Analysis of Dense Gas Effects in Compressible Turbulent Channel Flows

  • L. Sciacovelli
  • P. CinnellaEmail author
  • X. Gloerfelt
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)


In this work we investigate the influence of dense gas effects on compressible wall-bounded turbulence. Turbulent flows of dense gases represent a research field of great importance for a wide range of applications in engineering. Dense gases are single-phase fluids with a molecular complexity such that the fundamental derivative of gas dynamics (Thompson, Phys Fluids, 14:1843–1849, 1979, [1]) \(\varGamma := 1 + \frac{\rho }{c} \left. \frac{\partial c}{\partial \rho }\right| _s\) (where \(\rho \) is the density, p the pressure, s the entropy, and c the sound speed), which measures the rate of change of the sound speed in isentropic transformations, is less than one in a range of thermodynamic conditions close to the saturation curve. In such conditions, the speed of sound increases in isentropic expansions and decreases in isentropic compressions, unlike the case of perfect gases. For dense gases, the perfect gas model is no longer valid, and more complex equations of state must be used to account for their peculiar thermodynamic behavior. Moreover, in the dense gas regime, the dynamic viscosity \(\mu \) and the thermal conductivity \(\lambda \) depend on temperature and pressure through complex relationships. Similarly, the approximation of nearly constant Prandtl number Pr=\(\mu c_p/\lambda \) is no longer valid. Numerical simulations of turbulent dense gas flows of engineering interest are based on the (Reynolds-Averaged Navier–Stokes) RANS equations, which need to be supplemented by a model for the Reynolds stress tensor and turbulent heat flux. The accuracy of RANS models for dense-gas flows has not been properly assessed up to date, due to the lack of both experimental and numerical reference data.



This work was granted access to the HPC resources of GENCI (Grand Equipement National de Calcul Intensif) under the allocation 7332.


  1. 1.
    Thompson, P.A.: A fundamental derivative in gasdynamics. Phys. Fluids 14, 1843–1849 (1979)CrossRefGoogle Scholar
  2. 2.
    Sciacovelli, L., Cinnella, P., Content, C., Grasso, F.: Dense gas effects in inviscid homogeneous isotropic turbulence. J. Fluid Mech. 800, 140–179 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Sciacovelli, L., Cinnella, P., Grasso, F.: Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence. J. Fluid Mech. (2017). In pressGoogle Scholar
  4. 4.
    Sciacovelli, L., Cinnella, P., Gloerfelt, X.: DNS of supersonic turbulent channel flows of dense gases. J. Fluid Mech. 821, 153–199 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Martin, J., Hou, Y.: Development of an equation of state for gases. AIChE J. 1, 142–151 (1955)CrossRefGoogle Scholar
  6. 6.
    Chung, T.H., Ajlan, M., Lee, L.L., Starling, K.E.: Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity. Ind. Eng. Chem. Res. 27, 671–679 (1988)CrossRefGoogle Scholar
  7. 7.
    Huang, P.G., Coleman, G.N., Bradshaw, P.: Compressible turbulent channel flows: DNS results and modeling. J. Fluid Mech. 305, 185–218 (1995)CrossRefGoogle Scholar
  8. 8.
    Patel, A., Peeters, J.W.R., Boersma, B.J., Pecnik, R.: Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27, 095101 (2015)CrossRefGoogle Scholar
  9. 9.
    Launder, B.E., Sharma, B.I.: Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transf. 1, 131–138 (1971)Google Scholar
  10. 10.
    Chien, K.Y.: Predictions of channel and boundary-layer flow with a low-Reynolds turbulence model. AIAA J. 20, 33–38 (1982)CrossRefGoogle Scholar
  11. 11.
    Durbin, P.A.: Near-Wall turbulence closure modeling without “damping functions”. Theoret. Comput. Fluid Dyn. 3, 1–13 (1991)zbMATHGoogle Scholar
  12. 12.
    Shih, T.H.: An improved \(k-\varepsilon \) model for near-wall turbulence and comparison with direct numerical simulation. NASA TM 103221 (1990)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratoire DynFluidArts et Métiers ParisTechParisFrance
  2. 2.California Institute of TechnologyPasadenaUSA

Personalised recommendations