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Crank–Nicolson scheme in native OpenFOAM source libraries was not able to provide 2nd order temporal accuracy of velocity and pressure since the volume flux of convective nonlinear terms was 1st accurate in time. In the present study the simplest way of getting the volume flux with 2nd order accuracy was proposed by using old fluxes. A possible num...
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... n is the kinematic viscosity and r is the density of fluid. The present numerical domain is Àp x; y p while a cyclic boundary condition is imposed on each boundary of numerical domain. The initial fields are given at t ¼ 0 as shown in Fig. 2. To check the temporal and spatial accuracy of OpenFOAM computations are carried out with various computational time steps on several uniform meshes as listed in Table 1. The numerical errors of velocity and pressure are calculated with L 2 norm at t ¼ 1s. Fig. 3 shows a spatial convergence of ve- locity and pressure errors when 1st ...
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In this work, the critical parameters for the shear thickening fluid flow past a channel confined circular cylinder have been investigated numerically. The flow governing equations have been solved by using the finite volume based open source solver (OpenFOAM). In particular, critical parameters (i.e., Reynolds number) has been investigated for flo...
In this paper, the forced oscillation of a circular cylinder, known as the Radiation problem, close to the free-surface is studied for a range of Reynolds (Re) and Keulegan-Carpenterr (KC) numbers , using a semi-analytical linear solution and a fully non-linear Navier-Stokes solver. The fully non-linear solution is obtained using the OpenFOAM packa...
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... Most publications assessing OpenFOAM's accuracy focus on newly developed numerical tools based on the OpenFOAM library, e.g. Hassanaly et al. (2018); Komen et al. (2020); Gärtner et al. (2020), but rarely on its built-in capabilities (Lee (2017); Noriega et al. (2018)). It is therefore important to not only assess OpenFOAM's numerical accuracy, but also to provide a direct comparison with other, well established high-fidelity codes for chemically reacting flows. ...
OpenFOAM is one of the most widely used open-source computational fluid dynamics tools and often employed for chemical engineering applications. However, there is no systematic assessment of OpenFOAM’s numerical accuracy and parallel performance for chemically reacting flows. For the first time, this work provides a direct comparison between OpenFOAM’s built-in flow solvers as well as its reacting flow extension EBIdnsFoam with four other, well established high-fidelity combustion codes. Quantification of OpenFOAM’s numerical accuracy is achieved with a benchmark suite that has recently been established by Abdelsamie et al. (Comput Fluids 223:104935, 2021. https://doi.org/10.1016/j.compfluid.2021.104935) for combustion codes. Fourth-order convergence can be achieved with OpenFOAM’s own cubic interpolation scheme and excellent agreement with other high-fidelity codes is presented for incompressible flows as well as more complex cases including heat conduction and molecular diffusion in multi-component mixtures. In terms of computational performance, the simulation of incompressible non-reacting flows with OpenFOAM is slower than the other codes, but similar performance is achieved for reacting flows with excellent parallel scalability. For the benchmark case of hydrogen flames interacting with a Taylor–Green vortex, differences between low-Mach and compressible solvers are identified which highlight the need for more investigations into reliable benchmarks for reacting flow solvers. The results from this work provide the first contribution of a fully implicit compressible combustion solver to the benchmark suite and are thus valuable to the combustion community. The OpenFOAM cases are publicly available and serve as guide for achieving the highest numerical accuracy as well as a basis for future developments.
... Focusing on the planar configuration, several test rigs have been developed to study the primary breakup in airblast atomizers, generally using an airfoilshaped solid section as a prefilmer. Inamura et al. [10,11] used this sort 45 of test rig with water as a working fluid under different operating conditions, establishing the primary breakup mechanism of these devices. Matas et al. [12] used a similar setup to study the shear instability of a planar air-water mixing layer, demonstrating the direct influence of gas turbulence on this instability and showing that mean gas flow quantities do not fully characterize its features. ...
... All chosen discretization schemes are 2 nd order in time and space. As far as time discretization is concerned, a backward scheme (also known as 2 nd order upwind Euler scheme [45]) is used, which replaces the time derivative of a flow property ϕ as given by Eq. (8): ...
... Concerning the numerical set up, we used the Crank-Nicolson time scheme, Lee [41], and the convection terms are discretized by the Gaussian integration with linear interpolation (second-order schemes in space and time) as in Silva et al. [42]. The VanLeer limiter [43] guarantees that the volume fraction remains bounded and we kept the channel (with average velocity ∞ , see Fig. 1). ...
... In this study, the Courant (CFL) number is limited to 1. The time discretisation is carried out by using an implicit backward scheme 35 , which is second-order accurate, for both fluid and structure equations. The fluid divergence and gradient terms are solved using the second order Gauss linear scheme. ...
The study presents a numerical investigation of two-dimensional partly flexible plate dynamics. The structure is immersed in a turbulent fluid flow with a Reynolds number based on its chord of 10^4. The plate is animated by a forced pitching movement. The flexibility effects of the plate's leading edge are analyzed, as it deforms under the hydrodynamic loads. The fluid–structure interaction effects are considered by solving a coupled problem using a strong implicit procedure. Both fluid and solid dynamics are solved. The numerical results of the present study are validated with experimental ones with a good agreement between both approaches for the lower reduced frequencies. Differences are observable for high frequency that could be imputable to the three-dimensional aspects of the experiment. It has been shown that with an appropriate choice of the rigidity of the structure, it is possible to mitigate the unsteady load fluctuations without affecting the load mean values too much. Indeed, at low pitching frequency (drag mode), the leading-edge vortex generation is impacted by the flexible leading edge. As a result, it tends to decrease the hydrodynamic force fluctuation amplitude without really impacting the mean force value. Conversely, at high pitching frequency (propulsive mode), it was found that a flexible leading edge tends to increase both the magnitudes of the hydrodynamic forces and their mean values. Finally, it is shown that the load fluctuation mitigation, or amplification, is maximum for a specific flexibility value depending on the pitching frequency.
... To date, the OpenFOAM platform [3, 4] has been extensively applied towards simulating a wide range of engineering applications, including fire scenarios (e.g., [5,6,7,8,9,10]) with relatively good level of success. Some studies reporting on the influence of the numerical schemes used within the OpenFOAM platform (e.g., [11,12,13,14,15,16,17,18,19]), as well as with the use of FireFOAM specifically (e.g., [20,21,22,23]), already exist in the literature, nevertheless their influence when modelling actual fire-related scenarios has not been extensively reported. The main objective of this work is to investigate the accuracy of a selection of native numerical schemes of OpenFOAM, often employed in numerical simulations of fire scenarios. ...
The influence of the numerical schemes used for discretization of the convective terms in the momentum equations and in the transport equations for scalars is investigated. To this purpose, a set of problems with exact solutions, the Taylor–Green vortex problem, an isotropic decaying turbulence problem, along with two well-known fire configurations, namely the Sandia’s helium plume and McCaffrey’s fire plume experiments, are considered for evaluation purposes. Overall, the influence of the employed numerical schemes in both equations is shown to be significant on computational meshes that are typically employed in the context of fire simulations. As expected, the discretization errors diminish when sufficiently fine grid resolutions are considered. The native schemes of OpenFOAM, filteredLinear2 and limitedLinear, are found to be relatively accurate, when compared to other numerical schemes in the literature: while maintaining boundedness of the solution, they introduce only small amounts of numerical dissipation.
... Lee [19] improved the TDM performance of Crank Nicolson in OpenFOAM software. Lee [19] could increase the accuracy of the model by developing the method of interpolation and using the combined explicit and implicit scheme. ...
... Lee [19] improved the TDM performance of Crank Nicolson in OpenFOAM software. Lee [19] could increase the accuracy of the model by developing the method of interpolation and using the combined explicit and implicit scheme. In this modeling, the new Crank Nicolson method improves the precision of the cylindrical backflow simulation, compared to the default Crank Nicolson's method and the first-order Euler method [20]. ...
... In Table 3, the puffing frequency, which in some way expresses the fluctuation behavior of pool fire, is presented for different methods of spatial and temporal discretization in a flow rate per unit area of 0.066 kg/m 2 .sec. In Table 3, in addition to the experimental data [34], the value of puffing frequency is obtained from the two empirical correlations of Zukoski and Cetegen [17], according to Eqs. (19) and (20), respectively. The predicted values for Zukoski and Cetegen's correlations are about 5% and 10% of the deviation, respectively. ...
The identification of the type of regime has an essential effect on the selection of sub-grid scale and discretization methods, regarding the accuracy and computational time. In order to investigate the role of sub-grid scale and time discretization method in a pool fire modeling by the Large Eddy Simulation (LES), three sub-grid scales Smagorinsky, one-equation and Wall-Adapting Local Eddy-Viscosity (WALE) and three time discretization methods of first-order Euler method, second-order Crank Nicolson and backward second-order were investigated. The results indicate that WALE and one-equation sub-grid scale have an acceptable prediction, while Smagorinsky has a significant error with the experimental results. Different time discretization methods have little effects on the results of mean velocity and mean turbulent parameters of the pool fire. By considering the instantaneous distribution of parameters, all three methods perform similar results where the kinetic energy is less than 5 m²/s². In areas where the perturbation is aggravated, the two second-order discretization methods have the same error with a little difference by the first-order Euler method. The accuracies of second-order methods are about 10% for the velocity prediction, compared to the experimental results, while the error of the Euler method is 15%.
... In our simulations we use this scheme for gradient terms discretization, as far we have built the mesh as a structured mesh, but it could be interesting to see the differences with the least square method. More details about the accuracy in time and space for OpenFoam can be found in [Lee17]. The discretization schemes used in time and space are all of first and second order. ...
The more stringent regulation about aeronautical engines emission posed by ICAO requires always more predictive design tools. The droplets diameter distribution produced during the atomization process is a key parameter in order to predict the pollutant emission released during the combustion process. Thus the study of the atomization phenomenon with itsmulti-scale nature is a relevant and an important challenge. For this reason the objective of this work are: first to review the existent models in the literature to understand their key features in order to define a classification that gives guidelines on the modeling choices; second to apply industrial oriented approaches on an aeronautical configuration, in order to propose an improvement of the available design tools. A systematic classification of the models is done with respect to the length-scale considered to represent the interface characteristics. From this point of view, it is possible to distinguish two kinds of approaches: the separated phases representation and the mixed phases representation. The diffuse interface approaches belongs on the second category together with many other approaches, compressible and incompressible, that share the same characteristic: they considers a mixture that contains both phases. An air-assisted liquid sheet configuration has been built to test different models in order to define a metric of comparison. Two different models using the sharp interface approach (ARCHER and InterFoam ), two models using the diffuse interface approach (CEDRE and ELSA ) and an hybrid model (ICMelsa ) have been considered on this test case. A comparison on two parts, based on statistical quantities, has been proposed. A fist part called "classical study", compare the first order statistics showing that all approaches lead to very similar results, as soon as certain level of mesh resolution is achieved. At the contrary the second order statics present noticeable differences. These results motivate a second part called "phase analysis" to study the link between the small scale representation of the interface and the second-order statics. In particular, the phase marker variance and the associated segregation level are found to be sensible indicators of the interface description. A 1D signal analysis shows that they can be used to detect any departure from the separated phases representation.Then the importance of the phase indicator variance is demonstrated on other second-order statistics: Reynolds stress components and turbulent liquid flux. Thus, second-order statistics are partly described with direct mixed phases representations and require complementary model to be fully recovered. A first attempt, based on a linear approach, is proposed to model the level of segregation of mixed phases representation. It is based on the filtering of a fully segregated signal at a given scale. In a second part of this thesis, an industrial test case (a pressure swirling injector) proposed by SAFRAN Aircraft Engines is studied. Three industrial oriented models, among those studied in the first part, have been applied to simulate this injector flow (InterFoam , ELSA , ICMelsa). Their present numerical approaches are able to work with complex geometries, with a computational effort representative of the industrial current standards. The results of the three models (liquid film thickness, breakup length and Sauter Mean Diameter) have been compared with respect to the available experimental data. Eventually, a proposal to improve the ICMelsa model multi-scale have been successfully tested on the liquid sheet configuration and implemented to further improve the results of the SAFRAN Aircraft Engines industrial case. These results have shown that we are very close to predict the characteristics of a spray produced by a real aeronautical injection system.
... In most studies [7][8][9], the effect of discretization on a non-reacting flow is commonly investigated. Not much research, on the other hand, has been done on the impact of the discretization method on LES in fire dynamic modeling; Trisjono et al. [10] recommended central scheme for advection term in LES of turbulent reacting flows. ...
Using discretization technique is one of the challenges associated with numerical modeling. In the Large Eddy Simulation (LES) method, this issue becomes more critical because it affects the sub-grid scale (SGS) model and creates errors. Using an LES method, we investigated the numerical errors and compatibility of different discretization methods with SGS in pool fire modeling. First-order, central, and second-order upwind and linear upwind stabilized transport (LUST) schemes were examined in Smagorinsky (S_SGS) and k-equation (K_SGS) sub-grid scales. First-order upwind and second-order upwind methods estimated the velocity field, temperature, and perturbation with a significant error, so that in the plume area, there was 90% error with the first-order upwind and 50% error with the second-order upwind concerning the results of the mean square horizontal velocity perturbation. With an error of 20%, the LUST method had a better agreement with the experimental results. Besides, SGS did not have a significant effect on the results of this method. However, the second-order upwind method was more consistent with the S_SGS model. To improve the results of upwind methods, Quadratic Upstream Interpolation for Convective Kinematics and Monotonic Upwind Scheme for Conservation Laws discretization methods are recommended.
... As boundedness is not guaranteed with central differencing, an upwind-blended scheme provides boundedness resulting in better numerical stability and accuracy. Time discretisation is achieved with a second-order implicit, backwarddifferencing scheme [30], where: ...
... It is worth to remind that in the Finite Volume (FV) approach, both the computational grid and the discretization of the operators implicitly act as a top-hat filter to the equations [100]. Since most of the CFD solvers in the FV framework are usually limited to second order accuracy [101], the SCT and the SMT term coming from filtering of the equations would be probably biased by the discretization schemes and by the grid [102,103], even when explicit filtering is applied. ...
The development of a single-fluid solver supporting phase-change and able to capture the evolution of three fluids, two of which are miscible, into the sharp interface capturing Volume of Fluid (VOF) approximation, is presented. The transport of each phase-fraction is solved independently by a flux-corrected transport method to ensure the boundedness of the void fraction over the domain. The closure of the system of equations is achieved by a cavitation model, that handles the phase change between the liquid and the fuel vapor and it also accounts for the interaction with the non-condensable gases. Boundedness and conservativeness of the solver in the transport of the volume fraction are verified on two numerical benchmarks: a two-dimensional bubble rising in a liquid column and a cavitating/condensing liquid column. Finally, numerical predictions from large-eddy simulations are compared against experimental results available from literature; in particular, validation against high-speed camera visualizations and Laser Doppler Velocimetry (LDV) measurements of cavitating microscopic in-nozzle flows in a fuel injector is reported.
