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A Priori Tests of RANS Models for Turbulent Channel Flows of a Dense Gas

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Abstract

Dense gas effects, encountered in many engineering applications, lead to unconventional variations of the thermodynamic and transport properties in the supersonic flow regime, which in turn are responsible for considerable modifications of turbulent flow behavior with respect to perfect gases. The most striking differences for wall-bounded turbulence are the decoupling of dynamic and thermal effects for gases with high specific heats, the liquid-like behavior of the viscosity and thermal conductivity, which tend to decrease away from the wall, and the increase of density fluctuations in the near wall region. The present work represents a first attempt of quantifying the influence of such dense gas effects on modeling assumptions employed for the closure of the Reynolds-averaged Navier–Stokes equations, with focus on the eddy viscosity and turbulent Prandtl number models. For that purpose, we use recent direct numerical simulation results for supersonic turbulent channel flows of PP11 (a heavy fluorocarbon representative of dense gases) at various bulk Mach and Reynolds numbers to carry out a priori tests of the validity of some currently-used models for the turbulent stresses and heat flux. More specifically, we examine the behavior of the modeled eddy viscosity for some low-Reynolds variants of the \(k-\varepsilon \) model and compare the results with those found for a perfect gas at similar conditions. We also investigate the behavior of the turbulent Prandtl number in dense gas flow and compare the results with the predictions of two well-established turbulent Prandtl number models.

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References

  1. Kirillov, N.: Analysis of modern natural gas liquefaction technologies. Chem. Pet. Eng. 40(7-8), 401–406 (2004)

    Article  Google Scholar 

  2. Zamfirescu, C., Dincer, I.: Performance investigation of high-temperature heat pumps with various BZT working fluids. Thermochim. Acta 488, 66–77 (2009)

    Article  Google Scholar 

  3. Brown, B., Argrow, B.: Application of Bethe-Zel’dovich-Thompson fluids in organic Rankine cycle engines. J. Propuls. Power 16(6), 1118–1124 (2000)

    Article  Google Scholar 

  4. Congedo, P., Corre, C., Cinnella, P.: Numerical investigation of dense-gas effects in turbomachinery. Comput. Fluids 49(1), 290–301 (2011)

    Article  MathSciNet  Google Scholar 

  5. Thompson, P.: A fundamental derivative in gasdynamics. Phys. Fluids 14(9), 1843–1849 (1971)

    Article  Google Scholar 

  6. Cinnella, P., Congedo, P.: Inviscid and viscous aerodynamics of dense gases. J. Fluid Mech. 580, 179–217 (2007)

    Article  MathSciNet  Google Scholar 

  7. Sciacovelli, L., Cinnella, P., Content, C., Grasso, F.: Dense gas effects in inviscid homogeneous isotropic turbulence. J. Fluid Mech. 800(1), 140–179 (2016)

    Article  MathSciNet  Google Scholar 

  8. Sciacovelli, L., Cinnella, P., Grasso, F.: Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence. J. Fluid Mech. 825, 515–549 (2017)

    Article  MathSciNet  Google Scholar 

  9. Sciacovelli, L., Cinnella, P., Gloerfelt, X.: Direct numerical simulations of supersonic turbulent channel flows of dense gases. J. Fluid Mech. 821, 153–199 (2017)

    Article  MathSciNet  Google Scholar 

  10. Huang, P., Coleman, G., Bradshaw, P.: Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218 (1995)

    Article  Google Scholar 

  11. Patel, V., Rodi, W., Scheuerer, G.: Turbulence models for near-wall and low reynolds number flows: A review. AIAA J. 23(9), 1308–1319 (1985)

    Article  MathSciNet  Google Scholar 

  12. Launder, B.: Second moment closure: Methodology and practice. Tech. rep., Proceedings of the Ecole d’Eté d’Analyse Numérique–Modélisation Numérique de la Turbulence. Clamart, France (1982)

    Google Scholar 

  13. Shih, T.: An improved k-epsilon model for near-wall turbulence and comparison with direct numerical simulation. Tech. rep., NASA TM 103221 (1990)

  14. Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low reynolds number. J. Fluid Mech. 177, 133–166 (1987)

    Article  Google Scholar 

  15. Durbin, P.A.: Near-wall turbulence closure modeling without ”damping functions”. Theor. Comput. Fluid Dyn. 3(1), 1–13 (1991)

    MathSciNet  MATH  Google Scholar 

  16. Hoyas, S., Jiménez, J.: Scaling of the velocity fluctuations in turbulent channels up to \(Re_{\tau = 2003}\). Phys. Fluids 18(011), 702 (2006)

    Google Scholar 

  17. Karimpour, F., Venayagamoorthy, S.: Some insights for the prediction of near-wall turbulence. J. Fluid Mech. 723, 126–139 (2013)

    Article  Google Scholar 

  18. He, S., Kim, W., Bae, J.: Assessment of performance of turbulence models in predicting supercritical pressure heat transfer in a vertical tube. Int. J. Heat Mass Transf. 51, 4659–4675 (2008)

    Article  Google Scholar 

  19. Pecnik, R., Patel, A.: Scaling and modelling of turbulence in variable property channel flows. J. Fluid Mech. 823, R1–1–11 (2017)

    Article  MathSciNet  Google Scholar 

  20. Irrenfried, C., Steiner, H.: DNS based analytical P-function model for RANS with heat transfer at high prandtl numbers. Int. J. Heat Mass Transf. 66, 217–225 (2017)

    Google Scholar 

  21. Gerolymos, G., Vallet, I.: Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow. J. Fluid Mech. 757, 701–746 (2014)

    Article  MathSciNet  Google Scholar 

  22. Martin, J., Hou, Y.: Development of an equation of state for gases. AIChE J. 1(2), 142–151 (1955)

    Article  Google Scholar 

  23. Chung, T., Ajlan, M., Lee, L., Starling, K.: Generalized multiparameter correlation for nonpolar and polar fluid transport properties. Ind. Eng. Chem. Res. 27 (4), 671–679 (1988)

    Article  Google Scholar 

  24. Cramer, M., Park, S.: On the suppression of shock-induced separation in bethe–zel’dovich–thompson fluids. J. Fluid Mech. 393, 1–21 (1999)

    Article  MathSciNet  Google Scholar 

  25. Cramer, M., Tarkenton, G.: Transonic flows of Bethe-Zel’dovich-Thompson fluids. J. Fluid Mech. 240, 197–228 (1992)

    Article  MathSciNet  Google Scholar 

  26. Poling, B., Prausnitz, J., O’Connell, J., Reid, R.: The properties of gases and liquids, vol. 5. McGraw-Hill, New York (2001)

    Google Scholar 

  27. Cramer, M.: Negative nonlinearity in selected fluorocarbons. Phys. Fluids A 1 (11), 1894–1897 (1989)

    Article  Google Scholar 

  28. Gloerfelt, X., Berland, J.: Turbulent boundary-layer noise: direct radiation at mach number 0.5. J. Fluid Mech. 723, 318–351 (2013)

    Article  MathSciNet  Google Scholar 

  29. Bogey, C., Bailly, C.: A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194(1), 194–214 (2004)

    Article  Google Scholar 

  30. Bogey, C., De Cacqueray, N., Bailly, C.: A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations. J. Comput. Phys. 228(5), 1447–1465 (2009)

    Article  MathSciNet  Google Scholar 

  31. Foysi, H., Sarkar, S., Friedrich, R.: Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509, 207–216 (2004)

    Article  Google Scholar 

  32. Modesti, D., Pirozzoli, S.: Reynolds and mach number effects in compressible turbulent channel flow. Int. J. Heat Fluid Flow 59, 33–49 (2016)

    Article  Google Scholar 

  33. Morinishi, Y., Tamano, S., Nakabayashi, K.: Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech. 502, 273–308 (2004)

    Article  Google Scholar 

  34. Zonta, F., Marchioli, C., Soldati, A.: Modulation of turbulence in forced convection by temperature-dependent viscosity. J. Fluid Mech. 697, 150–174 (2012)

    Article  Google Scholar 

  35. Lee, J., Jung, S., Sung, H., Zaki, T.: Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity. J. Fluid Mech. 726, 196–225 (2013)

    Article  MathSciNet  Google Scholar 

  36. Patel, A., Peeters, J., Boersma, B., Pecnik, R.: Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27 (9), 095,101 (2015)

    Article  Google Scholar 

  37. Trettel, A., Larsson, J.: Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28(2), 026,102 (2016)

    Article  Google Scholar 

  38. Launder, B., Sharma, B.: Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Trans. 1(2), 131–137 (1974)

    Article  Google Scholar 

  39. Chien, K.Y.: Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model. AIAA J. 20(1), 33–38 (1982)

    Article  Google Scholar 

  40. Lam, C., Bremhorst, K.: A modified form of the k-ε model for predicting wall turbulence. J. Fluids Eng. 103(3), 456–460 (1981)

    Article  Google Scholar 

  41. Jones, W., Launder, B.: The prediction of laminarization with a two-equation model of turbulence. Int. J. Heat Mass Transf. 15(2), 301–314 (1972)

    Article  Google Scholar 

  42. Cebeci, T.: A model for eddy conductivity and turbulent Prandtl number. J. Heat Transf. 95, 227–234 (1973)

    Article  Google Scholar 

  43. Na, T., Habib, I.: Heat transfer in turbulent pipe flow based on a new mixing length model. Appl. Sci. Res. 28, 302–314 (1973)

    Article  Google Scholar 

  44. Pirozzoli, S., Bernardini, M., Orlandi, P.: Passive scalars in turbulent channel flow at high Reynolds number. J. Fluid Mech. 788, 614–639 (2016)

    Article  MathSciNet  Google Scholar 

  45. Kays, W., Crawford, M., Weigand, B.: Convective heat and mass transfer. McGraw–Hill, New York (1980)

    Google Scholar 

  46. Kays, W.: Turbulent Prandtl number – where are we ASME J. Heat Transf. 116 (2), 284–295 (1994)

    Article  Google Scholar 

Download references

Acknowledgements

This work was granted access to the HPC resources of GENCI (Grand Equipement National de Calcul Intensif) under the allocation 7332. The authors are grateful to Dr. Davide Modesti for providing the turbulent Prandtl number profile at \(Re_{\tau ,cl}^{*}= 677\). The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Mechanical and Civil Engineering Department, California Institute of Technology, Pasadena, CA, USA

    Luca Sciacovelli

  2. Laboratoire DynFluid, Arts et Métiers ParisTech, Paris, France

    Paola Cinnella & Xavier Gloerfelt

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  1. Luca Sciacovelli
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  2. Paola Cinnella
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  3. Xavier Gloerfelt
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Correspondence to Luca Sciacovelli.

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Sciacovelli, L., Cinnella, P. & Gloerfelt, X. A Priori Tests of RANS Models for Turbulent Channel Flows of a Dense Gas. Flow Turbulence Combust 101, 295–315 (2018). https://doi.org/10.1007/s10494-018-9938-y

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