Sub-millimetre wave range -Doppler radar as a diagnostic tool for gas -solids systems - solids concentration measurements Marlene Bonmanna Diana Carolina Guío -Pérezb Tomas Bryllerta David Pallarèsb Martin Seemannb Filip Johnssonb Jan

2025-05-02 0 0 995.22KB 18 页 10玖币

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Sub-millimetre wave range-Doppler radar as a diagnostic tool for gas-solids systems - solids

concentration measurements

Marlene Bonmanna, Diana Carolina Guío-Pérezb, Tomas Bryllerta, David Pallarèsb, Martin Seemannb, Filip Johnssonb, Jan

Stakea

a Department of Microtechnology and Nanoscience, Terahertz and Millimetre Wave Laboratory

Chalmers University of Technology, SE-412 96 Gothenburg, Sweden

b Department of Space, Earth and Environment, Division of Energy Technology

Chalmers University of Technology, SE-412 96 Gothenburg, Sweden

Abstract

Current non-intrusive measurement techniques for characterising the solids flow in gas-solids suspensions are

limited by the low temporal or low spatial resolution of the sample volume, or in the case of optical methods, by

a short range of sight. In this work, a sub-millimetre wave range-Doppler radar is developed and validated for non-

intrusive sensing of solids concentrations in a gas-solids particle system with known characteristics. The radar system

combines favourable features, such as the ability to see through at optical frequencies opaque materials, to measure

the local solids velocity and the reflected radar power with a spatial resolution of a few cubic centimetres over

distances of a few metres. In addition, the radar hardware offers flexibility in terms of installation. After signal

processing, the output of the radar is range-velocity images of the solids flowing along the radar’s line-of-sight. The

image frame rate can be close to real-time, allowing the solids flow dynamics to be observed.

While the well-established Doppler principle is used to measure the solids velocity, this paper introduces a method

to relate the received radar signal power to the solids volumetric concentrations () of different particulate

materials. The experimental set-up provides a steady stream of free-falling solids that consist of glass spheres, bronze

spheres or natural sand grains with known particle size distributions and with particle diameters in the range of 50–

300 µm. Thus, the values of  found using the radar measurements are validated using the values of retrieved

from closure of the mass balance derived from the measured mass flow rate of the solids stream and the solids

velocity. The results show that the radar system provides reliable measurements of , with a mean relative error of

approximately 25% for all the tested materials, particle sizes and mass flow rates, yielding values of  ranging from

0.2×10-4 m3/m3 up to 40×10-4 m3/m3 and solids velocities within the range of 0–4.5 m/s. This demonstrates the

ability of the radar technology to diagnose the solids flow in gas-solids suspensions using a unique combination of

penetration length, accuracy, and spatial and velocity resolution. In future work, the radar technique will be applied

to study non-controlled solids flow at a larger scale, and to understand flow conditions relevant to industrial reactor

applications, e.g., fluidised bed, entrained flow, and cyclone units.

Keywords: sub-millimetre wave, Doppler radar, FMCW-pulse Doppler radar, gas-solids flow, solids concentration

measurement, particle velocity measurement

1. Introduction

In a wide range of industrial processes, the transport and mixing of gas-solids phases play essential roles. These

processes range from the pneumatic transport of particulate materials in, for example, food processing [1] and

pharmaceutics [2], to the fluidised bed technology used, for example, in combustion plants [3]. Measuring the

velocities and concentrations of solids is essential for understanding the mechanisms that govern the solids flow and

for validation of numerical modelling approaches [4, 5] that attempt to describe the complex gas-solids dynamics.

Ideally, a measurement technique to diagnose the solids flow in a gas-solids suspension should:

(i) Be non-intrusive, avoiding the insertion of objects that affect the solids flow to be measured.

(ii) Resolve the dynamics of the flow. It should provide sufficiently high resolutions in the time (time-scales longer

than 10-1 s cover most of the power spectra of fast gas-solids flows (see for example [6]) and space (with particle

scale length being the ultimate target) dimensions.

(iii) Provide penetration into the gas-solids suspension so that the flow can also be diagnosed in locations that lack

optical access.

(iv) Be sufficiently robust to withstand the harsh erosional (and sometimes corrosive) flow conditions.

(v) Be associated with a low cost of implementation.

Among the non-intrusive techniques currently available, the most commonly used are time-averaged pressure

measurements, from which the axial profiles of the cross-sectional average concentrations of solids can be obtained

with a spatial resolution that ranges from decimetres to several metres (e.g., [7]). Specific characteristics, such as

bubble dynamics and regime changes, can be extracted from time-resolved pressure measurements (e.g., [8], [9],

and [10]). Some non-intrusive tomographic techniques applied in gas-solid systems involve x-rays, γ-rays, electrical

capacitance, and phase-Doppler anemometers. They can be used for mapping solids flow (velocity, concentration,

or both) in narrow bench-scale units with a spatial resolution in the order of a few centimetres [11, 12, 13 and

references therein, 14]. Such dynamic tomographic measurements have limited applicability to large-scale units,

owing to the higher integrated absorption of the signal and the rapidly increasing number of sensor pairs needed to

retain the same level of spatial resolution. In addition, the intended positioning of the sensor pairs is often restricted

by geometric constraints, which may reduce the flexibility and accuracy of the technique. Moreover, the

measurement accuracy largely depends on the reconstruction algorithm. Direct tracking techniques, such as

electrostatic induction sensors or particle image velocimetry (PIV) [15, 12], offer higher spatial resolution (1 mm).

However, these techniques are restricted to measurements of flows at moderate temperatures and are limited by

the need for an optically free line-of-sight to the measurement volume. Therefore, solids velocity measurements

made with electrostatic induction sensors or particle image velocimetry PIV are rarely used for dense flows.

Radar technology combines several of the desired properties listed above, in that it is non-invasive, has long

penetration lengths, and excellent velocity and spatial resolutions. Some authors [16, 17] have demonstrated non-

intrusive measurements of multi-disperse solids streams using a multi-static dual-frequency (91.5 GHz, 150.3 GHz)

radar system. They observed proportionality between the solids mass load and reflected signal power. The radar

technique has also been used to measure particle size distributions (). Even though the radar mode cannot

measure the velocity of the solids, Baer and co-workers [18] have demonstrated that two 80-GHz frequency-

modulated continuous-wave (FMCW) radars can be used to find the cross-sectional average concentration of the

solids volume fraction and velocity across a 200-mm-wide conveying installation. The

is derived from the time

of flight of the radar signal and the velocity from two-point measurements using the correlation between the two

radar signals along the solids flow. However, the configurations involving two transmitter-receiver sets and several

radars, respectively, require accurate radar alignment, making them less-suitable for performing measurements in

industrial units. Furthermore, the spatial resolution is restricted, being defined by the overlap of the two radar beams

[16, 17] and across the whole 200-mm tube [18].

Radar systems that utilise only one antenna for transmitting and receiving the radar signals operating in pulsed-

FMCW mode offer an alternative to overcome the complication of radar antenna alignment and to allow (besides

local solids concentration measurements) for local solids velocity measurements using the Doppler principle.

Cooper and Chattopadhyay [19] have described a 680-GHz radar that can simultaneously monitor the distance and

velocity of small solids particles in a sandstorm. However, the radar was not adapted for industrial applications.

The recently developed radar technology with sub-millimetre wave frequencies (325–350GHz) [20] offers high

spatial resolution and has a relatively compact footprint (40×30×20 cm3). Thus, it allows the performance of

measurements while pointing the radar beam in any desired direction and simplifies the installation for industrial

measurements. In addition, it operates at higher frequencies than previous radar systems [16, 17, 18]. In the case of

the 680-GHz radar used previously [19], this increases the measurement sensitivity for smaller solids particles and

increases the spatial resolution. At the same time, the radar operates below optical frequencies (400–750 THz),

which means that the radar beam has a greater depth of penetration than optical measurement methods. Therefore,

this sub-millimetre wave radar technology is highly promising for non-intrusive monitoring of solids concentrations

and velocities, allowing the characterisation of volumes in the order of 10-3 m3 (resulting from a beam cross-section

in the order of 0.01–0.1 m2 and a spatial resolution along the direction of the beam of 10-2 m), with a velocity

resolution in the order of 10-2 m/s and a time resolution of 10-2 s (frame rate in the order of 10–100 Hz). The

abilities of FMCW-pulse Doppler radar systems to measure accurately the velocities of objects are generally accepted

and, specifically for the radar system used in this work, have been previously reported in the literature [20]. Thus,

there is a need to verify the ability of such radar systems to measure accurately the solids concentrations, thereby

providing an all-in-one measurement of the solids flux.

The aim of this work was to evaluate the use of radar technology as a diagnostic tool for the characterisation

of solids flows. Here, the 340–GHz sub-millimetre wave FMCW-pulse Doppler radar system described previously

[20] is used to measure the solids velocity and concentration along a free-falling solids stream with known mass

flow rate, stream diameter and solids properties. Radar-based measurements of the solids concentration are

compared to their corresponding reference values calculated from closure of the mass balance using the values of

the measured mass flow rate and the solids velocity (obtained through the Doppler method and, thus, considered

to be reliable). The radar measurement is tested with solids of different sizes, shapes, and material/dielectric constants

and with varying solids concentrations.

2. Theory

Figure 1 illustrates the general principle of a radar beam intersecting a gas-solids suspension, where the geometrical

dimensions of the gas-solids suspension with solids volume concentration  exceeds the radar beam-width

 , where  is the distance (range) to the radar antenna and  is the angular beam-width. The radar

beam-width  defines the cross-range resolution of the radar, whereas the spatial resolution in the propagation

direction of the radar beam is determined by the range resolution , thereby yielding the sample volume  

 for a given range increment. For each , the solids velocity distribution and  are measured.

The solids velocity is indicated by

, the Doppler velocity, whereas  is measured by the radar and is the projection

towards the radar (i.e., radial velocity).

Figure 1. Radar beam intersecting a gas-solids suspension.

The radar signal is transmitted and then reflected back to the radar antenna by the solids. The relationship

between the reflected signal power and  is derived from the radar equation. The radar equation [21] expresses

the signal power reflected from an individual scatterer:



, (1)

where  is the peak transmit power,  is the antenna gain,  is the wavelength of the signal, and  is the back-

scattering cross-section.

The back-scattering cross-section for an individual solids particle with radius  is calculated as:

   (2)

where  is the back-scattering efficiency calculated using the Mie theory formalism for an approximately spherical

particle [22]. However, when the radar beam intersects a solids cloud all the individual solids particles within the

radar beam contribute to the total back-scattering cross-section, . Furthermore, multiple scattering effects,

i.e., the impact of second-order scattering of photons that do not leave the radar’s field-of-view after having

scattered once with solids in the radar beam, gain relevance as the solids concentration increases, thereby altering

the back-scattered signal. Multiple scattering effects are negligible for sub-wavelength-sized solids when the mean-

free path (inverse of the extinction coefficient) between scattering events is larger than the radar’s field-of-view

(radar footprint) [23]. Theoretically, for approximately wavelength-sized solids, Mishchenko et al. [24] have

estimated a solids volume fraction of 2.4×10-3 as a rough threshold value for validity. The suspensions diagnosed in

this work fulfil most often this criterion, as discussed in the

Results

section. Thus, neglecting multiple scattering

effects, the total back-scattering cross-section can be expressed as:

   



 , (3)

where  is the solids number concentration (the number of solids particles per unit volume), and  is the

PSD function.

As the radar beam is travelling through the gas-solids suspension, it is reflected. It travels back to the radar

antenna, experiencing two-way attenuation due to extinction (scattering and absorption). The intensity of the radar

beam,, is reduced according to [22, 25]:

  



, (4)

where  is the attenuation coefficient and  is the range interval that the beam has travelled. The attenuation

coefficient  is related to the total extinction cross-section,  as   . The extinction cross-

section for an individual solid particle with radius  can be calculated as:

  , (5)

with  being the extension efficiency of an individual solid particle calculated using the Mie formalism, and,

neglecting multiple scattering effects, the  for the gas-solids suspension is:

   



  (6)

However, when making a compromise between the control of the conducted measurements and the size of

the measurement set-up, it should be noted that under experimental conditions, as in this work, the radar beam

with radius  is not always fully immersed in a solids stream with radius  throughout the whole

measured distance (i.e.,

rradar

rstream

in some regions, see details in Section 3). This violates the requirement for the

applicability of Eq. (4). To correct for this, the first right-hand side term of Eq. (1) is introduced. In addition, a

scaling factor  is introduced in the attenuation term to scale . Furthermore, in a real radar system, several

additional factors influence the measurement, such as the radar hardware components (the gain in receiver

amplifiers, loss in wires, filters, and antennas) and signal gain and losses introduced by the digital signal processing

needed to extract the velocity and range data. As these factors are generally not known with sufficient precision,

the radar instrument needs to be calibrated to estimate the absolute values of the solids concentration (for details of

the calibration, see Section 3.2.2). In summary, calibration allows the incorporation of all of the above into a single

factor,.

With all the considerations mentioned above, Eq. (1) is re-written as:



 

 



 



 





(7)

As the last step, the measured solids volume fraction can be calculated as:

  (8)

where the solids mean volume is given by:

 





 . (9)

3. Methodology

The following sub-sections describe the procedure for validating the radar measurements of solids

concentrations, the experimental set-up for establishing a controlled solids stream, the radar system and its

calibration.

3.1 Validation procedure

The radar measures the reflected power along a solids stream with mass flow rate . For a stable and steady flow

of solids, the relationship between and  is given by closure of the mass balance:

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Sub-millimetrewaverange-Dopplerradarasadiagnostictoolforgas-solidssystems-solidsconcentrationmeasurementsMarleneBonmanna,DianaCarolinaGuío-Pérezb,TomasBryllerta,DavidPallarèsb,MartinSeemannb,FilipJohnssonb,JanStakeaaDepartmentofMicrotechnologyandNanoscience,TerahertzandMillimetreWaveLaboratoryChalme...

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Sub-millimetre wave range -Doppler radar as a diagnostic tool for gas -solids systems - solids concentration measurements Marlene Bonmanna Diana Carolina Guío -Pérezb Tomas Bryllerta David Pallarèsb Martin Seemannb Filip Johnssonb Jan.pdf

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Sub-millimetre wave range -Doppler radar as a diagnostic tool for gas -solids systems - solids concentration measurements Marlene Bonmanna Diana Carolina Guío -Pérezb Tomas Bryllerta David Pallarèsb Martin Seemannb Filip Johnssonb Jan

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