Preface

This book discusses some recent advances in fusion energy research, including the development of new theory, models, and algorithms, and their application in solving practical computational science and engineering problems. Although it is now established that fusion power can make an enduring contribution to future energy supply, offering many benefits of both renewable and resource-limited energy sources, several challenges still need to be addressed before fusion energy can become a commercial reality. Conducting materials need to have extremely high heat tolerances and low enough vapor pressure to reduce plasma contamination. The extreme temperatures and strong magnetic fields inside a nuclear fusion reactor can make the power generation process highly prone to instabilities. Sudden changes in plasma positions during plasma instabilities may lead to disruptions characterized by a loss of magnetic confinement with subsequent release of the magnetic and thermal energy stored in the plasma to surrounding structures. The development of new models and computational techniques that enable us to control these instabilities is critical to establishing the future of nuclear fusion as an efficient alternative energy source.

From a computational viewpoint, fusion devices are challenging to model. The problem is inherently multiphysics due to the electromagnetic interaction of fusion plasma with the surrounding conducting structures. Although most fusion devices have a nominal toroidal geometry, the geometry of the conductors can be rather complex due to several deviations from this ideal situation (holes, cuts, slits, ports, etc.), for example, to make the interior of the machine accessible. A detailed three-dimensional description of the structures is needed to provide an accurate estimate of the effects of current flows, giving rise to models that can be extremely demanding in terms of the computational burden. Fast parallel techniques are often required to make the computations more affordable.

This book includes contributions on several interesting topics, describing new technology and solutions, presenting the development of new models and algorithms, and discussing both engineering challenges and their respective underlying physics, together with examples of both simulations and experimental results from realistic tokamaks configurations. Researchers, engineers, and graduate students in both pure and applied physics, mathematics, and engineering may benefit from this volume. We express appreciation to IntechOpen for their professional support, especially Author Service Manager Ms. Marica Novaković for her patience and continued help in the preparation of this volume.

## **Bruno Carpentieri**

**Chapter 1**

Modeling

**1. Introduction**

Introductory Chapter: Large

Eddy Simulation for Turbulence

*Aamir Shahzad, Muhammad Kashif and Fazeelat Hanif*

Laminar and non-laminar are two major types of flows and are discussed mainly in fluid mechanics. Streamline and turbulent flows are examples of laminar and non-laminar flows; however, a laminar flow can be transformed into non-laminar by applying some kind of perturbations (such as temperature, pressure, force field, etc.) and/or by employing some gradient. This type of conversion process from laminar to non-laminar flow produces new patterns in between the two states, and these patterns are unstable, and it generates the flow instabilities in the fluid. Only large eddies (large-scale motions) are directly computed in large eddy simulation (LES); therefore, to create the three-dimensional (3D) unsteady governing equations for large-scale motions, a low-pass spatial filter is used for the instantaneous conservation equations. LES has wide range of applications for compressible flows, turbulent combustion, aeroacoustics, turbulent/transitional flows, and atmospheric sciences. In comparison to LES for cases involving incompressible flows, much less work has been performed on LES for compressible flows, and there are numerous difficulties/problems in this field. Extra work/requirements are needed for supersonic flows with shock waves in order to accurately and steadily capture the shock while also providing the spatial accuracy necessary to simulate a number of fine-scale turbulence structures. Low-order techniques are typically used to address shock waves, frequently using upwind schemes that are not particularly suitable for LES. Favre filtering is typically used in compressible flows to prevent the entry of sub-grid scale (SGS) terms into the continuity equation; therefore, knowledge and expertise obtained in incompressible flows may not be applicable. SGS modeling for compressible flows is significantly more difficult as a result of the additional equations that must be solved, such as the energy equation for the compressible case, and the necessity to represent additional SGS terms, such as the SGS heat flux [1]. With applications in a variety of combustion issues, LES of turbulent combustion first emerged in the 1990s and has grown significantly in the last 10 years. The majority of combustion chemistry takes place in SGS; therefore, models must be created because chemical reactions typically take place on sizes much smaller than those of LES meshes. However, even with very straightforward SGS combustion models, LES has showed considerable potential in this field and clearly outperformed the Reynolds-averaged Navier-Stokes (RANS) approach. However, due to the complexity of turbulent combustion, which includes chemical reactions, turbulence/chemistry interactions, liquid fuel atomization, liquid fuel injection, droplet breakup and evaporation, small-scale

Faculty of Computer Science, Free University of Bozen-Bolzano, Bolzano, Italy

## **Dr. Aamir Shahzad**

Professor (Associate), Modeling and Simulation Laboratory, Department of Physics, Government College University, Faisalabad, Pakistan

## **Chapter 1**
