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A comparative study of subgrid-scale stress models in the context of a transitional boundary layer

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Abstract

In this paper, four important subgrid-scale (SGS) stress models are investigated in order to assess their predictive performance on modeling of the SGS physics. The analysis is conducted using the a priori method based on a comprehensive direct numerical simulation (DNS) data set of a transitional boundary layer flow over a flat plate. The study includes examination of the correlations between the modeled SGS stress tensor and that directly computed from the DNS data, investigation of the effects of filter sizes on modeled SGS stresses, and evaluation of forward and backward scatter of the kinetic energy of the flow in the transitional and turbulent regions.

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Abbreviations

a, b :

Scalar quantities

C f :

Skin friction coefficient

C S :

Model coefficient for DSM

C L :

Model coefficient for SM

C L , C S :

Model coefficients for DTPMM

C S , C W , C N :

Model coefficients for DNM

G(x − y):

Filter kernel function

H ij :

Tensor

L ij , \({\mathcal{L}_{ij}}\) :

Leonard-type stress tensor

M ij , W ij , N ij :

Differential tensors

p :

Pressure

Re θ :

Reynolds number based on momentum thickness

\({\bar{S}_{ij}}\) :

Resolved strain rate tensor: (\({\partial \bar{u}_i/\partial x_j+\partial \bar{u}_j/\partial x_i}\))/2

\({|\bar{S}|}\) :

Norm of \({\bar{S}_{ij}}\) : \({(2\bar{S}_{ij} \bar{S}_{ij})^{1/2}}\)

t :

Time

α ij , λ ij , ζ ij :

Test-grid level base tensors

β ij , γ ij , η ij :

Grid level base tensors

γ :

Filter parameter

δ ij :

Kronecker delta

Δ:

Filter size

\({\epsilon}\) :

Ratio between filter sizes

ε sgs :

Kinetic energy transfer rate between filtered and subgrid scales

ν :

Kinematic viscosity

\({\bar{\Omega}_{ij}}\) :

Resolved rotation rate tensor: (\({\partial \bar{u}_i/\partial x_j-\partial \bar{u}_j/\partial x_i}\))/2

ρ :

Density

ρ (a,b):

Correlation function between two scalar quantities a and b

ρ ij :

Correlation coefficient between two tensorial components

θ :

Momentum thickness

τ ij :

Grid level SGS stress tensor

\({(\cdot)_i, (\cdot)_j, (\cdot)_{ij}}\) :

Vectors or second-order tensors: i, j = 1, 2, 3

\({(\cdot)_{ij}^*}\) :

A trace-free tensor: \({(\cdot)_{ij}^*=(\cdot)_{ij}-(\cdot)_{kk}\delta_{ij}/3}\)

\({\bar{(\cdot)}}\) :

Grid level filter; or a filtered quantity

\({\tilde{(\cdot)}}\) :

Test-grid level filter

\({(\cdot)^+}\) :

Wall coordinates

\({\langle\cdot\rangle}\) :

Time- and spanise-averaged quantity

References

  1. Piomelli U., Zang T.A., Speziale C.G., Hussaini M.Y.: On the large-eddy simulation of transitional wall-bounded flows. Phys. Fluids A 2, 257–265 (1990)

    Article  Google Scholar 

  2. Domaradzki J.A., Metcalfe R.W., Rogallo R.S., Riley J.J.: Analysis of subgrid-scale eddy viscosity with use of results from direct numerical simulations. Phys. Rev. Lett. 58, 547–550 (1987)

    Article  Google Scholar 

  3. Piomelli U., Cabot W.H., Moin P., Lee S.: Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3, 1766–1771 (1991)

    Article  MATH  Google Scholar 

  4. Domaradzki J.A. , Liu W., Barchet M.E.: An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence. Phys. Fluids A 5, 1747–1759 (1993)

    Article  Google Scholar 

  5. Liu S., Meneveau C., Katz J.: On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119 (1994)

    Article  Google Scholar 

  6. Kerr R.M., Domaradzki J.A., Barbier G.: Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence. Phys. Fluids 8, 197–208 (1996)

    Article  MATH  Google Scholar 

  7. Tao B., Katz J., Meneveau C.: Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements. J. Fluid Mech. 457, 35–78 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Wu, X., Moin, P.: Transitional and turbulent boundary layer with heat transfer. Phys. Fluids 22, 085105, 1–8 (2010)

    Google Scholar 

  9. Lilly D.K.: A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633–635 (1992)

    Article  Google Scholar 

  10. Salvetti M.V., Banerjee S.: A priori tests of a new dynamic subgrid-scale model for finite-difference large-eddy simulations. Phys. Fluids 7, 2831–2847 (1995)

    Article  MATH  Google Scholar 

  11. Wang, B.-C., Bergstrom, D.: A dynamic nonlinear subgrid-scale stress model. Phys. Fluids 17, 035109, 1–15 (2005)

    Google Scholar 

  12. Wu X., Moin P.: Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Wu X.: Establishing the generality of three phenomena using a boundary layer with free-stream passing wakes. J. Fluid Mech. 664, 193–219 (2010)

    Article  MATH  Google Scholar 

  14. Sagaut P., Grohens R.: Discrete filters for large eddy simulation. Int. J. Numer. Meth. Fluids 31, 1195–1220 (1999)

    Article  MATH  Google Scholar 

  15. Germano M., Piomelli U., Moin P., Cabot W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765 (1991)

    Article  MATH  Google Scholar 

  16. Bardina, J., Ferziger, H., Reynolds, W.C.: Improved turbulence models based on large-eddy simulation of homogeneous, incompressible, turbulent flows. Stanford University Technical Report TF-19 (1983)

  17. Speziale C.G.: On nonlinear k−l and k−ɛ models of turbulence. J. Fluid Mech. 178, 459–475 (1987)

    Article  MATH  Google Scholar 

  18. Wang B.-C., Yee E., Bergstrom D., Iida O.: New dynamic subgrid-scale heat flux models for large-eddy simulation of thermal convection based on the general gradient diffusion hypothesis. J. Fluid Mech. 604, 125–163 (2008)

    Article  MATH  Google Scholar 

  19. Wang B.-C., Yee E., Yin J., Bergstrom D.J.: A general dynamic linear tensor-diffusivity subgrid-scale heat flux model for large-eddy simulation of turbulent thermal flows. Numer. Heat Trans. Part B 51, 205–227 (2007)

    Article  Google Scholar 

  20. Wang B.-C., Yee E., Bergstrom D.: Geometrical description of subgrid-scale stress tensor based on Euler axis/angle. AIAA J. 44, 1106–1110 (2006)

    Article  Google Scholar 

  21. Xun Q.-Q., Wang B.-C., Yee E.: Large-eddy simulation of turbulent heat convection in a spanwise rotating channel flow. Int. J. Heat Mass Trans. 54, 698–716 (2011)

    Article  MATH  Google Scholar 

  22. Molla, M., Wang, B.-C., Kuhn, D.: Characteristics of pulsatile channel flows undergoing transition triggered by an idealized stenosis. Phys. Fluids 24, 121901, 1–25 (2012)

    Google Scholar 

  23. Smagorinsky J.: General circulation experiments with the primitive equations I. the basic experiment. Mon. Weath. Rev. 91, 99–164 (1963)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

    M. Saeedi, B.-C. Wang & Z. Yang

Authors
  1. M. Saeedi
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  2. B.-C. Wang
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  3. Z. Yang
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Correspondence to B.-C. Wang.

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Saeedi, M., Wang, BC. & Yang, Z. A comparative study of subgrid-scale stress models in the context of a transitional boundary layer. Acta Mech 225, 2595–2609 (2014). https://doi.org/10.1007/s00707-013-1078-9

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  • DOI: https://doi.org/10.1007/s00707-013-1078-9

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