Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-19T06:19:29.217Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study

Published online by Cambridge University Press:  23 November 2007

LAURENT C. SELLE ,
NORA A. OKONG'O ,
JOSETTE BELLAN  and
KENNETH G. HARSTAD
LAURENT C. SELLE
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
NORA A. OKONG'O
Affiliation:
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
JOSETTE BELLAN
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
KENNETH G. HARSTAD
Affiliation:
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 593 , 25 December 2007 , pp. 57 - 91
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
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
Clark, R., Ferziger, J. & Reynolds, W. 1979 Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1–16.CrossRefGoogle Scholar
Gonzales-Bagnoli, M. G., Shapiro, A. A. & Stenby, E. H. 2003 Evaluation of the thermodynamic models for the thermal diffusion factor. Phil. Mag. 83 (17–18), 2171–2183.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., Miller, R. S. & Bellan, J. 1997 Efficient high-pressure state equations. AIChE J. 43 (6), 1605–1610.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. & Bellan, J. 2001 The D2 variation for isolated LOX drops and polydisperse clusters in hydrogen at high temperature and pressures. Combust. Flame 124 (4), 535–550.CrossRefGoogle Scholar
Hirshfelder, J., Curtis, C. & Bird, R. 1964 Molecular Theory of Gases and Liquids. John Wiley and Sons.Google 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 modelling.. J. Fluid Mech. 523, 37–78.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., Schik, A., Schweitzer, C. & Schaffler, M. 1996 Injection and mixing processes in high pressure LOX/GH2 rocket combustors. AIAA Paper 96-2620.CrossRefGoogle Scholar
Mayer, W., Ivancic, B., Schik, A. & Hornung, U. 1998 Propellant atomization in LOX/GH2 rocket combustors. AIAA Paper 98-3685.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
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 Computing 17, 181–188.CrossRefGoogle Scholar
Oefelein, J. C. & Yang, V. 1998 Modeling high-pressure mixing and combustion processes in liquid rocket engines. J. Propul. Power 14, 843–857.CrossRefGoogle Scholar
Oefelein, J. C. 2005 Thermophysical characteristics of shear-coaxial LOX-H2 flames at supercritical pressure. Proc. Combust. Inst. 30, 2929–2937.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., 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. Exps. 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 Paper 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
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.CrossRefGoogle Scholar
Segal, C. 2007 Subcritical to supercritical jet mixing. AIAA Paper 2007-0569.Google 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
Selle, L. C. & Bellan, J. 2007 Scalar dissipation modeling for passive and active scalars: a priori study using Direct Numerical Simulation. Proc. Comb. Inst. 31, 1665–1673.CrossRefGoogle Scholar
Smagorinksy, J. 1993 Some historical remarks on the use of nonlinear viscosities. In Large Eddy Simulation of Complex Engineering and Geophysical Flows (Galperin, B. & Orszag, S.), chap. 1, pp. 3–36. Cambridge University Press.Google Scholar
Su, L. K. & Clemens, N. T. 2003 The structure of fine-scale scalar mixing in gas-phase planar turbulent jets. J. Fluid Mech. 488, 1–29.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
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.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
Zong, N., Meng, H., Hsieh, S.-Y. & Yang, V. 2004 A numerical study of cryogenic fluid injection and mixing under supercritical conditions. Phys. Fluids 16 (12), 4248–4261.CrossRefGoogle Scholar