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An estimate for the coefficient of self-diffusion can be derived whenever the Eulerian velocity spectrum is known. The result is more general than those previously obtained. A comparison is made with computed test-particle diffusion in an inviscid two-dimensional Navier-Stokes fluid.
The prediction of boiling incipience is a critical issue for a reactor. Vapor lock causes operating instability and undesirable temperature rise, especially for small channels. This study uses the Eulerian multiphase flow boiling model to predict the onset of nucleate boiling in a millimeter scale rectangular channel. Two wall boiling models, namely the RPI (Rensselaer Polytechnic Institute) and the non-equilibrium sub cooled model are applied. Computational fluid dynamics is employed for this study to investigate the impact of operating conditions like liquid flow rate, operating pressure, heat flux, velocity profile, turbulence model, and inlet liquid temperature. Here, the effect of fundamental boiling parameters on the surface wall temperature and vapor volume fraction is also studied. The parameters under consideration are the bubble departure diameter, bubble departure frequency, nucleate site density, quenching time period, and interface heat transfer coefficients. A series of CFD calculations is conducted by varying the considered variables systematically in a wide range of flow conditions covering laminar, transition, and turbulent flows. The sub-component heat fluxes like the liquid convective, the vapor convective, the evaporative, and the quenching terms are monitored to infer the boiling dynamics in the transition region from the single-phase flow to the nucleate boiling zone. It is found that the CFD approach to detecting the boiling incipience point agrees reasonably with available experimental data. However, its limitations, like inaccuracy for lower flow rates and early transition to boiling flow, are also noticed due to the nature of the considered RPI model.
Numerical calculations have been carried out for gas-particle confined turbulent flows using a recently developed two-phase turbulence closure model. The present modeling scheme utilizes Eulerian formulations of the transport equations and accounts for the combined effects of interphase slip and turbulent dispersion of particles. A multiple-scale turbulence model is used for the turbulent field modeling of the underlying fluid flow. For the particle size and particle loading considered in this study, the fluid turbulence transport equations must be modified to include the damping effects of particles. Predictions and comparisons are made in the fully developed gas-solid pipe flow and the confined particle-laden jet. Numerical results are in reasonably good agreement with the published experimental information.
The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.
With dry bay fires persisting as a significant contributor to aircraft vulnerability despite chronicled developments in survivability technologies, an accurate fire prediction capability remains paramount for credible vulnerability assessments. Physics based modeling of the hydrodynamic ram (HRAM) fluid deposition process is a key component of such capability, wherein capturing the first instance of fluid spurt, referred to herein as shallow jet spurts, is a core focus. Such pre-spurts as they have been formerly identified have only been witnessed sporadically in HRAM spurt experiments. In this work, ALE3D, a first-principles multi-physics code was employed to model the shallow jet spurt phenomenon with spherical projectiles impacting water-filled tanks faced with aluminum panels, such that the underlying physics and sensitivities could be explored. Development and verification of the 2D axisymmetric model is described relative to trends observed in a prior experimental campaign. Results from the verified model suggest shallow jet spurts have at least a quadratic sensitivity to the fundamental vibrational mode of the impact plate across impact velocities 610–1829 m/s (2000–6000 ft/s). It is further explained how shallow jet spurts are arrested for impacts at the two extremes of plate rigidity. This research constitutes the first fluid-structure modeling of shallow jet spurts which future three-dimensional analyses will expound upon.
The hydrodynamic response of liquid-filled storage tanks subjected to translational earthquake shaking has been the focus of studies for more than 75 years. In service, tanks experience six components of seismic input, with rocking due to support flexibility and/or rotational components of ground motion. Published theory for predicting hydrodynamic responses in rigid cylindrical tanks due to rotational seismic input is examined. Analytical solutions for pressure in the fluid and on the tank wall, and base moment are modified to account for the effects of angular displacements at the base. A finite element model of a water-filled cylindrical tank using the Arbitrary Lagrangian and Eulerian (ALE) solver in LS-DYNA is used to demonstrate the efficacy of the proposed expressions for three base rocking motions. Results from the modified analytical solutions and the finite element model are in excellent agreement.
Particle-based thermal energy storage (TES) systems are an emerging energy storage technology. The technological advances have reduced costs, making TES more competitive and reliable in the marketplace but an efficient and reliable operation is heavily dependent on coherent heat transfer between air to particles or vice versa. The particle-based TES technologies provide an intermediate system that can store energy for short (0-10 h), long (10-200 h) and seasonal (> 200 h) timescales. The TES systems store energy by converting electricity to thermal energy; electricity can be directly sourced intermittent generation technologies and/or the grid, helping manage peak loads and other mismatches in supply and demand. The overall efficiency of the TES system depends on the performance of system components (particle storage silos and particle transfer mechanism etc.). The particle heat exchanger is one of the key system components that affects the system efficiency. The pressurized fluidized bed heat exchanger (PFB HX) performance is challenging to predict due to the chaotic behavior of particle and fluid interaction. This research presents a computational study of a novel direct-contact, counter-flow and air-to-particles PFB HX, that contributes in advancing the particle-based long-duration TES technologies. For the current analysis an unsteady Eulerian-Eulerian CFD model was developed and validated against experiments performed at the National Laboratory of the Rockies for two particle sizes (600 ..mu..m and 825 ..mu..m ). Following validation, parametric simulations were conducted to evaluate the effects of interphase drag models (Syamlal-O'Brien and Gidaspow), particle size, bed height and the influence of a frictional-viscosity term on hydrodynamics and heat transfer between the air & particles. The key findings from the analysis are: (1) for the studied operating window Syamlal-O'Brien provides superior agreement with measured gas temperatures (errors generally < 10%) while Gidaspow shows large deviations for the coarse particle case; (2) model predictions are most sensitive in the lower 0.2 m above the air distributor where bubble initiation and local mixing dominate interphase heat transfer; (3) representation of the distributor (number of inlet ports) materially affects predicted local mixing and temperature stratification; and (4) the Eulerian-Eulerian framework reproduces bulk thermal trends but shows regime dependent limitations for coarse particles, motivating mesoscale informed closures for scale-up analysis for future studies. These results provide validated guidance for drag selection and distributor design in particle-based thermal energy storage applications. Collectively, the validated model and parametric results quantify key drivers of PHB-HX performance and provide practical guidance for design and optimization. The results provide confidence in the model predictability and provide a step forward to improve on heat exchange performance. The demonstrated performance and modeling approach support the deployment and further development of this novel PHB-HX concept for robust, particle-based long-duration thermal energy storage systems.
This paper presents computational fluid dynamics (CFD) models for simulating self-pressurization and spray-bar pressure control processes in a large-scale liquid hydrogen storage tank under normal gravity conditions. For self-pressurization, the model employs the kinetics-based Schrage equation alongside the volume-of-fluid (VOF) method to account for interfacial mass transfer. The CFD predictions of pressure and temperature are compared with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) experiment, and the predicted interfacial mass transfer rates are also presented. A CFD model simulating pressure control using a spray bar has also been developed. An Eulerian-Lagrangian approach models the interactions between discrete droplets and the continuous ullage (vapor) phase. The spray model is coupled with the VOF method by tracking droplets in the ullage and removing them when they reach the liquid interface. The T-sat model calculates droplet-ullage heat and mass transfer, where droplets warm up to the saturation temperature corresponding to the ullage vapor pressure before evaporating while remaining at the saturation temperature. The evolution of tank pressure, vapor temperature, and liquid temperature predicted by the CFD model is validated against data from the MHTB spray-bar mixing experiment. Overall, the CFD models agree with experimental data, demonstrating their capability to simulate self-pressurization and pressure control processes in large-scale cryogenic storage tanks. These models can be valuable tools for designing and optimizing cryogenic fluid management systems in future applications.
This paper presents computational fluid dynamics (CFD) models for simulating self-pressurization and spray-bar pressure control processes in a large-scale liquid hydrogen storage tank under normal gravity conditions. For self-pressurization, the model employs the kinetics-based Schrage equation alongside the volume-of-fluid (VOF) method to account for interfacial mass transfer. The CFD predictions of pressure and temperature are compared with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) experiment, and the predicted interfacial mass transfer rates are also presented. A CFD model simulating pressure control using a spray bar has also been developed. An Eulerian-Lagrangian approach models the interactions between discrete droplets and the continuous ullage (vapor) phase. The spray model is coupled with the VOF method by tracking droplets in the ullage and removing them when they reach the liquid interface. The T-sat model calculates droplet-ullage heat and mass transfer, wherein droplets warm up to the saturation temperature corresponding to the ullage vapor pressure before evaporating while remaining at the saturation temperature. The evolution of tank pressure, vapor temperature, and liquid temperature predicted by the CFD model is validated against data from the MHTB spray-bar mixing experiment. Overall, the CFD models agree with experimental data, demonstrating their capability to simulate self-pressurization and pressure control processes in large-scale cryogenic storage tanks. These models can be valuable tools for designing and optimizing cryogenic fluid management systems in future applications.
Numerical tests of the inviscid equilibrium theory of Kraichnan (1975) are described. The mathematical description applies equally well to the two-dimensional electrostatic guiding center plasma and to the two-dimensional inviscid Navier-Stokes fluid. The predictions of this analytic theory are discussed. A pair of coupled equations are derived for the two-time vorticity autocorrelation in Fourier space and the infinitesimal unit response function G of Kraichnan in the so-called Eulerian direct interaction approximation. Kraichnan's assertion that thermodynamic limits exist for the negative temperature states is questioned.
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
Heat transfer in directly-irradiated high-temperature solid–gas flows laden with polydisperse particles is investigated using a novel transient three-dimensional computational fluid dynamics model. The model couples particle–gas hydrodynamics of solid–gas flows laden with polydisperse particles, radiative heat transfer in non-grey absorbing, emitting and anisotropically-scattering multi-component participating media, conduction heat transfer in the gas phase, and interfacial convection heat transfer. The multiphase particle-in-cell method is used to predict high-fidelity solid–gas flow characteristics, such as the local discrete particle size distribution, with increased computational efficiency by combining the advantages of both Eulerian and Lagrangian methods. The multi-component radiative transfer model is implemented using an advanced collision-based Monte Carlo ray-tracing method. The number of the prescribed discrete particle components is found to be the key parameter affecting the computational accuracy and efficiency, which primarily depends on the size distribution of the particles. For the model particle–gas flow featuring free-falling Gamma-distributed ceramic particles exposed to concentrated solar irradiation, the particle volume fraction, radiative, fluid flow and thermal characteristics appear to converge with the increasing number of the discrete particle components. Five particle components are sufficient to obtain physically meaningful results. A further increase in the number of the particle components only slightly increases the accuracy of the numerical predictions at the expense of a rapidly increasing computational time. For five particle components, the particle vertical velocity at the receiver exit for particles with the diameter of 43.4 μm is 57% of that for the particles with the diameter of 202.8 μm. The temperatures of these two particle components increase from the initial ambient values by factors of 2 and 1.2, respectively, during the simulation time. In conclusion, the model developed allows for increased fidelity of particle–gas flow simulations with significant radiative effects.
Bubble column bioreactors are being actively considered for gas fermentation applications, specifically for CO2 utilization, and sugars to fuels conversion. Their main advantages include good mass transfer without any moving parts and low-cost of operation and maintenance. However, the design and scale-up of such reactors is challenging specifically for carbon capture applications where a mixture of gases (e.g. CO2/CO/H2) with variable solubilities is used. The overall performance of scaled-up bioreactors (e.g., mass transfer rate) is largely affected by gas holdup, bubble size distribution (BSD), and multiphase hydrodynamics. We investigate the effect of gas sparger designs on the performance of these large-scale bioreactors using computational fluid dynamics simulations in this work, so as to improve CO2 conversion at scale. The gas distribution systems in bubble column reactors not only determines operational regime, but also affects the evolution of the BSD, which in turn influences interfacial mass transfer and ultimately the efficiency of the gas-liquid exchange process. In addition to the BSD, uniformity in gas sparging affects gas holdup and bubble residence time which constitute important metrics of performance in gas-liquid systems. In this work, we use computational models to simulate high fidelity representations of different sparger designs and their effect on the operation of a bubble column reactor. Four different types of spargers have been selected for the computational study (Fig. 1): ladder, multi-ring, single-ring and toroidal. Their effect on superficial velocity, gas holdup mixing efficiency, and BSD will be evaluated in this work. The model uses a multiphase Eulerian framework similar to [1] and include a composition of mixtures of H2/CO/CO2 gases, common in fermentation applications.
The Lagrangian formalism is widely used to simulate hydrodynamic responses in complex engineering applications, particularly those involving strong shock waves. However, as the mesh moves with the fluid, it can become highly distorted, requiring a regularization step. This involves constructing a new grid and remapping conservative quantities onto it to restore mesh quality. This work introduces a regularization method for block-structured meshes within a 3D ALE (Arbitrary Lagrangian-Eulerian) code. The proposed approach prevents mesh tangling while preserving the anisotropic features of the initial Lagrangian mesh. This regularization technique incorporates aspect ratio-based weights to control mesh smoothing. Unlike uniform rezoning techniques, this weighted approach maintains proximity to the Lagrangian mesh while improving mesh quality. Here, the method effectively handles concave geometries by mitigating the grid attraction phenomenon, which typically leads to mesh concentration along concave edges. Numerical experiments demonstrate its efficiency in regularizing severely deformed meshes, and its integration within the ALE framework is validated on challenging hydrodynamic test cases, including the triple point problem.
In the United States transportation sector, Light-Duty Vehicles (LDVs) are the largest energy consumers and CO 2 emitters. Electrification of LDVs is posed as a potential solution, but SI engines can still contribute to decarbonization. Car manufacturers have turned to unconventional engine operation to increase the efficiency of Spark-Ignition (SI) engines and reduce the carbon emissions of their fleets. Dilute, lean, and stratified-charge engine operation has the potential for engine efficiency improvements at the expense of increased cyclic variability and combustion instability. At such demanding engine conditions, the spark ignition event is key for flame initiation and propagation and for enhanced combustion stability. Reliable and accurate spark ignition models can help design ignition systems that reduce cyclic variability. Multiple computational spark-ignition models exist that perform well under conventional conditions, but the underlying physics needs to be expanded, for unconventional engine operation. In this paper, a hybrid Lagrangian–Eulerian Spark-Ignition (LESI) model is coupled with different turbulent flame propagation models for engine simulations. LESI relies on Lagrangian arc tracking and Eulerian energy deposition. The LESI model is coupled with the Well-Stirred Reactor (WSR), Thickened Flame Model (TFM), and g-equation model and used to simulate several cycles of a Direct-Injection Spark-Ignition (DISI) engine using a commercial Computational Fluid Dynamics (CFD) engine solver. The results showcase the successful coupling of LESI with the combustion models. Global engine metrics, such as pressure and Apparent Heat Release Rate (AHRR), for each simulation setup are compared to experimental engine results, for validation. In addition, results highlight the successful prediction of spark channel movement by comparing simulation images to experimental optical engine images. Finally, the successful coupling of LESI to combustion models, making it a usable model in the engine modeling community, is emphasized and future development details are discussed.
Abstract Rates and extents of mineral precipitation in porous media are difficult to predict, in part because laboratory experiments are problematic. It is similarly challenging to implement numerical methods that model this process due to the need to dynamically evolve the interface of solid material. We developed a multiphase solver that implements a micro-continuum simulation approach based on the Darcy–Brinkman–Stokes equation to study mineral precipitation. We used the volume-of-fluid technique in sharp interface implementation to capture the propagation of the solid mineral surface. Additionally, we utilize an adaptive mesh refinement method to improve the resolution of near interface simulation domain dynamically. The developed solver was validated against both analytical solution and Arbitrary Lagrangian–Eulerian approach to ensure its accuracy on simulating the propagation of the solid interface. The precipitation of barite (BaSO 4 ) was chosen as a model system to test the solver using variety of simulation parameters: different geometrical constraints, flow conditions, reaction rate and ion diffusion. The growth of a single barite crystal was simulated to demonstrate the solver’s capability to capture the crystal face specific directional growth.