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Über dieses Buch

The master thesis of David Roos Launchbury deals with the implementation and validation of a numerical solver for incompressible large eddy simulation (LES) with heat transfer in OpenFOAM. Academic and industrial cases, ranging from flow between parallel plates to film cooling, are investigated utilising existing and newly-implemented turbulence models. Simulations using no turbulence models, i.e. under-resolved DNS (UDNS) simulations, are performed for comparison. Very good results are obtained in all cases with variations among the individual models, with the UDNS simulations performing surprisingly well. The study shows that the developed software is able to simulate complex cases reliably and accurately.



1. Introduction

One of the major limitations when performing fluid dynamics simulation has been, and will always be, the available resources to do such calculations. In recent years the computational power of computers and the availability of large parallel clusters have drastically increased and with that, simulations have become more and more complex. This allows for more detailed studies of physical phenomena in challenging environments and geometries, but only if the software tools are enhanced along with the hardware improvements. The focus of this work lies on improving a previously developed solver (see [19]) to be used for the simulation of highly turbulent flows using a method known as large eddy simulation (LES).
David Roos Launchbury

2. Large Eddy Simulation

The behaviour of fluids can be described by the well-known mathematical model known as the Navier-Stokes equations. The original equations include formulations for the conservation of momentum, energy and mass, therefore leading to three momentum equations, one energy equation and one continuity equation. The form presented below is a simplification of these equations for incompressible flows and a constant viscosity. For a detailed derivation of the Navier-Stokes equations as well as the simplifications applied for incompressibility, many textbooks on fluid dynamics are available, eg. [12], [22] or [5].
David Roos Launchbury

3. Subgrid Models

The following sections describe the individual models used in the context of this work and how they approximate these subgrid stresses. First and foremost, all models shown here are based on the eddy-viscosity assumption, ie. it is assumed that the effects of the subgrid stresses cause increased transport and dissipation and can therefore be approximated (Boussinesqapproximation, see [12]) by increasing the laminar viscosity by a turbulent counterpart.
David Roos Launchbury

4. Solver

In the previous work [19] a new solver for time-dependent incompressible flows was developed. It uses an explicit, third-order accurate time integration method based on the third-order Runge-Kutta scheme. It also offers the possibility of treating the viscous terms implicitly by applying a hybrid time integration scheme consisting of the Runge-Kutta and the Crank-Nicolson method (see [14]). It was shown that the solver is able to reach the predicted orders of accuracy by performing an order-verification study using the method of manufactured solution [38]. The full details of the numerical schemes as well as the verification procedure and results can be found in [19].
David Roos Launchbury

5. Validation

The solver along with the previously described turbulence models were validated by performing a series of different test cases. These cases were selected in such a manner that different physical phenomena can be investigated. They are also cases where stationary RANS models usually give unsatisfactory results due to the inadequacy of the turbulence models.
David Roos Launchbury

6. Parallel Performance

Large eddy simulations are computationally expensive. Apart from a fine mesh resolution a large number of timesteps is required to get significant results. This is due to the fact that not only does the simulation have to reach a statistically steady state (eg. fully developed flow), it then needs to run long enough to provide meaningful average values. This is even more the case when transient statistics such as shedding frequencies are needed (eg. around a square cylinder, see section 5.3) as the resolution of the frequency spectrum depends on the total number of samples available. For these reasons parallel computing is a necessary tool in order to deal with large eddy simulations.
David Roos Launchbury

7. Recommendations for LES Simulations

This chapter provides a few guidelines when dealing with large eddy simulations in general as well as specifically in OpenFOAM.
David Roos Launchbury

8. Conclusions

In this work, the basic third-order time-accurate explicit solver for Open-FOAM previously developed in [19] was improved in such a way that it is now possible to simulate complex cases using the technique of large eddy simulation (LES). As a first step, the theoretical background of the LES procedure was explained. Afterwards, the turbulence models used in the context of this work are briefly described. More detailed information is given on the sigma subgrid model developed by [30], which was implemented from scratch as a part of the present study.
David Roos Launchbury

9. Unresolved Issues

During the course of this work a few issues have surfaced concerning solver stability. The implementation of the new pressure-velocity coupling scheme has delivered excellent results in the channel, square cylinder and ribbed channel cases but has lead to solver divergence in the film cooling simulation. The velocity values inside the cooling hole were increasing beyond the stability limit given by the CFL condition, therefore causing the simulation to abort. This phenomenon could be observed on different grids and even at very low timesteps which lead to the conclusion that it is not just a matter of stability but a bug in the code.
David Roos Launchbury

10. Outlook

As a first step it is imperative that the problems described in the previous section are addressed.
Further, the ongoing discussion on mesh resolution will be followed, especially the results of the work by [13] as, if successful, they could provide a powerful tool to estimate the required LES grid size based on a RANS simulation.
David Roos Launchbury


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