Transonic airfoil analysis and design in nonuniform flow

A nonuniform transonic airfoil code is developed for applications in analysis, inverse design and direct optimization involving an airfoil immersed in propfan slipstream. Problems concerning the numerical stability, convergence, divergence and solution oscillations are discussed. The code is validated by comparing with some known results in incompressible flow. A parametric investigation indicates that the airfoil lift-drag ratio can be increased by decreasing the thickness ratio. A better performance can be achieved if the airfoil is located below the slipstream center. Airfoil characteristics designed by the inverse method and a direct optimization are compared. The airfoil designed with the method of direct optimization exhibits better characteristics and achieves a gain of 22 percent in lift-drag ratio with a reduction of 4 percent in thickness

A fully resolved active musculo-mechanical model for esophageal transport

Esophageal transport is a physiological process that mechanically transports an ingested food bolus from the pharynx to the stomach via the esophagus, a multi-layered muscular tube. This process involves interactions between the bolus, the esophagus, and the neurally coordinated activation of the esophageal muscles. In this work, we use an immersed boundary (IB) approach to simulate peristaltic transport in the esophagus. The bolus is treated as a viscous fluid that is actively transported by the muscular esophagus, which is modeled as an actively contracting, fiber-reinforced tube. A simplified version of our model is verified by comparison to an analytic solution to the tube dilation problem. Three different complex models of the multi-layered esophagus, which differ in their activation patterns and the layouts of the mucosal layers, are then extensively tested. To our knowledge, these simulations are the first of their kind to incorporate the bolus, the multi-layered esophagus tube, and muscle activation into an integrated model. Consistent with experimental observations, our simulations capture the pressure peak generated by the muscle activation pulse that travels along the bolus tail. These fully resolved simulations provide new insights into roles of the mucosal layers during bolus transport. In addition, the information on pressure and the kinematics of the esophageal wall due to the coordination of muscle activation is provided, which may help relate clinical data from manometry and ultrasound images to the underlying esophageal motor function

Numerical ABL Wind Tunnel Simulations with Direct Modeling of Roughness Elements through Immersed Boundary Condition Method

Reproduction of atmospheric boundary layer wind tunnel experiments by numerical simulation is achieved in this work by directly modeling with immersed boundary method the geometrical elements placed in the wind tunnel's floor to induce the desired characteristics to the boundary layer.The wind tunnel has a cross section of 2.2 m x 2.25 m, with an inlet region 14 m long and a working region 2 m long. Boundary layer development is shaped up with a series of cubical elements, 3 cm in side, placed in a regular staggered arrangement with a 15 cm spacement. Vortex induction, Standen spires type elements, of 13,4 cm height, and a wall of 31.5 cm height are placed at the inlet. This arrangement is used to reproduce a representative urban site boundary layer (figure 1).The numerical model is implemented on the basis of the open source modelcaffa3d.MBRi [Usera et al 2008], which uses a finite volume method over block structured grids, coupled with various LES approaches for turbulence modeling and parallelization through domain decomposition with MPI [Mendina et al 2013]. Simulations were setup with approximately 2 million cells per block, with a 26 block arrangement. The computational grid is horizontally uniform with a resolution of 1.04 cm x 1.04 cm and nonuniform in vertical direction with the grid points concentrated near the floor . The grid spacing is geometrically stretched away from the floor with a minimum value of 1mm. The time step is 0.1 second and the computation is distributed in 26 cores on the Cluster-FING infraestructure [www.fing.edu.uy/cluster]. The Immersed boundary method approach followed the work of [Liao et al 2009]. Numerical simulation results are compared to wind tunnel measurements for the mean velocity profiles (figure 2), rms profiles and spectrums, providing good overall agreement. We conclude that the Immersed Boundary Condition method is a promising approach to numerically reproduce ABL Boundary Layer development methods used in physical modeling.Agencia Nacional de Investigación e Innovació

Second order convergence of a modified MAC scheme for Stokes interface problems

Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution study, the rigorous convergence proofs are usually limited to particular reformulations and boundary conditions. In this paper, a rigorous error analysis of the marker and cell (MAC) scheme for Stokes interface problems with constant viscosity in the framework of the finite difference method is presented. Without reformulating the problem into elliptic PDEs, the main idea is to use a discrete Ladyzenskaja-Babuska-Brezzi (LBB) condition and construct auxiliary functions, which satisfy discretized Stokes equations and possess at least second order accuracy in the neighborhood of the moving interface. In particular, the method, for the first time, enables one to prove second order convergence of the velocity gradient in the discrete $\ell^2$-norm, in addition to the velocity and pressure fields. Numerical experiments verify the desired properties of the methods and the expected order of accuracy for both two-dimensional and three-dimensional examples