Finite Volume Computational Fluid Dynamics Research Articles

CPU–GPU heterogeneous code acceleration of a finite volume Computational Fluid Dynamics solver

This research focuses on accelerating the finite-volume Computational Fluid Dynamics (CFD) solver, SENSEI, through concurrent CPU–GPU heterogeneous computing, leveraging multiple CPUs and GPUs. An overview of SENSEI, its discretization, and the heterogeneous computing workflow utilizing MPI and OpenACC are provided. A performance model for CPU–GPU heterogeneous computing, incorporating ghost cell exchange usually applied in stencil computations, is introduced to estimate the performance. This work explores the scaling performance of CPU–GPU heterogeneous computing in comparison to a pure multi-CPU/GPU setup using a supersonic inlet test case. The results emphasize the advantages of leveraging both CPU and GPU computational power concurrently. Highlighting the collaborative synergy of CPUs and GPUs as co-workers, this work shows improved performance over exclusive use of pure CPUs or GPUs, with the proposed performance model ensuring a fair estimation of these advantages. This work concludes by offering suggestions for application users interested in accelerating scientific computing simulations and providing feedback for hardware architects designing improved CPU–GPU heterogeneous systems for heterogeneous computing.

CFD assessment of RANS turbulence modeling for solidification in internal flows against experiments and higher fidelity LBM-LES phase change model

Generation-IV nuclear reactors’ potential coolant candidates include molten salts and liquid metals. Owing to their high melting temperature, both the design and safety assessments of these reactors need to take into consideration potential solidification events during normal or abnormal operation. This work assesses the Finite Volume Computational Fluid Dynamics (FV-CFD) enthalpy-porosity method combined with the Reynolds Averaged Navier Stokes (RANS) model k−ω to model internal solidification under turbulent flow conditions for high and low Prandtl numbers at a moderate computational cost, which is required for full-core nuclear reactor analyses. Concerning high Prandtl numbers, the predictions of macroscopic quantities generated by the FV-CFD RANS model are contrasted against a well-known internal solidification experiment on water (Thomason et al., 1978). A key factor in the satisfactory agreement between the CFD RANS model and the experiment is the addition of an interface turbulence-damping source to the specific dissipation rate equation (ω). For the low Prandtl numbers involved in liquid metals, there is a lack of high-fidelity experiments due to the complicated measurements. Thus, to perform the FV-CFD RANS model assessment, we develop and validate a high-fidelity phase-change model based on the Lattice Boltzmann Method (LBM) with a Large Eddy Simulation (LES) turbulence model. To the author’s knowledge, this is the first attempt to integrate LES turbulence models with phase-change solidification in the LBM context. Considering the computational time advantage of the FV-CFD RANS model over higher fidelity models and the good agreement of its predictions against experiments and the LES model demonstrated, this work demonstrates that FV-CFD RANS is an attractive tool to model internal turbulent solidification.

Simulating the Effect of Electric Bias Voltages on the Electrical Characteristics of Oxyfuel Preheat Flame Using Reduced Combustion Mechanism

Abstract A three-dimensional computational model is presented in this paper that illustrates the detailed electrical characteristics, and the current–voltage (i–v) relationship throughout the preheating process of premixed methane-oxygen oxyfuel cutting flame subject to electric bias voltages. As such, the equations describing combustion, electrochemical transport for charged species, and potential are solved through a commercially available finite volume computational fluid dynamics (CFD) code. The reactions of the methane-oxygen (CH4–O2) flame were combined with a reduced mechanism, and additional ionization reactions that generate three chemi-ions, H3O+, HCO+, and e−, to describe the chemistry of ions in flames. The electrical characteristics such as ion migrations and ion distributions are investigated for a range of electric potential, V ∈ [−5 V, +5 V]. Since the physical flame is comprised of twelve Bunsen-like conical flames, inclusion of the third dimension imparts the resolution of fluid mechanics and the interaction among the individual cones. It was concluded that charged “sheaths” are formed at both torch and workpiece surfaces, subsequently forming three distinct regimes in the i–v relationship. The i–v characteristics obtained from this study have been compared to the previous experimental and two-dimensional computational model for premixed flame. In this way, the overall model generates a better understanding of the physical behavior of the oxyfuel-cutting flames, along with more validated i–v characteristics. Such understanding might provide critical information toward achieving an autonomous oxyfuel-cutting process.

Advanced Lubrication Simulations of an Entire Test Rig: Optimization of the Nozzle Orientation to Maximize the Lubrication Capability

In the framework of the H2020 project IDERPLANE, aimed at providing innovative, effective, and validated criteria for the design and assessment of more reliable planet bearings for aerospace application analyzing the problem from a damage tolerance perspective, the present paper presents the numerical study and optimization of a test rig specifically designed for the experiments on the full-test article. Specifically, for the first time ever, an entire system including shafts, gears and bearings with all the rolling elements have been studied with a Finite Volume Computational Fluid Dynamics approach. This ambitious challenge was addressed with the implementation of a new mesh handling technique, namely the Global Remeshing Approach with Mesh Clustering (GRAMC). The aim was to optimize the lubrication of the test article to avoid unexpected failures during the experimental campaign. Three different oil jet directions have been studied and the most effective one, namely the axial one, was selected for the final test rig design.

Lattice Boltzmann solidification modeling of forced convection internal flows applied to Gen-IV nuclear reactor coolants

Generation-IV nuclear reactors involve novel coolants such as molten salts and lead. One of the issues that must be assessed with these coolants is the risk of solidification during reactor operation owing to their high melting temperature. However, the numerical simulation of solidification problems is computationally demanding. In this work, we assess the applicability of Lattice Boltzmann Method (LBM) to nuclear coolants solidification problems under laminar internal forced flow conditions. The double distribution Total Enthalpy-Partially Saturated Method is implemented in the open-source code OpenLB and compared against more standard Finite-Volume Computational Fluid Dynamics (FV-CFD) results, which uses the enthalpy-porosity Eulerian Multiphase method, in commercial code Star-CCM+. The test cases comprise the solidification of two fluids with significantly different Prandtl numbers, molten salt and lead, in a 3D pipe geometry in laminar flow conditions with an initial Reynolds number of 100. The solid interface advances from the cooled wall towards the bulk of the pipe reducing the area of flow passage as the transient evolves. Results of LBM velocity fields, solid fraction profiles, temperature fields, and pressure fields are in good agreement with FV-CFD results for both coolants. Furthermore, LBM stability and accuracy limits are independently explored for molten salts and lead using Two-Relaxation Time (TRT) and Bhatnagar-Gross-Krook (BGK) collision operators. Simulation time between FV-CFD and LBM is also contrasted for both coolants. In this work, LBM solvers use explicit time schemes with a regular grid, whereas FV-CFD solutions are able to include implicit time schemes and near-wall mesh refinement. For molten salt flows (high Prandtl number) FV-CFD allows for considerably larger timesteps than LBM, which is limited by the maximum lattice Mach number limitation and stability considerations. For lead flows (low Prandtl number), the implicit scheme in FV-CFD is limited in terms of accuracy for large timesteps due to the limiting Fourier-number. On the other hand, LBM does not present notable stability issues for lead and the lattice Mach number limit is not as relevant as for the molten salt case for this Reynolds number, allowing for faster simulation times than FV-CFD.

Analysis of heat transfer enhancement due to helical static mixing elements inside cooling channels in machine tools

In this contribution, the effectiveness of helical static mixers in different arrangements and flow configurations/regimes is explored. By means of a thorough numerical analysis, the application limits of helical static mixers for the heat transfer enhancement inside cooling channels of machine tools are provided. The numerical simulations were processed with the commercial finite volume Computational Fluid Dynamics (CFD) code, ANSYS Fluent 2020 R2. This study shows that there exists an optimal range of application for static mixers as heat exchange intensifier depending on the flow speed, the transmitted heat flow and the thermal conductivity of the tool. The investigations of this contribution are restricted to single-phase flow in circular cross-sections and straight channel geometries. As a representative application example for a machine tooling, the cooling of a simple injection mold is investigated. The research carried out reveals that the application of static mixing elements for enhancement of heat transfer is very effective, particularly for fluid flow with low to medium Reynolds numbers, close-contour cooling, high values of heat fluxes, and high thermal conductivity of the tooling material.

On the Effectiveness of Scale-Averaged RANS and Scale-Resolved IDDES Turbulence Simulation Approaches in Predicting the Pressure Field over a NASCAR Racecar

Racecar aerodynamic development requires well-correlated simulation data for rapid and incremental development cycles. Computational Fluid Dynamics (CFD) simulations and wind tunnel testing are industry-wide tools to perform such development, and the best use of these tools can define a race team’s ability to compete. With CFD usage being limited by the sanctioning bodies, large-scale mesh and large-time-step CFD simulations based on Reynolds-Averaged Navier–Stokes (RANS) approaches are popular. In order to provide the necessary aerodynamic performance advantages sought by CFD development, increasing confidence in the validity of CFD simulations is required. A previous study on a Scale-Averaged Simulation (SAS) approach using RANS simulations of a Gen-6 NASCAR, validated against moving-ground, open-jet wind tunnel data at multiple configurations, produced a framework with good wind tunnel correlation (within 2%) in aerodynamic coefficients of lift and drag predictions, but significant error in front-to-rear downforce balance (negative lift) predictions. A subsequent author’s publication on a Scale-Resolved Simulation (SRS) approach using Improved Delayed Detached Eddy Simulation (IDDES) for the same geometry showed a good correlation in front-to-rear downforce balance, but lift and drag were overpredicted relative to wind tunnel data. The current study compares the surface pressure distribution collected from a full-scale wind tunnel test on a Gen-6 NASCAR to the SAS and SRS predictions (both utilizing SST k−ω turbulence models). CFD simulations were performed with a finite-volume commercial CFD code, Star-CCM+ by Siemens, utilizing a high-resolution CAD model of the same vehicle. A direct comparison of the surface pressure distributions from the wind tunnel and CFD data clearly showed regions of high and low correlations. The associated flow features were studied to further explore the strengths and areas of improvement needed in the CFD predictions. While RANS was seen to be more accurate in terms of lift and drag, it was a result of the cancellation of positive and negative errors. Whereas IDDES overpredicted lift and drag and requires an order of magnitude more computational resources, it was able to capture the trend of surface pressure seen in the wind tunnel measurements.

Reliable renewable power production by modeling of geothermal assisted solar chimney power plant

The growing concern about the impact of climate change has highlighted the importance of renewable resources. Wind, geothermal, and solar energy are some of the most natural renewable energy sources, dominated by their availability and efficiency. Currently, medium-low enthalpy geothermal is exploited less than high-enthalpy geothermal resources. In addition, the variable nature of solar radiation is a significant problem for the solar systems resulting from the solar chimney power plant's discontinued operation. These geothermal resources can feed into the solar chimney power plant to generate electricity and resolve the solar system discontinuously. In the present research, a geothermal hot spring with a temperature of 75 °C in Khorasan, Iran, has been investigated as a case study. By developing a finite volume Computational Fluid Dynamics model, the system performance has been evaluated. Hybridizing these two energy sources declares a significant improvement in the power plant's performance. Increasing the thermal flux of hybrid systems by 200 kW/m2 designates a 17% increase in power generation of the geothermal-solar system at a specific hour of the day, in comparison with a stand-alone solar chimney. Moreover, a geothermal–solar chimney power plant in the coldest month of the year showed the same output power as solar chimney power plants could generate in the warmest month of the year. Annual averaged thermal flux productivity under the hybrid system is 585.12% larger than sole geothermal spring production. The hybrid system model produces 319.5 MWh while the stand-alone system generates 263.9 MWh of energy throughout the year. Economic analysis shows that the proposed system is one-tenth affordable considering energy prices in Iran.

Neural-network-based Riemann solver for real fluids and high explosives; application to computational fluid dynamics

The Riemann problem is fundamental to most computational fluid dynamics (CFD) codes for simulating compressible flows. The time to obtain the exact solution to this problem for real fluids is high because of the complexity of the fluid model, which includes the equation of state; as a result, approximate Riemann solvers are used in lieu of the exact ones, even for ideal gases. We used fully connected feedforward neural networks to find the solution to the Riemann problem for calorically imperfect gases, supercritical fluids, and high explosives and then embedded these network into a one-dimensional finite volume CFD code. We showed that for real fluids, the neural networks can be more than five orders of magnitude faster than the exact solver, with prediction errors below 0.8%. The same neural networks embedded in a CFD code yields very good agreement with the overall exact solution, with a speed-up of three orders of magnitude with respect to the same CFD code that use the exact Riemann solver to resolve the flux at the interfaces. Compared to the Rusanov flux reconstruction method, the neural network is half as fast but yields a higher accuracy and is able to converge to the exact solution with a coarser grid.

CFD simulation of floating body motion with mooring dynamics: Coupling MoorDyn with OpenFOAM

It is increasingly popular to use Computational Fluid Dynamics (CFD) models to study floating structures subjected to ocean waves, especially when it comes to applications of floating offshore wind turbines and Wave Energy Converters (WECs). Mooring dynamics are currently lacking in most of these applications. This paper presents a coupled simulation study of moored floating body motion by coupling two open-source libraries: a finite volume CFD toolbox, OpenFOAM, and a lumped-mass mooring model, MoorDyn. The instantaneous floating body position and velocity are passed from the body motion solver in the CFD model to the mooring model to calculate the fairlead kinematics. The mooring reaction forces, which are calculated by MoorDyn after updating the mooring system states, are then returned to the body motion solver to update the floating body motion. Both mesh deformation and overset mesh methods are used as the mesh motion solver in the CFD model to account for the floating body motion. The coupled model was validated against experimental measurements for a floating box moored with four catenary lines under the action of regular waves, which came from a preliminary test campaign for WECs. Apart from the lumped-mass mooring model, the present work also coupled a quasi-static mooring model and a finite element model with the floating body motion solver in OpenFOAM. The mooring line tensions predicted by these models were compared. The coupled model equipped with three mooring line codes may be further used to carry out survivability studies of FOWTs and WECs subject to severe sea states.

Mini-Hydropower Plant Based on Lenyov Hydrobelt and Volume-Sectional Hydraulic Engine

The use of the energy of small watercourses with the help of small hydropower plants is one of the promising directions for the development of renewable energy. This article presents the designs of two different hydraulic engines, each of which has its own advantage. Therefore, the task of calculating the real parameters of the design of a mini-hydropower plant based on Lenyov hydrobelt has been solved. Theoretical calculations were validated numerically by the finite volume method and computational fluid dynamics modeling; both methods gave similar results. According to the results of calculations, this design based on the Lenyov hydrobelt with the capacity of 16 kW is advisable to place in a river with a flow velocity of at least 4.5 m/s. The article also presents an alternative type of developed mini-hydropower plant, -a volume-sectional hydraulic engine. The proposed rotary-type positive displacement hydraulic engine can operate at low pressure on a flat surface. The advantage of the hydraulic engine is the sectional operation of several working chambers. It was established that a high water velocity and a large volume of passing water was not required. The total force acting in the hydraulic engine is 5430.19 N. Due to the use of conical inlet channels, the water flow velocity was increased and the water flow became directional. The frequency of rotation of the hydraulic engine shaft at a river flow velocity of 4 m/s was 60.43 rpm. The received power in these modes was 22.25 kW.

Coupling Lattice-Boltzmann and Finite Volume CFD Methods for Efficient Co-Simulation of Two-Phase Flow in the Porous Transport Layers of PEM Water Electrolyzers

Polymer electrolyte membrane water electrolysis (PEMWE) can be modeled using computational fluid dynamics (CFD) for research and development purposes. Continua that contain multiple phases or represent porous media are typically treated as homogeneous regions with bulk-average properties. Per this assumption, the finite volume method (FVM) can be employed to solve such problems with simple geometries. This is computationally inexpensive, and it can be utilized to assist the design of macroscopic cell components such as flow fields. However, this method is limited in its ability to link porous transport layer (PTL) morphology to local phase composition and cell performance.The Lattice-Boltzmann method (LBM) has demonstrated the ability to accurately simulate two-phase flow in detailed porous media for fuel cells1,2. Being a particle-based CFD method enables it to resolve the liquid/gas interphase within the pores of replica PTL samples at higher computing speed than other methods. Figure 1 shows an example of oxygen evolution inside the Ti powder PTL sample for a PEMWE device at an average current density of 2 A/cm2. This outcome can aid in the development of porous media for both fuel cell and electrolysis applications3.We always strive to build the simplest possible models that fully describe a system at the length scale of interest. Macroscale FVM simulations can be used to aid the investigation of porous media properties and morphology by providing a realistic current distribution. Meanwhile, experimentally validated LBM simulations produce output data that are useful for modeling two-phase flow in a homogeneous region using the FVM. Satjaritanun, S. Hirano, I. V. Zenyuk, J. W. Weidner, N. Tippayawong, and S. Shimpalee, J. Electrochem. Soc., 167, 013516 (2019).Satjaritanun, S. Hirano, A. D. Shum, I. V. Zenyuk, A. Z. Weber, J. W. Weidner, and S. Shimpalee, J. Electrochem. Soc., 165, F1115 (2018).Satjaritanun, M. O'Brien, D. Kulkarni, S. Shimpalee, C. Capuano, K. E. Ayers, N. Danilovic, D. Y. Parkinson, and I. V. Zenyuk, iScience, 12, 101783 (2020). Figure 1

Development and Validation of an Aerothermoelastic Analysis Capability

Coupled aerothermoelastic simulations are required for the accurate simulation of many high-speed flow problems. Hence, the multidisciplinary analysis of such problems is the main focus of the current work. In this study, flow simulations are carried out using a three-dimensional implicit finite volume computational fluid dynamics solver developed in house that has been well tested and validated through numerous previous studies. For the thermal and structural solutions, a finite element solver is used, which is also developed and validated in house. The coupled aerothermoelastic platform is validated in this work through two applications. In the first application, we compare computed solutions for flow over a hypersonic cylindrical leading edge with available experimental data. In the second application, we look at solutions for flow over an aerodynamically heated panel.

Verification of multiphysics coupling techniques for modeling of molten salt reactors

Crucial to the development of molten salt reactor (MSR) designs is the application of multiphysics codes to model the tightly coupled neutronics and thermal-hydraulics behaviour of the liquid fuel. However, the verification and validation of such codes is not a trivial task, in particular for fast reactor designs, where no experimental data are available. In absence of experimental data, a benchmark was developed by LPSC/CNRS-Grenoble for multiphysics codes dedicated to MSR studies. In this study we present two independent multiphysics approaches and apply them to this benchmark. The first approach utilizes the Serpent2 multiphysics interface, allowing for high fidelity coupling of the finite volume computational fluid dynamics code OpenFOAM and Serpent2. In this approach, Serpent2 serves as the neutronics solver and is coupled to an OpenFOAM based thermal-hydraulics solver and supplemented by a delayed neutron precursors transport solver implemented in OpenFOAM. The main advantage of this coupling approach is that it allows for using a high accuracy Monte-Carlo approach to solve the neutron transport equations. The second approach is a novel approach that utilizes the SEALION framework. The SEALION code employs a specialized thermal hydraulics solver based on OpenFOAM, coupled with a custom-made modified point kinetics neutronics solver, that explicitly accounts for the altered neutron importance due to the transport of delayed neutron precursors. The main advantage of this approach is that it allows for a pre-determination of the temperature feedback effects using Monte-Carlo codes, such as Serpent2. Both approaches are verified against results from the benchmark and the overall agreement between the results demonstrates the validity of both approaches.

Effects of mesh loop modes on performance of unstructured finite volume GPU simulations

In unstructured finite volume method, loop on different mesh components such as cells, faces, nodes, etc is used widely for the traversal of data. Mesh loop results in direct or indirect data access that affects data locality significantly. By loop on mesh, many threads accessing the same data lead to data dependence. Both data locality and data dependence play an important part in the performance of GPU simulations. For optimizing a GPU-accelerated unstructured finite volume Computational Fluid Dynamics (CFD) program, the performance of hot spots under different loops on cells, faces, and nodes is evaluated on Nvidia Tesla V100 and K80. Numerical tests under different mesh scales show that the effects of mesh loop modes are different on data locality and data dependence. Specifically, face loop makes the best data locality, so long as access to face data exists in kernels. Cell loop brings the smallest overheads due to non-coalescing data access, when both cell and node data are used in computing without face data. Cell loop owns the best performance in the condition that only indirect access of cell data exists in kernels. Atomic operations reduced the performance of kernels largely in K80, which is not obvious on V100. With the suitable mesh loop mode in all kernels, the overall performance of GPU simulations can be increased by 15%-20%. Finally, the program on a single GPU V100 can achieve maximum 21.7 and average 14.1 speed up compared with 28 MPI tasks on two Intel CPUs Xeon Gold 6132.

A virtual sensor simulation system of a flower greenhouse coupled with a new temperature microclimate model using three-dimensional CFD

Greenhouse culture, as a high-yield and efficient production technology, has become an important means to increase crop yield and quality. Greenhouse environmental monitoring is a key practice affecting the yield and quality of greenhouse crops. Meeting the growth needs of crops while reducing the cost of environmental monitoring has become an urgent and difficult scientific problem. Sensor technology with the addition of computational fluid dynamics (CFD) technique is a new method for addressing this issue. However, this CFD approach generally cannot monitor the greenhouse environment in real time. This study aims to establish a virtual sensor system based on the external environment of a climate model to form a closed-loop network using a finite volume CFD code (ANSYS FLUENT 19.0). An experiment is conducted on a flower greenhouse, and a 3D transient CFD is implemented including a meshing and turbulence model in the MATLAB interface program. Furthermore, a temperature model based on the external greenhouse environment is established using a regression method from the model, and a virtual sensor model of greenhouse temperature is established using a feedback method. The results show that the simulation satisfied the temperature distribution law, revealing that virtual sensors and physical sensors can work together to monitor the greenhouse environment.

Numerical simulations of flow patterns in the human left ventricle model with a novel dynamic mesh morphing approach based on radial basis function

We present a new numerical simulation framework for prediction of flow patterns in the human left ventricle model. In this study, a radial basis function (RBF) mesh morphing method is developed and applied within the finite-volume computational fluid dynamics (CFD) approach. The numerical simulations are designed to closely mimic details of recent tomographic particle image velocimetry (TomoPIV) experiments. The numerically simulated dynamic motions of the left ventricle and tri-leaflet biological mitral valve are emulated through the RBF morphing method. The arbitrary Lagrangian-Eulerian (ALE) based CFD is performed with the RBF-defined deforming wall boundaries. The results obtained show a good agreement with experiments, confirming the reliability and accuracy of the developed simulation framework.

Stress-Blended Eddy Simulation/Flamelet Generated Manifold Simulation of Film-Cooled Surface Heat Transfer and Near-Wall Reaction

Abstract Accurate numerical prediction of surface heat transfer in the presence of film cooling within aero-engine sub-components, such as blade effusion holes and combustor liners, has long been a goal of the aero-engine industry. It requires accurate simulation of the turbulent mixing and reaction processes between freestream and the cooling flow. In this study, the stress-blended eddy simulation (SBES) turbulence model is used together with the flamelet generated manifold (FGM) combustion model to calculate the surface heat flux upstream and downstream of an effusion cooling hole. The SBES model employs a blending function to automatically switch between Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) based on the local flow features, and thus significantly reduces the computational cost compared to a full LES simulation. All simulations are run using ansys fluent®, a commercial finite-volume computational fluid dynamics (CFD) solver. The test case corresponds to an experimental rig run at Massachusetts Institute of Technology (MIT), which is essentially a flat plate brushed by a uniform freestream of argon with ethylene seeded inside, and is cooled by either a reacting air or a non-reacting nitrogen jet inclined at 35 deg to the freestream. Calculations are performed for both reacting and non-reacting jet cooling cases across a range of jet-to-stream blowing ratios and compared with the experimental data. The effects of mesh resolution are also investigated. Calculations are also performed across a range of Damköhler number (i.e., flow to chemical time ratio) from zero to 30, with unity blowing ratio, and the differences in the maximum surface heat flux magnitude in the reacting and non-reacting cases at a specific location downstream of the hole are investigated. Results from these analyses show good correlation with the experimental heat flux data upstream and downstream of the cooling hole, including the heat flux augmentation due to local reaction. Results from the Damköhler number sweep also show a good match with the experimental data across the range investigated.

Development of a coupling between a system thermal–hydraulic code and a reduced order CFD model

The nuclear community has coupled several three-dimensional Computational Fluid Dynamics (CFD) solvers with one-dimensional system thermal–hydraulic (STH) codes. This work proposes to replace the CFD solver by a reduced order model (ROM) to reduce the computational cost. The system code RELAP5-MOD3.3 and a ROM of the finite volume CFD solver OpenFOAM are coupled by a partitioned domain decomposition coupling algorithm using an implicit coupling scheme. The velocity transported over a coupling boundary interface is imposed in the ROM using a penalty method. The coupled models are evaluated on open and closed pipe flow configurations. The results of the coupled simulations with the ROM are close to those with the CFD solver. Also for new parameter sets, the coupled RELAP5/ROM models are capable of predicting the coupled RELAP5/CFD results with good accuracy. Finally, coupling with the ROM is 3–5 times faster than coupling with the CFD solver.

Comparison of pore-scale capillary pressure to macroscale capillary pressure using direct numerical simulations of drainage under dynamic and quasi-static conditions

Conventional macroscale two-phase flow equations for porous media (such as Darcy's law and Richards Equation) require a constitutive relation for capillary pressure (Pc). The capillary pressure relation significantly impacts the behavior and prediction of fluid flow in porous media, and needs to accurately characterize the capillary forces. In a typical laboratory experiment, a functional macroscopic capillary pressure-saturation (Pc-Sw) relationship is measured as the difference between the pressures of the non-wetting-phase reservoir at the inlet (Pnw) and wetting-phase reservoir at the outlet (Pw) of a porous medium. It is well-known that this traditional macroscopic capillary pressure definition is valid only at equilibrium conditions and if the phases are connected. Under non-equilibrium (dynamic) conditions, when the fluids are moving, the macroscopic capillary pressure measured in experiments implicitly includes the pressure head caused by viscous effects.The goal of the present effort is to understand how well the traditional macroscopic capillary pressure definition represents the pore-scale capillary forces under different flow conditions. Using direct numerical simulations (DNS) of two-phase flow in a porous medium, we evaluate the capillary pressure at the pore-scale, and compare it to the macroscopic capillary pressure, Pc(Sw), that is typically measured in experiments using pressure transducers. The pore-scale capillary pressure is the pressure difference across the interface between two fluids as the fluids move through a porous medium; the interface pressure differences at fluid-fluid invasion front are averaged across all the pores of the porous medium to yield a representative pore-scale capillary pressure curve, referred to as the interface capillary pressure. The pore-scale interface capillary pressure represents the “true” capillary forces in the system, since depends only on the pore morphology (shape) and interfacial energy of the two fluids, and does not account for the viscous dissipation. In experiments it is difficult to measure the interface capillary pressure jump without accounting for the viscous pressure head, which is at least an order of magnitude larger. Upscaling the pore-scale capillary pressure is an essential step for complete characterization of capillary-dominant two-phase flow in a porous medium at the laboratory scale.Drainage is simulated under equilibrium (quasi-static) and non-equilibrium (dynamic) conditions for various capillary numbers. The Navier–Stokes (NS) equations are solved in the pore space using the open-source finite-volume computational fluid dynamics (CFD) code, OpenFOAM. The Volume-of-Fluid (VOF) method is employed to track the evolution of the fluid–fluid interfaces, and a contact angle is used to account for the effect of wall adhesion. The simulations are first validated with published experimental data for dynamic and quasi-static drainage in a micromodel. From the microscale simulations, the interface capillary pressure is determined, and compared to the macroscopic capillary pressure under equilibrium and non-equilibrium conditions. Our results show the traditionally-measured macroscopic capillary pressure curves exhibit a strong dependence on the capillary number under dynamic flow conditions. In contrast, the interface capillary pressure-saturation relation, which relies on pore-scale pressure differences at the invasion front, is almost invariant of flow conditions (dynamic and quasi-static).