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DOE OSTI2021

Comparative study with two reduced test facilities for air-cooled RCCS scaling law

Korea Atomic Energy Research Institute (KAERI) and Argonne National Laboratory (ANL) conducted steady-state tests at constant heat flux conditions to investigate the scale effect on heat removal behavior of the air-cooled Reactor Cavity Cooling System (RCCS). Two differently scaled-down test facilities were used in this study, KAERI’s ¼ scale with 4.0-m cavity height, and ANL’s ½ scale with 6.8-m cavity height. Two scaling laws were proposed to simulate the radiation across the cavity and the buoyancy-driven duct flow in the riser, respectively. The test matrix for KAERI and ANL test facilities focused on the scaling effect of the heated riser length with constant heat flux at the PMR200 RCCS design. The test results showed that mixed convection in the riser duct is an important factor for accurately extrapolating the thermo-fluid behavior in the prototype from the test results in the scale-down facilities. The system analysis code, GAMMA+, with improved heat transfer models predicted fairly well the air-cooled RCCS test data from two facilities. GAMMA+ analysis results showed that the predicted radiation fractions on the heated plate in the scale-down test conditions were larger than those on the reactor vessel in the prototype. The scaling law for air-cooled RCCS was improved by considering the mixed convection in the riser duct and the same radiation fraction on the heated plate. The mixed convection effect was calculated by the height ratio. The same radiation fraction provided a conservative extrapolation from the scale-down test results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

June 2022 Permeability Measurements in P-Tunnel, Nevada National Security Site

This document describes gas permeability measurements made in June 2022 in P-Tunnel at the Nevada National Security Site (NNSS). Four boreholes (AC-1, GI-5, GI-6, and HF-1) were tested with a dual packer system. The pressure versus flow rate data that were collected are analyzed using a numerical simulation method that captures compressible gas flow in partially saturated porous media using a close approximation to the geometry of the test setup. The first part of this document begins with data collection and a description of the packer assembly followed by details on data acquisition, measurement instrumentation, and equipment followed by a description of pre-test system verification. Next, the implementation of testing in the field is described, including how specific locations were chosen for testing. The second part of this document describes the numerical simulations used to back-out permeability from the pressure versus flow rate data. First, the numerical model is described, including assumptions. Next the details of the mesh that represents the experiment are described. A method for generating type curves in pressure versus flow rate space is presented and finally the data are mapped to permeability. We conclude with a discussion of the results.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Online and noninvasive monitoring of battery health at negative-half cell in all-vanadium redox flow batteries using ultrasound

Hydrogen evolution is one of the major side reactions that is detrimental to the health of all-vanadium redox flow batteries, especially for long-term cycling. Effective, low-cost, and accurate online prediction and detection methods for hydrogen generation are not yet available. In this work, we designed an online, noninvasive ultrasonic probing approach for monitoring the state of charge (SoC), predicting the hydrogen generation, and detecting hydrogen gas bubbles in anolyte solutions. The technique employs a pulse-echo method to measure the sound speed and the acoustic attenuation coefficient of the anolyte solution. Through static offline experiments and online in operando experiments, we have demonstrated that when hydrogen gas is generated in anolyte solutions, large variations are observed in both sound speed and acoustic attenuation coefficient measurements. We found that the variations of acoustic attenuation coefficient are highly correlated (correlation coefficients >0.9) with the gas flow rate. In conclusion, the designed acoustic method can monitor the SoC of anolyte, predict the hydrogen generation, and detect the presence of gas bubbles in an anolyte solution and, thus, provide information about the state of health for operation and management of flow battery systems.

25 ENERGY STORAGE↗

DOE OSTI2021

Performance evaluation of a Terry GS-2 steam impulse turbine with air-water mixtures

Terry steam turbines are widely used in various industries because of their robust design. Within the nuclear power generation industry, they are used in the Reactor Core Isolation Cooling System to remove decay heat during reactor isolation events. During the Fukushima Daiichi nuclear power station disaster in Japan in 2011, the Reactor Core Isolation Cooling System and associated Terry turbine operated for over 70 hours in Unit 2; this runtime is well beyond the expected operating duration. Theories suggest the turbine was subjected to a two-phase inlet flow, which could degrade the turbine performance. In this work, an experimental test rig was constructed to test a full-scale Terry model GS-2 steam turbine under two-phase air/water flows. Steady-state efficiency and torque performance maps of the turbine were developed over a range of turbine inlet pressures (1.38–4.83 bar or 20–70 psia), air mass fractions (0.05–1.0) and rotational speeds up to 4000 RPM. Furthermore, turbine performance followed expected trends with torque varying linearly and efficiency varying quadratically with rotational speed. In addition, high-speed images of the two-phase flow entering the turbine were also analyzed to understand how changes in inlet pressure and air mass fraction affect the flow regime and homogenization. The present tests with air–water two-phase mixtures are an important step towards providing an understanding of the full-scale Terry turbine’s behavior and performance curves under two-phase conditions. The results of this work will be combined with air/water and steam/water data gathered using a small-scale Terry ZS-1 steam turbine in order to understand the scaling relationship between large and small size Terry turbines and fluid pairs. The combined data set will enable further development of analytical models over a wide range of conditions and may be used to provide technical justification for expanded use of the Terry turbines in nuclear power plant safety systems and other systems.

42 ENGINEERING↗

DOE OSTI2020

How equation of state selection impacts accuracy near the critical point: Forced convection supercritical CO 2 flow over a cylinder

Increasing application of supercritical fluids leads to increased use of numerical simulations to guide designs. However, the impact of Equations of State (EoS) selection on computational cost and accuracy is not well understood. Laminar flow around a heated cylinder is used as a test case. A robust matrix of 99-simulations is used to analyze the flow of carbon dioxide just above the critical point at the isobaric condition of 8 MPa and temperatures between 305 and 390 K. Four EoS were studied: Ideal Gas Law, cubic EoS’s Peng-Robinson and Soave-Redlich-Kwong, and the Span-Wagner EoS. Results were identical for isothermal cases, but for heated or cooled cases, the high-fidelity Span-Wagner EoS simulations presented drastically different wake structures. Compared to the high-fidelity SW EoS, cEoS’s underestimated Nu values by up to 38% and cEoS’s underestimated CD values by 18–42%. In conclusion, the Span-Wagner EoS required only 17% more computation time then the cubic EoS simulations, making the Span-Wagner EoS recommended for engineering design.

42 ENGINEERING↗

DOE OSTI2021

Hanford Waste Treatment Plant LAB Facility Stack Effluent Monitoring: Sampling Probe Location Qualification Evaluation

The WTP LAB stack monitor locations were qualified using scale model stacks to mitigate the risk of identifying that sampling locations do not meet the qualification criteria on the full-scale stack. As required by the ANSI/HPS N13.1-1999 standard, the scale model and its sampling location were geometrically similar to the actual stack and the Reynolds numbers for both the actual and model stacks were >10,000. An additional criterion is that the DV of the full-scale stack must be between 1/6 DV and 6 DV of the scale model stack tests. Verification tests of the LAB stacks were performed at normal operating conditions. The maximum 6 DV value from the scale model testing determines the maximum conditions for which the full-scale stack may be operated and remain in compliance with the stack verification criterion. The remaining criteria for the stack verification to be considered valid involve the flow angle and velocity uniformity results. First, the flow angle at the full-scale stack must be = 20°. Second, the velocity uniformity at the full-scale stack must be = 20% COV. Finally, the velocity uniformity results for the actual and scale model stacks must agree within 5% COV. In general, these criteria were met through the full-scale stack tests at the LAB facility. Some specific items for each scale model and full-scale stack comparison should be noted in assessing the validity of the verification tests. The LB-C2 scale model stacks were performed with single fan operations at then-minimum flow conditions. These conditions resulted in DV values that were too low to meet the DV range criterion, and therefore are unable to be used in qualifying single fan operations on the full-scale stack. However, the single fan operations demonstrated COV values for velocity uniformity as well as flow angles that were comparable to the dual-fan operations at high flows. Overall, the test conditions and test results were within the range of acceptable values based on current design flow rates. Single fan operations are expected to only occur infrequently for maintenance needs and is therefore not a planned operating condition at this time. The LB-S1 scale model stacks were performed at three fan combinations, and in each combination, at least one test was performed at the then-minimum flow conditions as well as at then-maximum flow conditions. While the then-minimum flow conditions result in a DV range that is lower than the verification test DV value, and therefore does not meet the criterion, these tests are un-necessary for the verification test acceptance. The normal and maximum flow conditions from the scale model stack tests meet the DV range criterion, and the velocity uniformity test results compare favorably with the full-scale stack results. The LB-S2 scale model stacks were performed at nominally the same maximum flow condition; however, the 6 DV value for Fan A operation was slightly lower than the full-scale stack test DV. The COV values from the scale model stacks were comparable between the Fan A and Fan B results, and the overall test conditions are within the range of acceptable values. The stack verification is therefore considered acceptable for both Fan A and Fan B operations. The verification tests were performed at flows that were appreciably higher than the design conditions, and further elevated flow rates would be beyond the range of acceptable DV. Based on these stack verification test results, the three LAB filtered exhaust stacks meet the qualification criteria provided in the ANSI/HPS N13.1-1999 standard. Further changes to the system configuration or operating conditions that are outside the bounds described in this and the scale model test reports (Glissmeyer, Flaherty, and Piepel (2001), Glissmeyer and Geeting (2013)) may require additional tests and additional analyses to determine compliance with the standard.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Validation of strongly coupled geomechanics and gas hydrate reservoir simulation with multiscale laboratory tests

In this work, we validate a coupled flow-geomechanics simulator for gas hydrate deposits, named T+M AM , performing two meter-scale laboratory experiments of gas hydrates for production by depressurization, replicating the gas hydrate deposit in the Ulleung Basin, East Sea, South Korea. The first experiment with a sand-only specimen is a 1D 1 m-scale depressurization test based on the excess gas method, which represents the grain coating hydrate growth. On the other hand, the second is a 3D 1.5 m-scale test with the excess water method for a sand-mud alternating layer system, representing the pore filling hydrate growth. We measure production and displacement at the top with different depressurization levels. In particular, the 3D test exhibits high coupling strength of substantial deformation induced by incompressibility of water and high deformability of the specimen. For validation, we match pressure, flow rate, and displacement between the experimental data and numerical results. Thus, we identify that T+M AM is a reliable simulator, which can be applied to fields in both permafrost and deep oceanic hydrate deposits of strongly coupled flow and geomechanics systems. This validation also implies that other coupled simulators based on the same coupling formulation as T+M AM can be validated when individual flow and geomechanics simulators are stable and reliable.

02 PETROLEUM↗

DOE OSTI2021

Revisions of ORNL 188 W Process Based on Nonradiological Experiments

Tungsten-188 is in widespread use in the 188 W(t 1/2 = 69 d)/ 188 Re(t 1/2 =16.9 h) biomedical generator. Oak Ridge National Laboratory (ORNL) has been providing this product to the world since 1999. At ORNL, 188 W is produced via irradiation in ORNL’s High Flux Isotope Reactor (HFIR). Enriched 186 W targets in the form of sintered metallic pellets or rings achieve a compact loading in the irradiation vessel, providing a high yield per unit target. The enrichment of the target is >90% 186 W and this isotope undergoes double neutron capture to produce the desired 188W product. While 188 W is produced by neutron bombardment, 191 Os(t 1/2 = 15.4 d) is simultaneously produced as a byproduct requiring separation from 188 W by post irradiation treatment. In the current processing pathway, the irradiated W metal pellets or rings are first converted into an oxide form of WO 3 by heating the irradiated W metal target at 750°C in a quartz reaction vessel inside a vertical furnace under a constant flow of air. During heating, W metal reacts with oxygen in the air to produce WO 3 , which is soluble in 6 M NaOH for later purification process. This oxidation process also converts 188 Os (the decay daughter of 188 W) and 191 Os (the irradiation produced byproduct) into OsO 4 , a highly volatile and toxic gas. The gaseous effluents driven from the quartz reaction vessel are passed through a scrubbing array to remove OsO 4 before the air is discharged from the process. This heterogeneous oxidation method simultaneously achieves two goals: 1). converting metal target to a soluble oxide form and 2). separating volatile OsO 4 away from the solid WO 3 product, although harmful 191 OsO 4 is unfavorable but being taken care of by the down road scrubbing array. In the past twenty years the existing OsO 4 scrubbing array served well in preventing OsO 4 from being released into the environment, until July of 2020 when a minor amount of 191 Os was found to have been released into the environment which resulted in a standby of building 4501 from July 2020 to February 2021.Since October 20 of 2020 a team of researchers from groups of RSTD and NEFD were organized to work for the following tasks: (1) Fully understand the root causes of the July incident of 191 Os release and create a redesigned 191 Os scrubbing array to eliminate the possibility of 191 Os release in future 188 W processes; (2) In Phase-1 tests, select a correct air (O 2 ) flow rate in 188 W process, that provides sufficient oxygen for the oxidation of tungsten metal, while still allowing sufficient resonance time for 191 Os removal by the scrubbers; (3) In Phase-2 tests, confirm the efficiency of the redesigned scrubbing array to absorb excessive amount of non-rad OsO 4 (generated from Os metal powder) at the selected air flow; (4) In Phase-3 tests, simulate the hot cell 188 W process by heating pressed non-rad W-Os pellets in a quartz vessel of new design and the new array under operation parameters selected in Phase-1 and -2; (5) Complete a new operation procedure for 188 W process in hot cell and a TM report as a summary of the Os Mitigation Project. This TM report summarizes the investigation on root causes from technical aspects in July 191 Os release and the correspondent improvement towards the redesigned 191 Os scrubbing system. The report presents the efforts made on selection of optimal operational parameter with the new scrubbing array and the quartz vessel of new design, based on experiment data obtained in Phase-1, -2 and -3 tests. Further renovations for 188 W process and additional improvement of W target treatment will also be discussed.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2021

Novel Membrane-Based Corrosion Sensors For Operating In Natural Gas Pipelines

Membrane-based electrochemical sensors (MBES) provide an attractive option for real-time continuous humidity and corrosion rate measurements inside of natural gas pipelines. The MBES, can use electrochemical techniques such as linear polarization resistance and electrochemical impedance spectroscopy even when a conductive aqueous phase is intermittent or unavailable. We now present field-test performance data of our MBES operated inside a multiphase water and natural gas flow facility. The MBES measured internal corrosion and conductivity at the top, bottom, and side of the pipe spool. Tests were carried out with flow rates of 4.6, 9.1, and 18.3 m/s, temperatures of 21, 29, and 35 °C, and a pressure of 1000 psia. All sensors followed similar trends in open circuit potential, corrosion rate, and conductivity over time. Neither flow rate, temperature, nor build-up of metal-based solids on the sensor surfaces impacted the quality of the electrochemical measurements. The field-test results confirm that the membrane-based electrochemical sensors are suitable for monitoring internal corrosion of operational natural-gas pipelines.

Duffy, Timothy↗

DOE OSTI2023

Benchmark Specifications for TREAT Tests M5, M6, and M7

Detailed information describing three TREAT tests performed on metallic fuels has been collected and organized for use as a benchmark in evaluating the performance of metallic fuel models and codes. The tests, designated M5, M6, and M7, subjected EBR-II-irradiated fuel pins to a single type of overpower transient (at prototypical conditions with full coolant flow and an exponential power rise on an 8 second period) in flowing sodium loops. Six fuel pins were tested; five were ternary (U-19Pu-10Zr) alloy fuel clad in D9 with burnup ranging from 0.8 to 9.8 at. %, and one was binary alloy fuel (U-10Zr) clad in HT9 with 2.9 at. % burnup. The information gathered from the test records is expected to be useful for pre-transient characterization of the irradiated fuel pins as well as the transient analysis of the metallic fuel when subjected to severe accident conditions. This report presents benchmark specifications for the M5, M6, and M7 TREAT tests, identifies where primary sources of benchmark-related information can be found, and includes background information to help a user of the data understand their applicability and limitations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Intracore Natural Circulation Study in the High Temperature Test Facility

The development of the Modular High-Temperature Gas-Cooled Reactor is a significant milestone in advanced nuclear reactor technology. One of the concerns for the reactor’s safe operation is the effects of a loss-of-flow accident (LOFA) where the coolant circulators are tripped, and forced coolant flow through the core is lost. Depending on the steam generator placement, loop or intracore natural circulation develops to help transfer heat from the core to the reactor cavity, cooling system. This paper investigates the fundamental physical phenomena associated with intracore coolant natural circulation flow in a one-sixth Computational Fluid Dynamics (CFD) model of the Oregon State University High Temperature Test Facility (OSU HTTF) following a loss-of-flow accident transient. This study employs conjugate heat transfer and steady-state flow along with an SST k-ω turbulence model to characterize the phenomenon of core channel-to-channel natural convection. Previous studies have revealed the importance of complex flow distribution in the inlet and outlet plenums with the potential to generate hot coolant jets. For this reason, complete upper and lower plenum volumes are included in the analyzed computational domain. CFD results also include parametric studies performed for a mesh sensitivity analysis, generated using the STAR-CCM+ software. The resulting channel axial velocities and flow directions support the test facility scaling analysis and similarity group distortions calculation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

MC Formula Protocol for H35HF Fueling

A publicly available and verified high-flow fueling protocol for H35 medium-duty (MD) and heavy-duty (HD) hydrogen-powered buses and trucks does not exist. This could lead to transit agencies needing to select suppliers for purchase of new fleet vehicles, and to multiple providers responding with incompatible vehicle designs in the future. With the expansion of MD/HD vehicles using 35 MPa storage, there will be a need for publicly accessible H35HF stations, and these will require the use of a standardized prescriptive fueling protocol. The development of a fully tested and validated H35 high-flow (H35HF) MC Formula fueling protocol for MD and HD buses and trucks can provide guidelines to design H35 stations and vehicles, enable other manufacturers and vehicle original equipment manufacturers (OEMs) to enter this space, and ultimately accelerate to popularize the hydrogen market.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

DOE OSTI2023

Utilizing the maximum likelihood estimator for flow analysis

We explore the possibility of evaluating flow harmonics by employing the maximum likelihood estimator (MLE). For a given finite multiplicity, the MLE simultaneously furnishes estimations for all the parameters of the underlying distribution function while efficiently suppressing the variance of measures. Also, the method provides a means to assess a specific class of mixed harmonics, which is not straightforwardly feasible by the approaches primarily based on particle correlations. The results are analyzed using the Wald, likelihood ratio, and score tests of hypotheses. Besides, the resultant flow harmonics obtained using MLE are compared with those derived using particle correlations and event plane methods. Here, the dependencies of extracted flow harmonics on the multiplicity of individual events and the total number of events are analyzed. It is shown that the proposed approach works efficiently to deal with the deficiency in detector acceptability. Moreover, we elaborate on a fictitious scenario where the event plane is not a well-defined quantity in the distribution function. For the latter case, the MLE is shown to largely perform better than the two-particle correlation estimator. In this regard, one concludes that the MLE furnishes a meaningful alternative to the existing approaches for flow analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Coregistered positron emission particle tracking (PEPT) and X-ray computed tomography (CT) for engineering flow measurements

Increasingly, fully 3D experimental measurements of flow in complex engineering geometries are required to validate computational fluid dynamics models that support and inform reactor design and licensing. One barrier to such measurements is the complexity of typical reactor components and subsequent lack of optical access in these systems. To overcome this, the deployment of coregistered positron emission particle tracking (PEPT) and X-ray computed tomography (CT) is explored for flow measurement in reactor thermal hydraulic components and model (scaled) systems. Through this methodology, fully 3D flow information (via PEPT) and detailed internal geometry (via CT) are captured in opaque systems such as pipes, rod bundles, packed beds, etc. The reconstructed flow field and geometry can then be overlain to reveal detailed flow features around internal structures within a given test section. This is enabled through the use of a combined preclinical PET/CT scanner with overlapping PET and CT fields of view. Such measurements are useful for characterizing flow inside such intricate nuclear thermal hydraulic components as core geometries and heat exchangers, among others, and providing valuable 3D validation data for CFD models. In this work, basic tests of this 3D flow/geometry mapping are presented, and the implications of such measurements are discussed. Further, preliminary measurements are made with both point sources and flow in a simple pipe flow geometry to evaluate the capabilities of this technique. PEPT and CT features are coregistered with up to 0.1 mm precision, and pipe flow mean velocity and Reynolds stresses are reconstructed with similar accuracy to previous PEPT demonstrations. The utility of PEPT/CT is shown herein, and suggestions for future measurements are made.

3D flow measurement↗

DOE OSTI2023

Emissions and Flame Structure Assessment of Aeroengine Micromixing Injectors for Lean Direct Injection of Hydrogen and Hydrogen/Natural Gas Blends

Abstract The present study focuses on whether adapting low emissions liquid fuel injection concepts can be applied to gaseous mixtures. The goal is to develop an injector with specific geometric characteristics that will achieve the lowest emissions. This is conducted by evaluating emissions and flame diagnostics on a set of test hardware that has been developed for combustion of pure hydrogen and hydrogen/methane mixtures. The current test hardware adapts lean direct injection concepts from aeroengine injectors to a ground-based engine based on target flows associated with a Solar Turbines Industrial Engine gas turbine. A statistical test plan was developed to assess these geometric characteristics using a three level Box Behnken design. The test plan investigates the effect of injector flow splits, air swirl, fuel swirl, pressure drop, preheat temperature, fuel composition, and the adiabatic flame temperature on the flame structure and emissions performance. A total of 16 injectors were considered for a total of 688 test points for emission and imaging data. Emissions data were reported on a mass basis in ng/J and chemical reactor network analysis were conducted to further interpret emissions behavior. Images were also captured to analyze the flame structure features of interest including reaction volume, flame length, flame spread, and flame width. With these results, a predictive model for emissions was made to conclude the most optimal injector configuration is to have the highest level of air split (more volume of air through the injector plate versus the injector) and air swirl angle for both methane and hydrogen gas mixtures. The predictive emissions level for all of these cases were below 10 ng/J.

08 HYDROGEN↗

DOE OSTI2020

A method to test the coupling strength of the linear and nonlinear contributions to higher-order flow harmonics via event shape engineering

A Multi-Phase Transport (AMPT) model is used to study the efficacy of shape-engineered events to delineate the degree of coupling between the linear and nonlinear contributions to the higher-order flow harmonics v 4 and v 5 . Here, the study shows that the nonlinear contributions are strongly shape-dependent while the linear contributions are shape-independent, indicating little if any, coupling between the linear and nonlinear flow coefficients. The experimental verification of such patterns could be an invaluable tool for robust extraction of the linear and mode-coupled flow coefficients, especially for beam energies where the charged particle multiplicity and the event statistics precludes the use of current methods to establish the coupling strength.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Towards Commercialization of Hydrophone Flow Shields to Improve Passive Acoustic Data Quality (CRADA 678) (Final Report)

This project performed testing, market research, and manufacturing refinement to ready patent-pending hydrophone flow shields developed at PNNL for commercialization. The flow shields reduce the impact of flow noise on underwater sound recordings in areas of strong flow, like tidal channels or rivers. Flow noise is a challenge in many applications where it is necessary to measure underwater sound, including measuring the sound produced by marine energy converters and monitoring marine mammals. This project addressed several key questions about flow shield performance that are high-priority for potential customers and refined existing manufacturing processes to be scalable for market-level production. Specifically, this project conducted both laboratory and field evaluations of the flow shields to comprehensively evaluate their performance. Overall, the results indicate that the flow shields reduce flow noise by over 20 dB at frequencies below 50 Hz at flow speeds greater than 0.5 m/s and are proven to survive deployments more than 6 months long.

42 ENGINEERING↗

DOE OSTI2022

Neural-network learning of SPOD latent dynamics

Here, we aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower -dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts.

97 MATHEMATICS AND COMPUTING↗