet to find the corresponding local vapor quality (from an energy balance) and thus the location of this process condition on the map. The... 

Equation (6.27) was obtained for circular channels. Rectangular channels with four or three conductive walls are shown in Eig. 6.10. 

If the value of rB,oNB Ts, (D -c 1) the integral characteristics for the circular channels, the rectangular channels with four and three heated walls, respectively,... 

Figure 2.29 Dimensionless entropy generation rate as a function of Reynolds number for a circular channel of 610 pm diameter and different ratios of the fluid inlet temperature and the wall temperature, taken from [104. ...

The two plates were not manufactured via the same route and were not made of the same material [7]. Typically, rectangular channels in silicon are realized by sawing, whereas semi-circular channels are made in glass by wet-chemical etching. Such glass/silicon plates are joined by anodic bonding. 

From Eqs. (93) the values of gr could be found, similarly to solving the integral equation in Model I. Aris (A9) has also generalized this discrete model with circular channels to a continuous model with channels of any shape. Unfortunately, the equations for the continuous case can not easily be solved. 

The mixing ability of microfluidic systems was tested using a rotary pump, a circular channel with inputs and outputs that can be peristaltically pumped, opeued, and closed. It was found that after only a few minutes of active mixing (due to pumping), a uniform mixture of particles is obtained that would have taken hours to achieve by diffusion. This is also useful for accelerating diffusion-... 

With the exception of a spatially dependent body force f, there is no source or sink term in the vorticity transport equation. Therefore the source of vorticity is usually at boundaries, with the shear at solid walls being the most common means to produce vorticity. To illustrate the behavior of vorticity generation at a wall, consider the axisymmetric flow in a circular channel as illustrated in Fig. 3.12. 

Fig. 3.12 Axial velocity and circumferential vorticity profiles in a circular channel with axisymmetric flow.

Consider the fully developed steady flow of an incompressible around a circular channel that has an inner radius of n and an outer radius of rD (Fig. 4.28). The objective is to derive a general relationship for the friction factor as a function of flow parameters (i.e., Reynolds number) and channel geometry (i.e., hydraulic diameter Dh and the ratio = r, /r0). A friction factor /, which is a nondimensional measure of the wall shear stress, may be defined as... 

Beginning with the constant-viscosity, incompressible Navier Stokes equations, write a reduced form of the radial and circumferential momentum equations that is appropriate to represent the fully developed flow in the circular channel. 

Show that the analysis just derived for the circular channel has the correct parallel-plate limiting behavior for channel widths that are small compared to the radius, that is, small gaps where r0 - n (r,- + r0)/2. 

Fig. 7.6 Nondimensional velocity profiles in the entry region of a circular channel.

When some solid propint grains, particularly those with relatively long circular channels available for gas flow, are fired in rockets, there are frequently observed certain periodic pressure oscillations. These resonating pressures sometimes reach amplitudes high enough to cause the grain to crack and, in some cases, ultimately to rupture the rocket chamber. 

Flow in a circular channel with a significant relative length 1/H (here 1 — is the length of circular head H = R2 — Rt is the width of clearance, i.e., the difference between the inner radius of the outer cylinder, the tip, and the outer radius of the inner cylinder, the core) was simulated by the flow of a polymer between two parallel plates removed from one another to a distance H (see Fig. la). The resultant flow occurs due to the pressure difference AP = P, — P2 and motion of the upper plate with velocity U0 in the direction transverse to the axial flow. In this case boundary conditions in the Cartesian system of coordinates are ... 

Rheodynamics of non-linear viscous fluids flowing in circular channels with moving walls is described most comprehensively in 1S-34). With respect to the above conclusion (see sect 2.2.1) that the high elasticity of a melt influences insignificantly flow rate parameters of a flow, the combined shear is discussed in 24128-30,341 on the basis of a general approach to the analysis of viscosimetric flows developed by B. Colleman and W. Noll. 

Schulman ZP, Zadvornyh VN, Litvinov AI (1987) Rheodynamics of nonlinearly viscoplastic fluids in circular channels with movable walls. Acad, of Sc. Bel. SSR, Minsk, Preprint 45 51 c... 

---