High-Order Unstructured Lagrangian One-Step WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems: Applications to Compressible Multi-Phase Flows

In this article we present the first better than second order accurate unstructured Lagrangian-type one-step WENO finite volume scheme for the solution of hyperbolic partial differential equations with non-conservative products. The method achieves high order of accuracy in space together with essentially non-oscillatory behavior using a nonlinear WENO reconstruction operator on unstructured triangular meshes. High order accuracy in time is obtained via a local Lagrangian space-time Galerkin predictor method that evolves the spatial reconstruction polynomials in time within each element. The final one-step finite volume scheme is derived by integration over a moving space-time control volume, where the non-conservative products are treated by a path-conservative approach that defines the jump terms on the element boundaries. The entire method is formulated as an Arbitrary-Lagrangian-Eulerian (ALE) method, where the mesh velocity can be chosen independently of the fluid velocity. The new scheme is applied to the full seven-equation Baer-Nunziato model of compressible multi-phase flows in two space dimensions. The use of a Lagrangian approach allows an excellent resolution of the solid contact and the resolution of jumps in the volume fraction. The high order of accuracy of the scheme in space and time is confirmed via a numerical convergence study. Finally, the proposed method is also applied to a reduced version of the compressible Baer-Nunziato model for the simulation of free surface water waves in moving domains. In particular, the phenomenon of sloshing is studied in a moving water tank and comparisons with experimental data are provided

Single and multiphase CFD approaches for modelling partially baffled stirred vessels: comparison of experimental data with numerical predictions

Whilst the use of CFD to study mixing vessels is now common-place, there are still many specialised applications that are yet to be addressed. Here we present CFD and PIV results for a hydrodynamic study of a partially baffled vessel with a free surface. The standard k.ε and SSG Reynolds Stress turbulence models are used and the numerical predictions of the mean flow field are compared with experimental data for single phase modelling. At low rotation rates a flat free surface is observed and the flow is simulated using a single phase model, whilst at high rotation rates an Eulerian–Eulerian multiphase model is used to capture the free surface location, even under conditions when gas is drawn down to the impeller. It is shown that there are significant transient effects that mean many of the “rules of thumb” that have been developed for fully baffled vessels must be revisited. In particular such flows have central vortices that are unsteady and complex, transient flow-induced vortical structures generated by the impeller–baffle interactions and require a significant number of simulated agitator rotations before meaningful statistical analysis can be performed. Surprisingly, better agreement between CFD and experimental data was obtained using the k.ε than the SSG Reynolds stress model. The multiphase inhomogeneous approach used here with simplified physics assumptions gives good agreement for power consumption, and with PIV measurements with flat and deformed free surfaces, making this affordable method practical to avoid the erroneous modelling assumption of a flat free surface often made in such cases

Ballbot-Inspired orbital refueling depot and fluid-slosh effects on Spacecraft attitude dynamics

Orbital refueling has become a subject of increasing interest as longer, deep space missions and manned missions to the Moon and Mars are being contemplated once again. For fueling depots to become part of the infrastructure in space capable of enhancing deployment and service operations, there remains a slew of technical, operational, and engineering challenges which must be overcome. In this thesis, focus is placed mainly on the issue of fluid slosh and its effects on the spacecraft dynamics and the design of an attitude control system. In pursuit of overcoming the attitude tracking errors and instability from the fluid slosh, a novel satellite design is presented based on an omnidirectional ball-balanced robot (ball-bot) which aims at minimizing the control effort required to stabilize the satellite while also maximizing the amount of fuel it can carry. The satellite is comprised of two primary elements: a spherical tank, containing the fuel payload and a cuboid bus, containing the attitude control system (ACS) and other subsystems. The satellite bus is mobile and can displace itself over the surface of the sphere and has a sunshield which is deployed in orbit which shields the spherical tank from solar radiation. The cube is mobile and can displace itself on the surface of the sphere to point to the sun ensuring the protection of the fuel payload. A presentation of the state-of-the-art of orbital fuel depots is first presented, and subsequently, a contextualization of orbital dynamics, along with the mathematical modeling of the satellite, is carried out, complemented by a discussion about the limitations of the work and the assumptions of the model. A simulation of the satellite¿s dynamics with the fluid slosh is conducted using Simulink and the sun-tracking of the cuboid-bus with Mathematica. Finally, a set of conclusions are presented and recommendations for future research and improvements, based on the conclusions, are made.Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructur

Modeling Thermal Turbulence Using Implicit Large Eddy Simulation

A general description of a thermally coupled fluid flow is given by the incompressible Navier-Stokes equations coupled with the heat equation using Boussinesq approximation, whose mathematical structure is much well understood. A variational multiscale finite element approximation has been considered for the formulation of incompressible Navier-Stokes equation and heat equation. The complexity of these problems makes their numerical solution very difficult as the standard finite element method is unstable. In the incompressible Navier Stokes equations, two well known sources of numerical instabilities are the incompressibility constraint and the presence of the convective term. Many stabilization techniques used nowadays are based on scale separation, splitting the unknown into a coarse part induced by the discretization of the domain and a fine subgrid part. The modeling of the subgrid scale and its influence leads to a modified coarse scale problem providing stability. In convection-diffusion problem once global instabilities have been overcome by a stabilization method, there are still local oscillations near layers due to the lack of monotonicity of the method. Shock capturing techniques are often employed to deal with them. Proper choice of stabilization and shock capturing techniques can eliminate the local instabilities near layers of convection-diffusion equation. A very important issue of the formulation presented in this thermally coupled incompressible flow is the possibility to model turbulent flows. Some terms involving the velocity subgrid scale arise from the convective term in the Navier-Stokes equations which can be understood as the contribution from the Reynolds tensor of a LES approach and the contribution from the cross stress tensor. This opens the door of modeling thermal turbulence using LES automatically inherited by the formulation used in this work. Different classical benchmark problems are numerically solved in this thesis work for the convection-diffusion equation to show the capabilities of different combination of stabilization and shock capturing methods. In the case of thermally coupled incompressible flows some numerical and industrial examples are exhibited to check the performance of the different combination of stabilization and shock capturing methods and to compare them. The objective is to conclude which method works better to approximate the exact solution and eliminate instabilities and local oscillations

A Chimera method based on a Dirichlet/Neumann(Robin) coupling for the Navier–Stokes equations

We present a Chimera method for the numerical solution of incompressible flows past objects in relative motion. The Chimera method is implemented as an iteration-by-subdomain method based on Dirichlet/Neumann(Robin) coupling. The DD method we propose is not only geometric but also algorithmic, for the solution on each subdomain is obtained on separate processes and the exchange of information between the subdomains is carried out by a master code. This strategy is very flexible as it requires almost no modification to the original numerical code. Therefore, only the master code has to be adapted to the numerical codes and the strategies used on each subdomain. As a basic flow solver, we a use stabilized finite element method

On computations of the integrated space shuttle flowfield using overset grids

Numerical simulations using the thin-layer Navier-Stokes equations and chimera (overset) grid approach were carried out for flows around the integrated space shuttle vehicle over a range of Mach numbers. Body-conforming grids were used for all the component grids. Testcases include a three-component overset grid - the external tank (ET), the solid rocket booster (SRB) and the orbiter (ORB), and a five-component overset grid - the ET, SRB, ORB, forward and aft attach hardware, configurations. The results were compared with the wind tunnel and flight data. In addition, a Poisson solution procedure (a special case of the vorticity-velocity formulation) using primitive variables was developed to solve three-dimensional, irrotational, inviscid flows for single as well as overset grids. The solutions were validated by comparisons with other analytical or numerical solution, and/or experimental results for various geometries. The Poisson solution was also used as an initial guess for the thin-layer Navier-Stokes solution procedure to improve the efficiency of the numerical flow simulations. It was found that this approach resulted in roughly a 30 percent CPU time savings as compared with the procedure solving the thin-layer Navier-Stokes equations from a uniform free stream flowfield