Introductory Chapter: Large Eddy Simulation for Turbulence Modeling

1. Introduction

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 molecular fuel air mixing, large-scale turbulent fuel air mixing, and chemical reactions in aircraft engines, there are significant challenges in this area. Many of these processes take place at various ranges of length and time [1]. LES also has wide range of applications in gas turbine. Reduced life cycle costs for the operator and decreased environmental effect during engine production and operation are crucial factors for gas turbine manufacturers. Many gas turbine components use a stable RANS approach; however, when it comes to the rotor-stator interaction in turbomachinery, we frequently use an unsteady RANS (URANS) approach where the governing flow equations are phase averaged assuming a constant rate of rotation [2]. LES-related techniques are being used more frequently as a result of the inability of RANS models to produce accurate off-design aerodynamics forecasts, noise source information, and predictive capability for the control of drag, noise, and mixing processes in general. The huge advances in accessible computing power over the past few years have provided additional encouragement for the usage of LES [3].

1.1 LES for aeroacoustics

A major amount of the noise that is produced by air and land transportation, such as fan noise, jet noise, high-speed train noise, and airframe noise, is a growing environmental concern. Turbulence is a prominent source of aerodynamic noise. Because LES directly computes large scale fluctuations, which are known to add the most to the noise generated in many issues, LES is a very helpful technique in aeroacoustics. Applications of LES for foretelling aerodynamic noise likely began in the 1990s and have since grown to be a very active area of research. LES shows considerable promise for aeroacoustics computations, from improving source modeling for acoustic analogies to practical prediction and designing of engineering systems in the near future. It also advances fundamental understanding of noise creation. LES algorithms should be able to reliably mimic the flow physics that captures the transfer of energy from turbulent to acoustic modes if properly built and validated. The proper SGS modeling, numerical issues such as high-order accuracy and careful usage of the boundary conditions, and practical engineering configurations where flow Reynolds numbers are typically very high make it impractical to use LES for both noise source capturing and its propagation and are all still significant challenges. Additionally, standard validation study against approved experimental databases can be carried out for relatively basic LES applications. Since intricate statistics such as two-point space-time correlations are essential to flow-generated sound, more attention should be given while validating LES applications in aeroacoustics, according to the theory. As a result, the validation may begin with the most basic facts before moving on to more intricate and acoustically important statistics [1].

1.2 LES for turbulent/transitional flows

Turbulence has an important property, which is scale invariance. Certain characteristics of the flow are said to be scale invariant if they hold true across various motion scales. Such symmetry can be explained as an especially straightforward relation between small and large scales, making it a crucial component in turbulence models [4]. LES, a different strategy, was first suggested by Smagorinsky in 1963. The traditional RANS approach, which requires solving additional modeled transport equations to determine the so-called Reynolds stresses as a result of the averaging procedure, is not used by LES. When compared with direct numerical simulation (DNS), the computational cost of LES is significantly lower since only small-scale SGS motions are represented and the large-scale motions of turbulent flow are computed directly. LES is more perfect than the RANS approach as the large eddies contain most of the turbulent energy and are accountable for most of the turbulent mixing and momentum transfer, and these eddies are captured directly by LES in full detail where they are modeled in the RANS approach. Moreover, the small scales tend to be more homogeneous and isotropic than the large ones, and thus, the SGS motions modeling should be easier than all scales modeling within a single model such as in the RANS approach [1]. There are two main types of SGS models for LES of turbulent flows. The models that yield expressions for SGS terminology such as a heat flux or stress tensor and typically include eddy viscosity notions fall under one group. The SGS stresses are secondary values, which are directly computed from the definitions in the other category, which describes the unresolved primitive variables such as velocity or temperature [5]. For most meteorological applications, large eddies, which hold the majority of the turbulent kinetic energy (TKE) also referred as energy-containing eddies, are the most significant scales for atmospheric planetary boundary layer (PBL) turbulence, as an example, and are in charge of most turbulent transport concerned. It is a simulation that specifically determines (or eliminates) large eddies when LES roughly reflects the effects of smaller ones. As LES’s grid resolution increases, less are present, a greater spectrum of turbulent eddies is resolved, and LES-generated flows are parameterized, and they become more representative throughout the flow field. Thus, now LES is the most promising/feasible numerical mean for realistic turbulent/transitional flows simulation [6]. LES inlet conditions were also generated on the basis of implementation of digital filter generator (DFG). The test case was the LES of a channel flow with a continuously repeated constriction. The DFG was used to construct three-time series that would be used as LES inlet conditions in the future. Along with entering the first and second moments of the velocity field over the inlet plane from the periodic boundary condition (PBC) simulation in the first, the DFG’s input turbulence scales were set to be spatially homogeneous with values determined using a channel inlet height-weighted area average. The turbulence scales were allowed to change in the second and third time series. Their variation is again inferred from the PBC simulation and is related to wall normal direction. Then, LES’s inlet boundary conditions were created using these distinct time series. These changing turbulent scales have increased the simulation accuracy, which has significant uses [7].

1.3 LES for atmospheric science

Prior LES research mostly concentrated on a turbulent PBL with flat terrain and no clouds. Due to the enormous thermal plumes present and the lack of other flow conditions, this flow regime is best suited to LES without involving complex physical phenomena (such as latent heating and radiation). However, in recent years, LES has been broadened to study more challenging and complicated PBL regimes, which are pertinent to forecasts for severe weather and climate, or more recent applications for wind energy [6].

2. History, current state, and future challenges of LES

2.1 History

Smagorinsky first proposed LES in 1963 for forecasting air flow, and early uses likewise fell under this category. Deardoff and Schumann introduced LES to engineering-related flow for the first time in 1970 and 1975, respectively. From the 1960s to roughly the middle of the 1980s, LES took a while to develop, and the applications primarily consisted of straightforward, building-block flows, such as homogeneous turbulence, plane channel flows, mixing layers, and so on. However, as computing power increased, a very fast development and sharp increase in LES applications began around the middle of the 1980s, particularly after the 1990s with substantial growth of the LES community and a wide range of LES applications shifting from simple flows to complex flows, including multi-phase flow, heat transfer, and fluid dynamics, aeroacoustics, transmission, combustion, etc. In addition to the rise in computing power, it is now evident that RANS approaches naturally have limitations and can’t deal with certain categories of sophisticated turbulent flow issues, and LES has developed quickly and has a wide range of applications [1].

2.2 Current state

As was indicated in the preceding section, the LES was initially applied successfully to examine the specifics of flow problems with low Reynolds numbers and generally simple geometry, such as homogeneous turbulence, mixing layers, and flat channel flows. Despite the fact that LES is used in such academic or essential setups still exists today, primarily for model validation and a basic comprehension of flow physics, etc. When the RANS technique has failed, emphasis has changed to more intricate arrangements with flow characteristics. Particularly, corporate interest in applying LES to complicated engineering flows has been stimulated by decades of advancement in LES and the advent of cheap workstation clusters and massively parallel computers. Nevertheless, the RANS technique has not been substituted by LES, and it seems unlikely that it will be for some time due to two key factors, computational analytical tool for real-world engineering challenges firstly, notwithstanding the present computing ability for practical purposes, performing LES routinely still costs far too much in terms of computing; secondly, LES is not yet mature enough for users without sufficient results can be achieved with the level of solution accuracy that can be anticipated using experience and knowledge. Currently, LES has wide range of applications in turbulent flows, gas turbine, jet noise, aeroacoustics, and atmospheric science [1].

2.3 Future challenges

In the future, LES will be properly used for a wider series of flow problems and for more difficult problems with more multi-disciplinary uses. Nevertheless, numerous major issues/challenges related with LES and its applications such as wall layer modeling, SGS modeling, LES of turbulent combustion, generation methods for inflow boundary conditions, etc., are still existing. Before LES can become a trustworthy, strong engineering analysis tool that can be utilized as a substitute for RANS, there are still important problems that need to be overcome. It is extremely improbable that LES will entirely overtake RANS and become a design tool for the foreseeable future, without considerable years of LES experience [1].

Actually, the PBL is more complex as compared with LES for simulation of systems; however, this complexity is generated due to heterogeneous nature of the considering surface. For instance, the earth land surface is described by spatially varying elements, urban expansion, and undulating grounds, which can merge circulations and therefore alter the turbulence dynamics. These complex surfaces may significantly affect turbulence transport in many climate applications, for example, vegetation development, pollution, cloud formation, and storm formation. In summary, the LES is more employed than realistic PBL for multi-dimensional environmental flows.

large eddy simulation	LES
Sub-grid scale	SGS
Reynolds-averaged Navier-Stokes	RANS
Direct numerical simulation	DNS
Turbulent kinetic energy	TKE
Planetary boundary layer	PBL
Digital filter generator	DFG
Periodic boundary condition	PBC