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Multiphase two dimensional mixing and combustion of flow fields suspended in gaseous medium for propulsion systems problems, obtaining governing equations
Multiphase two dimensional mixing and combustion of flow fields suspended in gaseous medium for propulsion systems problems, obtaining governing equations
Measurement of phase volume fractions in water-containing multiphase flows is necessary for the optimization of a host of industrial flow processes. Many water-containing multiphase flows can be classified as either water-dispersed or water-continuous mixtures. A recently developed approach based on Hanai’s mixture formula and utilizing electrical capacitance tomography (ECT) sensors have shown good potential for obtaining water volume fraction estimates in two-phase water-containing flows with different water salinity levels. However, the proposed approach was investigated via controlled experiments restricted to static configurations while, in practice, multiphase flows can be dynamic and unpredictable. In this work, we perform a flow loop study of the proposed ECT-based method for volume fraction estimation in oil–water two-phase flows. Here, we evaluate the performance of the proposed method in both water-dispersed and water-continuous flow regimes by employing different types of capacitive sensors in cylindrical arrangements and parallel-plate rectangular arrangements.
In virtual design and scale up of pilot-scale carbon capture systems, the coupled reactive multiphase flow problem must be solved to predict the adsorber’s performance and capture efficiency under various operation conditions. This paper focuses on the detailed computational fluid dynamics (CFD) modeling of a pilot-scale fluidized bed adsorber equipped with vertical cooling tubes. Multiphase Flow with Interphase eXchanges (MFiX), an open-source multiphase flow CFD solver, is used for the simulations with custom code to simulate the chemical reactions and filtered models to capture the effect of the unresolved details in the coarser mesh for simulations with reasonable simulations and manageable computational effort. Previously developed two filtered models for horizontal cylinder drag, heat transfer, and reaction kinetics have been modified to derive the 2D filtered models representing vertical cylinders in the coarse-grid CFD simulations. The effects of the heat exchanger configurations (i.e., horizontal or vertical) on the adsorber’s hydrodynamics and CO2 capture performance are then examined. The simulation result subsequently is compared and contrasted with another predicted by a one-dimensional three-region process model.
MFiX (Multiphase Flow with Interphase eXchanges) is an open-source multiphase flow solver developed at the National Energy Technology Laboratory. Within the code, users have access to a single phase or interpenetrating continua-based multiphase two-fluid model (TFM), a discrete element model (DEM), and a particle-in-cell model (PIC). TFM, DEM, and PIC can all be used to create multiphase simulations that include hydrodynamics, chemical reactions, and heat transfer.
This study characterized and modeled heterogeneous surface wettability in sandstone and investigated the role of spatial heterogeneity and correlation length of surface wettability on relative permeability in a supercritical CO 2 (scCO 2 )-brine-rock system. Understanding the role of wettability heterogeneity on relative permeability is essential to geological CO 2 sequestration, oil and gas recovery, and contaminated groundwater remediation. Although numerous studies have attempted to understand the influences of surface wettability, capillary number (Ca), and viscosity ratio, the role of the spatial variation and correlation length of surface wettability on two-phase flow in three-dimensional (3D) porous media has not been unraveled due to the challenges in the measurement and representation of realistic rock surface wettability. In this work, we conducted in-situ measurements of surface contact angle (CA) in a Bentheimer sandstone after CO 2 flooding using micro-computed tomography (micro-CT), and found that the pore-scale CA distribution on rock surfaces followed a log-normal distribution associated with a spatial correlation length. Based on the statistical information from CT scanning, a Gaussian random field was used to model CA distributions that had desired standard deviations and spatial correlation lengths, which were then adjusted within a certain range of values for sensitivity analyses to study their combined effects on the two-phase flow in the porous medium using the lattice Boltzmann (LB) method. The LB two-phase flow simulation was accelerated using hybrid, multicore parallel computing to overcome the challenges in simulating multiphase flow in a large 3D domain having 800 × 800 × 600 nodes. The simulation results showed that the surface wettability heterogeneity (i.e., standard deviation of CA) had a lesser effect on the relative permeability of the wetting fluid (water) but a more significant impact on the relative permeability of the non-wetting fluid (scCO 2 ). The Corey model was used to fit the LB-simulated relative permeability curves of water and scCO 2 and showed that the variations in the relative permeability curves for both water and scCO 2 increased as the standard deviation and spatial correlation length of CA increased. This study illustrated that the assumption of homogeneous surface wettability may cause errors in multiphase flow simulations. Furthermore, the impacts of both the standard deviation and spatial correlation length of CAs should be accounted for. This is the first study that explored the spatial correlation lengths associated with CA distributions on sandstone surfaces and comprehensively investigated the roles of both spatial variation and correlation length of CA on two-phase flow properties in 3D porous media. The optimized LB multiphase flow model was proved a powerful tool to study the interplays and combined effects of these statistical parameters, which had critical applications in numerous natural and engineering processes that involved multiphase flow in porous media.
Carbon dioxide (CO 2 ) is a significant contributor of greenhouse gases emissions responsible for global warming. The fossil-fueled power plant is one of the major sources of CO 2 emission worldwide and needs to be mitigated. Post-combustion carbon capture by chemical absorption can be a promising technology to reduce CO 2 emission from power plants. The absorption is carried out via countercurrent flow in the packed columns. Although monoethanolamine (MEA) is a popular solvent, it has also limitations such as high volatility of solvent, corrosivity that leads to product degradation and damage to apparatuses, low CO 2 loading capacity, etc. Therefore, alternate solvents are being explored as prospective materials for carbon capture. A water-lean solvent, CO 2 binding organic liquids (CO2BOL), is currently being developed as a prospective material in carbon capture at the Pacific Northwest National Laboratory. Since the development of the material is at the primitive stage, it needs extensive investigation before industrial deployments. Hydrodynamics and mass transfer phenomena in the packed column using CO 2 BOL is unknown. Computational fluid dynamics (CFD) can be a useful tool to understand these phenomena in the packed column. Before employing the extensive CFD investigations, one needs to carefully validate CFD predictions for accurate flow predictions. This report demonstrates the validation of multiphase flow simulations against the experimental results for both structured and random packed columns. The reactive multiphase flow simulations using volume of fluid method were conducted at a wide range of liquid loads and contacts angles. The effective area is one of the critical factors dictating interphase mass transfer due to chemical reactions. Accordingly, CFD-predicted effective areas were compared with the experimental results of Tsai et al. [1] for Mellapak 250.Y structured packing. Both results matched well at different liquid loads in the presence of fast chemical kinetics using caustic solvents. Further, reactive multiphase flow simulations were also conducted in pall ring random packing to compute effective areas in the presence of fast chemical reactions. The CFD-predicted effective area compared well with correlation developed by Song et al. [2]. With successful validations, the current simulation framework can be further used for prediction of hydrodynamics and mass transfer phenomena using CO 2 BOL solvents in the packed column. Subsequently, it would be helpful in design optimization of a packed column. In addition to validation of the CFD model, this report also explains the mechanism for enhanced liquid side mass transfer for a structured packed column as compared to the wetted wall column.
The objective of this investigation has been to develop an algorithm (or algorithms) for the improvement of the accuracy and efficiency of the computer fluid dynamics (CFD) models to study the fundamental physics of combustion chamber flows, which are necessary ultimately for the design of propulsion systems such as SSME and STME. During this three year study (May 19, 1978 - May 18, 1992), a unique algorithm was developed for all speed flows. This newly developed algorithm basically consists of two pressure-based algorithms (i.e. PISOC and MFICE). This PISOC is a non-iterative scheme and the FICE is an iterative scheme where PISOC has the characteristic advantages on low and high speed flows and the modified FICE has shown its efficiency and accuracy to compute the flows in the transonic region. A new algorithm is born from a combination of these two algorithms. This newly developed algorithm has general application in both time-accurate and steady state flows, and also was tested extensively for various flow conditions, such as turbulent flows, chemically reacting flows, and multiphase flows.
We shall present results of a recent collaborative effort between the authors attempting to implement the numerical flux scheme, AUSM+ and its new developments, into a widely used NASA code, OVERFLOW. This paper is intended to give a thorough and systematic documentation about the solutions of default test cases using the AUSNI+ scheme. Hence we will address various aspects of numerical solutions, such as accuracy, convergence rate, and effects of turbulence models, over a variety of geometries, speed regimes. We will briefly describe the numerical schemes employed in the calculations, including the capability of solving for low-speed flows and multiphase flows by employing the concept of numerical speed of sound. As a bonus, this low Mach number formulations also enhances convergence to steady solutions for flows even at transonic speed. Calculations for complex 3D turbulent flows were performed with several turbulence models and the results display excellent agreements with measured data.
A survey is presented of diagnostic techniques and measurements made in multiphase reacting flows. The special problems encountered by the presence of liquid droplets, soot and solid particles in high temperature chemically reacting turbulent environments are outlined. The principal measurement techniques that have been tested in spray flames are spark photography, laser anemometry, thermocouples and suction probes. Spark photography provides measurement of drop size, drop size distribution, drop velocity, and angle of flight. Photographs are analysed automatically by image analysers. Photographic techniques are reliable, inexpensive and proved. Laser anemometers have been developed for simultaneous measurement of velocity and size of individual particles in sprays under conditions of vaporization and combustion. Particle/gas velocity differentials, particle Reynolds numbers, local drag coefficients and direct measurement of vaporization rates can be made by laser anemometry. Gas temperature in sprays is determined by direct in situ measurement of time constants immediately prior to measurement with compensation and signal analysis by micro-processors. Gas concentration is measured by suction probes and gas phase chromatography. Measurements of particle size, particle velocity, gas temperature, and gas concentration made in airblast and pressure atomised liquid spray flames are presented.
Here, in this paper, a Volume of Fluid method which uses a Stratified Flow model for flux calculation is proposed to solve a compressible multiphase flow in a way that has high parallel efficiency. The solver is part of an open-source computing tool to study fuel entrainment and combustion in the application of paraffin-based hybrid rocket motors. This paper focuses on the compressible Volume of Fluid solver for the liquid and gaseous phases in this environment. This solver uses perfect gas and stiffened gas models for equation of state, with the ability to easily add other models as desired. Additionally a comparison of a Riemann solver versus an AUSM+up scheme is conducted, showing improvement with the later in the solution of multiphase flows. This solver successfully reproduces shock tube cases with the expected accuracy, as well as simulating two-dimensional shear and gravity-driven flows. Results also show that the code is able to utilize a Stratified Flow model to evaluate shear flow without the need for interface reconstruction or gradient calculations. Finally, it is shown that the solver has near-ideal scaling under strong scaling tests as well as good performance in static scaling, giving improved performance over current options and implying future advancement of high-performance computing efficiency for multiphase flow solvers.
Geologic carbon sequestration (GCS) is a safety-critical technology that aims to reduce the amount of carbon dioxide in the atmosphere, which also places high demands on reliability. Multiphase flow in porous media is essential to understand CO 2 migration and pressure fields in the subsurface associated with GCS. However, numerical simulation for such problems in 4D is computationally challenging and expensive, due to the multiphysics and multiscale nature of the highly nonlinear governing partial differential equations (PDEs). It prevents us from considering multiple subsurface scenarios and conducting real-time optimization. Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the recently developed framework of the multiple-input deep neural operators (MIONet) and incorporates the Fourier neural operator (FNO) in the network architecture. Once Fourier-MIONet is trained, it can predict the evolution of saturation and pressure of the multiphase flow under various reservoir conditions, such as permeability and porosity heterogeneity, anisotropy, injection configurations, and multiphase flow properties. Compared to the enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown parameters, and it can be trained in significantly less time (about 3.5 times faster) with much lower CPU memory (<15%) and GPU memory (<35%) requirements, to achieve similar prediction accuracy. In addition to the lower computational cost, Fourier-MIONet can be trained with only 6 snapshots of time to predict the PDE solutions for 30 years. Furthermore, we observed that Fourier-MIONet can maintain good accuracy when predicting out-of-distribution (OOD) data. The excellent generalizability of Fourier-MIONet is enabled by its adherence to the physical principle that the solution to a PDE is continuous over time. Furthermore, the developed Fourier-MIONet makes it possible to solve the long-time evolution of geological carbon sequestration in a large-scale three-dimensional space accurately and efficiently.
This paper focuses on multiphase radial distribution networks with mixed wye and delta connections, and proposes a semidefinite relaxation of the AC optimal power flow (OPF) problem. Two multiphase power-flow models are developed to facilitate the integration of delta-connected generation units/loads in the OPF problem. The first model extends traditional branch flow models - and it is referred to as extended branch flow model (EBFM). The second model leverages a linear relationship between per-phase power injections and delta connections, which holds under a balanced voltage approximation (BVA). Based on these models, pertinent OPF problems are formulated and relaxed to semidefinite programs (SDPs). Numerical studies on IEEE test feeders show that SDP relaxations can be solved efficiently by a generic optimization solver. Numerical evidences indicate that solving the resultant SDP under BVA is faster than under EBFM. Moreover, both SDP solutions are numerically exact with respect to voltages and branch flows. It is also shown that the SDP solution under BVA has a small optimality gap, while the BVA model is accurate in the sense that it reflects actual system voltages.
A numerical simulator entitled TOUGH-UDEC is presented for the assessment of coupled thermal-hydraulic-mechanical processes in fractured porous media. Two existing well-established codes, TOUGH2 and UDEC, are coupled to model multiphase fluid flows, heat transfers, and discontinuous deformations in fractured porous media by means of discrete fracture representation. TOUGH2 is widely used for the modeling of heat transfers and multiphase multicomponent fluid flows, and UDEC is a well-known distinct element code for rock mechanics. The two codes are solved sequentially, with coupling parameters passed to each equation at specific intervals. After solving thermal-hydraulic equations within the TOUGH2 code, pressure and temperature information is imported into the UDEC model. Upon solving the mechanical equation within the UDEC code the calculated fracture apertures are converted to the equivalent permeability and porosity values for a TOUGH2 flow analysis. The solution is calculated by iteratively following an explicit sequence for numerical efficiency. Verifications are presented to demonstrate the capabilities of the coupled TOUGH-UDEC simulator. Three application examples of (1) shear dilation due to increased pore pressure, (2) thermal stress and (3) CO 2 injection, show that the new simulator can be an effective tool for geoengineering applications involving shear activation of fractures and faults.
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.
Submeter-scale geologic heterogeneity greatly affects CO 2 plume migration and retention. In this work, we present meter-scale laboratory experiments that can capture the impact of realistic submeter-scale geologic heterogeneity on multiphase flow and trapping. We produce realistic sedimentary formations consisting of ripple deposits with varying grain size contrast and wettability in a meter-scale slab chamber. Then, we conduct multiphase flow experiments with analog fluids through these structures and measure the saturation patterns, capillary heterogeneity trapping (CHT), and overall trapping performance. When we alter the ripple bedform architecture, variations in trapped saturation and CHT (10–20%) increment are exhibited. Similar growth in trapping performance is also observed when grain size contrast increases. Finally, wettability changes (water- to oil-wet) can increase nonwetting saturation and CHT up to 5% and 10–20%, respectively. These results emphasize the importance of correctly characterizing the impact of small-scale heterogeneities and wettability changes. We believe this is the first time that multiphase flow experiments were conducted in meter-scale domains with realistic ripple bedforms and heterogeneous wettability to investigate plume migration and trapping.
A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a typical chaotic structure in the flow field is observed at a Reynolds number of 10000, which indicates that the proposed model is a promising tool for direct numerical simulation of two-phase flows.
The water-gas relative permeability is an important parameter to characterize multiphase flow in sediments. To study the water-gas relative permeability of hydrate-bearing porous media, multiphase flow simulations were carried out at the pore scale using the lattice Boltzmann method. In this work, the effects of hydrate saturation and hydrate-growth habits on the water-gas relative permeability, which is scaled by the relative permeability considering the hydrate only, were evaluated in a two-dimensional porous medium. Results show that the increase of hydrate saturation causes the decrease of water-gas effective permeability as expected. However, the effect of hydrate saturation on the water-gas relative permeability is different from that of hydrate saturation on the water-gas effective permeability. The water-gas relative permeability increases with the increase of hydrate saturation in the pore-filling case. The water-gas relative permeability decreases with the increase of hydrate saturation in the grain-coating case. The wettability of solid phase has a different effect on the relative permeability of wetting phase and nonwetting phase. The Jamin effect (phase blocking) was observed and may exist in the production of gas from natural gas hydrate reservoirs. This seriously affects the multiphase flow characteristics. The changes of microscale fluid distribution effect the changes of water-gas relative permeability. The relationship between the water-gas relative permeability and the characterization parameters of microscale fluid distribution was analyzed.