Papers by Keyword: Immersed Boundary Method

Abstract: Inlet and outlet pressure drop effects can contribute significantly to the total pressure drop in porous media if thin solid matrices are used. However, these effects are usually ignored and few are the studies that focus on this topic. This paper uses a numerical simulation approach to determine the importance of the inlet and outlet pressure drop effects on the total pressure drop in a staggered arrangement of square cylinders with equal sizes, d_c. The Navier-Stokes equations are solved at the pore level for several matrix lengths (from d_c to 34d_c) and for several Reynolds numbers based on d_c and maximum velocity of the velocity inlet profile (from 36 to 120). Accurate results of the velocity and pressure fields are obtained through the use of the immersed boundary method in combination with the finite differences method, 4^th-order compact schemes for spatial discretization and 4^th-order Runge-Kutta temporal discretization. The results presented in this paper confirm that the classical models (e.g., Hazen-Dupuit-Darcy model) are only valid when the solid matrix has a length above a certain value, called the critical length. For shorter porous media, the pressure drop does not vary linearly with the matrix length. The deviations to the model that occur at the shortest porous media are explained by the entrance and exit contributions to the total pressure drop that, in these cases, are not negligible when compared to the bulk pressure drop. For the staggered array of square cylinders and range of Reynolds numbers considered, the critical porous medium length is 16d_c. A practical outcome of the present study is the quantification of the influence of the pressure tap locations on the measurements of pressure drop in porous media. When the matrix is short when compared to the particle diameter, care must be taken with the pressure taps placement: they should be located outside the porous matrix and not too close to its inlet and outlet sections. If the matrix is thick enough when compared to the particle diameter, the taps can be placed either inside or outside the matrix. Also, if the influence of the side walls on the total pressure drop is not high (i.e., the walls are at a relative large distance when compared to the particle diameter), there is no practical need to correct the measured pressure values to account for the influence of the walls. This correction should be considered for the shortest matrices though.

Abstract: This paper presents direct numerical simulations for the flow through regular porous media composed of equal size staggered square cylinders obtained with a compact finite differences immersed boundary method. Different moderate Reynolds numbers are simulated in order to capture the dependence of the pressure drop with the Reynolds number in the Forchheimer regime. The pressure drop predictions agree well with the Hazen-Dupuit-Darcy model; however, when compared to a widely used semi-empirical correlation, the modified Ergun equation, the agreement is poor. A better agreement is found if the particle diameter is taken to be equal to the cylinder diameter. From the intrinsic-averaged pressure calculated along the flow direction, it can be seen that, for the porous media studied, the bulk pressure drop dominates and the entrance and exit effects are negligible.

Abstract: This work presents the extension of a compact finite difference immersed boundary method for the detailed calculation of fluid flow and heat transfer in porous media. The unsteady incompressible Navier-Stokes and energy conservation equations are solved with fourth-order Runge-Kutta temporal discretization and fourth-order compact schemes for spatial discretization, which allows achieving highly accurate calculations. Verification proves that the method is higher than third-order accurate. Three test cases were used for the validation of the method: (i) isothermal flow around a square cylinder in a plane parallel channel, (ii) isothermal flow through an infinite row of square cylinders and iii) flow and heat transfer around a square cylinder in a plane parallel channel. The validation tests establish confidence in the application of the method to porous media. As an example of such an application, direct numerical simulations are conducted for a staggered array of equal size square cylinders. Although the problem is rather complex from the geometrical point of view, a Cartesian grid is employed, with all its advantages. The potential of applying an immersed boundary method to the solution of a multiphase problem with complex internal boundaries is demonstrated.

Abstract: The immersed boundary method (IBM) for the simulation of the interaction between fluid and flexible boundaries in combination with the lattice Boltzmann method (LBM) is described. The LBM is used to compute the flow field, the interaction between fluid and flexible boundaries to be treated by the IBM. To analyze the key factors of combination method and implementation process. An example is presented to verify the efficiency and accuracy of the described algorithm. These will provide a base for large scale simulation involving flexible boundaries in the future.

Abstract: Inspired by the propulsion of organisms in a viscous fluid, we develop a two-dimensional computational model to study the propulsive and fluid dynamic features of an organism modeled as an elastic filament in viscous fluid using immersed boundary (IB) finite volume method. The elastic filament is modeled using discrete number of IB points. The elastic forces are computed based on an elastic energy function. The Navier-Stokes equations governing the fluid flow are solved on a staggered Cartesian grid system using the fractional step based finite volume method. The computational model is validated by comparing the numerical simulation results pertinent to the swimming of an infinite with that of the existing analytical results. The interplay of propulsive and fluiddynamic features of the organism in the viscous fluid is well captured using the developed model.

Abstract: An immersed boundary method based on the ghost-cell approach is presented in this paper. The compressible Navier-Stokes equations are discretized using a flux-splitting method for inviscid fluxes and second-order central-difference for the viscous components. High-order accuracy is achieved by using weighted essentially non-oscillatory (WENO) and Runge-Kutta schemes. Boundary conditions are reconstructed by a serial of linear interpolation and inverse distance weighting interpolation of flow variables in fluid domain. Two classic flow problems (flow over a circular cylinder, and a NACA 0012 airfoil) are simulated using the present immersed boundary method, and the predictions show good agreement with previous computational results.

Abstract: In this paper, numerical simulation of flow around a cylinder using the feedback force immersed boundary method is carried out. The feasibility of algorithm is verified by the numerical simulation of flow past two cylinders in tandem arrangement. The Cartesian adaptive mesh refinement is used in the whole flow field, and the dynamic distribution characteristics of flow field around a single cylinder and double cylinders are obtained when Re=100. Compared with the results in other literatures, the simulation shows a good agreement.

Abstract: Immersed boundary method is one of the important numerical methods for solving the interaction between flexible hyper elastic structure with large deformation and viscous fluid. Based on previous research results, hyper elastic finite elementmodeling of erythrocyte with film thickness was established. Study on the dynamic characteristics of erythrocyte under shear flow, linkage dynamic characteristics of erythrocyte, plasma and vessel wall by using the immersed boundary method. The research results agree with experimental observations and some other researcher's calculated values, Interpret the mechanism ofhemokinesis in portion micro vessels simultaneously, have a great value to clinical medicine and biomechanics research.

Abstract: A compact finite differences method is used to calculate two-dimensional viscous flows through complex geometries. The immersed boundaries are set through body forces that allow for the imposition of boundary conditions that coincide with the computational grid. Two different flow configurations are simulated. First, the flow through a row of cylinders with square cross-sections is calculated and used as a validation study. The computed average drag coefficient and Strouhal number are compared to data available in the literature, showing a good agreement between the results. The second flow configuration analyzed is the flow through a porous matrix composed of equal size staggered square cylinders. Flow visualization results are shown and various flow regimes identified. Different inlet boundary conditions are compared. The drag coefficient is larger when a uniform inlet velocity is prescribed and the variability between cylinders is lower.

Abstract: This paper presents a fluid-cell interaction algorithm using the immersed boundary coupled fictitious domain method. We discuss the application of this method to the numerical investigation of motion and deformation of erythrocytes in two-dimensional stenotic microvessels. The erythrocytes are modeled as biconcave-shaped closed membranes filled with cytoplasm. Simulation results of multiple erythrocytes traversing the stenosis in Poiseuille flow are presented. This algorithm is applicable to a large class of problems involving fluid flow with complex geometry and fluid-cell interactions.