Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-10T16:40:04.625Z Has data issue: false hasContentIssue false
  • English
  • Français

A posteriori study using a DNS database describing fluid disintegration and binary-species mixing under supercritical pressure: heptane and nitrogen

Published online by Cambridge University Press:  09 February 2010

EZGI S. TASKINOGLU  and
JOSETTE BELLAN
EZGI S. TASKINOGLU
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
JOSETTE BELLAN*
Affiliation:
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
Get access Rights & Permissions [Opens in a new window]

Abstract

A large eddy simulation (LES) a posteriori study is conducted for a temporal mixing layer which initially contains different species in the lower and upper streams and in which the initial pressure is larger than the critical pressure of either species. A vorticity perturbation, initially imposed, promotes roll-up and a double pairing of four initial spanwise vortices to reach a transitional state. The 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. Unlike all LES models to date, the differential equations contain, additional to the subgrid-scale (SGS) fluxes, a new SGS term denoted a ‘pressure correction’ (p correction) in the momentum equation. This additional term results from filtering the Navier–Stokes equations and represents the gradient of the difference between the filtered p and p computed from the filtered flow field. A previous a priori analysis, using a direct numerical simulation (DNS) database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of regions of high density-gradient magnitude that populated the entire flow; in that study, the appropriateness of several SGS-flux models was assessed, and a model for the p-correction term was proposed.

In the present study, the constant-coefficient SGS-flux models of the a priori investigation are tested a posteriori in LES devoid of, or including, the SGS p-correction term. A new p-correction model, different from that of the a priori study, is used, and the results of the two p-correction models are compared. The results reveal that the former is less computationally intensive and more accurate than the latter in reproducing global and structural features of the flow. The constant-coefficient SGS-flux models encompass the Smagorinsky (SMC) model, in conjunction with the Yoshizawa (YO) model for the trace, the gradient (GRC) model and the scale similarity (SSC) models, all exercised with the a priori study constant-coefficient values calibrated at the transitional state. Further, dynamic SGS-flux model LESs are performed with the p correction included in all cases. The dynamic models are the Smagorinsky (SMD) model, in conjunction with the YO model, the gradient (GRD) model and ‘mixed’ models using SMD in combination with GRC or SSC utilized with their theoretical coefficient values. The LES comparison is performed with the filtered-and-coarsened DNS (FC-DNS) which represents an ideal LES solution. The constant-coefficient models including the p correction (SMCP, GRCP and SSCP) are substantially superior to those devoid of it; the SSCP model produces the best agreement with the FC-DNS template. For duplicating the local flow structure, the predictive superiority of the dynamic mixed models is demonstrated over the SMD model; however, even better predictions in capturing vortical features are obtained with the GRD model. The GRD predictions improve when LES is initiated at a time past the initial range in which the p-correction term rivals in magnitude the leading-order term in the momentum equation. Finally, the ability of the LES to predict the FC-DNS irreversible entropy production is assessed. It is shown that the SSCP model is the best at recovering the domain-averaged irreversible entropy production. The sensitivity of the predictions to the initial conditions and grid size is also investigated.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 645 , 25 February 2010 , pp. 211 - 254
Copyright
Copyright © Cambridge University Press 2010

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. Paper 80-1357. AIAA.CrossRefGoogle Scholar
Bellan, J. 2006 Theory, modelling and analysis of turbulent supercritical mixing. Combust. Sci. Technol. 178, 253–281.CrossRefGoogle Scholar
Berselli, L. C., Iliescu, T. & Layton, W. J. 2006 Mathematics of Large Eddy Simulation of Turbulent Flows. Springer.Google 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. Paper 99-0206. AIAA.CrossRefGoogle Scholar
Chow, F. K. & 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.Google 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. & 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.Google 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.Google Scholar
Harstad, K. & Bellan, J. 1998 Isolated fluid oxygen drop behaviour 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
Hirshfelder, J., Curtis, C. & Bird, R. 1964 Molecular Theory of Gases and Liquids. John Wiley.Google Scholar
Honein, A. E. & Moin, P. 2004 Higher entropy conservation and numerical stability of compressible turbulence simulations. J. Comput. Phys. 201, 531–545.Google Scholar
Keizer, J. 1987 Statistical Thermodynamics of Nonequilibrium Processes. Springer.Google Scholar
Kennedy, C. & Carpenter, M. 1994 Several new numerical methods for compressible shear layer simulations. Appl. Numer. Math. 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
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., Schik, A., Schweitzer, C. & Schaffler, M. 1996 Injection and mixing processes in high pressure LOX/GH2 rocket combustors. Paper 96-2620. AIAA.Google Scholar
Mayer, W., Ivancic, B., Schik, A. & Hornung, U. 1998 Propellant atomization in LOX/GH2 rocket combustors. Paper 98-3685. AIAA.Google Scholar
Meyer, J., Geurts, B. J. & Baelmans, M. 2003 Database analysis of errors in large-eddy simulation. Phys. Fluids 15 (9), 2740–2755.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.Google Scholar
Muller, S. M. & Scheerer, D. 1991 A method to parallelize tridiagonal solvers. Par. Comput. 17, 181–188.CrossRefGoogle Scholar
Oefelein, J. C. 2005 Thermophysical characteristics of shear-coaxial LOX-H2 flames at supercritical pressure. Proc. Combust. Inst. 30, 2929–2937.Google Scholar
Oefelein, J. C. & Yang, V. 1998 modelling high-pressure mixing and combustion processes in liquid rocket engines. J. Propul. Power 14, 843–857.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2000 Entropy production of emerging turbulent scales in a temporal supercritical n-heptane/nitrogen three-dimensional mixing layer. Proc. Combust. Inst. 28, 497–504.Google Scholar
Okong'o, N. & Bellan, J. 2002 a 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. 2002 b Direct numerical simulation of a transitional supercritical binary mixing layer: heptane and nitrogen. J. Fluid Mech. 464, 1–34.Google 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 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.Google Scholar
Okong'o, N. & Bellan, J. 2004 b Turbulence and fluid-front area production in binary-species, supercritical, transitional mixing layers. Phys. Fluids 16 (5), 1467–1492.Google 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.Google Scholar
Oschwald, M. & Schik, A. 1999 Supercritical nitrogen free jet investigated by spontaneous Raman scattering. Exp. Fluids 27, 497–506.Google Scholar
Oschwald, M., Schik, A., Klar, M. & Mayer, W. 1999 Investigation of coaxial LN2/GH2-injection at supercritical pressure by spontaneous Raman scattering. Paper AIAA-99-2887. AIAA.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.Google Scholar
Prausnitz, J., Lichtenthaler, R. & de 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. A 45 (4), 2370–2379Google Scholar
Segal, C. & Polikhov, S. 2008 Subcritical to supercritical mixing. Phys. Fluids 20, 052101-7.Google Scholar
Selle, L. C., Okong'o, N. A., Bellan, J. & Harstad, K. G. 2007 modelling of subgrid scale phenomena in supercritical transitional mixing layers: an a priori study. J. Fluid Mech. 593, 57–91.CrossRefGoogle Scholar
Smagorinksy, J. 1963 General circulation experiments with the primitive equations. Part 1. basic experiments. Mon. Weather Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Smagorinksy, 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.), chapter 1, pp. 3–36. Cambridge University Press.Google Scholar
Speziale, C. G., Erlebacher, G., Zang, T. A. & Hussaini, M. Y. 1988 The subgrid-scale modelling of compressible turbulence. Phys. Fluids A 31, 940–942.Google Scholar
Tennekes, H. & Lumley, J. L. 1989 A First Course in Turbulence. MIT Press.Google Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1996 a Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer. Intl J. Num. Meth. Fluids 22, 297–311.Google Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1996 b Large eddy simulation of the temporal mixing layer using the Clark model. Theoret. Comput. Fluid Dyn. 8, 309–324.Google 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 modelling. Phys. Fluids 29 (7), 2152–2164.CrossRefGoogle Scholar
Zang, Y., Street, R. L. & Koseff, J. R. 1993 A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Phys. Fluids A 5, 3186–3196.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