Turbulence Physics and Modeling

Local Dissipation Scales in Turbulent Flows

People: Ryan King, Joerg Schumacher, and Peter Hamlington

The dissipation of kinetic energy by viscosity in fully developed turbulence occurs primarily at the smallest scales of the flow, where viscous effects overwhelm inertial processes. All such dissipation is assumed to occur near a single mean scale in the classical picture of turbulence developed by Kolmogorov. Prior numerical and experimental studies have shown, however, that the dissipation rate is highly intermittent, resulting in local values of the dissipation that can be orders of magnitude larger than the mean, even for turbulent flows at moderate Reynolds numbers. Such high amplitudes are, by definition, the result of very large velocity gradients, or tiny shear layers across which the velocity varies significantly. The dissipation can thus be connected to a locally varying scale associated with fluctuations in the velocity gradient field. This gives a range of fluctuating scales over which dissipation occurs. Previously, we have measured local dissipation scale distributions and high-order statistics of the energy dissipation rate are in turbulent channel flow using very high resolution direct numerical simulations at Reynolds numbers Re=180, 381, and 590. Now we are working to measure local dissipation scale distributions in homogeneously sheared turbulence in order to specially isolate the effects of large-scale mean shear on the scales at which dissipation occurs in turbulent flows.

Relevant Publications:
• Hamlington, P.E., Krasnov, D., Boeck, T., and Schumacher, J. (2012) Statistics of the energy dissipation rate and local enstrophy in turbulent channel flow. Physica D: Nonlinear Phenomena, Vol. 241, pp. 169-177. (pdf)
• Hamlington, P.E., Krasnov, D., Boeck, T. and Schumacher, J. (2012) Local dissipation scales and energy dissipation statistics in turbulent channel flow. Journal of Fluid Mechanics, Vol. 701, pp. 419-429. (pdf)

Closure Model Analysis for Non-Equilibrium Turbulence in Rapidly Strained Flows

People: Peter Hamlington and Matthias Ihme

The turbulence response to mean-flow deformation is examined using rapid distortion theory and a hierarchy of closure models for the Reynolds stress anisotropy. The study is carried out from a fundamental perspective in order to gain insights into the properties of turbulence in non-equilibrium flows subjected to rapid straining. In particular, we examine the evolu- tion of the turbulence kinetic energy, turbulence eddy time scale, Reynolds stresses, and anisotropy in internal combustion engines and rapid compres- sion machines. These quantities are examined as a function of the degree of non-equilibrium in the flow, which is parameterized by the ratio of char- acteristic turbulence and mean-flow deformation time scales. A systematic analysis of a hierarchy of closure models is used to motivate the use of a non- equilibrium quasi-algebraic model for the anisotropy; this model is shown to be in good agreement with more computationally complex fully differ- ential models. By comparing results from rapid distortion theory and the hierarchy of Reynolds stress models, we also provide prescriptions for the applicability of the various model approaches based on the magnitude of the non-equilibrium parameter. We connect these prescriptions with experimen- tal data for internal combustion engines operating at realistic conditions.

Relevant Publications:

Physics-Based Nonlocal and Nonequilibrium Turbulence Modeling

People: Peter Hamlington and Werner J.A. Dahm

A new physics-based anisotropy closure including nonlocal and nonequilibrium effects in turbulent flows has been obtained. The new closure is motivated by fundamental studies of the vorticity alignment in turbulent flows. The fundamental vorticity alignment studies indicate that the anisotropy dynamics may be understood as a quasi-linear system. Nonlocal effects in this system are accounted for through a new nonlocal formulation for the rapid pressure-strain correlation. Using this formulation, a nonlocal transport equation for the anisotropy is obtained, and solution of a quasi-linear version of this equation gives a new closure for the anisotropy that includes nonlocal and nonequilibrium effects in turbulent flows. The new closure is written in an analogous form to the local equilibrium closure originally proposed by Boussinesq, except that the mean strain rate is replaced with a nonlocal, nonequilibrium effective strain rate. The effective strain is naturally written as a convolution integral over the entire straining history of the flow, although a time-local formulation for the effective strain rate that can be implemented in computational fluid dynamics codes is also outlined. Application of the new closure to a range of nonequilibrium and nonlocal tests provides significantly improved predictions of the anisotropy compared to standard approaches based on the local equilibrium closure. With respect to the nonequilibrium tests, particular focus is placed on periodically-sheared turbulence, where the degree of nonequilibrium is determined by the shearing frequency in the flow. The nonlocal tests include fully-developed turbulent channel flow and the zero pressure gradient turbulent boundary layer. Practical implementation of the new closure in existing computational frameworks is outlined, and computational results are presented for the boundary layer case.

Relevant Publications:
• Hamlington, P.E., Schumacher, J., and Dahm, W.J.A. (2008) Local and nonlocal strain rate fields and vorticity alignment in turbulent flows. Physical Review E, Vol. 77, 026303. (pdf)
• Hamlington, P.E. and Dahm, W.J.A. (2008) Reynolds stress closure for nonequilibrium effects in turbulent flows. Physics of Fluids, Vol. 20, 115101. (pdf)
• Hamlington, P.E., Schumacher, J., and Dahm, W.J.A. (2008) Direct assessment of vorticity alignment with local and nonlocal strain rates in turbulent flows. Physics of Fluids, Vol. 20, 111703. (pdf)
• Hamlington, P.E. and Dahm, W.J.A. (2009) Frequency response of periodically sheared homogeneous turbulence. Physics of Fluids, Vol. 21, 055107. (pdf)
• Hamlington, P.E. and Dahm, W.J.A. (2009) Nonlocal form of the rapid pressure-strain correlation in turbulent flows. Physical Review E, Vol. 80, 046311. (pdf)