Mellado, Juan Pedro

Sarkar, Sutanu

English

CaltechCONF

Large Eddy Simulation of Jets with Density VariationJ. P. Mellado and S. SarkarUC San Diego1. IntroductionThe mixing of jets into an ambient with different density occurs in many applications in-cluding energy and propulsion systems as well as in nature. When the momentum is high, thesituation of interest here, the influence of variable density effects dominates that of buoyancy.In nonreacting jets, the ratio of densities of the jet inflow and the ambient, s = ρj/ρ∞, is theoverall control parameter. It has been proposed [7, 6] that the asymptotic self-similar evolutionis that of an equivalent constant-density round jet with the nozzle diameter, d, replaced byds1/2. The axial decay rate of centerline values of concentration and velocity is thus larger for alighter-than-ambient jet. In reacting jets, an equivalent diameter, d(ρf/ρ∞)1/2 with ρf denotingthe density at the flame has been proposed [7]. It has been reported by [5] that the spreadingrate of the concentration field is independent of the density ratio. The same is found to be truefor the centerline decay if the effective diameter is used. Instabilities are also of interest[3, 1];side jets, corresponding to a self-excited mode, appear when s < 0.7.2. ResultsThe evolution of a plane jet exiting from a nozzle of height h with a temperature variationand corresponding density variation is simulated. The filtered Navier-Stokes equations (com-pressible) are solved in a flow domain of size 30h×16h×8.4h, employing 164×128×64 points. Adynamic mixed model is used for the subgrid terms. The molecular transport terms are droppedso that, in principle, the molecular Reynolds number is infinite.As an example, results on the evolution of the centerline velocity, ∆Uc, are shown. Fig. 1(a)shows that, as expected for a plane jet, (∆U0/∆Uc)2 eventually increases linearly as a functionof x/h. Also, in agreement with published literature, a lighter-than-ambient jet exhibits a largervelocity decay. Fig. 1(b) replots the results using an equivalent slot width which, for a plane jet,turnns out to be hs. There is no collapse between the different cases showing that the observedvariable-density effect in the region x/h < 15 differs from that in the self-similar far field. Inthe full presentation, we will report on the evolution of all Reynolds stresses, the approach toasymptotic self-similarity, and the development of flow instabilities.In combustion formulations based on a conserved scalar, nonlinear dependencies such as ρ(Z)and Yi(Z) in the case of infinitely-fast chemistry and, similarly, ρ(Z;χ) and Yi(Z, χ) in the caseof a flamelet approach introduce new subgrid terms. Here, χ denotes the scalar dissipation. Thebeta-pdf approach to determine the subgrid contribution based on a a scale-similarity model forthe local, pointwise subgrid variance is often used. [4] propose a different approach, ARM, basedon approximate deconvolution along with input of the Reynolds-averaged subgrid variance. Ina detailed comparison of the two approaches by [2] in a plane jet, it has been found that ARMperforms better than beta pdf for global nonlinearities such as polynomials, Zn. Fig. 2 showsthe crosswise profile of the averaged subgrid contribution for the case of ρ(Z). (The strangelyimproved agreement with increased filter size is specific to this nonlinearity and does not occurin general!) For nonlinearities that are strongly localized in scalar space such as the Arrheniusdependence on temperature, a combination of ARM (for obtaining the local subgrid variance)plus beta pdf works better than using ARM by itself. We will further discuss the relativeperformance of ARM and beta pdf in the full presentation.10 5 10 15 20x/h0246810(∆U 0/∆U c)20 20 40 60 80x/(hs)0246810(∆U 0/∆U c)2Figure 1: Centerline velocity decay for different density ratios: s = 1.00 (circles), s = 0.50(squares), and s = 0.25 (triangles). On the right, the effective nozzle width, hs, is used.0.0 0.5 1.0 1.5 2.0y/δZ0.000.080.160.240.32〈ρ(Z)sg〉(a)0.0 0.5 1.0 1.5 2.0y/δZ0.000.080.160.240.32〈ρ(Z)sg〉(b)Figure 2: Prediction of the SGS part of ρ(Z) by (a) the ARM model, (b) the beta-PDF model,at a downstream location x/h = 11.0. Hollow symbols correspond to exact values and solidsymbols to model predictions. Circles, squares and triangles denote filter sizes of 4, 8 and 16,respectively. Dashed line in (b) corresponds to beta-PDF with exact, pointwise subgrid variancefor ∆f/∆g = 4. Vertical solid line indicates stoichiometric position, 〈Z〉 = 0.055.References[1] D. M. Kyle and K. R. Sreenivasan. The instability and breakdown of a round variable-density jet.J. Fluid Mech., 249:619–664, 1993.[2] J. P. Mellado, S. Sarkar, and C. Pantano. Reconstruction subgrid models for nonpremixed com-bustion, in press. Phys. Fluids, 2003.[3] P. A. Monkewitz, D. W. Bechert, B. Barsikov, and B. Lehmann. Self-excited oscillations and mixingin a heated round jet. J. Fluid Mech., 213:611–639, 1990.[4] C. Pantano and S. Sarkar. A subgrid model for nonlinear functions of a scalar. Phys. Fluids,13:3803–3819, 2001.[5] C. D. Richards and W. M. Pitts. Global density effects on the self-preservation behaviour ofturbulent free jets. J. Fluid Mech., 254:417–435, 1993.[6] F. P. Ricou and D. B. Spalding. Measurements of entrainment by axisymmetrical turbulent jets.J. Fluid Mech., 11:21–32, 1961.[7] M. W. Thring and M. P. Newby. Combustion length of enclosed turbulent jet flames. FourthSymposium (Intl.) on Combustion, pages 789–796, 1953.2

Large Eddy Simulation of Jets with Density Variation

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