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Efficient and Flexible Sensitivity Matrix Computation for Adaptive Electrical Capacitance Volume Tomography

Electrical capacitance tomography is a widely used sensor modality for flow imaging in many industrial settings. Adaptive Electrical Capacitance Volume Tomography (AECVT) extends the capabilities of traditional ECT by enabling direct volumetric imaging and an improved resolution. Construction of the sensitivity matrix is a necessary step to obtain flow images. This step requires computation of the electric field inside the sensing domain, which is done via a typical field solver such as the finite element method. In this work, we present an efficient and flexible method to construct the sensitivity matrix for Adaptive Electrical Capacitance Volume Tomography (AECVT) based on individual electrode segment excitations and their judicious combination to form desired matrix elements. We illustrate how the proposed method yields the same sensitivity matrix as the traditional method but at a much lower computational cost. Once all segment contributions are obtained, we also indicate how the proposed method, unlike the traditional approach, can generate the sensitivity matrix on demand for an arbitrary combination of synthetic electrodes and obviating the need for any additional field computations. Finally, we present image reconstruction results for two different experimental scenarios where the mutual capacitance data and the corresponding sensitivity vectors are obtained through the proposed measurement combination scheme.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Toward Water Volume Fraction Calculation in Multiphase Flows Using Electrical Capacitance Tomography Sensors

Real-time monitoring of water volume fraction in multiphase flows is an important problem for a number of industrial applications. The water phase in the multiphase flows may correspond to either the dispersed phase or the continuous phase. In the past, several lowcost and nonintrusive techniques based on the electrical capacitance tomography (ECT) has been developed to image and monitor in real-time multiphase flows containing water. Furthermore, such monitoring becomes increasingly challenging for high salinity levels, and no reliable ECTbased method is presently available which could work for obtaining water volume fraction in multiphase flows for all water salinity levels. In this paper, we propose a new approach based on the Hanai’s formula for complex dielectric constant and taking advantage of the Maxwell- Wagner-Sillars effect to obtain, to a good approximation, water volume fractions in multiphase flows containing water as either dispersed or continuous phase.

02 PETROLEUM↗

Relevance Vector Machine Image Reconstruction Algorithm for Electrical Capacitance Tomography With Explicit Uncertainty Estimates

We present a Relevance Vector Machine (RVM) based algorithm for electrical capacitance tomography (ECT) applications that can concurrently provide image reconstruction results and uncertainty estimates about the reconstruction. To illustrate the RVM operation in ECT, we simulate typical ECT scenarios, making explicit the connection between the reconstructed pixel values and the corresponding uncertainty estimates in each case. We compare the RVM reconstruction performance with that of the Iterative Landweber Method (ILM) and the least absolute shrinkage and selection operator (LASSO) in all the considered scenarios. The results show that, in addition to the key advantage of providing uncertainty measures, RVM can achieve similar reconstruction results with either lower or similar computational complexity.

42 ENGINEERING↗

Preliminary Results From Propellant Mass Gauging in Microgravity with Electrical Capacitance Tomography

This presentation is a shortened and simplified version of the original from Jed Storey intended for usage with an a.i. Solutions' "Lunch-and-learn" audience. It reviews the setup, execution, and some preliminary results from the Electrical Capacitive Tomography experiment conducted by NASA KSC Launch Services Program flown aboard a Zero-G aircraft earlier this year. The original is STRIVES submission 20220010165. Some extra images and videos have been added and some detailed content removed since the purpose of this presentation is less technical than that of it's parent.

mass gauging↗

Microgravity Electrical Capacitance Tomography Data Set

Propellants mass gauging technologies designed to work in an accelerated environment, where the propellant remains settled at one end of the propellant tank, do not work well in a microgravity environment because the propellant is not necessarily settled. While some microgravity mass gauging technologies exist at various TRLs, most of them have major disadvantages. Improvements in microgravity propellant mass gauging will result in improvements to many areas of propellant management, which influences performance and mission assurance. Electrical Capacitance Tomography (ECT) is a sensing technology that has been used in the oil/gas industry for decades to measure multi-phase flow rate in pipes. ECT, when installed in a tank, is able to reconstruct the liquid distribution inside of the tank, which can then be integrated to obtain mass. ECT mass gauging recently achieved high accuracy in laboratory testing on the ground, and while ECT mass gauging will theoretically work during all phases of flight, it had not yet been tested in microgravity. The NASA KSC Launch Services Program, with support from the Flight Opportunities Program, successfully flew an ECT tank liquid mass gauging system experiment on a Zero-G parabolic flight aircraft. The experiment hardware was rented from a company; NASA LSP did no technology development work for this project. This STRIVES entry is for the entire raw data set, which consists of approximately 25GB of csv files of capacitance and motion data from the ground and flight tests of the experiment. The data set will be available on the NASA LSP Electronic Slosh Data Catalog (ESDC), and the public may request the data set from the authors (POC: Jed Storey, jedediah.m.nasa.gov).

mass gauging↗

Preliminary Results from Propellant Mass Gauging with Electrical Capacitance Tomography

Propellants mass gauging technologies designed to work in an accelerated environment, where the propellant remains settled at one end of the propellant tank, do not work well in a microgravity environment because the propellant is not necessarily settled. While some microgravity mass gauging technologies exist at various TRLs, most of them have major disadvantages. Improvements in microgravity propellant mass gauging will result in improvements to many areas of propellant management, which influences performance and mission assurance. Electrical Capacitance Tomography (ECT) is a sensing technology that is able to reconstruct the liquid distribution inside of a tank, which can then be integrated to obtain mass. ECT mass gauging recently achieved high accuracy in laboratory testing, <0.1% liquid volume measurement error, even during sloshing. While ECT mass gauging will theoretically work during all phases of flight, it had not yet been tested in microgravity. The NASA KSC Launch Services Program, with support from the Flight Opportunities Program, successfully flew an ECT liquid mass gauging system experiment on a Zero-G parabolic flight aircraft. Basics of ECT measurement theory, details of the experiment setup and flights, and preliminary results will be discussed. The preliminary results suggest that, even in the current prototype generation, ECT sensor systems will be useful as a propellant mass gauging technology in both an accelerated and microgravity environment.

mass gauging↗

Propellant Mass Gauging in Microgravity with Electrical Capacitance Tomography

Advancements in microgravity propellant mass gauging will result in improvements to many areas of propellant management, which influences space vehicle performance and mission assurance. Propellant mass gauging technologies designed to work in an accelerated environment, where the propellant remains settled at one end of the propellant tank, do not always work well in a microgravity environment because the propellant is not necessarily settled. While some microgravity mass gauging technologies exist at various stages of development, most of them have major disadvantages. Electrical Capacitance Tomography (ECT) is a sensing technology that is able to reconstruct the liquid distribution inside of a tank, which can then be integrated to obtain mass. While ECT mass gauging will theoretically work during all phases of flight, it had not yet been tested in microgravity. The NASA Kennedy Space Center Launch Services Program, with support from the Flight Opportunities Program, successfully tested an ECT liquid mass gauging system experiment on a parabolic flight aircraft in May 2022. Basics of ECT measurement theory, details of the experiment setup, data processing, ground test results, and the flight test result will be discussed. The results suggest that ECT sensor systems will be useful as a propellant mass gauging technology in both accelerated and microgravity environments.

electrical capacitance tomography↗

Velocity Profiling of a Gas–Solid Fluidized Bed Using Electrical Capacitance Volume Tomography

In this study, a method of producing velocity profile maps from electrical capacitance volume tomography (ECVT) measurements by reconstructing displacement from measured changes in capacitance is developed and applied to fluidized bed systems. The mapping of the reconstruction leverages the gradient of the sensitivity distribution of the ECVT sensor to circumvent the need for image cross correlation techniques. Experimental data of both bubbling and slugging fluidized beds are collected in a cold flow model. Adaptation of the technique is discussed in detail, and velocity profiles are obtained for a range of gas flow rates. The produced velocity maps are compared against the established methods of cross correlation and against empirical correlations from the literature and are found to agree well in tracking slug and bubble velocity. The exception is when the tracked object is large relative to the ECVT sensor dimensions, a scenario that can be avoided through proper sensor design. The quantities of average velocity, momentum, and solid and gas volume fraction are derived from the image and velocity profiles. The results demonstrate and extend the power of ECVT as a measurement tool for the study and monitoring of gas–solid fluidized beds by providing a computationally cheaper alternative to 3-D cross correlation for deriving velocity profiles.

47 OTHER INSTRUMENTATION↗

Electronic Scanning Strategies in Adaptive Electrical Capacitance Volume Tomography: Tradeoffs and Prospects

Electrical Capacitance Volume Tomography (ECVT) has been applied for imaging of multiphase flows found in industrial applications. The ill-posed nature of the image reconstruction problem in ECVT and the consequent low resolution can be alleviated by employing electronic scanning enabled by electrode segmentation and reconfiguration during data acquisition. Here we study electronic scanning strategies that mimic physical rotation and shifting of the sensor along its symmetry axis. First, we study the feasibility of electronic scanning by analyzing the capacitance transducer circuit in SPICE. Then, we simulate electronic scanning using the finite element method for different electrode shapes, for which we compare the image reconstruction results and acquisition time. We find a noticeable improvement in image resolution for the scanning cases over conventional ECVT. Lastly, among the scanning cases, we emphasize a particular electrode shape that provides the best image resolution along with the minimal amount of acquisition time.

47 OTHER INSTRUMENTATION↗

Review of Selected Advances in Electrical Capacitance Volume Tomography for Multiphase Flow Monitoring

Electrical Capacitance Volume Tomography (ECVT) has emerged as an attractive technology for addressing instrumentation requirements in various energy-related multiphase flow systems. ECVT can monitor multiple flow conditions and reconstruct real-time 3D images from capacitance measurements using a large set of electrode plates placed around the processes column enclosing the sensed flow system. ECVT is non-intrusive and allows the measurement of changes in mutual capacitance between all possible plate pair combinations. The objective of this paper is to provide a comprehensive review of recent advances in ECVT, enabling robust monitoring of multiphase flows, especially water-containing multiphase flows.

02 PETROLEUM↗

Electrical Capacitance Volume Tomography with High-Contrast Dielectrics

The Electrical Capacitance Volume Tomography (ECVT) system has been designed to complement the tools created to sense the presence of water in nonconductive spacecraft materials, by helping to not only find the approximate location of moisture but also its quantity and depth. The ECVT system has been created for use with a new image reconstruction algorithm capable of imaging high-contrast dielectric distributions. Rather than relying solely on mutual capacitance readings as is done in traditional electrical capacitance tomography applications, this method reconstructs high-resolution images using only the self-capacitance measurements. The image reconstruction method assumes that the material under inspection consists of a binary dielectric distribution, with either a high relative dielectric value representing the water or a low dielectric value for the background material. By constraining the unknown dielectric material to one of two values, the inverse math problem that must be solved to generate the image is no longer ill-determined. The image resolution becomes limited only by the accuracy and resolution of the measurement circuitry. Images were reconstructed using this method with both synthetic and real data acquired using an aluminum structure inserted at different positions within the sensing region. The cuboid geometry of the system has two parallel planes of 16 conductors arranged in a 4 4 pattern. The electrode geometry consists of parallel planes of copper conductors, connected through custom-built switch electronics, to a commercially available capacitance to digital converter. The figure shows two 4 4 arrays of electrodes milled from square sections of copper-clad circuit-board material and mounted on two pieces of glass-filled plastic backing, which were cut to approximately square shapes, 10 cm on a side. Each electrode is placed on 2.0-cm centers. The parallel arrays were mounted with the electrode arrays approximately 3 cm apart. The open ends were surrounded by a metal guard to reduce the sensitivity of the electrodes to outside interference and to help maintain the spacing between the arrays. Other uses for this innovation potentially include quantifying the amount of commodity remaining in the fuel and oxidizer tanks while on-orbit without having to fire spacecraft engines. Another orbit application is moisture sensing in plant-growth experiments because microgravity causes moisture in soil to distribute itself in unusual ways. At the moment, the hardware and image reconstruction technique may only be of interest to people involved in nondestructive evaluation. The reconstructed image takes almost a full week to reproduce with existing computer power. However, because computer power and speeds follows Moore s Law, execution times are likely to become acceptable within the next five to eight years. The code was written in Mathematica for dedicated use with the ECVT system. In its present form, it is not suitable to be used directly as a consumer product. However, the code could be likely improved by rewriting it in a compiled language such as C or Fortran.

Nurge, Mark↗

The Development of a Generalized Riser Flow Regime Map Based Upon Higher Moment and Chaotic Statistics Using Electrical Capacitance Volume Tomography (ECVT)

Dynamic analyses have been applied to the temporal signals from an Electro Capacitance Volume Tomography instrument located near mid-height on the riser of an industrial-scale cold-flow circulating fluidized bed to characterize gas-solids flow behavior in the riser. Twelve capacitance electrodes surround the cylindrical riser over a height of 1.3 m. The instrument used a neural network deconvolution algorithm to determine the spatially resolved solids fraction recorded at 52 Hz. Experiments were carried out over a range of gas and solids flows in the transport regime using a Geldart Group B bed material, high density polyethylene with mean particle size of 880 μm. The radial solids distribution was found to vary from one-time step to the next between profiles typical of laminar and turbulent flow. The duration of time spent in each of these flow profiles depended upon the operating regime – dilute, core-annular, or fast fluidized bed. The chaotic structure of the temporal data was characterized using the three conventional approaches: the first 4 moments from the distribution of signal in time, system memory parameters from the autocorrelation function and the Hurst exponent, and analysis of the correlationentropy and correlation dimension of the attractor. These signal analysis techniques were used to clearly distinguish differences between different transport operating regimes. Specifically, it was experimentally observed that a riser transitions from core annular flow profile to dilute and dense regimes via increasing the frequency of short term transients to either dilute or dense flow profiles, respectively. A regime map was generated based upon these dynamics using solids flux and gas velocity axes. Fast fluidized, core annular, and dilute each exhibited different degree of dynamic characteristics typical of fluid dominated or particle compromising behavior. It should be noted that the magnitude for the different statistics was in the same range regardless of the regime, it was the radial profile for the statistic that changed and subsequently identified that there was a change in the regime. Finally, a reduced regime map was developed consisting of plotting the gas velocity normalized by the upper transport velocity versus the solids flux normalized by the saturation carrying capacity. The use of this reduced plot allowed the data from widely different conditions to be plotted and compared on the same<p>graph. Note that in many instances, some of the statistics identified the operating point as being in one regime while others indicated that it was in another indicating a transition region between dilute or core annular regimes and between the core annular and fast fluidization regimes. This now provides a tool that can be used to optimize process performance, identify changes in operating states, or replicate process dynamics during process scaling or changing operating parameters. </p>

Breault, Ronald↗

Electrical Capacitance Volume Tomography for the Packed Bed Reactor ISS Flight Experiment

Fixed packed bed reactors are compact, require minimum power and maintenance to operate, and are highly reliable. These features make this technology a highly desirable unit operation for long duration life support systems in space. NASA is developing an ISS experiment to address this technology with particular focus on water reclamation and air revitalization. Earlier research and development efforts funded by NASA have resulted in two hydrodynamic models which require validation with appropriate instrumentation in an extended microgravity environment. To validate these models, the instantaneous distribution of the gas and liquid phases must be measured.Electrical Capacitance Volume Tomography (ECVT) is a non-invasive imaging technology recently developed for multi-phase flow applications. It is based on distributing flexible capacitance plates on the peripheral of a flow column and collecting real-time measurements of inter-electrode capacitances. Capacitance measurements here are directly related to dielectric constant distribution, a physical property that is also related to material distribution in the imaging domain. Reconstruction algorithms are employed to map volume images of dielectric distribution in the imaging domain, which is in turn related to phase distribution. ECVT is suitable for imaging interacting materials of different dielectric constants, typical in multi-phase flow systems. ECVT is being used extensively for measuring flow variables in various gas-liquid and gas-solid flow systems. Recent application of ECVT include flows in risers and exit regions of circulating fluidized beds, gas-liquid and gas-solid bubble columns, trickle beds, and slurry bubble columns. ECVT is also used to validate flow models and CFD simulations. The technology is uniquely qualified for imaging phase concentrations in packed bed reactors for the ISS flight experiments as it exhibits favorable features of compact size, low profile sensors, high imaging speed, and flexibility to fit around columns of various shapes and sizes. ECVT is also safer than other commonly used imaging modalities as it operates in the range of low frequencies (1 MHz) and does not radiate radioactive energy. In this effort, ECVT is being used to image flow parameters in a packed bed reactor for an ISS flight experiment.

Tomography↗