Skip to main content Accessibility help
×
Home

Direct numerical simulations of supersonic turbulent channel flows of dense gases

Published online by Cambridge University Press:  19 May 2017

L. Sciacovelli
Affiliation:
Laboratoire DynFluid, Arts et Métiers ParisTech, 75013 Paris, FR, France Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari, IT, Italy
P. Cinnella
Affiliation:
Laboratoire DynFluid, Arts et Métiers ParisTech, 75013 Paris, FR, France
X. Gloerfelt
Affiliation:
Laboratoire DynFluid, Arts et Métiers ParisTech, 75013 Paris, FR, France
Corresponding
E-mail address:

Abstract

The influence of dense-gas effects on compressible wall-bounded turbulence is investigated by means of direct numerical simulations of supersonic turbulent channel flows. Results are obtained for PP11, a heavy fluorocarbon representative of dense gases, the thermophysics properties of which are described by using a fifth-order virial equation of state and advanced models for the transport properties. In the dense-gas regime, the speed of sound varies non-monotonically in small perturbations and the dependency of the transport properties on the fluid density (in addition to the temperature) is no longer negligible. A parametric study is carried out by varying the bulk Mach and Reynolds numbers, and results are compared to those obtained for a perfect gas, namely air. Dense-gas flow exhibits almost negligible friction heating effects, since the high specific heat of the fluids leads to a loose coupling between thermal and kinetic fields, even at high Mach numbers. Despite negligible temperature variations across the channel, the mean viscosity tends to decrease from the channel walls to the centreline (liquid-like behaviour), due to its complex dependency on fluid density. On the other hand, strong density fluctuations are present, but due to the non-standard sound speed variation (opposite to the mean density evolution across the channel), the amplitude is maximal close to the channel wall, i.e. in the viscous sublayer instead of the buffer layer like in perfect gases. As a consequence, these fluctuations do not alter the turbulence structure significantly, and Morkovin’s hypothesis is well respected at any Mach number considered in the study. The preceding features make high Mach wall-bounded flows of dense gases similar to incompressible flows with variable properties, despite the significant fluctuations of density and speed of sound. Indeed, the semi-local scaling of Patel et al. (Phys. Fluids, vol. 27 (9), 2015, 095101) or Trettel & Larsson (Phys. Fluids, vol. 28 (2), 2016, 026102) is shown to be well adapted to compare results from existing surveys and with the well-documented incompressible limit. Additionally, for a dense gas the isothermal channel flow is also almost adiabatic, and the Van Driest transformation also performs reasonably well. The present observations open the way to the development of suitable models for dense-gas turbulent flows.

Type
Papers
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below.

References

Anderson, W. K. 1991 Numerical study on using sulfur hexafluoride as a wind tunnel test gas. AIAA J. 29 (12), 21792180.CrossRefGoogle Scholar
Aubard, G., Gloerfelt, X. & Robinet, J.-C. 2013 Large-eddy simulation of broadband unsteadiness in a shock/boundary-layer interaction. AIAA J. 51 (10), 23952409.CrossRefGoogle Scholar
Bae, J. H., Yoo, J. Y. & Choi, H. 2005 Direct numerical simulation of turbulent supercritical flows with heat transfer. Phys. Fluids 17 (10), 105104.CrossRefGoogle Scholar
Bogey, C. & Bailly, C. 2004 A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194 (1), 194214.CrossRefGoogle Scholar
Bogey, C. & Bailly, C. 2009 Turbulence and energy budget in a self-preserving round jet: direct evaluation using large eddy simulation. J. Fluid Mech. 627, 129160.CrossRefGoogle Scholar
Bogey, C., De Cacqueray, N. & Bailly, C. 2009 A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations. J. Comput. Phys. 228 (5), 14471465.CrossRefGoogle Scholar
Bogey, C., Marsden, O. & Bailly, C. 2012 Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 105. J. Fluid Mech. 701, 352385.CrossRefGoogle Scholar
Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9 (1), 3352.CrossRefGoogle Scholar
Brown, B. P. & Argrow, B. M. 2000 Application of Bethe–Zel’dovich–Thompson fluids in organic Rankine cycle engines. J. Propul. Power 16 (6), 11181124.CrossRefGoogle Scholar
Brun, C., Boiarciuc, M. P., Hakerborn, M. & Comte, P. 2008 Large eddy simulation of compressible channel flow – arguments in favour of universality of compressible turbulent wall bounded flows. Theor. Comput. Fluid Dyn. 22, 189212.CrossRefGoogle Scholar
Bufi, E. A. & Cinnella, P. 2015 Efficient uncertainty quantification of turbulent flows through supersonic ORC nozzle blades. Energy Procedia 82, 186193.CrossRefGoogle Scholar
Chang, P. A. III, Piomelli, U. & Blake, W. K. 1999 Relationship between wall pressure and velocity-field sources. Phys. Fluids 11 (11), 34343448.CrossRefGoogle Scholar
Chernyshenko, S. I. & Baig, M. F. 2005 The mechanism of streak formation in near-wall turbulence. J. Fluid Mech. 544 (1), 99131.CrossRefGoogle Scholar
Chu, B.-T. & Kovasznay, L. S. G. 1958 Non-linear interactions in a viscous heat-conducting compressible gaz. J. Fluid Mech. 3, 494514.CrossRefGoogle Scholar
Chung, T. H., Ajlan, M., Lee, L. L. & Starling, K. E. 1988 Generalized multiparameter correlation for nonpolar and polar fluid transport properties. Indust. Engng Chem. Res. 27 (4), 671679.CrossRefGoogle Scholar
Chung, T. H., Lee, L. L. & Starling, K. E. 1984 Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity. Indust. Engng Chem. Fundamentals 23 (1), 813.CrossRefGoogle Scholar
Cinnella, P. & Congedo, P. M. 2007 Inviscid and viscous aerodynamics of dense gases. J. Fluid Mech. 580, 179217.CrossRefGoogle Scholar
Coleman, G. N., Kim, J. & Moser, R. D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159183.CrossRefGoogle Scholar
Congedo, P. M., Corre, C. & Cinnella, P. 2011 Numerical investigation of dense-gas effects in turbomachinery. Comput. Fluids 49 (1), 290301.CrossRefGoogle Scholar
Cramer, M. S. 1989 Negative nonlinearity in selected fluorocarbons. Phys. Fluids 1 (11), 18941897.CrossRefGoogle Scholar
Cramer, M. S. & Bahmani, F. 2014 Effect of large bulk viscosity on large-Reynolds-number flows. J. Fluid Mech. 751, 142163.CrossRefGoogle Scholar
Cramer, M. S. & Kluwick, A. 1984 On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 142 (1), 937.CrossRefGoogle Scholar
Cramer, M. S. & Park, S. 1999 On the suppression of shock-induced separation in Bethe–Zel’dovich–Thompson fluids. J. Fluid Mech. 393, 121.CrossRefGoogle Scholar
Cramer, M. S. & Tarkenton, G. M. 1992 Transonic flows of Bethe–Zel’dovich–Thompson fluids. J. Fluid Mech. 240, 197228.CrossRefGoogle Scholar
Cramer, M. S. 2012 Numerical estimates for the bulk viscosity of ideal gases. Phys. Fluids 24 (6), 066102.CrossRefGoogle Scholar
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME J. Fluids Engng 100 (2), 215223.CrossRefGoogle Scholar
Donzis, D. A. & Jagannathan, S. 2013 Fluctuations of thermodynamic variables in stationary compressible turbulence. J. Fluid Mech. 733, 221244.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martin, M. P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419445.CrossRefGoogle Scholar
Foysi, H., Sarkar, S. & Friedrich, R. 2004 Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509, 207216.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73L76.CrossRefGoogle Scholar
Gerolymos, G. A., Sénéchal, D. & Vallet, I. 2010 Performance of very-high-order upwind schemes for DNS of compressible wall-turbulence. Intl J. Numer. Meth. Fluids 63 (7), 769810.Google Scholar
Gerolymos, G. A. & Vallet, I. 2014 Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow. J. Fluid Mech. 757, 701746.CrossRefGoogle Scholar
Gloerfelt, X. & Berland, J. 2013 Turbulent boundary-layer noise: direct radiation at Mach number 0.5. J. Fluid Mech. 723, 318351.CrossRefGoogle Scholar
Gomez, T., Flutet, V. & Sagaut, P. 2009 Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows. Phys. Rev. E 79 (3), 035301.Google ScholarPubMed
Guardone, A. & Argrow, B. M. 2005 Nonclassical gasdynamic region of selected fluorocarbons. Phys. Fluids 17 (11), 116102.CrossRefGoogle Scholar
Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J. Fluid Mech. 414, 133.CrossRefGoogle Scholar
Huang, P. G., Bradshaw, P. & Coakley, T. J. 1993 Skin friction and velocity profile family for compressible turbulent boundary layers. AIAA J. 31 (9), 16001604.CrossRefGoogle Scholar
Huang, P. G., Coleman, G. N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185218.CrossRefGoogle Scholar
Incropera, F. P. & DeWitt, D. P. 2007 Fundamentals of Heat and Mass Transfer, 6th edn. Wiley.Google Scholar
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421451.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.CrossRefGoogle Scholar
Lagha, M., Kim, J., Eldredge, J. D. & Zhong, X. 2011 A numerical study of compressible turbulent boundary layers. Phys. Fluids 23 (1), 015106.CrossRefGoogle Scholar
Laufer, J.1969 Thoughts on compressible turbulent boundary layers. NASA S.P. 216.Google Scholar
Lechner, R., Sesterhenn, J. & Friedrich, R. 2001 Turbulent supersonic channel flow. J. Turbul. 2 (1), 001–001.CrossRefGoogle Scholar
Lee, J., Jung, S. Y., Sung, H. J. & Zaki, T. A. 2013 Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity. J. Fluid Mech. 726, 196225.CrossRefGoogle Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395415.CrossRefGoogle Scholar
Li, X., Hashimoto, K., Tominaga, Y., Tanahashi, M. & Miyauchi, T. 2008 Numerical study of heat transfer mechanism in turbulent supercritical CO2 channel flow. J. Therm. Sci. Technol. 3 (1), 112123.CrossRefGoogle Scholar
Martin, J. J. & Hou, Y. C. 1955 Development of an equation of state for gases. AIChE J. 1 (2), 142151.CrossRefGoogle Scholar
Mathijssen, T., Gallo, M., Casati, E., Nannan, N. R., Zamfirescu, C., Guardone, A. & Colonna, P. 2015 The flexible asymmetric shock tube (FAST): a Ludwieg tube facility for wave propagation measurements in high-temperature vapours of organic fluids. Exp. Fluids 56 (10), 112.CrossRefGoogle Scholar
Modesti, D. & Pirozzoli, S. 2016 Reynolds and Mach number effects in compressible turbulent channel flow. Intl J. Heat Fluid Flow 59, 3349.CrossRefGoogle Scholar
Monaco, J. F., Cramer, M. S. & Watson, L. T. 1997 Supersonic flows of dense gases in cascade configurations. J. Fluid Mech. 330, 3159.CrossRefGoogle Scholar
Moneghan, R. J.1953 A review and assessment of various formulae for tubulent skin friction in compressible flow. Tech. Rep. Aeronautical Research Council. Current Paper 142.Google Scholar
Morinishi, Y., Tamano, S. & Nakabayashi, K. 2004 Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech. 502, 273308.CrossRefGoogle Scholar
Morkovin, M. V. 1961 Effect of compressibility on turbulent flows. In Mécanique de la Turbulence (ed. Favre, A.), pp. 367380. CNRS.Google Scholar
Moser, R., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to re 𝜏 = 590. Phys. Fluids 11, 943945.CrossRefGoogle Scholar
Neufeld, P. D., Janzen, A. R. & Aziz, R. A. 1972 Empirical equations to calculate 16 of the transport collision integrals 𝛺(l, s)∗ for the Lennard-Jones (12–6) potential. J. Chem. Phys. 57 (3), 11001102.CrossRefGoogle Scholar
Nicoud, F. & Poinsot, T. 1999 DNS of a channel flow with variable properties. In Proceedings of First International Symposium on Turbulence and Shear Flow Phenomena, TSFP-1, Santa Barbara, USA, TSFP.Google Scholar
Patel, A., Peeters, J. W. R., Boersma, B. J. & Pecnik, R. 2015 Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27 (9), 095101.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120168.CrossRefGoogle Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2. 25. Phys. Fluids 16 (3), 530545.CrossRefGoogle Scholar
Poling, B. E., Prausnitz, J. M., O’Connell, J. P. & Reid, R. C. 2001 The Properties of Gases and Liquids, vol. 5. McGraw-Hill.Google Scholar
Rubesin, M. W.1990 Extra compressibility terms for Favre-averaged two-equation models of inhomogeneous turbulent flows. NASA Contractor Rep. 177556.Google Scholar
Sarkar, S. 1995 The stabilizing effect of compressibility in turbulent shear flow. J. Fluid Mech. 282, 163186.CrossRefGoogle Scholar
Sciacovelli, L. & Cinnella, P. 2015 Numerical simulation of dense gas compressible homogeneous isotropic turbulence. In 15th European Turbulence Conference, EUROMECH/ETC15.Google Scholar
Sciacovelli, L., Cinnella, P., Content, C. & Grasso, F. 2016a Dense gas effects in inviscid homogeneous isotropic turbulence. J. Fluid Mech. 800 (1), 140179.CrossRefGoogle Scholar
Sciacovelli, L., Cinnella, P. & Grasso, F.2016b Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence. J. Fluid Mech. (submitted).Google Scholar
Sewall, E. A. & Tafti, D. K. 2008 A time-accurate variable property algorithm for calculating flows with large temperature variations. Comput. Fluids 37, 5163.CrossRefGoogle Scholar
Sieder, E. N. & Tate, G. E. 1936 Heat transfer and pressure drop of liquids in tubes. Indust. Engng Chem. 28 (12), 14291435.CrossRefGoogle Scholar
Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid Mech. 26, 287319.CrossRefGoogle Scholar
Spinelli, A., Pini, M., Dossena, V., Gaetani, P. & Casella, F. 2013 Design, simulation, and construction of a test rig for organic vapors. Trans. ASME J. Engng Gas Turbines Power 135 (4), 042304.CrossRefGoogle Scholar
Tamano, S. & Morinishi, Y. 2006 Effect of different thermal wall boundary conditions on compressible turbulent channel flow at M = 1. 5. J. Fluid Mech. 548, 361373.CrossRefGoogle Scholar
Teitel, M. & Antonia, R. A. 1993 Heat transfer in fully developed turbulent channel flow: comparison between experiment and direct numerical simulations. Intl J. Heat Mass Transfer 36 (6), 17011706.CrossRefGoogle Scholar
Thompson, P. A. 1971 A fundamental derivative in gasdynamics. Phys. Fluids 14 (9), 18431849.CrossRefGoogle Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28 (2), 026102.CrossRefGoogle Scholar
Van Driest, E. R. 1951 Turbulent boundary layer in compressible fluids. J. Aero. Sci. 18 (3), 145160.CrossRefGoogle Scholar
Wallace, J. M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48, 131158.CrossRefGoogle Scholar
Wei, L. & Pollard, A. 2011 Interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows. J. Fluid Mech. 673, 118.CrossRefGoogle Scholar
Zonta, F. 2013 Nusselt number and friction factor in thermally stratified turbulent channel flow under Non-Oberbeck-Boussinesq conditions. Intl J. Heat Fluid Flow 44, 489494.CrossRefGoogle Scholar
Zonta, F., Marchioli, C. & Soldati, A. 2012 Modulation of turbulence in forced convection by temperature-dependent viscosity. J. Fluid Mech. 697, 150174.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 13
Total number of PDF views: 385 *
View data table for this chart

* Views captured on Cambridge Core between 19th May 2017 - 25th January 2021. This data will be updated every 24 hours.

Hostname: page-component-898fc554b-p5tlp Total loading time: 0.566 Render date: 2021-01-25T14:47:01.166Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Direct numerical simulations of supersonic turbulent channel flows of dense gases
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Direct numerical simulations of supersonic turbulent channel flows of dense gases
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Direct numerical simulations of supersonic turbulent channel flows of dense gases
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *