Langley Research Center Turbulence Modeling Resource

DNS: High-Order Moments in Unstrained and Strained Channel Flow

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The data on this page were provided by E. Jeyapaul and G. Coleman.

This DNS was conducted to extract all terms in the budgets for higher (3rd and 4th) order moments for both unstrained and strained turbulent channel flow. The strained flow was in adverse-pressure gradient (APG). Data are included for the unstrained case as well as at 7 different times in the strained flow's evolution. The nominal Re_tau of the flow to which the strain is applied was approximately 392 (based on friction velocity and channel half-width), the bulk Re (based on bulk mixed-mean velocity and full channel width) was approximately 13750, and the initial Reynolds number (based on centerline velocity and channel half-width) was approximately 7910.

The flow was computed on a grid with over 21 million grid points (384 x 193 x 288, or 256 x 193 x 192 spectral modes) using the incompressible Navier-Stokes equations in a pseudo-spectral code. For the unstrained case, the grid spacings corresponded to approximately Delta x⁺=10 and Delta z⁺=6.5. The minimum y-spacing (adjacent to the wall) corresponded to Delta y⁺=0.1, The data were averaged over 159 statistically independent realizations. For the strained APG flow, uniform irrotational temporal deformations were applied to the flow domain of a conventional direct numerical simulation channel code. The velocity difference between the inner and outer layer was also controlled by accelerating the walls in the streamwise plane, in order to duplicate the defining features of both the inner and outer regions of an APG boundary layer. A relatively weak APG was specified, with uniform strain magnitude (deceleration in streamwise direction and divergence in wall-normal direction) set to 31% of the ratio of the initial friction velocity to the initial channel half-width. Initial channel size was 2*pi*delta by 2*delta by pi*delta (where delta is the channel half-width). Additional details concerning the data, code, and computational methodology can be found in:

• Jeyapaul, E., Coleman, G. N., and Rumsey, C. L., "Higher-Order and Length-Scale Statistics from DNS of a Decelerated Planar Wall-Bounded Turbulent Flow," International Journal of Heat and Fluid Flow, Vol. 54, 2015, pp. 14-27, https://doi.org/10.1016/j.ijheatfluidflow.2015.04.002.
• Jeyapaul, E., Coleman, G. N., and Rumsey, C. L., "Assessment of Higher-order RANS Closures in a Decelerated Planar Wall-bounded Turbulent Flow," AIAA-2014-2088, June 2014, https://doi.org/10.2514/6.2014-2088.
• Coleman, G. N., Kim, J., and Spalart, P. R., "Direct numerical simulation of a decelerated wall-bounded turbulent shear flow," J. Fluid Mech, Vol. 495, 2003, pp. 1-18, https://doi.org/10.1017/S0022112003005883.
• Sciberras, M. A. and Coleman, G. N., "Testing of Reynolds-stress-transport closures by comparison with DNS of an idealized adverse-pressure-gradient boundary layer," European Journal of Mechanics B/Fluids, Vol. 26, 2007, pp. 551-582, https://doi.org/10.1016/j.euromechflu.2006.11.001.

The data files include:

• Basic 2nd-order statistics, including mean velocity components, velocity gradients, RMS turbulent fluctuations, TKE, shear stress components, turbulent shear stress components.
• 2nd-order pressure statistics, including abs(Pbar), abs(dP/dy), PP_bar, rms_P
• 2nd-order budgets for vv, ww, uu, uv, TKE
• 2nd-order S(u), S(v), S(w), S(p), F(u), F(v), F(w), F(p)
• 3rd-order correlations, including uuv, uvv, vvv, uuu
• 3rd-order budgets for uuu, uuv, uvv, vvv
• 4th-order correlations, including u3v, u2v2, uv3, v4, u4
• 4th-order budgets for uuuu, uuuv, uuvv, uvvv, vvvv
• 5th-order correlations, including u4v, u3v2, u2v3, uv4, v5, u5, w5
• Other miscellaneous correlations

The DNS data files are provided below (updated 7/29/2014):

• Unstrained channel data
• APG strained channel data, strain time A₂₂t= 0.020
• APG strained channel data, strain time A₂₂t= 0.100
• APG strained channel data, strain time A₂₂t= 0.191
• APG strained channel data, strain time A₂₂t= 0.281
• APG strained channel data, strain time A₂₂t= 0.365
• APG strained channel data, strain time A₂₂t= 0.675
• APG strained channel data, strain time A₂₂t= 0.772

PDF of the fluctuation velocity at three different strain times are given here:

• Unstrained channel PDF data
• APG strained channel PDF data, strain time A₂₂t= 0.365
• APG strained channel PDF data, strain time A₂₂t= 0.772

Equations and an explanation of the terms in the data files are given here:

• HOMchannel_v03.pdf
• explanation_of_terms.txt (updated 7/29/2014)

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Recent significant updates:
7/29/2014 - updated all DNS files (fixed bug in rms_p); explanation of all changes given in explanation_of_terms.txt
6/11/2014 - updated all DNS files, nondimensionalized now by u_tau(0) rather than Uref=26.330*utau(0); added PDF data
5/19/2014 - updated Retau value to be more precise; made minor addition to explanation_of_terms.txt

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Last Updated: 11/05/2021