Skip to main content
SpringerLink
Log in

A three-equation turbulence model for high-speed flows

  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Adding a new equation to the two-equation K-ω turbulence model framework, this paper proposed a three-equation turbulence model to determine the density variance for high-speed aero-optics and high-speed compressible turbulent flows. Simulations were performed with the new model for supersonic and hypersonic flat-plate turbulent boundary layer and hypersonic ramp flows. The results showed that the prediction with the present model agrees well with the experimental data and is significantly better than the Lutz’s model in predicting the density variance for the flat-plate flows. Furthermore, the present model can produce more accurate skin pressure and skin heat flux distributions than the original K-ω model in simulating hypersonic compression ramp flows with separation and reattachment and shock/boundary layer interactions. Without introducing a variety of ad hoc wall damping and wall-reflection terms, the proposed three-equation turbulence model is applicable to high-speed aero-optics and turbulent flows of real vehicles of complex configuration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wang M, Mani A, Gordeyev S. Physics and computation of aero-optics. Annu Rev Fluid Mech, 2012, 44: 299–321

    Article  MathSciNet  Google Scholar 

  2. Pond J E, Sutton G W. Aero-optic performance of an aircraft forward-facing optical turret. J Aircraft, 2006, 43: 600–607

    Article  Google Scholar 

  3. Pond J E. Side mounded IR window aero-optic and aerothermal analysis. SPIE, 1999, 3705: 266–275

    Article  Google Scholar 

  4. Kovasznay L S G. Turbulence in supersonic flow. J Aeronaut Sci, 1953, 20: 657–674

    MATH  Google Scholar 

  5. Chu B T, Kovasznay L S G. Nonlinear interactions in a viscous heat-conducting compressible gas. J Fluid Mech, 1958, 3: 494–514

    Article  MathSciNet  Google Scholar 

  6. Yoshizawa A. Three-equation modeling of inhomogeneous compressible turbulence based on a two-scale direct-interaction approximation. Phys Fluids A, 1990, 5: 838–850

    Article  MathSciNet  Google Scholar 

  7. Panda J. Experimental investigation of turbulent density fluctuations and noise generation from heated jets. J Fluid Mech, 2007, 591: 73–96

    Article  MATH  Google Scholar 

  8. Pirozzoli S, Bernardini M. Direct numerical simulation database for impinging shock wave turbulent boundary-layer interaction. AIAA J, 2011, 49: 1307–1312

    Article  Google Scholar 

  9. Xu C Y, Chen L W, Lu X Y. Large eddy simulation of the compressible flow past a wavy cylinder. J Fluid Mech, 2010, 665: 238–273

    Article  MATH  Google Scholar 

  10. Wilcox D C. Turbulence Modeling for CFD. 3nd ed. California: DCW Industries Inc., 2006

    Google Scholar 

  11. Dong M, Zhou H. The improvement of turbulence modeling for the aerothermal computation of hypersonic turbulent boundary layers. Sci China Phys Mech Astron, 2010, 53: 369–379

    Article  MathSciNet  Google Scholar 

  12. Georgiadis N J, Rizzetta D P, Fureby C. Large-eddy simulation: current capabilities, recommended practices, and future research. AIAA J, 2010, 48: 1772–1784

    Article  Google Scholar 

  13. Roy C J, Blottner F G. Review and assessment of turbulence models for hypersonic flows. Prog Aerosp Sci, 2006, 42: 469–530

    Article  Google Scholar 

  14. Lutz S A. Modeling of density fluctuations in supersonic turbulent boundary layer. AIAA J, 1989, 27: 822–823

    Article  Google Scholar 

  15. Lejeune C, Kourta A, Chassaing P. Modelling of high-speed turbulent flows. AIAA Paper, 1996, 1996–2041

    Google Scholar 

  16. Taulbee D, VanOsdol J. Modeling turbulent compressible flows: the mass fluctuating velocity and squared density. AIAA Paper, 1991, 1991–0524

    Google Scholar 

  17. Wei H, Chen C P. A nonequilibrium algebraic model for turbulent density fluctuations. Int J Heat Mass Transfer, 1996, 39: 3989–3991

    Article  MATH  Google Scholar 

  18. Huang P G, Bradshaw P, Coakley T J. Turbulence models for compressible boundary layers. AIAA J, 1994, 32: 735–740

    Article  MATH  Google Scholar 

  19. Lele S K. Compressibility effects on turbulence. Annu Rev Fluid Mech, 1994, 26: 211–254

    Article  MathSciNet  Google Scholar 

  20. Sarkar S. The stabilizing effect of compressibility in turbulent shear flow. J Fluid Mech, 1995, 282: 163–186

    Article  MATH  Google Scholar 

  21. Thacker W D, Sarkar S, Gatski T B. Analyzing the influence of compressibility on the rapid pressure-strain rate correlation in turbulent shear flows. Theor Comput Fluid Dyn, 2007, 21: 171–199

    Article  MATH  Google Scholar 

  22. Wang X, Zhong X. Effect of compressibility on strong shock and turbulence interactions. AIAA Paper, 2012, 2012–1243

    Google Scholar 

  23. Wang S Z, Gao Z X, Lee C H. Numerical investigation of compressibility effects in turbulent channel flows using large eddy simulation. Sci China Phys Mech Astron, 2012, 55: 305–315

    Article  Google Scholar 

  24. Wilcox D C. Reassessment of the scale-determining equation for advanced turbulence models. AIAA J, 1988, 26: 1299–1310

    Article  MathSciNet  MATH  Google Scholar 

  25. Sarkar S. The pressure-dilatation correlation in compressible flows. Phys Fluids A, 1992, 4: 2674–2682

    Article  Google Scholar 

  26. Speziale C G, Abid R, Anderson E C. Critical evaluation of two-equation models for near-wall turbulence. AIAA J, 1992, 30: 324–331

    Article  MATH  Google Scholar 

  27. Yee H C, Klopfer G H, Montagne J L. High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows. J Comput Phys, 1990, 88: 31–61

    Article  MathSciNet  MATH  Google Scholar 

  28. Liu J Y, Lee C H. Comparison of two-equation turbulent models for hypersonic flow simulations (in Chinese). J Beijing Univ Aeron Astron, 2007, 33: 1131–1135

    Google Scholar 

  29. Kistler A L. Fluctuation measurements in a supersonic turbulent boundary layer. Phys Fluids, 1959, 2: 290–296

    Article  MATH  Google Scholar 

  30. Laderman A J, Demetriades A. Turbulent shear stresses in compressible boundary layers. AIAA J, 1979, 17: 736–744

    Article  Google Scholar 

  31. Laderman A J, Demetriades A. Mean and fluctuating flow measurements in the hypersonic boundary layer over a cooled wall. J Fluid Mech, 1974, 63: 121–144

    Article  Google Scholar 

  32. Settles G S, Dodson L J. Hypersonic shock/boundary-layer interaction database. NASA-CR-177577, 1991

    Google Scholar 

  33. Coleman G T, Stollery J L. Heat transfer from hypersonic turbulent flow at a wedge compression corner. J Fluid Mech, 1972, 56: 741–752

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aircraft Engineering College, Nanchang Hangkong University, Nanchang, 330063, China

    JingYuan Liu

Authors
  1. JingYuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to JingYuan Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, J. A three-equation turbulence model for high-speed flows. Sci. China Technol. Sci. 56, 803–811 (2013). https://doi.org/10.1007/s11431-013-5178-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-013-5178-5

Keywords

Search

Navigation