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Ma, Yang; Cheng, Yongpan; Zhang, Dongjie; Zhang, Ke; Wang, Fan
doi: 10.1002/fld.5044pmid: N/A
The breaking up of gas filament in liquid is important in many industrial and scientific applications. In this study, a transient axisymmetric model with the level set method is built up to examine the dynamics of a contracting gas filament, and to determine the effects of the aspect ratio, Ohnesorge (Oh) number, and viscosity ratio on its breakup mode. The filament undergoes no break, middle break, or end‐pinching modes with increasing aspect ratio at either a low or a high Oh number, and one critical initial aspect ratio is observed for each Oh number. The fate of the filament is determined by the interaction of capillary waves on its surface, and can be predicted accurately by using the one‐dimensional wave superposition method. The decreasing viscosity ratio of liquid over gas reduces the critical initial aspect ratio for the fate transition between the no break and breakup modes, and this effect is reduced at a low viscosity ratio. These findings may be helpful in fabricating gas bubbles and their breakup suppression.
doi: 10.1002/fld.5045pmid: N/A
An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds‐averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open‐source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR‐F6 wing‐body‐nacelle‐pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.
Nomura, Reika; Takase, Shinsuke; Moriguchi, Shuji; Terada, Kenjiro; LeVeque, Randall J.
doi: 10.1002/fld.5046pmid: N/A
This study presents a method for determining the drag parameter in the 2D shallow water (SW) equation for flows through a coastal forest by conducting a series of 3D numerical simulations (3D NSs). Following the theory of multiscale modeling, an evaluation method procedure is proposed. We first prepare a local test domain that contains a sufficient number of trees to constitute part of a coastal forest. Then, 3D NSs are conducted in this test domain with various inflow conditions. Based on the corresponding results, the momentum losses over the test domain are converted into the drag parameter of the global SW equation. A response surface of the drag parameter is constructed as a function of the flow conditions. The stabilized finite element method is employed for both the local and the global NSs, and the phase‐field method is utilized to represent 3D free surfaces. Comparisons between the 2D SW calculation results and the 3D NS results are also performed to verify the validity of the proposed method.
Papageorgiou, Anastasios K.; Papoutsis‐Kiachagias, Evangelos M.; Giannakoglou, Kyriakos C.
doi: 10.1002/fld.5047pmid: N/A
This article contributes to the development of methods for shape optimization under uncertainties, associated with the flow conditions, based on intrusive Polynomial Chaos Expansion (iPCE) and continuous adjoint. The iPCE to the Navier–Stokes equations for laminar flows of incompressible fluids is developed to compute statistical moments of the Quantity of Interest which are, then, compared with those obtained through the Monte Carlo method. The optimization is carried out using a continuous adjoint‐enabled, gradient‐based loop. Two different formulations for the continuous adjoint to the iPCE PDEs are derived, programmed, and verified. Intrusive PCE methods for the computation of the statistical moments require mathematical development, derivation of a new system of governing equations and their numerical solution. The development is presented for a chaos order of two and two uncertain variables and can be used as a guide to those willing to extend this development to a different set of uncertain variables or chaos order. The developed method and software, programmed in OpenFOAM, is applied to two optimization problems pertaining to the flow around isolated airfoils with uncertain farfield conditions.
Goudon, Thierry; Llobell, Julie; Minjeaud, Sebastian
doi: 10.1002/fld.5048pmid: N/A
We set up a numerical strategy for the simulation of the Euler equations, in the framework of finite volume staggered discretizations where numerical densities, energies, and velocities are stored on different locations. The main difficulty relies on the treatment of the total energy, which mixes quantities stored on different grids. The proposed method is strongly inspired, on the one hand, from the kinetic framework for the definition of the numerical fluxes, and, on the other hand, from the discrete duality finite volume (DDFV) framework, which has been designed for the simulation of elliptic equations on complex meshes. The time discretization is explicit and we exhibit stability conditions that guaranty the positivity of the discrete densities and internal energies. Moreover, while the scheme works on the internal energy equation, we can define a discrete total energy which satisfies a local conservation equation. We provide a set of numerical simulations to illustrate the behavior of the scheme.
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