Multiscale finite-volume method for density-driven flow in porous media

The multiscale finite-volume (MSFV) method has been developed to solve multiphase flow problems on large and highly heterogeneous domains efficiently. It employs an auxiliary coarse grid, together with its dual, to define and solve a coarse-scale pressure problem. A set of basis functions, which are local solutions on dual cells, is used to interpolate the coarse-grid pressure and obtain an approximate fine-scale pressure distribution. However, if flow takes place in presence of gravity (or capillarity), the basis functions are not good interpolators. To treat this case correctly, a correction function is added to the basis function interpolated pressure. This function, which is similar to a supplementary basis function independent of the coarse-scale pressure, allows for a very accurate fine-scale approximation. In the coarse-scale pressure equation, it appears as an additional source term and can be regarded as a local correction to the coarse-scale operator: It modifies the fluxes across the coarse-cell interfaces defined by the basis functions. Given the closure assumption that localizes the pressure problem in a dual cell, the derivation of the local problem that defines the correction function is exact, and no additional hypothesis is needed. Therefore, as in the original MSFV method, the only closure approximation is the localization assumption. The numerical experiments performed for density-driven flow problems (counter-current flow and lock exchange) demonstrate excellent agreement between the MSFV solutions and the corresponding fine-scale reference solution

Probability Density Function Modeling of Multi-Phase Flow in Porous Media with Density-Driven Gravity Currents

A probability density function (PDF) based approach is employed to model multi-phase flow with interfacial mass transfer (dissolution) in porous media. The joint flow statistics is represented by a mass density function (MDF), which is transported in the physical and probability spaces via Fokker-Planck equation. This MDF-equation requires Lagrangian evolutions of the random flow variables; these evolutions are stochastic processes honoring the micro-scale flow physics. To demonstrate the concept, we consider an example of immiscible two-phase flow with the non-equilibrium dissolution of single component from one phase into the other-a model for solubility trapping during CO2 storage in brine aquifer. Since CO2-rich brine is denser than pure brine, density-driven countercurrent flow is set up in the brine phase. The stochastic models mimicking the physics of countercurrent flow lead to a modeled MDF-equation, which is solved using our recently developed stochastic particle method for multi-phase flow (Tyagi etal. J Comput Phys 227:6696-6714, 2008). In addition, we derive Eulerian equations for stochastic moments (mean, variance, etc.) and show that unlike the MDF-equation the system of moment equations is not closed. In classical Darcy formulation, for example, the mean concentration equation is closed by neglecting variance. However, with several one- and two-dimensional simulations, it is demonstrated that the PDF and Darcy modeling approaches give significantly different results. While the PDF-approach properly accounts for the long correlation length scales and the concentration variance in density-driven countercurrent flow, the same phenomenon cannot be captured accurately with a standard Darcy mode

Energy Extraction from Onflow Inhomogeneity in the Spanwise Direction. A Theoretical Study

Potential of energy extraction from onflow inhomogeneity in spanwise direction was investigated theoretically. Trajectory optimization was performed for a 5 meter span UAV with morphing capability as well as without it. Results show that energy extraction from inhomogeneity in spanwise direction is of little practical relevance compared to gust soaring. Morphing can be effectively used for drag reduction and stabilization while flying in a turbulent windfiel

Joint PDF Closure of Turbulent Premixed Flames

In this paper, a novel model for turbulent premixed combustion in the corrugated flamelet regime is presented, which is based on transporting a joint probability density function (PDF) of velocity, turbulence frequency and a scalar vector. Due to the high dimensionality of the corresponding sample space, the PDF equation is solved with a Monte-Carlo method, where individual fluid elements are represented by computational particles. Unlike in most other PDF methods, the source term not only describes reaction rates, but accounts for "ignition” of reactive unburnt fluid elements due to propagating embedded quasi laminar flames within a turbulent flame brush. Unperturbed embedded flame structures and a constant laminar flame speed (as expected in the corrugated flamelet regime) are assumed. The probability for an individual particle to "ignite” during a time step is calculated based on an estimate of the mean flame surface density (FSD), latter gets transported by the PDF method. Whereas this model concept has recently been published [21], here, a new model to account for local production and dissipation of the FSD is proposed. The following particle properties are introduced: a flag indicating whether a particle represents the unburnt mixture; a flame residence time, which allows to resolve the embedded quasi laminar flame structure; and a flag indicating whether the flame residence time lies within a specified range. Latter is used to transport the FSD, but to account for flame stretching, curvature effects, collapse and cusp formation, a mixing model for the residence time is employed. The same mixing model also accounts for molecular mixing of the products with a co-flow. To validate the proposed PDF model, simulation results of three piloted methane-air Bunsen flames are compared with experimental data and very good agreement is observe

Probability density function approach for modelling multi-phase flow with ganglia in porous media

A probabilistic approach to model macroscopic behaviour of non-wetting-phase ganglia or blobs in multi-phase flow through porous media is proposed. The key idea is to consider a set of stochastic Markov processes that can mimic the microscopic multi-phase dynamics. These processes are characterized by equilibrium probability density functions (PDFs) and correlation times, which can be obtained from micro-scale simulation studies or experiments. A Lagrangian viewpoint is adopted, where stochastic particles represent infinitesimal fluid elements and evolve in the physical and probability space. Ganglion mobilization and trapping are modelled by a two-state jump process with transition probabilities given as functions of ganglion size. Coalescence and breakup of ganglia influence the ganglion size distribution, which is modelled by a Langevin type equation. The joint probability density function (JPDF) of the chosen stochastic variables is governed by a high-dimensional Chapman-Kolmogorov equation. This equation can be used to derive moment (e.g. saturation, mean mobility etc.) transport equations, which in general do not form a closed system. However, in some special cases, which arise in the limit of one time scale being smaller or larger than the others, a closed set of moment transport equations can be obtained. For slowly varying and quasi-uniform flows, the saturation transport equation appears in closed form with the mean mobility fully determined, if the equilibrium PDFs are known. Furthermore, it is shown how statistical parameters such as mobilization and trapping rates and equilibrium PDFs can be obtained from the birth-death type approach, in which ganglia breakup and coalescence are explicitly considered. A two-equation transport model (one equation for the total saturation and one for the trapped saturation) is obtained in the limit of very fast coalescence and breakup processes. This model is employed to mimic hysteresis in relative permeability-saturation curves; a well known phenomenon observed in the successive processes of imbibition and drainage. For the general case, the JPDF-equation is solved using the stochastic particle method, which was proposed in our previous paper (Tyagi etal.J.Comput.Phys.227, 2008, 6696-6714). Several one- and two-dimensional numerical simulation results are presented to show the influence of correlation times on the averaged macroscopic flow behaviou

Variational assimilation of sparse time-averaged data for efficient adjoint-based optimization of unsteady RANS simulations

Data assimilation (DA) plays a crucial role in extracting valuable information from flow measurements in fluid dynamics problems. Often only time-averaged data is available, which poses challenges for DA in the context of unsteady flow problems. Recent works have shown promising results in optimizing Reynolds-averaged Navier-Stokes (RANS) simulations of stationary flows using sparse data through variational data assimilation, enabling the reconstruction of mean flow profiles. In this study we perform three-dimensional variational data assimilation of sparse time-averaged data into an unsteady RANS (URANS) simulation by means of a stationary divergence-free forcing term in the URANS equations. Efficiency and speed of our method are enhanced by employing coarse URANS simulations and leveraging the stationary discrete adjoint method for the time-averaged URANS equations. The data assimilation codes were developed in-house using OpenFOAM for the URANS simulations as well as for the solution of the adjoint problem, and Python for the gradient-based optimization. Our results demonstrate that data assimilation of sparse time-averaged velocity measurements not only enables accurate mean flow reconstruction, but also improves the flow dynamics, specifically the vortex shedding frequency. To validate the efficacy of our approach, we applied it to turbulent flows around cylinders of various shapes at Reynolds numbers ranging from 3000 to 22000. Our findings indicate that data points near the cylinder play a crucial role in improving the vortex shedding frequency, while additional data points further downstream are necessary to also reconstruct the time-averaged velocity field in the wake region

Stress Urinary Incontinence post-Holmium Laser Enucleation of the Prostate: a Single-Surgeon Experience.

PURPOSE: To identify incidence and predictors of stress urinary incontinence (SUI) following Holmium laser enucleation of the prostate (HoLEP). MATERIALS AND METHODS: We performed a retrospective review of 589 HoLEP patients from 2012-2018. Patients were assessed at pre-operative and post-operative visits. Univariate and multivariate regression analyses were performed to identify predictors of SUI. RESULTS: 52/589 patients (8.8%) developed transient SUI, while 9/589 (1.5%) developed long-term SUI. tSUI resolved for 46 patients (88.5%) within the first six weeks and in 6 patients (11.5%) between 6 weeks to 3 months. Long-term SUI patients required intervention, achieving continence at 16.4 months on average, 44 men (70.9%) with incontinence were catheter dependent preoperatively. Mean prostatic volume was 148.7mL in tSUI patients, 111.6mL in long-term SUI, and 87.9mL in others (p \u3c 0.0001). On univariate analysis, laser energy used (p \u3c 0.0001), laser on time (p=0.0204), resected prostate weight (p \u3c 0.0001), overall International Prostate Symptom Score (IPSS) (p=0.0005), and IPSS QOL (p=0.02) were associated with SUI. On multivariate analysis, resected prostate weight was predictive of any SUI and tSUI, with no risk factors identified for long-term SUI. CONCLUSION: Post-HoLEP SUI occurs in ~10% of patients, with 1.5% continuing beyond six months. Most patients with tSUI recover within the first six weeks. Prostate size \u3e100g and catheter dependency are associated with increased risk tSUI. Larger prostate volume is an independent predictor of any SUI, and tSUI

Nursing sensitive outcomes: identifying a definition, exploration of conceptual challenges and an overview of the literature

Introduction/background: A literature review on nursing sensitive outcomes has been conducted as part of a larger research project. The literature was reviewed to: - identify a definition of nursing sensitive outcomes - determine the conceptual models used to describe nursing sensitive outcomes - identify significant contributions made by researchers on the development and use of nursing sensitive outcomes in clinical practice.The overall aim of the research project is to develop a set of indicators that provides a balanced view of nursing care and its contribution to patient outcomes. It is anticipated that this research will broaden the debate on nursing sensitive outcomes so that the contribution that nursing care makes to patient outcomes is able to be identified and measured

Robust variational data assimilation of sparse velocity reference data in RANS simulations through a divergence-free forcing term

The Reynolds-averaged Navier-Stokes (RANS) equations offer a computationally efficient way of solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can compromise their accuracy. In order to address this issue, recent research has explored data-driven techniques like data assimilation and machine learning. We present an efficient variational data assimilation (DA) approach to enhance steady-state RANS simulations based on eddy viscosity closure models. Our method introduces a corrective forcing term based on a potential field that is divergence-free and enhances simulation accuracy. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation. The implementation is built on a two-dimensional coupled RANS solver in \emph{OpenFOAM}, which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is employed to minimize the difference between the simulation results and the reference data. To assess this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the DA, sparsely distributed data from averaged high-fidelity simulation results are used. The findings indicate that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. It is sturdy with respect to varying the regularization parameters and the number of reference data points, and runs efficiently by leveraging coarse meshes.Comment: 23 pages, 13 figure