L-shaped probes

Figure 1. Sampling devices A, L-shaped probe B, straight probes C, side-wall sampling and D, side-wall sampling with a projection. (Reproduced with permission from reference 23. Copyright 1989 Gulf Publishing Company.)...

Thin L-shaped probes are commonly used to measure solids concentration profile in slurry pipelines (28-33), However, serious sampling errors arise as a result of particle inertia. To illustrate the effect of particle inertia on the performance of L-shaped probes, consider the fiuid streamlines ahead (upstream) of a sampling probe located at the center of a pipe, as shown in Figure 2. The probe has zero thickness, and its axis coincides with that of the pipe. The fluid ahead of the sampler contains particles of different sizes and densities. Figure 2A shows the fluid streamlines for sampling with a velocity equal to the upstream local velocity (isokinetic sampling). Of course, the probe does not disturb the flow field ahead of the sampler, and consequently, sample solids concentration and composition equal those upstream of the probe. 

The preceding discussion shows that the sampling efficiency for thin L-shaped probes is a function of two parameters the deviation from the isokinetic conditions and the response of the particles to the deflection of the fluid streamlines upstream of the sampler. The deviation from the isokinetic conditions is a function of the velocity ratio (U/Uq), whereas the particle response is a function of the ratio of particle inertia to fluid drag. This ratio in a dimensionless form is known as the particle inertia parameter, the Stokes number, or the Barth number (K), defined as ... 

The effect of particle bouncing on the sampling efficiency of thick L-shaped probes was first noted in gas-solid systems by Whitely and Reed (44). They found that sampling efficiency for thick L-shaped probes was higher than unity at U/Uq = 1. To estimate the sampling efficiency due to particle bouncing at the isokinetic velocity, Belyaev and Levin (25) and Yoshida et al. (45) proposed an empirical equation. This equation can be written in a slightly different form as... 

The increase in the sample concentration at the isokinetic conditions resembles that of thick L-shaped probes. Particles rebounding from the probe wall probably enter the probe and thus cause higher concentrations at sampling velocities equal to and greater than isokinetic. 

Figure 15. Sampling efficiency for circular and thin-walled L-shaped probes. (Reproduced with permission from reference 46. Copyright 1985.)...

Particle Bouncing. A second source of sampling errors occurs as a result of particle bouncing effects. A typical example of this effect is sampling particles of high inertia using thick (blunt) L-shaped probes. In this case, particles may hit the probe wall, lose some of their inertia, and enter the probe. Consequently, the sample solids concentration is higher than the upstream local concentration, even when U U0 = 1. 

Figure 13 shows the sampling efficiency versus the velocity ratio for L-shaped probes having a tip angle 6 of 18° and probe relative wall thicknesses of 0.4, 0.8, and 1.2. The 0.08-mm sand at 6.3 vol% discharge solids concentration, and 2.63 m/s bulk velocity was used in these experiments. At this tip angle, the increase of C C0 at U U0= 1 is eliminated. 

To account for particle rebound and inertia effects simultaneously, a modification was introduced by Nasr-El-Din and Shook (51). Figure 15 compares the calculated sampling efficiency for a thick L-shaped probe having a relative wall thickness of 0.8, considering the inertial effect alone and with the particle bouncing effect, with the experimental measurements. Clearly, the agreement is much better when particle inertia and bouncing effects are considered. 

A second example of the particle bouncing effect is sampling using straight probes. Although thick L-shaped probes are more practical than thin probes, they require a relatively large aperture in the wall of the pipe. Straight probes are robust, simple to construct, require a minimum... 

To measure local particle velocity in slurry pipelines, Brown et al. (88) modified Beck et al. s (86, 87) conductivity method. They developed a new conductivity probe where four electrodes are mounted on an L-shaped probe. The probe has two field electrodes and two sets of sensor electrodes separated by a known distance (Figure 24). The probe is capable of measuring particle velocity in vertical and horizontal slurry... 

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