Large-Eddy-Simulation of Complex Flows Using the Immersed Boundary Method

In the literature immersed boundary methods are employed tosimulate complex flows around moving arbitrary bodies without thenecessity of remeshing. These methods employ a regular Eulerian meshto simulate the fluid flow and a Lagrangian representation of theboundary of the bodies. The two representations can be coupled throughan immersed boundary condition constraining the fluid to exactlyfollow the boundary of the bodies (immersed boundaries). Typicallysuch methods suffer from accuracy problems, that arise from spuriousmass fluxes over the immersed boundary (IB), pressure boundaryconditions or high density ratios. The mirroring IB method Mark(2008); Mark and van Wachem (2008) resolves these problems by ensuringzero mass flux over the IB instead of employing a pressure boundarycondition. In this work the mirroring IB method together with a hybridIB condition are implemented and validated in IBOFLOW. IBOFLOW is anincompressible finite-volume based fluid flow solver. TheNavier-Stokes' equations are coupled with the SIMPLEC Doormaal andRaithby (1984) method and discretized on a Cartesian octree grid thatcan be dynamically refined and coarsened, enabling grid refinement tofollow moving bodies. The variables are stored in a co-locatedconfiguration and pressure weighted flux interpolation Rhie and Chow(1983) is employed to prevent pressure oscillations. In theimplemented IB method the immersed bodies are represented by ananalytical description or by a triangulation. The method models thepresence of the bodies inside the fluid by an implicitly formulated IBcondition, which constrains the fluid velocity to the boundaryvelocity with second-order accuracy. The original mirroring IBcondition mirrors the velocity field over the local IB and the hybridIB condition mirrors and extrapolates the fluid velocity onto the IB.These IB conditions generate a fictitious velocity field inside thebodies, which is excluded in the continuity equation to ensure zeromass flux over the boundary. The fluid flow over an immersed sphere issimulated to validate and compare the different IB conditions. Thesimulated drag force is compared to experimental findings withexcellent agreement and a detailed convergence study of the error ofthe fluid velocity integrated over the immersed boundary is performedto show the strictly second-order accuracy of the implemented IBconditions. It is shown that the error is reduced with the hybrid IBcondition compared to the original mirroring IB condition. Inaddition, a sedimenting sphere with a moving grid refinement issimulated to validate the hybrid method and show the potential of thedynamic octree grid.

Composite B-spline regularized delta functions for the immersed boundary method: Divergence-free interpolation and gradient-preserving force spreading.

An immersed boundary formulation incorporating a two-layer wall model approach for RANS simulations with complex geometry

In this paper we show how the Immersed Boundary (IB) method can be used with the Large-Eddy-Simulation (LES) to compute moderately high Reynolds number flows in complex geometric configurations. The resulting combination gives an easy-to-use, inexpensive and accurate technique which can be an important step towards the application of computational fluid dynamics (CFD) to industrially relevant problems. This paper aims at describing the main features of the method, some of the important drawbacks and possible solutions. Several representative examples are discussed in order to show the flexibility and the range of the applicability of this technique.

A numerical study of the MRT-LBM for the shallow water equation in high Reynolds number flows: An application to real-world tsunami simulation

In the past decade a large degree of advancement has been made in CFD labs worldwide, towards the development of Immersed Boundary (IB) CFD methods. The IB method belongs to a new class of numerical methods sometime called mesh-less methods, as no standard meshes that conform to the geometry (or body) need to be generated. The discrete points where the calculation is performed can be freely distributed in the computational domain without great concern for the position of the geometry. The geometry is immersed into a Cartesian grid and the methodology accounts for the effects of the presence of the body in the flow field. The IB method therefore frees up the user from the time consuming and often complicated need for meshing. Plenty of proofs of accuracy and validations are presented yearly at the most prestigious CFD conferences and are available on the internet. Oil and Gas CFD applications are concerned with a variety of internal flow problems. Most of those problems present geometrical complexities, valves for instance, that make a standard body-fitted generation of good quality meshes almost an impossible task. And bad inputs, such as low quality meshes, always determine bad outputs, low quality results. In this paper the KARALIT CFD code based on a class of IB methodology akin to ghost cell methods, is applied to a class of applications encountered often in oil and gas plants, namely a pipeline connecting an arbitrary number of valves, or other devices. While complex valves and devices do make the standard body-fitted approach extremely tedious and difficult, on the other side pipelines are naturally and easily modeled using standard body-fitted cylindrical meshes. The hybrid CFD approach presented will show an automatic implementation of mixed type domain: pipes cylindrical body-fitted meshes are automatically generated by the method and automatically connected to the devices which are treated with the IB method. Examples of lines with arbitrary number of devices will be shown. Result and key performance parameters are provided from the IB CFD calculations and key conclusions about the line characteristic are drawn.

Numerical simulation of flow around a smooth circular cylinder at very high Reynolds numbers

SUMMARYIn this study, an immersed boundary (IB) method based on a direct forcing is coupled with a high‐order weighted‐essentially non‐oscillatory (WENO) scheme to simulate fluid–solid interaction (FSI) problems with complex geometries. The IB is a general simulation method for FSI, whereas the WENO is an efficient scheme for fluid flow simulations and shock waves, and both of them work on regular cartesian grids. The effectiveness and the accuracy of the coupled scheme are first analyzed on well‐documented supersonic test problems for a wide range of Mach numbers. The results are in good agreement with both analytical and experimental data. A comprehensive analysis of the interaction of the moving shock through an array of cylinder matrix is then conducted by varying the number of cylinders in the matrix block while keeping the same opening passage. The relaxation length between two adjacent columns of cylinders is kept identical to study uniquely the effect of surface‐to‐volume ratio of the obstacle matrix. It is shown that the configuration with higher surface‐to‐volume ratio produces more post‐shock flow instabilities downstream of the matrix block. The complex shock/shock and shock/vortex interactions are well resolved by the present computation. It is being observed that after the passage of the shock through the cylinder matrix, eddies of different length scales are generated, but the later stage of shock/vortex and shocklet/vortexlet interactions are different for the two cases. The analysis of the PSD of the total kinetic energy globally conforms to Richardson's inviscid cascade. An intermittent peaked PDF of downstream instantaneous vorticity field is obtained in the limit of Re → ∞ . The baroclinic production of vorticity is found to be feeble as previously founded by Sun and Takayama (J. Fluid Mech. 2003; 478:237–256). Copyright © 2011 John Wiley & Sons, Ltd.

The results of thermal interactions between a solid particle and a fluid have two folds: the motion of fluid affects the heat transfer and energy balance of a particle; and the heat transfer from particles influences the fluid motion. When the temperature of a particle and its surrounding fluid is not the same, heat is transferred between the particle and the fluid. The heat flux influences the properties of the surrounding fluid and changes the dynamics of the sedimentation of the particle. To study the effect of non-isothermal flows to the motion of a particle, we have developed a Direct Numerical Simulation (DNS) method that is capable of solving both the momentum equation and heat transfer equation for the computation of thermal interaction between particles and fluid. This numerical method makes use of a finite difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. In particular, the IB concept has been extended to treat thermal boundary condition at the particle surface. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, which tracks particles, and a force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between particle and fluid. In this paper, the IB based DNS method has been applied to study the fluidization of 12,000 circular particles, the unsteady conduction of a sphere in a stagnant fluid, and the sedimentation of a non-isothermal sphere in a viscous fluid at different Grashof number. Our simulation results show that the sedimentation velocity of the particle depends strongly on the thermal interaction of particle and fluid due to the strong buoyancy force exerted on the particle.

This paper gives a discussion on the Computational Fluid Dynamics (CFD) applications in offshore engineering. Accurate hydrodynamic quantities are essential for engineering design. Offshore structures are generally subject to high Reynolds number flows. These high Reynolds number flow conditions (Re > 106 ) are difficult and expensive to achieve in an experimental setup. Therefore, it is attractive to use CFD to provide the essential hydrodynamic quantities for practical design. Verification and validation studies are important for determining the validity of the CFD prediction. A procedure of performing CFD simulation is shown. Different types of turbulence modelling are discussed. Three examples of high Reynolds number CFD simulations, covering flow around offshore structural components and waves past partially-submerged horizontal cylinders, are shown and discussed.

Aerodynamic characteristics of a guided rocket projectile are numerically simulated. Simulations are performed in a range of flight conditions using a commercial CFD software FLUENT, and variations of lift coefficients and drag coefficients with Mach numbers and angles of attack were demonstrated. The numerical results also indicate that the angle of canard deflection has significant influence on the flow field near tailfins.

Pore-scale modeling of flow in porous and fractured media is a first key step to provide a firm knowledge basis for effective aquifer management practices in environmental applications or to improved reservoir performance in the oil and gas field. We present a performance comparison of two numerical approaches for the pore-scale simulation of fully saturated flow in natural porous media. Real samples of rocks at the millimeter scale whose complex pore space geometry is reconstructed through X-ray computer tomography are considered. The governing flow equation in the system are solved by employing a Body-Fitted (BF) grid and an Immersed Boundary (IB) method, as respectively embedded in FLUENT and EULAG (Prusa et al., 2008) software environments. The BF technique allows solving the flow problem within the real pore space and is widely adopted in computational fluid dynamics since it allows to fit complex geometries while preserving accuracy, up to a certain level of detail. The method is associated with some limitations in the presence of extremely complex geometrical setting of the kind encountered in natural or reconstructed micro scale porous systems, mainly due to the time-demanding mesh generation stage. On the other hand, IB methods can take full advantage of uniform Cartesian grid implementations describing both the fluid and solid regions in the domain. Grain size distributions are modeled by considering an additional forcing term in the governing flow equation. This term inhibits Sow through the solid matrix and hence acts to enforce the no-slip condition at solid walls. The effectiveness of such term, i.e., its ability to prevent mass flow rate within the solid domain, is controlled by a parameter, a, which is directly related to the characteristic time scale of the forcing action. First, the performance of each model is analyzed separately on the same rock samples. Grid dependence is tested for the BF method upon comparing simulations at three different levels of resolution. A detailed sensitivity analysis is performed to assess the role of the parameter α in the IB method simulations. Finally, the two models are compared in terms of resulting flow fields, mass-conservation capability, hydraulic conductivity estimates and computational resources requirement.

The objective of this brief review is to showcase recent applications of sharp-interface immersed boundary (IB) method to computationally challenging problems in fluid–structure interaction (FSI). The sharp-interface IB method is briefly reviewed and a scheme to strongly couple the flow and structural solver is discussed. The following applications have been discussed. First, the vortex-induced vibration of a cylinder has been presented. Second, FSI benchmarks of an elastic and a viscoelastic splitter attached on a cylinder involving large-scale flow-induced deformation have been presented. Third, numerical simulations of a FSI benchmark in a heated channel, demonstrating augmentation in convective heat transfer, have been reviewed. Finally, the flow-induced deformation of a thin elastic plate due to blast loading has been presented. In all of these FSI problems, the IB method has been successfully employed to simulate the coupled fluid and structural dynamics.

Handling of complex geometries with fluid–solid interaction has been one of the exigent issues in computational fluid dynamics (CFD) because most engineering problems have complex geometries with fluid–solid interaction for the purpose. Two different approaches have been developed for the same hitherto: (i) The unstructured grid method and (ii) the immersed boundary method (IBM). This paper details the IBM for the numerical investigation of two-dimensional laminar flow over a backward facing step and various geometrically configured triangular steps in hydro-dynamically developing regions (entrance region) as well in the hydro-dynamically developed regions through a channel at different Reynolds numbers. The present numerical method is rooted in a finite volume approach on a staggered grid in concert with a fractional step method. Geometrical obstructions are treated as an immersed boundary (IB), both momentum forcing and mass source terms are applied on the obstruction to satisfy the no-slip boundary condition and also to satisfy the continuity for the mesh containing the immersed boundary. Initially, numerically obtained velocity profiles and stream line plots for fluid flow over backward facing step is depicted to show its excellent agreement with the published results in various literatures. There after profiles and plots in the channel with triangular steps are also being unveiled with in depth elucidation. Results are presented for different Reynolds numbers.

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the structure and Eulerian variables to describe the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methods require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. These tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100--1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50--200 times more efficient than the explicit method.