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2024 AIChE Annual Meeting conference presentation detailing the analysis of legacy solids concentration measure data taken via optical fiber probe in NETL's 12-inch Cold Flow Circulating Fluidized Bed (CFCFB), including discussion of the variation in statistical and chaotic parameters as a function of different fluidization regimes.
Nuclear thermal propulsion is an evolving technology that can be utilized for long-distance space travel. This technology yields the advantage of a high thrust and specific impulse, but requires an examination of the potential design adjustments necessary to enhance its feasibility. The development of nuclear thermal propulsion requires a comprehensive understanding of the system-level behavior during transient and steady-state operation. This paper extends our previous research by including the proper handling of turbomachinery with multi-channel thermal hydraulic simulations only for steady-state solutions. The system-level approach presented here enables the treatment of the turbopump components through non-dimensional analysis that eliminates the assumption of constant efficiencies. All the other components within the system (e.g., reflector and core) can be discretized to multiple channels and layers, in which the full thermal hydraulic solution is established. The approach chosen here enables the realistic modeling of the propellant flow within the expander cycle by capturing the pressure losses, mass flow rate splits, and enthalpy gain for various operational conditions. The verification of the package is completed through point comparisons of previous investigations into similar system designs. Furthermore, sensitivity studies are used to benchmark the capabilities of the package and investigate solution variations due to the perturbation of operational conditions and regimes. The sensitivity studies performed here are important to capture variation in flow characteristics (e.g., temperature, pressure, mass flow rates) for different design objectives such as the thrust and specific impulse. This work demonstrates that system-level simulations lacking multi-channel capability and proper turbomachinery treatment may yield higher uncertainties in understanding the engine’s response and characteristics to changing various requirements. This is extremely important when screening the design space of such propulsion systems and when transient simulations are required.
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The multi-machine ITPA Global H-mode Confinement Database has been upgraded with new data from JET with the ITER-like wall and ASDEX Upgrade with the full tungsten wall. This paper describes the new database and presents results of regression analysis to estimate the global energy confinement scaling in H-mode plasmas using a standard power law. Various subsets of the database are considered, focusing on type of wall and divertor materials, confinement regime (all H-modes, ELMy H or ELM-free) and ITER-like constraints. Apart from ordinary least squares, two other, robust regression techniques are applied, which take into account uncertainty on all variables. Regression on data from individual devices shows that, generally, the confinement dependence on density and the power degradation are weakest in the fully metallic devices. Using the multi-machine scalings, predictions are made of the confinement time in a standard ELMy H-mode scenario in ITER. The uncertainty on the scaling parameters is discussed with a view to practically useful error bars on the parameters and predictions. One of the derived scalings for ELMy H-modes on an ITER-like subset is studied in particular and compared to the IPB98(y,2) confinement scaling in engineering and dimensionless form. Transformation of this new scaling from engineering variables to dimensionless quantities is shown to result in large error bars on the dimensionless scaling. Regression analysis in the space of dimensionless variables is therefore proposed as an alternative, yielding acceptable estimates for the dimensionless scaling. The new scaling, which is dimensionally correct within the uncertainties, suggests that some dependencies of confinement in the multi- machine database can be reconciled with parameter scans in individual devices. This includes vanishingly small dependence of confinement on line-averaged density and normalized plasma pressure (β), as well as a noticeable, positive dependence on effective atomic mass and plasma triangularity. Extrapolation of this scaling to ITER yields a somewhat lower confinement time compared to the IPB98(y, 2) prediction, possibly related to the considerably weaker dependence on major radius in the new scaling (slightly above linear). Further studies are needed to compare more flexible regression models with the power law used here. In addition, data from more devices concerning possible ‘hidden variables’ could help to determine their influence on confinement, while adding data in sparsely populated areas of the parameter space may contribute to further disentangling some of the global confinement dependencies in tokamak plasmas.
In the present study, a high throughput (HT) methodology is applied to rapidly assess the surface characteristics of 83 additively manufactured 316L stainless steel. The variation in surface roughness (S a ) showed a good correlation with a dimensionless number (π) and provided direct linkages to the internal porosity defects. Lack-of-fusion regime relates to high surface roughness (S a > 5 µm), low dimensionless number (π < 61), and the presence of cavities in between the melt pool tracks. Balling regime correlates to high surface roughness (S a > 5 µm), intermediate dimensionless number (61 < π < 146), and non-uniform melt pool track width. Keyhole regime shows low surface roughness (S a < 5 µm), high dimensionless number (π > 146), and a curved melt pool track. This approach accelerates the process parameter discovery and minimizes the porosity defects for the LPBF process. The impact of the defects on the as-processed tensile mechanical properties demonstrates that samples with porosity exhibit up to 10% less tensile strength and 30% less ductility than optimal samples.
Abstract Wind-wave development is governed by the fetch- or duration-limited growth principle that is expressed as a pair of similarity functions relating the dimensionless elevation variance (wave energy) and spectral peak frequency to fetch or duration. Combining the pair of similarity functions, the fetch or duration variable can be removed to form a dimensionless function of elevation variance and spectral peak frequency, which is interpreted as the wave energy evolution with wave age. The relationship is initially developed for quasi-neural stability and quasi-steady wind forcing conditions. Further analyses show that the same fetch, duration, and wave-age similarity functions are applicable to unsteady wind forcing conditions, including rapidly accelerating and decelerating mountain gap wind episodes and tropical cyclone (TC) wind fields. Here it is shown that with the dimensionless frequency converted to dimensionless wavenumber using the surface wave dispersion relationship, the same similarity function is applicable in all water depths. Field data collected in shallow to deep waters and mild to TC wind conditions and synthetic data generated by spectrum model computations are assembled to illustrate the applicability. For the simulation work, the finite-depth wind-wave spectrum model and its shoaling function are formulated for variable spectral slopes. Given wind speed, wave age, and water depth, the measured and spectrum-computed significant wave heights and the associated growth parameters are in good agreement in forcing conditions from mild to TC winds and in all depths from deep ocean to shallow lake. Significance Statement This paper presents a growth function and spectrum model to describe wind-wave development in all water depths. Their applicability covers a wide range of wind forcing conditions including steady, accelerating, decelerating, and tropical cyclone events. Support for the unified spectrum model and growth function is presented with field observations and numerical computations.
The dimensionless isotope mass scaling experiment between pure Deuterium and pure Tritium plasmas with matched $\rho^*$, $\nu^*$ , β n , q and $T_e/T_i$ has been achieved in JET L-mode with dominant electron heating (NBI+ohmic) conditions. 28% higher scaled energy confinement time $B_t\tau_{E,\mathrm{th}}/A$ is found in favour of the Tritium plasma. This can be cast in the form of the dimensionless energy confinement scaling law as $\Omega_i \tau_{E,\mathrm{th}} \sim A^{0.48 \pm 0.16}$. This significant isotope mass scaling is consequently seen in the scaled one-fluid heat diffusion coefficient $A \chi_{\mathrm{eff}}/B_t$ which is around 50% lower in the Tritium plasma throughout the whole plasma radius. The isotope mass dependence in the particle transport channel is negligible, supported also by the perturbative particle transport analysis with gas puff modulation. The comparison of the edge particle fuelling or ionisation profiles from the EDGE2D-EIRENE simulations show that the absolute density differences that are necessary for the dimensionless match in the confined plasma dominate over any isotope mass dependencies of particle fuelling and ionization profiles at the plasma edge. Local GENE simulation results indicate a mild anti-gyroBohm effect at $\rho_\mathrm{tor}$ = 0.6 and thereby a small isotope mass dependence in favour of Tritium on heat transport and a negligible effect on particle transport. A significant fraction of the isotope scaling and reduced heat transport observed in the Tritium plasma is not captured in the GENE and ASTRA-TGLF-SAT2 simulations by simply changing the isotope mass for the same input profiles.
In a recent study, (1) we performed the self-consistent field (SCF) calculations of a dissipative particle dynamics (DPD) model of conformationally asymmetric diblock copolymer A-B melts to study the stability of various Frank–Kasper (FK) phases formed by such A-B melts. While all the equations in ref (1) are correct, we did not calculate the dimensionless (mean-field) Helmholtz free energies per chain βf c = βu c,χ + βu c,κ – s c /k B and the dimensionless stresses dβf c /dθ of ordered phases accurately. For example, the dimensionless (nonbonded) internal energy per chain due to the system compressibility βu c,κ = (N/2κ)∑ q βû 0 (|q|)(ϕ̂ A (q) + ϕ̂ B (q) – δ q,0 )(ϕ̂ A (−q) + ϕ̂ B (−q) – δ– q,0 ) should be calculated in the reciprocal space as given (note that βû 0 (|q|) is obtained analytically, and that since ϕ A (r) is real 𝜙̂ A (−𝐪)= $\overline{𝜙̂ A}$(𝐪), i.e., the complex conjugate of ϕ̂ A (q)); this corresponds to numerically evaluating βu c,κ = (N/2κ)∫dr(ϕ A (r) + ϕ B (r) – 1)ψ(r) with ψ(r) ≡ (∫dr′βu 0 (|r–r′|)(ϕ A (r′) + ϕ B (r′) – 1)/V in the real space via the (composite) trapezoidal rule. While the trapezoidal rule is less accurate than the Romberg integration (2) in general, the opposite occurs when the integration domain is periodic; this was pointed out by Matsen in ref (3) and explained in detail in refs (4and5). With our ignorance of this exceptional convergence property of the trapezoidal rule for periodic functions, we calculated all convolutions having the form of ψ(r) in the reciprocal space via the fast Fourier transforms (6) but those having the form of βu c,κ in the real space via Romberg integration; the latter leads to inaccurate results and unfortunately incorrect phase diagrams reported in ref (1), which are corrected here.
Abstract Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction . For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.
Abstract Diagramming pathways of dimensionless power is a potent method for extrapolating between operating points on present-day tokamaks and future burning plasma devices. The heat transport power, current drive power, H-mode threshold power and other ‘plasma physics’ powers can be expressed in dimensionally correct (or normalized) form as Pa 3/4 , where P is the power and a is the plasma minor radius, with the relative gyroradius ( ρ * ) dependence ranging from gyro-Bohm-like for transport ( P a 3 / 4 ∝ ρ * − 3 / 2 ), Bohm-like for current drive ( P a 3 / 4 ∝ ρ * − 5 / 2 ) and worse than Bohm-like for H-mode threshold ( P a 3 / 4 ∝ ρ * − 3 ). The D–T fusion power cannot be normalized in the same fashion since it is governed by nuclear physics, but at fixed B T it scales like P a 3 / 4 ∝ ρ * − 9 / 2 . Other ‘mixed physics’ powers can be incorporated into the dimensionless power framework by holding B T fixed in the same manner. Diagramming these dimensionless powers vs ρ * shows how the pathway to a steady-state reactor can be optimized relative to various operational boundaries. Using a steady-state hybrid discharge with β N = 3.2 from DIII-D as the starting point, a multi-parameter optimization finds an attractive pathway to steady-state operation on ITER using 76 MW of current drive power (fusion gain of Q fus = 8), along with a pathway to Q fus = 20 in a JET-sized steady-state reactor with B T = 10 T.
We study the separation performance using membrane modules through dimensional analysis (DA). We formulate the main process equations to identify relevant dimensionless numbers inherent in the physics. In particular, we identify that the critical step in the separation process is mass transfer through the selective layer. Remarkably, the dimensionless feed flow (DFfeed) emerges as a crucial factor in describing this process. Not only does DFfeed directly appear in the governing equations, but it also holds a physical significance associated with the time scales for the mass transfer across the feed side and through the selective layer. Regarding the output performance variables, we consider the recovery, stage cut, productivity and purity. In this context, we profit from experimental data and CFD simulations to evaluate the separation performance of the modules when varying the input flowrate, the scale of the module, and the CO2 permeance. These datasets enable us to establish correlations between performance metrics and the dimensionless feed flow (DFfeed). Using simple power functions of DFfeed, we obtain R2 coefficients exceeding 0.99, indicating the accuracy of the correlations built in the present work. In the future, we wish to use DA to understand key transport mechanisms, predict and control module performance, and challenge the universality of these findings by testing various gas separations across different membrane modules beyond our case study.
In the current analysis, we study the separation performance using membrane modules through dimensional analysis (DA). We formulate the main process equations to identify relevant dimensionless numbers inherent in the physics. In particular, we identify that the critical step in the separation process is mass transfer through the selective layer. Remarkably, the dimensionless feed flow (DFfeed) emerges as a crucial factor in describing this process. Not only does DFfeed directly appear in the governing equations, but it also holds a physical significance associated with the time scales for the mass transfer across the feed side and through the selective layer. Regarding the output performance variables, we consider the recovery, stage cut, productivity and purity. In this context, we profit from experimental data and CFD simulations to evaluate the separation performance of the modules when varying the input flowrate, the scale of the module, and the CO2 permeance. These datasets enable us to establish correlations between performance metrics and the dimensionless feed flow. Using simple power functions of DFfeed, we obtain R2 coefficients exceeding 0.99, indicating the accuracy of the correlations built in the present work. In the future, we wish to use DA to understand key transport mechanisms, predict and control module performance, and challenge the universality of these findings by testing various gas separations across different membrane modules beyond our case study.
NuScale Power has completed full length helical coil steam generator (HCSG) tests at SIET Laboratories in Piacenza, Italy. The test program included an investigation of the onset and evolution of density wave oscillations (DWO). This paper describes the mechanisms leading to the onset of DWO as inferred from tests performed in the full-height TF-2 counter-flow test facility. This research supports the concept that the onset of DWO is caused by liquid bridging inside the boiling length of the tubes. Using a separate cylinders approximation, a DWO onset correlation is obtained by performing a steady-state momentum balance on the density front created by liquid bridging. This yields a momentum balance equation in terms of a set of dimensionless superficial velocities, a corresponding dimensionless pressure drop term and an average void fraction. Envelope theory is then used to obtain a critical void fraction which is substituted into the dimensionless momentum balance to obtain a DWO onset correlation similar to the Wallis counter-current flooding correlation. A comparison of the DWO onset correlation to the TF-2 DWO experimental data is presented and shows excellent agreement when the average equilibrium vapor quality is greater than 0.2.
Unsteady heat transfer characterization on the combustion surfaces of Rotational Detonation Engines (RDE) is not well understood. It is generally thought that the complex nature of the unsteady, reacting, compressible fluid flow inside the combustion anulus of the RDE causes the convective heat transfer coefficient to be significantly higher than it is in other applications. Empirical models that have been used to analyze this strictly apply to steady flows where dimensionless groups can be employed. The reacting flow fields that are characteristic of RDEs are inherently compressible, three dimensional, unsteady, and turbulent, having properties that change by orders of magnitude throughout the flow field. They will therefore contain multiple length scales and time scales operating everywhere in the flow during all times. Because of this it is not likely that the RDE flow fields will lend themselves to explanation using simple dimensionless parameters. The dimensionless groups have meaning only in situations where length scales and time scales are singular and well defined. In spite of this it may be possible to get a relatively good idea of what the convection heat transfer coefficient is. In this work a numerical study is performed where the inside wall surface temperature distribution in the RDE outer body is systematically changed over a given range that would be characteristic of the start-up flows inside an RDE. For each case, temperature distributions inside the outer containment wall of the RDE was calculated and compared with experimental data. The closet match can then be used to directly calculate the convection heat transfer coefficient on the inside surface of the RDE.
Abstract Decoupling and understanding the various mass, charge, and heat transport phenomena involved in the electrocatalytic transformation of small molecules (i.e., CO 2 , CO, H 2 , N 2 , NH 3 , O 2 , and CH 4 ) is challenging but it can be readily achieved using dimensionless quantities (i.e., Reynolds, Sherwood, Schmidt, Damköhler, Nusselt, Prandtl, and Peclet Numbers) to simplify the characterization of systems with multiple interacting physical phenomena. Herein we report the development of a gastight rotating cylinder electrode cell with well‐defined mass transport characteristics that can be applied to experimentally decouple mass transfer effects from intrinsic kinetics in electrocatalytic systems. The gastight rotating cylinder electrode cell enables the dimensionless analysis of electrocatalytic systems and should enable the rigorous research and development of electrocatalytic technologies.
Here, we have discovered that one of the original articles findings, that the actual choice of the dimensionless parameter χ ∥i0 for the ion heat conductivity seemed to play no role for the simulation results, was not physical. Instead, due to a mistake in the handling of input parameters, χ ∥i0 was actually not used in the code – the dimensionless electron heat conductivity χ ∥e0 was used instead.
Powder-bed fusion (PBF) processes refer to a subset of Additive Manufacturing (AM) techniques where powder is spread on the build-plate before melting (by a laser or electron beam). While PBF processes are attractive due to their ability for realizing complex structures that are either difficult or impossible to create through conventional means, the parts fabricated with these techniques can exhibit defects such as pores, inclusions, and excessive surface roughness. To minimize these defects, much research has been dedicated towards process maturation by optimizing laser or electron beam parameters. However, these developmental efforts typically do not address the recoating process where achieving dense and uniform layers of powder is a necessity for ensuring process repeatability and part quality. While the recoating process can be studied through experimentation, the dynamics of particle movement are difficult to analyze experimentally. Therefore, here, in this study, powder spreading in PBF was simulated through the Discrete Element Method (DEM) to elucidate the mechanisms that control powder-bed quality. Utilizing the Buckingham Pi theorem, a dimensionless metric referred to as the spreading index is developed that combines powder-bed density, roughness, and particle size to assess the quality of powder layers. The formulated spreading index is then related to several dimensionless quantities that provide insight into the mechanisms dominating powder spreading in PBF. The DEM simulations conducted in this work focused on the scenario where powder is spread onto an existing powder bed and revealed that a reduction in the recoating velocity causes an increase in the spreading index while little to no impact on the spreading index was observed when varying layer thickness from 30 μm to 75 μm.Particle size effects on the powder-bed quality were also investigated.
The very high-temperature reactors (VHTRs) are highly ranked among candidates of Generation IV of nuclear reactors due to their high efficiency, safety, the resistance to proliferation, and reliability. The VHTRs are preferentially fueled by Tristructural-isometric (TRISO) coated fuel particles which has fuel kernels of fissile material coated by four coating layers: a porous buffer pyrolysis carbon layer (buffer PyC), an inner dense pyrolysis carbon layer (IPyC), a silicon carbide layer (SiC) and an outer dense pyrolysis carbon layer (OPyC). The heart of the operation and safety of the VHTRs significantly depends on the reliability of the coating layers of TRISO particles to retain metallic and gaseous fission products within the particles. The technique used for coating TRISO particles are gas-solids spouted beds via chemical vapor deposition (CVD). Fabrication of high-quality low-defect TRISO fuel particles fuel at larger scale spouted beds is required to support the commercialization of the VHTRs. In this work, our new developed mechanistic scale-up methodology of gas-solids spouted beds based on matching the radial profile of gas-holdup has been demonstrated and validated using radioactive particle tracking (RPT). Two spouted beds of small and larger scales were used in the study. Three sets of conditions were carried out which include the conditions of the reference case in the large scale, conditions that provide similar gas holdup radial profile to that of the reference case and conditions that provided dissimilar gas holdup radial in the small-scale spouted beds. The results confirm the validation of the scale-up methodology in terms of the dimensionless values of the spout diameter, cumulative probability distribution of the solids particles penetration into the spout, fraction of cycle time in each region of the bed, the radial profiles of the dimensionless values of the root-mean-square particle velocities and solids eddy diffusivity. Finally, the results further advance the knowledge and understanding of the gas-solids spouted beds provide deeper insight into their solids dynamics and presenting important benchmarking data for validating computational fluid dynamics codes and models. At last, procedures are established for the implementation of the new scale-up methodology.