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Subgrid-scale models and large-eddy simulation of oxygen stream disintegration and mixing with a hydrogen or helium stream at supercritical pressure

Published online by Cambridge University Press:  11 May 2011

EZGI S. TAŞKINOĞLU  and
JOSETTE BELLAN
EZGI S. TAŞKINOĞLU
Affiliation:
Mechanical Engineering Department, California Institute of Technology, Pasadena, CA 91125, USA
JOSETTE BELLAN*
Affiliation:
Mechanical Engineering Department, California Institute of Technology, Pasadena, CA 91125, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
*
†Email address for correspondence: josette.bellan@jpl.nasa.gov
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Abstract

For flows at supercritical pressure, p, the large-eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid-scale (SGS) fluxes but also new SGS terms, each denoted as a ‘correction’. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations and represent differences, other than contributed by the convection terms, between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) which is the difference between the filtered divergence of the molecular heat flux and the divergence of the molecular heat flux computed as a function of the filtered flow field. We revisit here a previous a priori study where we only had partial success in modelling the q-correction term and show that success can be achieved using a different modelling approach. This a priori analysis, based on a temporal mixing-layer direct numerical simulation database, shows that the focus in modelling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES molecular heat-flux calculation. Furthermore, an a posteriori study is conducted for temporal mixing layers initially containing oxygen (O) in the lower stream and hydrogen (H) or helium (He) in the upper stream to examine the benefit of the new model. Results show that for any LES including SGS-flux models (constant-coefficient gradient or scale-similarity models; dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/gradient models), the inclusion of the q-correction in LES leads to the theoretical maximum reduction of the SGS molecular heat-flux difference; the remaining error in modelling this new subgrid term is thus irreducible. The impact of the q-correction model first on the molecular heat flux and then on the mean, fluctuations, second-order correlations and spatial distribution of dependent variables is also demonstrated. Discussions on the utilization of the models in general LES are presented.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 156 - 193
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Bardina, J., Ferziger, J. & Reynolds, W. 1980 Improved subgrid scale models for large eddy simulation. AIAA Paper 80-1357.CrossRefGoogle Scholar
Bellan, J. 2006 Theory, modeling and analysis of turbulent supercritical mixing. Combust. Sci. Technol. 178, 253–281.CrossRefGoogle Scholar
Bellan, J. & Selle, L. C. 2009 Large eddy simulation composition equations for single-phase and two-phase fully multicomponent flows. Proc. Combust. Inst. 32, 2239–2246.CrossRefGoogle Scholar
Carati, D., Winckelmans, G. S. & Jeanmart, H. 2001 On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation. J. Fluid Mech. 442, 119–138.CrossRefGoogle Scholar
Chehroudi, B., Talley, D. & Coy, E. 1999 Initial growth rate and visual characteristics of a round jet into a sub- to supercritical environment of relevance to rocket, gas turbine and diesel engines. AIAA Paper 99-0206.Google Scholar
Chow, F. K. & P. Moin, P. 2003 A further study of numerical errors in large-eddy simulations. J. Comput. Phys. 184, 366–380.CrossRefGoogle Scholar
Clark, R., Ferziger, J. & Reynolds, W. 1979 Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91 (1), 1–16.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
Geurts, B. J. 1997 Inverse modeling for large-eddy simulation. Phys. Fluids 9 (12), 3585–3587.CrossRefGoogle Scholar
Geurts, B. J. & Frohlich, J. 2002 A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14 (6), L41–L44.CrossRefGoogle Scholar
Ghosal, S. 1996 An analysis of numerical errors in large-eddy simulations of turbulence. J. Comput. Phys. 125, 187–206.CrossRefGoogle Scholar
Hannoun, I. A., Fernando, H. J. S. & List, E. J. 1988 Turbulence structure near a sharp density interface. J. Fluid Mech. 189, 189–209.CrossRefGoogle Scholar
Harstad, K. & Bellan, J. 1998 Isolated fluid oxygen drop behavior in fluid hydrogen at rocket chamber pressures. Intl J. Heat Mass Transfer 41, 3537–3550.CrossRefGoogle Scholar
Harstad, K. & Bellan, J. 2000 An all-pressure fluid-drop model applied to a binary mixture: heptane in nitrogen. Intl J. Multiphase Flow 26 (10), 1675–1706.CrossRefGoogle Scholar
Harstad, K., Miller, R. S. & Bellan, J. 1997 Efficient high-pressure state equations. AIChE J. 43 (6), 1605–1610.CrossRefGoogle Scholar
Keizer, J., 1987 Statistical Thermodynamics of Nonequilibrium Processes. Springer.CrossRefGoogle Scholar
Kennedy, C. & Carpenter, M. 1994 Several new numerical methods for compressible shear layer simulations. Appl. Numer. Maths 14, 397–433.CrossRefGoogle Scholar
Leboissetier, A., Okong'o, N. & Bellan, J. 2005 Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 2. A posteriori modeling. J. Fluid Mech. 523, 37–78.CrossRefGoogle Scholar
Lilly, D. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633–635.CrossRefGoogle Scholar
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119.CrossRefGoogle Scholar
Mayer, W., Ivancic, B., Schik, A. & Hornung, U. 1998 Propellant atomization in LOX/GH2 rocket combustors. AIAA Paper 98-3685.CrossRefGoogle Scholar
Mayer, W., Schik, A., Schweitzer, C. & Schaffler, M. 1996 Injection and mixing processes in high pressure LOX/GH2 rocket combustors. AIAA Paper 96-2620.CrossRefGoogle Scholar
Miller, R., Harstad, K. & Bellan, J. 2001 Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen. J. Fluid Mech. 436, 1–39.CrossRefGoogle Scholar
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids 3 (11), 2746–2757.CrossRefGoogle Scholar
Moser, R. & Rogers, M. 1991 Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A 3 (5), 1128–1134.CrossRefGoogle Scholar
Moser, R. & Rogers, M. 1993 The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence. J. Fluid Mech. 247, 275–320.CrossRefGoogle Scholar
Muller, S. M. & Scheerer, D. 1991 A method to parallelize tridiagonal solvers. Parallel Comput. 17, 181–188.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2002 a Direct numerical simulation of a transitional supercritical binary mixing layer: heptane and nitrogen. J. Fluid Mech. 464, 1–34.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2002 b Consistent boundary conditions for multicomponent real gas mixtures based on characteristic waves. J. Comput. Phys. 176, 330–344.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2003 Real gas effects of mean flow and temporal stability of binary-species mixing layers. AIAA J. 41 (12), 2429–2443.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2004 a Turbulence and fluid-front area production in binary-species, supercritical, transitional mixing layers. Phys. Fluids 16 (5), 1467–1492.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2004 b Consistent large eddy simulation of a temporal mixing layer laden with evaporating drops. Part 1. Direct numerical simulation, formulation and a priori analysis. J. Fluid Mech. 499, 1–47.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2004 c Perturbation and initial Reynolds number effects on transition attainment of supercritical mixing layers. Comput, Fluids 33 (8), 1023–1046.CrossRefGoogle Scholar
Okong'o, N., Harstad, K. & Bellan, J. 2002 Direct numerical simulations of O2/H2 temporal mixing layers under supercritical conditions. AIAA J. 40 (5), 914–926.CrossRefGoogle Scholar
Oschwald, M. & Schik, A. 1999 Supercritical nitrogen free jet investigated by spontaneous Raman scattering. Exp. Fluids 27, 497–506.CrossRefGoogle Scholar
Oschwald, M., Schik, A., Klar, M. & Mayer, W. 1999 Investigation of coaxial LN2/GH2-injection at supercritical pressure by spontaneous Raman scattering. AIAA 99-2887.CrossRefGoogle Scholar
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453–477.CrossRefGoogle Scholar
Pope, S. B. 2004 Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6, 35–59.CrossRefGoogle Scholar
Prausnitz, J., Lichtenthaler, R. & deAzevedo, E. Azevedo, E. 1986 Molecular Thermodynamics for Fluid-Phase Equilibrium. Prentice-Hall.Google Scholar
Pruett, C., Sochacki, J. & Adams, N. 2001 On Taylor-series expansions of residual stress. Phys. Fluids 13 (9), 2578–2589.CrossRefGoogle Scholar
Sarman, S. & Evans, D. J. 1992 Heat flux and mass diffusion in binary Lennard–Jones mixtures. Phys. Rev. A45 (4), 2370–2379CrossRefGoogle Scholar
Segal, C. & Polikhov, S. 2008 Subcritical to supercritical mixing. Phys. Fluids 20, 052101–7.CrossRefGoogle Scholar
Selle, L. C., Okong'o, N. A., Bellan, J. & Harstad, K. G. 2007 Modeling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study. J. Fluid Mech. 593, 57–91.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Part 1. Basic experiments. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Smagorinsky, J. 1993 Some historical remarks on the use of nonlinear viscosities. In Large Eddy Simulation of Complex Engineering and Geophysical Flows (ed. Galperin, B. & Orszag, S.), chap. 1, pp. 3–36. Cambridge University Press.Google Scholar
Stolz, S. & Adams, N. A. 1999 An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11 (7), 1699–1701.CrossRefGoogle Scholar
Stolz, S., Adams, N. A. & Kleiser, L. 2001 An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Phys. Fluids 13 (4), 997–1015.CrossRefGoogle Scholar
Taşkinoğlu, E. S. & Bellan, J. 2010 A posteriori study using a DNS database describing fluid disintegration and binary-species mixing under supercritical pressure: heptane and nitrogen. J. Fluid Mech. 645, 211–254.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1989 A First Course in Turbulence. MIT Press.Google Scholar
Tucker, P. K., Menon, S., Merkle, C. L., Oefelein, J. C. & Yang, V. 2008 Validation of high-fidelity CFD simulations for rocket injector design. AIAA Paper 2008-5226, presented at the 44th Joint Propulsion Conference, Hartford, CT.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1995 A priori tests of large eddy simulation of the compressible plane mixing layer. J. Engng Maths 29, 299–327.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1996 Large eddy simulation of the temporal mixing layer using the Clark model. Theor. Comput. Fluid Dyn. 8, 309–324.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1997 Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357–390.CrossRefGoogle Scholar
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29 (7), 2152–2164.CrossRefGoogle Scholar