**8. References**

20 Will-be-set-by-IN-TECH

Figure 6 shows the typical values of *c* and *Y*CH4 computed using Fluent for flame F3 at *x*/*D* = 8.5 as a function of normalised radial distance, *r*/*D*. The experimental measurements and the results computed earlier are also shown for comparison. This flame has lower Reynolds and Karlovitz numbers compared to F1 and hence thermo-chemical effects are dominant compared to turbulence effects. The experimental data clearly shows that the peak value of mean temperature in F3 is larger compared to F1 (cf. Figs. 5 and 6). The relative role of the turbulence and thermo-chemistry is supposed to be naturally captured by the scalar dissipation rate based modelling of turbulent premixed flames, which is reflected well in the results shown in Fig. 6. There is some under prediction of the mean temperature in the calculations using Fluent compared to the previous results, which is due to, as noted earlier, over prediction of the entrainment rate. However, the agreement is good for *r*/*D* ≤ 1.0 and

Fig. 6. The radial variation of *c* and *Y*CH4 (in %) in flame F3; Fluent results (—), experimental

In this chapter, a brief overview of various combustion modelling approaches to simulate lean premixed and partially premixed flames is given. The focus is limited to RANS framework because of its high usage in industry currently. The strained flamelet formulation developed recently is discussed in some detail and important details in implementing this model into a commercial CFD code are discussed. The results obtained for pilot stabilised turbulent Bunsen flames using Fluent with strained flamelet model are compared to experimental measurements and earlier CFD results. These published CFD results (Kolla & Swaminathan, 2010b) are obtained using another CFD code employing different numerical schemes and solver methodologies. A good comparison among the Fluent and previous CFD results and the experimental measurements is observed. These comparisons, gives good confidence on the implementation of the strained flamelets model and the associated source and sink terms in the commercial CFD code, Fluent. This initial work serves as a foundation for further studies of lean premixed, partially premixed combustion in industry relevant combustor geometries and, turbulence and thermo-chemical conditions using this modelling framework. Also, this implementation provides opportunities to study self induced combustion oscillations, interaction of flame and sound, interaction of flame generated sound waves with combustor geometries, etc., since a compressible formulation is used in the implementation. The influence of non-unity Lewis number on this combustion

the trend is captured correctly for *r*/*D* > 1 for the flame F3.

measurements (◦) and previously published results (- -).

**6. Summary and future scope**

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**1. Introduction**

Hydrodynamic stability has been a subject extensively investigated in fluid dynamics (see Lin 1966, Drazin & Reid 1982; Godreche & Manneville 1998; Schmid & Henningson 2001, and references therein). We still lack, however, a stability analysis capable of operationally handling results from experiments and numerical simulations, or data taken directly from nature. These "real problems", as we will hereafter refer to, are in general highly nonlinear and localized in space and time. In other words, the signal tends to be temporally intermittent, the regions of interest may be finitely and irregularly defined, and the definition domain could be on the move. Specific examples include atmospheric cyclogenesis, ocean eddy shedding, vortex shedding behind bluff bodies, emergence of turbulent spots, among many others. In this study, we present a new approach to address this old issue, and show subsequently how this approach can be conveniently used for the investigation of a variety of fluid flow problems

**Multiscale Window Interaction and Localized** 

*1Harvard University, School of Engineering and Applied Sciences, Cambridge, MA* 

*2Central University of Finance and Economics, Beijing* 

*4Nanjing Institute of Meteorology, Nanjing* 

*3Stanford University, Center for Turbulence Research, Stanford, CA* 

**Nonlinear Hydrodynamic Stability Analysis** 

X. San Liang\*

*1,3USA 2,4China* 

**8**

Localization and admissibility of finite amplitude perturbation are the two basic requirements for the approach. Classically, stability in terms of normal modes (e.g., Drazin & Reid 1982) organizes the whole domain together to make one dynamical system; stability defined in the sense of Lyapunov is measured by a norm (energy) of the perturbation over the whole spatial domain (cf. section 2). These definitions do not retain local features. On the other hand, many analyses have been formulated aiming at localized features, among which the geometrical optics stability method (Lifschitz 1994) and the Green function approach for convective/absolute instability study (Briggs 1964; Huerre & Monkewitz 1990; Pierrehumbert & Swanson 1995) now become standard. These approaches, though localized, usually rely on

We integrate the philosophies of the above two schools to build our own methodology, which retains full physics, and admits arbitrary perturbation, particularly perturbation of local dynamics, finite amplitude and variable spatial scales. The basic idea is that: The Lyapunov type norm (energy) could be "localized" to make a spatio-temporal field-like metric. In doing

which would otherwise be very difficult, if not impossible, to investigate.

small perturbation approximation to make linearization possible.

\*URL:http://people.seas.harvard.edu/∼san

