On the existence of a Generalized Langevin model representation for second-moment closures

Naud

Flow Turbulence Combust

et al. 2008

Self Cite

Two transported PDF strategies, joint velocity-scalar PDF (JVSPDF) and joint scalar PDF (JSPDF), are investigated for bluff-body stabilized jet-type turbulent diffusion flames with a variable degree of turbulence-chemistry interaction. Chemistry is modeled by means of the novel reaction-diffusion manifold (REDIM) technique. A detailed chemistry mechanism is reduced, including diffusion effects, with N 2 and CO 2 mass fractions as reduced coordinates. The second-moment closure RANS turbulence model and the modified Curl's micro-mixing model are not varied. Radiative heat loss effects are ignored. The results for mean velocity and velocity fluctuations in physical space are very similar for both PDF methods. They agree well with experimental data up to the neck zone. Each of the two PDF approaches implies a different closure for the velocity-scalar correlation. This leads to differences in the radial profiles in physical space of mean scalars and mixture fraction variance, due to different scalar flux modeling. Differences are visible in mean mixture fraction and mean temperature, as well as in mixture fraction variance. In principle, the JVSPDF simulations can be closer to physical reality, as a differential model is implied for the scalar fluxes, whereas the gradient diffusion hypothesis is implied in JSPDF simulations. Yet, in JSPDF simulations, turbulent diffusion can be tuned by means of the turbulent Schmidt number. In the neck zone, where the turbulent flow field results deteriorate, the joint scalar PDF results are in somewhat better agreement with experimental data, for the test cases considered. In composition space, where results are reported as scatter plots, differences between the two PDF strategies are small in the calculations at hand, with a little more local extinction in the joint scalar PDF results.

Section: Turbulence Modelmentioning

confidence: 99%

Joint Scalar versus Joint Velocity-Scalar PDF Simulations of Bluff-Body Stabilized Flames with REDIM

Naud

Flow Turbulence Combust

et al. 2008

Self Cite

“…Note that we follow the general formalism introduced in [4], such that the trace of the tensors T (n) ij is zero in variable density flows, and where the tensors T (9) ij and T (10) ij (and the GLM coefficients ξ i ) are introduced in order to allow GLM representations of Reynolds-stress models that include terms which are cubic in b ij . It is useful to write Eq.…”

Section: Glm General Formulationmentioning

confidence: 99%

“…This is a useful way to derive consistent and realisable second-moment closures [3]. The other way around, the Langevin model can be specified such that it corresponds to a given Reynoldsstress model [2,4]. Still, the choice for a Langevin model corresponding to a given Reynolds-stress model is not unique.…”

Section: Introductionmentioning

confidence: 99%

Generalised Langevin Model in Correspondence with a Chosen Standard Scalar-Flux Second-Moment Closure

Naud

Flow Turbulence Combust

2010

In the context of transported joint velocity-scalar probability density function methods, the correspondence between Generalised Langevin Models (GLM) for Lagrangian particle velocity evolution and Eulerian Reynolds-stress turbulence models has been established in the 1990's by S.B. Pope. It was shown that the GLM representation of a given Reynolds stress model is not unique. It was also shown that a given GLM together with a given mixing model for particle composition evolution implies a differential scalar-flux model. In this paper, we study how extra constraints can be applied on the choice of the GLM coefficients in order to imply a chosen scalar-flux model. This correspondence between GLM-implied and standard scalar-flux models is based on the linear relaxation term and on the mean velocity gradient contributions in the rapid term. In general, GLM-implied models possibly involve more terms (including anisotropy effects in the scalar-flux decay rate and some high-order terms in the rapid-pressure-scrambling term). The proposed form of the GLM supposes a non-constant value for the diffusion coefficient C0, originally identified as a Kolmogorov constant. Here, the value of C0 is determined in order to yield the Monin model for linear relaxation of the scalar-flux, and the constant in the rapid-pressure contribution is related to the choice of the parameter β in the GLM. We finally show how GLM-implied scalar-flux models are in general dependent on the choice of the mixing model and how the proposed GLM can reduce this dependency. These developments are illustrated by results obtained from calculations of the Sydney bluff-body stabilised flame HM1.Response to Reviewers: First of all, we would like to thank the reviewers for their comments which helped to improve the paper. #1We included all the suggestions of Reviewer #1. About remark 5: we used the more general formalism introduced by Wouters [REF. 4] that allows to deal with variable density flows, and with Reynoldsstress models that include cubic terms (we added a remark in the text after Equation (27) at the beginning of Section 4.1). #2The remarks of Reviewer #2 allowed us to distinguish more clearly in the text two aspects: 1. setting the C_0 value depending on the Monin linear relaxation term and 2. removing the effect of the mixing model as much as possible. This lead to some modifications of the text. The modification of β in order to be in agreement with Launder's model for the rapid-pressure-scrambling term is indeed pragmatic. We added some clarifications on this aspect on page 12 in the paragraph "Rapid-pressure-scrambling term". About the "philosophical questions" raised by the reviewer, here are some remarks on the modification of C_0 in order to lead the Monin linear return to isotropy (the main contribution of this paper). As mentioned by the reviewer "the scalar field is dynamically passive". With Taylor's hypothesis, we see the relation between the Monin constant and the GLM coefficient C_0. As discussed in the paper, there is no re...

“…From the comparative study presented in [16], the isotropisation of production model by Launder, Reece and Rodi (LRR-IPM) [17] is used with the modified constant value C ǫ1 = 1.6, instead of the standard value C ǫ1 = 1.44. Consistently, the Lagrangian isotropisation of production model (LIPM) is used in the velocity-scalar PDF approach to describe velocity evolution a i [18,19].…”

Section: Turbulence Modelmentioning

confidence: 99%

Scalar PDF and velocity-scalar PDF modelling of the bluff-body stabilised flame HM1 using ILDM

Naud¹,

Proceedings of the International Symposium on Turbulence, Heat and Mass Transfer

et al. 2006

-Velocity-scalar and scalar PDF results are compared for the bluff-body stabilised flame HM1 using ILDM chemistry based on mixture fraction, and CO 2 and H 2 O mass fractions. The same Reynolds stress turbulence model and the same modified Curl mixing model are used. No effect of radiative heat loss is included. The results for mean velocity and Reynolds stresses are satisfactory and very similar for both calculations. Each PDF modelling approach implies a different closure for the velocity-scalar correlation. In the present calculations this leads to significant differences in the radial profiles of mean scalars and of mixture fraction variance (different scalar flux modelling): velocity-scalar PDF results (differential scalar flux model) are better than scalar PDF results (gradient diffusion). Results in composition space (scatter plots) confirm the higher quality of the velocity-scalar PDF.