A unified fluid-structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-α scheme are used for the spatial and temporal discretization. The membrane discretization is based on curvilinear surface elements that can describe large deformations and rotations, and also provide a straightforward description for contact. The fluid is described by the incompressible Navier-Stokes equations, and its discretization is based on stabilized Petrov-Galerkin FE. The coupling between fluid and structure uses a conforming sharp interface discretization, and the resulting non-linear FE equations are solved monolithically within the Newton-Raphson scheme. An arbitrary Lagrangian-Eulerian formulation is used for the fluid in order to account for the mesh motion around the structure. The formulation is very general and admits diverse applications that include contact at free surfaces. This is demonstrated by two analytical and three numerical examples exhibiting strong coupling between fluid and structure. The examples include balloon inflation, droplet rolling and flapping flags. They span a Reynolds-number range from 0.001 to 2000. One of the examples considers the extension to rotation-free shells using isogeometric FE.
Swirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners, turbines and jet engines. To simulate the highly nonlinear dynamics of the flow, it is necessary to use high-order numerical methods, leading to increased computational cost. To be able to perform simulations in acceptable turn-around time, an available LES code for solving the filtered compressible Navier-Stokes equations in cylindrical coordinates using compact finite-difference schemes was parallelized for massively-parallel architectures. The parallelization was done following the ghost-cell approach for filtering in the three spatial directions. The inter-process communication is handled using the message passing interface (MPI). The weak and strong scaling properties of the code indicate that it can be used for massively parallel simulations using several thousand processors.
Circular jet flows play an important role for many technical applications. Realistic simulations of such flows require modelling of the nozzle geometry to represent the turbulent state of the boundary layer at the nozzle exit. An available high-order finitedifference code for solving the compressible Navier-Stokes equations on a cylindrical grid was adapted to account for the nozzle geometry within the simulation domain. The code was parallelized using the message-passing interface MPI to be able to complete the simulations within acceptable turn-around times. Validation of the implementation was performed by checking the convergence behaviour of the spatial discretization schemes.
a b s t r a c tVortex breakdown of swirling, round jet flows is investigated in the compressible, subsonic regime by means of Direct Numerical Simulation (DNS). This is achieved by solving the compressible Navier-Stokes equations on a cylindrical grid using high-order spatial and temporal discretization schemes. TheReynolds number is Re = ρ The integral swirl number at the inflow is S int = 0.85. The parameters are chosen properly so as to make comparisons with existing experiments at lower Mach numbers possible while still enabling a study of compressible and baroclinic effects. Different from previous numerical investigations, a nozzle immersed in the fluid is included in the computational domain and is modelled as an isothermal no-slip wall, either rotating with the mean azimuthal flow direction or kept at rest. The present investigation aims to clarify the role played by the nozzle wall motion for the vortex breakdown of the swirling jet. We study the nozzle flow as well as the swirling jet flow simultaneously, a novelty for numerical investigations of vortex breakdown in swirling jets. Depending on the nozzle wall motion, the flow differs significantly upstream of the vortex breakdown: for the rotating nozzle, the flow inside the nozzle is purely laminar and the azimuthal boundary layer at the outer nozzle wall gives rise to the axisymmetric mode n = 0 and a single-helix type instability with azimuthal wave number n = 1. With the nozzle at rest, a transitional flow is observed within the nozzle where a helical instability with azimuthal wave number n = 12 dominates, growing in the boundary layer at the nozzle wall. For both nozzle setups, the helical instabilities observed for the nozzle flow interact with the developing vortex breakdown and the conical shear-layer downstream of the nozzle. For the nozzle at rest, this interaction results in a vortex breakdown configuration which is shifted in the upstream direction and which has a smaller radial and streamwise extent compared to the rotating nozzle case and the recirculation intensity is higher. The dominant frequency is highly influenced by the flow upstream of the vortex breakdown and is substantially higher for the nozzle at rest. Although the nozzle flow field differs for the two configurations and therefore alters the vortex breakdown downstream, a single-helix type instability n = 1 governing the vortex breakdown is found for both cases. This provides strong evidence for the robustness of the instability mechanisms leading to vortex breakdown.
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