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Ind. Eng. Chem. Res. 2004, 43, 5620-5631
CREC Fiber-Optic Probes for Particle Velocity and Particle Clustering: Design Principles and Calibration Procedures Samuel R. Nova, Stefan Krol, and Hugo I. de Lasa* Chemical Reactor Engineering Centre, Faculty of Engineering, University of Western Ontario, 1151 Richmond Street, London, Ontario, Canada N6A 5B9
The present study describes the novel CREC-GS-Optiprobe design. This new sensor allows for the characterization of clustering phenomena in gas-solid fluidized beds with minimum intrusion effects. This sensor is composed of the following components and functionalities: (a) an optical fiber acts as a laser beam emitter; (b) a GRIN (graded-refractive-index) lens, separated from the emitter fiber at a selected distance, creates a region of high light intensity far from the tip of the probe; and (c) a second optical fiber, placed adjacent to the GRIN lens, acts as a receiver to collect the light rays reflected by the moving particles crossing the region of high light intensity. The GRIN lens forms a 285-µm-diameter region of high light intensity at a distance of 5.4 mm from the tip of the sensor. The equations used in the design of the CREC-GS-Optiprobe were derived assuming paraxial optics. The calibration methods that are reported in this study were designed to improve probe performance. Reflection tests demonstrated that the probe develops a region of high light intensity where the beam converges into a waist. After probe calibration and alignment, the acquired signals display distinctive peaks, showing the simultaneous detection of particle clusters on both probes. 1. Introduction The measurement of particle concentration, particle velocity, and cluster size is becoming an essential area for the successful study of fluidized beds. In this respect, there are a number of existing techniques for the measurement of particle velocity, particle cluster size, solid concentration, and other properties in fluidized beds.1-6 Some of these techniques use an external radiation source for the measurement of the aforementioned fluidized-bed properties. The principle exploited in these methods is the projection of a beam of electromagnetic or acoustic radiation across the flow stream from an external source. Several kinds of radiation and electromagnetic waves, including light and ultrasound, can be used.4,5 In these cases, the measurement of the gassolid flow properties is based on the modulation of this beam by either the fluid or the particles in the flow. When two beams of radiation are spaced axially along the flow, the cross-correlation function of the modulated beam signals can be used to estimate the velocity of the particles. In particular, optical methods make use of light as an external radiation source and rely on the absorption, scattering, or reflection of the incident light by the solid particles to generate signals that can be cross-correlated.5 Additionally, the use of infrared lasers in combination with optical fibers creates a valuable optical method for research on the hydrodynamics of fluidized beds, specifically in downer reactors. Reflection methods are employed predominantly in gas-solid flow systems where the loadings of particles are high and where the light penetration is reduced to such a degree that the absorption or scattering methods cannot be used.5 * To whom correspondence should be addressed. Tel.: +1519-661-2144. Fax: +1-519-850-2931. E-mail: hdelasa@ eng.uwo.ca.
Researchers have used light absorption and light reflection to measure particle velocities and solid concentrations in gas-solid flow systems.7,8 In some of these studies, a five-fiber optical probe shaped as an aerofoil has been used to measure particle velocity in circulating fluidized beds.9,10 Moreover, the combination of optical fiber probes and a nonisokinetic suction probe has been adapted to estimate local solid concentrations in fluidized beds.11 Optical fibers work in the region of the electromagnetic spectrum that encompasses wavelengths from 200 to 20 000 nm, including the visible light region (from 400 to 700 nm) and the near-infrared region (from 700 to 1600 nm) where silica glass fibers present better light transmission.12 An important property of optical fibers is the acceptance angle. The acceptance angle is the angle over which light rays entering the fiber are guided along its core center. The numerical aperture (NA) and the acceptance angle (θ) of an optical fiber are interrelated. The acceptance angle of an optical fiber depends on the refractive indexes of the core and cladding materials.12 GRIN lenses (graded-refractive-index, gradient-index, or graded-index lenses) are small cylindrical glass rods with the capability of refracting light and forming a real image of the light source. 13 The light source can be the light-emitting end of an optical fiber. The refractive index of the GRIN lens material varies parabolically as a function of the radius, from a maximum on the rod axis to a minimum at the outer surface. As a result of this index variation, a ray evolving through the GRIN lens follows a sinusoidal path. The wavelength of this sinusoidal path is called the pitch (P). In a GRIN lens with a pitch equal to 1, rays complete a full sine cycle through the entire length of the lens. Therefore, the pitch of a GRIN lens is proportional to its length. Depending on their lengths, various GRIN lenses with
10.1021/ie0306980 CCC: $27.50 © 2004 American Chemical Society Published on Web 07/03/2004
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5621
Figure 1. Schematics of the emitter side of a CREC-GS-Optiprobe showing the region of high light intensity.
different pitch fractions display different light ray trajectories and therefore different optical characteristics. The introduction of a GRIN lens into optical fiber probes provides the capability of focusing the incident light to change the depths of the measuring region according to the solid particle concentration in the suspension.14 On this basis, a new probe was designed with the capability of focusing the entire incident light into a narrow point far from the tip of the probe, as proposed by de Lasa et al.15 The CREC-GS-Optiprobe, developed at Chemical Reactor Engineering Centre, University of Western Ontario (CREC-UWO), belongs to the class of fiber-optic reflective sensors. This probe provides a well-defined region of high light intensity. This design minimizes probe intrusion, allowing for detailed resolution of the particle phenomena occurring in the suspension. To maximize probe performance, a new version of the probe is proposed here that incorporates a GRIN lens, which definitely optimizes the optical characteristics of both the emitter and receiver optical fibers. 2. Design and Operating Principle of the CREC-GS-Optiprobe 2.1. General Design Considerations. CREC-GSOptiprobes are relatively simple devices with the capability of being used for the fluid dynamic characterization of fluidized-bed reactors. Advantages of the CRECGS-Optiprobe, over other reflective sensors, can be summarized as follows: (a) The geometric configuration optimizes the optical characteristics of both the emitter and receiver optical fibers. (b) The GRIN lens incorporated into the probe creates a focal point far from the tip of the sensor, thereby minimizing flow disturbances in the measurements resulting from bouncing particles and the boundary layer formed in the front face of the probe. The CREC-GS-Optiprobe has the following components and features: (a) The first component is an emitter fiber followed by a GRIN lens (Figure 1). The emitter fiber is spaced from the GRIN lens at an optimal object distance (l0) suitable for producing a sensing region at a desired image distance (l1) where the beam energy is concentrated. The image distance can be adjusted by selecting the adequate object distance and, in this way, setting the sensing region sufficiently far from the tip of the sensor. (b) A receiver fiber is positioned adjacent to the GRIN lens, with the adequate numerical aperture to receive mostly light rays reflected by particles crossing the sensing region (Figure 2 and Table 1). In this manner,
Figure 2. General features and operating principles of the CRECGS-Optiprobe. l0, object distance (distance between the emitter fiber and the GRIN lens); l1, image distance (location of the sensing region from the GRIN lens); d, spacing between the GRIN lens and the receiver fiber core; s, distance defining the visible domain of the receiver optical fiber; 2θh, acceptance angle of the receiver optical fiber. Table 1. Properties of the Emitter and Receiver Fibers optical fiber property numerical aperture (NA) half acceptance angle (θh) θh average fiber diameter (µm) fiber core diameter (µm)
maximum value
minimum value
0.4 23.6°
0.27 15.7° 19.65° 850 400
light rays reflected by other particles, outside this focal point, are ignored. (c) Another important characteristic is the spacing between the GRIN lens and the receiver optical fiber core (Figure 2). The distance d defines the probe visible domain. The visible domain or sensing region is located at a distance from the lens that is greater than s, the “critical distance” of the probe (a characteristic dimension defining the probe visible domain boundary).16 This visible domain for the receiver fiber can be practically established by adjusting d, the distance between the GRIN lens and the receiver fiber. Because the visible domain is placed at a critical distance from the tip of the GRIN lens, the sensor, in principle, could detect all rays coming from a particle located at a distance greater than the critical distance. On the other hand, all rays coming from a particle located at a distance less than s pass unnoticed by the sensor. 16 Moreover, calibration of the CREC-GSOptiprobe is important given that the sensor components have to be adjusted to ensure that the image distance (l1) is equal to or greater than the probe critical distance. Figure 3 illustrates the different components of a CREC-GS-Optiprobe assembly: (a) optical fibers (emitter and receiver), (b) GRIN lens, and (c) supporting and protecting tubings. Calculations of the dimensions various components can be accomplished using classical optics. On this basis, the acceptance angle of an optical fiber is defined as the maximum angle over which light rays entering the fiber are guided along its core (refer to Figure 4). The numerical aperture of an optical fiber can be related to the half acceptance angle, θh, through the equation
NA ) sin(θh) ) xn02 - n12 ) n0 sin(θc)
(1)
where n0 is the refractive index of the fiber core, n1 is
5622 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
Figure 5. Schematics of the GRIN lens optics showing the location of the critical object distance l0c and the sensing region. Figure 3. Schematics of the CREC-GS-Optiprobe showing the emitter optical fiber, receiver optical fiber, and GRIN lens. The object distance l0, the distance between the emitter optical fiber and the front of the GRIN lens, can be adjusted with the movable calibration tubing to place the region of high light intensity at the required image distance.
Figure 4. Acceptance angle (2θh) and half acceptance angle (θh) of an optical fiber with numerical aperture NA ) 0.4. Three ray cases are represented: (a) Ray with an angle equal to the half acceptance angle of the fiber (θi ) θh ) 23.6°); this ray is guided through the fiber (θr ) 15.5°, θc ) 15.5°, and θcr ) 74.5°). (b) Ray with an angle smaller than the half acceptance angle of the fiber (θi ) 10° and θr ) 6.7°); this ray is also guided through the fiber. (c) Ray with an angle larger than the fiber half acceptance angle (θi ) 30.9° and θr ) 20° when passing from the air to the fiber core; θi ) 70° and θr ) 77.2° when passing from the fiber core to the cladding); this ray leaks out of the fiber.
the refractive index of the cladding, and θc is the confinement angle in the fiber core. 2.2. Emitter Fiber Design Equations. Similarly to the acceptance angle of the fiber, the emitting angle is the angle over which light exits the fiber. Rays emerging from the emitter fiber (Figures 5 and 6) reach the front face of the GRIN lens, which is located at a well-selected object distance (l0). The area illuminated by the beam at the distance l0 has a radius of r0 (refer to Figure 6). Considering that one-half of the emitting angle is equal to the half acceptance angle, the radius of the area illuminated by the beam (r0) can be calculated as a function of the object distance (l0) according to the
Figure 6. Optimal separation d distance between the GRIN lens and the core of the receiver optical fiber to maximize the reception of the light reflected from the sensing region.
following relationship
r0 ) l0 tan(θh) +
dc 2
(2)
where dc is the diameter of the fiber core, typically 400 µm. As a general rule, the radius of the illuminated spot should be comparable to the so-called effective radius of the GRIN lens to minimize power losses. This GRIN lens effective radius is the radius of the spot over the front face of the lens that collects the maximum amount of light from a beam projected from a single point located at the distance l0 (Figure 5). All rays that fall within this effective radius cross the entire length of the GRIN lens and eventually emerge at the back face of the lens. The effective radius of a GRIN lens can be related to the diameter of the fiber core, dc, with this effective radius being estimated by assuming that the diameter of the light source is negligible in relation to the diameter of the GRIN lens. According to Snell’s law for
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5623
a ray reaching the front face of the GRIN lens (see Figure 5)
nair sin(θ0) ) N0 sin(θ′0)
(3)
By assuming that the light source is a single point lying on the lens optical axis, far from the lens front face, a sharp angle is formed between the lens axis and a ray falling exactly at the radius of the lens. In fact, the paraxial approximation can be applied for small angles to simplify the algebra. Hence, sin(θ) can be approximated as being equal to the angle θ. In addition, if the refractive index of the air (nair) is approximated as being equal to 1, eq 3 can be simplified to
θ0 ) N0θ′0
(4)
Furthermore, if the angle θ0 is small, then the angle θ0 can also be approximated using the following relationship
θ0 ≈ tan(θ0) )
y0 l0
(5)
Substituting the approximation for θ0 in eq 5 into eq 4 and solving for the refractive angle, θ′0, inside the GRIN lens at the front face results in the expression
θ′0 )
y0 N0l0
(6)
2.3. GRIN Lens Design Equations. The radial position y and the angle θ′ of any ray crossing the inside of the GRIN lens are given by the next set of equations as functions of the axial position (z) in the lens for the entire length of the lens (L)
y(z) ) y0 cos(xAz) +
sin(xAz) θ′0 xA
θ′(z) ) - xAsin(xAz)y0 + cos(xAz)θ′0
(7) (8)
where y0 and θ′0 are the position and the angle inside the lens at the front face (at z ) 0), respectively. 2.3.1. GRIN Lens Characteristic Equations. Equations 7 and 8 can also be rewritten in compact mathematical form as (refer to Appendix A)
y(z) ) Y0 sin(xAz + δ)
(9)
θ′(z) ) T0 cos(xAz + δ)
(10)
where
Y0 )
x
y02 +
θ′02 A
T0 ) xAY0 δ ) arctan
( ) y0xA θ′0
(11) (12) (13)
Alternatively, by using θ′0 from eq 6, the phase angle δ
can be expressed as
δ ) arctan(xAN0l0)
(14)
Thus, a GRIN lens with radius R accepts rays that fall inside its effective acceptance radius. Those rays should cross the entire length of the GRIN lens to eventually emerge at the back face of the lens. For this to happen, the radial distance of those rays (eq 9) must be less than or equal to the lens radius (R) throughout the entire length of the lens, i.e., those rays must effectively comply with the constraint
y(z) e R
(15)
for any axial position z within the range 0 e z e L, where the upper limit L is the total length of the GRIN lens. 2.3.2. GRIN Lens Focal Point. It is quite apparent that, when a ray enters the GRIN lens with a small angle and close to the lens axis, the ray appears at the back face of the lens. However, a problem arises when a ray enters the lens with a wider angle and at a radial position far from the lens axis, in that case this ray might not emerge at the back face of the lens. The outcome of this situation strongly depends on the value of the distance l0 with reference to a certain critical value, l0c (the GRIN lens front focal length), and consequently three possible cases are expected: Case 1. 0 < l0 < l0c. When the distance l0 is small (but not zero), rays entering the GRIN lens with a wide angle of incidence (θ0) move away from the lens axis, and consequently, they escape through the cylindrical wall of the lens. As the distance l0 approaches the value of l0c, the rays entering the GRIN lens become more parallel to the lens axis because of their narrower angle of incidence (θ0); consequently, more of these rays cross the entire length of the lens, and a smaller number of rays are lost through the lens cylindrical wall. Case 2. l0 ) l0c. If the distance l0 is increased further with respect to case 1, l0 reaches the critical value l0c. At this point, the rays entering the GRIN lens emerge at the back face of the lens with a trajectory approximately parallel to the lens axis. Particularly, at the location z ) L, the so-called extreme rays, which are the rays making tangential contact with the lens cylindrical wall, emerge exactly at the rim of the back face of the lens defined by the coordinates (L, R). Because zm is defined as the lens axial position where the extreme rays contact the cylindrical wall of the lens tangentially, then zm ) L in this case. Case 3. l0 > l0c. If the distance l0 is increased further with respect to l0c, the extreme rays are bent inward toward the lens axis within the range zm < z < L after tangentially contacting the cylindrical wall of the lens at zm. Because the rays are deflected toward the lens axis as they pass through the GRIN lens, after emerging from the lens, they are concentrated at one point located at the distance l1 from the back face of the lens. In this way, an image of the light source is created at the distance l1 with these emerging rays. Therefore, for a point light source located at a distance l0 from the lens, the radial position of the extreme rays at z ) 0 determines an effective acceptance radius for the corresponding distance l0. At the same time, the axial position zm where the extreme ray contacts the cylindrical wall of the lens depends on how much the ray is bent inward toward the lens axis. This extent of
5624 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
bending depends on the refractive index distribution of the lens material (Appendix B). 2.3.3. GRIN Lens Acceptance Radius. To estimate the effective acceptance radius of the GRIN lens, it is necessary to determine the limiting condition zm ) L. At this value of zm, any extreme ray tangent to the lens cylindrical wall displays a maximum value. The radial position of an extreme ray at the axial position zm ) L is equal to the lens radius [y(L) ) R]. Because this is the maximum value of the GRIN lens sinusoidal function (eq 9), it is apparent that y(L) ) Y0 ) R and the sine of the argument inside the brackets is equal to 1. Under this limiting condition, a phase value δ ) δc exists for which eq 9 gives
sin(xAL + δc) ) 1
π 2
sin(xAL)
xAN0l0
(23)
Solving for y0a, an expression for the lens acceptance radius as a function of the distance l0 can be established for the range 0 < l0 < l0c
y0a )
R sin(xAL) N0l0xA
(24)
+ cos(xAL)
(16)
Furthermore, for case 3, where l0 > l0c, an expression for the effective acceptance radius can be obtained from eq 11. Within this range, the key piece of information is that the sinusoidal path of an extreme ray has a wave amplitude equal to the GRIN lens radius at z ) zm
(17)
y(zm) ) Y0 ) R
which means that
xAL + δc )
R ) y0a cos(xAL) + y0a
(25)
Substituting eqs 6 and 25 into eq 11 gives
and consequently
δc )
π - xAL 2
(18)
In addition, δc is related to the critical object distance l0c through eq 14 as follows
1
xAN0l0c
) tan(xAL)
(19)
and solving for l0c gives
l0c )
1
xAN0 tan(xAL)
(20)
At this distance l0c, known as the front focal length, the equality part of eq 15 is satisfied at the axial position zm ) L. Now, let us obtain the effective acceptance radius as a function of l0 for the first case when 0 < l0 < l0c. Within this range, a ray emerging exactly at the rim of the back face of the lens (z ) L) determines the effective radius at the front face of the lens. Therefore, the radial position of this ray at z ) L is the lens radius, or
y(z) ) y(L) ) R
(21)
In the first case, the ray emerging exactly at y(L) ) R determines the effective acceptance radius when 0 < l0 < l0c, even though it is not tangent to the cylindrical wall of the lens. For this ray, the amplitude Y0 calculated from eq 9 is greater than the lens radius (R). Therefore, by applying the condition given in eq 21 to eq 9, the lens acceptance radius (y0a) can be calculated as
sin(xAL) θ′0 R ) y0a cos(xAL) + xA
(22)
Substitution of θ′0 from eq 6 into eq 22 results in the following expression
R)
x
y0a2
2
y0a +
N02l02A
(26)
and solving for y0a yields
y0a )
R
x
1+
1 2 2 N0 l0 A
(27)
2.3.4. GRIN Lens as a Component of the CRECGS-Optiprobe. For a CREC-GS-Optiprobe to concentrate all of the laser beam energy into a narrow region, it is necessary to set the distance l0 of its GRIN lens to a value greater than l0c. Therefore, eq 27 also gives the height of the pupil for the case of a CREC-GS-Optiprobe. If the GRIN lens has a length L and a pitch P, then the expression relating the length of the lens to the pitch is given by
L)
2πP xA
(28)
Finally, for the rays exiting the back face of the GRIN lens, Snell’s law applies
N0 sin(θ′1) ) nair sin(θ1)
(29)
and applying the paraxial approximation to the small angles θ′1 and θ1 gives
N0θ′1 ) nairθ1
(30)
By approximating nair ≈ 1 and solving for θ′1, the following relation is obtained
θ′1 )
θ1 N0
(31)
By substituting eqs 6, 27, and 28 into eq 7, the height of the pupil at the outgoing point (y1) can be estimated in terms of l0 and lens optical properties as
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5625
y1 )
[
sin(2πP)
R
x
1+
xAN0l0 1 2 2 N0 l0 A
]
+ cos(2πP)
Table 2. GRIN Lens Parameters
(32)
Given that θ′(L) ) θ′1, by substituting eqs 6, 27, 28, and 31 into eq 8, the angle of the extreme ray can be expressed as
θ1 )
R
x
1+
[
1 2 2 N0 l0 A
]
cos(2πP) - xAN0 sin(2πP) l0
l1 )
Furthermore, the characteristic dimension of the sensing region h can be calculated using GRIN lens optics and the equation
h ) Os|MT|
(35)
where Os is the size of the object acting as the light source for the GRIN lens and from which the lens creates an image of size h and |MT| is the absolute value of the transverse magnification of the GRIN lens (Figure 6). Note that, in this case, the core of the emitter optical fiber is the object from which the lens creates the inverted image at the distance l1. This inverted image, projected at the distance l1, constitutes the region of high light intensity of the sensor. The transverse magnification, MT, representing the ratio between the size of the projected image and the true size of the object, can be calculated using the optical properties of the selected GRIN lens and the equation
MT )
nair nair cos(LxA) - N0l0xA sin(LxA)
(36)
where nair is the refractive index of the incident medium, in this case, the refractive index of air; L is the length of the GRIN lens; l0 is the distance between the GRIN lens and the emitter optical fiber; and xA is the gradient constant, which is a measure of the refractive index distribution in the GRIN lens at a given laser wavelength (λ ) 830 nm). xA can be evaluated from the expression
xA ) AA +
BA 2
+
λ
CA λ4
(37)
where AA, BA, and CA are constants provided by the GRIN lens supplier and λ is the laser wavelength in micrometers. N0 is the base refractive index or the value of the refractive index at the GRIN lens optical axis. N0 can be calculated with the equation
N0 ) AN +
BN λ2
maximum value
minimum value
units
0.29451 3.503 × 10-3 4.0137 × 10-4
0.29154 4.7287 × 10-3 4.8665 × 10-5
mm-1 µm2 mm-1 µm4 mm-1
1.5868 8.14 × 10-3 2.052 2 0.1
µm2 mm mm
Table 3. Calculated GRIN Lens Parameters
(34)
tan(θ1)
AA BA CA AN BN L D P
standard value
(33)
In addition, the image distance l1 (distance at which the maximum energy is concentrated) can be calculated as
y1
GRIN lens parameter
(38)
where AN and BN are constants provided by the GRIN
GRIN lens parameter
maximum value
minimum value
average value
xA LxA N0
0.3004
0.2981
0.2993 0.6141 1.5986
units mm-1
lens supplier and λ is the wavelength of the laser beam in micrometers. The constants AA, BA, CA, AN, BN, and L and the other optical parameters for the selected GRIN lens, such as the lens diameter (D) and the lens pitch (P), are reported in Table 2. These parameters were used for the design of the CREC-GS-Optiprobe system. In this case, the wavelength of the laser employed is 830 nm. Therefore, from eqs 37 and 38 and the GRIN lens parameters listed in Table 2, the parameters reported in Table 3 are obtained. 2.4. Receiver Fiber Design Equations. On the basis of the eq 1, it can be established that a receiver optical fiber with an average numerical aperture (NA) has a half acceptance angle of θh. With the aim of maximizing the reception of the receiver optical fiber, it is necessary to ensure that the cone defined by the half acceptance angle of the receiver optical fiber covers the entire characteristic dimension of the sensing region h and also that the numerical aperture of the optical fiber is large enough to allow the parallel placement of the receiver optical fiber at a distance greater than the radius of the GRIN lens. Thus, the side (dop) opposite from the half acceptance angle can be calculated from l1 and θh as
dop ) l1 tan θh
(39)
Simultaneously, the opposite side (dop) can be considered as the sum of the following contributions (refer to Figure 6)
dop ) d + R +
h 2
(40)
where d represents the distance between the GRIN lens and the core of the receiver optical fiber, R is the radius of the lens, and h is the characteristic dimension of the sensing region. Substituting eq 39 into eq 40 and solving for d gives
d ) l1 tan(θh) - R -
h 2
(41)
Thus, this distance d between the GRIN lens and the receiver optical fiber gives the maximum reception of the light from a reflecting screen that is placed at a distance l1 from the back face of the lens. 3. Optoelectronic System Regarding the optoelectronic system, the connections of the optical fibers and the various electronic compo-
5626 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
of 1.5986 at the lens axis (N0). The GRIN lenses and the ends of the emitter optical fibers are spaced by 8.05 mm. This is the value of the object distance (l0) represented in Figure 1. 4. Calibration of the CREC-GS-Optiprobes Required for High Performance
Figure 7. Fiber-optic configuration system for cross-correlation analysis. (1) Probe port, (2, 4) laser diode assemblies, (3, 5) mechanical fiber holders, (6) laser power supply unit, (7, 8) silicon photodetector heads, (9) two-channel amplifier, (10) two-channel notch filter, (11) shielded connector block, (12) computer with LabVIEW software.
nents used are described in Figure 7. The power supply unit provides a voltage between 4.5 and 5.5 V dc to operate the two laser diode assemblies. The laser diode assemblies used in the present study emit an infrared laser beam with a wavelength of 830 nm and a power of 20 mW. The upstream signal is obtained as follows: First, a laser beam from one of the laser diode assemblies illuminates one end of an optical fiber. Then, the laser beam is conducted through the fiber and emitted at the other end connected to the upstream CREC-GSOptiprobe. At this point, the beam strikes a GRIN lens mounted inside the probe head. As mentioned previously, the laser beam emerging from the GRIN lens is focused into a point far from the tip of the probe within the gas-solid flow. Only the particles crossing through this detection region reflect enough light to be collected by the receiver optical fiber. The collected light is then transmitted through the receiver fiber and sent to a silicon photodetector, where the optical signal is converted into an electrical signal. The downstream signal is obtained in the same way. Next, both the upstream and downstream signals are sent to a voltage amplifier and a notch filter for signal conditioning. The electrical signals require amplification because the signals coming from the photodetectors are too weak for signal processing and analysis. The notch filter eliminates periodic interferences modulating the flow from the compressed-air system.5 Once the signal conditioning is completed, the signals are sent to a PC computer via a shielded I/O connector block to be processed and analyzed with the LabVIEW software package. The GRIN lenses used have the following dimensions and optical parameters: diameter of 2.00 mm, length (L) of 2.052 mm at 0.1 pitch (P), index gradient constant xA of 0.2993 mm-1 at 830 nm (λ), and refractive index
Manufacturing of the sensor parts is rather difficult given their small dimensions. Inherent errors in the probe construction could yield incorrect results. Consequently, direct calibration of the probe is needed to achieve more accurate measurements and better probe performance. For the calibration of the probe, a three-stage calibration procedure was developed comprising (a) experimental determination of the maximum detection distance; (b) experimental determination of the probe image distance, l1; and (c) axial alignment of the two probes. The measurement of particle velocities is achieved by obtaining the cross-correlation function of a pair of time series from two sensors spaced axially along the flow stream. The cross-correlation function describes the general dependence of the values of one set of data on the other. The cross-correlation method of velocity measurement for particles is based on the determination of the transit time of a measurable disturbance, in this case, the disturbance created by a particle moving along the flow over a known distance. The time delay of the maximum value of the cross-correlation function allows a proper assessment to be made of the particle transit time between the two sensors. As described previously, important CREC-GSOptiprobe features and characteristics are related to the probe performance. The geometrical and optical sensor properties allow measurements to be recorded in a region far from the sensor tip where there is a minimum of intrusion effects.18 However, given the miniature size of the probe, with component dimensions in the range of a few millimeters, machining of the probe with deviations smaller than 20% is extremely difficult to achieve. Thus, calibration of the probe is a must to compensate for these inaccuracies.19 The selection of the proper value for the parameter d, which is defined as the spacing between the GRIN lens and the core of the receiver fiber, is one of the key design considerations of the CREC-GS-Optiprobe16 (Figure 6). Nevertheless, the final spacing between these two components was d ) 0.785 mm after the probe was manufactured versus the required value of d ) 0.2 mm.16 Because of this variation, it was expected that the characteristic distance s, the distance defining the boundary of the probe visible domain, would be different. Therefore, it was required that the exact distance s for a manufactured distance d of 0.785 mm be determined experimentally. To find this new distance s, first, an FCC screen was constructed (Figure 8). A sample of FCC particles used in the fluidized bed was sieved on a wire screen bin with an aperture of 38 µm. The small solids that went through the screen were discarded, and the gross solids remaining on the 38-µm bin were kept to construct the FCC screen. A sufficient amount of adhesive was spread on a piece of black cardboard, and the sieved FCC particulate was distributed over the adhesive to cover the cardboard with FCC catalyst. A small rectangular
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5627
Figure 9. Optimal calibration of the CREC-GS-Optiprobe. d, spacing between the GRIN lens and the receiver fiber core (0.785 mm); dsc, screen separation (5.4 mm); l1, image distance (5.4 mm for an object distance of l0 ) 8.05 mm); s, visible domain limit (5.375 mm); h, transversal dimension of the sensing region (285.4 µm); θi, ray incidence angle (19.65°); θh, average half acceptance angle of the optical fiber (19.65°); NA, numerical aperture of the optical fiber (see Table 1).
Figure 8. FCC screen making process.
piece of this FCC-catalyst-covered cardboard was cut and mounted on a small frame. Because of the geometry of the probe, and in particular because of the separation distance between the GRIN lens and the core of the receiver optical fiber (distance d), a point exists, far from the probe tip, where the receiver optical fiber collects a maximum amount of light from a reflecting plane. This optimal detection distance s is different from the GRIN lens image distance l1 (Figure 2) as described by Krol et al.16 To optimize the performance of the probe, it was necessary to find the corresponding value of the distance s for a distance d of 0.785 mm and then, through manipulation of l0, to set the image distance (l1) equal to a value that complied with the condition l1 g s. Thus, by placing the GRIN lens image distance (l1) at a distance slightly greater than the new optimal detection distance s, the reception performance of the CREC-GS-Optiprobe was maximized. To find this new optimal detection distance s, the intensity of the light detected by the receiver optical fiber was measured for several separation distances between the probe and the FCC screen (dsc). The FCC screen and the CREC-GS-Optiprobe, supported on an optical bench, were mounted on a rail carrier. The optical bench allowed separation changes between the sensor tip and the FCC screen to be made with an accuracy of displacement of 10 µm (Figure 9). The emitter optical fiber was fed with a series of light pulses to quantify the light intensity at a given separation distance (dsc). Cutting the laser beam with a black chopper disk with 48 holes produced this series of light pulses. A dc electrical motor powered by an ac/dc adapter, which was connected to a variable autotrans-
Figure 10. Image distance l1 versus the object distance l0 for the GRIN lens described in Table 2 and used in the construction of the CREC-GS-Optiprobe (eq 42).
former to adjust the disk revolution frequency, rotated the chopper disk. The chopper disk was necessary to avoid a flat-line signal in the optoelectronic system when making amplitude readings of the light intensity. To find the optimum detection point of the probe, three object distance (l0) were selected (Figure 2). For calibration purposes, these object distances (l0) had to meet the condition of giving image distances (l1) different from the distance s (i.e., different from s ) 5.2 mm).16 This condition had to be fulfilled to find the point at which the receiver fiber captured the maximum amount of light due to both the numerical aperture of the receiver optical fiber and the spacing between the GRIN lens and the core of the receiver optical fiber. Figure 10 gives the variation of l1, the image distance, with respect to changes in l0, the object distance, for the specific GRIN lens incorporated into the CREC-GSOptiprobe. These results were obtained using GRIN lens optics. In this way, the GRIN lens parameters l0 and l1 can be related.13 On the basis of these assumptions, the
5628 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
Figure 11. Intensity of the light accepted by the receiver optical fiber of a CREC-GS-Optiprobe for different separation distances between the probe and a screen of FCC particles (d ) 0.785 mm and maximum NA ) 0.4).
following equation can be proposed
l1 )
(n1n2/xA) sin(LxA) - n2N0l0 cos(LxA) n1N0 cos(LxA) - N02l0xA sin(LxA)
(42)
where n1 and n2 are the refractive indexes of the media found at the front and at the back of the GRIN lens, respectively; L is the length of the GRIN lens; l0 is the object distance, which is the distance between the GRIN lens and the emitter optical fiber; and xA is the gradient constant, which is a measure of the refractive index distribution in the GRIN lens at a given laser wavelength (λ ) 830 nm). The medium found at both the front and back of the GRIN lens is air, which has a refractive index of 1. On the basis of eq 42, the three pairs of object distances (l0) and image distances (l1) satisfied the condition of having their image distances far inside the visible domain of the receiver optical fiber (l1 > s ) 5.2 mm). The selected values of l0 were 6.7, 6.8, and 7.1 mm, which gave image distance values of 6.49, 6.40, and 6.15 mm, respectively (Figure 10), with all of these image distance values being considerably greater than the s distance (l1 > 5.2 mm). Then, for each value of l0 given above, the light intensity was measured for different separation distances between the tip of the CREC-GS-Optiprobe and the FCC screen (dsc). A dsc range was selected from 0 mm to a value larger than the respective image distance, and voltage amplitude readings, representing the light intensity, were made at every 0.25 mm of separation (Figure 11). Figure 11 shows the three curves corresponding to the three object distances selected. The three curves display a maximum light intensity at around the same screen separation value (dsc ) 5.375 mm). This result, consistently observed in the three curves, is a direct consequence of the separation distance d and the numerical aperture of the receiver optical fiber used (Table 1) and is not a consequence of the GRIN lens image distance value, given that for the three l0 values selected, the image distances are located far from the 5.375-mm distance range. The shape of the curves reported in Figure 11 is the combined effect of the shape of the laser beam and the numerical aperture value of the receiver optical fiber. In fact, the laser beam has a conical shape, with this
Figure 12. Intensity of the light reflected by a single FCC particle mounted on a black screen.
cone formed between the focal point and the back face of the GRIN lens. The maximum light intensity of the laser beam is found at the image distance. For distances smaller than the image distance, the illumination area is larger, and consequently, the light intensity per unit area is lower. Moreover, the numerical aperture of the receiver optical fiber defines an acceptance cone, and only the light entering the fiber core within this acceptance cone is guided along the fiber. In addition, when the screen is too far from the probe, the intensity of the light scattered on the screen and reaching the receiver optical fiber is lower. On the basis of the results presented in Figure 11, it was concluded that the new s distance was 5.375 mm and that the optimal distance between the CREC-GSOptiprobe and a FCC screen, at which the receiver optical fiber presented a maximum detection of the light reflected by the screen, was 5.4 mm. Once this distance was established, the next step was to determine the object distance that generated an image distance at 5.4 mm. It can be observed from Figure 10 that the value of the object distance that generates the required image distance of 5.4 mm is 8.05 mm. Thus, by placing the emitter optical fiber at a distance of 8.05 mm from the GRIN lens, the focal point was located 5.4 mm from the probe tip, with this focal point matching the optimum detection point of the probe. To verify the outcome of the CREC-GS-Optiprobe calibration, a procedure similar to the one described above was followed but now with a black screen holding a single FCC particle. The separation between the tip of the probe and the black screen holding the single FCC particle was increased gradually from 0 to 10 mm, with voltage amplitude readings made every 0.25 mm. The intensity of the light reflected by the FCC particle at a given screen separation was calculated as the difference between the light intensity reflected by the FCC particle and the light intensity reflected by the background (the black screen). Figure 12 reports the results for one of the probes. The axial alignment of the focal points of both probes is critical. Probe misalignment, in either the x or y direction, means that the particles crossing the focal point of probe upstream never reach the focal point of the probe downstream. Probe alignment in the y direction is easily achieved by placing both probes at the same column depth, given
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5629
that the focal points of both probes were placed at the same distance (5.4 mm). The probe port allows the probes to be aligned in the x direction by rotating the probes a few degrees either clockwise or counterclockwise, and in this way, the focal points can be displaced a few micrometers to the left or to the right. To determine whether to move the focal point to the left of to the right, a plumb line (a 0.12mm-diameter white string with a weight) was used. The color of the string is important as the string must reflect the light of a pulsating laser beam. In this manner, the light reflected by the white string creates two peaks when the probes are vertically aligned. In this way, by rotating the probes, adequate vertical alignment can be ensured in the x direction. 5. Results Given the various focusing, positioning, and calibration procedures performed as described above, the intensity of the signal detected by the receiver optical fiber improved significantly. Figure 12 confirms that there is a narrow focal region (measurement region) at 5.4 mm from the tip of the CREC-GS-Optiprobe. Under actual flow conditions, a signal peak is usually obtained from a string of particles crossing the measurement region. This is because the string of particles crosses the laser beam 5.4 mm from the tip of the probe and the light reflected by the particles is detected by the receiver optical fiber without interference. Because the width of a signal peak depends on many factors such as the polishing quality of the ends of the optical fibers, the numerical aperture of the receiver optical fiber, and the optical and geometrical characteristics of the FCC particles, it was necessary to establish the relationship between the actual length of the cluster crossing the measurement region and the width of the signal peak generated by the particle cluster. Moreover, regarding the connection between the cluster size and the width of the peak in the recorded signal, it is important to mention that the length of a trail of particles is not necessarily represented by the width of the signal peak at its baseline. Therefore, it was required to find the level of the peak at which its width better represented the cluster length. The approach selected to find the position on the peak representing the cluster length was achieved through the use of a 10-cm-diameter rotating disk holding a train of FCC particles simulating the structure of a cluster. This method is close to the techniques reported by Krol et al.,16 Zhu et al.,10 and Liu et al.20 While developing these experiments, in the context of this study, care was taken to ensure that the focal point of the CREC-GSOptiprobe was placed on the disk surface. Therefore, the disk was positioned 5.4 mm from the probe tip and rotated at a controlled speed with a known angular velocity. To enhance the signal from the reflection of the incident light on the FCC particles, the rotating disk was made of black matte plastic. The angular velocities of the disk reproduced the cluster velocities expected in a downflow acrylic unit (2-4 m/s). The velocity of the train of FCC particles held on the rotating disk was calculated using (a) the time gap between two consecutive signal peaks (displayed on the computer) and (b) the circumference of the circle defined by the radial position of the train of particles mounted on the disk.
From tests at different disk speeds, it was observed that around 50% of the signal peak height better reproduced the length of the train of particles mounted on the disk. Therefore, the peak width measured at a level of 50% of the total peak height was used in the calculations for the cluster size estimation. A CREC-GS-Optiprobe system was successfully implemented to characterize the gas-solid flow patterns in a downflow unit.21,22 It was found that a spacing of 0.604 cm between the sensors provided an adequate probe separation for measuring the cluster velocity ((10% accuracy) and this given the expected errors in axial distance between sensors and cross-correlation time shift. Even if the CREC-GS-Optiprobe system were tried for low concentrations of solids (lower than 1%), there would be no apparent restriction on the solids volumetric concentration given the characteristics of the design of the CREC-GS-Optiprobe as the measuring region can be modified according to the concentration of solids. For low solids concentrations, the measuring region can be situated far from the tip of the probe, whereas for high solids concentrations, the measuring region can be brought closer to the tip of the probe. 6. Conclusions The following are the most important conclusions of the present study: (a) The GRIN lens is a useful element in the design of fiber-optic reflective sensors. (b) The equations used for the design of the CRECGS-Optiprobe are derived using the paraxial approximation to predict precisely the position of the region where the beam converges into a waist. (c) In the design of the CREC-GS-Optiprobe, the combination between the image distance and the separation distance between the GRIN lens and the receiver optical fiber creates a point of high light intensity. (d) This point of high light intensity is situated far enough from the probe tip that the intrusive effects are minimized, as was demonstrated experimentally, (e) A number of focusing, positioning, and calibration methodologies were developed to ensure a good measurement of particle cluster velocities and a proper sizing of clusters in downflow reactors. Nomenclature xA ) index gradient constant of a GRIN lens (mm-1) AA ) parameter of eq 37 for calculating the gradient constant (mm-1) Ad ) difference in amplitude of the signal generated by an FCC particle mounted on a black screen and the signal generated by the black screen alone (V) AI ) amplitude of the light intensity signal (V) AN ) parameter of eq 38 for calculating the base refractive index BA ) parameter of eq 37 for calculating the gradient constant (µm2 mm-1) BN ) parameter of eq 38 for calculating the base refractive index (µm2) CA ) parameter of eq 37 for calculating the gradient constant (µm4 mm-1) D ) GRIN lens diameter (mm) d ) distance between the GRIN lens and the receiver optical fiber core (mm) dc ) diameter of the optical fiber core (mm)
5630 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 dop ) side opposite from the half acceptance angle (θh) of the receiver optical fiber for a right triangle whose adjacent side is the image distance (l1) (mm) dsc ) separation distance between the probe and the light reflecting screen (mm) dsp ) separation distance between the probe and a single FCC particle mounted on a black screen (mm) h ) characteristic dimension of the CREC-GS-Optiprobe sensing region (µm) L ) GRIN lens length (mm) l0 ) object distance or distance between the emitter optical fiber and the GRIN lens (mm) l0c ) critical object distance or front focal length of the GRIN lens (mm) l1 ) image distance at the back of the GRIN lens (mm) MT ) transverse magnification of the GRIN lens (µm) N0 ) base refractive index at the axis of the GRIN lens N(r) ) refractive index distribution in a GRIN lens as a function of the radius n0 ) refractive index of the fiber core n1 ) refractive index of the incident medium: air or optical fiber cladding n2 ) refractive index of the refractive medium: GRIN lens or optical fiber core nair ) refractive index of air ni ) refractive index of the initial medium nr ) refractive index of the refractive medium NA ) numerical aperture of the GRIN lens or optical fiber Os ) size of the object located at the back of the GRIN lens (µm) P ) pitch of the GRIN lens or fraction of the length needed for the light of a certain wavelength to complete one sine cycle (0 < P e 1) R ) GRIN lens radius (mm) r ) radial position in the GRIN lens (mm) r0 ) radius of the area illuminated by the emitter optical fiber (mm) s ) characteristic distance defining the probe visible domain boundary (mm) T0 ) amplitude for the cosine function in the ray-tracking equations Y0 ) amplitude for the sine function in the ray-tracking equations (mm) y0 ) radial position of the ray inside the GRIN lens at the front face (mm) y0a ) GRIN lens acceptance radius at its front face (mm) y(z) ) radial position of the ray inside the GRIN lens (mm) z ) axial position of the ray inside the GRIN lens (mm) zm ) axial position at which the ray tangentially reaches the GRIN lens wall (mm) Greek Letters R ) any angle (degrees or radians) β ) any angle (degrees or radians) δ ) phase angle for the sine function in the ray-tracking equations (radians) θ0 ) angle of the ray originating at a source point (emitter fiber) (radians) θ1 ) angle of the ray originating at the back face of the GRIN lens (radians) θ′0 ) angle of a ray inside the GRIN lens at its front face (radians) θ′1 ) angle of a ray inside the GRIN lens at its back face (radians) θc ) confinement angle in the fiber core (degrees) θcr ) critical angle at which total internal reflection bounces the light back (degrees) θh ) half acceptance angle (degrees) θi ) angle of incidence of a ray measured from a line normal to the surface (degrees or radians)
θr ) angle of refraction of a ray measured from a line normal to the surface (degrees or radians) θref ) angle of reflection of a ray measured from a line normal to the surface (degrees or radians) θ′(z) ) angle of a ray inside the GRIN lens (radians) λ ) wavelength of infrared radiation (µm)
Appendix A. Amplitude Y0 and Phase δ in a GRIN Lens The ray-tracking equations, eqs 7 and 8, determine the position and angle of a ray crossing through a GRIN lens. These two equations are expressed in terms of y0, the radial position, and θ′0, the angle of the beam with respect to the lens axis, where both parameters are measured at the front face of the lens. To obtain eqs 9 and 10, these two parameters are replaced by the amplitude Y0 and the phase δ
y0 ) Y0 sin δ θ′0
xA
) Y0 cos δ
(A.1) (A.2)
Substituting eqs A.1 and A.2 into eq 7, one obtains
y(z) ) Y0[cos(xAz) sin δ + sin(xAz) cos δ]
(A.3)
By application of the trigonometric formula
sin(R + β) ) sin(R) cos(β) + cos(R) sin(β) (A.4) eq A.3 furnishes eq 9
y(z) ) Y0 sin(xAz + δ)
(9)
Proceeding similarly for eq 8, we obtain
θ′(z) ) Y0xA[cos(xAz) cos(δ) - sin(xAz) sin(δ)] (A.5) which, through application of the trigonometric formula
cos(R + β) ) cos(R) cos(β) - sin(R) sin(β)
(A.6)
gives
θ′(z) ) Y0xA cos(xAz + δ)
(A.7)
Now, defining
T0 ) Y0xA
(12)
θ′(z) ) T0 cos(xAz + δ)
(10)
eq 10 is obtained as
Moreover, to get eq 11, first eqs A.1 and A.2 can be squared to give
y02 ) Y02 sin2(δ)
(A.8)
θ′02 ) Y02 cos2(δ) A
(A.9)
Then, eqs A.8 and A.9 can be added as follows
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5631
y02 +
θ′02 ) Y02[sin2(δ) + cos2(δ)] A
(A.10)
which can be solved for Y0 to give eq 11
Y0 )
x
y02 +
θ′02 A
(11)
Finally, for the derivation of eq 13, eq A.1 is divided by eq A.2 to yield
y0 sin δ ) tan δ ) θ′0 cos δ
( )
(A.11)
xA
and solving for δ gives
( )
δ ) arctan
y0xA θ′0
(13)
Appendix B: Refractive Index Variation in a GRIN Lens GRIN lenses are small glass rods with the capability of collecting light from a source and refracting that light to form a usable image of the light source. The light path through a GRIN lens is continually altered through a smooth variation of the refractive index. The refractive index of the rod material of the GRIN lens varies parabolically as a function of the radius, from a maximum on the rod axis to a minimum at the outer surface. The refractive index changes with the radial position in the lens according to
A N(r) ) N0 1 - r2 2
(
)
(B.1)
where N0 is the base refractive index or the optical refractive index at the lens axis, A is the squared gradient constant, and r is the radial position in the lens. As a result of this index variation, a ray passing through the GRIN lens follows a sinusoidal path. The period of this sinusoidal path is called the pitch (P). Literature Cited (1) Beck, M. S.; Drane, J.; Plaskowski, A.; Wainwright, N. Particle Velocity and Mass Flow Measurement in Pneumatic Conveyors. Powder Technol. 1968/1969, 2, 269. (2) Oki, K.; Walawender, W. P.; Fan, L. T. The Measurement of Local Velocity of Solid Particles. Powder Technol. 1977, 18, 171. (3) Nieuwland, J. J.; Meijer, R.; Kuipers, J. A. M.; van Swaaij, W. P. M. Measurements of Solids Concentration and Axial Solids Velocity in Gas-Solid Two-Phase Flows. Powder Technol. 1996, 87, 127.
(4) Jin, Y.; Zheng, Y.; Wei, F. State-of-the-Art Review of Downer Reactors. In Circulating Fluidized Bed Technology VII; Grace, J. R., Zhu, J., de Lasa, H., Eds.; Canadian Society for Chemical Engineering: Ottawa, Canada, 2002. (5) Beck, M. S.; Plaskowski, A. Cross Correlation Flowmeters: Their Design and Application; Adam Hilger: Bristol, U.K., 1987. (6) Tuzla, K.; Sharma, A. K.; Chen, J. C.; Schiewe, T.; Wirth, K. E.; Molerus, O. Transient Dynamics of Solid Concentration in Downer Fluidized Bed. Powder Technol. 1998, 100, 166. (7) Sobocinski, D. A.; Young, B. J.; de Lasa, H. I. New FiberOptic Method for Measuring Velocities of Strands and Solids HoldUp in Gas-Solids Downflow Reactors. Powder Technol. 1995, 83, 1. (8) Herbert, P. M.; Gauthier, T. A.; Briens, C. L.; Bergougnou, M. A. Application of Fiber Optic Reflection Probes to the Measurement of Local Particle Velocity and Concentration in Gas-Solid Flow. Powder Technol. 1994, 80, 243. (9) Zhou, J.; Grace, J. R.; Lim, C. J.; Brereton, C. M H. Particle Velocity Profiles in a Circulating Fluidized Bed Riser of Square Cross-Section. Chem. Eng. Sci. 1995, 50, 237. (10) Zhu, J.-X.; Li, G.-Z.; Qin, S.-Z.; Li, F.-Y.; Zhang, H.; Yang, Y.-L. Direct Measurements of Particle Velocities in Gas-Solids Suspension Flow Using a Novel Five-Fiber Optical Probe. Powder Technol. 2001, 115, 184. (11) Aguillo´n, J.; Shakourzadeh, K.; Guigon, P. A New Method for Local Solid Concentration Measurement in Circulating Fluidized Bed. Powder Technol. 1996, 86, 251. (12) Hecht, J. Understanding Fiber Optics; Sams Publishing: Indianapolis, IN, 1993. (13) Nippon Sheet Glass America, Inc., Somerset, NJ; Manufacturer’s literature on the SELFOC microlens: SELFOC Product Guide. (14) Lounge, M. Y.; Iyer, S. A.; Giannelis, E. P.; Lischer, D. J.; Chang, H. Optical Fiber Measurements of Particle Velocity Using Laser-Induced Phosphorescence. Appl. Opt. 1991, 30, 1976. (15) de Lasa, H.; Young, B.; Krol, S. Fiber Optic Sensor for Sensing Particle Movement in a Catalytic Reactor. US Patent 5,740,291, 1998. (16) Krol, S.; Pekediz, A.; de Lasa, H. Particle Clustering in Down Flow Reactors. Powder Technol. 2000, 108, 6. (17) Zhu, J.-X.; Yu, Z.-Q.; Jin, Y.; Grace, J. R.; Issangya, A. Cocurrent Downflow Circulating Fluidized Bed (Downer) Reactorss A State of the Art Review. Can. J. Chem. Eng. 1995, 73, 662. (18) Nova, S. R. Fibre Optic Sensors for Multiphase Reactors. M.E.Sc. Thesis, The University of Western Ontario, London, ON, Canada, 2001. (19) Zhang, H.; Johnston, P. M.; Zhu, J.-X.; de Lasa, H. I.; Bergougnou, M. A. A Novel Calibration Procedure for a Fibre Optic Solid Concentration Probe. Powder Technol. 1998, 100, 260. (20) Liu, J.; Grace, J. R.; Bi, X.; Novel Multifunctional OpticalFibre Probe: I. Development and Validation. AIChE J. 2003, 49, 1405. (21) Nova, S.; Krol, S.; de Lasa, H. Particle Velocity and Particle Clustering in Downflow Reactors. Powder Technol., manuscript submitted. (22) Nova, S.; Krol, S.; de Lasa, H. Particle Velocity and Particle Clustering in Downflow Reactors: Measurements Using a CRECGS-Optiprobe. In Fluidization XI: Present and Future for Fluidization Engineering; Arena, U., Chirone, R., Miccio, M., Salatino, P., Eds.; Engineering Conferences International: New York, 2004; p 379.
Received for review September 5, 2003 Revised manuscript received March 18, 2004 Accepted March 24, 2004 IE0306980
