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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

CO 2 and Renewable Electricity into Chemicals: Formic Acid Production from Coal Flue Gas

Formic acid (FA) is an industrial chemical. It is used as a preservative for silage, as a digestive aid for animals, as a fluid for fracking, as a pharmaceutical intermediate and in leather tanning. The global formic acid market is valued at 777.4 million USD in 2020 and is expected to reach 851.8 million USD by the end of 2026. A new major formic acid application is the use of formic acid as a key feedstock for the bioprocessing industry. It has the potential to grow tremendously if we can lower the cost of formic acid production compared with the current fossil-fuel one. Recently, Dioxide Materials has developed a technology that can directly convert CO 2 to pure formic acid with a three-compartment CO 2 electrolyzer. However, the electrolyzer performance needs further improvement for the technology to be commercially viable. The major objective of this project is to develop the electrolyzer technology to enable formic acid as a feedstock for the bioprocessing industry to be economically manufactured from flue gas from a coal fired pilot plant. In particular, the project is to understand how to run the electrolyzer for the conversion of CO 2 into formic acid using flue gas from a coal fired power plant as a source of CO 2 . The work will include characterizing how the performance of the electrolyzer changes with low CO 2 concentration and impurities, developing new cell designs that can still operate with feedstocks with low CO 2 concentrations, testing simulated flue gas in the electrolyzer system and developing filters to remove any impurities that arise.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2012

Presentation to JAEA Visitors, July 24, 2012 [Slides]

There are 7 Reasons for characterizing spent fuel nuclide concentrations: (1) Provide IAEA with the capability to independently verify the mass of plutonium at any site that has spent fuel; (2) Shipper/receiver difference; (3) Determination of the input accountability mass of an electrochemical (pyro-chemical) processing facility; (4) Continuity of knowledge at spent fuel storage site; (5) Optimal reloads through knowledge of true actinide content; (6) Burnup credit for fuel transport and storage; and (7) Provide confidence to the public that the shipment of spent fuel around the world is being undertaken in a rigorous manner, assuring that material is not diverted during shipment. Types of fuel of interest are: Fast Reactor Fuel, Normal burnup low enriched uranium (LEU), Mixed oxide (MOX), Low burnup LEU, and Research reactor. MCNPX calculates the slowing down and the energy spread for a given time. The principles are: (1) Neutrons slow down in LSDS; (2) Slow neutrons capture preferentially on a fission resonance; (3) Fission emits high-energy neutrons; (4) High-energy neutrons detected in threshold detector (that is not sensitive to slow neutrons) (e.g., 238 U, 232 Th); and (5) The detection time is characteristic of the slow neutron energy. Following each PSR pulse, the entire signal is digitized in 2 nanosecond intervals, and subsequently analyzed Analysis involves applying a digital filter to extract fission pulses in a background of initial oscillations and noise throughout. Some of the noise is not random. Depending on the threshold setting and filter parameters, both the normalization and the trend change. Original PNNL LSDS design required a 1-meter radius cylindrical LSDS. Much higher efficiency would allow us to use a (1.2m) LSDS (this is the LANL LSDS size), or a less intense source, or a combination of both. We still estimate 10 16 total neutrons from the source to obtain 2-3% precision in 239 Pu and 235 U assay.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

A Fast Reactor Irradiation Experiment Design in the ATR

Modern modeling techniques were used to investigate a proposed method for fast neutron irradiations in an existing thermal-spectrum reactor, the Advanced Test Reactor (ATR). This method builds upon pre-existing ideas, where fast flux is increased by surrounding the specimens with fissionable “booster fuel” but diverges from historical approaches by using an already developed fuel element design used in the Belgian Reactor 2 (BR2) as the booster fuel while leveraging modern 3-D modeling and simulation techniques. Design evaluations and neutronics simulations were performed to evaluate the performance of a BR2 fuel element irradiated in an ATR flux trap with test pins in the central channel of the BR2 fuel element. These efforts have yielded promising results. Adding a BR2 fuel element in the northeast (NE) flux trap of ATR was predicted to result in a 150% increase to the incident fast neutron flux with a fast (>0.1 MeV) to thermal (<0.625 eV) neutron flux ratio ranging from approximately 50 to 150, dependent on the material used for thermal neutron filtering and volume of moderator within the central channel of the BR2 element. The predicted annual fast neutron fluence (>0.1 MeV) ranges from 7.9 × 1021 to 9.1 × 1021 n/cm2. Given the relatively large fast to thermal neutron flux ratio, the calculated radial power profiles within 4.3 mm outer diameter U10Zr fueled specimens irradiated within the BR2 booster fuel element are adequate representations of those within fast neutron reactors. The predicted radial power profiles are not flat, but they are more prototypic than those seen in advanced fuels tests which began in ATR in 2003. Another distinct advantage of this experiment design is that full-scale test pins can be irradiated to augment the ongoing series of reduced scale advanced fuels tests. The proposed experiment design irradiated within a BR2 fuel element in a flux trap of ATR offers an improved alternative to the current testing of advanced reactor fuels in ATR. Selected results from this design evaluation are presented.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

Analysis of Samples Collected from the Surface of Interim Storage Canisters at Calvert Cliffs in June 2017: Revision 01.

In June 2017, dust and salt samples were collected from the surface of Spent Nuclear Fuel (SNF) dry storage canisters at the Calvert Cliffs Nuclear Power Plant. The samples were delivered to Sandia National laboratories for analysis. Two types of samples were collected: filter-backed Scotch-Brite TM pads were used to collect dry dust samples for characterization of salt and dust morphologies and distributions; and Saltsmart TM test strips were used to collect soluble salts for determining salt surface loadings per unit area. After collection, the samples were sealed into plastic sleeves for shipping. Condensation within the sleeves containing the Scotch-Brite TM samples remobilized the salts, rendering them ineffective for the intended purpose, and also led to mold growth, further compromising the samples; for these reasons, the samples were not analyzed. The SaltSmart TM samples were unaffected and were analyzed by ion chromatography for major anions and cations. The results of those analyses are presented here.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Water Solubility of Plutonium and Uranium Compounds and Residues at TA-55

Understanding the water solubility of plutonium and uranium compounds and residues at TA-55 is necessary to provide a technical basis for appropriate criticality safety, safety basis and accountability controls. Individual compound solubility was determined using published solubility data and solution thermodynamic modeling. Residue solubility was estimated using a combination of published technical reports and process knowledge of constituent compounds. The scope of materials considered includes all compounds and residues at TA-55 as of March 2016 that contain Pu-239 or U-235 where any single item in the facility has more than 500 g of nuclear material. This analysis indicates that the following materials are not appreciably soluble in water: plutonium dioxide (IDC=C21), plutonium phosphate (IDC=C66), plutonium tetrafluoride (IDC=C80), plutonium filter residue (IDC=R26), plutonium hydroxide precipitate (IDC=R41), plutonium DOR salt (IDC=R42), plutonium incinerator ash (IDC=R47), uranium carbide (IDC=C13), uranium dioxide (IDC=C21), U 3 O 8 (IDC=C88), and uranium filter residue (IDC=R26). This analysis also indicates that the following materials are soluble in water: plutonium chloride (IDC=C19) and uranium nitrate (IDC=C52). Equilibrium calculations suggest that PuOCl is water soluble under certain conditions, but some plutonium processing reports indicate that it is insoluble when present in electrorefining residues (R65). Plutonium molten salt extraction residues (IDC=R83) contain significant quantities of PuCl 3 , and are expected to be soluble in water. The solubility of the following plutonium residues is indeterminate due to conflicting reports, insufficient process knowledge or process-dependent composition: calcium salt (IDC=R09), electrorefining salt (IDC=R65), salt (IDC=R71), silica (IDC=R73) and sweepings/screenings (IDC=R78). Solution thermodynamic modeling also indicates that fire suppression water buffered with a commercially-available phosphate buffer would significantly reduce the solubility of PuCl 3 by the precipitation of PuPO 4 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

An Experimental Comparison of Cyclic Variations in Diesel–Natural Gas and POMDME–Natural Gas Dual Fuel Combustion

Abstract Cyclic variations in internal combustion engines are caused by various factors, including combustion mixture stratification, in-cylinder flows, local fluctuations in air-fuel ratio, etc. Cyclic variations have a profound impact on engine performance and emissions. In this study, cyclic variations in dual fuel combustion are analyzed, comparing diesel–natural gas (NG) and polyoxymethylene dimethyl ether (POMDME)-NG dual fuel combustion. Cyclic variability was initially quantified using the coefficient of variation of gross indicated mean effective pressure (IMEPg) computed from experimental cylinder pressure data. The cases analyzed in this study had a coefficient of variation (COV) of IMEPg greater than or around 5%, which was the lower limit of onset of instability for this engine. Experiments were performed at two fixed start of injection (SOI) of high-cetane fuel: 310 CAD and 350 CAD. For all experiments, a constant load of 5 bar IMEPg was maintained, and the intake boost pressure and rail pressure were fixed at 1.5 bar and 500 bar, respectively. For each case, 1000 cycles of cylinder pressure data were recorded, filtered, and processed using an in-house heat release analysis code for each cycle. A comparison between individual cycles and the “ensemble averaged cycle” was made for both diesel–NG and POMDME–NG combustion. For the early SOI of 310 CAD, the peak cylinder pressure fluctuations of individual cycle were found to be ± 15 bar for both fuel combinations, compared to the ensemble averaged cycle, and < 1/10th of the cycles had an IMEPg lower than 0.05 bar of the ensemble averaged cycle. However, the peak pressure fluctuations were found to be lower for POMDME–NG (±3 bar) than diesel–NG dual fuel combustion at 350 CAD SOI, indicating lower cyclic variations. The higher reactivity of POMDME helped reduce fluctuations in combustion phasing at the retarded SOI. The presence of cycles of deterioration and cycles of recovery were also observed with diesel–NG combustion for 310 CAD SOI, and the scatter in the IMEPg return map was similar for both fuel combinations. The IMEPg return map for POMDME–NG combustion was less scattered at the 350 CAD SOI.

Engineering↗
DOE OSTI2021

Transient Efficiency Flexibility and Reliability Optimization of Coal-Fired Power Plants (Model-Based Estimation Library Report)

This document pertains to the reporting requirements of DOE contract FE-0031767. The document covers the development of a model-based estimation (MBE) library for generating digital twins of coal-fired power plants (CFPPs). The models used by the MBE are transient and physics-based. Model classes in the library that correspond to different components in CFPPs are presented with physical explanations and representative results. MBE library provides Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF) algorithms. The MBE library is generic and can be used to represent a variety of CFPPs. A digital twin of a CFPP will be created as the reduced-order model of that CFPP is embedded in the developed MBE architecture.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2014

Determination of filter pore size for use in HB line phase II production of plutonium oxide

H-Canyon and HB-Line are tasked with the production of plutonium oxide (PuO 2 ) from a feed of plutonium (Pu) metal. The PuO 2 will provide feed material for the Mixed Oxide (MOX) Fuel Fabrication Facility. After dissolution of the Pu metal in H-Canyon, plans are to transfer the solution to HB-Line for purification by anion exchange. Anion exchange will be followed by plutonium(IV) oxalate precipitation, filtration, and calcination to form PuO 2 . The filtrate solutions, remaining after precipitation, contain low levels of Pu ions, oxalate ions, and may include solids. These solutions are transferred to H-Canyon for disposition. To mitigate the criticality concern of Pu solids in a Canyon tank, past processes have used oxalate destruction or have pre-filled the Canyon tank with a neutron poison. The installation of a filter on the process lines from the HB-Line filtrate tanks to H-Canyon Tank 9.6 is proposed to remove plutonium oxalate solids. This report describes SRNL’s efforts to determine the appropriate pore size for the filters needed to perform this function. Information provided in this report aids in developing the control strategies for solids in the process.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Baseline Postirradiation Examination of the FUTURIX-FTA Experiments

Postirradiation Examination (PIE) results from the baseline examination of the FUTURIX-FTA irradiation experiment are presented in this report. The FUTURIX-FTA irradiation was designed to study the fuel performance of candidate transmutation fuels. The FUTURIX-FTA experiment was conducted in the true fast neutron spectrum conditions of the Phénix sodium fast test reactor in France. FUTURIX-FTA contained several compositions that were also irradiated as part of the AFC-1 test in cadmium filtered positions in the Idaho National Laboratory (INL) Advanced Test Reactor (ATR) that approximate the neutron spectrum of a fast reactor. This experiment was a joint collaboration between the Department of Energy (DOE) in the U.S. and the Commissariat á l'Energie Atomique et aux Energies Alternatives (CEA) in France. A joint agreement between DOE and CEA was established in 2004 to conduct an irradiation experiment of metallic and nitride fuels in the Phénix reactor at CEA. Both the FUTURIX-FTA tests and the AFC-1 tests were conducted for the DOE Advanced Fuels Campaign (AFC) that is part of Fuel Cycle Research & Development (FCRD) program. These programs seek to develop and demonstrate the technologies needed to transmute long-lived transuranic actinide isotopes contained in spent nuclear fuel via fast reactor technology. The long term goal of this work is to reduce the radiotoxicity of future high level waste repositories. Post-irradiation examination of irradiated fuels experiments provides data related to in reactor fuel performance and input into future fuel design choices. The compositions of the FUTURIX-FTA pins were designed to test if minor actinides could be incorporated into the fuel of a fast reactor without significantly changing fuel performance observed for previously well studied fuels. The fuel performance of metallic fuel in fast reactors has been well documented. Likewise the irradiation performance of nitride fuels in fast reactors has also been documented. However the existing database for nitride fuels is much smaller than the database for metal fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Fast response, optical radiance measurements of low intensity impurity emission in WEST plasmas with staggered wavelength filters

Fast response acquisition of atomic line emission through the use of a filterscope has been implemented on the WEST tokamak at multiple poloidal locations. Filterscopes consist of a fiber-optic-based transmission from the tokamak to specifically engineered optical bandpasses and photomultiplier tubes (PMT) that collect the emission intensity to measure a radiance, L [W/cm2/str], over the specified bandpass. This diagnostic records plasma-wall interaction (PWI) properties (e.g. impurity emission and recycling of main fuel ions) up to a max acquisition rate of 100 kHz. These PMT radiometric measurements are calibrated into a line-normalized radiance, LN [photons/sec/cm2/str], similar to traditional spectrometers, which can later be converted to a particle flux. Low intensity emission peaks are difficult to quantify due to often comparable continuum levels, thus a secondary filter shifted to a judiciously-selected, line-free region (~1 nm away) allows for background subtraction. The system currently installed on WEST targets tungsten (W) gross sputtering specifically by monitoring, with a filter pair, the spectral region near the neutral W line emission (W I 400.9 nm). The line and background filters of the pair are centered at 400.6 nm and 403.1 nm, respectively. Through a set beam splitters on each sight line, the filter pair are measuring from the same location. The two L signals near W I are then subtracted from each other yielding only the W I LN. W I LN data from a recent WEST experimental campaign is presented and compared with plasma parameters and traditional spectrometer measurements of W I line emission to demonstrate the capabilities of this staggered-filter filterscope method. Specifically, the choice of WEST-specific bandpass curves for the W I LN will be illustrated based on this latter comparison.

Neff, Anton↗
DOE OSTI2021

Model predictive combustion control of a Gasoline Compression Ignition engine

Gasoline Compression Ignition is a novel combustion concept that derives its superiority from the high compression ratio of a compression ignition engine as well as the properties of gasoline fuel, such as longer ignition delay and higher volatility compared to diesel. Here, this combustion concept was experimentally tested on a 12.4L Class 8 truck engine. Based on these experimental data, prior efforts by the authors focused on the development of an engine model for a heavy-duty engine operating on a low-reactivity fuel. This engine model was leveraged within this study to investigate a combustion control strategy at different engine conditions and injection methods and was augmented to incorporate cycle-to-cycle combustion variations. State estimation is performed by means of a Kalman filter which feeds into a model predictive controller. The model predictive controller chooses control actions based on a predefined cost function under consideration of bounds reflecting physical constraints. The engine model was utilized to establish a state-space model that serves the Kalman filter and model predictive controller for estimation and prediction. A comparative study investigating control actions and engine behavior was performed with and without limiting in-cylinder peak pressure as well as combustion noise, which is of particular interest for early pilot injection strategies. In addition, the proposed control architecture was investigated at two different levels of cycle-to-cycle variations and compared to the performance of a control structure with input disturbance rejection. For increased cycle-to-cycle variations, disturbance estimation reduces state fluctuations and control effort. In general, this investigation highlights control aspects specific to a compression-ignited combustion regime with low-reactivity fuel. The control algorithm is able to maintain the desired references for brake mean effective pressure and combustion phasing while controlling peak in-cylinder pressure and combustion noise.

42 ENGINEERING↗
DOE OSTI2013

Simulated Fuel Economy and Emissions Performance during City and Interstate Driving for a Heavy-Duty Hybrid Truck

We compare simulated fuel economy and emissions for both conventional and hybrid class 8 heavy-duty diesel trucks operating over multiple urban and highway driving cycles. Both light and heavy freight loads were considered, and all simulations included full aftertreatment for NOx and particulate emissions controls. The aftertreatment components included a diesel oxidation catalyst (DOC), urea-selective catalytic NOx reduction (SCR), and a catalyzed diesel particulate filter (DPF). Our simulated hybrid powertrain was configured with a pre-transmission parallel drive, with a single electric motor between the clutch and gearbox. A conventional HD truck with equivalent diesel engine and aftertreatment was also simulated for comparison. Our results indicate that hybridization can significantly increase HD fuel economy and improve emissions control in city driving. However, there is less potential hybridization benefit for HD highway driving. A major factor behind the reduced hybridization benefit for highway driving is that there are fewer opportunities to utilize regenerative breaking. Our aftertreatment simulations indicate that opportunities for passive DPF regeneration are much greater for both hybrid and conventional trucks during highway driving due to higher sustained exhaust temperatures. When passive DPF regeneration is extensively utilized, the fuel penalty for particulate control is virtually eliminated, except for the 0.4%-0.9% fuel penalty associated with the slightly higher exhaust backpressure.

Daw, C. Stuart↗
DOE OSTI2018

Ex Situ Catalytic Fast Pyrolysis of Lignocellulosic Biomass to Hydrocarbon Fuels: 2018 State of Technology and Future Research

This report will update modeled costs for a fixed bed ex situ catalytic fast pyrolysis process for the conversion of biomass to liquid hydrocarbon fuels based on recent bench-scale experimental results. It will also update previously published information for this conversion pathway in the DOE Bioenergy Technologies Office 2016 Multi-Year Program Plan with current understanding of research goals achievable by 2022 and associated modeled cost reductions. All costs will be updated to a consistent set of assumptions in 2016 dollars.

09 BIOMASS FUELS↗
NASA NTRS1992

Dynamics and control of hypersonic aeropropulsive/aeroelastic vehicles

The guidance and control of hypersonic vehicles is examined by studying the airframe/engine/structural-dynamic interactions of a generic vehicle with scramjet propulsion. The pitch-attitude dynamics are described for the vehicle configuration that can sustain hypersonic flight at near-orbital altitudes. These aerospacecraft have strong airframe/engine/elastic coupling in attitude dynamics and engine responses with static instability with respect to pitch. An integrated airframe-engine control system is presented for the control of the system's strong aeropropulsive/aeroelastic coupling. The control methodology utilizes feedback of measured/synthesized values of angle of attack, blended pitch rate, thrust, and combustor-inlet pressure. The multiinput/multioutput engine controller requires high-bandwidth actuation of the fuel-flow control and the effective diffuser ratio. The proposed control laws do not provide optimized performance in terms of pitch response suggesting that additional control crossfeeds and filtering is needed.

Schmidt, David K.↗
NASA NTRSDate not supplied

Flame Structure Comparison using Jet-A and an isoparaffinic fuel in a lean direct injection flame tube combustor

This paper offers a first look at some recently acquired optical data. The effect of reference velocity on flame thickness, fuel atomization, and relative speciation of OH, CH, C2, and soot for two National Jet Fuel Combustion Program (NJFCP) fuels are explored in this paper. The NJFCP fuels are an average Jet-A, designated A-2 with a derived cetane number (DCN) of 49, and an isoparaffinic kerosene, C-4. C-4 fuel is made up primarily of C9 - C13, and C16 isoparaffins and is a combination of 60% Sasol IPK and 40% GEVO alcohol-to-jet (ATJ). C-4 has a DCN of 28. Both fuels begin distillation at about the same temperature, but C-4 completes about 30 degrees Celsius lower than A-2. Chemiluminescence images were acquired in a 5-atm gas turbine flame tube combustor using the NASA 7-point lean direct injector (LDI). The flame characteristics were determined through imaging with three scientific cameras. OH*, CH*, and C2* chemiluminescence were collected through narrow bandpass filters centered at 313nm, 430nm and 515nm onto an intensified high-speed camera framed at 8-kHz. A second high-speed camera collected color flame images at rates between 40 and 50 kHz. An ICCD camera framed at 20 Hz was used to record planar laser scatter from liquid fuel. Differences in speciation for the chemiluminescent species was observed between the two fuels. Some reasons for the differences are explored in this paper.

gas turbine combustion↗
DOE OSTI2025

Studies of optical and chemical properties of aged and fresh biomass burning absorbing aerosols for climate models

Particulate emissions from burning fuels from sub-Saharan Africa is currently poorly characterized. With increasing population and industrialization, emissions are expected to grow. Optical methods for measuring light absorption in the ultraviolet (UV) and visible (vis) regions of the spectrum are crucial for understanding the optical properties of BB aerosols (Bond and Bergstrom, 2006; Lack and Cappa, 2010; Moschos et al., 2021). One such instrument is the dual-spot AE33 model aethalometer is a common filter-based instrument that can be used to measure aerosol absorption properties (Hansen et al., 1984). This instrument has many figures of merit; however, the method's limitations include potential biases from scattering within the filter material, multiple scattering effects of the particles, filter loading (i.e. particle shadowing), and the need for wavelength-specific correction factors (Cλ), which depend on accurate intercomparison with other in situ techniques (Bond et al., 1999; Collaud Coen et al., 2010). This work aims to: 1. Optically characterize BB aerosol generated from African fuel 2. Correct the aethalometer at multiple wavelengths 3. Parametrize these correction factors. 4. Combusting the same fuels with two difference tube furnace systems assess the general applicability of this flexible means of producing BB aerosol. This was accomplished by conducting laboratory studies at Los Alamos National Laboratory (LANL) and North Carolina A&T State University (NCA&T), where aethalometer measurements were compared to in situ optical measurements. Mass cross sections of BB aerosol from these under-studied fuels will be determined along with their wavelength dependence.

09 BIOMASS FUELS↗
DOE OSTI2012

A petascale direct numerical simulation study of the modelling of flame wrinkling for large-eddy simulations in intense turbulence

A new set of petascale direct numerical simulations (DNS) modelling lean hydrogen combustion with detailed chemistry in a temporally evolving slot-jet configuration is presented as a database for the development and validation of models for premixed turbulent combustion. The jet Reynolds number is 10,000, requiring grid numbers up to nearly seven billion, which was achieved by computation on 120,000 processor cores. In contrast to many prior DNS studies, a mean shear exists that drives strong turbulent mixing within the flame structure. Three cases are simulated with different Damköhler numbers, while Reynolds number is held fixed. Basic statistics are presented showing that integrated burning rates up to approximately six times the laminar burning rate are obtained. It is shown that increased flame surface area accounts for most of the enhanced burning while increases in the burning rate per unit area also play an important contribution. The database is then used to assess a new model of flame wrinkling intended for large-eddy simulations (LES). The approach draws on concepts from fractal geometry, requiring the modelling of an inner cut-off scale representing the smallest scale of flame wrinkling, and the fractal dimension controlling the resolution dependence of the unresolved flame surface area. In contrast to previous modelling, it is argued that the inner cut-off should be filter-size invariant in an inertial range. Then, dimensional and physical reasoning together with Damköhler’s limiting scaling laws for the turbulent flame speed are used to infer the cut-off and fractal dimension in limiting regimes. Two methods of determining the fractal dimension are proposed: a static, algebraic expression or a dynamic approach exploiting a Germano-type identity. Finally the model is compared against the DNS in a priori tests and is found to give excellent results, quantitatively capturing the trends with time, space, filter size and Damköhler number.

Energy & Fuels↗