Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T09:54:42.619Z Has data issue: false hasContentIssue false
  • English
  • Français

The determination of turbulence-model statistics from the velocity–acceleration correlation

Published online by Cambridge University Press:  30 September 2014

Stephen B. Pope
Stephen B. Pope*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: s.b.pope@cornell.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

For inhomogeneous turbulent flows at high Reynolds number, it is shown that the redistribution term in Reynolds-stress turbulence models can be determined from the velocity–acceleration correlation. It is further shown that the drift coefficient in the generalized Langevin model (which is used in probability density function (PDF) methods) can be determined from the Reynolds stresses and the velocity–acceleration correlation. These observations are valuable, since the second moments of velocity and acceleration can be measured in experiments, in direct numerical simulations and in well-resolved large-eddy simulations (LES), and hence these turbulence-model quantities can be determined. The redistribution is closely related to the pressure–rate-of-strain, and the unknown in the PDF equation is closely related to the conditional mean pressure gradient (conditional on velocity). In contrast to the velocity–acceleration moments, these pressure statistics are much more difficult to obtain, and our knowledge of them is quite limited. It is also shown that the generalized Langevin model can be re-expressed to provide a direct connection between the drift term and the fluid acceleration. All of these results are first obtained using the constant-property Navier–Stokes equations, but it is then shown that the results are simply extended to variable-density flows.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 757 , 25 October 2014 , R1
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Coriton, B., Steinberg, A. M. & Frank, J. H. 2014 High-speed tomographic PIV and OH PLIF measurements in turbulent reactive flows. Exp. Fluids 55, 1743.CrossRefGoogle Scholar
Elsinga, G. E., Wieneke, B., Scarano, F. & van Oudheusden, B. W. 2006 Tomographic particle image velocimetry. Exp. Fluids 41, 933–947.CrossRefGoogle Scholar
Gerashchenko, S., Sharp, N. S., Neuscamman, S. & Warhaft, Z. 2008 Lagrangian measurements of inertial particle accelerations in a turbulent boundary layer. J. Fluid Mech. 617, 255–281.CrossRefGoogle Scholar
Haworth, D. C. 2010 Progress in probability density function methods for turbulent reacting flows. Prog. Energy Combust. Sci. 36, 168–259.CrossRefGoogle Scholar
Haworth, D. C. & Pope, S. B. 1986 A generalized Langevin model for turbulent flows. Phys. Fluids 29, 387–405.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019.CrossRefGoogle ScholarPubMed
Mann, J., Søren, O. & Andersen, J. S.1999 Experimental study of relative, turbulent dispersion. Tech. Rep. R-1036(EN). Risø National Laboratory, Roskilde, Denmark.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to ${\mathit{Re}}_{\tau } = 590$ . Phys. Fluids 11, 943–946.CrossRefGoogle Scholar
Nguyen, K. X., Horst, T. W., Oncley, S. P. & Tong, C. 2013 Measurements of the budgets of the subgrid-scale stress and temperature in a convective atmospheric surface layer. J. Fluid Mech. 729, 388–422.CrossRefGoogle Scholar
Pope, S. B. 1994 On the relationship between stochastic Lagrangian models of turbulence and second-moment closures. Phys. Fluids 6, 973–985.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pope, S. B. 2002 Stochastic Lagrangian models of velocity in homogeneous turbulent shear flow. Phys. Fluids 14, 1696–1702.CrossRefGoogle Scholar
Pope, S. B. 2011 Simple models of turbulent flows. Phys. Fluids 23, 011301.CrossRefGoogle Scholar
Pope, S. B. 2013 Small scales, many species and the manifold challenges of turbulent combustion. Proc. Combust. Inst. 34, 1–31.CrossRefGoogle Scholar
Rogallo, R. S. & Moin, P. 1985 Numerical simulation of turbulent flows. Annu. Rev. Fluid Mech. 17, 99–137.Google Scholar
Sawford, B. L. & Yeung, P. K. 2000 Eulerian acceleration statistics as a discriminator between Lagrangian stochastic models in uniform shear flow. Phys. Fluids 12, 2033–2045.CrossRefGoogle Scholar
Sawford, B. L. & Yeung, P. K. 2010 Conditional relative acceleration statistics and relative dispersion modeling. Flow Turbul. Combust. 85, 345–362.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to $ R_{\theta } = 1410$ . J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Terashima, O., Onishi, K., Sakai, Y., Nagata, K. & Ito, Y. 2014 Simultaneous measurement of all three velocity components and pressure in a plane jet. Meas. Sci. Technol. 25, 055301.CrossRefGoogle Scholar
Vedula, P. & Yeung, P. K. 1999 Similarity scaling of pressure and acceleration statistics in numerical simulations of turbulence. Phys. Fluids 11, 1208–1220.CrossRefGoogle Scholar
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.CrossRefGoogle Scholar