Grid Sensitivity Study Research Articles

Grid sensitivity studies in hydraulically fractured low permeability reservoirs

The accuracy and hence the validity of reservoir simulation results largely depend on the grid system used in the simulation. It is observed that when there is a large difference in permeability between two adjacent layers, conventional grid systems do not accurately predict reservoir behaviors. Grid refinement is used near the well bore and fractures to better resolve the fluid flow between grid blocks. Logarithmically refined grids are commonly applied near the well bore region as there are large changes in pressure and saturation in this zone. Grid refinement must be applied even more carefully when dealing with the production of condensates. Effects of grid refinement on simulation results such as cumulative gas, cumulative oil, condensate–gas ratio (CGR) or gas–oil ratio (GOR), and planar pressure distribution were studied using a generic reservoir model with one horizontal well and one vertical planar fracture for wet gas, gas–condensate and black oil fluids. These results were generated using a full-feature compositional simulator. The results from these studies were used to develop empirical relationships between the dimensionless fracture conductivity and the grid size necessary to achieve converging results.

Towards jet acoustic prediction within the Launch Ascent and Vehicle Aerodynamics framework

Understanding the acoustic environment generated during lift-off is critical for successfully designing new space vehicles. In order for modeling and simulation tools to effectively assist in the development of the vehicles, validation must be performed on simplified model problems. In this paper, time-accurate implicit large eddy and detached eddy simulations coupled with a linear acoustic propagation method are applied to a Mach 1.8 perfectly expanded jet impinging on a flat plate at 45 degrees. The Launch Ascent and Vehicle Aerodynamics (LAVA) code used to simulate this problem is a high-fidelity unsteady simulation tool for modeling fluid dynamics, conjugate heat transfer, and acoustics. A detailed description of the linear acoustic propagation tool is provided. The narrow band far-field sound pressure levels predicted using LAVA are compared to existing experimental data. POD and spectral methods are applied to analyze the noise sources due to coherent flow structures and jet impingement. Grid and time-step sensitivity studies are performed to assess the spatial and temporal requirements for accurate jet acoustic simulation. Sensitivity of the predicted far-field sound pressure levels to position of the acoustic propagation surface is also assessed.

A Study of a Powder Coating Gun near Field: A Case of Staggered Concentric Jet Flow

This paper examines, experimentally and numerically, an isothermal coaxial air jet, created by an innovative nozzle design for an air propane torch, used for the thermal deposition of polymers. This design includes staggering the origins of the central and annular jets and creating an annular air jet with an inward radial velocity component. The experimental work used a Pitot tube to measure axial velocity on the jet centerline and in the fully developed flow. The static gauge pressure in the near field was also measured and found to be positive, an unexpected result. The numerical work used Gambit and Fluent. An extensive grid sensitivity study was conducted and it was found that results from a relatively coarse mesh were substantially the same as results from a mesh with almost 11 times the number of control volumes. A thorough evaluation of all of the RANS models in Fluent 6.3.26 found that the flow fields they calculated showed at most partial agreement with the experimental results. The greatest difference between numerical and experimental results was the incorrect prediction by all RANS models of a recirculation zone in the near field on the jet axis. Experimental work showed it did not exist.

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

Summary Many naturally fractured reservoirs around the world have depleted significantly, and improved-oil-recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs (NFRs) is still challenging because of permeability anisotropies and contrasts. Nonphysical abstractions inherent in conventional dual-porosity and dual-permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies for discrete fracture modeling may suffer from large simulation run times, and the industry has not used such approaches widely, even though they give more-accurate representations of fractured reservoirs than dual-continuum models. We developed an embedded discrete fracture model (DFM) for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual-continuum models and also incorporates the effect of each fracture explicitly. The model is compatible with existing finite-difference reservoir simulators. In contrast to dual-continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity of a typical NFR. The accuracy of the embedded DFM is confirmed by comparing the results with the fine-grid, explicit-fracture simulations for a case study including orthogonal fractures and a case with a nonaligned fracture. We also perform a grid-sensitivity study to show the convergence of the method as the grid is refined. Our simulations indicate that to achieve accurate results, the embedded discrete fracture model may only require moderate mesh refinement around the fractures and hence offers a computationally efficient approach. Furthermore, examples of waterflooding, gas injection, and primary depletion are presented to demonstrate the performance and applicability of the developed method for simulating fluid flow in NFRs.

Finite volume method for non-equilibrium radiative heat transfer

Radiative heat transfer is an important physical phenomenon, especially in the high speed and high temperature flow regimes, making its application important in space exploration vehicles. This paper presents the development and validation of computational tools for modeling the radiative heat transfer that can be either employed by itself or coupled with a computational fluid dynamics solver to analyze aerothermodynamics environments. A generalized mesh is used for discretization of the spatial domain and a finite volume method is used for solving the radiative heat transfer equation. Solution of the radiative heat transfer equation in an angular domain is carried out in a parallel environment. This numerical approach is validated with different benchmark test cases for gray gas radiation in various geometries. To enable the simulation of non-gray gas radiation, the full spectrum correlated-k model is implemented into the radiation solver. A grid sensitivity study is conducted to analyze the dependency of mesh resolution in spatial and angular domains on solution accuracy. The results of the validation studies, grid sensitivity studies, and parallel performance of the implementation are presented in this paper.

Isothermal Air-Ingress Validation Experiments

Idaho National Laboratory has conducted air-ingress experiments as part of a campaign to validate computational fluid dynamics (CFD) calculations for very high-temperature gas-cooled reactor (VHTR) analysis. An isothermal test loop was designed to recreate exchange or stratified flow that occurs in the lower plenum of VHTR after a break in the primary loop allows helium to leak out and reactor building air to enter the reactor core. The experiment was designed to measure stratified flow in the inlet pipe connecting to the lower plenum of the General Atomics gas turbine-modular helium reactor (GT-MHR). Instead of helium and air, brine and sucrose were used as heavy fluids, and water was used as the lighter fluid to create, using scaling laws, the appropriate flow characteristics of the lower plenum immediately after depressurization. These results clearly indicate that stratified flow is established even for very small density differences.Corresponding CFD results were validated with the experimental data. A grid sensitivity study on CFD models was also performed using the Richardson extrapolation and the grid convergence index method for the numerical accuracy of CFD calculations. The calculated current speed showed very good agreement with the experimental data, indicating that current CFD methods are suitable for simulating density gradient stratified flow phenomena in an air-ingress accident.

CFD analysis on a three by three nuclear fuel bundle with five spacer grid assemblies

This study has been conducted to investigate the flow characteristics for SMART 3×3 rod bundle with various turbulence models, namely, κ-ɛ model, κ-ω shear stress transport (SST) model and Baseline (BSL) Reynolds stress model. Commercial code CFX 12.0 was used for the simulation, and pressure drop, second flow intensity, flow velocity and temperature fields were predicted. For the development of an adequate computational model to simulate such a complex geometry, a grid sensitivity study was first examined. In addition, a pressure drop test for SMART rod bundle was shortly introduced, which test was done at Korea Atomic Energy Research Institute and compared with simulation results. From the comparison, with the SST model and BSL model similar pressure drop values were obtained. Maximum surface temperatures in the cross-section increase with the increase in the steps of the span (spacer grid assembly) and the temperature immediately decreases just after the mixing vane and then the temperature slowly rises. Compared with experimental results, the SST model had a similar maximum temperature pattern along rod axis. Also, it was interesting to find that the turbulence model did not affect the secondary flow intensity while affecting the flow velocity values. As a result, the most appropriate turbulence model and the grids were able to be determined.

Considerations on the Numerical Modeling and Performance of Axial Swirlers Under Relight Conditions

Numerical modeling of aero engine combustors under relight conditions is a matter of continuously increasing importance due to the demanding engine certification regulations. In order to reduce the complexity and the cost of the numerical modeling, common practice is to replace the atomizer’s swirlers with velocity profiles boundary conditions, very often scaled down from nominal operating conditions assuming similarity of the swirler flowfield. The current numerical study focuses on the flowfield characteristics of an axially swirled atomizer operating within a windmilling engine environment. The scalability of the velocity profile from higher power settings is examined. Observations on the performance of the axial swirler under relight conditions are also made. Experimental data was used as a validation platform for the numerical solver, after a grid sensitivity study and a turbulence model selection process. Boundary conditions for simulating the windmilling environment were extracted from experimental work. The swirler axial and tangential velocity profiles were normalized using the swirler inlet velocity. Results showed that both profiles are only scalable for windmilling conditions of high flight Mach number (≥ 0.5). At low flight Mach numbers, the actual profile had a lower velocity than that predicted through scaling. The swirl number was found to deteriorate significantly with the flight velocity following a linear trend, reducing significantly the expected flame quality. As a consequence the burner is forced to operate at the edge of its stability loop with low certainty regarding its successful relight.

Numerical Studies on Heat Release Rate in Room Fire on Liquid Fuel under Different Ventilation Factors

Heat release rate (HRR) of the design fire is the most important parameter in assessing building fire hazards. However, HRR in room fire was only studied by computational fluid dynamics (CFD) in most of the projects determining fire safety provisions by performance-based design. In contrast to ten years ago, officers in the Far East are now having better knowledge of CFD. Two common questions are raised on CFD-predicted results on describing free boundaries; and on computing grid size. In this work, predicting HRR by the CFD model was justified with experimental room pool fire data reported earlier. The software fire dynamics simulator (FDS) version 5 was selected as the CFD simulation tool. Prescribed input heating rate based on the experimental results was used with the liquid fuel model in FDS. Five different free boundary conditions were investigated to predict HRR. Grid sensitivity study was carried out using one stretched mesh and multiple uniform meshes with different grid sizes. As it is difficult to have the entire set of CFD predicted results agreed with experiments, macroscopic flow parameters on the mass flow rate through door opening predicted by CFD were also justified by another four conditions with different ventilation factors.

Large eddy simulations of jet flow interaction within staggered rod bundles

This work is a numerical investigation of experimental work on dual isothermal jet injection into a staggered rod bundle, mimicking phenomena present in the lower plenum of the very high temperature gas cooled reactor. Large eddy simulations were used to model the unsteady flow of the experimental conditions. As a basis, steady state simulations as well as time averaged comparisons were made with the standard and realizable k–ɛ formulations. Grid sensitivity studies were performed over six grids with the most refined grid comprised of roughly 26.5 million semi-structured polyhedral cells. The continuous wavelet transform was used for instantaneous signal decomposition of results taken within the domain in an effort to devise a better approach to validating CFD predictions of the complex flows in the lower plenum of the VHTR.

Experimental and computational investigation of local scour around bridge piers

Experiments and numerical simulations are carried out to study clear-water scour around three bridge piers with cylindrical, square, and diamond cross-sectional shape, respectively. To handle movable-bed channels with embedded hydraulic structures, the fluid–structure interaction curvilinear immersed boundary (FSI-CURVIB) method is employed. The hydrodynamic model solves the unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed with the k-ω turbulence model using a second-order accurate fractional step method. Bed erosion is simulated by solving the sediment continuity equation in the bed-load layer using a second-order accurate unstructured, finite-volume formulation with a sand-slide, bed-slope-limiting algorithm. Grid sensitivity studies are carried out to investigate the effect of grid resolution on the predictive capability of the model. Comparisons of the simulations with the experimental data show that for all three cases the agreement is reasonable. A major finding of this work, however, is that the predictive capability of the URANS morphodynamic model improves dramatically for the diamond shape pier for which sediment transport is driven primarily by the shear layers shed from the pier sharp edges. For piers with blunt leading edge, on the other hand, as the circular and square shapes, the URANS model cannot resolve the energetic horseshoe vortex system at the pier/bed junction and thus significantly underpredicts both the scour depth at the nose of the pier and the rate of scour growth. It is also shown that ad hoc empirical corrections that modify the calculated critical bed shear stress to enhance scour rate in the pier leading edge need to be applied with caution as their predictive capabilities are not universal but rather depend on the pier shape and the region of the flow.

Numerical Study on Turbulent Structure of Transverse Jet into Supersonic Flow

We investigated the three-dimensional turbulent structure of a transverse air jet injected into a Mach 1.9 supersonic crossflow and evaluated the jet mixing state using a large-eddy simulation (LES). A grid sensitivity study and detailed comparisons with acetone planer laser-induced fluorescence data validated our LES. The LES results reproduced the injectant mixing field, not only in the averaged distribution of the injectant concentration, but also in the large-scale turbulent features. Large-scale vortices in the windward side of the jet plume caused large protrusions of injectant and were the main cause of the turbulent diffusion of injectant toward the crossflow in the near-field. The windward large-scale vortex structure consisted of a string of hairpin-like vortices meandering along the jet trajectory. The head of these hairpin vortices tilted toward the upstream and upward directions. The instantaneous combustible injectant mass flux was evaluated by assuming the injectant air to be ethylene. A large amount of combustible injectant existed inside the large-scale protrusions induced by the windward large-scale vortex structure. The combustible injectant mass flow rate passing through the cross-section has substantial fluctuations over time, mainly due to the intermittent appearance of the windward largescale vortices.

Numerical Study of the Thermosolutal Convection Induced Macrosegregation during Columnar Solidification

As a response to “call for contribution to a numerical problem for 2D columnar solidification of binary alloys” [Bellet et al., Int. J. Therm. Sci., Vol. 48(11)(2009), p. 2013], the macrosegregation in a Pb-18wt.%Sn benchmark casting is numerically studied with a two-phase columnar solidification model developed by the current authors. The studies were done with 2D calculations in response to the call, and a 3D calculation was performed to confirm the consistency with the 2D case. A grid-sensitivity study was done to ensure the reliability and accuracy of the present results. The segregation mechanism due to thermosolutal convection was analyzed and the uncertainties resulting from the inaccurate thermophysical properties, modelling and process parameters are discussed. The numerical model was evaluated by comparison with experiments.

Large-Eddy Simulation: Current Capabilities, Recommended Practices, and Future Research

Usage of large-eddy simulation (LES) methods for calculation of turbulent flows has increased substantially in recent years. This paper attempts to 1) provide an assessment of the current capabilities of LES, 2) outline some recommended practices for using LES, and 3) identify future research needs. The assessment considers flow problems for which LES can be successfully applied today and flow problems for which LES still has limitations. The availability of LES and hybrid Reynolds-averaged Navier-Stokes (RANS)/LES in general-purpose codes is discussed. Several important issues for which the LES community has not yet reached a consensus are discussed. These include grid sensitivity studies, application of unstructured grid methods, upwind-biased solvers, and turbulence (subgrid) modeling including continuous hybrid RANS/LES approaches. A section on recommended practices and key considerations tries to provide guidance on some of the important items that need to be addressed in using LES. The paper concludes with a discussion of future research directions, with a focus on work needed to advance the capabilities and reliability of LES for analysis of turbulent flows.

Improved Lattice Boltzmann Without Parasitic Currents for Rayleigh-Taylor Instability

Over the last decade the Lattice Boltzmann Method (LBM) has gained significant interest as a numerical solver for multiphase flows. However most of the LB variants proposed to date are still faced with discreteness artifacts in the form of spurious currents around fluid-fluid interfaces. In the recent past, Lee et al. have proposed a new LB scheme, based on a higher order differencing of the non-ideal forces, which appears to virtually free of spurious currents for a number of representative situations. In this paper, we analyze the Lee method and show that, although strictly speaking, it lacks exact mass conservation, in actual simulations, the mass-breaking terms exhibit a self-stabilizing dynamics which leads to their disappearance in the long-term evolution. This property is specifically demonstrated for the case of a moving droplet at low-Weber number, and contrasted with the behaviour of the Shan-Chen model. Furthermore, the Lee scheme is for the first time applied to the problem of gravity-driven Rayleigh-Taylor instability. Direct comparison with literature data for different values of the Reynolds number, shows again satisfactory agreement. A grid-sensitivity study shows that, while large grids are required to converge the fine-scale details, the large-scale features of the flow settle-down at relatively low resolution. We conclude that the Lee method provides a viable technique for the simulation of Rayleigh-Taylor instabilities on a significant parameter range of Reynolds and Weber numbers.

Three-Dimensional Unsteady RANS Modeling of Discontinuous Gravity Currents in Rectangular Domains

Discontinuous gravity currents in rectangular channels are modeled numerically by solving the 3D unsteady Reynolds- averaged Navier-Stokes URANS equations closed with a buoyancy corrected low-Reynolds number LRN k- model using second- order accurate finite-volume numerics. It is shown that, on moderately fine computational meshes with 10 6 grid nodes and with careful modeling of the near-wall flow, the URANS model can capture the essential large-scale 3D dynamics of gravity current flows, which previously had been resolved only by DNS and/or large-eddy simulation LES on very fine computational meshes. These 3D dynamics include the onset of the well-known lobe-and-cleft instability at the current head, the onset of large-scale Kelvin-Helmholtz billows at the head of the gravity current, and the breakdown of the interfacial billows in the rear part of the current head due to intense three- dimensional mixing. The computed results underscore the importance of careful modeling of the near wall flow in URANS simulations. The standard k- model with wall functions fails to capture the aforementioned complex 3D dynamics, which are only resolved by the LRN k- model on grids that resolve the near-wall region. Furthermore, numerical experiments show that including in the simulation the lateral no-slip end walls of the channel has a profound effect on the accuracy of the computed solutions. End-wall effects enhance the three-dimensionality of the flow, result in increased mixing of the dense and the ambient fluids behind the head of gravity currents, and yield results in good agreement with measurements. On the other hand, when end-wall effects are omitted, by imposing periodicity in the spanwise direction, three-dimensional mixing is suppressed and the breakdown of interfacial billows is significantly underestimated. Grid sensitivity studies are also carried out using three successively refined meshes and show that the URANS LRN model yields grid- converged solutions at affordable computational resources. As URANS modeling requires only a fraction of the computational cost of DNS or LES with near-wall resolution, the present results underscore the potential of unsteady statistical turbulence models for predicting and elucidating the physics of gravity current flows in complex geometries and at Reynolds numbers of engineering relevance.

Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition

An experimental investigation concerning the most energetic turbulent features of the flow exiting from an axisymmetric converging nozzle at Mach 0.85 and ambient temperature is discussed using planar optical measurement techniques. The arrangement of the particle image velocimetry (PIV) system allows for all three components of the velocity field to be captured along the (r, θ)-plane of the jet at discrete streamwise locations betweenx/D=3.0 and 8.0 in 0.25 diameter increments. The ensemble-averaged (time-suppressed) two-point full Reynolds stress matrix is constructed from which the integral eigenvalue problem of the proper orthogonal decomposition (POD) is applied using both scalar and vector forms of the technique. A grid sensitivity study indicates that the POD eigenvalues converge safely to within 1% of their expected value when the discretization of the spatial grid is less than 30% of the integral length scale or 10% of the shear-layer width. The first POD eigenvalue from the scalar decomposition of the streamwise component is shown to agree with previous investigations for a range of Reynolds numbers and Mach numbers with a peak in azimuthal mode 5 atx/D=3.0, and a gradual shift to azimuthal mode 2 byx/D=8.0. The eigenvalues from the scalar POD of the radial and azimuthal components are shown to be much lower-dimensional with most of their energy residing in the first few azimuthal modes, that is modes 0, 1 and 2, with little change in the relative energies along the streamwise direction. From the vector decomposition, the azimuthal eigenspectra of the first two POD modes shift from a peak in azimuthal mode 5 atx/D=3.0, followed by a gradual decay to azimuthal mode 2 atx/D=8.0, the differences in the peak energies being very subtle. The conclusion from these findings is that when the Mach number is subsonic and the Reynolds number sufficiently large, the structure of the turbulent jet behaves independently of these factors.

Grid Influence on the Propeller Open-Water Performance and Flow Field

A grid sensitivity study for a conventional propeller in open-water condition uses three grids and compares with experimental data. Thrust and torque are rather insensitive to the grid resolution, but local quantities such as pressure coefficient and velocity are grid sensitive. An uncertainty analysis method reveals that the data are not in the asymptotic range which might be partly due to the complexity of the propeller flow.

Study of the effects of wing sweep on the aerodynamic performance of a blended wing body aircraft

This article presents a study of the effects of wing sweep on the aerodynamic performance of a blended wing body (BWB) aircraft that is based on an aerodynamically optimized design with a fixed planform and pitching moment constraint. Sixteen BWB geometries with varying wing sweep angles ranging from −40° (forward sweep) to 55° sweep were evaluated, while keeping the aerofoil profiles and twist distribution unchanged from the original optimized geometry. This gives some insight into the effects of one of the key planform design parameters. Numerical simulations were carried out using Euler solutions of the flow field with adaptive unstructured grids. Grid sensitivity studies were carried out, along with grid adaptation, on all geometries for solution accuracy. Results show that within 10° −55° sweep, there is significant variation in the lift-to-drag ratio ( LID), whereas for sweep values from −40° to 10°, the L/D ratio remained relatively constant. To maintain the design lift for varying wing sweep, the angle of attack of the aircraft needs to be changed. It was found that this variation followed an approximately parabolic curve, with a minimum incidence of 4.91° at 25° wing sweep. Furthermore, it was seen that the coefficient of moments versus the sweep angle varied almost linearly for all geometries under investigation.

Comparison of Hybrid Turbulence Models for a Circular Cylinder and a Cavity

Three hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation turbulence models are applied to the flow over a three-dimensional circular cylinder and a generic weapons bay. Time-step and grid sensitivity studies are performed. The time-step study indicates that 100-200 steps per primary shedding cycle are required for temporal accuracy using a second-order implicit algorithm. The grid study indicates that these new turbulence models can achieve a reasonably grid-independent solution in simulation of unsteady turbulent flows. As the mesh resolution is increased, smaller scale turbulent structures become visible. A computational mesh with a grid resolution resulting in a ratio of the turbulent length scale to grid length scale greater than 2 produced a reasonable simulation with all three hybrid models for both cases.