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DOE OSTI2015

Shale gas and non-aqueous fracturing fluids: Opportunities and challenges for supercritical CO₂

Hydraulic fracturing of shale formations in the United States has led to a domestic energy boom. Currently, water is the only fracturing fluid regularly used in commercial shale oil and gas production. Industry and researchers are interested in non-aqueous working fluids due to their potential to increase production, reduce water requirements, and to minimize environmental impacts. Using a combination of new experimental and modeling data at multiple scales, we analyze the benefits and drawbacks of using CO₂ as a working fluid for shale gas production. We theorize and outline potential advantages of CO₂ including enhanced fracturing and fracture propagation, reduction of flow-blocking mechanisms, increased desorption of methane adsorbed in organic-rich parts of the shale, and a reduction or elimination of the deep re-injection of flow-back water that has been linked to induced seismicity and other environmental concerns. We also examine likely disadvantages including costs and safety issues associated with handling large volumes of supercritical CO₂. The advantages could have a significant impact over time leading to substantially increased gas production. In addition, if CO₂ proves to be an effective fracturing fluid, then shale gas formations could become a major utilization option for carbon sequestration.

03 NATURAL GAS↗

DOE OSTI2019

Designing and transforming yield-stress fluids

We review progress in designing and transforming multi-functional yield-stress fluids and give a perspective on the current state of knowledge that supports each step in the design process. We focus mainly on the rheological properties that make yield-stress fluids so useful and the trade-offs which need to be considered when working with these materials. Thinking in terms of "design with" and "design of' yield-stress fluids motivates how we can organize our scientific understanding of this field. "Design with" involves identification of rheological property requirements independent of the chemical formulation, e.g. for 3D direct-write printing which needs to accommodate a wide range of chemistry and material structures. "Design of includes microstructural considerations: conceptual models relating formulation to properties, quantitative models of formulation-structureproperty relations, and chemical transformation strategies for converting effective yield-stress fluids to be more useful solid engineering materials. Finally, future research directions are suggested at the intersection of chemistry, soft-matter physics, and material science in the context of our desire to design useful Theologically-complex functional materials.

36 MATERIALS SCIENCE↗

DOE OSTI2017

An immersed boundary method for fluid–structure interaction with compressible multiphase flows

This paper presents a two-dimensional immersed boundary method for fluid–structure interaction with compressible multiphase flows involving large structure deformations. This method involves three important parts: flow solver, structure solver and fluid–structure interaction coupling. In the flow solver, the compressible multiphase Navier–Stokes equations for ideal gases are solved by a finite difference method based on a staggered Cartesian mesh, where a fifth-order accuracy Weighted Essentially Non-Oscillation (WENO) scheme is used to handle spatial discretization of the convective term, a fourth-order central difference scheme is employed to discretize the viscous term, the third-order TVD Runge–Kutta scheme is used to discretize the temporal term, and the level-set method is adopted to capture the multi-material interface. In this work, the structure considered is a geometrically non-linear beam which is solved by using a finite element method based on the absolute nodal coordinate formulation (ANCF). The fluid dynamics and the structure motion are coupled in a partitioned iterative manner with a feedback penalty immersed boundary method where the flow dynamics is defined on a fixed Lagrangian grid and the structure dynamics is described on a global coordinate. We perform several validation cases (including fluid over a cylinder, structure dynamics, flow induced vibration of a flexible plate, deformation of a flexible panel induced by shock waves in a shock tube, an inclined flexible plate in a hypersonic flow, and shock-induced collapse of a cylindrical helium cavity in the air), and compare the results with experimental and other numerical data. The present results agree well with the published data and the current experiment. Finally, we further demonstrate the versatility of the present method by applying it to a flexible plate interacting with multiphase flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Perspectives on using implicit type constitutive relations in the modelling of the behaviour of non-Newtonian fluids

We discuss the benefits of using the so-called implicit type constitutive relations introduced by K. R. Rajagopal, J. Fluid Mech. 550, 243-249 (2006) and K. R. Rajagopal, Appl. Math. 48, 279-319 (2003) in the description of the behaviour of non-Newtonian fluids. In particular, we focus on the benefits of using the implicit type constitutive relations in the mathematical modelling of fluids in which the shear stress/shear rate dependence is given by an S-shaped curve, and in modelling of fluids that exhibit nonzero normal stress differences. We also discuss a thermodynamical framework that allows one to cope with the implicit type constitutive relations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface

For a spherical interface of radius R separating two different homogeneous regions of incompressible viscous fluids under the action of a radially directed acceleration, we perform a linear stability analysis in terms of spherical surface harmonics Y n to derive the dispersion relation. The instability behavior is investigated by computing the growth rates and the most-unstable modes as a function of the spherical harmonic degree n. This general methodology is applicable to the entire parameter space spanned by the Atwood number, the viscosity ratio, and the dimensionless number B = (α R Ρ² 2 /μ² ² )¹ / ³ R (where α R , Ρ 2 and μ 2 are the local radial acceleration at the interface, and the density and viscosity of the denser overlying fluid, respectively). While the mathematical formulation here is general, this paper focuses on instability that arises at a spherical viscous fluid/vacuum interface as there is a great deal to be learned from the effects of one-fluid viscosity and sphericity alone. To quantify and understand the effect that curvature and radial accelerationhave on the Rayleigh-Taylor instability, a comparison of the growth rates, under homologous driving conditions, between the planar and spherical interfaces is performed. The derived dispersion relation for the planar interface accounts for an underlying finite fluid region of thickness L and normal acceleration α R . Under certain conditions, the development of the most-unstable modes at a spherical interface can take place via the superposition of two adjacent spherical harmonics Y n and Y n+1 . This bimodality in the evolution of disturbances in the linear regime does not have a counterpart in the planar configuration where the most-unstable modes are associated with a unique wave number.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Fluid vs. kinetic magnetic reconnection with strong guide fields

The fast rates of magnetic reconnection found in both nature and experiments are important to understand theoretically. Recently, it was demonstrated that two-fluid magnetic reconnection remains fast in the strong guide field regime, regardless of the presence of fast-dispersive waves. This conclusion is in agreement with recent results from kinetic simulations, and is in contradiction to the findings in an earlier two-fluid study, where it was suggested that fast-dispersive waves are necessary for fast reconnection. In this paper, we give a more detailed derivation of the analytic model presented in a recent letter and present additional simulation results to support the conclusions that the magnetic reconnection rate in this regime is independent of both collisional dissipation and system-size. In particular, we present a detailed comparison between fluid and kinetic simulations, finding good agreement in both the reconnection rate and overall length of the current layer. Finally, we revisit the earlier two-fluid study, which arrived at different conclusions, and suggest an alternative interpretation for the numerical results presented therein.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Unsteady hydromagnetic flow of dusty fluid and heat transfer over a vertical stretching sheet with thermal radiation

In this paper, the hydromagnetic flow of dusty fluid over a vertical stretching sheet with thermal radiation is investigated. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformation. These nonlinear ordinary differential equations are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method (RKF45 Method). The behavior of velocity and temperature profiles of hydromagnetic fluid flow of dusty fluid is analyzed and discussed for different parameters of interest such as unsteady parameter, fluid-particle interaction parameter, the magnetic parameter, radiation parameter and Prandtl number on the flow.

42 ENGINEERING↗

DOE OSTI2026

Filament extension atomizers: A study of integration potential into spray dryers for high-viscosity and non-Newtonian fluids

Filament extension atomizers (FEAs) are an emerging class of spray nozzles designed to atomize high-viscosity and non-Newtonian fluids that are challenging for conventional pressure or two-fluid nozzles. In this study, we investigate the influence of roller geometry, surface velocity, roller material, and fluid rheology on the atomization performance of FEA systems using concentrated whey protein suspensions (50–70 wt. %). Extensional and shear rheology experiments, along with high-speed imaging and particle image velocimetry, reveal that filament breakup dynamics are governed by competition between inertial, capillary, and viscoelastic stresses. High roller rotational velocity leads to narrower spray cones, contradicting rheology experiments and suggests a significant inertial contribution to filament breakup. Smaller rollers operating at the same rotational velocity led to broader spray cones consistent with expectations. An FEA nozzle was integrated into a conventional dryer producing particles in the 100 μm range. Results suggest that FEA technology enables atomization of highly viscous fluids at industrially relevant spray cone angles similar to those generated by pressure nozzles, offering a pathway to improve energy efficiency in spray drying by enabling higher solids loading feedstocks. Furthermore, these insights provide critical guidance for optimizing FEA nozzle designs and process parameters across a range of applications.

Energy efficiency↗

DOE OSTI2025

Thermal-Fluid and Thermal-Structural Response of the T-Tube Modular Divertor to Spatiotemporally Varying Heat Loads

Tungsten (W) is the leading candidate for divertor target plates because of its high melting point (>3000°C), thermal conductivity, and ultimate tensile stress. While W and its alloys are the only solid materials that can survive the high heat fluxes incident on the divertor, W’s low-ductility high ductile-to-brittle transition temperature of ~600°C and relatively low recrystallization temperature (RT) of ~1300°C pose structural (among other) challenges. The objective of this work is to estimate the thermal-fluid and thermal-structural performance of the helium (He)-cooled T-tube divertor, which was originally developed by the Advanced Reactor Innovation and Evaluation Study (ARIES) using numerical simulations. Here, predictions of temperature distributions across the plasma-facing structural component and surface pressures from computational fluid dynamics simulations are used to determine stress distributions using commercial structural finite element modeling software over a range of fusion-relevant conditions. The maximum allowable incident heat fluxes are determined based on the temperature limits imposed by the ITER elastic Structural Design Criteria for In-vessel Components (SDC-IC) and the maximum RT over a range of He mass flow rates and presented in the form of performance design charts. Our recent work found that thermal- structural criteria accounting for the low ductility of W in a finger-type modular divertor constrain the maximum incident heat fluxes to values well below the ITER specifications, and those based on considering only the RT demonstrate that integrated thermal-fluid and elastic structural performance evaluation are required for accurate assessment of divertor performance. This novel analysis of the T-tube considers how nonuniform and transient incident heat fluxes affect its thermal-fluid and thermal-structural performance, as well as the effect of volumetric heating, which can be as great as 27% of the power incident on the divertor surface. The W tile of the T-tube, with its relatively large plasma-facing area of ~15 cm 2 , will likely experience significant spatial variations in incident heat flux. This work therefore assesses whether steady-state incident heat flux profiles with a peak of 10 MW/m 2 and maximum heat flux gradients of 200 MW/m 2 per m exceed the structural limits imposed by the ITER elastic SDC-IC and the maximum RT over a range of fusion-relevant conditions. The effect of transient heat fluxes typical of plasma detachment and reattachment from the target plate due, for example, to gas injection are also evaluated

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Local well-posedness and singularity formation in non-Newtonian compressible fluids

We investigate the initial value problem of a very general class of 3 + 1 non-Newtonian compressible fluids in which the viscous stress tensor with shear and bulk viscosity relaxes to its Navier–Stokes values. These fluids correspond to the non-relativistic limit of well-known Israel–Stewart-like theories used in the relativistic fluid dynamic simulations of high-energy nuclear and astrophysical systems. After establishing the local well-posedness of the Cauchy problem, we show for the first time in the literature that there exists a large class of initial data for which the corresponding evolution breaks down in finite time due to the formation of singularities. This implies that a large class of non-Newtonian fluids do not have finite solutions defined at all times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Parametric electroconvection in a weakly conducting fluid in a horizontal parallel-plate capacitor

We study the flows of a nonuniformly heated weakly conducting fluid in an ac electric field of a horizontal parallel-plate capacitor. Analysis is carried out for fluids in which the charge formation is governed by electroconductive mechanism associated with the temperature dependence of the electrical conductivity of the medium. Periodic and chaotic regimes of fluid flow are investigated in the limiting case of instantaneous charge relaxation and for a finite relaxation time. Bifurcation diagrams and electroconvective regimes charts are constructed. The regions where fluid oscillations synchronize with the frequency of the external field are determined. Hysteretic transitions between electroconvection regimes are studied. The scenarios of transition to chaotic oscillations are analyzed. Depending on the natural frequency of electroconvective system and the external field frequency, the transition from periodic to chaotic oscillations can occur via quasiperiodicity, a subharmonic cascade, or intermittence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3 + 1 Spacetime Perspective

A kinetic theory of classical particles serves as a unified basis for developing a geometric 3 + 1 spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases on as common a footing as possible reveals that the particle four-momentum is better regarded as comprising momentum and inertia rather than momentum and energy; and, consequently, that the object now known as the stress-energy or energy-momentum tensor is more properly understood as a stress-inertia or inertia-momentum tensor. In dealing with both fiducial and comoving frames as fluid dynamics requires, tensor decompositions in terms of the four-velocities of observers associated with these frames render use of coordinate-free geometric notation not only fully viable, but conceptually simplifying. A particle number four-vector, three-momentum ( 1 , 1 ) tensor, and kinetic energy four-vector characterize a simple fluid and satisfy balance equations involving spacetime divergences on both Minkowski and Galilei/Newton spacetimes. Reduced to a fully 3 + 1 form, these equations yield the familiar conservative formulations of special relativistic and non-relativistic fluid dynamics as partial differential equations in inertial coordinates, and in geometric form will provide a useful conceptual bridge to arbitrary-Lagrange–Euler and general relativistic formulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Experimental and numerical studies of seismic fluid-structure interaction in a base-supported cylindrical vessel

Seismic design and qualification of advanced reactors will rely heavily on the use of verified and validated numerical models capable of capturing the interaction of the vessel, its contained fluid, and the internal equipment: fluid-structure interaction (FSI) analysis. Analytical solutions can be used for preliminary sizing and design of such vessels but their application is limited to simple geometries and boundary conditions, and small amplitude, translational (and rotational) inputs. To validate numerical models for seismic FSI analysis in finite element codes, a comprehensive set of experiments was performed on a liquid-filled cylindrical vessel, using a 6 degree-of-freedom earthquake simulator. Results in terms of sloshing frequency, damping ratio in sloshing modes, and hydrodynamic responses (wave height, hydrodynamic pressure, base shear, and base moment) for multi-directional earthquake simulator inputs are reported and compared with analytical solutions for liquid-filled vessels. The impact of seismic (base) isolation on hydrodynamic responses was studied using earthquake simulator inputs generated using a virtual isolation system. Data from the experiments are used to validate a numerical model of the fluid-filled vessel using the Arbitrary Lagrangian Eulerian (ALE) solver in the commercial finite element program LS-DYNA. Validation studies are presented for multi-directional seismic inputs, including rocking motions. Lagrangian modeling approaches using an elastic material formulation for the fluid are also investigated and their limitations and possible applications are identified. Here, the results are broadly applicable to the seismic response of base supported, liquid-filled vessels.

58 GEOSCIENCES↗

DOE OSTI2022

Development, verification, and validation of comprehensive acoustic fluid-structure interaction capabilities in an open-source computational platform

The acoustic fluid-structure interaction (FSI) formulation is a practical numerical approach for the seismic analysis of fluid-filled tanks. However, there are no verification and validation studies reported in the literature that demonstrate the ability of an acoustic FSI numerical model to predict responses important to structural and mechanical design for intense translational and rotational earthquake inputs. Herein, an acoustic FSI formulation is implemented in the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE), and is formally verified and validated using analytical solutions and code-to-code verification, and experimental data, respectively. The analytical solutions are for small amplitude, unidirectional seismic inputs. The code-to-code verification utilizes a previously verified and validated Arbitrary Lagrangian-Eulerian (ALE) numerical model in the commercial finite element code LS-DYNA. The validation studies utilize a comprehensive data set assembled from results of 3D earthquake-simulator tests of a fluid-filled vessel. The acoustic numerical model in MOOSE is verified and validated for hydrodynamic pressures and support reactions except for cases that involve significant convective response. For small amplitude inputs, numerically predicted wave heights match those of the analytical solutions. The numerical model is not verified and validated for wave height calculations under intense 3D seismic inputs. The run times for the acoustic FSI simulations in MOOSE are an order of magnitude, or more, shorter than for the corresponding ALE simulations in LS-DYNA. The utility of the MOOSE acoustic FSI implementation is demonstrated by seismic analysis of a building equipped with a fluid-filled, advanced nuclear reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Characteristics of Fluid‐Solid Interaction Constitutive Models Within Poroelastodynamics at Higher Strain‐Rates and Large Deformations Implemented in 1D

The large deformation, mixed formulation, finite element (FE) modeling approach presented in Irwin et al. 2024 is extended herein to include improved constitutive models for representing dynamic solid-fluid interactions at higher strain rates (𝒪⁢(1⁢0 2 −1⁢0 3 )⁢s −1 ) and larger overpressure magnitudes (𝒪⁡(1⁢0 2 )⁢kPa) within a biphasic soft porous material using Theory of Porous Media (TPM) at finite strain. Specifically, these constitutive modeling improvements are the following: (i) a more physically robust constitutive model for pore fluid seepage velocity via inclusion of pore fluid viscous stress, and (ii) a modified deformation-dependent-permeability model and updated hyperelastic constitutive model better suited for handling larger volumetric compressions and extensions. The novelty of the present work is mainly the contribution (i): inclusion of pore fluid viscous stress at higher strain-rate and large deformations, which requires 𝐶 1 continuity in the weak formulation, accomplished by employing Hermite cubic interpolation functions within a mixed nonlinear poromechanical finite element formulation. In (ii), the model is updated to weakly enforce solid phase incompressibility, such that this assumption is not violated numerically, which provides improved numerical stability for achieving larger overpressure magnitudes on 𝒪⁡(1⁢0 2 ) kPa, which were not achievable with the previous Kozeny–Carman model in Irwin et al. 2024. Also in (ii), the volumetric part of the solid skeleton free energy function is modified to ensure proper bounds on the solid skeleton Jacobian of deformation 𝐽 s related to incompressibility of the solid phase. Uniaxial strain, unidirectional flow examples at higher strain rates (𝒪⁢(1⁢0 2 −1⁢0 3 )⁢s −1 ) and larger deformations (up to 0.2 (or 20%) nominal axial strain) demonstrate the improved physical representation—and numerical stability—of these constitutive model improvements.

42 ENGINEERING↗

DOE OSTI2022

A two-fluid single-column model of turbulent shallow convection. Part II: Single-column model formulation and numerics

The two-fluid single-column model of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy is introduced as a prognostic variable, dependence on a diagnosed boundary-layer height is removed, and subfilter fluxes are approximated using a two-fluid version of a Mellor–Yamada scheme. Three mechanisms for entrainment and detrainment processes are introduced, which represent entrainment of unstable air at the surface, forced detrainment of air at the top of the boundary/cloud layers, and turbulent mixing that relaxes the convective fluid to a reference profile. A semi-implicit Eulerian discretization replaces the semi-implicit semi-Lagrangian implementation of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) to improve numerical stability and conservation. The equations for the implicit time step are solved using a quasi-Newton method, which is shown to perform well in numerical tests for conservation and convergence. The two-fluid single-column model presented in this article will be applied to simulations of shallow cumulus convection in Part III.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Ensemble Kalman filter for data assimilation coupled with low-resolution computations techniques applied in fluid dynamics

This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.

Data Assimilation↗