Flow Measurement Techniques Research Articles

Capacitance-based mass flow rate measurement of two-phase hydrogen in a 0.5 in. tube

Mass flow rate is a critical measurement parameter when designing cryogenic hydrogen fluid systems. It is important in custody transfer applications for calculating financial obligations, fundamental fluid property research/modeling, and fluid system design applications to optimize chill down performance, maintain thermal equilibriums, and provide feedback control for pumps and valves. However, due to the large temperature differential between cryogenic fluids and the environment, there is often multiphase flow during system chilldown and steady state operation. Current available cryogenic flow measurement techniques are not equipped to deal with the complex multiphase flow inherent in cryogenic fluid systems, resulting in significant measurement errors. This mass flow measurement inaccuracy can cause financial loss, system instability, and even component failure, resulting in a strong market demand for a multiphase cryogenic mass flow meter to optimize and control sophisticated and costly cryogenic systems. This paper presents a solution in the form of a novel capacitance-based technique for measuring the multiphase mass flow rate of cryogenic hydrogen in a terrestrial environment. The device was calibrated and tested on a ½” tube multiphase hydrogen flow loop at a cryogenic hydrogen test facility. An error of ± 2 % full scale was achieved across a range of flow conditions, including transient and steady states.

A comparison of machine learning methods for recovering noisy and missing 4D flow MRI data.

Experimental blood flow measurement techniques are invaluable for a better understanding of cardiovascular disease formation, progression, and treatment. One of the emerging methods is time-resolved three-dimensional phase-contrast magnetic resonance imaging (4D flow MRI), which enables noninvasive time-dependent velocity measurements within large vessels. However, several limitations hinder the usability of 4D flow MRI and other experimental methods for quantitative hemodynamics analysis. These mainly include measurement noise, corrupt or missing data, low spatiotemporal resolution, and other artifacts. Traditional filtering is routinely applied for denoising experimental blood flow data without any detailed discussion on why it is preferred over other methods. In this study, filtering is compared to different singular value decomposition (SVD)-based machine learning and autoencoder-type deep learning methods for denoising and filling in missing data (imputation). An artificially corrupted and voxelized computational fluid dynamics (CFD) simulation as well as in vitro 4D flow MRI data are used to test the methods. SVD-based algorithms achieve excellent results for the idealized case but severely struggle when applied to in vitro data. The autoencoders are shown to be versatile and applicable to all investigated cases. For denoising, the in vitro 4D flow MRI data, the denoising autoencoder (DAE), and the Noise2Noise (N2N) autoencoder produced better reconstructions than filtering both qualitatively and quantitatively. Deep learning methods such as N2N can result in noise-free velocity fields even though they did not use clean data during training. This work presents one of the first comprehensive assessments and comparisons of various classical and modern machine-learning methods for enhancing corrupt cardiovascular flow data in diseased arteries for both synthetic and experimental test cases.

Reproducibility of a single-volume dynamic CT myocardial blood flow measurement technique: validation in a swine model

BackgroundWe prospectively assessed the reproducibility of a novel low-dose single-volume dynamic computed tomography (CT) myocardial blood flow measurement technique.MethodsThirty-four pairs of measurements were made under rest and stress conditions in 13 swine (54.3 ± 12.3 kg). One or two acquisition pairs were acquired in each animal with a 10-min delay between each pair. Contrast (370 mgI/mL; 0.5 mL/kg) and a diluted contrast/saline chaser (0.5 mL/kg; 30:70 contrast/saline) were injected peripherally at 5 mL/s, followed by bolus tracking and acquisition of a single volume scan (100 kVp; 200 mA) with a 320-slice CT scanner. Bolus tracking and single volume scan data were used to derive perfusion in mL/min/g using a first-pass analysis model; the coronary perfusion territories of the left anterior descending (LAD), left circumflex (LCx), and right coronary artery (RCA) were automatically assigned using a previously validated minimum-cost path technique. The reproducibility of CT myocardial perfusion measurement within the LAD, LCx, RCA, and the whole myocardium was assessed via regression analysis. The average CT dose index (CTDI) of perfusion measurement was recorded.ResultsThe repeated first (Pmyo1) and second (Pmyo2) single-volume CT perfusion measurements were related by Pmyo2 = 1.01Pmyo1 − 0.03(ρ = 0.96; RMSE = 0.08 mL/min/g; RMSE = 0.07 mL/min/g) for the whole myocardium, and by Preg2 = 0.86Preg1 + 0.13(ρ = 0.87; RMSE = 0.31 mL/min/g; RMSE = 0.29 mL/min/g) for the LAD, LCx, and RCA perfusion territories. The average CTDI of the single-volume CT perfusion measurement was 10.5 mGy.ConclusionThe single-volume CT blood flow measurement technique provides reproducible low-dose myocardial perfusion measurement using only bolus tracking data and a single whole-heart volume scan.Relevance statementThe single-volume CT blood flow measurement technique is a noninvasive tool that reproducibly measures myocardial perfusion and provides coronary CT angiograms, allowing for simultaneous anatomic-physiologic assessment of myocardial ischemia.Key PointsA low-dose single-volume dynamic CT myocardial blood flow measurement technique is reproducible.Motion misregistration artifacts are eliminated using a single-volume CT perfusion technique.This technique enables combined anatomic-physiologic assessment of coronary artery disease.Graphical

Two-Field Excitation for Contactless Inductive Flow Tomography.

Contactless inductive flow tomography (CIFT) is a flow measurement technique allowing for visualization of the global flow in electrically conducting fluids. The method is based on the principle of induction by motion: very weak induced magnetic fields arise from the fluid motion under the influence of a primary excitation magnetic field and can be measured precisely outside of the fluid volume. The structure of the causative flow field can be reconstructed from the induced magnetic field values by solving the according linear inverse problem using appropriate regularization methods. The concurrent use of more than one excitation magnetic field is necessary to fully reconstruct three-dimensional liquid metal flows. In our laboratory demonstrator experiment, we impose two excitation magnetic fields perpendicular to each other to a mechanically driven flow of the liquid metal alloy GaInSn. In the first approach, the excitation fields are multiplexed. Here, the temporal resolution of the measurement needs to be kept as high as possible. Consecutive application by multiplexing enables determining the flow structure in the liquid with a temporal resolution down to 3 s with the existing equipment. In another approach, we concurrently apply two sinusoidal excitation fields with different frequencies. The signals are disentangled on the basis of the lock-in principle, enabling a successful reconstruction of the liquid metal flow.

Unbalanced Optimal Transport For Stochastic Particle Tracking

Non-invasive flow measurement techniques, such as particle tracking velocimetry, resolve 3D velocity fields by pairing tracer particle positions in successive time steps. These trajectories are crucial for evaluating physical quantities like vorticity, shear stress, pressure, and coherent structures. Traditional approaches deterministically reconstruct particle positions and extract particle tracks using tracking algorithms. However, reliable track estimation is challenging due to measurement noise caused by high particle density, particle image overlap, and falsely reconstructed 3D particle positions. To overcome this challenge, probabilistic approaches quantify the epistemic uncertainty in particle positions, typically using a Gaussian probability distribution. However, the standard deterministic tracking algorithms relying on nearest-neighbor search do not directly extend to the probabilistic setting. Moreover, such algorithms do not necessarily find globally consistent solutions robust to reconstruction errors. This paper aims to develop a globally consistent nearest-neighborhood algorithm that robustly extracts stochastic particle tracks from the reconstructed Gaussian particle distributions in all frames. Our tracking algorithm relies on the unbalanced optimal transport theory in the metric space of Gaussian measures. Specifically, we optimize a binary transport plan for efficiently moving the Gaussian distributions of reconstructed particle positions between time frames. We achieve this by computing the partial Wasserstein distance in the metric space of Gaussian measures. Our tracking algorithm is robust to position reconstruction errors since it automatically detects the number of particles that should be matched through hyperparameter optimization. Notably, our tracking algorithm also readily applies to the standard deterministic PTV case. Finally, we validate our method using an in vitro flow experiment using a 3D-printed cerebral aneurysm.

Quantification of two-phase flow in a microchannel heat exchanger header based on capacitance measurement

The two-phase distribution has always been one of the research focuses of microchannel heat exchangers, because the maldistribution could seriously affect the heat transfer performance. This paper developed a capacitive method to quantify the two-phase distribution of vapor-liquid flow in the aluminum header of a microchannel heat exchanger. A flexible capacitance sensor was used to quantify the two-phase distribution with R134a. The inlet mass fluxes vary from 17.47 kg m−2 s−1 to 52.42 kg m−2 s−1 and inlet vapor qualities range from 0.2 to 0.6. The normalized time-averaged capacitance signal was processed by a Gaussian function to obtain the mathematical expectation and the standard deviation. The local vapor quality in the header was solved for using a correlation derived from the pre-experiments. The distribution of local vapor quality showed that gases were concentrated upstream of the header, while liquids were concentrated in the middle and lower reaches. The local vapor quality reached a minimum and remained constant at 0.1 in the middle and lower reaches, unaffected by changes in inlet conditions. As the mass flux increased, both the local vapor quality maximum point and the minimum point in the header were shifted back toward the downstream. Additionally, the increase of mass flux caused the fluctuation of the standard deviation increased, which meant the stability of the flow decreased. The two-phase flow measurement technique based on flexible capacitance sensors proposed in this study realized the extension of the capacitive method from the experimental stage to the industrial application stage.

A novel flow rate measurement method for fire hose based on vibration signal and neural network

During fire incidents, it is imperative to monitor the flow rate of the fire hoses. Due to the constraints imposed by the fire scene, vibration-based flow measurement technique has shown great potential. However, usage of single frequency or statistic feature to predict flow rate is prone to influenced by outer noise. In this study, we constructed a dataset for fire-hose flow rate prediction task with a flow rate range of 0.35 L/s to 20.00 L/s, and sample frequency of 50 kHz. On that basis, a new variant of residual network, i.e., an RBU-STMS has been developed, integrating soft thresholding and feature pyramid mechanism. Evaluation result on the dataset has proven the effectiveness of the developed model which yields improvement of 3.85 % and 4.05 % by incorporating the two mechanisms individually and an overall improvement of 5.00 % by combining both mechanisms, compared to the conventional residual network. Furthermore, the proposed model exhibits a considerable tolerance to noisy inputs, with a predicted error rate of only 8.06 % when subjected to a 10 % standard deviation of random noise in the input, remaining below the 10 % threshold.

Dynamic Light Scattering in Biomedical Applications: feature issue introduction

The feature Issue on “Dynamic Light Scattering in Biomedical Applications” presents a compilation of research breakthroughs and technological advancements that have shaped the field of biophotonics, particularly in the non-invasive exploration of biological tissues. Highlighting the significance of dynamic light scattering (DLS) alongside techniques like laser Doppler flowmetry (LDF), diffusing wave spectroscopy (DWS), and laser speckle contrast imaging (LSCI), this issue underscores the versatile applications of these methods in capturing the intricate dynamics of microcirculatory blood flow across various tissues. Contributions explore developments in fluorescence tomography, the integration of machine learning for data processing, enhancements in microscopy for cancer detection, and novel approaches in optical biophysics, among others. Innovations featured include a high-resolution speckle contrast tomography system for deep blood flow imaging, a rapid estimation technique for real-time tissue perfusion imaging, and the use of convolutional neural networks for efficient blood flow mapping. Additionally, studies delve into the impact of skin strain on spectral reflectance, the sensitivity of cerebral blood flow measurement techniques, and the potential of photobiomodulation for enhancing brain function. This issue not only showcases the latest theoretical and experimental strides in DLS-based imaging but also anticipates the continued evolution of these modalities for groundbreaking applications in disease detection, diagnosis, and monitoring, marking a pivotal contribution to the field of biomedical optics.

The Sun’s Large-Scale Flows I: Measurements of Differential Rotation & Torsional Oscillation

We have developed a comprehensive catalog of the variable differential rotation measured near the solar photosphere. This catalog includes measurements of these flows obtained using several techniques: direct Doppler, granule tracking, magnetic pattern tracking, global helioseismology, as well as both time-distance and ring-diagram methods of local helioseismology. We highlight historical differential rotation measurements to provide context, and thereafter provide a detailed comparison of the MDI-HMI-GONG-Mt. Wilson overlap period (April 2010 – Jan 2011) and investigate the differences between velocities obtained from different techniques and attempt to explain discrepancies. A comparison of the rotation rate obtained by magnetic pattern tracking with the rotation rates obtained using local and global helioseismic techniques shows that magnetic pattern tracking measurements correspond to helioseismic flows located at a depth of 25 to 28 Mm. In addition, we show the torsional oscillation from Sunspot Cycles 23 and 24 and discuss properties that are consistent across measurement techniques. We find that acceleration derived from torsional oscillation is a better indicator of long-term trends in torsional oscillation compared to the residual velocity magnitude. Finally, this analysis will pave the way toward understanding systematic effects associated with various flow measurement techniques and enable more accurate determination of the global patterns of flows and their regular and irregular variations.

Lagrangian particle tracking in the presence of obstructing objects

Volumetric flow measurement techniques have become the state-of-the-art for characterizing a broad range of different flow fields. Still, certain major limitations are present, which hinders the application of these techniques for some of the more complex flow configurations. In particular, flow measurements involving the presence of obstructing objects require time consuming measurement strategies and careful adjustment of the experimental equipment to avoid inaccurate measurement results. Within this study, these limitations are mitigated by the use of a known object’s shape and position in the form of depth maps for commonly used Lagrangian particle tracking schemes like Shake-the-Box (STB) as well as in volume self-calibration methods. The incorporation of these depth maps is computationally inexpensive and straight forward to implement. In order to evaluate the performance of this novel object-aware Lagrangian particle tracking (OA-LPT) approach, synthetic as well as experimental test data is created and the reconstruction quality is evaluated. It is shown, that OA-LPT is capable of providing full flow-field information, whereas the default STB implementation fails to correctly reconstruct particles in the partly-occluded regions.

Assessment of a Flow-Measurement Technique for the Printability of Extrusion-Based Bioprinting

Assessment of a Flow-Measurement Technique for the Printability of Extrusion-Based Bioprinting

Contagion effects of permissionless, worthless cryptocurrency tokens: Evidence from the collapse of FTX

This paper investigates the price discovery relationships between FTT Token, issued by the cryptocurrency exchange FTX, and a set of assets and liabilities held by FTX amid a period of catastrophic financial decline by applying novel information flow measurement techniques. Results indicate that during key phases associated with the collapse of FTX, FTT Token had an informational lead over multiple assets, including cryptocurrencies such as Ethereum. Furthermore, we identify significant interactions between the FTT Token and both Robinhood shares and the token Serum, raising concerns about the direct influence of permissionless, technically valueless tokens on other assets and the potential challenges to market stability and investor protection. Our findings underscore the need for stronger policy-making, regulatory, and ethical considerations in cryptocurrency markets.

Dynamic Contrast-enhanced CT Lymphangiography to Quantify Thoracic Duct Lymphatic Flow.

Background CT lymphangiography has been used to image the lymphatic anatomy and assess lymphatic abnormalities. There is, however, a need to develop a method for quantification of lymphatic flow rate in the thoracic duct (TD). Purpose To develop and validate a TD lymphatic flow measurement technique using dynamic contrast-enhanced CT lymphangiography. Materials and Methods Lymphatic flow rate was measured with two techniques: a first-pass analysis technique based on a single compartment model and a thresholding technique distinguishing between opacified and nonopacified voxels within the TD. The measurements were validated in a swine animal model between November 2021 and September 2022. CT images were acquired at 100 kV and 200 mA using a fast-pitched helical scan mode covering the entire TD following contrast material injection into the bilateral inguinal lymph nodes. Two helical CT scans, acquired at the base and peak contrast enhancement of the TD, were used to measure lymphatic flow rate. A US flow probe surgically placed around the TD provided the reference standard measurement. CT lymphatic flow measurements were compared with the reference US flow probe measurements using regression and Bland-Altman analysis. Repeatability was determined using repeated flow measurements within approximately 10 minutes of each other. Results Eleven swine (10 male; mean weight, 43.6 kg ± 2.6 [SD]) were evaluated with 71 dynamic CT acquisitions. The lymphatic flow rates measured using the first-pass analysis and thresholding techniques were highly correlated with the reference US flow probe measurements (r = 0.99 and 0.91, respectively) and showed good agreement with the reference standard, with Bland-Altman analysis showing small mean differences of 0.04 and 0.05 mL/min, respectively. The first-pass analysis and thresholding techniques also showed good agreement for repeated flow measurements (r = 0.94 and 0.90, respectively), with small mean differences of 0.09 and 0.03 mL/min, respectively. Conclusion The first-pass analysis and thresholding techniques could be used to accurately and noninvasively quantify TD lymphatic flow using dynamic contrast-enhanced CT lymphangiography. © RSNA, 2023 See also the editorial by Choyke in this issue.

High-resolution light-field particle imaging velocimetry with color-and-depth encoded illumination

Three-dimensional and three-components (3D-3C) measurement of flow velocity vector is important for the investigation of mechanism underlying flow structure. Light-field particle imaging velocimetry (LF-PIV) is a newly emerged technique for flow velocity measurement. However, LF-PIV suffers low axial resolution, prohibiting it for high fidelity imaging. To overcome this limitation, we proposed to employ color-depth-encoded illumination in light-field PIV (Code LF-PIV) to refine the particle's axial location with the color-depth information of the illumination beam. Code LF-PIV is the first system that integrates the snapshot acquisition of light-field acquisition and the high resolution capability of color coded illumination. Compared to conventional light-field PIV, Code LF-PIV can achieve much higher axial resolution due to the new illumination strategy. Compared to traditional coded illumination PIV, such as Rainbow PIV, Code LF-PIV has higher flexibility for variant imaging applications because of the elimination of customized diffractive optical element. We demonstrated the superiority of our system by imaging fixed particle, randomly distributed cavities inside crystal cube, and the square lid-driven cavity flow, where our Code LF system has increased the axial resolution by a factor of 23 when compared to the conventional LF system, and has achieved a comparable axial resolution as the depth super-resolved Rainbow PIV. Comprehensive evaluation of the imaging results demonstrated that Code LF-PIV combines the advantages of the high resolution of color-depth coded method with the convenient volumetric imaging of light-field camera, making Code LF-PIV a useful technique for high-resolution and large-scale flow measurement.

Controlled-release testing of the static chamber methodology for direct measurements of methane emissions

Abstract. Direct measurements of methane emissions at the component level provide the level of detail necessary for the development of actionable mitigation strategies. As such, there is a need to understand the magnitude of component-level methane emission sources and to test methane quantification methods that can capture methane emissions at the component level used in national inventories. The static chamber method is a direct measurement technique that has been applied to measure large and complex methane sources, such as oil and gas infrastructure. In this work, we compile methane emission factors from the Intergovernmental Panel on Climate Change (IPCC) Emission Factor Database in order to understand the magnitude of component-level methane flow rates, review the tested flow rates and measurement techniques from 40 controlled-release experiments, and perform 64 controlled-release tests of the static chamber methodology with mass flow rates of 1.02, 10.2, 102, and 512 g h−1 of methane. We vary the leak properties, chamber shapes, chamber sizes, and use of fans to evaluate how these factors affect the accuracy of the static chamber method. We find that 99 % of the component-level methane emission rates from the IPCC Emission Factor Database are below 100 g h−1 and that 77 % of the previously available controlled-release experiments did not test for methane mass flow rates below 100 g h−1. We also find that the static chamber method quantified methane flow rates with an overall accuracy of +14/-14 % and that optimal chamber configurations (i.e., chamber shape, volume, and use of fans) can improve accuracy to below ±5 %. We note that smaller chambers (≤20 L) performed better than larger-volume chambers (≥20 L), regardless of the chamber shape or use of fans. However, we found that the use of fans can substantially increase the accuracy of larger chambers, especially at higher methane mass flow rates (≥100 g h−1). Overall, our findings can be used to engineer static chamber systems for future direct measurement campaigns targeting a wide range of sources, including landfills, sewerage utility holes, and oil and natural gas infrastructure.

Ultrasound Speckle Decorrelation-Based Blood Flow Measurements.

Ultrasound imaging is the preferred noninvasive technique to measure blood flow to diagnose cardiovascular disease such as heart failure, carotid stenosis, and renal failure. Conventional ultrasound techniques such as Doppler ultrasound, ultrasound imaging velocimetry, vector Doppler and transverse oscillation beamforming have been used for blood flow velocity profile measurement. However, these techniques were limited to measuring blood flow velocities within the 2-D lateral (across the ultrasound beam) plane of a vessel, and the blood flow velocity profile was derived by assuming that blood vessels have a circular cross-section with axis symmetry. This assumption is incorrect because most vessels have complex geometries, such as tortuosity and branches, and an asymmetric flow profile in the presence of vascular plaque. Consequently, ultrasound speckle decorrelation has been proposed to measure blood flow from transverse views of blood vessels wherein the ultrasound beam is perpendicular to the vessel axis. In this review, we present a summary of recent progress in ultrasound speckle decorrelation-based blood flow measurement techniques.

Experimental investigation of liquid metal droplet flow affected by a time-dependent magnetic field

Abstract The present study investigates experimentally the effects of a time-dependent and spatially inhomogeneous magnetic field on liquid metal droplet flow down an inclined substrate. The flow is solely excited by the electromagnetic interactions between the electrically conducting melt and the applied magnetic field. The metal droplet consists of the eutectic alloy GaInSn which is liquid at room temperature. The magnetic field is generated in the gap between two metallic disks that are equipped with a special geometric arrangement of permanent magnets and put into a measured rotation. During the experiments, a droplet of a measured volume is positioned on an electrically non-conducting substrate that is slightly inclined against the horizontal direction. Droplet and substrate are placed in between the two rotating magnetic disks. In our experiments, we record the electromagnetically excited flow of the droplet downwards onto the substrate using a high-speed camera system. Applying standard techniques of digital image processing, we measure both the displacement position and velocity of the droplet as a function of time. We observe that, depending on the rotation rate of the disks and angle of inclination, the magnetic field eventually triggers this spreading process. In more detail, by evaluating the recorded data, we find that the magnetic field excites capillary waves at the free surface of the droplet. These surface waves contribute to a redistribution of volume towards the contact line formed at the downward-facing end tip of the droplet. This mode of transport steepens the contact angle, allowing the droplet to move. Besides the fundamental aspect of this work, the present study may contribute to the electromagnetic control of both the production of metallic microfibers and metallurgic coating processes as well as to the non-contact electromagnetic flow measurement technique of Lorentz force velocimetry applied to liquid metal free-surface flows.

Development of a unique two hole flow meter for big data analysis in flow measurement techniques

The world of aerodynamics relies on experimentation and obtaining practical results to solve complex real-life problems. In most cases, the aerodynamic tool used to study the flow and its related characteristic is a wind tunnel. Wind tunnels generally explain the flow behavior over different bodies. But before performing experimentations with a wind tunnel, calibration needs to be carried out. In this paper, a spherical flow analyzer with two holes has been introduced and the computational and experimental results are recorded and validated.

Using pressure-driven flow systems to evaluate laser speckle contrast imaging.

Microfluidic flow phantom studies are commonly used for characterizing the performance of laser speckle contrast imaging (LSCI) instruments. The selection of the flow control system is critical for the reliable generation of flow during testing. The majority of recent LSCI studies using microfluidics used syringe pumps for flow control. We quantified the uncertainty in flow generation for a syringe pump and a pressure-regulated flow system. We then assessed the performance of both LSCI and multi-exposure speckle imaging (MESI) using the pressure-regulated flow system across a range of flow speeds. The syringe pump and pressure-regulated flow systems were evaluated during stepped flow profile experiments in a microfluidic device using an inline flow sensor. The uncertainty associated with each flow system was calculated and used to determine the reliability for instrument testing. The pressure-regulated flow system was then used to characterize the relative performance of LSCI and MESI during stepped flow profile experiments while using the inline flow sensor as reference. The pressure-regulated flow system produced much more stable and reproducible flow outputs compared to the syringe pump. The expanded uncertainty for the syringe pump was 8 to higher than that of the pressure-regulated flow system across the tested flow speeds. Using the pressure-regulated flow system, MESI outperformed single-exposure LSCI at all flow speeds and closely mirrored the flow sensor measurements, with average errors of and , respectively. Pressure-regulated flow systems should be used instead of syringe pumps when assessing the performance of flow measurement techniques with microfluidic studies. MESI offers more accurate relative flow measurements than traditional LSCI across a wide range of flow speeds.

Removal of the effect of the high solids holdup ring in the fluidized bed on electromagnetic tomography

Electromagnetic tomography (EMT) system based on tunneling magneto resistance (TMR) sensor, as a non-invasive multiphase flow measurement technique, can effectively detect the solid-phase distribution in the gas–liquid–solid three-phase fluidized bed with magnetic catalysts by reconstructing the permeability distribution image. The radial distribution of solid particles in the gas–liquid–solid three-phase fluidized bed with uneven fluidization is non-uniform, in which a high solids holdup ring exists near the wall of the riser. When the TMR-EMT system is used directly for image reconstruction, the high solids holdup ring will greatly reduce the image quality, further leading to the inability to detect phase information in the riser. To improve the reconstructed image by the TMR-EMT system, a removal method for the high solids holdup ring is proposed. The method firstly estimates the equivalent thickness of the high solids holdup ring based on the boundary measurement data. Then the influence of the high solids holdup ring on the boundary measurement data is subtracted. By the removal method, the internal phase distribution information is prominent. The simulation and experimental results demonstrate that the proposed method can realize the permeability distribution detection by the TMR-EMT system in the presence of the high solids holdup ring.