Full Multiphase Research Articles

Scaling and modeling of the heat transfer across the free surface of a thermocapillary liquid bridge

PurposeThis paper aims to derive a reduced-order model for the heat transfer across the interface between a millimetric thermocapillary liquid bridge from silicone oil and the surrounding ambient gas.Design/methodology/approachNumerical solutions for the two-fluid model are computed covering a wide parametric space, making a total of 2,800 numerical flow simulations. Based on the computed data, a reduced single-fluid model for the liquid phase is devised, in which the heat transfer between the liquid and the gas is modeled by Newton’s heat transfer law, albeit with a space-dependent Biot function Bi(z), instead of a constant Biot number Bi.FindingsAn explicit robust fit of Bi(z) is obtained covering the whole range of parameters considered. The single-fluid model together with the Biot function derived yields very accurate results at much lesser computational cost than the corresponding two-phase fully-coupled simulation required for the two-fluid model.Practical implicationsUsing this novel Biot function approach instead of a constant Biot number, the critical Reynolds number can be predicted much more accurately within single-phase linear stability solvers.Originality/valueThe Biot function for thermocapillary liquid bridges is derived from the full multiphase problem by a robust multi-stage fit procedure. The derived Biot function reproduces very well the theoretical boundary layer scalings.

Oscillation dynamics of the air-core in a hydrocyclone

Tangential introduction of liquid results in a swirling flow within a cylindro-conical hydrocyclone. Upon continuous feeding with water, the central axial region experiences local low pressure across the height yielding the formation of an air-core, which executes meandering motion similar to the oscillation of an elastic string. We investigated the vortical flow and the induced oscillating behavior of an air column submerged in a water flow field inside a hydrocyclone. Through a series of experiments in a transparent hydrocyclone and subsequent full scale multiphase flow simulations with the Reynolds stress model, we analyzed the morphological characteristics of the air-core (mean and fluctuating properties). Air-core oscillations are characterized in terms of spatial wavelength and frequency. We show that hydrodynamics driven oscillating behavior of the air-core shares an analogy with the vibration of an elastic beam. Following this analogy, we obtain a scaling relationship between the wavelength and air-core radius, which is in good agreement with our experimental data and numerical results.

Ram Pressure Stripping of the Multiphase ISM: A Detailed View from TIGRESS Simulations

Ram pressure stripping (RPS) is a process that removes the interstellar medium (ISM) quickly, playing a vital role in galaxy evolution. Previous RPS studies have treated the ISM as single-phase or lack the resolution and physical processes to properly capture the full multiphase ISM. To improve this simplification, we introduce an inflowing, hot intracluster medium (ICM) into a self-consistently modeled ISM in a local patch of star-forming galactic disks using the TIGRESS framework. Our simulations reveal that the workings of RPS are not only direct acceleration of the ISM by ICM ram pressure but also mixing-driven momentum transfer involving significant phase transition and radiative cooling. The hot ICM passes through the low-density channels of the porous, multiphase ISM; shreds the cool ISM; and creates mixing layers. The ICM momentum is transferred through the mixing layers while populating the intermediate-temperature gas and radiating thermal energy away. The mixed gas extends beyond galactic disks and forms stripped tails that cool back unless the ICM fluxes are large enough to prevent cooling until they escape the simulation domain. The mixing-driven momentum transfer predicts that the more ICM mixes in, the faster the ISM moves, resulting in the anticorrelation of outflow velocity and gas metallicity of the stripped ISM. The compression of the ISM disks due to the ICM ram pressure enhances star formation rates up to 50% compared to the model without ICM. With the ICM ram pressure higher than the disk anchoring pressure, star formation is quenched within ∼100 Myr.

Investigation of post-injection strategies for diesel engine Catalyst Heating Operation using a vapor-liquid-equilibrium-based spray model

Most multidimensional engine simulations spend much time solving for non-equilibrium spray dynamics (atomization, collision, vaporization). However, their accuracy is limited by significant grid dependency, and the need for extensive calibration. This is critical for modeling cold-start diesel fuel post injections, which occur at low temperatures and pressures, far from typical model validation ranges. At the same time, resolving micron-scale spray phenomena would render full Eulerian multiphase calculations prohibitive. In this study, an improved phase equilibrium based approach was implemented and assessed for simulating diesel catalyst heating operation strategies. A phase equilibrium solver based on the model by Yue and Reitz [1] was implemented: a fully multiphase CFD solver is employed with an engineering-size engine grid, and fuel injection is modeled using the standard Lagrangian parcels approach. Mass and energy from the liquid parcels are released to the Eulerian multiphase mixture according to an equilibrium-based liquid jet model. An improved phase equilibrium solver was developed to handle large real-gas mixtures such as those from accurate chemical kinetics mechanisms. The liquid-jet model was improved such that momentum transfer to the Eulerian solver better reproduces the physical spray jet structure. Validation of liquid/vapor penetration predictions showed that the model yields accurate results with very limited tuning and low sensitivity to the few calibration constants. In-cylinder simulations of diesel catalyst heating operation strategies showed that capturing spray structure is paramount when short, transient injection pulses and low temperatures are present. Furthermore, the EP model provides improved predictions of post-injection spray structure and ignitability, while conventional spray modeling does not capture the increase of liquid penetration during the expansion stroke. Finally, the only important EP model calibration constant, Cliq, does not affect momentum transfer, but it changes the local charge cooling distribution through the local energy transfer, which makes it candidate to additional research. The results confirm that non-equilibrium spray processes do not need to be resolved in engineering simulations of high-pressure diesel sprays.

A multiphase CMAQ version 5.0 adjoint.

We present the development of a multiphase adjoint for the Community Multiscale Air Quality (CMAQ) model, a widely used chemical transport model. The adjoint model provides location- and time-specific gradients that can be used in various applications such as backward sensitivity analysis, source attribution, optimal pollution control, data assimilation, and inverse modeling. The science processes of the CMAQ model include gas-phase chemistry, aerosol dynamics and thermodynamics, cloud chemistry and dynamics, diffusion, and advection. Discrete adjoints are implemented for all the science processes, with an additional continuous adjoint for advection. The development of discrete adjoints is assisted with algorithmic differentiation (AD) tools. Particularly, the Kinetic PreProcessor (KPP) is implemented for gas-phase and aqueous chemistry, and two different automatic differentiation tools are used for other processes such as clouds, aerosols, diffusion, and advection. The continuous adjoint of advection is developed manually. For adjoint validation, the brute-force or finite-difference method (FDM) is implemented process by process with box- or column-model simulations. Due to the inherent limitations of the FDM caused by numerical round-off errors, the complex variable method (CVM) is adopted where necessary. The adjoint model often shows better agreement with the CVM than with the FDM. The adjoints of all science processes compare favorably with the FDM and CVM. In an example application of the full multiphase adjoint model, we provide the first estimates of how emissions of particulate matter (PM2.5) affect public health across the US.

Investigation on separation performance of vane-type gas-liquid tube separator

In this work, gas phase distribution characteristic and separation performance of a new vane-type gas-liquid separator were carefully investigated using electrical resistance tomography and numerical simulation. The diameter of the separator was 100 mm and the flow rate ranges from 12.0 to 23.0 m3/h. The gas flow rate ranges from 1.2 to 4.0 m3/h. In the experiment, electrical resistance tomography was applied to test section void fraction distribution. Coriolis mass flow meter was applied to obtain separation efficiency by testing separator exits mixture density. In the numerical simulation, full Eulerian multiphase model, together with RNG k-? turbulent model and dispersed phase zero equation models were applied. Results show that the vane-type gas-liquid separator's performance is influenced by gas core size. The separator performs well in all the cases, considering separation efficiency is over 85%, and achieves nearly 100% through adjustment of split ratio. All these findings are beneficial for vane-type gas-liquid separator design and optimization.

A General Mathematical Formulation for the Determination of Differential Leakage Factors in Electrical Machines With Symmetrical and Asymmetrical Full or Dead-Coil Multiphase Windings

This paper presents a simple and general mathematical formulation for the determination of the differential leakage factor for both symmetrical and asymmetrical full and dead-coil windings of electrical machines. The method can be applied to all multiphase windings and considers Gorges polygons in conjunction with masses geometry in order to find an easy and affordable way to compute the differential leakage factor, avoiding the adoption of traditional methods that refer to the Ossanna's infinite series, which has to be obviously truncated under the bound of a predetermined accuracy. Moreover, the method described in this paper allows the easy determination of both the minimum and maximum values of the differential leakage factor, as well as its average value and the time trend. The proposed method, which does not require infinite series, is validated by means of several examples in order to practically demonstrate the effectiveness and the easiness of application of this procedure.

Automated quantification of mitral valve geometry on multi-slice computed tomography in patients with dilated cardiomyopathy – Implications for transcatheter mitral valve replacement

ObjectivesThe primary aim of this study was to quantify the dimensions and geometry of the mitral valve complex in patients with dilated cardiomyopathy and significant mitral regurgitation. The secondary aim was to evaluate the validity of an automated segmentation algorithm for assessment of the mitral valve compared to manual assessment on computed tomography. BackgroundTranscatheter mitral valve replacement (TMVR) is an evolving technique which relies heavily on the lengthy evaluation of cardiac computed tomography (CT) datasets. Limited data is available on the dimensions and geometry of the mitral valve in pathological states throughout the cardiac cycle, which may have implications for TMVR device design, screening of suitable candidates and annular sizing prior to TMVR. MethodsA retrospective study of 15 of patients with dilated cardiomyopathy who had undergone full multiphase ECG gated cardiac CT. A comprehensive evaluation of mitral valve geometry was performed at 10 phases of the cardiac cycle using the recommended D-shaped mitral valve annulus (MA) segmentation model using manual and automated CT interpretation platforms. Mitral annular dimensions and geometries were compared between manual and automated methods. ResultsMitral valve dimensions in patients with dilated cardiomyopathy were similar to previously reported values (MAarea Diastole: 12.22 ± 1.90 cm2), with dynamic changes in size and geometry between systole and diastole of up to 5%. The distance from the centre of the MA to the left ventricular apex demonstrated moderate agreement between automated and manual methods (ρc = 0.90) with other measurements demonstrating poor agreement between the two methods (ρc = 0.75–0.86). ConclusionsVariability of mitral valve annulus measurements are small during the cardiac cycle. Novel automated algorithms to determine cardiac cycle variations in mitral valve geometry may offer improved segmentation accuracy as well as improved CT interpretation times.

Efficient flow diagnostics proxies for polymer flooding

Flow diagnostics refers to a family of numerical methods that within a few seconds can compute visually intuitive quantities illuminating flow patterns and well connections for full 3D reservoir models. The starting point is a flow field, extracted from a previous multiphase simulation or computed by solving a simplified pressure equation with fixed mobilities. Time-of-flight (TOF) and stationary tracer equations are then solved to determine approximate time lines and influence regions. From these, one can derive sweep or drainage regions, injector–producer regions, and well allocation factors, as well as dynamic heterogeneity measures that characterize sweep and displacement efficiency and correlate (surprisingly) well with oil recovery from waterflooding processes. This work extends flow diagnostics to polymer flooding. Our aim is to develop inexpensive flow proxies that can be used to optimize well placement, drilling sequence, and injection strategies. In particular, we seek proxies that can distinguish the effects of improved microscopic and macroscopic displacement. To account for the macroscopic effect of polymer injection, representative flow fields are computed by solving the reservoir equations with linearized flux functions. Although this linearization has a pronounced smearing effect on water and polymer fronts, we show that the heterogeneity of the total flux field is adequately represented. Subsequently, transform the flow equations to streamline coordinates, map saturations from physical coordinates to time-of-flight, and (re)solve a representative 1D flow problem for each well-pair region. A recovery proxy is then obtained by accumulating each 1D solution weighted by a distribution function that measures the variation in residence times for all flow paths inside each well-pair region. We apply our new approach to 2D and 3D reservoir simulation models, and observe close agreements between the suggested approximations and results obtained from full multiphase simulations. Furthermore, we demonstrate how two different versions of the proxy can be utilized to differentiate between macroscopic and microscopic sweep improvements resulting from polymer injection. For the examples considered, we demonstrate that macroscopic sweep improvements alone correlate better with measures for heterogeneity than the combined improvements.

High-Performance Modeling of Carbon Dioxide Sequestration by Coupling Reservoir Simulation and Molecular Dynamics

Summary The present work describes a parallel computational framework for carbon dioxide (CO2) sequestration simulation by coupling reservoir simulation and molecular dynamics (MD) on massively parallel high-performance-computing (HPC) systems. In this framework, a parallel reservoir simulator, reservoir-simulation toolbox (RST), solves the flow and transport equations that describe the subsurface flow behavior, whereas the MD simulations are performed to provide the required physical parameters. Technologies from several different fields are used to make this novel coupled system work efficiently. One of the major applications of the framework is the modeling of large-scale CO2 sequestration for long-term storage in subsurface geological formations, such as depleted oil and gas reservoirs and deep saline aquifers, which has been proposed as one of the few attractive and practical solutions to reduce CO2 emissions and address the global-warming threat. Fine grids and accurate prediction of the properties of fluid mixtures under geological conditions are essential for accurate simulations. In this work, CO2 sequestration is presented as a first example for coupling reservoir simulation and MD, although the framework can be extended naturally to the full multiphase multicomponent compositional flow simulation to handle more complicated physical processes in the future. Accuracy and scalability analysis are performed on an IBM BlueGene/P and on an IBM BlueGene/Q, the latest IBM supercomputer. Results show good accuracy of our MD simulations compared with published data, and good scalability is observed with the massively parallel HPC systems. The performance and capacity of the proposed framework are well-demonstrated with several experiments with hundreds of millions to one billion cells. To the best of our knowledge, the present work represents the first attempt to couple reservoir simulation and molecular simulation for large-scale modeling. Because of the complexity of subsurface systems, fluid thermodynamic properties over a broad range of temperature, pressure, and composition under different geological conditions are required, although the experimental results are limited. Although equations of state can reproduce the existing experimental data within certain ranges of conditions, their extrapolation out of the experimental data range is still limited. The present framework will definitely provide better flexibility and predictability compared with conventional methods.

A multi-component two-phase flow algorithm for use in landfill processes modelling

This paper describes the finite difference algorithm that has been developed for the flow sub-model of the University of Southampton landfill degradation and transport model LDAT. The liquid and gas phase flow components are first decoupled from the solid phase of the full multi-phase, multi-component landfill process constitutive equations and are then rearranged into a format that can be applied as a calculation procedure within the framework of a three dimensional array of finite difference rectangular elements.The algorithm contains a source term which accommodates the non-flow landfill processes of degradation, gas solubility, and leachate chemical equilibrium, sub-models that have been described in White and Beaven (2013).The paper includes an illustration of the application of the flow sub-model in the context of the leachate recirculation tests carried out at the Beddington landfill project. This illustration demonstrates the ability of the sub-model to track movement in the gas phase as well as the liquid phase, and to simulate multi-directional flow patterns that are different in each of the phases.

Comparison of single and two-phase models for nanofluid convection at the entrance of a uniformly heated tube

Macroscopic modeling of hydrodynamic and thermal behavior of nanofluid flows at the entry region of uniformly heated pipe is studied. Single-phase models with and without thermal dispersion effect, Eulerian–Eulerian, and Eulerian–Mixture two-phase models are evaluated by comparing predicted convective heat transfer coefficients and friction factors with experimental results from literature. Solutions with two different velocity–pressure coupling algorithms, Full Multiphase Coupled, and Phase Coupled Semi-Implicit Method for Pressure Linked Equations are also compared in terms of accuracy and computational cost. Dispersion model that uses velocity gradient to define dispersion conductivity is found to be more effective at entry region compared to other single-phase models. However, two-phase models predict convective heat transfer coefficient and friction factor more accurately at the entry region. Moreover, computational cost of Eulerian–Eulerian two-phase model can be reduced up to 50% by implementing Full Multiphase Coupled scheme.

The use of mixture model theory in CFD for the chemical reaction between CO2 and soda lime in closed circuit rebreather scrubbers

A mixture model simulation is presented by modeling the axial scrubber in a Closed Circuit Rebreather (CCR). The mixture model is a good substitute for the full Eulerian multiphase model because the interphase laws are unknown in this case. Analysis of mesh size, mesh type and inflation are made to independently characterize their accuracy by means of convergence before further comparisons with experimental data. The importance of mesh refinement is demonstrated near the wall with satisfactory results seen on the near grid wall of the boundary where a finer mesh is utilized. The contribution of inflation and grid independence to the accuracy of the model is presented in the results section.

Study of Flow Field, Power and Mixing Time in a Two-Phase Stirred Vessel with Dual Rushton Impellers: Experimental Observation and CFD Simulation

An agitated two-phase flow is studied numerically and experimentally in a mixing vessel agitated with two six-blade Rushton turbines. In Computational Fluid Dynamics (CFD), the full Eulerian multiphase approach coupled with the standard turbulence model is performed to deal with two-phase flow. The impeller rotation was modelled by the Multiple Reference Frame (MRF) approach. The simulation was used to investigate the flow field, power and mixing time in single and two-phase cases. The results of the calculations have been verified with the data that was measured by particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) technique. The predicted results show good agreement with the experimental data. The computational model presented in this study could be useful for explaining the two-phase flow patterns on the mixing process and extending the applications of multiphase stirred reactors.

Mixing and evaporation of liquid droplets injected into an air stream flowing at all speeds

This paper deals with the formulation, implementation, and testing of three numerical techniques based on (i) a full multiphase approach, (ii) a multisize-group (MUSIG) approach, and (iii) a heterogeneous MUSIG (H-MUSIG) approach for the prediction of mixing and evaporation of liquid droplets injected into a stream of air. The numerical procedures are formulated following an Eulerian approach, within a pressure-based fully conservative finite volume method equally applicable in the subsonic, transonic, and supersonic regimes, for the discrete and continuous phases. The k-ε two-equation turbulence model is used to account for the droplet and gas turbulence with modifications to account for compressibility at high speeds. The performances of the various methods are compared by solving for two configurations involving streamwise and cross-stream sprayings into subsonic and supersonic streams. Results, which are displayed in the form of droplet velocity vectors, contour plots, and axial profiles, indicate that solutions obtained by the various techniques exhibit a similar behavior. Differences in values are relatively small with the largest being associated with droplet volume fractions and vapor mass fraction in the gas phase. This is attributed to the fact that with MUSIG and H-MUSIG, no droplet diameter equation is solved and the diameter of the various droplet phases is held constant, as opposed to the full multiphase approach.

Numerical Analysis of a Two-Phase Flow and Mixing Process in a Stirred Tank

An agitated two-phase flow and the mixing progress in an oil-water stirred tank are studied numerically using FLUENT software. The stirred cylindrical tank is equipped with an axial-type turbine and a radial-type impeller. The full Eulerian multiphase approach coupled with the standard turbulence model is performed to deal with two-phase flow with a higher volume fraction of the second (dispersed) phase. The computation is completed by using unstructured meshes in a multiple reference frame (MRF). For the initial condition of the simulation, oil is set on the top part of the tank with 30% of the total fluid volume. The simulation is conducted to get distributions of two-phase flow speed, pressure and volume fraction and to successfully illustrate how the mixing of two-phase components progresses in the stirred tank. The computational results obtained in this study would be useful for explaining the two-phase flow patterns on the mixing process and extending the applications of multiphase stirred reactors.

The mechanical properties and corrosion behaviors of ultra-low carbon microalloying steel

The continuous cooling transformation (CCT) microstructure evolution in low carbon Mo–Nb–Cu–B microalloying steel (LCS) was investigated by thermo-simulation test. It was found that the full multi-phase of intermediate transformation products could be obtained at cooling rate greater than approximately 2 °C/s. In order to get bainitic microstructures, the thermo-mechanical control process (TMCP) was worked out according to CCT microstructure characteristics. After TMCP, 750 MPa grade steel twice over that of weathering steel 09CuPCrNi (WS) with ferrite and pearlite structures could be achieved. The corrosion behaviors of LCS and WS were also studied by wet-dry cycle corrosion test. The results showed that LCS had higher corrosion resistance than WS, attributed to suppression of the formation of pearlite.

A New Method for an Inhomogeneity with Stepwise Graded Interphase under Thermomechanical Loadings

The solution for a circular inhomogeneity embedded in an infinite elastic matrix with a multilayered interphase plays a fundamental role in many practical and theoretical problems. Therefore, improved analysis methods for this problem are of great interest. In this paper, a new procedure is presented to obtain the exact stress fields within the inhomogeneity and the matrix under thermomechanical loadings, without the need of solving the full multiphase composite problem. With this short-cut method, the problem is reduced to a single linear algebraic equation and two coupled linear algebraic equations which determine the only three real coefficients of the stress field within the inhomogeneity. In particular, the average stresses within the inhomogeneity can be calculated directly from the three real coefficients. Further, the other three unknown real coefficients associated with the stress field in the matrix can be determined subsequently. Hence, the influence of the stepwise graded interphase on the stress fields is manifested by its effect on the six real coefficients. All these results hold for stepwise graded interphase composed of any number of interphase layers. Several examples serve to illustrate the method and its advantages over other existing approaches. The explicit solutions are used to study the design of harmonic elastic inclusions, and the effect of a compliant interphase layer on thermal-mismatch induced residual stresses.

Macroscale continuum mechanics for multiphase porous-media flow including phases, interfaces, common lines and common points

This paper provides the tools needed for analysis of multiphase flow in porous media. Contributions are in four areas. First, theorems are provided that allow global scale integral equations to be localized at the porous medium scale. This is a more general approach than the traditional averaging of microscale point equations. Second, conservation equations for mass, momentum, energy and entropy for phases, interfaces, common lines, and common points are obtained. The inclusion of common lines and common points completes the full description of multiphase flow in porous media. Third, the entropy inequality is developed for the full multiphase system. The interaction terms between phases, interfaces, common lines, and common points provide a clear direction as to whether the entropy equation for each of these components may be used in the development of a constitutive theory or if the constitutive theory will depend on a combined entropy inequality statement. Fourth, the simplification of the system of equations is presented for the case of massless interfaces and common lines where these constituents are still capable of sustaining stress and containing energy. These latter forms are particularly useful in consideration of capillary pressure terms when the mass of the interface may be considered negligible.

An asymptotic theory for hot spot formation and transition to detonation for reactive granular materials

The transition to detonation in energetic granular materials is a complex multiphase process. The idea is proposed and developed that, under appropriate conditions, the resonant interaction of a fast-moving compaction burning front with a gas acoustic mode is an essential process in triggering the transition to detonation. The approach involves the study of solutions of a simple quantitative asymptotic model consisting of two nonlinear coupled partial differential equations that has been derived recently in an asymptotic limit from the full reactive multiphase equations. These equations retain some of the resonant mechanisms involving the gas acoustics and the compaction burn front. An analysis of the properties of solutions of the simplified system is developed. This analysis, involving simple resonant mechanisms, is able to qualitatively capture a number of phenomena observed in experiments and large-scale simulations for the equations for multiphase flow. The phenomena documented here include development of the transition to detonation in the region trailing the burning front, development of the resonant gas acoustic hot spot within the burning front, and stability of the fast moving burning front without transition. All these cases occur in the model in parameter regimes with physical significance that is identified through the asymptotic procedure.