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Semi-smooth Newton methods for nonlinear complementarity formulation of compositional two-phase flow in porous media
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Load following characteristics of a molten salt fast reactor under two-phase flow conditions
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Investigation of air-water two-phase flow characteristics in a 25.4 mm diameter circular pipe
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Symmetry and scaling in one-dimensional compressible two-phase flow
Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. We focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.
Direct Numerical Simulation of Single- and Two-Phase Flows for Nuclear Engineering Geometries
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Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows
In this work, the effects of the particle volume fraction gradient on fluid-particle interactions are studied. The phase interaction force is decomposed into three terms. For the first term, namely the symmetrized force density, we present theoretical reasoning and numerical evidence to assume that it is independent of the particle volume fraction gradient. The second term is the particle volume fraction gradient times a newly introduced diffusion stress. The third term is the divergence of the particle-fluid-particle (PFP) stress. If this assumption of independence of the particle volume fraction gradient for the first term can be verified, to the first order of the ratio of the mean distance between particles to the macroscopic lengthscale, all three terms can be studied and modeled in flows with uniform particle distributions. Models thus obtained are applicable to statistically inhomogeneous flows, with the second and third terms accounting for statistical inhomogeneity. To verify this assumption, numerical simulations of flows passing fixed arrays of particles are performed. Both uniform and nonuniform particle volume fractions are studied and compared for disperse multiphase flows with the particle Reynolds numbers ranging from 1 to 100, and particle volume fraction ranging from 1% to 26% in statistically steady states. It is found that the symmetrized force (first) term can be well approximated by the drag force obtained from studies of uniform flows. The diffusion stress is positive along the flow direction and negative in the directions perpendicular to the flow. In the case of moving particles, this stress could potentially cause particle aggregation in the flow direction and dispersion in the directions perpendicular to the flow. Finally, the diffusion stress is only important when there is a volume fraction gradient, while the PFP stress can be important in inhomogeneous flows with either nonuniform particle concentrations or nonuniform average relative velocities between the phases.
Derivation of A Representative Elementary Volume (REV) for Upscaled Two-Phase Flow in Porous Media
Relative permeability plays an important role in the upscaling of multiphase flow in porous media from the pore scale to the Darcy scale. The entire concept of relative permeability is contingent on the existence of a representative elementary volume (REV). As we move to smaller samples to measure relative permeability, such as with digital core analysis, the concept of a classical REV has become increasingly unlikely when using the conventional approach to defining a representative volume. The “‘conventional”’ understanding of an REV is that a large enough volume must be considered such that spatial variability averages out. In digital rock methods, such as pore-scale simulations based on micro-computed tomography (CT) images, the domain size is typically 2 to 4 mm. This is approximately the length scale of a single-phase flow REV using the classic REV approach. However, the single-phase perspective does not consider the complex dynamics and fluctuations often observed in multiphase flow systems, even at centimeter-scale experiments and/or simulations. A fundamental question is, therefore, whether the domain size commonly used in digital rock simulations can provide a consistent energy budget such that the concept of relative permeability exists. Based on first principles, relative permeability accounts for the rate of energy dissipated in a stationary process. If the dynamics are fluctuating, the energy dissipated can vary but will average out over a long enough timescale. The key to determining the validity of the relative permeability is the timescale of the measurement, not the spatial scale. The conventional REV theory assumes that spatial, temporal, and ensemble averages are equivalent in an ergodic system, but it does not provide a way to test this assumption. We provide a formal way to identify the timescale where the relative permeability accurately captures energy dissipation as a way to validate relative permeability measurements and quantitatively assess their accuracy. This result will be tested for a practical SCAL test, determining how long a flow experiment needs to be run to accurately characterize the rate of energy dissipation by the flow. The outcome will be a best practice guide for the determination of relative permeability from core-scale experiments and/or digital core simulations that ensure the energy budget is fully accounted for in the relative permeability coefficient.
TWO-PHASE FLOW AND ACOUSTIC PHENOMENA IN GASES AND LIQUIDS LITERATURE SEARCH, NO. 177
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Maximum two-phase flow rates of subcooled nitrogen through a sharp-edged orifice
Data are presented of an experiment in which subcooled liquid nitrogen was discharged through a sharp-edged orifice at flow rates near the maximum. The data covered a range of inlet stagnation pressures from slightly above saturation to twice the thermodynamic critical pressure. The data were taken along five separate inlet stagnation isotherms ranging from 0.75 to 1.035 times the thermodynamic critical temperature. The results indicate that subcooled liquids do not choke or approach maximum flow in an asymptotic manner even though the back pressure is well below saturation; and orifice flow coefficients are not constant as is frequently assumed. A metastable jet appears to exist which breaks down if the difference between back pressure and saturation pressure is large enough.
Maximum two-phase flow rates of subcooled nitrogen through a sharp-edged orifice
An experiment was conducted and data are presented in which subcooled liquid nitrogen was discharged through a sharp-edged orifice at flow rates near the maximum. The data covered a range of inlet stagnation pressure from slightly above saturation to twice the thermodynamic critical pressure. The data were taken along five separate inlet stagnation isotherms ranging from 0.75 to 1.035 times the thermodynamic critical temperature. The results indicate that: (1) subcooled liquids do not choke or approach maximum flow in an asymptotic manner even though the back pressure is well below saturation; (2) orifice flow coefficients are not constant as is frequently assumed. A metastable jet appears to exist which breaks down if the difference between back pressure and saturation pressure is large enough.
Babcock and Wilcox's experience with two-phase flow mixtures of coal and gas
The performance of pulverized coal injection systems in operation on blast furnaces is described in terms of application to coal gasification, fluidized bed combustion, and magnetohydrodynamics.
Simultaneous velocity and particle size measurement in two phase flows by Laser Anemometry
A technique for particle size measurement by using Laser Doppler Anemometry is discussed. An additional gate photomultiplier has been introduced at right angles to the optical axis in order to select only those particles passing through the central region of the measurement control volume. Particle sizing measurements have been made in sprays of glass particles using the modified Laser Anemometry system. Measurements in fuel sprays are also reported and compared with the results obtained by a photographic technique. The application of the particle sizing technique to opaque particles is investigated and suitable optical arrangements are suggested. Light scattering characteristics of Laser Anemometry systems for different optical geometries are calculated to select the optimum optical arrangement for the particle sizing measurements.
Two-phase flow measurements of a spray in a turbulent flow
The dynamics of spray drop interaction with a turbulent coflowing air stream were investigated using a Phase Doppler Particle Analyzer that determines both drop size and velocity. Detailed measurements obtained included spray drop size, axial and radial velocity, angle of trajectory, drop Reynolds number, and size-velocity correlations. The gas-phase flow field was also ascertained via the behavior of the smallest drops. Also investigated were the drag coefficients of droplets in a turbulent air cross flow for both monodispersions and polydispersions. Most notable aspects of the coflow included the effect of air streams with velocities significantly different from the spray sheet. Local changes in number density were produced as a result of lateral convection and streamwise accelerations and decelerations of various drop size classes. The complexity of the spray field interaction illustrated by this data effectively describes the development of the spray due to the influence of the airflow. The droplet drag measurements showed similar behavior for monodispersed and polydispersed flows and similar trends to previously obtained data. The measurements also pointed out further studies which would assist in creating an improved drag law for polydispersed drops in a turbulent environment.
A combined Eulerian-Lagrangian two-phase flow analysis of SSME HPOTP nozzle plug trajectories. II - Results
An analysis of Space Shuttle Main Engine high-pressure oxygen turbopump nozzle plug trajectories has been performed, using a Lagrangian method to track nozzle plug particles expelled from a turbine through a high Reynolds number flow in a turnaround duct with turning vanes. Axisymmetric and parametric analyses reveal that if nozzle plugs exited the turbine they would probably impact the LOX heat exchanger with impact velocities which are significantly less than the penetration velocity. The finding that only slight to moderate damage will result from nozzle plug failure in flight is supported by the results of a hot-fire engine test with induced nozzle plug failures.
Effect of particle velocity fluctuations on the inertia coupling in two-phase flow
Consistent forms for the interfacial force, the interfacial pressure, the Reynolds stresses and the particle stress have been derived for the inviscid, irrotational incompressible flow of fluid in a dilute suspension of spheres. The particles are assumed to have a velocity distribution, giving rise to an effective pressure and stress in the particle phase. The velocity fluctuations also contribute in the fluid Reynolds stress and in the (elastic) stress field inside the spheres. The relation of these constitutive equations to the force on an individual sphere is discussed.
Two-phase flow research using the learjet apparatus
Low-gravity, gas-liquid flow research can be conducted aboard the NASA Lewis Learjet, the Lewis DC-9, or the Johnson Space Center KC-135. Air and water solutions serve as the test liquids in cylindrical test sections with an inner diameter of 1.27 cm and lengths up to 1.5 m. Superficial velocities range from 0.1 to 1.1 m/sec for liquids and from 0.1 to 25 m/sec for air. Flow rate, differential pressure, void fraction, film thickness, wall-shear stress, and acceleration data are measured and recorded throughout the 20 sec duration of the experiment. Flow is visualized by photographing at 400 frames with a high-speed, 16-mm camera.