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636 records · Page 36

Dynamics and control of coherent structures in the turbulent wall layer: An overview

We expand the velocity field in the vicinity of the wall in empirical eigenfunctions obtained from experiment. Truncating our system and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. We find a rich dynamical behavior, including in particular a heteroclinic attracting orbit giving rise to intermittency. The intermittent jump from one attracting point to the other resembles in many respects the bursts observed in experiments. Specifically, the time between jumps and the duration of the jumps, is approximately that observed in a burst; the jump begins with the formation of a narrowed and intensified updraft, like the ejection phase of a burst, and is followed by a gentle, diffuse downdraft like the sweep phase of a burst. The magnitude of the Reynolds stress spike produced during a burst is limited by our truncation. The behavior is quite robust, much of it being due to the symmetries present (Aubry's group has examined dimensions up to 128 with persistence of the global behavior). We have examined eigenvalues and coefficients obtained from experiment, and from exact simulation, which differ in magnitude. Similar behavior is obtained in both cases; in the latter case, the heteroclinic orbits connect limit cycles instead of fixed points, corresponding to cross-stream waving of the streamwise rolls. The bifurcation diagram remains structurally similar, but somewhat distorted. The role of the pressure term is made clear - it triggers the intermittent jumps, which otherwise would occur at longer and longer intervals, as the system trajectory is attracted closer and closer to the heteroclinic cycle. The pressure term results in the jumps occurring at essentially random times, and the magnitude of the signal determines the average timing. Stretching of the wall region shows that the model is consistent with observations of polymer drag reduction. Change of the third order coefficients, corresponding to acceleration or deceleration of the mean flow, changes the heteroclinic cycles from attracting to repelling, increasing or decreasing the stability, in agreement with observations. The existence of fixed points is an artifact introduced by the projection; however, a decoupled model still displays the rich dynamics. Numerous assumptions made in Aubry et al. (1988) can now be proved exactly. Feeding back eigenfuncitons with the proper phase can delay the bursting, (the heteroclinic jump to the other fixed point), decreasing the drag. It is also possible to speed up the bursting, increasing mixing to control separation. Our approach is optimal for short time tracking in control.

Berkooz, Gal↗

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↗

Parameters Impacting Columnated Granular Soil Pneumatic Seal Performance

The ability of a column of loose granular soil to form a pneumatic seal was investigated by varying the diameter of the soil column, the effective column height, and the level of compaction in the soil. The soil column diameter was tested at three levels using pipes with inner diameters measuring 5.08, 10.16, and 15.24 centimeters (2, 4, and 6 inches). Soil was filled in each pipe to form 15, 30, and 45 centimeter (6, 12, and 18 inch) tall soil columns. Each diameter/height configuration was also tested at three levels of soil compaction, compared by calculating the bulk density of the soil with mass and volume measurements. GRC-1a simulant was used, with approximate low/medium/high bulk densities of 1.6, 1.75, and 1.9 g/cc achieved with a combination of vibration and tamping. The order of tests for a given column diameter was randomized and repeated three times. With the top of the soil open to atmosphere at room temperature, compressed air was injected through a small diffuser at the column base with several small downward-facing holes. The number and size of these holes was scaled such that a constant total inlet orifice area to column cross sectional area ratio was maintained for each column diameter. Inlet air pressure was slowly increased via a precision regulator to preserve quasi-static equilibrium in the soil column to minimize the impact of dynamics. Air pressure was increased all the way through the static and bubbling regimes until slugging or turbulent behavior was observed in the soil to ensure that the entire static regime had been captured during data collection. A three-factor, three-level analysis of variance (ANOVA) statistical analysis was performed on the resulting data to determine the extent to which each physical parameter impacted the soil column seal performance. It was concluded that there is statistically significant evidence that column height, and the interaction between column height and diameter impact soil seal performance. In all other cases there was insufficient data to identify a statistically significant causal relationship. Additionally, plots were generated comparing experimental data to the predictive formula developed by Ogino et al. for fluidized beds in 1993. Because this model was developed for industrial spouted fluidized beds, the accuracy of its output prior to fluidization in the static seal ‘edge case’ is unknown, especially considering in this application the working gas was diffused across the column base rather than being injected through a spout. Further, the fidelity of the model had not yet been tested with lunar soil simulants. Plotting the Ogino et al. model alongside test data allows for a more intuitive sense of the impact of test parameters on soil seal performance, as well as providing a quick means to further tune this predictive model for more accurate use with static seals across granular lunar soil simulants. The model provided by Ogino et al. was further tuned using test data to determine the degree to which a spouted bed model could be applied to a slightly modified set of testing conditions: lunar soil simulants and a more diffuse, homogeneous application of pneumatic pressure. A Matlab script was created to test different values for the leading coefficient and exponents in Ogino’s formula. The script swept preset ranges, then iterated with higher resolutions across narrower ranges to converge on the optimal value for each parameter. The resulting adjusted model was compared to the original, as well as test data with noticeable improvements across the entire test domain.

Jack Stewart↗

Machine learning changes the rules for flux limiters

Learning to integrate non-linear equations from highly resolved direct numerical simulations has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock capturing methods. Focusing on flux limiters provides a specific plug-and-play component for existing numerical methods. Since their introduction, an array of flux limiters has been designed. Using the coarse-grained Burgers' equation, we show that flux-limiters may be rank-ordered in terms of their log-error relative to high-resolution data. We then develop a theory to find an optimal flux-limiter and present flux-limiters that outperform others tested for integrating Burgers' equation on lattices with [Formula: see text], and 2x, 3x, 4x, and 8x coarse-grainings. We train a continuous piecewise linear limiter by minimizing the mean-squared misfit to six-grid point segments of high-resolution data, averaged over all segments. While flux limiters are generally designed to have an output of φ(r) = 1 at a flux ratio of r = 1, our limiters are not bound by this rule and yet produce a smaller error than standard limiters. Here we find that our machine learned limiters have distinctive features that may provide new rules-of-thumb for the development of improved limiters. Additionally, we use our theory to learn flux-limiters that outperform standard limiters across a range of values (as opposed to at a specific fixed value) of coarse-graining, number of discretized bins, and diffusion parameter. This demonstrates the ability to produce flux limiters that should be more broadly useful than standard limiters for general applications.

97 MATHEMATICS AND COMPUTING↗

Techno-Economic Analysis of Recycling Strategies for Catalyst and Acid During Catalytic Graphitization

With the aim of meeting the urgent demand for active anode materials (AAM) in energy storage systems, bio-based graphite (biographite) emerges as an affordable solution to de-risk the turbulent supply chain of critical minerals. Anode grade biographite requires high crystallinity and purity, which can be achieved by catalytic graphitization with iron, followed by acid washing. Therefore, a well-conceived process integration that recycles catalyst can be the starting point to commercialization. This study evaluates closed-loop catalyst recovery, and byproducts valorization scenarios through a technoeconomic framework to help understand the scale-up potential of biographite. For the acid washing, three reactors in series meet the required biographite purity at 99.95%. Iron and acid recovery can reduce material consumption and waste generation by ~95%, albeit at the expense of ~80% increase in capital costs. Recovery scenarios present similar capital and operational expenses, yielding minimum selling prices (MSP) near $6 kg-1 of biographite. Monte Carlo methodology reveals that feedstock price accounts for ~60% of MSP variance, followed by plant capacity ~20%. The likelihood of reaching a competitive profit margin of 30% in the U.S. AAM market sits at 85% average for recovery scenarios, and 103% when iron oxide is sold as byproduct. Additionally, an IRR >= 15% can be achieved for half of Monte Carlo simulations, representing promising early-stage results. Biographite production offers a strategic pathway to stabilize the anode market beyond China by integrating established technologies for a scalable, economically viable, and sustainable process. The role of catalyst recovery and byproducts utilization is critical for advancing the biomaterials industry.

97 MATHEMATICS AND COMPUTING↗

Flight Mechanics Modeling and Simulation of the Earth Entry System

Introduction: The Mars Sample Return (MSR) Campaign being planned by NASA and ESA has the ambitious goal to return Mars samples back to Earth. This international collaboration had developed a concept of operations that included a ESA-designed Earth Return Orbiter (ERO) and NASA-designed Capture, Containment, and Return System (CCRS). The Earth Entry System (EES), consisting of a protective aeroshell that houses the samples as well as sample containment vessels, would conduct entry, descent, and landing (EDL) on a direct Earth trajectory. The EES would enter on a spin-stabilized ballistic trajectory with the goal to passively achieve aerodynamic stability throughout all regions of flight. The EDL sequence would end with the EES impacting the soft playa soil of the Utah Test and Training Range (UTTR). As of the submission of this abstract, the MSR campaign is undergoing a re-architecture leading to a pause in EES development. However, the novel approaches developed in flight mechanics modeling and simulation can significantly benefit the greater IPPW community in the development of Earth return vehicles. This paper will present the latest state of EES flight mechanics modeling and simulation. The paper will highlight the simulation architecture developed and key lessons learned from understanding of EDL trajectory sensitivities. Modeling and Simulation: Figure 1 provides a high-level concept of operations for the approach, entry, descent, and landing (AEDL) phase of the CCRS-portion of MSR. The objective of EES flight mechanics is to model and simulate the EES trajectory from ERO separation to ground impact at UTTR. A variety of flight mechanics simulation models were utilized to model both exo-atmopsheric and atmospheric portions of flight. 42, a 6-DOF simulation developed at Goddard Space Flight Center, is utilized for propagating the attitude of EES during exo-atmospheric flight. 42 allows for a variety of spin eject mechanism scenarios to be simulated for analysis. 10 minutes prior to entry, the 42 states are handed off to the EDL sims. The prime EDL sim utilized by EES is the Program to Optimize Simulated Trajectories II (POST2), a 6-DOF sim developed at Langley Research Center, and the independent verification and validation EDL sim utilized is DSENDS, a 6-DOF sim developed at Jet Propulsion Laboratory. Figure 2 provides a visualization of the flight mechanics simulation model flow through various points in the AEDL phase. Due to the existence of a variety of sim models, the EES flight mechanics team developed processes for data hand-off. These processes included the development of a centralized coordinate frame document, utilization of a single, centralized simulation input document for all sims to reference, and hand-off files containing both the technical data to be ingested by other flight mechanics sims as well as annotations of modeling assumptions utilized to generate the data. Figure~\ref{fig:post2simarchitecture} provides an overview of the POST2 sim architecture wherein POST2 ingests numerous subsystem models and input files. The dispersed state file generated by MONTE provides the position/velocity state of the trajectory while the 42 Handoff file provides the attitude. The aerodynamics database, delivered by the EES aeroscience team, is utilized to simulate the aerodynamic forces and moments experienced during EDL. A custom atmosphere model, developed by EES atmosphere team, is utilized to simulate the anticipated atmosphere environment around the region of Earth through which the EES trajectory flys. These inputs and subsystem models can be varied depending on the AEDL flight mechanics scenario being simulated. Monte Carlo simulations are utilized to generate statistical AEDL performance metrics in the form of scorecards and violin plots. Furthermore, outputs from the POST2 simulation are utilized for follow-on analyses including aerothermal and landing performance. \section{Flight Mechanics Lessons Learned} Though the EES flight mechanics team uncovered a variety of lessons learned through the analysis conducted to support CCRS through preliminary design review, this paper will highlight the most important lessons. A key AEDL performance goal is to ensure the landing footprint of EES remains on the UTTR south range. A common modeling strategy used in EDL analysis is One-Variable-At-a-Time (OVAT). OVAT analysis provides insight into the key drivers that affect AEDL performance metrics. Figure 3 shows the landing ellipses for single dispersion sources as compared to the baseline aggregate of all dispersions. The figure shows that atmosphere winds alone dominate the size of the footprint ellipse (note: EES does not use a parachute unlike previous Earth-return missions and is in wind-driven free fall for ~5min). The significance of the wind led the EES flight mechanics team to pursue the development of a Custom Atmosphere Model [4], in lieu of EarthGRAM [1], built on actual radiosonde wind measurements around the UTTR-region. This decision was driven by the realism in the generated footprint ellipses and lessons-learned from Stardust [5]. These findings will be invaluable for future Earth-return missions in providing an early understanding of the key drivers affecting footprint size and modeling considerations for which to account. Another lesson learned is tied to the AEDL performance goal of achieving passive stability throughout all regions of flight. It is well understood that blunt-body aeroshells are less stable as they transition from supersonic to subsonic. Eliminating a backshell does help improvestability; however, other phenomena such as roll-induced instability during terminal descent can still arise. The EES flight mechanics team developed stability metrics as tools to better understand the causes of and better predict the onset of dynamic instability. These tools were built upon analytical models developed by Jaffe [3] and Murphy [2]. The tools were shown to both be very accurate in correlation with actual unstable cases and useful in developing stability margin policies based on the vehicle design and simulation considerations (e.g. sphere-cone angle change, mass change, wind turbulence). These tools allowed for the current EES design to demonstrate the ability to achieve passive stability and can be an invaluable tool for consideration in the design of parachute-less Earth-return vehicles.

Rohan Deshmukh↗